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If you are not located in the United States, you -will have to check the laws of the country where you are located before -using this eBook. - -Title: History of the inductive sciences, from the earliest to the - present time - -Author: William Whewell - -Release Date: August 5, 2022 [eBook #68693] - -Language: English - -Produced by: Ed Brandon - -*** START OF THE PROJECT GUTENBERG EBOOK HISTORY OF THE INDUCTIVE -SCIENCES, FROM THE EARLIEST TO THE PRESENT TIME *** - - -HISTORY -OF THE -INDUCTIVE SCIENCES. - -VOLUME I. - - -HISTORY -OF THE -INDUCTIVE SCIENCES, -FROM -THE EARLIEST TO THE PRESENT TIME. -BY WILLIAM WHEWELL, D. D., -MASTER OF TRINITY COLLEGE, CAMBRIDGE. -_THE THIRD EDITION, WITH ADDITIONS._ -IN TWO VOLUMES. - - -VOLUME I. - - -NEW YORK: -D. APPLETON AND COMPANY, -549 & 551 BROADWAY. -1875. - - - - -TO SIR JOHN FREDERICK WILLIAM HERSCHEL, -K.G.H. - - -MY DEAR HERSCHEL, -IT is with no common pleasure that I take up my pen to dedicate -these volumes to you. They are the result of trains of thought which -have often been the subject of our conversation, and of which the -origin goes back to the period of our early companionship at the -University. And if I had ever wavered in my purpose of combining -such reflections and researches into a whole, I should have derived -a renewed impulse and increased animation from your delightful -Discourse on a kindred subject. For I could not have read it without -finding this portion of philosophy invested with a fresh charm; and -though I might be well aware that I could not aspire to that large -share of popularity which your work so justly gained, I should still -have reflected, that something was due to the subject itself, and -should have hoped that my own aim was so far similar to yours, that -the present work might have a chance of exciting an interest in some -of your readers. That it will interest you, I do not at all hesitate -to believe. - -If you were now in England I should stop here: but when a friend is -removed for years to a far distant land, we seem to acquire a right -to speak openly of his good qualities. I cannot, therefore, prevail -upon myself to lay down my pen without alluding to the affectionate -admiration of your moral and social, as well as intellectual -excellencies, which springs up in the hearts of your friends, -whenever you are thought of. They are much delighted to look upon -the halo of deserved fame which plays round your head but still -more, to recollect, {6} as one of them said, that your head is far -from being the best part about you. - -May your sojourn in the southern hemisphere be as happy and -successful as its object is noble and worthy of you; and may your -return home be speedy and prosperous, as soon as your purpose is -attained. - -Ever, my dear Herschel, yours, - -W. WHEWELL. -March 22, 1837. - -P.S. So I wrote nearly ten years ago, when you were at the Cape of -Good Hope, employed in your great task of making a complete standard -survey of the nebulæ and double stars visible to man. Now that you -are, as I trust, in a few weeks about to put the crowning stone upon -your edifice by the publication of your "Observations in the -Southern Hemisphere," I cannot refrain from congratulating you upon -having had your life ennobled by the conception and happy execution -of so great a design, and once more offering you my wishes that you -may long enjoy the glory you have so well won. - -W. W. -TRINITY COLLEGE, NOV. 22, 1846. - - - -{{7}} -PREFACE -TO THE THIRD EDITION. - - -IN the Prefaces to the previous Editions of this work, several -remarks were made which it is not necessary now to repeat to the -same extent. That a History of the Sciences, executed as this is, -has some value in the eyes of the Public, is sufficiently proved by -the circulation which it has obtained. I am still able to say that I -have seen no objection urged against the plan of the work, and -scarcely any against the details. The attempt to throw the history -of each science into EPOCHS at which some great and cardinal -discovery was made, and to arrange the subordinate events of each -history as belonging to the PRELUDES and the SEQUELS of such Epochs, -appears to be assented to, as conveniently and fairly exhibiting the -progress of scientific truth. Such a view being assumed, as it was a -constant light and guide to the writer in his task, so will it also, -I think, make the view of the reader far more clear and -comprehensive than it could otherwise be. With regard to the manner -in which this plan has been carried into effect with reference to -particular writers and their researches, as I have said, I have seen -scarcely any objection made. I was aware, as I stated at the outset, -of the difficulty and delicacy of the office which I had undertaken; -but I had various considerations to encourage me to go through it; -and I had a trust, which I {8} have as yet seen nothing to disturb, -that I should be able to speak impartially of the great scientific -men of all ages, even of our own. - -I have already said, in the Introduction, that the work aimed at -being, not merely a narration of the facts in the history of -Science, but a basis for the Philosophy of Science. It seemed to me -that our study of the modes of discovering truth ought to be based -upon a survey of the truths which have been discovered. This maxim, -so stated, seems sufficiently self-evident; yet it has, even up to -the present time, been very rarely acted on. Those who discourse -concerning the nature of Truth and the mode of its discovery, still, -commonly, make for themselves examples of truths, which for the most -part are utterly frivolous and unsubstantial (as in most Treatises -on Logic); or else they dig up, over and over, the narrow and -special field of mathematical truth, which certainly cannot, of -itself, exemplify the general mode by which man has attained to the -vast body of certain truth which he now possesses. - -Yet it must not be denied that the Ideas which form the basis of -Mathematical Truth are concerned in the formation of Scientific -Truth in general; and discussions concerning these Ideas are by no -means necessarily barren of advantage. But it must be borne in mind -that, besides these Ideas, there are also others, which no less lie -at the root of Scientific Truth; and concerning which there have -been, at various periods, discussions which have had an important -bearing on the progress of Scientific Truth;--such as discussions -concerning the nature and necessary attributes of Matter, of Force, -of Atoms, of Mediums, of Kinds, of Organization. The controversies -which have taken place concerning these have an important place in -the history of Natural Science in {9} its most extended sense. Yet -it appeared convenient to carry on the history of Science, so far as -it depends on Observation, in a line separate from these discussions -concerning Ideas. The account of these discussions and the -consequent controversies, therefore, though it be thoroughly -historical, and, as appears to me, a very curious and interesting -history, is reserved for the other work, the _Philosophy of the -Inductive Sciences_. Such a history has, in truth, its natural place -in the Philosophy of Science; for the Philosophy of Science at the -present day must contain the result and summing up of all the truth -which has been disentangled from error and confusion during these -past controversies. - -I have made a few Additions to the present Edition; partly, with a -view of bringing up the history, at least of some of the Sciences, -to the present time,--so far as those larger features of the History -of Science are concerned, with which alone I have here to deal,--and -partly also, especially in the First Volume, in order to rectify and -enlarge some of the earlier portions of the history. Several works -which have recently appeared suggested reconsideration of various -points; and I hoped that my readers might be interested in the -reflections so suggested. - -I will add a few sentences from the Preface to the First Edition. - -"As will easily be supposed, I have borrowed largely from other -writers, both of the histories of special sciences and of philosophy -in general.[1\P] I have done this without {10} scruple, since the -novelty of my work was intended to consist, not in its superiority -as a collection of facts, but in the point of view in which the -facts were placed. I have, however, in all cases, given references -to my authorities, and there are very few instances in which I have -not verified the references of previous historians, and studied the -original authors. According to the plan which I have pursued, the -history of each science forms a whole in itself, divided into -distinct but connected members, by the _Epochs_ of its successive -advances. If I have satisfied the competent judges in each science -by my selection of such epochs, the scheme of the work must be of -permanent value, however imperfect may be the execution of any of -its portions. - -[Note 1\P: Among these, I may mention as works to which I have -peculiar obligations, Tennemann's Geschichte der Philosophie; -Degerando's Histoire Comparée des Systèmes de Philosophie; -Montucla's Histoire des Mathématiques, with Delalande's continuation -of it; Delambre's Astronomie Ancienne, Astronomie du Moyen Age, -Astronomie Moderne, and Astronomie du Dix-huitième Siècle; Bailly's -Histoire d'Astronomie Ancienne, and Histoire d'Astronomie Moderne; -Voiron's Histoire d'Astronomie (published as a continuation of -Bailly), Fischer's Geschichte der Physik, Gmelin's Geschichte der -Chemie, Thomson's History of Chemistry, Sprengel's History of -Medicine, his History of Botany, and in all branches of Natural -History and Physiology, Cuvier's works; in their historical, as in -all other portions, most admirable and instructive.] - -"With all these grounds of hope, it is still impossible not to see -that such an undertaking is, in no small degree, arduous, and its -event obscure. But all who venture upon such tasks must gather trust -and encouragement from reflections like those by which their great -forerunner prepared himself for his endeavors;--by recollecting that -they are aiming to advance the best interests and privileges of man; -and that they may expect all the best and wisest of men to join them -in their aspirations and to aid them in their labors. - -"'Concerning ourselves we speak not; but as touching the matter -which we have in hand, this we ask;--that men deem it not to be the -setting up of an Opinion, but the performing of a Work; and that -they receive this as a certainty--that we are not laying the -foundations of any sect or doctrine, but of the profit and dignity -of mankind:--Furthermore, {11} that being well disposed to what -shall advantage themselves, and putting off factions and prejudices, -they take common counsel with us, to the end that being by these our -aids and appliances freed and defended from wanderings and -impediments, they may lend their hands also to the labors which -remain to be performed:--And yet, further, that they be of good -hope; neither feign and imagine to themselves this our Reform as -something of infinite dimension and beyond the grasp of mortal man, -when, in truth, it is, of infinite error, the end and true limit; -and is by no means unmindful of the condition of mortality and -humanity, not confiding that such a thing can be carried to its -perfect close in the space of one single day, but assigning it as a -task to a succession of generations.'--BACON--INSTAURATIO MAGNA, -_Præf. ad fin._ - -"'If there be any man who has it at heart, not merely to take his -stand on what has already been discovered, but to profit by that, -and to go on to something beyond;--not to conquer an adversary by -disputing, but to conquer nature by working;--not to opine probably -and prettily, but to know certainly and demonstrably;--let such, as -being true sons of nature (if they will consent to do so), join -themselves to us; so that, leaving the porch of nature which endless -multitudes have so long trod, we may at last open a way to the inner -courts. And that we may mark the two ways, that old one, and our new -one, by familiar names, we have been wont to call the one the -_Anticipation of the Mind_, the other, the _Interpretation of -Nature_.'--INST. MAG. _Præf. ad Part._ ii. - - - -{{13}} -CONTENTS -OF THE FIRST VOLUME. - - PAGE -~Preface to the Third Edition. 7~ -~Index of Proper Names. 23~ -~Index of Technical Terms. 33~ - -INTRODUCTION. 41 - -BOOK I. - -HISTORY OF THE GREEK SCHOOL PHILOSOPHY, WITH REFERENCE TO PHYSICAL -SCIENCE. - -CHAPTER I.--PRELUDE TO THE GREEK SCHOOL PHILOSOPHY. - -_Sect._ 1. First Attempts of the Speculative Faculty in Physical -Inquiries. 55 -_Sect._ 2. Primitive Mistake in Greek Physical Philosophy. 60 - -CHAPTER II.--THE GREEK SCHOOL PHILOSOPHY. - -_Sect._ 1. The General Foundation of the Greek School Philosophy. 63 -_Sect._ 2. The Aristotelian Physical Philosophy. 67 -_Sect._ 3. Technical Forms of the Greek Schools. 73 - 1. Technical Forms of the Aristotelian Philosophy. 73 - 2. " " " Platonists. 75 - 3. " " " Pythagoreans. 77 - 4. " " " Atomists and Others. 78 - -CHAPTER III.--FAILURE OF THE PHYSICAL PHILOSOPHY OF THE GREEK -SCHOOLS. - -_Sect._ 1. Result of the Greek School Philosophy. 80 -_Sect._ 2. Cause of the Failure of the Greek Physical Philosophy. 83 -{14} - -BOOK II. - -HISTORY OF THE PHYSICAL SCIENCES IN ANCIENT GREECE. - -Introduction. 95 - -CHAPTER I.--EARLIEST STAGES OF MECHANICS AND HYDROSTATICS. - -_Sect._ 1. Mechanics. 96 -_Sect._ 2. Hydrostatics. 98 - -CHAPTER II.--EARLIEST STAGES OF OPTICS. 100 - -CHAPTER III.--EARLIEST STAGES OF HARMONICS. 105 - -BOOK III. - -HISTORY OF GREEK ASTRONOMY. - -Introduction. 111 - -CHAPTER I.--EARLIEST STAGES OF ASTRONOMY. - -_Sect._ 1. Formation of the Notion of a Year. 112 -_Sect._ 2. Fixation of the Civil Year. 113 -_Sect._ 3. Correction of the Civil Year (Julian Calendar). 117 -_Sect._ 4. Attempts at the Fixation of the Month. 118 -_Sect._ 5. Invention of Lunisolar Years. 120 -_Sect._ 6. The Constellations. 124 -_Sect._ 7. The Planets. 126 -_Sect._ 8. The Circles of the Sphere. 128 -_Sect._ 9. The Globular Form of the Earth. 132 -_Sect._ 10. The Phases of the Moon. 134 -_Sect._ 11. Eclipses. 135 -_Sect._ 12. Sequel to the Early Stages of Astronomy. 136 - -CHAPTER II.--PRELUDE TO THE INDUCTIVE EPOCH OF HIPPARCHUS. 138 -{15} - -CHAPTER III.--INDUCTIVE EPOCH OF HIPPARCHUS. - -_Sect._ 1. Establishment of the Theory of Epicycles and - Eccentrics. 145 -_Sect._ 2. Estimate of the Value of the Theory of Eccentrics and - Epicycles. 151 -_Sect._ 3. Discovery of the Precession of the Equinoxes. 155 - -CHAPTER IV.--SEQUEL TO THE INDUCTIVE EPOCH OF HIPPARCHUS. - -_Sect._ 1. Researches which verified the Theory. 157 -_Sect._ 2. Researches which did not verify the Theory. 159 -_Sect._ 3. Methods of Observation of the Greek Astronomers. 161 -_Sect._ 4. Period from Hipparchus to Ptolemy. 166 -_Sect._ 5. Measures of the Earth. 169 -_Sect._ 6. Ptolemy's Discovery of Evection. 170 -_Sect._ 7. Conclusion of the History of Greek Astronomy. 175 -_Sect._ 8. Arabian Astronomy. 176 - -BOOK IV. - -HISTORY OF PHYSICAL SCIENCE IN THE MIDDLE AGES. - -Introduction. 185 - -CHAPTER I.--ON THE INDISTINCTNESS OF IDEAS OF THE MIDDLE AGES. - -1. Collections of Opinions. 187 -2. Indistinctness of Ideas in Mechanics. 188 -3. " " shown in Architecture. 191 -4. " " in Astronomy. 192 -5. " " shown by Skeptics. 192 -6. Neglect of Physical Reasoning in Christendom. 195 -7. Question of Antipodes. 195 -8. Intellectual Condition of the Religious Orders. 197 -9. Popular Opinions. 199 - -CHAPTER II.--THE COMMENTATORIAL SPIRIT OF THE MIDDLE AGES. 201 - -1. Natural Bias to Authority. 202 -2. Character of Commentators. 204 -3. Greek Commentators of Aristotle. 205 -{16} -4. Greek Commentators of Plato and Others. 207 -5. Arabian Commentators of Aristotle. 208 - -CHAPTER III.--OF THE MYSTICISM OF THE MIDDLE AGES. 211 - -1. Neoplatonic Theosophy. 212 -2. Mystical Arithmetic. 216 -3. Astrology. 218 -4. Alchemy. 224 -5. Magic. 225 - -CHAPTER IV.--OF THE DOGMATISM OF THE STATIONARY PERIOD. - -1. Origin of the Scholastic Philosophy. 228 -2. Scholastic Dogmas. 230 -3. Scholastic Physics. 235 -4. Authority of Aristotle among the Schoolmen. 236 -5. Subjects omitted. Civil Law. Medicine. 238 - -CHAPTER V.--PROGRESS OF THE ARTS IN THE MIDDLE AGES. - -1. Art and Science. 239 -2. Arabian Science. 242 -3. Experimental Philosophy of the Arabians. 243 -4. Roger Bacon. 245 -5. Architecture of the Middle Ages. 246 -6. Treatises on Architecture. 248 - -BOOK V. - -HISTORY OF FORMAL ASTRONOMY AFTER THE STATIONARY PERIOD. - -Introduction. 255 - -CHAPTER I.--PRELUDE TO THE INDUCTIVE EPOCH OF COPERNICUS. 257 - -CHAPTER II.--INDUCTION OF COPERNICUS. THE HELIOCENTRIC THEORY -ASSERTED ON FORMAL GROUNDS. 262 -{17} - -CHAPTER III--SEQUEL TO COPERNICUS. THE RECEPTION AND DEVELOPMENT -OF THE COPERNICAN THEORY. - -_Sect._ 1. First Reception of the Copernican Theory. 269 -_Sect._ 2. Diffusion of the Copernican Theory. 272 -_Sect._ 3. The Heliocentric Theory confirmed by Facts. Galileo's - Astronomical Discoveries. 276 -_Sect._ 4. The Copernican System opposed on Theological Grounds. 286 -_Sect._ 5. The Heliocentric Theory confirmed on Physical - Considerations. (Prelude to Kepler's Astronomical - Discoveries.) 287 - -CHAPTER IV.--INDUCTIVE EPOCH OF KEPLER. - -_Sect._ 1. Intellectual Character of Kepler. 290 -_Sect._ 2. Kepler's Discovery of his Third Law. 293 -_Sect._ 3. Kepler's Discovery of his First and Second Laws. - Elliptical Theory of the Planets. 296 - -CHAPTER V.--SEQUEL TO THE EPOCH OF KEPLER. RECEPTION, VERIFICATION, -AND EXTENSION OF THE ELLIPTICAL THEORY. - -_Sect._ 1. Application of the Elliptical Theory to the Planets. 302 -_Sect._ 2. " " " " " Moon. 303 -_Sect._ 3. Causes of the further Progress of Astronomy. 305 - -_THE MECHANICAL SCIENCES._ - -BOOK VI. - -HISTORY OF MECHANICS, INCLUDING FLUID MECHANICS. - -Introduction. 311 - -CHAPTER I.--PRELUDE TO THE EPOCH OF GALILEO. - -_Sect._ 1. Prelude to the Science of Statics. 312 -_Sect._ 2. Revival of the Scientific Idea of Pressure. - --Stevinus.--Equilibrium of Oblique Forces. 316 -_Sect._ 3. Prelude to the Science of Dynamics.--Attempts at the - First Law of Motion. 319 -{18} - -CHAPTER II.--INDUCTIVE EPOCH OF GALILEO.--DISCOVERY OF THE LAWS OF -MOTION IN SIMPLE CASES. - -_Sect._ 1. Establishment of the First Law of Motion. 322 -_Sect._ 2. Formation and Application of the Motion of Accelerating - Force. Laws of Falling Bodies. 324 -_Sect._ 3. Establishment of the Second Law of Motion.--Curvilinear - Motions. 330 -_Sect._ 4. Generalization of the Laws of Equilibrium.--Principle - of Virtual Velocities. 331 -_Sect._ 5. Attempts at the Third Law of Motion.--Notion of - Momentum. 334 - -CHAPTER III.--SEQUEL TO THE EPOCH OF GALILEO.--PERIOD OF -VERIFICATION AND DEDUCTION. 340 - -CHAPTER IV.--DISCOVERY OF THE MECHANICAL PRINCIPLES OF FLUIDS. - -_Sect._ 1. Rediscovery of the Laws of Equilibrium of Fluids. 345 -_Sect._ 2. Discovery of the Laws of Motion of Fluids. 348 - -CHAPTER V.--GENERALIZATION OF THE PRINCIPLES OF MECHANICS. - -_Sect._ 1. Generalization of the Second Law of Motion.--Central - Forces. 352 -_Sect._ 2. Generalization of the Third Law of Motion.--Centre - of Oscillation.--Huyghens. 356 - -CHAPTER VI.--SEQUEL TO THE GENERALIZATION OF THE PRINCIPLES OF -MECHANICS.--PERIOD OF MATHEMATICAL DEDUCTION.--ANALYTICAL -MECHANICS. 362 - -1. Geometrical Mechanics.--Newton, &c. 363 -2. Analytical Mechanics.--Euler. 363 -3. Mechanical Problems. 364 -4. D'Alembert's Principle. 365 -5. Motion in Resisting Media.--Ballistics. 365 -6. Constellation of Mathematicians. 366 -7. The Problem of Three Bodies. 367 -8. Mécanique Céleste, &c. 371 -9. Precession.--Motion of Rigid Bodies. 374 -10. Vibrating Strings. 375 -11. Equilibrium of Fluids.--Figure of the Earth.--Tides. 376 -12. Capillary Action. 377 -13. Motion of Fluids. 378 -14. Various General Mechanical Principles. 380 -15. Analytical Generality.--Connection of Statics and Dynamics. 381 -{19} - -BOOK VII. - -HISTORY OF PHYSICAL ASTRONOMY. - -CHAPTER I.--PRELUDE TO THE INDUCTIVE EPOCH OF NEWTON. 385 - -CHAPTER II.--THE INDUCTIVE EPOCH OF NEWTON.--DISCOVERY OF THE -UNIVERSAL GRAVITATION OF MATTER, ACCORDING TO THE LAW OF THE -INVERSE SQUARE OF THE DISTANCE. 399 - -1. Sun's Force on Different Planets. 399 -2. Force in Different Points of an Orbit. 400 -3. Moon's Gravity to the Earth. 402 -4. Mutual Attraction of all the Celestial Bodies. 406 -5. " " " Particles of Matter. 411 - Reflections on the Discovery. 414 - Character of Newton. 416 - -CHAPTER III.--SEQUEL TO THE EPOCH OF NEWTON.--RECEPTION OF THE -NEWTONIAN THEORY. - -_Sect._ 1. General Remarks. 420 -_Sect._ 2. Reception of the Newtonian Theory in England. 421 -_Sect._ 3. " " " " Abroad. 429 - -CHAPTER IV.--SEQUEL TO THE EPOCH OF NEWTON, CONTINUED. VERIFICATION -AND COMPLETION OF THE NEWTONIAN THEORY. - -_Sect._ 1. Division of the Subject. 433 -_Sect._ 2. Application of the Newtonian Theory to the Moon. 434 -_Sect._ 3. " " " " Planets, - Satellites, and Earth. 438 -_Sect._ 4. Application of the Newtonian Theory to Secular - Inequalities. 444 -_Sect._ 5. " " " " to the new Planets.446 -_Sect._ 6. " " " " to Comets. 449 -_Sect._ 7. " " " " to the Figure of - the Earth. 452 -_Sect._ 8. Confirmation of the Newtonian Theory by Experiments on - Attraction. 456 -_Sect._ 9. Application of the Newtonian Theory to the Tides. 457 - -CHAPTER V.--DISCOVERIES ADDED TO THE NEWTONIAN THEORY. - -_Sect._ 1. Tables of Astronomical Refraction. 462 -_Sect._ 2. Discovery of the Velocity of Light.--Römer. 463 -{20} -_Sect._ 3. Discovery of Aberration.--Bradley. 464 -_Sect._ 4. Discovery of Nutation. 465 -_Sect._ 5. Discovery of the Laws of Double Stars.--The Two - Herschels. 467 - -CHAPTER VI.--THE INSTRUMENTS AND AIDS OF ASTRONOMY DURING THE -NEWTONIAN PERIOD. - -_Sect._ 1. Instruments. 470 -_Sect._ 2. Observatories. 476 -_Sect._ 3. Scientific Societies. 478 -_Sect._ 4. Patrons of Astronomy. 479 -_Sect._ 5. Astronomical Expeditions. 480 -_Sect._ 6. Present State of Astronomy. 481 - -_ADDITIONS TO THE THIRD EDITION._ - -INTRODUCTION 489 - -BOOK I.--THE GREEK SCHOOL PHILOSOPHY. - -THE GREEK SCHOOLS. - -The Platonic Doctrine of Ideas. 491 - -FAILURE OF THE GREEK PHYSICAL PHILOSOPHY. - -Bacon's Remarks on the Greeks. 494 -Aristotle's Account of the Rainbow. 495 - -BOOK II.--THE PHYSICAL SCIENCES IN ANCIENT GREECE. - -Plato's Timæus and Republic. 497 -Hero of Alexandria. 501 - -BOOK III.--THE GREEK ASTRONOMY. - -Introduction. 503 - -EARLIEST STAGES OF ASTRONOMY. - -The Globular Form of the Earth. 505 -The Heliocentric System among the Ancients. 506 -The Eclipse of Thales. 508 -{21} - -BOOK IV.--PHYSICAL SCIENCE IN THE MIDDLE AGES. - -General Remarks. 511 - -PROGRESS IN THE MIDDLE AGES. - -Thomas Aquinas. 512 -Roger Bacon. 512 - -BOOK V.--FORMAL ASTRONOMY. - -PRELUDE TO COPERNICUS. - -Nicolas of Cus. 523 - -THE COPERNICAN THEORY. - -The Moon's Rotation. 524 -M. Foucault's Experiments. 525 - -SEQUEL TO COPERNICUS. - -English Copernicans. 526 -Giordano Bruno. 530 -Did Francis Bacon reject the Copernican Doctrine? 530 -Kepler persecuted. 532 -The Papal Edicts against the Copernican System repealed. 534 - -BOOK VI.--MECHANICS. - -PRINCIPLES AND PROBLEMS. - -Significance of Analytical Mechanics. 536 -Strength of Materials. 538 -Roofs--Arches--Vaults. 541 - -BOOK VII.--PHYSICAL ASTRONOMY. - -PRELUDE TO NEWTON. - -The Ancients. 544 -Jeremiah Horrox. 545 -Newton's Discovery of Gravitation. 546 -{22} - -THE PRINCIPIA. - -Reception of the _Principia_. 548 -Is Gravitation proportional to Quantity of Matter? 549 - -VERIFICATION AND COMPLETION OF THE NEWTONIAN THEORY. - -Tables of the Moon and Planets. 550 -The Discovery of Neptune. 554 -The Minor Planets. 557 -Anomalies in the Action of Gravitation. 560 -The Earth's Density. 561 -Tides. 562 -Double Stars. 563 - -INSTRUMENTS. - -Clocks. 565 - - - -{{23}} -INDEX OF PROPER NAMES. - -The letters _a_, _b_, indicate vol. I., vol. II., respectively. - -Abdollatif, _b._ 443. -Aboazen, _a._ 222. -Aboul Wefa, _a._ 180. -Achard, _b._ 174. -Achillini, _b._ 445. -Adam Marsh, _a._ 198. -Adanson, _b._ 404, 405. -Adelbold, _a._ 198. -Adelhard Goth, _a._ 198. -Adet, _b._ 279. -Achilles Tatius, _a._ 127. -Æpinus, _b._ 197, 203, 209. -Agassiz, _b._ 429, 521, 540. -Agatharchus, _b._ 53. -Airy, _a._ 372, 442, 477; _b._ 67, 120. -Albategnius, _a._ 177, 178. -Albertus Magnus, _a._ 229, 237; _b._ 367. -Albumasar, _a._ 222. -Alexander Aphrodisiensis, _a._ 206. -Alexander the Great, _a._ 144. -Alfarabi, _a._ 209. -Alfred, _a._ 198. -Algazel, _a._ 194. -Alhazen, _a._ 243; _b._ 54. -Alis-ben-Isa, _a._ 169. -Alkindi, _a._ 211, 226. -Almansor, _a._ 177. -Almeric, _a._ 236. -Alpetragius, _a._ 179 -Alphonso X., _a._ 151, 178. -Amauri, _a._ 236. -Ammonius Saccas, _a._ 206, 212. -Ampère, _b._ 183, 243, 244, 246, 284. -Anaxagoras, _a._ 78; _b._ 53. -Anaximander, _a._ 130, 132, 135. -Anaximenes, _a._ 56. -Anderson, _a._ 342. -Anna Comnena, _a._ 207. -Anselm, _a._ 229. -Arago, _b._ 72, 81, 100, 114, 254. -Aratus, _a._ 167. -Archimedes, _a._ 96, 99, 312, 316. -Arduino, _b._ 514. -Aristarchus, _a._ 137, 259. -Aristyllus, _a._ 144. -Aristophanes, _a._ 120. -Aristotle, _a._ 57, 334; _b._ 24, 58, 361, 412, 417, 420, 438, 444, -455, 583. -Arnold de Villâ Novâ, _a._ 228. -Arriaga, _a._ 335. -Artedi, _b._ 423. -Artephius, _a._ 226. -Aryabatta, _a._ 260. -Arzachel, _a._ 178. -Asclepiades, _b._ 439. -Asclepigenia, _a._ 215. -Aselli, _b._ 453. -Avecibron, _a._ 232. -Averroes, _a._ 194, 210. -Avicenna, _a._ 209. -Avienus, _a._ 169. -Aubriet, _b._ 387. -Audouin, _b._ 483. -Augustine, _a._ 197, 220, 232. -Autolycus, _a._ 130, 131. -Auzout, _a._ 474. - -Babbage, Mr. _b._ 254, 555. -Bachman, _b._ 386. -Bacon, Francis, _a._ 278, 383, 412; _b._ 25, 32, 165. -Bacon, Roger, _b._ 55. -Bailly, _a._ 199, 445. -Baliani, _a._ 326, 347. -Banister, _b._ 380. -Barlow, _b._ 67, 223, 245, 254. {24} -Bartholin, _b._ 70. -Barton, _b._ 125. -Bauhin, John, _b._ 381. -Bauhin, Gaspard, _b._ 381. -Beaumont, Elie de, _b._ 527, 532, 533, 539, 583, 588. -Beccaria, _b._ 199. -Beccher, _b._ 268. -Bede, _a._ 198, 232. -Bell, Sir Charles, _b._ 463. -Bélon, _b._ 421, 476. -Benedetti, _a._ 314, 321, 324, 336. -Bentley, _a._ 422, 424. -Berard, _b._ 154. -Bergman, _b._ 266, 281, 321. -Bernard of Chartres, _a._ 229. -Bernoulli, Daniel, _a._ 375, 378, 379, 380, 430; _b._ 32, 37, 39. -Bernoulli, James, _a._ 358. -Bernoulli, James, the younger, _b._ 42. -Bernoulli, John, _a._ 359, 361, 363, 366, 375, 393, 430; _b._ 32. -Bernoulli, John, the younger, _b._ 32. -Berthollet, _b._ 267, 278, 281. -Berzelius, _b._ 284, 289, 304, 335, 347, 348. -Bessel, _a._ 272. -Betancourt, _b._ 173. -Beudant, _b._ 348. -Bichat, _b._ 463. -Bidone, _a._ 350. -Biela, _a._ 452. -Biker, _b._ 174. -Biot, _b._ 75, 76, 81, 223, 249. -Black, _b._ 160, 272, 281. -Blair, _b._ 67. -Bloch, _b._ 425. -Blondel, _a._ 342. -Bock, _b._ 371. -Boëthius, _a._ 197, 208. -Boileau, _a._ 390. -Bonaparte, _b._ 241, 296. -Bonaventura, _a._ 233. -Bontius, _b._ 422. -Borelli, _a._ 323, 387, 393, 405, 406. -Bossut, _a._ 350. -Boué, Ami, _b._ 523. -Bouguer, _a._ 377. -Bouillet, _b._ 166. -Bourdon, _b._ 461. -Bournon, _b._ 326. -Bouvard, _a._ 443. -Boyle, _a._ 395; _b._ 80, 163, 263. -Boze, _b._ 198. -Bradley, _a._ 438, 441, 456, 463, 465. -Brander, _b._ 508, 516. -Brassavola, _b._ 368. -Brewster, Sir David, _b._ 65, 75, 81, 113, 119, 123, 331, 332. -Briggs, _a._ 276. -Brisbane, Sir Thomas, _a._ 478. -Brocchi, _b._ 519, 576, 589. -Brochant de Villiers, _b._ 527, 532. -Broderip, _b._ 562. -Brongniart, Alexandre, _b._ 516, 530. -Brongniart, Adolphe, _b._ 539. -Brook, Taylor, _a._ 359, 375; _b._ 31. -Brooke, Mr., _b._ 325. -Brougham, Lord, _b._ 80, 112. -Brown, Robert, _b._ 409, 474. -Brunfels, _b._ 368. -Bruno, Giordano, _a._ 272. -Buat, _a._ 350. -Buch, Leopold von, _b._ 523, 527, 539, 557. -Buckland, Dr., _b._ 534. -Budæus, _a._ 74. -Buffon, _b._ 317, 460, 476. -Bullfinger, _a._ 361. -Bullialdus, _a._ 172, 397. -Burckhardt, _a._ 442, 448. -Burg, _b._ 443. -Burkard, _b._ 459. -Burnet, _b._ 559, 584. - -Cabanis, _b._ 489. -Cæsalpinus, _b._ 316, 371, 373. -Calceolarius, _b._ 508. -Calippus, _a._ 123, 140. -Callisthenes, _a._ 144. -Camerarius, Joachim, _b._ 372. -Camerarius, Rudolph Jacob, _b._ 458, 459. -Campanella, _a._ 224, 237. -Campani, _a._ 474. -Camper, _b._ 476. -Canton, _b._ 197, 198, 219. -Capelli, _a._ 435. -Cappeller, _b._ 318. {25} -Cardan, _a._ 313, 319, 330, 335. -Carlini, _a._ 456. -Carne, _b._ 538. -Caroline, Queen, _a._ 422. -Carpa, _b._ 445. -Casræus, _a._ 326. -Cassini, Dominic, _a._ 454, 462, 479; _b._ 33. -Cassini, J., _a._ 439, 463. -Castelli, _a._ 340, 342, 346, 348. -Catelan, _a._ 358. -Cavallieri, _a._ 430. -Cavendish, _a._ 456; _b._ 204, 273, 278. -Cauchy, _a._ 379; _b._ 43, 127. -Caus, Solomon de, _a._ 332. -Cesare Cesariano, _a._ 249. -Chalid ben Abdolmalic, _a._ 169. -Chatelet, Marquise du, _a._ 361. -Chaussier, _b._ 463. -Chladni, _b._ 40, 41. -Christie, _b._ 254. -Christina, _a._ 390. -Chrompré, _b._ 304. -Cicero, _a._ 119. -Cigna, _a._ 376; _b._ 202. -Clairaut, _a._ 367, 377, 410, 437, 451, 454; _b._ 67. -Clarke, _a._ 361, 424. -Cleomedes, _a._ 161, 167. -Clusius, _b._ 378. -Cobo, _b._ 379. -Colombe, Ludovico delle, _a._ 346. -Colombus, Realdus, _b._ 446, 450. -Columna, Fabius, _b._ 381. -Commandinus, _a._ 316. -Comparetti, _b._ 79. -Condamine, _a._ 453. -Constantine of Africa, _b._ 367. -Conti, Abbé de, _a._ 360. -Conybeare, _b._ 519, 525. -Copernicus, _a._ 257. -Cosmas Indicopleustes, _a._ 196. -Cotes, _a._ 366, 425. -Coulomb, _b._ 204, 207, 209, 221. -Crabtree, _a._ 276, 302, 304. -Cramer, _b._ 35. -Cronstedt, _b._ 341. -**Cruickshank, _b._ 240. -Cumming, Prof., _b._ 252. -Cunæus, _b._ 196. -Cuvier, _b._ 421, 422, 466, 478, 481, 487, 492, 516, 517, 520, 522. - -D'Alembert, _a._ 361, 365, 367, 372, 374, 376, 378, 446; _b._ 33, 37. -D'Alibard, _b._ 198. -Dalton, Dr. John, _b_. 157, 169, 174, 285 &c., 288, &c. -Daniell, _b._ 178, 554. -Dante, _a._ 200. -D'Arcy, _a._ 380. -Davy, _b._ 291, 293, 295, 301. -Daubenton, _b._ 476. -Daubeny, Dr., _b._ 550. -Daussy, _a._ 459. -De Candolle, Prof., _b._ 408, 473. -Dechen, M. von, _b._ 533. -Defrance, _b._ 516, 518. -Degerando, _a._ 194, 228. -De la Beche, Sir H., _b._ 519. -Delambre, _a._ 442, 447. -De la Rive, Prof., _b._ 187. -Delisle, _a._ 431. -De Luc, _b._ 167, 177. -Démeste, _b._ 319. -Democritus, _a._ 78; _b._ 360. -Derham, _b._ 165. -Desaguliers, _b._ 193. -Descartes, _a._ 323, 328, 338, 343, 354, 387, 423; _b._ 56, 59, 220. -Des Hayes, _b._ 519. -Desmarest, _b._ 512, 515. -Dexippus, _a._ 208. -Digges, _a._ 331. -Dillenius, _b._ 402. -Diogenes Laërtius, _a._ 187. -Dioscorides, _b._ 364, 367. -Dollond, _a._475; _b._ 67. -Dominis, Antonio de, _b._ 59. -Dubois, _b._ 445. -Dufay, _b._ 194, &c., 201. -Du Four, _b._ 79. -Dufrénoy, _b._ 527, 532. -Dulong, _b._ 150, 187. -Duns Scotus, _a._ 233, 237. -Dunthorne, _a._ 435. -Dupuis, _a._ 125. -Durret, _a._ 288. {26} -Dutens, _a._ 82. -Duvernay, _b._ 475. - -Ebn Iounis, _a._ 177. -Encke, _a._ 451, 467, 483. -Eratosthenes, _a._ 158. -Ericsen, _b._ 167. -Eristratus _b._ 453. -Etienne, _b._ 445. -Evelyn, _a._ 422. -Euclid, _a._ 100, 101, 131, 132. -Eudoxus, _a._ 140, 143. -Euler, _a._ 363, 367, 370, 377, 380, 437; _b._ 32, 40. -Eusebius, _a._ 195. -Eustachius, _b._ 445, 453. -Eustratus, _a._ 207. - -Fabricius, _a._ 207. -Fabricius of Acquapendente, _b._ 456. -Fabricius, David, _a._ 300. -Fallopius, _b._ 445. -Faraday, Dr., _b._ 245, 254, 291, 292, 296, 302. -Fermat, _a._ 341, 353. -Fitton, Dr., _b._ 524. -Flacourt, _b._ 379. -Flamsteed, _a._ 304, 409, 410, 419, 427, 435. -Fleischer, _b._ 57. -Fontaine, _a._ 372. -Fontenelle, _a._ 439; _b._ 265, 509. -Forbes, Prof. James, _b._ 155. -Forster, Rev. Charles, _a._ 243. -Fourcroy, _b._ 278, 281. -Fourier, _b._ 141, 147, 152, 180. -Fowler, _b._ 242. -Fracastoro, _b._ 507. -Francis I. (king of France), _a._ 237. -Franklin, _b._ 195, 197, 202. -Fraunhofer, _a._ 472, 475; _b._ 68, 98. 128. -Frederic II., Emperor, _a._ 236. -Fresnel, _b._ 72, 92, 96, 102, 114, 115, 179. -Fries, _b._ 418. -Frontinus, _a._ 250. -Fuchs, _b._ 334, 369. -Fuchsel, _b._ 513. - -Gærtner, _b._ 404. -Galen, _b._ 440, 443, 444, 445, 462, 464. -Galileo, _a._ 276, 319, 322, 324, &c., 336, 342, 345. -Gall, _b._ 463, 465. -Galvani, _b._ 238, 240. -Gambart, _a._ 451. -Gascoigne, _a._ 470. -Gassendi, _a._ 288, 341, 390, 392; _b._ 33. -Gauss, _a._ 372, 448. -Gay-Lussac, _b._ 158, 169, 179, 283, 290. -Geber, _a._ 178, 224. -Gellibrand, _b._ 219. -Geminus, _a._ 118, 143, 166. -Generelli, Cirillo, _b._ 587. -Geoffroy (botanist), _b._ 459. -Geoffroy (chemist), _b._ 265. -Geoffroy Saint-Hilaire, _b._ 477, 480, 483. -George Pachymerus, _a._ 207. -Gerbert, _a._ 198. -Germain, Mlle. Sophie, _b._ 43. -Germanicus, _a._ 168. -Gessner, _b._ 316, 372, 508. -Ghini, _b._ 376. -Gibbon, _a._ 242. -Gilbert, _a._ 274, 394; _b._ 192, 217, 219, 224. -Giordano Bruno, _a._ 272, 273. -Girard, _a._ 350. -Girtanner, _b._ 169. -Giseke, _b._ 398. -Glisson, _b._ 466. -Gmelin, _b._ 348. -Godefroy of St. Victor, _a._ 231. -Goldfuss, _b._ 519. -Göppert, _b._ 578. -Göthe, _b._ 63, 469, 473. -Gough, _b._ 171. -Graham, _a._ 471; _b._ 219. -Grammatici, _b._ 435. -Grazia, Vincenzio di, _a._ 346. -Greenough, _b._ 527. -Gregory, David, _a._ 426, 435. -Gregory VII., Pope, _a._ 227. -Gregory IX., Pope, _a._ 237. -Gren, _b._ 174. -Grew, _b._ 457, 475. -Grey, _b._ 194. -Grignon, _b._ 319. -Grimaldi, _a._ 341; _b._ 60, 79. {27} -Grotthuss, _b._ 304. -Guericke, Otto, _b._ 33, 193. -Guettard, _b._ 510. -Gulielmini, _b._ 317. -Guyton de Morveau, _b._ 278, 281. - -Hachette, _b._ 350. -Hadley, _a._ 474. -Haidinger, _b._ 330. -Halicon, _a._ 150. -Haller, _b._ 401, 466. -Halley, _a._ 354, 355, 396, 398, 421, 426, 435, 443, 450, 454, 480; -_b._ 225. -Haly, _a._ 222. -Hamilton, Sir W. (mathem.), _b._ 124, 130. -Hampden, Dr., _a._ 228. -Hansen, _a._ 372, 374. -Hansteen, _b._ 219. -Harding, _a._ 448. -Harris, Mr. Snow, _b._ 209. -Harrison, _a._ 473. -Hartsoecker, _a._ 474. -Harvey, _b._ 446, 449, 456. -Hausmann, _b._ 329. -Haüy, _b._ 320, &c., 325, 342. -Hawkesbee, _b._ 193, 195. -Hegel, _a._ 415. -Helmont, _b._ 262. -Henckel, _b._ 318. -Henslow, Professor, _b._ 474. -Heraclitus, _a._ 56. -Herman, Paul, _b._ 379. -Hermann, Contractus, _a._ 198. -Hermann, James, _a._ 359, 362, 363; _b._ 386, 387. -Hermolaus Barbarus, _a._ 75. -Hernandez, _b._ 379. -Herodotus, _a._ 57; _b._ 361, 506. -Herophilus, _b._ 441. -Herrenschneider, _b._ 145. -Herschel, Sir John, _a._ 467; _b._ 67, 81, 254, 333, 555, 559. -Herschel, Sir William, _a._ 446; _b._ 80. -Hevelius, _a._ 450, 471, 480. -Higgins, _b._ 287. -Hill, _b._ 319, 403. -Hipparchus, _a._ 144. -Hippasus, _a._ 107. -Hippocrates, _b._ 438. -Hoff, K. E. A. von, _b._ 545, 550. -Hoffmann, _b._ 527. -Home, _b._ 518. -Homer, _b._ 438. -Hooke, _a._ 324, 353, 354, 387, 395, 396, 401, 406; _b._ 29, 41, 62, -77, 79, 85. -Hopkins, Mr. W., _b._ 40, 557. -Horrox, _a._ 276, 303, 395. -Hoskins, _a._ 355. -Howard, Mr. Luke, _b._ 179. -Hudson, _b._ 403. -Hugo of St. Victor, _a._ 231. -Humboldt, Alexander von, _b._ 219, 523, 538, 549. -Humboldt, Wilhelm von, _b._ 240. -Hunter, John, _b._ 476. -Hutton (fossilist), _b._ 519. -Hutton (geologist), _a._ 456; _b._ 515, 584. -Huyghens, _a._ 337, 343, 353, 357, 377, 387, 412; _b._ 33, 62, 70, -86, 87. -Hyginus, _a._ 168. - -Iamblichus, _a._ 214. -Ideler, _a._ 113. -Ivory, _a._ 372. - -Jacob of Edessa, _a._ 209. -Jameson, Professor, _b._ 338, 514. -Job, _a._ 124. -John of Damascus, _a._ 206. -John Philoponus, _a._ 206. -John of Salisbury, _a._ 232, 234. -John Scot Erigena, _a._ 229. -Jordanus Nemorarius, _a._ 314, 331. -Joseph, _a._ 226. -Julian, _a._ 215. -Jung, Joachim, _b._ 384. -Jussieu, Adrien de, _b._ 407. -Jussieu, Antoine Laurent de, _b._ 406. -Jussieu, Bernard de, _b._ 406. - -Kæmpfer, _b._ 379. -Kant, _b._ 490. -Kazwiri, _b._ 583. -Keckerman, _a._ 235. -Keill, _a._ 367, 426; _b._ 264. -Kelland, Mr. Philip, _b._ 127, 130. {28} -Kempelen, _b._ 47. -Kepler, _a._ 263, 271, 290, 353, 383, &c., 415, 462; _b._ 55, 56. -Kircher, _a._ 218. -Kirwan, _b._ 274, 278. -Klaproth, _b._ 279. -Klingenstierna, _a._ 475; _b._ 67. -Knaut, Christopher, _b._ 386. -Knaut, Christian, _b._ 386. -König, _b._ 519. -Krafft, _b._ 142, 225. -Kratzenstein, _b._ 166. -Kriege, _b._ 380. - -Lacaille, _a._ 442, 454. -Lactantius, _a._ 195. -Lagrange, _a._ 367, 369, 375, 381, 444; _b._ 35, 37, 39. -Lamé, _b._ 129. -La Hire, _a._ 439, 463. -Lalande, _a._ 440, 447. -Lamarck, _b._ 408, 478, 518. -Lambert, _b._ 40, 142, 221. -Landen, _a._ 375. -Lansberg, _a._ 288, 302, 303. -Laplace, _a._ 370, &c., 444, 457; _b._ 36, 140, 147, 184. -Lasus, _a._ 107. -Latreille, _b._ 485. -Lavoisier, _b._ 274, 275, 276, &c., 280. -Laughton, _a._ 424. -Launoy, _a._ 236. -Laurencet, _b._ 484. -Lawrence, _b._ 565. -Lecchi, _a._ 350. -Leeuwenhoek, _b._ 457, 460. -Legendre, _b._ 223. -L'Hôpital, _a._ 358. -Leibnitz, _a._ 360, 391. -Le Monnier, _a._ 435, 437, 463. -Leonardo da Vinci, _a._ 251, 318; _b._ 507, 586. -Leonicenus, _b._ 368. -Le Roi, _b._ 167, 178. -Leslie, _b._ 145, 151, 181. -Levy, _b._ 331. -Leucippus, _a._ 78, 84. -Lexell, _a._ 447, 452. -Lhwyd, _b._ 508. -Libri, _b._ 151. -Lindenau, _a._ 440. -Lindley, _b._ 474, 519. -Linnæus, _b._ 318, 388, 423. -Linus, _b._ 61. -Lister, _b._ 509, 511. -Littrow, _a._ 477. -Lloyd, Professor, _b._ 125, 130. -Lobel, _b._ 381, 408. -Locke, _a._ 422. -Longomontanus, _a._ 297, 302. -Louville, _a._ 431, 439. -Lubbock, _a._ 372, 373, 459. -Lucan, _a._ 190. -Lucas, _b._ 62. -Lyell, _b._ 500, 529, 545, 560, 562, 590. - -Macleay, _b._ 418. -Magini, _a._ 270. -Mairan, _a._ 361. -Malpighi, _b._ 456. -Malus, _b._ 71, 74. -Manilius, _a._ 168. -Maraldi, _a._439; _b._ 79. -Marcet, _b._ 187. -Margrave, _b._ 422. -Marinus (anatomist), _b._ 462. -Marinus (Neoplatonist), _a._ 215. -Marriotte, _a._ 343. -Marsilius Ficinus, _a._ 238. -Martianus Capella, _a._ 259. -Martyn, T., _b._ 402. -Mæstlin, _a._ 271, 287. -Matthioli, _b._ 381. -Maupertuis, _a._ 367, 431, 453. -Mayer, Tobias, _a._ 165; _b._ 146, 206, 221. -Mayo, Herbert, _b._ 464. -Mayow, _b._ 277. -Mazeas, _b._ 80, 199. -MacCullagh, Professor, _b._ 123, 130. -Meckel, _b._ 486. -Melloni, _b._ 154. -Menelaus, _a._ 167. -Mersenne, _a._ 328, 342, 347, 390; _b._ 28. -Messa, _b._ 445. -Meton, _a._ 121. -Meyranx, _b._ 484. -Michael Scot, _a._ 226. -Michell, _b._ 511. {29} -Michelotti, _a._ 350. -Miller, Professor, _b._ 331. -Milton, _a._ 200, 275, 340. -Mitscherlich, _b._ 334. -Mohs, _b._ 326, 329, 345, &c., 349, 351. -Mondino, _b._ 445. -Monge, _b._ 274. -Monnet, _b._ 510. -Monnier, _b._ 197. -Monteiro, _b._ 331. -Montfaucon, _b._ 196. -Morin, _a._ 288. -Morison, _b._ 383. -Moro, Lazzaro, _b._ 587. -Morveau, Guyton de, _b._ 278, 281. -Mosotti, _b._ 211. -Munro, _b._ 476. -Murchison, Sir Roderic, _b._ 530. -Muschenbroek, _b._ 166. - -Napier, _a._ 276, 306. -Naudæus, _a._ 226. -Naumann, _b._ 331, 352. -Newton, _a._ 343, 349, 353, 355, 363, 399, &c., 420, 432, 463; _b._ -33, 39, 59, 70, 73, 77, 88, 142, 450. -Nicephorus Blemmydes, _a._ 207. -Nicholas de Cusa, _a._ 261. -Nicomachus, _a._ 104. -Nigidius Figulus, _a._ 219. -Nobili, _b._ 154. -Nollet, _b._ 196. -Nordenskiöld, _b._ 350. -Norman, _b._ 218. -Norton, _a._ 331. -Numa, _a._ 118, 261. - -Odoardi, _b._ 513, 515. -Oersted, Professor, _b._ 243. -Œyenhausen, _b._ 533. -Oken, Professor, _b._ 477. -Olbers, _a._ 448. -Orpheus, _a._ 214. -Osiander, _a._ 268. -Ott, _b._ 145. -Otto Guericke, _b._ 193, 195. -Ovid, _b._ 506. - -Pabst von Ohain, _b._ 341. -Packe, _b._ 509. -Pallas, _b._ 476, 513. -Papin, _b._ 173. -Pappus, _a._ 188. -Paracelsus, _a._ 226; _b._ 262. -Pardies, _b._ 61. -Pascal, _a._ 346. -Paulus III., Pope, _a._ 267. -Pecquet, _b._ 453. -Pepys, _a._ 422. -Perrier, _a._ 348. -Peter of Apono, _a._ 226. -Peter Bungo, _a._ 217. -Peter Damien, _a._ 231. -Peter the Lombard, _a._ 231. -Peter de Vineis, _a._ 237. -Petit, _b._ 149, 187. -Petrarch, _a._ 237. -Philip, Dr. Wilson, _b._ 454. -Phillips, William, _b._ 325, 343, 525. -Philolaus, _a._ 259. -Photius, _a._ 208. -Piazzi, _a._ 447, 485. -Picard, _a._ 404, 464, 470; _b._ 33. -Piccolomini, _a._ 336. -Pictet, _b._ 168. -Picus of Mirandula, _a._ 226, 238. -Plana, _a._ 372. -Playfair, _a._ 423. -Pliny, _a._ 150, 187, 219; _b._ 316, 359, 364. -Plotinus, _a._ 207, 213. -Plunier, _b._ 380. -Plutarch, _a._ 77, 187. -Poisson, _a._ 372, 377; _b._ 40, 43, 182, 208, 222. -Polemarchus, _a._ 141, 142. -Poncelet, _a._ 350. -Pond, _a._ 477. -Pontanus, Jovianus, _b._ 458. -Pontécoulant, _a._ 372. -Pope, _a._ 427. -Porphyry, _a._ 205, 207. -Posidonius, _a._ 169. -Potter, Mr. Richard, _b._ 126, 130. -Powell, Prof., _b._ 128, 130, 154. -Prevost, Pierre, _b._ 143. -Prevost, Constant, _b._ 589. -Prichard, Dr., _b._ 500, 565. {30} -Priestley, _b._ 271, 273, 279. -Proclus, _a._ 204, 207, 214, 217, 222. -Prony, _a._ 350; _b._ 174. -Proust, _b._ 267. -Prout, Dr., _b._ 289, 454. -Psellus, _a._ 208. -Ptolemy _a._ 149, &c.; _b._ 26 -Ptolemy Euergetes, _a._ 155. -Purbach, _a._ 299. -Pythagoras, _a._ **65, 78, 127, 217. -Pytheas, _a._ 162. - -Quetelet, M., _b._ 130. - -Raleigh, _b._ 378. -Ramsden, _a._ 471. -Ramus, _a._ 237, 301. -Raspe, _b._ 514, 516. -Ray, _b._ 384, 422. -Raymund Lully, _a._ 226. -Reaumur, _b._ 509. -Recchi, _b._ 379. -Redi, _b._ 475. -Reichenbach, _a._ 472. -Reinhold, _a._ 269. -Rennie, Mr. George, _a._ 350. -Rheede, _b._ 379. -Rheticus, _a._ 266, 269. -Riccioli, _a._ 288, 341. -Richman, _b._ 142, 199. -Richter, _b._ 286. -Riffault, _b._ 304. -Riolan, _b._ 448. -Rivinus, _b._ 386. -Rivius, _a._ 250, 326. -Robert Grostête, _a._ 198, 226. -Robert of Lorraine, _a._ 198. -Robert Marsh, _a._ 199. -Roberval, _b._ 33. -Robins, _a._ 342. -Robinson, Dr., _a._ 477. -Robison, _a._ 169. 173, 206. -Roger Bacon, _a._ 199, 226, 244. -Rohault, _a._ 391, 423. -Romé de Lisle, _b._ 318, 319, 320, 324, 328. -Römer, _a._ 464, 480; _b._ 33. -Rondelet, _b._ 421. -Roscoe, _b._ 409. -Ross, Sir John, _b._ 219. -Rothman, _a._ 264. -Rouelle, _b._ 512, 515. -Rousseau, _b._ 401. -Rudberg, _b._ 127. -Ruellius, _b._ 368. -Rufus, _b._ 441. -Rumphe, _b._ 379. - -Saluces, _a._ 376. -Salusbury, _a._ 276. -Salviani, _b._ 421 -Santbach, _a._ 325. -Santorini, _b._ 462. -Saron, _a._ 446. -Savart, _b._ 40, 44, 245. -Savile, _a._ 205. -Saussure, _b._ 177, 513. -Sauveur, _b._ 30, 37. -Scheele, _b._ 271. -Schelling, _b._ 63. -Schlottheim, _b._ 514, 519. -Schmidt, _b._ 557. -Schomberg, Cardinal, _a._ 267. -Schweigger, _b._ 251. -Schwerd, _b._ 125. -Scilla, _b._ 508. -Scot, Michael, _b._ 367. -Scrope, Mr. Poulett, _b._ 550. -Sedgwick, Professor, _b._ 533, 538. -Sedillot, M., _a._ 179. -Seebeck, Dr., _b._ 75, 81, 252. -Segner, _a._ 375. -Seneca, _a._ 168, 259, 346. -Sergius, _a._ 209. -Servetus, _b._ 446. -Sextus Empiricus, _a._ 193. -S'Gravesande, _a._ 361. -Sharpe, _b._ 174. -Sherard, _b._ 379. -Simon of Genoa, _b._ 367. -Simplicius, _a._ 204, 206. -Sloane, _b._ 380. -Smith, Mr. Archibald, _b._ 130. -Smith, Sir James Edward, _b._ 403. -Smith, William, _b._ 515, 521. -Snell, _b._ 56, 57. -Socrates, _b._ 442. -Solomon, _a._ 227**; _b._ 361. {31} -Sorge, _b._ 38. -Sosigenes, _a._ 118, 168. -Southern, _b._ 174. -Sowerby, _b._ 519. -Spallanzani, _b._ 454. -Spix, _b._ 477. -Sprengel, _b._ 473. -Stahl, _b._ 268. -Stancari, _b._ 29. -Steno, _b._ 317, 507, 512. -Stephanus, _b._ 445. -Stevinus, _a._ 317, 336, 345, 357. -Stillingfleet, _b._ 403. -Stobæus, _a._ 208. -Stokes, Mr. C. _b._ 578. -Strabo, _a._ 203; _b._ 363, 587. -Strachey, _b._ 511. -Stukeley, _b._ 511. -Svanberg, _b._ 149. -Surian, _b._ 380. -Sylvester II. (Pope), _a._ 198, 227. -Sylvius, _b._ 263, 445, 446. -Symmer, _b._ 202. -Syncellus, _a._ 117. -Synesius, _a._ 166. - -Tacitus, _a._ 220. -Tartalea, _b._ 315, 321, 325. -Tartini, _b._ 38. -Taylor, Brook, _a._ 359, 375; _b._ 31. -Tchong-Kang, _a._ 135, 162. -Telaugé, _a._ 217. -Tennemann, _a._ 228. -Thales, _a._ 56, 57, 63, 130. -Thebit, _a._ 226. -Thenard, _b._ 283. -Theodore Metochytes, _a._ 207. -Theodosius, _a._ 168. -Theophrastus, _a._ 205; _b._ 360, 362, 363, 370. -Thomas Aquinas, _a._ 226, 232, 237. -Thomson, Dr., _b._ 288, 289. -Tiberius, _a._ 220. -Timocharis, _a._ 144. -Torricelli, _a._ 336, 340, 347, 349. -Tournefort, _b._ 386, 458. -Tostatus, _a._ 197. -Totaril, Cardinal, _a._ 237. -Tragus, _b._ 368. -Trithemius, _a._ 228. -Troughton, _a._ 471. -Turner, _b._ 289. -Tycho Brahe, _a._ 297, 302; _b._ 55, 56. - -Ubaldi, _a._ 313. -Ulugh Beigh, _a._ 178. -Ungern-Sternberg, Count, _b._ 550. -Uranus, _a._ 209. -Ure, Dr., _b._ 174. -Usteri, _b._ 473. - -Vaillant, Sebastian, _b._ 459. -Vallisneri, _b._ 508. -Van Helmont, _b._ 262. -Varignon, _a._ 344; _b._ 454. -Varolius, _b._ 463. -Varro, Michael, _a._ 314, 319, 326, 332. -Vesalius, _b._ 444, 445, 462. -Vicq d'Azyr, _b._ 463, 476. -Vieussens, _b._ 463. -Vincent, _a._ 355. -Vincent of Beauvais, _b._ 367. -Vinci, Leonardo da, _a._ 251, 318; _b._ 507. -Virgil (bishop of Salzburg), _a._ 197. -Virgil (a necromancer), _a._ 227. -Vitello, _b._ 56. -Vitruvius, _a._ 249, 251; _b._ 25. -Viviani, _a._ 337, 340. -Voet, _a._ 390. -Voigt, _b._ 473. -Volta, _b._ 238, 240. -Voltaire, _a._ 361, 431. -Voltz, _b._ 533. -Von Kleist, _b._ 196. - -Wallerius, _b._ 319. -Wallis, _a._ 276, 341, 343, 387, 395; _b._ 37. -Walmesley, _a._ 440. -Warburton, _a._ 427. -Ward, Seth, _a._ 276, 396. -Wargentin, _a._ 441. -Watson, _b._ 195, 196, 202. -Weber, Ernest and William, _b._ 43. -Weiss, Prof., _b._ 326, 327. -Wells, _b._ 170, 177, 242. -Wenzel, _b._ 286. {32} -Werner, _b._ 318, 337, 341, 514, 520, 521, 528, 584. -Wheatstone, _b._ 44. -Wheler, _b._ 379. -Whewell, _a._ 459; _b._ 330. -Whiston, _a._ 424. -Wilcke, _b._ 161, 198, 204. -Wilkins (Bishop), _a._ 275, 332, 395. -William of Hirsaugen, _a._ 198. -Willis, Rev. Robert, _a._ 246; _b._ 40, 47. -Willis, Thomas, _b._ 462, 463, 465. -Willoughby, _b._ 422, 423. -Wolf, Caspar Frederick, _b._ 472. -Wolff, _a._ 361; _b._ 165. -Wollaston, _b._ 68, 70, 71, 81, 288, 325. -Woodward, _b._ 508, 511, 584. -Wren, _a._ 276, 343, 395; _b._ 421. -Wright, _a._ 435. - -Xanthus, _b._ 360. - -Yates, _b._ 219. -Young, Thomas, _a._ 350; _b._ 43, 92, &c., 111, 112. - -Zabarella, _a._ 235. -Zach, _a._ 448. -Ziegler, _b._ 174. -Zimmerman, _b._ 557. - - - -{{33}} -INDEX OF TECHNICAL TERMS. - - -Aberration, _a._ 464. -Absolute and relative, _a._ 69. -Accelerating force, _a._ 326. -Achromatism, _b._ 66. -Acid, _b._ 263. -Acoustics, _b._ 24. -Acronycal rising and setting, _a._ 131. -Action and reaction, _a._ 343. -Acuation, _b._ 319. -Acumination, _b._ 319. -Acute harmonics, _b._ 37. -Ætiology, _b._ 499. -Affinity (in Chemistry), _b._ 265. - " (in Natural History), _b._ 418. -Agitation, Centre of, _a._ 357. -Alidad, _a._ 184. -Alineations, _a._ 158, 161. -Alkali, _b._ 262. -Almacantars, _a._ **181. -Almagest, _a._ 170. -Almanac, _a._ **181. -Alphonsine tables, _a._ 178. -Alternation (of formations), _b._ 538. -Amphoteric silicides, _b._ 352. -Analogy (in Natural History), _b._ 418. -Analysis (chemical), _b._ 262. - " (polar, of light), _b._ 80. -Angle of cleavage, _b._ 322. - " incidence, _b._ 53. - " reflection, _b._ 53. -Animal electricity, _b._ 238. -Anïon, _b._ 298. -Annus, _a._ 113. -Anode, _b._ 298. -Anomaly, _a._ 139, 141. -Antarctic circle, _a._ 131. -Antichthon, _a._ 82. -Anticlinal line, _b._ 537. -Antipodes, _a._ 196. -Apogee, _a._ 146. -Apotelesmatic astrology, _a._ 222. -Apothecæ, _b._ 366. -Appropriate ideas, _a._ 87. -Arctic circle, _a._ 131. -Armed magnets, _b._ 220. -Armil, _a._ 163. -Art and science, _a._ 239. -Articulata, _b._ 478. -Artificial magnets, _b._ 220. -Ascendant, _a._ 222. -Astrolabe, _a._ 164. -Atmology, _b._ 137, 163. -Atom, _a._ 78. -Atomic theory, _b._ 285. -Axes of symmetry (of crystals), _b._ 327. -Axis (of a mountain chain), _b._ 537. -Azimuth, _a._ **181. -Azot, _b._ 276. - -Ballistics, _a._ 365. -Bases (of salts), _b._264. -Basset (of strata), _b._ 512. -Beats, _b._ 29. - -Calippic period, _a._ 123. -Caloric, _b._ 143. -Canicular period, _a._ 118. -Canon, _a._ 147. -Capillary action, _a._ 377. -Carbonic acid gas, _b._ 276 -Carolinian tables, _a._ 304. -Catasterisms, _a._ 158. -Categories, _a._ 206. -Cathïon, _b._ 298. -Cathode, _b._ 298. -Catïon, _b._ 298. -Causes, Material, formal, efficient, final, _a._ 73. {34} -Centrifugal force, _a._ 330. -Cerebral system, _b._ 463. -Chemical attraction, _b._ 264. -Chyle, _b._ 453. -Chyme, _b._ 453. -Circles of the sphere, _a._ 128. -Circular polarization, _b._ 82, 119. - " progression (in Natural History), _b._ 418. -Civil year, _a._ 117. -Climate, _b._ 146. -Coexistent vibrations, _a._ 376. -Colures, _a._ 131. -Conditions of existence (of animals), _b._ 483, 492. -Conducibility, _b._ 143. -Conductibility, _b._ 143. -Conduction, _b._ 139. -Conductivity, _b._ 143. -Conductors, _b._ 194. -Conical refraction, _b._ 124. -Conservation of areas, _a._ 380. -Consistence (in Thermotics), _b._ 160. -Constellations, _a._ 124. -Constituent temperature, _b._ 170. -Contact-theory of the Voltaic pile, _b._ 295. -Cor (of plants), _b._ 374. -Cosmical rising and setting, _a._ 131. -Cotidal lines, _a._ 460. -Craters of elevation, _b._ 556. - -Dæmon, _a._ 214. -D'Alembert's principle, _a._ 365. -Day, _a._ 112. -Decussation of nerves, _b._ 462. -Deduction, _a._ 48. -Deferent, _a._ 175. -Definite proportions (in Chemistry), _b._ 285. -Delta, _b._ 546. -Dephlogisticated air, _b._ 273. -Depolarization, _b._ 80. - " of heat, _b._ 155. -Depolarizing axes, _b._ 81. -Descriptive phrase (in Botany), _b._ 393. -Dew, _b._ 177. -Dichotomized, _a._ 137. -Diffraction, _b._ 79. -Dimorphism, _b._ 336. -Dioptra, _a._ 165. -Dipolarization, _b._ 80, 82. -Direct motion of planets, _a._ 138. -Discontinuous functions, _b._ 36. -Dispensatoria, _b._ 366. -Dispersion (of light), _b._ 126. -Doctrine of the sphere, _a._ 130. -Dogmatic school (of medicine), _b._ 439. -Double refraction, _b._ 69. - -Eccentric, _a._ 145. -Echineis, _a._ 190. -Eclipses, _a._ 135. -Effective forces, _a._ 359. -Elective attraction, _b._ 265. -Electrical current, _b._ 242. -Electricity, _b._ 192. -Electrics, _b._ 194. -Electrical tension, _b._ 242. -Electro-dynamical, _b._ 246. -Electrodes, _b._ 298. -Electrolytes, _b._ 298. -Electro-magnetism, _b._ 243. -Elements (chemical), _b._ 309. -Elliptical polarization, _b._ 122, 123. -Empiric school (of medicine), _b._ 439. -Empyrean, _a._ 82. -Enneads, _a._ 213. -Entelechy, _a._ 74. -Eocene, _b._ 529. -Epicycles, _a._ 140, 145 -Epochs, _a._ 46. -Equant, _a._ 175. -Equation of time, _a._ 159. -Equator, _a._ 130. -Equinoctial points, _a._ 131. -Escarpment, _b._ 537. -Evection, _a._ 171, 172. -Exchanges of heat, Theory of, _b._ 143. - -Facts and ideas, _a._ 43. -Faults (in strata), _b._ 537. -Final causes, _b._ 442, 492. -Finite intervals (hypothesis of), _b._ 126. -First law of motion, _a._ 322. -Fits of easy transmission, _b._ 77, 89. -Fixed air, _b._ 272. -Fixity of the stars, _a._ 158. {35} -Formal optics, _b._ 52. -Franklinism, _b._ 202. -Fresnel's rhomb, _b._ 105. -Fringes of shadows, _b._ 79, 125. -Fuga vacui, _a._ 347. -Full months, _a._ 122. -Function (in Physiology), _b._ 435. - -Galvanism, _b._ 239. -Galvanometer, _b._ 251. -Ganglionic system, _b._ 463. -Ganglions, _b._ 463. -Generalization, _a._ 46. -Geocentric theory, _a._ 258. -Gnomon, _a._ 162. -Gnomonic, _a._ 137. -Golden number, _a._ 123. -Grave harmonics, _b._ 38. -Gravitate, _a._ 406. - -Habitations (of plants), _b._ 562. -Hæcceity, _a._ 233. -Hakemite tables, _a._ 177. -Halogenes, _b._ 308. -Haloide, _b._ 352. -Harmonics, Acute, _b._ 37. - " Grave, _b._ 38. -Heat, _b._ 139. - " Latent, _b._ 160. -Heccædecaëteris, _a._ 121. -Height of a homogeneous atmosphere, _b._ 34. -Heliacal rising and setting, _a._ 131. -Heliocentric theory, _a._ 258. -Hemisphere of Berosus, _a._ 162. -Hollow months, _a._ 122. -Homoiomeria, _a._ 78. -Horizon, _a._ 131. -Horoscope, _a._ 222. -Horror of a vacuum, _a._ 346. -Houses (in Astrology), _a._ 222. -Hydracids, _b._ 283. -Hygrometer, _b._ 177. -Hygrometry, _b._ 138. -Hypostatical principles, _b._ 262. - -Iatro-chemists, _b._ 263. -Ideas of the Platonists, _a._ 75. -Ilchanic tables, _a._ 178. -Impressed forces, _a._ 359. -Inclined plane, _a._ 313. -Induction (electric), _b._ 197. - " (logical), _a._ 43. -Inductive, _a._ 42. - " charts, _a._ 47. - " epochs, _a._ 46. -Inflammable air, _b._ 273. -Influences, _a._ 219. -Intercalation, _a._ 118. -Interferences, _b._ 86, 93. -Ionic school, _a._ 56. -Isomorphism, _b._ 334. -Isothermal lines, _b._ 146, 538. -Italic school, _a._ 56. - -Joints (in rocks), _b._ 537. -Judicial astrology, _a._ 222. -Julian calendar, _a._ 118. - -Lacteals, _b._ 453. -Latent heat, _b._ 160. -Laws of motion, first, _a._ 322. - " " second, _a._ 330. - " " third, _a._ 334. -Leap year, _a._ 118. -Leyden phial, _b._ 196. -Librations (of planets), _a._ 297. -Libration of Jupiter's Satellites, _a._ 441. -Limb of an instrument, _a._ 162. -Longitudinal vibrations, _b._ 44. -Lunisolar year, _a._ 120. -Lymphatics, _b._ 453. - -Magnetic elements, _b._ 222. - " equator, _b._ 219. -Magnetism, _b._ 217. -Magneto-electric induction, _b._ 256. -Matter and form, _a._ 73. -Mean temperature, _b._ 146. -Mechanical mixture of gases, _b._ 172. -Mechanico-chemical sciences, _b._ 191. -Meiocene, _b._ 529. -Meridian line, _a._ 164. -Metals, _b._ 306, 307. -Meteorology, _b._ 138. -Meteors, _a._ 86. -Methodic school (of medicine), _b._ 439. {36} -Metonic cycle, _a._ 122. -Mineral alkali, _b._ 264. -Mineralogical axis, _b._ 537. -Minutes, _a._ 163. -Miocene, _b._ 529. -Mollusca, _b._ 478. -Moment of inertia, _a._ 356. -Momentum, _a._ 337, 338. -Moon's libration, _a._ 375. -Morphology, _b._ 469, 474. -Movable polarization, _b._ 105. -Multiple proportions (in Chemistry), _b._ 285. -Music of the spheres, _a._ 82. -Mysticism, _a._ 209, 211. - -Nadir, _a._ **182. -Nebular hypothesis, _b._ 501. -Neoplatonists, _a._ 207. -Neutral axes, _b._ 81. -Neutralization (in Chemistry), _b._ 263. -Newton's rings, _b._ 77, 124. - " scale of color, _b._ 77. -Nitrous air, _b._ 273. -Nomenclature, _b._ 389. -Nominalists, _a._ 238. -Non-electrics, _b._ 194. -Numbers of the Pythagoreans, _a._ 82, 216. -Nutation, _a._ 465. -Nycthemer, _a._ 159. - -Octaëteris, _a._ 121. -Octants, _a._ 180. -Oolite, _b._ 529. -Optics, _b._ 51, &c. -Organical sciences, _b._ 435. -Organic molecules, _b._ 460. -Organization, _b._ 435. -Oscillation, Centre of, _a._ 356. -Outcrop (of strata), _b._ 512. -Oxide, _b._ 282. -Oxyd, _b._ 282. -Oxygen, _b._ 276. - -Palæontology, _b._ 519. -Palætiological sciences, _b._ 499. -Parallactic instrument, _a._ 165. -Parallax, _a._ 159. -Percussion, Centre of, _a._ 357. -Perfectihabia, _a._ 75. -Perigee, _a._ 146. -Perijove, _a._ 446. -Periodical colors, _b._ 93. -Phases of the moon, _a._ 134. -Philolaic tables, _a._ 304. -Phlogisticated air, _b._ 273. -Phlogiston, _b._ 268. -Phthongometer, _b._ 47. -Physical optics, _b._ 52. -Piston, _a._ 346. -Plagihedral faces, _b._ 82. -Plane of maximum areas, _b._ 380. -Pleiocene, _b._ 529. -Plesiomorphous, _b._ 335. -Plumb line, _a._ 164. -Pneumatic trough, _b._ 273. -Poikilite, _b._ 530. -Polar decompositions, _b._ 293. -Polarization, _b._ 72, 74. - " Circular, _b._ 82, 119. - " Elliptical, _b._ 122, 124. - " Movable, _b._ 105. - " Plane, _b._ 120. - " of heat, _b._ 153. -Poles (voltaic), _b._ 298. - " of maximum cold, _b._ 146. -Potential levers, _a._ 318. -Power and act, _a._ 74. -Precession of the equinoxes, _a._ 155. -Predicables, _a._ 205. -Predicaments, _a._ 206. -Preludes of epochs, _a._ 46. -Primary rocks, _b._ 513. -Primitive rocks, _b._ 513. -Primum calidum, _a._ 77. -Principal plane (of a rhomb), _b._ 73. -Principle of least action, _a._ 380. -Prosthapheresis, _a._ 146. -Provinces (of plants and animals), _b._ 562. -Prutenic tables, _a._ 270. -Pulses, _b._ 33. -Pyrites, _b._ 352. - -Quadrant, _a._ 164 -Quadrivium, _a._ 199. -Quiddity, _a._ 234. {37} -Quinary division (in Natural History), _b._ 418. -Quintessence, _a._ 73. - -Radiata, _b._ 478. -Radiation, _b._ 139. -Rays, _b._ 58. -Realists, _a._ 238. -Refraction, _b._ 54. - " of heat, _b._ 155. -Remora, _a._ 190. -Resinous electricity, _b._ 195. -Rete mirabile, _b._ 463. -Retrograde motion of planets, _a._ 139. -Roman calendar, _a._ 123. -Rotatory vibrations, _b._ 44. -Rudolphine tables, _a._ 270, 302. - -Saros, _a._ 136. -Scholastic philosophy, _a._ 230. -School philosophy, _a._ 50. -Science, _a._ 42. -Secondary rocks, _b._ 513. - " mechanical sciences, _b._ 23. -Second law of motion, _a._ 330. -Seconds, _a._ 163. -Secular inequalities, _a._ 370. -Segregation, _b._ 558. -Seminal contagion, _b._ 459. - " proportions, _a._ 79. -Sequels of epochs, _a._ 47. -Silicides, _b._ 352. -Silurian rocks, _b._ 530. -Simples, _b._ 367. -Sine, _a._ 181. -Solar heat, _b._ 145. -Solstitial points, _a._ 131. -Solution of water in air, _b._ 166. -Sothic period, _a._ 118. -Spagiric art, _b._ 262. -Specific heat, _b._ 159. -Sphere, _a._ 130. -Spontaneous generation, _b._ 457. -Statical electricity, _b._ 208. -Stationary periods, _a._ 48. - " planets, _a._ 139. -Stations (of plants), _b._ 562. -Sympathetic sounds, _b._ 37. -Systematic Botany, _b._ 357. -Systematic Zoology, _b._ 412. -Systems of crystallization, _b._ 328. - -Tables, Solar, (of Ptolemy), _a._ 146. - " Hakemite, _a._ 177. - " Toletan, _a._ 177. - " Ilchanic, _a._ 178. - " Alphonsine, _a._ 178. - " Prutenic, _a._ 270. - " Rudolphine, _a._ 302. - " Perpetual (of Lansberg), _a._ 302. - " Philolaic, _a._ 304. - " Carolinian, _a._ 304. -Tangential vibrations, _b._ 45. -Tautochronous curves, _a._ 372. -Technical terms, _b._ 389. -Temperament, _b._ 47. -Temperature, _b._ 139. -Terminology, _b._ 389. -Tertiary rocks, _b._ 513. -Tetractys, _a._ 77. -Theory of analogues, _b._ 483. -Thermomultiplier, _b._ 154. -Thermotics, _b._ 137. -Thick plates. Colors of, _b._ 79. -Thin plates. Colors of, _b._ 77. -Third law of motion, _a._ 334. -Three principles (in Chemistry), _b._ 261. -Toletan tables, _a._ 177. -Transition rocks, _b._ 530. -Transverse vibrations, _b._ 44, 93, 101. -Travertin, _b._ 546. -Trepidation of the fixed stars, _a._ 179. -Trigonometry, _a._ 167. -Trivial names, _b._ 392. -Trivium, _a._ 199. -Tropics, _a._ 131. -Truncation (of crystals), _b._ 319. -Type (in Comparative Anatomy), _b._ 476. - -Uniform force, _a._ 327. -Unity of Composition (in Comparative Anatomy), _b._ 483. -Unity of plan (in Comparative Anatomy), _b._ 483. - -Variation of the moon, _a._ 179, 303. {38} -Vegetable alkali, _b._ 264. -Vertebrata, _b._ 478. -Vibrations, _b._ 44. -Vicarious elements, _b._ 334. - " solicitations, _a._ 359. -Virtual velocities, _a._ 333. -Vitreous electricity, _b._ 195. -Volatile alkali, _b._ 264. -Volta-electrometer, _b._ 299. -Voltaic electricity, _b._ 239. - " pile, _b._ 239. -Volumes, Theory of, _b._ 290. -Voluntary, violent, and natural motion, _a._ 319. -Vortices, _a._ 388. - -Week, _a._ 127. - -Year, _a._ 112. - -Zenith, _a._ 181. -Zodiac, _a._ 131. -Zones, _a._ 136. - - - -{{39}} -A -HISTORY -OF THE -INDUCTIVE SCIENCES. - -INTRODUCTION. - - -"A just story of learning, containing the antiquities and originals -of KNOWLEDGES, and their sects; their inventions, their diverse -administrations and managings; their flourishings, their -oppositions, decays, depressions, oblivions, removes; with the -causes and occasions of them, and all other events concerning -learning, throughout all ages of the world; I may truly affirm to be -wanting. - -"The use and end of which work I do not so much design for -curiosity, or satisfaction of those that are the lovers of learning: -but chiefly for a more serious and grave purpose; which is this, in -few words--that it will make learned men more wise in the use and -administration of learning." -BACON, _Advancement of Learning_, book ii. - - - -{{41}} -INTRODUCTION. - - -IT is my purpose to write the History of some of the most important -of the Physical Sciences, from the earliest to the most recent -periods. I shall thus have to trace some of the most remarkable -branches of human knowledge, from their first germ to their growth -into a vast and varied assemblage of undisputed truths; from the -acute, but fruitless, essays of the early Greek Philosophy, to the -comprehensive systems, and demonstrated generalizations, which -compose such sciences as the Mechanics, Astronomy, and Chemistry, of -modern times. - -The completeness of historical view which belongs to such a design, -consists, not in accumulating all the details of the cultivation of -each science, but in marking the larger features of its formation. -The historian must endeavor to point out how each of the important -advances was made, by which the sciences have reached their present -position; and when and by whom each of the valuable truths was -obtained, of which the aggregate now constitutes a costly treasure. - -Such a task, if fitly executed, must have a well-founded interest -for all those who look at the existing condition of human knowledge -with complacency and admiration. The present generation finds itself -the heir of a vast patrimony of science; and it must needs concern -us to know the steps by which these possessions were acquired, and -the documents by which they are secured to us and our heirs forever. -Our species, from the time of its creation, has been travelling -onwards in pursuit of truth; and now that we have reached a lofty -and commanding position, with the broad light of day around us, it -must be grateful to look back on the line of our vast progress;--to -review the journey, begun in early twilight amid primeval wilds; for -a long time continued with slow advance and obscure prospects; and -gradually and in later days followed along more open and lightsome -paths, in a wide and fertile region. The historian of science, from -early periods to the present times, may hope for favor on the score -of the mere subject of his narrative, and in virtue of the curiosity -which the men {42} of the present day may naturally feel respecting -the events and persons of his story. - -But such a survey may possess also an interest of another kind; it -may be instructive as well as agreeable; it may bring before the -reader the present form and extent, the future hopes and prospects -of science, as well as its past progress. The eminence on which we -stand may enable us to see the land of promise, as well as the -wilderness through which we have passed. The examination of the -steps by which our ancestors acquired our intellectual estate, may -make us acquainted with our expectations as well as our -possessions;--may not only remind us of what we have, but may teach -us how to improve and increase our store. It will be universally -expected that a History of Inductive Science should point out to us -a philosophical distribution of the existing body of knowledge, and -afford us some indication of the most promising mode of directing -our future efforts to add to its extent and completeness. - -To deduce such lessons from the past history of human knowledge, was -the intention which originally gave rise to the present work. Nor is -this portion of the design in any measure abandoned; but its -execution, if it take place, must be attempted in a separate and -future treatise, _On the Philosophy of the Inductive Sciences_. An -essay of this kind may, I trust, from the progress already made in -it, be laid before the public at no long interval after the present -history.[1\1] - -[Note 1\1: The _Philosophy of the Inductive Sciences_ was published -shortly after the present work.] - -Though, therefore, many of the principles and maxims of such a work -will disclose themselves with more or less of distinctness in the -course of the history on which we are about to enter, the systematic -and complete exposition of such principles must be reserved for this -other treatise. My attempts and reflections have led me to the -opinion, that justice cannot be done to the subject without such a -division of it. - -To this future work, then, I must refer the reader who is disposed -to require, at the outset, a precise explanation of the terms which -occur in my title. It is not possible, without entering into this -philosophy, to explain adequately how science which is INDUCTIVE -differs from that which is not so; or why some portions of -_knowledge_ may properly be selected from the general mass and -termed SCIENCE. It will be sufficient at present to say, that the -sciences of which we have {43} here to treat, are those which are -commonly known as the _Physical Sciences_; and that by _Induction_ -is to be understood that process of collecting general truths from -the examination of particular facts, by which such sciences have -been formed. - -There are, however, two or three remarks, of which the application -will occur so frequently, and will tend so much to give us a clearer -view of some of the subjects which occur in our history, that I will -state them now in a brief and general manner. - -_Facts and Ideas_.[2\1]--In the first place then, I remark, that, to -the formation of science, two things are requisite;--Facts and -Ideas; observation of Things without, and an inward effort of -Thought; or, in other words, Sense and Reason. Neither of these -elements, by itself can constitute substantial general knowledge. -The impressions of sense, unconnected by some rational and -speculative principle, can only end in a practical acquaintance with -individual objects; the operations of the rational faculties, on the -other hand, if allowed to go on without a constant reference to -external things, can lead only to empty abstraction and barren -ingenuity. Real speculative knowledge demands the combination of the -two ingredients;--right reason, and facts to reason upon. It has -been well said, that true knowledge is the interpretation of nature; -and therefore it requires both the interpreting mind, and nature for -its subject; both the document, and the ingenuity to read it aright. -Thus invention, acuteness, and connection of thought, are necessary -on the one hand, for the progress of philosophical knowledge; and on -the other hand, the precise and steady application of these -faculties to facts well known and clearly conceived. It is easy to -point out instances in which science has failed to advance, in -consequence of the absence of one or other of these requisites; -indeed, by far the greater part of the course of the world, the -history of most times and most countries, exhibits a condition thus -stationary with respect to knowledge. The facts, the impressions on -the senses, on which the first successful attempts at physical -knowledge proceeded, were as well known long before the time when -they were thus turned to account, as at that period. The motions of -the stars, and the effects of weight, were familiar to man before -the rise of the Greek Astronomy and Mechanics: but the "diviner -mind" was still absent; the act of thought had not been exerted, by -which these facts were bound together under the form of laws and -principles. And even at {44} this day, the tribes of uncivilized and -half-civilized man, over the whole face of the earth, have before -their eyes a vast body of facts, of exactly the same nature as those -with which Europe has built the stately fabric of her physical -philosophy; but, in almost every other part of the earth, the -process of the intellect by which these facts become science, is -unknown. The scientific faculty does not work. The scattered stones -are there, but the builder's hand is wanting. And again, we have no -lack of proof that mere activity of thought is equally inefficient -in producing real knowledge. Almost the whole of the career of the -Greek schools of philosophy; of the schoolmen of Europe in the -middle ages; of the Arabian and Indian philosophers; shows us that -we may have extreme ingenuity and subtlety, invention and -connection, demonstration and method; and yet that out of these -germs, no physical science may be developed. We may obtain, by such -means, Logic and Metaphysics, and even Geometry and Algebra; but out -of such materials we shall never form Mechanics and Optics, -Chemistry and Physiology. How impossible the formation of these -sciences is without a constant and careful reference to observation -and experiment;--how rapid and prosperous their progress may be when -they draw from such sources the materials on which the mind of the -philosopher employs itself;--the history of those branches of -knowledge for the last three hundred years abundantly teaches us. - -[Note 2\1: For the _Antithesis of Facts and Ideas_, see the -_Philosophy_, book i. ch. 1, 2, 4, 5.] - -Accordingly, the existence of clear Ideas applied to distinct Facts -will be discernible in the History of Science, whenever any marked -advance takes place. And, in tracing the progress of the various -provinces of knowledge which come under our survey, it will be -important for us to see that, at all such epochs, such a combination -has occurred; that whenever any material step in general knowledge -has been made,--whenever any philosophical discovery arrests our -attention,--some man or men come before us, who have possessed, in -an eminent degree, a clearness of the ideas which belong to the -subject in question, and who have applied such ideas in a vigorous -and distinct manner to ascertained facts and exact observations. We -shall never proceed through any considerable range of our narrative, -without having occasion to remind the reader of this reflection. - -_Successive Steps in Science_.[3\1]--But there is another remark -which we must also make. Such sciences as we have here to do with -are, {45} commonly, not formed by a single act;--they are not -completed by the discovery of one great principle. On the contrary, -they consist in a long-continued advance; a series of changes; a -repeated progress from one principle to another, different and often -apparently contradictory. Now, it is important to remember that this -contradiction is apparent only. The principles which constituted the -triumph of the preceding stages of the science, may appear to be -subverted and ejected by the later discoveries, but in fact they are -(so far as they were true) taken up in the subsequent doctrines and -included in them. They continue to be an essential part of the -science. The earlier truths are not expelled but absorbed, not -contradicted but extended; and the history of each science, which -may thus appear like a succession of revolutions, is, in reality, a -series of developments. In the intellectual, as in the material -world, - - Omnia mutantur nil interit . . . . . - Nec manet ut fuerat nec formas servat easdem, - Sed tamen ipsa eadem est. - - All changes, naught is lost; the forms are changed, - And that which has been is not what it was, - Yet that which has been is. - -Nothing which was done was useless or unessential, though it ceases -to be conspicuous and primary. - -[Note 3\1: Concerning _Successive Generalizations in Science_ see -the _Philosophy_, book i. ch. 2, sect. 11.] - -Thus the final form of each science contains the substance of each -of its preceding modifications; and all that was at any antecedent -period discovered and established, ministers to the ultimate -development of its proper branch of knowledge. Such previous -doctrines may require to be made precise and definite, to have their -superfluous and arbitrary portions expunged, to be expressed in new -language, to be taken up into the body of science by various -processes;--but they do not on such accounts cease to be true -doctrines, or to form a portion of the essential constituents of our -knowledge. - -_Terms record Discoveries_.[4\1]--The modes in which the earlier -truths of science are preserved in its later forms, are indeed -various. From being asserted at first as strange discoveries, such -truths come at last to be implied as almost self-evident axioms. -They are recorded by some familiar maxim, or perhaps by some new -word or phrase, which becomes part of the current language of the -philosophical world; and thus asserts a principle, while it appears -merely to indicate a transient {46} notion;--preserves as well as -expresses a truth;--and, like a medal of gold, is a treasure as well -as a token. We shall frequently have to notice the manner in which -great discoveries thus stamp their impress upon the terms of a -science; and, like great political revolutions, are recorded by the -change of the current coin which has accompanied them. - -[Note 4\1: Concerning _Technical Terms_, see _Philosophy_, book i. -ch. 3.] - -_Generalization_.--The great changes which thus take place in the -history of science, the revolutions of the intellectual world, have, -as a usual and leading character, this, that they are steps of -_generalization_; transitions from particular truths to others of a -wider extent, in which the former are included. This progress of -knowledge, from individual facts to universal laws,--from particular -propositions to general ones,--and from these to others still more -general, with reference to which the former generalizations are -particular,--is so far familiar to men's minds, that, without here -entering into further explanation, its nature will be understood -sufficiently to prepare the reader to recognize the exemplifications -of such a process, which he will find at every step of our advance. - -_Inductive Epochs; Preludes; Sequels_.--In our history, it is the -_progress_ of knowledge only which we have to attend to. This is the -main action of our drama; and all the events which do not bear upon -this, though they may relate to the cultivation and the cultivators -of philosophy, are not a necessary part of our theme. Our narrative -will therefore consist mainly of successive steps of generalization, -such as have just been mentioned. But among these, we shall find -some of eminent and decisive importance, which have more peculiarly -influenced the fortunes of physical philosophy, and to which we may -consider the rest as subordinate and auxiliary. These primary -movements, when the Inductive process, by which science is formed, -has been exercised in a more energetic and powerful manner, may be -distinguished as the _Inductive Epochs_ of scientific history; and -they deserve our more express and pointed notice. They are, for the -most part, marked by the great discoveries and the great -philosophical names which all civilized nations have agreed in -admiring. But, when we examine more clearly the history of such -discoveries, we find that these epochs have not occurred suddenly -and without preparation. They have been preceded by a period, which -we may call their _Prelude_ during which the ideas and facts on -which they turned were called into action;--were gradually evolved -into clearness and connection, permanency and certainty; till at -last the discovery which marks the epoch, seized and fixed forever -the truth which had till then been obscurely and {47} doubtfully -discerned. And again, when this step has been made by the principal -discoverers, there may generally be observed another period, which -we may call the _Sequel_ of the Epoch, during which the discovery -has acquired a more perfect certainty and a more complete -development among the leaders of the advance; has been diffused to -the wider throng of the secondary cultivators of such knowledge, and -traced into its distant consequences. This is a work, always of time -and labor, often of difficulty and conflict. To distribute the -History of science into such Epochs, with their Preludes and -Sequels, if successfully attempted, must needs make the series and -connections of its occurrences more distinct and intelligible. Such -periods form resting-places, where we pause till the dust of the -confused march is laid, and the prospect of the path is clear. - -_Inductive Charts_.[5\1]--Since the advance of science consists in -collecting by induction true general laws from particular facts, and -in combining several such laws into one higher generalization, in -which they still retain their truth; we might form a Chart, or -Table, of the progress of each science, by setting down the -particular facts which have thus been combined, so as to form -general truths, and by marking the further union of these general -truths into others more comprehensive. The Table of the progress of -any science would thus resemble the Map of a River, in which the -waters from separate sources unite and make rivulets, which again -meet with rivulets from other fountains, and thus go on forming by -their junction trunks of a higher and higher order. The -representation of the state of a science in this form, would -necessarily exhibit all the principal doctrines of the science; for -each general truth contains the particular truths from which it was -derived, and may be followed backwards till we have these before us -in their separate state. And the last and most advanced -generalization would have, in such a scheme, its proper place and -the evidence of its validity. Hence such an _Inductive Table_ of -each science would afford a criterion of the correctness of our -distribution of the inductive Epochs, by its coincidence with the -views of the best judges, as to the substantial contents of the -science in question. By forming, therefore, such Inductive Tables of -the principal sciences of which I have here to speak, and by -regulating by these tables, my views of the history of the sciences, -I conceive that I have secured the distribution of my {48} history -from material error; for no merely arbitrary division of the events -could satisfy such conditions. But though I have constructed such -charts to direct the course of the present history, I shall not -insert them in the work, reserving them for the illustration of the -philosophy of the subject; for to this they more properly belong, -being a part of the _Logic of Induction_. - -[Note 5\1: Inductive charts of the History of Astronomy and of -Optics, such as are here referred to, are given in the _Philosophy_, -book xi. ch. 6.] - -_Stationary Periods_.--By the lines of such maps the real advance of -science is depicted, and nothing else. But there are several -occurrences of other kinds, too interesting and too instructive to -be altogether omitted. In order to understand the conditions of the -progress of knowledge, we must attend, in some measure, to the -failures as well as the successes by which such attempts have been -attended. When we reflect during how small a portion of the whole -history of human speculations, science has really been, in any -marked degree, progressive, we must needs feel some curiosity to -know what was doing in these _stationary_ periods; what field could -be found which admitted of so wide a deviation, or at least so -protracted a wandering. It is highly necessary to our purpose, to -describe the baffled enterprises as well as the achievements of -human speculation. - -_Deduction_.--During a great part of such stationary periods, we -shall find that the process which we have spoken of as essential to -the formation of real science, the conjunction of clear Ideas with -distinct Facts, was interrupted; and, in such cases, men dealt with -ideas alone. They employed themselves in reasoning from principles, -and they arranged, and classified, and analyzed their ideas, so as -to make their reasonings satisfy the requisitions of our rational -faculties. This process of drawing conclusions from our principles, -by rigorous and unimpeachable trains of demonstration, is termed -_Deduction_. In its due place, it is a highly important part of -every science; but it has no value when the fundamental principles, -on which the whole of the demonstration rests, have not first been -obtained by the induction of facts, so as to supply the materials of -substantial truth. Without such materials, a series of -demonstrations resembles physical science only as a shadow resembles -a real object. To give a real significance to our propositions, -Induction must provide what Deduction cannot supply. From a pictured -hook we can hang only a pictured chain. - -_Distinction of common Notions and Scientific Ideas_.[6\1]--When the -{49} notions with which men are conversant in the common course of -practical life, which give meaning to their familiar language, and -employment to their hourly thoughts, are compared with the Ideas on -which exact science is founded, we find that the two classes of -intellectual operations have much that is common and much that is -different. Without here attempting fully to explain this relation -(which, indeed, is one of the hardest problems of our philosophy), -we may observe that they have this in common, that both are acquired -by acts of the mind exercised in connecting external impressions, -and may be employed in conducting a train of reasoning; or, speaking -loosely (for we cannot here pursue the subject so as to arrive at -philosophical exactness), we may say, that all notions and ideas are -obtained by an _inductive_, and may be used in a _deductive_ -process. But scientific Ideas and common Notions differ in this, -that the former are precise and stable, the latter vague and -variable; the former are possessed with clear insight, and employed -in a sense rigorously limited, and always identically the same; the -latter have grown up in the mind from a thousand dim and diverse -suggestions, and the obscurity and incongruity which belong to their -origin hang about all their applications. Scientific Ideas can often -be adequately exhibited for all the purposes of reasoning, by means -of Definitions and Axioms; all attempts to reason by means of -Definitions from common Notions, lead to empty forms or entire -confusion. - -[Note 6\1: Scientific Ideas depend upon certain _Fundamental Ideas_, -which are enumerated in the _Philosophy_, book i. ch. 8.] - -Such common Notions are sufficient for the common practical conduct -of human life: but man is not a practical creature merely; he has -within him a _speculative_ tendency, a pleasure in the contemplation -of ideal relations, a love of knowledge as knowledge. It is this -speculative tendency which brings to light the difference of common -Notions and scientific Ideas, of which we have spoken. The mind -analyzes such Notions, reasons upon them, combines and connects -them; for it feels assured that intellectual things ought to be able -to bear such handling. Even practical knowledge, we see clearly, is -not possible without the use of the reason; and the speculative -reason is only the reason satisfying itself of its own consistency. -The speculative faculty cannot be controlled from acting. The mind -cannot but claim a right to speculate concerning all its own acts -and creations; yet, when it exercises this right upon its common -practical notions, we find that it runs into barren abstractions and -ever-recurring cycles of subtlety. Such Notions are like waters -naturally stagnant; however much we urge and agitate them, they only -revolve in stationary {50} whirlpools. But the mind is capable of -acquiring scientific Ideas, which are better fitted to undergo -discussion and impulsion. When our speculations are duly fed from -the springheads of Observation, and frequently drawn off into the -region of Applied Science, we may have a living stream of consistent -and progressive knowledge. That science may be both real as to its -import, and logical as to its form, the examples of many existing -sciences sufficiently prove. - -_School Philosophy_.--So long, however, as attempts are made to form -sciences, without such a verification and realization of their -fundamental ideas, there is, in the natural series of speculation, -no self-correcting principle. A philosophy constructed on notions -obscure, vague, and unsubstantial, and held in spite of the want of -correspondence between its doctrines and the actual train of -physical events, may long subsist, and occupy men's minds. Such a -philosophy must depend for its permanence upon the pleasure which -men feel in tracing the operations of their own and other men's -minds, and in reducing them to logical consistency and systematical -arrangement. - -In these cases the main subjects of attention are not external -objects, but speculations previously delivered; the object is not to -interpret nature, but man's mind. The opinions of the Masters are -the facts which the Disciples endeavor to reduce to unity, or to -follow into consequences. A series of speculators who pursue such a -course, may properly be termed a _School_, and their philosophy a -_School Philosophy_; whether their agreement in such a mode of -seeking knowledge arise from personal communication and tradition, -or be merely the result of a community of intellectual character and -propensity. The two great periods of School Philosophy (it will be -recollected that we are here directing our attention mainly to -physical science) were that of the Greeks and that of the Middle -Ages;--the period of the first waking of science, and that of its -midday slumber. - -What has been said thus briefly and imperfectly, would require great -detail and much explanation, to give it its full significance and -authority. But it seemed proper to state so much in this place, in -order to render more intelligible and more instructive, at the first -aspect, the view of the attempted or effected progress of science. - -It is, perhaps, a disadvantage inevitably attending an undertaking -like the present, that it must set out with statements so abstract; -and must present them without their adequate development and proof. -Such an Introduction, both in its character and its scale of -execution, may be compared to the geographical sketch of a country, -with which {51} the historian of its fortunes often begins his -narration. So much of Metaphysics is as necessary to us as such a -portion of Geography is to the Historian of an Empire; and what has -hitherto been said, is intended as a slight outline of the Geography -of that Intellectual World, of which we have here to study the -History. - -The name which we have given to this History--A HISTORY OF THE -INDUCTIVE SCIENCES--has the fault of seeming to exclude from the -rank of Inductive Sciences those which are not included in the -History; as Ethnology and Glossology, Political Economy, Psychology. -This exclusion I by no means wish to imply; but I could find no -other way of compendiously describing my subject, which was intended -to comprehend those Sciences in which, by the observation of facts -and the use of reason, systems of doctrine have been established -which are universally received as truths among thoughtful men; and -which may therefore be studied as examples of the manner in which -truth is to be discovered. Perhaps a more exact description of the -work would have been, _A History of the principal Sciences hitherto -established by Induction_. I may add that I do not include in the -phrase "Inductive Sciences," the branches of Pure Mathematics -(Geometry, Arithmetic, Algebra, and the like), because, as I have -elsewhere stated (_Phil. Ind. Sc._, book ii. c. 1), these are not -_Inductive_ but _Deductive_ Sciences. They do not infer true -theories from observed facts, and more general from more limited -laws: but they trace the conditions of all theory, the properties of -space and number; and deduce results from ideas without the aid of -experience. The History of these Sciences is briefly given in -Chapters 13 and 14 of the Second Book of the _Philosophy_ just -referred to. - - -I may further add that the other work to which I refer, the -_Philosophy of the Inductive Sciences_, is in a great measure -historical, no less than the present _History_. That work contains -the history of the Sciences so far as it depends on _Ideas_; the -present work contains the history so far as it depends upon -_Observation_. The two works resulted simultaneously from the same -examination of the principal writers on science in all ages, and may -serve to supplement each other. - - - -{{53}} -BOOK I. - -HISTORY -OF THE -GREEK SCHOOL PHILOSOPHY, -WITH REFERENCE TO -PHYSICAL SCIENCE. - - - Τίς γὰρ ἀρχὰ δέξατο ναυτιλίας; - Τίς δὲ κίνδυνος κρατεροῖς ἀδάμαντος δῆσεν ἄλοις; - . . . . . . Ἐπεὶ δ' ἐμβόλου - Κρέμασαν ἀγκύρας ὕπερθεν - Χρυσέαν χείρεσσι λαβὼν φιάλαν - Ἀρχὸς ἐν πρύμνᾳ πατέρ Οὐρανιδᾶν - Ἐγχεικέραυνον Ζῆνα, καὶ ὠκυπόρους - Κυμάτων ῥίπας, ἀνέμων τ' ἐκάλει, - Ἀματά τ' εὔφρονα, καὶ - Φιλίαν νόστοιο μοῖραν. - PINDAR. _Pyth._ iv. 124, 349. - - - Whence came their voyage? them what peril held - With adamantine rivets firmly bound? - * * * * * * - But soon as on the vessel's bow - The anchor was hung up, - Then took the Leader on the prow - In hands a golden cup, - And on great Father Jove did call, - And on the Winds and Waters all, - Swept by the hurrying blast; - And on the Nights, and Ocean Ways, - And on the fair auspicious Days, - And loved return at last. - - - -{{55}} -BOOK I. - - -HISTORY OF THE GREEK SCHOOL PHILOSOPHY, WITH REFERENCE TO PHYSICAL -SCIENCE. - - - - -CHAPTER I. - -PRELUDE TO THE GREEK SCHOOL PHILOSOPHY. - - -_Sect._ 1.--_First Attempts of the Speculative Faculty in Physical -Inquiries._ - -AT an early period of history there appeared in men a propensity to -pursue speculative inquiries concerning the various parts and -properties of the material world. What they saw excited them to -meditate, to conjecture, and to reason: they endeavored to account for -natural events, to trace their causes, to reduce them to their -principles. This habit of mind, or, at least that modification of it -which we have here to consider, seems to have been first unfolded -among the Greeks. And during that obscure introductory interval which -elapsed while the speculative tendencies of men were as yet hardly -disentangled from the practical, those who were most eminent in such -inquiries were distinguished by the same term of praise which is -applied to sagacity in matters of action, and were called _wise_ -men--σοφοὶ. But when it came to be clearly felt by such persons that -their endeavors were suggested by the love of knowledge, a motive -different from the motives which lead to the wisdom of active life, a -name was adopted of a more appropriate, as well as of a more modest -signification, and they were termed _philosophers_, or lovers of -wisdom. This appellation is said[7\1] to have been first assumed by -Pythagoras. Yet he, in Herodotus, instead of having this title, is -called a powerful _sophist_--Ἑλλήνων οὐ τῷ ἀσθενεστάτῳ σοφιστῇ -Πυθαγόρῃ;[8\1] the historian using this word, as it would seem, -without intending to imply that misuse of reason which the term -afterwards came to denote. The historians of literature {56} placed -Pythagoras at the origin of the Italic School, one of the two main -lines of succession of the early Greek philosophers: but the other, -the Ionic School, which more peculiarly demands our attention, in -consequence of its character and subsequent progress, is deduced from -Thales, who preceded the age of _Philosophy_, and was one of the -_sophi_, or "wise men of Greece." - -[Note 7\1: Cic. Tusc. v. 3.] - -[Note 8\1: Herod. iv. 95.] - -The Ionic School was succeeded in Greece by several others; and the -subjects which occupied the attention of these schools became very -extensive. In fact, the first attempts were, to form systems which -should explain the laws and causes of the material universe; and to -these were soon added all the great questions which our moral -condition and faculties suggest. The physical philosophy of these -schools is especially deserving of our study, as exhibiting the -character and fortunes of the most memorable attempt at universal -knowledge which has ever been made. It is highly instructive to -trace the principles of this undertaking; for the course pursued was -certainly one of the most natural and tempting which can be -imagined; the essay was made by a nation unequalled in fine mental -endowments, at the period of its greatest activity and vigor; and -yet it must be allowed (for, at least so far as physical science is -concerned, none will contest this), to have been entirely -unsuccessful. We cannot consider otherwise than as an utter failure, -an endeavor to discover the causes of things, of which the most -complete results are the Aristotelian physical treatises; and which, -after reaching the point which these treatises mark, left the human -mind to remain stationary, at any rate on all such subjects, for -nearly two thousand years. - -The early philosophers of Greece entered upon the work of physical -speculation in a manner which showed the vigor and confidence of the -questioning spirit, as yet untamed by labors and reverses. It was -for later ages to learn that man must acquire, slowly and patiently, -letter by letter, the alphabet in which nature writes her answers to -such inquiries. The first students wished to divine, at a single -glance, the whole import of her book. They endeavored to discover -the origin and principle of the universe; according to Thales, -_water_ was the origin of all things, according to Anaximenes, -_air_; and Heraclitus considered _fire_ as the essential principle -of the universe. It has been conjectured, with great plausibility, -that this tendency to give to their Philosophy the form of a -Cosmogony, was owing to the influence of the poetical Cosmogonies -and Theogonies which had been produced and admired at a still -earlier age. Indeed, such wide and ambitious {57} doctrines as -those which have been mentioned, were better suited to the dim -magnificence of poetry, than to the purpose of a philosophy which -was to bear the sharp scrutiny of reason. When we speak of the -_principles_ of things, the term, even now, is very ambiguous and -indefinite in its import, but how much more was that the case in the -first attempts to use such abstractions! The term which is commonly -used in this sense (ἀρχὴ), signified at first _the beginning_; and -in its early philosophical applications implied some obscure mixed -reference to the mechanical, chemical, organic, and historical -causes of the visible state of things, besides the theological views -which at this period were only just beginning to be separated from -the physical. Hence we are not to be surprised if the sources from -which the opinions of this period appear to be derived are rather -vague suggestions and casual analogies, than any reasons which will -bear examination. Aristotle conjectures, with considerable -probability, that the doctrine of Thales, according to which water -was the universal element, resulted from the manifest importance of -moisture in the support of animal and vegetable life.[9\1] But such -precarious analyses of these obscure and loose dogmas of early -antiquity are of small consequence to our object. - -[Note 9\1: Metaph. i. 3.] - -In more limited and more definite examples of inquiry concerning the -causes of natural appearances, and in the attempts made to satisfy -men's curiosity in such cases, we appear to discern a more genuine -prelude to the true spirit of physical inquiry. One of the most -remarkable instances of this kind is to be found in the speculations -which Herodotus records, relative to the cause of the floods of the -Nile. "Concerning the nature of this river," says the father of -history,[10\1] "I was not able to learn any thing, either from the -priests or from any one besides, though I questioned them very -pressingly. For the Nile is flooded for a hundred days, beginning -with the summer solstice; and after this time it diminishes, and is, -during the whole winter, very small. And on this head I was not able -to obtain any thing satisfactory from any one of the Egyptians, when -I asked what is the power by which the Nile is in its nature the -reverse of other rivers." - -[Note 10\1: Herod. ii. 19.] - -We may see, I think, in the historian's account, that the Grecian -mind felt a craving to discover the reasons of things which other -nations did not feel. The Egyptians, it appears, had no theory, and -felt no want of a theory. Not so the Greeks; they had their reasons -to render, though they were not such as satisfied Herodotus. "Some -{58} of the Greeks," he says, "who wish to be considered great -philosophers (Ἑλλήνων τινες ἐπισήμοι βουλόμενοι γενέσθαι σοφίην), -have propounded three ways of accounting for these floods. Two of -them," he adds, "I do not think worthy of record, except just so far -as to mention them." But as these are some of the earliest Greek -essays in physical philosophy, it will be worth while, even at this -day, to preserve the brief notice he has given of them, and his own -reasonings upon the same subject. - -"One of these opinions holds that the Etesian winds [which blew from -the north] are the cause of these floods, by preventing the Nile -from flowing into the sea." Against this the historian reasons very -simply and sensibly. "Very often when the Etesian winds do not blow, -the Nile is flooded nevertheless. And moreover, if the Etesian winds -were the cause, all other rivers, which have their course opposite -to these winds, ought to undergo the same changes as the Nile; which -the rivers of Syria and Libya so circumstanced do not." - -"The next opinion is still more unscientific (ἀνεπιστημονεστέρη), -and is, in truth, marvellous for its folly. This holds that the -ocean flows all round the earth, and that the Nile comes out of the -ocean, and by that means produces its effects." "Now," says the -historian, "the man who talks about this ocean-river, goes into the -region of fable, where it is not easy to demonstrate that he is -wrong. I know of no such river. But I suppose that Homer and some of -the earlier poets invented this fiction and introduced it into their -poetry." - -He then proceeds to a third account, which to a modern reasoner -would appear not at all unphilosophical in itself, but which he, -nevertheless, rejects in a manner no less decided than the others. -"The third opinion, though much the most plausible, is still more -wrong than the others; for it asserts an impossibility, namely, that -the Nile proceeds from the melting of the snow. Now the Nile flows -out of Libya, and through Ethiopia, which are very hot countries, -and thus comes into Egypt, which is a colder region. How then can it -proceed from snow?" He then offers several other reasons "to show," -as he says, "to any one capable of reasoning on such subjects (ἀνδρί -γε λογίζεσθαι τοιούτων πέρι οἵῳ τε ἔοντι), that the assertion cannot -be true. The winds which blow from the southern regions are hot; the -inhabitants are black; the swallows and kites (ἰκτῖνοι) stay in the -country the whole year; the cranes fly the colds of Scythia, and -seek their warm winter-quarters there; which would not be if it -snowed ever so little." He adds another reason, founded apparently -upon {59} some limited empirical maxim of weather-wisdom taken from -the climate of Greece. "Libya," he said, "has neither rain nor ice, -and therefore no snow; _for_, in five days after a fall of snow -there must be a fall of rain; so that if it snowed in those regions -it must rain too." I need not observe that Herodotus was not aware -of the difference between the climate of high mountains and plains -in a torrid region; but it is impossible not to be struck both with -the activity and the coherency of thought displayed by the Greek -mind in this primitive physical inquiry. - -But I must not omit the hypothesis which Herodotus himself proposes, -after rejecting those which have been already given. It does not -appear to me easy to catch his exact meaning, but the statement will -still be curious. "If," he says, "one who has condemned opinions -previously promulgated may put forward his own opinion concerning so -obscure a matter, I will state why it seems to me that the Nile is -flooded in summer." This opinion he propounds at first with an -oracular brevity, which it is difficult to suppose that he did not -intend to be impressive. "In winter the sun is carried by the seasons -away from his former course, and goes to the upper parts of Libya. And -_there, in short, is the whole account;_ for that region to which this -divinity (the sun) is nearest, must naturally be most scant of water, -and the river-sources of that country must be dried up." - -But the lively and garrulous Ionian immediately relaxes from this -apparent reserve. "To explain the matter more at length," he -proceeds, "it is thus. The sun when he traverses the upper parts of -Libya, does what he commonly does in summer;--he _draws_ the water -to him (ἕλκει ἐπ' ἑωϋτὸν τὸ ὕδωρ), and having thus drawn it, he -pushes it to the upper regions (of the air probably), and then the -winds take it and disperse it till they dissolve in moisture. And -thus the winds which blow from those countries, Libs and Notus, are -the most moist of all winds. Now when the winter relaxes and the sun -returns to the north, he still draws water from all the rivers, but -they are increased by showers and rain torrents so that they are in -flood till the summer comes; and then, the rain falling and the sun -still drawing them, they become small. But the Nile, not being fed -by rains, yet being drawn by the sun, is, alone of all rivers, much -more scanty in the winter than in the summer. For in summer it is -drawn like all other rivers, but in winter it alone has its supplies -shut up. And in this way, I have been led to think the sun is the -cause of the occurrence in question." We may remark that the -historian here appears to {60} ascribe the inequality of the Nile at -different seasons to the influence of the sun upon its springs -alone, the other cause of change, the rains being here excluded; and -that, on this supposition, the same relative effects would be -produced whether the sun increase the sources in winter by melting -the snows, or diminish them in summer by what he calls _drawing_ -them upwards. - -This specimen of the early efforts of the Greeks in physical -speculations, appears to me to speak strongly for the opinion that -their philosophy on such subjects was the native growth of the Greek -mind, and owed nothing to the supposed lore of Egypt and the East; -an opinion which has been adopted with regard to the Greek -Philosophy in general by the most competent judges on a full survey -of the evidence.[11\1] Indeed, we have no evidence whatever that, at -any period, the African or Asiatic nations (with the exception -perhaps of the Indians) ever felt this importunate curiosity with -regard to the definite application of the idea of cause and effect -to visible phenomena; or drew so strong a line between a fabulous -legend and a reason rendered; or attempted to ascend to a natural -cause by classing together phenomena of the same kind. We may be -well excused, therefore, for believing that they could not impart to -the Greeks what they themselves did not possess; and so far as our -survey goes, physical philosophy has its origin, apparently -spontaneous and independent, in the active and acute intellect of -Greece. - -[Note 11\1: Thirlwall, _Hist. Gr._, ii. 130; and, as there quoted, -Ritter, _Geschichte der Philosophie_, i. 159-173.] - - -_Sect._ 2.--_Primitive Mistake in Greek Physical Philosophy._ - -WE now proceed to examine with what success the Greeks followed the -track into which they had thus struck. And here we are obliged to -confess that they very soon turned aside from the right road to -truth, and deviated into a vast field of error, in which they and -their successors have wandered almost to the present time. It is not -necessary here to inquire why those faculties which appear to be -bestowed upon us for the discovery of truth, were permitted by -Providence to fail so signally in answering that purpose; whether, -like the powers by which we seek our happiness, they involve a -responsibility on our part, and may be defeated by rejecting the -guidance of a higher faculty; or whether these endowments, though -they did not {61} immediately lead man to profound physical -knowledge, answered some nobler and better purpose in his -constitution and government. The fact undoubtedly was, that the -physical philosophy of the Greeks soon became trifling and -worthless; and it is proper to point out, as precisely as we can, in -what the fundamental mistake consisted. - -To explain this, we may in the first place return for a moment to -Herodotus's account of the cause of the floods of the Nile. - -The reader will probably have observed a remarkable phrase used by -Herodotus, in his own explanation of these inundations. He says that -the sun _draws_, or attracts, the water; a metaphorical term, -obviously intended to denote some more general and abstract -conception than that of the visible operation which the word -primarily signifies. This abstract notion of "drawing" is, in the -historian, as we see, very vague and loose; it might, with equal -propriety, be explained to mean what we now understand by mechanical -or by chemical attraction, or pressure, or evaporation. And in like -manner, all the first attempts to comprehend the operations of -nature, led to the introduction of abstract conceptions, often -vague, indeed, but not, therefore, unmeaning; such as _motion_ and -_velocity_, _force_ and _pressure_, _impetus_ and _momentum_ (ῥοπὴ). -And the next step in philosophizing, necessarily was to endeavor to -make these vague abstractions more clear and fixed, so that the -logical faculty should be able to employ them securely and -coherently. But there were two ways of making this attempt; the one, -by examining the words only, and the thoughts which they call up; -the other, by attending to the facts and things which bring these -abstract terms into use. The latter, the method of _real_ inquiry, -was the way to success; but the Greeks followed the former, the -_verbal_ or _notional_ course, and failed. - -If Herodotus, when the notion of the sun's attracting the waters of -rivers had entered into his mind, had gone on to instruct himself, -by attention to facts, in what manner this notion could be made more -definite, while it still remained applicable to all the knowledge -which could be obtained, he would have made some progress towards a -true solution of his problem. If, for instance, he had tried to -ascertain whether this Attraction which the sun exerted upon the -waters of rivers, depended on his influence at their fountains only, -or was exerted over their whole course, and over waters which were -not parts of rivers, he would have been led to reject his -hypothesis; for he would have found, by observations sufficiently -obvious, that the sun's Attraction, as shown in such cases, is a -tendency to lessen all expanded and {62} open collections of -moisture, whether flowing from a spring or not; and it would then be -seen that this influence, operating on the whole surface of the -Nile, must diminish it as well as other rivers, in summer, and -therefore could not be the cause of its overflow. He would thus have -corrected his first loose conjecture by a real study of nature, and -might, in the course of his meditations, have been led to available -notions of Evaporation, or other natural actions. And, in like -manner, in other cases, the rude attempts at explanation, which the -first exercise of the speculative faculty produced, might have been -gradually concentrated and refined, so as to fall in, both with the -requisitions of reason and the testimony of sense. - -But this was not the direction which the Greek speculators took. On -the contrary; as soon as they had introduced into their philosophy -any abstract and general conceptions, they proceeded to scrutinize -these by the internal light of the mind alone, without any longer -looking abroad into the world of sense. They took for granted that -philosophy must result from the relations of those notions which are -involved in the common use of language, and they proceeded to seek -their philosophical doctrines by studying such notions. They ought -to have reformed and fixed their usual conceptions by Observation; -they only analyzed and expanded them by Reflection: they ought to -have sought by trial, among the Notions which passed through their -minds, some one which admitted of exact application to Facts; they -selected arbitrarily, and, consequently, erroneously, the Notions -according to which Facts should be assembled and arranged: they -ought to have collected clear Fundamental Ideas from the world of -things by _inductive_ acts of thought; they only derived results by -_Deduction_ from one or other of their familiar Conceptions.[12\1] - -[Note 12\1: The course by which the Sciences were formed, and which -is here referred to as that which the Greeks did _not_ follow, is -described in detail in the _Philosophy_, book xi., _Of the -Construction of Science_.] - -When this false direction had been extensively adopted by the Greek -philosophers, we may treat of it as the method of their _Schools_. -Under that title we must give a further account of it. {63} - - - - -CHAPTER II. - -THE GREEK SCHOOL PHILOSOPHY. - - -_Sect._ 1.--_The general Foundation of the Greek School Philosophy._ - -THE physical philosophy of the Greek Schools was formed by looking -at the material world through the medium of that common language -which men employ to answer the common occasions of life; and by -adopting, arbitrarily, as the grounds of comparison of facts, and of -inference from them, notions more abstract and large than those with -which men are practically familiar, but not less vague and obscure. -Such a philosophy, however much it might be systematized, by -classifying and analyzing the conceptions which it involves, could -not overcome the vices of its fundamental principle. But before -speaking of these defects, we must give some indications of its -character. - -The propensity to seek for principles in the common usages of -language may be discerned at a very early period. Thus we have an -example of it in a saying which is reported of Thales, the founder -of Greek philosophy.[13\1] When he was asked, "What is the -_greatest_ thing?" he replied, "_Place_; for all other things are -_in_ the world, but the world is _in_ it." In Aristotle we have the -consummation of this mode of speculation. The usual point from which -he starts in his inquiries is, that we say thus or thus in common -language. Thus, when he has to discuss the question, whether there -be, in any part of the universe, a Void, or space in which there is -nothing, he inquires first in how many senses we say that one thing -is _in_ another. He enumerates many of these;[14\1] we say the part -is in the whole, as the finger is _in_ the hand; again we say, the -species is in the genus, as man is included _in_ animal; again, the -government of Greece is _in_ the king; and various other senses are -described or exemplified, but of all these _the most proper_ is when -we say a thing is _in_ a vessel, and generally, _in place_. He next -examines what _place_ is, and comes to this conclusion, that "if -about a body there be another body including it, it is in place, and -if not, not." A body _moves_ when it changes its place; but {64} he -adds, that if water be in a vessel, the vessel being at rest, the -parts of the water may still move, for they are included by each -other; so that while the whole does not change its place, the parts -may change their places in a circular order. Proceeding then to the -question of a _void_, he, as usual, examines the different senses in -which the term is used, and adopts, as the most proper, _place -without matter_; with no useful result, as we shall soon see. - -[Note 13\1: Plut. _Conv. Sept. Sap._ Diog. Laert. i. 35.] - -[Note 14\1: Physic. Ausc. iv. 3.] - -Again,[15\1] in a question concerning mechanical action, he says, -"When a man moves a stone by pushing it with a stick, _we say_ both -that the man moves the stone, and that the stick moves the stone, -but the latter _more properly_." - -[Note 15\1: Physic. Ausc. viii. 5.] - -Again, we find the Greek philosophers applying themselves to extract -their dogmas from the most general and abstract notions which they -could detect; for example,--from the conception of the Universe as -One or as Many things. They tried to determine how far we may, or -must, combine with these conceptions that of a whole, of parts, of -number, of limits, of place, of beginning or end, of full or void, -of rest or motion, of cause and effect, and the like. The analysis -of such conceptions with such a view, occupies, for instance, almost -the whole of Aristotle's _Treatise on the Heavens_. - -The Dialogue of Plato, which is entitled _Parmenides_, appears at -first as if its object were to show the futility of this method of -philosophizing; for the philosopher whose name it bears, is -represented as arguing with an Athenian named Aristotle,[16\1] and, -by a process of metaphysical analysis, reducing him at least to this -conclusion, "that whether _One_ exist, or do not exist, it follows -that both it and other things, with reference to themselves and to -each other, all and in all respects, both are and are not, both -appear and appear not." Yet the method of Plato, so far as concerns -truths of that kind with which we are here concerned, was little -more efficacious than that of his rival. It consists mainly, as may -be seen in several of the dialogues, and especially in the _Timæus_, -in the application of notions as loose as those of the Peripatetics; -for example, the conceptions of the Good, the Beautiful, the -Perfect; and these are rendered still more arbitrary, by assuming an -acquaintance with the views of the Creator of the universe. The -philosopher is thus led to maxims which agree with those {65} of the -Aristotelians, that there can be no void, that things seek their own -place, and the like.[17\1] - -[Note 16\1: This Aristotle is not the Stagirite, who was forty-five -years younger than Plato, but one of the "thirty tyrants," as they -were called.] - -[Note 17\1: Timæus, p. 80.] - -Another mode of reasoning, very widely applied in these attempts, -was the doctrine of contrarieties, in which it was assumed, that -adjectives or substantives which are in common language, or in some -abstract mode of conception, opposed to each other, must point at -some fundamental antithesis in nature, which it is important to -study. Thus Aristotle[18\1] says, that the Pythagoreans, from the -contrasts which number suggests, collected ten principles,--Limited -and Unlimited, Odd and Even, One and Many, Right and Left, Male and -Female, Rest and Motion, Straight and Curved, Light and Darkness, -Good and Evil, Square and Oblong. We shall see hereafter, that -Aristotle himself deduced the doctrine of Four Elements, and other -dogmas, by oppositions of the same kind. - -[Note 18\1: Metaph. 1. 5.] - -The physical speculator of the present day will learn without -surprise, that such a mode of discussion as this, led to no truths -of real or permanent value. The whole mass of the Greek philosophy, -therefore, shrinks into an almost imperceptible compass, when viewed -with reference to the progress of physical knowledge. Still the -general character of this system, and its fortunes from the time of -its founders to the overthrow of their authority, are not without -their instruction, and, it may be hoped, not without their interest. -I proceed, therefore, to give some account of these doctrines in -their most fully developed and permanently received form, that in -which they were presented by Aristotle. - - -_Sect._ 2.--_The Aristotelian Physical Philosophy._ - -THE principal physical treatises of Aristotle are, the eight Books -of "Physical Lectures," the four Books "Of the Heavens," the two -Books "Of Production and Destruction:" for the Book "Of the World" -is now universally acknowledged to be spurious; and the -"Meteorologies," though full of physical explanations of natural -phenomena, does not exhibit the doctrines and reasonings of the -school in so general a form; the same may be said of the "Mechanical -Problems." The treatises on the various subjects of Natural History, -"On Animals," "On the Parts of Animals," "On Plants," "On -Physiognomonics," "On Colors," "On Sound," contain an extraordinary -{66} accumulation of facts, and manifest a wonderful power of -systematizing; but are not works which expound principles, and -therefore do not require to be here considered. - -The Physical Lectures are possibly the work concerning which a -well-known anecdote is related by Simplicius, a Greek commentator of -the sixth century, as well as by Plutarch. It is said, that -Alexander the Great wrote to his former tutor to this effect; "You -have not done well in publishing these lectures; for how shall we, -your pupils, excel other men, if you make that public to all, which -we learnt from you?" To this Aristotle is said to have replied: "My -Lectures are published and not published; they will be intelligible -to those who heard them, and to none besides." This may very easily -be a story invented and circulated among those who found the work -beyond their comprehension; and it cannot be denied, that to make -out the meaning and reasoning of every part, would be a task very -laborious and difficult, if not impossible. But we may follow the -import of a large portion of the Physical Lectures with sufficient -clearness to apprehend the character and principles of the -reasoning; and this is what I shall endeavor to do. - -The author's introductory statement of his view of the nature of -philosophy falls in very closely with what has been said, that he -takes his facts and generalizations as they are implied in the -structure of language. "We must in all cases proceed," he says, -"from what is known to what is unknown." This will not be denied; -but we can hardly follow him in his inference. He adds, "We must -proceed, therefore, from universal to particular. And something of -this," he pursues, "may be seen in language; for names signify -things in a general and indefinite manner, as _circle_, and by -defining we unfold them into particulars." He illustrates this by -saying, "thus children at first call all men _father_, and all women -_mother_, but afterwards distinguish." - -In accordance with this view, he endeavors to settle several of the -great questions concerning the universe, which had been started -among subtle and speculative men, by unfolding the meaning of the -words and phrases which are applied to the most general notions of -things and relations. We have already noticed this method. A few -examples will illustrate it further:--Whether there was or was not a -_void_, or place without matter, had already been debated among -rival sects of philosophers. The antagonist arguments were briefly -these:--There must be a void, because a body cannot move into a -space except it is {67} empty, and therefore without a void there -could be no motion:--and, on the other hand, there is no void, for -the intervals between bodies are filled with air, and air is -something. These opinions had even been supported by reference to -experiment. On the one hand, Anaxagoras and his school had shown, -that air, when confined, resisted compression, by squeezing a blown -bladder, and pressing down an inverted vessel in the water; on the -other hand, it was alleged that a vessel full of fine ashes held as -much water as if the ashes were not there, which could only be -explained by supposing void spaces among the ashes. Aristotle -decides that there is no void, on such arguments as this:[19\1]--In -a void there could be no difference of up and down; for as in -nothing there are no differences, so there are none in a privation -or negation; but a void is merely a privation or negation of matter; -therefore, in a void, bodies could not move up and down, which it is -in their nature to do. It is easily seen that such a mode of -reasoning, elevates the familiar forms of language and the -intellectual connections of terms, to a supremacy over facts; making -truth depend upon whether terms are or are not privative, and -whether we say that bodies fall _naturally_. In such a philosophy -every new result of observation would be compelled to conform to the -usual combinations of phrases, as these had become associated by the -modes of apprehension previously familiar. - -[Note 19\1: Physic. Ausc. iv. 7, p. 215.] - -It is not intended here to intimate that the common modes of -apprehension, which are the basis of common language, are limited -and casual. They imply, on the contrary, universal and necessary -conditions of our perceptions and conceptions; thus all things are -necessarily apprehended as existing in Time and Space, and as -connected by relations of Cause and Effect; and so far as the -Aristotelian philosophy reasons from these assumptions, it has a -real foundation, though even in this case the conclusions are often -insecure. We have an example of this reasoning in the eighth -Book,[20\1] where he proves that there never was a time in which -change and motion did not exist; "For if all things were at rest, -the first motion must have been produced by some change in some of -these things; that is, there must have been a change before the -first change;" and again, "How can _before_ and _after_ apply when -time is not? or how can time be when motion is not? If," he adds, -"time is a numeration of motion, and if time be eternal, motion must -be eternal." But he sometimes {68} introduces principles of a more -arbitrary character; and besides the general relations of thought, -takes for granted the inventions of previous speculators; such, for -instance, as the then commonly received opinions concerning the -frame of the world. From the assertion that motion is eternal, -proved in the manner just stated, Aristotle proceeds by a curious -train of reasoning, to identify this eternal motion with the diurnal -motion of the heavens. "There must," he says, "be something which is -the First Mover:"[21\1] this follows from the relation of causes and -effects. Again, "Motion must go on constantly, and, therefore, must -be either continuous or successive. Now what is continuous is more -properly said to take place _constantly_, than what is successive. -Also the continuous is better; but we always suppose that which is -better to take place in nature, if it be possible. The motion of the -First Mover will, therefore, be continuous, if such an eternal -motion be possible." We here see the vague judgment of _better_ and -_worse_ introduced, as that of _natural_ and _unnatural_ was before, -into physical reasonings. - -[Note 20\1: Ib. viii. 1, p. 258.] - -[Note 21\1: Physic. Ausc. viii. 6. p. 258.] - -I proceed with Aristotle's argument.[22\1] "We have now, therefore, -to show that there may be an infinite single, continuous motion, and -that this is circular." This is, in fact, proved, as may readily be -conceived, from the consideration that a body may go on perpetually -revolving uniformly in a circle. And thus we have a demonstration, -on the principles of this philosophy, that there is and must be a -First Mover, revolving eternally with a uniform circular motion. - -[Note 22\1: Ib. viii. 8.] - -Though this kind of philosophy may appear too trifling to deserve -being dwelt upon, it is important for our purpose so far as to -exemplify it, that we may afterwards advance, confident that we have -done it no injustice. - -I will now pass from the doctrines relating to the motions of the -heavens, to those which concern the material elements of the -universe. And here it may be remarked that the tendency (of which we -are here tracing the development) to extract speculative opinions -from the relations of words, must be very natural to man; for the -very widely accepted doctrine of the Four Elements which appears to -be founded on the opposition of the adjectives _hot_ and _cold_, -_wet_ and _dry_, is much older than Aristotle, and was probably one -of the earliest of philosophical dogmas. The great master of this -philosophy, however, puts the opinion in a more systematic manner -than his predecessors. {69} - -"We seek," he says,[23\1] "the principles of sensible things, that -is, of tangible bodies. We must take, therefore, not all the -contrarieties of quality, but those only which have reference to the -touch. Thus black and white, sweet and bitter, do not differ as -tangible qualities, and therefore must be rejected from our -consideration. - -[Note 23\1: De Gen. et Corrupt. ii. 2.] - -"Now the contrarieties of quality which refer to the touch are -these: hot, cold; dry, wet; heavy, light; hard, soft; unctuous, -meagre; rough, smooth; dense, rare." He then proceeds to reject all -but the four first of these, for various reasons; heavy and light, -because they are not active and passive qualities; the others, -because they are combinations of the four first, which therefore he -infers to be the four elementary qualities. - -"[24\1] Now in four things there are six combinations of two; but the -combinations of two opposites, as hot and cold, must be rejected; we -have, therefore, four elementary combinations, which agree with the -four apparently elementary bodies. Fire is hot and dry; air is hot and -wet (for steam is air); water is cold and wet, earth is cold and dry." - -[Note 24\1: Ib. iii. 8.] - -It may be remarked that this disposition to assume that some common -elementary quality must exist in the cases in which we habitually -apply a common adjective, as it began before the reign of the -Aristotelian philosophy, so also survived its influence. Not to -mention other cases, it would be difficult to free Bacon's -_Inquisitio in naturam calidi_, "Examination of the nature of heat," -from the charge of confounding together very different classes of -phenomena under the cover of the word _hot_. - -The correction of these opinions concerning the elementary -composition of bodies belongs to an advanced period in the history -of physical knowledge, even after the revival of its progress. But -there are some of the Aristotelian doctrines which particularly -deserve our attention, from the prominent share they had in the very -first beginnings of that revival; I mean the doctrines concerning -motion. - -These are still founded upon the same mode of reasoning from -adjectives; but in this case, the result follows, not only from the -opposition of the words, but also from the distinction of their -being _absolutely_ or _relatively_ true. "Former writers," says -Aristotle, "have considered heavy and light _relatively_ only, -taking cases, where both things have weight, but one is lighter than -the other; and they imagined that, in {70} this way, they defined -what was _absolutely_ (ἁπλῶς) heavy and light." We now know that -things which rise by their lightness do so only because they are -pressed upwards by heavier surrounding bodies; and this assumption -of absolute levity, which is evidently gratuitous, or rather merely -nominal, entirely vitiated the whole of the succeeding reasoning. -The inference was, that fire must be absolutely light, since it -tends to take its place above the other three elements; earth -absolutely heavy, since it tends to take its place below fire, air, -and water. The philosopher argued also, with great acuteness, that -air, which tends to take its place below fire and above water, must -do so _by its nature_, and not in virtue of any combination of heavy -and light elements. "For if air were composed of the parts which -give fire its levity, joined with other parts which produce gravity, -we might assume a quantity of air so large, that it should be -lighter than a small quantity of fire, having more of the light -parts." It thus follows that each of the four elements tends to its -own place, fire being the highest, air the next, water the next, and -earth the lowest. - -The whole of this train of errors arises from fallacies which have a -verbal origin;--from considering light as opposite to heavy; and -from considering levity as a quality of a body, instead of regarding -it as the effect of surrounding bodies. - -It is worth while to notice that a difficulty which often -embarrasses persons on their entrance upon physical -speculations,--the difficulty of conceiving that up and down are -different directions in different places,--had been completely got -over by Aristotle and the Greek philosophers. They were steadily -convinced of the roundness of the earth, and saw that this truth led -to the conclusion that all heavy bodies tend in converging -directions to the centre. And, they added, as the heavy tends to the -centre, the light tends to the exterior, "for Exterior is opposite -to Centre as heavy is to light."[25\1] - -[Note 25\1: De Cœlo, iv. 4.] - -The tendencies of bodies downwards and upwards, their weight, their -fall, their floating or sinking, were thus accounted for in a manner -which, however unsound, satisfied the greater part of the -speculative world till the time of Galileo and Stevinus, though -Archimedes in the mean time published the true theory of floating -bodies, which is very different from that above stated. Other parts -of the doctrines of motion were delivered by the Stagirite in the -same spirit and with the same success. The motion of a body which is -thrown along the {71} ground diminishes and finally ceases; the -motion of a body which falls from a height goes on becoming quicker -and quicker; this was accounted for on the usual principle of -opposition, by saying that the former is a _violent_, the latter a -_natural_ motion. And the later writers of this school expressed the -characters of such motions in verse. The rule of natural motion -was[26\1] - Principium tepeat, medium cum fine calebit. - Cool at the first, it warm and warmer glows. -And of violent motion, the law was-- - Principium fervet, medium calet, ultima friget. - Hot at the first, then barely warm, then cold. - -[Note 26\1: Alsted. Encyc. tom. i. p. 687.] - -It appears to have been considered by Aristotle a difficult problem -to explain why a stone thrown from the hand continues to move for -some time, and then stops. If the hand was the cause of the motion, -how could the stone move at all when left to itself? if not, why -does it ever stop? And he answers this difficulty by saying,[27\1] -"that there is a motion communicated to the air, the successive -parts of which urge the stone onwards; and that each part of this -medium continues to act for some while after it has been acted on, -and the motion ceases when it comes to a particle which cannot act -after it has ceased to be acted on." It will be readily seen that -the whole of this difficulty, concerning a body which moves forward -and is retarded till it stops, arises from ascribing the -retardation, not to the real cause, the surrounding resistances, but -to the body itself. - -[Note 27\1: Phys. Ausc. viii. 10.] - -One of the doctrines which was the subject of the warmest discussion -between the defenders and opposers of Aristotle, at the revival of -physical knowledge, was that in which he asserts,[28\1] "That body -is heavier than another which in an equal bulk moves downward -quicker." The opinion maintained by the **Aristotelians at the time of -Galileo was, that bodies fall quicker exactly in proportion to their -weight. The master himself asserts this in express terms, and -reasons upon it.[29\1] Yet in another passage he appears to -distinguish between weight and actual motion downwards.[30\1] "In -physics, we call bodies heavy and light from their _power_ of -motion; but these names are not applied to their actual operations -(ἐνέργειαις) except any one thinks {72} _momentum_ (ῥοπὴ) to be a -word of both applications. But heavy and light are, as it were, the -_embers_ or _sparks_ of motion, and therefore proper to be treated -of here." - -[Note 28\1: De Cœlo, iv. 1, p. 308.] - -[Note 29\1: Ib. iii. 2.] - -[Note 30\1: Ib. iv. 1, p. 307.] - -The distinction just alluded to, between Power or Faculty of Action, -and actual Operation or Energy, is one very frequently referred to -by Aristotle; and though not by any means useless, may easily be so -used as to lead to mere verbal refinements instead of substantial -knowledge. - -The Aristotelian distinction of Causes has not any very immediate -bearing upon the parts of physics of which we have here mainly -spoken; but it was so extensively accepted, and so long retained, -that it may be proper to notice it.[31\1] "One kind of Cause is the -matter of which any thing is made, as bronze of a statue, and silver -of a vial; another is the form and pattern, as the Cause of an -octave is the ratio of two to one; again, there is the Cause which -is the origin of the production, as the father of the child; and -again, there is the End, or that for the sake of which any thing is -done, as health is the cause of walking." These four kinds of Cause, -the _material_, the _formal_, the _efficient_, and the _final_, were -long leading points in all speculative inquiries; and our familiar -forms of speech still retain traces of the influence of this -division. - -[Note 31\1: Phys. ii. 3.] - -It is my object here to present to the reader in an intelligible -shape, the principles and mode of reasoning of the Aristotelian -philosophy, not its results. If this were not the case, it would be -easy to excite a smile by insulating some of the passages which are -most remote from modern notions. I will only mention, as specimens, -two such passages, both very remarkable. - -In the beginning of the book "On the Heavens," he proves[32\1] the -world to be _perfect_, by reasoning of the following kind: "The -bodies of which the world is composed are solids, and therefore have -three dimensions: now three is the most perfect number; it is the -first of numbers, for of _one_ we do not speak as a number; of _two_ -we say _both_; but _three_ is the first number of which we say -_all_; moreover, it has a beginning, a middle, and an end." - -[Note 32\1: De Cœlo, i. 1.] - -The reader will still perceive the verbal foundations of opinions -thus supported. - -"The simple elements must have simple motions, and thus fire and air -have their natural motions upwards, and water and earth have {73} -their natural motions downwards; but besides these motions, there is -motion in a circle, which is unnatural to these elements, but which -is a more perfect motion than the other, because a circle is a -perfect line, and a straight line is not; and there must be -something to which this motion is natural. From this it is evident," -he adds, with obvious animation, "that there is some essence of body -different from those of the four elements, more divine than those, -and superior to them. If things which move in a circle move contrary -to nature, it is marvellous, or rather absurd, that this, the -unnatural motion, should alone be continuous and eternal; for -unnatural motions decay speedily. And so, from all this, we must -collect, that besides the four elements which we have here and about -us, there is another removed far off, and the more excellent in -proportion as it is more distant from us." This fifth element was -the "_quinta essentia_," of after writers, of which we have a trace -in our modern literature, in the word _quintessence_. - - -_Sect._ 3.--_Technical Forms of the Greek Schools._ - -WE have hitherto considered only the principle of the Greek Physics; -which was, as we have seen, to deduce its doctrines by an analysis -of the notions which common language involves. But though the -Grecian philosopher began by studying words in their common -meanings, he soon found himself led to fix upon some special shades -or applications of these meanings as the permanent and standard -notion, which they were to express; that is, he made his language -_technical_. The invention and establishment of technical terms is -an important step in any philosophy, true or false; we must, -therefore, say a few words on this process, as exemplified in the -ancient systems. - -1. _Technical Forms of the Aristotelian Philosophy._--We have -already had occasion to cite some of the distinctions introduced by -Aristotle, which may be considered as technical; for instance, the -classification of Causes as _material_, _formal_, _efficient_, and -_final_; and the opposition of Qualities as _absolute_ and -_relative_. A few more of the most important examples may suffice. -An analysis of objects into _Matter_ and _Form_, when metaphorically -extended from visible objects to things conceived in the most -general manner, became an habitual hypothesis of the Aristotelian -school. Indeed this metaphor is even yet one of the most significant -of those which we can employ, to suggest one of the most comprehensive -and fundamental antitheses with which philosophy has to do;--the -opposition of sense and reason, of {74} impressions and laws. In this -application, the German philosophers have, up to the present time, -rested upon this distinction a great part of the weight of their -systems; as when Kant says, that Space and Time are the _Forms of -Sensation_. Even in our own language, we retain a trace of the -influence of this Aristotelian notion, in the word _Information_, when -used for that knowledge which may be conceived as moulding the mind -into a definite shape, instead of leaving it a mere mass of -unimpressed susceptibility. - -Another favorite Aristotelian antithesis is that of _Power_ and -_Act_ (δύναμις, ἐνέργεια). This distinction is made the basis of -most of the physical philosophy of the school; being, however, -generally introduced with a peculiar limitation. Thus, Light is -defined to be "the Act of what is lucid, as being lucid. And if," it -is added, "the lucid be so in power but not in act, we have -darkness." The reason of the limitation, "as being lucid," is, that -a lucid body may act in other ways; thus a torch may move as well as -shine, but its moving is not its act _as being a lucid_ body. - -Aristotle appears to be well satisfied with this explanation, for he -goes on to say, "Thus light is not Fire, nor any body whatever, or -the emanation of any body (for that would be a kind of body), but it -is the presence of something like Fire in the body; it is, however, -impossible that two bodies should exist in the same place, so that -it is not a body;" and this reasoning appears to leave him more -satisfied with his doctrine, that Light is an _Energy_ or _Act_. - -But we have a more distinctly technical form given to this notion. -Aristotle introduced a word formed by himself to express the act -which is thus opposed to inactive power: this is the celebrated word -ἐντελέχεια. Thus the noted definition of Motion in the third book of -the Physics,[33\1] is that it is "the _Entelechy_, or Act, of a -movable body in respect of being movable;" and the definition of the -Soul is[34\1] that it is "the _Entelechy_ of a natural body which -has life by reason of its power." This word has been variously -translated by the followers of Aristotle, and some of them have -declared it untranslatable. _Act_ and _Action_ are held to be -inadequate substitutes; the _very act_, _ipse cursus actionis_, is -employed by some; _primus actus_ is employed by many, but another -school use _primus actus_ of a non-operating form. Budæus uses -_efficacia_. Cicero[35\1] translates it "quasi quandam continuatam -motionem, et perennem;" but this paraphrase, though it may {75} fall -in with the description of the soul, which is the subject with which -Cicero is concerned, does not appear to agree with the general -applications of the term. Hermolaus Barbarus is said to have been so -much oppressed with this difficulty of translation, that he -consulted the evil spirit by night, entreating to be supplied with a -more common and familiar substitute for this word: the mocking -fiend, however, suggested only a word equally obscure, and the -translator, discontented with this, invented for himself the word -_perfectihabia_. - -[Note 33\1: Phys. iii. 1.] - -[Note 34\1: De Animâ, ii. 1.] - -[Note 35\1: Tusc. i. 10.] - -We need not here notice the endless apparatus of technicalities -which was, in later days, introduced into the Aristotelian -philosophy; but we may remark, that their long continuance and -extensive use show us how powerful technical phraseology is, for the -perpetuation either of truth or error. The Aristotelian terms, and -the metaphysical views which they tend to preserve, are not yet -extinct among us. In a very recent age of our literature it was -thought a worthy employment by some of the greatest writers of the -day, to attempt to expel this system of technicalities by ridicule. - -"Crambe regretted extremely that _substantial forms_, a race of -harmless beings, which had lasted for many years, and afforded a -comfortable subsistence to many poor philosophers, should now be -hunted down like so many wolves, without a possibility of retreat. -He considered that it had gone much harder with them than with -_essences_, which had retired from the schools into the -apothecaries' shops, where some of them had been advanced to the -degree of _quintessences_.**"[36\1] - -[Note 36\1: Martinus Scriblerus, cap. vii.] - -We must now say a few words on the technical terms which others of -the Greek philosophical sects introduced. - -2. _Technical Forms of the Platonists._--The other sects of the Greek -philosophy, as well as the Aristotelians, invented and adopted -technical terms, and thus gave fixity to their tenets and consistency -to their traditionary systems; of these I will mention a few. - -A technical expression of a contemporary school has acquired perhaps -greater celebrity than any of the terms of Aristotle. I mean the -_Ideas_ of Plato. The account which Aristotle gives of the origin of -these will serve to explain their nature.[37\1] "Plato," says he, -"who, in his youth, was in habits of communication first with -Cratylus and the Heraclitean opinions, which represent all the -objects of sense as being in a perpetual flux, so that concerning -these no science nor certain {76} knowledge can exist, entertained -the same opinions at a later period also. When, afterwards, Socrates -treated of moral subjects, and gave no attention to physics, but, in -the subjects which he did discuss, arrived at universal truths, and -before any man, turned his thoughts to definitions, Plato adopted -similar doctrines on this subject also; and construed them in this -way, that these truths and definitions must be applicable to -something else, and not to sensible things: for it was impossible, -he conceived, that there should be a general common definition of -any sensible object, since such were always in a state of change. -The things, then, which were the subjects of universal truths he -called _Ideas_; and held that objects of sense had their names -according to Ideas and after them; so that things participated in -that Idea which had the same name as was applied to them." - -[Note 37\1: Arist. Metaph. i. 6. The same account is repeated, and -the subject discussed, Metaph. xii. 4.] - -In agreement with this, we find the opinions suggested in the -_Parmenides_ of Plato, the dialogue which is considered by many to -contain the most decided exposition of the doctrine of Ideas. In -this dialogue, Parmenides is made to say to Socrates, then a young -man,[38\1] "O Socrates, philosophy has not yet claimed you for her -own, as, in my judgment, she will claim you, and you will not -dishonor her. As yet, like a young man as you are, you look to the -opinions of men. But tell me this: it appears to you, as you say, -that there are certain _Kinds_ or _Ideas_ (εἰδὴ) of which things -partake and receive applications according to that of which they -partake: thus those things which partake of _Likeness_ are called -_like_; those things which partake of _Greatness_ are called -_great_; those things which partake of _Beauty_ and _Justice_ are -called _beautiful_ and _just_." To this Socrates assents. And in -another part of the dialogue he shows that these Ideas are not -included in our common knowledge, from whence he infers that they -are objects of the Divine mind. - -[Note 38\1: Parmenid. p. 131.] - -In the Phædo the same opinion is maintained, and is summed up in -this way, by a reporter of the last conversation of Socrates,[39\1] -εἶναι τι ἕκαστον τῶν εἰδῶν, καὶ τούτων τ' ἄλλα μεταλαμβάνοντα αὐτῶν -τούτων τὴν ἐπωνυμίαν ἴσχειν; "that each _Kind_ has an existence, and -that other things partake of these Kinds, and are called according -to the Kind of which they partake." - -[Note 39\1: Phædo, p. 102.] - -The inference drawn from this view was, that in order to obtain true -and certain knowledge, men must elevate themselves, as much as -possible, to these Ideas of the qualities which they have to -consider: {77} and as things were thus called after the Ideas, the -Ideas had a priority and pre-eminence assigned them. The _Idea_ of -Good, Beautiful, and Wise was the "First Good," the "First -Beautiful," the "First Wise." This dignity and distinction were -ultimately carried to a large extent. Those Ideas were described as -eternal and self-subsisting, forming an "Intelligible World," full -of the models or archetypes of created things. But it is not to our -purpose here to consider the Platonic Ideas in their theological -bearings. In physics they were applied in the same form as in -morals. The _primum calidum_, _primum frigidum_ were those Ideas of -fundamental Principles by participation of which, all things were -hot or cold. - -This school did not much employ itself in the development of its -principles as applied to physical inquiries: but we are not without -examples of such speculations. Plutarch's Treatise Περὶ τοῦ Πρώτου -Ψυχροῦ, "On the First Cold," may be cited as one. It is in reality a -discussion of a question which has been agitated in modern times -also;--whether cold be a positive quality or a mere privation. "Is -there, O Favorinus," he begins, "a First Power and Essence of the -Cold, as Fire is of the Hot; by a certain presence and participation -of which all other things are cold: or is rather coldness a -privation of heat, as darkness is of light, and rest of motion?" - -3. _Technical Forms of the Pythagoreans._--The _Numbers_ of the -Pythagoreans, when propounded as the explanation of physical -phenomena, as they were, are still more obscure than the Ideas of -the Platonists. There were, indeed, considerable resemblances in the -way in which these two kinds of notions were spoken of. Plato called -his Ideas _unities_, _monads_; and as, according to him, Ideas, so, -according to the Pythagoreans, Numbers, were the causes of things -being what they are.[40\1] But there was this difference, that -things shared the nature of the Platonic Ideas "by participation," -while they shared the nature of Pythagorean Numbers "by imitation." -Moreover, the Pythagoreans followed their notion out into much -greater development than any other school, investing particular -numbers with extraordinary attributes, and applying them by very -strange and forced analogies. Thus the number Four, to which they -gave the name of _Tetractys_, was held to be the most perfect -number, and was conceived to correspond to the human soul, in some -way which appears to be very imperfectly understood by the -commentators of this philosophy. {78} - -[Note: 40\1: Arist. Metaph. i. 6.] - -It has been observed by a distinguished modern scholar,[41\1] that -the place which Pythagoras ascribed to his numbers is intelligible -only by supposing that he confounded, first a numerical unit with a -geometrical point, and then this with a material atom. But this -criticism appears to place systems of physical philosophy under -requisitions too severe. If all the essential properties and -attributes of things were fully represented by the relations of -number, the philosophy which supplied such an explanation of the -universe, might well be excused from explaining also that existence -of objects which is distinct from the existence of all their -qualities and properties. The Pythagorean love of numerical -speculations might have been combined with the doctrine of atoms, -and the combination might have led to results well worth notice. But -so far as we are aware, no such combination was attempted in the -ancient schools of philosophy; and perhaps we of the present day are -only just beginning to perceive, through the disclosures of -chemistry and crystallography, the importance of such a line of -inquiry. - -[Note 41\1: Thirlwall's _Hist. Gr._ ii. 142.] - -4. _Technical Forms of the Atomists and Others._--The atomic -doctrine, of which we have just spoken, was one of the most definite -of the physical doctrines of the ancients, and was applied with most -perseverance and knowledge to the explanation of phenomena. Though, -therefore, it led to no success of any consequence in ancient times, -it served to transmit, through a long series of ages, a habit of -really physical inquiry; and, on this account, has been thought -worthy of an historical disquisition by Bacon.[42\1] - -[Note 42\1: Parmenidis et Telesii et præcipue Democriti Philosophia, -&c., Works, vol. ix. 317.] - -The technical term, _Atom_, marks sufficiently the nature of the -opinion. According to this theory, the world consists of a -collection of simple particles, of one kind of matter, and of -indivisible smallness (as the name indicates), and by the various -configurations and motions of these particles, all kinds of matter -and all material phenomena are produced. - -To this, the Atomic Doctrine of Leucippus and Democritus, was -opposed the _Homoiomeria_ of Anaxagoras; that is, the opinion that -material things consist of particles which are homogeneous in each -kind of body, but various in different kinds: thus for example, -since by food the flesh and blood and bones of man increase, the -author of this doctrine held that there are in food particles of -flesh, and blood, {79} and bone. As the former tenet points to the -corpuscular theories of modern times, so the latter may be -considered as a dim glimpse of the idea of chemical analysis. The -Stoics also, who were, especially at a later period, inclined to -materialist views, had their technical modes of speaking on such -subjects. They asserted that matter contained in itself tendencies -or dispositions to certain forms, which dispositions they called -λόγοι **σπερματικοὶ, _seminal proportions_, or _seminal reasons_. - -Whatever of sound view, or right direction, there might be in the -notions which suggested these and other technical expressions, was, -in all the schools of philosophy (so far as physics was concerned) -quenched and overlaid by the predominance of trifling and barren -speculations; and by the love of subtilizing and commenting upon the -works of earlier writers, instead of attempting to interpret the -book of nature. Hence these technical terms served to give fixity -and permanence to the traditional dogmas of the sect, but led to no -progress of knowledge. - -The advances which were made in physical science proceeded, not from -these schools of philosophy (if we except, perhaps, the obligations -of the science of Harmonics to the Pythagoreans), but from reasoners -who followed an independent path. The sequel of the ambitious hopes, -the vast schemes, the confident undertakings of the philosophers of -ancient Greece, was an entire failure in the physical knowledge of -which it is our business to trace the history. Yet we are not, on -that account, to think slightingly of these early speculators. They -were men of extraordinary acuteness, invention, and range of -thought; and, above all, they had the merit of first completely -unfolding the speculative faculty--of starting in that keen and -vigorous chase of knowledge out of which all the subsequent culture -and improvement of man's intellectual stores have arisen. The sages -of early Greece form the heroic age of science. Like the first -navigators in their own mythology, they boldly ventured their -untried bark in a distant and arduous voyage, urged on by the hopes -of a supernatural success; and though they missed the imaginary -golden prize which they sought, they unlocked the gates of distant -regions, and opened the seas to the keels of the thousands of -adventurers who, in succeeding times, sailed to and fro, to the -indefinite increase of the mental treasures of mankind. - -But inasmuch as their attempts, in one sense, and at first, failed, -we must proceed to offer some account of this failure, and of its -nature and causes. {80} - - - - -CHAPTER III. - -FAILURE OF THE PHYSICAL PHILOSOPHY OF THE GREEK SCHOOLS. - - -_Sect._ 1.--_Result of the Greek School Philosophy_. - -THE methods and forms of philosophizing which we have described as -employed by the Greek Schools, failed altogether in their -application to physics. No discovery of general laws, no explanation -of special phenomena, rewarded the acuteness and boldness of these -early students of nature. Astronomy, which made considerable -progress during the existence of the sects of Greek philosophers, -gained perhaps something by the authority with which Plato taught -the supremacy and universality of mathematical rule and order; and -the truths of Harmonics, which had probably given rise to the -Pythagorean passion for numbers, were cultivated with much care by -that school. But after these first impulses, the sciences owed -nothing to the philosophical sects; and the vast and complex -accumulations and apparatus of the Stagirite do not appear to have -led to any theoretical physical truths. - -This assertion hardly requires proof, since in the existing body of -science there are no doctrines for which we are indebted to the -Aristotelian School. Real truths, when once established, remain to -the end of time a part of the mental treasure of man, and may be -discerned through all the additions of later days. But we can point -out no physical doctrine now received, of which we trace the -anticipation in Aristotle, in the way in which we see the Copernican -system anticipated by Aristarchus, the resolution of the heavenly -appearances into circular motions suggested by Plato, and the -numerical relations of musical intervals ascribed to Pythagoras. But -it may be worth while to look at this matter more closely. - -Among the works of Aristotle are thirty-eight chapters of -"Problems," which may serve to exemplify the progress he had really -made in the reduction of phenomena to laws and causes. Of these -Problems, a large proportion are physiological, and these I here -pass by, as not illustrative of the state of physical knowledge. But -those which are properly physical are, for the most part, questions -concerning such {81} facts and difficulties as it is the peculiar -business of theory to explain. Now it may be truly said, that in -scarcely any one instance are the answers, which Aristotle gives to -his questions, of any value. For the most part, indeed, he propounds -his answer with a degree of hesitation or vacillation which of -itself shows the absence of all scientific distinctness of thought; -and the opinions so offered never appear to involve any settled or -general principle. - -We may take, as examples of this, the problems of the simplest kind, -where the principles lay nearest at hand--the mechanical ones. -"Why," he asks,[43\1] "do small forces move great weights by means -of a lever, when they have thus to move the lever added to the -weight? Is it," he suggests, "because a greater radius moves -faster?" "Why does a small wedge split great weights?[44\1] Is it -because the wedge is composed of two opposite levers?" "Why,[45\1] -when a man rises from a chair, does he bend his leg and his body to -acute angles with his thigh? Is it because a right angle is -connected with equality and rest?" "Why[46\1] can a man throw a -stone further with a sling than with his hand? Is it that when he -throws with his hand he moves the stone from rest, but when he uses -the sling he throws it already in motion?" "Why,[47\1] if a circle -be thrown on the ground, does it first describe a straight line and -then a spiral, as it falls? Is it that the air first presses equally -on the two sides and supports it, and afterwards presses on one side -more?" "Why[48\1] is it difficult to distinguish a musical note from -the octave above? Is it that proportion stands in the place of -equality?" It must be allowed that these are very vague and -worthless surmises; for even if we were, as some commentators have -done, to interpret some of them so as to agree with sound -philosophy, we should still be unable to point out, in this author's -works, any clear or permanent apprehension of the general principles -which such an interpretation implies. - -[Note 43\1: Mech. Prob. 4.] - -[Note 44\1: Ib. 18.] - -[Note 45\1: Ib. 31.] - -[Note 46\1: Ib. 13.] - -[Note 47\1: Περὶ Ἄψυχα. 11.] - -[Note 48\1: Περὶ Ἁρμον. 14.] - -Thus the Aristotelian physics cannot be considered as otherwise than -a complete failure. It collected no general laws from facts; and -consequently, when it tried to explain facts, it had no principles -which were of any avail. - -The same may be said of the physical speculations of the other -schools of philosophy. They arrived at no doctrines from which they -could deduce, by sound reasoning, such facts as they saw; though -they {82} often venture so far to trust their principles as to infer -from them propositions beyond the domain of sense. Thus, the -principle that each element seeks _its own place_, led to the -doctrine that, the place of fire being the highest, there is, above -the air, a Sphere of Fire--of which doctrine the word _Empyrean_, -used by our poets, still conveys a reminiscence. The Pythagorean -tenet that ten is a perfect number,[49\1] led some persons to assume -that the heavenly bodies are in number ten; and as nine only were -known to them, they asserted that there was an _antichthon_, or -_counter-earth_, on the other side of the sun, invisible to us. -Their opinions respecting numerical ratios, led to various other -speculations concerning the distances and positions of the heavenly -bodies: and as they had, in other cases, found a connection between -proportions of distance and musical notes, they assumed, on this -suggestion, _the music of the spheres_. - -[Note 49\1: Arist. Metaph. i. 5.] - -Although we shall look in vain in the physical philosophy of the -Greek Schools for any results more valuable than those just -mentioned, we shall not be surprised to find, recollecting how much -an admiration for classical antiquity has possessed the minds of -men, that some writers estimate their claims much more highly than -they are stated here. Among such writers we may notice Dutens, who, -in 1766, published his "Origin of the Discoveries attributed to the -Moderns; in which it is shown that our most celebrated Philosophers -have received the greatest part of their knowledge from the Works of -the Ancients." The thesis of this work is attempted to be proved, as -we might expect, by very large interpretations of the general -phrases used by the ancients. Thus, when Timæus, in Plato's -dialogue, says of the Creator of the world,[50\1] "that he infused -into it two powers, the origins of motions, both of that of the same -thing and of that of different things;" Dutens[51\1] finds in this a -clear indication of the projectile and attractive forces of modern -science. And in some of the common declamation of the Pythagoreans -and Platonists concerning the general prevalence of numerical -relations in the universe, he discovers their acquaintance with the -law of the inverse square of the distance by which gravitation is -regulated, though he allows[52\1] that it required all the -penetration of Newton and his followers to detect this law in the -scanty fragments by which it is transmitted. - -[Note 50\1: Tim. 96.] - -[Note 51\1: 3d ed. p. 83.] - -[Note 52\1: Ib. p. 88.] - -Argument of this kind is palpably insufficient to cover the failure -of the Greek attempts at a general physical philosophy; or rather we -{83} may say, that such arguments, since they are as good as can be -brought in favor of such an opinion, show more clearly how entire -the failure was. I proceed now to endeavor to point out its causes. - - -_Sect._ 2.--_Cause of the Failure of the Greek Physical Philosophy._ - -THE cause of the failure of so many of the attempts of the Greeks to -construct physical science is so important, that we must endeavor to -bring it into view here; though the full development of such -subjects belongs rather to the Philosophy of Induction. The subject -must, at present, be treated very briefly. - -I will first notice some errors which may naturally occur to the -reader's mind, as possible causes of failure, but which, we shall be -able to show, were not the real reasons in this case. - -The cause of failure was _not the neglect of facts_. It is often -said that the Greeks disregarded experience, and spun their -philosophy out of their own thoughts alone; and this is supposed by -many to be their essential error. It is, no doubt, true, that the -disregard of experience is a phrase which may be so interpreted as -to express almost any defect of philosophical method; since -coincidence with experience is requisite to the truth of all theory. -But if we fix a more precise sense on our terms, I conceive it may -be shown that the Greek philosophy did, in its opinions, recognize -the necessity and paramount value of observations; did, in its -origin, proceed upon observed facts; and did employ itself to no -small extent in classifying and arranging phenomena. We must -endeavor to illustrate these assertions, because it is important to -show that these steps alone do not necessarily lead to science. - -1. The acknowledgment of experience as the main ground of physical -knowledge is so generally understood to be a distinguishing feature -of later times, that it may excite surprise to find that Aristotle, -and other ancient philosophers, not only asserted in the most -pointed manner that all our knowledge must begin from experience, -but also stated in language much resembling the habitual phraseology -of the most modern schools of philosophizing, that particular facts -must be _collected_; that from these, general principles must be -obtained by _induction_; and that these principles, when of the most -general kind, are _axioms_. A few passages will show this. - -"The way[53\1] must be the same," says Aristotle, in speaking of the -rules of reasoning, "with respect to philosophy, as it is with -respect to {84} any art or science whatever; we must collect the -facts, and the things to which the facts happen, in each subject, -and provide as large a supply of these as possible." He then -proceeds to say that "we are not to look at once at all this -collected mass, but to consider small and definite portions" . . . -"And thus it is the office of observation to supply principles in -each subject; for instance, astronomical observation supplies the -principles of astronomical science. For the phenomena being properly -assumed, the astronomical demonstrations were from these discovered. -And the same applies to every art and science. So that if we take -the facts (τὰ ὑπάρχοντα) belonging to each subject, it is _our_ task -to mark out clearly the course of the demonstrations. For if _in our -natural history_ (κατὰ τὴν ἱστορίαν) we have omitted nothing of the -facts and properties which belong to the subject, we shall learn -what we can demonstrate and what we cannot." - -[Note 53\1: Anal. Prior. i. 30.] - -These facts, τὰ ὑπάρχοντα, he, at other times, includes in the term -_sensation_. Thus, he says,[54\1] "It is obvious that if any -sensation is wanting, there must be also some knowledge wanting -which we are thus prevented from having, since we arrive at -knowledge either by induction or by demonstration. Demonstration -proceeds from universal propositions, Induction from particulars. -But we cannot have universal theoretical propositions except from -induction; and we cannot make inductions without having sensation; -for sensation has to do with particulars." - -[Note 54\1: Anal. Post. i. 18.] - -In another place,[55\1] after stating that principles must be prior -to, and better known than conclusions, he distinguishes such -principles into absolutely prior, and prior relative to us: "The -prior principles, relative to us, are those which are nearer to the -sensation; but the principles absolutely prior are those which are -more remote from the sensation. The most general principles are the -more remote, the more particular are nearer. The general principles -which are necessary to knowledge are _axioms_." - -[Note 55\1: Ib. i. 2.] - -We may add to these passages, that in which he gives an account of -the way in which Leucippus was led to the doctrine of atoms. After -describing the opinions of some earlier philosophers, he says,[56\1] -"Thus, proceeding in violation of sensation, and disregarding it, -because, as they held, they must follow reason, some came to the -conclusion that the universe was one, and infinite, and at rest. As -it appeared, however, that though this ought to be by reasoning, it -{85} would go near to madness to hold such opinions in practice (for -no one was ever so mad as to think fire and ice to be one), -Leucippus, therefore, pursued a line of reasoning which was in -accordance with sensation, and which was not irreconcilable with the -production and decay, the motion and multitude of things." It is -obvious that the school to which Leucippus belonged (the Eclectic) -must have been, at least in its origin, strongly impressed with the -necessity of bringing its theories into harmony with the observed -course of nature. - -[Note 56\1: De Gen. et Cor. i. 8.] - -2. Nor was this recognition of the fundamental value of experience a -mere profession. The Greek philosophy did, in its beginning, proceed -upon observation. Indeed it is obvious that the principles which it -adopted were, in the first place, assumed in order to account for -some classes of facts, however imperfectly they might answer their -purpose. The principle of things seeking their own places, was -invented in order to account for the falling and floating of bodies. -Again, Aristotle says, that heat is that which brings together -things of the same kind, cold is that which brings together things -whether of the same or of different kinds: it is plain that in this -instance he intended by his principle to explain some obvious facts, -as the freezing of moist substances, and the separation of -heterogeneous things by fusion; for, as he adds, if fire brings -together things which are akin, it will separate those which are not -akin. It would be easy to illustrate the remark further, but its -truth is evident from the nature of the case; for no principles -could be accepted for a moment, which were the result of an -arbitrary caprice of the mind, and which were not in some measure -plausible, and apparently confirmed by facts. - -But the works of Aristotle show, in another way, how unjust it would -be to accuse him of disregarding facts. Many large treatises of his -consist almost entirely of collections of facts, as for instance, -those "On Colors," "On Sounds," and the collection of Problems to -which we have already referred; to say nothing of the numerous -collection of facts bearing on natural history and physiology, which -form a great portion of his works, and are even now treasuries of -information. A moment's reflection will convince us that the -physical sciences of our own times, for example. Mechanics and -Hydrostatics, are founded almost entirely upon facts with which the -ancients were as familiar as we are. The defect of their philosophy, -therefore, wherever it may lie, consists neither in the speculative -depreciation of the value of facts, nor in the practical neglect of -their use. - -3. Nor again, should we hit upon the truth, if we were to say that -{86} Aristotle, and other ancient philosophers, did indeed collect -facts; but that they took no steps in classifying and comparing -them; and that thus they failed to obtain from them any general -knowledge. For, in reality, the treatises of Aristotle which we have -mentioned, are as remarkable for the power of classifying and -systematizing which they exhibit, as for the industry shown in the -accumulation. But it is not classification of facts merely which can -lead us to knowledge, except we adopt that special arrangement, -which, in each case, brings into view the principles of the subject. -We may easily show how unprofitable an arbitrary or random -classification is, however orderly and systematic it may be. - -For instance, for a long period all unusual fiery appearances in the -sky were classed together as _meteors_. Comets, shooting-stars, and -globes of fire, and the aurora borealis in all its forms, were thus -grouped together, and classifications of considerable extent and -minuteness were proposed with reference to these objects. But this -classification was of a mixed and arbitrary kind. Figure, color, -motion, duration, were all combined as characters, and the -imagination lent its aid, transforming these striking appearances -into fiery swords and spears, bears and dragons, armies and -chariots. The facts so classified were, notwithstanding, worthless; -and would not have been one jot the less so, had they and their -classes been ten times as numerous as they were. No rule or law that -would stand the test of observation was or could be thus discovered. -Such classifications have, therefore, long been neglected and -forgotten. Even the ancient descriptions of these objects of -curiosity are unintelligible, or unworthy of trust, because the -spectators had no steady conception of the usual order of such -phenomena. For, however much we may fear to be misled by -preconceived opinions, the caprices of imagination distort our -impressions far more than the anticipations of reason. In this case -men had, indeed we may say with regard to many of these meteors, -they still have, no science: not for want of facts, nor even for -want of classification of facts; but because the classification was -one in which no real principle was contained. - -4. Since, as we have said before, two things are requisite to -science,--Facts and Ideas; and since, as we have seen. Facts were -not wanting in the physical speculations of the ancients, we are -naturally led to ask, Were they then deficient in Ideas? Was there a -want among them of mental activity, and logical connection of -thought? But it is so obvious that the answer to this inquiry must -be in the negative, that we need not dwell upon it. No one who knows -any thing of the {87} history of the ancient Greek mind, can -question, that in acuteness, in ingenuity, in the power of close and -distinct reasoning, they have never been surpassed. The common -opinion, which considers the defect of their philosophical character -to reside rather in the exclusive activity of such qualities, than -in the absence of them, is at least so far just. - -5. We come back again, therefore, to the question, What was the -radical and fatal defect in the physical speculations of the Greek -philosophical schools? - -To this I answer: The defect was, that though they had in their -possession Facts and Ideas, _the Ideas were not distinct and -appropriate to the Facts_. - -The peculiar characteristics of scientific ideas, which I have -endeavored to express by speaking of them as _distinct_ and -_appropriate to the facts_, must be more fully and formally set -forth, when we come to the philosophy of the subject. In the mean -time, the reader will probably have no difficulty in conceiving -that, for each class of Facts, there is some special set of Ideas, -by means of which the facts can be included in general scientific -truths; and that these Ideas, which may thus be termed -_appropriate_, must be possessed with entire distinctness and -clearness, in order that they may be successfully applied. It was -the want of Ideas having this reference to material phenomena, which -rendered the ancient philosophers, with very few exceptions, -helpless and unsuccessful speculators on physical subjects. - -This must be illustrated by one or two examples. One of the facts -which Aristotle endeavors to explain is this; that when the sun's -light passes through a hole, whatever be the form of the hole, the -bright image, if formed at any considerable distance from the hole, -is round, instead of imitating the figure of the hole, as shadows -resemble their objects in form. We shall easily perceive this -appearance to be a necessary consequence of the circular figure of -the sun, if we conceive light to be diffused from the luminary by -means of straight rays proceeding from every point of the sun's disk -and passing through every point within the boundary of the hole. By -attending to the consequences of this mode of conception, it will be -seen that each point of the hole will be the vertex of a double cone -of rays which has the sun's disk for its base on one side and an -image of the sun on the other; and the figure of the image of the -hole will be determined by supposing a series of equal bright -circles, images of the sun, to be placed along the boundary of an -image equal to the hole itself. The figure of the image thus -determined will partake of the form of the hole, and {88} of the -circular form of the sun's image: but these circular images become -larger and larger as they are further from the hole, while the -central image of the hole remains always of the original size; and -thus at a considerable distance from the hole, the trace of the -hole's form is nearly obliterated, and the image is nearly a perfect -circle. Instead of this distinct conception of a cone of rays which -has the sun's disk for its basis, Aristotle has the following loose -conjecture.[57\1] "Is it because light is emitted in a conical form; -and of a cone, the base is a circle; so that on whatever the rays of -the sun fall, they appear more circular?" And thus though he applies -the notion of rays to this problem, he possesses this notion so -_indistinctly_ that his explanation is of no value. He does not -introduce into his explanation the consideration of the sun's -circular figure, and is thus prevented from giving a true account of -this very simple optical phenomenon. - -[Note 57\1: Problem. 15, ὁσα μαθηματίκης, &c.] - -6. Again, to pass to a more extensive failure: why was it that -Aristotle, knowing the property of the lever, and many other -mechanical truths, was unable to form them into a science of -mechanics, as Archimedes afterwards did? - -The reason was, that, instead of considering rest and motion -directly, and distinctly, with reference to the Idea of Cause, that -is Force, he wandered in search of reasons among other ideas and -notions, which could not be brought into steady connection with the -facts;--the ideas of properties of circles, of proportions of -velocities,--the notions of "strange" and "common," of "natural" and -"unnatural." Thus, in the Proem to his Mechanical Problems, after -stating some of the difficulties which he has to attack, he says, -"Of all such cases, the circle contains the principle of the cause. -And this is what might be looked for; for it is nothing absurd, if -something _wonderful_ is derived from something more wonderful -still. Now the most wonderful thing is, that opposites should be -combined; and the circle is constituted of such combinations of -opposites. For it is constructed by a stationary point and a moving -line, which are contrary to each other in nature; and hence we may -the less be surprised at the resulting contrarieties. And in the -first place, the circumference of the circle, though a line without -breadth, has opposite qualities; for it is both _convex_ and -_concave_. In the next place, it has, at the same time, opposite -motions, for it moves forward and backward at the same time. For the -circumference, setting out from any point, comes to the same point -again, so {89} that by a continuous progression, the last point -becomes the first. So that, as was before stated, it is not -surprising that the circle should be the principle of all wonderful -properties." - -Aristotle afterwards proceeds to explain more specially how he -applies the properties of the circle in this case. "The reason," he -says, in his fourth Problem, "why a force, acting at a greater -distance from the fulcrum, moves a weight more easily, is, that it -describes a greater circle." He had already asserted that when a -body at the end of a lever is put in motion, it may be considered as -having two motions; one in the direction of the tangent, and one in -the direction of the radius; the former motion is, he says, -_according to nature_, the latter, _contrary to nature_. Now in the -smaller circle, the motion, contrary to nature, is more considerable -than it is in the larger circle. "Therefore," he adds, "the mover or -weight at the larger arm will be transferred further by the same -force than the weight moved, which is at the extremity of the -shorter arm." - -These loose and inappropriate notions of "natural" and "unnatural" -motions, were unfit to lead to any scientific truths; and, with the -habits of thought which dictated these speculations a perception of -the true grounds of mechanical properties was impossible. - -7. Thus, in this instance, the error of Aristotle was the neglect of -the Idea _appropriate_ to the facts, namely, the Idea of Mechanical -Cause, which is Force; and the substitution of vague or inapplicable -notions involving only relations of space or emotions of wonder. The -errors of those who failed similarly in other instances, were of the -same kind. To detail or classify these would lead us too far into -the philosophy of science; since we should have to enumerate the -Ideas which are appropriate, and the various classes of Facts on -which the different sciences are founded,--a task not to be now -lightly undertaken. But it will be perceived, without further -explanation, that it is necessary, in order to obtain from facts any -general truth, that we should apply to them that appropriate Idea, -by which permanent and definite relations are established among them. - -In such Ideas the ancients were very poor, and the stunted and -deformed growth of their physical science was the result of this -penury. The Ideas of Space and Time, Number and Motion, they did -indeed possess distinctly; and so far as these went, their science -was tolerably healthy. They also caught a glimpse of the Idea of a -Medium by which the qualities of bodies, as colors and sounds, are -perceived. But the idea of Substance remained barren in their hands; -{90} in speculating about elements and qualities, they went the -wrong way, assuming that the properties of Compounds must _resemble_ -those of the Elements which determine them; and their loose notions -of Contrariety never approached the form of those ideas of Polarity, -which, in modern times, regulate many parts of physics and -chemistry. - -If this statement should seem to any one to be technical or -arbitrary, we must refer, for the justification of it, to the -Philosophy of Science, of which we hope hereafter to treat. But it -will appear, even from what has been here said, that there are -certain Ideas or Forms of mental apprehension, which may be applied -to Facts in such a manner as to bring into view fundamental -principles of science; while the same Facts, however arrayed or -reasoned about, so long as these appropriate ideas are not employed, -cannot give rise to any exact or substantial knowledge. - -[2d Ed.] This account of the cause of failure in the physical -speculations of the ancient Greek philosophers has been objected to -as unsatisfactory. I will offer a few words in explanation of it. - -The mode of accounting for the failure of the Greeks in physics is, -in substance;--that the Greeks in their physical speculations fixed -their attention upon the wrong aspects and relations of the -phenomena; and that the aspects and relations in which phenomena are -to be viewed in order to arrive at scientific truths may be arranged -under certain heads, which I have termed _Ideas_; such as Space, -Time, Number, Cause, Likeness. In every case, there is an Idea to -which the phenomena may be referred, so as to bring into view the -Laws by which they are governed; this Idea I term the _appropriate_ -Idea in such case; and in order that the reference of the phenomena -to the Law may be clearly seen, the Idea must be _distinctly_ -possessed. - -Thus the reason of Aristotle's failure in his attempts at Mechanical -Science is, that he did not refer the facts to the appropriate Idea, -namely Force, the Cause of Motion, but to relations of Space and the -like; that is, he introduces _Geometrical_ instead of _Mechanical_ -Ideas. It may be said that we learn little by being told that -Aristotle's failure in this and the like cases arose from his -referring to the wrong class of Ideas; or, as I have otherwise -expressed it, fixing his attention upon the wrong aspects and -relations of the facts; since, it may be said, this is only to state -in other words that he _did_ fail. But this criticism is, I think, -ill-founded. The account which I have given is not only a statement -that Aristotle, and others who took a like course, did fail; but -also, that they failed in one certain point out of several {91} -which are enumerated. They did not fail because they neglected to -observe facts; they did not fail because they omitted to class -facts; they did not fail because they had not ideas to reason from; -but they failed because they did not take the right ideas in each -case. And so long as they were in the wrong in this point, no -industry in collecting facts, or ingenuity in classing them and -reasoning about them, could lead them to solid truth. - -Nor is this account of the nature of their mistake without its -instruction for us; although we are not to expect to derive from the -study of their failure any technical rule which shall necessarily -guide us to scientific discovery. For their failure teaches us that, -in the formation of science, an Error in the Ideas is as fatal to -the discovery of Truth as an Error in the Facts; and may as -completely impede the progress of knowledge. I have in Books II. to -X. of the _Philosophy_, shown historically how large a portion of -the progress of Science consists in the establishment of Appropriate -Ideas as the basis of each science. Of the two main processes by -which science is constructed, as stated in Book XI. of that work, -namely the _Explication of Conceptions_ and the _Colligation of -Facts_, the former must precede the latter. In Book XII. chap. 5, of -the _Philosophy_, I have stated the maxim concerning appropriate -Ideas in this form, that _the Idea and the Facts must be -homogeneous_. - -When I say that the failure of the Greeks in physical science arose -from their not employing _appropriate_ Ideas to connect the facts, I -do not use the term "appropriate" in a loose popular sense; but I -employ it as a somewhat technical term, to denote _the_ appropriate -Idea, out of that series of Ideas which have been made (as I have -shown in the _Philosophy_) the foundation of sciences; namely, -Space, Time, Number, Cause, Likeness, Substance, and the rest. It -appears to me just to say that Aristotle's failure in his attempts -to deal with problems of equilibrium, arose from his referring to -circles, velocities, notions of natural and unnatural, and the -like,--conceptions depending upon Ideas of Space, of Nature, -&c.--which are not appropriate to these problems, and from his -missing the Idea of Mechanical Force or Pressure, which is the -appropriate Idea. - -I give this, not as an account of _all_ failures in attempts at -science, but only as the account of such radical and fundamental -failures as this of Aristotle; who, with a knowledge of the facts, -failed to connect them into a really scientific view. If I had to -compare rival theories of a more complex kind, I should not -necessarily say that one involved {92} an appropriate Idea and the -other did not, though I might judge one to be true and the other to -be false. For instance, in comparing the emissive and the undulatory -theory of light, we see that both involve the same Idea;--the Idea -of a Medium acting by certain mechanical properties. The question -there is, What is the true view of the mechanism of the Medium? - -It may be remarked, however, that the example of Aristotle's failure -in physics, given in p. 87, namely, his attempted explanation of the -round image of a square hole, is a specimen rather of _indistinct_ -than of inappropriate ideas. - -The geometrical explanation of this phenomenon, which I have there -inserted, was given by Maurolycus, and before him, by Leonardo da -Vinci. - -We shall, in the next Book, see the influence of the appropriate -general Ideas, in the formation of various sciences. It need only be -observed, before we proceed, that, in order to do full justice to -the physical knowledge of the Greek Schools of philosophy, it is not -necessary to study their course after the time of their founders. -Their fortunes, in respect of such acquisitions as we are now -considering, were not progressive. The later chiefs of the Schools -followed the earlier masters; and though they varied much, they -added little. The Romans adopted the philosophy of their Greek -subjects; but they were always, and, indeed, acknowledged themselves -to be, inferior to their teachers. They were as arbitrary and loose -in their ideas as the Greeks, without possessing their invention, -acuteness, and spirit of system. - -In addition to the vagueness which was combined with the more -elevated trains of philosophical speculation among the Greeks, the -Romans introduced into their treatises a kind of declamatory -rhetoric, which arose probably from their forensic and political -habits, and which still further obscured the waning gleams of truth. -Yet we may also trace in the Roman philosophers to whom this charge -mostly applies (Lucretius, Pliny, Seneca), the national vigor and -ambition. There is something Roman in the public spirit and -anticipation of universal empire which they display, as citizens of -the intellectual republic. Though they speak sadly or slightingly of -the achievements of their own generation, they betray a more abiding -and vivid belief in the dignity and destined advance of human -knowledge as a whole, than is obvious among the Greeks. - -We must, however, turn back, in order to describe steps of more -definite value to the progress of science than those which we have -hitherto noticed. - - - -{{93}} -BOOK II. - -HISTORY -OF THE -PHYSICAL SCIENCES -IN -ANCIENT GREECE. - - - - - Ναρθηκοπλήρωτον δὲ θηρῶμαι πυρὸς - Πηγὴν κλοπαίαν, ἣ διδάσκαλος τέχνης - Πάσης βροτοῖς πεφῆνε καὶ μέγας πόρος. - Prom. Vinct. 109. - - I brought to earth the spark of heavenly fire, - Concealed at first, and small, but spreading soon - Among the sons of men, and burning on, - Teacher of art and use, and fount of power. - - - -{{95}} -INTRODUCTION. - - -IN order to the acquisition of any such exact and real knowledge of -nature as that which we properly call Physical Science, it is -requisite, as has already been said, that men should possess Ideas -both distinct and appropriate, and should apply them to ascertained -Facts. They are thus led to propositions of a general character, -which are obtained by Induction, as will elsewhere be more fully -explained. We proceed now to trace the formation of Sciences among -the Greeks by such processes. The provinces of knowledge which thus -demand our attention are, Astronomy, Mechanics and Hydrostatics, -Optics and Harmonics; of which I must relate, first, the earliest -stages, and next, the subsequent progress. - -Of these portions of human knowledge, Astronomy is, beyond doubt or -comparison, much the most ancient and the most remarkable; and -probably existed, in somewhat of a scientific form, in Chaldea and -Egypt, and other countries, before the period of the intellectual -activity of the Greeks. But I will give a brief account of some of -the other Sciences before I proceed to Astronomy, for two reasons; -first, because the origin of Astronomy is lost in the obscurity of a -remote antiquity; and therefore we cannot exemplify the conditions -of the first rise of science so well in that subject as we can in -others which assumed their scientific form at known periods; and -next, in order that I may not have to interrupt, after I have once -begun it, the history of the only progressive Science which the -ancient world produced. - -It has been objected to the arrangement here employed that it is not -symmetrical; and that Astronomy, as being one of the Physical -Sciences, ought to have occupied a chapter in this Second Book, -instead of having a whole Book to itself (Book III). I do not pretend -that the arrangement is symmetrical, and have employed it only on the -ground of convenience. The importance and extent of the history of -Astronomy are such that this science could not, with a view to our -purposes, be made co-ordinate with Mechanics or Optics. {96} - - - - -CHAPTER I. - -EARLIEST STAGES OF MECHANICS AND HYDROSTATICS. - - -_Sect._ 1.--_Mechanics._ - -ASTRONOMY is a science so ancient that we can hardly ascend to a -period when it did not exist; Mechanics, on the other hand, is a -science which did not begin to be till after the time of Aristotle; -for Archimedes must be looked upon as the author of the first sound -knowledge on this subject. What is still more curious, and shows -remarkably how little the continued progress of science follows -inevitably from the nature of man, this department of knowledge, -after the right road had been fairly entered upon, remained -absolutely stationary for nearly two thousand years; no single step -was made, in addition to the propositions established by Archimedes, -till the time of Galileo and Stevinus. This extraordinary halt will -be a subject of attention hereafter; at present we must consider the -original advance. - -The great step made by Archimedes in Mechanics was the establishing, -upon true grounds, the general proposition concerning a straight -lever, loaded with two heavy bodies, and resting upon a fulcrum. The -proposition is, that two bodies so circumstanced will balance each -other, when the distance of the smaller body from the fulcrum is -greater than the distance of the other, in exactly the same -proportion in which the weight of the body is less. - -This proposition is proved by Archimedes in a work which is still -extant, and the proof holds its place in our treatises to this day, -as the simplest which can be given. The demonstration is made to -rest on assumptions which amount in effect to such Definitions and -Axioms as these: That those bodies are of equal weight which balance -each other at equal arms of a straight lever; and that in every -heavy body there is a definite point called a _Centre of Gravity_, -in which point we may suppose the weight of the body collected. - -The principle, which is really the foundation of the validity of the -demonstration thus given, and which is the condition of all -experimental knowledge on the subject, is this: that when two equal -weights are supported on a lever, they act on the fulcrum of the lever -with the {97} same effect as if they were both together supported -immediately at that point. Or more generally, we may state the -principle to be this: that the pressure by which a heavy body is -supported continues the same, however we alter the form or position of -the body, so long as the magnitude and material continue the same. - -The experimental truth of this principle is a matter of obvious and -universal experience. The weight of a basket of stones is not -altered by shaking the stones into new positions. We cannot make the -direct burden of a stone less by altering its position in our hands; -and if we try the effect on a balance or a machine of any kind, we -shall see still more clearly and exactly that the altered position -of one weight, or the altered arrangement of several, produces no -change in their effect, so long as their point of support remains -unchanged. - -This general fact is obvious, when we possess in our minds the ideas -which are requisite to apprehend it clearly. But when we are so -prepared, the truth appears to be manifest, even independent of -experience, and is seen to be a rule to which experience must -conform. What, then, is the leading idea which thus enables us to -reason effectively upon mechanical subjects? By attention to the -course of such reasonings, we perceive that it is the idea of -_Pressure_; Pressure being conceived as a measurable effect of heavy -bodies at rest, distinguishable from all other effects, such as -motion, change of figure, and the like. It is not here necessary to -attempt to trace the history of this idea in our minds; but it is -certain that such an idea may be distinctly formed, and that upon it -the whole science of statics may be built. _Pressure_, _load_, -_weight_, are names by which this idea is denoted when the effect -tends directly downwards; but we may have pressure without motion, -or _dead pull_, in other cases, as at the critical instant when two -nicely-matched wrestlers are balanced by the exertion of the utmost -strength of each. - -Pressure in any direction may thus exist without any motion -whatever. But the causes which produce such pressure are capable of -producing motion, and are generally seen producing motion, as in the -above instance of the wrestlers, or in a pair of scales employed in -weighing; and thus men come to consider pressure as the exception, -and motion as the rule: or perhaps they image to themselves the -motion which _might_ or _would_ take place; for instance, the motion -which the arms of a lever _would_ have if they _did_ move. They turn -away from the case really before them, which is that of bodies at -rest, and balancing each other, and pass to another case, which is -arbitrarily {98} assumed to represent the first. Now this arbitrary -and capricious evasion of the question we consider as opposed to the -introduction of the distinct and proper idea of Pressure, by means -of which the true principles of this subject can be apprehended. - -We have already seen that Aristotle was in the number of those who -thus evaded the difficulties of the problem of the lever, and -consequently lost the reward of success. He failed, as has before -been stated, in consequence of his seeking his principles in -notions, either vague and loose, as the distinction of natural and -unnatural motions, or else inappropriate, as the circle which the -weight _would_ describe, the velocity which it _would_ have if it -moved; circumstances which are not part of the fact under -consideration. The influence of such modes of speculation was the -main hindrance to the prosecution of the true Archimedean form of -the science of Mechanics. - -The mechanical doctrine of Equilibrium, is _Statics_. It is to be -distinguished from the mechanical doctrine of Motion, which is -termed _Dynamics_, and which was not successfully treated till the -time of Galileo. - - -_Sect._ 2.--_Hydrostatics._ - -ARCHIMEDES not only laid the foundations of the Statics of solid -bodies, but also solved the principal problem of _Hydrostatics_, or -the Statics of Fluids; namely, the conditions of the floating of -bodies. This is the more remarkable, since not only did the -principles which Archimedes established on this subject remain -unpursued till the revival of science in modern times, but, when -they were again put forward, the main proposition was so far from -obvious that it was termed, and is to this day called, the -_hydrostatic paradox_. The true doctrine of Hydrostatics, however, -assuming the Idea of Pressure, which it involves, in common with the -Mechanics of solid bodies, requires also a distinct Idea of a Fluid, -as a body of which the parts are perfectly movable among each other -by the slightest partial pressure, and in which all pressure exerted -on one part is transferred to all other parts. From this idea of -Fluidity, necessarily follows that multiplication of pressure which -constitutes the hydrostatic paradox; and the notion being seen to be -verified in nature, the consequences were also realized as facts. -This notion of Fluidity is expressed in the postulate which stands -at the head of Archimedes' "Treatise on Floating Bodies." And from -this principle are deduced the solutions, not only of the simple -problems of the science, but of some problems of considerable -complexity. {99} - -The difficulty of holding fast this Idea of Fluidity so as to trace -its consequences with infallible strictness of demonstration, may be -judged of from the circumstance that, even at the present day, men -of great talents, not unfamiliar with the subject, sometimes admit -into their reasonings an oversight or fallacy with regard to this -very point. The importance of the Idea when clearly apprehended and -securely held, may be judged of from this, that the whole science of -Hydrostatics in its most modern form is only the development of the -Idea. And what kind of attempts at science would be made by persons -destitute of this Idea, we may see in the speculations of Aristotle -concerning light and heavy bodies, which we have already quoted; -where, by considering light and heavy as opposite qualities, -residing in things themselves, and by an inability to apprehend the -effect of surrounding fluids in supporting bodies, the subject was -made a mass of false or frivolous assertions, which the utmost -ingenuity could not reconcile with facts, and could still less -deduce from the asserted doctrines any new practical truths. - -In the case of Statics and Hydrostatics, the most important -condition of their advance was undoubtedly the distinct apprehension -of these two _appropriate Ideas_--_Statical Pressure_, and -_Hydrostatical Pressure_ as included in the idea of Fluidity. For -the Ideas being once clearly possessed, the experimental laws which -they served to express (that the whole pressure of a body downwards -was always the same; and that water, and the like, were fluids -according to the above idea of fluidity), were so obvious, that -there was no doubt nor difficulty about them. These two ideas lie at -the root of all mechanical science; and the firm possession of them -is, to this day, the first requisite for a student of the subject. -After being clearly awakened in the mind of Archimedes, these ideas -slept for many centuries, till they were again called up in Galileo, -and more remarkably in Stevinus. This time, they were not destined -again to slumber; and the results of their activity have been the -formation of two Sciences, which are as certain and severe in their -demonstrations as geometry itself and as copious and interesting in -their conclusions; but which, besides this recommendation, possess -one of a different order,--that they exhibit the exact impress of -the laws of the physical world, and unfold a portion of the rules -according to which the phenomena of nature take place, and must take -place, till nature herself shall alter. {100} - - - - -CHAPTER II. - -EARLIEST STAGES OF OPTICS. - - -THE progress made by the ancients in Optics was nearly proportional -to that which they made in Statics. As they discovered the true -grounds of the doctrine of Equilibrium, without obtaining any sound -principles concerning Motion, so they discovered the law of the -Reflection of light, but had none but the most indistinct notions -concerning Refraction. - -The extent of the principles which they really possessed is easily -stated. They knew that vision is performed by _rays_ which proceed -in straight lines, and that these rays are _reflected_ by certain -surfaces (mirrors) in such manner that the angles which they make -with the surface on each side are equal. They drew various -conclusions from these premises by the aid of geometry; as, for -instance, the convergence of rays which fall on a concave speculum. - -It may be observed that the _Idea_ which is here introduced, is that -of visual _rays_, or lines along which vision is produced and light -carried. This idea once clearly apprehended, it was not difficult to -show that these lines are straight lines, both in the case of light -and of sight. In the beginning of Euclid's "Treatise on Optics," some -of the arguments are mentioned by which this was established. We are -told in the Proem, "In explaining what concerns the sight, he adduced -certain arguments from which he inferred that all light is carried in -straight lines. The greatest proof of this is shadows, and the bright -spots which are produced by light coming through windows and cracks, -and which could not be, except the rays of the sun were carried in -straight lines. So in fires, the shadows are greater than the bodies -if the fire be small, but less than the bodies if the fire be -greater." A clear comprehension of the principle would lead to the -perception of innumerable proofs of its truth on every side. - -The Law of Equality of Angles of Incidence and Reflection was not -quite so easy to verify; but the exact resemblance of the object and -its image in a plane mirror, (as the surface of still water, for -instance), which is a consequence of this law, would afford -convincing evidence of its truth in that case, and would be -confirmed by the examination of other cases. {101} - -With these true principles was mixed much error and indistinctness, -even in the best writers. Euclid, and the Platonists, maintained -that vision is exercised by rays proceeding _from_ the eye, not _to_ -it; so that when we see objects, we learn their form as a blind man -would do, by feeling it out with his staff. This mistake, however, -though Montucla speaks severely of it, was neither very -discreditable nor very injurious; for the mathematical conclusions -on each supposition are necessarily the same. Another curious and -false assumption is, that those visual rays are not close together, -but separated by intervals, like the fingers when the hand is -spread. The motive for this invention was the wish to account for -the fact, that in looking for a small object, as a needle, we often -cannot see it when it is under our nose; which it was conceived -would be impossible if the visual rays reached to all points of the -surface before us. - -These errors would not have prevented the progress of the science. -But the Aristotelian physics, as usual, contained speculations more -essentially faulty. Aristotle's views led him to try to describe the -kind of causation by which vision is produced, instead of the laws -by which it is exercised; and the attempt consisted, as in other -subjects, of indistinct principles, and ill-combined facts. -According to him, vision must be produced by a Medium,--by something -_between_ the object and the eye,--for if we press the object on the -eye, we do not see it; this Medium is Light, or "the transparent in -action;" darkness occurs when the transparency is potential, not -actual; color is not the "absolute visible," but something which is -_on_ the absolute visible; color has the power of setting the -transparent in action; it is not, however, all colors that are seen -by means of light, but only the proper color of each object; for -some things, as the heads, and scales, and eyes of fish, are seen in -the dark; but they are not seen with their proper color.**[1\2] - -[Note 1\2: De Anim. ii. **7.] - -In all this there is no steady adherence either to one notion, or to -one class of facts. The distinction of Power and Act is introduced -to modify the Idea of Transparency, according to the formula of the -school; then Color is made to be something unknown in addition to -Visibility; and the distinction of "proper" and "improper" colors is -assumed, as sufficient to account for a phenomenon. Such -classifications have in them nothing of which the mind can take -steady hold; nor is it difficult to see that they do not come under -those {102} conditions of successful physical speculation, which we -have laid down. - -It is proper to notice more distinctly the nature of the Geometrical -Propositions contained in Euclid's work. The _Optica_ contains -Propositions concerning Vision and Shadows, derived from the -principle that the rays of light are rectilinear: for instance, the -Proposition that the shadow is greater than the object, if the -illuminating body be less and _vice versa_. The _Catoptrica_ -contains Propositions concerning the effects of Reflection, derived -from the principle that the Angles of Incidence and Reflection are -equal: as, that in a convex mirror the object appears convex, and -smaller than the object. We see here an example of the promptitude -of the Greeks in deduction. When they had once obtained a knowledge -of a principle, they followed it to its mathematical consequences -with great acuteness. The subject of concave mirrors is pursued -further in Ptolemy's _Optics_. - -The Greek writers also cultivated the subject of _Perspective_ -speculatively, in mathematical treatises, as well as practically, in -pictures. The whole of this theory is a consequence of the principle -that vision takes place in straight lines drawn from the object to -the eye. - -"The ancients were in some measure acquainted with the Refraction as -well as the Reflection of Light," as I have shown in Book IX. Chap. -2 [2d Ed.] of the _Philosophy_. The current knowledge on this -subject must have been very slight and confused; for it does not -appear to have enabled them to account for one of the simplest -results of Refraction, the magnifying effect of convex transparent -bodies. I have noticed in the passage just referred to, Seneca's -crude notions on this subject; and in like manner Ptolemy in his -_Optics_ asserts that an object placed in water must always appear -larger then when taken out. Aristotle uses the term ἀνακλάσις -(_Meteorol_. iii. 2), but apparently in a very vague manner. It is -not evident that he distinguished Refraction from Reflection. His -Commentators however do distinguish these as διακλάσις and -ἀνακλάσις. See Olympiodorus in Schneider's _Eclogæ Physicæ_, vol. i. -p. 397. And Refraction had been the subject of special attention -among the Greek Mathematicians. Archimedes had noticed (as we learn -from the same writer) that in certain cases, a ring which cannot be -seen over the edge of the empty vessel in which it is placed, -becomes visible when the vessel is filled with water. The same fact -is stated in the _Optics_ of Euclid. We do not find this fact -explained in that work as we now have it; but in Ptolemy's _Optics_ -the fact is explained by a flexure of the visual ray: it is {103} -noticed that this flexure is different at different angles from the -perpendicular, and there is an elaborate collection of measures of -the flexure at different angles, made by means of an instrument -devised for the purpose. There is also a collection of similar -measures of the refraction when the ray passes from air to glass, -and when it passes from glass to water. This part of Ptolemy's work -is, I think, the oldest extant example of a collection of -experimental measures in any other subject than astronomy; and in -astronomy our measures are the result of _observation_ rather than -of _experiment_. As Delambre says (_Astron. Anc._ vol. ii. p. 427), -"On y voit des expériences de physique bien faites, ce qui est sans -exemple chez les anciens." - -Ptolemy's Optical work was known only by Roger Bacon's references to -it (_Opus Majus_, p. 286, &c.) till 1816; but copies of Latin -translations of it were known to exist in the Royal Library at Paris, -and in the Bodleian at Oxford. Delambre has given an account of the -contents of the Paris copy in his _Astron. Anc._ ii. 414, and in the -_Connoissance des Temps_ for 1816; and Prof. Rigaud's account of the -Oxford copy is given in the article _Optics_, in the _Encyclopædia -Britannica_. Ptolemy shows great sagacity in applying the notion of -Refraction to the explanation of the displacement of astronomical -objects which is produced by the atmosphere,--_Astronomical -Refraction_, as it is commonly called. He represents the visual ray as -refracted in passing from the _ether_, which is above the air, into -the air; the air being bounded by a spherical surface which has for -its centre "the centre of all the elements, the centre of the earth;" -and the refraction being a flexure towards the line drawn -perpendicular to this surface. He thus constructs, says Delambre, the -same figure on which Cassini afterwards founded the whole of his -theory; and gives a theory more complete than that of any astronomer -previous to him. Tycho, for instance, believed that astronomical -refraction was caused only by the _vapors_ of the atmosphere, and did -not exist above the altitude of 45°. - -Cleomedes, about the time of Augustus, had guessed at Refraction, as -an explanation of an eclipse in which the sun and moon are both seen -at the same time. "Is it not possible," he says, "that the ray which -proceeds from the eye and traverses moist and cloudy air may bend -downwards to the sun, even when he is below the horizon?" And Sextus -Empiricus, a century later, says, "The air being dense, by the -refraction of the visual ray, a constellation may be seen above the -horizon when it is yet below the horizon." But from what follows, it -{104} appears doubtful whether he clearly distinguished Refraction -and Reflection. - -In order that we may not attach too much value to the vague -expressions of Cleomedes and Sextus Empiricus, we may remark that -Cleomedes conceives such an eclipse as he describes not to be -possible, though he offers an explanation of it if it be: (the fact -must really occur whenever the moon is seen in the horizon in the -middle of an eclipse:) and that Sextus Empiricus gives his -suggestion of the effect of refraction as an argument why the -Chaldean astrology cannot be true, since the constellation which -appears to be rising at the moment of a birth is not the one which -is truly rising. The Chaldeans might have answered, says Delambre, -that the star begins to shed its influence, not when it is really in -the horizon, but when its light is seen. (_Ast. Anc._ vol. i. p. -231, and vol. ii. p. 548.) - -It has been said that Vitellio, or Vitello, whom we shall hereafter -have to speak of in the history of Optics, took his Tables of -Refractions from Ptolemy. This is contrary to what Delambre states. -He says that Vitello may be accused of plagiarism from Alhazen, and -that Alhazen did not borrow his Tables from Ptolemy. Roger Bacon had -said (_Opus Majus_, p. 288), "Ptolemæus in libro de Opticis, id est, -de Aspectibus, seu in Perspectivâ suâ, qui prius quam Alhazen dedit -hanc sententiam, quam a Ptolemæo acceptam Alhazen exposuit." This -refers only to the opinion that visual rays proceed from the eye. -But this also is erroneous; for Alhazen maintains the contrary: -"Visio fit radiis a visibili extrinsecus ad visum manantibus." -(_Opt._ Lib. i. cap. 5.) Vitello says of his Table of Refractions, -"Acceptis instrumentaliter, prout potuimus propinquius, angulis -omnium refractionum . . . invenimus quod semper iidem sunt anguli -refractionum: . . . secundum hoc fecimus has tabulas." "Having -measured, by means of instruments, as exactly as we could, the whole -range of the angles of refraction, we found that the refraction is -always the same for the same angle; and hence we have constructed -these Tables." {105} - - - - -CHAPTER III. - -EARLIEST STAGES OF HARMONICS. - - -AMONG the ancients, the science of Music was an application of -Arithmetic, as Optics and Mechanics were of Geometry. The story -which is told concerning the origin of their arithmetical music, is -the following, as it stands in the Arithmetical Treatise of -Nicomachus. - -Pythagoras, walking one day, meditating on the means of measuring -musical notes, happened to pass near a blacksmith's shop, and had -his attention arrested by hearing the hammers, as they struck the -anvil, produce the sounds which had a musical relation to each -other. On listening further, he found that the intervals were a -Fourth, a Fifth, and an Octave; and on weighing the hammers, it -appeared that the one which gave the Octave was _one-half_ the -heaviest, the one which gave the Fifth was _two-thirds_, and the one -which gave the Fourth was _three-quarters_. He returned home, -reflected upon this phenomenon, made trials, and finally discovered, -that if he stretched musical strings of equal lengths, by weights -which have the proportion of one-half, two-thirds, and -three-fourths, they produced intervals which were an Octave, a -Fifth, and a Fourth. This observation gave an arithmetical measure -of the principal Musical Intervals, and made Music an arithmetical -subject of speculation. - -This story, if not entirely a philosophical fable, is undoubtedly -inaccurate; for the musical intervals thus spoken of would not be -produced by striking with hammers of the weights there stated. But -it is true that the notes of strings have a definite relation to the -forces which stretch them; and this truth is still the groundwork of -the theory of musical concords and discords. - -Nicomachus says that Pythagoras found the weights to be, as I have -mentioned, in the proportion of 12, 6, 8, 9; and the intervals, an -Octave, corresponding to the proportion 12 to 6, or 2 to 1; a Fifth, -corresponding to the proportion 12 to 8, or 3 to 2; and a Fourth, -corresponding to the proportion 12 to 9, or 4 to 3. There is no -doubt that this statement of the ancient writer is inexact as to the -physical fact, for the rate of vibration of a string, on which its -note depends, is, {106} other things being equal, not as the weight, -but as the square root of the weight. But he is right as to the -essential point, that those ratios of 2 to 1, 3 to 2, and 4 to 3, -are the characteristic ratios of the Octave, Fifth, and Fourth. In -order to produce these intervals, the appended weights must be, not -as 12, 9, 8, and 6, but as 12, 6¾, 5⅓, and 3. - -The numerical relations of the other intervals of the musical scale, -as well as of the Octave, Fifth, and Fourth, were discovered by the -Greeks. Thus they found that the proportion in a Major Third was 5 -to 4; in a Minor Third, 6 to 5; in a Major Tone, 9 to 8; in a -Semitone or _Diesis_, 16 to 15. They even went so far as to -determine the _Comma_, in which the interval of two notes is so -small that they are in the proportion of 81 to 80. This is the -interval between two notes, each of which may be called the -Seventeenth above the key-note;--the one note being obtained by -ascending a Fifth four times over; the other being obtained by -ascending through two Octaves and a Major Third. The want of exact -coincidence between these two notes is an inherent arithmetical -imperfection in the musical scale, of which the consequences are -very extensive. - -The numerical properties of the musical scale were worked out to a -very great extent by the Greeks, and many of their Treatises on this -subject remain to us. The principal ones are the seven authors -published by Meibomius.[2\2] These arithmetical elements of Music -are to the present day important and fundamental portions of the -Science of Harmonics. - -[Note 2\2: _Antiquæ Musicæ Scriptores septem_, 1652.] - -It may at first appear that the truth, or even the possibility of -this history, by referring the discovery to accident, disproves our -doctrine, that this, like all other fundamental discoveries, -required a distinct and well-pondered Idea as its condition. In -this, however, as in all cases of supposed accidental discoveries in -science, it will be found, that it was exactly the possession of -such an Idea which made the accident possible. - -Pythagoras, assuming the truth of the tradition, must have had an -exact and ready apprehension of those relations of musical sounds, -which are called respectively an Octave, a Fifth, and a Fourth. If -he had not been able to conceive distinctly this relation, and to -apprehend it when heard, the sounds of the anvil would have struck -his ears to no more purpose than they did those of the smiths -themselves. He {107} must have had, too, a ready familiarity with -numerical ratios; and, moreover (that in which, probably, his -superiority most consisted), a disposition to connect one notion -with the other--the musical relation with the arithmetical, if it -were found possible. When the connection was once suggested, it was -easy to devise experiments by which it might be confirmed. - -"The philosophers of the Pythagorean School,[3\2] and in particular, -Lasus of Hermione, and Hippasus of Metapontum, made many such -experiments upon strings; varying both their lengths and the weights -which stretched them; and also upon vessels filled with water, in a -greater or less degree." And thus was established that connection of -the Idea with the Fact, which this Science, like all others, -requires. - -[Note 3\2: Montucla, iii. 10.] - - -I shall quit the Physical Sciences of Ancient Greece, with the above -brief statement of the discovery of the fundamental principles which -they involved; not only because such initial steps must always be -the most important in the progress of science, but because, in -reality, the Greeks made no advances beyond these. There took place -among them no additional inductive processes, by which new facts -were brought under the dominion of principles, or by which -principles were presented in a more comprehensive shape than before. -Their advance terminated in a single stride. Archimedes had stirred -the intellectual world, but had not put it in progressive motion: -the science of Mechanics stopped where he left it. And though, in -some objects, as in Harmonics, much was written, the works thus -produced consisted of deductions from the fundamental principles, by -means of arithmetical calculations; occasionally modified, indeed, -by reference to the pleasures which music, as an art, affords, but -not enriched by any new scientific truths. - -[3d Ed.] We should, however, quit the philosophy of the ancient -Greeks without a due sense of the obligations which Physical Science -in all succeeding ages owes to the acute and penetrating spirit in -which their inquiries in that region of human knowledge were -conducted, and to the large and lofty aspirations which were -displayed, even in their failure, if we did not bear in mind both -the multifarious and comprehensive character of their attempts, and -some of the causes which limited their progress in positive science. -They speculated and {108} theorized under a lively persuasion that a -Science of every part of nature was possible, and was a fit object -for the exercise of man's best faculties; and they were speedily led -to the conviction that such a science must clothe its conclusions in -the language of mathematics. This conviction is eminently -conspicuous in the writings of Plato. In the _Republic_, in the -_Epinomis_, and above all in the _Timæus_, this conviction makes him -return, again and again, to a discussion of the laws which had been -established or conjectured in his time, respecting Harmonics and -Optics, such as we have seen, and still more, respecting Astronomy, -such as we shall see in the next Book. Probably no succeeding step -in the discovery of the Laws of Nature was of so much importance as -the full adoption of this pervading conviction, that there must be -Mathematical Laws of Nature, and that it is the business of -Philosophy to discover these Laws. This conviction continues, -through all the succeeding ages of the history of science, to be the -animating and supporting principle of scientific investigation and -discovery. And, especially in Astronomy, many of the erroneous -guesses which the Greeks made, contain, if not the germ, at least -the vivifying life-blood, of great truths, reserved for future ages. - -Moreover, the Greeks not only sought such theories of special parts -of nature, but a general Theory of the Universe. An essay at such a -theory is the _Timæus_ of Plato; too wide and too ambitious an -attempt to succeed at that time; or, indeed, on the scale on which -he unfolds it, even in our time; but a vigorous and instructive -example of the claim which man's Intellect feels that it may make to -understand the universal frame of things, and to render a reason for -all that is presented to it by the outward senses. - -Further; we see in Plato, that one of the grounds of the failure in -this attempt, was the assumption that the _reason why_ every thing is -what it is and as it is, must be that so it is _best_, according to -some view of better or worse attainable by man. Socrates, in his -dying conversation, as given in the _Phædo_, declares this to have -been what he sought in the philosophy of his time; and tells his -friends that he turned away from the speculations of Anaxagoras -because they did not give him such reasons for the constitution of -the world; and Plato's _Timæus_ is, in reality, an attempt to supply -this deficiency, and to present a Theory of the Universe, in which -every thing is accounted for by such reasons. Though this is a -failure, it is a noble as well as an instructive failure. - - - -{{109}} -BOOK III. - -HISTORY -OF -GREEK ASTRONOMY. - - -Τόδε δὲ μηδείς ποτε φοβηθῇ τῶν Ἑλλήνων, ὡς οὐ χρὴ περὶ τὰ θεῖα ποτὲ -πραγματεύεσθαι θνητοὺς ὄντας· πᾶν δε τούτου διανοηθῆναι τοὐναντίον, -ὡς οὔτε ἄφρον ἔστι ποτὲ τὸ θεῖον, οὔτε ἀγνοεῖ που τὴν ἀνθρωπίνην -φυσιν· ἀλλ' οἶδεν ὅτι, διδάσκοντος αὐτοῦ, ξυνακολουθήσει καὶ -μαθήσεται τὰ διδάσκομενα.--PLATO, _Epinomis_, p. 988. - -Nor should any Greek have any misgiving of this kind; that it is not -fitting for us to inquire narrowly into the operations of Superior -Powers, such as those by which the motions of the heavenly bodies -are produced: but, on the contrary, men should consider that the -Divine Powers never act without purpose, and that they know the -nature of man: they know that by their guidance and aid, man may -follow and comprehend the lessons which are vouchsafed him on such -subjects. - - - -{{111}} -INTRODUCTION. - - -THE earliest and fundamental conceptions of men respecting the -objects with which Astronomy is concerned, are formed by familiar -processes of thought, without appearing to have in them any thing -technical or scientific. Days, Years, Months, the Sky, the -Constellations, are notions which the most uncultured and incurious -minds possess. Yet these are elements of the Science of Astronomy. -The reasons why, in this case alone, of all the provinces of human -knowledge, men were able, at an early and unenlightened period, to -construct a science out of the obvious facts of observation, with -the help of the common furniture of their minds, will be more -apparent in the course of the philosophy of science: but I may here -barely mention two of these reasons. They are, first, that the -familiar act of thought, exercised for the common purposes of life, -by which we give to an assemblage of our impressions such a unity as -is implied in the above notions and terms, a Month, a Year, the Sky, -and the like, is, in reality, an _inductive act_, and shares the -nature of the processes by which all sciences are formed; and, in -the next place, that the ideas appropriate to the induction in this -case, are those which, even in the least cultivated minds, are very -clear and definite; namely, the ideas of Space and Figure, Time and -Number, Motion and Recurrence. Hence, from their first origin, the -modifications of those ideas assume a scientific form. - -We must now trace in detail the peculiar course which, in -consequence of these causes, the knowledge of man respecting the -heavenly bodies took, from the earliest period of his history. {112} - - - - -CHAPTER I. - -EARLIEST STAGES OF ASTRONOMY. - - -_Sect._ 1.--_Formation of the Notion of a Year._ - -THE notion of a _Day_ is early and obviously impressed upon man in -almost any condition in which we can imagine him. The recurrence of -light and darkness, of comparative warmth and cold, of noise and -silence, of the activity and repose of animals;--the rising, -mounting, descending, and setting of the sun;--the varying colors of -the clouds, generally, notwithstanding their variety, marked by a -daily progression of appearances;--the calls of the desire of food -and of sleep in man himself, either exactly adjusted to the period -of this change, or at least readily capable of being accommodated to -it;--the recurrence of these circumstances at intervals, equal, so -far as our obvious judgment of the passage of time can decide; and -these intervals so short that the repetition is noticed with no -effort of attention or memory;--this assemblage of suggestions makes -the notion of a Day necessarily occur to man, if we suppose him to -have the conception of Time, and of Recurrence. He naturally marks -by a term such a portion of time, and such a cycle of recurrence; he -calls each portion of time, in which this series of appearances and -occurrences come round, a _Day_; and such a group of particulars are -considered as appearing or happening _in_ the same day. - -_A Year_ is a notion formed in the same manner; implying in the same -way the notion of recurring facts; and also the faculty of arranging -facts in time, and of appreciating their recurrence. But the notion -of a Year, though undoubtedly very obvious, is, on many accounts, -less so than that of a Day. The repetition of similar circumstances, -at equal intervals, is less manifest in this case, and the intervals -being much longer, some exertion of memory becomes requisite in -order that the recurrence may be perceived. A child might easily be -persuaded that successive years were of unequal length; or, if the -summer were cold, and the spring and autumn warm, might be made to -believe, if all who spoke in its hearing agreed to support the -delusion, that one year was two. It would be impossible to practise -such a deception with regard to the day, without the use of some -artifice beyond mere words. {113} - -Still, the recurrence of the appearances which suggest the notion of -a Year is so obvious, that we can hardly conceive man without it. -But though, in all climes and times, there would be a recurrence, -and at the same interval in all, the recurring appearances would be -extremely different in different countries; and the contrasts and -resemblances of the seasons would be widely varied. In some places -the winter utterly alters the face of the country, converting grassy -hills, deep leafy woods of various hues of green, and running -waters, into snowy and icy wastes, and bare snow-laden branches; -while in others, the field retains its herbage, and the tree its -leaves, all the year; and the rains and the sunshine alone, or -various agricultural employments quite different from ours, mark the -passing seasons. Yet in all parts of the world the yearly cycle of -changes has been singled out from all others, and designated by a -peculiar name. The inhabitant of the equatorial regions has the sun -vertically over him at the end of every period of six months, and -similar trains of celestial phenomena fill up each of these -intervals, yet we do not find years of six months among such -nations. The Arabs alone,[1\3] who practise neither agriculture nor -navigation, have a year depending upon the moon only; and borrow the -word from other languages, when they speak of the solar year. - -[Note 1\3: Ideler, _Berl. Trans._ 1813, p. 51.] - -In general, nations have marked this portion of time by some word -which has a reference to the returning circle of seasons and -employments. Thus the Latin _annus_ signified a ring, as we see in -the derivative _annulus_: the Greek term ἐνιαυτὸς implies something -which _returns into itself_: and the word as it exists in Teutonic -languages, of which our word _year_ is an example, is said to have -its origin in the word _yra_ which means a ring in Swedish, and is -perhaps connected with the Latin _gyrus_. - - -_Sect._ 2.--_Fixation of the Civil Year._ - -THE year, considered as a recurring cycle of seasons and of general -appearances, must attract the notice of man as soon as his attention -and memory suffice to bind together the parts of a succession of the -length of several years. But to make the same term imply a certain -fixed number of days, we must know how many days the cycle of the -seasons occupies; a knowledge which requires faculties and artifices -beyond what we have already mentioned. For instance, men cannot -reckon as far as any number at all approaching the number of days in -the year, without possessing a system of numeral terms, and methods -{114} of practical numeration on which such a system of terms is -always founded.[2\3] The South American Indians, the Koussa Caffres -and Hottentots, and the natives of New Holland, all of whom are said -to be unable to reckon further than the fingers of their hands and -feet,[3\3] cannot, as we do, include in their notion of a year the -fact of its consisting of 365 days. This fact is not likely to be -known to any nation except those which have advanced far beyond that -which may be considered as the earliest scientific process which we -can trace in the history of the human race, the formation of a -method of designating the successive numbers to an indefinite -extent, by means of names, framed according to the decimal, quinary, -or vigenary scale. - -[Note 2\3: _Arithmetic_ in _Encyc. Metrop._ (by Dr. Peacock), Art. 8.] - -[Note 3\3: Ibid. Art. 32.] - -But even if we suppose men to have the habit of recording the -passage of each day, and of counting the score thus recorded, it -would be by no means easy for them to determine the exact number of -days in which the cycle of the seasons recurs; for the -indefiniteness of the appearances which mark the same season of the -year, and the changes to which they are subject as the seasons are -early or late, would leave much uncertainty respecting the duration -of the year. They would not obtain any accuracy on this head, till -they had attended for a considerable time to the motions and places -of the sun; circumstances which require more precision of notice -than the general facts of the degrees of heat and light. The motions -of the sun, the succession of the places of his rising and setting -at different times of the year, the greatest heights which he -reaches, the proportion of the length of day and night, would all -exhibit several cycles. The turning back of the sun, when he had -reached the greatest distance to the south or to the north, as shown -either by his rising or by his height at noon, would perhaps be the -most observable of such circumstances. Accordingly the τροπαὶ -ἠελίοιο, the turnings of the sun, are used repeatedly by Hesiod as a -mark from which he reckons the seasons of various employments. -"Fifty days," he says, "after the turning of the sun, is a -seasonable time for beginning a voyage."[4\3] - -[Note 4\3: Ἤματα πεντήκοντα μετὰ τροπὰς ἠελίοιο - Ἐς τέλος ἐλθόντος θέρεος.--_Op. et Dies_, 661.] - -The phenomena would be different in different climates, but the -recurrence would be common to all. Any one of these kinds of -phenomena, noted with moderate care for a year, would show what was -the number of days of which a year consisted; and if several years -{115} were included in the interval through which the scrutiny -extended, the knowledge of the length of the year so acquired would -be proportionally more exact. - -Besides those notices of the sun which offered exact indications of -the seasons, other more indefinite natural occurrences were used; as -the arrival of the swallow (χελιδών) and the kite (ἰκτίν), The -birds, in Aristophanes' play of that name, mention it as one of -their offices to mark the seasons; Hesiod similarly notices the cry -of the crane as an indication of the departure of winter.[5\3] - -[Note 5\3: Ideler, i. 240.] - -Among the Greeks the seasons were at first only summer and winter -(θέρος and χειμών), the latter including all the rainy and cold -portion of the year. The winter was then subdivided into the χειμών -and ἔαρ (winter proper and spring), and the summer, less definitely, -into θέρος and ὀπώρα (summer and autumn). Tacitus says that the -Germans knew neither the blessings nor the name of autumn, "Autumni -perinde nomen ac bona ignorantur." Yet _harvest_, _herbst_, is -certainly an old German word.[6\3] - -[Note 6\3: Ib. i. 243.] - -In the same period in which the sun goes through his cycle of -positions, the stars also go through a cycle of appearances -belonging to them; and these appearances were perhaps employed at as -early a period as those of the sun, in determining the exact length -of the year. Many of the groups of fixed stars are readily -recognized, as exhibiting always the same configuration; and -particular bright stars are singled out as objects of attention. -These are observed, at particular seasons, to appear in the west -after sunset; but it is noted that when they do this, they are found -nearer and nearer to the sun every successive evening, and at last -disappear in his light. It is observed also, that at a certain -interval after this, they rise visibly before the dawn of day -renders the stars invisible; and after they are seen to do this, -they rise every day at a longer interval before the sun. The risings -and settings of the stars under these circumstances, or under others -which are easily recognized, were, in countries where the sky is -usually clear, employed at an early period to mark the seasons of -the year. Eschylus[7\3] makes Prometheus mention this among the -benefits of which {116} he, the teacher of arts to the earliest race -of men, was the communicator. - -[Note 7\3: Οὔκ ἤν γαρ αὐτοῖς οὔτε χείματος τέκμαρ, - Οὔτ' ἀνθεμώδους ἦρος, οὔδε καρπίμου - Θέρους βέβαιον· ἀλλ' ἄτερ γνώμης τὸ πᾶν - Ἔπρασσον, ἔστε δή σφιν ἀνατολὰς ἐγὼ - Ἄστρων ἔδειξα, τάς τε δυσκρίτους δύσεις.--_Prom. V._ 454.] - -Thus, for instance, the rising[8\3] of the Pleiades in the evening -was a mark of the approach of winter. The rising of the waters of -the Nile in Egypt coincided with the heliacal rising of Sirius, -which star the Egyptians called Sothis. Even without any artificial -measure of time or position, it was not difficult to carry -observations of this kind to such a degree of accuracy as to learn -from them the number of days which compose the year; and to fix the -precise season from the appearance of the stars. - -[Note 8\3: Ideler (Chronol. i. 242) says that _this_ rising of the -Pleiades took place at a time of the year which corresponds to our -11th May, and the setting to the 20th October; but this does not -agree with the forty days of their being "concealed," which, from -the context, must mean, I conceive, the interval between their -setting and rising. Pliny, however, says, "Vergiliarum exortu æstas -incipit, occasu hiems; _semestri_ spatio intra se messes -vindemiasque et omnium maturitatem complexæ." (H. N. xviii. 69.) - -The autumn of the Greeks, ὀπώρα, was earlier than our autumn, for -Homer calls Sirius ἀστὴρ ὀπωρινός, which rose at the end of July.] - -A knowledge concerning the stars appears to have been first -cultivated with the last-mentioned view, and makes its first -appearance in literature with this for its object. Thus Hesiod -directs the husbandman when to reap by the rising, and when to -plough by the setting of the Pleiades.[9\3] In like manner -Sirius,[10\3] Arcturus,[11\3] the Hyades and Orion,[12\3] are -noticed. {117} - -[Note 9\3: Πληίαδων Ἀτλαγενέων ἐπιτελλομενάων. - Ἄρχεσθ' ἀμητοῦ· ἀρότοιο δὲ, δυσομενάων. - Αἵ δή τοι νύκτας τε καὶ ἤματα τεσσεράκοντα - Κεκρύφαται, αὔτις δὲ περιπλομένου ἐνιαυτοῦ - Φαίνονται. _Op. et Dies_, l. 381.] - -[Note 10\3: Ib. l. 413.] - -[Note 11\3: Εὖτ' ἂν δ' ἑξήκοντα μετὰ τροπὰς ἠελίοιο - Χειμέρι', ἐκτελέσῃ Ζεὺς ἤματα, δή ῥα τότ' ἀστὴρ - Ἀρκτοῦρος, προλιπὼν ἱερὸν ῥόον Ὠκεανοῖο - Πρῶτον παμφαίνων ἐπιτέλλεται ἀκροκνέφαιος. - _Op. et Dies_, l. 562. - - Εὖτ' ἂν δ' Ὠρίων καὶ Σείριος ἐς μέσον ἔλθῃ - Οὐρανὸν, Ἀρκτοῦρον δ' ἐσὶδῃ ῥοδοδάκτυλος ἠὼς. - Ib. 607.] - -[Note 12\3: . . . . . . . αὐτὰρ ἐπὴν δὴ - Πληϊάδες Ὑάδες τε τὸ τε σθένος Ὠρίωνος - Δύνωσιν. Ib. 612. - -These methods were employed to a late period, because the Greek -months, being lunar, did not correspond to the seasons. Tables of -such motions were called παραπήγματα.--Ideler, _Hist. -Untersuchungen_, p. 209.] - -By such means it was determined that the year consisted, at least, -nearly, of 365 days. The Egyptians, as we learn from -Herodotus,[13\3] claimed the honor of this discovery. The priests -informed him, he says, "that the Egyptians were the first men who -discovered the year, dividing it into twelve equal parts; and this -they asserted that they discovered from the stars." Each of these -parts or months consisted of 30 days, and they added 5 days more at -the end of the year, "and thus the circle of the seasons come -round." It seems, also, that the Jews, at an early period, had a -similar reckoning of time, for the Deluge which continued 150 days -(Gen. vii. 24), is stated to have lasted from the 17th day of the -second month (Gen. vii. 11) to the 17th day of the seventh month -(Gen. viii. 4), that is, 5 months of 30 days. - -[Note 13\3: Ib. ii. 4.] - -A year thus settled as a period of a certain number of days is -called a _Civil Year_. It is one of the earliest discoverable -institutions of States possessing any germ of civilization; and one -of the earliest portions of human systematic knowledge is the -discovery of the length of the civil year, so that it should agree -with the natural year, or year of the seasons. - - -_Sect._ 3.--_Correction of the Civil Year._ (_Julian Calendar._) - -IN reality, by such a mode of reckoning as we have described, the -circle of the seasons would not come round exactly. The real length of -the year is very nearly 365 days and a quarter. If a year of 365 days -were used, in four years the year would begin a day too soon, when -considered with reference to the sun and stars; and in 60 years it -would begin 15 days too soon: a quantity perceptible to the loosest -degree of attention. The civil year would be found not to coincide -with the year of the seasons; the beginning of the former would take -place at different periods of the latter; it would _wander_ into -various seasons, instead of remaining fixed to the same season; the -term _year_, and any number of years, would become ambiguous: some -correction, at least some comparison, would be requisite. - -We do not know by whom the insufficiency of the year of 365 days was -first discovered;[14\3] we find this knowledge diffused among all -civilized nations, and various artifices used in making the -correction. The method which we employ, and which consists in -reckoning an {118} additional day at the end of February every fourth -or _leap_ year, is an example of the principle of _intercalation_, by -which the correction was most commonly made. Methods of intercalation -for the same purpose were found to exist in the new world. The -Mexicans added 13 days at the end of every 52 years. The method of the -Greeks was more complex (by means of the _octaëteris_ or cycle of 8 -years); but it had the additional object of accommodating itself to -the motions of the moon, and therefore must be treated of hereafter. -The Egyptians, on the other hand, knowingly permitted their civil year -to _wander_, at least so far as their religious observances were -concerned. "They do not wish," says Geminus,[15\3] "the same -sacrifices of the gods to be made perpetually at the same time of the -year, but that they should go through all the seasons, so that the -same feast may happen in summer and winter, in spring and autumn." The -period in which any festival would thus pass through all the seasons -of the year is 1461 years; for 1460 years of 365¼ days are equal to -1461 years of 365 days. This period of 1461 years is called the -_Sothic_ Period, from Sothis, the name of the Dog-star, by which their -_fixed_ year was determined; and for the same reason it is called the -_Canicular_ Period.[16\3] - -[Note 14\3: Syncellus (_Chronographia_, p. 123) says that according -to the legend, it was King Aseth who first added the 5 additional -days to 360, for the year, in the eighteenth century, B. C.] - -[Note 15\3: _Uranol._ p. 33.] - -[Note 16\3: Censorinus _de Die Natali_, c. 18.] - -Other nations did not regulate their civil year by intercalation at -short intervals, but rectified it by a _reform_ when this became -necessary. The Persians are said to have added a month of 30 days -every 120 years. The Roman calendar, at first very rude in its -structure, was reformed by Numa, and was directed to be kept in -order by the perpetual interposition of the augurs. This, however, -was, from various causes, not properly done; and the consequence -was, that the reckoning fell into utter disorder, in which state it -was found by Julius Cæsar, when he became dictator. By the advice of -Sosigenes, he adopted the mode of intercalation of one day in 4 -years, which we still retain; and in order to correct the -derangement which had already been produced, he added 90 days to a -year of the usual length, which thus became what was called _the -year of confusion_. The _Julian Calendar_, thus reformed, came into -use, January 1, B. C. 45. - - -_Sect._ 4.--_Attempts at the Fixation of the Month._ - -THE circle of changes through which the moon passes in about thirty -days, is marked, in the earliest stages of language, by a word which -implies the space of time which one such circle occupies; just {119} -as the circle of changes of the seasons is designated by the word -_year_. The lunar changes are, indeed, more obvious to the sense, -and strike a more careless person, than the annual; the moon, when -the sun is absent, is almost the sole natural object which attracts -our notice; and we look at her with a far more tranquil and -agreeable attention than we bestow on any other celestial object. -Her changes of form and place are definite and striking to all eyes; -they are uninterrupted, and the duration of their cycle is so short -as to require no effort of memory to embrace it. Hence it appears to -be more easy, and in earlier stages of civilization more common, to -count time by _moons_ than by years. - -The words by which this period of time is designated in various -languages, seem to refer us to the early history of language. Our -word _month_ is connected with the word _moon_, and a similar -connection is noticeable in the other branches of the Teutonic. The -Greek word μὴν in like manner is related to μήνη, which though not -the common word for the moon, is found in Homer with that -signification. The Latin word _mensis_ is probably connected with -the same group.[17\3] - -[Note 17\3: Cicero derives this word from the verb _to measure_: -"quia _mensa_ spatia conficiunt, _menses_ nominantur;" and other -etymologists, with similar views, connect the above-mentioned words -with the Hebrew _manah_, to measure (with which the Arabic word -_almanach_ is connected). Such a derivation would have some analogy -with that of _annus_, &c., noticed above: but if we are to attempt -to ascend to the earliest condition of language, we must conceive it -probable that men would have a name for a most conspicuous visible -object, _the moon_, before they would have a verb denoting the very -abstract and general notion, _to measure_.] - -The month is not any exact number of days, being more than 29, and -less than 30. The latter number was first tried, for men more -readily select numbers possessing some distinction of regularity. It -existed for a long period in many countries. A very few months of 30 -days, however, would suffice to derange the agreement between the -days of the months and the moon's appearance. A little further trial -would show that months of 29 and 30 days alternately, would -preserve, for a considerable period, this agreement. - -The Greeks adopted this calendar, and, in consequence, considered -the days of their month as representing the changes of the moon: the -last day of the month was called ἔνη καὶ νέα, "the old and new" as -belonging to both the waning and the reappearing moon:[18\3] and -their {120} festivals and sacrifices, as determined by the calendar, -were conceived to be necessarily connected with the same periods of -the cycles of the sun and moon. "The laws and the oracles," says -Geminus, "which directed that they should in sacrifices observe -three things, months, days, years, were so understood." With this -persuasion, a correct system of intercalation became a religious -duty. - -[Note 18\3: Aratus says of the moon, in a passage quoted by Geminus, -p. 33: - Αἴει δ' ἄλλοθεν ἄλλα παρακλίνουσα μετωπὰ - Εἴρῃ, ὁποσταίη μήνος περιτέλλεται ἡὼς - As still her shifting visage changing turns, - By her we count the monthly round of morns.] - -The above rule of alternate months of 29 and 30 days, supposes the -length of the months 29 days and a half, which is not exactly the -length of a lunar month. Accordingly the Months and the Moon were -soon at variance. Aristophanes, in "The Clouds," makes the Moon -complain of the disorder when the calendar was deranged. - - Οὐκ ἄγειν τὰς ἡμέρας - Οὐδὲν ὀρθῶς, ἀλλ' ἀνω τε καὶ κάτω κυδοιδοπᾶν - Ὥστ' ἀπειλεῖν φησὶν αὐτῇ τοὐς θεοὺς ἑκάστοτε - Ἡνίκ' ἂν ψευσθῶσι δείπνου κἀπίωσιν οἴκαδε - Τῆς ἑορτῆς μὴ τυχόντες κατὰ λόγον τῶν ἡμερῶν. - _Nubes_, 615-19. - - CHORUS OF CLOUDS. - - The Moon by us to you her greeting sends, - But bids us say that she's an ill-used moon, - And takes it much amiss that you should still - Shuffle her days, and turn them topsy-turvy: - And that the gods (who know their feast-days well) - By your false count are sent home supperless, - And scold and storm at her for your neglect.[19\3] - -[Note 19\3: This passage is supposed by the commentators to be -intended as a satire upon those who had introduced the cycle of -Meton (spoken of in Sect. 5), which had been done at Athens a few -years before "The Clouds" was acted.] - -The correction of this inaccuracy, however, was not pursued -separately, but was combined with another object, the securing a -correspondence between the lunar and solar years, the main purpose -of all early cycles. - - -_Sect._ 5.--_Invention of Lunisolar Years._ - -THERE are 12 complete lunations in a year; which according to the -above rule (of 29½ days to a lunation) would make 354 days, leaving -12¼ days of difference between such a lunar year and a solar year. -It is said that, at an early period, this was attempted to be -corrected by interpolating a month of 30 days every alternate year; -and Herodotus[20\3] relates a conversation of Solon, implying a -still ruder mode of {121} intercalation. This can hardly be -considered as an improvement in the Greek calendar already -described. - -[Note 20\3: B. i. c. 15.] - -The first cycle which produced any near correspondence of the -reckoning of the moon and the sun, was the _Octaëteris_, or period -of 8 years: 8 years of 354 days, together with 3 months of 30 days -each, making up (in 99 lunations) 2922 days; which is exactly the -amount of 8 years of 365¼ days each. Hence this period would answer -its purpose, so far as the above lengths of the lunar and solar -cycles are exact; and it might assume various forms, according to -the manner in which the three intercalary months were distributed. -The customary method was to add a thirteenth month at the end of the -third, fifth, and eighth year of the cycle. This period is ascribed -to various persons and times; probably different persons proposed -different forms of it. Dodwell places its introduction in the 59th -Olympiad, or in the 6th century, B. C.: but Ideler thinks the -astronomical knowledge of the Greeks of that age was too limited to -allow of such a discovery. - -This cycle, however, was imperfect. The duration of 99 lunations is -something more than 2922 days; it is more nearly 2923½; hence in 16 -years there was a deficiency of 3 days, with regard to the motions -of the moon. This cycle of 16 years (_Heccædecaëteris_), with 3 -interpolated days at the end, was used, it is said, to bring the -calculation right with regard to the moon; but in this way the -origin of the year was displaced with regard to the sun. After 10 -revolutions of this cycle, or 160 years, the interpolated days would -amount to 30, and hence the end of the lunar year would be a month -in advance of the end of the solar. By terminating the lunar year at -the end of the preceding month, the two years would again be brought -into agreement: and we have thus a cycle of 160 years.[21\3] - -[Note 21\3: Geminus. Ideler.] - -This cycle of 160 years, however, was calculated from the cycle of -16 years; and it was probably never used in civil reckoning; which -the others, or at least that of 8 years, appear to have been. - -The cycles of 16 and 160 years were corrections of the cycle of 8 -years; and were readily suggested, when the length of the solar and -lunar periods became known with accuracy. But a much more exact -cycle, independent of these, was discovered and introduced by -Meton,[22\3] 432 years B. C. This cycle consisted of 19 years, and -is so correct and convenient, that it is in use among ourselves to -this day. The time occupied by 19 years, and by 235 lunations, is -very nearly the same; {122} (the former time is less than 6940 days -by 9½ hours, the latter, by 7½ hours). Hence, if the 19 years be -divided into 235 months, so as to agree with the changes of the -moon, at the end of that period the same succession may begin again -with great exactness. - -[Note 22\3: Ideler, _Hist. Unters._ p. 208.] - -In order that 235 months, of 30 and 29 days, may make up 6940 days, -we must have 125 of the former, which were called _full_ months, and -110 of the latter, which were termed _hollow_. An artifice was used -in order to distribute 110 hollow months among 6940 days. It will be -found that there is a hollow month for each 63 days nearly. Hence if -we reckon 30 days to every month, but at every 63d day leap over a -day in the reckoning, we shall, in the 19 years, omit 110 days; and -this accordingly was done. Thus the 3d day of the 3d month, the 6th -day of the 5th month, the 9th day of the 7th, must be omitted, so as -to make these months "hollow." Of the 19 years, seven must consist -of 13 months; and it does not appear to be known according to what -order these seven years were selected. Some say they were the 3d, -6th, 8th, 11th, 14th, 17th, and 19th; others, the 3d, 5th, 8th, -11th, 13th, 16th, and 19th. - -The near coincidence of the solar and lunar periods in this cycle of -19 years, was undoubtedly a considerable discovery at the time when -it was first accomplished. It is not easy to trace the way in which -such a discovery was made at that time; for we do not even know the -manner in which men then recorded the agreement or difference -between the calendar day and the celestial phenomenon which ought to -correspond to it. It is most probable that the length of the month -was obtained with some exactness by the observation of eclipses, at -considerable intervals of time from each other; for eclipses are -very noticeable phenomena, and must have been very soon observed to -occur only at new and full moon.[23\3] - -[Note 23\3: Thucyd. vii. 50. Ἡ σελήνη ἐκλείπει· ἐτύγχανε γὰρ -_πανσέληνος_ οὖσα. iv. 52, Τοῦ ἡλίου ἐκλιπές τι ἐγένετο _περὶ -νουμηνίαν_. ii. 28. Νουμηνίᾳ κατὰ _σελήνην_ (ὥσπερ καὶ μόνον δοκεῖ -εἶναι γίγνεσθαι δυνατὸν) ὁ ἡλίος ἐξέλιπε μετὰ μεσημβρίαν καὶ πάλιν -ἀν ἐπληρώθη, γενόμενος μηνοειδὴς καὶ ἀστέρων τινῶν ἐκφανέντων.] - -The exact length of a certain number of months being thus known, the -discovery of a cycle which should regulate the calendar with -sufficient accuracy would be a business of arithmetical skill, and -would depend, in part, on the existing knowledge of arithmetical -methods; but in making the discovery, a natural arithmetical -sagacity was probably more efficacious than method. It is very -possible that the _Cycle of Meton_ is correct more nearly than its -author was aware, and {123} nearly than he could ascertain from any -evidence and calculation known to him. It is so exact that it is -still used in calculating the new moon for the time of Easter; and -the _Golden Number_, which is spoken of in stating such rules, is -the number of this Cycle corresponding to the current year.[24\3] - -[Note 24\3: The same cycle of 19 years has been used by the Chinese -for a very great length of time; their civil year consisting, like -that of the Greeks, of months of 29 and 30 days. The Siamese also -have this period. (_Astron._ Lib. U. K.)] - -Meton's Cycle was corrected a hundred years later (330 B. C.), by -Calippus, who discovered the error of it by observing an eclipse of -the moon six years before the death of Alexander.[25\3] In this -corrected period, four cycles of 19 years were taken, and a day left -out at the end of the 76 years, in order to make allowance for the -hours by which, as already observed, 6940 days are greater than 19 -years, and than 235 lunations: and this _Calippic period_ is used in -Ptolemy's Almagest, in stating observations of eclipses. - -[Note 25\3: Delamb. _A. A._ p. 17.] - -The Metonic and Calippic periods undoubtedly imply a very -considerable degree of accuracy in the knowledge which the -astronomers, to whom they are due, had of the length of the month; -and the first is a very happy invention for bringing the solar and -lunar calendars into agreement. - -The Roman Calendar, from which our own is derived, appears to have -been a much less skilful contrivance than the Greek; though scholars -are not agreed on the subject of its construction, we can hardly -doubt that months, in this as in other cases, were intended -originally to have a reference to the moon. In whatever manner the -solar and lunar motions were intended to be reconciled, the attempt -seems altogether to have failed, and to have been soon abandoned. -The Roman months, both before and after the Julian correction, were -portions of the year, having no reference to full and new moons; and -we, having adopted this division of the year, have thus, in our -common calendar, the traces of one of the early attempts of mankind -to seize the law of the succession of celestial phenomena, in a case -where the attempt was a complete failure. - -Considered as a part of the progress of our astronomical knowledge, -improvements in the calendar do not offer many points to our -observation, but they exhibit a few very important steps. Calendars -which, belonging apparently to unscientific ages and nations, -possess a great degree of accordance with the true motions of the -sun and moon (like {124} the solar calendar of the Mexicans, and the -lunar calendar of the Greeks), contain the only record now extant of -discoveries which must have required a great deal of observation, of -thought, and probably of time. The later improvements in calendars, -which take place when astronomical observation has been attentively -pursued, are of little consequence to the history of science; for -they are generally founded on astronomical determinations, and are -posterior in time, and inferior in accuracy, to the knowledge on -which they depend. But cycles of correction, which are both short -and close to exactness, like that of Meton, may perhaps be the -original form of the knowledge which they imply; and certainly -require both accurate facts and sagacious arithmetical reasonings. -The discovery of such a cycle must always have the appearance of a -happy guess, like other discoveries of laws of nature. Beyond this -point, the interest of the study of calendars, as bearing on our -subject, ceases: they may be considered as belonging rather to Art -than to Science; rather as an application of a part of our knowledge -to the uses of life, than a means or an evidence of its extension. - - -_Sect._ 6.--_The Constellations._ - -SOME tendency to consider the stars as formed into groups, is -inevitable when men begin to attend to them; but how men were led to -the fanciful system of names of Stars and of Constellations, which -we find to have prevailed in early times, it is very difficult to -determine. Single stars, and very close groups, as the Pleiades, -were named in the time of Homer and Hesiod, and at a still earlier -period, as we find in the book of Job.[26\3] - -[Note 26\3: Job xxxviii. 31. "Canst thou bind the sweet influences -of Chima (the Pleiades), or loose the bands of Kesil (Orion)? Canst -thou bring forth Mazzaroth (Sirius) in his season? or canst thou -guide Ash (or Aisch) (Arcturus) with his sons?" - -And ix. 9. "Which maketh Arcturus, Orion, and Pleiades, and the -chambers of the south." - -Dupuis, vi. 545, thinks that Aisch was αἴξ, the goat and kids. See -Hyde, _Ulughbeigh_.] - -Two remarkable circumstances with respect to the Constellations are, -first, that they appear in most cases to be arbitrary combinations; -the artificial figures which are made to include the stars, not -having any resemblance to their obvious configurations; and second, -that these figures, in different countries, are so far similar, as -to imply some communication. The arbitrary nature of these figures -shows that they {125} were rather the work of the imaginative and -mythological tendencies of man, than of mere convenience and love of -arrangement. "The constellations," says an astronomer of our own -time,[27\3] "seem to have been almost purposely named and delineated -to cause as much confusion and inconvenience as possible. -Innumerable snakes twine through long and contorted areas of the -heavens, where no memory can follow them: bears, lions, and fishes, -large and small, northern and southern, confuse all nomenclature. A -better system of constellations might have been a material help as -an artificial memory." When men indicate the stars by figures, -borrowed from obvious resemblances, they are led to combinations -quite different from the received constellations. Thus the common -people in our own country find a wain or wagon, or a plough, in a -portion of the great bear.[28\3] - -[Note 27\3: Sir J. Herschel.] - -[Note 28\3: So also the Greeks, Homer, _Il._ XVIII. 487. - Ἄρκτον ἢν καὶ ἄμαξαν ἐπίκλησιν καλέουσιν. - The Northern Bear which oft the Wain they call. -Ἄρκτος was the traditional name; ἄμαξα, that suggested by the -form.] - -The similarity of the constellations recognized in different -countries is very remarkable. The Chaldean, the Egyptian, and the -Grecian skies have a resemblance which cannot be overlooked. Some -have conceived that this resemblance may be traced also in the -Indian and Arabic constellations, at least in those of the -zodiac.[29\3] But while the figures are the same, the names and -traditions connected with them are different, according to the -histories and localities of each country;[30\3] the river among the -stars which the Greeks called the Eridanus, the Egyptians asserted -to be the Nile. Some conceive that the Signs of the _Zodiac_, or -path along which the sun and moon pass, had its divisions marked by -signs which had a reference to the course of the seasons, to the -motion of the sun, or the employments of the husbandman. If we take -the position of the heavens, which, from the knowledge we now -possess, we are sure they must have had 15,000 years ago, the -significance of the signs of the zodiac, in which the sun was, as -referred to the Egyptian year, becomes very marked,[31\3] and has -led some to suppose that the zodiac was invented at such a period. -Others have rejected this as an improbably great antiquity, and have -thought it more likely that the constellation assigned to each -season was that which, at that season, rose at the beginning of the -night: {126} thus the balance (which is conceived to designate the -equality of days and nights) was placed among the stars which rose -in the evening when the spring began: this would fix the origin of -these signs 2500 years before our era. - -[Note 29\3: Dupuis, vi. 548. The Indian zodiac contains, in the -place of our Capricorn, a ram _and_ a fish, which proves the -resemblance without chance of mistake. Bailly, i. p. 157.] - -[Note 30\3: Dupuis, vi. 549.] - -[Note 31\3: Laplace, _Hist. Astron._ p. 8.] - -It is clear, as has already been said, that Fancy, and probably -Superstition, had a share in forming the collection of -constellations. It is certain that, at an early period, -superstitious notions were associated with the stars.[32\3] -Astrology is of very high antiquity in the East. The stars were -supposed to influence the character and destiny of man, and to be in -some way connected with superior natures and powers. - -[Note 32\3: Dupuis, vi. 546.] - -We may, I conceive, look upon the formation of the constellations, -and the notions thus connected with them, as a very early attempt to -find a meaning in the relations of the stars; and as an utter -failure. The first effort to associate the appearances and motions -of the skies by conceptions implying unity and connection, was made -in a wrong direction, as may very easily be supposed. Instead of -considering the appearances only with reference to space, time, -number, in a manner purely rational, a number of other elements, -imagination, tradition, hope, fear, awe of the supernatural, belief -in destiny, were called into action. Man, still young, as a -philosopher at least, had yet to learn what notions his successful -guesses on these subjects must involve, and what they must exclude. -At that period, nothing could be more natural or excusable than this -ignorance; but it is curious to see how long and how obstinately the -belief lingered (if indeed it be yet extinct) that the motions of -the stars, and the dispositions and fortunes of men, may come under -some common conceptions and laws, by which a connection between the -one and the other may be established. - -We cannot, therefore, agree with those who consider Astrology in the -early ages as "only a degraded Astronomy, the abuse of a more -ancient science."[33\3] It was the first step to astronomy by -leading to habits and means of grouping phenomena; and, after a -while, by showing that pictorial and mythological relations among -the stars had no very obvious value. From that time, the inductive -process went on steadily in the true road, under the guidance of -ideas of space, time, and number. - -[Note 33\3: Ib. vi. 546.] - - -_Sect._ 7.--_The Planets._ - -WHILE men were becoming familiar with the fixed stars, the planets -must have attracted their notice. Venus, from her brightness, and -{127} from her accompanying the sun at no great distance, and thus -appearing as the morning and evening star, was very conspicuous. -Pythagoras is said to have maintained that the evening and morning -star are the same body, which certainly must have been one of the -earliest discoveries on this subject; and indeed we can hardly -conceive men noticing the stars for a year or two without coming to -this conclusion. - -Jupiter and Mars, sometimes still brighter than Venus, were also -very noticeable. Saturn and Mercury were less so, but in fine -climates they and their motion would soon be detected by persons -observant of the heavens. To reduce to any rule the movements of -these luminaries must have taken time and thought; probably before -this was done, certainly very early, these heavenly bodies were -brought more peculiarly under those views which we have noticed as -leading to astrology. - -At a time beyond the reach of certain history, the planets, along -with the sun and moon, had been arranged in a certain recognized -order by the Egyptians or some other ancient nation. Probably this -arrangement had been made according to the slowness of their motions -among the stars; for though the motion of each is very variable, the -gradation of their velocities is, on the whole, very manifest; and -the different rate of travelling of the different planets, and -probably other circumstances of difference, led, in the ready fancy -of early times, to the attribution of a peculiar character to each -luminary. Thus Saturn was held to be of a cold and gelid nature; -Jupiter, who, from his more rapid motion, was supposed to be lower -in place, was temperate; Mars, fiery, and the like.[34\3] - -[Note 34\3: Achilles Tatius (_Uranol._ pp. 135, 136), gives the -Grecian and Egyptian names of the planets. - Egyptian. Greek. -Saturn Νεμεσέως Κρόνου ἀστὴρ φαίνων -Jupiter Ὀσίριδος Δῖος φαέθων -Mars Ἡρακλεοῦς Ἀρέος πυρόεις -Venus Ἀφροδίτης ἑώσφορος -Mercury Ἀπόλλωνος Ἑρμοῦ στίλβων] - -It is not necessary to dwell on the details of these speculations, -but we may notice a very remarkable evidence of their antiquity and -generality in the structure of one of the most familiar of our -measures of time, the _Week_. This distribution of time according to -periods of seven days, comes down to us, as we learn from the Jewish -scriptures, from the beginning of man's existence on the earth. The -same usage is found over all the East; it existed among the -Arabians, Assyrians, {128} Egyptians.[35\3] The same week is found -in India among the Bramins; it has there, also, its days marked by -those of the heavenly bodies; and it has been ascertained that the -same day has, in that country, the name corresponding with its -designation in other nations. - -[Note 35\3: Laplace, _Hist. Astron._ p. 16.] - -The notion which led to the usual designations of the days of the -week is not easily unravelled. The days each correspond to one of -the heavenly bodies, which were, in the earliest systems of the -world, conceived to be the following, enumerating them in the order -of their remoteness from the earth:[36\3] Saturn, Jupiter, Mars, the -Sun, Venus, Mercury, the Moon. At a later period, the received -systems placed the seven luminaries in _the seven spheres_. The -knowledge which was implied in this view, and the time when it was -obtained, we must consider hereafter. The order in which the names -are assigned to the days of the week (beginning with Saturday) is, -Saturn, the Sun, the Moon, Mars, Mercury, Jupiter, Venus; and -various accounts are given of the manner in which one of these -orders is obtained from the other; all the methods proceeding upon -certain arbitrary arithmetical processes, connected in some way with -astrological views. It is perhaps not worth our while here to -examine further the steps of this process; it would be difficult to -determine with certainty why the former order of the planets was -adopted, and how and why the latter was deduced from it. But there -is something very remarkable in the universality of the notions, -apparently so fantastic, which have produced this result; and we may -probably consider the Week, with Laplace,[37\3] as "the most ancient -monument of astronomical knowledge." This period has gone on without -interruption or irregularity from the earliest recorded times to our -own days, traversing the extent of ages and the revolutions of -empires; the names of the ancient deities which were associated with -the stars have been replaced by those of the objects of the worship -of our Teutonic ancestors, according to their views of the -correspondence of the two mythologies; and the Quakers, in rejecting -these names of days, have cast aside the most ancient existing relic -of astrological as well as idolatrous superstition. - -[Note 36\3: _Philol. Mus._ No. 1.] - -[Note 37\3: _Hist. Ast._ p. 17.] - - -_Sect._ 8.--_The Circles of the Sphere._ - -THE inventions hitherto noticed, though undoubtedly they were steps -in astronomical knowledge, can hardly be considered as purely -abstract and scientific speculations; for the exact reckoning of -time is one of {129} the wants, even of the least civilized nations. -But the distribution of the places and motions of the heavenly -bodies by means of a celestial sphere with imaginary lines drawn -upon it, is a step in _speculative_ astronomy, and was occasioned -and rendered important by the scientific propensities of man. - -It is not easy to say with whom this notion originated. Some parts -of it are obvious. The appearance of the sky naturally suggests the -idea of a concave Sphere, with the stars fixed on its surface. Their -motions during any one night, it would be readily seen, might be -represented by supposing this Sphere to turn round a Pole or Axis; -for there is a conspicuous star in the heavens which apparently -stands still (the Pole-star); all the others travel round this in -circles, and keep the same positions with respect to each other. -This stationary star is every night the same, and in the same place; -the other stars also have the same relative position; but their -general position at the same time of night varies gradually from -night to night, so as to go through its cycle of appearances once a -year. All this would obviously agree with the supposition that the -sky is a concave sphere or dome, that the stars have fixed places on -this sphere, and that it revolves perpetually and uniformly about -the Pole or fixed point. - -But this supposition does not at all explain the way in which the -appearances of different nights succeed each other. This, however, -may be explained, it appears, by supposing the _sun_ also _to move -among the stars_ on the surface of the concave sphere. The sun by -his brightness makes the stars invisible which are on his side of -the heavens: this we can easily believe; for the moon, when bright, -also puts out all but the largest stars; and we see the stars -appearing in the evening, each in its place, according to their -degree of splendor, as fast as the declining light of day allows -them to become visible. And as the sun brings day, and his absence -night, if he move through the circuit of the stars in a year, we -shall have, in the course of that time, every part of the starry -sphere in succession presented to us as our nocturnal sky. - -This notion, _that the sun moves round among the stars in a year_, -is the basis of astronomy, and a considerable part of the science is -only the development and particularization of this general -conception. It is not easy to ascertain either the exact method by -which the path of the sun among the stars was determined, or the -author and date of the discovery. That there is some difficulty in -tracing the course of the sun among the stars will be clearly seen, -when it is considered that no {130} star can ever be seen at the -same time with the sun. If the whole circuit of the sky be divided -into twelve parts or _signs_, it is estimated by Autolycus, the -oldest writer on these subjects whose works remain to us,[38\3] that -the stars which occupy one of these parts are absorbed by the solar -rays, so that they cannot be seen. Hence the stars which are seen -nearest to the place of the setting and the rising sun in the -evening and in the morning, are distant from him by the half of a -sign: the evening stars being to the west, and the morning stars to -the east of him. If the observer had previously obtained a knowledge -of the places of all the principal stars, he might in this way -determine the position of the sun each night, and thus trace his -path in a year. - -[Note 38\3: Delamb. _A. A._ p. xiii.] - -In this, or some such way, the sun's path was determined by the -early astronomers of Egypt. Thales, who is mentioned as the father -of Greek astronomy, probably learnt among the Egyptians the results -of such speculations, and introduced them into his own country. His -knowledge, indeed, must have been a great deal more advanced than -that which we are now describing, if it be true, as is asserted, -that he predicted an eclipse. But his having done so is not very -consistent with what we are told of the steps which his successors -had still to make. - -The Circle of the Signs, in which the sun moves among the stars, is -obliquely situated with regard to the circles in which the stars -move about the poles. Pliny[39\3] states that Anaximander,[40\3] a -scholar of Thales, was the first person who pointed out this -obliquity, and thus, as he says, "opened the gate of nature." -Certainly, the person who first had a clear view of the nature of -the sun's path in the celestial sphere, made that step which led to -all the rest; but it is difficult to conceive that the Egyptians and -Chaldeans had not already advanced so far. - -[Note 39\3: Lib. ii. c. (viii.)] - -[Note 40\3: Plutarch, _De Plac. Phil._ lib. ii. cap. xii. says -Pythagoras was the author of this discovery.] - -The diurnal motion of the celestial sphere, and the motion of the -moon in the circle of the signs, gave rise to a mathematical -science, _the Doctrine of the Sphere_, which was one of the earliest -branches of applied mathematics. A number of technical conceptions -and terms were soon introduced. The _Sphere_ of the heavens was -conceived to be complete, though we see but a part of it; it was -supposed to turn about the visible _pole_ and another pole opposite -to this, and these poles were connected by an imaginary _Axis_. The -circle which divided the sphere exactly midway between these poles -was called the _Equator_ (ἰσημέρινος). {131} The two circles -parallel to this which bounded the sun's path among the stars were -called _Tropics_ (τροπικαί), because the sun _turns_ back again -towards the equator when he reaches them. The stars which never set -are bounded by a circle called the _Arctic Circle_ (ἄρκτικος, from -ἄρκτος, the Bear, the constellation to which some of the principal -stars within that circle belong.) A circle about the opposite pole -is called _Antarctic_, and the stars which are within it can never -rise to us.[41\3] The sun's path or circle of the signs is called -the _Zodiac_, or circle of animals; the points where this circle -meets the equator are the _Equinoctial Points_, the days and nights -being equal when the sun is in them; the _Solstitial Points_ are -those where the sun's path touches the tropics; his motion to the -south or to the north ceases when he is there, and he appears in -that respect to stand still. The _Colures_ (κόλουροι, mutilated) are -circles which pass through the poles and through the equinoctial and -solstitial points; they have their name because they are only -visible in part, a portion of them being below the horizon. - -[Note 41\3: The Arctic and Antarctic Circles of modern astronomers -are different from these.] - -The _Horizon_ (ὁρίζων) is commonly understood as the boundary of the -visible earth and heaven. In the doctrine of the sphere, this -boundary is _a great circle_, that is, a circle of which the plane -passes through the centre of the sphere; and, therefore, an entire -hemisphere is always above the horizon. The term occurs for the -first time in the work of Euclid, called _Phænomena_ (Φαινόμενα). We -possess two treatises written by Autolycus[42\3] (who lived about -300 B. C.) which trace _deductively_ the results of the doctrine of -the sphere. Supposing its diurnal motion to be uniform, in a work -entitled Περὶ Κινουμένης Σφαῖρας, "On the Moving Sphere," he -demonstrates various properties of the diurnal risings, settings, -and motions of the stars. In another work, Περὶ Ἐπιτολῶν καὶ Δύσεων, -"On Risings and Settings,"[43\3] _tacitly_ assuming the sun's motion -in his circle to be uniform, he proves certain propositions, with -regard to those risings and settings of the stars, which take place -at the same time when the sun rises and sets,[44\3] or _vice -versâ_;[45\3] and also their _apparent_ risings and settings when -they cease to be visible after sunset, or begin to be visible after -sunrise.[46\3] {132} Several of the propositions contained in the -former of these treatises are still necessary to be understood, as -fundamental parts of astronomy. - -[Note 42\3: Delambre, _Astron. Ancienne_, p. 19.] - -[Note 43\3: Delambre, _Astron. Anc._ p. 25.] - -[Note 44\3: _Cosmical_ rising and setting.] - -[Note 45\3: _Acronycal_ rising and setting; (ἀκρονυκίος, happening -at the extremity of the night.)] - -[Note 46\3: _Heliacal_ rising and setting.] - -The work of Euclid, just mentioned, is of the same kind. -Delambre[47\3] finds in it evidence that Euclid was merely a -book-astronomer, who had never observed the heavens. - -[Note 47\3: _Ast. Anc._ p. 53.] - -We may here remark the first instance of that which we shall find -abundantly illustrated in every part of the history of science; that -man is _prone_ to become a deductive reasoner;--that as soon as he -obtains principles which can be traced to details by logical -consequence, he sets about forming a body of science, by making a -system of such reasonings. Geometry has always been a favorite mode -of exercising this propensity: and that science, along with -Trigonometry, Plane and Spherical, to which the early problems of -astronomy gave rise, have, up to the present day, been a constant -field for the exercise of mathematical ingenuity; a few simple -astronomical truths being assumed as the basis of the reasoning. - - -_Sect._ 9.--_The Globular Form of the Earth._ - -THE establishment of the globular form of the earth is an important -step in astronomy, for it is the first of those convictions, -directly opposed to the apparent evidence of the senses, which -astronomy irresistibly proves. To make men believe that _up_ and -_down_ are different directions in different places; that the sea, -which seems so level, is, in fact, convex; that the earth, which -appears to rest on a solid foundation, is, in fact, not supported at -all; are great triumphs both of the power of discovering and the -power of convincing. We may readily allow this, when we recollect -how recently the doctrine of the _antipodes_, or the existence of -inhabitants of the earth, who stand on the opposite side of it, with -their feet turned towards ours, was considered both monstrous and -heretical. - -Yet the different positions of the horizon at different places, -necessarily led the student of spherical astronomy towards this -notion of the earth as a round body. Anaximander[48\3] is said by -some to have held the earth to be globular, and to be detached or -suspended; he is also stated to have constructed a sphere, on which -were shown the extent of land and water. As, however, we do not know -the arguments upon which he maintained the earth's globular form, we -cannot judge of the {133} value of his opinion; it may have been no -better founded than a different opinion ascribed to him by Laertius, -that the earth had the shape of a pillar. Probably, the authors of -the doctrine of the globular form of the earth were led to it, as we -have said, by observing the different height of the pole at -different places. They would find that the space which they passed -over from north to south on the earth, was proportional to the -change of place of the horizon in the celestial sphere; and as the -horizon is, at every place, in the direction of the earth's -apparently level surface, this observation would naturally suggest -to them the opinion that the earth is placed within the celestial -sphere, as a small globe in the middle of a much larger one. - -[Note 48\3: See Brucker, _Hist. Phil._ vol. i. p. 486.] - -We find this doctrine so distinctly insisted on by Aristotle, that we -may almost look on him as the establisher of it.[49\3] "As to the -figure of the earth, it must necessarily be spherical." This he -proves, first by the tendency of things, in all places, downwards. He -then adds,[50\3] "And, moreover, from the phenomena according to the -sense: for if it were not so, the eclipses of the moon would not have -such sections as they have. For in the configurations in the course of -a month, the deficient part takes all different shapes; it is -straight, and concave, and convex; but in eclipses it always has the -line of division convex; wherefore, since the moon is eclipsed in -consequence of the interposition of the earth, the periphery of the -earth must be the cause of this by having a spherical form. And again, -from the appearances of the stars, it is clear, not only that the -earth is round, but that its size is not very large: for when we make -a small removal to the south or the north, the circle of the horizon -becomes palpably different, so that the stars overhead undergo a great -change, and are not the same to those that travel to the north and to -the south. For some stars are seen in Egypt or at Cyprus, but are not -seen in the countries to the north of these; and the stars that in the -north are visible while they make a complete circuit, there undergo a -setting. So that from this it is manifest, not only that the form of -the earth is round, but also that it is a part of not a very large -sphere: for otherwise the difference would not be so obvious to -persons making so small a change of place. Wherefore we may judge that -those persons _who connect the region in the neighborhood of the -pillars of Hercules with that towards India, and who assert that in -this way the sea is_ ONE, do not assert things very improbable. They -confirm this conjecture moreover by the {134} elephants, which are -said to be of the same species (γένος) towards each extreme; as if -this circumstance was a consequence of the conjunction of the -extremes. The mathematicians, who try to calculate the measure of the -circumference, make it amount to 400,000 stadia; whence we collect -that the earth is not only spherical, but is not large compared with -the magnitude of the other stars." - -[Note 49\3: Arist. _de Cœlo_, lib. ii. cap. xiv. ed. Casaub. p. -290.] - -[Note 50\3: p. 291 C.] - -When this notion was once suggested, it was defended and confirmed -by such arguments as we find in later writers: for instance,[51\3] -that the tendency of all things was to fall to the place of heavy -bodies, and that this place being the centre of the earth, the whole -earth had no such tendency; that the inequalities on the surface -were so small as not materially to affect the shape of so vast a -mass; that drops of water naturally form themselves into figures -with a convex surface; that the end of the ocean would fall if it -were not rounded off; that we see ships, when they go out to sea, -disappearing downwards, which shows the surface to be convex. These -are the arguments still employed in impressing the doctrines of -astronomy upon the student of our own days; and thus we find that, -even at the early period of which we are now speaking, truths had -begun to accumulate which form a part of our present treasures. - -[Note 51\3: Pliny, _Nat. Hist._ ii. LXV.] - - -_Sect._ 10.--_The Phases of the Moon._ - -WHEN men had formed a steady notion of the Moon as a solid body, -revolving about the earth, they had only further to conceive it -spherical, and to suppose the sun to be beyond the region of the -moon, and they would find that they had obtained an explanation of -the varying forms which the bright part of the moon assumes in the -course of a month. For the convex side of the crescent-moon, and her -full edge when she is gibbous, are always turned towards the sun. -And this explanation, once suggested, would be confirmed, the more -it was examined. For instance, if there be near us a spherical -stone, on which the sun is shining, and if we place ourselves so -that this stone and the moon are seen in the same direction (the -moon appearing just over the top of the stone), we shall find that -the visible part of the stone, which is then illuminated by the sun, -is exactly similar in form to the moon, at whatever period of her -changes she may be. The stone and the moon being in the same -position with respect to us, and both being enlightened by the sun, -the bright parts are the same in figure; {135} the only difference -is, that the dark part of the moon is usually not visible at all. - -This doctrine is ascribed to Anaximander. Aristotle was fully aware -of it.[52\3] It could not well escape the Chaldeans and Egyptians, -if they speculated at all about the causes of the appearances in the -heavens. - -[Note 52\3: Probl. Cap. XV. Art. 7.] - - -_Sect._ 11.--_Eclipses._ - -ECLIPSES of the sun and moon were from the earliest tunes regarded -with a peculiar interest. The notions of superhuman influences and -relations, which, as we have seen, were associated with the -luminaries of the sky, made men look with alarm at any sudden and -striking change in those objects; and as the constant and steady -course of the celestial revolutions was contemplated with a feeling -of admiration and awe, any marked interruption and deviation in this -course, was regarded with surprise and terror. This appears to be -the case with all nations at an early stage of their civilization. - -This impression would cause Eclipses to be noted and remembered; and -accordingly we find that the records of Eclipses are the earliest -astronomical information which we possess. When men had discovered -some of the laws of succession of other astronomical phenomena, for -instance, of the usual appearances of the moon and sun, it might -then occur to them that these unusual appearances also might -probably be governed by some rule. - -The search after this rule was successful at an early period. The -Chaldeans were able to predict Eclipses of the Moon. This they did, -probably, by means of their Cycle of 223 months, or about 18 years; -for at the end of this time, the eclipses of the moon begin to return, -at the same intervals and in the same order as at the beginning.[53\3] -Probably this was the first instance of the prediction of peculiar -astronomical phenomena. The Chinese have, indeed, a legend, in which -it is related that a solar eclipse happened in the reign of -Tchongkang, above 2000 years before Christ, and that the emperor was -so much irritated against two great officers of state, who had -neglected to predict this eclipse, that he put them to death. But this -cannot be accepted as a real event: for, during the next ten -centuries, we find no single observation or fact connected with -astronomy in the Chinese {136} histories; and their astronomy has -never advanced beyond a very rude and imperfect condition. - -[Note 53\3: The eclipses of the sun are more difficult to calculate; -since they depend upon the place of the spectator on the earth.] - -We can only conjecture the mode in which the Chaldeans discovered -their Period of 18 years; and we may make very different -suppositions with regard to the degree of science by which they were -led to it. We may suppose, with Delambre,[54\3] that they carefully -recorded the eclipses which happened, and then, by the inspection of -their registers, discovered that those of the moon recurred after a -certain period. Or we may suppose, with other authors, that they -sedulously determined the motions of the moon, and having obtained -these with considerable accuracy, sought and found a period which -should include cycles of these motions. This latter mode of -proceeding would imply a considerable degree of knowledge. - -[Note 54\3: _A. A._ p. 212.] - -It appears probable rather that such a period was discovered by -noticing the _recurrence_ of eclipses, than by studying the moon's -_motions_. After 6585⅓ days, or 223 lunations, the same eclipses -nearly will recur. It is not contested that the Chaldeans were -acquainted with this period, which they called _Saros_; or that they -calculated eclipses by means of it. - - -_Sect._ 12.--_Sequel to the Early Stages of Astronomy._ - -EVERY stage of science has its train of practical applications and -systematic inferences, arising both from the demands of convenience -and curiosity, and from the pleasure which, as we have already said, -ingenuous and active-minded men feel in exercising the process of -deduction. The earliest condition of astronomy, in which it can be -looked upon as a science, exhibits several examples of such -applications and inferences, of which we may mention a few. - -_Prediction of Eclipses._--The Cycles which served to keep in order -the Calendar of the early nations of antiquity, in some instances -enabled them also, as has just been stated, to predict Eclipses; and -this application of knowledge necessarily excited great notice. -Cleomedes, in the time of Augustus, says, "We never see an eclipse -happen which has not been predicted by those who made use of the -Tables." (ὑπὸ τῶν κανονικῶν.) - -_Terrestrial Zones._--The globular form of the earth being assented -to, the doctrine of the sphere was applied to the earth as well as -the heavens; and the earth's surface was divided by various -imaginary {137} circles; among the rest, the equator, the tropics, -and circles, at the same distance from the poles as the tropics are -from the equator. One of the curious consequences of this division -was the _assumption_ that there must be some marked difference in -the stripes or _zones_ into which the earth's surface was thus -divided. In going to the south, Europeans found countries hotter and -hotter, in going to the north, colder and colder; and it was -supposed that the space between the tropical circles must be -uninhabitable from heat, and that within the polar circles, again, -uninhabitable from cold. This fancy was, as we now know, entirely -unfounded. But the principle of the globular form of the earth, when -dealt with by means of spherical geometry, led to many true and -important propositions concerning the lengths of days and nights at -different places. These propositions still form a part of our -Elementary Astronomy. - -_Gnomonic._--Another important result of the doctrine of the sphere -was _Gnomonic_ or _Dialling_. Anaximenes is said by Pliny to have -first taught this art in Greece; and both he and Anaximander are -reported to have erected the first dial at Lacedemon. Many of the -ancient dials remain to us; some of these are of complex forms, and -must have required great ingenuity and considerable geometrical -knowledge in their construction. - -_Measure of the Sun's Distance._--The explanation of the phases of the -moon led to no result so remarkable as the attempt of Aristarchus of -Samos to obtain from this doctrine a measure of the Distance of the -Sun as compared with that of the Moon. If the moon was a perfectly -smooth sphere, when she was exactly midway between the new and full in -position (that is, a quadrant from the sun), she would be somewhat -more than a half moon; and the place when she was _dichotomized_, that -is, was an exact semicircle, the bright part being bounded by a -straight line, would depend upon the sun's distance from the earth. -Aristarchus endeavored to fix the exact place of this Dichotomy; but -the irregularity of the edge which bounds the bright part of the moon, -and the difficulty of measuring with accuracy, by means then in use, -either the precise time when the boundary was most nearly a straight -line, or the exact distance of the moon from the sun at that time, -rendered his conclusion false and valueless. He collected that the sun -is at 18 times the distance of the moon from us; we now know that he -is at 400 times the moon's distance. - -It would be easy to dwell longer on subjects of this kind; but we -have already perhaps entered too much in detail. We have been {138} -tempted to do this by the interest which the mathematical spirit of -the Greeks gave to the earliest astronomical discoveries, when these -were the subjects of their reasonings; but we must now proceed to -contemplate them engaged in a worthier employment, namely, in adding -to these discoveries. - - - - -CHAPTER II. - -PRELUDE TO THE INDUCTIVE EPOCH OF HIPPARCHUS. - - -WITHOUT pretending that we have exhausted the consequences of the -elementary discoveries which we have enumerated, we now proceed to -consider the nature and circumstances of the next great discovery -which makes an Epoch in the history of Astronomy; and this we shall -find to be the Theory of Epicycles and Eccentrics. Before, however, -we relate the establishment of this theory, we must, according to -the general plan we have marked out, notice some of the conjectures -and attempts by which it was preceded, and the growing acquaintance -with facts, which made the want of such an explanation felt. - -In the steps previously made in astronomical knowledge, no ingenuity -had been required to devise the view which was adopted. The motions of -the stars and sun were most naturally and almost irresistibly -conceived as the results of motion in a revolving sphere; the -indications of position which we obtain from different places on the -earth's surface, when clearly combined, obviously imply a globular -shape. In these cases, the first conjectures, the supposition of the -simplest form, of the most uniform motion, required no -after-correction. But this manifest simplicity, this easy and obvious -explanation, did not apply to the movement of all the heavenly bodies. -The Planets, the "wandering stars," could not be so easily understood; -the motion of each, as Cicero says, "undergoing very remarkable -changes in its course, going before and behind, quicker and slower, -appearing in the evening, but gradually lost there, and emerging again -in the morning."[55\3] A continued attention to these stars would, -however, {139} detect a kind of intricate regularity in their motions, -which might naturally be described as "a dance." The Chaldeans are -stated by Diodorus[56\3] to have observed assiduously the risings and -settings of the planets, from the top of the temple of Belus. By doing -this, they would find the times in which the forward and backward -movements of Saturn, Jupiter, and Mars recur; and also the time in -which they come round to the same part of the heavens.[57\3] Venus and -Mercury never recede far from the sun, and the intervals which elapse -while either of them leaves its greatest distance from the sun and -returns again to the greatest distance on the same side, would easily -be observed. - -[Note 55\3: Cic. _de Nat. D._ lib. ii. p. 450. "Ea quæ Saturni -stella dicitur, φαίνωνque a Græcis nominatur, quæ a terra abest -plurimum, xxx fere annis cursum suum conficit; in quo cursu multa -mirabiliter efficiens, tum antecedendo, tum retardando, tum -vespertinis temporibus delitescendo, tum matutinis se rursum -aperiendo, nihil immutat sempiternis sæculorum ætatibus, quin eadem -iisdem temporibus efficiat." And so of the other planets.] - -[Note 56\3: _A. A._ i. p. 4.] - -[Note 57\3: Plin. _H. N._ ii. p. 204.] - -Probably the manner in which the motions of the planets were -originally reduced to rule was something like the following:--In -about 30 of our years, Saturn goes 29 times through his _Anomaly_, -that is, the succession of varied motions by which he sometimes goes -forwards and sometimes backwards among the stars. During this time, -he goes once round the heavens, and returns nearly to the same -place. This is the cycle of his apparent motions. - -Perhaps the eastern nations contented themselves with thus referring -these motions to cycles of time, so as to determine their recurrence. -Something of this kind was done at an early period, as we have seen. - -But the Greeks soon attempted to frame to themselves a sensible image -of the mechanism by which these complex motions were produced; nor did -they find this difficult. Venus, for instance, who, upon the whole, -moves from west to east among the stars, is seen, at certain -intervals, to return or move _retrograde_ a short way back from east -to west, then to become for a short time _stationary_, then to turn -again and resume her _direct_ motion westward, and so on. Now this can -be explained by supposing that she is placed in the rim of a wheel, -which is turned edgeways to us, and of which the centre turns round in -the heavens from west to east, while the wheel, carrying the planet in -its motion, moves round its own centre. In this way the motion of the -wheel about its centre, would, in some situations, counterbalance the -general motion of the centre, and make the planet retrograde, while, -on the whole, the westerly motion would prevail. Just as if we suppose -that a person, holding a lamp in his hand in the dark, and at a {140} -distance, so that the lamp alone is visible, should run on turning -himself round; we should see the light sometimes stationary, sometimes -retrograde, but on the whole progressive. - -A mechanism of this kind was imagined for each of the planets, and the -wheels of which we have spoken were in the end called _Epicycles_. - -The application of such mechanism to the planets appears to have -arisen in Greece about the time of Aristotle. In the works of Plato we -find a strong taste for this kind of mechanical speculation. In the -tenth book of the "Polity," we have the apologue of Alcinus the -Pamphylian, who, being supposed to be killed in battle, revived when -he was placed on the funeral pyre, and related what he had seen during -his trance. Among other revelations, he beheld the machinery by which -all the celestial bodies revolve. The axis of these revolutions is the -adamantine distaff which Destiny holds between her knees; on this are -fixed, by means of different sockets, flat rings, by which the planets -are carried. The order and magnitude of these spindles are minutely -detailed. Also, in the "Epilogue to the Laws" (_Epinomis_), he again -describes the various movements of the sky, so as to show a distinct -acquaintance with the general character of the planetary motions; and, -after speaking of the Egyptians and Syrians as the original -cultivators of such knowledge, he adds some very remarkable -exhortations to his countrymen to prosecute the subject. "Whatever we -Greeks," he says, "receive from the barbarians, we improve and -perfect; there is good hope and promise, therefore, that Greeks will -carry this knowledge far beyond that which was introduced from -abroad." To this task, however, he looks with a due appreciation of -the qualities and preparation which it requires. "An astronomer must -be," he says, "the wisest of men; his mind must be duly disciplined in -youth; especially is mathematical study necessary; both an -acquaintance with the doctrine of number, and also with that other -branch of mathematics, which, closely connected as it is with the -science of the _heavens_, we very absurdly call _geometry_, the -measurement of the _earth_."[58\3] - -[Note 58\3: _Epinomis_, pp. 988, 990.] - -Those anticipations were very remarkably verified in the subsequent -career of the Greek Astronomy. - -The theory, once suggested, probably made rapid progress. -Simplicius[59\3] relates, that Eudoxus of Cnidus introduced the -hypothesis of revolving circles or spheres. Calippus of Cyzicus, -having visited {141} Polemarchus, an intimate friend of Eudoxus, -they went together to Athens, and communicated to Aristotle the -invention of Eudoxus, and with his help improved and corrected it. - -[Note 59\3: Lib. ii. _de Cœlo_. Bullialdus, p. 18.] - -Probably at first this hypothesis was applied only to account for -the general phenomena of the progressions, retrogradations, and -stations of the planet; but it was soon found that the motions of -the sun and moon, and the circular motions of the planets, which the -hypothesis supposed, had other _anomalies_ or irregularities, which -made a further extension of the hypothesis necessary. - -The defect of uniformity in these motions of the sun and moon, -though less apparent than in the planets, is easily detected, as -soon as men endeavor to obtain any accuracy in their observations. -We have already stated (Chap. I.) that the Chaldeans were in -possession of a period of about eighteen years, which they used in -the calculation of eclipses, and which might have been discovered by -close observation of the moon's motions; although it was probably -rather hit upon by noting the recurrence of eclipses. The moon moves -in a manner which is not reducible to regularity without -considerable care and time. If we trace her path among the stars, we -find that, like the path of the sun, it is oblique to the equator, -but it does not, like that of the sun, pass over the same stars in -successive revolutions. Thus its _latitude_, or distance from the -equator, has a cycle different from its revolution among the stars; -and its _Nodes_, or the points where it cuts the equator, are -perpetually changing their position. In addition to this, the moon's -motion in her own path is not uniform; in the course of each -lunation, she moves alternately slower and quicker, passing -gradually through the intermediate degrees of velocity; and goes -through the cycle of these changes in something less than a month; -this is called a revolution of _Anomaly_. When the moon has gone -through a complete number of revolutions of Anomaly, and has, in the -same time, returned to the same position with regard to the sun, and -also with regard to her Nodes, her motions with respect to the sun -will thenceforth be the same as at the first, and all the -circumstances on which lunar eclipses depend being the same, the -eclipses will occur in the same order. In 6585⅓ days there are 239 -revolutions of anomaly, 241 revolutions with regard to one of the -Nodes, and, as we have said, 223 lunations or revolutions with -regard to the sun. Hence this Period will bring about a succession -of the same lunar eclipses. - -If the Chaldeans observed the moon's motion among the stars with any -considerable accuracy, so as to detect this period by that means, -{142} they could hardly avoid discovering the anomaly or unequal -motion of the moon; for in every revolution, her daily progression -in the heavens varies from about twenty-two to twenty-six times her -own diameter. But there is not, in their knowledge of this Period, -any evidence that they had measured the amount of this variation; -and Delambre[60\3] is probably right in attributing all such -observations to the Greeks. - -[Note 60\3: _Astronomie Ancienne_, i. 212.] - -The sun's motion would also be seen to be irregular as soon as men -had any exact mode of determining the lengths of the four seasons, -by means of the passage of the sun through the equinoctial and -solstitial points. For spring, summer, autumn, and winter, which -would each consist of an equal number of days if the motions were -uniform, are, in fact, found to be unequal in length. - -It was not very difficult to see that the mechanism of epicycles -might be applied so as to explain irregularities of this kind. A -wheel travelling round the earth, while it revolved upon its centre, -might produce the effect of making the sun or moon fixed in its rim -go sometimes faster and sometimes slower in appearance, just in the -same way as the same suppositions would account for a planet going -sometimes forwards and sometimes backwards: the epicycles of the sun -and moon would, for this purpose, be less than those of the planets. -Accordingly, it is probable that, at the time of Plato and -Aristotle, philosophers were already endeavoring to apply the -hypothesis to these cases, though it does not appear that any one -fully succeeded before Hipparchus. - -The problem which was thus present to the minds of astronomers, and -which Plato is said to have proposed to them in a distinct form, -was, "To reconcile the celestial phenomena by the combination of -equable circular motions." That the circular motions should be -equable as well as circular, was a condition, which, if it had been -merely tried at first, as the most simple and definite conjecture, -would have deserved praise. But this condition, which is, in -reality, inconsistent with nature, was, in the sequel, adhered to -with a pertinacity which introduced endless complexity into the -system. The history of this assumption is one of the most marked -instances of that love of simplicity and symmetry which is the -source of all general truths, though it so often produces and -perpetuates error. At present we can easily see how fancifully the -notion of simplicity and perfection was interpreted, in the -arguments by which the opinion was defended, that the {143} real -motions of the heavenly bodies must be circular and uniform. The -Pythagoreans, as well as the Platonists, maintained this dogma. -According to Geminus, "They supposed the motions of the sun, and the -moon, and the five planets, to be circular and equable: for they -would not allow of such disorder among divine and eternal things, as -that they should sometimes move quicker, and sometimes slower, and -sometimes stand still; for no one would tolerate such anomaly in the -movements, even of a man, who was decent and orderly. The occasions -of life, however, are often reasons for men going quicker or slower, -but in the incorruptible nature of the stars, it is not possible -that any cause can be alleged of quickness and slowness. Whereupon -they propounded this question, how the phenomena might be -represented by equable and circular motions." - -These conjectures and assumptions led naturally to the establishment -of the various parts of the Theory of Epicycles. It is probable that -this theory was adopted with respect to the Planets at or before the -time of Plato. And Aristotle gives us an account of the system thus -devised.[61\3] "Eudoxus," he says, "attributed four spheres to each -Planet: the first revolved with the fixed stars (and this produced -the diurnal motion); the second gave the planet a motion along the -ecliptic (the mean motion in longitude); the third had its axis -perpendicular[62\3] to the ecliptic (and this gave the inequality of -each planetary motion, really arising from its special motion about -the sun); the fourth produced the oblique motion transverse to this -(the motion in latitude)." He is also said to have attributed a -motion in latitude and a corresponding sphere to the Sun as well as -to the Moon, of which it is difficult to understand the meaning, if -Aristotle has reported rightly of the theory; for it would be absurd -to ascribe to Eudoxus a knowledge of the motions by which the sun -deviates from the ecliptic. Calippus conceived that two additional -spheres must be given to the sun and to the moon, in order to -explain the phenomena: probably he was aware of the inequalities of -the motions of these luminaries. He also proposed an additional -sphere for each planet, to account, we may suppose, for the results -of the eccentricity of the orbits. - -[Note 61\3: Metaph. xi. 8.] - -[Note 62\3: Aristotle says "has its poles in the ecliptic," but this -must be a mistake of his. He professes merely to receive these -opinions from the mathematical astronomers, "ἐκ τῆς οἰκειοτάτης -φιλοσοφίας τῶν μαθηματικῶν."] - -The hypothesis, in this form, does not appear to have been reduced -to measure, and was, moreover, unnecessarily complex. The resolution -{144} of the oblique motion of the moon into two separate motions, -by Eudoxus, was not the simplest way of conceiving it; and Calippus -imagined the connection of these spheres in some way which made it -necessary nearly to double their number; in this manner his system -had no less than 55 spheres. - -Such was the progress which the _Idea_ of the hypothesis of -epicycles had made in men's minds, previously to the establishment -of the theory by Hipparchus. There had also been a preparation for -this step, on the other side, by the collection of _Facts_. We know -that observations of the Eclipses of the Moon were made by the -Chaldeans 367 B. C. at Babylon, and were known to the Greeks; for -Hipparchus and Ptolemy founded their Theory of the Moon on these -observations. Perhaps we cannot consider, as equally certain, the -story that, at the time of Alexander's conquest, the Chaldeans -possessed a series of observations, which went back 1903 years, and -which Aristotle caused Callisthenes to bring to him in Greece. All -the Greek observations which are of any value, begin with the school -of Alexandria. Aristyllus and Timocharis appear, by the citations of -Hipparchus, to have observed the Places of Stars and Planets, and -the Times of the Solstices, at various periods from B. C. 295 to B. -C. 269. Without their observations, indeed, it would not have been -easy for Hipparchus to establish either the Theory of the Sun or the -Precession of the Equinoxes. - -In order that observations at distant intervals may be compared with -each other, they must be referred to some common era. The Chaldeans -dated by the era of Nabonassar, which commenced 749 B. C. The Greek -observations were referred to the Calippic periods of 76 years, of -which the first began 331 B. C. These are the dates used by -Hipparchus and Ptolemy. {145} - - - - -CHAPTER III. - -INDUCTIVE EPOCH OF HIPPARCHUS. - - -_Sect._ 1.--_Establishment of the Theory of Epicycles and -Eccentrics._ - -ALTHOUGH, as we have already seen, at the time of Plato, the Idea of -Epicycles had been suggested, and the problem of its general -application proposed, and solutions of this problem offered by his -followers; we still consider Hipparchus as the real discoverer and -founder of that theory; inasmuch as he not only guessed that it -_might_, but showed that it _must_, account for the phenomena, both -as to their nature and as to their quantity. The assertion that "he -only discovers who proves," is just; not only because, until a -theory is proved to be the true one, it has no pre-eminence over the -numerous other guesses among which it circulates, and above which -the proof alone elevates it; but also because he who takes hold of -the theory so as to apply calculation to it, possesses it with a -distinctness of conception which makes it peculiarly his. - -In order to establish the Theory of Epicycles, it was necessary to -assign the magnitudes, distances, and positions of the circles or -spheres in which the heavenly bodies were moved, in such a manner as -to account for their apparently irregular motions. We may best -understand what was the problem to be solved, by calling to mind -what we now know to be the real motions of the heavens. The true -motion of the earth round the sun, and therefore the apparent annual -motion of the sun, is performed, not in a circle of which the earth -is the centre, but in an ellipse or oval, the earth being nearer to -one end than to the other; and the motion is most rapid when the sun -is at the nearer end of this oval. But instead of an oval, we may -suppose the sun to move uniformly in a circle, the earth being now, -not in the centre, but nearer to one side; for on this supposition, -the sun will appear to move most quickly when he is nearest to the -earth, or in his _Perigee_, as that point is called. Such an orbit -is called an _Eccentric_, and the distance of the earth from the -centre of the circle is called the _Eccentricity_. It may easily be -shown by geometrical reasoning, that the inequality of apparent -motion so produced, is exactly the same in {146} detail, as the -inequality which follows from the hypothesis of a small _Epicycle_, -turning uniformly on its axis, and carrying the sun in its -circumference, while the centre of this epicycle moves uniformly in -a circle of which the earth is the centre. This identity of the -results of the hypothesis of the Eccentric and the Epicycle is -proved by Ptolemy in the third book of the "Almagest." - -_The Sun's Eccentric._--When Hipparchus had clearly conceived these -hypotheses, as _possible_ ways of accounting for the sun's motion, -the task which he had to perform, in order to show that they -deserved to be adopted, was to assign a place to the _Perigee_, a -magnitude to the _Eccentricity_, and an _Epoch_ at which the sun was -at the perigee; and to show that, in this way, he had produced a -true representation of the motions of the sun. This, accordingly, he -did; and having thus determined, with considerable exactness, both -the law of the solar irregularities, and the numbers on which their -amount depends, he was able to assign the motions and places of the -sun for any moment of future time with corresponding exactness; he -was able, in short, to construct _Solar Tables_, by means of which -the sun's place with respect to the stars could be correctly found -at any time. These tables (as they are given by Ptolemy)[63\3] give -the _Anomaly_, or inequality of the sun's motion; and this they -exhibit by means of the _Prosthapheresis_, the quantity of which, at -any distance of the sun from the _Apogee_, it is requisite to add to -or subtract from the arc, which he would have described if his -motion had been equable. - -[Note 63\3: Syntax. 1. iii.] - -The reader might perhaps expect that the calculations which thus -exhibited the motions of the sun for an indefinite future period -must depend upon a considerable number of observations made at all -seasons of the year. That, however, was not the case; and the genius -of the discoverer appeared, as such genius usually does appear, in -his perceiving how small a number of facts, rightly considered, were -sufficient to form a foundation for the theory. The number of days -contained in two seasons of the year sufficed for this purpose to -Hipparchus. "Having ascertained," says Ptolemy, "that the time from -the vernal equinox to the summer tropic is 94½ days, and the time -from the summer tropic to the autumnal equinox 92½ days, from these -phenomena alone he demonstrates that the straight line joining the -centre of the sun's eccentric path with the centre of the zodiac -(the spectator's eye) is nearly the 24th part of the radius of the -eccentric path; and that {147} its _apogee_ precedes the summer -solstice by 24½ degrees nearly, the zodiac containing 360." - -The exactness of the Solar Tables, or _Canon_, which was founded on -these data, was manifested, not only by the coincidence of the sun's -calculated place with such observations as the Greek astronomers of -this period were able to make (which were indeed very rude), but by -its enabling them to calculate solar and lunar eclipses; phenomena -which are a very precise and severe trial of the accuracy of such -tables, inasmuch as a very minute change in the apparent place of -the sun or moon would completely alter the obvious features of the -eclipse. Though the tables of this period were by no means perfect, -they bore with tolerable credit this trying and perpetually -recurring test; and thus proved the soundness of the theory on which -the tables were calculated. - -_The Moon's Eccentric._--The moon's motions have many -irregularities; but when the hypothesis of an Eccentric or an -Epicycle had sufficed in the case of the sun, it was natural to try -to explain, in the same way, the motions of the moon; and it was -shown by Hipparchus that such hypotheses would account for the more -obvious anomalies. It is not very easy to describe the several ways -in which these hypotheses were applied, for it is, in truth, very -difficult to explain in words even the mere facts of the moon's -motion. If she were to leave a visible bright line behind her in the -heavens wherever she moved, the path thus exhibited would be of an -extremely complex nature; the circle of each revolution slipping -away from the preceding, and the traces of successive revolutions -forming a sort of band of net-work running round the middle of the -sky.[64\3] In each revolution, the motion in longitude is affected -by an anomaly of the same nature as the sun's anomaly already spoken -of; but besides this, the path of the moon deviates from the -ecliptic to the north and to the south of the ecliptic, and thus she -has a motion in latitude. This motion in latitude would be -sufficiently known if we knew the period of its _restoration_, that -is, the time which the moon occupies in moving from any latitude -till she is restored to the same latitude; as, for instance, from -the ecliptic on one side of the heavens to the ecliptic on the same -side of the heavens again. But it is found that the period of the -restoration of the latitude is not the same as the period of the -restoration of the longitude, that is, as the period of the moon's -revolution among the {148} stars; and thus the moon describes a -different path among the stars in every successive revolution, and -her path, as well as her velocity, is constantly variable. - -[Note 64\3: The reader will find an attempt to make the nature of -this path generally intelligible in the _Companion to the British -Almanac_ for 1814.] - -Hipparchus, however, reduced the motions of the moon to rule and to -Tables, as he did those of the sun, and in the same manner. He -determined, with much greater accuracy than any preceding -astronomer, the mean or average equable motions of the moon in -longitude and in latitude; and he then represented the anomaly of -the motion in longitude by means of an eccentric, in the same manner -as he had done for the sun. - -But here there occurred still an additional change, besides those of -which we have spoken. The Apogee of the Sun was always in the same -place in the heavens; or at least so nearly so, that Ptolemy could -detect no error in the place assigned to it by Hipparchus 250 years -before. But the Apogee of the Moon was found to have a motion among -the stars. It had been observed before the time of Hipparchus, that -in 6585⅓ days, there are 241 revolutions of the moon with regard to -the stars, but only 239 revolutions with regard to the anomaly. This -difference could be suitably represented by supposing the eccentric, -in which the moon moves, to have itself an angular motion, -perpetually carrying its apogee in the same direction in which the -moon travels; but this supposition being made, it was necessary to -determine, not only the eccentricity of the orbit, and place of the -apogee at a certain time, but also the rate of motion of the apogee -itself, in order to form tables of the moon. - -This task, as we have said, Hipparchus executed; and in this instance, -as in the problem of the reduction of the sun's motion to tables, the -data which he found it necessary to employ were very few. He deduced -all his conclusions from six eclipses of the moon.[65\3] Three of -these, the records of which were brought from Babylon, where a -register of such occurrences was kept, happened in the 366th and 367th -years from the era of Nabonassar, and enabled Hipparchus to determine -the eccentricity and apogee of the moon's orbit at that time. The -three others were observed at Alexandria, in the 547th year of -Nabonassar, which gave him another position of the orbit at an -interval of 180 years; and he thus became acquainted with the motion -of the orbit itself, as well as its form.[66\3] {149} - -[Note 65\3: Ptol. _Syn._ iv. 10.] - -[Note 66\3: Ptolemy uses the hypothesis of an epicycle for the -moon's first inequality; but Hipparchus employs an eccentric.] - -The moon's motions are really affected by several other -inequalities, of very considerable amount, besides those which were -thus considered by Hipparchus; but the lunar paths, constructed on -the above data, possessed a considerable degree of correctness, and -especially when applied, as they were principally, to the -calculation of eclipses; for the greatest of the additional -irregularities which we have mentioned disappear at new and full -moon, which are the only times when eclipses take place. - -The numerical explanation of the motions of the sun and moon, by -means of the Hypothesis of Eccentrics, and the consequent -construction of tables, was one of the great achievements of -Hipparchus. The general explanation of the motions of the planets, -by means of the hypothesis of epicycles, was in circulation -previously, as we have seen. But the special motions of the planets, -in their epicycles, are, in reality, affected by anomalies of the -same kind as those which render it necessary to introduce eccentrics -in the cases of the sun and moon. - -Hipparchus determined, with great exactness, the _Mean Motions_ of -the Planets; but he was not able, from want of data, to explain the -planetary _Irregularities_ by means of Eccentrics. The whole mass of -good observations of the planets which he received from preceding -ages, did not contain so many, says Ptolemy, as those which he has -transmitted to us of his own. "Hence[67\3] it was," he adds, "that -while he labored, in the most assiduous manner to represent the -motions of the sun and moon by means of equable circular motions; -with respect to the planets, so far as his works show, he did not -even make the attempt, but merely put the extant observations in -order, added to them himself more than the whole of what he received -from preceding ages, and showed the insufficiency of the hypothesis -current among astronomers to explain the phenomena." It appears that -preceding mathematicians had already pretended to construct "a -Perpetual Canon," that is, Tables which should give the places of -the planets at any future time; but these being constructed without -regard to the eccentricity of the orbits, must have been very -erroneous. - -[Note 67\3: _Synt._ ix. 2.] - -Ptolemy declares, with great reason, that Hipparchus showed his -usual love of truth, and his right sense of the responsibility of -his task, in leaving this part of it to future ages. The Theories of -the Sun and Moon, which we have already described, constitute him a -great astronomical discoverer, and justify the reputation he has -always {150} possessed. There is, indeed, no philosopher who is so -uniformly spoken of in terms of admiration. Ptolemy, to whom we owe -our principal knowledge of him, perpetually couples with his name -epithets of praise: he is not only an excellent and careful -observer, but "a[68\3] most truth-loving and labor-loving person," -one who had shown extraordinary sagacity and remarkable desire of -truth in every part of science. Pliny, after mentioning him and -Thales, breaks out into one of his passages of declamatory -vehemence: "Great men! elevated above the common standard of human -nature, by discovering the laws which celestial occurrences obey, -and by freeing the wretched mind of man from the fears which -eclipses inspired--Hail to you and to your genius, interpreters of -heaven, worthy recipients of the laws of the universe, authors of -principles which connect gods and men!" Modern writers have spoken -of Hipparchus with the same admiration; and even the exact but -severe historian of astronomy, Delambre, who bestows his praise so -sparingly, and his sarcasm so generally;--who says[69\3] that it is -unfortunate for the memory of Aristarchus that his work has come to -us entire, and who cannot refer[70\3] to the statement of an eclipse -rightly predicted by Halicon of Cyzicus without adding, that if the -story be true, Halicon was more lucky than prudent;--loses all his -bitterness when he comes to Hipparchus.[71\3] "In Hipparchus," says -he, "we find one of the most extraordinary men of antiquity; the -_very greatest_, in the sciences which require a combination of -observation with geometry." Delambre adds, apparently in the wish to -reconcile this eulogium with the depreciating manner in which he -habitually speaks of all astronomers whose observations are inexact, -"a long period and the continued efforts of many industrious men are -requisite to produce good instruments, but energy and assiduity -depend on the man himself." - -[Note 68\3: _Synt._ ix. 2.] - -[Note 69\3: _Astronomie Ancienne_, i. 75.] - -[Note 70\3: Ib. i. 17.] - -[Note 71\3: Ib. i. 186.] - -Hipparchus was the author of other great discoveries and -improvements in astronomy, besides the establishment of the Doctrine -of Eccentrics and Epicycles; but this, being the greatest advance in -the _theory_ of the celestial motions which was made by the -ancients, must be the leading subject of our attention in the -present work; our object being to discover in what the progress of -real theoretical knowledge consists, and under what circumstances it -has gone on. {151} - - -_Sect._ 2.--_Estimate of the Value of the Theory of Eccentrics and -Epicycles._ - -IT may be useful here to explain the value of the theoretical step -which Hipparchus thus made; and the more so, as there are, perhaps, -opinions in popular circulation, which might lead men to think -lightly of the merit of introducing or establishing the Doctrine of -Epicycles. For, in the first place, this doctrine is now -acknowledged to be false; and some of the greatest men in the more -modern history of astronomy owe the brightest part of their fame to -their having been instrumental in overturning this hypothesis. And, -moreover, in the next place, the theory is not only false, but -extremely perplexed and entangled, so that it is usually looked upon -as a mass of arbitrary and absurd complication. Most persons are -familiar with passages in which it is thus spoken of.[72\3] - - . . . . . He his fabric of the heavens - Hath left to their disputes, perhaps to move - His laughter at their quaint opinions wide; - Hereafter, when they come to model heaven - And calculate the stars, how will they wield - The mighty frame! how build, unbuild, contrive, - To save appearances! how gird the sphere - With centric and eccentric scribbled o'er, - Cycle in epicycle, orb in orb! - -And every one will recollect the celebrated saying of Alphonso X., -king of Castile,[73\3] when this complex system was explained to -him; that "if God had consulted him at the creation, the universe -should have been on a better and simpler plan." In addition to this, -the system is represented as involving an extravagant conception of -the nature of the orbs which it introduces; that they are -crystalline spheres, and that the vast spaces which intervene -between the celestial luminaries are a solid mass, formed by the -fitting together of many masses perpetually in motion; an -imagination which is presumed to be incredible and monstrous. - -[Note 72\3: _Paradise Lost_, viii.] - -[Note 73\3: A. D. 1252.] - -We must endeavor to correct or remove these prejudices, not only in -order that we may do justice to the Hipparchian, or, as it is -usually called, Ptolemaic system of astronomy, and to its founder; -but for another reason, much more important to the purpose of this -work; {152} namely, that we may see how theories may be highly -estimable, though they contain false representations of the real -state of things, and may be extremely useful, though they involve -unnecessary complexity. In the advance of knowledge, the value of -the true part of a theory may much outweigh the accompanying error, -and the use of a rule may be little impaired by its want of -simplicity. The first steps of our progress do not lose their -importance because they are not the last; and the outset of the -journey may require no less vigor and activity than its close. - -That which is true in the Hipparchian theory, and which no -succeeding discoveries have deprived of its value, is the -_Resolution_ of the apparent motions of the heavenly bodies into an -assemblage of circular motions. The test of the truth and reality of -this Resolution is, that it leads to the construction of theoretical -Tables of the motions of the luminaries, by which their places are -given at any time, agreeing nearly with their places as actually -observed. The assumption that these circular motions, thus -introduced, are all exactly uniform, is the fundamental principle of -the whole process. This assumption is, it may be said, false; and we -have seen how fantastic some of the arguments were, which were -originally urged in its favor. But _some_ assumption is necessary, -in order that the motions, at different points of a revolution, may -be somehow connected, that is, in order that we may have any theory -of the motions; and no assumption more simple than the one now -mentioned can be selected. The merit of the theory is this;--that -obtaining the amount of the eccentricity, the place of the apogee, -and, it may be, other elements, from _few_ observations, it deduces -from these, results agreeing with _all_ observations, however -numerous and distant. To express an inequality by means of an -epicycle, implies, not only that there is an inequality, but -further,--that the inequality is at its greatest value at a certain -known place,--diminishes in proceeding from that place by a known -law,--continues its diminution for a known portion of the revolution -of the luminary,--then increases again; and so on: that is, the -introduction of the epicycle represents the inequality of motion, as -completely as it can be represented with respect to its _quantity_. - -We may further illustrate this, by remarking that such a Resolution -of the unequal motions of the heavenly bodies into equable circular -motions, is, in fact, equivalent to the most recent and improved -processes by which modern astronomers deal with such motions. Their -universal method is to resolve all unequal motions into a series of -{153} _terms_, or expressions of partial motions; and these terms -involve _sines_ and _cosines_, that is, certain technical modes of -measuring circular motion, the circular motion having some constant -relation to the time. And thus the problem of the resolution of the -celestial motions into equable circular ones, which was propounded -above two thousand years ago in the school of Plato, is still the -great object of the study of modern astronomers, whether observers -or calculators. - -That Hipparchus should have succeeded in the first great steps of -this resolution for the sun and moon, and should have seen its -applicability in other cases, is a circumstance which gives him one -of the most distinguished places in the roll of great astronomers. -As to the charges or the sneers against the complexity of his -system, to which we have referred, it is easy to see that they are -of no force. As a system of _calculation_, his is not only good, -but, as we have just said, in many cases no better has yet been -discovered. If, when the actual motions of the heavens are -calculated in the best possible way, the process is complex and -difficult, and if we are discontented at this, nature, and not the -astronomer, must be the object of our displeasure. This plea of the -astronomers must be allowed to be reasonable. "We must not be -repelled," says Ptolemy,[74\3] "by the complexity of the hypotheses, -but explain the phenomena as well as we can. If the hypotheses -satisfy each apparent inequality separately, the combination of them -will represent the truth; and why should it appear wonderful to any -that such a complexity should exist in the heavens, when we know -nothing of their nature which entitles us to suppose that any -inconsistency will result?" - -[Note 74\3: _Synt._ xiii. 2.] - -But it may be said, we now know that the motions are more simple -than they were thus represented, and that the Theory of Epicycles -was false, as a conception of the real construction of the heavens. -And to this we may reply, that it does not appear that the best -astronomers of antiquity conceived the cycles and epicycles to have -a material existence. Though the dogmatic philosophers, as the -Aristotelians, appear to have taught that the celestial spheres were -real solid bodies, they are spoken of by Ptolemy as imaginary;[75\3] -and it is clear, from his proof of the identity of the results of -the hypothesis of an eccentric and an epicycle, that they are -intended to pass for no more than geometrical conceptions, in which -view they are true representations of the apparent motions. {154} - -[Note 75\3: Ibid. iii. 3.] - -It is true, that the real motions of the heavenly bodies are simpler -than the apparent motions; and that we, who are in the habit of -representing to our minds their real arrangement, become impatient -of the seeming confusion and disorder of the ancient hypotheses. But -this real arrangement never could have been detected by -philosophers, if the apparent motions had not been strictly examined -and successfully analyzed. How far the connection between the facts -and the true theory is from being obvious or easily traced, any one -may satisfy himself by endeavoring, from a general conception of the -moon's real motions, to discover the rules which regulate the -occurrences of eclipses; or even to explain to a learner, of what -nature the apparent motions of the moon among the stars will be. - -The unquestionable evidence of the merit and value of the Theory of -Epicycles is to be found in this circumstance;--that it served to -embody all the most exact knowledge then extant, to direct -astronomers to the proper methods of making it more exact and -complete, to point out new objects of attention and research; and -that, after doing this at first, it was also able to take in, and -preserve, all the new results of the active and persevering labors -of a long series of Greek, Latin, Arabian, and modern European -astronomers, till a new theory arose which could discharge this -office. It may, perhaps, surprise some readers to be told, that the -author of this next _great_ step in astronomical theory, Copernicus, -adopted the theory of epicycles; that is, he employed that which we -have spoken of as its really valuable characteristic. "We[76\3] must -confess," he says, "that the celestial motions are circular, or -compounded of several circles, since their inequalities observe a -fixed law and recur in value at certain intervals, which could not -be, except that they were circular; for a circle alone can make that -which has been, recur again." - -[Note 76\3: Copernicus. _De Rev._ 1. i. c. 4.] - -In this sense, therefore, the Hipparchian theory was a real and -indestructible truth, which was not rejected, and replaced by -different truths, but was adopted and incorporated into every -succeeding astronomical theory; and which can never cease to be one -of the most important and fundamental parts of our astronomical -knowledge. - -A moment's reflection will show that, in the events just spoken of, -the introduction and establishment of the Theory of Epicycles, those -characteristics were strictly exemplified, which we have asserted to -be the conditions of every real advance in progressive science; -namely, {155} the application of distinct and appropriate Ideas to a -real series of Facts. The distinctness of the geometrical -conceptions which enabled Hipparchus to assign the Orbits of the Sun -and Moon, requires no illustration; and we have just explained how -these ideas combined into a connected whole the various motions and -places of those luminaries. To make this step in astronomy, required -diligence and care, exerted in collecting observations, and -mathematical clearness and steadiness of view, exercised in seeing -and showing that the theory was a successful analysis of them. - - -_Sect._ 3.--_Discovery of the Precession of the Equinoxes._ - -THE same qualities which we trace in the researches of Hipparchus -already examined,--diligence in collecting observations, and -clearness of idea in representing them,--appear also in other -discoveries of his, which we must not pass unnoticed. The Precession -of the Equinoxes, in particular, is one of the most important of -these discoveries. - -The circumstance here brought into notice was a Change of Longitude -of the Fixed Stars. The longitudes of the heavenly bodies, being -measured from the point where the sun's annual path cuts the -equator, will change if that path changes. Whether this happens, -however, is not very easy to decide; for the sun's path among the -stars is made out, not by merely looking at the heavens, but by a -series of inferences from other observable facts. Hipparchus used -for this purpose eclipses of the moon; for these, being exactly -opposite to the sun, afford data in marking out his path. By -comparing the eclipses of his own time with those observed at an -earlier period by Timocharis, he found that the bright star, Spica -Virginis, was six degrees behind the equinoctial point in his own -time, and had been eight degrees behind the same point at an earlier -epoch. The suspicion was thus suggested, that the longitudes of all -the stars increase perpetually; but Hipparchus had too truly -philosophical a spirit to take this for granted. He examined the -places of Regulus, and those of other stars, as he had done those of -Spica; and he found, in all these instances, a change of place which -could be explained by a certain alteration of position in the -circles to which the stars are referred, which alteration is -described as the Precession of the Equinoxes. - -The distinctness with which Hipparchus conceived this change of -relation of the heavens, is manifested by the question which, as we -are told by Ptolemy, he examined and decided;--that this motion of -the {156} heavens takes place about the poles of the ecliptic, and -not about those of the equator. The care with which he collected -this motion from the stars themselves, may be judged of from this, -that having made his first observations for this purpose on Spica -and Regulus, zodiacal stars, his first suspicion was that the stars -of the zodiac alone changed their longitude, which suspicion he -disproved by the examination of other stars. By his processes, the -idea of the nature of the motion, and the evidence of its existence, -the two conditions of a discovery, were fully brought into view. The -scale of the facts which Hipparchus was thus able to reduce to law, -may be in some measure judged of by recollecting that the -precession, from his time to ours, has only carried the stars -through one sign of the zodiac; and that, to complete one revolution -of the sky by the motion thus discovered, would require a period of -25,000 years. Thus this discovery connected the various aspects of -the heavens at the most remote periods of human history; and, -accordingly, the novel and ingenious views which Newton published in -his chronology, are founded on this single astronomical fact, the -Precession of the Equinoxes. - -The two discoveries which have been described, the mode of -constructing Solar and Lunar Tables, and the Precession, were -advances of the greatest importance in astronomy, not only in -themselves, but in the new objects and undertakings which they -suggested to astronomers. The one discovery detected a constant law -and order in the midst of perpetual change and apparent disorder; -the other disclosed mutation and movement perpetually operating -where every thing had been supposed fixed and stationary. Such -discoveries were well adapted to call up many questionings in the -minds of speculative men; for, after this, nothing could be supposed -constant till it had been ascertained to be so by close examination; -and no apparent complexity or confusion could justify the -philosopher in turning away in despair from the task of -simplification. To answer the inquiries thus suggested, new methods -of observing the facts were requisite, more exact and uniform than -those hitherto employed. Moreover, the discoveries which were made, -and others which could not fail to follow in their train, led to -many consequences, required to be reasoned upon, systematized, -completed, enlarged. In short, the _Epoch of Induction_ led, as we -have stated that such epochs must always lead, to a _Period of -Development_, _of Verification_, _Application_, _and Extension_. -{157} - - - -CHAPTER IV. - -SEQUEL TO THE INDUCTIVE EPOCH OF HIPPARCHUS. - - -_Sect._ 1.--_Researches which verified the Theory._ - -THE discovery of the leading Laws of the Solar and Lunar Motions, -and the detection of the Precession, may be considered as the great -positive steps in the Hipparchian astronomy;--the parent -discoveries, from which many minor improvements proceeded. The task -of pursuing the collateral and consequent researches which now -offered themselves,--of bringing the other parts of astronomy up to -the level of its most improved portions,--was prosecuted by a -succession of zealous observers and calculators, first, in the -school of Alexandria, and afterwards in other parts of the world. We -must notice the various labors of this series of astronomers; but we -shall do so very briefly; for the ulterior development of doctrines -once established is not so important an object of contemplation for -our present purpose, as the first conception and proof of those -fundamental truths on which systematic doctrines are founded. Yet -Periods of Verification, as well as Epochs of Induction, deserve to -be attended to; and they can nowhere be studied with so much -advantage as in the history of astronomy. - -In truth, however, Hipparchus did not leave to his successors the -task of pursuing into detail those views of the heavens to which his -discoveries led him. He examined with scrupulous care almost every -part of the subject. We must briefly mention some of the principal -points which were thus settled by him. - -The verification of the laws of the changes which he assigned to the -skies, implied that the condition of the heavens was constant, -except so far as it was affected by those changes. Thus, the -doctrine that the changes of position of the stars were rightly -represented by the precession of the equinoxes, supposed that the -stars were fixed with regard to each other; and the doctrine that -the unequal number of days, in certain subdivisions of months and -years, was adequately explained by the theory of epicycles, assumed -that years and days were always of constant lengths. But Hipparchus -was not content with assuming these bases of his theory, he -endeavored to prove them. {158} - -1. _Fixity of the Stars._--The question necessarily arose after the -discovery of the precession, even if such a question had never -suggested itself before, whether the stars which were called -_fixed_, and to which the motions of the other luminaries are -referred, do really retain constantly the same relative position. In -order to determine this fundamental question, Hipparchus undertook -to construct a _Map_ of the heavens; for though the result of his -survey was expressed in words, we may give this name to his -Catalogue of the positions of the most conspicuous stars. These -positions are described by means of _alineations_; that is, three or -more such stars are selected as can be touched by an apparent -straight line drawn in the heavens. Thus Hipparchus observed that -the southern claw of Cancer, the bright star in the same -constellation which precedes the head of the Hydra, and the bright -star Procyon, were nearly in the same line. Ptolemy quotes this and -many other of the configurations which Hipparchus had noted, in -order to show that the positions of the stars had not changed in the -intermediate time; a truth which the catalogue of Hipparchus thus -gave astronomers the means of ascertaining. It contained 1080 stars. - -The construction of this catalogue of the stars by Hipparchus is an -event of great celebrity in the history of astronomy. Pliny,[77\3] -who speaks of it with admiration as a wonderful and superhuman task -("ausus rem etiam Deo improbam, annumerare posteris stellas"), -asserts the undertaking to have been suggested by a remarkable -astronomical event, the appearance of a new star; "novam stellam et -alium in ævo suo genitam deprehendit; ejusque motu, qua die fulsit, -ad dubitationem est adductus anne hoc sæpius fieret, moverenturque -et eæ quas putamus affixas." There is nothing inherently improbable -in this tradition, but we may observe, with Delambre,[78\3] that we -are not informed whether this new star remained in the sky, or soon -disappeared again. Ptolemy makes no mention of the star or the -story; and his catalogue contains no _bright_ star which is not -found in the "Catasterisms" of Eratosthenes. These Catasterisms were -an enumeration of 475 of the principal stars, according to the -constellations in which they are, and were published about sixty -years before Hipparchus. - -[Note 77\3: _Nat. Hist._ lib. ii. (xxvi.)] - -[Note 78\3: _A. A._ i. 290.] - -2. _Constant Length of Years._--Hipparchus also attempted to -ascertain whether successive years are all of the same length; and -though, with his scrupulous love of accuracy,[79\3] he does not -appear to have {159} thought himself justified in asserting that the -years were always exactly equal, he showed, both by observations of -the time when the sun passed the equinoxes, and by eclipses, that -the difference of successive years, if there were any difference, -must be extremely slight. The observations of succeeding -astronomers, and especially of Ptolemy, confirmed this opinion, and -proved, with certainty, that there is no progressive increase or -diminution in the duration of the year. - -[Note 79\3: Ptolem. _Synt._ iii. 2.] - -3. _Constant Length of Days. Equation of Time._--The equality of -days was more difficult to ascertain than that of years; for the -year is measured, as on a natural scale, by the number of days which -it contains; but the day can be subdivided into hours only by -artificial means; and the mechanical skill of the ancients did not -enable them to attain any considerable accuracy in the measure of -such portions of time; though clepsydras and similar instruments -were used by astronomers. The equality of days could only be proved, -therefore, by the consequences of such a supposition; and in this -manner it appears to have been assumed, as the fact really is, that -the apparent revolution of the stars is accurately uniform, never -becoming either quicker or slower. It followed, as a consequence of -this, that the solar days (or rather the _nycthemers_, compounded of -a night and a day) would be unequal, in consequence of the sun's -unequal motion, thus giving rise to what we now call the _Equation -of Time_,--the interval by which the time, as marked on a dial, is -before or after the time, as indicated by the accurate timepieces -which modern skill can produce. This inequality was fully taken -account of by the ancient astronomers; and they thus in fact assumed -the equality of the sidereal days. - - -_Sect._ 2.--_Researches which did not verify the Theory._ - -SOME of the researches of Hipparchus and his followers fell upon the -weak parts of his theory; and if the observations had been -sufficiently exact, must have led to its being corrected or rejected. - -Among these we may notice the researches which were made concerning -the _Parallax_ of the heavenly bodies, that is, their apparent -displacement by the alteration of position of the observer from one -part of the earth's surface to the other. This subject is treated of -at length by Ptolemy; and there can be no doubt that it was well -examined by Hipparchus, who invented a _parallactic instrument_ for -that purpose. The idea of parallax, as a geometrical possibility, -was indeed too obvious to be overlooked by geometers at any time; -and when the doctrine of the sphere was established, it must have -appeared strange {160} to the student, that every place on the -earth's surface might alike be considered as the centre of the -celestial motions. But if this was true with respect to the motions -of the fixed stars, was it also true with regard to those of the sun -and moon? The displacement of the sun by parallax is so small, that -the best observers among the ancients could never be sure of its -existence; but with respect to the moon, the case is different. She -may be displaced by this cause to the amount of twice her own -breadth, a quantity easily noticed by the rudest process of -instrumental observation. The law of the displacement thus produced -is easily obtained by theory, the globular form of the earth being -supposed known; but the amount of the displacement depends upon the -distance of the moon from the earth, and requires at least one good -observation to determine it. Ptolemy has given a table of the -effects of parallax, calculated according to the apparent altitude -of the moon, assuming certain supposed distances; these distances, -however, do not follow the real law of the moon's distances, in -consequence of their being founded upon the Hypothesis of the -Eccentric and Epicycle. - -In fact this Hypothesis, though a very close representation of the -truth, so far as the _positions_ of the luminaries are concerned, -fails altogether when we apply it to their _distances_. The radius -of the epicycle, or the eccentricity of the eccentric, are -determined so as to satisfy the observations of the apparent -_motions_ of the bodies; but, inasmuch as the hypothetical motions -are different altogether from the real motions, the Hypothesis does -not, at the same time, satisfy the observations of the _distances_ -of the bodies, if we are able to make any such observations. - -Parallax is one method by which the distances of the moon, at -different times, may be compared; her Apparent Diameters afford -another method. Neither of these modes, however, is easily capable -of such accuracy as to overturn at once the Hypothesis of epicycles; -and, accordingly, the Hypothesis continued to be entertained in -spite of such measures; the measures being, indeed, in some degree -falsified in consequence of the reigning opinion. In fact, however, -the imperfection of the methods of measuring parallax and magnitude, -which were in use at this period, was such, their results could not -lead to any degree of conviction deserving to be set in opposition -to a theory which was so satisfactory with regard to the more -certain observations, namely, those of the motions. - -The Eccentricity, or the Radius of the Epicycle, which would satisfy -{161} the inequality of the _motions_ of the moon, would, in fact, -double the inequality of the _distances_. The Eccentricity of the -moon's orbit is determined by Ptolemy as 1/12 of the radius of the -orbit; but its real amount is only half as great; this difference is -a necessary consequence of the supposition of uniform circular -motions, on which the Epicyclic Hypothesis proceeds. - -We see, therefore, that this part of the Hipparchian theory carries -in itself the germ of its own destruction. As soon as the art of -celestial measurement was so far perfected, that astronomers could -be sure of the apparent diameter of the moon within 1/30 or 1/40 of -the whole, the inconsistency of the theory with itself would become -manifest. We shall see, hereafter, the way in which this -inconsistency operated; in reality a very long period elapsed before -the methods of observing were sufficiently good to bring it clearly -into view. - - -_Sect._ 3._--Methods of Observation of the Greek Astronomers._ - -WE must now say a word concerning the Methods above spoken of. Since -one of the most important tasks of verification is to ascertain with -accuracy the magnitude of the quantities which enter, as elements, -into the theory which occupies men during the period; the -improvement of instruments, and the methods of observing and -experimenting, are principal features in such periods. We shall, -therefore, mention some of the facts which bear upon this point. - -The estimation of distances among the stars by the eye, is an -extremely inexact process. In some of the ancient observations, -however, this appears to have been the method employed; and stars -are described as being _a cubit_ or _two cubits_ from other stars. -We may form some notion of the scale of this kind of measurement, -from what Cleomedes remarks,[80\3] that the sun appears to be about -a foot broad; an opinion which he confutes at length. - -[Note 80\3: Del. _A. A._ i. 222.] - -A method of determining the positions of the stars, susceptible of a -little more exactness than the former, is the use of _alineations_, -already noticed in speaking of Hipparchus's catalogue. Thus, a -straight line passing through two stars of the Great Bear passes -also through the pole-star; this is, indeed, even now a method -usually employed to enable us readily to fix on the pole-star; and -the two stars β and α of Ursa Major, are hence often called "the -pointers." {162} - -But nothing like accurate measurements of any portions of the sky -were obtained, till astronomers adopted the method of making visual -coincidences of the objects with the instruments, either by means of -_shadows_ or of _sights_. - -Probably the oldest and most obvious measurements of the positions -of the heavenly bodies were those in which the elevation of the sun -was determined by comparing the length of the shadow of an upright -staff or _gnomon_, with the length of the staff itself. It -appears,[81\3] from a memoir of Gautil, first printed in the -_Connaissance des Temps_ for 1809, that, at the lower town of -Loyang, now called Hon-anfou, Tchon-kong found the length of the -shadow of the gnomon, at the summer solstice, equal to one foot and -a half, the gnomon itself being eight feet in length. This was about -1100 B. C. The Greeks, at an early period, used the same method. -Strabo says[82\3] that "Byzantium and Marseilles are on the same -parallel of latitude, because the shadows at those places have the -same proportion to the gnomon, according to the statement of -Hipparchus, who follows Pytheas." - -[Note 81\3: Lib. U. K. _Hist. Ast._ p. 5.] - -[Note 82\3: Del. _A. A._ i. 257.] - -But the relations of position which astronomy considers, are, for -the most part, angular distances; and these are most simply -expressed by the intercepted portion of a circumference described -about the angular point. The use of the gnomon might lead to the -determination of the angle by the graphical methods of geometry; but -the numerical expression of the circumference required some progress -in trigonometry; for instance, a table of the tangents of angles. - -Instruments were soon invented for measuring angles, by means of -circles, which had a border or _limb_, divided into equal parts. The -whole circumference was divided into 360 _degrees_: perhaps because -the circles, first so divided, were those which represented the -sun's annual path; one such degree would be the sun's daily advance, -more nearly than any other convenient aliquot part which could be -taken. The position of the sun was determined by means of the shadow -of one part of the instrument upon the other. The most ancient -instrument of this kind appears to be the _Hemisphere of Berosus_. A -hollow hemisphere was placed with its rim horizontal, and a style -was erected in such a manner that the extremity of the style was -exactly at the centre of the sphere. The shadow of this extremity, -on the concave surface, had the same position with regard to the -lowest point of the sphere which the sun had with regard to the -highest point of the heavens. {163} But this instrument was in fact -used rather for dividing the day into portions of time than for -determining position. - -Eratosthenes[83\3] observed the amount of the obliquity of the sun's -path to the equator: we are not informed what instruments he used -for this purpose; but he is said to have obtained, from the -munificence of Ptolemy Euergetes, two _Armils_, or instruments -composed of circles, which were placed in the portico at Alexandria, -and long used for observations. If a circular rim or hoop were -placed so as to coincide with the plane of the equator, the inner -concave edge would be enlightened by the sun's rays which came under -the front edge, when the sun was south of the equator, and by the -rays which came over the front edge, when the sun was north of the -equator: the moment of the transition would be the time of the -equinox. Such an instrument appears to be referred to by Hipparchus, -as quoted by Ptolemy.[84\3] "The circle of copper, which stands at -Alexandria in what is called the Square Porch, appears to mark, as -the day of the equinox, that on which the concave surface begins to -be enlightened from the other side." Such an instrument was called -an _equinoctial armil_. - -[Note 83\3: Delambre, _A. A._ i. 86.] - -[Note 84\3: Ptol. _Synt._ iii. 2.] - -A _solstitial armil_ is described by Ptolemy, consisting of two -circular rims, one sliding round within the other, and the inner one -furnished with two pegs standing out from its surface at right -angles, and diametrically opposite to each other. These circles -being fixed in the plane of the meridian, and the inner one turned, -till, at noon, the shadow of the peg in front falls upon the peg -behind, the position of the sun at noon would be determined by the -degrees on the outer circle. - -In calculation, the degree was conceived to be divided into 60 -_minutes_, the minute into 60 _seconds_, and so on. But in practice -it was impossible to divide the limb of the instrument into parts so -small. The armils of Alexandria were divided into no parts smaller -than sixths of degrees, or divisions of 10 minutes. - -The angles, observed by means of these divisions, were expressed as -a fraction of the circumference. Thus Eratosthenes stated the -interval between the tropics to be 11/83 of the circumference.[85\3] - -[Note 85\3: Delambre, _A. A._ i. 87. It is probable that his -observation gave him 47⅔ degrees. The fraction 47⅔/360 = 143/1080 = -11 ∙ 13/1080 = 11/(83+1/13), which is very nearly 11/83.] - -It was soon remarked that the whole circumference of the circle -{164} was not wanted for such observations. Ptolemy[86\3] says that -he found it more convenient to observe altitudes by means of a -square flat piece of stone or wood, with a _quadrant_ of a circle -described on one of its flat faces, about a centre near one of the -angles. A peg was placed at the centre, and one of the extreme radii -of the quadrant being perpendicular to the horizon, the elevation of -the sun above the horizon was determined by observing the point of -the arc of the quadrant on which the shadow of the peg fell. - -[Note 86\3: _Synt._ i. 1.] - -As the necessity of accuracy in the observations was more and more -felt, various adjustments of such instruments were practised. The -instruments were placed in the meridian by means of a _meridian -line_ drawn by astronomical methods on the floor on which they -stood. The plane of the instrument was made vertical by means of a -plumb-line: the bounding radius, from which angles were measured, -was also adjusted by the _plumb-line_.[87\3] - -[Note 87\3: The curvature of the plane of the circle, by warping, -was noticed. Ptol. iii. 2. p. 155, observes that his equatorial -circle was illuminated on the hollow side twice in the same day. (He -did not know that this might arise from refraction.)] - -In this manner, the places of the sun and of the moon could be -observed by means of the shadows which they cast. In order to -observe the stars,[88\3] the observer looked along the face of the -circle of the armil, so as to see its two edges apparently brought -together, and the star apparently touching them.[89\3] - -[Note 88\3: Delamb. _A. A._ i. 185.] - -[Note 89\3: Ptol. _Synt._ i. 1. Ὥσπερ κεκολλήμενος ἀμφοτέραις αὐτῶν -ταῖς ἐπιφανείαις ὁ ἀστὴρ ἐν τῷ δι' αὐτῶν ἐπιπέδῳ διοπτεύηται.] - -It was afterwards found important to ascertain the position of the -sun with regard to the ecliptic: and, for this purpose, an -instrument, called an _astrolabe_, was invented, of which we have a -description in Ptolemy.[90\3] This also consisted of circular rims, -movable within one another, or about poles; and contained circles -which were to be brought into the position of the ecliptic, and of a -plane passing through the sun and the poles of the ecliptic. The -position of the moon with regard to the ecliptic, and its position -in longitude with regard to the sun or a star, were thus determined. - -[Note 90\3: _Synt._ v. 1.] - -The astrolabe continued long in use, but not so long as the quadrant -described by Ptolemy; this, in a larger form, is the _mural -quadrant_, which has been used up to the most recent times. - -It may be considered surprising,[91\3] that Hipparchus, after having -{165} observed, for some time, right ascensions and declinations, -quitted equatorial armils for the astrolabe, which immediately -refers the stars to the ecliptic. He probably did this because, -after the discovery of precession, he found the latitudes of the -stars constant, and wanted to ascertain their motion in longitude. - -[Note 91\3: Del. _A. A._ 181.] - -To the above instruments, may be added the _dioptra_, and the -_parallactic instrument_ of Hipparchus and Ptolemy. In the latter, -the distance of a star from the zenith was observed by looking -through two sights fixed in a rule, this being annexed to another -rule, which was kept in a vertical position by a plumb-line; and the -angle between the two rules was measured. - -The following example of an observation, taken from Ptolemy, may -serve to show the form in which the results of the instruments, just -described, were usually stated.[92\3] - -[Note 92\3: Del. _A. A._ ii. 248.] - -"In the 2d year of Antoninus, the 9th day of Pharmouthi, the sun -being near setting, the last division of Taurus being on the -meridian (that is, 5½ equinoctial hours after noon), the moon was in -3 degrees of Pisces, by her distance from the sun (which was 92 -degrees, 8 minutes); and half an hour after, the sun being set, and -the quarter of Gemini on the meridian, Regulus appeared, by the -other circle of the astrolabe, 57½ degrees more forwards than the -moon in longitude." From these data the longitude of Regulus is -calculated. - -From what has been said respecting the observations of the -Alexandrian astronomers, it will have been seen that their -instrumental observations could not be depended on for any close -accuracy. This defect, after the general reception of the -Hipparchian theory, operated very unfavorably on the progress of the -science. If they could have traced the moon's place distinctly from -day to day, they must soon have discovered all the inequalities -which were known to Tycho Brahe; and if they could have measured her -parallax or her diameter with any considerable accuracy, they must -have obtained a confutation of the epicycloidal form of her orbit. -By the badness of their observations, and the imperfect agreement of -these with calculation, they not only were prevented making such -steps, but were led to receive the theory with a servile assent and -an indistinct apprehension, instead of that rational conviction and -intuitive clearness which would have given a progressive impulse to -their knowledge. {166} - - -_Sect._ 4.--_Period from Hipparchus to Ptolemy._ - -WE have now to speak of the cultivators of astronomy from the time -of Hipparchus to that of Ptolemy, the next great name which occurs -in the history of this science; though even he holds place only -among those who verified, developed, and extended the theory of -Hipparchus. The astronomers who lived in the intermediate time, -indeed, did little, even in this way; though it might have been -supposed that their studies were carried on under considerable -advantages, inasmuch as they all enjoyed the liberal patronage of -the kings of Egypt.[93\3] The "divine school of Alexandria," as it -is called by Synesius, in the fourth century, appears to have -produced few persons capable of carrying forwards, or even of -verifying, the labors of its great astronomical teacher. The -mathematicians of the school wrote much, and apparently they -observed sometimes; but their observations are of little value; and -their books are expositions of the theory and its geometrical -consequences, without any attempt to compare it with observation. -For instance, it does not appear that any one verified the -remarkable discovery of the precession, till the time of Ptolemy, -250 years after; nor does the statement of this motion of the -heavens appear in the treatises of the intermediate writers; nor -does Ptolemy quote a single observation of any person made in this -long interval of time; while his references to those of Hipparchus -are perpetual; and to those of Aristyllus and Timocharis, and of -others, as Conon, who preceded Hipparchus, are not unfrequent. - -[Note 93\3: Delamb. _A. A._ ii. 240.] - -This Alexandrian period, so inactive and barren in the history of -science, was prosperous, civilized, and literary; and many of the -works which belong to it are come down to us, though those of -Hipparchus are lost. We have the "Uranologion" of Geminus,[94\3] a -systematic treatise on Astronomy, expounding correctly the -Hipparchian Theories and their consequences, and containing a good -account of the use of the various Cycles, which ended in the -adoption of the Calippic Period. We have likewise "The Circular -Theory of the Celestial Bodies" of Cleomedes,[95\3] of which the -principal part is a development of the doctrine of the sphere, -including the consequences of the globular form of the earth. We -have also another work on "Spherics" by Theodosius of -Bithynia,[96\3] which contains some of the most important -propositions of the subject, and has been used as a book of {167} -instruction even in modern times. Another writer on the same subject -is Menelaus, who lived somewhat later, and whose Three Books on -Spherics still remain. - -[Note 94\3: B. C. 70.] - -[Note 95\3: B. C. 60.] - -[Note 96\3: B. C. 50.] - -One of the most important kinds of deduction from a geometrical -theory, such as that of the doctrine of the sphere, or that of -epicycles, is the calculation of its numerical results in particular -cases. With regard to the latter theory, this was done in the -construction of Solar and Lunar Tables, as we have already seen; and -this process required the formation of a _Trigonometry_, or system -of rules for calculating the relations between the sides and angles -of triangles. Such a science had been formed by Hipparchus, who -appears to be the author of every great step in ancient -astronomy.[97\3] He wrote a work in twelve books, "On the -Construction of the Tables of Chords of Arcs;" such a table being -the means by which the Greeks solved their triangles. The Doctrine -of the Sphere required, in like manner, a _Spherical Trigonometry_, -in order to enable mathematicians to calculate its results; and this -branch of science also appears to have been formed by -Hipparchus,[98\3] who gives results that imply the possession of -such a method. Hypsicles, who was a contemporary of Ptolemy, also -made some attempts at the solution of such problems: but it is -extraordinary that the writers whom we have mentioned as coming -after Hipparchus, namely, Theodosius, Cleomedes, and Menelaus, do -not even mention the calculation of triangles,[99\3] either plain or -spherical; though the latter writer[100\3] is said to have written -on "the Table of Chords," a work which is now lost. - -[Note 97\3: Delamb. _A. A._ ii. 37.] - -[Note 98\3: _A. A._ i. 117.] - -[Note 99\3: _A. A._ i. 249.] - -[Note 100\3: _A. A._ ii. 37.] - -We shall see, hereafter, how prevalent a disposition in literary -ages is that which induces authors to become commentators. This -tendency showed itself at an early period in the school of -Alexandria. Aratus,[101\3] who lived 270 B. C. at the court of -Antigonus, king of Macedonia, described the celestial constellations -in two poems, entitled "Phænomena," and "Prognostics." These poems -were little more than a versification of the treatise of Eudoxus on -the acronycal and heliacal risings and settings of the stars. The -work was the subject of a comment by Hipparchus, who perhaps found -this the easiest way of giving connection and circulation to his -knowledge. Three Latin translations of this poem gave the Romans the -means of becoming acquainted with it: the first is by Cicero, of -which we have numerous fragments {168} extant;[102\3] Germanicus -Cæsar, one of the sons-in-law of Augustus, also translated the poem, -and this translation remains almost entire. Finally, we have a -complete translation by Avienus.[103\3] The "Astronomica" of -Manilius, the "Poeticon Astronomicon" of Hyginus, both belonging to -the time of Augustus, are, like the work of Aratus, poems which -combine mythological ornament with elementary astronomical -exposition; but have no value in the history of science. We may pass -nearly the same judgment upon the explanations and declamations of -Cicero, Seneca, and Pliny, for they do not apprise us of any -additions to astronomical knowledge; and they do not always indicate -a very clear apprehension of the doctrines which the writers adopt. - -[Note 101\3: _A. A._ i. 74.] - -[Note 102\3: Two copies of this translation, illustrated by drawings -of different ages, one set Roman, and the other Saxon, according to -Mr. Ottley, are described in the _Archæologia_, vol. xviii.] - -[Note 103\3: Montucla, i. 221.] - -Perhaps the most remarkable feature in the two last-named writers, -is the declamatory expression of their admiration for the -discoverers of physical knowledge; and in one of them, Seneca, the -persuasion of a boundless progress in science to which man was -destined. Though this belief was no more than a vague and arbitrary -conjecture, it suggested other conjectures in detail, some of which, -having been verified, have attracted much notice. For instance, in -speaking of comets,[104\3] Seneca says, "The time will come when -those things which are now hidden shall be brought to light by time -and persevering diligence. Our posterity will wonder that we should -be ignorant of what is so obvious." "The motions of the planets," he -adds, "complex and seemingly confused, have been reduced to rule; -and some one will come hereafter, who will reveal to us the paths of -comets." Such convictions and conjectures are not to be admired for -their wisdom; for Seneca was led rather by enthusiasm, than by any -solid reasons, to entertain this opinion; nor, again, are they to be -considered as merely lucky guesses, implying no merit; they are -remarkable as showing how the persuasion of the universality of law, -and the belief of the probability of its discovery by man, grow up -in men's minds, when speculative knowledge becomes a prominent -object of attention. - -[Note 104\3: Seneca, _Qu. N._ vii. 25.] - -An important practical application of astronomical knowledge was -made by Julius Cæsar, in his correction of the calendar, which we -have already noticed; and this was strictly due to the Alexandrian -School: Sosigenes, an astronomer belonging to that school, came from -Egypt to Rome for the purpose. {169} - - -_Sect._ 5.--_Measures of the Earth._ - -THERE were, as we have said, few attempts made, at the period of -which we are speaking, to improve the accuracy of any of the -determinations of the early Alexandrian astronomers. One question -naturally excited much attention at all times, the _magnitude_ of -the earth, its figure being universally acknowledged to be a globe. -The Chaldeans, at an earlier period, had asserted that a man, -walking without stopping, might go round the circuit of the earth in -a year; but this might be a mere fancy, or a mere guess. The attempt -of Eratosthenes to decide this question went upon principles -entirely correct. Syene was situated on the tropic; for there, on -the day of the solstice, at noon, objects cast no shadow; and a well -was enlightened to the bottom by the sun's rays. At Alexandria, on -the same day, the sun was, at noon, distant from the zenith by a -fiftieth part of the circumference. Those two cities were north and -south from each other: and the distance had been determined, by the -royal overseers of the roads, to be 5000 stadia. This gave a -circumference of 250,000 stadia to the earth, and a radius of about -40,000. Aristotle[105\3] says that the mathematicians make the -circumference 400,000 stadia. Hipparchus conceived that the measure -of Eratosthenes ought to be increased by about one-tenth.[106\3] -Posidonius, the friend of Cicero, made another attempt of the same -kind. At Rhodes, the star Canopus but just appeared above the -horizon; at Alexandria, the same star rose to an altitude of 1/48th -of the circumference; the direct distance on the meridian was 5000 -stadia, which gave 240,000 for the whole circuit. We cannot look -upon these measures as very precise; the stadium employed is not -certainly known; and no peculiar care appears to have been bestowed -on the measure of the direct distance. - -[Note 105\3: _De Cœlo_, ii. ad fin.] - -[Note 106\3: Plin. ii. (cviii.)] - -When the Arabians, in the ninth century, came to be the principal -cultivators of astronomy, they repeated this observation in a manner -more suited to its real importance and capacity of exactness. Under -the Caliph Almamon,[107\3] the vast plain of Singiar, in -Mesopotamia, was the scene of this undertaking. The Arabian -astronomers there divided themselves into two bands, one under the -direction of Chalid ben Abdolmalic, and the other having at its head -Alis ben Isa. These two parties proceeded, the one north, the other -south, determining the distance by the actual application of their -measuring-rods to the ground, {170} till each was found, by -astronomical observation, to be a degree from the place at which -they started. It then appeared that these terrestrial degrees were -respectively 56 miles, and 56 miles and two-thirds, the mile being -4000 cubits. In order to remove all doubt concerning the scale of -this measure, we are informed that the cubit is that called the -black cubit, which consists of 27 inches, each inch being the -thickness of six grains of barley. - -[Note 107\3: Montu. 357.] - - -_Sect._ 6.--_Ptolemy's Discovery of Evection._ - -BY referring, in this place, to the last-mentioned measure of the -earth, we include the labors of the Arabian as well as the -Alexandrian astronomers, in the period of mere detail, which forms -the sequel to the great astronomical revolution of the Hipparchian -epoch. And this period of verification is rightly extended to those -later times; not merely because astronomers were then still employed -in determining the magnitude of the earth, and the amount of other -elements of the theory,--for these are some of their employments to -the present day,--but because no great intervening discovery marks a -new epoch, and begins a new period;--because no great revolution in -the theory added to the objects of investigation, or presented them -in a new point of view. This being the case, it will be more -instructive for our purpose to consider the general character and -broad intellectual features of this period, than to offer a useless -catalogue of obscure and worthless writers, and of opinions either -borrowed or unsound. But before we do this, there is one writer whom -we cannot leave undistinguished in the crowd; since his name is more -celebrated even than that of Hipparchus; his works contain -ninety-nine hundredths of what we know of the Greek astronomy; and -though he was not the author of a new theory, he made some very -remarkable steps in the verification, correction, and extension of -the theory which he received. I speak of Ptolemy, whose work, "The -Mathematical Construction" (of the heavens), contains a complete -exposition of the state of astronomy in his time, the reigns of -Adrian and Antonine. This book is familiarly known to us by a term -which contains the record of our having received our first knowledge -of it from the Arabic writers. The "_Megiste_ Syntaxis," or Great -Construction, gave rise, among them, to the title _Al Magisti_, or -_Almagest_, by which the work is commonly described. As a -mathematical exposition of the Theory of Epicycles and Eccentrics, -of the observations and calculations which were employed in {171} -order to apply this theory to the sun, moon, and planets, and of the -other calculations which are requisite, in order to deduce the -consequences of this theory, the work is a splendid and lasting -monument of diligence, skill, and judgment. Indeed, all the other -astronomical works of the ancients hardly add any thing whatever to -the information we obtain from the Almagest; and the knowledge which -the student possesses of the ancient astronomy must depend mainly -upon his acquaintance with Ptolemy. Among other merits, Ptolemy has -that of giving us a very copious account of the manner in which -Hipparchus established the main points of his theories; an account -the more agreeable, in consequence of the admiration and enthusiasm -with which this author everywhere speaks of the great master of the -astronomical school. - -In our present survey of the writings of Ptolemy, we are concerned -less with his exposition of what had been done before him, than with -his own original labors. In most of the branches of the subject, he -gave additional exactness to what Hipparchus had done; but our main -business, at present, is with those parts of the Almagest which -contain new steps in the application of the Hipparchian hypothesis. -There are two such cases, both very remarkable,--that of the moon's -_Evection_, and that of the _Planetary Motions_. - -The law of the moon's anomaly, that is, of the leading and obvious -inequality of her motion, could be represented, as we have seen, -either by an eccentric or an epicycle; and the amount of this -inequality had been collected by observations of eclipses. But -though the hypothesis of an epicycle, for instance, would bring the -moon to her proper place, so far as eclipses could show it, that is, -at new and full moon, this hypothesis did not rightly represent her -motions at other points of her course. This appeared, when Ptolemy -set about measuring her distances from the sun at different times. -"These," he[108\3] says, "sometimes agreed, and sometimes -disagreed." But by further attention to the facts, a rule was -detected in these differences. "As my knowledge became more complete -and more connected, so as to show the order of this new inequality, -I perceived that this difference was small, or nothing, at new and -full moon; and that at both the _dichotomies_ (when the moon is half -illuminated) it was small, or nothing, if the moon was at the apogee -or perigee of the epicycle, and was greatest when she was in the -middle of the interval, and therefore when the first {172} inequality -was greatest also." He then adds some further remarks on the -circumstances according to which the moon's place, as affected by -this new inequality, is before or behind the place, as given by the -epicyclical hypothesis. - -[Note 108\3: _Synth._ v. 2.] - -Such is the announcement of the celebrated discovery of the moon's -second inequality, afterwards called (by Bullialdus) the _Evection_. -Ptolemy soon proceeded to represent this inequality by a combination -of circular motions, uniting, for this purpose, the hypothesis of an -epicycle, already employed to explain the first inequality, with the -hypothesis of an eccentric, in the circumference of which the centre -of the epicycle was supposed to move. The mode of combining these -was somewhat complex; more complex we may, perhaps, say, than was -absolutely requisite;[109\3] the apogee of the eccentric moved -backwards, or contrary to the order of the signs, and the centre of -the epicycle moved forwards nearly twice as fast upon the -circumference of the eccentric, so as to reach a place nearly, but -not exactly, the same, as if it had moved in a concentric instead of -an eccentric path. Thus the centre of the epicycle went twice round -the eccentric in the course of one month: and in this manner it -satisfied the condition that it should vanish at new and full moon, -and be greatest when the moon was in the quarters of her monthly -course.[110\3] - -[Note 109\3: If Ptolemy had used the hypothesis of an eccentric -instead of an epicycle for the first inequality of the moon, an -epicycle would have represented the second inequality more simply -than his method did.] - -[Note 110\3: I will insert here the explanation which my German -translator, the late distinguished astronomer Littrow, has given of -this point. The Rule of this Inequality, the Evection, may be most -simply expressed thus. If _a_ denote the excess of the Moon's -Longitude over the Sun's, and _b_ the Anomaly of the Moon reckoned -from her Perigee, the Evection is equal to 1°. 3. sin (2_a_ - _b_). -At New and Full Moon, _a_ is 0 or 180°, and thus the Evection is -- 1°.3.sin _b_. At both quarters, or dichotomies, _a_ is 90° or 270°, -and consequently the Evection is + 1°.3 . sin _b_. The Moon's -Elliptical Equation of the centre is at all points of her orbit -equal to 6°.3.sin _b_. The Greek Astronomers before Ptolemy observed -the moon only at the time of eclipses; and hence they necessarily -found for the sum of these two greatest inequalities of the moon's -motion the quantity 6°.3. sin _b_ - 1°.3.sin _b_, or 5°.sin _b_: and -as they took this for the moon's equation of the centre, which -depends upon the eccentricity of the moon's orbit, we obtain from -this too small equation of the centre, an eccentricity also smaller -than the truth. Ptolemy, who first observed the moon in her -quarters, found for the sum of those Inequalities at those points -the quantity 6°.3.sin _b_ + 1°.3.sin _b_, or 7°.6.sin _b_; and thus -made the eccentricity of the moon as much too great at the quarters -as the observers of eclipses had made it too small. He hence -concluded that the eccentricity of the Moon's orbit is variable, -which is not the case.] - -The discovery of the Evection, and the reduction of it to the {173} -epicyclical theory, was, for several reasons, an important step in -astronomy; some of these reasons may be stated. - -1. It obviously suggested, or confirmed, the suspicion that the -motions of the heavenly bodies might be subject to _many_ -inequalities:--that when one set of anomalies had been discovered -and reduced to rule, another set might come into view;--that the -discovery of a rule was a step to the discovery of deviations from -the rule, which would require to be expressed in other rules;--that -in the application of theory to observation, we find, not only the -_stated phenomena_, for which the theory does account, but also -_residual phenomena_, which remain unaccounted for, and stand out -beyond the calculation;--that thus nature is not simple and regular, -by conforming to the simplicity and regularity of our hypotheses, -but leads us forwards to apparent complexity, and to an accumulation -of rules and relations. A fact like the Evection, explained by an -Hypothesis like Ptolemy's, tended altogether to discourage any -disposition to guess at the laws of nature from mere ideal views, or -from a few phenomena. - -2. The discovery of Evection had an importance which did not come -into view till long afterwards, in being the first of a numerous -series of inequalities of the moon, which results from the -_Disturbing Force_ of the sun. These inequalities were successfully -discovered; and led finally to the establishment of the law of -universal gravitation. The moon's first inequality arises from a -different cause;--from the same cause as the inequality of the sun's -motion;--from the motion in an ellipse, so far as the central -attraction is undisturbed by any other. This first inequality is -called the Elliptic Inequality, or, more usually, the _Equation of -the Centre_.[111\3] All the planets have such inequalities, but the -Evection is peculiar to the moon. The discovery of other -inequalities of the moon's motion, the Variation and Annual -Equation, made an immediate sequel in the order of the subject to -{174} the discoveries of Ptolemy, although separated by a long -interval of time; for these discoveries were only made by Tycho -Brahe in the sixteenth century. The imperfection of astronomical -instruments was the great cause of this long delay. - -[Note 111\3: The Equation of the Centre is the difference between -the place of the Planet in its elliptical orbit, and that place -which a Planet would have, which revolved uniformly round the Sun as -a centre in a circular orbit in the same time. An imaginary Planet -moving in the manner last described, is called the _mean_ Planet, -while the actual Planet which moves in the ellipse is called the -_true_ Planet. The Longitude of the mean Planet at a given time is -easily found, because its motion is uniform. By adding to it the -Equation of the Centre, we find the Longitude of the true Planet, -and thus, its place in its orbit.--_Littrow's Note_. - -I may add that the word _Equation_, used in such cases, denotes in -general a quantity which must be added to or subtracted from a mean -quantity, to make it _equal_ to the true quantity; or rather, a -quantity which must be added to or subtracted from a variably -increasing quantity to make it increase _equably_.] - -3. The Epicyclical Hypothesis was found capable of accommodating -itself to such new discoveries. These new inequalities could be -represented by new combinations of eccentrics and epicycles: all the -real and imaginary discoveries by astronomers, up to Copernicus, -were actually embodied in these hypotheses; Copernicus, as we have -said, did not reject such hypotheses; the lunar inequalities which -Tycho detected might have been similarly exhibited; and even -Newton[112\3] represents the motion of the moon's apogee by means of -an epicycle. As a mode of expressing the law of the irregularity, -and of calculating its results in particular cases, the epicyclical -theory was capable of continuing to render great service to -astronomy, however extensive the progress of the science might be. -It was, in fact, as we have already said, the modern process of -representing the motion by means of a series of circular functions. - -[Note 112\3: _Principia_, lib. iii. prop. xxxv.] - -4. But though the doctrine of eccentrics and epicycles was thus -admissible as an Hypothesis, and convenient as a means of expressing -the laws of the heavenly motions, the successive occasions on which it -was called into use, gave no countenance to it as a Theory; that is, -as a true view of the nature of these motions, and their causes. By -the steps of the progress of this Hypothesis, it became more and more -complex, instead of becoming more simple, which, as we shall see, was -the course of the true Theory. The notions concerning the position and -connection of the heavenly bodies, which were suggested by one set of -phenomena, were not confirmed by the indications of another set of -phenomena; for instance, those relations of the epicycles which were -adopted to account for the Motions of the heavenly bodies, were not -found to fall in with the consequences of their apparent Diameters and -Parallaxes. In reality, as we have said, if the relative distances of -the sun and moon at different times could have been accurately -determined, the Theory of Epicycles must have been forthwith -overturned. The insecurity of such measurements alone maintained the -theory to later times.[113\3] {175} - -[Note 113\3: The alteration of the apparent diameter of the moon is -so great that it cannot escape us, even with very moderate -instruments. This apparent diameter contains, when the moon is -nearest the earth, 2010 seconds; when she is furthest off 1762 -seconds; that is, 248 seconds, or 4 minutes 8 seconds, less than in -the former case. [The two quantities are in the proportion of 8 to -7, nearly.]--_Littrow's Note_.] - - -_Sect._ 7.--_Conclusion of the History of Greek Astronomy._ - -I MIGHT now proceed to give an account of Ptolemy's other great -step, the determination of the Planetary Orbits; but as this, though -in itself very curious, would not illustrate any point beyond those -already noticed, I shall refer to it very briefly. The planets all -move in ellipses about the sun, as the moon moves about the earth; -and as the sun apparently moves about the earth. They will therefore -each have an Elliptic Inequality or Equation of the centre, for the -same reason that the sun and moon have such inequalities. And this -inequality may be represented, in the cases of the planets, just as -in the other two, by means of an eccentric; the epicycle, it will be -recollected, had already been used in order to represent the more -obvious changes of the planetary motions. To determine the amount of -the Eccentricities and the places of the Apogees of the planetary -orbits, was the task which Ptolemy undertook; Hipparchus, as we have -seen, having been destitute of the observations which such a process -required. The determination of the Eccentricities in these cases -involved some peculiarities which might not at first sight occur to -the reader. The **elcliptical motion of the planets takes place about -the sun; but Ptolemy considered their movements as altogether -independent of the sun, and referred them to the earth alone; and -thus the apparent eccentricities which he had to account for, were -the compound result of the Eccentricity of the earth's orbit, and of -the proper eccentricity of the orbit of the Planet. He explained -this result by the received mechanism of an eccentric _Deferent_, -carrying an Epicycle; but the motion in the Deferent is uniform, not -about the centre of the circle, but about another point, the -_Equant_. Without going further into detail, it may be sufficient to -state that, by a combination of Eccentrics and Epicycles, he did -account for the leading features of these motions; and by using his -own observations, compared with more ancient ones (for instance, -those of Timocharis for Venus), he was able to determine the -Dimensions and Positions of the orbits.[114\3] {176} - -[Note 114\3: Ptolemy determined the Radius and the Periodic Time of -his two circles for each Planet in the following manner: For the -_inferior_ Planets, that is, Mercury and Venus, he took the Radius of -the Deferent equal to the Radius of the Earth's orbit, and the Radius -of the Epicycle equal to that of the Planet's orbit. For these -Planets, according to his assumption, the Periodic Time of the Planet -in its Epicycle was to the Periodic Time of the Epicyclical Centre on -the Deferent, as the _synodical_ Revolution of the Planet to the -_tropical_ Revolution of the Earth above the Sun. For the three -_superior_ Planets, Mars, Jupiter, and Saturn, the Radius of the -Deferent was equal to the Radius of the Planet's orbit, and the Radius -of the Epicycle was equal to the Radius of the Earth's orbit; the -Periodic Time on the Planet in its Epicycle was to the Periodic Time -of the Epicyclical Centre on the Deferent, as the _synodical_ -Revolution of the Planet to the _tropical_ Revolution of the same -Planet. - -Ptolemy might obviously have made the geometrical motions of all the -Planets correspond with the observations by one of these two modes -of construction; but he appears to have adopted this double form of -the theory, in order that in the inferior, as well as in the -superior Planets, he might give the smaller of the two Radii to the -Epicycle: that is, in order that he might make the smaller circle -move round the larger, not _vice versâ_.--_Littrow's Notes._] - -I shall here close my account of the astronomical progress of the -Greek School. My purpose is only to illustrate the principles on -which the progress of science depends, and therefore I have not at -all pretended to touch upon every part of the subject. Some portion -of the ancient theories, as, for instance, the mode of accounting -for the motions of the moon and planets in latitude, are -sufficiently analogous to what has been explained, not to require -any more especial notice. Other parts of Greek astronomical -knowledge, as, for instance, their acquaintance with refraction, did -not assume any clear or definite form, and can only be considered as -the prelude to modern discoveries on the same subject. And before we -can with propriety pass on to these, there is a long and remarkable, -though unproductive interval, of which some account must be given. - - -_Sect._ 8.--_Arabian Astronomy._ - -THE interval to which I have just alluded may be considered as -extending from Ptolemy to Copernicus; we have no advance in Greek -astronomy after the former; no signs of a revival of the power of -discovery till the latter. During this interval of 1350 -years,[115\3] the principal cultivators of astronomy were the -Arabians, who adopted this science from the Greeks whom they -conquered, and from whom the conquerors of western Europe again -received back their treasure, when the love of science and the -capacity for it had been awakened in their minds. In the intervening -time, the precious deposit had undergone little change. The Arab -astronomer had been the scrupulous but unprofitable servant, who -kept his talent without apparent danger of loss, but also without -prospect of increase. There is little in {177} Arabic literature -which bears upon the _progress_ of astronomy; but as the little that -there is must be considered as a sequel to the Greek science, I -shall notice one or two points before I treat of the stationary -period in general. - -[Note 115\3: Ptolemy died about A. D. 150. Copernicus was living -A. D. 1500.] - -When the sceptre of western Asia had passed into the hands of the -Abasside caliphs,[116\3] Bagdad, "the city of peace," rose to -splendor and refinement, and became the metropolis of science under -the successors of Almansor the Victorious, as Alexandria had been -under the successors of Alexander the Great. Astronomy attracted -peculiarly the favor of the powerful as well as the learned; and -almost all the culture which was bestowed upon the science, appears -to have had its source in the patronage, often also in the personal -studies, of Saracen princes. Under such encouragement, much was -done, in those scientific labors which money and rank can command. -Translations of Greek works were made, large instruments were -erected, observers were maintained; and accordingly as observation -showed the defects and imperfection of the extant tables of the -celestial motions, new ones were constructed. Thus under Almansor, -the Grecian works of science were collected from all quarters, and -many of them translated into Arabic.[117\3] The translation of the -"Megiste Syntaxis" of Ptolemy, which thus became the Almagest, is -ascribed to Isaac ben Homain in this reign. - -[Note 116\3: Gibbon, x. 31.] - -[Note 117\3: Id. x. 36.] - -The greatest of the Arabian Astronomers comes half a century later. -This is Albategnius, as he is commonly called; or more exactly, -Mohammed ben Geber Albatani, the last appellation indicating that he -was born at Batan, a city of Mesopotamia.[118\3] He was a Syrian -prince, whose residence was at Aracte or Racha in Mesopotamia: a -part of his observations were made at Antioch. His work still -remains to us in Latin. "After having read," he says, "the Syntaxis -of Ptolemy, and learnt the methods of calculation employed by the -Greeks, his observations led him to conceive that some improvements -might be made in their results. He found it necessary to add to -Ptolemy's observations as Ptolemy had added to those of Abrachis" -(Hipparchus). He then published Tables of the motions of the sun, -moon, and planets, which long maintained a high reputation. - -[Note 118\3: Del. _Astronomie du Moyen Age_, 4.] - -These, however, did not prevent the publication of others. Under the -Caliph Hakem (about A. D. 1000) Ebon Iounis published Tables of the -Sun, Moon, and Planets, which were hence called the _Hakemite -Tables_. Not long after, Arzachel of Toledo published the _Toletan_ -{178} Tables. In the 13th century, Nasir Eddin published Tables of -the Stars, dedicated to Ilchan, a Tartar prince, and hence termed -the _Ilchanic_ Tables. Two centuries later, Ulugh Beigh, the -grandson of Tamerlane, and prince of the countries beyond the Oxus, -was a zealous practical astronomer; and his Tables, which were -published in Europe by Hyde in 1665, are referred to as important -authority by modern astronomers. The series of Astronomical Tables -which we have thus noticed, in which, however, many are omitted, -leads us to the _Alphonsine_ Tables, which were put forth in 1488, -and in succeeding years, under the auspices of Alphonso, king of -Castile; and thus brings us to the verge of modern astronomy. - -For all these Tables, the Ptolemaic hypotheses were employed; and, -for the most part, without alteration. The Arabs sometimes felt the -extreme complexity and difficulty of the doctrine which they -studied; but their minds did not possess that kind of invention and -energy by which the philosophers of Europe, at a later period, won -their way into a simpler and better system. - -Thus Alpetragius states, in the outset of his "Planetarum Theorica," -that he was at first astonished and stupefied with this complexity, -but that afterwards "God was pleased to open to him the occult secret -in the theory of his orbs, and to make known to him the truth of their -essence and the rectitude of the quality of their motion." His system -consists, according to Delambre,[119\3] in attributing to the planets -a spiral motion from east to west, an idea already refuted by Ptolemy. -Geber of Seville criticises Ptolemy very severely,[120\3] but without -introducing any essential alteration into his system. The Arabian -observations are in many cases valuable; both because they were made -with more skill and with better instruments than those of the Greeks; -and also because they illustrate the permanence or variability of -important elements, such as the obliquity of the ecliptic and the -inclination of the moon's orbit. - -[Note 119\3: Delambre, _M. A._ p. 7.] - -[Note 120\3: _M. A._ p. 180, &c.] - -We must, however, notice one or two peculiar Arabian doctrines. The -most important of these is the discovery of the Motion of the Son's -Apogee by Albategnius. He found the Apogee to be in longitude 82 -degrees; Ptolemy had placed it in longitude 65 degrees. The -difference of 17 degrees was beyond all limit of probable error of -calculation, though the process is not capable of great precision; -and the inference of the Motion of the Apogee was so obvious, that -we cannot {179} agree with Delambre, in doubting or extenuating the -claim of Albategnius to this discovery, on the ground of his not -having expressly stated it. - -In detecting this motion, the Arabian astronomers reasoned rightly -from facts well observed: they were not always so fortunate. -Arzachel, in the 11th century, found the apogee of the sun to be -less advanced than Albategnius had found it, by some degrees; he -inferred that it had receded in the intermediate time; but we now -know, from an acquaintance with its real rate of moving, that the -true inference would have been, that Albategnius, whose method was -less trustworthy than that of Arzachel, had made an error to the -amount of the difference thus arising. A curious, but utterly false -hypothesis was founded on observations thus erroneously appreciated; -namely, the _Trepidation of the fixed stars_. Arzachel conceived -that a uniform Precession of the equinoctial points would not -account for the apparent changes of position of the stars, and that -for this purpose, it was necessary to conceive two circles of about -eight degrees radius described round the equinoctial points of the -immovable sphere, and to suppose the first points of Aries and Libra -to describe the circumference of these circles in about 800 years. -This would produce, at one time a progression, and at another a -regression, of the apparent equinoxes, and would moreover change the -latitude of the stars. Such a motion is entirely visionary; but the -doctrine made a sect among astronomers, and was adopted in the first -edition of the Alphonsine Tables, though afterwards rejected. - -An important exception to the general unprogressive character of -Arabian science has been pointed out recently by M. Sedillot.[121\3] -It appears that Mohammed-Aboul Wefa-al-Bouzdjani, an Arabian -astronomer of the tenth century, who resided at Cairo, and observed -at Bagdad in 975, discovered a third inequality of the moon, in -addition to the two expounded by Ptolemy, the Equation of the -Centre, and the Evection. This third inequality, the _Variation_, is -usually supposed to have been discovered by Tycho Brahe, six -centuries later. It is an inequality of the moon's motion, in virtue -of which she moves quickest when she is at new or full, and slowest -at the first and third quarter; in consequence of this, from the -first quarter to the full, she is behind her mean place; at the -full, she does not differ from her mean place; from the full to the -third quarter, she is before her true {180} place; and so on; and -the greatest effect of the inequality is in the _octants_, or points -half-way between the four quarters. In an Almagest of Aboul Wefa, a -part of which exists in the Royal Library at Paris, after describing -the two inequalities of the moon, he has a Section ix., "Of the -Third Anomaly of the moon called _Muhazal_ or _Prosneusis_." He -there says, that taking cases when the moon was in apogee or -perigee, and when, consequently, the effect of the two first -inequalities vanishes, he found, _by observation of the moon_, when -she was nearly _in trine_ and _in sextile_ with the sun, that she -was a degree and a quarter from her calculated place. "And hence," -he adds, "I perceived that this anomaly exists independently of the -two first: and this can only take place by a declination of the -diameter of the epicycle with respect to the centre of the zodiac." - -[Note 121\3: Sedillot, Nouvelles Rech. sur l'Hist. de l'Astron. chez -les Arabes. _Nouveau Journal Asiatique_. 1836.] - -We may remark that we have here this inequality of the moon made out -in a really philosophical manner; a residual quantity in the moon's -longitude being detected by observation, and the cases in which it -occurs selected and grouped by an inductive effort of the mind. The -advance is not great; for Aboul Wefa appears only to have detected -the existence, and not to have fixed the law or the exact quantity -of the inequality; but still it places the scientific capacity of -the Arabs in a more favorable point of view than any circumstance -with which we were previously acquainted. - -But this discovery of Aboul Wefa appears to have excited no notice -among his contemporaries and followers: at least it had been long -quite forgotten when Tycho Brahe rediscovered the same lunar -inequality. We can hardly help looking upon this circumstance as an -evidence of a servility of intellect belonging to the Arabian -period. The learned Arabians were so little in the habit of -considering science as progressive, and looking with pride and -confidence at examples of its progress, that they had not the -courage to believe in a discovery which they themselves had made, -and were dragged back by the chain of authority, even when they had -advanced beyond their Greek masters. - -As the Arabians took the whole of their theory (with such slight -exceptions as we have been noticing) from the Greeks, they took from -them also the mathematical processes by which the consequences of -the theory were obtained. Arithmetic and Trigonometry, two main -branches of these processes, received considerable improvements at -their hands. In the former, especially, they rendered a service to -the world which it is difficult to estimate too highly, in -abolishing the {181} cumbrous Sexagesimal Arithmetic of the Greeks, -and introducing the notation by means of the digits 1, 2, 3, 4, 5, -6, 7, 8, 9, 0, which we now employ.[122\3] These numerals appear to -be of Indian origin, as is acknowledged by the Arabs themselves; and -thus form no exception to the sterility of the Arabian genius as to -great scientific inventions. Another improvement, of a subordinate -kind, but of great utility, was Arabian, being made by Albategnius. -He introduced into calculation the _sine_, or half-chord of the -double arc, instead of the chord of the arc itself, which had been -employed by the Greek astronomers. There have been various -conjectures concerning the origin of the word _sine_; the most -probable appears to be that _sinus_ is the Latin translation of the -Arabic word _gib_, which signifies a fold, the two halves of the -chord being conceived to be folded together. - -[Note 122\3: Mont. i. 376.] - -The great obligation which Science owes to the Arabians, is to have -preserved it during a period of darkness and desolation, so that -Europe might receive it back again when the evil days were past. We -shall see hereafter how differently the European intellect dealt -with this hereditary treasure when once recovered. - -Before quitting the subject, we may observe that Astronomy brought -back, from her sojourn among the Arabs, a few terms which may still -be perceived in her phraseology. Such are the _zenith_, and the -opposite imaginary point, the _nadir_;--the circles of the sphere -termed _almacantars_ and _azimuth_ circles. The _alidad_ of an -instrument is its index, which possesses an angular motion. Some of -the stars still retain their Arabic names; _Aldebran_, _Rigel_, -_Fomalhaut_; many others were known by such appellations a little -while ago. Perhaps the word _almanac_ is the most familiar vestige -of the Arabian period of astronomy. - -It is foreign to my purpose to note any efforts of the intellectual -faculties among other nations, which may have taken place -independently of the great system of progressive European culture, -from which all our existing science is derived. Otherwise I might -speak of the astronomy of some of the Orientals, for example, the -Chinese, who are said, by Montucla (i. 465), to have discovered the -first equation of the moon, and the proper motion of the fixed stars -(the Precession), in the third century of our era. The Greeks had -made these discoveries 500 years earlier. - - - -{{183}} -BOOK IV. - - -HISTORY -OF -PHYSICAL SCIENCE IN THE MIDDLE AGES; -OR, -VIEW OF THE STATIONARY PERIOD -OF -INDUCTIVE SCIENCE. - - - - In vain, in vain! the all-composing hour - Resistless falls . . . . - . . . . . - As one by one, at dread Medea's strain, - The sickening stars fade off th' ethereal plain; - As Argus' eyes, by Hermes' wand opprest, - Closed one by one to everlasting rest; - Thus at her felt approach and secret might, - Art after art goes out, and all is night. - See skulking Truth to her old cavern fled, - Mountains of casuistry heaped on her head; - Philosophy, that reached the heavens before, - Shrinks to her hidden cause, and is no more. - Physic of Metaphysic begs defence, - And Metaphysic calls for aid to Sense: - See Mystery to Mathematics fly! - In vain! they gaze, turn giddy, rave, and die. - - _Dunciad_, B. iv. - - - -{{185}} -INTRODUCTION. - - -WE have now to consider more especially a long and barren period, -which intervened between the scientific activity of ancient Greece -and that of modern Europe; and which we may, therefore, call the -Stationary Period of Science. It would be to no purpose to enumerate -the various forms in which, during these times, men reproduced the -discoveries of the inventive ages; or to trace in them the small -successes of Art, void of any principle of genuine Philosophy. Our -object requires rather that we should point out the general and -distinguishing features of the intellect and habits of those times. -We must endeavor to delineate the character of the Stationary -Period, and, as far as possible, to analyze its defects and errors; -and thus obtain some knowledge of the causes of its barrenness and -darkness. - -We have already stated, that real scientific progress requires -distinct general Ideas, applied to many special and certain Facts. -In the period of which we now have to speak, men's Ideas were -obscured; their disposition to bring their general views into -accordance with Facts was enfeebled. They were thus led to employ -themselves unprofitably, among indistinct and unreal notions. And -the evil of these tendencies was further inflamed by moral -peculiarities in the character of those times;--by an abjectness of -thought on the one hand, which could not help looking towards some -intellectual superior, and by an impatience of dissent on the other. -To this must be added an enthusiastic temper, which, when introduced -into speculation, tends to subject the mind's operations to ideas -altogether distorted and delusive. - -These characteristics of the stationary period, its obscurity of -thought, its servility, its intolerant disposition, and its -enthusiastic temper, will be treated of in the four following -chapters, on the Indistinctness of Ideas, the Commentatorial Spirit, -the Dogmatism, and the Mysticism of the Middle Ages. {186} - - - - -CHAPTER I. - -ON THE INDISTINCTNESS OF IDEAS OF THE MIDDLE AGES. - - -THAT firm and entire possession of certain clear and distinct -general ideas which is necessary to sound science, was the character -of the minds of those among the ancients who created the several -sciences which arose among them. It was indispensable that such -inventors should have a luminous and steadfast apprehension of -certain general relations, such as those of space and number, order -and cause; and should be able to apply these notions with perfect -readiness and precision to special facts and cases. It is necessary -that such scientific notions should be more definite and precise -than those which common language conveys; and in this state of -unusual clearness, they must be so familiar to the philosopher, that -they are the language in which he thinks. The discoverer is thus led -to doctrines which other men adopt and follow out, in proportion as -they seize the fundamental ideas, and become acquainted with the -leading facts. Thus Hipparchus, conceiving clearly the motions and -combinations of motion which enter into his theory, saw that the -relative lengths of the seasons were sufficient data for determining -the form of the sun's orbit; thus Archimedes, possessing a steady -notion of mechanical pressure, was able, not only to deduce the -properties of the lever and of the centre of gravity, but also to -see the truth of those principles respecting the distribution of -pressure in fluids, on which the science of hydrostatics depends. - -With the progress of such distinct ideas, the inductive sciences -rise and flourish; with the decay and loss of such distinct ideas, -these sciences become stationary, languid, and retrograde. When men -merely repeat the terms of science, without attaching to them any -clear conceptions;--when their apprehensions become vague and -dim;--when they assent to scientific doctrines as a matter of -tradition, rather than of conviction, on trust rather than on -sight;--when science is considered as a collection of opinions, -rather than a record of laws by which the universe is really -governed;--it must inevitably happen, that men will lose their hold -on the knowledge which the great discoverers who preceded them have -brought to light. They are not able to push forwards the truths on -which they lay so {187} feeble and irresolute a hand; probably they -cannot even prevent their sliding back towards the obscurity from -which they had been drawn, or from being lost altogether. Such -indistinctness and vacillation of thought appear to have prevailed -in the stationary period, and to be, in fact, intimately connected -with its stationary character. I shall point out some indications of -the intellectual peculiarity of which I speak. - -1. _Collections of Opinions._--The fact, that mere Collections of -the opinions of physical philosophers came to hold a prominent place -in literature, already indicated a tendency to an indistinct and -wandering apprehension of such opinions. I speak of such works as -Plutarch's five Books "on the Opinions of Philosophers," or the -physical opinions which Diogenes Laërtius gives in his "Lives of the -Philosophers." At an earlier period still, books of this kind -appear; as for instance, a large portion of Pliny's Natural History, -a work which has very appropriately been called the Encyclopædia of -Antiquity; even Aristotle himself is much in the habit of -enumerating the opinions of those who had preceded him. To present -such statements as an important part of physical philosophy, shows -an erroneous and loose apprehension of its nature. For the only -proof of which its doctrines admit, is the possibility of applying -the general theory to each particular case; the authority of great -men, which in moral and practical matters may or must have its -weight, is here of no force; and the technical precision of ideas -which the terms of a sound physical theory usually demand, renders a -mere statement of the doctrines very imperfectly intelligible to -readers familiar with common notions only. To dwell upon such -collections of opinions, therefore, both implies, and produces, in -writers and readers, an obscure and inadequate apprehension of the -full meaning of the doctrines thus collected; supposing there be -among them any which really possess such a clearness, solidity, and -reality, as to make them important in the history of science. Such -diversities of opinion convey no truth; such a multiplicity of -statements of what has been _said_, in no degree teaches us what -_is_; such accumulations of indistinct notions, however vast and -varied, do not make up one distinct idea. On the contrary, the habit -of dwelling upon the verbal expressions of the views of other -persons, and of being content with such an apprehension of doctrines -as a transient notice can give us, is fatal to firm and clear -thought: it indicates wavering and feeble conceptions, which are -inconsistent with speculation. {188} - -We may, therefore, consider the prevalence of Collections of the -kind just referred to, as indicating a deficiency of philosophical -talent in the ages now under review. As evidence of the same -character, we may add the long train of publishers of Abstracts, -Epitomes, Bibliographical Notices, and similar writers. All such -writers are worthless for all purposes of _science_, and their -labors may be considered as dead works; they have in them no -principle of philosophical vitality; they draw their origin and -nutriment from the death of true physical knowledge; and resemble -the swarms of insects that are born from the perishing carcass of -some noble animal. - -2. _Indistinctness of Ideas in Mechanics._--But the indistinctness -of thought which is so fatal a feature in the intellect of the -stationary period, may be traced more directly in the works, even of -the best authors, of those times. We find that they did not retain -steadily the ideas on which the scientific success of the previous -period had depended. For instance, it is a remarkable circumstance -in the history of the science of Mechanics, that it did not make any -advance from the time of Archimedes to that of Stevinus and Galileo. -Archimedes had established the doctrine of the lever; several -persons tried, in the intermediate time, to prove the property of -the inclined plane, and none of them succeeded. But let us look to -the attempts; for example, that of Pappus, in the eighth Book of his -Mathematical Collections, and we may see the reason of the failure. -His Problem shows, in the very terms in which it is propounded, the -want of a clear apprehension of the subject. "Having given the power -which will draw a given weight along the horizontal plane, to find -the additional power which will draw the same weight along a given -inclined plane." This is proposed without previously defining how -Powers, producing such effects, are to be measured; and as if the -speed with which the body were drawn, and the nature of the surface -of the plane, were of no consequence. The proper elementary Problem -is, To find the force which will _support_ a body on a smooth -inclined plane; and no doubt the solution of Pappus has more -reference to this problem than to his own. His reasoning is, -however, totally at variance with mechanical ideas on any view of -the problem. He supposes the weight to be formed into a sphere; and -this sphere being placed in contact with the inclined plane, he -assumes that the effect will be the same as if the weight were -supported on a horizontal lever, the fulcrum being the point of -contact of the sphere with the plane, and the power acting at the -circumference of the sphere. Such an assumption implies an entire -{189} absence of those distinct ideas of force and mechanical -pressure, on which our perception of the identity or difference of -different modes of action must depend;--of those ideas by the help -of which Archimedes had been able to demonstrate the properties of -the lever, and Stevinus afterwards discovered the true solution of -the problem of the inclined plane. The motive to Pappus's assumption -was probably no more than this;--he perceived that the additional -power, which he thus obtained, vanished when the plane became -horizontal, and increased as the inclination became greater. Thus -his views were vague; he had no clear conception of mechanical -action, and he tried a geometrical conjecture. This is not the way -to real knowledge. - -Pappus (who lived about A. D. 400) was one of the best -mathematicians of the Alexandrian school; and, on subjects where his -ideas were so indistinct, it is not likely that any much clearer -were to be found in the minds of his contemporaries. Accordingly, on -all subjects of speculative mechanics, there appears to have been an -entire confusion and obscurity of thought till modern times. Men's -minds were busy in endeavoring to systematize the distinctions and -subtleties of the Aristotelian school, concerning Motion and Power; -and, being thus employed among doctrines in which there was involved -no definite meaning capable of real exemplification, they, of -course, could not acquire sound physical knowledge. We have already -seen that the physical opinions of Aristotle, even as they came from -him, had no proper scientific precision. His followers, in their -endeavors to perfect and develop his statements, never attempted to -introduce clearer ideas than those of their master; and as they -never referred, in any steady manner, to facts, the vagueness of -their notions was not corrected by any collision with observation. -The physical doctrines which they extracted from Aristotle were, in -the course of time, built up into a regular system; and though these -doctrines could not be followed into a practical application without -introducing distinctions and changes, such as deprived the terms of -all steady signification, the dogmas continued to be repeated, till -the world was persuaded that they were self-evident; and when, at a -later period, experimental philosophers, such as Galileo and Boyle, -ventured to contradict these current maxims, their new principles -sounded in men's ears as strange as they now sound familiar. Thus -Boyle promulgated his opinions on the mechanics of fluids, as -"Hydrostatical _Paradoxes_, proved and illustrated by experiments." -And the opinions which he there opposes, are those which the -Aristotelian philosophers habitually propounded as certain {190} and -indisputable; such, for instance, as that "in fluids the upper parts -do not gravitate on the lower;" that "a lighter fluid will not -gravitate on a heavier;" that "levity is a positive quality of -bodies as well as gravity." So long as these assertions were left -uncontested and untried, men heard and repeated them, without -perceiving the incongruities which they involved: and thus they long -evaded refutation, amid the vague notions and undoubting habits of -the stationary period. But when the controversies of Galileo's time -had made men think with more acuteness and steadiness, it was -discovered that many of these doctrines were inconsistent with -themselves, as well as with experiment. We have an example of the -confusion of thought to which the Aristotelians were liable, in -their doctrine concerning falling bodies. "Heavy bodies," said they, -"must fall quicker than light ones; for weight is the cause of their -fall, and the weight of the greater bodies is greater." They did not -perceive that, if they considered the weight of the body as a power -acting to produce motion, they must consider the body itself as -offering a resistance to motion; and that the effect must depend on -the proportion of the power to the resistance; in short, they had no -clear idea of _accelerating force_. This defect runs through all -their mechanical speculations, and renders them entirely valueless. - -We may exemplify the same confusion of thought on mechanical -subjects in writers of a less technical character. Thus, if men had -any distinct idea of mechanical action, they could not have accepted -for a moment the fable of the Echineis or Remora, a little fish -which was said to be able to stop a large ship merely by sticking to -it.[1\4] Lucan refers to this legend in a poetical manner, and -notices this creature only in bringing together a collection of -monstrosities; but Pliny relates the tale gravely, and moralizes -upon it after his manner. "What," he cries,[2\4] "is more violent -than the sea and the winds? what a greater work of art than a ship? -Yet one little fish (the Echineis) can hold back all these when they -all strain the same way. The winds may {191} blow, the waves may -rage; but this small creature controls their fury, and stops a -vessel, when chains and anchors would not hold it: and this it does, -not by hard labor, but merely by adhering to it. Alas, for human -vanity! when the turreted ships which man has built, that he may -fight from castle-walls, at sea as well as at land, are held captive -and motionless by a fish a foot and a half long! Such a fish is said -to have stopped the admiral's ship at the battle of Actium, and -compelled Antony to go into another. And in our own memory, one of -these animals held fast the ship of Caius, the emperor, when he was -sailing from Astura to Antium. The stopping of this ship, when all -the rest of the fleet went on, caused surprise; but this did not -last long, for some of the men jumped into the water to look for the -fish, and found it sticking to the rudder; they showed it to Caius, -who was indignant that this animal should interpose its prohibition -to his progress, when impelled by four hundred rowers. It was like a -slug; and had no power, after it was taken into the ship." - -[Note 1\4: Lucan is describing one of the poetical compounds -produced in incantations. - Huc quicquid fœtu genuit Natura sinistro - Miscetur: non spuma canum quibus unda timori est, - Viscera non lyncis, non duræ nodus hyænæ - Defuit, et cervi pasti serpente medullæ; - In mediis _Echineis_ aquis, oculique draconum. - Etc. _Pharsalia_, **vi. 670.] - -[Note 2\4: Plin. _Hist. N._ xxxii. 5.] - -A very little advance in the power of thinking clearly on the force -which it exerted in pulling, would have enabled the Romans to see -that the ship and its rowers must pull the adhering fish by the hold -the oars had upon the water; and that, except the fish had a hold -equally strong on some external body, it could not resist this force. - -3. _Indistinctness of Ideas shown in Architecture._--Perhaps it may -serve to illustrate still further the extent to which, under the -Roman empire, men's notions of mechanical relations became faint, -wavered, and disappeared, if we observe the change which took place -in architecture. All architecture, to possess genuine beauty, must -be mechanically consistent. The decorative members must represent a -structure which has in it a principle of support and stability. Thus -the Grecian colonnade was a straight horizontal beam, resting on -vertical props; and the pediment imitated a frame like a roof, where -oppositely inclined beams support each other. These forms of -building were, therefore, proper models of art, because they implied -supporting forces. But to be content with colonnades and pediments, -which, though they imitated the forms of the Grecian ones, were -destitute of their mechanical truth, belonged to the decline of art; -and showed that men had lost the idea of force, and retained only -that of shape. Yet this was what the architects of the Roman empire -did. Under their hands, the pediment was severed at its vertex, and -divided into separate halves, so that it was no longer a mechanical -possibility. The entablature no longer lay straight from pillar to -pillar, but, projecting over each {192} column, turned back to the -wall, and adhered to it in the intervening space. The splendid -remains of Palmyra, Balbec, Petra, exhibit endless examples of this -kind of perverse inventiveness; and show us, very instructively, how -the decay of art and of science alike accompany this indistinctness -of ideas which we are now endeavoring to illustrate. - -4. _Indistinctness of Ideas in Astronomy._--Returning to the -sciences, it may be supposed, at first sight, that, with regard to -astronomy, we have not the same ground for charging the stationary -period with indistinctness of ideas on that subject, since they were -able to acquire and verify, and, in some measure, to apply, the -doctrines previously established. And, undoubtedly, it must be -confessed that men's notions of the relations of space and number -are never very indistinct. It appears to be impossible for these -chains of elementary perception ever to be much entangled. The later -Greeks, the Arabians, and the earliest modern astronomers, must have -conceived the hypotheses of the Ptolemaic system with tolerable -completeness. And yet, we may assert, that during the stationary -period, men did not possess the notions, even of space and number, -in that vivid and vigorous manner which enables them to discover new -truths. If they had perceived distinctly that the astronomical -theorist had merely to do with _relative_ motions, they must have -been led to see the possibility, at least, of the Copernican system; -as the Greeks, at an earlier period, had already perceived it. We -find no trace of this. Indeed, the mode in which the Arabian -mathematicians present the solutions of their problems, does not -indicate that clear apprehension of the relations of space, and that -delight in the contemplation of them, which the Greek geometrical -speculations imply. The Arabs are in the habit of giving conclusions -without demonstrations, precepts without the investigations by which -they are obtained; as if their main object were practical rather -than speculative,--the calculation of results rather than the -exposition of theory. Delambre[3\4] has been obliged to exercise -great ingenuity, in order to discover the method by which Ibn Iounis -proved his solution of certain difficult problems. - -[Note 3\4: Delamb. _M. A._ p. 125-8.] - -5. _Indistinctness of Ideas shown by Skeptics._--The same -unsteadiness of ideas which prevents men from obtaining clear views, -and steady and just convictions, on special subjects, may lead them -to despair of or deny the possibility of acquiring certainty at all, -and may thus make them skeptics with regard to all knowledge. Such -skeptics {193} are themselves men of indistinct views, for they -could not otherwise avoid assenting to the demonstrated truths of -science; and, so far as they may be taken as specimens of their -contemporaries, they prove that indistinct ideas prevail in the age -in which they appear. In the stationary period, moreover, the -indefinite speculations and unprofitable subtleties of the schools -might further impel a man of bold and acute mind to this universal -skepticism, because they offered nothing which could fix or satisfy -him. And thus the skeptical spirit may deserve our notice as -indicative of the defects of a system of doctrine too feeble in -demonstration to control such resistance. - -The most remarkable of these philosophical skeptics is Sextus -Empiricus; so called, from his belonging to that medical sect which -was termed the _empirical_, in contradistinction to the _rational_ -and _methodical_ sects. His works contain a series of treatises, -directed against all the divisions of the science of his time. He -has chapters against the Geometers, against the Arithmeticians, -against the Astrologers, against the Musicians, as well as against -Grammarians, Rhetoricians, and Logicians; and, in short, as a modern -writer has said, his skepticism is employed as a sort of frame-work -which embraces an encyclopedical view of human knowledge. It must be -stated, however, that his objections are rather to the metaphysical -grounds, than to the details of the sciences; he rather denies the -possibility of speculative truth in general, than the experimental -truths which had been then obtained. Thus his objections to geometry -and arithmetic are founded on abstract cavils concerning the nature -of points, letters, unities, &c. And when he comes to speak against -astrology, he says, "I am not going to consider that perfect science -which rests upon geometry and arithmetic; for I have already shown -the weakness of those sciences: nor that faculty of prediction (of -the motions of the heavens) which belongs to the pupils of Eudoxus, -and Hipparchus, and the rest, which some call Astronomy; for that is -an observation of phenomena, like agriculture or navigation: but -against the Art of Prediction from the time of birth, which the -Chaldeans exercise." Sextus, therefore, though a skeptic by -profession, was not insensible to the difference between -experimental knowledge and mystical dogmas, though even the former -had nothing which excited his admiration. - -The skepticism which denies the evidence of the truths of which the -best established physical sciences consist, must necessarily involve -a very indistinct apprehension of those truths; for such truths, -properly exhibited, contain their own evidence, and are the best -antidote {194} to this skepticism. But an incredulity or contempt -towards the asserted truths of physical science may arise also from -the attention being mainly directed to the certainty and importance -of religious truths. A veneration for revealed religion may thus -assume the aspect of a skepticism with regard to natural knowledge. -Such appears to be the case with Algazel or Algezeli, who is adduced -by Degerando[4\4] as an example of an Arabian skeptic. He was a -celebrated teacher at Bagdad in the eleventh century, and he -declared himself the enemy, not only of the mixed Peripatetic and -Platonic philosophy of the time, but of Aristotle himself. His work -entitled _The Destructions of the Philosophers_, is known to us by -the refutation of it which Averrhoes published, under the title of -_Destruction of Algazel's Destructions of the Philosophers_. It -appears that he contested the fundamental principles both of the -Platonic and of the Aristotelian schools, and denied the possibility -of a known connection between cause and effect; thus making a -prelude, says Degerando, to the celebrated argumentation of Hume. - -[Note 4\4: Degerando, _Hist. Comp. de Systèmes_, iv. 224.] - -[2d Ed.] Since the publication of my first edition, an account of -Algazel or Algazzali and his works has been published under the -title of _Essai sur les Ecoles Philosophiques chez les Arabes, et -notamment sur la Doctrine d'Algazzali_, par August Schmölders. -Paris. 1842. From this book it appears that Degerando's account of -Algazzali is correct, when he says[5\4] that "his skepticism seems -to have essentially for its object to destroy all systems of merely -rational theology, in order to open an indefinite career, not only -to faith guided by revelation, but also to the free exaltation of a -mystical enthusiasm." It is remarked by Dr. Schmölders, following M. -de Hammer-Purgstall, that the title of the work referred to in the -text ought rather to be _Mutual Refutation of the Philosophers_: and -that its object is to show that Philosophy consists of a mass of -systems, each of which overturns the others. The work of Algazzali -which Dr. Schmölders has published, _On the Errors of Sects, &c._, -contains a kind of autobiographical account of the way in which the -author was led to his views. He does not reject the truths of -science, but he condemns the mental habits which are caused by -laying too much stress upon science. Religious men, he says, are, by -such a course, led to reject all science, even what relates to -eclipses of the moon and sun; and men of science are led to hate -religion.[6\4] {195} - -[Note 5\4: _Hist. Comp._ iv. p. 227.] - -[Note 6\4: _Essai_, p. 33.] - -6. _Neglect of Physical Reasoning in Christendom._--If the Arabians, -who, during the ages of which we are speaking, were the most eminent -cultivators of science, entertained only such comparatively feeble -and servile notions of its doctrines, it will easily be supposed, -that in the Christendom of that period, where physical knowledge was -comparatively neglected, there was still less distinctness and -vividness in the prevalent ideas on such subjects. Indeed, during a -considerable period of the history of the Christian Church, and by -many of its principal authorities, the study of natural philosophy -was not only disregarded but discommended. The great practical -doctrines which were presented to men's minds, and the serious -tasks, of the regulation of the will and affections, which religion -impressed upon them, made inquiries of mere curiosity seem to be a -reprehensible misapplication of human powers; and many of the -fathers of the Church revived, in a still more peremptory form, the -opinion of Socrates, that the only valuable philosophy is that which -teaches us our moral duties and religious hopes.[7\4] Thus Eusebius -says,[8\4] "It is not through ignorance of the things admired by -them, but through contempt of their useless labor, that we think -little of these matters, turning our souls to the exercise of better -things." When the thoughts were thus intentionally averted from -those ideas which natural philosophy involves, the ideas inevitably -became very indistinct in their minds; and they could not conceive -that any other persons could find, on such subjects, grounds of -clear conviction and certainty. They held the whole of their -philosophy to be, as Lactantius[9\4] asserts it to be, "empty and -false." "To search," says he, "for the causes of natural things; to -inquire whether the sun be as large as he seems, whether the moon is -convex or concave, whether the stars are fixed in the sky or float -freely in the air; of what size and of what material are the -heavens; whether they be at rest or in motion; what is the magnitude -of the earth; on what foundations it is suspended and balanced;--to -dispute and conjecture on such matters, is just as if we chose to -discuss what we think of a city in a remote country, of which we -never heard but the name." It is impossible to express more forcibly -that absence of any definite notions on physical subjects which led -to this tone of thought. - -[Note 7\4: Brucker, iii. 317.] - -[Note 8\4: _Præp. Ev._ xv. 61.] - -[Note 9\4: _Inst._ 1. iii. init.] - -7. _Question of Antipodes._--With such habits of thought, we are not -to be surprised if the relations resulting from the best established -theories were apprehended in an imperfect and incongruous manner. -{196} We have some remarkable examples of this; and a very notable -one is the celebrated question of the existence of _Antipodes_, or -persons inhabiting the opposite side of the globe of the earth, and -consequently having the soles of their feet directly opposed to -ours. The doctrine of the globular form of the earth results, as we -have seen, by a geometrical necessity, from a clear conception of -the various points of knowledge which we obtain, bearing upon that -subject. This doctrine was held distinctly by the Greeks; it was -adopted by all astronomers, Arabian and European, who followed them; -and was, in fact, an inevitable part of every system of astronomy -which gave a consistent and intelligible representation of -phenomena. But those who did not call before their minds any -distinct representation at all, and who referred the whole question -to other relations than those of space, might still deny this -doctrine; and they did so. The existence of inhabitants on the -opposite side of the terraqueous globe, was a fact of which -experience alone could teach the truth or falsehood; but the -religious relations, which extend alike to all mankind, were -supposed to give the Christian philosopher grounds for deciding -against the possibility of such a race of men. Lactantius,[10\4] in -the fourth century, argues this matter in a way very illustrative of -that impatience of such speculations, and consequent confusion of -thought, which we have mentioned. "Is it possible," he says, "that -men can be so absurd as to believe that the crops and trees on the -other side of the earth hang downwards, and that men there have -their feet higher than their heads? If you ask of them how they -defend these monstrosities--how things do not fall away from the -earth on that side--they reply, that the nature of things is such -that heavy bodies tend towards the centre, like the spokes of a -wheel, while light bodies, as clouds, smoke, fire, tend from the -centre towards the heavens on all sides. Now I am really at a loss -what to say of those who, when they have once gone wrong, steadily -persevere in their folly, and defend one absurd opinion by another." -It is obvious that so long as the writer refused to admit into his -thoughts the fundamental conception of their theory, he must needs -be at a loss what to say to their arguments without being on that -account in any degree convinced of their doctrines. - -[Note 10\4: _Inst._ 1. iii. 23.] - -In the sixth century, indeed, in the reign of Justinian, we find a -writer (Cosmas Indicopleustes[11\4]) who does not rest in this -obscurity of {197} representation; but in this case, the -distinctness of the pictures only serves to show his want of any -clear conception as to what suppositions would explain the -phenomena. He describes the earth as an oblong floor, surrounded by -upright walls, and covered by a vault, below which the heavenly -bodies perform their revolutions, going round a certain high -mountain, which occupies the northern parts of the earth, and makes -night by intercepting the light of the sun. In Augustin[12\4] (who -flourished A. D. 400) the opinion is treated on other grounds; and -without denying the globular form of the earth, it is asserted that -there are no inhabitants on the opposite side, because no such race -is recorded by Scripture among the descendants of Adam.[13\4] -Considerations of the same kind operated in the well-known instance -of Virgil, Bishop of Salzburg, in the eighth century. When he was -reported to Boniface, Archbishop of Mentz, as holding the existence -of Antipodes, the prelate was shocked at the assumption, as it -seemed to him, of a world of human beings, out of the reach of the -conditions of salvation; and application was made to Pope Zachary -for a censure of the holder of this dangerous doctrine. It does not, -however, appear that this led to any severity; and the story of the -deposition of Virgil from his bishopric, which is circulated by -Kepler and by more modern writers, is undoubtedly altogether false. -The same scruples continued to prevail among Christian writers to a -later period; and Tostatus[14\4] notes the opinion of the rotundity -of the earth as an "unsafe" doctrine, only a few years before -Columbus visited the other hemisphere. - -[Note 11\4: Montfaucon, _Collectio Nova Patrum_, t. ii. p. 113. -Cosmas Indicopleustes. Christianorum Opiniones de Mundo, sive -Topographia Christiana.] - -[Note 12\4: _Civ. D._ xvi. 9.] - -[Note 13\4: It appears, however, that scriptural arguments were -found on the other side. St. Jerome says (_Comm. in Ezech._ i. 6), -speaking of the two cherubims with four faces, seen by the prophet, -and the interpretation of the vision: "Alii vero qui philosophorum -stultam sequuntur sapientiam, duo hemispheria in duobus templi -cherubim, nos et antipodes, quasi supinos et cadentes homines -suspicantur."] - -[Note 14\4: Montfauc. _Patr._ t. ii.] - -8. _Intellectual Condition of the Religious Orders._--It must be -recollected, however, that though these were the views and tenets of -many religious writers, and though they may be taken as indications of -the prevalent and characteristic temper of the times of which we -speak, they never were universal. Such a confusion of thought affects -the minds of many persons, even in the most enlightened times; and in -what we call the Dark Ages, though clear views on such subjects might -be more rare, those who gave their minds to science, entertained the -true opinion of the figure of the earth. Thus Boëthius[15\4] (in the -sixth century) urges the smallness of the globe of the earth, {198} -compared with the heavens, as a reason to repress our love of glory. -This work, it will be recollected, was translated into the Anglo-Saxon -by our own Alfred. It was also commented on by Bede, who, in what he -says on this passage, assents to the doctrine, and shows an -acquaintance with Ptolemy and his commentators, both Arabian and -Greek. Gerbert, in the tenth century, went from France to Spain to -study astronomy with the Arabians, and soon surpassed his masters. He -is reported to have fabricated clocks, and an astrolabe of peculiar -construction. Gerbert afterwards (in the last year of the first -thousand from the birth of Christ) became pope, by the name of -Sylvester II. Among other cultivators of the sciences, some of whom, -from their proficiency, must have possessed with considerable -clearness and steadiness the elementary ideas on which it depends, we -may here mention, after Montucla,[16\4] Adelbold, whose work On the -Sphere was addressed to Pope Sylvester, and whose geometrical -reasonings are, according to Montucla,[17\4] vague and chimerical; -Hermann Contractus, a monk of St Gall, who, in 1050, published -astronomical works; William of Hirsaugen, who followed his example in -1080; Robert of Lorraine, who was made Bishop of Hereford by William -the Conqueror, in consequence of his astronomical knowledge. In the -next century, Adelhard Goth, an Englishman, travelled among the Arabs -for purposes of study, as Gerbert had done in the preceding age; and -on his return, translated the Elements of Euclid, which he had brought -from Spain or Egypt. Robert Grostête, Bishop of Lincoln, was the -author of an Epitome on the Sphere; Roger Bacon, in his youth the -contemporary of Robert, and of his brother Adam Marsh, praises very -highly their knowledge in mathematics. - -[Note 15\4: Boëthius, _Cons._ ii. pr. 7.] - -[Note 16\4: Mont. i. 502.] - -[Note 17\4: Ib. i. 503.] - -"And here," says the French historian of mathematics, whom I have -followed in the preceding relation, "it is impossible not to reflect -that all those men who, if they did not augment the treasure of the -sciences, at least served to transmit it, were monks, or had been -such originally. Convents were, during these stormy ages, the asylum -of sciences and letters. Without these religious men, who, in the -silence of their monasteries, occupied themselves in transcribing, -in studying, and in imitating the works of the ancients, well or -ill, those works would have perished; perhaps not one of them would -have come down to us. The thread which connects us with the Greeks -and Romans would have been snapt asunder; the precious productions -of {199} ancient literature would no more exist for us, than the -works, if any there were, published before the catastrophe that -annihilated that highly scientific nation, which, according to -Bailly, existed in remote ages in the centre of Tartary, or at the -roots of Caucasus. In the sciences we should have had all to create; -and at the moment when the human mind should have emerged from its -stupor and shaken off its slumbers, we should have been no more -advanced than the Greeks were after the taking of Troy." He adds, -that this consideration inspires feelings towards the religious -orders very different from those which, when he wrote, were -prevalent among his countrymen. - -Except so far as their religious opinions interfered, it was natural -that men who lived a life of quiet and study, and were necessarily -in a great measure removed from the absorbing and blinding interests -with which practical life occupies the thoughts, should cultivate -science more successfully than others, precisely because their ideas -on speculative subjects had time and opportunity to become clear and -steady. The studies which were cultivated under the name of the -Seven Liberal Arts, necessarily tended to favor this effect. The -_Trivium_,[18\4] indeed, which consisted of Grammar, Logic, and -Rhetoric, had no direct bearing upon those ideas with which physical -science is concerned; but the _Quadrivium_, Music, Arithmetic, -Geometry, Astronomy, could not be pursued with any attention, -without a corresponding improvement of the mind for the purposes of -sound knowledge.[19\4] - -[Note 18\4: Bruck. iii. 597.] - -[Note 19\4: Roger Bacon, in his _Specula Mathematica_, cap. i., says -"Harum scientiarum porta et clavis est mathematica, quam sancti a -principio mundi invenerunt, etc. Cujus negligentia _jam per triginta -vel quadraginta annos_ destruxit totum studium Latinorum." I do not -know on what occasion this neglect took place.] - -9. _Popular Opinions._--That, even in the best intellects, something -was wanting to fit them for scientific progress and discovery, is -obvious from the fact that science was so long absolutely -stationary. And I have endeavored to show that one part of this -deficiency was the want of the requisite clearness and vigor of the -fundamental scientific ideas. If these were wanting, even in the -most powerful and most cultivated minds, we may easily conceive that -still greater confusion and obscurity prevailed in the common class -of mankind. They actually adopted the belief, however crude and -inconsistent, that the form of the earth and heavens really is what -at any place it appears to be; that the earth is flat, and the -waters of the sky sustained above a material floor, through which in -showers they descend. Yet the true doctrines of {200} astronomy -appear to have had some popular circulation. For instance, a French -poem of the time of Edward the Second, called _Ymage du Monde_, -contains a metrical account of the earth and heavens, according to -the Ptolemaic views; and in a manuscript of this poem, preserved in -the library of the University of Cambridge, there are -representations, in accordance with the text, of a spherical earth, -with men standing upright upon it on every side; and by way of -illustrating the tendency of all things to the centre, perforations -of the earth, entirely through its mass, are described and depicted; -and figures are exhibited dropping balls down each of these holes, -so as to meet in the interior. And, as bearing upon the perplexity -which attends the motions of _up_ and _down_, when applied to the -globular earth, and the change of the direction of gravity which -would occur in passing the centre, the readers of Dante will -recollect the extraordinary manner in which the poet and his guide -emerge from the bottom of the abyss; and the explanation which -Virgil imparts to him of what he there sees. After they have crept -through the aperture in which Lucifer is placed, the poet says, - "Io levai gli occhi e credetti vedere - Lucifero com' io l' avea lasciato, - E vidile le gambe in su tenere." - . . . . . "Questi come è fitto - Si sottasopra!" . . . . . - "Quando mi volsi, tu passast' il punto - Al qual si traggon d' ogni parte i pesi." - _Inferno_, xxxiv. - - . . . . . "I raised mine eyes, - Believing that I Lucifer should see - Where he was lately left, but saw him now - With legs held upward." . . . . . - "How standeth he in posture thus reversed?" - . . . . . . . . . . . . . . - "Thou wast on the other side so long as I - Descended; when I turned, thou didst o'erpass - That point to which from every part is dragged - All heavy substance." CARY. - -This is more philosophical than Milton's representation, in a more -scientific age, of Uriel sliding to the earth on a sunbeam, and -sliding back again, when the sun had sunk below the horizon. - . . . . . "Uriel to his charge - Returned on that bright beam whose point now raised, - Bore him slope downward to the sun, now fallen - Beneath the Azores." _Par. Lost_, B. iv. {201} - -The philosophical notions of up and down are too much at variance -with the obvious suggestions of our senses, to be held steadily and -justly by minds undisciplined in science. Perhaps it was some -misunderstood statement of the curved surface of the ocean, which -gave rise to the tradition of there being a part of the sea directly -over the earth, from which at times an object has been known to fall -or an anchor to be let down. Even such whimsical fancies are not -without instruction, and may serve to show the reader what that -vagueness and obscurity of ideas is, of which I have been -endeavoring to trace the prevalence in the dark ages. - -We now proceed to another of the features which appears to me to -mark, in a very prominent manner, the character of the stationary -period. - - - - -CHAPTER II. - -THE COMMENTATORIAL SPIRIT OF THE MIDDLE AGES. - - -WE have already noticed, that, after the first great achievements of -the founders of sound speculation, in the different departments of -human knowledge, had attracted the interest and admiration which those -who became acquainted with them could not but give to them, there -appeared a disposition among men to lean on the authority of some of -these teachers;--to study the opinions of others as the only mode of -forming their own;--to read nature through books;--to attend to what -had been already thought and said, rather than to what really is and -happens. This tendency of men's minds requires our particular -consideration. Its manifestations were very important, and highly -characteristic of the stationary period; it gave, in a great degree, a -peculiar bias and direction to the intellectual activity of many -centuries; and the kind of labor with which speculative men were -occupied in consequence of this bias, took the place of that -examination of realities which must be their employment, in order that -real knowledge may make any decided progress. - -In some subjects, indeed, as, for instance, in the domains of -morals, poetry, and the arts, whose aim is the production of beauty, -this opposition between the study of former opinion and present -reality, may not be so distinct; inasmuch as it may be said by some, -that, in these subjects, opinions are realities; that the thoughts -and feelings which {202} prevail in men's minds are the material -upon which we must work, the particulars from which we are to -generalize, the instruments which we are to use; and that, -therefore, to reject the study of antiquity, or even its authority, -would be to show ourselves ignorant of the extent and mutual bearing -of the elements with which we have to deal;--would be to cut asunder -that which we ought to unite into a vital whole. Yet even in the -provinces of history and poetry, the poverty and servility of men's -minds during the middle ages, are shown by indications so strong as -to be truly remarkable; for instance, in the efforts of the -antiquarians of almost every European country to assimilate the -early history of their own state to the poet's account of the -foundation of Rome, by bringing from the sack of Troy, Brutus to -England, Bavo to Flanders, and so on. But however this may be, our -business at present is, to trace the varying spirit of the -_physical_ philosophy of different ages; trusting that, hereafter, -this prefatory study will enable us to throw some light upon the -other parts of philosophy. And in physics the case undoubtedly was, -that the labor of observation, which is one of the two great -elements of the progress of knowledge, was in a great measure -superseded by the collection, the analysis, the explanation, of -previous authors and opinions; experimenters were replaced by -commentators; criticism took the place of induction; and instead of -great discoverers we had learned men. - -1. _Natural Bias to Authority._--It is very evident that, in such a -bias of men's studies, there is something very natural; however -strained and technical this erudition may have been, the -propensities on which it depends are very general, and are easily -seen. Deference to the authority of thoughtful and sagacious men, a -disposition which men in general neither reject nor think they ought -to reject in practical matters, naturally clings to them, even in -speculation. It is a satisfaction to us to suppose that there are, -or have been, minds of transcendent powers, of wide and wise views, -superior to the common errors and blindness of our nature. The -pleasure of admiration, and the repose of confidence, are -inducements to such a belief. There are also other reasons why we -willingly believe that there are in philosophy great teachers, so -profound and sagacious, that, in order to arrive at truth, we have -only to learn their thoughts, to understand their writings. There is -a peculiar interest which men feel in dealing with the thoughts of -their fellow-men, rather than with brute matter. Matter feels and -excites no sympathies: in seeking for mere laws of nature, there is -nothing of mental intercourse with the great spirits of the past, as -there is in {203} studying Aristotle or Plato. Moreover, a large -portion of this employment is of a kind the most agreeable to most -speculative minds; it consists in tracing the consequences of -assumed principles: it is deductive like geometry: and the -principles of the teachers being known, and being undisputed, the -deduction and application of their results is an obvious, -self-satisfying, and inexhaustible exercise of ingenuity. - -These causes, and probably others, make criticism and commentation -flourish, when invention begins to fail, oppressed and bewildered by -the acquisitions it has already made; and when the vigor and hope of -men's minds are enfeebled by civil and political changes. -Accordingly,[20\4] the Alexandrian school was eminently -characterized by a spirit of erudition, of literary criticism, of -interpretation, of imitation. These practices, which reigned first -in their full vigor in "the Museum," are likely to be, at all times, -the leading propensities of similar academical institutions. - -[Note 20\4: Degerando, _Hist. des Syst. de Philos._ iii. p. 134.] - -How natural it is to select a great writer as a paramount authority, -and to ascribe to him extraordinary profundity and sagacity, we may -see, in the manner in which the Greeks looked upon Homer; and the -fancy which detected in his poems traces of the origin of all arts -and sciences, has, as we know, found favor even in modern times. To -pass over earlier instances of this feeling, we may observe, that -Strabo begins his Geography by saying that he agrees with -Hipparchus, who had declared Homer to be the first author of our -geographical knowledge; and he does not confine the application of -this assertion to the various and curious topographical information -which the Iliad and Odyssey contain, concerning the countries -surrounding the Mediterranean; but in phrases which, to most -persons, might appear the mere play of a poetical fancy, or a casual -selection of circumstances, he finds unquestionable evidence of a -correct knowledge of general geographical truths. Thus,[21\4] when -Homer speaks of the sun "rising from the soft and deep-flowing -ocean," of his "splendid blaze plunging in the ocean;" of the -northern constellation - "Alone unwashen by the ocean wave;" -and of Jupiter, "who goes to the ocean to feast with the blameless -Ethiopians;" Strabo is satisfied from these passages that Homer knew -the dry land to be surrounded with water: and he reasons in like -manner with respect to other points of geography. {204} - -[Note 21\4: Strabo, i. p. 5.] - -2. _Character of Commentators._--The spirit of commentation, as has -already been suggested, turns to questions of taste, of metaphysics, -of morals, with far more avidity than to physics. Accordingly, critics -and grammarians were peculiarly the growth of this school; and, though -the commentators sometimes chose works of mathematical or physical -science for their subject (as Proclus, who commented on Euclid's -Geometry, and Simplicius, on Aristotle's Physics), these commentaries -were, in fact, rather metaphysical than mathematical. It does not -appear that the commentators have, in any instance, illustrated the -author by bringing his assertions of facts to the test of experiment. -Thus, when Simplicius comments on the passage concerning a vacuum, -which we formerly adduced, he notices the argument which went upon the -assertion, that a vessel full of ashes would contain as much water as -an empty vessel; and he mentions various opinions of different -authors, but no trial of the fact. Eudemus had said, that the ashes -contained something hot, as quicklime does, and that by means of this, -a part of the water was evaporated; others supposed the water to be -condensed, and so on.[22\4] - -[Note 22\4: Simplicius, p. 170.] - -The Commentator's professed object is to explain, to enforce, to -illustrate doctrines assumed as true. He endeavors to adapt the work -on which he employs himself to the state of information and of opinion -in his own time; to elucidate obscurities and technicalities; to -supply steps omitted in the reasoning; but he does not seek to obtain -additional truths or new generalizations. He undertakes only to give -what is virtually contained in his author; to develop, but not to -create. He is a cultivator of the thoughts of others: his labor is not -spent on a field of his own; he ploughs but to enrich the granary of -another man. Thus he does not work as a freeman, but as one in a -servile condition; or rather, his is a menial, and not a productive -service: his office is to adorn the appearance of his master, not to -increase his wealth. - -Yet though the Commentator's employment is thus subordinate and -dependent, he is easily led to attribute to it the greatest -importance and dignity. To elucidate good books is, indeed, a useful -task; and when those who undertake this work execute it well, it -would be most unreasonable to find fault with them for not doing -more. But the critic, long and earnestly employed on one author, may -easily underrate the relative value of other kinds of mental -exertion. He may {205} ascribe too large dimensions to that which -occupies the whole of his own field of vision. Thus he may come to -consider such study as the highest aim, and best evidence of human -genius. To understand Aristotle, or Plato, may appear to him to -comprise all that is possible of profundity and acuteness. And when -he has travelled over a portion of their domain, and satisfied -himself that of this he too is master, he may look with complacency -at the circuit he has made, and speak of it as a labor of vast -effort and difficulty. We may quote, as an expression of this -temper, the language of Sir Henry Savile, in concluding a course of -lectures on Euclid, delivered at Oxford.[23\4] "By the grace of God, -gentlemen hearers, I have performed my promise; I have redeemed my -pledge. I have explained, according to my ability, the definitions, -postulates, axioms, and _first eight propositions_ of the Elements -of Euclid. Here, sinking under the weight of years, I lay down my -art and my instruments." - -[Note 23\4: Exolvi per Dei gratiam, Domini auditores, promissum; -liberavi fldem meam; explicavi pro meo modulo, definitiones, -petitiones, communes sententias, et _octo priores propositiones_ -Elementorum Euclidis. Hic, annis fessus, cyclos artemque repono.] - -We here speak of the peculiar province of the Commentator; for -undoubtedly, in many instances, a commentary on a received author -has been made the vehicle of conveying systems and doctrines -entirely different from those of the author himself; as, for -instance, when the New Platonists wrote, taking Plato for their -text. The labors of learned men in the stationary period, which came -under this description, belong to another class. - -3. _Greek Commentators on Aristotle._--The commentators or disciples -of the great philosophers did not assume at once their servile -character. At first their object was to supply and correct, as well -as to explain their teacher. Thus among the earlier commentators of -Aristotle, Theophrastus invented five moods of syllogism in the -first figure, in addition to the four invented by Aristotle, and -stated with additional accuracy the rules of hypothetical -syllogisms. He also not only collected much information concerning -animals, and natural events, which Aristotle had omitted, but often -differed with his master; as, for instance, concerning the saltness -of the sea: this, which the Stagirite attributed to the effect of -the evaporation produced by the sun's rays, was ascribed by -Theophrastus to beds of salt at the bottom. Porphyry,[24\4] who -flourished in the third century, wrote a book on the _Predicables_, -which was found to be so suitable a complement {206} to the -_Predicaments_ or Categories of Aristotle, that it was usually -prefixed to that treatise; and the two have been used as an -elementary work together, up to modern times. The Predicables are -the five steps which the gradations of generality and particularity -introduce;--_genus_, _species_, _difference_, _individual_, -_accident_:--the Categories are the ten heads under which assertions -or predications may be arranged:--_substance_, _quantity_, -_relation_, _quality_, _place_, _time_, _position_, _habit_, -_action_, _passion_. - -[Note 24\4: Buhle, Arist. i. 284.] - -At a later period, the Aristotelian commentators became more -servile, and followed the author step by step, explaining, according -to their views, his expressions and doctrines; often, indeed, with -extreme prolixity, expanding his clauses into sentences, and his -sentences into paragraphs. Alexander Aphrodisiensis, who lived at -the end of the second century, is of this class; "sometimes useful," -as one of the recent editors of Aristotle says;[25\4] "but by the -prolixity of his interpretation, by his perverse itch for himself -discussing the argument expounded by Aristotle, for defending his -opinions, and for refuting or reconciling those of others, he rather -obscures than enlightens." At various times, also, some of the -commentators, and especially those of the Alexandrian school, -endeavored to reconcile, or combined without reconciling, opposing -doctrines of the great philosophers of the earlier times. -Simplicius, for instance, and, indeed, a great number of the -Alexandrian Philosophers,[26\4] as Alexander, Ammonius, and others, -employed themselves in the futile task of reconciling the doctrines -of the Pythagoreans, of the Eleatics, of Plato, and of the Stoics, -with those of Aristotle. Boethius[27\4] entertained the design of -translating into Latin the whole of Aristotle's and Plato's works, -and of showing their agreement; a gigantic plan, which he never -executed. Others employed themselves in disentangling the confusion -which such attempts produced, as John the Grammarian, surnamed -Philoponus, "the Labor-loving;" who, towards the end of the seventh -century, maintained that Aristotle was entirely misunderstood by -Porphyry and Proclus,[28\4] who had pretended to incorporate his -doctrines into those of the New Platonic school, or even to -reconcile him with Plato himself on the subject of _ideas_. Others, -again, wrote Epitomes, Compounds, Abstracts; and endeavored to throw -the works of the philosopher into some simpler and more obviously -regular form, as John of Damascus, in {207} the middle of the eighth -century, who made abstracts of some of Aristotle's works, and -introduced the study of the author into theological education. These -two writers lived under the patronage of the Arabs; the former was -favored by Amrou, the conqueror of Egypt; the latter was at first -secretary to the Caliph, but afterwards withdrew to a -monastery.[29\4] - -[Note 25\4: Ib. i. 288.] - -[Note 26\4: Ib. i. 311.] - -[Note 27\4: Degerando, _Hist. des Syst._ iv. 100.] - -[Note 28\4: Ib. iv. 155.] - -[Note 29\4: Deg. iv. 150.] - -At this period the Arabians became the fosterers and patrons of -philosophy, rather than the Greeks. Justinian had, by an edict, -closed the school of Athens, the last of the schools of heathen -philosophy. Leo, the Isaurian, who was a zealous Iconoclast, -abolished also the schools where general knowledge had been taught, -in combination with Christianity,[30\4] yet the line of the -Aristotelian commentators was continued, though feebly, to the later -ages of the Greek empire. Anna Comnena[31\4] mentions a Eustratus -who employed himself upon the dialectic and moral treatises, and -whom she does not hesitate to elevate above the Stoics and -Platonists, for his talent in philosophical discussions. Nicephorus -Blemmydes wrote logical and physical epitomes for the use of John -Ducas; George Pachymerus composed an epitome of the philosophy of -Aristotle, and a compend of his logic; Theodore Metochytes, who was -famous in his time alike for his eloquence and his learning, has -left a paraphrase of the books of Aristotle on Physics, on the Soul, -the Heavens,[32\4] &c. Fabricius states that this writer has a -chapter, the object of which is to prove, that all philosophers, and -Aristotle and Plato in particular, have disdained the authority of -their predecessors. He could hardly help remarking in how different -a spirit philosophy had been pursued since their time. - -[Note 30\4: Ib. iv. 163.] - -[Note 31\4: Ib. 167.] - -[Note 32\4: Ib. 168.] - -4. _Greek Commentators of Plato and others._--I have spoken -principally of the commentators of Aristotle, for he was the great -subject of the commentators proper; and though the name of his -rival, Plato, was graced by a list of attendants, hardly less -numerous, these, the Neoplatonists, as they are called, had -introduced new elements into the doctrines of their nominal master, -to such an extent that they must be placed in a different class. We -may observe here, however, how, in this school as in the -Peripatetic, the race of commentators multiplied itself. Porphyry, -who commented on Aristotle, was commented on by Ammonius; Plotinus's -Enneads were commented on by Proclus and Dexippus. Psellus[33\4] the -elder was a paraphrast of {208} Aristotle; Psellus the younger, in -the eleventh century, attempted to restore the New Platonic school. -The former of these two writers had for his pupils two men, the -emperor Leo, surnamed the Philosopher, and Photius the patriarch, -who exerted themselves to restore the study of literature at -Constantinople. We still possess the Collection of Extracts of -Photius, which, like that of Stobæus and others, shows the tendency -of the age to compilations, abstracts, and epitomes,--the extinction -of philosophical vitality. - -[Note 33\4: Deg. iv. 169.] - -5. _Arabian Commentators of Aristotle._--The reader might perhaps -have expected, that when the philosophy of the Greeks was carried -among a new race of intellects, of a different national character -and condition, the train of this servile tradition would have been -broken; that some new thoughts would have started forth; that some -new direction, some new impulse, would have been given to the search -for truth. It might have been anticipated that we should have had -schools among the Arabians which should rival the Peripatetic, -Academic, and Stoic among the Greeks;--that they would preoccupy the -ground on which Copernicus and Galileo, Lavoisier and Linnæus, won -their fame;--that they would make the next great steps in the -progressive sciences. Nothing of this, however, happened. The -Arabians cannot claim, in science or philosophy, any really great -names; they produced no men and no discoveries which have materially -influenced the course and destinies of human knowledge; they tamely -adopted the intellectual servitude of the nation which they -conquered by their arms; they joined themselves at once to the -string of slaves who were dragging the car of Aristotle and -Plotinus. Nor, perhaps, on a little further reflection, shall we be -surprised at this want of vigor and productive power, in this period -of apparent national youth. The Arabians had not been duly prepared -rightly to enjoy and use the treasures of which they became -possessed. They had, like most uncivilized nations, been -passionately fond of their indigenous poetry; their imagination had -been awakened, but their rational powers and speculative tendencies -were still torpid. They received the Greek philosophy without having -passed through those gradations of ardent curiosity and keen -research, of obscurity brightening into clearness, of doubt -succeeded by the joy of discovery, by which the Greek mind had been -enlarged and exercised. Nor had the Arabians ever enjoyed, as the -Greeks had, the individual consciousness, the independent volition, -the intellectual freedom, arising from the freedom of political -institutions. They had not felt the contagious mental activity of a -small city,--the elation arising from the general {209} sympathy in -speculative pursuits diffused through an intelligent and acute -audience; in short, they had not had a national education such as -fitted the Greeks to be disciples of Plato and Hipparchus. Hence, -their new literary wealth rather encumbered and enslaved, than -enriched and strengthened them: in their want of taste for -intellectual freedom, they were glad to give themselves up to the -guidance of Aristotle and other dogmatists. Their military habits -had accustomed them to look to a leader; their reverence for the -book of their law had prepared them to accept a philosophical Koran -also. Thus the Arabians, though they never translated the Greek -poetry, translated, and merely translated, the Greek philosophy; -they followed the Greek philosophers without deviation, or, at -least, without any philosophical deviations. They became for the -most part Aristotelians;--studied not only Aristotle, but the -commentators of Aristotle; and themselves swelled the vast and -unprofitable herd. - -The philosophical works of Aristotle had, in some measure, made -their way in the East, before the growth of the Saracen power. In -the sixth century, a Syrian, Uranus,[34\4] encouraged by the love of -philosophy manifested by Cosroes, had translated some of the -writings of the Stagirite; about the same time, Sergius had given -some translations in Syriac. In the seventh century, Jacob of Edessa -translated into this language the Dialectics, and added Notes to the -work. Such labors became numerous; and the first Arabic translations -of Aristotle were formed upon these Persian or Syriac texts. In this -succession of transfusions, some mistakes must inevitably have been -introduced. - -[Note 34\4: Deg. iv. 196.] - -The Arabian interpreters of Aristotle, like a large portion of the -Alexandrian ones, gave to the philosopher a tinge of opinions -borrowed from another source, of which I shall have to speak under -the head of _Mysticism_. But they are, for the most part, -sufficiently strong examples of the peculiar spirit of commentation, -to make it fitting to notice them here. At the head of them -stands[35\4] Alkindi, who appears to have lived at the court of -Almamon, and who wrote commentaries on the Organon of Aristotle. But -Alfarabi was the glory of the school of Bagdad; his knowledge -included mathematics, astronomy, medicine, and philosophy. Born in -an elevated rank, and possessed of a rich patrimony, he led an -austere life, and devoted himself altogether to study and -meditation. He employed himself particularly in unfolding the import -of Aristotle's treatise On the Soul.[36\4] Avicenna (Ebn Sina) {210} -was at once the Hippocrates and the Aristotle of the Arabians; and -certainly the most extraordinary man that the nation produced. In -the course of an unfortunate and stormy life, occupied by politics -and by pleasures, he produced works which were long revered as a -sort of code of science. In particular, his writings on medicine, -though they contain little besides a compilation of Hippocrates and -Galen, took the place of both, even in the universities of Europe; -and were studied as models at Paris and Montpelier, till the end of -the seventeenth century, at which period they fell into an almost -complete oblivion. Avicenna is conceived, by some modern -writers,[37\4] to have shown some power of original thinking in his -representations of the Aristotelian Logic and Metaphysics. Averroes -(Ebn Roshd) of Cordova, was the most illustrious of the Spanish -Aristotelians, and became the guide of the schoolmen,[38\4] being -placed by them on a level with Aristotle himself, or above him. He -translated Aristotle from the first Syriac version, not being able -to read the Greek text. He aspired to, and retained for centuries, -the title of the _Commentator_; and he deserves this title by the -servility with which he maintains that Aristotle[39\4] carried the -sciences to the highest possible degree, measured their whole -extent, and fixed their ultimate and permanent boundaries; although -his works are conceived to exhibit a trace of the New Platonism. -Some of his writings are directed against an Arabian skeptic, of the -name of Algazel, whom we have already noticed. - -[Note 35\4: Ib. iv. 187.] - -[Note 36\4: Ib. iv. 205.] - -[Note 37\4: Deg. iv. 206.] - -[Note 38\4: Ib. iv. 247. Averroes died A. D. 1206.] - -[Note 39\4: Ib. iv. 248.] - -When the schoolmen had adopted the supremacy of Aristotle to the -extent in which Averroes maintained it, their philosophy went -further than a system of mere commentation, and became a system of -dogmatism; we must, therefore, in another chapter, say a few words -more of the Aristotelians in this point of view, before we proceed -to the revival of science; but we must previously consider some -other features in the character of the Stationary Period. {211} - - - - -CHAPTER III. - -OF THE MYSTICISM OF THE MIDDLE AGES. - - -IT has been already several times hinted, that a new and peculiar -element was introduced into the Greek philosophy which occupied the -attention of the Alexandrian school; and that this element tinged a -large portion of the speculations of succeeding ages. We may speak -of this peculiar element as _Mysticism_; for, from the notion -usually conveyed by this term, the reader will easily apprehend the -general character of the tendency now spoken of; and especially when -he sees its effect pointed out in various subjects. Thus, instead of -referring the events of the external world to space and time, to -sensible connection and causation, men attempted to reduce such -occurrences under spiritual and supersensual relations and -dependencies; they referred them to superior intelligences, to -theological conditions, to past and future events in the moral -world, to states of mind and feelings, to the creatures of an -imaginary mythology or demonology. And thus their physical Science -became Magic, their Astronomy became Astrology, the study of the -Composition of bodies became Alchemy, Mathematics became the -contemplation of the Spiritual Relations of number and figure, and -Philosophy became Theosophy. - -The examination of this feature in the history of the human mind is -important for us, in consequence of its influence upon the -employments and the thoughts of the times now under our notice. This -tendency materially affected both men's speculations and their -labours in the pursuit of knowledge. By its direct operation, it -gave rise to the newer Platonic philosophy among the Greeks, and to -corresponding doctrines among the Arabians; and by calling into a -prominent place astrology, alchemy, and magic, it long occupied most -of the real observers of the material world. In this manner it -delayed and impeded the progress of true science; for we shall see -reason to believe that human knowledge lost more by the perversion -of men's minds and the misdirection of their efforts, than it gained -by any increase of zeal arising from the peculiar hopes and objects -of the mystics. - -It is not our purpose to attempt any general view of the progress -and fortunes of the various forms of Mystical Philosophy; but only -to exhibit some of its characters, in so far as they illustrate -those {212} tendencies of thought which accompanied the -retrogradation of inductive science. And of these, the leading -feature which demands our notice is that already alluded to; namely, -the practice of referring things and events, not to clear and -distinct relations, obviously applicable to such cases;--not to -general rules capable of direct verification; but to notions vague, -distant, and vast, which we cannot bring into contact with facts, -because they belong to a different region from the facts; as when we -connect natural events with moral or historical causes, or seek -spiritual meanings in the properties of number and figure. Thus the -character of Mysticism is, that it refers particulars, not to -generalizations homogeneous and immediate, but to such as are -heterogeneous and remote; to which we must add, that the process of -this reference is not a calm act of the intellect, but is -accompanied with a glow of enthusiastic feeling. - -1. _Neoplatonic Theosophy._--The _Newer Platonism_ is the first -example of this Mystical Philosophy which I shall consider. The main -points which here require our notice are, the doctrine of an -Intellectual World resulting from the act of the Divine Mind, as the -only reality; and the aspiration after the union of the human soul -with this Divine Mind, as the object of human existence. The "Ideas" -of Plato were Forms of our knowledge; but among the Neoplatonists -they became really existing, indeed the only really existing, -Objects; and the inaccessible scheme of the universe which these -ideas constitute, was offered as the great subject of philosophical -contemplation. The desire of the human mind to approach towards its -Creator and Preserver, and to obtain a spiritual access to Him, -leads to an employment of the thoughts which is well worth the -notice of the religious philosopher; but such an effort, even when -founded on revelation and well regulated, is not a means of advance -in physics; and when it is the mere result of natural enthusiasm, it -may easily obtain such a place in men's minds as to unfit them for -the successful prosecution of natural philosophy. The temper, -therefore, which introduces such supernatural communion into the -general course of its speculations, may be properly treated as -mystical, and as one of the causes of the decline of science in the -Stationary Period. The Neoplatonic philosophy requires our notice as -one of the most remarkable forms of this Mysticism. - -Though Ammonius Saccas, who flourished at the end of the second -century, is looked upon as the beginner of the Neoplatonists, his -disciple Plotinus is, in reality, the great founder of the school, -both by his {213} works, which still remain to us, and by the -enthusiasm which his character and manners inspired among his -followers. He lived a life of meditation, gentleness, and -self-denial, and died in the second year of the reign of Claudius -(A. D. 270). His disciple, Porphyry, has given us a Life of him, -from which we may see how well his habitual manners were suited to -make his doctrines impressive. "Plotinus, the philosopher of our -time," Porphyry thus begins his biography, "appeared like a person -ashamed that he was in the body. In consequence of this disposition, -he could not bear to talk concerning his family, or his parents, or -his country. He would not allow himself to be represented by a -painter or statuary; and once, when Aurelius entreated him to permit -a likeness of him to be taken, he said, 'Is it not enough for us to -carry this image in which nature has enclosed us, but we must also -try to leave a more durable image of this image, as if it were so -great a sight?' And he retained the same temper to the last. When he -was dying, he said, 'I am trying to bring the divinity which is in -us to the divinity which is in the universe.'" He was looked upon by -his successors with extraordinary admiration and reverence; and his -disciple Porphyry collected from his lips, or from fragmental notes, -the six _Enneads_ of his doctrines (that is, parts each consisting -of _nine_ Books), which he arranged and annotated. - -We have no difficulty in finding in this remarkable work examples of -mystical speculation. The Intelligible World of realities or essences -corresponds to the world of sense[40\4] in the classes of things which -it includes. To the Intelligible World, man's mind ascends, by a -triple road which Plotinus figuratively calls that of the Musician, -the Lover, the Philosopher.[41\4] The activity of the human soul is -identified by analogy with the motion of the heavens. "This activity -is about a middle point, and thus it is circular; but a middle point -is not the same in body and in the soul: in that, the middle point is -local; in this, it is that on which the rest depends. There is, -however, an analogy; for as in one case, so in the other, there must -be a middle point, and as the sphere revolves about its centre, the -soul revolves about God through its affections." - -[Note 40\4: vi. Ennead, iii. 1.] - -[Note 41\4: ii. E. ii. 2.] - -The conclusion of the work is,[42\4] as might be supposed, upon the -approach to, union with, and fruition of God. The author refers -again to the analogy between the movements of the soul and those of -the heavens. "We move round him like a choral dance; even when we -{214} look from him we revolve about him: we do not always look at -him, but when we do, we have satisfaction and rest, and the harmony -which belongs to that divine movement. In this movement, the mind -beholds the fountain of life, the fountain of mind, the origin of -being, the cause of good, the root of the soul."[43\4] "There will -be a time when this vision shall be continual; the mind being no -more interrupted, nor suffering any perturbation from the body. Yet -that which beholds is not that which is disturbed; and when this -vision becomes dim, it does not obscure the knowledge which resides -in demonstration, and faith, and reasoning; but the vision itself is -not reason, but greater than reason, and before reason."[44\4] - -[Note 42\4: vi. Enn. ix. 8.] - -[Note 43\4: vi. Enn. ix. 9.] - -[Note 44\4: vi. Enn. ix. 10.] - -The fifth book of the third Ennead has for its subject the Dæmon -which belongs to each man. It is entitled "Concerning Love;" and the -doctrine appears to be, that the Love, or common source of the -passions which is in each man's mind, is "the Dæmon which they say -accompanies each man."[45\4] These dæmons were, however (at least by -later writers), invested with a visible aspect and with a personal -character, including a resemblance of human passions and motives. It -is curious thus to see an untenable and visionary generalization -falling back into the domain of the senses and the fancy, after a -vain attempt to support itself in the region of the reason. This -imagination soon produced pretensions to the power of making these -dæmons or genii visible; and the Treatise on the Mysteries of the -Egyptians, which is attributed to Iamblichus, gives an account of -the secret ceremonies, the mysterious words, the sacrifices and -expiations, by which this was to be done. - -[Note 45\4: Ficinus, _Comm._ in v. Enn. iii.] - -It is unnecessary for us to dwell on the progress of this school; to -point out the growth of the Theurgy which thus arose; or to describe -the attempts to claim a high antiquity for this system, and to make -Orpheus, the poet, the first promulgator of its doctrines. The -system, like all mystical systems, assumed the character rather of -religion than of a theory. The opinions of its disciples materially -influenced their lives. It gave the world the spectacle of an -austere morality, a devotional exaltation, combined with the -grossest superstitions of Paganism. The successors of Iamblichus -appeared rather to hold a priesthood, than the chair of a -philosophical school.[46\4] They were persecuted by Constantine and -Constantius, as opponents of Christianity. Sopater, a {215} Syrian -philosopher of this school, was beheaded by the former emperor on a -charge that he had bound the winds by the power of magic.[47\4] But -Julian, who shortly after succeeded to the purple, embraced with -ardor the opinions of Iamblichus. Proclus (who died A. D. 487) was -one of the greatest of the teachers of this school;[48\4] and was, -both in his life and doctrines, a worthy successor of Plotinus, -Porphyry, and Iamblichus. We possess a biography, or rather a -panegyric of him, by his disciple Marinus, in which he is exhibited -as a representation of the ideal perfection of the philosophic -character, according to the views of the Neoplatonists. His virtues -are arranged as physical, moral, purificatory, theoretic, and -theurgic. Even in his boyhood, Apollo and Minerva visited him in his -dreams: he studied oratory at Alexandria, but it was at Athens that -Plutarch and Lysianus initiated him in the mysteries of the New -Platonists. He received a kind of consecration at the hands of the -daughter of Plutarch, the celebrated Asclepigenia, who introduced -him to the traditions of the Chaldeans, and the practices of -theurgy; he was also admitted to the mysteries of Eleusis. He became -celebrated for his knowledge and eloquence; but especially for his -skill in the supernatural arts which were connected with the -doctrines of his sect. He appears before us rather as a hierophant -than a philosopher. A large portion of his life was spent in -evocations, purifications, fastings, prayers, hymns, intercourse -with apparitions, and with the gods, and in the celebration of the -festivals of Paganism, especially those which were held in honor of -the Mother of the Gods. His religious admiration extended to all -forms of mythology. The philosopher, said he, is not the priest of a -single religion, but of all the religions of the world. Accordingly, -he composed hymns in honor of all the divinities of Greece, Rome, -Egypt, Arabia;--Christianity alone was excluded from his favor. - -[Note 46\4: Deg. iii. 407] - -[Note 47\4: Gibbon, iii. 352.] - -[Note 48\4: Deg. iii. 419.] - -The reader will find an interesting view of the _School of -Alexandria_, in M. Barthelemy Saint-Hilaire's _Rapport_ on the -_Mémoires_ sent to the Academy of Moral and Political Sciences at -Paris, in consequence of its having, in 1841, proposed this as the -subject of a prize, which was awarded in 1844. M. Saint-Hilaire has -prefixed to this _Rapport_ a dissertation on the Mysticism of that -school. He, however, uses the term _Mysticism_ in a wider sense than -my purpose, which regarded mainly the bearing of the doctrines of -this school upon the progress of the Inductive Sciences, has led me -to do. Although he finds much to {216} admire in the Alexandrian -philosophy, he declares that they were incapable of treating -scientific questions. The extent to which this is true is well -illustrated by the extract which he gives from Plotinus, on the -question, "Why objects appear smaller in proportion as they are more -distant." Plotinus denies that the reason of this is that the angles -of vision become smaller. His reason for this denial is curious -enough. If it were so, he says, how could the heaven appear smaller -than it is, since it occupies the whole of the visual angle? - -2. _Mystical Arithmetic._--It is unnecessary further to exemplify, -from Proclus, the general mystical character of the school and time -to which he belonged; but we may notice more specially one of the -forms of this mysticism, which very frequently offers itself to our -notice, especially in him; and which we may call _Mystical -Arithmetic_. Like all the kinds of Mysticism, this consists in the -attempt to connect our conceptions of external objects by general -and inappropriate notions of goodness, perfection, and relation to -the divine essence and government; instead of referring such -conceptions to those appropriate ideas, which, by due attention, -become perfectly distinct, and capable of being positively applied -and verified. The subject which is thus dealt with, in the doctrines -of which we now speak, is Number; a notion which tempts men into -these visionary speculations more naturally than any other. For -number is really applicable to moral notions--to emotions and -feelings, and to their objects--as well as to the things of the -material world. Moreover, by the discovery of the principle of -musical concords, it had been found, probably most unexpectedly, -that numerical relations were closely connected with sounds which -could hardly be distinguished from the expression of thought and -feeling; and a suspicion might easily arise, that the universe, both -of matter and of thought, might contain many general and abstract -truths of some analogous kind. The relations of number have so wide -a bearing, that the ramifications of such a suspicion could not -easily be exhausted, supposing men willing to follow them into -darkness and vagueness; which it is precisely the mystical tendency -to do. Accordingly, this kind of speculation appeared very early, -and showed itself first among the Pythagoreans, as we might have -expected, from the attention which they gave to the theory of -harmony: and this, as well as some other of the doctrines of the -Pythagorean philosophy, was adopted by the later Platonists, and, -indeed, by Plato himself, whose speculations concerning number have -decidedly a mystical character. The mere mathematical relations of -numbers,--as odd and even, perfect and imperfect, {217} abundant and -defective,--were, by a willing submission to an enthusiastic bias, -connected with the notions of good and beauty, which were suggested -by the terms expressing their relations; and principles resulting -from such a connection were woven into a wide and complex system. It -is not necessary to dwell long on this subject; the mere titles of -the works which treated of it show its nature. Archytas[49\4] is -said to have written a treatise on the number _ten_: Telaugé, the -daughter of Pythagoras, wrote on the number _four_. This number, -indeed, which was known by the name of the _Tetractys_, was very -celebrated in the school of Pythagoras. It is mentioned in the -"Golden Verses," which are ascribed to him: the pupil is conjured to -be virtuous, - Ναὶ μὰ τὸν ἁμετέρᾳ ψυχᾷ παραδόντα τετρακτὺν - Παγὰν ἀεννάου φύσεως . . . . - By him who stampt _The Four_ upon the mind,-- - _The Four_, the fount of nature's endless stream. - -[Note 49\4: Mont. ii. 123.] - -In Plato's works, we have evidence of a similar belief in religious -relations of Number; and in the new Platonists, this doctrine was -established as a system. Proclus, of whom we have been speaking, -founds his philosophy, in a great measure, on the relation of Unity -and Multiple; from this, he is led to represent the causality of the -Divine Mind by three Triads of abstractions; and in the development -of one part of this system, the number seven is introduced.[50\4] -"The intelligible and intellectual gods produce all things -triadically; for the monads in these latter are divided according to -number; and what the monad was in the former, the number is in these -latter. And the intellectual gods produce all things hebdomically; -for they evolve the intelligible, and at the same time intellectual -triads, into intellectual hebdomads, and expand their contracted -powers into intellectual variety." Seven is what is called by -arithmeticians a _prime_ number, that is, it cannot be produced by -the multiplication of other numbers. In the language of the New -Platonists, the number seven is said to be a virgin, and without a -mother, and it is therefore sacred to Minerva. The number six is a -perfect number, and is consecrated to Venus. - -[Note 50\4: Procl. v. 3, Taylor's translation.] - -The relations of space were dealt with in like manner, the -Geometrical properties being associated with such physical and -metaphysical notions as vague thought and lively feeling could -anyhow connect with them. We may consider, as an example of -this,[51\4] Plato's opinion {218} concerning the particles of the -four elements. He gave to each kind of particle one of the five -regular solids, about which the geometrical speculations of himself -and his pupils had been employed. The particles of fire were -pyramids, because they are sharp, and tend upwards; those of earth -are cubes, because they are stable, and fill space; the particles of -air are octahedral, as most nearly resembling those of fire; those -of water are the icositetrahedron, as most nearly spherical. The -dodecahedron is the figure of the element of the heavens, and shows -its influence in other things, as in the twelve signs of the zodiac. -In such examples we see how loosely space and number are combined or -confounded by these mystical visionaries. - -[Note 51\4: Stanley, _Hist. Phil._] - -These numerical dreams of ancient philosophers have been imitated by -modern writers; for instance, by Peter Bungo and Kircher, who have -written De Mysteriis Numerorum. Bungo treats of the mystical -properties of each of the numbers in order, at great length. And -such speculations have influenced astronomical theories. In the -first edition of the Alphonsine Tables,[52\4] the precession was -represented by making the first point of Aries move, in a period of -7000 years, through a circle of which the radius was 18 degrees, -while the circle moved round the ecliptic in 49,000 years; and these -numbers, 7000 and 49,000, were chosen probably by Jewish -calculators, or with reference to Jewish Sabbatarian notions. - -[Note 52\4: Montucla, i. 511.] - -3. _Astrology._--Of all the forms which mysticism assumed, none was -cultivated more assiduously than astrology. Although this art -prevailed most universally and powerfully during the stationary -period, its existence, even as a detailed technical system, goes -back to a very early age. It probably had its origin in the East; it -is universally ascribed to the Babylonians and Chaldeans; the name -_Chaldean_ was, at Rome, synonymous with _mathematicus_, or -astrologer; and we read repeatedly that this class of persons were -expelled from Italy by a decree of the senate, both during the times -of the republic and of the empire.[53\4] The recurrence of this act -of legislation shows that it was not effectual: "It is a class of -men," says Tacitus, "which, in our city, will always be prohibited, -and will always exist." In Greece, it does not appear that the state -showed any hostility to the professors of this art. They undertook, -it would seem, then, as at a later period, to determine the course -of a man's character and life from the configuration of the stars at -the moment of his birth. We do not possess any of the {219} -speculations of the early astrologers; and we cannot therefore be -certain that the notions which operated in men's minds when the art -had its birth, agreed with the views on which it was afterwards -defended, when it became a matter of controversy. But it appears -probable, that, though it was at later periods supported by physical -analogies, it was originally suggested by mythological belief. The -Greeks spoke of the _influences_ or _effluxes_ (ἀπόῤῥοιας) which -proceeded from the stars; but the Chaldeans had probably thought -rather of the powers which they exercised as _deities_. In whatever -manner the sun, moon, and planets came to be identified with gods -and goddesses, it is clear that the characters ascribed to these -gods and goddesses regulate the virtues and powers of the stars -which bear their names. This association, so manifestly visionary, -was retained, amplified, and pursued, in an enthusiastic spirit, -instead of being rejected for more distinct and substantial -connections; and a pretended science was thus formed, which bears -the obvious stamp of mysticism. - -[Note 53\4: Tacit. _Ann._ ii. 32. xii. 52. _Hist._ I. 22, II. 62.] - -That common sense of mankind which teaches them that theoretical -opinions are to be calmly tried by their consequences and their -accordance with facts, appears to have counteracted the prevalence -of astrology in the better times of the human mind. Eudoxus, as we -are informed by Cicero,[54\4] rejected the pretensions of the -Chaldeans; and Cicero himself reasons against them with arguments as -sensible and intelligent as could be adduced by a writer of the -present day; such as the different fortunes and characters of -persons born at the same time; and the failure of the predictions, -in the case of Pompey, Crassus, Cæsar, to whom the astrologers had -foretold glorious old age and peaceful death. He also employs an -argument which the reader would perhaps not expect from him,--the -very great remoteness of the planets as compared with the distance -of the moon. "What contagion can reach us," he asks, "from a -distance almost infinite?" - -[Note 54\4: Cic. _de Div._ ii. 42.] - -Pliny argues on the same side, and with some of the same -arguments.[55\4] "Homer," he says, "tells us that Hector and -Polydamus were born the same night;--men of such different fortune. -And every hour, in every part of the world, are born lords and -slaves, kings and beggars." - -[Note 55\4: _Hist. Nat._ vii. 49.] - -The impression made by these arguments is marked in an anecdote told -concerning Publius Nigidius Figulus, a Roman of the time of Julius -Cæsar, whom Lucan mentions as a celebrated astrologer. It is {220} -said, that when an opponent of the art urged as an objection the -different fates of persons born in two successive instants, Nigidius -bade him make two contiguous marks on a potter's wheel, which was -revolving rapidly near them. On stopping the wheel, the two marks were -found to be really far removed from each other; and Nigidius is said -to have received the name of Figulus (the potter), in remembrance of -this story, His argument, says St. Augustine, who gives us the -narrative, was as fragile as the ware which the wheel manufactured. - -As the darkening times of the Roman empire advanced, even the -stronger minds seem to have lost the clear energy which was -requisite to throw off this delusion. Seneca appears to take the -influence of the planets for granted; and even Tacitus[56\4] seems -to hesitate. "For my own part," says he, "I doubt; but certainly the -majority of mankind cannot be weaned from the opinion, that, at the -birth of each man, his future destiny is fixed; though some things -may fall out differently from the predictions, by the ignorance of -those who profess the art; and that thus the art is unjustly blamed, -confirmed as it is by noted examples in all ages." The occasion -which gives rise to these reflections of the historian is the -mention of Thrasyllus, the favorite astrologer of the Emperor -Tiberius, whose skill is exemplified in the following narrative. -Those who were brought to Tiberius on any important matter, were -admitted to an interview in an apartment situated on a lofty cliff -in the island of Capreæ. They reached this place by a narrow path, -accompanied by a single freedman of great bodily strength; and on -their return, if the emperor had conceived any doubts of their -trustworthiness, a single blow buried the secret and its victim in -the ocean below. After Thrasyllus had, in this retreat, stated the -results of his art as they concerned the emperor, Tiberius asked him -whether he had calculated how long he himself had to live. The -astrologer examined the aspect of the stars, and while he did this, -as the narrative states, showed hesitation, alarm, increasing -terror, and at last declared that, "the present hour was for him -critical, perhaps fatal." Tiberius embraced him, and told him "he -was right in supposing he had been in danger, but that he should -escape it;" and made him thenceforth his confidential counsellor. - -[Note 56\4: _Ann._ vi. 22.] - -The belief in the power of astrological prediction which thus obtained -dominion over the minds of men of literary cultivation and practical -energy, naturally had a more complete sway among the speculative {221} -but unstable minds of the later philosophical schools of Alexandria, -Athens, and Rome. We have a treatise on astrology by Proclus, which -will serve to exemplify the mystical principle in this form. It -appears as a commentary on a work on the same subject called -"Tetrabiblos," ascribed to Ptolemy; though we may reasonably doubt -whether the author of the "Megale Syntaxis" was also the writer of the -astrological work. A few notices of the commentary of Proclus will -suffice.[57\4] The science is defended by urging how powerful we know -the physical effects of the heavenly bodies to be. "The sun regulates -all things on earth;--the birth of animals, the growth of fruits, the -flowing of waters, the change of health, according to the seasons: he -produces heat, moisture, dryness, cold, according to his approach to -our zenith. The moon, which is the nearest of all bodies to the earth, -gives out much _influence_; and all things, animate and inanimate, -sympathize with her: rivers increase and diminish according to her -light; the advance of the sea, and its recess, are regulated by her -rising and setting; and along with her, fruits and animals wax and -wane, either wholly or in part." It is easy to see that by pursuing -this train of associations (some real and some imaginary) very vaguely -and very enthusiastically, the connections which astrology supposes -would receive a kind of countenance. Proclus then proceeds to -state[58\4] the doctrines of the science. "The sun," he says, "is -productive of heat and dryness; this power is moderate in its nature, -but is more perceived than that of the other luminaries, from his -magnitude, and from the change of seasons. The nature of the moon is -for the most part moist; for being the nearest to the earth, she -receives the vapors which rise from moist bodies, and thus she causes -bodies to soften and rot. But by the illumination she receives from -the sun, she partakes in a moderate degree of heat. Saturn is cold and -dry, being most distant both from the heating power of the sun, and -the moist vapors of the earth. His cold, however, is most prevalent, -his dryness is more moderate. Both he and the rest receive additional -powers from the configurations which they make with respect to the sun -and moon." In the same manner it is remarked that Mars is dry and -caustic, from his fiery nature, which, indeed, his color shows. -Jupiter is well compounded of warm and moist, as is Venus. Mercury is -variable in his character. From these notions were derived others -concerning the beneficial or hurtful effect of these stars. Heat and -{222} moisture are generative and creative elements; hence the -ancients, says Proclus, deemed Jupiter, and Venus, and the Moon to -have a good power; Saturn and Mercury, on the other hand, had an evil -nature. - -[Note 57\4: I. 2.] - -[Note 58\4: I. 4.] - -Other distinctions of the character of the stars are enumerated, -equally visionary, and suggested by the most fanciful connections. -Some are masculine, and some feminine: the Moon and Venus are of the -latter kind. This appears to be merely a mythological or -etymological association. Some are diurnal, some nocturnal: the Moon -and Venus are of the latter kind, the Sun and Jupiter of the former; -Saturn and Mars are both. - -The fixed stars, also, and especially those of the zodiac, had -especial influences and subjects assigned to them. In particular, each -sign was supposed to preside over a particular part of the body; thus -Aries had the head assigned to it, Taurus the neck, and so on. - -The most important part of the sky in the astrologer's consideration, -was that sign of the zodiac which rose at the moment of the child's -birth; this was, properly speaking, the _horoscope_, the _ascendant_, -or the _first house_; the whole circuit of the heavens being divided -into twelve _houses_, in which life and death, marriage and children, -riches and honors, friends and enemies, were distributed. - -We need not attempt to trace the progress of this science. It -prevailed extensively among the Arabians, as we might expect from the -character of that nation. Albumasar, of Balkh in Khorasan, who -flourished in the ninth century, who was one of their greatest -astronomers, was also a great astrologer; and his work on the latter -subject, "De Magnis Conjunctionibus, Annorum Revolutionibus ac eorum -Perfectionibus," was long celebrated in Europe. Aboazen Haly (the -writer of a treatise "De Judiciis Astrorum"), who lived in Spain in -the thirteenth century, was one of the classical authors on this -subject. - -It will easily be supposed that when this _apotelesmatic_ or -_judicial_ astrology obtained firm possession of men's minds, it -would be pursued into innumerable subtle distinctions and -extravagant conceits; and the more so, as experience could offer -little or no check to such exercises of fancy and subtlety. For the -correction of rules of astrological divination by comparison with -known events, though pretended to by many professors of the art, was -far too vague and fallible a guidance to be of any real advantage. -Even in what has been called Natural Astrology, the dependence of -the weather on the heavenly bodies, it is easy to see what a vast -accumulation of well-observed facts is requisite to establish {223} -any true rule; and it is well known how long, in spite of facts, -false and groundless rules (as the dependence of the weather on the -moon) may keep their hold on men's minds. When the facts are such -loose and many-sided things as human characters, passions, and -happiness, it was hardly to be expected that even the most powerful -minds should be able to find a footing sufficiently firm, to enable -them to resist the impression of a theory constructed of sweeping -and bold assertions, and filled out into a complete system of -details. Accordingly, the connection of the stars with human persons -and actions was, for a long period, undisputed. The vague, obscure, -and heterogeneous character of such a connection, and its unfitness -for any really scientific reasoning, could, of course, never be got -rid of; and the bewildering feeling of earnestness and solemnity, -with which the connection of the heavens with man was contemplated, -never died away. In other respects, however, the astrologers fell -into a servile commentatorial spirit; and employed themselves in -annotating and illustrating the works of their predecessors to a -considerable extent, before the revival of true science. - -It may be mentioned, that astrology has long been, and probably is, -an art held in great esteem and admiration among other eastern -nations besides the Mohammedans; for instance, the Jews, the -Indians, the Siamese, and the Chinese. The prevalence of vague, -visionary, and barren notions among these nations, cannot surprise -us; for with regard to them we have no evidence, as with regard to -Europeans we have, that they are capable, on subjects of physical -speculation, of originating sound and rational general principles. -The Arts may have had their birth in all parts of the globe; but it -is only Europe, at particular favored periods of its history, which -has ever produced Sciences. - -We are, however, now speaking of a long period, during which this -productive energy was interrupted and suspended. During this period -Europe descended, in intellectual character, to the level at which -the other parts of the world have always stood. Her Science was then -a mixture of Art and Mysticism; we have considered several forms of -this Mysticism, but there are two others which must not pass -unnoticed, Alchemy and Magic. - -We may observe, before we proceed, that the deep and settled -influence which Astrology had obtained among them, appears perhaps -most strongly in the circumstance, that the most vigorous and -clear-sighted minds which were concerned in the revival of science, -did not, for a long period, shake off the persuasion that there was, -in this art, some element of truth. Roger Bacon, Cardan, Kepler, -Tycho Brahe, {224} Francis Bacon, are examples of this. These, or -most of them, rejected all the more obvious and extravagant -absurdities with which the subject had been loaded; but still -conceived that some real and valuable truth remained when all these -were removed. Thus Campanella,[59\4] whom we shall have to speak of -as one of the first opponents of Aristotle, wrote an "Astrology -purified from all the Superstitions of the Jews and Arabians, and -treated physiologically." - -[Note 59\4: Bacon, _De Aug._ iii. 4.] - -4. _Alchemy._--Like other kinds of Mysticism, Alchemy seems to have -grown out of the notions of moral, personal, and mythological -qualities, which men associated with terms, of which the primary -application was to physical properties. This is the form in which -the subject is presented to us in the earliest writings which we -possess on the subject of chemistry;--those of Geber[60\4] of -Seville, who is supposed to have lived in the eighth or ninth -century. The very titles of Geber's works show the notions on which -this pretended science proceeds. They are, "Of the Search of -Perfection;" "Of the Sum of Perfection, or of the Perfect -Magistery;" "Of the Invention of Verity, or Perfection." The basis -of this phraseology is the distinction of metals into more or less -_perfect_; gold being the most perfect, as being the most valuable, -most beautiful, most pure, most durable; silver the next; and so on. -The "Search of Perfection" was, therefore, the attempt to convert -other metals into gold; and doctrines were adopted which represented -the metals as all compounded of the same elements, so that this was -theoretically possible. But the mystical trains of association were -pursued much further than this; gold and silver were held to be the -most noble of metals; gold was their King, and silver their Queen. -Mythological associations were called in aid of these fancies, as -had been done in astrology. Gold was Sol, silver was Luna, the moon; -copper, iron, tin, lead, were assigned to Venus, Mars, Jupiter, -Saturn. The processes of mixture and heat were spoken of as personal -actions and relations, struggles and victories. Some elements were -conquerors, some conquered; there existed preparations which -possessed the power of changing the whole of a body into a substance -of another kind: these were called _magisteries_.[61\4] When gold -and quicksilver are combined, the king and the queen are married, to -produce children of their own kind. It will easily be conceived, -that when chemical operations were described in phraseology of this -sort, the enthusiasm of the {225} fancy would be added to that of -the hopes, and observation would not be permitted to correct the -delusion, or to suggest sounder and more rational views. - -[Note 60\4: Thomson's _Hist. of Chem._ i. 117.] - -[Note 61\4: Boyle, Thomson's _Hist. Ch._ i. 25. Carolus Musitanus.] - -The exaggeration of the vague notion of perfection and power in the -object of the alchemist's search, was carried further still. The -same preparation which possessed the faculty of turning baser metals -into gold, was imagined to be also a universal medicine, to have the -gift of curing or preventing diseases, prolonging life, producing -bodily strength and beauty: the _philosophers' stone_ was finally -invested with every desirable efficacy which the fancy of the -"philosophers" could devise. - -It has been usual to say that Alchemy was the mother of Chemistry; -and that men would never have made the experiments on which the real -science is founded, if they had not been animated by the hopes and -the energy which the delusive art inspired. To judge whether this is -truly said, we must be able to estimate the degree of interest which -men feel in purely speculative truth, and in the real and -substantial improvement of art to which it leads. Since the fall of -Alchemy, and the progress of real Chemistry, these motives have been -powerful enough to engage in the study of the science, a body far -larger than the Alchemists ever were, and no less zealous. There is -no apparent reason why the result should not have been the same, if -the progress of true science had begun sooner. Astronomy was long -cultivated without the bribe of Astrology. But, perhaps, we may -justly say this;--that, in the stationary period, men's minds were -so far enfeebled and degraded, that pure speculative truth had not -its full effect upon them; and the mystical pursuits in which some -dim and disfigured images of truth were sought with avidity, were -among the provisions by which the human soul, even when sunk below -its best condition, is perpetually directed to something above the -mere objects of sense and appetite;--a contrivance of compensation, -as it were, in the intellectual and spiritual constitution of man. - -5. _Magic._--Magical Arts, so far as they were believed in by those -who professed to practise them, and so far as they have a bearing in -science, stand on the same footing as astrology; and, indeed, a -close alliance has generally been maintained between the two -pursuits. Incapacity and indisposition to perceive natural and -philosophical causation, an enthusiastic imagination, and such a -faith as can devise and maintain supernatural and spiritual -connexions, are the elements of this, as of other forms of -Mysticism. And thus, that temper which led men to aim at the -magician's supposed authority over the elements, {226} is an -additional exemplification of those habits of thought which -prevented the progress of real science, and the acquisition of that -command over nature which is founded on science, during the interval -now before us. - -But there is another aspect under which the opinions connected with -this pursuit may serve to illustrate the mental character of the -Stationary Period. - -The tendency, during the middle ages, to attribute the character of -Magician to almost all persons eminent for great speculative or -practical knowledge, is a feature of those times, which shows how -extensive and complete was the inability to apprehend the nature of -real science. In cultivated and enlightened periods, such as those of -ancient Greece, or modern Europe, knowledge is wished for and admired, -even by those who least possess it: but in dark and degraded periods, -superior knowledge is a butt for hatred and fear. In the one case, -men's eyes are open; their thoughts are clear; and, however high the -philosopher may be raised above the multitude, they can catch glimpses -of the intervening path, and see that it is free to all, and that -elevation is the reward of energy and labor. In the other case, the -crowd are not only ignorant, but spiritless; they have lost the -pleasure in knowledge, the appetite for it, and the feeling of dignity -which it gives: there is no sympathy which connects them with the -learned man: they see him above them, but know not how he is raised or -supported: he becomes an object of aversion and envy, of vague -suspicion and terror; and these emotions are embodied and confirmed by -association with the fancies and dogmas of superstition. To consider -superior knowledge as Magic, and Magic as a detestable and criminal -employment, was the form which these feelings of dislike assumed; and -at one period in the history of Europe, almost every one who had -gained any eminent literary fame, was spoken of as a magician. -Naudæus, a learned Frenchman, in the seventeenth century, wrote "An -Apology for all the Wise Men who have been unjustly reported -Magicians, from the Creation to the present Age." The list of persons -whom he thus thinks it necessary to protect, are of various classes -and ages. Alkindi, Geber, Artephius, Thebit, Raymund Lully, Arnold de -Villâ Novâ, Peter of Apono, and Paracelsus, had incurred the black -suspicion as physicians or alchemists. Thomas Aquinas, Roger Bacon, -Michael Scott, Picus of Mirandula, and Trithemius, had not escaped it, -though ministers of religion. Even dignitaries, such as Robert -Grosteste, Bishop of Lincoln, Albertus Magnus, Bishop of Ratisbon, -{227} Popes Sylvester the Second, and Gregory the Seventh, had been -involved in the wide calumny. In the same way in which the vulgar -confounded the eminent learning and knowledge which had appeared in -recent times, with skill in dark and supernatural arts, they converted -into wizards all the best-known names in the rolls of fame; as -Aristotle, Solomon, Joseph, Pythagoras; and, finally, the poet Virgil -was a powerful and skilful necromancer, and this fancy was exemplified -by many strange stories of his achievements and practices. - -The various results of the tendency of the human mind to mysticism, -which we have here noticed, form prominent features in the -intellectual character of the world, for a long course of centuries. -The theosophy and theurgy of the Neoplatonists, the mystical -arithmetic of the Pythagoreans and their successors, the predictions -of the astrologers, the pretences of alchemy and magic, represent, -not unfairly, the general character and disposition of men's -thoughts, with reference to philosophy and science. That there were -stronger minds, which threw off in a greater or less degree this -train of delusive and unsubstantial ideas, is true; as, on the other -hand, Mysticism, among the vulgar or the foolish, often went to an -extent of extravagance and superstition, of which I have not -attempted to convey any conception. The lesson which the preceding -survey teaches us is, that during the Stationary Period, Mysticism, -in its various forms, was a leading character, both of the common -mind, and of the speculations of the most intelligent and profound -reasoners; and that this Mysticism was the opposite of that habit of -thought which we have stated Science to require; namely, clear -Ideas, distinctly employed to connect well-ascertained Facts; -inasmuch as the Ideas in which it dealt were vague and unstable, and -the temper in which they were contemplated was an urgent and -aspiring enthusiasm, which could not submit to a calm conference -with experience upon even terms. The fervor of thought in some -degree supplied the place of reason in producing belief; but -opinions so obtained had no enduring value; they did not exhibit a -permanent record of old truths, nor a firm foundation for new. -Experience collected her stores in vain, or ceased to collect them, -when she had only to pour them into the flimsy folds of the lap of -Mysticism; who was, in truth, so much absorbed in looking for the -treasures which were to fall from the skies, that she heeded little -how scantily she obtained, or how loosely she held, such riches as -might be found near her. {228} - - - - -CHAPTER IV. - -OF THE DOGMATISM OF THE STATIONARY PERIOD. - - -IN speaking of the character of the age of commentators, we noticed -principally the ingenious servility which it displays;--the -acuteness with which it finds ground for speculation in the -expression of other men's thoughts;--the want of all vigor and -fertility in acquiring any real and new truths. Such was the -character of the reasoners of the stationary period from the first; -but, at a later day, this character, from various causes, was -modified by new features. The servility which had yielded itself to -the yoke, insisted upon forcing it on the necks of others: the -subtlety which found all the truth it needed in certain accredited -writings, resolved that no one should find there, or in any other -region, any other truths; speculative men became tyrants without -ceasing to be slaves; to their character of Commentators they added -that of Dogmatists. - -1. _Origin of the Scholastic Philosophy._--The causes of this change -have been very happily analyzed and described by several modern -writers.[62\4] The general nature of the process may be briefly -stated to have been the following. - -[Note 62\4: Dr. Hampden, in the Life of Thomas Aquinas, in the -_Encyc. Metrop._ Degerando, _Hist. Comparée_, vol. iv. Also -Tennemann, _Hist. of Phil._ vol. viii. Introduction.] - -The tendencies of the later times of the Roman empire to a -commenting literature, and a second-hand philosophy, have already -been noticed. The loss of the dignity of political freedom, the want -of the cheerfulness of advancing prosperity, and the substitution of -the less philosophical structure of the Latin language for the -delicate intellectual mechanism of the Greek, fixed and augmented -the prevalent feebleness and barrenness of intellect. Men forgot, or -feared, to consult nature, to seek for new truths, to do what the -great discoverers of other times had done; they were content to -consult libraries, to study and defend old opinions, to talk of what -great geniuses had said. They sought their philosophy in accredited -treatises, and dared not question such doctrines as they there found. - -The character of the philosophy to which they were thus led, was -determined by this want of courage and originality. There are various -{229} antagonist principles of opinion, which seem alike to have their -root in the intellectual constitution of man, and which are maintained -and developed by opposing sects, when the intellect is in vigorous -action. Such principles are, for instance,--the claims of Authority -and of Reason to our assent;--the source of our knowledge in -Experience or in Ideas;--the superiority of a Mystical or of a -Skeptical turn of thought. Such oppositions of doctrine were found in -writers of the greatest fame; and two of those, who most occupied the -attention of students, Plato and Aristotle, were, on several points of -this nature, very diverse from each other in their tendency. The -attempt to reconcile these philosophers by Boëthius and others, we -have already noticed; and the attempt was so far successful, that it -left on men's minds the belief in the possibility of a great -philosophical system which should be based on both these writers, and -have a claim to the assent of all sober speculators. - -But, in the mean time, the Christian Religion had become the leading -subject of men's thoughts; and divines had put forward its claims to -be, not merely the guide of men's lives, and the means of -reconciling them to their heavenly Master, but also to be a -Philosophy in the widest sense in which the term had been used;--a -consistent speculative view of man's condition and nature, and of -the world in which he is placed. - -These claims had been acknowledged; and, unfortunately, from the -intellectual condition of the times, with no due apprehension of the -necessary ministry of Observation, and Reason dealing with -observation, by which alone such a system can be embodied. It was -held without any regulating principle, that the philosophy which had -been bequeathed to the world by the great geniuses of heathen -antiquity, and the Philosophy which was deduced from, and implied -by, the Revelations made by God to man, must be identical; and, -therefore, that Theology is the only true philosophy. Indeed, the -Neoplatonists had already arrived, by other roads, at the same -conviction. John Scot Erigena, in the reign of Alfred, and -consequently before the existence of the Scholastic Philosophy, -properly so called, had reasserted this doctrine.[63\4] Anselm, in -the eleventh century, again brought it forward;[64\4] and Bernard de -Chartres, in the thirteenth.[65\4] - -[Note 63\4: Deg. iv. 351.] - -[Note 64\4: Ib. iv. 388.] - -[Note 65\4: Ib. iv. 418.] - -This view was confirmed by the opinion which prevailed, concerning -the nature of philosophical truth; a view supported by the theory -{230} of Plato, the practice of Aristotle, and the general -propensities of the human mind: I mean the opinion that all science -may be obtained by the use of reasoning alone;--that by analysing -and combining the notions which common language brings before us, we -may learn all that we can know. Thus Logic came to include the whole -of Science; and accordingly this Abelard expressly maintained.[66\4] -I have already explained, in some measure, the fallacy of this -belief, which consists, as has been well said,[67\4] "in mistaking -the universality of the theory of language for the generalization of -facts." But on all accounts this opinion is readily accepted; and it -led at once to the conclusion, that the Theological Philosophy which -we have described, is complete as well as true. - -[Note 66\4: Deg. iv. 407.] - -[Note 67\4: _Enc. Met._ 807.] - -Thus a Universal Science was established, with the authority of a -Religious Creed. Its universality rested on erroneous views of the -relation of words and truths; its pretensions as a science were -admitted by the servile temper of men's intellects; and its -religious authority was assigned it, by making all truth part of -religion. And as Religion claimed assent within her own jurisdiction -under the most solemn and imperative sanctions, Philosophy shared in -her imperial power, and dissent from their doctrines was no longer -blameless or allowable. Error became wicked, dissent became heresy; -to reject the received human doctrines, was nearly the same as to -doubt the Divine declarations. The _Scholastic Philosophy_ claimed -the assent of all believers. - -The external form, the details, and the text of this philosophy, -were taken, in a great measure, from Aristotle; though, in the -spirit, the general notions, and the style of interpretation, Plato -and the Platonists had no inconsiderable share. Various causes -contributed to the elevation of Aristotle to this distinction. His -Logic had early been adopted as an instrument of theological -disputation; and his spirit of systematization, of subtle -distinction, and of analysis of words, as well as his disposition to -argumentation, afforded the most natural and grateful employment to -the commentating propensities. Those principles which we before -noted as the leading points of his physical philosophy, were -selected and adopted; and these, presented in a most technical form, -and applied in a systematic manner, constitute a large portion of -the philosophy of which we now speak, so far as it pretends to deal -with physics. - -2. _Scholastic Dogmas._--But before the complete ascendancy of -Aristotle was thus established, when something of an intellectual -waking {231} took place after the darkness and sleep of the ninth -and tenth centuries, the Platonic doctrines seem to have had, at -first, a strong attraction for men's minds, as better falling in -with the mystical speculations and contemplative piety which -belonged to the times. John Scot Erigena[68\4] may be looked upon as -the reviver of the New Platonism in the tenth century. Towards the -end of the eleventh, Peter Damien,[69\4] in Italy, reproduced, -involved in a theological discussion, some Neoplatonic ideas. -Godefroy[70\4] also, censor of St. Victor, has left a treatise, -entitled _Microcosmus_; this is founded on a mystical analogy, often -afterwards again brought forward, between Man and the Universe. -"Philosophers and theologians," says the writer, "agree in -considering man as a little world; and as the world is composed of -four elements, man is endowed with four faculties, the senses, the -imagination, reason, and understanding." Bernard of Chartres,[71\4] -in his _Megascosmus_ and _Microcosmus_, took up the same notions. -Hugo, abbot of St. Victor, made a contemplative life the main point -and crown of his philosophy; and is said to have been the first of -the scholastic writers who made psychology his special study.[72\4] -He says the faculties of the mind are "the senses, the imagination, -the reason, the memory, the understanding, and the intelligence." - -[Note 68\4: Deg. iv. 35.] - -[Note 69\4: Ib. iv. 367.] - -[Note 70\4: Ib. iv. 413.] - -[Note 71\4: Ib. iv. 419.] - -[Note 72\4: Ib. iv. 415.] - -Physics does not originally and properly form any prominent part of -the Scholastic Philosophy, which consists mainly of a series of -questions and determinations upon the various points of a certain -technical divinity. Of this kind is the _Book of Sentences_ of Peter -the Lombard (bishop of Paris), who is, on that account, usually -called "Magister Sententiarum;" a work which was published in the -twelfth century, and was long the text and standard of such -discussions. The questions are decided by the authority of Scripture -and of the Fathers of the Church, and are divided into four Books, -of which the first contains questions concerning God and the -doctrine of the Trinity in particular; the second is concerning the -Creation; the third, concerning Christ and the Christian Religion; -and the fourth treats of Religious and Moral Duties. In the second -book, as in many of the writers of this time, the nature of Angels -is considered in detail, and the Orders of their Hierarchy, of which -there were held to be nine. The physical discussions enter only as -bearing upon the scriptural history of the creation, and cannot be -taken as a specimen of the work; but I may observe, that in speaking -of the division of the waters above the {232} firmament, he gives -one opinion, that of Bede, that the former waters are the solid -crystalline heavens in which the stars are fixed,[73\4] "for -crystal, which is so hard and transparent, is made of water." But he -mentions also the opinion of St. Augustine, that the waters above -the heavens are in a state of vapor, (_vaporaliter_) and in minute -drops; "if, then, water can, as we see in clouds, be so minutely -divided that it may be thus supported as vapor on air, which is -naturally lighter than water; why may we not believe that it floats -above that lighter celestial element in still minuter drops and -still lighter vapors? But in whatever manner the waters are there, -we do not doubt that they are there." - -[Note 73\4: Lib. ii. Distinct. xiv. _De opere secundæ diei_.] - -The celebrated _Summa Theologicæ_ of Thomas Aquinas is a work of the -same kind; and anything which has a physical bearing forms an -equally small part of it. Thus, of the 512 Questions of the _Summa_, -there is only one (Part I., Quest. 115), "on Corporeal Action," or -on any part of the material world; though there are several -concerning the celestial Hierarchies, as "on the Act of Angels," -"on the Speaking of Angels," "on the Subordination of Angels," -"on Guardian Angels," and the like. This, of course, would not be -remarkable in a treatise on Theology, except this Theology were -intended to constitute the whole of Philosophy. - -We may observe, that in this work, though Plato, Avecibron, and many -other heathen as well as Christian philosophers, are adduced as -authority, Aristotle is referred to in a peculiar manner as "the -philosopher." This is noticed by John of Salisbury, as attracting -attention in his time (he died A.D. 1182). "The various Masters of -Dialectic," says he,[74\4] "shine each with his peculiar merit; but -all are proud to worship the footsteps of Aristotle; so much so, -indeed, that the name of _philosopher_, which belongs to them all, has -been pre-eminently appropriated to him. He is called the philosopher -_autonomatice_, that is, by excellence." - -[Note 74\4: _Metalogicus_, lib. ii. cap. 16.] - -The Question concerning Corporeal Action, in Aquinas, is divided -into six Articles; and the conclusion delivered upon the first -is,[75\4] that "Body being compounded of power and act, is active as -well as passive." Against this it is urged, that quantity is an -attribute of body, and that quantity prevents action; that this -appears in fact, since a larger body is more difficult to move. The -author replies, that {233} "quantity does not prevent corporeal form -from action altogether, but prevents it from being a universal -agent, inasmuch as the form is individualized, which, in matter -subject to quantity, it is. Moreover, the illustration deduced from -the ponderousness of bodies is not to the purpose; first, because -the addition of quantity is not the cause of gravity, as is proved -in the fourth book, De Cœlo and De Mundo" (we see that he quotes -familiarly the physical treatises of Aristotle); "second, because it -is false that ponderousness makes motion slower; on the contrary, in -proportion as any thing is heavier, the more does it move with its -proper motion; thirdly, because action does not take place by local -motion, as Democritus asserted; but by this, that something is drawn -from power into act." - -[Note 75\4: _**Summa_, P. i. Q. 115. Art. 1.] - -It does not belong to our purpose to consider either the theological -or the metaphysical doctrines which form so large a portion of the -treatises of the schoolmen. Perhaps it may hereafter appear, that -some light is thrown on some of the questions which have occupied -metaphysicians in all ages, by that examination of the history of -the Progressive Sciences in which we are now engaged; but till we -are able to analyze the leading controversies of this kind, it would -be of little service to speak of them in detail. It may be noticed, -however, that many of the most prominent of them refer to the great -question, "What is the relation between actual things and general -terms?" Perhaps in modern times, the actual things would be more -commonly taken as the point to start from; and men would begin by -considering how classes and universals are obtained from -individuals. But the schoolmen, founding their speculations on the -received modes of considering such subjects, to which both Aristotle -and Plato had contributed, travelled in the opposite direction, and -endeavored to discover how individuals were deduced from genera and -species;--what was "the Principle of Individuation." This was -variously stated by different reasoners. Thus Bonaventura[76\4] -solves the difficulty by the aid of the Aristotelian distinction of -Matter and Form. The individual derives from the Form the property -of _being something_, and from the Matter the property of being that -_particular thing_. Duns Scotus,[77\4] the great adversary of Thomas -Aquinas in theology, placed the principle of Individuation in "a -certain determining positive entity," which his school called -_Hæcceity_ or _thisness_. "Thus an individual man is Peter, because -his _humanity_ is combined with_ Petreity_." The force {234} of -abstract terms is a curious question, and some remarkable -experiments in their use had been made by the Latin Aristotelians -before this time. In the same way in which we talk of the _quantity_ -and _quality_ of a thing, they spoke of its _quiddity_.[78\4] - -[Note 76\4: Deg. iv. 573.] - -[Note 77\4: Ib. iv. 523.] - -[Note 78\4: Deg. iv. 494.] - -We may consider the reign of mere disputation as fully established -at the time of which we are now speaking; and the only kind of -philosophy henceforth studied was one in which no sound physical -science had or could have a place. The wavering abstractions, -indistinct generalizations, and loose classifications of common -language, which we have already noted as the fountain of the physics -of the Greek Schools of philosophy, were also the only source from -which the Schoolmen of the middle ages drew their views, or rather -their arguments: and though these notional and verbal relations were -invested with a most complex and pedantic technicality, they did -not, on that account, become at all more precise as notions, or more -likely to lead to a single real truth. Instead of acquiring distinct -ideas, they multiplied abstract terms; instead of real -generalizations, they had recourse to verbal distinctions. The whole -course of their employments tended to make them, not only ignorant -of physical truth, but incapable of conceiving its nature. - -Having thus taken upon themselves the task of raising and discussing -questions by means of abstract terms, verbal distinctions, and -logical rules alone, there was no tendency in their activity to come -to an end, as there was no progress. The same questions, the same -answers, the same difficulties, the same solutions, the same verbal -subtleties,--sought for, admired, cavilled at, abandoned, -reproduced, and again admired,--might recur without limit. John of -Salisbury[79\4] observes of the Parisian teachers, that, after -several years' absence, he found them not a step advanced, and still -employed in urging and parrying the same arguments; and this, as Mr. -Hallam remarks,[80\4] "was equally applicable to the period of -centuries." The same knots were tied and {235} untied; the same -clouds were formed and dissipated. The poet's censure of "the Sons -of Aristotle," is just as happily expressed: - They stand - Locked up together hand in hand - Every one leads as he is led, - The same bare path they tread, - And dance like Fairies a fantastic round, - But neither change their motion nor their ground. - -[Note 79\4: He studied logic at Paris, at St. Geneviève, and then -left them. "Duodecennium mihi elapsum est diversis studiis -occupatum. Jucundum itaque visum est veteres quos reliqueram, et -quos adhuc Dialectica detinebat in monte, (Sanctæ Genovefæ) revisere -socios, conferre cum eis super ambiguitatibus pristinis; ut nostrûm -invicem collatione mutuâ commetiremur profectum. Inventi sunt, qui -fuerant, et ubi; neque enim ad palmam visi sunt processisse ad -quæstiones pristinis dirimendas, neque propositiunculam unam -adjecerant. Quibus urgebant stimulis eisdem et ipsi urgebantur," &c. -_Metalogicus_, lib. ii. cap. 10.] - -[Note 80\4: _Middle Ages_, iii. 537.] - -It will therefore be unnecessary to go into any detail respecting -the history of the School Philosophy of the thirteenth, fourteenth, -and fifteenth centuries. We may suppose it to have been, during the -intermediate time, such as it was at first and at last. An occasion -to consider its later days will be brought before us by the course -of our subject. But, even during the most entire ascendency of the -scholastic doctrines, the elements of change were at work. While the -doctors and the philosophers received all the ostensible homage of -men, a doctrine and a philosophy of another kind were gradually -forming: the practical instincts of man, their impatience of -tyranny, the progress of the useful arts, the promises of alchemy, -were all disposing men to reject the authority and deny the -pretensions of the received philosophical creed. Two antagonist -forms of opinion were in existence, which for some time went on -detached, and almost independent of each other; but, finally, these -came into conflict, at the time of Galileo; and the war speedily -extended to every part of civilized Europe. - -3. _Scholastic Physics._--It is difficult to give briefly any -appropriate examples of the nature of the Aristotelian physics which -are to be found in the works of this time. As the gravity of bodies -was one of the first subjects of dispute when the struggle of the -rival methods began, we may notice the mode in which it was -treated.[81\4] "Zabarella maintains that the proximate cause of the -motion of elements is the _form_, in the Aristotelian sense of the -term: but to this sentence we," says Keckerman, "cannot agree; for -in all other things the _form_ is the proximate cause, not of the -_act_, but of the power or faculty from which the act flows. Thus in -man, the rational soul is not the cause of the act of laughing, but -of the risible faculty or power." Keckerman's system was at one time -a work of considerable authority: it was published in 1614. By -comparing and systematizing what he finds in Aristotle, he is led to -state his results in the form of definitions {236} and theorems. -Thus, "gravity is a motive quality, arising from cold, density, and -bulk, by which the elements are carried downwards." "Water is the -lower, intermediate element, cold and moist." The first theorem -concerning water is, "The moistness of the water is controlled by -its coldness, so that it is less than the moistness of the air; -though, according to the sense of the vulgar, water appears to -moisten more than air." It is obvious that the two properties of -fluids, to have their parts easily moved, and to wet other bodies, -are here confounded. I may, as a concluding specimen of this kind, -mention those propositions or maxims concerning fluids, which were -so firmly established, that, when Boyle propounded the true -mechanical principles of fluid action, he was obliged to state his -opinions as "hydrostatical _paradoxes_." These were,--that fluids do -not gravitate _in proprio loco_; that is, that water has no gravity -in or on water, since it is in its own place;--that air has no -gravity on water, since it is above water, which is its proper -place;--that earth in water tends to descend, since its place is -below water;--that the water rises in a pump or siphon, because -nature abhors a vacuum;--that some bodies have a positive levity in -others, as oil in water; and the like. - -[Note 81\4: Keckerman, p. 1428.] - -4. _Authority of Aristotle among the Schoolmen._--The authority of -Aristotle, and the practice of making him the text and basis of the -system, especially as it regarded physics, prevailed during the period -of which we speak. This authority was not, however, without its -fluctuations. Launoy has traced one part of its history in a book _On -the various Fortune of Aristotle in the University of Paris_. The most -material turns of this fortune depend on the bearing which the works -of Aristotle were supposed to have upon theology. Several of -Aristotle's works, and more especially his metaphysical writings, had -been translated into Latin, and were explained in the schools of the -University of Paris, as early as the beginning of the thirteenth -century.[82\4] At a council held at Paris in 1209, they were -prohibited, as having given occasion to the heresy of Almeric (or -Amauri), and because "they might give occasion to other heresies not -yet invented." The Logic of Aristotle recovered its credit some years -after this, and was publicly taught in the University of Paris in the -year 1215; but the Natural Philosophy and Metaphysics were prohibited -by a decree of Gregory the Ninth, in 1231. The Emperor Frederic the -Second employed a number of learned men to translate into Latin, from -the Greek and {237} Arabic, certain books of Aristotle, and of other -ancient sages; and we have a letter of Peter de Vineis, in which they -are recommended to the attention of the University of Bologna: -probably the same recommendation was addressed to other Universities. -Both Albertus Magnus and Thomas Aquinas wrote commentaries on -Aristotle's works; and as this was done soon after the decree of -Gregory the Ninth, Launoy is much perplexed to reconcile the fact with -the orthodoxy of the two doctors. Campanella, who was one of the first -to cast off the authority of Aristotle, says, "We are by no means to -think that St. Thomas _aristotelized_; he only expounded Aristotle, -that he might correct his errors; and I should conceive he did this -with the license of the Pope." This statement, however, by no means -gives a just view of the nature of Albertus's and Aquinas's -commentaries. Both have followed their author with profound -deference.[83\4] For instance, Aquinas[84\4] attempts to defend -Aristotle's assertion, that if there were no resistance, a body would -move through a space in no time; and the same defence is given by -Scotus. - -[Note 82\4: Mosheim, iii. 157.] - -[Note 83\4: Deg. N. 475.] - -[Note 84\4: F. Piccolomini, ii. 835.] - -We may imagine the extent of authority and admiration which -Aristotle would attain, when thus countenanced, both by the powerful -and the learned. In universities, no degree could be taken without a -knowledge of the philosopher. In 1452, Cardinal Totaril established -this rule in the University of Paris.[85\4] When Ramus, in 1543, -published an attack upon Aristotle, it was repelled by the power of -the court, and the severity of the law. Francis the First published -an edict, in which he states that he had appointed certain judges, -who had been of opinion,[86\4] "que le dit Ramus avoit été -téméraire, arrogant et impudent; et que parcequ'en son livre des -animadversions il reprenait Aristotle, estait évidemment connue et -manifeste son ignorance." The books are then declared to be -suppressed. It was often a complaint of pious men, that theology was -corrupted by the influence of Aristotle and his commentators. -Petrarch says,[87\4] that one of the Italian learned men conversing -with him, after expressing much contempt for the apostles and -fathers, exclaimed, "Utinam tu Averroen pati posses, ut videres -quanto ille tuis his nugatoribus major sit!" - -[Note 85\4: Launoy, pp. 108, 128.] - -[Note 86\4: Launoy, p. 132.] - -[Note 87\4: Hallam, _M. A._ iii. 536.] - -When the revival of letters began to take place, and a number of men -of ardent and elegant minds, susceptible to the impressions of -beauty of style and dignity of thought, were brought into contact -with Greek literature, Plato had naturally greater charms for them. -A {238} powerful school of Platonists (not Neoplatonists) was formed -in Italy, including some of the principal scholars and men of genius -of the time; as Picus of Mirandula in the middle, Marsilius Ficinus -at the end, of the fifteenth century. At one time, it appeared as if -the ascendency of Aristotle was about to be overturned; but, in -physics at least, his authority passed unshaken through this trial. -It was not by disputation that Aristotle could be overthrown; and -the Platonists were not persons whose doctrines led them to use the -only decisive method in such cases, the observation and unfettered -interpretation of facts. - -The history of their controversies, therefore, does not belong to -our design. For like reasons we do not here speak of other authors, -who opposed the scholastic philosophy on general theoretical grounds -of various kinds. Such examples of insurrection against the -dogmatism which we have been reviewing, are extremely interesting -events in the history of the philosophy of science. But, in the -present work, we are to confine ourselves to the history of science -itself; in the hope that we may thus be able, hereafter, to throw a -steadier light upon that philosophy by which the succession of -stationary and progressive periods, which we are here tracing, may be -in some measure explained. We are now to close our account of the -stationary period, and to enter upon the great subject of the -progress of physical science in modern times. - -5. _Subjects omitted. Civil Law, Medicine._--My object has been to -make my way, as rapidly as possible, to this period of progress; and -in doing this, I have had to pass over a long and barren track, -where almost all traces of the right road disappear. In exploring -this region, it is not without some difficulty that he who is -travelling with objects such as mine, continues a steady progress in -the proper direction; for many curious and attractive subjects of -research come in his way: he crosses the track of many a -controversy, which in its time divided the world of speculators, and -of which the results may be traced, even now, in the conduct of -moral, or political, or metaphysical discussions; or in the common -associations of thought, and forms of language. The wars of the -Nominalists and Realists; the disputes concerning the foundations of -morals, and the motives of human actions; the controversies -concerning predestination, free will, grace, and the many other -points of metaphysical divinity; the influence of theology and -metaphysics upon each other, and upon other subjects of human -curiosity; the effects of opinion upon politics, and of political -condition upon opinion; the influence of literature and philosophy -{239} upon each other, and upon society; and many other -subjects;--might be well worth examination, if our hope of success -did not reside in pursuing, steadily and directly, those inquiries -in which we can look for a definite and certain reply. We must even -neglect two of the leading studies of those times, which occupied -much of men's time and thoughts, and had a very great influence on -society; the one dealing with Notions, the other with Things; the -one employed about moral rules, the other about material causes, but -both for practical ends; I mean, the study of the _Civil Law_, and -of _Medicine_. The second of these studies will hereafter come -before us, as one of the principal occasions which led to the -cultivation of chemistry; but, in itself, its progress is of too -complex and indefinite a nature to be advantageously compared with -that of the more exact sciences. The Roman Law is held, by its -admirers, to be a system of deductive science, as exact as the -mathematical sciences themselves; and it may, therefore, be useful -to consider it, if we should, in the sequel, have to examine how far -there can exist an analogy between moral and physical science. But, -after a few more words on the middle ages, we must return to our -task of tracing the progress of the latter. - - - - -CHAPTER V. - -PROGRESS OF THE ARTS IN THE MIDDLE AGES. - - -ART AND SCIENCE.--I shall, before I resume the history of science, say -a few words on the subject described in the title of this chapter, -both because I might otherwise be accused of doing injustice to the -period now treated of; and also, because we shall by this means bring -under our notice some circumstances which were important as being the -harbingers of the revival of progressive knowledge. - -The accusation of injustice towards the state of science in the -middle ages, if we were to terminate our survey of them with what -has hitherto been said, might be urged from obvious topics. How do -we recognize, it might be asked, in a picture of mere confusion and -mysticism of thought, of servility and dogmatism of character, the -powers and acquirements to which we owe so many of the most -important inventions which we now enjoy? Parchment and paper, -printing and engraving, improved glass and steel, gunpowder, clocks, -telescopes, {240} the mariner's compass, the reformed calendar, the -decimal notation, algebra, trigonometry, chemistry, counterpoint, an -invention equivalent to a new creation of music;--these are all -possessions which we inherit from that which has been so -disparagingly termed the Stationary Period. Above all, let us look -at the monuments of architecture of this period;--the admiration and -the despair of modern architects, not only for their beauty, but for -the skill disclosed in their construction. With all these evidences -before us, how can we avoid allowing that the masters of the middle -ages not only made some small progress in Astronomy, which has, -grudgingly as it would seem, been admitted in a former Book; but -also that they were no small proficients in other sciences, in -Optics, in Harmonics, in Physics, and, above all, in Mechanics? - -If, it may be added, we are allowed, in the present day, to refer to -the perfection of our arts as evidence of the advanced state of our -physical philosophy;--if our steam-engines, our gas-illumination, our -buildings, our navigation, our manufactures, are cited as triumphs of -science;--shall not prior inventions, made under far heavier -disadvantages,--shall not greater works, produced in an earlier state -of knowledge, also be admitted as witnesses that the middle ages had -their share, and that not a small or doubtful one, of science? - -To these questions I answer, by distinguishing between Art, and -Science in that sense of general Inductive Systematic Truth, which -it bears in this work. To separate and compare, with precision, -these two processes, belongs to the Philosophy of Induction; and the -attempt must be reserved for another place: but the leading -differences are sufficiently obvious. Art is practical, Science is -speculative: the former is seen in doing; the latter rests in the -contemplation of what is known. The Art of the builder appears in -his edifice, though he may never have meditated on the abstract -propositions on which its stability and strength depends. The -Science of the mathematical mechanician consists in his seeing that, -under certain conditions, bodies must sustain each other's pressure, -though he may never have applied his knowledge in a single case. - -Now the remark which I have to make is this:--in all cases the Arts -are prior to the related Sciences. Art is the parent, not the -progeny, of Science; the realization of principles in practice forms -part of the prelude, as well as of the sequel, of theoretical -discovery. And thus the inventions of the middle ages, which have -been above enumerated, though at the present day they may be -portions of our sciences, are no evidence that the sciences then -existed; but only that {241} those powers of practical observation -and practical skill were at work, which prepare the way for -theoretical views and scientific discoveries. - -It may be urged, that the great works of art do virtually take for -granted principles of science; and that, therefore, it is unreasonable -to deny science to great artists. It may be said, that the grand -structures of Cologne, or Amiens, or Canterbury, could not have been -erected without a profound knowledge of mechanical principles. - -To this we reply, that _such_ knowledge is manifestly not of the -nature of that which we call _science_. If the beautiful and skilful -structures of the middle ages prove that mechanics then existed as a -science, mechanics must have existed as a science also among the -builders of the Cyclopean walls of Greece and Italy, or of our own -Stonehenge; for the masses which are there piled on each other, could -not be raised without considerable mechanical skill. But we may go -much further. The actions of every man who raises and balances -weights, or walks along a pole, take for granted the laws of -equilibrium; and even animals constantly avail themselves of such -principles. Are these, then, acquainted with mechanics as a science? -Again, if actions which are performed by taking advantage of -mechanical properties prove a knowledge of the science of mechanics, -they must also be allowed to prove a knowledge of the science of -geometry, when they proceed on geometrical properties. But the most -familiar actions of men and animals proceed upon geometrical truths. -The Epicureans held, as Proclus informs us, that even asses knew that -two sides of a triangle are greater than the third. And animals may -truly be said to have a practical knowledge of this truth; but they -have not, therefore, a science of geometry. And in like manner among -men, if we consider the matter strictly, a practical assumption of a -principle does not imply a speculative knowledge of it. - -We may, in another way also, show how inadmissible are the works of -the Master Artists of the middle ages into the series of events which -mark the advance of Science. The following maxim is applicable to a -history, such as we are here endeavoring to write. We are employed in -tracing the progress of such general principles as constitute each of -the sciences which we are reviewing; and no facts or subordinate -truths belong to our scheme, except so far as they tend to or are -included in these higher principles; nor are they important to us, any -further than as they prove such principles. Now with regard to -processes of art like those which we have referred to, namely, the -inventions of the middle ages, let us ask, _what_ principle each of -them {242} illustrates? What chemical doctrine rests for its support -on the phenomena of gunpowder, or glass, or steel? What new harmonical -truth was illustrated in the Gregorian chant? What mechanical -principle unknown to Archimedes was displayed in the printing-press? -The practical value and use, the ingenuity and skill of these -inventions is not questioned; but what is their place in the history -of speculative knowledge? Even in those cases in which they enter into -such a history, how minute a figure do they make! how great is the -contrast between their practical and theoretical importance! They may -in their operation have changed the face of the world; but in the -history of the principles of the sciences to which they belong, they -may be omitted without being missed. - -As to that part of the objection which was stated by asking, why, if -the arts of our age prove its scientific eminence, the arts of the -middle ages should not be received as proof of theirs; we must reply -to it, by giving up some of the pretensions which are often put -forwards on behalf of the science of our times. The perfection of -the mechanical and other arts among us proves the advanced condition -of our sciences, only in so far as these arts have been perfected by -the application of some great scientific truth, with a clear insight -into its nature. The greatest improvement of the steam-engine was -due to the steady apprehension of an atmological doctrine by Watt; -but what distinct theoretical principle is illustrated by the -beautiful manufactures of porcelain, or steel, or glass? A chemical -view of these compounds, which would explain the conditions of -success and failure in their manufacture, would be of great value in -art; and it would also be a novelty in chemical theory; so little is -the present condition of those processes a triumph of science, -shedding intellectual glory on our age. And the same might be said -of many, or of most, of the processes of the arts as now practised. - -2. _Arabian Science._--Having, I trust, established the view I have -stated, respecting the relation of Art and Science, we shall be able -very rapidly to dispose of a number of subjects which otherwise -might seem to require a detailed notice. Though this distinction has -been recognized by others, it has hardly been rigorously adhered to, -in consequence of the indistinct notion of _science_ which has -commonly prevailed. Thus Gibbon, in speaking of the knowledge of the -period now under our notice, says,[88\4] "Much useful experience had -been acquired in {243} the practice of arts and manufactures; but -the _science_ of chemistry owes its origin and improvement to the -industry of the Saracens. They," he adds, "first invented and named -the alembic for the purposes of distillation, analyzed the -substances of the three kingdoms of nature, tried the distinction -and affinities of alkalies and acids, and converted the poisonous -minerals into soft and salutary medicines." The formation and -realization of the notions of _analysis_ and of _affinity_, were -important steps in chemical science, which, as I shall hereafter -endeavor to show, it remained for the chemists of Europe to make at -a much later period. If the Arabians had done this, they might with -justice have been called the authors of the science of chemistry; -but no doctrines can be adduced from their works which give them any -title to this eminent distinction. Their claims are dissipated at -once by the application of the maxim above stated. _What_ analysis -of theirs tended to establish any received principle of chemistry? -_What_ true doctrine concerning the differences and affinities of -acids and alkalies did they teach? We need not wonder if Gibbon, -whose views of the boundaries of scientific chemistry were probably -very wide and indistinct, could include the arts of the Arabians -within its domain; but they cannot pass the frontier of science if -philosophically defined, and steadily guarded. - -[Note 88\4: _Decline and Fall_, vol. x. p. 43.] - -The judgment which we are thus led to form respecting the chemical -knowledge of the middle ages, and of the Arabians in particular, may -serve to measure the condition of science in other departments; for -chemistry has justly been considered one of their strongest points. -In botany, anatomy, zoology, optics, acoustics, we have still the -same observations to make, that the steps in science which, in the -order of progress, next followed what the Greeks had done, were left -for the Europeans of the sixteenth and seventeenth centuries. The -merits and advances of the Arabian philosophers in astronomy and -pure mathematics, we have already described. - -3. _Experimental Philosophy of the Arabians._--The estimate to which -we have thus been led, of the scientific merits of the learned men -of the middle ages, is much less exalted than that which has been -formed by many writers; and, among the rest, by some of our own -time. But I am persuaded that any attempt to answer the questions -just asked, will expose the untenable nature of the higher claims -which have been advanced in favor of the Arabians. We can deliver no -just decision, except we will consent to use the terms of science in -a strict and precise sense: and if we do this, we shall find little, -either in the {244} particular discoveries or general processes of -the Arabians, which is important in the history of the Inductive -Sciences.[89\4] - -[Note 89\4: If I might take the liberty of criticising an author who -has given a very interesting view of the period in question -(_Mahometanism Unveiled_, by the Rev. Charles Forster, 1829), I -would remark, that in his work this caution is perhaps too little -observed. Thus, he says, in speaking of Alhazen (vol. ii. p. 270), -"the theory of the telescope may be found in the work of this -astronomer;" and of another, "the uses of magnifying glasses and -telescopes, and the principle of their construction, are explained -in the Great Work of (Roger) Bacon, with a truth and clearness which -have commanded universal admiration." Such phrases would be much too -strong, even if used respecting the optical doctrines of Kepler, -which were yet incomparably more true and clear than those of Bacon. -To employ such language, in such cases, is to deprive such terms as -_theory_ and _principle_ of all meaning.] - -The credit due to the Arabians for improvements in the general -methods of philosophizing, is a more difficult question; and cannot -be discussed at length by us, till we examine the history of such -methods in the abstract, which, in the present work, it is not our -intention to do. But we may observe, that we cannot agree with -those who rank their merits high in this respect. We have already -seen, that their minds were completely devoured by the worst habits -of the stationary period,--Mysticism and Commentation. They followed -their Greek leaders, for the most part, with abject servility, and -with only that kind of acuteness and independent speculation which -the Commentator's vocation implies. And in their choice of the -standard subjects of their studies, they fixed upon those works, the -Physical Books of Aristotle, which have never promoted the progress -of science, except in so far as they incited men to refute them; an -effect which they never produced on the Arabians. That the Arabian -astronomers made some advances beyond the Greeks, we have already -stated: the two great instances are, the discovery of the Motion of -the Sun's Apogee by Albategnius, and the discovery (recently brought -to light) of the existence of the Moon's Second Inequality, by Aboul -Wefa. But we cannot but observe in how different a manner they -treated these discoveries, from that with which Hipparchus or -Ptolemy would have done. The Variation of the Moon, in particular, -instead of being incorporated into the system by means of an -Epicycle, as Ptolemy had done with the Evection, was allowed, almost -immediately, so far as we can judge, to fall into neglect and -oblivion: so little were the learned Arabians prepared to take their -lessons from observation as well as from books. That in many -subjects they made experiments, may easily be allowed: there never -was a period of the earth's history, and least of all a period of -commerce {245} and manufactures, luxury and art, medicine and -engineering, in which there were not going on innumerable processes, -which may be termed Experiments; and, in addition to these, the -Arabians adopted the pursuit of alchemy, and the love of exotic -plants and animals. But so far from their being, as has been -maintained,[90\4] a people whose "experimental intellect" fitted -them to form sciences which the "abstract intellect" of the Greeks -failed in producing, it rather appears, that several of the sciences -which the Greeks had founded, were never even comprehended by the -Arabians. I do not know any evidence that these pupils ever attained -to understand the real principles of Mechanics, Hydrostatics, and -Harmonics, which their masters had established. At any rate, when -these sciences again became progressive, Europe had to start where -Europe had stopped. There is no Arabian name which any one has -thought of interposing between Archimedes the ancient, and Stevinus -and Galileo the moderns. - -[Note 90\4: _Mahometanism Unveiled_, ii. 271.] - -4. _Roger Bacon._--There is one writer of the middle ages, on whom -much stress has been laid, and who was certainly a most remarkable -person. Roger Bacon's works are not only so far beyond his age in -the knowledge which they contain, but so different from the temper -of the times, in his assertion of the supremacy of experiment, and -in his contemplation of the future progress of knowledge, that it is -difficult to conceive how such a character could then exist. That he -received much of his knowledge from Arabic writers, there can be no -doubt; for they were in his time the repositories of all -traditionary knowledge. But that he derived from them his -disposition to shake off the authority of Aristotle, to maintain the -importance of experiment, and to look upon knowledge as in its -infancy, I cannot believe, because I have not myself hit upon, nor -seen quoted by others, any passages in which Arabian writers express -such a disposition. On the other hand, we do find in European -writers, in the authors of Greece and Rome, the solid sense, the -bold and hopeful spirit, which suggest such tendencies. We have -already seen that Aristotle asserts, as distinctly as words can -express, that all knowledge must depend on observation, and that -science must be collected from facts by induction. We have seen, -too, that the Roman writers, and Seneca in particular, speak with an -enthusiastic confidence of the progress which science must make in -the course of ages. When Roger Bacon holds similar language in the -thirteenth century, the resemblance is probably rather a sympathy of -character, than a matter of direct derivation; but I know of nothing -{246} which proves even so much as this sympathy in the case of -Arabian philosophers. - -A good deal has been said of late of the coincidences between his -views, and those of his great namesake in later times, Francis -Bacon.[91\4] The resemblances consist mainly in such points as I -have just noticed; and we cannot but acknowledge, that many of the -expressions of the Franciscan Friar remind us of the large thoughts -and lofty phrases of the Philosophical Chancellor. How far the one -can be considered as having anticipated the method of the other, we -shall examine more advantageously, when we come to consider what the -character and effect of Francis Bacon's works really are.[92\4] - -[Note 91\4: Hallam's _Middle Ages_, iii. 549. Forster's _Mahom. U._ -ii. 313.] - -[Note 92\4: In the _Philosophy of the Inductive Sciences_, I have -given an account at considerable length of Roger Bacon's mode of -treating Arts and Sciences; and have also compared more fully his -philosophy with that of Francis Bacon; and I have given a view of -the bearing of this latter upon the progress of Science in modern -times. See _Phil. Ind. Sc._ book xii. chaps. 7 and 11. See also the -Appendix to this volume.] - -5. _Architecture of the Middle Ages._--But though we are thus -compelled to disallow several of the claims which have been put -forwards in support of the scientific character of the middle ages, -there are two points in which we may, I conceive, really trace the -progress of scientific ideas among them; and which, therefore, may -be considered as the prelude to the period of discovery. I mean -their practical architecture, and their architectural treatises. - -In a previous chapter of this book, we have endeavored to explain how -the indistinctness of ideas, which attended the decline of the Roman -empire, appears in the forms of their architecture;--in the disregard, -which the decorative construction exhibits, of the necessary -mechanical conditions of support. The original scheme of Greek -ornamental architecture had been horizontal masses resting on vertical -columns: when the arch was introduced by the Romans, it was concealed, -or kept in a state of subordination: and the lateral support which it -required was supplied latently, marked by some artifice. But the -struggle between the _mechanical_ and the _decorative -construction_[93\4] ended in the complete disorganization of the -classical style. The {247} inconsistencies and extravagances of which -we have noticed the occurrence, were results and indications of the -fall of good architecture. The elements of the ancient system had lost -all principle of connection and regard to rule. Building became not -only a mere art, but an art exercised by masters without skill, and -without feeling for real beauty. - -[Note 93\4: See Mr. Willis's admirable _Remarks on the Architecture -of the Middle Ages_, chap. ii. - -Since the publication of my first edition, Mr. Willis has shown that -much of the "mason-craft" of the middle ages consisted in the -geometrical methods by which the artists wrought out of the blocks -the complex forms of their decorative system. - -To the general indistinctness of speculative notions on mechanical -subjects prevalent in the middle ages, there may have been some -exceptions, and especially so long as there were readers of -Archimedes. Boëthius had translated the mechanical works of -Archimedes into Latin, as we learn from the enumeration of his works -by his friend Cassiodorus (_Variar._ lib i. cap. 45), "_Mechanicum_ -etiam Archimedem latialem siculis reddidisti." But _Mechanicus_ was -used in those times rather for one skilled in the art of -constructing wonderful machines than in the speculative theory of -them. The letter from which the quotation is taken is sent by King -Theodoric to Boëthius, to urge him to send the king a water-clock.] - -When, after this deep decline, architecture rose again, as it did in -the twelfth and succeeding centuries, in the exquisitely beautiful -and skilful forms of the Gothic style, what was the nature of the -change which had taken place, so far as it bears upon the progress -of science? It was this:--the idea of true mechanical relations in -an edifice had been revived in men's minds, as far as was requisite -for the purposes of art and beauty: and this, though a very -different thing from the possession of the idea as an element of -speculative science, was the proper preparation for that -acquisition. The notion of support and stability again became -conspicuous in the decorative construction, and universal in the -forms of building. The eye which, looking for beauty in definite and -significant relations of parts, is never satisfied except the -weights appear to be duly supported,[94\4] was again gratified. -Architecture threw off its barbarous characters: a new decorative -construction was matured, not thwarting and controlling, but -assisting and harmonizing with the mechanical construction. All the -ornamental parts were made to enter into the apparent construction. -Every member, almost every moulding, became a sustainer of weight; -and by the multiplicity of props assisting each other, and the -consequent subdivision of weight, the eye was satisfied of the -stability of the structure, notwithstanding the curiously-slender -forms of the separate parts. The arch and the vault, no longer -trammelled by an incompatible system of decoration, but favoured by -more tractable forms, were only limited by the skill of the -builders. Everything showed that, practically at least, men -possessed and applied, with steadiness and pleasure, the idea of -mechanical pressure and support. - -[Note 94\4: Willis, pp. 15-21. I have throughout this description of -the formation of the Gothic style availed myself of Mr. Willis's -well-chosen expressions.] - -The possession of this idea, as a principle of art, led, in the -course of time, to its speculative development as the foundation of -a science; {248} and thus Architecture prepared the way for -Mechanics. But this advance required several centuries. The interval -between the admirable cathedrals of Salisbury, Amiens, Cologne, and -the mechanical treatises of Stevinus, is not less than three hundred -years. During this time, men were advancing towards science; but in -the mean time, and perhaps from the very beginning of the time, art -had begun to decline. The buildings of the fifteenth century, -erected when the principles of mechanical support were just on the -verge of being enunciated in general terms, exhibit those principles -with a far less impressive simplicity and elegance than those of the -thirteenth. We may hereafter inquire whether we find any other -examples to countenance the belief, that the formation of Science is -commonly accompanied by the decline of Art. - -The leading principle of the style of the Gothic edifices was, not -merely that the weights were supported, but that they were seen to -be so; and that not only the mechanical relations of the larger -masses, but of the smaller members also, were displayed. Hence we -cannot admit, as an origin or anticipation of the Gothic, a style in -which this principle is not manifested. I do not see, in any of the -representations of the early Arabic buildings, that distribution of -weights to supports, and that mechanical consistency of parts, which -would elevate them above the character of barbarous architecture. -Their masses are broken into innumerable members, without -subordination or meaning, in a manner suggested apparently by -caprice and the love of the marvellous. "In the construction of -their mosques, it was a favorite artifice of the Arabs to sustain -immense and ponderous masses of stone by the support of pillars so -slender, that the incumbent weight seemed, as it were, suspended in -the air by an invisible hand."[95\4] This pleasure in the -contemplation of apparent impossibilities is a very general -disposition among mankind; but it appears to belong to the infancy, -rather than the maturity of intellect. On the other hand, the -pleasure in the contemplation of what is clear, the craving for a -thorough insight into the reasons of things, which marks the -European mind, is the temper which leads to science. - -[Note 95\4: _Mahometanism Unveiled_, ii. 255.] - -6. _Treatises on Architecture._--No one who has attended to the -architecture which prevailed in England, France, and Germany, from -the twelfth to the fifteenth century, so far as to comprehend its -beauty, harmony, consistency, and uniformity, even in the minutest -parts and most obscure relations, can look upon it otherwise than as -a {249} remarkably connected and definite artificial system. Nor can -we doubt that it was exercised by a class of artists who formed -themselves by laborious study and practice, and by communication -with each other. There must have been bodies of masters and of -scholars, discipline, traditions, precepts of art. How these -associated artists diffused themselves over Europe, and whether -history enables us to trace them in a distinct form, I shall not -here discuss. But the existence of a course of instruction, and of a -body of rules of practice, is proved beyond dispute by the great -series of European cathedrals and churches, so nearly identical in -their general arrangements, and in their particular details. The -question then occurs, have these rules and this system of -instruction anywhere been committed to writing? Can we, by such -evidence, trace the progress of the scientific idea, of which we see -the working in these buildings? - -We are not to be surprised, if, during the most flourishing and -vigorous period of the art of the middle ages, we find none of its -precepts in books. Art has, in all ages and countries, been taught -and transmitted by practice and verbal tradition, not by writing. It -is only in our own times, that the thought occurs as familiar, of -committing to books all that we wish to preserve and convey. And, -even in our own times, most of the Arts are learned far more by -practice, and by intercourse with practitioners, than by reading. -Such is the case, not only with Manufactures and Handicrafts, but -with the Fine Arts, with Engineering, and even yet, with that art, -Building, of which we are now speaking. - -We are not, therefore, to wonder, if we have no treatises on -Architecture belonging to the great period of the Gothic -masters;--or if it appears to have required some other incitement -and some other help, besides their own possession of their practical -skill, to lead them to shape into a literary form the precepts of -the art which they knew so well how to exercise:--or if, when they -did write on such subjects, they seem, instead of delivering their -own sound practical principles, to satisfy themselves with pursuing -some of the frivolous notions and speculations which were then -current in the world of letters. - -Such appears to be the case. The earliest treatises on Architecture -come before us under the form which the commentatorial spirit of the -middle ages inspired. They are Translations of Vitruvius, with -Annotations. In some of these, particularly that of Cesare -Cesariano, published at Como, in 1521, we see, in a very curious -manner, how the habit of assuming that, in every department of -literature, the ancients {250} must needs be their masters, led -these writers to subordinate the members of their own architecture -to the precepts of the Roman author. We have Gothic shafts, -mouldings, and arrangements, given as parallelisms to others, which -profess to represent the Roman style, but which are, in fact, -examples of that mixed manner which is called the style of the -_Cinque cento_ by the Italians, of the _Renaissance_ by the French, -and which is commonly included in our _Elizabethan_. But in the -early architectural works, besides the superstitions and mistaken -erudition which thus choked the growth of real architectural -doctrines, another of the peculiar elements of the middle ages comes -into view;--its mysticism. The dimensions and positions of the -various parts of edifices and of their members, are determined by -drawing triangles, squares, circles, and other figures, in such a -manner as to bound them; and to these geometrical figures were -assigned many abstruse significations. The plan and the front of the -Cathedral at Milan are thus represented in Cesariano's work, bounded -and subdivided by various equilateral triangles; and it is easy to -see, in the earnestness with which he points out these relations, -the evidence of a fanciful and mystical turn of thought.[96\4] - -[Note 96\4: The plan which he has given, fol. 14, he has entitled -"Ichnographia Fundamenti sacræ Ædis baricephalæ, Germanico more, à -Trigono ac Pariquadrato perstructa, uti etiam ea quæ nunc Milani -videtur." - -The work of Cesariano was translated into German by Gualter Rivius, -and published at Nuremberg, in 1548, under the title of _Vitruvius -Teutsch_, with copies of the Italian diagrams. A few years ago, in an -article in the _Wiener Jahrbücher_ (Oct.-Dec., 1821), the reviewer -maintained, on the authority of the diagrams in Rivius's book, that -Gothic architecture had its origin in Germany and not in England.] - -We thus find erudition and mysticism take the place of much of that -development of the architectural principles of the middle ages which -would be so interesting to us. Still, however, these works are by no -means without their value. Indeed many of the arts appear to -flourish not at all the worse, for being treated in a manner -somewhat mystical; and it may easily be, that the relations of -geometrical figures, for which fantastical reasons are given, may -really involve principles of beauty or stability. But independently -of this, we find, in the best works of the architects of all ages -(including engineers), evidence that the true idea of mechanical -pressure exists among them more distinctly than among men in -general, although it may not be developed in a scientific form. This -is true up to our own time, and the arts which such persons -cultivate could not be successfully {251} exercised if it were not -so. Hence the writings of architects and engineers during the middle -ages do really form a prelude to the works on scientific mechanics. -Vitruvius, in his _Architecture_, and Julius Frontinus, who, under -Vespasian, wrote _On Aqueducts_, of which he was superintendent, -have transmitted to us the principal part of what we know respecting -the practical mechanics and hydraulics of the Romans. In modern -times the series is resumed. The early writers on architecture are -also writers on engineering, and often on hydrostatics: for example, -Leonardo da Vinci wrote on the equilibrium of water. And thus we are -led up to Stevinus of Bruges, who was engineer to Prince Maurice of -Nassau, and inspector of the dykes in Holland; and in whose work, on -the processes of his art, is contained the first clear modern -statement of the scientific principles of hydrostatics. - -Having thus explained both the obstacles and the prospects which the -middle ages offered to the progress of science, I now proceed to the -history of the progress, when that progress was once again resumed. - - - -{{253}} -BOOK V. - - - -HISTORY -OF -FORMAL ASTRONOMY -AFTER THE STATIONARY PERIOD. - - - . . . Cyclopum educta caminis - Mœnia conspicio, atque adverso fornice portas. - . . . . . - His demum exactis, perfecto munere Divæ, - Devenere locos lætos et amœna vireta - Fortunatorum nemorum sedesque beatas. - Largior hic campos æther et lumine vestit - Purpureo: solemque suum, sua sidera norunt. - VIRGIL, _Æn._ vi. 630. - - - They leave at length the nether gloom, and stand - Before the portals of a better land: - To happier plains they come, and fairer groves, - The seats of those whom heaven, benignant, loves; - A brighter day, a bluer ether, spreads - Its lucid depths above their favored heads; - And, purged from mists that veil our earthly skies, - Shine suns and stars unseen by mortal eyes. - - - -{{255}} -INTRODUCTION. - - -_Of Formal and Physical Astronomy._ - -WE have thus rapidly traced the causes of the almost complete blank -which the history of physical science offers, from the decline of -the Roman empire, for a thousand years. Along with the breaking up -of the ancient forms of society, were broken up the ancient energy -of thinking, the clearness of idea, and steadiness of intellectual -action. This mental declension produced a servile admiration for the -genius of the better periods, and thus, the spirit of Commentation: -Christianity established the claim of truth to govern the world; and -this principle, misinterpreted and combined with the ignorance and -servility of the times, gave rise to the Dogmatic System: and the -love of speculation, finding no secure and permitted path on solid -ground, went off into the regions of Mysticism. - -The causes which produced the inertness and blindness of the -stationary period of human knowledge, began at last to yield to the -influence of the principles which tended to progression. The -indistinctness of thought, which was the original feature in the -decline of sound knowledge, was in a measure remedied by the steady -cultivation of Pure Mathematics and Astronomy, and by the progress of -inventions in the Arts, which call out and fix the distinctness of our -conceptions of the relations of natural phenomena. As men's minds -became clear, they became less servile: the perception of the nature -of truth drew men away from controversies about mere opinion; when -they saw distinctly the relations of _things_, they ceased to give -their whole attention to what had been _said_ concerning them; and -thus, as science rose into view, the spirit of commentation lost its -way. And when men came to feel what it was to think for themselves on -subjects of science, they soon rebelled against the right of others to -impose opinions upon them. When they threw off their blind admiration -for the ancients, they were disposed to cast away also their passive -obedience to the ancient system of doctrines. When they were no longer -inspired by the spirit of commentation, they were no longer submissive -to the dogmatism of the schools. When they began to feel that they -could {256} discover truths, they felt also a persuasion of a right -and a growing will so to do. - -Thus the revived clearness of ideas, which made its appearance at -the revival of letters, brought on a struggle with the authority, -intellectual and civil, of the established schools of philosophy. -This clearness of idea showed itself, in the first instance, in -Astronomy, and was embodied in the system of Copernicus; but the -contest did not come to a crisis till a century later, in the time -of Galileo and other disciples of the new doctrine. It is our -present business to trace the principles of this series of events in -the history of philosophy. - -I do not profess to write a history of Astronomy, any further than -is necessary in order to exhibit the principles on which the -progression of science proceeds; and, therefore, I neglect -subordinate persons and occurrences, in order to bring into view the -leading features of great changes. Now in the introduction of the -Copernican system into general acceptation, two leading views -operated upon men's minds; the consideration of the system as -exhibiting the apparent motions of the universe, and the -consideration of this system with reference to its causes;--the -_formal_ and the _physical_ aspect of the Theory;--the relations of -Space and Time, and the relations of Force and Matter. These two -divisions of the subject were at first not clearly separated; the -second was long mixed, in a manner very dim and obscure, with the -first, without appearing as a distinct subject of attention; but at -last it was extricated and treated in a manner suitable to its -nature. The views of Copernicus rested mainly on the formal -condition of the universe, the relations of space and time; but -Kepler, Galileo, and others, were led, by controversies and other -causes, to give a gradually increasing attention to the physical -relations of the heavenly bodies; an impulse was given to the study -of Mechanics (the Doctrine of Motion), which became very soon an -important and extensive science; and in no long period, the -discoveries of Kepler, suggested by a vague but intense belief in -the physical connection of the parts of the universe, led to the -decisive and sublime generalizations of Newton. - -The distinction of _formal_ and _physical_ Astronomy thus becomes -necessary, in order to treat clearly of the discussions which the -propounding of the Copernican theory occasioned. But it may be -observed that, besides this great change, Astronomy made very great -advances in the same path which we have already been tracing, -namely, the determination of the quantities and laws of the -celestial motions, in so far as they were exhibited by the ancient -theories, or {257} might be represented by obvious modifications of -those theories. I speak of new Inequalities, new Phenomena, such as -Copernicus, Galileo, and Tycho Brahe discovered. As, however, these -were very soon referred to the Copernican rather than the Ptolemaic -hypothesis, they may be considered as developments rather of the new -than of the old Theory; and I shall, therefore, treat of them, -agreeably to the plan of the former part, as the sequel of the -Copernican Induction. - - - - -CHAPTER I. - -PRELUDE TO THE INDUCTIVE EPOCH OF COPERNICUS. - - -THE Doctrine of Copernicus, that the Sun is the true centre of the -celestial motions, depends primarily upon the consideration that -such a supposition explains very simply and completely all the -obvious appearances of the heavens. In order to see that it does -this, nothing more is requisite than a distinct conception of the -nature of Relative Motion, and a knowledge of the principal -Astronomical Phenomena. There was, therefore, no reason why such a -doctrine might not be _discovered_, that is, suggested as a theory -plausible at first sight, long before the time of Copernicus; or -rather, it was impossible that this guess, among others, should not -be propounded as a solution of the appearances of the heavens. We -are not, therefore, to be surprised if we find, in the earliest -times of Astronomy, and at various succeeding periods, such a system -spoken of by astronomers, and maintained by some as true, though -rejected by the majority, and by the principal writers. - -When we look back at such a difference of opinion, having in our -minds, as we unavoidably have, the clear and irresistible -considerations by which the Copernican Doctrine is established _for -us_, it is difficult for us not to attribute superior sagacity and -candor to those who held that side of the question, and to imagine -those who clung to the Ptolemaic Hypothesis to have been blind and -prejudiced; incapable of seeing the beauty of simplicity and -symmetry, or indisposed to resign established errors, and to accept -novel and comprehensive truths. Yet in judging thus, we are probably -ourselves influenced by prejudices arising from the knowledge and -received opinions of our own times. For is it, in reality, clear -that, before the time of Copernicus, the {258} _Heliocentric_ Theory -(that which places the centre of the celestial motions in the Sun) -had a claim to assent so decidedly superior to the Geocentric -Theory, which places the Earth in the centre? What is the basis of -the heliocentric theory?--That the _relative_ motions are _the -same_, on that and on the other supposition. So far, therefore, the -two hypotheses are exactly on the same footing. But, it is urged, on -the heliocentric side we have the advantage of simplicity:--true; -but we have, on the other side, the testimony of our senses; that -is, the geocentric doctrine (which asserts that the Earth rests and -the heavenly bodies move) is the obvious and spontaneous -interpretation of the appearances. Both these arguments, -_simplicity_ on the one side, and _obviousness_ on the other, are -vague, and we may venture to say, both indecisive. We cannot -establish any strong preponderance of probability in favor of the -former doctrine, without going much further into the arguments of -the question. - -Nor, when we speak of the superior _simplicity_ of the Copernican -theory, must we forget, that though this theory has undoubtedly, in -this respect, a great advantage over the Ptolemaic, yet that the -Copernican system itself is very complex, when it undertakes to -account, as the Ptolemaic did, for the _Inequalities_ of the Motions -of the sun, moon, and planets; and, that in the hands of Copernicus, -it retained a large share of the eccentrics and epicycles of its -predecessor, and, in some parts, with increased machinery. The -heliocentric theory, without these appendages, would not approach -the Ptolemaic, in the accurate explanation of facts; and as those -who had placed the sun in the centre had never, till the time of -Copernicus, shown how the inequalities were to be explained on that -supposition, we may assert that after the promulgation of the theory -of eccentrics and epicycles on the geocentric hypothesis, there was -no _published_ heliocentric theory which could bear a comparison -with that hypothesis. - -It is true, that all the contrivances of epicycles, and the like, by -which the geocentric hypothesis was made to represent the phenomena, -were susceptible of an easy adaptation to a heliocentric method, _when -a good mathematician had once proposed to himself the problem_: and -this was precisely what Copernicus undertook and executed. But, till -the appearance of his work, the heliocentric system had never come -before the world except as a hasty and imperfect hypothesis; which -bore a favorable comparison with the phenomena, so long as their -general features only were known; but which had been completely thrown -into the shade by the labor and intelligence bestowed upon {259} the -Hipparchian or Ptolemaic theories by a long series of great -astronomers of all civilized countries. - -But, though the astronomers who, before Copernicus, held the -heliocentric opinion, cannot, on any good grounds, be considered as -much more enlightened than their opponents, it is curious to trace the -early and repeated manifestations of this view of the universe. The -distinct assertion of the heliocentric theory among the Greeks is an -evidence of the clearness of their thoughts, and the vigour of their -minds; and it is a proof of the feebleness and servility of intellect -in the stationary period, that, till the period of Copernicus, no one -was found to try the fortune of this hypothesis, modified according to -the improved astronomical knowledge of the time. - -The most ancient of the Greek philosophers to whom the ancients -ascribe the heliocentric doctrine, is Pythagoras; but Diogenes -Laertius makes Philolaus, one of the followers of Pythagoras, the -first author of this doctrine. We learn from Archimedes, that it was -held by his contemporary, Aristarchus. "Aristarchus of Samos," says -he,[1\5] "makes this supposition,--that the fixed stars and the sun -remain at rest, and that the earth revolves round the sun in a -circle." Plutarch[2\5] asserts that this, which was only a -hypothesis in the hands of Aristarchus, was _proved_ by Seleucus; -but we may venture to say that, at that time, no such proof was -possible. Aristotle had recognized the existence of this doctrine by -arguing against it. "All things," says he,[3\5] "tend to the centre -of the earth, and rest there, and therefore the whole mass of the -earth cannot rest except there." Ptolemy had in like manner argued -against the diurnal motion of the earth: such a revolution would, he -urged, disperse into surrounding space all the loose parts of the -earth. Yet he allowed that such a supposition would facilitate the -explanation of some phenomena. Cicero appears to make Mercury and -Venus revolve about the sun, as does Martianus Capella at a later -period; and Seneca says[4\5] it is a worthy subject of -contemplation, whether the earth be at rest or in motion: but at -this period, as we may see from Seneca himself, that habit of -intellect which was requisite for the solution of such a question, -had been succeeded by indistinct views, and rhetorical forms of -speech. If there were any good mathematicians and good observers at -this period, they were employed in cultivating and verifying the -Hipparchian theory. - -[Note 1\5: Archim. _Arenarius._] - -[Note 2\5: _Quest. Plat._ Delamb. _A. A._ vi.] - -[Note 3\5: Quoted by Copernic. i. 7.] - -[Note 4\5: _Quest. Nat._ vii. 2.] - -Next to the Greeks, the Indians appear to have possessed that {260} -original vigor and clearness of thought, from which true science -springs. It is remarkable that the Indians, also, had their -heliocentric theorists. Aryabatta[5\5] (A. D. 1322), and other -astronomers of that country, are said to have advocated the doctrine -of the earth's revolution on its axis; which opinion, however, was -rejected by subsequent philosophers among the Hindoos. - -[Note 5\5: Lib. U. K. _Hist. Ast._ p. 11.] - -Some writers have thought that the heliocentric doctrine was -_derived_ by Pythagoras and other European philosophers, from some -of the oriental nations. This opinion, however, will appear to have -little weight, if we consider that the heliocentric hypothesis, in -the only shape in which the ancients knew it, was too obvious to -require much teaching; that it did not and could not, so far as we -know, receive any additional strength from any thing which the -oriental nations could teach; and that each astronomer was induced -to adopt or reject it, not by any information which a master could -give him, but by his love of geometrical simplicity on the one hand, -or the prejudices of sense on the other. Real science, depending on -a clear view of the relation of phenomena to general theoretical -ideas, cannot be communicated in the way of secret and exclusive -traditions, like the mysteries of certain arts and crafts. If the -philosopher do not _see_ that the theory is true, he is little the -better for having heard or read the words which assert its truth. - -It is impossible, therefore, for us to assent to those views which -would discover in the heliocentric doctrines of the ancients, traces -of a more profound astronomy than any which they have transmitted to -us. Those doctrines were merely the plausible conjectures of men -with sound geometrical notions; but they were never extended so as -to embrace the details of the existing astronomical knowledge; and -perhaps we may say, that the analysis of the phenomena into the -arrangements of the Ptolemaic system, was so much more obvious than -any other, that it must necessarily come first, in order to form an -introduction to the Copernican. - -The true foundation of the heliocentric theory for the ancients was, -as we have intimated, its perfect geometrical consistency with the -general features of the phenomena, and its simplicity. But it was -unlikely that the human mind would be content to consider the -subject under this strict and limited aspect alone. In its eagerness -for wide speculative views, it naturally looked out for other and -vaguer principles of connection and relation. Thus, as it had been -urged in {261} favor of the geocentric doctrine, that the heaviest -body must be in the centre, it was maintained, as a leading -recommendation of the opposite opinion, that it placed the Fire, the -noblest element, in the Centre of the Universe. The authority of -mythological ideas was called in on both sides to support these -views. Numa, as Plutarch[6\5] informs us, built a circular temple -over the ever-burning Fire of Vesta; typifying, not the earth, but -the Universe, which, according to the Pythagoreans, has the Fire -seated at its Centre. The same writer, in another of his works, -makes one of his interlocutors say, "Only, my friend, do not bring -me before a court of law on a charge of impiety; as Cleanthes said, -that Aristarchus the Samian ought to be tried for impiety, because -he removed the Hearth of the Universe." This, however, seems to have -been intended as a pleasantry. - -[Note 6\5: _De Facie in Orbe Lunæ_, 6.] - -The prevalent physical views, and the opinions concerning the causes -of the motions of the parts of the universe, were scarcely more -definite than the ancient opinions concerning the relations of the -four elements, till Galileo had founded the true Doctrine of Motion. -Though, therefore, arguments on this part of the subject were the -most important part of the controversy after Copernicus, the force -of such arguments was at his time almost balanced. Even if more had -been known on such subjects, the arguments would not have been -conclusive: for instance, the vast mass of the heavens, which is -commonly urged as a reason why the heavens do not move round the -earth, would not make such a motion impossible; and, on the other -hand, the motions of bodies at the earth's surface, which were -alleged as inconsistent with its motion, did not really disprove -such an opinion. But according to the state of the science of motion -before Copernicus, all reasonings from such principles were utterly -vague and obscure. - -We must not omit to mention a modern who preceded Copernicus, in the -assertion at least of the heliocentric doctrine. This was Nicholas -of Cusa (a village near Treves), a cardinal and bishop, who, in the -first half of the fifteenth century, was very eminent as a divine -and mathematician; and who in a work, _De Doctâ Ignorantiâ_, -propounded the doctrine of the motion of the earth; more, however, -as a paradox than as a reality. We cannot consider this as any -distinct anticipation of a profound and consistent view of the truth. - -We shall now examine further the promulgation of the Heliocentric -System by Copernicus, and its consequences. {262} - - - - -CHAPTER II. - -INDUCTION OF COPERNICUS.--THE HELIOCENTRIC THEORY ASSERTED ON FORMAL -GROUNDS. - - -IT will be recollected that the _formal_ are opposed to the -_physical_ grounds of a theory; the former term indicating that it -gives a satisfactory account of the relations of the phenomena in -Space and Time, that is, of the Motions themselves; while the latter -expression implies further that we include in our explanation the -Causes of the motions, the laws of Force and Matter. The strongest -of the considerations by which Copernicus was led to invent and -adopt his system of the universe were of the former kind. He was -dissatisfied, he says, in his Preface addressed to the Pope, with -the want of symmetry in the Eccentric Theory, as it prevailed in his -days; and weary of the uncertainty of the mathematical traditions. -He then sought through all the works of philosophers, whether any -had held opinions concerning the motions of the world, different -from those received in the established mathematical schools. He -found, in ancient authors, accounts of Philolaus and others, who had -asserted the motion of the earth. "Then," he adds, "I, too, began to -meditate concerning the motion of the earth; and though it appeared -an absurd opinion, yet since I knew that, in previous times, others -had been allowed the privilege of feigning what circles they chose, -in order to explain the phenomena, I conceived that I also might -take the liberty of trying whether, on the supposition of the -earth's motion, it was possible to find better explanations than the -ancient ones, of the revolutions of the celestial orbs. - -"Having then assumed the motions of the earth, which are hereafter -explained, by laborious and long observation I at length found, that -if the motions of the other planets be compared with the revolution of -the earth, not only their phenomena follow from the suppositions, but -also that the several orbs, and the whole system, are so connected in -order and magnitude, that no one part can be transposed without -disturbing the rest, and introducing confusion into the whole -universe." - -Thus the satisfactory explanation of the apparent motions of the -planets, and the simplicity and symmetry of the system, were the -{263} grounds on which Copernicus adopted his theory; as the craving -for these qualities was the feeling which led him to seek for a new -theory. It is manifest that in this, as in other cases of discovery, -a clear and steady possession of abstract Ideas, and an aptitude in -comprehending real Facts under these general conceptions, must have -been leading characters in the discoverer's mind. He must have had a -good geometrical head, and great astronomical knowledge. He must -have seen, with peculiar distinctness, the consequences which flowed -from his suppositions as to the relations of space and time,--the -apparent motions which resulted from the assumed real ones; and he -must also have known well all the irregularities of the apparent -motions for which he had to account. We find indications of these -qualities in his expressions. A steady and calm contemplation of the -theory is what he asks for, as the main requisite to its reception. -If you suppose the earth to revolve and the heaven to be at rest, -you will find, he says, "_si serio animadvertas_," if you think -steadily, that the apparent diurnal motion will follow. And after -alleging his reasons for his system, he says,[7\5] "We are, -therefore, not ashamed to confess, that the whole of the space -within the orbit of the moon, along with the centre of the earth, -moves round the sun in a year among the other planets; the magnitude -of the world being so great, that the distance of the earth from the -sun has no apparent magnitude when compared with the sphere of the -fixed stars." "All which things, though they be difficult and almost -inconceivable, and against the opinion of the majority, yet, in the -sequel, by God's favor, we will make clearer than the sun, at least -to those who are not ignorant of mathematics." - -[Note 7\5: Nicolai Copernici Torinensis _de Revolutionibus Orbium -Cœlestium Libri VI_. Norimbergæ, M.D.XLIII. p. 9.] - -It will easily be understood, that since the ancient geocentric -hypothesis ascribed to the planets those motions which were apparent -only, and which really arose from the motion of the earth round the -sun in the new hypothesis, the latter scheme must much simplify the -planetary theory. Kepler[8\5] enumerates eleven motions of the -Ptolemaic system, which are at once exterminated and rendered -unnecessary by the new system. Still, as the real motions, both of -the earth and the planets, are unequable, it was requisite to have -some mode of representing their inequalities; and, accordingly, the -ancient theory of eccentrics and epicycles was retained, so far as -was requisite for this purpose. The planets revolved round the sun -by means of a Deferent, and a {264} great and small Epicycle; or -else by means of an Eccentric and Epicycle, modified from Ptolemy's, -for reasons which we shall shortly mention. This mode of -representing the motions of the planets continued in use, until it -was expelled by the discoveries of Kepler. - -[Note 8\5: _Myst. Cosm._ cap. 1.] - -Besides the daily rotation of the earth on its axis, and its annual -circuit about the sun, Copernicus attributed to the axis a "motion -of declination," by which, during the whole annual revolution, the -pole was constantly directed towards the same part of the heavens. -This constancy in the absolute direction of the axis, or its moving -parallel to itself, may be more correctly viewed as not indicating -any separate motion. The axis continues in the same direction, -because there is nothing to make it change its direction; just as a -straw, lying on the surface of a cup of water, continues to point -nearly in the same direction when the cup is carried round a room. -And this was noticed by Copernicus's adherent, Rothman,[9\5] a few -years after the publication of the work _De Revolutionibus_. "There -is no occasion," he says, in a letter to Tycho Brahe, "for the -triple motion of the earth: the annual and diurnal motions suffice." -This error of Copernicus, if it be looked upon as an error, arose -from his referring the position of the axis to a limited space, -which he conceived to be carried round the sun along with the earth, -instead of referring it to fixed or absolute space. When, in a -Planetarium (a machine in which the motions of the planets are -imitated), the earth is carried round the sun by being fastened to a -material radius, it is requisite to give a motion to the axis by -_additional_ machinery, in order to enable it to _preserve_ its -parallelism. A similar confusion of geometrical conception, produced -by a double reference to absolute space and to the centre of -revolution, often leads persons to dispute whether the moon, which -revolves about the earth, always turning to it the same face, -revolves about her axis or not. - -[Note 9\5: Tycho. Epist. i. p. 184, A. D. 1590.] - -It is also to be noticed that the precession of the equinoxes made -it necessary to suppose the axis of the earth to be not _exactly_ -parallel to itself, but to deviate from that position by a slight -annual difference. Copernicus erroneously supposes the precession to -be unequable; and his method of explaining this change, which is -simpler than that of the ancients, becomes more simple still, when -applied to the true state of the facts. - -The tendencies of our speculative nature, which carry us onwards in -{265} pursuit of symmetry and rule, and which thus produced the -theory of Copernicus, as they produce all theories, perpetually show -their vigor by overshooting their mark. They obtain something by -aiming at much more. They detect the order and connection which -exist, by imagining relations of order and connection which have no -existence. Real discoveries are thus mixed with baseless -assumptions; profound sagacity is combined with fanciful conjecture; -not rarely, or in peculiar instances, but commonly, and in most -cases; probably in all, if we could read the thoughts of the -discoverers as we read the books of Kepler. To try wrong guesses is -apparently the only way to hit upon right ones. The character of the -true philosopher is, not that he never conjectures hazardously, but -that his conjectures are clearly conceived and brought into rigid -contact with facts. He sees and compares distinctly the ideas and -the things,--the relations of his notions to each other and to -phenomena. Under these conditions it is not only excusable, but -necessary for him, to snatch at every semblance of general rule;--to -try all promising forms of simplicity and symmetry. - -Copernicus is not exempt from giving us, in his work, an example of -this character of the inventive spirit. The axiom that the celestial -motions must be _circular_ and _uniform_, appeared to him to have -strong claims to acceptation; and his theory of the inequalities of -the planetary motions is fashioned upon it. His great desire was to -apply it more rigidly than Ptolemy had done. The time did not come -for rejecting this axiom, till the observations of Tycho Brahe and -the calculations of Kepler had been made. - -I shall not attempt to explain, in detail, Copernicus's system of -the planetary inequalities. He retained epicycles and eccentrics, -altering their centres of motion; that is, he retained what was -_true_ in the old system, _translating_ it into his own. The -peculiarities of his method consisted in making such a combination -of epicycles as to supply the place of the _equant_,[10\5] and to -make all the motions equable about the centres of motion. This -device was admired for a time, till Kepler's elliptic theory -expelled it, with all other forms of the theory of epicycles: but we -must observe that Copernicus was aware of some of the discrepancies -which belonged to that theory as it had, up to that time, been -propounded. In the case of Mercury's orbit, which is more eccentric -than that of the other planets, he makes suppositions which are -complex indeed, but which show his perception of the imperfection of -{266} the common theory; and he proposes a new theory of the moon, -for the very reason which did at last overturn the doctrine of -epicycles, namely, that the ratio of their distances from the earth -at different times was inconsistent with the circular -hypothesis.[11\5] - -[Note 10\5: See B. iii. Chap. **iv. Sect. 7.] - -[Note 11\5: _De Rev._ iv. c. 2.] - -It is obvious, that, along with his mathematical clearness of view, -and his astronomical knowledge, Copernicus must have had great -intellectual boldness and vigor, to conceive and fully develop a -theory so different as his was from all received doctrines. His pupil -and expositor, Rheticus, says to Schener, "I beg you to have this -opinion concerning that learned man, my Preceptor; that he was an -ardent admirer and follower of Ptolemy; but when he was compelled by -phenomena and demonstration, he thought he did well to aim at the same -mark at which Ptolemy had aimed, though with a bow and shafts of a -very different material from his. We must recollect what Ptolemy says, -Δεῖ δ' ἐλευθέρον εἶναι τῇ γνώμῃ τὸν μέλλοντα φιλοσοφεῖν. 'He who is to -follow philosophy must be a freeman in mind.'" Rheticus then goes on -to defend his master from the charge of disrespect to the ancients: -"That temper," he says, "is alien from the disposition of every good -man, and most especially from the spirit of philosophy, and from no -one more utterly than from my Preceptor. He was very far from rashly -rejecting the opinions of ancient philosophers, except for weighty -reasons and irresistible facts, through any love of novelty. His -years, his gravity of character, his excellent learning, his -magnanimity and nobleness of spirit, are very far from having any -liability to such a temper, which belongs either to youth, or to -ardent and light minds, or to those τῶν μέγα φρονούντων ἐπὶ θεωρίᾳ -μικρῂ, 'who think much of themselves and know little,' as Aristotle -says." Undoubtedly this deference for the great men of the past, -joined with the talent of seizing the spirit of their methods when the -letter of their theories is no longer tenable, _is_ the true mental -constitution of discoverers. - -Besides the intellectual energy which was requisite in order to -construct a system of doctrines so novel as those of Copernicus, some -courage was necessary to the publication of such opinions; certain, as -they were, to be met, to a great extent, by rejection and dispute, and -perhaps by charges of heresy and mischievous tendency. This last -danger, however, must not be judged so great as we might infer from -the angry controversies and acts of authority which occurred in {267} -Galileo's time. The Dogmatism of the stationary period, which -identified the cause of philosophical and religious truth, had not yet -distinctly felt itself attacked by the advance of physical knowledge; -and therefore had not begun to look with alarm on such movements. -Still, the claims of Scripture and of ecclesiastical authority were -asserted as paramount on all subjects; and it was obvious that many -persons would be disquieted or offended with the new interpretation of -many scriptural expressions, which the true theory would make -necessary. This evil Copernicus appears to have foreseen; and this and -other causes long withheld him from publication. He was himself an -ecclesiastic; and, by the patronage of his maternal uncle, was -prebendary of the church of St. John at Thorn, and a canon of the -church of Frauenburg, in the diocese of Ermeland.[12\5] He had been a -student at Bologna, and had taught mathematics at Rome in the year -1500; and he afterwards pursued his studies and observations at his -residence near the mouth of the Vistula.[13\5] His discovery of his -system must have occurred before 1507, for in 1543 he informs Pope -Paulus the Third, in his dedication, that he had kept his book by him -for four times the nine years recommended by Horace, and then only -published it at the earnest entreaty of his friend Cardinal Schomberg, -whose letter is prefixed to the work. "Though I know," he says, "that -the thoughts of a philosopher do not depend on the judgment of the -many, his study being to seek out truth in all things as far as that -is permitted by God to human reason: yet when I considered," he adds, -"how absurd my doctrine would appear, I long hesitated whether I -should publish my book, or whether it were not better to follow the -example of the Pythagoreans and others, who delivered their doctrines -only by tradition and to friends." It will be observed that he speaks -here of the opposition of the established school of Astronomers, not -of Divines. The latter, indeed, he appears to consider as a less -formidable danger. "If perchance," he says at the end of his preface, -"there be ματαιολόγοι, vain babblers, who knowing nothing of -mathematics, yet assume the right of judging on account of some place -of Scripture perversely wrested to their purpose, and who blame and -attack my undertaking; I heed them not, and look upon their judgments -as rash and contemptible." He then goes on to show that the globular -figure of the earth (which was, of course, at that time, an undisputed -point among astronomers), had been opposed on similar grounds by -Lactantius, who, {268} though a writer of credit in other respects, -had spoken very childishly in that matter. In another epistle prefixed -to the work (by Andreas Osiander), the reader is reminded that the -hypotheses of astronomers are not necessarily asserted to be true, by -those who propose them, but only to be a way of _representing_ facts. -We may observe that, in the time of Copernicus, when the motion of the -earth had not been connected with the physical laws of matter and -motion, it could not be considered so distinctly real as it -necessarily was held to be in after times. - -[Note 12\5: Rheticus, _Nar._ p. 94.] - -[Note 13\5: Riccioli.] - -The delay of the publication of Copernicus's work brought it to the -end of his life; he died in the year 1543, in which it was -published. It was entitled _De Revolutionibus Orbium Cœlestium Libri -VI_. He received the only copy he ever saw on the day of his death, -and never opened it: he had then, says Gassendi, his biographer, -other cares. His system was, however, to a certain extent, -promulgated, and his fame diffused before that time. Cardinal -Schomberg, in his letter of 1536, which has been already mentioned, -says, "Some years ago, when I heard tidings of your merit by the -constant report of all persons, my affection for you was augmented, -and I congratulated the men of our time, among whom you flourish in -so much honor. For I had understood that you were not only -acquainted with the discoveries of ancient mathematicians, but also -had formed a new system of the world, in which you teach that the -Earth moves, the Sun occupies the lowest, and consequently, the -middle place, the sphere of the fixed stars remains immovable and -fixed, and the Moon, along with the elements included in her sphere, -placed between the orbits (_cœlum_) of Mars and Venus, travels round -the sun in a yearly revolution."[14\5] The writer goes on to say -that he has heard that Copernicus has written a book -(_Commentarios_), in which this system is applied to the -construction of Tables of the Planetary Motions (_erraticarum -stellarum_). He then proceeds to entreat him earnestly to publish -his lucubrations. {269} - -[Note 14\5: This passage has so important a place in the history, that -I will give it in the original:--"Intellexeram te non modo veterum -mathematicorum inventa egregie callere sed etiam novam mundi rationem -constituisse: Qua doceas terram moveri: solem imum mundi, atque medium -locum obtinere: cœlum octavum immotum atque fixum perpetuo manere: -Lunam se una cum inclusis suæ spheræ elementis, inter Martis et -Veneris cœlum sitam, anniversario cursu circum solem convertere. Atque -de hac tota astronomiæ ratione commentarios a te confectos esse, ac -erraticarum stellarum motus calculis subductos tabulis te contulisse, -maxima omnium cum admiratione. Quamobrem vir doctissime, nisi tibi -molestus sum, te etiam atque etiam oro vehementer ut hoc tuum inventum -studiosis communices, et tuas de mundi sphæra lucubrationes, una cum -Tabulis et si quid habes præterea quod ad eandem rem pertineat primo -quoque tempore ad me mittas."] - -This letter is dated 1536, and implies that the work of Copernicus -was then written, and known to persons who studied astronomy. -Delambre says that Achilles Gassarus of Lindau, in a letter dated -1540, sends to his friend George Vogelin of Constance, the book _De -Revolutionibus_. But Mr. De Morgan[15\5] has pointed out that the -printed work which Gassarus sent to Vogelin was the _Narratio_ by -Rheticus of Feldkirch, a eulogium of Copernicus and his system -prefixed to the second edition of the _De Revolutionibus_, which -appeared in 1566. In this Narration, Rheticus speaks of the work of -Copernicus as a Palingenesia, or New Birth of astronomy. Rheticus, -it appears, had gone to Copernicus for the purpose of getting -knowledge about triangles and trigonometrical tables, and had had -his attention called to the heliocentric theory, of which he became -an ardent admirer. He speaks of his "Preceptor" with strong -admiration, as we have seen. "He appears to me," says he, "more to -resemble Ptolemy than any other astronomers." This, it must be -recollected, was selecting the highest known subject of comparison. - -[Note 15\5: _Ast. Mod._ i. p. 138. I owe this and many other -corrections to the personal kindness of Mr. De Morgan.] - - - - -CHAPTER III. - -SEQUEL TO COPERNICUS.--THE RECEPTION AND DEVELOPMENT OF THE -COPERNICAN THEORY. - - -_Sect._ 1.--_First Reception of the Copernican Theory._ - -THE theories of Copernicus made their way among astronomers, in the -manner in which true astronomical theories always obtain the assent -of competent judges. They led to the construction of Tables of the -motion of the sun, moon, and planets, as the theories of Hipparchus -and Ptolemy had done; and the verification of the doctrines was to -be looked for, from the agreement of these Tables with observation, -through a sufficient course of time. The work _De Revolutionibus_ -contains such Tables. In 1551 Reinhold improved and republished -Tables founded on the principles of Copernicus. "We owe," he says in -his preface, "great obligations to Copernicus, both for his -laborious {270} observations, and for restoring the doctrine of the -Motions. But though his geometry is perfect, the good old man -appears to have been, at times, careless in his numerical -calculations. I have, therefore, recalculated the whole, from a -comparison of his observations with those of Ptolemy and others, -following nothing but the general plan of Copernicus's -demonstrations." These "Prutenic Tables" were republished in 1571 -and 1585, and continued in repute for some time; till superseded by -the Rudolphine Tables of Kepler in 1627. The name _Prutenic_, or -Prussian, was employed by the author as a mark of gratitude to his -benefactor Albert, Markgrave of Brandenbourg. The discoveries of -Copernicus had inspired neighboring nations with the ambition of -claiming a place in the literary community of Europe. In something -of the same spirit, Rheticus wrote an _Encomium Borussiæ_, which was -published along with his _Narratio_. - -The Tables founded upon the Copernican system were, at first, much -more generally adopted than the heliocentric doctrine on which they -were founded. Thus Magini published at Venice, in 1587, _New -Theories of the Celestial Orbits, agreeing with the Observations of -Nicholas Copernicus_. But in the preface, after praising Copernicus, -he says, "Since, however, he, either for the sake of showing his -talents, or induced by his own reasons, has revived the opinion of -Nicetas, Aristarchus, and others, concerning the motion of the -earth, and has disturbed the established constitution of the world, -which was a reason why many rejected, or received with dislike, his -hypothesis, I have thought it worth while, that, rejecting the -suppositions of Copernicus, I should accommodate other causes to his -observations, and to the Prutenic Tables." - -This doctrine, however, was, as we have shown, received with favor -by many persons, even before its general publication. The doctrine -of the motion of the earth was first publicly maintained at Rome by -Widmanstadt,[16\5] who professed to have received it from -Copernicus, and explained the System before the Pope and the -Cardinals, but did not teach it to the public. - -[Note 16\5: See Venturi, _Essai sur les Ouvrages -Physico-Mathématiques de Leonard da Vinci, avec des Fragmens tirés -de ses Manuscrits apportés d'Italie_. Paris, 1797; and, as there -quoted, _Marini Archiatri Pontificii_, tom. ii. p. 251.] - -Leonardo da Vinci, who was an eminent mathematician, as well as -painter, about 1510, explained how a body, by describing a kind of -spiral, might descend towards a revolving globe, so that its -apparent motion relative to a point in the surface of the globe, -might be in a {271} straight line leading to the centre. He thus -showed that he had entertained in his thoughts the hypothesis of the -earth's rotation, and was employed in removing the difficulties -which accompanied this supposition, by means of the consideration of -the composition of motions. - -In like manner we find the question stirred by other eminent men. -Thus John Muller of Konigsberg, a celebrated astronomer who died in -1476, better known by the name of Regiomontanus, wrote a -dissertation on the subject "Whether the earth be in motion or at -rest," in which he decides _ex professo_[17\5] against the motion. -Yet such discussions must have made generally known the arguments -for the heliocentric theory. - -[Note 17\5: Schoneri _Opera_, part ii. p. 129.] - -We have already seen the enthusiasm with which Rheticus, who was -Copernicus's pupil in the latter years of his life, speaks of him. -"Thus," says he, "God has given to my excellent preceptor a reign -without end; which may He vouchsafe to guide, govern, and increase, -to the restoration of astronomical truth. Amen." - -Of the immediate converts of the Copernican system, who adopted it -before the controversy on the subject had attracted attention, I -shall only add **Mæstlin, and his pupil, Kepler. **Mæstlin published -in 1588 an _Epitome Astronomiæ_, in which the immobility of the -earth is asserted; but in 1596 he edited Kepler's _Mysterium -Cosmographicum_, and the _Narratio_ of Rheticus: and in an epistle -of his own, which he inserts, he defends the Copernican system by -those physical reasonings which we shall shortly have to mention, as -the usual arguments in this dispute. Kepler himself, in the outset -of the work just named, says, "When I was at Tübingen, attending to -Michael Mæstlin, being disturbed by the manifold inconveniences of -the usual opinion concerning the world, I was so delighted with -Copernicus, of whom he made great mention in his lectures, that I -not only defended his opinions in our disputations of the candidates, -but wrote a thesis concerning the First Motion which is produced by -the revolution of the earth." This must have been in 1590. - -The differences of opinion respecting the Copernican system, of which -we thus see traces, led to a controversy of some length and extent. -This controversy turned principally upon physical considerations, -which were much more distinctly dealt with by Kepler, and others of -the followers of Copernicus, than they had been by the {272} -discoverer himself. I shall, therefore, give a separate consideration -to this part of the subject. It may be proper, however, in the first -place, to make a few observations on the progress of the doctrine, -independently of these physical speculations. - - -_Sect._ 2.--_Diffusion of the Copernican Theory._ - -THE diffusion of the Copernican opinions in the world did not take -place rapidly at first. Indeed, it was necessarily some time before -the progress of observation and of theoretical mechanics gave the -heliocentric doctrine that superiority in argument, which now makes us -wonder that men should have hesitated when it was presented to them. -Yet there were some speculators of this kind, who were attracted at -once by the enlarged views of the universe which it opened to them. -Among these was the unfortunate Giordano Bruno of Nola, who was burnt -as a heretic at Rome in 1600. The heresies which led to his unhappy -fate were, however, not his astronomical opinions, but a work which he -published in England, and dedicated to Sir Philip Sydney, under the -title of _Spaccio della Bestia Trionfante_, and which is understood to -contain a bitter satire of religion and the papal government. Montucla -conceives that, by his rashness in visiting Italy after putting forth -such a work, he compelled the government to act against him. Bruno -embraced the Copernican opinions at an early period, and connected -with them the belief in innumerable worlds besides that which we -inhabit; as also certain metaphysical or theological doctrines which -he called the Nolan philosophy. In 1591 he published _De -innumerabilibus, immenso, et infigurabili, seu de Universo et Mundis_, -in which he maintains that each star is a sun, about which revolve -planets like our earth; but this opinion is mixed up with a large mass -of baseless verbal speculations. - -Giordano Bruno is a disciple of Copernicus on whom we may look with -peculiar interest, since he probably had a considerable share in -introducing the new opinions into England;[18\5] although other -persons, as Recorde, Field, Dee, had adopted it nearly thirty years -earlier; and Thomas Digges ten years before, much more expressly. -Bruno visited this country in the reign of Queen Elizabeth, and -speaks of her and of her councillors in terms of praise, which -appear to show that {273} his book was intended for English readers; -though he describes the mob which was usually to be met with in the -streets of London with expressions of great disgust: "Una plebe la -quale in essere irrespettevole, incivile, rozza, rustica, selvatica, -et male allevata, non cede ad altra che pascer possa la terra nel -suo seno."[19\5] The work to which I refer is _La Cena de le -Cenere_, and narrates what took place at a supper held on the -evening of Ash Wednesday (about 1583, see p. 145 of the book), at -the house of Sir Fulk Greville, in order to give "Il Nolano" an -opportunity of defending his peculiar opinions. His principal -antagonists are two "Dottori d' Oxonia," whom Bruno calls Nundinio -and Torquato. The subject is not treated in any very masterly manner -on either side; but the author makes himself have greatly the -advantage not only in argument, but in temper and courtesy: and in -support of his representations of "pedantesca, ostinatissima -ignoranza et presunzione, mista con una rustica incivilità, che -farebbe prevaricar la pazienza di Giobbe," in his opponents, he -refers to a public disputation which he had held at Oxford with -these doctors of theology, in presence of Prince Alasco, and many of -the English nobility.[20\5] - -[Note 18\5: See Burton's _Anat. Mel._ Pref. "Some prodigious tenet -or paradox of the earth's motion," &c. "Bruno," &c.] - -[Note 19\5: _Opere di Giordano Bruno_, vol. i. p. 146.] - -[Note 20\5: Ib. vol. i. p. 179.] - -Among the evidences of the difficulties which still lay in the way -of the reception of the Copernican system, we may notice Bacon, who, -as is well known, never gave a full assent to it. It is to be -observed, however, that he does not reject the opinion of the -earth's motion in so peremptory and dogmatical a manner as he is -sometimes accused of doing: thus in the _Thema Cœli_ he says, "The -earth, then, being supposed to be at rest (for that now appears to -us the _more true_ opinion)." And in his tract _On the Cause of the -Tides_, he says, "If the tide of the sea be the extreme and -diminished limit of the diurnal motion of the heavens, it will -follow that the earth is immovable; or at least that it moves with a -much slower motion than the water." In the _Descriptio Globi -Intellectualis_ he gives his reasons for not accepting the -heliocentric theory. "In the system of Copernicus there are many and -grave difficulties: for the threefold motion with which he encumbers -the earth is a serious inconvenience; and the separation of the sun -from the planets, with which he has so many affections in common, is -likewise a harsh step; and the introduction of so many immovable -bodies into nature, as when he makes the sun and the stars -immovable, the bodies which are peculiarly lucid and radiant; and -his making the moon adhere to the earth in a sort of epicycle; and -some {274} other things which he assumes, are proceedings which mark -a man who thinks nothing of introducing fictions of any kind into -nature, provided his calculations turn out well." We have already -explained that, in attributing _three_ motions to the earth, -Copernicus had presented his system encumbered with a complexity not -really belonging to it. But it will be seen shortly, that Bacon's -fundamental objection to this system was his wish for a system which -could be supported by sound physical considerations; and it must be -allowed, that at the period of which we are speaking, this had not -yet been done in favor of the Copernican hypothesis. We may add, -however, that it is not quite clear that Bacon was in full -possession of the details of the astronomical systems which that of -Copernicus was intended to supersede; and that thus he, perhaps, did -not see how much less harsh were these fictions, as he called them, -than those which were the inevitable alternatives. Perhaps he might -even be liable to a little of that indistinctness, with respect to -strictly geometrical conceptions, which we have remarked in -Aristotle. We can hardly otherwise account for his not seeing any -use in resolving the apparently irregular motion of a planet into -separate regular motions. Yet he speaks slightingly of this -important step.[21\5] "The motion of planets, which is constantly -talked of as the motion of regression, or renitency, from west to -east, and which is ascribed to the planets as a proper motion, is -not true; but only arises from appearance, from the greater advance -of the starry heavens towards the west, by which the planets are -left behind to the east." Undoubtedly those who spoke of such a -motion of _regression_ were aware of this; but they saw how the -motion was simplified by this way of conceiving it, which Bacon -seems not to have seen. Though, therefore, we may admire Bacon for -the steadfastness with which he looked forward to physical astronomy -as the great and proper object of philosophical interest, we cannot -give him credit for seeing the full value and meaning of what had -been done, up to his time, in Formal Astronomy. - -[Note 21\5: _Thema Cœli_, p. 246.] - -Bacon's contemporary, Gilbert, whom he frequently praises as a -philosopher, was much more disposed to adopt the Copernican -opinions, though even he does not appear to have made up his mind to -assent to the whole of the system. In his work. _De Magnete_ -(printed 1600), he gives the principal arguments in favor of the -Copernican system, and decides that the earth revolves on its -axis.[22\5] He connects {275} this opinion with his magnetic -doctrines; and especially endeavors by that means to account for the -precession of the equinoxes. But he does not seem to have been -equally confident of its annual motion. In a posthumous work, -published in 1661 (_De Mundo Nostra Sublunari Philosophia Nova_) he -appears to hesitate between the systems of Tycho and -Copernicus.[23\5] Indeed, it is probable that at this period many -persons were in a state of doubt on such subjects. Milton, at a -period somewhat later, appears to have been still undecided. In the -opening of the eighth book of the _Paradise Lost_, he makes Adam -state the difficulties of the Ptolemaic hypothesis, to which the -archangel Raphael opposes the usual answers; but afterwards suggests -to his pupil the newer system: - . . . . What if seventh to these - The planet earth, so steadfast though she seem, - Insensibly three different motions move? - _Par. Lost_, b. viii. - -[Note 22\5: Lib. vi. cap. 3, 4.] - -[Note 23\5: Lib. ii. cap. 20.] - -Milton's leaning, however, seems to have been for the new system; we -can hardly believe that he would otherwise have conceived so -distinctly, and described with such obvious pleasure, the motion of -the earth: - Or she from west her silent course advance - With inoffensive pace, that spinning sleeps - On her soft axle, while she paces even, - And bears thee soft with the smooth air along. - _Par. Lost_, b. viii. - -Perhaps the works of the celebrated Bishop Wilkins tended more than -any others to the diffusion of the Copernican system in England, -since even their extravagances drew a stronger attention to them. In -1638, when he was only twenty-four years old, he published a book -entitled _The Discovery of a New World; or a Discourse tending to -prove that it is probable there may be another habitable World in -the Moon; with a Discourse concerning_ the possibility of a passage -thither. The latter part of his subject was, of course, an obvious -mark for the sneers and witticisms of critics. Two years afterwards, -in 1640, appeared his _Discourse concerning a new Planet; tending to -prove that it is probable our Earth is one of the Planets_: in which -he urged the reasons in favor of the heliocentric system; and -explained away the opposite arguments, especially those drawn from -the {276} supposed declarations of Scripture. Probably a good deal -was done for the establishment of those opinions by Thomas -Salusbury, who was a warm admirer of Galileo, and published, in -1661, a translation of several of his works bearing upon this -subject. The mathematicians of this country, in the seventeenth -century, as Napier and Briggs, Horrox and Crabtree, Oughtred and -Seth Ward, Wallis and Wren, were probably all decided Copernicans. -Kepler dedicates one of his works to Napier, and Ward invented an -approximate method of solving Kepler's problem, still known as "the -simple elliptical hypothesis." Horrox wrote, and wrote well, in -defence of the Copernican opinion, in his _Keplerian Astronomy -defended and promoted_, composed (in Latin) probably about 1635, but -not published till 1673, the author having died at the age of -twenty-two, and his papers having been lost. But Salusbury's work -was calculated for another circle of readers. "The book," he says in -the introductory address, "being, for subject and design, intended -chiefly for gentlemen, I have been as careless of using a studied -pedantry in my style, as careful in contriving a pleasant and -beautiful impression." In order, however, to judge of the advantage -under which the Copernican system now came forward, we must consider -the additional evidence for it which was brought to light by -Galileo's astronomical discoveries. - - -_Sect._ 3.--_The Heliocentric Theory confirmed by Facts.--Galileo's -Astronomical Discoveries._ - -THE long interval which elapsed between the last great discoveries -made by the ancients and the first made by the moderns, had afforded -ample time for the development of all the important consequences of -the ancient doctrines. But when the human mind had been thoroughly -roused again into activity, this was no longer the course of events. -Discoveries crowded on each other; one wide field of speculation was -only just opened, when a richer promise tempted the laborers away into -another quarter. Hence the history of this period contains the -beginnings of many sciences, but exhibits none fully worked out into a -complete or final form. Thus the science of Statics, soon after its -revival, was eclipsed and overlaid by that of Dynamics; and the -Copernican system, considered merely with reference to the views of -its author, was absorbed in the commanding interest of Physical -Astronomy. - -Still, advances were made which had an important bearing on the {277} -heliocentric theory, in other ways than by throwing light upon its -physical principles. I speak of the new views of the heavens which the -Telescope gave; the visible inequalities of the moon's surface; the -moon-like phases of the planet Venus; the discovery of the Satellites -of Jupiter, and of the Ring of Saturn. These discoveries excited at -the time the strongest interest; both from the novelty and beauty of -the objects they presented to the sense; from the way in which they -seemed to gratify man's curiosity with regard to the remote parts of -the universe; and also from that of which we have here to speak, their -bearing upon the conflict of the old and the new philosophy, the -heliocentric and geocentric theories. It may be true, as Lagrange and -Montucla say, that the laws which Galileo discovered in Mechanics -implied a profounder genius than the novelties he detected in the sky: -but the latter naturally attracted the greater share of the attention -of the world, and were matter of keener discussion. - -It is not to our purpose to speak here of the details and of the -occasion of the invention of the Telescope; it is well known that -Galileo constructed his about 1609, and proceeded immediately to apply -it to the heavens. The discovery of the Satellites of Jupiter was -almost immediately the reward of his activity; and these were -announced in his _Nuncius Sidereus_, published at Venice in 1610. The -title of this work will best convey an idea of the claim it made to -public notice: "The _Sidereal Messenger_, announcing great and very -wonderful spectacles, and offering them to the consideration of every -one, but especially of philosophers and astronomers; which have been -observed by _Galileo Galilei_, &c. &c., by the assistance of a -perspective glass lately invented by him; namely, in the face of the -moon, in innumerable fixed stars in the milky-way, in nebulous stars, -but especially in four planets which revolve round Jupiter at -different intervals and periods with a wonderful celerity; which, -hitherto not known to any one, the author has recently been the first -to detect, and has decreed to call the _Medicean stars_." - -The interest this discovery excited was intense: and men were at this -period so little habituated to accommodate their convictions on -matters of science to newly observed facts, that several of the -"paper-philosophers," as Galileo termed them, appear to have thought -they could get rid of these new objects by writing books against them. -The effect which the discovery had upon the reception of the -Copernican system was immediately very considerable. It showed that -the real universe was very different from that which ancient -philosophers had imagined, {278} and suggested at once the thought -that it contained mechanism more various and more vast than had yet -been conjectured. And when the system of the planet Jupiter thus -offered to the bodily eye a model or image of the solar system -according to the views of Copernicus, it supported the belief of such -an arrangement of the planets, by an analogy all but irresistible. It -thus, as a writer[24\5] of our own times has said, "gave the _holding -turn_ to the opinions of mankind respecting the Copernican system." We -may trace this effect in Bacon, even though he does not assent to the -motion of the earth. "We affirm," he says,[25\5] "the _sun-following -arrangement_ (solisequium) of Venus and Mercury; since it has been -found by Galileo that Jupiter also has attendants." - -[Note 24\5: Sir J. Herschel.] - -[Note 25\5: _Thema Cœli_, ix. p. 253.] - -The _Nuncius Sidereus_ contained other discoveries which had the -same tendency in other ways. The examination of the moon showed, or -at least seemed to show, that she was a solid body, with a surface -extremely rugged and irregular. This, though perhaps not bearing -directly upon the question of the heliocentric theory, was yet a -blow to the Aristotelians, who had, in their philosophy, made the -moon a body of a kind altogether different from this, and had given -an abundant quantity of reasons for the visible marks on her -surface, all proceeding on these preconceived views. Others of his -discoveries produced the same effect; for instance, the new stars -invisible to the naked eye, and those extraordinary appearances -called Nebulæ. - -But before the end of the year, Galileo had new information to -communicate, bearing more decidedly on the Copernican controversy. -This intelligence was indeed decisive with regard to the motion of -Venus about the sun; for he found that that planet, in the course of -her revolution, assumes the same succession of phases which the moon -exhibits in the course of a month. This he expressed by a Latin -verse: - Cynthiæ figuras æmulatur mater amorum: - The Queen of Love like Cynthia shapes her forms: -transposing the letters of this line in the published account, -according to the practice of the age; which thus showed the ancient -love for combining verbal puzzles with scientific discoveries, while -it betrayed the newer feeling, of jealousy respecting the priority -of discovery of physical facts. - -It had always been a formidable objection to the Copernican theory -that this appearance of the planets had not been observed. The -author {279} of that theory had endeavored to account for this, by -supposing that the rays of the sun passed freely through the body of -the planet; and Galileo takes occasion to praise him for not being -deterred from adopting the system which, on the whole, appeared to -agree best with the phenomena, by meeting with some appearances -which it did not enable him to explain.[26\5] Yet while the fate of -the theory was yet undecided, this could not but be looked upon as a -weak point in its defences. - -[Note 26\5: Drinkwater-Bethune, _Life of Galileo_, p. 35.] - -The objection, in another form also, was embarrassing alike to the -Ptolemaic and Copernican systems. Why, it was asked, did not Venus -appear four times as large when nearest to the earth, as when -furthest from it? The author of the Epistle prefixed to Copernicus's -work had taken refuge in this argument from the danger of being -supposed to believe in the reality of the system; and Bruno had -attempted to answer it by saying, that luminous bodies were not -governed by the same laws of perspective as opake ones. But a more -satisfactory answer now readily offered itself. Venus does not -appear four times as large when she is four times as near, because -her _bright part_ is _not_ four times as large, though her visible -diameter is; and as she is too small for us to see her shape with -the naked eye, we judge of her size only by the quantity of light. - -The other great discoveries made in the heavens by means of -telescopes, as that of Saturn's ring and his satellites, the spots -in the sun, and others, belong to the further progress of astronomy. -But we may here observe, that this doctrine of the motion of Mercury -and Venus about the sun was further confirmed by Kepler's -observation of the transit of the former planet over the sun in -1631. Our countryman Horrox was the first person who, in 1639, had -the satisfaction of seeing a transit of Venus. - -These events are a remarkable instance of the way in which a -discovery in art (for at this period, the making of telescopes must -be mainly so considered) may influence the progress of science. We -shall soon have to notice a still more remarkable example of the way -in which two sciences (Astronomy and Mechanics) may influence and -promote the progress of each other. {280} - - -_Sect._ 4.--_The Copernican System opposed on Theological Grounds._ - -THE doctrine of the Earth's motion round the Sun, when it was -asserted and promulgated by Copernicus, soon after 1500, excited no -visible alarm among the theologians of his own time. Indeed, it was -received with favor by the most intelligent ecclesiastics; and -lectures in support of the heliocentric doctrine were delivered in -the ecclesiastical colleges. But the assertion and confirmation of -this doctrine by Galileo, about a century later, excited a storm of -controversy, and was visited with severe condemnation. Galileo's own -behavior appears to have provoked the interference of the -ecclesiastical authorities; but there must have been a great change -in the temper of the times to make it possible for his adversaries -to bring down the sentence of the Inquisition upon opinions which -had been so long current without giving any serious offence. - -[2d Ed.] [It appears to me that the different degree of toleration -accorded to the heliocentric theory in the time of Copernicus and of -Galileo, must be ascribed in a great measure to the controversies -and alarms which had in the mean time arisen out of the Reformation -in religion, and which had rendered the Romish Church more jealous -of innovations in received opinions than it had previously been. It -appears too that the discussion of such novel doctrines was, at that -time at least, less freely tolerated in Italy than in other -countries. In 1597, Kepler writes to Galileo thus: "Confide Galilæe -et progredere. Si bene conjecto, pauci de præcipuis Europæ -Mathematicis a nobis secedere volent; tanta vis est veritatis. Si -tibi Italia minus est idonea ad publicationem et si aliqua habitures -es impedimenta, forsan Germania nobis hanc libertatem -concedet."--Venturi, _Mem. di Galileo_, vol. i. p. 19. - -I would not however be understood to assert the condemnation of new -doctrines in science to be either a general or a characteristic -practice of the Romish Church. Certainly the intelligent and -cultivated minds of Italy, and many of the most eminent of her -ecclesiastics among them, have always been the foremost in promoting -and welcoming the progress of science: and, as I have stated, there -were found among the Italian ecclesiastics of Galileo's time many of -the earliest and most enlightened adherents of the Copernican -system. The condemnation of the doctrine of the earth's motion, is, -so far as I am aware, the only instance in which the Papal authority -has pronounced a decree upon a point of science. And the most candid -of the {281} adherents of the Romish Church condemn the assumption -of authority in such matters, which in this one instance, at least, -was made by the ecclesiastical tribunals. The author of the _Ages of -Faith_ (book viii. p. 248) says, "A congregation, it is to be -lamented, declared the new system to be opposed to Scripture, and -therefore heretical." In more recent times, as I have elsewhere -remarked,[27\5] the Church of Authority and the Church of Private -Judgment have each its peculiar temptations and dangers, when there -appears to be a discrepance between Scripture and Philosophy. - -[Note 27\5: _Phil. Ind. Sci._ book x. chap. 4.] - -But though we may acquit the popes and cardinals in Galileo's time -of stupidity and perverseness in rejecting manifest scientific -truths, I do not see how we can acquit them of dissimulation and -duplicity. Those persons appear to me to defend in a very strange -manner the conduct of the ecclesiastical authorities of that period, -who boast of the liberality with which Copernican professors were -placed by them in important offices, at the very time when the -motion of the earth had been declared by the same authorities -contrary to Scripture. Such merits cannot make us approve of their -conduct in demanding from Galileo a public recantation of the system -which they thus favored in other ways, and which they had repeatedly -told Galileo he might hold as much as he pleased. Nor can any one, -reading the plain language of the Sentence passed upon Galileo, and -of the Abjuration forced from him, find any value in the plea which -has been urged, that the opinion was denominated a _heresy_ only in -a wide, improper, and technical sense. - -But if we are thus unable to excuse the conduct of Galileo's judges, -I do not see how we can give our unconditional admiration to the -philosopher himself. Perhaps the conventional decorum which, as we -have seen, was required in treating of the Copernican system, may -excuse or explain the furtive mode of insinuating his doctrines -which he often employs, and which some of his historians admire as -subtle irony, while others blame it as insincerity. But I do not see -with what propriety Galileo can be looked upon as a "Martyr of -Science." Undoubtedly he was very desirous of promoting what he -conceived to be the cause of philosophical truth; but it would seem -that, while he was restless and eager in urging his opinions, he was -always ready to make such submissions as the spiritual tribunals -required. He would really have acted as a martyr, if he had uttered -{282} his "E pur si muove," in the place of his abjuration, not -after it. But even in this case he would have been a martyr to a -cause of which the merit was of a mingled scientific character; for -his own special and favorite share in the reasonings by which the -Copernican system was supported, was the argument drawn from the -flux and reflux of the sea, which argument is altogether false. He -considered this as supplying a mechanical ground of belief, without -which the mere astronomical reasons were quite insufficient; but in -this case he was deserted by the mechanical sagacity which appeared -in his other speculations.] - -The heliocentric doctrine had for a century been making its way into -the minds of thoughtful men, on the general ground of its simplicity -and symmetry. Galileo appears to have thought that now, when these -original recommendations of the system had been reinforced by his -own discoveries and reasonings, it ought to be universally -acknowledged as a truth and a reality. And when arguments against -the fixity of the sun and the motion of the earth were adduced from -the expressions of Scripture, he could not be satisfied without -maintaining his favorite opinion to be conformable to Scripture as -well as to Philosophy; and he was very eager in his attempts to -obtain from authority a declaration to this effect. The -ecclesiastical authorities were naturally averse to express -themselves in favor of a novel opinion, startling to the common -mind, and contrary to the most obvious meaning of the words of the -Bible; and when they were compelled to pronounce, they decided -against Galileo and his doctrines. He was accused before the -Inquisition in 1615; but at that period the result was that he was -merely recommended to confine himself to the mathematical reasonings -upon the system, and to abstain from meddling with the Scripture. -Galileo's zeal for his opinions soon led him again to bring the -question under the notice of the Pope, and the result was a -declaration of the Inquisition that the doctrine of the earth's -motion appeared to be contrary to the Sacred Scripture. Galileo was -prohibited from defending and teaching this doctrine in any manner, -and promised obedience to this injunction. But in 1632 he published -his **"_Dialogo delli due Massimi Sistemi del Mondo, Tolemaico e -Copernicano_:" and in this he defended the heliocentric system by -all the strongest arguments which its admirers used. Not only so, -but he introduced into this _Dialogue_ a character under the name of -Simplicius, in whose mouth was put the defence of all the ancient -dogmas, and who was represented as defeated at all points in the -discussion; {283} and he prefixed to the _Dialogue_ a Notice, _To -the Discreet Reader_, in which, in a vein of transparent irony, he -assigned his reasons for the publication. "Some years ago," he says, -"a wholesome edict was promulgated at Rome, which, in order to check -the perilous scandals of the present age, imposed silence upon the -Pythagorean opinion of the motion of the earth. There were not -wanting," he adds, "persons who rashly asserted that this decree was -the result, not of a judicious inquiry, but of a passion -ill-informed; and complaints were heard that counsellors, utterly -unacquainted with astronomical observations, ought not to be -allowed, with their undue prohibitions, to clip the wings of -speculative intellects. At the hearing of rash lamentations like -these, my zeal could not keep silence." And he then goes on to say -that he wishes, by the publication of his _Dialogue_ to show that -the subject had been fully examined at Rome. The result of this was -that Galileo was condemned for his infraction of the injunction laid -upon him in 1616; his _Dialogue_ was prohibited; he himself was -commanded to abjure on his knees the doctrine which he had taught; -and this abjuration he performed. - -This celebrated event must be looked upon rather as a question of -decorum than a struggle in which the interests of truth and free -inquiry were deeply concerned. The general acceptance of the -Copernican System was no longer a matter of doubt. Several persons -in the highest positions, including the Pope himself, looked upon -the doctrine with favorable eyes; and had shown their interest in -Galileo and his discoveries. They had tried to prevent his involving -himself in trouble by discussing the question on scriptural grounds. -It is probable that his knowledge of those favorable dispositions -towards himself and his opinions led him to suppose that the -slightest color of professed submission to the Church in his belief, -would enable his arguments in favor of the system to pass unvisited: -the notice which I have quoted, in which the irony is quite -transparent and the sarcasm glaringly obvious, was deemed too flimsy -a veil for the purpose of decency, and indeed must have aggravated -the offence. But it is not to be supposed that the inquisitors -believed Galileo's abjuration to be sincere, or even that they -wished it to be so. It is stated that when Galileo had made his -renunciation of the earth's motion, he rose from his knees, and -stamping on the earth with his foot, said, _E pur si muove_--"And -yet it _does_ move." This is sometimes represented as the heroic -soliloquy of a mind cherishing its conviction of the truth in spite -of persecution; I think we may more naturally conceive it uttered as -a playful {284} epigram in the ear of a cardinal's secretary, with a -full knowledge that it would be immediately repeated to his master. - -[2d Ed.] [Throughout the course of the proceedings against him, -Galileo was treated with great courtesy and indulgence. He was -condemned to a formal imprisonment and a very light discipline. "Te -damnamus ad formalem carcerem hujus S. Officii ad tempus arbitrio -nostro limitandum; et titulo pœnitentiæ salutaris præcipimus ut -tribus annis futuris recites **semel in hebdomadâ septem psalmos -penitentiales." But this confinement was reduced to his being placed -under some slight restrictions, first at the house of Nicolini, the -ambassador of his own sovereign, and afterwards at the country seat -of Archbishop Piccolomini, one of his own warmest friends. - -It has sometimes been asserted or insinuated that Galileo was -subjected to bodily torture. An argument has been drawn from the -expressions used in his sentence: "Cum vero nobis videretur non esse -a te integram veritatem pronunciatam circa tuam intentionem; -judicavimus necesse esse venire ad rigorosum examen tui, in quo -respondisti catholicè." It has been argued by M. Libri (_Hist. des -Sciences Mathématiques en Italie_, vol. IV. p. 259), and M. Quinet -(_L'Ultramontanisme_, IV. Leçon, p. 104), that the _rigorosum -examen_ necessarily implies bodily torture, notwithstanding that no -such thing is mentioned by Galileo and his contemporaries, and -notwithstanding the consideration with which he was treated in all -other respects: but M. Biot more justly remarks (_Biogr. Univ._ Art. -_Galileo_), that such a procedure is incredible. - -To the opinion of M. Biot, we may add that of Delambre, who rejects -the notion of Galileo's having been put to the torture, as -inconsistent with the general conduct of the authorities towards -him, and as irreconcilable with the accounts of the trial given by -Galileo himself, and by a servant of his, who never quitted him for -an instant. He adds also, that it is inconsistent with the words of -his sentence, "ne tuus iste gravis et perniciosus error ac -transgressio remaneat _omnino impunitus_;" for the error would have -been already very far from impunity, if Galileo had been previously -subjected to the rack. He adds, very reasonably, "il ne faut noircir -personne sans preuve, pas même l'Inquisition;"--we must not -calumniate even the Inquisition.] - -The ecclesiastical authorities having once declared the doctrine of -the earth's motion to be contrary to Scripture and heretical, long -adhered in form to this declaration, and did not allow the Copernican -system to be taught in any other way than as an "hypothesis." The -{285} Padua edition of Galileo's works, published in 1744, contains -the _Dialogue_ which now, the editors say, "Esce finalmente a pubblico -libero uso colle debite licenze," is now at last freely published with -the requisite license; but they add, "quanto alla Quistione principale -del moto della terra, anche noi ci conformiamo alla ritrazione et -protesta dell' Autore, dichiarando nella piu solenne forma, che non -può, nè dee ammetersi se non come pura Ipotesi Mathematice, che serve -a spiegare piu agevolamento certi fenomeni;" "neither can nor ought to -be admitted except as a convenient hypothesis." And in the edition of -Newton's _Principia_, published in 1760, by Le Sueur and Jacquier, of -the Order of Minims, the editors prefix to the Third Book their -_Declaratio_, that though Newton assumes the hypothesis of the motion -of the earth, and therefore they had used similar language, they were, -in doing this, assuming a character which did not belong to them. -"Hinc alienam coacti sumus gerere personam." They add, "Cæterum latis -a summis Pontificibus contra telluris motum Decretis, nos obsequi -profitemur." - -By thus making decrees against a doctrine which in the course of -time was established as an indisputable scientific truth, the See of -Rome was guilty of an unwise and unfortunate stretch of -ecclesiastical authority. But though we do not hesitate to pronounce -such a judgment on this case, we may add that there is a question of -no small real difficulty, which the progress of science often brings -into notice, as it did then. The Revelation on which our religion is -founded, seems to declare, or to take for granted, opinions on -points on which Science also gives her decision; and we then come to -this dilemma,--that doctrines, established by a scientific use of -reason, may seem to contradict the declarations of Revelation, -according to our view of its meaning;--and yet, that we cannot, in -consistency with our religious views, make reason a judge of the -truth of revealed doctrines. In the case of Astronomy, on which -Galileo was called in question, the general sense of cultivated and -sober-minded men has long ago drawn that distinction between -religious and physical tenets, which is necessary to resolve this -dilemma. On this point, it is reasonably held, that the phrases -which are employed in Scripture respecting astronomical facts, are -not to be made use of to guide our scientific opinions; they may be -supposed to answer their end if they fall in with common notions, -and are thus effectually subservient to the moral and religions -import of Revelation. But the establishment of this distinction was -not accomplished without long and distressing controversies. Nor, if -we wish to {286} include all cases in which the same dilemma may -again come into play is it easy to lay down an adequate canon for -the purpose. For we can hardly foresee, beforehand, what part of the -past history of the universe may eventually be found to come within -the domain of science; or what bearing the tenets, which science -establishes, may have upon our view of the providential and revealed -government of the world. But without attempting here to generalize -on this subject, there are two reflections which may be worth our -notice: they are supported by what took place in reference to -Astronomy on the occasion of which we are speaking; and may, at -other periods, be applicable to other sciences. - -In the first place, the meaning which any generation puts upon the -phrases of Scripture, depends, more than is at first sight supposed -upon the received philosophy of the time. Hence, while men imagine -that they are contending for Revelation, they are, in fact, -contending for their own interpretation of Revelation, unconsciously -adapted to what they believe to be rationally probable. And the new -interpretation, which the new philosophy requires, and which appears -to the older school to be a fatal violence done to the authority of -religion, is accepted by their successors without the dangerous -results which were apprehended. When the language of Scripture, -invested with its new meaning, has become familiar to men, it is -found that the ideas which it calls up, are quite as reconcilable as -the former ones were with the soundest religious views. And the -world then looks back with surprise at the error of those who -thought that the essence of Revelation was involved in their own -arbitrary version of some collateral circumstance. At the present -day we can hardly conceive how reasonable men should have imagined -that religious reflections on the stability of the earth, and the -beauty and use of the luminaries which revolve round it, would be -interfered with by its being acknowledged that this rest and motion -are apparent only. - -In the next place, we may observe that those who thus adhere -tenaciously to the traditionary or arbitrary mode of understanding -Scriptural expressions of physical events, are always strongly -condemned by succeeding generations. They are looked upon with -contempt by the world at large, who cannot enter into the obsolete -difficulties with which they encumbered themselves; and with pity by -the more considerate and serious, who know how much sagacity and -rightmindedness are requisite for the conduct of philosophers and -religious men on such occasions; but who know also how weak and vain -is the attempt {287} to get rid of the difficulty by merely -denouncing the new tenets as inconsistent with religious belief, and -by visiting the promulgators of them with severity such as the state -of opinions and institutions may allow. The prosecutors of Galileo -are still up to the scorn and aversion of mankind: although, as we -have seen, they did not act till it seemed that their position -compelled them to do so, and then proceeded with all the gentleness -and moderation which were compatible with judicial forms. - - -_Sect._ 5.--_The Heliocentric Theory confirmed on Physical -considerations.--_(_Prelude to Kepler's Astronomical Discoveries._) - -BY physical views, I mean, as I have already said, those which -depend on the causes of the motions of matter, as, for instance, the -consideration of the nature and laws of the force by which bodies -fall downwards. Such considerations were necessarily and immediately -brought under notice by the examination of the Copernican theory; -but the loose and inaccurate notions which prevailed respecting the -nature and laws of force, prevented, for some time, all distinct -reasoning on this subject, and gave truth little advantage over -error. The formation of a new Science, the Science of Motion and its -Causes, was requisite, before the heliocentric system could have -justice done it with regard to this part of the subject. - -This discussion was at first carried on, as was to be expected, in -terms of the received, that is, the Aristotelian doctrines. Thus, -Copernicus says that terrestrial things appear to be at rest when they -have a motion according to nature, that is, a circular motion; and -ascend or descend when they have, in addition to this, a rectilinear -motion by which they **endeavor to get into their own place. But his -disciples soon began to question the Aristotelian dogmas, and to seek -for sounder views by the use of their own reason. "The great argument -against this system," says Mæstlin, "is that heavy bodies are said to -move to the centre of the universe, and light bodies from the centre. -But I would ask, where do we get this experience of heavy and light -bodies? and how is our knowledge on these subjects extended so far -that we can reason with certainty concerning the centre of the whole -universe? Is not the only residence and home of all the things which -are heavy and light to us, the earth and the air which surrounds it? -and what is the earth and the ambient air, with respect to the -immensity of the universe? It is a point, a punctule, or something, if -there be any thing, still less. As our light and heavy bodies tend to -{288} the centre of our earth, it is credible that the sun, the moon, -and the other lights, have a similar affection, by which they remain -round as we see them; but none of these centres is necessarily the -centre of the universe." - -The most obvious and important physical difficulty attendant upon -the supposition of the motion of the earth was thus stated: If the -earth move, how is it that a stone, dropped from the top of a high -tower, falls exactly at the foot of the tower? since the tower being -carried from west to east by the diurnal revolution of the earth, -the stone must be left behind to the west of the place from which it -was let fall. The proper answer to this was, that the motion which -the falling body received from its tendency downwards was -_compounded_ with the motion which, before it fell, it had in virtue -of the earth's rotation: but this answer could not be clearly made -or apprehended, till Galileo and his pupils had established the laws -of such Compositions of motion arising from different forces. -Rothman, Kepler, and other defenders of the Copernican system, gave -their reply somewhat at a venture, when they asserted that the -motion of the earth was communicated to bodies at its surface. -Still, the facts which indicate and establish this truth are -obvious, when the subject is steadily considered; and the -Copernicans soon found that they had the superiority of argument on -this point as well as others. The attacks upon the Copernican system -by Durret, Morin, Riccioli, and the defence of it by Galileo, -Lansberg, Gassendi,[28\5] left on all candid reasoners a clear -impression in favour of the system. Morin attempted to stop the -motion of the earth, which he called breaking its wings; his _Alæ -Terræ Fractæ_ was published in 1643, and answered by Gassendi. And -Riccioli, as late as 1653, in his _Almagestum Novum_, enumerated -fifty-seven Copernican arguments, and pretended to refute them all: -but such reasonings now made no converts; and by this time the -mechanical objections to the motion of the earth were generally seen -to be baseless, as we shall relate when we come to speak of the -progress of Mechanics as a distinct science. In the mean time, the -beauty and simplicity of the heliocentric theory were perpetually -winning the admiration even of those who, from one cause or other, -refused their assent to it. Thus Riccioli, the last of its -considerable opponents, allows its superiority in these respects; -and acknowledges (in 1653) that the Copernican belief appears rather -to increase than diminish under the condemnation of the decrees of -the Cardinals. He applies to it the lines of Horace:[29\5] {289} - Per damna per cædes, ab ipso - Sumit opes animumque ferro. - Untamed its pride, unchecked its course, - From foes and wounds it gathers force. - -[Note 28\5: Del. _A. M._ vol. i. p. 594.] - -[Note 29\5: _Almag. Nov._ p. 102.] - -We have spoken of the influence of the motion of the earth on the -motions of bodies at its surface; but the notion of a physical -connection among the parts of the universe was taken up by Kepler in -another point of view, which would probably have been considered as -highly fantastical, if the result had not been, that it led to by -far the most magnificent and most certain train of truths which the -whole expanse of human knowledge can show. I speak of the persuasion -of the existence of numerical and geometrical laws connecting the -distances, times, and forces of the bodies which revolve about the -central sun. That steady and intense conviction of this governing -principle, which made its development and verification the leading -employment of Kepler's most active and busy life, cannot be -considered otherwise than as an example of profound sagacity. That -it was connected, though dimly and obscurely, with the notion of a -central agency or influence of some sort, emanating from the sun, -cannot be doubted. Kepler, in his first essay of this kind, the -_Mysterium Cosmographicum_, says, "The motion of the earth, which -Copernicus had proved by _mathematical_ reasons, I wanted to prove -by _physical_, or, if you prefer it, metaphysical." In the twentieth -chapter of that work, he endeavors to make out some relation between -the distances of the Planets from the Sun and their velocities. The -inveterate yet vague notions of forces which preside in this -attempt, may be judged of by such passages as the following:--"We -must suppose one of two things; either that the moving spirits, in -proportion as they are more removed from the sun, are more feeble; -or that there is one moving spirit in the centre of all the orbits, -namely, in the sun, which urges each body the more vehemently in -proportion as it is nearer; but in more distant spaces languishes in -consequence of the remoteness and attenuation of its virtue." - -We must not forget, in reading such passages, that they were written -under a belief that force was requisite to keep up, as well as to -change the motion of each planet; and that a body, moving in a -circle, would _stop_ when the force of the central point ceased, -instead of moving off in a tangent to the circle, as we now know it -would do. The force which Kepler supposes is a tangential force, in -the direction of the body's motion, and nearly perpendicular to the -radius; the {290} force which modern philosophy has established, is -in the direction of the radius, and nearly perpendicular to the -body's path. Kepler was right no further than in his suspicion of a -connection between the cause of motion and the distance from the -centre; not only was his knowledge imperfect in all particulars, but -his most general conception of the mode of action of a cause of -motion was erroneous. - -With these general convictions and these physical notions in his -mind, Kepler endeavored to detect numerical and geometrical -relations among the parts of the solar system. After extraordinary -labor, perseverance, and ingenuity, he was eminently successful in -discovering such relations; but the glory and merit of interpreting -them according to their physical meaning, was reserved for his -greater successor, Newton. - - - - -CHAPTER IV. - -INDUCTIVE EPOCH OF KEPLER. - - -_Sect._ 1.--_Intellectual Character of Kepler._ - -SEVERAL persons,[30\5] especially in recent times, who have taken a -view of the discoveries of Kepler, appear to have been surprised and -somewhat discontented that conjectures, apparently so fanciful and -arbitrary as his, should have led to important discoveries. They -seem to have been alarmed at the _Moral_ that their readers might -draw, from the tale of a Quest of Knowledge, in which the Hero, -though fantastical and self-willed, and violating in his conduct, as -they conceived, all right rule and sound philosophy, is rewarded -with the most signal triumphs. Perhaps one or two reflections may in -some measure reconcile us to this result. {291} - -[Note 30\5: Laplace, _Précis de l'Hist. d'Ast._ p. 94. "Il est -affligeant pour l'esprit humain de voir ce grand homme, même dans ses -derniers ouvrages, se complaire avec délices dans ses chimériques -spéculations, et les regarder comme l'âme et la vie de l'astronomie." - -_Hist. of Ast._, L. U. K., p. 53. "This success [of Kepler] may well -inspire with dismay those who are accustomed to consider experiment -and rigorous induction as the only means to interrogate nature with -success." - -_Life of Kepler_, L. U. K., p. 14, "Bad philosophy." P. 15, -"Kepler's miraculous good fortune in seizing truths across the -wildest and most absurd theories." P. 54, "The danger of attempting -to follow his method in the pursuit of truth."] - -In the first place, we may observe that the leading thought which -suggested and animated all Kepler's attempts was true, and we may -add, sagacious and philosophical; namely, that there must be _some_ -numerical or geometrical relations among the times, distances, and -velocities of the revolving bodies of the solar system. This settled -and constant conviction of an important truth regulated all the -conjectures, apparently so capricious and fanciful, which he made -and examined, respecting particular relations in the system. - -In the next place, we may venture to say, that advances in knowledge -are not commonly made without the previous exercise of some boldness -and license in guessing. The discovery of new truths requires, -undoubtedly, minds careful and scrupulous in examining what is -suggested; but it requires, no less, such as are quick and fertile -in suggesting. What is Invention, except the talent of rapidly -calling before us many possibilities, and selecting the appropriate -one? It is true, that when we have rejected all the inadmissible -suppositions, they are quickly forgotten by most persons; and few -think it necessary to dwell on these discarded hypotheses, and on -the process by which they were condemned, as Kepler has done. But -all who discover truths must have reasoned upon many errors, to -obtain each truth; every accepted doctrine must have been one -selected out of many candidates. In making many conjectures, which -on trial proved erroneous, Kepler was no more fanciful or -unphilosophical than other discoverers have been. Discovery is not a -"cautious" or "rigorous" process, in the sense of abstaining from -such suppositions. But there are great differences in different -cases, in the facility with which guesses are proved to be errors, -and in the degree of attention with which the error and the proof -are afterwards dwelt on. Kepler certainly was remarkable for the -labor which he gave to such self-refutations, and for the candor and -copiousness with which he narrated them; his works are in this way -extremely curious and amusing; and are a very instructive exhibition -of the mental process of discovery. But in this respect, I venture -to believe, they exhibit to us the usual process (somewhat -caricatured) of inventive minds: they rather exemplify the _rule_ of -genius than (as has generally been hitherto taught) the _exception_. -We may add, that if many of Kepler's guesses now appear fanciful and -absurd, because time and observation have refuted them, others, -which were at the time equally gratuitous, have been confirmed by -succeeding discoveries in a manner which makes them appear -marvellously sagacious; as, for instance, his assertion of the -rotation of {292} the sun on his axis, before the invention of the -telescope, and his opinion that the obliquity of the ecliptic was -decreasing, but would, after a long-continued diminution, stop, and -then increase again.[31\5] Nothing can be more just, as well as more -poetically happy, than Kepler's picture of the philosopher's pursuit -of scientific truth, conveyed by means of an allusion to Virgil's -shepherd and shepherdess: - Malo me Galatea petit, lasciva puella - Et fugit ad salices et se cupit ante videri. - Coy yet inviting, Galatea loves - To sport in sight, then plunge into the groves; - The challenge given, she darts along the green, - Will not be caught, yet would not run unseen. - -[Note 31\5: Bailly, _A. M._ iii. 175.] - -We may notice as another peculiarity of Kepler's reasonings, the -length and laboriousness of the processes by which he discovered the -errors of his first guesses. One of the most important talents -requisite for a discoverer, is the ingenuity and skill which devises -means for rapidly testing false suppositions as they offer themselves. -This talent Kepler did not possess: he was not even a good -arithmetical calculator, often making mistakes, some of which he -detected and laments, while others escaped him to the last. But his -defects in this respect were compensated by his courage and -perseverance in undertaking and executing such tasks; and, what was -still more admirable, he never allowed the labor he had spent upon any -conjecture to produce any reluctance in abandoning the hypothesis, as -soon as he had evidence of its inaccuracy. The only way in which he -rewarded himself for his trouble, was by describing to the world, in -his lively manner, his schemes, exertions, and feelings. - -The _mystical_ parts of Kepler's opinions, as his belief in -astrology, his persuasion that the earth was an animal, and many of -the loose moral and spiritual as well as sensible analyses by which -he represented to himself the powers which he supposed to prevail in -the universe, do not appear to have interfered with his discovery, -but rather to have stimulated his invention, and animated his -exertions. Indeed, where there are clear scientific ideas on one -subject in the mind, it does not appear that mysticism on others is -at all unfavorable to the successful prosecution of research. - -I conceive, then, that we may consider Kepler's character as -containing the general features of the character of a scientific -discoverer, {293} though some of the features are exaggerated, and -some too feebly marked. His spirit of invention was undoubtedly very -fertile and ready, and this and his perseverance served to remedy -his deficiency in mathematical artifice and method. But the peculiar -physiognomy is given to his intellectual aspect by his dwelling in a -most prominent manner on those erroneous trains of thought which -other persons conceal from the world, and often themselves forget, -because they find means of stopping them at the outset. In the -beginning of his book (_Argumenta Capitum_) he says, "if Christopher -Columbus, if Magellan, if the Portuguese, when they narrate their -wanderings, are not only excused, but if we do not wish these -passages omitted, and should lose much pleasure if they were, let no -one blame me for doing the same." Kepler's talents were a kindly and -fertile soil, which he cultivated with abundant toil and vigor; but -with great scantiness of agricultural skill and implements. Weeds -and the grain throve and flourished side by side almost -undistinguished; and he gave a peculiar appearance to his harvest, -by gathering and preserving the one class of plants with as much -care and diligence as the other. - - -_Sect._ 2.--_Kepler's Discovery of his Third Law._ - -I SHALL now give some account of Kepler's speculations and -discoveries. The first discovery which he attempted, the relation -among the successive distances of the planets from the sun, was a -failure; his doctrine being without any solid foundation, although -propounded by him with great triumph, in a work which he called -_Mysterium Cosmographicum_, and which was published in 1596. The -account which he gives of the train of his thoughts on this subject, -namely, the various suppositions assumed, examined, and rejected, is -curious and instructive, for the reasons just stated; but we shall -not dwell upon these essays, since they led only to an opinion now -entirely abandoned. The doctrine which professed to give the true -relation of the orbits of the different planets, was thus -delivered:[32\5] "The orbit of the earth is a circle: round the -sphere to which this circle belongs, describe a dodecahedron; the -sphere including this will give the orbit of Mars. Round Mars -describe a tetrahedron; the circle including this will be the orbit -of Jupiter. Describe a cube round Jupiter's orbit; the circle -including this will be the orbit of Saturn. Now inscribe in the -Earth's orbit an icosahedron; the circle inscribed in it will be the -orbit of Venus. {294} Inscribe an octahedron in the orbit of Venus; -the circle inscribed in it will be Mercury's orbit. This is the -reason of the number of the planets." The five kinds of polyhedral -bodies here mentioned are the only "Regular Solids." - -[Note 32\5: L. U. K. Kepler, 6.] - -But though this part of the _Mysterium Cosmographicum_ was a -failure, the same researches continued to occupy Kepler's mind; and -twenty-two years later led him to one of the important rules known -to us as "Kepler's Laws;" namely, to the rule connecting the mean -distances of the planets from the sun with the times of their -revolutions. This rule is expressed in mathematical terms, by saying -that the squares of the periodic times are in the same proportion as -the cubes of the distances; and was of great importance to Newton in -leading him to the law of the sun's attractive force. We may -properly consider this discovery as the sequel of the train of -thought already noticed. In the beginning of the _Mysterium_, Kepler -had said, "In the year 1595, I brooded with the whole energy of my -mind on the subject of the Copernican system. There were three -things in particular of which I pertinaciously sought the causes why -they are not other than they are; the number, the size, and the -motion of the orbits." We have seen the nature of his attempt to -account for the two first of these points. He had also made some -essays to connect the motions of the planets with their distances, -but with his success in this respect he was not himself completely -satisfied. But in the fifth book of the _Harmonice Mundi_, published -in 1619, he says, "What I prophesied two-and-twenty years ago as -soon as I had discovered the Five Solids among the Heavenly Bodies; -what I firmly believed before I had seen the _Harmonics_ of Ptolemy; -what I promised my friends in the title of this book (_On the most -perfect Harmony of the Celestial Motions_) which I named before I -was sure of my discovery; what sixteen years ago I regarded as a -thing to be sought; that for which I joined Tycho Brahe, for which I -settled in Prague, for which I have devoted the best part of my life -to astronomical contemplations; at length I have brought to light, -and have recognized its truth beyond my most sanguine expectations." - -The rule thus referred to is stated in the third Chapter of this fifth -Book. "It is," he says, "a most certain and exact thing that the -proportion which exists between the periodic times of any two planets -is precisely the sesquiplicate of the proportion of their mean -distances; that is, of the radii of the orbits. Thus, the period of -the earth is one year, that of Saturn thirty years; if any one trisect -the proportion, that {295} is, take the cube root of it, and double -the proportion so found, that is, square it, he will find the exact -proportion of the distances of the Earth and of Saturn from the sun. -For the cube root of 1 is 1, and the square of this is 1; and the cube -root of 30 is greater than 3, and therefore the square of it is -greater than 9. And Saturn at his mean distance from the sun is at a -little more than 9 times the mean distance of the Earth." - -When we now look back at the time and exertions which the -establishment of this law cost Kepler, we are tempted to imagine that -he was strangely blind in not seeing it sooner. His object, we might -reason, was to discover a law connecting the distances and the -periodic times. What law of connection could be more simple and -obvious, we might say, than that one of these quantities should vary -as some _power_ of the other, or as some _root_; or as some -combination of the two, which in a more general view, may still be -called a _power_? And if the problem had been viewed in this way, the -question must have occurred, to _what_ power of the periodic times are -the distances proportional? And the answer must have been, the trial -being made, that they are proportional to the square of the cube root. -This _ex-post-facto_ obviousness of discoveries is a delusion to which -we are liable with regard to many of the most important principles. In -the case of Kepler, we may observe, that the process of connecting two -classes of quantities by comparing their _powers_, is obvious only to -those who are familiar with general algebraical views; and that in -Kepler's time, algebra had not taken the place of geometry, as the -most usual vehicle of mathematical reasoning. It may be added, also, -that Kepler always sought his _formal_ laws by means of _physical_ -reasonings; and these, though vague or erroneous, determined the -nature of the mathematical connection which he assumed. Thus in the -_Mysterium_ he had been led by his notions of moving virtue of the sun -to this conjecture, among others--that, in the planets, the increase -of the periods will be double of the difference of the distances; -which supposition he found to give him an approach to the actual -proportion of the distances, but one not sufficiently close to satisfy -him. - -The greater part of the fifth Book of the _Harmonics of the -Universe_ consists in attempts to explain various relations among -the distances, times, and eccentricities of the planets, by means of -the ratios which belong to certain concords and discords. This -portion of the work is so complex and laborious, that probably few -modern readers have had courage to go through it. Delambre -acknowledged that his patience {296} often failed him during the -task;[33\5] and subscribes to the judgment of Bailly: "After this -sublime effort, Kepler replunges himself in the relations of music -to the motions, the distance, and the eccentricities of the planets. -In all these harmonic ratios there is not one true relation; in a -crowd of ideas there is not one truth: he becomes a man after being -a spirit of light." Certainly these speculations are of no value, -but we may look on them with toleration, when we recollect that -Newton has sought for analogies between the spaces occupied by the -prismatic colors and the notes of the gamut.[34\5] The numerical -relations of Concords are so peculiar that we can easily suppose -them to have other bearings than those which first offer themselves. - -[Note 33\5: _A. M._ a. 358.] - -[Note 34\5: _Optics_, b. ii. p. iv. Obs. 5.] - -It does not belong to my present purpose to speak at length of the -speculations concerning the forces producing the celestial motions -by which Kepler was led to this celebrated law, or of those which he -deduced from it, and which are found in the _Epitome Astronomiæ -Copernicanæ_, published in 1622. In that work also (p. 554), he -extended this law, though in a loose manner, to the satellites of -Jupiter. These _physical_ speculations were only a vague and distant -prelude to Newton's discoveries; and the law, as a _formal_ rule, -was complete in itself. We must now attend to the history of the -other two laws with which Kepler's name is associated. - - -_Sect._ 3.--_Kepler's Discovery of his First and Second -Laws.--Elliptical Theory of the Planets._ - -THE propositions designated as Kepler's First and Second Laws are -these: That the orbits of the planets are elliptical; and, That the -areas described, or _swept_, by lines drawn from the sun to the -planet, are proportional to the times employed in the motion. - -The occasion of the discovery of these laws was the attempt to -reconcile the theory of Mars to the theory of eccentrics and -epicycles; the event of it was the complete overthrow of that -theory, and the establishment, in its stead, of the Elliptical -Theory of the planets. Astronomy was now ripe for such a change. As -soon as Copernicus had taught men that the orbits of the planets -were to be referred to the sun, it obviously became a question, what -was the true form of these orbits, and the rule of motion of each -planet in its own orbit. Copernicus represented the motions in -longitude by means of {297} eccentrics and epicycles, as we have -already said; and the motions in latitude by certain _librations_, -or alternate elevations and depressions of epicycles. If a -mathematician had obtained a collection of true positions of a -planet, the form of the orbit and the motion of the star would have -been determined with reference to the sun as well as to the earth; -but this was not possible, for though the _geocentric_ position, or -the direction in which the planet was seen, could be observed, its -distance from the earth was not known. Hence, when Kepler attempted -to determine the orbit of a planet, he combined the observed -geocentric places with successive modifications of the theory of -epicycles, till at last he was led, by one step after another, to -change the epicyclical into the elliptical theory. We may observe, -moreover, that at every step he endeavored to support his new -suppositions by what he called, in his fanciful phraseology, -"sending into the field a reserve of new physical reasonings on the -rout and dispersion of the veterans;"[35\5] that is, by connecting -his astronomical hypotheses with new imaginations, when the old ones -became untenable. We find, indeed, that this is the spirit in which -the pursuit of knowledge is generally carried on with success; those -men arrive at truth who eagerly endeavor to connect remote points of -their knowledge, not those who stop cautiously at each point till -something compels them to go beyond it. - -[Note 35\5: I will insert this passage, as a specimen of Kepler's -fanciful mode of narrating the defeats which he received in the war -which he carried on with Mars. "Dum in hunc modum de Martis motibus -triumpho, eique ut planè devicto tabularum carceres et equationum -compedes necto, diversis nuntiatur locis, futilem victoriam ut -bellam totâ mole recrudescere. Nam domi quidam hostis ut captivus -contemptus, rupit omnia equationum vincula, carceresque tabularum -effregit. Foris speculatores profligerunt meas causarum physicarum -arcessitas copias earumque jugum excusserunt resumtà libertate. -Jamque parum abfuit quia hostis fugitivus sese cum rebellibus suis -conjungeret meque in desperationem adigeret: nisi raptim, nova -rationum physicarum subsidia, fusis et palantibus veteribus, -submisissem, et qua se captivus proripuisset, omni diligentia, -edoctus vestigiis ipsius nullâ morâ interpositâ inhæsisserem."] - -Kepler joined Tycho Brahe at Prague in 1600, and found him and -Longomontanus busily employed in correcting the theory of Mars; and -he also then entered upon that train of researches which he -published in 1609 in his extraordinary work _On the Motions of -Mars_. In this work, as in others, he gives an account, not only of -his success, but of his failures, explaining, at length, the various -suppositions which he had made, the notions by which he had been led -to invent or to entertain them, the processes by which he had proved -their {298} falsehood, and the alternations of hope and sorrow, of -vexation and triumph, through which he had gone. It will not be -necessary for us to cite many passages of these kinds, curious and -amusing as they are. - -One of the most important truths contained in the motions of Man is -the discovery that the plane of the orbit of the planet should be -considered with reference to the sun itself, instead of referring it -to any of the other centres of motion which the eccentric hypothesis -introduced: and that, when so considered, it had none of the -librations which Ptolemy and Copernicus had attributed to it. The -fourteenth chapter of the second part asserts, "Plana eccentricorum -esse ἀτάλαντα;" that the planes are _unlibrating_; retaining always -the same inclination to the ecliptic, and the same _line of nodes_. -With this step Kepler appears to have been justly delighted. -"Copernicus," he says, "not knowing the value of what he possessed -(his system), undertook to represent Ptolemy, rather than nature, to -which, however, he had approached more nearly than any other person. -For being rejoiced that the quantity of the latitude of each planet -was increased by the approach of the earth to the planet, according to -his theory, he did not venture to reject the rest of Ptolemy's -increase of latitude, but in order to express it, devised librations -of the planes of the eccentric, depending not upon its own eccentric, -but (most improbably) upon the orbit of the earth, which has nothing -to do with it. I always fought against this impertinent tying together -of two orbits, even before I saw the observations of Tycho; and I -therefore rejoice much that in this, as in others of my preconceived -opinions, the observations were found to be on my side." Kepler -established his point by a fair and laborious calculation of the -results of observations of Mars made by himself and Tycho Brahe; and -had a right to exult when the result of these calculations confirmed -his views of the symmetry and simplicity of nature. - -We may judge of the difficulty of casting off the theory of eccentrics -and epicycles, by recollecting that Copernicus did not do it at all, -and that Kepler only did it after repeated struggles; the history of -which occupies thirty-nine Chapters of his book. At the end of them he -says, "This prolix disputation was necessary, in order to prepare the -way to the natural form of the equations, of which I am now to -treat.[36\5] My first error was, that the path of a planet is a -perfect circle;--an opinion which was a more mischievous thief of my -time, {299} in proportion as it was supported by the authority of all -philosophers, and apparently agreeable to metaphysics." But before he -attempts to correct this erroneous part of his hypothesis, he sets -about discovering the law according to which the different parts of -the orbit are described in the case of the earth, in which case the -eccentricity is so small that the effect of the oval form is -insensible. The result of this inquiry was[37\5] the Rule, that the -time of describing any arc of the orbit is proportional to the area -intercepted between the curve and two lines drawn from the sun to the -extremities of the arc. It is to be observed that this rule, at first, -though it had the recommendation of being selected after the -unavoidable abandonment of many, which were suggested by the notions -of those times, was far from being adopted upon any very rigid or -cautious grounds. A rule had been proved at the apsides of the orbit, -by calculation from observations, and had then been extended by -conjecture to other parts of the orbit; and the rule of the areas was -only an approximate and inaccurate mode of representing this rule, -employed for the purpose of brevity and convenience, in consequence of -the difficulty of applying, geometrically, that which Kepler now -conceived to be the true rule, and which required him to find the sum -of the lines drawn from the sun to _every_ point of the orbit. When he -proceeded to apply this rule to Mars, in whose orbit the oval form is -much more marked, additional difficulties came in his way; and here -again the true supposition, that the _oval_ is of that special kind -called _ellipse_, was adopted at first only in order to simplify -calculation,[38\5] and the deviation from exactness in the result was -attributed to the inaccuracy of those approximate processes. The -supposition of the oval had already been forced upon Purbach in the -case of Mercury, and upon Reinhold in the case of the Moon. The centre -of the epicycle was made to describe an egg-shaped figure in the -former case, and a lenticular figure in the latter.[39\5] - -[Note 36\5: _De Stellâ Martis_, iii. 40.] - -[Note 37\5: _De Stellâ Martis_, p. 194.] - -[Note 38\5: Ib. iv. c. 47.] - -[Note 39\5: L. U. K. Kepler, p. 30.] - -It may serve to show the kind of labor by which Kepler was led to -his result, if we here enumerate, as he does in his forty-seventh -Chapter,[40\5] six hypotheses, on which he calculated the longitude -of Mars, in order to see which best agreed with observation. - -[Note 40\5: _De Stellâ Martis_, p. 228.] - -1. The simple eccentricity. - -2. The bisection of the eccentricity, and the duplication of the -superior part of the equation. {300} - -3. The bisection of the eccentricity, and a stationary point of -equations, after the manner of Ptolemy. - -4. The vicarious hypothesis by a free section of the eccentricity -made to agree as nearly as possible with the truth. - -5. The physical hypothesis on the supposition of a perfect circle. - -6. The physical hypothesis on the supposition of a perfect ellipse. - -By the physical hypothesis, he meant the doctrine that the time of a -planet's describing any part of its orbit is proportional to the -distance of the planet from the sun, for which supposition, as we -have said, he conceived that he had assigned physical reasons. - -The two last hypotheses came the nearest to the truth, and differed -from it only by about eight minutes, the one in excess and the other -in defect. And, after being much perplexed by this remaining error, -it at last occurred to him[41\5] that he might take another -ellipsis, exactly intermediate between the former one and the -circle, and that this must give the path and the motion of the -planet. Making this assumption, and taking the areas to represent -the times, he now saw[42\5] that both the longitude and the -distances of Mars would agree with observation to the requisite -degree of accuracy. The rectification of the former hypothesis, when -thus stated, may, perhaps, appear obvious. And Kepler informs us -that he had nearly been anticipated in this step (c. 55). "David -Fabricius, to whom I had communicated my hypothesis of cap. 45, was -able, by his observations, to show that it erred in making the -distances too short at mean longitudes; of which he informed me by -letter while I was laboring, by repeated efforts, to discover the -true hypothesis. So nearly did he get the start of me in detecting -the truth." But this was less easy than it might seem. When Kepler's -first hypothesis was enveloped in the complex construction requisite -in order to apply it to each point of the orbit, it was far more -difficult to see where the error lay, and Kepler hit upon it only by -noticing the coincidences of certain numbers, which, as he says, -raised him as if from sleep, and gave him a new light. We may -observe, also, that he was perplexed to reconcile this new view, -according to which the planet described an exact ellipse, with his -former opinion, which represented the motion by means of libration -in an epicycle. "This," he says, "was my greatest trouble, that, -though I considered and reflected till I was almost mad, I could not -find why the planet to which, with so much probability, and with -such an exact {301} accordance of the distances, libration in the -diameter of the epicycle was attributed, should, according to the -indication of the equations, go in an elliptical path. What an -absurdity on my part! as if libration in the diameter might not be a -way to the ellipse!" - -[Note 41\5: _De Stellâ Martis_, c. 58.] - -[Note 42\5: Ibid. p. 235.] - -Another scruple respecting this theory arose from the impossibility of -solving, by any geometrical construction, the problem to which Kepler -was thus led, namely, "To divide the area of a semicircle in a given -ratio, by a line drawn from any point of the diameter." This is still -termed "Kepler's Problem," and is, in fact, incapable of exact -geometrical solution. As, however, the calculation can be performed, -and, indeed, was performed by Kepler himself, with a sufficient degree -of accuracy to show that the elliptical hypothesis is true, the -insolubility of this problem is a mere mathematical difficulty in the -deductive process, to which Kepler's induction gave rise. - -Of Kepler's physical reasonings we shall speak more at length on -another occasion. His numerous and fanciful hypotheses had -discharged their office, when they had suggested to him his many -lines of laborious calculation, and encouraged him under the -exertions and disappointments to which these led. The result of this -work was the formal laws of the motion of Mars, established by a -clear induction, since they represented, with sufficient accuracy, -the best observations. And we may allow that Kepler was entitled to -the praise which he claims in the motto on his first leaf. Ramus had -said that if any one would construct an astronomy without -hypothesis, he would be ready to resign to him his professorship in -the University of Paris. Kepler quotes this passage, and adds, "it -is well, Ramus, that you have run from this pledge, by quitting life -and your professorship;[43\5] if you held it still, I should, with -justice, claim it." This was not saying too much, since he had -entirely overturned the hypothesis of eccentrics and epicycles, and -had obtained a theory which was a mere representation of the motions -and distances as they were observed. {302} - -[Note 43\5: Ramus perished in the Massacre of St. Bartholomew.] - - - - -CHAPTER V. - -SEQUEL TO THE EPOCH OF KEPLER. RECEPTION, VERIFICATION, AND -EXTENSION OF THE ELLIPTICAL THEORY. - - -_Sect._ 1.--_Application of the Elliptical Theory to the Planets._ - -THE extension of Kepler's discoveries concerning the orbit of Mars -to the other planets, obviously offered itself as a strong -probability, and was confirmed by trial. This was made in the first -place upon the orbit of Mercury; which planet, in consequence of the -largeness of its eccentricity, exhibits more clearly than the others -the circumstances of the elliptical motion. These and various other -supplementary portions of the views to which Kepler's discoveries -had led, appeared in the latter part of his _Epitome Astronomiæ -Copernicanæ_, published in 1622. - -The real verification of the new doctrine concerning the orbits and -motions of the heavenly bodies was, of course, to be found in the -construction of tables of those motions, and in the continued -comparison of such tables with observation. Kepler's discoveries had -been founded, as we have seen, principally on Tycho's observations. -Longomontanus (so called as being a native of Langberg in Denmark), -published in 1621, in his _Astronomia Danica_, tables founded upon -the theories as well as the observations of his countryman. -Kepler[44\5] in 1627 published his tables of the planets, which he -called _Rudolphine Tables_, the result and application of his own -theory. In 1633, Lansberg, a Belgian, published also _Tabulæ -Perpetuæ_, a work which was ushered into the world with considerable -pomp and pretension, and in which the author cavils very keenly at -Kepler and Brahe. We may judge of the impression made upon the -astronomical world in general by these rival works, from the account -which our countryman Jeremy Horrox has given of their effect on him. -He had been seduced by the magnificent promises of Lansberg, and the -praises of his admirers, which are prefixed to the work, and was -persuaded that the common opinion which preferred Tycho and Kepler -to him was a prejudice. In 1636, however, he became acquainted with -Crabtree, another young {303} astronomer, who lived in the same part -of Lancashire. By him Horrox was warned that Lansberg was not to be -depended on; that his hypotheses were vicious, and his observations -falsified or forced into agreement with his theories. He then read -the works and adopted the opinions of Kepler; and after some -hesitation which he felt at the thought of attacking the object of -his former idolatry, he wrote a dissertation on the points of -difference between them. It appears that, at one time, he intended -to offer himself as the umpire who was to adjudge the prize of -excellence among the three rival theories of Longomontanus, Kepler, -and Lansberg; and, in allusion to the story of ancient mythology, -his work was to have been called _Paris Astronomicus_; we easily see -that he would have given the golden apple to the Keplerian goddess. -Succeeding observations confirmed his judgment: and the _Rudolphine -Tables_, thus published seventy-six years after the Prutenic, which -were founded on the doctrines of Copernicus, were for a long time -those universally used. - -[Note 44\5: Rheticus, _Narratio_, p. 98.] - - -_Sect._ 2.--_Application of the Elliptical Theory to the Moon._ - -THE reduction of the Moon's motions to rule was a harder task than -the formation of planetary tables, if accuracy was required; for the -Moon's motion is affected by an incredible number of different and -complex inequalities, which, till their law is detected, appear to -defy all theory. Still, however, progress was made in this work. The -most important advances were due to Tycho Brahe. In addition to the -first and second inequalities of the moon (the _Equation of the -Centre_, known very early, and the _Evection_, which Ptolemy had -discovered), Tycho proved that there was another inequality, which -he termed the _Variation_,[45\5] which depended on the moon's -position with respect to the sun, and which at its maximum was forty -minutes and a half, about a quarter of the evection. He also -perceived, though not very distinctly, the necessity of another -correction of the moon's place depending on the sun's longitude, -which has since been termed the _Annual Equation_. - -[Note 45\5: We have seen (chap. iii.), that Aboul-Wefa, in the -tenth century, had already noticed this inequality; but his -discovery had been entirely forgotten long before the time of Tycho, -and has only recently been brought again into notice.] - -These steps concerned the Longitude of the Moon; Tycho also made -important advances in the knowledge of the Latitude. The Inclination -of the Orbit had hitherto been assumed to be the same at all {304} -times; and the motion of the Node had been supposed uniform. He -found that the inclination increased and diminished by twenty -minutes, according to the position of the line of nodes; and that -the nodes, though they regress upon the whole, sometimes go forwards -and sometimes go backwards. - -Tycho's discoveries concerning the moon are given in his -_Progymnasmata_, which was published in 1603, two years after the -author's death. He represents the Moon's motion in longitude by -means of certain combinations of epicycles and eccentrics. But after -Kepler had shown that such devices are to be banished from the -planetary system, it was impossible not to think of extending the -elliptical theory to the moon. Horrox succeeded in doing this; and -in 1638 sent this essay to his friend Crabtree. It was published in -1673, with the numerical elements requisite for its application -added by Flamsteed. Flamsteed had also (in 1671-2) compared this -theory with observation, and found that it agreed far more nearly -than the _Philolaic Tables_ of Bullialdus, or the _Carolinian -Tables_ of Street (_Epilogus ad Tabulas_). Moreover Horrox, by -making the centre of the ellipse revolve in an epicycle, gave an -explanation of the evection, as well as of the equation of the -centre.[46\5] - -[Note 46\5: Horrox (_Horrockes_ as he himself spelt his name) gave a -first sketch of his theory in letters to his friend Crabtree in -1638: in which the variation of the eccentricity is not alluded to. -But in Crabtree's letter to Gascoigne in 1642, he gives Horrox's -rule concerning it; and Flamsteed in his _Epilogue_ to the Tables, -published by Wallis along with Horrox's works in 1673, gave an -explanation of the theory which made it amount very nearly to a -revolution of the centre of the ellipse in an epicycle. Halley -afterwards made a slight alteration; but hardly, I think, enough to -justify Newton's assertion (_Princip._ Lib. iii. Prop. 35, Schol.), -"Halleius centrum ellipseos in epicyclo locavit." See Baily's -_Flamsteed_, p. 683.] - -Modern astronomers, by calculating the effects of the perturbing -forces of the solar system, and comparing their calculations with -observation, have added many new corrections or equations to those -known at the time of Horrox; and since the Motions of the heavenly -bodies were even then affected by these variations as yet -undetected, it is clear that the Tables of that time must have shown -some errors when compared with observation. These errors much -perplexed astronomers, and naturally gave rise to the question -whether the motions of the heavenly bodies really were exactly -regular, or whether they were not affected by accidents as little -reducible to rule as wind and weather. Kepler had held the opinion -of the _casualty_ of such errors; but Horrox, far more -philosophically, argues against this opinion, though he {305} allows -that he is much embarrassed by the deviations. His arguments show a -singularly clear and strong apprehension of the features of the -case, and their real import. He says,[47\5] "these errors of the -tables are alternately in excess and defect; how could this constant -compensation happen if they were casual? Moreover, the alternation -from excess to defect is most rapid in the Moon, most slow in -Jupiter and Saturn, in which planets the error continues sometimes -for years. If the errors were casual, why should they not last as -long in the Moon as in Saturn? But if we suppose the tables to be -right in the mean motions, but wrong in the equations, these facts -are just what must happen; since Saturn's inequalities are of long -period, while those of the Moon are numerous, and rapidly changing." -It would be impossible, at the present moment, to reason better on -this subject; and the doctrine, that all the apparent irregularities -of the celestial motions are really regular, was one of great -consequence to establish at this period of the science. - -[Note 47\5: _Astron. Kepler._ Proleg. p. 17.] - - -_Sect._ 3.--_Causes of the further Progress of Astronomy._ - -WE are now arrived at the time when theory and observation sprang -forwards with emulous energy. The physical theories of Kepler, and -the reasonings of other defenders of the Copernican theory, led -inevitably, after some vagueness and perplexity, to a sound science -of Mechanics; and this science in time gave a new face to Astronomy. -But in the mean time, while mechanical mathematicians were -generalizing from the astronomy already established, astronomers -were accumulating new facts, which pointed the way to new theories -and new generalizations. Copernicus, while he had established the -permanent length of the year, had confirmed the motion of the sun's -apogee, and had shown that the eccentricity of the earth's orbit, -and the obliquity of the ecliptic, were gradually, though slowly, -diminishing. Tycho had accumulated a store of excellent -observations. These, as well as the laws of the motions of the moon -and planets already explained, were materials on which the Mechanics -of the Universe was afterwards to employ its most matured powers. In -the mean time, the telescope had opened other new subjects of notice -and speculation; not only confirming the Copernican doctrine by the -phases of Venus, and the analogical examples of Jupiter and Saturn, -which with their Satellites {306} appeared like models of the Solar -System; but disclosing unexpected objects, as the Ring of Saturn, -and the Spots of the Sun. The art of observing made rapid advances, -both by the use of the telescope, and by the sounder notions of the -construction of instruments which Tycho introduced. Copernicus had -laughed at Rheticus, when he was disturbed about single minutes; and -declared that if he could be sure to ten minutes of space, he should -be as much delighted as Pythagoras was when he discovered the -property of the right-angled triangle. But Kepler founded the -revolution which he introduced on a quantity less than this. -"Since," he says,[48\5] "the Divine Goodness has given us in Tycho -an observer so exact that this error of eight minutes is impossible, -we must be thankful to God for this, and turn it to account. And -these eight minutes, which we must not neglect, will, of themselves, -enable us to reconstruct the whole of astronomy." In addition to -other improvements, the art of numerical calculation made an -inestimable advance by means of Napier's invention of Logarithms; -and the progress of other parts of pure mathematics was proportional -to the calls which astronomy and physics made upon them. - -[Note 48\5: _De Stellâ Martis_, c. 19.] - -The exactness which observation had attained enabled astronomers -both to verify and improve the existing theories, and to study the -yet unsystematized facts. The science was, therefore, forced along -by a strong impulse on all sides, and its career assumed a new -character. Up to this point, the history of European Astronomy was -only the sequel of the history of Greek Astronomy; for the -heliocentric system, as we have seen, had had a place among the -guesses, at least, of the inventive and acute intellects of the -Greek philosophers. But the discovery of Kepler's Laws, accompanied, -as from the first they were, with a conviction that the relations -thus brought to light were the effects and exponents of physical -causes, led rapidly and irresistibly to the Mechanical Science of -the skies, and collaterally, to the Mechanical Science of the other -parts of Nature: Sound, and Light, and Heat; and Magnetism, and -Electricity, and Chemistry. The history of these Sciences, thus -treated, forms the sequel of the present work, and will be the -subject of the succeeding volumes. And since, as I have said, our -main object in this work is to deduce, from the history of science, -the philosophy of scientific discovery, it may be regarded as -fortunate for our purpose that the history, after this point, so far -changes its aspect as to offer new materials for such speculations. -The details of {307} a history of astronomy, such as the history of -astronomy since Newton has been, though interesting to the special -lovers of that science, would be too technical, and the features of -the narrative too monotonous and unimpressive, to interest the -general reader, or to suggest a comprehensive philosophy of science. -But when we pass from the Ideas of Space and Time to the Ideas of -Force and Matter, of Mediums by which action and sensation are -produced, and of the Intimate Constitution of material bodies, we -have new fields of inquiry opened to us. And when we find that in -these fields, as well as in astronomy, there are large and striking -trains of unquestioned discovery to be narrated, we may gird -ourselves afresh to the task of writing, and I hope, of reading, the -remaining part of the History of the Inductive Sciences, in the -trust that it will in some measure help us to answer the important -questions, What is Truth? and, How is it to be discovered? - - - -{{309}} -BOOK VI. - -_THE MECHANICAL SCIENCES._ - - -HISTORY OF MECHANICS, -INCLUDING -FLUID MECHANICS. - - - - ΚΡΑΤΟΣ ΒIΑ ΤΕ, σφῷν μὲν ἐντολὴ Διὸς - Ἔχει Τέλος δὴ, κ' οὐδὲν ἐμποδῶν ἔτι - ÆSCHYLUS. _Prom. Vinct._ 13. - - You, FORCE and POWER, have done your destined task: - And naught impedes the work of other hands. - - - -{{311}} -INTRODUCTION. - - -WE enter now upon a new region of the human mind. In passing from -Astronomy to Mechanics we make a transition from the _formal_ to the -_physical_ sciences;--from time and space to force and matter;--from -_phenomena_ to _causes_. Hitherto we have been concerned only with -the paths and orbits, the periods and cycles, the angles and -distances, of the objects to which our sciences applied, namely, the -heavenly bodies. How these motions are produced;--by what agencies, -impulses, powers, they are determined to be what they are;--of what -nature are the objects themselves;--are speculations which we have -hitherto not dwelt upon. The history of such speculations now comes -before us; but, in the first place, we must consider the history of -speculations concerning motion in general, terrestrial as well as -celestial. We must first attend to Mechanics, and afterwards return -to Physical Astronomy. - -In the same way in which the development of Pure Mathematics, which -began with the Greeks, was a necessary condition of the progress of -Formal Astronomy, the creation of the science of Mechanics now -became necessary to the formation and progress of Physical -Astronomy. Geometry and Mechanics were studied for their own sakes; -but they also supplied ideas, language, and reasoning to other -sciences. If the Greeks had not cultivated Conic Sections, Kepler -could not have superseded Ptolemy; if the Greeks had cultivated -Dynamics,[1\6] Kepler might have anticipated Newton. {312} - -[Note 1\6: _Dynamics_ is the science which treats of the Motions of -Bodies; _Statics_ is the science which treats of the Pressure of -Bodies which are in equilibrium, and therefore at rest.] - - - - -CHAPTER I. - -PRELUDE TO THE EPOCH OF GALILEO. - - -_Sect._ 1.--_Prelude to the Science of Statics._ - -SOME steps in the science of Motion, or rather in the science of -Equilibrium, had been made by the ancients, as we have seen. -Archimedes established satisfactorily the doctrine of the Lever, -some important properties of the Centre of Gravity, and the -fundamental proposition of Hydrostatics. But this beginning led to -no permanent progress. Whether the distinction between the -principles of the doctrine of Equilibrium and of Motion was clearly -seen by Archimedes, we do not know; but it never was caught hold of -by any of the other writers of antiquity, or by those of the -Stationary Period. What was still worse, the point which Archimedes -had won was not steadily maintained. - -We have given some examples of the general ignorance of the Greek -philosophers on such subjects, in noticing the strange manner in -which Aristotle refers to mathematical properties, in order to -account for the equilibrium of a lever, and the attitude of a man -rising from a chair. And we have seen, in speaking of the indistinct -ideas of the Stationary Period, that the attempts which were made to -extend the statical doctrine of Archimedes, failed, in such a manner -as to show that his followers had not clearly apprehended the idea -on which his reasoning altogether depended. The clouds which he had, -for a moment, cloven in his advance, closed after him, and the -former dimness and confusion settled again on the land. - -This dimness and confusion, with respect to all subjects of -mechanical reasoning, prevailed still, at the period we now have to -consider; namely, the period of the first promulgation of the -Copernican opinions. This is so important a point that I must -illustrate it further. - -Certain general notions of the connection of cause and effect in -motion, exist in the human mind at all periods of its development, and -are implied in the formation of language and in the most familiar -employments of men's thoughts. But these do not constitute a _science_ -of {313} Mechanics, any more than the notions of _square_ and _round_ -make a Geometry, or the notions of _months_ and _years_ make an -Astronomy. The unfolding these Notions into distinct Ideas, on which -can be founded principles and reasonings, is further requisite, in -order to produce a science; and, with respect to the doctrines of -Motion, this was long in coming to pass; men's thoughts remained long -entangled in their primitive and unscientific confusion. - -We may mention one or two features of this confusion, such as we -find in authors belonging to the period now under review. - -We have already, in speaking of the Greek School Philosophy, noticed -the attempt to explain some of the differences among Motions, by -classifying them into Natural Motions and Violent Motions; and we have -spoken of the assertion that heavy bodies fall quicker in proportion -to their greater weight. These doctrines were still retained: yet the -views which they implied were essentially erroneous and unsound; for -they did not refer distinctly to a measurable Force as the cause of -all motion or change of motion; and they confounded the causes which -_produce_ and those which _preserve_, motion. Hence such principles -did not lead immediately to any advance of knowledge, though efforts -were made to apply them, in the cases both of terrestrial Mechanics -and of the motions of the heavenly bodies. - -The effect of the Inclined Plane was one of the first, as it was one -of the most important, propositions, on which modern writers employed -themselves. It was found that a body, when supported on a sloping -surface, might be sustained or raised by a force or exertion which -would not have been able to sustain or raise it without such support. -And hence, _The Inclined Plane_ was placed in the list of Mechanical -Powers, or simple machines by which the efficacy of forces is -increased: the question was, in what proportion this increase of -efficiency takes place. It is easily seen that the force requisite to -sustain a body is smaller, as the slope on which it rests is smaller; -Cardan (whose work, _De Proportionibus Numerorum, Motuum, Ponderum,_ -&c., was published in 1545) asserts that the force is double when the -angle of inclination is double, and so on for other proportions; this -is probably a guess, and is an erroneous one. Guido Ubaldi, of -Marchmont, published at Pesaro, in 1577, a work which he called -_Mechanicorum Liber_, in which he endeavors to prove that an acute -wedge will produce a greater mechanical effect than an obtuse one, -without determining in what proportion. There is, he observes, "a -certain repugnance" between the direction in which the side of the -wedge tends to {314} move the obstacle, and the direction in which it -really does move. Thus the Wedge and the Inclined Plane are connected -in principle. He also refers the Screw to the Inclined Plane and the -Wedge, in a manner which shows a just apprehension of the question. -Benedetti (1585) treats the Wedge in a different manner; not exact, -but still showing some powers of thought on mechanical subjects. -Michael Varro, whose _Tractatus de Motu_ was published at Geneva in -1584, deduces the wedge from the composition of hypothetical motions, -in a way which may appear to some persons an anticipation of the -doctrine of the Composition of Forces. - -There is another work on subjects of this kind, of which several -editions were published in the sixteenth century, and which treats -this matter in nearly the same way as Varro, and in favour of which a -claim has been made[2\6] (I think an unfounded one), as if it -contained the true principle of this problem. The work is "Jordanus -Nemorarius _De Ponderositate_." The date and history of this author -were probably even then unknown; for in 1599, Benedetti, correcting -some of the errors of Tartalea, says they are taken "a Jordano quodam -antiquo." The book was probably a kind of school-book, and much used; -for an edition printed at Frankfort, in 1533, is stated to be _Cum -gratia et privilegio Imperiali, Petro Apiano mathematico Ingolstadiano -ad xxx annos concesso_. But this edition does not contain the Inclined -Plane. Though those who compiled the work assert in words something -like the inverse proportion of Weights and their Velocities, they had -not learnt at that time how to apply this maxim to the Inclined Plane; -nor were they ever able to render a sound reason for it. In the -edition of Venice, 1565, however, such an application is attempted. -The reasonings are founded on the Aristotelian assumption, "that -bodies descend more quickly in proportion as they are heavier." To -this principle are added some others; as, that "a body is heavier in -proportion as it descends more directly to the centre," and that, in -proportion as a body descends more obliquely, the intercepted part of -the direct descent is smaller. By means of these principles, the -"descending force" of bodies, on inclined planes, was compared, by a -process, which, so far as it forms a line of proof at all, is a -somewhat curious example of confused and vicious reasoning. When two -bodies are supported on two inclined planes, and are connected by a -string passing over the junction of the planes, so that when one -descends the other ascends, {315} they must move through equal spaces -on the planes; but on the plane which is more oblique (that is, more -nearly horizontal), the vertical descent will be smaller in the same -proportion in which the plane is longer. Hence, by the Aristotelian -principle, the weight of the body on the longer plane is less; and, to -produce an equality of effect, the body must be greater in the same -proportion. We may observe that the Aristotelian principle is not only -false, but is here misapplied; for its genuine meaning is, that when -bodies _fall freely_ by gravity, they move quicker in proportion as -they are heavier; but the rule is here applied to the motions which -bodies _would_ have, if they were moved by a force extraneous to their -gravity. The proposition was supposed by the Aristotelians to be true -of _actual_ velocities; it is applied by Jordanus to _virtual_ -velocities, without his being aware what he was doing. This confusion -being made, the result is got at by taking for granted that bodies -_thus_ proved to be equally _heavy_, have equal powers of descent on -the inclined planes; whereas, in the previous part of the reasoning, -the weight was supposed to be proportional to the descent in the -vertical direction. It is obvious, in all this, that though the author -had adopted the false Aristotelian principle, he had not settled in -his own mind whether the motions of which it spoke were actual or -virtual motions;--motions in the direction of the inclined plane, or -of the intercepted parts of the vertical, corresponding to these; nor -whether the "descending force" of a body was something different from -its weight. We cannot doubt that, if he had been required to point -out, with any exactness, the cases to which his reasoning applied, he -would have been unable to do so; not possessing any of those clear -fundamental Ideas of Pressure and Force, on which alone any real -knowledge on such subjects must depend. The whole of Jordanus's -reasoning is an example of the confusion of thought of his period, and -of nothing more. It no more supplied the want of some man of genius, -who should give the subject a real scientific foundation, than -Aristotle's knowledge of the proportion of the weights on the lever -superseded the necessity of Archimedes's proof of it. - -[Note 2\6: Mr. Drinkwater's _Life of Galileo_, in the Lib. Usef. Kn. -p. 83.] - -We are not, therefore, to wonder that, though this pretended theorem -was copied by other writers, as by Tartalea, in his _Quesiti et -Inventioni Diversi_, published in 1554, no progress was made in the -real solution of any one mechanical problem by means of it. Guido -Ubaldi, who, in 1577, writes in such a manner as to show that he had -taken a good hold of his subject for his time, refers to Pappus's -solution of the problem of the Inclined Plane, but makes no mention -of that of {316} Jordanus and Tartalea.[3\6] No progress was likely -to occur, till the mathematicians had distinctly recovered the -genuine Idea of Pressure, as a Force producing equilibrium, which -Archimedes had possessed, and which was soon to reappear in Stevinus. - -[Note 3\6: Ubaldi mentions and blames Jordanus's way of treating the -Lever. (See his Preface.)] - -The properties of the Lever had always continued known to -mathematicians, although, in the dark period, the superiority of the -proof given by Archimedes had not been recognized. We are not to be -surprised, if reasonings like those of Jordanus were applied to -demonstrate the theories of the Lever with apparent success. Writers -on Mechanics were, as we have seen, so vacillating in their mode of -dealing with words and propositions, that their maxims could be made -to prove any thing which was already known to be true. - -We proceed to speak of the beginning of the real progress of -Mechanics in modern times. - - -_Sect._ 2.--_Revival of the Scientific Idea of -Pressure.--Stevinus.--Equilibrium of Oblique Forces._ - -THE doctrine of the Centre of Gravity was the part of the mechanical -speculations of Archimedes which was most diligently prosecuted -after his time. Pappus and others, among the ancients, had solved -some new problems on this subject, and Commandinus, in 1565, -published _De Centro Gravitatis Solidorum_. Such treatises -contained, for the most part, only mathematical consequences of the -doctrines of Archimedes; but the mathematicians also retained a -steady conviction of the mechanical property of the Centre of -Gravity, namely, that all the weight of the body might be collected -there, without any change in the mechanical results; a conviction -which is closely connected with our fundamental conceptions of -mechanical action. Such a principle, also, will enable us to -determine the result of many simple mechanical arrangements; for -instance, if a mathematician of those days had been asked whether a -solid ball could be made of such a form, that, when placed on a -horizontal plane, it should go on rolling forwards without limit -merely by the effect of its own weight, he would probably have -answered, that it could not; for that the centre of gravity of the -ball would seek the lowest position it could find, and that, when it -had found this, the ball could have no tendency to roll any further. -And, in making this assertion, the supposed reasoner would not be -{317} anticipating any wider proof of the impossibility of a -_perpetual motion_ drawn from principles subsequently discovered, -but would be referring the question to certain fundamental -convictions, which, whether put into Axioms or not, inevitably -accompany our mechanical conceptions. - -In the same way, Stevinus of Bruges, in 1586, when he published his -_Beghinselen der Waaghconst_ (Principles of Equilibrium), had been -asked why a loop of chain, hung over a triangular beam, could not, -as he asserted it could not, go on moving round and round -perpetually, by the action of its own weight, he would probably have -answered, that the weight of the chain, if it produced motion at -all, must have a tendency to bring it into some certain position, -and that when the chain had reached this position, it would have no -tendency to go any further; and thus he would have reduced the -impossibility of such a perpetual motion, to the conception of -gravity, as a force tending to produce equilibrium; a principle -perfectly sound and correct. - -Upon this principle thus applied, Stevinus did establish the -fundamental property of the Inclined Plane. He supposed a loop of -string, loaded with fourteen equal balls at equal distances, to hang -over a triangular support which was composed of two inclined planes -with a horizontal base, and whose sides, being unequal in the -proportion of two to one, supported four and two balls respectively. -He showed that this loop must hang at rest, because any motion would -only bring it into the same condition in which it was at first; and -that the festoon of eight balls which hung down below the triangle -might be removed without disturbing the equilibrium; so that four -balls on the longer plane would balance two balls on the shorter -plane; or in other words, the weights would be as the lengths of the -planes intercepted by the horizontal line. - -Stevinus showed his firm possession of the truth contained in this -principle, by deducing from it the properties of forces acting in -oblique directions under all kinds of conditions; in short, he -showed his entire ability to found upon it a complete doctrine of -equilibrium; and upon his foundations, and without any additional -support, the mathematical doctrines of Statics might have been -carried to the highest pitch of perfection they have yet reached. -The formation of the science was finished; the mathematical -development and exposition of it were alone open to extension and -change. - -[2d Ed.] ["Simon Stevin of Bruges," as he usually designates himself -in the title-page of his work, has lately become an object of -general interest in his own country, and it has been resolved to -erect a {318} statue in honor of him in one of the public places of -his native city. He was born in 1548, as I learn from M. Quetelet's -notice of him, and died in 1620. Montucla says that he died in 1633; -misled apparently by the preface to Albert Girard's edition of -Stevin's works, which was published in 1634, and which speaks of a -death which took place in the preceding year; but on examination it -will be seen that this refers to Girard, not to Stevin. - -I ought to have mentioned, in consideration of the importance of the -proposition, that Stevin distinctly states the _triangle of forces_; -namely, that three forces which act upon a point are in equilibrium -when they are parallel and proportional to the three sides of any -plane triangle. This includes the principle of the _Composition of -Statical Forces_. Stevin also applies his principle of equilibrium -to cordage, pulleys, funicular polygons, and especially to the bits -of bridles; a branch of mechanics which he calls _Chalinothlipsis_. - -He has also the merit of having seen very clearly, the distinction -of statical and dynamical problems. He remarks that the question, -"What force will _support_ a loaded wagon on an inclined plane? is a -statical question, depending on simple conditions; but that the -question, What force will _move_ the wagon? requires additional -considerations to be introduced. - -In Chapter iv. of this Book, I have noticed Stevin's share in the -rediscovery of the _Laws of the Equilibrium of Fluids_. He -distinctly explains the _hydrostatic paradox_, of which the -discovery is generally ascribed to Pascal. - -Earlier than Stevinus, Leonardo da Vinci must have a place among the -discoverers of the Conditions of Equilibrium of Oblique Forces. He -published no work on this subject; but extracts from his manuscripts -have been published by Venturi, in his _Essai sur les Ouvrages -Physico-Mathematiques de Leonard da Vinci, avec des Fragmens tirés -de ses Manuscrits apportés d'Italie_, Paris, 1797: and by Libri, in -his _Hist. des Sc. Math. en Italie_, 1839. I have also myself -examined these manuscripts in the Royal Library at Paris. - -It appears that, as early as 1499, Leonardo gave a perfectly correct -statement of the proportion of the forces exerted by a cord which -acts obliquely and supports a weight on a lever. He distinguishes -between the real lever, and the _potential levers_, that is, the -perpendiculars drawn from the centre upon the directions of the -forces. This is quite sound and satisfactory. These views must in -all probability have been sufficiently promulgated in Italy to -influence the speculations of Galileo; {319} whose reasonings -respecting the lever much resemble those of Leonardo.--Da Vinci also -anticipated Galileo in _asserting_ that the time of descent of a -body down an inclined plane is to the time of descent down its -vertical length in the proportion of the length of the plane to the -height. But this cannot, I think, have been more than a guess: there -is no vestige of a proof given.] - -The contemporaneous progress of the other branch of mechanics, the -Doctrine of Motion, interfered with this independent advance of -Statics; and to that we must now turn. We may observe, however, that -true propositions respecting the composition of forces appear to -have rapidly diffused themselves. The _Tractatus de Motu_ of Michael -Varro of Geneva, already noticed, printed in 1584, had asserted, -that the forces which balance each other, acting on the sides of a -right-angled triangular wedge, are in the proportion of the sides of -the triangle; and although this assertion does not appear to have -been derived from a distinct idea of pressure, the author had hence -rightly deduced the properties of the wedge and the screw. And -shortly after this time, Galileo also established the same results -on different principles. In his Treatise _Delle Scienze Mecaniche_ -(1592), he refers the Inclined Plane to the Lever, in a sound and -nearly satisfactory manner; imagining a lever so placed, that the -motion of a body at the extremity of one of its arms should be in -the same direction as it is upon the plane. A slight modification -makes this an unexceptionable proof. - - -_Sect._ 3.--_Prelude to the Science of Dynamics.--Attempts at the -First Law of Motion._ - -WE have already seen, that Aristotle divided Motions into Natural -and Violent. Cardan endeavored to improve this division by making -three classes: _Voluntary_ Motion, which is circular and uniform, -and which is intended to include the celestial motions; _Natural_ -Motion, which is stronger towards the end, as the motion of a -falling body,--this is in a straight line, because it is motion to -an end, and nature seeks her ends by the shortest road; and thirdly, -_Violent_ Motion, including in this term all kinds different from -the former two. Cardan was aware that such Violent Motion might be -produced by a very small force; thus he asserts, that a spherical -body resting on a horizontal plane may be put in motion by any force -which is sufficient to cleave the air; for which, however, he -erroneously assigns as a reason, {320} the smallness of the point of -contact.[4\6] But the most common mistake of this period was, that -of supposing that as force is requisite to move a body, so a -perpetual supply of force is requisite to keep it in motion. The -whole of what Kepler called his "physical" reasoning, depended upon -this assumption. He endeavored to discover the forces by which the -motions of the planets about the sun might be produced; but, in all -cases, he considered the velocity of the planet as produced by, and -exhibiting the effect of, a force which acted in the direction of -the motion. Kepler's essays, which are in this respect so feeble and -unmeaning, have sometimes been considered as disclosing some distant -anticipation of Newton's discovery of the existence and law of -central forces. There is, however, in reality, no other connection -between these speculations than that which arises from the use of -the term _force_ by the two writers in two utterly different -meanings. Kepler's Forces were certain imaginary qualities which -appeared in the actual motion which the bodies had; Newton's Forces -were causes which appeared by the change of motion: Kepler's Forces -urged the bodies forwards; Newton's deflected the bodies from such a -progress. If Kepler's Forces were destroyed, the body would -instantly stop; if Newton's were annihilated, the body would go on -uniformly in a straight line. Kepler compares the action of his -Forces to the way in which a body might be driven round, by being -placed among the sails of a windmill; Newton's Forces would be -represented by a rope pulling the body to the centre. Newton's Force -is merely mutual attraction; Kepler's is something quite different -from this; for though he perpetually illustrates his views by the -example of a magnet, he warns us that the sun differs from the -magnet in this respect, that its force is not attractive, but -directive.[5\6] Kepler's essays may with considerable reason be -asserted to be an anticipation of the Vortices of Descartes; but -they can with no propriety whatever be said to anticipate Newton's -Dynamical Theory. - -[Note 4\6: In speaking of the force which would draw a body up an -inclined plane he observes, that "per communem animi sententiam," -when the plane becomes horizontal, the requisite force is nothing.] - -[Note 5\6: _Epitome Astron. Copern._ p. 176.] - -The confusion of thought which prevented mathematicians from seeing -the difference between producing and preserving motion, was, indeed, -fatal to all attempts at progress on this subject. We have already -noticed the perplexity in which Aristotle involved himself, by his -endeavors to find a reason for the continued motion of a stone {321} -after the moving power had ceased to act; and that he had ascribed -it to the effect of the air or other medium in which the stone -moves. Tartalea, whose _Nuova Scienza_ is dated 1550, though a good -_pure_ mathematician, is still quite in the dark on mechanical -matters. One of his propositions, in the work just mentioned, is (B. -i. Prop. 3), "The more a heavy body recedes from the beginning, or -approaches the end of violent motion, the slower and more inertly it -goes;" which he applies to the horizontal motion of projectiles. In -like manner most other writers about this period conceived that a -cannon-ball goes forwards till it loses all its projectile motion, -and then falls downwards. Benedetti, who has already been mentioned, -must be considered as one of the first enlightened opponents of this -and other Aristotelian errors or puzzles. In his _Speculationum -Liber_ (Venice, 1585), he opposes Aristotle's mechanical opinions, -with great expressions of respect, but in a very sweeping manner. -His chapter xxiv. is headed, "Whether this eminent man was right in -his opinion concerning violent and natural motion." And after -stating the Aristotelian opinion just mentioned, that the body is -impelled by the air, he says that the air must impede rather than -impel the body, and that[6\6] "the motion of the body, separated -from the mover, arises by a certain natural impression from the -impetuosity (_ex impetuositate_) received from the mover." He adds, -that in natural motions this _impetuosity_ continually increases by -the continued action of the cause,--namely, the propension of going -to the place assigned it by nature; and that thus the velocity -increases as the body moves from the beginning of its path. This -statement shows a clearness of conception with regard to the cause -of accelerated motion, which Galileo himself was long in acquiring. - -[Note 6\6: P. 184.] - -Though Benedetti was thus on the way to the First Law of -Motion,--that all motion is uniform and rectilinear, except so far -as it is affected by extraneous forces;--this Law was not likely to -be either generally conceived, or satisfactorily proved, till the -other Laws of Motion, by which the action of Forces is regulated, -had come into view. Hence, though a partial apprehension of this -principle had preceded the discovery of the Laws of Motion, we must -place the establishment of the principle in the period when those -Laws were detected and established, the period of Galileo and his -followers. {322} - - - - -CHAPTER II. - -INDUCTIVE EPOCH OF GALILEO.--DISCOVERY OF THE LAWS OF MOTION IN -SIMPLE CASES. - - -_Sect._ 1.--_Establishment of the First Law of Motion._ - -AFTER mathematicians had begun to doubt or reject the authority of -Aristotle, they were still some time in coming to the conclusion, -that the distinction of Natural and Violent Motions was altogether -untenable;--that the velocity of a body in motion increased or -diminished in consequence of the action of extrinsic causes, not of -any property of the motion itself;--and that the apparently -universal fact, of bodies growing slower and slower, as if by their -own disposition, till they finally stopped, from which Motions had -been called Violent, arose from the action of external obstacles not -immediately obvious, as the friction and the resistance of the air -when a ball runs on the ground, and the action of gravity, when it -is thrown upwards. But the truth to which they were at last led, -was, that such causes would account for _all_ the diminution of -velocity which bodies experience when apparently left to themselves -and that without such causes, the motion of all bodies would go on -forever, in a straight line and with a uniform velocity. - -Who first announced this Law in a general form, it may be difficult -to point out; its exact or approximate truth was necessarily taken -for granted in all complete investigations on the subject of the -laws of motion of falling bodies, and of bodies projected so as to -describe curves. In Galileo's first attempt to solve the problem of -falling bodies, he did not carry his analysis back to the notion of -force, and therefore this law does not appear. In 1604 he had an -erroneous opinion on this subject and we do not know when he was -led to the true doctrine which he published in his _Discorso_, in -1638. In his third Dialogue he gives the instance of water in a -vessel, for the purpose of showing that circular motion has a -tendency to continue. And in his first Dialogue on the Copernican -System[7\6] (published in 1630), he asserts {323} Circular Motion -alone to be naturally uniform, and retains the distinction between -Natural and Violent Motion. In the _Dialogues on Mechanics_, -however, published in 1638, but written apparently at an earlier -period, in treating of Projectiles,[8\6] he asserts the true Law. -"Mobile super planum horizontale projectum mente concipio omni -secluso impedimento; jam constat ex his quæ fusius alibi dicta sunt, -illius motum equabilem et perpetuum super ipso plano futurum esse, -si planum in infinitum extendatur." "Conceive a movable body upon a -horizontal plane, and suppose all obstacles to motion to be removed; -it is then manifest, from what has been said more at large in -another place, that the body's motion will be uniform and perpetual -upon the plane, if the plane be indefinitely extended." His pupil -Borelli, in 1667 (in the treatise _De Vi Percussionis_), states the -proposition generally, that "Velocity is, by its nature, uniform, -and perpetual;" and this opinion appears to have been, at that time, -generally diffused, as we find evidence in Wallis and others. It is -commonly said that Descartes was the first to state this generally. -His _Principia_ were published in 1644; but his proofs of this First -Law of Motion are rather of a theological than of a mechanical kind. -His reason for this Law is,[9\6] "the immutability and simplicity of -the operation by which God preserves motion in matter. For he only -preserves it precisely as it is in that moment in which he preserves -it, taking no account of that which may have been previously." -Reasoning of this abstract and _à priori_ kind, though it may be -urged in favor of true opinions after they have been inductively -established, is almost equally capable of being called in on the -side of error, as we have seen in the case of Aristotle's -philosophy. We ought not, however, to forget that the reference to -these abstract and _à priori_ principles is an indication of the -absolute universality and necessity which we look for in complete -Sciences, and a result of those faculties by which such Science is -rendered possible, and suitable to man's intellectual nature. - -[Note 7\6: Dial. **i. p. 40.] - -[Note 8\6: **p. 141.] - -[Note 9\6: _Princip._ p. 34.] - -The induction by which the First Law of Motion is established, -consists, as induction consists in all cases, in conceiving clearly -the Law, and in perceiving the subordination of Facts to it. But the -Law speaks of bodies not acted upon by any external force,--a case -which never occurs in fact; and the difficulty of the step consisted -in bringing all the common cases in which motion is gradually -extinguished, under the notion of the action of a retarding force. -In order to do this, {324} Hooke and others showed that, by -diminishing the obvious resistances, the retardation also became -less; and men were gradually led to a distinct appreciation of the -Resistance, Friction, &c., which, in all terrestrial motions, -prevent the Law from being evident; and thus they at last -established by experiment a Law which cannot be experimentally -exemplified. The natural uniformity of motion was proved by -examining all kinds of cases in which motion was not uniform. Men -culled the abstract Rule out of the concrete Experiment; although -the Rule was, in every case, mixed with other Rules, and each Rule -could be collected from the Experiment only by supposing the others -known. The perfect simplicity which we necessarily seek for in a law -of nature, enables us to disentangle the complexity which this -combination appears at first sight to occasion. - -The First Law of Motion asserts that the motion of a body, when left -to itself will not only be uniform, but rectilinear also. This -latter part of the law is indeed obvious of itself as soon as we -conceive a body detached from all special reference to external -points and objects. Yet, as we have seen, Galileo asserted that the -naturally uniform motion of bodies was that which takes place in a -circle. Benedetti, however, in 1585, had entertained sound notions -on this subject. In commenting on Aristotle's question, why we -obtain an advantage in throwing by using a sling, he says,[10\6] that -the body, when whirled round, tends to go on in a straight line. In -Galileo's second Dialogue, he makes one of his interlocutors -(Simplicio), when appealed to on this subject, after thinking -intently for a little while, give the same opinion; and the -principle is, from this time, taken for granted by the authors who -treat of the motion of projectiles. Descartes, as might be supposed, -gives the same reason for this as for the other part of the law, -namely, the immutability of the Deity. - -[Note 10\6: "Corpus vellet recta iter peragere." -_**Speculationum Liber_, p. 160.] - - -_Sect._ 2.--_Formation and Application of the Notion of Accelerating -Force.--Laws of Falling Bodies._ - -WE have seen how rude and vague were the attempts of Aristotle and -his followers to obtain a philosophy of bodies falling downwards or -thrown in any direction. If the First Law of Motion had been clearly -known, it would then, perhaps, have been seen that the way to -understand and analyze the motion of any body, is to consider the -{325} Causes of _change_ of motion which at each instant operate -upon it; and thus men would have been led to the notion of -Accelerating Forces, that is, Forces which act upon bodies already -in motion, and accelerate, retard, or deflect their motions. It was, -however, only after many attempts that they reached this point. They -began by considering the _whole motion_ with reference to certain -ill-defined abstract Notions, instead of considering, with a clear -apprehension of the conditions of Causation, the _successive parts_ -of which the motion consists. Thus, they spoke of the tendency of -bodies to the Centre, or to their Own Place;--of Projecting Force, -of Impetus, of Retraction;--with little or no profit to knowledge. -The indistinctness of their notions may, perhaps, be judged of from -their speculations concerning projectiles. Santbach,[11\6] in 1561, -imagined that a body thrown with great velocity, as, for instance, a -ball from a cannon, went in a straight line till all its velocity -was exhausted, and then fell directly downwards. He has written a -treatise on gunnery, founded on this absurd assumption. To this -succeeded another doctrine, which, though not much more -philosophical than the former, agreed much better with the -phenomena. Nicolo Tartalea (_Nuova Scienza_, Venice, 1550; _Quesiti -et Inventioni Diversi_, 1554) and **Gualter Rivius (_Architectura_, -&c., Basil, 1582) represented the path of a cannon-ball as -consisting, first of a straight line in the direction of the -original projection, then of an arc of a circle in which it went on -till its motion became vertical downwards, and then of a vertical -line in which it continued to fall. The latter of these writers, -however, was aware that the path must, from the first, be a curve; -and treated it as a straight line, only because the curvature is -very slight. Even Santbach's figure represents the path of the ball -as partially descending before its final fall, but then it descends -by _steps_, not in a curve. Santbach, therefore, did not conceive -the _Composition_ of the effect of gravity with the existing motion, -but supposed them to act alternately; Rivius, however, understood -this Composition, and saw that gravity must act as a deflecting -force at every point of the path. Galileo, in his second -Dialogue,[12\6] makes Simplicius come to the same conclusion. -"Since," he says, "there is nothing to support the body, when it -quits that which projects it, it cannot be but that its proper -gravity must operate," and it must immediately begin to decline -downwards. {326} - -[Note 11\6: _Problematum Astronomicorum et Geometricorum Sectiones_ -vii. &c. &c. Auctore Daniele Santbach, Noviomago. Basileæ, 1561.] - -[Note 12\6: P. 147.] - -The Force of Gravity which thus produces deflection and curvature in -the path of a body thrown _obliquely_, constantly increases the -velocity of a body when it falls _vertically_ downwards. The -universality of this increase was obvious, both from reasoning and in -fact; the law of it could only be discovered by closer consideration; -and the full analysis of the problem required a distinct measure of -the quantity of Accelerating Force. Galileo, who first solved this -problem, began by viewing it as a question of fact, but conjectured -the solution by taking for granted that the rule must be the simplest -possible. "Bodies," he says,[13\6] "will fall in the most simple way, -because Natural Motions are always the most simple. When a stone -falls, if we consider the matter attentively, we shall find that there -is no addition, no increase, of the velocity more simple than that -which is always added in the same manner," that is, when equal -additions take place in equal times; "which we shall easily understand -if we attend to the close connection of motion and time." From this -Law, thus assumed, he deduced that the spaces described from the -beginning of the motion must be as the squares of the times; and, -again, assuming that the laws of descent for balls rolling down -inclined planes, must be the same as for bodies falling freely, he -verified this conclusion by experiment. - -[Note 13\6: _Dial. Sc._ iv. p. 91.] - -It will, perhaps, occur to the reader that this argument, from the -simplicity of the assumed law, is somewhat insecure. It is not -always easy for us to discern what that greatest simplicity is, -which nature adopts in her laws. Accordingly, Galileo was led wrong -by this way of viewing the subject before he was led right. He at -first supposed, that the Velocity which the body had acquired at any -point must be proportional to the _Space_ described from the point -where the motion began. This false law is as simple in its -enunciation as the true law, that the Velocity is proportional to -the _Time_: it had been asserted as the true law by M. Varro (_De -Motu Tractatus_, Genevæ, 1584), and by Baliani, a gentleman of -Genoa, who published it in 1638. It was, however, soon rejected by -Galileo, though it was afterwards taken up and defended by Casræus, -one of Galileo's opponents. It so happens, indeed, that the false -law is not only at variance with fact, but with itself: it involves -a mathematical self-contradiction. This circumstance, however, was -accidental: it would be easy to state laws of the increase of -velocity which should be simple, and yet false in fact, though quite -possible in their own nature. {327} - -The Law of Velocity was hitherto, as we have seen, treated as a law -of phenomena, without reference to the Causes of the law. "The cause -of the acceleration of the motions of falling bodies is not," -Galileo observes, "a necessary part of the investigation. Opinions -are different. Some refer it to the approach to the centre; others -say that there is a certain extension of the centrical medium, -which, closing behind the body, pushes it forwards. For the present, -it is enough for us to demonstrate certain properties of Accelerated -Motion, the acceleration being according to the very simple Law, -that the Velocity is proportional to the Time. And if we find that -the properties of such motion are verified by the motions of bodies -descending freely, we may suppose that the assumption agrees with -the laws of bodies falling freely by the action of gravity."[14\6] - -[Note 14\6: Gal. _Op._ iii. 91, 92.] - -It was, however, an easy step to conceive this acceleration as -caused by the continual action of Gravity. This account had already -been given by Benedetti, as we have seen. When it was once adopted, -Gravity was considered as a _constant_ or _uniform_ force; on this -point, indeed, the adherents of the law of Galileo and of that of -Casræus were agreed; but the question was, what _is_ a Uniform -Force? The answer which Galileo was led to give was obviously -this;--_that_ is a Uniform Force which generates equal velocities in -equal successive times; and this principle leads at once to the -doctrine, that Forces are to be compared by comparing the Velocities -generated by them in equal times. - -Though, however, this was a consequence of the rule by which Gravity -is represented as a Uniform Force, the subject presents some -difficulty at first sight. It is not immediately obvious that we may -thus measure forces by the Velocity _added_ in a given time, without -taking into account the velocity they have already. If we -communicate velocity to a body by the hand or by a spring, the -effect we produce in a second of time is lessened, when the body has -already a velocity which withdraws it from the pressure of the -agent. But it appears that this is not so in the case of gravity; -the velocity added in one second is the same, whatever downward -motion the body already possesses. A body falling from rest acquires -a velocity, in one second, of thirty-two feet; and if a cannon-ball -were shot downwards with a velocity of 1000 feet a second, it would -equally, at the end of one second, have received an accession of 32 -feet to its velocity. - -This conception of Gravity as a Uniform Force,--as constantly and -{328} equally _increasing_ the velocity of a descending body,--will -become clear by a little attention; but it undoubtedly presents -difficulty at first. Accordingly, we find that Descartes did not -accept it. "It is certain," he says, "that a stone is not equally -disposed to receive a new motion or increase of velocity when it is -already moving very quickly, and when it is moving slowly." - -Descartes showed, by other expressions, that he had not caught hold -of the true notion of accelerating force. Thus, he says in a letter -to Mersenne, "I am astonished at what you tell me, of having found, -by experiment, that bodies thrown up in the air take neither more -nor less time to rise than to fall again; and you will excuse me if -I say that I look upon the experiment as a very difficult one to -make accurately." Yet it is clear from the Notion of a Constant -Force that (omitting the resistance of the air) this equality must -take place; for the Force which will gradually destroy the whole -velocity in a certain time in ascending, will, in the same time, -generate again the same velocity by the same gradations inverted; -and therefore the same space will be passed over in the same time in -the descent and in the ascent. - -Another difficulty arose from a necessary consequence of the Laws of -Falling Bodies thus established;--the proposition, namely, that in -acquiring its motion, a body passes through every intermediate degree -of velocity, from the smallest conceivable, up to that which it at -last acquires. When a body falls from rest, it begins to fall with -_no_ velocity; the velocity increases with the time; and in -one-thousandth part of a second, the body has only acquired -one-thousandth part of the velocity which it has at the end of one -second. - -This is certain, and manifest on consideration; yet there was at first -much difficulty raised on the subject of this assertion; and disputes -took place concerning the velocity with which a body _begins_ to fall. -On this subject also Descartes did not form clear notions. He writes -to a correspondent, "I have been revising my notes on Galileo, in -which I have not said expressly that falling bodies do not pass -through every degree of slowness, but I said that this cannot be known -without knowing what Weight is, which comes to the same thing; as to -your example, I grant that it proves that every degree of velocity is -infinitely divisible, but not that a falling body actually passes -through all these divisions." - -The Principles of the Motion of Falling Bodies being thus established -by Galileo, the Deduction of the principal mathematical consequences -was, as is usual, effected with great rapidity, and is to be found -{329} in his works, and in those of his scholars and successors. The -motion of bodies falling freely was, however, in such treatises, -generally combined with the motion of bodies Falling along Inclined -Planes; a part of the theory of which we have still to speak. - -The Notion of Accelerating Force and of its operation, once formed, -was naturally applied in other cases than that of bodies falling -freely. The different velocities with which heavy and light bodies -fall were explained by the different resistance of the air, which -diminishes the accelerating force;[15\6] and it was boldly asserted, -that in a vacuum a lock of wool and a piece of lead would fall equally -quickly. It was also maintained[16\6] that any falling body, however -large and heavy, would always have its velocity in some degree -diminished by the air in which it falls, and would at last be reduced -to a state of uniform motion, as soon as the resistance upwards became -equal to the accelerating force downwards. Though the law of progress -of a body to this limiting velocity was not made out till the -_Principia_ of Newton appeared, the views on which Galileo made this -assertion are perfectly sound, and show that he had clearly conceived -the nature and operation of accelerating and retarding force. - -[Note 15\6: Galileo, iii. 43.] - -[Note 16\6: iii. 54.] - -When Uniform Accelerating Forces had once been mastered, there -remained only mathematical difficulties in the treatment of Variable -Forces. A Variable Force was measured by the _Limit_ of the -increment of the Velocity, compared with the increment of the Time; -just as a Variable Velocity was measured by the Limit of the -increment of the Space compared with that of the Time. - -With this introduction of the Notion of Limits, we are, of course, led -to the Higher Geometry, either in its geometrical or its analytical -form. The general laws of bodies falling by the action of any Variable -Forces were given by Newton in the Seventh Section of the _Principia_. -The subject is there, according to Newton's preference of geometrical -methods, treated by means of the Quadrature of Curves; the Doctrine of -Limits being exhibited in a peculiar manner in the First Section of -the work, in order to prepare the way for such applications of it. -Leibnitz, the Bernouillis, Euler, and since their time, many other -mathematicians, have treated such questions by means of the analytical -method of limits, the Differential Calculus. The Rectilinear Motion of -bodies acted upon by variable forces is, of course, a simpler problem -than their Curvilinear Motion, to which we have now to proceed. But it -{330} may be remarked that Newton, having established the laws of -Curvilinear Motion independently, has, in a great part of his Seventh -Section, deduced the simpler case of the Rectilinear Motion from the -move complex problem, by reasonings of great ingenuity and beauty. - - -_Sect._ 3.--_Establishment of the Second Law of Motion.--Curvilinear -Motions._ - -A SLIGHT degree of distinctness in men's mechanical notions enabled -them to perceive, as we have already explained, that a body which -traces a curved line must be urged by some force, by which it is -constantly made to deviate from that rectilinear path, which it -would pursue if acted upon by no force. Thus, when a body is made to -describe a circle, as when a stone is whirled round in a sling, we -find that the string does exert such a force on the stone; for the -string is stretched by the effort, and if it be too slender, it may -thus be broken. This _centrifugal force_ of bodies moving in circles -was noticed even by the ancients. The effect of force to produce -curvilinear motion also appears in the paths described by -projectiles. We have already seen that though Tartalea did not -perceive this correctly, Rivius, about the same time, did. - -To see that a transverse force would produce a curve, was one step; -to determine what the curve is, was another step, which involved the -discovery of the Second Law of Motion. This step was made by -Galileo. In his _Dialogues on Motion_, he asserts that a body -projected horizontally will retain a uniform motion in the -horizontal direction, and will have, compounded with this, a -uniformly accelerated motion downwards, that is, the motion of a -body falling vertically from rest; and will thus describe the curve -called a parabola. - -The Second Law of Motion consists of this assertion in a general -form;--namely, that in all cases the motion which the force will -produce is compounded with the motion which the body previously has. -This was not obvious; for Cardan had maintained,[17\6] that "if a -body is moved by two motions at once, it will come to the place -resulting from their composition slower than by either of them." The -proof of the truth of the law to Galileo's mind was, so far as we -collect from the Dialogue itself, the simplicity of the supposition, -and his clear perception of the causes which, in some cases, -produced an obvious deviation in practice {331} from this -theoretical result. For it may be observed, that the curvilinear -paths ascribed to military projectiles by Rivius and Tartalea, and -by other writers who followed them, as Digges and Norton in our own -country, though utterly different from the theoretical form, the -parabola, do, in fact, approach nearer the true paths of a cannon or -musket ball than a parabola would do; and this approximation more -especially exists in that which at first sight appears most absurd -in the old theory; namely, the assertion that the ball, which -ascends in a sloping direction, finally descends vertically. In -consequence of the resistance of the air, this is really the path of -a projectile; and when the velocity is very great, as in military -projectiles, the deviation from the parabolic form is very manifest. -This cause of discrepancy between the theory, which does not take -resistance into the account, and the fact, Galileo perceived; and -accordingly he says,[18\6] that the velocities of the projectiles, -in such cases, may be considered as excessive and supernatural. With -the due allowance to such causes, he maintained that his theory was -verified, and might be applied in practice. Such practical -applications of the doctrine of projectiles no doubt had a share in -establishing the truth of Galileo's views. We must not forget, -however, that the full establishment of this second law of motion -was the result of the theoretical and experimental discussions -concerning the motion of the earth: its fortunes were involved in -those of the Copernican system; and it shared the triumph of that -doctrine. This triumph was already decisive, indeed, in the time of -Galileo, but not complete till the time of Newton. - -[Note 17\6: _Op._ vol. iv. p. 490.] - -[Note 18\6: _Op._ vol. iii. p. 147.] - - -_Sect._ 4.--_Generalization of the Laws of Equilibrium.--Principle -of Virtual Velocities._ - -IT was known, even as early as Aristotle, that the two weights which -balance each other on the lever, if they move at all, move with -velocities which are in the inverse proportions of the weights. The -peculiar resources of the Greek language, which could state this -relation of inverse proportionality in a single word (ἀντιπέπονθεν), -fixed it in men's minds, and prompted them to generalize from this -property. Such attempts were at first made with indistinct ideas, -and on conjecture only, and had, therefore, no scientific value. -This is the judgment which we must pass on the book of Jordanus -Nemorarius, which {332} we have already mentioned. Its reasonings -are professedly on Aristotelian principles, and exhibit the common -Aristotelian absence of all distinct mechanical ideas. But in Varro, -whose _Tractatus de Motu_ appeared in 1584, we find the principle, -in a general form, not satisfactorily proved, indeed, but much more -distinctly conceived. This is his first theorem: "Duarum virium -connexarum quarum (si moveantur) motus erunt ipsis ἀντιπεπονθῶς -proportionales, neutra alteram movebit, sed equilibrium facient." -The proof offered of this is, that the resistance to a force is as -the motion produced; and, as we have seen, the theorem is rightly -applied in the example of the wedge. From this time it appears to -have been usual to prove the properties of machines by means of this -principle. This is done, for instance, in _Les Raisons des Forces -Mouvantes_, the production of Solomon de Caus, engineer to the -Elector Palatine, published at Antwerp in 1616; in which the effect -of Toothed-Wheels and of the Screw is determined in this manner, but -the Inclined Plane is not treated of. The same is the case in Bishop -Wilkins's _Mathematical Magic_, in 1648. - -When the true doctrine of the Inclined Plane had been established, -the laws of equilibrium for all the simple machines or Mechanical -Powers, as they had usually been enumerated in books on Mechanics, -were brought into view; for it was easy to see that the _Wedge_ and -the _Screw_ involved the same principle as the _Inclined Plane_, and -the _Pulley_ could obviously be reduced to the _Lever_. It was, -also, not difficult for a person with clear mechanical ideas to -perceive how any other combination of bodies, on which pressure and -traction are exerted, may be reduced to these simple machines, so as -to disclose the relation of the forces. Hence by the discovery of -Stevinus, all problems of equilibrium were essentially solved. - -The conjectural generalization of the property of the lever, which -we have just mentioned, enabled mathematicians to express the -solution of all these problems by means of one proposition. This was -done by saying, that in raising a weight by any machine, we _lose_ -in Time what we _gain_ in Force; the weight raised moves as much -_slower_ than the power, as it is _larger_ than the power. This was -explained with great clearness by Galileo, in the preface to his -_Treatise on Mechanical Science_, published in 1592. - -The motions, however, which we here suppose the parts of the machine -to have, are not motions which the forces produce; for at present we -are dealing with the case in which the forces balance each other, -and therefore produce no motion. But we ascribe to the {333} Weights -and Powers hypothetical motions, arising from some other cause; and -then, by the construction of the machine, the velocities of the -Weights and Powers must have certain definite ratios. These -velocities, being thus hypothetically supposed and not actually -produced, are called _Virtual_ Velocities. And the general law of -equilibrium is, that in any machine, the Weights which balance each -other, are reciprocally to each other as their Virtual Velocities. -This is called the _Principle of Virtual Velocities_. - -This Principle (which was afterwards still further generalized) is, -by some of the admirers of Galileo, dwelt upon as one of his great -services to Mechanics. But if we examine it more nearly, we shall -see that it has not much importance in our history. It is a -generalization, but a generalization established rather by -enumeration of cases, than by any induction proceeding upon one -distinct Idea, like those generalizations of Facts by which Laws are -primarily established. It rather serves verbally to conjoin Laws -previously known, than to exhibit a connection in them: it is rather -a help for the memory than a proof for the reason. - -The Principle of Virtual Velocities is so far from implying any -clear possession of mechanical ideas, that any one who knows the -property of the Lever, whether he is capable of seeing the reason -for it or not, can see that the greater weight moves slower in the -exact proportion of its greater magnitude. Accordingly, Aristotle, -whose entire want of sound mechanical views we have shown, has yet -noticed this truth. When Galileo treats of it, instead of offering -any reasons which could independently establish this principle, he -gives his readers a number of analogies and illustrations, many of -them very loose ones. Thus the raising a great weight by a small -force, he illustrates by supposing the weight broken into many small -parts, and conceiving those parts raised one by one. By other -persons, the analogy, already intimated, of gain and loss is -referred to as an argument for the principle in question. Such -images may please the fancy, but they cannot be accepted as -mechanical reasons. - -Since Galileo neither first enunciated this rule, nor ever proved it -as an independent principle of Mechanics, we cannot consider the -discovery of it as one of his mechanical achievements. Still less -can we compare his reference to this principle with Stevinus's proof -of the Inclined Plane; which, as we have seen, was rigorously -inferred from the sound axiom, that a body cannot put itself in -motion. If we were to assent to the really self-evident axioms of -Stevinus, only in virtue {334} of the unproved verbal generalization -of Galileo, we should be in great danger of allowing ourselves to be -referred successively from one truth to another, without any -reasonable hope of ever arriving at any thing ultimate and -fundamental. - -But though this Principle of Virtual Velocity cannot be looked upon -as a great discovery of Galileo, it is a highly useful rule; and the -various forms under which he and his successors urged it, tended -much to dissipate the vague wonder with which the effects of -machines had been looked upon; and thus to diffuse sounder and -clearer notions on such subjects. - -The Principle of Virtual Velocities also affected the progress of -mechanical science in another way: it suggested some of the -analogies by the aid of which the Third Law of Motion was made out; -leading to the adoption of the notion of _Momentum_ as the -arithmetical product of weight and velocity. Since on a machine on -which a weight of two pounds at one part balances three pounds at -another part, the former weight would move through three inches -while the latter would move through two inches; we see (since three -multiplied into two is equal to two multiplied into three) that the -_Product_ of the weight and the velocity is the same for the two -balancing weights; and if we call this Product _Momentum_, the Law -of Equilibrium is, that when two weights balance on a machine, the -Momentum of the two would be the same, if they were put in motion. - -The Notion of Momentum was here employed in connection with Virtual -Velocities; but it also came under consideration in treating of -Actual Velocities, as we shall soon see. - - -_Sect._ 5.--_Attempts at the Third Law of Motion.--Notion of -Momentum._ - -IN the questions we have hitherto had to consider respecting Motion, -no regard is had to the Size of the body moved, but only to the -Velocity and Direction of the motion. We must now trace the progress -of knowledge respecting the mode in which the Mass of the body -influences the effect of Force. This is a more difficult and complex -branch of the subject; but it is one which requires to be noticed, -as obviously as the former. Questions belonging to this department -of Mechanics, as well as to the others, occur in Aristotle's -Mechanical Problems. "Why," says he, "is it, that neither very small -nor very large bodies go far when we throw them; but, in order that -this may {335} happen, the thing thrown must have a certain -proportion to the agent which throws it? Is it that what is thrown -or pushed must react[19\6] against that which pushes it; and that a -body so large as not to yield at all, or so small as to yield -entirely, and not to react, produces no throw or push?" The same -confusion of ideas prevailed after his time; and mechanical -questions were in vain discussed by means of general and abstract -terms, employed with no distinct and steady meaning; such as -_impetus_, _power_, _momentum_, _virtue_, _energy_, and the like. -From some of these speculations we may judge how thorough the -confusion in men's heads had become. Cardan perplexes himself with -the difficulty, already mentioned, of the comparison of the forces -of bodies at rest and in motion. If the Force of a body depends on -its velocity, as it appears to do, how is it that a body at rest has -any Force at all, and how can it resist the slightest effort, or -exert any pressure? He flatters himself that he solves the question, -by asserting that bodies at rest have an occult motion. "Corpus -movetur occulto motu quiescendo."--Another puzzle, with which he -appears to distress himself rather more wantonly, is this: "If one -man can draw half of a certain weight, and another man also one -half; when the two act together, these proportions should be -compounded; so that they ought to be able to draw one half of one -half, or one quarter only." The talent which ingenious men had for -getting into such perplexities, was certainly at one time very -great. Arriaga,[20\6] who wrote in 1639, is troubled to discover how -several flat weights, lying one upon another on a board, should -produce a greater pressure than the lowest one alone produces, since -that alone touches the board. Among other solutions, he suggests -that the board affects the upper weight, which it does not touch, by -determining its _ubication_, or _whereness_. - -[Note 19\6: ἀντερείδειν.] - -[Note 20\6: Rod. de Arriaga, _Cursus Philosophicus_. Paris, 1639.] - -Aristotle's doctrine, that a body ten times as heavy as another, -will fall ten times as fast, is another instance of the confusion of -Statical and Dynamical Forces: the Force of the greater body, while -_at rest_, is ten times as great as that of the other; but the Force -as measured by the _velocity_ produced, is equal in the two cases. -The two bodies would fall downwards with the same rapidity, except -so far as they are affected by accidental causes. The merit of -proving this by experiment, and thus refuting the Aristotelian -dogma, is usually ascribed to Galileo, who made his experiment from -the famous leaning tower of Pisa, about 1590. But others about the -same time had not {336} overlooked so obvious a fact--F. -Piccolomini, in his _Liber Scientiæ de Natura_, published at Padua, -in 1597, says, "On the subject of the motion of heavy and light -bodies, Aristotle has put forth various opinions, which are contrary -to sense and experience, and has delivered rules concerning the -proportion of quickness and slowness, which are palpably false. For -a stone twice as great does _not_ move twice as fast." And Stevinus, -in the Appendix to his Statics, describes his having made the -experiment, and speaks with great correctness of the apparent -deviations from the rule, arising from the resistance of the air. -Indeed, the result followed by very obvious reasoning; for ten -bricks, in contact with each other, side by side, would obviously -fall in the same time as one; and these might be conceived to form a -body ten times as large as one of them. Accordingly, Benedetti, in -1585, reasons in this manner with regard to bodies of different -size, though he retains Aristotle's error as to the different -velocity of bodies of different density. - -The next step in this subject is more clearly due to Galileo; he -discovered the true proportion which the Accelerating Force of a -body falling down an inclined plane bears to the Accelerating Force -of the same body falling freely. This was at first a happy -conjecture; it was then confirmed by experiments, and, finally, -after some hesitation, it was referred to its true principle, the -Third Law of Motion, with proper elementary simplicity. The -Principle here spoken of is this:--that for the same body, the -Dynamical effect of force is as the Statical effect; that is, the -Velocity which any force generates in a given time when it puts the -body in motion, is proportional to the Pressure which the same force -produces in a body at rest. The Principle, so stated, appears very -simple and obvious; yet this was not the form in which it suggested -itself either to Galileo or to other persons who sought to prove it. -Galileo, in his _Dialogues on Motion_, assumes, as his fundamental -proposition on this subject, one much less evident than that we have -quoted, but one in which that is involved. His Postulate is,[21\6] -that when the same body falls down different planes of the same -height, the velocities acquired are equal. He confirms and -illustrates this by a very ingenious experiment on a pendulum, -showing that the weight swings to the same height whatever path it -be compelled to follow. Torricelli, in his treatise published 1644, -says that he had heard that Galileo had, towards the end of his -life, proved his {337} assumption, but that, not having seen the -proof, he will give his own. In this he refers us to the right -principle, but appears not distinctly to conceive the proof, since -he estimates _momentum_ indiscriminately by the statical Pressure of -a body, and by its Velocity when in motion; as if these two -quantities were self-evidently equal. Huyghens, in 1673, expresses -himself dissatisfied with the proof by which Galileo's assumption -was supported in the later editions of his works. His own proof -rests on this principle;--that if a body fall down one inclined -plane, and proceed up another with the velocity thus acquired, it -cannot, under any circumstances, ascend to a higher position than -that from which it fell. This principle coincides very nearly with -Galileo's experimental illustration. In truth, however, Galileo's -principle, which Huyghens thus slights, may be looked upon as a -satisfactory statement of the true law namely, that, in the same -body, the velocity produced is as the pressure which produces it. -"We are agreed," he says,[22\6] "that, in a movable body, the -_impetus_, _energy_, _momentum_, or _propension to motion_, is as -great as is the _force_ or _least resistance_ which suffices to -_support_ it." The various terms here used, both for dynamical and -statical Force, show that Galileo's ideas were not confused by the -ambiguity of any one term, as appears to have happened to some -mathematicians. The principle thus announced, is, as we shall see, -one of great extent and value; and we read with interest the -circumstances of its discovery, which are thus narrated.[23\6] When -Viviani was studying with Galileo, he expressed his dissatisfaction -at the want of any clear reason for Galileo's postulate respecting -the equality of velocities acquired down inclined planes of the same -heights; the consequence of which was, that Galileo, as he lay, the -same night, sleepless through indisposition, discovered the proof -which he had long sought in vain, and introduced it in the -subsequent editions. It is easy to see, by looking at the proof, -that the discoverer had had to struggle, not for intermediate steps -of reasoning between remote notions, as in a problem of geometry, -but for a clear possession of ideas which were near each other, and -which he had not yet been able to bring into contact, because he had -not yet a sufficiently firm grasp of them. Such terms as Momentum -and Force had been sources of confusion from the time of Aristotle; -and it required considerable steadiness of thought to compare the -forces of bodies at rest and in motion under the obscurity and -vacillation thus produced. {338} - -[Note 21\6: _Opere_, iii. 96.] - -[Note 22\6: Galileo, _Op._ iii. 104.] - -[Note 23\6: Drinkwater, _Life of Galileo_, p. 59.] - -The term _Momentum_ had been introduced to express the force of -bodies in motion, before it was known what that effect was. Galileo, -in his _Discorso intorno alle Cose che stanno in su l' Acqua_, says, -that "Momentum is the force, efficacy, or virtue, with which the -motion moves and the body moved resists, depending not upon weight -only, but upon the velocity, inclination, and any other cause of -such virtue." When he arrived at more precision in his views, he -determined, as we have seen, that, in the same body, the Momentum is -_proportional_ to the Velocity; and, hence it was easily seen that -in different bodies it was proportional to the Velocity and Mass -jointly. The principle thus enunciated is capable of very extensive -application, and, among other consequences, leads to a determination -of the results of the mutual Percussion of Bodies. But though -Galileo, like others of his predecessors and contemporaries, had -speculated concerning the problem of Percussion, he did not arrive -at any satisfactory conclusion; and the problem remained for the -mathematicians of the next generation to solve. - -We may here notice Descartes and his Laws of Motion, the publication -of which is sometimes spoken of as an important event in the history -of Mechanics. This is saying far too much. The _Principia_ of -Descartes did little for physical science. His assertion of the Laws -of Motion, in their most general shape, was perhaps an improvement -in form; but his Third Law is false in substance. Descartes claimed -several of the discoveries of Galileo and others of his -contemporaries; but we cannot assent to such claims, when we find -that, as we shall see, he did not understand, or would not apply, -the Laws of Motion when he had them before him. If we were to -compare Descartes with Galileo, we might say, that of the mechanical -truths which were easily attainable in the beginning of the -seventeenth century, Galileo took hold of as many, and Descartes of -as few, as was well possible for a man of genius. - -[2d Ed.] [The following remarks of M. Libri appear to be just. After -giving an account of the doctrines put forth on the subject of -Astronomy, Mechanics, and other branches of science, by Leonardo da -Vinci, Fracastoro, Maurolycus, Commandinus, Benedetti, he adds -(_Hist. des Sciences Mathématiques en Italie_, t. iii. p. 131): -"This short analysis is sufficient to show that, at the period at -which we are arrived, Aristotle no longer reigned unquestioned in -the Italian Schools. If we had to write the history of philosophy, -we should prove by a multitude of facts that it was the Italians who -overthrew the ancient idol of philosophers. Men go on incessantly -repeating that the {339} struggle was begun by Descartes, and they -proclaim him the legislator of modern philosophers. But when we -examine the philosophical writings of Fracastoro, of Benedetti, of -Cardan, and above all, those of Galileo; when we see on all sides -energetic protests raised against the peripatetic doctrines; we ask, -what there remained for the inventor of vortices to do, in -overturning the natural philosophy of Aristotle? In addition to -this, the memorable labors of the School of Cosenza, of Telesius, of -Giordano Bruno, of Campanella; the writings of Patricius, who was, -besides, a good geometer; of Nizolius, whom Leibnitz esteemed so -highly, and of the other metaphysicians of the same epoch,--prove -that the ancient philosophy had already lost its empire on that side -the Alps, when Descartes threw himself upon the enemy now put to the -rout. The yoke was cast off in Italy, and all Europe had only to -follow the example, without its being necessary to give a new -impulse to real science." - -In England, we are accustomed to hear Francis Bacon, rather than -Descartes, spoken of as the first great antagonist of the -Aristotelian schools, and the legislator of modern philosophy. But -it is true, both of one and the other, that the overthrow of the -ancient system had been effectively begun before their time by the -practical discoverers here mentioned, and others who, by experiment -and reasoning, established truths inconsistent with the received -Aristotelian doctrines. Gilbert in England, Kepler in Germany, as -well as Benedetti and Galileo in Italy, gave a powerful impulse to -the cause of real knowledge, before the influence of Bacon and -Descartes had produced any general effect. What Bacon really did was -this;--that by the august image which he presented of a future -Philosophy, the rival of the Aristotelian, and far more powerful and -extensive, he drew to it the affections and hopes of all men of -comprehensive and vigorous minds, as well as of those who attended -to special trains of discovery. He announced a New Method, not -merely a correction of special current errors; he thus converted the -Insurrection into a Revolution, and established a new philosophical -Dynasty. Descartes had, in some degree, the same purpose; and, in -addition to this, he not only proclaimed himself the author of a New -Method, but professed to give a complete system of the results of -the Method. His physical philosophy was put forth as complete and -demonstrative, and thus involved the vices of the ancient dogmatism. -Telesius and Campanella had also grand notions of an entire reform -in the method of philosophizing, as I have noticed in the -_Philosophy of the Inductive Sciences_, Book xii.] {340} - - - - -CHAPTER III. - -SEQUEL TO THE EPOCH OF GALILEO.--PERIOD OF VERIFICATION AND -DEDUCTION. - - -THE evidence on which Galileo rested the truth of the Laws of Motion -which he asserted, was, as we have seen, the simplicity of the laws -themselves, and the agreement of their consequences with facts; -proper allowances being made for disturbing causes. His successors -took up and continued the task of making repeated comparisons of the -theory with practice, till no doubt remained of the exactness of the -fundamental doctrines: they also employed themselves in simplifying, -as much as possible, the mode of stating these doctrines, and in -tracing their consequences in various problems by the aid of -mathematical reasoning. These employments led to the publication of -various Treatises on Falling Bodies, Inclined Planes, Pendulums, -Projectiles, Spouting Fluids, which occupied a great part of the -seventeenth century. - -The authors of these treatises may be considered as the School of -Galileo. Several of them were, indeed, his pupils or personal -friends. Castelli was his disciple and astronomical assistant at -Florence, and afterwards his correspondent. Torricelli was at first -a pupil of Castelli, but became the inmate and amanuensis of Galileo -in 1641, and succeeded him in his situation at the court of Florence -on his death, which took place a few months afterwards. Viviani -formed one of his family during the three last years of his life; -and surviving him and his contemporaries (for Viviani lived even -into the eighteenth century), has a manifest pleasure and pride in -calling himself the last of the disciples of Galileo. Gassendi, an -eminent French mathematician and professor, visited him in 1628; and -it shows us the extent of his reputation when we find Milton -referring thus to his travels in Italy:[24\6] "There it was that I -found and visited the famous Galileo, grown old, a prisoner in the -Inquisition, for thinking in astronomy otherwise than the Franciscan -and Dominican licensers thought." - -[Note 24\6: _Speech for the Liberty of Unlicensed Printing._] - -Besides the above writers, we may mention, as persons who pursued and -illustrated Galileo's doctrines, Borelli, who was professor at -Florence and Pisa; Mersenne, the correspondent of Descartes, who was -{341} professor at Paris; Wallis, who was appointed Savilian professor -at Oxford in 1649, his predecessor being ejected by the parliamentary -commissioners. It is not necessary for us to trace the progress of -purely mathematical inventions, which constitute a great part of the -works of these authors; but a few circumstances may be mentioned. - -The question of the proof of the Second Law of Motion was, from the -first, identified with the controversy respecting the truth of the -Copernican System; for this law supplied the true answer to the most -formidable of the objections against the motion of the earth; -namely, that if the earth were moving, bodies which were dropt from -an elevated object would be left behind by the place from which they -fell. This argument was reproduced in various forms by the opponents -of the new doctrine; and the answers to the argument, though they -belong to the history of Astronomy, and form part of the Sequel to -the Epoch of Copernicus, belong more peculiarly to the history of -Mechanics, and are events in the sequel to the Discoveries of -Galileo. So far, indeed, as the mechanical controversy was -concerned, the advocates of the Second Law of Motion appealed, very -triumphantly, to experiment. Gassendi made many experiments on this -subject publicly, of which an account is given in his _Epistolæ tres -de Motu Impresso a Motore Translato_[25\6] It appeared in these -experiments, that bodies let fall downwards, or cast upwards, -forwards, or backwards, from a ship, or chariot, or man, whether at -rest, or in any degree of motion, had always the same motion -relatively to the _motor_. In the application of this principle to -the system of the world, indeed, Gassendi and other philosophers of -his time were greatly hampered; for the deference which religious -scruples required, did not allow them to say that the earth really -moved, but only that the physical reasons against its motion were -invalid. This restriction enabled Riccioli and other writers on the -geocentric side to involve the subject in metaphysical difficulties; -but the conviction of men was not permanently shaken by these, and -the Second Law of Motion was soon assumed as unquestioned. - -[Note 25\6: Mont. ii. 199.] - -The Laws of the Motion of Falling Bodies, as assigned by Galileo, -were confirmed by the reasonings of Gassendi and Fermat, and the -experiments of Riccioli and Grimaldi; and the effect of resistance -was pointed out by **Mersenne and Dechales. The parabolic motion of -Projectiles was more especially illustrated by experiments on the -jet which spouts from an orifice in a vessel full of fluid. This -mode of experimenting {342} is well adapted to attract notice, since -the curve described, which is transient and invisible in the case of -a single projectile, becomes permanent and visible when we have a -continuous stream. The doctrine of the motions of fluids has always -been zealously cultivated by the Italians. Castelli's treatise, -_Della Misura dell' Acque Corrente_ (1638), is the first work on -this subject, and Montucla with justice calls him "the creator of a -new branch of hydraulics;"[26\6] although he mistakenly supposed the -velocity of efflux to be as the depth of the orifice from the -surface. **Mersenne and Torricelli also pursued this subject, and -after them, many others. - -[Note 26\6: Mont. ii. 201.] - -Galileo's belief in the near approximation of the curve described by -a cannon-ball or musket-ball to the theoretical parabola, was -somewhat too obsequiously adopted by succeeding practical writers on -artillery. They underrated, as he had done, the effect of the -resistance of the air, which is in effect so great as entirely to -change the form and properties of the curve. Notwithstanding this, -the parabolic theory was employed, as in Anderson's _Art of Gunnery_ -(1674); and Blondel, in his _Art de jeter les Bombes_ (1688), not -only calculated Tables on this supposition, but attempted to answer -the objections which had been made respecting the form of the curve -described. It was not till a later period (1740), when Robins made a -series of careful and sagacious experiments on artillery, and when -some of the most eminent mathematicians calculated the curve, taking -into account the resistance, that the Theory of Projectiles could be -said to be verified in fact. - -The Third Law of Motion was still in some confusion when Galileo died, -as we have seen. The next great step made in the school of Galileo was -the determination of the Laws of the motions of bodies in their Direct -Impact, so far as this impact affects the motion of translation. The -difficulties of the problem of Percussion arose, in part, from the -heterogeneous nature of Pressure (of a body at rest), and Momentum (of -a body in motion); and, in part, from mixing together the effects of -percussion on the parts of a body, as, for instance, cutting, -bruising, and breaking, with its effect in moving the whole. - -The former difficulty had been seen with some clearness by Galileo -himself. In a posthumous addition to his _Mechanical Dialogues_, he -says, "There are two kinds of resistance in a movable body, one -internal, as when we say it is more difficult to lift a weight of a -thousand pounds than a weight of a hundred; another respecting -space, as {343} when we say that it requires more force to throw a -stone one hundred paces than fifty."[27\6] Reasoning upon this -difference, he comes to the conclusion that "the Momentum of -percussion is infinite, since there is no resistance, however great, -which is not overcome by a force of percussion, however -small."[28\6] He further explains this by observing that the -resistance to percussion must occupy some portion of time, although -this portion may be insensible. This correct mode of removing the -apparent incongruity of continuous and instantaneous force, was a -material step in the solution of the problem. - -[Note 27\6: _Op._ iii. 210.] - -[Note 28\6: iii. 211.] - -The Laws of the mutual Impact of bodies were erroneously given by -Descartes in his _Principia_; and appear to have been first -correctly stated by Wren, Wallis, and Huyghens, who about the same -time (1669) sent papers to the Royal Society of London on the -subject. In these solutions, we perceive that men were gradually -coming to apprehend the Third Law of Motion in its most general -sense; namely, that the Momentum (which is proportional to the Mass -of the body and its Velocity jointly) may be taken for the measure -of the effect; so that this Momentum is as much diminished in the -striking body by the resistance it experiences, as it is increased -in the body struck by the Impact. This was sometimes expressed by -saying that "the Quantity of Motion remains unaltered," _Quantity of -Motion_ being used as synonymous with _Momentum_. Newton expressed -it by saying that "Action and Reaction are equal and opposite," -which is still one of the most familiar modes of expressing the -Third Law of Motion. - -In this mode of stating the Law, we see an example of a propensity -which has prevailed very generally among mathematicians; namely, a -disposition to present the fundamental laws of rest and of motion as -if they were equally manifest, and, indeed, identical. The close -analogy and connection which exists between the principles of -equilibrium and of motion, often led men to confound the evidence of -the two; and this confusion introduced an ambiguity in the use of -words, as we have seen in the case of Momentum, Force, and others. -The same may be said of _Action_ and _Reaction_, which have both a -statical and a dynamical signification. And by this means, the most -general statements of the laws of motion are made to coincide with -the most general statical propositions. For instance, Newton deduced -from his principles the conclusion, that by the mutual action of -bodies, the motion of their centre of gravity cannot be affected. -Marriotte, in his _Traité de la_ {344} _Percussion_ (1684), had -asserted this proposition for the case of direct impact. But by the -reasoners of Newton's time, the dynamical proposition, that the -motion of the centre of gravity is not altered by the actual free -motion and impact of bodies, was associated with the statical -proposition, that when bodies are in equilibrium, the centre of -gravity cannot be made to ascend or descend by the _virtual_ motions -of the bodies. This latter is a proposition which was assumed as -self-evident by Torricelli; but which may more philosophically be -proved from elementary statical principles. - -This disposition to identify the elementary laws of equilibrium and -of motion, led men to think too slightingly of the ancient solid and -sufficient foundation of Statics, the doctrine of the lever. When -the progress of thought had opened men's minds to a more general -view of the subject, it was considered as a blemish in the science -to found it on the properties of one particular machine. Descartes -says in his Letters, that "it is ridiculous to prove the pulley by -means of the lever." And Varignon was led by similar reflections to -the project of his _Nouvelle Mécanique_, in which the whole of -statics should be founded on the composition of forces. This project -was published in 1687; but the work did not appear till 1725, after -the death of the author. Though the attempt to reduce the -equilibrium of all machines to the composition of forces, is -philosophical and meritorious, the attempt to reduce the composition -of Pressures to the composition of _Motions_, with which Varignon's -work is occupied, was a retrograde step in the subject, so far as -the progress of distinct mechanical ideas was concerned. - -Thus, at the period at which we have now arrived, the Principles of -Elementary Mechanics were generally known and accepted; and there -was in the minds of mathematicians a prevalent tendency to reduce -them to the most simple and comprehensive form of which they -admitted. The execution of this simplification and extension, which -we term the generalization of the laws, is so important an event, -that though it forms part of the natural sequel of Galileo, we shall -treat of it in a separate chapter. But we must first bring up the -history of the mechanics of fluids to the corresponding point. {345} - - - - -CHAPTER IV. - -DISCOVERY OF THE MECHANICAL PRINCIPLES OF FLUIDS. - - -_Sect._ 1.--_Rediscovery of the Laws of Equilibrium of Fluids._ - -WE have already said, that the true laws of the equilibrium of -fluids were discovered by Archimedes, and rediscovered by Galileo -and Stevinus; the intermediate time having been occupied by a -vagueness and confusion of thought on physical subjects, which made -it impossible for men to retain such clear views as Archimedes had -disclosed. Stevinus must be considered as the earliest of the -authors of this rediscovery; for his work (_Principles of Statik and -Hydrostatik_) was published in Dutch about 1585; and in this, his -views are perfectly distinct and correct. He restates the doctrines -of Archimedes, and shows that, as a consequence of them, it follows -that the pressure of a fluid on the bottom of a vessel may be much -greater than the weight of the fluid itself: this he proves, by -imagining some of the upper portions of the vessel to be filled with -fixed solid bodies, which take the place of the fluid, and yet do -not alter the pressure on the base. He also shows what will be the -pressure on any portion of a base in an oblique position; and hence, -by certain mathematical artifices which make an approach to the -Infinitesimal Calculus, he finds the whole pressure on the base in -such cases. This mode of treating the subject would take in a large -portion of our elementary Hydrostatics as the science now stands. -Galileo saw the properties of fluids no less clearly, and explained -them very distinctly, in 1612, in his _Discourse on Floating -Bodies_. It had been maintained by the Aristotelians, that _form_ -was the cause of bodies floating; and collaterally, that ice was -_condensed_ water; apparently from a confusion of thought between -_rigidity_ and _density_. Galileo asserted, on the contrary, that -ice is _rarefied_ water, as appears by its floating: and in support -of this, he proved, by various experiments, that the floating of -bodies does not depend on their form. The happy genius of Galileo is -the more remarkable in this case, as the controversy was a good deal -perplexed by the mixture of phenomena of another kind, due to what -is usually called _capillary_ or _molecular attraction_. Thus it is -a fact, that a _ball_ {346} of ebony sinks in water, while a _flat -slip_ of the same material lies on the surface; and it required -considerable sagacity to separate such cases from the general rule. -Galileo's opinions were attacked by various writers, as Nozzolini, -Vincenzio di Grazia, Ludovico delle Colombe; and defended by his -pupil Castelli, who published a reply in 1615. These opinions were -generally adopted and diffused; but somewhat later, Pascal pursued -the subject more systematically, and wrote his _Treatise of the -Equilibrium of Fluids_ in 1653; in which he shows that a fluid, -inclosed in a vessel, necessarily presses equally in all directions, -by imagining two _pistons_ or sliding plugs, applied at different -parts, the surface of one being centuple that of the other: it is -clear, as he observes, that the force of one man acting at the first -piston, will balance the force of one hundred men acting at the -other. "And thus," says he, "it appears that a vessel full of water -is a new Principle of Mechanics, and a new Machine which will -multiply force to any degree we choose." Pascal also referred the -equilibrium of fluids to the "principle of virtual velocities," -which regulates the equilibrium of other machines. This, indeed, -Galileo had done before him. It followed from this doctrine, that -the pressure which is exercised by the lower parts of a fluid arises -from the weight of the upper parts. - -In all this there was nothing which was not easily assented to; but -the extension of these doctrines to the air required an additional -effort of mechanical conception. The pressure of the air on all -sides of us, and its weight above us, were two truths which had -never yet been apprehended with any kind of clearness. Seneca, -indeed,[29\6] talks of the "gravity of the air," and of its power of -diffusing itself when condensed, as the causes of wind; but we can -hardly consider such propriety of phraseology in him as more than a -chance; for we see the value of his philosophy by what he -immediately adds: "Do you think that we have forces by which we move -ourselves, and that the air is left without any power of moving? -when even water has a motion of its own, as we see in the growth of -plants." We can hardly attach much value to such a recognition of -the gravity and elasticity of the air. - -[Note 29\6: _Quæst. Nat._ v. 5.] - -Yet the effects of these causes were so numerous and obvious, that -the Aristotelians had been obliged to invent a principle to account -for them; namely, "Nature's Horror of a Vacuum." To this principle -were referred many familiar phenomena, as suction, breathing, the -{347} action of a pair of bellows, its drawing water if immersed in -water, its refusing to open when the rent is stopped up. The action -of a cupping instrument, in which the air is rarefied by fire; the -fact that water is supported when a full inverted bottle is placed -in a basin; or when a full tube, open below and closed above, is -similarly placed; the running out of the water, in this instance, -when the top is opened; the action of a siphon, of a syringe, of a -pump; the adhesion of two polished plates, and other facts, were all -explained by the _fuga vacui_. Indeed, we must contend that the -principle was a very good one, inasmuch as it brought together all -these facts which are really of the same kind, and referred them to -a common cause. But when urged as an ultimate principle, it was not -only _unphilosophical_, but _imperfect_ and _wrong_. It was -_unphilosophical_, because it introduced the notion of an emotion, -Horror, as an account of physical facts; it was _imperfect_, because -it was at best only a law of phenomena, not pointing out any -physical cause; and it was _wrong_, because it gave an unlimited -extent to the effect. Accordingly, it led to mistakes. Thus -Mersenne, in 1644, speaks of a siphon which shall go over a -mountain, being ignorant then that the effect of such an instrument -was limited to a height of thirty-four feet. A few years later, -however, he had detected this mistake; and in his third volume, -published in 1647, he puts his siphon in his _emendanda_, and speaks -correctly of the weight of air as supporting the mercury in the tube -of Torricelli. It was, indeed, by finding this horror of a vacuum to -have a limit at the height of thirty-four feet, that the true -principle was suggested. It was discovered that when attempts were -made to raise water higher than this. Nature tolerated a vacuum -above the water which rose. In 1643, Torricelli tried to produce -this vacuum at a smaller height, by using, instead of water, the -heavier fluid, quicksilver; an attempt which shows that the true -explanation, the balance of the weight of the water by another -pressure, had already suggested itself. Indeed, this appears from -other evidence. Galileo had already taught that the air has weight; -and Baliani, writing to him in 1630, says,[30\6] "If we were in a -vacuum, the weight of the air above our heads would be felt." -Descartes also appears to have some share in this discovery; for, in -a letter of the date of 1631, he explains the suspension of mercury -in a tube, closed at top, by the pressure of the column of air -reaching to the clouds. {348} - -[Note 30\6: Drinkwater's _Galileo_, p. 90.] - -Still men's minds wanted confirmation in this view; and they found -such confirmation, when, in 1647, Pascal showed practically, that if -we alter the length of the superincumbent column of air by going to -a high place, we alter the weight which it will support. This -celebrated experiment was made by Pascal himself on a church-steeple -in Paris, the column of mercury in the Torricellian tube being used -to compare the weights of the air; but he wrote to his -brother-in-law, who lived near the high mountain of Puy de Dôme in -Auvergne, to request him to make the experiment there, where the -result would be more decisive. "You see," he says, "that if it -happens that the height of the mercury at the top of the hill be -less than at the bottom (which I have many reasons to believe, -though all those who have thought about it are of a different -opinion), it will follow that the weight and pressure of the air are -the sole cause of this suspension, and not the horror of a vacuum: -since it is very certain that there is more air to weigh on it at -the bottom than at the top; while we cannot say that nature abhors a -vacuum at the foot of a mountain more than on its summit."--M. -Perrier, Pascal's correspondent, made the observation as he had -desired, and found a difference of three inches of mercury, "which," -he says, "ravished us with admiration and astonishment." - -When the least obvious case of the operation of the pressure and -weight of fluids had thus been made out, there were no further -difficulties in the progress of the theory of Hydrostatics. When -mathematicians began to consider more general cases than those of -the action of gravity, there arose differences in the way of stating -the appropriate principles: but none of these differences imply any -different conception of the fundamental nature of fluid equilibrium. - - -_Sect._ 2.--_Discovery of the Laws of Motion of Fluids._ - -THE art of conducting water in pipes, and of directing its motion -for various purposes, is very old. When treated systematically, it -has been termed _Hydraulics_: but _Hydrodynamics_ is the general -name of the science of the laws of the motions of fluids, under -those or other circumstances. The Art is as old as the commencement -of civilization: the Science does not ascend higher than the time of -Newton, though attempts on such subjects were made by Galileo and -his scholars. - -When a fluid spouts from an orifice in a vessel, Castelli saw that -the velocity of efflux depends on the depth of the orifice below the -{349} surface: but he erroneously judged the velocity to be exactly -proportional to the depth. Torricelli found that the fluid, under -the inevitable causes of defect which occur in the experiment, would -spout nearly to the height of the surface: he therefore inferred, -that the full velocity is that which a body would acquire in falling -through the depth; and that it is consequently proportional to the -square root of the depth.--This, however, he stated only as a result -of experience, or law of phenomena, at the end of his treatise, _De -Motu Naturaliter Accelerato_, printed in 1643. - -Newton treated the subject theoretically in the _Principia_ (1687); -but we must allow, as Lagrange says, that this is the least -satisfactory passage of that great work. Newton, having made his -experiments in another manner than Torricelli, namely, by measuring -the quantity of the efflux instead of its velocity, found a result -inconsistent with that of Torricelli. The velocity inferred from the -quantity discharged, was only that due to _half_ the depth of the -fluid. - -In the first edition of the _Principia_,[31\6] Newton gave a train -of reasoning by which he theoretically demonstrated his own result, -going upon the principle, that the momentum of the issuing fluid is -equal to the momentum which the column vertically over the orifice -would generate by its gravity. But Torricelli's experiments, which -had given the velocity due to the whole depth, were confirmed on -repetition: how was this discrepancy to be explained? - -[Note 31\6: B. ii. Prop. xxxvii.] - -Newton explained the discrepancy by observing the contraction which -the jet, or vein of water, undergoes, just after it leaves the -orifice, and which he called the _vena contracta_. At the orifice, -the velocity is that due to half the height; at the _vena contracta_ -it is that due to the whole height. The former velocity regulates -the quantity of the discharge; the latter, the path of the jet. - -This explanation was an important step in the subject; but it made -Newton's original proof appear very defective, to say the least. In -the second edition of the _Principia_ (1714), Newton attacked the -problem in a manner altogether different from his former -investigation. He there assumed, that when a round vessel, containing -fluid, has a hole in its bottom, the descending fluid may be -conceived to be a conoidal mass, which has its base at the surface of -the fluid, and its narrow end at the orifice. This portion of the -fluid he calls the _cataract_; and supposes that while this part -descends, the surrounding {350} parts remain immovable, as if they -were frozen; in this way he finds a result agreeing with Torricelli's -experiments on the velocity of the efflux. - -We must allow that the assumptions by which this result is obtained -are somewhat arbitrary; and those which Newton introduces in -attempting to connect the problem of issuing fluids with that of the -resistance to a body moving in a fluid, are no less so. But even up -to the present time, mathematicians have not been able to reduce -problems concerning the motions of fluids to mathematical principles -and calculations, without introducing some steps of this arbitrary -kind. And one of the uses of experiments on this subject is, to -suggest those hypotheses which may enable us, in the manner most -consonant with the true state of things, to reduce the motions of -fluids to those general laws of mechanics, to which we know they -must be subject. - -Hence the science of the Motion of Fluids, unlike all the other -primary departments of Mechanics, is a subject on which we still -need experiments, to point out the fundamental principles. Many such -experiments have been made, with a view either to compare the -results of deduction and observation, or, when this comparison -failed, to obtain purely empirical rules. In this way the resistance -of fluids, and the motion of water in pipes, canals, and rivers, has -been treated. Italy has possessed, from early times, a large body of -such writers. The earlier works of this kind have been collected in -sixteen quarto volumes. Lecchi and Michelotti about 1765, Bidone -more recently, have pursued these inquiries. Bossut, Buat, Hachette, -in France, have labored at the same task, as have Coulomb and Prony, -Girard and Poncelet. Eytelwein's German treatise (_Hydraulik_) -contains an account of what others and himself have done. Many of -these trains of experiments, both in France and Italy, were made at -the expense of governments, and on a very magnificent scale. In -England less was done in this way during the last century, than in -most other countries. The _Philosophical Transactions_, for -instance, scarcely contain a single paper on this subject founded on -experimental investigations.[32\6] Dr. Thomas Young, who was at the -head of his countrymen in so many branches of science, was one of -the first to call back attention to this: and Mr. Rennie and others -have recently made valuable experiments. In many of the questions -now spoken of, the accordance which engineers are able to obtain, -between their calculated and observed results, {351} is very great: -but these calculations are performed by means of empirical formulæ, -which do not connect the facts with their causes, and still leave a -wide space to be traversed, in order to complete the science. - -[Note 32\6: Rennie, _Report to Brit. Assoc._] - -In the mean time, all the other portions of Mechanics were reduced -to general laws, and analytical processes; and means were found of -including Hydrodynamics, notwithstanding the difficulties which -attend its special problems, in this common improvement of form. -This progress we must relate. - -[2d Ed.] [The hydrodynamical problems referred to above are, the -laws of a fluid issuing from a vessel, the laws of the motion of -water in pipes, canals, and rivers, and the laws of the resistance -of fluids. To these may be added, as an hydrodynamical problem -important in theory, in experiment, and in the comparison of the -two, the laws of waves. Newton gave, in the _Principia_, an -explanation of the waves of water (Lib. ii. Prop. 44), which appears -to proceed upon an erroneous view of the nature of the motion of the -fluid: but in his solution of the problem of sound, appeared, for -the first time, a correct view of the propagation of an undulation -in a fluid. The history of this subject, as bearing upon the theory -of sound, is given in Book viii.: but I may here remark, that the -laws of the motion of waves have been pursued experimentally by -various persons, as Bremontier (_Recherches sur le Mouvement des -Ondes_, 1809), Emy (_Du Mouvement des Ondes_, 1831), the Webers -(_Wellenlehre_, 1825); and by Mr. Scott Russell (_Reports of the -British Association_, 1844). The analytical theory has been carried -on by Poisson, Cauchy, and, among ourselves, by Prof. Kelland -(_Edin. Trans._) and Mr. Airy (in the article _Tides_, in the -_Encyclopædia Metropolitana_). And though theory and experiment have -not yet been brought into complete accordance, great progress has -been made in that work, and the remaining chasm between the two is -manifestly due only to the incompleteness of both.] - -Perhaps the most remarkable case of fluid motion recently discussed, -is one which Mr. Scott Russell has presented experimentally; and -which, though novel, is easily seen to follow from known principles; -namely, the _Great Solitary Wave_. A wave may be produced, which -shall move along a canal unaccompanied by any other wave: and the -simplicity of this case makes the mathematical conditions and -consequences more simple than they are in most other problems of -Hydrodynamics. {352} - - - - -CHAPTER V. - -GENERALIZATION OF THE PRINCIPLES OF MECHANICS. - - -_Sect._ 1.--_Generalization of the Second Law of Motion.--Central -Forces._ - -THE Second Law of Motion being proved for constant Forces which act -in parallel lines, and the Third Law for the Direct Action of -bodies, it still required great mathematical talent, and some -inductive power, to see clearly the laws which govern the motion of -any number of bodies, acted upon by each other, and by any forces, -anyhow varying in magnitude and direction. This was the task of the -generalization of the laws of motion. - -Galileo had convinced himself that the velocity of projection, and -that which gravity alone would produce, are "both maintained, -without being altered, perturbed, or impeded in their mixture." It -is to be observed, however, that the truth of this result depends -upon a particular circumstance, namely, that gravity, at all points, -acts in lines, which, as to sense, are parallel. When we have to -consider cases in which this is not true, as when the force tends to -the centre of a circle, the law of composition cannot be applied in -the same way; and, in this case, mathematicians were met by some -peculiar difficulties. - -One of these difficulties arises from the apparent inconsistency of -the statical and dynamical measures of force. When a body moves in a -circle, the force which urges the body to the centre is only a -_tendency_ to motion; for the body does not, in fact, approach to -the centre; and this mere tendency to motion is combined with an -actual motion, which takes place in the circumference. We appear to -have to compare two things which are heterogeneous. Descartes had -noticed this difficulty, but without giving any satisfactory -solution of it.[33\6] If we combine the actual motion to or from the -centre with the traverse motion about the centre, we obtain a result -which is false on mechanical principles. Galileo endeavored in this -way to find the curve described by a body which falls towards the -earth's centre, and is, at the same time, carried {353} round by the -motion of the earth; and obtained an erroneous result. Kepler and -Fermat attempted the same problem, and obtained solutions different -from that of Galileo, but not more correct. - -[Note 33\6: _Princip._ P. iii. 59.] - -Even Newton, at an early period of his speculations, had an -erroneous opinion respecting this curve, which he imagined to be a -kind of spiral. Hooke animadverted upon this opinion when it was -laid before the Royal Society of London in 1679, and stated, more -truly, that, supposing no resistance, it would be "an eccentric -ellipsoid," that is, a figure resembling an ellipse. But though he -had made out the approximate form of the curve, in some unexplained -way, we have no reason to believe that he possessed any means of -determining the mathematical properties of the curve described in -such a case. The perpetual composition of a central force with the -previous motion of the body, could not be successfully treated -without the consideration of the Doctrine of Limits, or something -equivalent to that doctrine. The first example which we have of the -right solution of such a problem occurs, so far as I know, in the -Theorems of Huyghens concerning Circular Motion, which were -published, without demonstration, at the end of his _Horologium -Oscillatorium_, in 1673. It was there asserted that when equal -bodies describe circles, if the times are equal, the centrifugal -forces will be as the diameters of the circles; if the velocities -are equal, the forces will be reciprocally as the diameters, and so -on. In order to arrive at these propositions, Huyghens must, -virtually at least, have applied the Second Law of Motion to the -limiting elements of the curve, according to the way in which -Newton, a few years later, gave the demonstration of the theorems of -Huyghens in the _Principia_. - -The growing persuasion that the motions of the heavenly bodies about -the sun might be explained by the action of central forces, gave a -peculiar interest to these mechanical speculations, at the period -now under review. Indeed, it is not easy to state separately, as our -present object requires us to do, the progress of Mechanics, and the -progress of Astronomy. Yet the distinction which we have to make is, -in its nature, sufficiently marked. It is, in fact, no less marked -than the distinction between speaking logically and speaking truly. -The framers of the science of motion were employed in establishing -those notions, names, and rules, in conformity to which _all_ -mechanical _truth must_ be expressed; but _what was the truth_ with -regard to the mechanism of the universe remained to be determined by -other means. Physical Astronomy, at the period of which we speak, -eclipsed and overlaid {354} theoretical Mechanics, as, a little -previously, Dynamics had eclipsed and superseded Statics. - -The laws of variable force and of curvilinear motion were not much -pursued, till the invention of Fluxions and of the Differential -Calculus again turned men's minds to these subjects, as easy and -interesting exercises of the powers of these new methods. Newton's -_Principia_, of which the first two Books are purely dynamical, is -the great exception to this assertion; inasmuch as it contains -correct solutions of a great variety of the most general problems of -the science; and indeed is, even yet, one of the most complete -treatises which we possess upon the subject. - -We have seen that Kepler, in his attempts to explain the curvilinear -motions of the planets by means of a central force, failed, in -consequence of his belief that a continued transverse action of the -central body was requisite to keep up a continual motion. Galileo -had founded his theory of projectiles on the principle that such an -action was not necessary; yet Borelli, a pupil of Galileo, when, in -1666, he published his theory of the Medicean Stars (the satellites -of Jupiter), did not keep quite clear of the same errors which had -vitiated Kepler's reasonings. In the same way, though Descartes is -sometimes spoken of as the first promulgator of the First Law of -Motion, yet his theory of Vortices must have been mainly suggested -by a want of an entire confidence in that law. When he represented -the planets and satellites as owing their motions to oceans of fluid -diffused through the celestial spaces, and constantly whirling round -the central bodies, he must have felt afraid of trusting the planets -to the operation of the laws of motion in free space. Sounder -physical philosophers, however, began to perceive the real nature of -the question. As early as 1666, we read, in the Journals of the -Royal Society, that "there was read a paper of Mr. Hooke's -explicating the inflexion of a direct motion into a curve by a -supervening attractive principle;" and before the publication of the -_Principia_ in 1687, Huyghens, as we have seen, in Holland, and, in -our own country, Wren, Halley, and Hooke, had made some progress in -the true mechanics of circular motion,[34\6] and had distinctly -contemplated the problem of the motion of a body in an ellipse by a -central force, though they could not solve it. Halley went to -Cambridge in 1684,[35\6] for the express purpose of consulting -Newton upon the subject of the production of the elliptical motion -of the planets by means of a central {355} force, and, on the 10th -of December,[36\6] announced to the Royal Society that he had seen -Mr. Newton's book, _De Motu Corporum_. The feeling that -mathematicians were on the brink of discoveries such as are -contained in this work was so strong, that Dr. Halley was requested -to remind Mr. Newton of his promise of entering them in the Register -of the Society, "for securing the invention to himself till such -time as he can be at leisure to publish it." The manuscript, with -the title _Philosophiæ Naturalis Principia Mathematica_, was -presented to the society (to which it was dedicated) on the 28th of -April, 1686. Dr. Vincent, who presented it, spoke of the novelty and -dignity of the subject; and the president (Sir J. Hoskins) added, -with great truth, "that the method was so much the more to be prized -as it was both invented and perfected at the same time." - -[Note 34\6: Newt. _Princip._ Schol. to Prop. iv.] - -[Note 35\6: Sir D. Brewster's _Life of Newton_, p. 154.] - -[Note 36\6: Id. p. 184.] - -The reader will recollect that we are here speaking of the -_Principia_ as a Mechanical Treatise only; we shall afterwards have -to consider it as containing the greatest discoveries of Physical -Astronomy. As a work on Dynamics, its merit is, that it exhibits a -wonderful store of refined and beautiful mathematical artifices, -applied to solve all the most general problems which the subject -offered. The _Principia_ can hardly be said to contain any new -inductive discovery respecting the principles of mechanics; for -though Newton's _Axioms or Laws of Motion_ which stand at the -beginning of the book, are a much clearer and more general statement -of the grounds of Mechanics than had yet appeared, they do not -involve any doctrines which had not been previously stated or taken -for granted by other mathematicians. - -The work, however, besides its unrivalled mathematical skill, -employed in tracing out, deductively, the consequences of the laws -of motion, and its great cosmical discoveries, which we shall -hereafter treat of, had great philosophical value in the history of -Dynamics, as exhibiting a clear conception of the new character and -functions of that science. In his Preface, Newton says, "Rational -Mechanics must be the science of the Motions which result from any -Forces, and of the Forces which are required for any Motions, -accurately propounded and demonstrated. For many things induce me to -suspect, that all natural phenomena may depend upon some Forces by -which the particles of bodies are either drawn towards each other, -and cohere, or repel and recede from each other: and these Forces -being hitherto unknown, philosophers have pursued their researches -in vain. And I hope {356} that the principles expounded in this work -will afford some light, either to this mode of philosophizing, or to -some mode which is more true." - -Before we pursue this subject further, we must trace the remainder -of the history of the Third Law. - - -_Sect._ 2.--_Generalization of the Third Law of Motion.--Centre of -Oscillation.--Huyghens._ - -THE Third Law of Motion, whether expressed according to Newton's -formula (by the equality of Action and Reaction), or in any other of -the ways employed about the same time, easily gave the solution of -mechanical problems in all cases of _direct_ action; that is, when -each body acted directly on others. But there still remained the -problems in which the action is _indirect_;--when bodies, in motion, -act on each other by the intervention of levers, or in any other -way. If a rigid rod, passing through two weights, be made to swing -about its upper point, so as to form a pendulum, each weight will -act and react on the other by means of the rod, considered as a -lever turning about the point of suspension. What, in this case, -will be the effect of this action and reaction? In what time will -the pendulum oscillate by the force of gravity? Where is the point -at which a single weight must be placed to oscillate in the same -time? in other words, where is the _Centre of Oscillation_? - -Such was the problem--an example only of the general problem of -indirect action--which mathematicians had to solve. That it was by -no means easy to see in what manner the law of the communication of -motion was to be extended from simpler cases to those where rotatory -motion was produced, is shown by this;--that Newton, in attempting -to solve the mechanical problem of the Precession of the Equinoxes, -fell into a serious error on this very subject. He assumed that, -when a part has to communicate rotatory movement to the whole (as -the protuberant portion of the terrestrial spheroid, attracted by -the sun and moon, communicates a small movement to the whole mass of -the earth), the quantity of the _motion_, "motus," will not be -altered by being communicated. This principle is true, if, by -_motion_, we understand what is called _moment of inertia_, a -quantity in which both the velocity of each particle and its -distance from the axis of rotation are taken into account: but -Newton, in his calculations of its amount, considered the velocity -only; thus making _motion_, in this case, identical with the -_momentum_ which he introduces in treating of the simpler case {357} -of the third law of motion, when the action is direct. This error -was retained even in the later editions of the _Principia_.[37\6] - -[Note 37\6: B. iii. Lemma iii. to Prop, xxxix.] - -The question of the centre of oscillation had been proposed by -Mersenne somewhat earlier,[38\6] in 1646. And though the problem was -out of the reach of any principles at that time known and -understood, some of the mathematicians of the day had rightly solved -some cases of it, by proceeding as if the question had been to find -the _Centre of Percussion_. The Centre of Percussion is the point -about which the momenta of all the parts of a body balance each -other, when it is in motion about any axis, and is stopped by -striking against an obstacle placed at that centre. Roberval found -this point in some easy cases; Descartes also attempted the problem; -their rival labors led to an angry controversy: and Descartes was, -as in his physical speculations he often was, very presumptuous, -though not more than half right. - -[Note 38\6: Mont. ii. 423.] - -Huyghens was hardly advanced beyond boyhood when Mersenne first -proposed this problem; and, as he says,[39\6] could see no principle -which even offered an opening to the solution, and had thus been -repelled at the threshold. When, however, he published his -_Horologium Oscillatorium_ in 1673, the fourth part of that work was -on the Centre of Oscillation or Agitation; and the principle which -he then assumed, though not so simple and self-evident as those to -which such problems were afterwards referred, was perfectly correct -and general, and led to exact solutions in all cases. The reader has -already seen repeatedly in the course of this history, complex and -derivative principles presenting themselves to men's minds, before -simple and elementary ones. The "hypothesis" assumed by Huyghens was -this; "that if any weights are put in motion by the force of -gravity, they _cannot_ move so that the centre of gravity of them -all shall rise _higher_ than the place from which it descended." -This being assumed, it is easy to show that the centre of gravity -will, under all circumstances, rise _as high_ as its original -position; and this consideration leads to a determination of the -oscillation of a compound pendulum. We may observe, in the principle -thus selected, a conviction that, in all mechanical action, the -centre of gravity may be taken as the representative of the whole -system. This conviction, as we have seen, may be traced in the -axioms of Archimedes and Stevinus; and Huyghens, when he proceeds -upon it, undertakes to show,[40\6] that he assumes only this, that a -heavy body cannot, of itself, move upwards. {358} - -[Note 39\6: _Hor. Osc._ Pref.] - -[Note 40\6: _Hor. Osc._ p. 121.] - -Clear as Huyghen's principle appeared to himself, it was, after some -time, attacked by the Abbé Catelan, a zealous Cartesian. Catelan -also put forth principles which he conceived were evident, and -deduced from them conclusions contradictory to those of Huyghens. -His principles, now that we know them to be false, appear to us very -gratuitous. They are these; "that in a compound pendulum, the sum of -the velocities of the component weights is equal to the sum of the -velocities which they would have acquired if they had been detached -pendulums;" and "that the time of the vibration of a compound -pendulum is an arithmetic mean between the times of the vibrations -of the weights, moving as detached pendulums." Huyghens easily -showed that these suppositions would make the centre of gravity -ascend to a greater height than that from which it fell; and after -some time, James Bernoulli stept into the arena, and ranged himself -on the side of Huyghens. As the discussion thus proceeded, it began -to be seen that the question really was, in what manner the Third -Law of Motion was to be extended to cases of indirect action; -whether by distributing the action and reaction according to -statical principles, or in some other way. "I propose it to the -consideration of mathematicians," says Bernoulli in 1686, "what law -of the communication of velocity is observed by bodies in motion, -which are sustained at one extremity by a fixed fulcrum, and at the -other by a body also moving, but more slowly. Is the excess of -velocity which must be communicated from the one body to the other -to be distributed in the same proportion in which a load supported -on the lever would be distributed?" He adds, that if this question -be answered in the affirmative, Huyghens will be found to be in -error; but this is a mistake. The principle, that the action and -reaction of bodies thus moving are to be distributed according to -the rules of the lever, is true; but Bernoulli mistook, in -estimating this action and reaction by the _velocity_ acquired at -any moment; instead of taking, as he should have done, the -_increment_ of velocity which gravity tended to impress in the next -instant. This was shown by the Marquis de l'Hôpital; who adds, with -justice, "I conceive that I have thus fully answered the call of -Bernoulli, when he says, I propose it to the consideration of -mathematicians, &c." - -We may, from this time, consider as known, but not as fully -established, the principle that "When bodies in motion affect each -other, the action and reaction are distributed according to the laws -of Statics;" although there were still found occasional difficulties -in the {359} generalization and application of the role. James -Bernoulli, in 1703, gave "a General Demonstration of the Centre of -Oscillation, drawn from the nature of the Lever." In this -demonstration[41\6] he takes as a fundamental principle, that bodies -in motion, connected by levers, balance, when the products of their -momenta and the lengths of the levers are equal in opposite -directions. For the proof of this proposition, he refers to Marriotte, -who had asserted it of weights acting by percussion,[42\6] and in -order to prove it, had balanced the effect of a weight on a lever by -the effect of a jet of water, and had confirmed it by other -experiments.[43\6] Moreover, says Bernoulli, there is no one who -denies it. Still, this kind of proof was hardly satisfactory or -elementary enough. John Bernoulli took up the subject after the death -of his brother James, which happened in 1705. The former published in -1714 his _Meditatio de Naturâ Centri Oscillationis_. In this memoir, -he assumes, as his brother had done, that the effects of forces on a -lever in motion are distributed according to the common rules of the -lever.[44\6] The principal generalization which he introduced was, -that he considered gravity as a force soliciting to motion, which -might have different intensities in different bodies. At the same -time, Brook Taylor in England solved the problem, upon the same -principles as Bernoulli; and the question of priority on this subject -was one point in the angry intercourse which, about this time, became -common between the English mathematicians and those of the Continent. -Hermann also, in his _Phoronomia_, published in 1716, gave a proof -which, as he informs us, he had devised before he saw John -Bernoulli's. This proof is founded on the statical equivalence of the -"_solicitations of gravity_" and the "_vicarious solicitations_" which -correspond to the actual motion of each part; or, as it has been -expressed by more modern writers, the equilibrium of the _impressed_ -and _effective forces_. - -[Note 41\6: _Op._ ii. 930.] - -[Note 42\6: _Choq. des Corps_, p. 296.] - -[Note 43\6: Ib. Prop. xi.] - -[Note 44\6: P. 172.] - -It was shown by John Bernoulli and Hermann, and was indeed easily -proved, that the proposition assumed by Huyghens as the foundation -of his solution, was, in fact, a consequence of the elementary -principles which belong to this branch of mechanics. But this -assumption of Huyghens was an example of a more general proposition, -which by some mathematicians at this time had been put forward as an -original and elementary law; and as a principle which ought to -supersede the usual measure of the forces of bodies in motion; this -principle they called "_the Conservation of Vis Viva_." The attempt -to {360} make this change was the commencement of one of the most -obstinate and curious of the controversies which form part of the -history of mechanical science. The celebrated Leibnitz was the -author of the new opinion. In 1686, he published, in the Leipsic -Acts, "A short Demonstration of a memorable Error of Descartes and -others, concerning the natural law by which they think that God -always preserves the same quantity of motion; in which they pervert -mechanics." The principle that the same quantity of motion, and -therefore of moving force, is always preserved in the world, follows -from the equality of action and reaction; though Descartes had, -after his fashion, given a theological reason for it; Leibnitz -allowed that the quantity of moving force remains always the same, -but denied that this force is measured by the quantity of motion or -momentum. He maintained that the same force is requisite to raise a -weight of one pound through four feet, and a weight of four pounds -through one foot, though the momenta in this case are as one to two. -This was answered by the Abbé de Conti; who truly observed, that -allowing the effects in the two cases to be equal, this did not -prove the forces to be equal; since the effect, in the first case, -was produced in a double time, and therefore it was quite consistent -to suppose the force only half as great. Leibnitz, however, -persisted in his innovation; and in 1695 laid down the distinction -between _vires mortuæ_, or pressures, and _vires vivæ_, the name he -gave to his own measure of force. He kept up a correspondence with -John Bernoulli, whom he converted to his peculiar opinions on this -subject; or rather, as Bernoulli says,[45\6] made him think for -himself, which ended in his proving directly that which Leibnitz had -defended by indirect reasons. Among other arguments, he had -pretended to show (what is certainly not true), that if the common -measure of forces be adhered to, a perpetual motion would be -possible. It is easy to collect many cases which admit of being very -simply and conveniently reasoned upon by means of the _vis viva_, -that is, by taking the force to be proportional to the _square_ of -the velocity, and not to the velocity itself. Thus, in order to give -the arrow _twice_ the velocity, the bow must be _four_ times as -strong; and in all cases in which no account is taken of the time of -producing the effect, we may conveniently use similar methods. - -[Note 45\6: _Op._ iii. 40.] - -But it was not till a later period that the question excited any -general notice. The Academy of Sciences of Paris in 1724 proposed -{361} as a subject for their prize dissertation the laws of the -impact of bodies. Bernoulli, as a competitor, wrote a treatise, upon -Leibnitzian principles, which, though not honored with the prize, -was printed by the Academy with commendation.[46\6] The opinions -which he here defended and illustrated were adopted by several -mathematicians; the controversy extended from the mathematical to -the literary world, at that time more attentive than usual to -mathematical disputes, in consequence of the great struggle then -going on between the Cartesian and the Newtonian system. It was, -however, obvious that by this time the interest of the question, so -far as the progress of Dynamics was concerned, was at an end; for -the combatants all agreed as to the results in each particular case. -The Laws of Motion were now established; and the question was, by -means of what definitions and abstractions could they be best -expressed;--a metaphysical, not a physical discussion, and therefore -one in which "the paper philosophers," as Galileo called them, could -bear a part. In the first volume of the _Transactions of the Academy -of St. Petersburg_, published in 1728, there are three Leibnitzian -memoirs by Hermann, Bullfinger, and Wolff. In England, Clarke was an -angry assailant of the German opinion, which S'Gravesande -maintained. In France, Mairan attacked the _vis viva_ in 1728; "with -strong and victorious reasons," as the Marquise du Chatelet -declared, in the first edition of her _Treatise on Fire_.[47\6] But -shortly after this praise was published, the Chateau de Cirey, where -the Marquise usually lived, became a school of Leibnitzian opinions, -and the resort of the principal partisans of the _vis viva_. "Soon," -observes Mairan, "their language was changed; the _vis viva_ was -enthroned by the side of the _monads_." The Marquise tried to -retract or explain away her praises; she urged arguments on the -other side. Still the question was not decided; even her friend -Voltaire was not converted. In 1741 he read a memoir _On the Measure -and Nature of Moving Forces_, in which he maintained the old -opinion. Finally, D'Alembert in 1743 declared it to be, as it truly -was, a mere question of words; and by the turn which Dynamics then -took, it ceased to be of any possible interest or importance to -mathematicians. - -[Note 46\6: _Discours sur les Loix de la Communication du Mouvement_.] - -[Note 47\6: Mont. iii. 640.] - -The representation of the laws of motion and of the reasonings -depending on them, in the most general form, by means of analytical -language, cannot be said to have been fully achieved till the time of -D'Alembert; but as we have already seen, the discovery of these laws -{362} had taken place somewhat earlier; and that law which is more -particularly expressed in D'Alembert's Principle (_the equality of the -action gained and lost_) was, it has been seen, rather led to by the -general current of the reasoning of mathematicians about the end of -the seventeenth century than discovered by any one. Huyghens, -Marriotte, the two Bernoulli's, L'Hôpital, Taylor, and Hermann, have -each of them their name in the history of this advance; but we cannot -ascribe to any of them any great real inductive sagacity shown in what -they thus contributed, except to Huyghens, who first seized the -principle in such a form as to find the centre of oscillation by means -of it. Indeed, in the steps taken by the others, language itself had -almost made the generalization for them at the time when they wrote; -and it required no small degree of acuteness and care to distinguish -the old cases, in which the law had already been applied, from the new -cases, in which they had to apply it. - - - - -CHAPTER VI. - -SEQUEL TO THE GENERALIZATION OF THE PRINCIPLES OF MECHANICS.--PERIOD -OF MATHEMATICAL DEDUCTION.--ANALYTICAL MECHANICS. - - -WE have now finished the history of the discovery of Mechanical -Principles, strictly so called. The three Laws of Motion, -generalized in the manner we have described, contain the materials -of the whole structure of Mechanics; and in the remaining progress -of the science, we are led to no new truth which was not implicitly -involved in those previously known. It may be thought, therefore, -that the narrative of this progress is of comparatively small -interest. Nor do we maintain that the application and development of -principles is a matter of so much importance to the philosophy of -science, as the advance towards and to them. Still, there are many -circumstances in the latter stages of the progress of the science of -Mechanics, which well deserve notice, and make a rapid survey of -that part of its history indispensable to our purpose. - -The Laws of Motion are expressed in terms of Space and Number; the -development of the consequences of these laws must, therefore, be -performed by means of the reasonings of mathematics; and the science -{363} of Mechanics may assume the various aspects which belong to the -different modes of dealing with mathematical quantities. Mechanics, -like pure mathematics, may be geometrical or may be analytical; that -is, it may treat space either by a direct consideration of its -properties, or by a symbolical representation of them: Mechanics, like -pure mathematics, may proceed from special cases, to problems and -methods of extreme generality;--may summon to its aid the curious and -refined relations of symmetry, by which general and complex conditions -are simplified;--may become more powerful by the discovery of more -powerful analytical artifices;--may even have the generality of its -principles further expanded, inasmuch as symbols are a more general -language than words. We shall very briefly notice a series of -modifications of this kind. - -1. _Geometrical Mechanics. Newton, &c._--The first great -systematical Treatise on Mechanics, in the most general sense, is -the two first Books of the _Principia_ of Newton. In this work, the -method employed is predominantly geometrical: not only space is not -represented symbolically, or by reference to number; but numbers, -as, for instance, those which measure time and force, are -represented by spaces; and the laws of their changes are indicated -by the properties of curve lines. It is well known that Newton -employed, by preference, methods of this kind in the exposition of -his theorems, even where he had made the discovery of them by -analytical calculations. The intuitions of space appeared to him, as -they have appeared to many of his followers, to be a more clear and -satisfactory road to knowledge, than the operations of symbolical -language. Hermann, whose _Phoronomia_ was the next great work on -this subject, pursued a like course; employing curves, which he -calls "the scale of velocities," "of forces," &c. Methods nearly -similar were employed by the two first Bernoullis, and other -mathematicians of that period; and were, indeed, so long familiar, -that the influence of them may still be traced in some of the terms -which are used on such subjects; as, for instance, when we talk of -"reducing a problem to quadratures," that is, to the finding the -area of the curves employed in these methods. - -2. _Analytical Mechanics. Euler._--As analysis was more cultivated, -it gained a predominancy over geometry; being found to be a far more -powerful instrument for obtaining results; and possessing a beauty -and an evidence, which, though different from those of geometry, had -great attractions for minds to which they became familiar. The -person who did most to give to analysis the generality and {364} -symmetry which are now its pride, was also the person who made -Mechanics analytical; I mean Euler. He began his execution of this -task in various memoirs which appeared in the _Transactions of the -Academy of Sciences at St. Petersburg_, commencing with its earliest -volumes; and in 1736, he published there his _Mechanics, or the -Science of Motion analytically expounded; in the way of a Supplement -to the Transactions of the Imperial Academy of Sciences_. In the -preface to this work, he says, that though the solutions of problems -by Newton and Hermann were quite satisfactory, yet he found that he -had a difficulty in applying them to new problems, differing little -from theirs; and that, therefore, he thought it would be useful to -extract an analysis out of their synthesis. - -3. _Mechanical Problems._--In reality, however, Euler has done much -more than merely give analytical methods, which may be applied to -mechanical problems: he has himself applied such methods to an -immense number of cases. His transcendent mathematical powers, his -long and studious life, and the interest with which he pursued the -subject, led him to solve an almost inconceivable number and variety -of mechanical problems. Such problems suggested themselves to him on -all occasions. One of his memoirs begins, by stating that, happening -to think of the line of Virgil, - Anchora de prorà jacitur stant litore puppes; - The anchor drops, the rushing keel is staid; -he could not help inquiring what would be the nature of the ship's -motion under the circumstances here described. And in the last few -days of his life, after his mortal illness had begun, having seen in -the newspapers some statements respecting balloons, he proceeded to -calculate their motions; and performed a difficult integration, in -which this undertaking engaged him. His Memoirs occupy a very large -portion of the _Petropolitan Transactions_ during his life, from 1728 -to 1783; and he declared that he should leave papers which might -enrich the publications of the Academy of Petersburg for twenty years -after his death;--a promise which has been more than fulfilled; for, -up to 1818, the volumes usually contain several Memoirs of his. He and -his contemporaries may be said to have exhausted the subject; for -there are few mechanical problems which have been since treated, which -they have not in some manner touched upon. - -I do not dwell upon the details of such problems; for the next great -step in Analytical Mechanics, the publication of D'Alembert's {365} -Principle in 1743, in a great degree superseded their interest. The -Transactions of the Academies of Paris and Berlin, as well as St. -Petersburg, are filled, up to this time, with various questions of -this kind. They require, for the most part, the determination of the -motions of several bodies, with or without weight, which pull or -push each other by means of threads, or levers, to which they are -fastened, or along which they can slide; and which, having a certain -impulse given them at first, are then left to themselves, or are -compelled to move in given lines and surfaces. The postulate of -Huyghens, respecting the motion of the centre of gravity, was -generally one of the principles of the solution; but other -principles were always needed in addition to this; and it required -the exercise of ingenuity and skill to detect the most suitable in -each case. Such problems were, for some time, a sort of trial of -strength among mathematicians: the principle of D'Alembert put an -end to this kind of challenges, by supplying a direct and general -method of resolving, or at least of throwing into equations, any -imaginable problem. The mechanical difficulties were in this way -reduced to difficulties of pure mathematics. - -4. _D'Alembert's Principle._--D'Alembert's Principle is only the -expression, in the most general form, of the principle upon which -John Bernoulli, Hermann, and others, had solved the problem of the -centre of oscillation. It was thus stated, "The motion _impressed_ -on each particle of any system by the forces which act upon it, may -be resolved into two, the _effective_ motion, and the motion gained -or _lost_: the effective motions will be the real motions of the -parts, and the motions gained and lost will be such as would keep -the system at rest." The distinction of _statics_, the doctrine of -equilibrium, and _dynamics_, the doctrine of motion, was, as we have -seen, fundamental; and the difference of difficulty and complexity -in the two subjects was well understood, and generally recognized by -mathematicians. D'Alembert's principle reduces every dynamical -question to a statical one; and hence, by means of the conditions -which connect the possible motions of the system, we can determine -what the actual motions must be. The difficulty of determining the -laws of equilibrium, in the application of this principle in complex -cases is, however, often as great as if we apply more simple and -direct considerations. - -5. _Motion in Resisting Media. Ballistics._--We shall notice more -particularly the history of some of the problems of mechanics. -Though John Bernoulli always spoke with admiration of Newton's -_Principia_, and of its author, he appears to have been well -disposed to point out {366} real or imagined blemishes in the work. -Against the validity of Newton's determination of the path described -by a body projected in any part of the solar system, Bernoulli urges -a cavil which it is difficult to conceive that a mathematician, such -as he was, could seriously believe to be well founded. On Newton's -determination of the path of a body in a resisting medium, his -criticism is more just. He pointed out a material error in this -solution: this correction came to Newton's knowledge in London, in -October, 1712, when the impression of the second edition of the -Principia was just drawing to a close, under the care of Cotes at -Cambridge; and Newton immediately cancelled the leaf and corrected -the error.[48\6] - -[Note 48\6: MS. Correspondence in Trin. Coll. Library.] - -This problem of the motion of a body in a resisting medium, led to -another collision between the English and the German mathematicians. -The proposition to which we have referred, gave only an indirect -view of the nature of the curve described by a projectile in the -air; and it is probable that Newton, when he wrote the _Principia_, -did not see his way to any direct and complete solution of this -problem. At a later period, in 1718, when the quarrel had waxed hot -between the admirers of Newton and Leibnitz, Keill, who had come -forward as a champion on the English side, proposed this problem to -the foreigners as a challenge. Keill probably imagined that what -Newton had not discovered, no one of his time would be able to -discover. But the sedulous cultivation of analysis by the Germans -had given them mathematical powers beyond the expectations of the -English; who, whatever might be their talents, had made little -advance in the effective use of general methods; and for a long -period seemed to be fascinated to the spot, in their admiration of -Newton's excellence. Bernoulli speedily solved the problem; and -reasonably enough, according to the law of honor of such challenges, -called upon the challenger to produce his solution. Keill was unable -to do this; and after some attempts at procrastination, was driven -to very paltry evasions. Bernoulli then published his solution, with -very just expressions of scorn towards his antagonist. And this may, -perhaps, be considered as the first material addition which was made -to the _Principia_ by subsequent writers. - -6. _Constellation of Mathematicians._--We pass with admiration along -the great series of mathematicians, by whom the science of -theoretical mechanics has been cultivated, from the time of Newton -to our own. There is no group of men of science whose fame is {367} -higher or brighter. The great discoveries of Copernicus, Galileo, -Newton, had fixed all eyes on those portions of human knowledge on -which their successors employed their labors. The certainty -belonging to this line of speculation seemed to elevate -mathematicians above the students of other subjects; and the beauty -of mathematical relations, and the subtlety of intellect which may -be shown in dealing with them, were fitted to win unbounded -applause. The successors of Newton and the Bernoullis, as Euler, -Clairaut, D'Alembert, Lagrange, Laplace, not to introduce living -names, have been some of the most remarkable men of talent which the -world has seen. That their talent is, for the most part, of a -different kind from that by which the laws of nature were -discovered, I shall have occasion to explain elsewhere; for the -present, I must endeavor to arrange the principal achievements of -those whom I have mentioned. - -The series of persons is connected by social relations. Euler was -the pupil of the first generation of Bernoullis, and the intimate -friend of the second generation; and all these extraordinary men, as -well as Hermann, were of the city of Basil, in that age a spot -fertile of great mathematicians to an unparalleled degree. In 1740, -Clairaut and Maupertuis visited John Bernoulli, at that time the -Nestor of mathematicians, who died, full of age and honors, in 1748. -Euler, several of the Bernoullis, Maupertuis, Lagrange, among other -mathematicians of smaller note, were called into the north by -Catharine of Russia and Frederic of Prussia, to inspire and instruct -academies which the brilliant fame then attached to science, had -induced those monarchs to establish. The prizes proposed by these -societies, and by the French Academy of Sciences, gave occasion to -many of the most valuable mathematical works of the century. - -7. _The Problem of Three Bodies._--In 1747, Clairaut and D'Alembert -sent, on the same day, to this body, their solutions of the celebrated -"Problem of Three Bodies," which, from that time, became the great -object of attention of mathematicians;--the bow in which each tried -his strength, and endeavored to shoot further than his predecessors. - -This problem was, in fact, the astronomical question of the effect -produced by the attraction of the sun, in disturbing the motions of -the moon about the earth; or by the attraction of one planet, -disturbing the motion of another planet about the sun; but being -expressed generally, as referring to one body which disturbs any two -others, it became a mechanical problem, and the history of it -belongs to the present subject. {368} - -One consequence of the synthetical form adopted by Newton in the -_Principia_, was, that his successors had the problem of the solar -system to begin entirely anew. Those who would not do this, made no -progress, as was long the case with the English. Clairaut says, that -he tried for a long time to make some use of Newton's labors; but -that, at last, he resolved to take up the subject in an independent -manner. This, accordingly, he did, using analysis throughout, and -following methods not much different from those still employed. We -do not now speak of the comparison of this theory with observation, -except to remark, that both by the agreements and by the -discrepancies of this comparison, Clairaut and other writers were -perpetually driven on to carry forwards the calculation to a greater -and greater degree of accuracy. - -One of the most important of the cases in which this happened, was -that of the movement of the Apogee of the Moon; and in this case, a -mode of approximating to the truth, which had been depended on as -nearly exact, was, after having caused great perplexity, found by -Clairaut and Euler to give only half the truth. This same Problem of -Three Bodies was the occasion of a memoir of Clairaut, which gained -the prize of the Academy of St. Petersburg in 1751; and, finally, of -his _Théorie de la Lune_, published in 1765. D'Alembert labored at -the same time on the same problem; and the value of their methods, -and the merit of the inventors, unhappily became a subject of -controversy between those two great mathematicians. Euler also, in -1753, published a _Theory of the Moon_, which was, perhaps, more -useful than either of the others, since it was afterwards the basis -of Mayer's method, and of his Tables. It is difficult to give the -general reader any distinct notion of these solutions. We may -observe, that the quantities which determine the moon's position, -are to be determined by means of certain algebraical equations, -which express the mechanical conditions of the motion. The -operation, by which the result is to be obtained, involves the -process of integration; which, in this instance, cannot be performed -in an immediate and definite manner; since the quantities thus to be -operated on depend upon the moon's position, and thus require us to -know the very thing which we have to determine by the operation. The -result must be got at, therefore, by successive approximations: we -must first find a quantity near the truth; and then, by the help of -this, one nearer still; and so on; and, in this manner, the moon's -place will be given by a converging series of terms. The form of -these terms depends upon the relations of position between the sun -{369} and moon, their apogees, the moon's nodes, and other -quantities; and by the variety of combinations of which these admit, -the terms become very numerous and complex. The magnitude of the -terms depends also upon various circumstances; as the relative force -of the sun and earth, the relative times of the solar and lunar -revolutions, the eccentricities and inclinations of the two orbits. -These are combined so as to give terms of different orders of -magnitudes; and it depends upon the skill and perseverance of the -mathematician how far he will continue this series of terms. For -there is no limit to their number: and though the methods of which -we have spoken do theoretically enable us to calculate as many terms -as we please, the labor and the complexity of the operations are so -serious that common calculators are stopped by them. None but very -great mathematicians have been able to walk safely any considerable -distance into this avenue,--so rapidly does it darken as we proceed. -And even the possibility of doing what has been done, depends upon -what we may call accidental circumstances; the smallness of the -inclinations and eccentricities of the system, and the like. "If -nature had not favored us in this way," Lagrange used to say, "there -would have been an end of the geometers in this problem." The -expected return of the comet of 1682 in 1759, gave a new interest to -the problem, and Clairaut proceeded to calculate the case which was -thus suggested. When this was treated by the methods which had -succeeded for the moon, it offered no prospect of success, in -consequence of the absence of the favorable circumstances just -referred to, and, accordingly, Clairaut, after obtaining the six -equations to which he reduces the solution,[49\6] adds, "Integrate -them who can" (Intègre maintenant qui pourra). New methods of -approximation were devised for this case. - -[Note 49\6: _Journal des Sçavans_, Aug. 1759.] - -The problem of three bodies was not prosecuted in consequence of its -analytical beauty, or its intrinsic attraction; but its great -difficulties were thus resolutely combated from necessity; because -in no other way could the theory of universal gravitation be known -to be true or made to be useful. The construction of _Tables of the -Moon_, an object which offered a large pecuniary reward, as well as -mathematical glory, to the successful adventurer, was the main -purpose of these labors. - -The _Theory of the Planets_ presented the Problem of Three Bodies in -a new form, and involved in peculiar difficulties; for the {370} -approximations which succeed in the Lunar theory fail here. -Artifices somewhat modified are required to overcome the -difficulties of this case. - -Euler had investigated, in particular, the motions of Jupiter and -Saturn, in which there was a secular acceleration and retardation, -known by observation, but not easily explicable by theory. Euler's -memoirs, which gained the prize of the French Academy, in 1748 and -1752, contained much beautiful analysis; and Lagrange published also -a theory of Jupiter and Saturn, in which he obtained results -different from those of Euler. Laplace, in 1787, showed that this -inequality arose from the circumstance that two of Saturn's years -are very nearly equal to five of Jupiter's. - -The problems relating to Jupiter's _Satellites_, were found to be -even more complex than those which refer to the planets: for it was -necessary to consider each satellite as disturbed by the other three -at once; and thus there occurred the Problem of _Five_ Bodies. This -problem was resolved by Lagrange.[50\6] - -[Note 50\6: Bailly, _Ast. Mod._ iii. 178.] - -Again, the newly-discovered _small Planets_, Juno, Ceres, Vesta, -Pallas, whose orbits almost coincide with each other, and are more -inclined and more eccentric than those of the ancient planets, give -rise, by their perturbations, to new forms of the problem, and -require new artifices. - -In the course of these researches respecting Jupiter, Lagrange and -Laplace were led to consider particularly the _secular Inequalities_ -of the solar system; that is, those inequalities in which the duration -of the cycle of change embraces very many revolutions of the bodies -themselves. Euler in 1749 and 1755, and Lagrange[51\6] in 1766, had -introduced the method of the _Variation of the Elements_ of the orbit; -which consists in tracing the effect of the perturbing forces, not as -directly altering the place of the planet, but as producing a change -from one instant to another, in the dimensions and position of the -Elliptical orbit which the planet describes.[52\6] Taking this view, -he {371} determines the secular changes of each of the _elements_ or -determining quantities of the orbit. In 1773, Laplace also attacked -this subject of secular changes, and obtained expressions for them. On -this occasion, he proved the celebrated proposition that, "the mean -motions of the planets are invariable:" that is, that there is, in the -revolutions of the system, no progressive change which is not finally -stopped and reversed; no increase, which is not, after some period, -changed into decrease; no retardation which is not at last succeeded -by acceleration; although, in some cases, millions of years may elapse -before the system reaches the turning-point. Thomas Simpson noticed -the same consequence of the laws of universal attraction. In 1774 and -1776, Lagrange[53\6] still labored at the secular equations; extending -his researches to the nodes and inclinations; and showed that the -invariability of the mean motions of the planets, which Laplace had -proved, neglecting the fourth powers of the eccentricities and -inclinations of the orbits,[54\6] was true, however far the -approximation was carried, so long as the squares of the disturbing -masses were neglected. He afterwards improved his methods;[55\6] and, -in 1783, he endeavored to extend the calculation of the changes of the -elements to the periodical equations, as well as the secular. - -[Note 51\6: Gautier, _Prob. de Trois Corps_, p. 155.] - -[Note 52\6: In the first edition of this History, I had ascribed to -Lagrange the invention of the Method of Variation of Elements in the -theory of Perturbations. But justice to Euler requires that we should -assign this distinction to him; at least, next to Newton, whose mode -of representing the paths of bodies by means of a _Revolving Orbit_, -in the Ninth Section of the _Principia_, may be considered as an -anticipation of the method of variation of elements. In the fifth -volume of the _Mécanique Céleste_, livre xv. p. 305, is an abstract of -Euler's paper of 1749; where Laplace adds, "C'est le premier essai de -la méthode de la variation des constantes arbitraires." And in page -310 is an abstract of the paper of 1756: and speaking of the method, -Laplace says, "It consists in regarding the elements of the elliptical -motion as variable in virtue of the perturbing forces. Those elements -are, 1, the axis major; 2, the epoch of the body being at the apse; 3, -the eccentricity; 4, the movement of the apse; 5, the inclination; 6, -the longitude of the node;" and he then proceeds to show how Euler did -this. It is possible that Lagrange knew nothing of Euler's paper. See -_Méc. Cél._ vol. v. p. 312. But Euler's conception and treatment of -the method are complete, so that he must be looked upon as the author -of it.] - -[Note 53\6: Gautier, p. 104.] - -[Note 54\6: Ib. p. 184.] - -[Note 55\6: Ib. p. 196.] - -8. _Mécanique Céleste_, _&c._--Laplace also resumed the -consideration of the secular changes; and, finally, undertook his -vast work, the _Mécanique Céleste_, which he intended to contain a -complete view of the existing state of this splendid department of -science. We may see, in the exultation which the author obviously -feels at the thought of erecting this monument of his age, the -enthusiasm which had been excited by the splendid course of -mathematical successes of which I have given a sketch. The two first -volumes of this great work appeared in 1799. The third and fourth -volumes were published in 1802 and 1805 respectively. Since its -publication, little has been added to the solution of the great -problems of which it treats. In 1808, Laplace presented to the -French Bureau des Longitudes, a Supplement to the _Mécanique -Céleste_; the object of which was to improve still further {372} the -mode of obtaining the secular variations of the elements. Poisson -and Lagrange proved the invariability of the major axes of the -orbits, as far as the second order of the perturbing forces. Various -other authors have since labored at this subject. Burckhardt, in -1808, extended the perturbing function as far as the sixth order of -the eccentricities. Gauss, Hansen, and Bessel, Ivory, MM. Lubbock, -Plana, Pontécoulant, and Airy, have, at different periods up to the -present time, either extended or illustrated some particular part of -the theory, or applied it to special cases; as in the instance of -Professor Airy's calculation of an inequality of Venus and the -earth, of which the period is 240 years. The approximation of the -Moon's motions has been pushed to an almost incredible extent by M. -Damoiseau, and, finally, Plana has once more attempted to present, -in a single work (three thick quarto volumes), all that has hitherto -been executed with regard to the theory of the Moon. - -I give only the leading points of the progress of analytical -dynamics. Hence I have not spoken in detail of the theory of the -Satellites of Jupiter, a subject on which Lagrange gained a prize -for a Memoir, in 1766, and in which Laplace discovered some most -curious properties in 1784. Still less have I referred to the purely -speculative question of _Tautochronous Curves_ in a resisting -medium, though it was a subject of the labors of Bernoulli, Euler, -Fontaine, D'Alembert, Lagrange, and Laplace. The reader will rightly -suppose that many other curious investigations are passed over in -utter silence. - -[2d Ed.] [Although the analytical calculations of the great -mathematicians of the last century had determined, in a -demonstrative manner, a vast series of inequalities to which the -motions of the sun, moon, and planets were subject in virtue of -their mutual attraction, there were still unsatisfactory points in -the solutions thus given of the great mechanical problems suggested -by the System of the Universe. One of these points was the want of -any evident mechanical significance in the successive members of -these series. Lindenau relates that Lagrange, near the end of his -life, expressed his sorrow that the methods of approximation -employed in Physical Astronomy rested on arbitrary processes, and -not on any insight into the results of mechanical action. But -something was subsequently done to remove the ground of this -complaint. In 1818, Gauss pointed out that secular equations may be -conceived to result from the disturbing body being distributed along -its orbit so as to form a ring, and thus made the result conceivable -more distinctly than as a mere result of calculation. And it appears -{373} to me that Professor Airy's treatise entitled _Gravitation_, -published at Cambridge in 1834, is of great value in supplying -similar modes of conception with regard to the mechanical origin of -many of the principal inequalities of the solar system. - -Bessel in 1824, and Hansen in 1828, published works which are -considered as belonging, along with those of Gauss, to a new era in -physical astronomy.[56\6] Gauss's _Theoria Motuum Corporum -Celestium_, which had Lalande's medal assigned to it by the French -Institute, had already (1810) resolved all problems concerning the -determination of the place of a planet or comet in its orbit in -function of the elements. The value of Hansen's labors respecting -the Perturbations of the Planets was recognized by the Astronomical -Society of London, which awarded to them its gold medal. - -[Note 56\6: _Abhand. der Akad. d. Wissensch. zu Berlin_. 1824; and -_Disquisitiones circa Theoriam Perturbationum_. See Jahn. _Gesch. -der Astron._ p. 84.] - -The investigations of M. Damoiseau, and of MM. Plana and Carlini, on -the Problem of the Lunar Theory, followed nearly the same course as -those of their predecessors. In these, as in the _Mécanique Céleste_ -and in preceding works on the same subject, the Moon's co-ordinates -(time, radius vector, and latitude) were expressed in function of -her true longitude. The integrations were effected in series, and -then by reversion of the series, the longitude was expressed in -function of the time; and then in the same manner the other two -co-ordinates. But Sir John Lubbock and M. Pontécoulant have made the -_mean_ longitude of the moon, that is, the time, the independent -variable, and have expressed the moon's co-ordinates in terms of -sines and cosines of angles increasing proportionally to the time. -And this method has been adopted by M. Poisson (_Mem. Inst._ xiii. -1835, p. 212). M. Damoiseau, like Laplace and Clairaut, had deduced -the successive coefficients of the lunar inequalities by numerical -equations. But M. Plana expresses explicitly each coefficient in -general terms of the letters expressing the constants of the -problem, arranging them according to the order of the quantities, -and substituting numbers at the end of the operation only. By -attending to this arrangement, MM. Lubbock and Pontécoulant have -verified or corrected a large portion of the terms contained in the -investigations of MM. Damoiseau and Plana. Sir John Lubbock has -calculated the polar co-ordinates of the Moon directly; M. Poisson, -on the other hand, has obtained the variable elliptical elements; M. -Pontécoulant conceives that the method of variation or arbitrary -{374} constants may most conveniently be reserved for secular -inequalities and inequalities of long periods. - -MM. Lubbock and Pontécoulant have made the mode of treating the -Lunar Theory and the Planetary Theory agree with each other, instead -of following two different paths in the calculation of the two -problems, which had previously been done. - -Prof. Hansen, also, in his _Fundamenta Nova Investigationis Orbitæ -veræ quam Luna perlustrat_ (_Gothæ_, 1838), gives a general method, -including the Lunar Theory and the Planetary Theory as two special -cases. To this is annexed a solution of the _Problem of Four Bodies_. - -I am here speaking of the Lunar and Planetary Theories as Mechanical -Problems only. Connected with this subject, I will not omit to -notice a very general and beautiful method of solving problems -respecting the motion of systems **of mutually attracting bodies, -given by Sir W. R. Hamilton, in the _Philosophical Transactions_ for -1834-5 ("On a General Method in Dynamics"). His method consists in -investigating the _Principal Function_ of the co-ordinates of the -bodies: this function being one, by the differentiation of which, -the co-ordinates of the bodies of the system may be found. Moreover, -an approximate value of this function being obtained, the same -formulæ supply a means of successive approximation without limit.] - -9. _Precession. Motion of Rigid Bodies._--The series of -investigations of which I have spoken, extensive and complex as it -is, treats the moving bodies as points only, and takes no account of -any peculiarity of their form or motion of their parts. The -investigation of the motion of a body of any magnitude and form, is -another branch of analytical mechanics, which well deserves notice. -Like the former branch, it mainly owed its cultivation to the -problems suggested by the solar system. Newton, as we have seen, -endeavored to calculate the effect of the attraction of the sun and -moon in producing the _precession of the equinoxes_; but in doing -this he made some mistakes. In 1747, D'Alembert solved this problem -by the aid of his "Principle;" and it was not difficult for him to -show, as he did in his _Opuscules_, in 1761, that the same method -enabled him to determine the motion of a body of any figure acted -upon by any forces. But, as the reader will have observed in the -course of this narrative, the great mathematicians of this period -were always nearly abreast of each other in their -advances.--Euler,[57\6] in the mean time, had published, in 1751, a -solution of the {375} problem of the precession; and in 1752, a -memoir which he entitled _Discovery of a New Principle of -Mechanics_, and which contains a solution of the general problem of -the alteration of rotary motion by forces. D'Alembert noticed with -disapprobation the assumption of priority which this title implied, -though allowing the merit of the memoir. Various improvements were -made in these solutions; but the final form was given them by Euler; -and they were applied to a great variety of problems in his _Theory -of the Motion of Solid and Rigid Bodies_, which was written[58\6] -about 1760, and published in 1765. The formulæ in this work were -much simplified by the use of a discovery of Segner, that every body -has three axes which were called Principal Axes, about which alone -(in general) it would permanently revolve. The equations which Euler -and other writers had obtained, were attacked as erroneous by Landen -in the Philosophical Transactions for 1785; but I think it is -impossible to consider this criticism otherwise than as an example -of the inability of the English mathematicians of that period to -take a steady hold of the analytical generalizations to which the -great Continental authors had been led. Perhaps one of the most -remarkable calculations of the motion of a rigid body is that which -Lagrange performed with regard to the _Moon's Libration_; and by -which he showed that the Nodes of the Moon's Equator and those of -her Orbit must always coincide. - -[Note 57\6: _Ac. Berl._ 1745, 1750.] - -[Note 58\6: See the preface to the book.] - -10. _Vibrating Strings._--Other mechanical questions, unconnected -with astronomy, were also pursued with great zeal and success. Among -these was the problem of a vibrating string, stretched between two -fixed points. There is not much complexity in the mechanical -conceptions which belong to this case, but considerable difficulty -in reducing them to analysis. Taylor, in his _Method of Increments_, -published in 1716, had annexed to his work a solution of this -problem; obtained on suppositions, limited indeed, but apparently -conformable to the most common circumstances of practice. John -Bernoulli, in 1728, had also treated the same problem. But it -assumed an interest altogether new, when, in 1747, D'Alembert -published his views on the subject; in which he maintained that, -instead of one kind of curve only, there were an infinite number of -different curves, which answered the conditions of the question. The -problem, thus put forward by one great mathematician, was, as usual, -taken up by the others, whose names the reader is now so familiar -with in such an association. In {376} 1748, Euler not only assented -to the generalization of D'Alembert, but held that it was not -necessary that the curves so introduced should be defined by any -algebraical condition whatever. From this extreme indeterminateness -D'Alembert dissented; while Daniel Bernoulli, trusting more to -physical and less to analytical reasonings, maintained that both -these generalizations were inapplicable in fact, and that the -solution was really restricted, as had at first been supposed, to -the form of the trochoid, and to other forms derivable from that. He -introduced, in such problems, the "Law of Coexistent Vibrations," -which is of eminent use in enabling us to conceive the results of -complex mechanical conditions, and the real import of many -analytical expressions. In the mean time, the wonderful analytical -genius of Lagrange had applied itself to this problem. He had formed -the Academy of Turin, in conjunction with his friends Saluces and -Cigna; and the first memoir in their Transactions was one by him on -this subject: in this and in subsequent writings he has established, -to the satisfaction of the mathematical world, that the functions -introduced in such cases are not necessarily continuous, but are -arbitrary to the same degree that the motion is so practically; -though capable of expression by a series of circular functions. This -controversy, concerning the degree of lawlessness with which the -conditions of the solution may be assumed, is of consequence, not -only with respect to vibrating strings, but also with respect to -many problems, belonging to a branch of Mechanics which we now have -to mention, the Doctrine of Fluids. - -11. _Equilibrium of Fluids. Figure of the Earth. Tides._--The -application of the general doctrines of Mechanics to fluids was a -natural and inevitable step, when the principles of the science had -been generalized. It was easily seen that a fluid is, for this -purpose, nothing more than a body of which the parts are movable -amongst each other with entire facility; and that the mathematician -must trace the consequences of this condition upon his equations. -This accordingly was done, by the founders of mechanics, both for -the cases of the equilibrium and of motion. Newton's attempt to -solve the problem of the _figure of the earth_, supposing it fluid, -is the first example of such an investigation: and this solution -rested upon principles which we have already explained, applied with -the skill and sagacity which distinguished all that Newton did. - -We have already seen how the generality of the principle, that -fluids press equally in all directions, was established. In applying -it to calculation, Newton took for his fundamental principle, the -equal {377} weight of columns of the fluid reaching to the centre; -Huyghens took, as his basis, the **perpendicularity of the resulting -force at each point to the surface of the fluid; Bouguer conceived -that both principles were necessary; and Clairaut showed that the -equilibrium of _all_ canals is requisite. He also was the first -mathematician who deduced from this principle the Equations of -Partial Differentials by which these laws are expressed; a step -which, as Lagrange says,[59\6] changed the face of Hydrostatics, and -made it a new science. Euler simplified the mode of obtaining the -Equations of Equilibrium for any forces whatever; and put them in -the form which is now generally adopted in our treatises. - -[Note 59\6: _Méc. Analyt._ ii. p. 180.] - -The explanation of the _Tides_, in the way in which Newton attempted -it in the third book of the _Principia_, is another example of a -hydrostatical investigation: for he considered only the form that -the ocean would have if it were at rest. The memoirs of Maclaurin, -Daniel Bernoulli, and Euler, on the question of the Tides, which -shared among them the prize of the Academy of Sciences in 1740, went -upon the same views. - -The _Treatise of the Figure of the Earth_, by Clairaut, in 1743, -extended Newton's solution of the same problem, by supposing a solid -nucleus covered with a fluid of different density. No peculiar -novelty has been introduced into this subject, except a method -employed by Laplace for determining the attractions of spheroids of -small eccentricity, which is, as Professor Airy has said,[60\6] "a -calculus the most singular in its nature, and the most powerful in -its effects, of any which has yet appeared." - -[Note 60\6: _Enc. Met._ Fig. of Earth, p. 192.] - -12. _Capillary Action._--There is only one other problem of the -statics of fluids on which it is necessary to say a word,--the -doctrine of Capillary Attraction. Daniel Bernoulli,[61\6] in 1738, -states that he passes over the subject, because he could not reduce -the facts to general laws: but Clairaut was more successful, and -Laplace and Poisson have since given great analytical completeness to -his theory. At present our business is, not so much with the -sufficiency of the theory to explain phenomena, as with the mechanical -problem of which this is an example, which is one of a very remarkable -and important character; namely, to determine the effect of -attractions which are exercised by all the particles of bodies, on the -hypothesis that the {378} attraction of each particle, though sensible -when it acts upon another particle at an extremely small distance from -it, becomes insensible and vanishes the moment this distance assumes a -perceptible magnitude. It may easily be imagined that the analysis by -which results are obtained under conditions so general and so -peculiar, is curious and abstract; the problem has been resolved in -some very extensive cases. - -[Note 61\6: _Hydrodyn._ Pref. p. 5.] - -13. _Motion of Fluids._--The only branch of mathematical mechanics -which remains to be considered, is that which is, we may venture to -say, hitherto incomparably the most incomplete of -all,--Hydrodynamics. It may easily be imagined that the mere -hypothesis of absolute relative mobility in the parts, combined with -the laws of motion and nothing more, are conditions too vague and -general to lead to definite conclusions. Yet such are the conditions -of the problems which relate to the motion of fluids. Accordingly, -the mode of solving them has been, to introduce certain other -hypotheses, often acknowledged to be false, and almost always in -some measure arbitrary, which may assist in determining and -obtaining the solution. The Velocity of a fluid issuing from an -orifice in a vessel, and the Resistance which a solid body suffers -in moving in a fluid, have been the two main problems on which -mathematicians have employed themselves. We have already spoken of -the manner in which Newton attacked both these, and endeavored to -connect them. The subject became a branch of Analytical Mechanics by -the labors of D. Bernoulli, whose _Hydrodynamica_ was published in -1738. This work rests upon the Huyghenian principle of which we have -already spoken in the history of the centre of oscillation; namely, -the equality of the _actual descent_ of the particles and the -_potential ascent_; or, in other words, the conservation of _vis -viva_. This was the first analytical treatise; and the analysis is -declared by Lagrange to be as elegant in its steps as it is simple -in its results. Maclaurin also treated the subject; but is accused -of reasoning in such a way as to show that he had determined upon -his result beforehand; and the method of John Bernoulli, who -likewise wrote upon it, has been strongly objected to by D'Alembert. -D'Alembert himself applied the principle which bears his name to -this subject; publishing a _Treatise on the Equilibrium and Motion -of Fluids_ in 1744, and on the _Resistance of Fluids_ in 1753. His -_Réflexions sur la Cause Générale des Vents_, printed in 1747, are -also a celebrated work, belonging to this part of mathematics. -Euler, in this as in other cases, was one of those who most -contributed to give analytical elegance to the subject. In addition -to the questions which {379} have been mentioned, he and Lagrange -treated the problems of the small vibrations of fluids, both -inelastic and elastic;--a subject which leads, like the question of -vibrating strings, to some subtle and abstruse considerations -concerning the significations of the integrals of partial -differential equations. Laplace also took up the subject of waves -propagated along the surface of water; and deduced a very celebrated -theory of the tides, in which he considered the ocean to be, not in -equilibrium, as preceding writers had supposed, but agitated by a -constant series of undulations, produced by the solar and lunar -forces. The difficulty of such an investigation may be judged of -from this, that Laplace, in order to carry it on, is obliged to -assume a mechanical proposition, unproved, and only conjectured to -be true; namely,[62\6] that, "in a system of bodies acted upon by -forces which are periodical, the state of the system is periodical -like the forces." Even with this assumption, various other arbitrary -processes are requisite; and it appears still very doubtful whether -Laplace's theory is either a better mechanical solution of the -problem, or a nearer approximation to the laws of the phenomena, -than that obtained by D. Bernoulli, following the views of Newton. - -[Note 62\6: _Méc. Cél._ t. ii. p. 218.] - -In most cases, the solutions of problems of hydrodynamics are not -satisfactorily confirmed by the results of observation. Poisson and -Cauchy have prosecuted the subject of waves, and have deduced very -curious conclusions by a very recondite and profound analysis. The -assumptions of the mathematician here do not represent the -conditions of nature; the rules of theory, therefore, are not a good -standard to which we may refer the aberrations of particular cases; -and the laws which we obtain from experiment are very imperfectly -illustrated by _à priori_ calculation. The case of this department -of knowledge, Hydrodynamics, is very peculiar; we have reached the -highest point of the science,--the laws of extreme simplicity and -generality from which the phenomena flow; we cannot doubt that the -ultimate principles which we have obtained are the true ones, and -those which really apply to the facts; and yet we are far from being -able to apply the principles to explain or find out the facts. In -order to do this, we want, in addition to what we have, true and -useful principles, intermediate between the highest and the -lowest;--between the extreme and almost barren generality of the -laws of motion, and the endless varieties and inextricable -complexity of fluid motions in special cases. {380} The reason of -this peculiarity in the science of Hydrodynamics appears to be, that -its general principles were not discovered with reference to the -science itself, but by extension from the sister science of the -Mechanics of Solids; they were not obtained by ascending gradually -from particulars, to truths more and more general, respecting the -motions of fluids; but were caught at once, by a perception that the -parts of fluids are included in that range of generality which we -are entitled to give to the supreme laws of motions of solids. Thus, -Solid Dynamics and Fluid Dynamics resemble two edifices which have -their highest apartment in common, and though we can explore every -part of the former building, we have not yet succeeded in traversing -the staircase of the latter, either from the top or from the bottom. -If we had lived in a world in which there were no solid bodies, we -should probably not have yet discovered the laws of motion; if we -had lived in a world in which there were no fluids, we should have -no idea how insufficient a complete possession of the general laws -of motion may be, to give us a true knowledge of particular results. - -14. _Various General Mechanical Principles._--The generalized laws -of motion, the points to which I have endeavored to conduct my -history, include in them all other laws by which the motions of -bodies can be regulated; and among such, several laws which had been -discovered before the highest point of generalization was reached, -and which thus served as stepping-stones to the ultimate principles. -Such were, as we have seen, the Principles of the Conservation of -_vis viva_, the Principle of the Conservation of the Motion of the -Centre of Gravity, and the like. These principles may, of course, be -deduced from our elementary laws, and were finally established by -mathematicians on that footing. There are other principles which may -be similarly demonstrated; among the rest, I may mention the -Principle of _the Conservation of areas_, which extends to any -number of bodies a law analogous to that which Kepler had observed, -and Newton demonstrated, respecting the areas described by each -planet round the sun. I may mention also, the Principle of the -_Immobility of the plane of maximum areas_, a plane which is not -disturbed by any mutual action of the parts of any system. The -former of these principles was published about the same time by -Euler, D. Bernoulli, and Darcy, under different forms, in 1746 and -1747; the latter by Laplace. - -To these may be added a law, very celebrated in its time, and the -occasion of an angry controversy, _the Principle of least action_. -{381} Maupertuis conceived that he could establish _à priori_, by -theological arguments, that all mechanical changes must take place -in the world so as to occasion the least possible quantity of -_action_. In asserting this, it was proposed to measure the Action -by the product of Velocity and Space; and this measure being -adopted, the mathematicians, though they did not generally assent to -Maupertuis' reasonings, found that his principle expressed a -remarkable and useful truth, which might be established on known -mechanical grounds. - -15. _Analytical Generality. Connection of Statics and -Dynamics._--Before I quit this subject, it is important to remark -the peculiar character which the science of Mechanics has now -assumed, in consequence of the extreme analytical generality which -has been given it. Symbols, and operations upon symbols, include the -whole of the reasoner's task; and though the relations of space are -the leading subjects in the science, the great analytical treatises -upon it do not contain a single diagram. The _Mécanique Analytique_ -of Lagrange, of which the first edition appeared in 1788, is by far -the most consummate example of this analytical generality. "The plan -of this work," says the author, "is entirely new. I have proposed to -myself to reduce the whole theory of this science, and the art of -resolving the problems which it includes, to general formulæ, of -which the simple development gives all the equations necessary for -the solution of the problem."--"The reader will find no figures in -the work. The methods which I deliver do not require either -constructions, or geometrical or mechanical reasonings; but only -algebraical operations, subject to a regular and uniform rule of -proceeding." Thus this writer makes Mechanics a branch of Analysis; -instead of making, as had previously been done, Analysis an -implement of Mechanics.[63\6] The transcendent generalizing genius -of Lagrange, and his matchless analytical skill and elegance, have -made this undertaking as successful as it is striking. - -[Note 63\6: Lagrange himself terms Mechanics, "An Analytical -Geometry of four dimensions." Besides the _three co-ordinates_ which -determine the place of a body in _space_, the _time_ enters as a -_fourth co-ordinate_. [Note by Littrow.]] - -The mathematical reader is aware that the language of mathematical -symbols is, in its nature, more general than the language of words: -and that in this way truths, translated into symbols, often suggest -their own generalizations. Something of this kind has happened in -Mechanics. The same Formula expresses the general condition of -Statics and that of Dynamics. The tendency to generalization which -is thus introduced by analysis, makes mathematicians unwilling to -{382} acknowledge a plurality of Mechanical principles; and in the -most recent analytical treatises on the subject, all the doctrines -are deduced from the single Law of Inertia. Indeed, if we identify -Forces with the Velocities which produce them, and allow the -Composition of Forces to be applicable to force _so understood_, it -is easy to see that we can reduce the Laws of Motion to the -Principles of Statics; and this conjunction, though it may not be -considered as philosophically just, is verbally correct. If we thus -multiply or extend the meanings of the term Force, we make our -elementary principles simpler and fewer than before; and those -persons, therefore, who are willing to assent to such a use of -words, can thus obtain an additional generalisation of dynamical -principles; and this, as I have stated, has been adopted in several -recent treatises. I shall not further discuss here how far this is a -real advance in science. - -Having thus rapidly gone through the history of Force and Attraction -in the abstract, we return to the attempt to interpret the phenomena -of the universe by the aid of these abstractions thus established. - -But before we do so, we may make one remark on the history of this -part of science. In consequence of the vast career into which the -Doctrine of Motion has been drawn by the splendid problems proposed to -it by Astronomy, the origin and starting-point of Mechanics, namely -Machines, had almost been lost out of sight. _Machines_ had become the -smallest part of _Mechanics_, as _Land-measuring_ had become the -smallest part of _Geometry_. Yet the application of Mathematics to the -doctrine of Machines has led, at all periods of the Science, and -especially in our own time, to curious and valuable results. Some of -these will be noticed in the _Additions_ to this volume. - - - -{{383}} -BOOK VII. - - - -THE MECHANICAL SCIENCES. -(CONTINUED.) - - -HISTORY -OF -PHYSICAL ASTRONOMY. - - - DESCEND from heaven, Urania, by that name - If rightly thou art called, whose voice divine - Following, above the Olympian hill I soar, - Above the flight of Pegasean wing. - The meaning, not the name, I call, for thou - Nor of the muses nine, nor on the top - Of old Olympus dwell'st: but heavenly-born, - Before the hills appeared, or fountain flowed, - Thou with Eternal Wisdom didst converse, - Wisdom, thy sister. - - _Paradise Lost_, B. vii. - - - -{{385}} -CHAPTER I. - -PRELUDE TO THE INDUCTIVE EPOCH OF NEWTON. - - -WE have now to contemplate the last and most splendid period of the -progress of Astronomy;--the grand completion of the history of the -most ancient and prosperous province of human knowledge;--the steps -which elevated this science to an unrivalled eminence above other -sciences;--the first great example of a wide and complex assemblage -of phenomena indubitably traced to their single simple cause;--in -short, the first example of the formation of a perfect Inductive -Science. - -In this, as in other considerable advances in real science, the -complete disclosure of the new truths by the principal discoverer, -was preceded by movements and glimpses, by trials, seekings, and -guesses on the part of others; by indications, in short, that men's -minds were already carried by their intellectual impulses in the -direction in which the truth lay, and were beginning to detect its -nature. In a case so important and interesting as this, it is more -peculiarly proper to give some view of this Prelude to the Epoch of -the full discovery. - -(_Francis Bacon._) That Astronomy should become Physical -Astronomy,--that the motions of the heavenly bodies should be traced -to their causes, as well as reduced to rule,--was felt by all -persons of active and philosophical minds as a pressing and -irresistible need, at the time of which we speak. We have already -seen how much this feeling had to do in impelling Kepler to the -train of laborious research by which he made his discoveries. -Perhaps it may be interesting to point out how strongly this -persuasion of the necessity of giving a physical character to -astronomy, had taken possession of the mind of Bacon, who, looking -at the progress of knowledge with a more comprehensive spirit, and -from a higher point of view than Kepler, could have none of his -astronomical prejudices, since on that subject he was of a different -school, and of far inferior knowledge. In his "Description of the -Intellectual Globe," Bacon says that while Astronomy had, up to that -time, had it for her business to inquire into the rules of the -heavenly motions, and Philosophy into their causes, they had both so -far worked without due appreciation of their respective tasks; -Philosophy neglecting facts, and Astronomy claiming assent to her -{386} mathematical hypotheses, which ought to be considered as mere -steps of calculation. "Since, therefore," he continues,[1\7] "each -science has hitherto been a slight and ill-constructed thing, we -must assuredly take a firmer stand; our ground being, that these two -subjects, which on account of the narrowness of men's views and the -traditions of professors have been so long dissevered, are, in fact, -one and the same thing, and compose one body of science." It must be -allowed that, however erroneous might be the points of Bacon's -positive astronomical creed, these general views of the nature and -position of the science are most sound and philosophical. - -[Note 1\7: Vol. ix. 221.] - -(_Kepler_) In his attempts to suggest a right physical view of the -starry heavens and their relation to the earth, Bacon failed, along -with all the writers of his time. It has already been stated that -the main cause of this failure was the want of a knowledge of the -true theory of motion;--the non-existence of the science of -Dynamics. At the time of Bacon and Kepler, it was only just -beginning to be possible to reduce the heavenly motions to the laws -of earthly motion, because the latter were only just then divulged. -Accordingly, we have seen that the whole of Kepler's physical -speculations proceed upon an ignorance of the first law of motion, -and assume it to be the main problem of the physical astronomer to -assign the cause which _keeps up_ the motions of the planets. -Kepler's doctrine is, that a certain Force or Virtue resides in the -sun, by which all bodies within his influence are carried round him. -He illustrates[2\7] the nature of this Virtue in various ways, -comparing it to Light, and to the Magnetic Power, which it resembles -in the circumstances of operating at a distance, and also in -exercising a feebler influence as the distance becomes greater. But -it was obvious that these comparisons were very imperfect; for they -do not explain how the sun produces in a body at a distance a motion -_athwart_ the line of emanation; and though Kepler introduced an -assumed rotation of the sun on his axis as the cause of this effect, -that such a cause could produce the result could not be established -by any analogy of terrestrial motions. But another image to which he -referred, suggested a much more substantial and conceivable kind of -mechanical action by which the celestial motions might be produced, -namely, a current of fluid matter circulating round the sun, and -carrying the planet with it, like a boat in a stream. In the Table -of Contents of the work on the planet Mars, the purport of the -chapter to which I have alluded is {387} stated as follows: "A -physical speculation, in which it is demonstrated that the vehicle -of that Virtue which urges the planets, circulates through the -spaces of the universe after the manner of a river or whirlpool -(_vortex_), moving quicker than the planets." I think it will be -found, by any one who reads Kepler's phrases concerning the _moving -force,--the magnetic nature,--the immaterial virtue_ of the sun, -that they convey no distinct conception, except so far as they are -interpreted by the expressions just quoted. A vortex of fluid -constantly whirling round the sun, kept in this whirling motion by -the rotation of the sun himself, and carrying the planets round the -sun by its revolution, as a whirlpool carries straws, could be -readily understood; and though it appears to have been held by -Kepler that this current and vortex was immaterial, he ascribes to -it the power of overcoming the inertia of bodies, and of putting -them and keeping them in motion, the only material properties with -which he had any thing to do. Kepler's physical reasonings, -therefore, amount, in fact, to the doctrine of Vortices round the -central bodies, and are occasionally so stated by himself; though by -asserting these vortices to be "an immaterial species," and by the -fickleness and variety of his phraseology on the subject, he leaves -this theory in some confusion;--a proceeding, indeed, which both his -want of sound mechanical conceptions, and his busy and inventive -fancy, might have led us to expect. Nor, we may venture to say, was -it easy for any one at Kepler's time to devise a more plausible -theory than the theory of vortices might have been made. It was only -with the formation and progress of the science of Mechanics that -this theory became untenable. - -[Note 2\7: _De Stellâ Martis_, P. 3. c. xxxiv.] - -(_Descartes_) But if Kepler might be excused, or indeed admired, for -propounding the theory of Vortices at his time, the case was -different when the laws of motion had been fully developed, and when -those who knew the state of mechanical science ought to have learned -to consider the motions of the stars as a mechanical problem, -subject to the same conditions as other mechanical problems, and -capable of the same exactness of solution. And there was an especial -inconsistency in the circumstance of the Theory of Vortices being -put forwards by Descartes, who pretended, or was asserted by his -admirers, to have been one of the discoverers of the true Laws of -Motion. It certainly shows both great conceit and great shallowness, -that he should have proclaimed with much pomp this crude invention -of the ante-mechanical period, at the time when the best -mathematicians of Europe, as Borelli in Italy, Hooke and Wallis in -England, Huyghens in Holland, {388} were patiently laboring to bring -the mechanical problem of the universe into its most distinct form, -in order that it might be solved at last and forever. - -I do not mean to assert that Descartes borrowed his doctrines from -Kepler, or from any of his predecessors, for the theory was -sufficiently obvious; and especially if we suppose the inventor to -seek his suggestions rather in the casual examples offered to the -sense than in the exact laws of motion. Nor would it be reasonable -to rob this philosopher of that credit, of the plausible deduction -of a vast system from apparently simple principles, which, at the -time, was so much admired; and which undoubtedly was the great cause -of the many converts to his views. At the same time we may venture -to say that a system of doctrine thus deduced from assumed -principles by a long chain of reasoning, and not verified and -confirmed at every step by detailed and exact facts, has hardly a -chance of containing any truth. Descartes said that he should think -it little to show how the world _is_ constructed, if he could not -also show that it _must_ of necessity have been so constructed. The -more modest philosophy which has survived the boastings of his -school is content to receive all its knowledge of facts from -experience, and never dreams of interposing its peremptory _must be_ -when nature is ready to tell us what _is_. The _à priori_ -philosopher has, however, always a strong feeling in his favor among -men. The deductive form of his speculations gives them something of -the charm and the apparent certainty of pure mathematics; and while -he avoids that laborious recurrence to experiments, and measures, -and multiplied observations, which is irksome and distasteful to -those who are impatient to grow wise at once, every fact of which -the theory appears to give an explanation, seems to be an unasked -and almost an infallible witness in its favor. - -My business with Descartes here is only with his physical Theory of -Vortices; which, great as was its glory at one time, is now utterly -extinguished. It was propounded in his _Principia Philosophiæ_, in -1644. In order to arrive at this theory, he begins, as might be -expected of him, from reasonings sufficiently general. He lays it -down as a maxim, in the first sentence of his book, that a person -who seeks for truth must, once in his life, doubt of all that he -most believes. Conceiving himself thus to have stripped himself of -all his belief on all subjects, in order to resume that part of it -which merits to be retained, he begins with his celebrated -assertion, "I think, therefore I am;" which appears to him a certain -and immovable principle, by means of {389} which he may proceed to -something more. Accordingly, to this he soon adds the idea, and -hence the certain existence, of God and his perfections. He then -asserts it to be also manifest, that a vacuum in any part of the -universe is impossible; the whole must be filled with matter, and -the matter must be divided into equal angular parts, this being the -most simple, and therefore the most natural supposition.[3\7] This -matter being in motion, the parts are necessarily ground into a -spherical form; and the corners thus rubbed off (like filings or -sawdust) form a second and more subtle matter.[4\7] There is, -besides, a third kind of matter, of parts more coarse and less -fitted for motion. The first matter makes luminous bodies, as the -sun, and the fixed stars; the second is the transparent substance of -the skies; the third is the material of opake bodies, as the earth, -planets, and comets. We may suppose, also,[5\7] that the motions of -these parts take the form of revolving circular currents,[6\7] or -_vortices_. By this means, the first matter will be collected to the -centre of each vortex, while the second, or subtle matter, surrounds -it, and, by its centrifugal effort, constitutes light. The planets -are carried round the sun by the motion of his vortex,[7\7] each -planet being at such a distance from the sun as to be in a part of -the vortex suitable to its solidity and mobility. The motions are -prevented from being exactly circular and regular by various causes; -for instance, a vortex may be pressed into an oval shape by -contiguous vortices. The satellites are, in like manner, carried -round their primary planets by subordinate vortices; while the -comets have sometimes the liberty of gliding out of one vortex into -the one next contiguous, and thus travelling in a sinuous course, -from system to system, through the universe. It is not necessary for -us to speak here of the entire deficiency of this system in -mechanical consistency, and in a correspondency to observation in -details and measures. Its general reception and temporary sway, in -some instances even among intelligent men and good mathematicians, -are the most remarkable facts connected with it. These may be -ascribed, in part, to the circumstance that philosophers were now -ready and eager for a physical astronomy commensurate with the -existing state of knowledge; they may have been owing also, in some -measure, to the character and position of Descartes. He was a man of -high claims in every department of speculation, and, in pure -mathematics, a genuine inventor of great eminence;--a man of family -and a soldier;--an inoffensive philosopher, attacked and persecuted -{390} for his opinions with great bigotry and fury by a Dutch -divine, Voet;--the favorite and teacher of two distinguished -princesses, and, it is said, the lover of one of them. This was -Elizabeth, the daughter of the Elector Frederick, and consequently -grand-daughter of our James the First. His other royal disciple, the -celebrated Christiana of Sweden, showed her zeal for his -instructions by appointing the hour of five in the morning for their -interviews. This, in the climate of Sweden, and in the winter, was -too severe a trial for the constitution of the philosopher, born in -the sunny valley of the Loire; and, after a short residence at -Stockholm, he died of an inflammation of the chest in 1650. He -always kept up an active correspondence with his friend Mersenne, -who was called, by some of the Parisians, "the Resident of Descartes -at Paris;" and who informed him of all that was done in the world of -science. It is said that he at first sent to Mersenne an account of -a system of the universe which he had devised, which went on the -assumption of a vacuum; Mersenne informed him that the _vacuum_ was -no longer the fashion at Paris; upon which he proceeded to remodel -his system, and to re-establish it on the principle of a _plenum_. -Undoubtedly he tried to avoid promulgating opinions which might -bring him into trouble. He, on all occasions, endeavored to explain -away the doctrine of the motion of the earth, so as to evade the -scruples to which the decrees of the pope had given rise; and, in -stating the theory of vortices, he says,[8\7] "There is no doubt -that the world was created at first with all its perfection; -nevertheless, it is well to consider how it might have arisen from -certain principles, although we know that it did not." Indeed, in -the whole of his philosophy, he appears to deserve the character of -being both rash and cowardly, "_pusillanimus simul et audax_," far -more than Aristotle, to whose physical speculations Bacon applies -this description.[9\7] - -[Note 3\7: _Prin._ p. 58.] - -[Note 4\7: Ib. p. 59.] - -[Note 5\7: Ib. p. 56.] - -[Note 6\7: Ib. p. 61.] - -[Note 7\7: Ib. c. 140, p. 114.] - -[Note 8\7: _Prin._ p. 56.] - -[Note 9\7: Bacon, _Descriptio Globi Intellectualis_.] - -Whatever the causes might be, his system was well received and -rapidly adopted. Gassendi, indeed, says that he found nobody who had -the courage to read the _Principia_ through;[10\7] but the system -was soon embraced by the younger professors, who were eager to -dispute in its favor. It is said[11\7] that the University of Paris -was on the point of publishing an edict against these new doctrines, -and was only prevented from doing so by a pasquinade which is worth -mentioning. It was composed by the poet Boileau (about 1684), and -professed to be a Request in favor of Aristotle, and an Edict issued -from Mount {391} Parnassus in consequence. It is obvious that, at -this time, the cause of Cartesianism was looked upon as the cause of -free inquiry and modern discovery, in opposition to that of bigotry, -prejudice, and ignorance. Probably the poet was far from being a -very severe or profound critic of the truth of such claims. "This -petition of the Masters of Arts, Professors and Regents of the -University of Paris, humbly showeth, that it is of public notoriety -that the sublime and incomparable Aristotle was, without contest, -the first founder of the four elements, fire, air, earth, and water; -that he did, by special grace, accord unto them a simplicity which -belongeth not to them of natural right;" and so on. "Nevertheless, -since, a certain time past, two individuals, named Reason and -Experience, have leagued themselves together to dispute his claim to -the rank which of justice pertains to him, and have tried to erect -themselves a throne on the ruins of his authority; and, in order the -better to gain their ends, have excited certain factious spirits, -who, under the names of Cartesians and Gassendists, have begun to -shake off the yoke of their master, Aristotle; and, contemning his -authority, with unexampled temerity, would dispute the right which -he had acquired of making true pass for false and false for -true;"--In fact, this production does not exhibit any of the -peculiar tenets of Descartes, although, probably, the positive -points of his doctrines obtained a footing in the University of -Paris, under the cover of this assault on his adversaries. The -Physics of Rohault, a zealous disciple of Descartes, was published -at Paris about 1670,[12\7] and was, for a time, the standard book -for students of this subject, both in France and in England. I do -not here speak of the later defenders of the Cartesian system, for, -in their hands, it was much modified by the struggle which it had to -maintain against the Newtonian system. - -[Note 10\7: Del. _A. M._ ii. 193.] - -[Note 11\7: _Enc. Brit._ art. _Cartesianism._] - -[Note 12\7: And a second edition in 1672.] - -We are concerned with Descartes and his school only as they form -part of the picture of the intellectual condition of Europe just -before the publication of Newton's discoveries. Beyond this, the -Cartesian speculations are without value. When, indeed, Descartes' -countrymen could no longer refuse their assent and admiration to the -Newtonian theory, it came to be the fashion among them to say that -Descartes had been the necessary precursor of Newton; and to adopt a -favorite saying of Leibnitz, that the Cartesian philosophy was the -antechamber of Truth. Yet this comparison is far from being happy: -it appeared rather as if these suitors had mistaken the door; for -those {392} who first came into the presence of Truth herself, were -those who never entered this imagined antechamber, and those who -were in the antechamber first, were the last in penetrating further. -In partly the same spirit, Playfair has noted it as a service which -Newton perhaps owed to Descartes, that "he had exhausted one of the -most tempting forms of error." We shall see soon that this -temptation had no attraction for those who looked at the problem in -its true light, as the Italian and English philosophers already did. -Voltaire has observed, far more truly, that Newton's edifice rested -on no stone of Descartes' foundations. He illustrates this by -relating that Newton only once read the work of Descartes, and, in -doing so, wrote the word "_error_," repeatedly, on the first seven -or eight pages; after which he read no more. This volume, Voltaire -adds, was for some time in the possession of Newton's nephew.[13\7] - -[Note 13\7: _Cartesianism_, Enc. Phil.] - -(_Gassendi._) Even in his own country, the system of Descartes was -by no means universally adopted. We have seen that though Gassendi -was coupled with Descartes as one of the leaders of the new -philosophy, he was far from admiring his work. Gassendi's own views -of the causes of the motions of the heavenly bodies are not very -clear, nor even very clearly referrible to the laws of mechanics; -although he was one of those who had most share in showing that -those laws apply to astronomical motions. In a chapter, headed[14\7] -"Quæ sit motrix siderum causa," he reviews several opinions; but the -one which he seems to adopt, is that which ascribes the motion of -the celestial globes to certain fibres, of which the action is -similar to that of the muscles of animals. It does not appear, -therefore, that he had distinctly apprehended, either the -continuation of the movements of the planets by the First Law of -Motion, or their deflection by the Second Law;--the two main steps -on the road to the discovery of the true forces by which they are -made to describe their orbits. - -[Note 14\7: Gassendi, _Opera_, vol. i. p. 639.] - -(_Leibnitz, &c._) Nor does it appear that in Germany mathematicians -had attained this point of view. Leibnitz, as we have seen, did not -assent to the opinions of Descartes, as containing the complete truth; -and yet his own views of the physics of the universe do not seem to -have any great advantage over these. In 1671 he published _A new -physical hypothesis, by which the causes of most phenomena are deduced -from a certain single universal motion supposed in our globe;--not to -be despised either by the Tychonians or the Copernicans_. He supposes -{393} the particles of the earth to have separate motions, which -produce collisions, and thus propagate[15\7] an "agitation of the -ether," radiating in all directions; and,[16\7] "by the rotation of -the sun on its axis, concurring with its rectilinear action on the -earth, arises the motion of the earth about the sun." The other -motions of the solar system are, as we might expect, accounted for in -a similar manner; but it appears difficult to invest such an -hypothesis with any mechanical consistency. - -[Note 15\7: Art. 5.] - -[Note 16\7: Ib. 8.] - -John Bernoulli maintained to the last the Cartesian hypothesis, -though with several modifications of his own, and even pretended to -apply mathematical calculation to his principles. This, however, -belongs to a later period of our history; to the reception, not to -the prelude, of the Newtonian theory. - -(_Borelli._) In Italy, Holland, and England, mathematicians appear -to have looked much more steadily at the problem of the celestial -motions, by the light which the discovery of the real laws of motion -threw upon it. In Borelli's _Theories of the Medicean Planets_, -printed at Florence in 1666, we have already a conception of the -nature of central action, in which true notions begin to appear. The -attraction of a body upon another which revolves about it is spoken -of and likened to magnetic action; not converting the attracting -force into a transverse force, according to the erroneous views of -Kepler, but taking it as a tendency of the bodies to meet. "It is -manifest," says he,[17\7] "that every planet and satellite revolves -round some principal globe of the universe as a fountain of virtue, -which so draws and holds them that they cannot by any means be -separated from it, but are compelled to follow it wherever it goes, -in constant and continuous revolutions." And, further on, he -describes[18\7] the nature of the action, as a matter of conjecture -indeed, but with remarkable correctness.[19\7] "We shall account for -these motions by supposing, that which can hardly be denied, that -the planets have a certain natural appetite for uniting themselves -with the globe round which they revolve, and that they really tend, -with all their efforts, to approach to such globe; the planets, for -instance, to the sun, the Medicean Stars to Jupiter. It is certain, -also, that circular motion gives a body a tendency to recede from -the centre of such revolution, as we find in a wheel, or a stone -whirled in a sling. Let us suppose, then, the planet to endeavor to -approach the sun; since, in the mean time, it requires, by the -circular motion, a force to recede from the same central body, it -comes to pass, that when {394} those two opposite forces are equal, -each compensates the other, and the planet cannot go nearer to the -sun nor further from him than a certain determinate space, and thus -appears balanced and floating about him." - -[Note 17\7: Cap. 2.] - -[Note 18\7: Ib. 11.] - -[Note 19\7: P. 47.] - -This is a very remarkable passage; but it will be observed, at the -same time, that the author has no distinct conception of the manner -in which the change of direction of the planet's motion is regulated -from one instant to another; still less do his views lead to any -mode of calculating the distance from the central body at which the -planet would be thus balanced, or the space through which it might -approach to the centre and recede from it. There is a great interval -from Borelli's guesses, even to Huyghens' theorems and a much -greater to the beginning of Newton's discoveries. - -(_England._) It is peculiarly interesting to us to trace the gradual -approach towards these discoveries which took place in the minds of -English mathematicians and this we can do with tolerable -distinctness. Gilbert, in his work, _De Magnete_, printed in 1600, -has only some vague notions that the magnetic virtue of the earth in -some way determines the direction of the earth's axis, the rate of -its diurnal rotation, and that of the revolution of the moon about -it.[20\7] He died in 1603, and, in his posthumous work, already -mentioned (_De Mundo nostro Sublunari Philosophia nova_, 1651), we -have already a more distinct statement of the attraction of one body -by another.[21\7] "The force which emanates from the moon reaches to -the earth, and, in like manner, the magnetic virtue of the earth -pervades the region of the moon: both correspond and conspire by the -joint action of both, according to a proportion and conformity of -motions; but the earth has more effect, in consequence of its -superior mass; the earth attracts and repels the moon, and the moon, -within certain limits, the earth; not so as to make the bodies come -together, as magnetic bodies do, but so that they may go on in a -continuous course." Though this phraseology is capable of -representing a good deal of the truth, it does not appear to have -been connected, in the author's mind, with any very definite notions -of mechanical action in detail. We may probably say the same of -Milton's language: - What if the sun - Be centre to the world; and other stars, - By his attractive virtue and their own - Incited, dance about him various rounds? - _Par. Lost_, B. viii. {395} - -[Note 20\7: Lib. vi. cap. 6, 7.] - -[Note 21\7: Ib. ii. c. 19.] - -Boyle, about the same period, seems to have inclined to the -Cartesian hypothesis. Thus, in order to show the advantage of the -natural theology which contemplates organic contrivances, over that -which refers to astronomy, he remarks: "It may be said, that in -bodies inanimate,[22\7] the contrivance is very rarely so exquisite -but that the various motions and occurrences of their parts may, -without much improbability, be suspected capable, after many essays, -to cast one another into several of those circumvolutions called by -Epicurus συστροφὰς and by Descartes, _vortices_; which being once -made, may continue a long time after the manner explained by the -latter." Neither Milton nor Boyle, however, can be supposed to have -had an exact knowledge of the laws of mechanics; and therefore they -do not fully represent the views of their mathematical -contemporaries. But there arose about this time a group of -philosophers, who began to knock at the door where Truth was to be -found, although it was left for Newton to force it open. These were -the founders of the Royal Society, Wilkins, Wallis, Seth Ward, Wren, -Hooke, and others. The time of the beginning of the speculations and -association of these men corresponds to the time of the civil wars -between the king and parliament in England and it does not appear a -fanciful account of their scientific zeal and activity, to say, that -while they shared the common mental ferment of the times, they -sought in the calm and peaceful pursuit of knowledge a contrast to -the vexatious and angry struggles which at that time disturbed the -repose of society. It was well if these dissensions produced any -good to science to balance the obvious evils which flowed from them. -Gascoigne, the inventor of the micrometer, a friend of Horrox, was -killed in the battle of Marston Moor. Milburne, another friend of -Horrox, who like him detected the errors of Lansberg's astronomical -tables, left papers on this subject, which were lost by the coming -of the Scotch army into England in 1639; in the civil war which -ensued, the anatomical collections of Harvey were plundered and -destroyed. Most of these persons of whom I have lately had to speak, -were involved in the changes of fortune of the Commonwealth, some on -one side, and some on the other. Wilkins was made Warden of Wadham -by the committee of parliament appointed for reforming the -University of Oxford; and was, in 1659, made Master of Trinity -College, Cambridge, by Richard Cromwell, but ejected thence the year -following, upon the restoration of the {396} royal sway. Seth Ward, -who was a Fellow of Sidney College, Cambridge, was deprived of his -Fellowship by the parliamentary committee; but at a later period -(1649) he took the engagement to be faithful to the Commonwealth, -and became Savilian Professor of Astronomy at Oxford. Wallis held a -Fellowship of Queen's College, Cambridge, but vacated it by -marriage. He was afterwards much employed by the royal party in -deciphering secret writings, in which art he had peculiar skill. Yet -he was appointed by the parliamentary commissioners Savilian -Professor of Geometry at Oxford, in which situation he was continued -by Charles II. after his restoration. Christopher Wren was somewhat -later, and escaped these changes. He was chosen Fellow of All-Souls -in 1652, and succeeded Ward as Savilian Professor of Astronomy. -These men, along with Boyle and several others, formed themselves -into a club, which they called the Philosophical, or the Invisible -College; and met, from about the year 1645, sometimes in London, and -sometimes in Oxford, according to the changes of fortune and -residence of the members. Hooke went to Christ Church, Oxford, in -1663, where he was patronized by Boyle, Ward, and Wallis; and when -the Philosophical College resumed its meetings in London, after the -Restoration, as the Royal Society, Hooke was made "curator of -experiments." Halley was of the next generation, and comes after -Newton; he studied at Queen's College, Oxford, in 1673; but was at -first a man of some fortune, and not engaged in any official -situation. His talents and zeal, however, made him an active and -effective ally in the promotion of science. - -[Note 22\7: Shaw's Boyle's _Works_, ii. 160.] - -The connection of the persons of whom we have been speaking has a -bearing on our subject, for it led, historically speaking, to the -publication of Newton's discoveries in physical astronomy. Rightly -to propose a problem is no inconsiderable step to its solution; and -it was undoubtedly a great advance towards the true theory of the -universe to consider the motion of the planets round the sun as a -mechanical question, to be solved by a reference to the laws of -motion, and by the use of mathematics. So far the English -philosophers appear to have gone, before the time of Newton. Hooke, -indeed, when the doctrine of gravitation was published, asserted -that he had discovered it previously to Newton; and though this -pretension could not be maintained, he certainly had perceived that -the thing to be done was, to determine the effect of a central force -in producing curvilinear motion; which effect, as we have already -seen, he illustrated by experiment as early as 1666. Hooke had also -spoken more clearly on this subject {397} in _An Attempt to prove -the Motion of the Earth from Observations_, published in 1674. In -this, he distinctly states that the planets would move in straight -lines, if they were not deflected by central forces; and that the -central attractive power increases in approaching the centre in -certain degrees, dependent on the distance. "Now what these degrees -are," he adds, "I have not yet experimentally verified;" but he -ventures to promise to any one who succeeds in this undertaking, a -discovery of the cause of the heavenly motions. He asserted, in -conversation, to Halley and Wren, that he had solved this problem, -but his solution was never produced. The proposition that the -attractive force of the sun varies inversely as the square of the -distance from the centre, had already been divined, if not fully -established. If the orbits of the planets were circles, this -proportion of the forces might be deduced in the same manner as the -propositions concerning circular motion, which Huyghens published in -1673; yet it does not appear that Huyghens made this application of -his principles. Newton, however, had already made this step some -years before this time. Accordingly, he says in a letter to Halley, -on Hooke's claim to this discovery,[23\7] "When Huygenius put out -his _Horologium Oscillatorium_, a copy being presented to me, in my -letter of thanks I gave those rules in the end thereof a particular -commendation for their usefulness in computing the forces of the -moon from the earth, and the earth from the sun." He says, moreover, -"I am almost confident by circumstances, that Sir Christopher Wren -knew the duplicate proportion when I gave him a visit; and then Mr. -Hooke, by his book _Cometa_, will prove the last of us three that -knew it." Hooke's _Cometa_ was published in 1678. These inferences -were all connected with Kepler's law, that the times are in the -sesquiplicate ratio of the major axes of the orbits. But Halley had -also been led to the duplicate proportion by another train of -reasoning, namely, by considering the force of the sun as an -emanation, which must become more feeble in proportion to the -increased spherical surface over which it is diffused, and therefore -in the inverse proportion of the square of the distances.[24\7] In -this view of the matter, however, the difficulty was to determine -what would be the motion of a body acted on by such a force, when -the orbit is not circular but oblong. The investigation of this case -was a problem which, we can {398} easily conceive, must have -appeared of very formidable complexity while it was unsolved, and -the first of its kind. Accordingly Halley, as his biographer says, -"finding himself unable to make it out in any geometrical way, first -applied to Mr. Hooke and Sir Christopher Wren, and meeting with no -assistance from either of them, he went to Cambridge in August -(1684), to Mr. Newton, who supplied him fully with what he had so -ardently sought." - -[Note 23\7: _Biog. Brit._, art. _Hooke._] - -[Note 24\7: Bullialdus, in 1645, had asserted that the force by -which the sun "prehendit et harpagat," takes hold of and grapples -the planets, must be as the inverse square of the distance.] - -A paper of Halley's in the _Philosophical Transactions_ for January, -1686, professedly inserted as a preparation for Newton's work, -contains some arguments against the Cartesian hypothesis of gravity, -which seem to imply that Cartesian opinions had some footing among -English philosophers; and we are told by Whiston, Newton's successor -in his professorship at Cambridge, that Cartesianism formed a part -of the studies of that place. Indeed, Rohault's _Physics_ was used -as a classbook at that University long after the time of which we -are speaking; but the peculiar Cartesian doctrines which it -contained were soon superseded by others. - -With regard, then, to this part of the discovery, that the force of -the sun follows the inverse duplicate proportion of the distances, -we see that several other persons were on the verge of it at the -same time with Newton; though he alone possessed that combination of -distinctness of thought and power of mathematical invention, which -enabled him to force his way across the barrier. But another, and so -far as we know, an earlier train of thought, led by a different path -to the same result; and it was the convergence of these two lines of -reasoning that brought the conclusion to men's minds with -irresistible force. I speak now of the identification of the force -which retains the moon in her orbit with the force of gravity by -which bodies fall at the earth's surface. In this comparison Newton -had, so far as I am aware, no forerunner. We are now, therefore, -arrived at the point at which the history of Newton's great -discovery properly begins. {399} - - - - -CHAPTER II. - -THE INDUCTIVE EPOCH OF NEWTON.--DISCOVERY OF THE UNIVERSAL -GRAVITATION OF MATTER, ACCORDING TO THE LAW OF THE INVERSE SQUARE OF -THE DISTANCE. - - -IN order that we may the more clearly consider the bearing of this, -the greatest scientific discovery ever made, we shall resolve it -into the partial propositions of which it consists. Of these we may -enumerate five. The doctrine of universal gravitation asserts, - -1. That the force by which the _different_ planets are attracted to -the sun is in the inverse proportion of the squares of their -distances; - -2. That the force by which the _same_ planet is attracted to the -sun, in different parts of its orbit, is also in the inverse -proportion of the squares of the distances; - -3. That the _earth_ also exerts such a force on the _moon_, and that -this force is identical with the force of _gravity_; - -4. That bodies thus act on _other_ bodies, besides those which -revolve round them; thus, that the sun exerts such a force on the -moon and satellites, and that the planets exert such forces on _one -another_; - -5. That this force, thus exerted by the general masses of the sun, -earth, and planets, arises from the attraction of _each particle_ of -these masses; which attraction follows the above law, and belongs to -all matter alike. - -The history of the establishment of these five truths will be given -in order. - -1. _Sun's Force on Different Planets._--With regard to the first of -the above five propositions, that the different planets are -attracted to the sun by a force which is inversely as the square of -the distance, Newton had so far been anticipated, that several -persons had discovered it to be true, or nearly true; that is, they -had discovered that if the orbits of the planets were circles, the -proportions of the central force to the inverse square of the -distance would follow from Kepler's third law, of the sesquiplicate -proportion of the periodic times. As we have seen, Huyghens' -theorems would have proved this, if they had been so applied; Wren -knew it; Hooke not only knew it, but claimed a prior knowledge to -Newton; and Halley had satisfied himself that it was at {400} least -nearly true, before he visited Newton. Hooke was reported to Newton -at Cambridge, as having applied to the Royal Society to do him -justice with regard to his claims; but when Halley wrote and -informed Newton (in a letter dated June 29, 1686), that Hooke's -conduct "had been represented in worse colors than it ought," Newton -inserted in his book a notice of these his predecessors, in order, -as he said, "to compose the dispute."[25\7] This notice appears in a -Scholium to the fourth Proposition of the _Principia_, which states -the general law of revolutions in circles. "The case of the sixth -corollary," Newton there says, "obtains in the celestial bodies, as -has been separately inferred by our countrymen, Wren, Hooke, and -Halley;" he soon after names Huyghens, "who, in his excellent -treatise _De Horologio Oscillatorio_, compares the force of gravity -with the centrifugal forces of revolving bodies." - -[Note 25\7: _Biog. Brit._ folio, art. _Hooke._] - -The two steps requisite for this discovery were, to propose the -motions of the planets as simply a mechanical problem, and to apply -mathematical reasoning so as to solve this problem, with reference to -Kepler's third law considered as a fact. The former step was a -consequence of the mechanical discoveries of Galileo and his school; -the result of the firm and clear place which these gradually obtained -in men's mind, and of the utter abolition of all the notions of solid -spheres by Kepler. The mathematical step required no small -mathematical powers; as appears, when we consider that this was the -first example of such a problem, and that the method of limits, under -all its forms, was at this time in its infancy, or rather, at its -birth. Accordingly, even this step, though much the easiest in the -path of deduction, no one before Newton completely executed. - -2. _Force in different Points of an Orbit._--The inference of the -law of the force from Kepler's two laws concerning the elliptical -motion, was a problem quite different from the preceding, and much -more difficult; but the dispute with respect to priority in the two -propositions was intermingled. Borelli, in 1666, had, as we have -seen, endeavored to reconcile the general form of the orbit with the -notion of a central attractive force, by taking centrifugal force -into the account; and Hooke, in 1679, had asserted that the result -of the law of the inverse square in the force of the earth would be -an ellipse,[26\7] or a curve like an ellipse.[27\7] But it does not -appear that this was any thing more than {401} a conjecture. Halley -says[28\7] that "Hooke, in 1683, told him he had demonstrated all -the laws of the celestial motions by the reciprocally duplicate -proportion of the force of gravity; but that, being offered forty -shillings by Sir Christopher Wren to produce such a demonstration, -his answer was, that he had it, but would conceal it for some time, -that others, trying and failing, might know how to value it when he -should make it public." Halley, however, truly observes, that after -the publication of the demonstration in the _Principia_, this reason -no longer held; and adds, "I have plainly told him, that unless he -produce another differing demonstration, and let the world judge of -it, neither I nor any one else can believe it." - -[Note 26\7: Newton's Letter, _Biog. Brit._, Hooke, p. 2660.] - -[Note 27\7: Birch's _Hist. R. S._, Wallis's Life.] - -[Note 28\7: _Enc. Brit._, Hooke, p. 2660.] - -Newton allows that Hooke's assertions in 1679 gave occasion to his -investigation on this point of the theory. His demonstration is -contained in the second and third Sections of the _Principia_. He -first treats of the general law of central forces in any curve; and -then, on account, as he states, of the application to the motion of -the heavenly bodies, he treats of the case of force varying -inversely as the square of the distance, in a more diffuse manner. - -In this, as in the former portion of his discovery, the two steps -were, the proposing the heavenly motions as a mechanical problem, -and the solving this problem. Borelli and Hooke had certainly made -the former step, with considerable distinctness; but the -mathematical solution required no common inventive power. - -Newton seems to have been much ruffled by Hooke's speaking slightly -of the value of this second step; and is moved in return to deny -Hooke's pretensions with some asperity, and to assert his own. He -says, in a letter to Halley, "Borelli did something in it, and wrote -modestly; he (Hooke) has done nothing; and yet written in such a way -as if he knew, and had sufficiently hinted all but what remained to -be determined by the drudgery of calculations and observations; -excusing himself from that labor by reason of his other business; -whereas he should rather have excused himself by reason of his -inability; for it is very plain, by his words, he knew not how to go -about it. Now is not this very fine? Mathematicians that find out, -settle, and do all the business, must content themselves with being -nothing but dry calculators and drudges; and another that does -nothing but pretend and grasp at all things, must carry away all the -inventions, as well of those that were to follow him as of those -that {402} went before." This was written, however, under the -influence of some degree of mistake; and in a subsequent letter, -Newton says, "Now I understand he was in some respects -misrepresented to me, I wish I had spared the postscript to my -last," in which is the passage just quoted. We see, by the melting -away of rival claims, the undivided honor which belongs to Newton, -as the real discoverer of the proposition now under notice. We may -add, that in the sequel of the third Section of the _Principia_, he -has traced its consequences, and solved various problems flowing -from it with his usual fertility and beauty of mathematical -resource; and has there shown the necessary connection of Kepler's -third law with his first and second. - -3. _Moon's Gravity to the Earth._--Though others had considered -cosmical forces as governed by the general laws of motion, it does not -appear that they had identified such forces with the force of -terrestrial gravity. This step in Newton's discoveries has generally -been the most spoken of by superficial thinkers; and a false kind of -interest has been attached to it, from the story of its being -suggested by the fall of an apple. The popular mind is caught by the -character of an eventful narrative which the anecdote gives to this -occurrence; and by the antithesis which makes a profound theory appear -the result of a trivial accident. How inappropriate is such a view of -the matter we shall soon see. The narrative of the progress of -Newton's thoughts, is given by Pemberton (who had it from Newton -himself) in his preface to his _View of Newton's Philosophy_, and by -Voltaire, who had it from Mrs. Conduit, Newton's niece.[29\7] "The -first thoughts," we are told, "which gave rise to his _Principia_, he -had when he retired from Cambridge, in 1666, on account of the plague -(he was then twenty-four years of age). As he sat alone in a garden, -he fell into a speculation on the power of gravity; that as this power -is not found sensibly diminished at the remotest distance from the -centre of the earth to which we can rise, neither at the tops of the -loftiest buildings, nor even on the summits of the highest mountains, -it appeared to him reasonable to conclude that this power must extend -much further than was usually thought: Why not as high as the moon? -said he to himself; and if so, her motion must be influenced by it; -perhaps she is retained in her orbit thereby." - -[Note 29\7: _Elémens de Phil. de Newton_, 3me partie, chap. iii.] - -The thought of cosmical gravitation was thus distinctly brought into -being; and Newton's superiority here was, that he conceived the -{403} celestial motions as distinctly as the motions which took -place close to him;--considered them as of the same kind, and -applied the same rules to each, without hesitation or obscurity. But -so far, this thought was merely a guess: its occurrence showed the -activity of the thinker; but to give it any value, it required much -more than a "why not?"--a "perhaps." Accordingly, Newton's "why not?" -was immediately succeeded by his "if so, what then?" His reasoning -was, that if gravity reach to the moon, it is probably of the same -kind as the central force of the sun, and follows the same rule with -respect to the distance. What is this rule? We have already seen -that, by calculating from Kepler's laws, and supposing the orbits to -be circles, the rule of the force appears to be the inverse -duplicate proportion of the distance; and this, which had been -current as a conjecture among the previous generation of -mathematicians, Newton had already proved by indisputable -reasonings, and was thus prepared to proceed in his train of -inquiry. If, then, he went on, pursuing his train of thought, the -earth's gravity extend to the moon, diminishing according to the -inverse square of the distance, will it, at the moon's orbit, be of -the proper magnitude for retaining her in her path? Here again came -in calculation, and a calculation of extreme interest; for how -important and how critical was the decision which depended on the -resulting numbers? According to Newton's calculations, made at this -time, the moon by her motion in her orbit, was deflected from the -tangent every minute through a space of thirteen feet. But by -noticing the space through which bodies would fall in one minute at -the earth's surface, and supposing this to be diminished in the -ratio of the inverse square, it appeared that gravity would, at the -moon's orbit, draw a body through more than fifteen feet. The -difference seems small, the approximation encouraging, the theory -plausible; a man in love with his own fancies would readily have -discovered or invented some probable cause of this difference. But -Newton acquiesced in it as a disproof of his conjecture, and "laid -aside at that time any further thoughts of this matter;**" thus -resigning a favorite hypothesis, with a candor and openness to -conviction not inferior to Kepler, though his notion had been taken -up on far stronger and sounder grounds than Kepler dealt in; and -without even, so far as we know, Kepler's regrets and struggles. Nor -was this levity or indifference; the idea, though thus laid aside, -was not finally condemned and abandoned. When Hooke, in 1679, -contradicted Newton on the subject of the curve described by a -falling body, and asserted it to be an ellipse, Newton {404} was led -to investigate the subject, and was then again conducted, by another -road, to the same law of the inverse square of the distance. This -naturally turned his thoughts to his former speculations. Was there -really no way of explaining the discrepancy which this law gave, -when he attempted to reduce the moon's motion to the action of -gravity? A scientific operation then recently completed, gave the -explanation at once. He had been mistaken in the magnitude of the -earth, and consequently in the distance of the moon, which is -determined by measurements of which the earth's radius is the base. -He had taken the common estimate, current among geographers and -seamen, that sixty English miles are contained in one degree of -latitude. But Picard, in 1670, had measured the length of a certain -portion of the meridian in France, with far greater accuracy than -had yet been attained and this measure enabled Newton to repeat his -calculations with these amended data. We may imagine the strong -curiosity which he must have felt as to the result of these -calculations. His former conjecture was now found to agree with the -phenomena to a remarkable degree of precision. This conclusion, thus -coming after long doubts and delays, and falling in with the other -results of mechanical calculation for the solar system, gave a stamp -from that moment to his opinions, and through him to those of the -whole philosophical world. - -[2d Ed.] [Dr. Robison (_Mechanical Philosophy_, p. 288) says that -Newton having become a member of the Royal Society, there learned -the accurate measurement of the earth by Picard, differing very much -from the estimation by which he had made his calculations in 1666. -And M. Biot, in his Life of Newton, published in the _Biographie -Universelle_, says, "According to conjecture, about the month of -June, 1682, Newton being in London at a meeting of the Royal -Society, mention was made of the new measure of a degree of the -earth's surface, recently executed in France by Picard; and great -praise was given to the care which had been employed in making this -measure exact." - -I had adopted this conjecture as a fact in my first edition; but it -has been pointed out by Prof. Rigaud (_Historical Essay on the First -Publication of the Principia_, 1838), that Picard's measurement was -probably well known to the Fellows of the Royal Society as early as -1675, there being an account of the results of it given in the -_Philosophical Transactions_ for that year. Newton appears to have -discovered the method of determining that a body might describe an -ellipse when acted upon by a force residing in the focus, and -varying {405} inversely as the square of the distance, in 1679, upon -occasion of his correspondence with Hooke. In 1684, at Halley's -request, he returned to the subject, and in February, 1685, there -was inserted in the Register of the Royal Society a paper of -Newton's (_Isaaci Newtoni Propositiones de Motu_) which contained -some of the principal Propositions of the first two Books of the -_Principia_. This paper, however, does not contain the Proposition -"Lunam gravitare in terram," nor any of the other propositions of -the third Book. The _Principia_ was printed in 1686 and 7, -apparently at the expense of Halley. On the 6th of April, 1687, the -third Book was presented to the Royal Society.] - -It does not appear, I think, that before Newton, philosophers in -general had supposed that terrestrial gravity was the very force by -which the moon's motions are produced. Men had, as we have seen, -taken up the conception of such forces, and had probably called them -gravity: but this was done only to explain, by analogy, what _kind_ -of forces they were, just as at other times they compared them with -magnetism; and it did not imply that terrestrial gravity was a force -which acted in the celestial spaces. After Newton had discovered -that this was so, the application of the term "gravity" did -undoubtedly convey such a suggestion; but we should err if we -inferred from this coincidence of expression that the notion was -commonly entertained before him. Thus Huyghens appears to use -language which may be mistaken, when he says,[30\7] that Borelli was -of opinion that the primary planets were urged by "gravity" towards -the sun, and the satellites towards the primaries. The notion of -terrestrial gravity, as being actually a cosmical force, is foreign -to all Borelli's speculations.[31\7] But Horrox, as early as 1635, -appears to have entertained the true view on this subject, although -vitiated by Keplerian errors concerning the connection between the -rotation of the central body and its effect on the body which -revolves about it. Thus he says,[32\7] that the emanation of the -earth carries a projected stone along with the motion of the earth, -just in the same way as it carries the moon in her orbit; and that -this force is greater on the stone than on the moon, because the -distance is less. - -[Note 30\7: _**Cosmotheoros_, l. 2. p. 720.] - -[Note 31\7: I have found no instance in which the word is so used by -him.] - -[Note 32\7: _Astronomia Kepleriana defensa et promota_, cap. 2. See -further on this subject in the _Additions_ to this volume.] - -The Proposition in which Newton has stated the discovery of which we -are now speaking, is the fourth of his third Book: "That the moon -gravitates to the earth, and by the force of gravity is perpetually -{406} deflected from a rectilinear motion, and retained in her -orbit." The proof consists in the numerical calculation, of which he -only gives the elements, and points out the method; but we may -observe, that no small degree of knowledge of the way in which -astronomers had obtained these elements, and judgment in selecting -among them, were necessary: thus, the mean distance of the moon had -been made as little as fifty-six and a half semidiameters of the -earth by Tycho, and as much as sixty-two and a half by Kircher: -Newton gives good reasons for adopting sixty-one. - -The term "gravity," and the expression "to gravitate," which, as we -have just seen, Newton uses of the moon, were to receive a still -wider application in consequence of his discoveries; but in order to -make this extension clearer, we consider it as a separate step. - -4. _Mutual Attraction of all the Celestial Bodies._--If the -preceding parts of the discovery of gravitation were comparatively -easy to conjecture, and difficult to prove, this was much more the -case with the part of which we have now to speak, the attraction of -other bodies, besides the central ones, upon the planets and -satellites. If the mathematical calculation of the unmixed effect of -a central force required transcendent talents, how much must the -difficulty be increased, when other influences prevented those first -results from being accurately verified, while the deviations from -accuracy were far more complex than the original action! If it had -not been that these deviations, though surprisingly numerous and -complicated in their nature, were very small in their quantity, it -would have been impossible for the intellect of man to deal with the -subject; as it was, the struggle with its difficulties is even now a -matter of wonder. - -The conjecture that there is some mutual action of the planets, had -been put forth by Hooke in his _Attempt to prove the Motion of the -Earth_ (1674). It followed, he said, from his doctrine, that not -only the sun and moon act upon the course and motion of the earth, -but that Mercury, Venus, Mars, Jupiter, and Saturn, have also, by -their attractive power, a considerable influence upon the motion of -the earth, and the earth in like manner powerfully affects the -motions of those bodies. And Borelli, in attempting to form -"theories" of the satellites of Jupiter, had seen, though dimly and -confusedly, the probability that the sun would disturb the motions -of these bodies. Thus he says (cap. 14), "How can we believe that -the Medicean globes are not, like other planets, impelled with a -greater velocity when they approach the sun: and thus they are acted -upon by two moving forces, one of {407} which produces their proper -revolution about Jupiter, the other regulates their motion round the -sun." And in another place (cap. 20), he attempts to show an effect -of this principle upon the inclination of the orbit; though, as -might be expected, without any real result. - -The case which most obviously suggests the notion that the sun -exerts a power to disturb the motions of secondary planets about -primary ones, might seem to be our own moon; for the great -inequalities which had hitherto been discovered, had all, except the -first, or elliptical anomaly, a reference to the position of the -sun. Nevertheless, I do not know that any one had attempted thus to -explain the curiously irregular course of the earth's attendant. To -calculate, from the disturbing agency, the amount of the -irregularities, was a problem which could not, at any former period, -have been dreamt of as likely to be at any time within the verge of -human power. - -Newton both made the step of inferring that there were such forces, -and, to a very great extent, calculated the effects of them. The -inference is made on mechanical principles, in the sixth Theorem of -the third Book of the _Principia_;--that the moon is attracted by -the sun, as the earth is;--that the satellites of Jupiter and Saturn -are attracted as the primaries are; in the same manner, and with the -same forces. If this were not so, it is shown that these attendant -bodies could not accompany the principal ones in the regular manner -in which they do. All those bodies at equal distances from the sun -would be equally attracted. - -But the complexity which must occur in tracing the results of this -principle will easily be seen. The satellite and the primary, though -nearly at the same distance, and in the same direction, from the -sun, are not exactly so. Moreover the difference of the distances -and of the directions is perpetually changing; and if the motion of -the satellite be elliptical, the cycle of change is long and -intricate: on this account alone the effects of the sun's action -will inevitably follow cycles as long and as perplexed as those of -the positions. But on another account they will be still more -complicated; for in the continued action of a force, the effect -which takes place at first, modifies and alters the effect -afterwards. The result at any moment is the sum of the results in -preceding instants: and since the terms, in this series of -instantaneous effects, follow very complex rules, the sums of such -series will be, it might be expected, utterly incapable of being -reduced to any manageable degree of simplicity. - -It certainly does not appear that any one but Newton could make -{408} any impression on this problem, or course of problems. No one -for sixty years after the publication of the _Principia_, and, with -Newton's methods, no one up to the present day, had added any thing -of any value to his deductions. We know that he calculated all the -principal lunar inequalities; in many of the cases, he has given us -his processes; in others, only his results. But who has presented, -in his beautiful geometry, or deduced from his simple principles, -any of the inequalities which he left untouched? The ponderous -instrument of synthesis, so effective in his hands, has never since -been grasped by one who could use it for such purposes; and we gaze -at it with admiring curiosity, as on some gigantic implement of war, -which stands idle among the memorials of ancient days, and makes us -wonder what manner of man he was who could wield as a weapon what we -can hardly lift as a burden. - -It is not necessary to point out in detail the sagacity and skill -which mark this part of the _Principia_. The mode in which the -author obtains the effect of a disturbing force in producing a -motion of the apse of an elliptical orbit (the ninth Section of the -first Book), has always been admired for its ingenuity and elegance. -The general statement of the nature of the principal inequalities -produced by the sun in the motion of a satellite, given in the -sixty-sixth Proposition, is, even yet, one of the best explanations -of such action; and the calculations of the quantity of the effects -in the third Book, for instance, the _variation_ of the moon, the -_motion of the nodes_ and its inequalities, the _change of -inclination_ of the orbit,--are full of beautiful and efficacious -artifices. But Newton's inventive faculty was exercised to an extent -greater than these published investigations show. In several cases -he has suppressed the demonstration of his method, and given us the -result only; either from haste or from mere weariness, which might -well overtake one who, while he was struggling with facts and -numbers, with difficulties of conception and practice, was aiming -also at that geometrical elegance of exposition, which he considered -as alone fit for the public eye. Thus, in stating the effect of the -eccentricity of the moon's orbit upon the motion of the apogee, he -says,[33\7] "The computations, as too intricate and embarrassed with -approximations, I do not choose to introduce." - -[Note 33\7: Schol. to Prop. 35, first edit.] - -The computations of the theoretical motion of the moon being thus -difficult, and its irregularities numerous and complex, we may ask -{409} whether Newton's reasoning was sufficient to establish this -part of his theory; namely, that her actual motions arise from her -gravitation to the sun. And to this we may reply, that it was -sufficient for that purpose,--since it showed that, from Newton's -hypothesis, inequalities must result, following the laws which the -moon's inequalities were known to follow;--since the amount of the -inequalities given by the theory agreed nearly with the rules which -astronomers had collected from observation;--and since, by the very -intricacy of the calculation, it was rendered probable, that the -first results might be somewhat inaccurate, and thus might give rise -to the still remaining differences between the calculations and the -facts. A _Progression of the Apogee_; a _Regression of the Nodes_; -and, besides the Elliptical, or first Inequality, an inequality, -following the law of the _Evection_, or second inequality discovered -by Ptolemy; another, following the law of the _Variation_ discovered -by Tycho;--were pointed out in the first edition of the _Principia_, -as the consequences of the theory. Moreover, the quantities of these -inequalities were calculated and compared with observation with the -utmost confidence, and the agreement in most instances was striking. -The Variation agreed with Halley's recent observations within a -minute of a degree.[34\7] The Mean Motion of the Nodes in a year -agreed within less than one-hundredth of the whole.[35\7] The -Equation of the Motion of the Nodes also agreed well.[36\7] The -Inclination of the Plane of the Orbit to the ecliptic, and its -changes, according to the different situations of the nodes, -likewise agreed.[37\7] The Evection has been already noticed as -encumbered with peculiar difficulties: here the accordance was less -close. The Difference of the daily progress of the Apogee in syzygy, -and its daily Regress in Quadratures, is, Newton says, "4¼ minutes -by the Tables, 6⅔ by our calculation." He boldly adds, "I suspect -this difference to be due to the fault of the Tables." In the second -edition (1711) he added the calculation of several other -inequalities, as the _Annual Equation_, also discovered by Tycho; -and he compared them with more recent observations made by Flamsteed -at Greenwich; but even in what has already been stated, it must be -allowed that there is a wonderful accordance of theory with -phenomena, both being very complex in the rules which they educe. - -[Note 34\7: B. iii. Prop. 29.] - -[Note 35\7: Prop. 32.] - -[Note 36\7: Prop. 33.] - -[Note 37\7: Prop. 35.] - -The same theory which gave these Inequalities in the motion of the -Moon produced by the disturbing force of the sun, gave also {410} -corresponding Inequalities in the motions of the Satellites of other -planets, arising from the same cause; and likewise pointed out the -necessary existence of irregularities in the motions of the Planets -arising from their mutual attraction. Newton gave propositions by -which the Irregularities of the motion of Jupiter's moons might be -deduced from those of our own;[38\7] and it was shown that the -motions of their nodes would be slow by theory, as Flamsteed had -found it to be by observation.[39\7] But Newton did not attempt to -calculate the effect of the mutual action of the planets, though he -observes, that in the case of Jupiter and Saturn this effect is too -considerable to be neglected;[40\7] and he notices in the second -edition,[41\7] that it follows from the theory of gravity, that the -aphelia of Mercury, Venus, the Earth, and Mars, slightly progress. - -[Note 38\7: B. i. Prop. 66.] - -[Note 39\7: B. iii. Prop. 23.] - -[Note 40\7: B. iii. Prop. 13.] - -[Note 41\7: Scholium to Prop. 14. B. iii.] - -In one celebrated instance, indeed, the deviation of the theory of -the _Principia_ from observation was wider, and more difficult to -explain; and as this deviation for a time resisted the analysis of -Euler and Clairaut, as it had resisted the synthesis of Newton, it -at one period staggered the faith of mathematicians in the exactness -of the law of the inverse square of the distance. I speak of the -Motion of the Moon's Apogee, a problem which has already been -referred to; and in which Newton's method, and all the methods which -could be devised for some time afterwards, gave only half the -observed motion; a circumstance which arose, as was discovered by -Clairaut in 1750, from the insufficiency of the method of -approximation. Newton does not attempt to conceal this discrepancy. -After calculating what the motion of apse would be, upon the -assumption of a disturbing force of the same amount as that which -the sun exerts on the moon, he simply says,[42\7] "the apse of the -moon moves about twice as fast." - -[Note 42\7: B. i. Prop. 44, second edit. There is reason to believe, -however, that Newton had, in his unpublished calculations, rectified -this discrepancy.] - -The difficulty of doing what Newton did in this branch of the -subject, and the powers it must have required, may be judged of from -what has already been stated;--that no one, with his methods, has -yet been able to add any thing to his labors: few have undertaken to -illustrate what he has written, and no great number have understood -it throughout. The extreme complication of the forces, and of the -conditions under which they act, makes the subject by far the most -thorny walk of mathematics. It is necessary to resolve the action -{411} into many elements, such as can be separated; to invent -artifices for dealing with each of these; and then to recompound the -laws thus obtained into one common conception. The moon's motion -cannot be conceived without comprehending a scheme more complex than -the Ptolemaic epicycles and eccentrics in their worst form; and the -component parts of the system are not, in this instance, mere -geometrical ideas, requiring only a distinct apprehension of -relations of space in order to hold them securely; they are the -foundations of mechanical notions, and require to be grasped so that -we can apply to them sound mechanical reasonings. Newton's -successors, in the next generation, abandoned the hope of imitating -him in this intense mental effort; they gave the subject over to the -operation of algebraical reasoning, in which symbols think for us, -without our dwelling constantly upon their meaning, and obtain for -us the consequences which result from the relations of space and the -laws of force, however complicated be the conditions under which -they are combined. Even Newton's countrymen, though they were long -before they applied themselves to the method thus opposed to his, -did not produce any thing which showed that they had mastered, or -could retrace, the Newtonian investigations. - -Thus the Problem of Three Bodies,[43\7] treated geometrically, -belongs exclusively to Newton; and the proofs of the mutual action -of the sun, planets, and satellites, which depend upon such -reasoning, could not be discovered by any one but him. - -[Note 43\7: See the history of the _Problem of Three Bodies_, -_ante_, in Book vi. Chap. vi. Sect. 7.] - -But we have not yet done with his achievements on this subject; for -some of the most remarkable and beautiful of the reasonings which he -connected with this problem, belong to the next step of his -generalization. - -5. _Mutual Attraction of all Particles of Matter._--That all the -parts of the universe are drawn and held together by love, or -harmony, or some affection to which, among other names, that of -attraction may have been given, is an assertion which may very -possibly have been made at various times, by speculators writing at -random, and taking their chance of meaning and truth. The authors of -such casual dogmas have generally nothing accurate or substantial, -either in their conception of the general proposition, or in their -reference to examples of it; and, therefore, their doctrines are no -concern of ours at present. But among those who were really the -first to think of the mutual {412} attraction of matter, we cannot -help noticing Francis Bacon; for his notions were so far from being -chargeable with the looseness and indistinctness to which we have -alluded, that he proposed an experiment[44\7] which was to decide -whether the facts were so or not;--whether the gravity of bodies to -the earth arose from an attraction of the parts of matter towards -each other, or was a tendency towards the centre of the earth. And -this experiment is, even to this day, one of the best which can be -devised, in order to exhibit the universal gravitation of matter: it -consists in the comparison of the rate of going of a clock in a deep -mine, and on a high place. Huyghens, in his book _De Causâ -Gravitatis_, published in 1690, showed that the earth would have an -oblate form, in consequence of the action of the centrifugal force; -but his reasoning does not suppose gravity to arise from the mutual -attraction of the parts of the earth. The apparent influence of the -moon upon the tides had long been remarked; but no one had made any -progress in truly explaining the mechanism of this influence; and -all the analogies to which reference had been made, on this and -similar subjects, as magnetic and other attractions, were rather -delusive than illustrative, since they represented the attraction as -something peculiar in particular bodies, depending upon the nature -of each body. - -[Note 44\7: _Nov. Org._ Lib. ii. Aph. 36.] - -That all such forces, cosmical and terrestrial, were the same single -force, and that this was nothing more than the insensible attraction -which subsists between one stone and another, was a conception -equally bold and grand; and would have been an incomprehensible -thought, if the views which we have already explained had not -prepared the mind for it. But the preceding steps having disclosed, -between all the bodies of the universe, forces of the same kind as -those which produce the weight of bodies at the earth, and, -therefore, such as exist in every particle of terrestrial matter; it -became an obvious question, whether such forces did not also belong -to all particles of planetary matter, and whether this was not, in -fact, the whole account of the forces of the solar system. But, -supposing this conjecture to be thus suggested, how formidable, on -first appearance at least, was the undertaking of verifying it! For -if this be so, every finite mass of matter exerts forces which are -the result of the infinitely numerous forces of its particles, these -forces acting in different directions. It does not appear, at first -sight, that the law by which the force is related to the distance, -will be the same for the particles as it is for the masses; and, in -reality, it {413} is not so, except in special cases. And, again, in -the instance of any effect produced by the force of a body, how are -we to know whether the force resides in the whole mass as a unit, or -in the separate particles? We may reason, as Newton does,[45\7] that -the rule which proves gravity to belong universally to the planets, -proves it also to belong to their parts; but the mind will not be -satisfied with this extension of the rule, except we can find -decisive instances, and calculate the effects of both suppositions, -under the appropriate conditions. Accordingly, Newton had to solve a -new series of problems suggested by this inquiry; and this he did. - -[Note 45\7: _Princip._ B. iii. Prop. 7.] - -These solutions are no less remarkable for the mathematical power -which they exhibit, than the other parts of the _Principia_. The -propositions in which it is shown that the law of the inverse square -for the particles gives the same law for spherical masses, have that -kind of beauty which might well have justified their being published -for their mathematical elegance alone, even if they had not applied to -any real case. Great ingenuity is also employed in other instances, as -in the case of spheroids of small eccentricity. And when the amount of -the mechanical action of masses of various forms has thus been -assigned, the sagacity shown in tracing the results of such action in -the solar system is truly admirable; not only the general nature of -the effect being pointed out, but its quantity calculated. I speak in -particular of the reasonings concerning the Figure of the Earth, the -Tides, the Precession of the Equinoxes, the Regression of the Nodes of -a ring such as Saturn's; and of some effects which, at that time, had -not been ascertained even as facts of observation; for instance, the -difference of gravity in different latitudes, and the Nutation of the -earth's axis. It is true, that in most of these cases, Newton's -process could be considered only as a rude approximation. In one (the -Precession) he committed an error, and in all, his means of -calculation were insufficient. Indeed these are much more difficult -investigations than the Problem of Three Bodies, in which three points -act on each other by explicit laws. Up to this day, the resources of -modern analysis have been employed upon some of them with very partial -success; and the facts, in all of them, required to be accurately -ascertained and measured, a process which is not completed even now. -Nevertheless the form and nature of the conclusions which Newton did -obtain, were such as to inspire a strong confidence in the competency -of his theory to explain {414} all such phenomena as have been spoken -of. We shall afterwards have to speak of the labors, undertaken in -order to examine the phenomena more exactly, to which the theory gave -occasion. - -Thus, then, the theory of the universal mutual gravitation of all -the particles of matter, according to the law of the inverse square -of the distances, was conceived, its consequences calculated, and -its results shown to agree with phenomena. It was found that this -theory took up all the facts of astronomy as far as they had -hitherto been ascertained; while it pointed out an interminable -vista of new facts, too minute or too complex for observation alone -to disentangle, but capable of being detected when theory had -pointed out their laws, and of being used as criteria or -confirmations of the truth of the doctrine. For the same reasoning -which explained the evection, variation, and annual equation of the -moon, showed that there must be many other inequalities besides -these; since these resulted from approximate methods of calculation, -in which small quantities were neglected. And it was known that, in -fact, the inequalities hitherto detected by astronomers did not give -the place of the moon with satisfactory accuracy; so that there was -room, among these hitherto untractable irregularities, for the -additional results of the theory. To work out this comparison was -the employment of the succeeding century; but Newton began it. Thus, -at the end of the proposition in which he asserts,[46\7] that "all -the lunar motions and their irregularities follow from the -principles here stated," he makes the observation which we have just -made; and gives, as examples, the different motions of the apogee -and nodes, the difference of the change of the eccentricity, and the -difference of the moon's variation, according to the different -distances of the sun. "But this inequality," he says, "in -astronomical calculations, is usually referred to the prosthaphæresis -of the moon, and confounded with it." - -[Note 46\7: B. iii. Prop. 22.] - -_Reflections on the Discovery._--Such, then, is the great Newtonian -Induction of Universal Gravitation, and such its history. It is -indisputably and incomparably the greatest scientific discovery ever -made, whether we look at the advance which it involved, the extent -of the truth disclosed, or the fundamental and satisfactory nature -of this truth. As to the first point, we may observe that any one of -the five steps into which we have separated the doctrine, would, of -itself, have been considered as an important advance;--would have -conferred distinction on the persons who made it, and the time to -which it belonged. All {415} the five steps made at once, formed not -a leap, but a flight,--not an improvement merely, but a -metamorphosis,--not an epoch, but a termination. Astronomy passed at -once from its boyhood to mature manhood. Again, with regard to the -extent of the truth, we obtain as wide a generalization as our -physical knowledge admits, when we learn that every particle of -matter, in all times, places, and circumstances, attracts every -other particle in the universe by one common law of action. And by -saying that the truth was of a fundamental and satisfactory nature, -I mean that it assigned, not a rule merely, but a cause, for the -heavenly motions; and that kind of cause which most eminently and -peculiarly we distinctly and thoroughly conceive, namely, mechanical -force. Kepler's laws were merely _formal_ rules, governing the -celestial motions according to the relations of space, time, and -number; Newton's was a _**causal_ law, referring these motions to -mechanical reasons. It is no doubt conceivable that future -discoveries may both extend and further explain Newton's -doctrines;--may make gravitation a case of some wider law, and may -disclose something of the mode in which it operates; questions with -which Newton himself struggled. But, in the mean time, few persons -will dispute, that both in generality and profundity, both in width -and depth, Newton's theory is altogether without a rival or -neighbor.[47\7] - -[Note 47\7: The value and nature of this step have long been -generally acknowledged wherever science is cultivated. Yet it would -appear that there is, in one part of Europe, a school of -philosophers who contest the merit of this part of Newton's -discoveries. "Kepler," says a celebrated German metaphysician,* -"discovered the laws of free motion; a discovery of immortal glory. -It has since been the fashion to say that Newton first found out the -proof of these rules. It has seldom happened that the glory of the -first discoverer has been more unjustly transferred to another -person." It may appear strange that any one in the present day -should hold such language; but if we examine the reasons which this -author gives, they will be found, I think, to amount to this: that -his mind is in the condition in which Kepler's was; and that the -whole range of mechanical ideas and modes of conception which made -the transition from Kepler and Newton possible, are extraneous to -the domain of his philosophy. Even this author, however, if I -understand him rightly, recognizes Newton as the author of the -doctrine of Perturbations. - -I have given a further account of these views, in a Memoir _On Hegel's -Criticism of Newton's Principia_. Cambridge Transactions, 1849. - -* Hegel, _Encyclopædia_, § 270.] - -The requisite conditions of such a discovery in the mind of its author -were, in this as in other cases, the idea, and its comparison with -facts;--the conception of the law, and the moulding this conception in -such a form as to correspond with known realities. The idea of -mechanical {416} force as the cause of the celestial motions, had, as -we have seen, been for some time growing up in men's minds; had gone -on becoming more distinct and more general; and had, in some persons, -approached the form in which it was entertained by Newton. Still, in -the mere conception of universal gravitation, Newton must have gone -far beyond his predecessors and contemporaries, both in generality and -distinctness; and in the inventiveness and sagacity with which he -traced the consequences of this conception, he was, as we have shown, -without a rival, and almost without a second. As to the facts which he -had to include in his law, they had been accumulating from the very -birth of astronomy; but those which he had more peculiarly to take -hold of were the facts of the planetary motions as given by Kepler, -and those of the moon's motions as given by Tycho Brahe and Jeremy -Horrox. - -We find here occasion to make a remark which is important in its -bearing on the nature of progressive science. What Newton thus used -and referred to as _facts_, were the _laws_ which his predecessors had -established. What Kepler and Horrox had put forth as "theories," were -now established truths, fit to be used in the construction of other -theories. It is in this manner that one theory is built upon -another;--that we rise from particulars to generals, and from one -generalization to another;--that we have, in short, successive steps -of induction. As Newton's laws assumed Kepler's, Kepler's laws assumed -as facts the results of the planetary theory of Ptolemy; and thus the -theories of each generation in the scientific world are (when -thoroughly verified and established,**) the facts of the next -generation. Newton's theory is the circle of generalization which -includes all the others;--the highest point of the inductive -ascent;--the catastrophe of the philosophic drama to which Plato had -prologized;--the point to which men's minds had been journeying for -two thousand years. - -_Character of Newton._--It is not easy to anatomize the constitution -and the operations of the mind which makes such an advance in -knowledge. Yet we may observe that there must exist in it, in an -eminent degree, the elements which compose the mathematical talent. It -must possess distinctness of intuition, tenacity and facility in -tracing logical connection, fertility of invention, and a strong -tendency to generalization. It is easy to discover indications of -these characteristics in Newton. The distinctness of his intuitions of -space, and we may add of force also, was seen in the amusements of his -youth; in his constructing clocks and mills, carts and dials, as well -as the facility with which he {417} mastered geometry. This fondness -for handicraft employments, and for making models and machines, -appears to be a common prelude of excellence in physical -science;[48\7] probably on this very account, that it arises from the -distinctness of intuitive power with which the child conceives the -shapes and the working of such material combinations. Newton's -inventive power appears in the number and variety of the mathematical -artifices and combinations which he devised, and of which his books -are full. If we conceive the operation of the inventive faculty in the -only way in which it appears possible to conceive it;--that while some -hidden source supplies a rapid stream of possible suggestions, the -mind is on the watch to seize and detain any one of these which will -suit the case in hand, allowing the rest to pass by and be -forgotten;--we shall see what extraordinary fertility of mind is -implied by so many successful efforts; what an innumerable host of -thoughts must have been produced, to supply so many that deserved to -be selected. And since the selection is performed by tracing the -consequences of each suggestion, so as to compare them with the -requisite conditions, we see also what rapidity and certainty in -drawing conclusions the mind must possess as a talent, and what -watchfulness and patience as a habit. - -[Note 48\7: As in Galileo, Hooke, Huyghens, and others.] - -The hidden fountain of our unbidden thoughts is for us a mystery; -and we have, in our consciousness, no standard by which we can -measure our own talents; but our acts and habits are something of -which we are conscious; and we can understand, therefore, how it was -that Newton could not admit that there was any difference between -himself and other men, except in his possession of such habits as we -have mentioned, perseverance and vigilance. When he was asked how he -made his discoveries, he answered, "by always thinking about them;" -and at another time he declared that if he had done any thing, it -was due to nothing but industry and patient thought: "I keep the -subject of my inquiry constantly before me, and wait till the first -dawning opens gradually, by little and little, into a full and clear -light." No better account can be given of the nature of the mental -_effort_ which gives to the philosopher the full benefit of his -powers; but the natural _powers_ of men's minds are not on that -account the less different. There are many who might wait through -ages of darkness without being visited by any dawn. - -The habit to which Newton thus, in some sense, owed his {418} -discoveries, this constant attention to the rising thought, and -development of its results in every direction, necessarily engaged -and absorbed his spirit, and made him inattentive and almost -insensible to external impressions and common impulses. The stories -which are told of his extreme absence of mind, probably refer to the -two years during which he was composing his _Principia_, and thus -following out a train of reasoning the most fertile, the most -complex, and the most important, which any philosopher had ever had -to deal with. The magnificent and striking questions which, during -this period, he must have had daily rising before him; the perpetual -succession of difficult problems of which the solution was necessary -to his great object; may well have entirely occupied and possessed -him. "He existed only to calculate and to think."[49\7] Often, lost -in meditation, he knew not what he did, and his mind appeared to -have quite forgotten its connection with the body. His servant -reported that, on rising in a morning, he frequently sat a large -portion of the day, half-dressed, on the side of his bed and that -his meals waited on the table for hours before he came to take them. -Even with his transcendent powers, to do what he did was almost -irreconcilable with the common conditions of human life; and -required the utmost devotion of thought, energy of effort, and -steadiness of will--the strongest character, as well as the highest -endowments, which belong to man. - -[Note 49\7: Biot.] - -Newton has been so universally considered as the greatest example of -a natural philosopher, that his moral qualities, as well as his -intellect, have been referred to as models of the philosophical -character; and those who love to think that great talents are -naturally associated with virtue, have always dwelt with pleasure -upon the views given of Newton by his contemporaries; for they have -uniformly represented him as candid and humble, mild and good. We -may take as an example of the impressions prevalent about him in his -own time, the expressions of Thomson, in the Poem on his -Death.[50\7] {419} - Say ye who best can tell, ye happy few, - Who saw him in the softest lights of life, - All unwithheld, indulging to his friends - The vast unborrowed treasures of his mind, - Oh, speak the wondrous man! how mild, how calm - How greatly humble, how divinely good, - How firm established on eternal truth! - Fervent in doing well, with every nerve - Still pressing on, forgetful of the past, - And panting for perfection; far above - Those little cares and visionary joys - That so perplex the fond impassioned heart - Of ever-cheated, ever-trusting man. - -[Note 50\7: In the same strain we find the general voice of the -time. For instance, one of Loggan's "Views of Cambridge" is -dedicated "Isaaco Newtono . . Mathematico, Physico, Chymico -consummatissimo; nec minus suavitate morum et candore animi . . . -spectabili." - -In opposition to the general current of such testimony, we have the -complaints of Flamsteed, who ascribes to Newton angry language and -harsh conduct in the matter of the publication of the Greenwich -Observations, and of Whiston. Yet even Flamsteed speaks well of his -general disposition. Whiston was himself so weak and prejudiced that -his testimony is worth very little.] - -[2d Ed.] [In the first edition of the _Principia_, published in -1687, Newton showed that the nature of all the then known -inequalities of the moon, and in some cases, their quantities, might -be deduced from the principles which he laid down but the -determination of the amount and law of most of the inequalities was -deferred to a more favorable opportunity, when he might be furnished -with better astronomical observations. Such observations as he -needed for this purpose had been made by Flamsteed, and for these he -applied, representing how much value their use would add to the -observations. "If," he says, in 1694, "you publish them without such -a theory to recommend them, they will only be thrown into the heap -of the observations of former astronomers, till somebody shall arise -that by perfecting the theory of the moon shall discover your -observations to be exacter than the rest; but when that shall be, -God knows: I fear, not in your lifetime, if I should die before it -is done. For I find this theory so very intricate, and the theory of -gravity so necessary to it, that I am satisfied it will never be -perfected but by somebody who understands the theory of gravity as -well, or better than I do." He obtained from Flamsteed the lunar -observations for which he applied, and by using these he framed the -Theory of the Moon which is given as his in David Gregory's -_Astronomiæ Elementa_.[51\7] He also obtained from Flamsteed the -diameters of the planets as observed at various times, and the -greatest elongation of Jupiter's Satellites, both of which, -Flamsteed says, he made use of in his _Principia_. - -[Note 51\7: In the Preface to a _Treatise on Dynamics_, Part i., -published in 1836, I have endeavored to show that Newton's modes of -determining several of the lunar inequalities admitted of an -accuracy not very inferior to the modern analytical methods.] - -Newton, in his letters to Flamsteed in 1694 and 5, acknowledges this -service.[52\7]**] {420} - -[Note 52\7: The quarrel on the subject of the publication of -Flamsteed's Observations took place at a later period. Flamsteed -wished to have his Observations printed complete and entire. Halley, -who, under the authority of Newton and others, had the management of -the printing, made many alterations and omissions, which Flamsteed -considered as deforming and spoiling the work. The advantages of -publishing a _complete_ series of observations, now generally -understood, were not then known to astronomers in general, though -well known to Flamsteed, and earnestly insisted upon in his -remonstrances. The result was that Flamsteed published his -Observations at his own expense, and finally obtained permission to -destroy the copies printed by Halley, which he did. In 1726, after -Flamsteed's death, his widow applied to the Vice-Chancellor of -Oxford, requesting that the volume printed by Halley might be -removed out of the Bodleian Library, where it exists, as being -"nothing more than an erroneous abridgment of Mr. Flamsteed's -works," and unfit to see the light.] - - - - -CHAPTER III. - -SEQUEL TO THE EPOCH OF NEWTON.--RECEPTION OF THE NEWTONIAN THEORY. - - -_Sect._ 1.--_General Remarks._ - -THE doctrine of universal gravitation, like other great steps in -science, required a certain time to make its way into men's minds; -and had to be confirmed, illustrated, and completed, by the labors -of succeeding philosophers. As the discovery itself was great beyond -former example, the features of the natural sequel to the discovery -were also on a gigantic scale; and many vast and laborious trains of -research, each of which might, in itself, be considered as forming a -wide science, and several of which have occupied many profound and -zealous inquirers from that time to our own day, come before us as -parts only of the verification of Newton's Theory. Almost every -thing that has been done, and is doing, in astronomy, falls -inevitably under this description; and it is only when the -astronomer travels to the very limits of his vast field of labor, -that he falls in with phenomena which do not acknowledge the -jurisdiction of the Newtonian legislation. We must give some account -of the events of this part of the history of astronomy; but our -narrative must necessarily be extremely brief and imperfect; for the -subject is most large and copious, and our limits are fixed and -narrow. We have here to do with the history of discoveries, only so -far as it illustrates their philosophy. And though the {421} -astronomical discoveries of the last century are by no means poor, -even in interest of this kind, the generalizations which they -involve are far less important for our object, in consequence of -being included in a previous generalization. Newton shines out so -brightly, that all who follow seem faint and dim. It is not -precisely the case which the poet describes-- - As in a theatre the eyes of men, - After some well-graced actor leaves the stage, - Are idly bent on him that enters next, - Thinking his prattle to be tedious: -but our eyes are at least less intently bent on the astronomers who -succeeded, and we attend to their communications with less -curiosity, because we know the end, if not the course of their -story; we know that their speeches have all closed with Newton's -sublime declaration, asserted in some new form. - -Still, however, the account of the verification and extension of any -great discovery is a highly important part of its history. In this -instance it is most important; both from the weight and dignity of -the theory concerned, and the ingenuity and extent of the methods -employed: and, of course, so long as the Newtonian theory still -required verification, the question of the truth or falsehood of -such a grand system of doctrines could not but excite the most -intense curiosity. In what I have said, I am very far from wishing -to depreciate the value of the achievements of modern astronomers, -but it is essential to my purpose to mark the subordination of -narrower to wider truths--the different character and import of the -labors of those who come before and after the promulgation of a -master-truth. With this warning I now proceed to my narrative. - - -_Sect._ 2.--_Reception of the Newtonian Theory in England._ - -THERE appears to be a popular persuasion that great discoveries are -usually received with a prejudiced and contentious opposition, and -the authors of them neglected or persecuted. The reverse of this was -certainly the case in England with regard to the discoveries of -Newton. As we have already seen, even before they were published, -they were proclaimed by Halley to be something of transcendent -value; and from the moment of their appearance, they rapidly made -their way from one class of thinkers to another, nearly as fast as -the nature of men's intellectual capacity allows. Halley, Wren, and -all the leading {422} members of the Royal Society, appear to have -embraced the system immediately and zealously. Men whose pursuits -had lain rather in literature than in science, and who had not the -knowledge and habits of mind which the strict study of the system -required, adopted, on the credit of their mathematical friends, the -highest estimation of the _Principia_, and a strong regard for its -author, as Evelyn, Locke, and Pepys. Only five years after the -publication, the principles of the work were referred to from the -pulpit, as so incontestably proved that they might be made the basis -of a theological argument. This was done by Dr. Bentley, when he -preached the Boyle's Lectures in London, in 1692. Newton himself, -from the time when his work appeared, is never mentioned except in -terms of profound admiration; as, for instance, when he is called by -Dr. Bentley, in his sermon,[53\7] "That very excellent and divine -theorist, Mr. Isaac Newton." It appears to have been soon suggested, -that the Government ought to provide in some way for a person who -was so great an honor to the nation. Some delay took place with -regard to this; but, in 1695, his friend Mr. Montague, afterwards -Earl of Halifax, at that time Chancellor of the Exchequer, made him -Warden of the Mint; and in 1699, he succeeded to the higher office -of Master of the Mint, a situation worth £1200 or £1500 a year, -which he filled to the end of his life. In 1703, he became President -of the Royal Society, and was annually re-elected to this office -during the remaining twenty-five years of his life. In 1705, he was -knighted in the Master's Lodge, at Trinity College, by Queen Anne, -then on a visit to the University of Cambridge. After the accession -of George the First, Newton's conversation was frequently sought by -the Princess, afterwards Queen Caroline, who had a taste for -speculative studies, and was often heard to declare in public, that -she thought herself fortunate in living at a time which enabled her -to enjoy the society of so great a genius. His fame, and the respect -paid him, went on increasing to the end of his life; and when, in -1727, full of years and glory, his earthly career was ended, his -death was mourned as a national calamity, with the forms usually -confined to royalty. His body lay in state in the Jerusalem chamber; -his pall was borne by the first nobles of the land and his earthly -remains were deposited in the centre of Westminster Abbey, in the -midst of the memorials of the greatest and wisest men whom England -has produced. - -[Note 53\7: Serm. vii. 221.] - -It cannot be superfluous to say a word or two on the reception of -{423} his philosophy in the universities of England. These are often -represented as places where bigotry and ignorance resist, as long as -it is possible to resist, the invasion of new truths. We cannot -doubt that such opinions have prevailed extensively, when we find an -intelligent and generally temperate writer, like the late Professor -Playfair of Edinburgh, so far possessed by them, as to be incapable -of seeing, or interpreting, in any other way, any facts respecting -Oxford and Cambridge. Yet, notwithstanding these opinions, it will -be found that, in the English universities, new views, whether in -science or in other subjects, have been introduced as soon as they -were clearly established;--that they have been diffused from the few -to the many more rapidly there than elsewhere occurs;--and that from -these points, the light of newly-discovered truths has most usually -spread over the land. In most instances undoubtedly there has been -something of a struggle, on such occasions, between the old and the -new opinions. Few men's minds can at once shake off a familiar and -consistent system of doctrines, and adopt a novel and strange set of -principles as soon as presented; but all can see that one change -produces many, and that change, in itself, is a source of -inconvenience and danger. In the case of the admission of the -Newtonian opinions into Cambridge and Oxford, however, there are no -traces even of a struggle. Cartesianism had never struck its roots -deep in this country; that is, the peculiar hypotheses of Descartes. -The Cartesian books, such, for instance, as that of Rohault, were -indeed in use; and with good reason, for they contained by far the -best treatises on most of the physical sciences, such as Mechanics, -Hydrostatics, Optics, and Formal Astronomy, which could then be -found. But I do not conceive that the Vortices were ever dwelt upon -as a matter of importance in our academic teaching. At any rate, if -they were brought among us, they were soon dissipated. Newton's -College, and his University, exulted in his fame, and did their -utmost to honor and aid him. He was exempted by the king from the -obligation of taking orders, under which the fellows of Trinity -College in general are; by his college he was relieved from all -offices which might interfere, however slightly, with his studious -employments, though he resided within the walls of the society -thirty-five years, almost without the interruption of a month.[54\7] -By the University he was elected their representative in parliament -in 1688, {424} and again in 1701; and though he was rejected in the -dissolution of 1705, those who opposed him acknowledged him[55\7] to -be "the glory of the University and nation," but considered the -question as a political one, and Newton as sent "to tempt them from -their duty, by the great and just veneration they had for him." -Instruments and other memorials, valued because they belonged to -him, are still preserved in his college, along with the tradition of -the chambers which he occupied. - -[Note 54\7: His name is nowhere found on the college-books, as -appointed to any of the offices which usually pass down the list of -resident fellows in rotation. This might be owing in part, however, -to his being Lucasian Professor. The constancy of his residence in -college appears from the _exit_ and _redit_ book of that time, which -is still preserved.] - -[Note 55\7: A pamphlet by Styan Thurlby.] - -The most active and powerful minds at Cambridge became at once -disciples and followers of Newton. Samuel Clarke, afterwards his -friend, defended in the public schools a thesis taken from his -philosophy, as early as 1694; and in 1697 published an edition of -Rohault's _Physics_, with notes, in which Newton is frequently -referred to with expressions of profound respect, though the leading -doctrines of the _Principia_ are not introduced till a later -edition, in 1703. In 1699, Bentley, whom we have already mentioned -as a Newtonian, became Master of Trinity College; and in the same -year, Whiston, another of Newton's disciples, was appointed his -deputy as professor of mathematics. Whiston delivered the Newtonian -doctrines, both from the professor's chair, and in works written for -the use of the University; yet it is remarkable that a taunt -respecting the late introduction of the Newtonian system into the -Cambridge course of education, has been founded on some peevish -expressions which he uses in his Memoirs, written at a period when, -having incurred expulsion from his professorship and the University, -he was naturally querulous and jaundiced in his views. In 1709-10, -Dr. Laughton, who was tutor in Clare Hall, procured himself to be -appointed moderator of the University disputations, in order to -promote the diffusion of the new mathematical doctrines. By this -time the first edition of the _Principia_ was become rare, and -fetched a great price. Bentley urged Newton to publish a new one; -and Cotes, by far the first, at that time, of the mathematicians of -Cambridge, undertook to superintend the printing, and the edition -was accordingly published in 1713. - -[2d Ed.] [I perceive that my accomplished German translator, -Littrow, has incautiously copied the insinuations of some modern -writers to the effect that Clarke's reference to Newton, in his -Edition of Rohault's _Physics_, was a mode of introducing Newtonian -doctrines covertly, when it was not allowed him to introduce such -novelties {425} openly. I am quite sure that any one who looks into -this matter will see that this supposition of any unwillingness at -Cambridge to receive Newton's doctrine is quite absurd, and can -prove nothing but the intense prejudices of those who maintain such -an opinion. Newton received and held his professorship amid the -unexampled admiration of all contemporary members of the University. -Whiston, who is sometimes brought as an evidence against Cambridge -on this point, says, "I with immense pains set myself with the -utmost zeal to the study of Sir Isaac Newton's wonderful discoveries -in his _Philosophiæ Naturalis Principia Mathematica_, one or two of -which _lectures I had heard him read in the public schools_, though -I understood them not at the time." As to Rohault's _Physics_, it -really did contain the best mechanical philosophy of the time;--the -doctrines which were held by Descartes in common with Galileo, and -with all the sound mathematicians who succeeded them. Nor does it -look like any great antipathy to novelty in the University of -Cambridge, that this book, which was quite as novel in its doctrines -as Newton's _Principia_, and which had only been published at Paris -in 1671, had obtained a firm hold on the University in less than -twenty years. Nor is there any attempt made in Clarke's notes to -conceal the novelty of Newton's discoveries, but on the contrary, -admiration is claimed for them as new. - -The promptitude with which the Mathematicians of the University of -Cambridge adopted the best parts of the mechanical philosophy of -Descartes, and the greater philosophy of Newton, in the seventeenth -century, has been paralleled in our own times, in the promptitude -with which they have adopted and followed into their consequences -the Mathematical Theory of Heat of Fourier and Laplace, and the -Undulatory Theory of Light of Young and Fresnel. - -In Newton's College, we possess, besides the memorials of him -mentioned above (which include two locks of his silver-white hair), -a paper in his own handwriting, describing the preparatory reading -which was necessary in order that our College students might be able -to read the _Principia_. I have printed this paper in the Preface to -my Edition of the First Three Sections of the _Principia_ in the -original Latin (1846). - -Bentley, who had expressed his admiration for Newton in his Boyle's -Lectures in 1692, was made Master of the College in 1699, as I have -stated; and partly, no doubt, in consequence of the Newtonian -sermons which he had preached. In his administration of the College, -he zealously stimulated and assisted the exertions of Cotes, -Whiston, and other disciples of Newton. Smith, Bentley's successor -as Master of {426} the College, erected a statue of Newton in the -College Chapel (a noble work of Roubiliac), with the inscription, -_Qui genus humanum ingenio superavit._] - -At Oxford, David Gregory and Halley, both zealous and distinguished -disciples of Newton, obtained the Savilian professorships of -astronomy and geometry in 1691 and 1703. - -David Gregory's _Astronomiæ Physicæ et Geometricæ Elementa_ issued -from the Oxford Press in 1702. The author, in the first sentence of -the Preface, states his object to be to explain the mechanics of the -universe (Physica Cœlestis), which Isaac Newton, the Prince of -Geometers, has carried to a point of elevation which all look up to -with admiration. And this design is executed by a full exposition of -the Newtonian doctrines and their results. Keill, a pupil of -Gregory, followed his tutor to Oxford, and taught the Newtonian -philosophy there in 1700, being then Deputy Sedleian Professor. He -illustrated his lectures by experiments, and published an -Introduction to the _Principia_ which is not out of use even yet. - -In Scotland, the Newtonian philosophy was accepted with great -alacrity, as appears by the instances of David Gregory and Keill. -David Gregory was professor at Edinburgh before he removed to Oxford, -and was succeeded there by his brother James. The latter had, as early -as 1690, printed a thesis, containing in twenty-two propositions, a -compend of Newton's _Principia_.[56\7] Probably these were intended as -theses for academical disputations; as Laughton at Cambridge -introduced the Newtonian philosophy into these exercises. The formula -at Cambridge, in use till very recently in these disputations, was -"_Rectè statuit Newtonus de Motu Lunæ_;" or the like. - -[Note 56\7: See Hutton's _Math. Dict._, art. _James Gregory_. If it -fell in with my plan to notice derivative works, I might speak of -Maclaurin's admirable _Account of Sir Isaac Newton's Discoveries_, -published in 1748. This is still one of the best books on the -subject. The late Professor Rigaud's _Historical Essay on the First -Publication of Sir Isaac Newton's "Principia"_ (Oxf. 1838) contains -a careful and candid view of the circumstances of that event.] - -The general diffusion of these opinions in England took place, not -only by means of books, but through the labors of various -experimental lecturers, like Desaguliers, who removed from Oxford to -London in 1713; when he informs us,[57\7] that "he found the -Newtonian philosophy generally received among persons of all ranks -and professions, and even among the ladies by the help of -experiments." {427} - -[Note 57\7: Desag. _Pref._] - -We might easily trace in our literature indications of the gradual -progress of the Newtonian doctrines. For instance, in the earlier -editions of Pope's _Dunciad_, this couplet occurred, in the -description of the effects of the reign of Dulness: - Philosophy, that reached the heavens before, - Shrinks to her hidden cause, and is no more. -"And this," says his editor, Warburton, "was intended as a censure -on the Newtonian philosophy. For the poet had been misled by the -prejudices of foreigners, as if that philosophy had recurred to the -occult qualities of Aristotle. This was the idea he received of it -from a man educated much abroad, who had read every thing, but every -thing superficially.[58\7] When I hinted to him how he had been -imposed upon, he changed the lines with great pleasure into a -compliment (as they now stand) on that divine genius, and a satire -on that very folly by which he himself had been misled." In 1743 it -was printed, - Philosophy, that leaned on heaven before, - Shrinks to her second cause, and is no more. -The Newtonians repelled the charge of dealing in occult -causes;[59\7] and, referring gravity to the will of the Deity, as -the First Cause, assumed a superiority over those whose philosophy -rested in second causes. - -[Note 58\7: I presume Bolingbroke is here meant.] - -[Note 59\7: See Cotes's Pref. to the _Principia_.] - -To the cordial reception of the Newtonian theory by the English -astronomers, there is only one conspicuous exception; which is, -however, one of some note, being no other than Flamsteed, the -Astronomer Royal, a most laborious and exact observer. Flamsteed at -first listened with complacency to the promises of improvements in -the Lunar Tables, which the new doctrines held forth, and was -willing to assist Newton, and to receive assistance from him. But -after a time, he lost his respect for Newton's theory, and ceased to -take any interest in it. He then declared to one of his -correspondents,[60\7] "I have determined to lay these crotchets of -Sir Isaac Newton's wholly aside." We need not, however, find any -difficulty in this, if we recollect that Flamsteed, though a good -observer, was no philosopher;--never understood by a Theory any -thing more than a Formula which should predict results;--and was -incapable of comprehending the object of Newton's theory, which was -to assign causes as well as rules, and to satisfy the conditions of -Mechanics as well as of Geometry. {428} - -[Note 60\7: Baily's _Account of Flamsteed, &c._, p. 309.] - -[2d Ed.] [I do not see any reason to retract what was thus said; but -it ought perhaps to be distinctly said that on these very accounts -Flamsteed's rejection of Newton's rules did not imply a denial of -the doctrine of gravitation. In the letter above quoted, Flamsteed -says that he has been employed upon the Moon, and that "the heavens -reject that equation of Sir I. Newton which Gregory and Newton -called his sixth: I had then [when he wrote before] compared but 72 -of my observations with the tables, now I have examined above 100 -more. I find them all firm in the same, and the seventh [equation] -too." And thereupon he comes to the determination above stated. - -At an earlier period Flamsteed, as I have said, had received -Newton's suggestions with great deference, and had regulated his own -observations and theories with reference to them. The calculation of -the lunar inequalities upon the theory of gravitation was found by -Newton and his successors to be a more difficult and laborious task -than he had anticipated, and was not performed without several -trials and errors. One of the equations was at first published (in -Gregory's _Astronomiæ Elementa_) with a wrong sign. And when Newton -had done all, Flamsteed found that the rules were far from coming up -to the degree of accuracy which had been claimed for them, that they -could give the moon's place true to 2 or 3 minutes. It was not till -considerably later that this amount of exactness was attained. - -The late Mr. Baily, to whom astronomy and astronomical literature -are so deeply indebted, in his _Supplement to the Account of -Flamsteed_, has examined with great care and great candor the -assertion that Flamsteed did not understand Newton's Theory. He -remarks, very justly, that what Newton himself at first presented as -his Theory, might more properly be called Rules for computing lunar -tables, than a physical Theory in the modern acceptation of the -term. He shows, too, that Flamsteed had read the _Principia_ with -attention.[61\7] Nor do I doubt that many considerable -mathematicians gave the same imperfect assent to Newton's doctrine -which Flamsteed did. But when we find that others, as Halley, David -Gregory, and Cotes, at once not only saw in the doctrine a source of -true formulæ, but also a magnificent physical discovery, we are -obliged, I think, to make Flamsteed, in this respect, an exception -to the first class of astronomers of his own time. - -[Note 61\7: _Supp._ p. 691.] - -Mr. Baily's suggestion that the annual equations for the corrections -of the lunar apogee and node were collected from Flamsteed's tables -{429} and observations independently of their suggestion by Newton -as the results of Theory (_Supp._ p. 692, Note, and p. 698), appears -to me not to be adequately supported by the evidence given.] - - -_Sect._ 3.--_Reception of the Newtonian Theory abroad._ - -THE reception of the Newtonian theory on the Continent, was much -more tardy and unwilling than in its native island. Even those whose -mathematical attainments most fitted them to appreciate its proofs, -were prevented by some peculiarity of view from adopting it as a -system; as Leibnitz, Bernoulli, Huyghens; who all clung to one -modification or other of the system of vortices. In France, the -Cartesian system had obtained a wide and popular reception, having -been recommended by Fontenelle with the graces of his style; and its -empire was so firm and well established in that country, that it -resisted for a long time the pressure of Newtonian arguments. -Indeed, the Newtonian opinions had scarcely any disciples in France, -till Voltaire asserted their claims, on his return from England in -1728: until then, as he himself says, there were not twenty -Newtonians out of England. - -The hold which the Philosophy of Descartes had upon the minds of his -countrymen is, perhaps, not surprising. He really had the merit, a -great one in the history of science, of having completely overturned -the Aristotelian system, and introduced the philosophy of matter and -motion. In all branches of mixed mathematics, as we have already -said, his followers were the best guides who had yet appeared. His -hypothesis of vortices, as an explanation of the celestial motions, -had an apparent advantage over the Newtonian doctrine, in this -respect;--that it referred effects to the most intelligible, or at -least most familiar kinds of mechanical causation, namely, pressure -and impulse. And above all, the system was acceptable to most minds, -in consequence of being, as was pretended, deduced from a few simple -principles by necessary consequences; and of being also directly -connected with metaphysical and theological speculations. We may -add, that it was modified by its mathematical adherents in such a -way as to remove most of the objections to it. A vortex revolving -about a centre could be constructed, or at least it was supposed -that it could be constructed, so as to produce a tendency of bodies -to the centre. In all cases, therefore, where a central force acted, -a vortex was supposed; but in reasoning to the results of this -hypothesis, it was {430} easy to leave out of sight all other -effects of the vortex, and to consider only the central force; and -when this was done, the Cartesian mathematician could apply to his -problems a mechanical principle of some degree of consistency. This -reflection will, in some degree, account for what at first seems so -strange;--the fact that the language of the French mathematicians is -Cartesian, for almost half a century after the publication of the -_Principia_ of Newton. - -There was, however, a controversy between the two opinions going on -all this time, and every day showed the insurmountable difficulties -under which the Cartesians labored. Newton, in the _Principia_, had -inserted a series of propositions, the object of which was to prove, -that the machinery of vortices could not be accommodated to one part -of the celestial phenomena, without contradicting another part. A -more obvious difficulty was the case of gravity of the earth; if -this force arose, as Descartes asserted, from the rotation of the -earth's vortex about its axis, it ought to tend directly to the -axis, and not to the centre. The asserters of vortices often tried -their skill in remedying this vice in the hypothesis, but never with -much success. Huyghens supposed the ethereal matter of the vortices -to revolve about the centre in all directions; Perrault made the -strata of the vortex increase in velocity of rotation as they recede -from the centre; Saurin maintained that the circumambient resistance -which comprises the vortex will produce a pressure passing through -the centre. The elliptic form of the orbits of the planets was -another difficulty. Descartes had supposed the vortices themselves -to be oval but others, as John Bernoulli, contrived ways of having -elliptical motion in a circular vortex. - -The mathematical prize-questions proposed by the French Academy, -naturally brought the two sets of opinions into conflict. The -Cartesian memoir of John Bernoulli, to which we have just referred, -was the one which gained the prize in 1730. It not unfrequently -happened that the Academy, as if desirous to show its impartiality, -divided the prize between the Cartesians and Newtonians. Thus in -1734, the question being, the cause of the inclination of the orbits -of the planets, the prize was shared between John Bernoulli, whose -Memoir was founded on the system of vortices, and his son Daniel, -who was a Newtonian. The last act of homage of this kind to the -Cartesian system was performed in 1740, when the prize on the -question of the Tides was distributed between Daniel Bernoulli, -Euler, Maclaurin, and Cavallieri; the last of whom had tried to -patch up and amend the Cartesian hypothesis on this subject. {431} - -Thus the Newtonian system was not adopted in France till the -Cartesian generation had died off; Fontenelle, who was secretary to -the Academy of Sciences, and who lived till 1756, died a Cartesian. -There were exceptions; for instance, Delisle, an astronomer who was -selected by Peter the Great of Russia, to found the Academy of St -Petersburg; who visited England in 1724, and to whom Newton then -gave his picture, and Halley his Tables. But in general, during the -interval, that country and this had a national difference of creed -on physical subjects. Voltaire, who visited England in 1727, notices -this difference in his lively manner. "A Frenchman who arrives in -London, finds a great alteration in philosophy, as in other things. -He left the world full [**a _plenum_], he finds it empty. At Paris -you see the universe composed of vortices of subtle matter, in -London we see nothing of the kind. With you it is the pressure of -the moon which causes the tides of the sea, in England it is the sea -which gravitates towards the moon; so that when you think the moon -ought to give us high water, these gentlemen believe that you ought -to have low water; which unfortunately we cannot test by experience; -for in order to do that, we should have examined the Moon and the -Tides at the moment of the creation. You will observe also that the -sun, which in France has nothing to do with the business, here comes -in for a quarter of it. Among you Cartesians, all is done by an -impulsion which one does not well understand; with the Newtonians, -it is done by an attraction of which we know the cause no better. At -Paris you fancy the earth shaped like a melon, at London it is -flattened on the two sides." - -It was Voltaire himself as we have said, who was mainly instrumental -in giving the Newtonian doctrines currency in France. He was at first -refused permission to print his _Elements of the Newtonian -Philosophy_, by the Chancellor, D'Aguesseaux, who was a Cartesian; but -after the appearance of this work in 1738, and of other writings by -him on the same subject, the Cartesian edifice, already without real -support or consistency, crumbled to pieces and disappeared. The first -Memoir in the _Transactions of the French Academy_ in which the -doctrine of central force is applied to the solar system, is one by -the Chevalier de Louville in 1720, _On the Construction and Theory of -Tables of the Sun_. In this, however, the mode of explaining the -motions of the planets by means of an original impulse and an -attractive force is attributed to Kepler, not to Newton. The first -Memoir which refers to the universal gravitation of matter is by -Maupertuis, in {432} 1736. But Newton was not unknown or despised in -France till this time. In 1699 he was admitted one of the very small -number of foreign associates of the French Academy of Sciences. Even -Fontenelle, who, as we have said, never adopted his opinions, spoke of -him in a worthy manner, in the _Eloge_ which he composed on the -occasion of his death. At a much earlier period too, Fontenelle did -homage to his fame. The following passage refers, I presume, to -Newton. In the _History_ of the Academy for 1708, which is written by -the secretary, he says,[62\7] in referring to the difficulty which the -comets occasion in the Cartesian hypothesis: "We might relieve -ourselves at once from all the embarrassment which arises from the -directions of these motions, by suppressing, as has been done _by one -of the greatest geniuses of the age_, all this immense fluid matter, -which we commonly suppose between the planets, and conceiving them -suspended in a perfect void." - -[Note 62\7: _Hist. Ac. Sc._ 1708. p. 103.] - -Comets, as the above passage implies, were a kind of artillery which -the Cartesian _plenum_ could not resist. When it appeared that the -paths of such wanderers traversed the vortices in all directions, it -was impossible to maintain that these imaginary currents governed -the movements of bodies immersed in them and the mechanism ceased -to have any real efficacy. Both these phenomena of comets, and many -others, became objects of a stronger and more general interest, in -consequence of the controversy between the rival parties; and thus -the prevalence of the Cartesian system did not seriously impede the -progress of sound knowledge. In some cases, no doubt, it made men -unwilling to receive the truth, as in the instance of the deviation -of the comets from the zodiacal motion; and again, when Römer -discovered that light was not instantaneously propagated. But it -encouraged observation and calculation, and thus forwarded the -verification and extension of the Newtonian system; of which process -we must now consider some of the incidents. {433} - - - - -CHAPTER IV. - -SEQUEL TO THE EPOCH OF NEWTON, CONTINUED.--VERIFICATION AND -COMPLETION OF THE NEWTONIAN THEORY. - - -_Sect._ 1.--_Division of the Subject._ - -THE verification of the Law of Universal Gravitation as the -governing principle of all cosmical phenomena, led, as we have -already stated, to a number of different lines of research, all long -and difficult. Of these we may treat successively, the motions of -the Moon, of the Sun, of the Planets, of the Satellites, of Comets; -we may also consider separately the Secular Inequalities, which at -first sight appear to follow a different law from the other changes; -we may then speak of the results of the principle as they affect -this Earth, in its Figure, in the amount of Gravity at different -places, and in the phenomena of the Tides. Each of these subjects -has lent its aid to confirm the general law: but in each the -confirmation has had its peculiar difficulties, and has its separate -history. Our sketch of this history must be very rapid, for our aim -is only to show what is the kind and course of the confirmation -which such a theory demands and receives. - -For the same reason we pass over many events of this period which -are highly important in the history of astronomy. They have lost -much of their interest for us, and even for common readers, because -they are of a class with which we are already familiar, truths -included in more general truths to which our eyes now most readily -turn. Thus, the discovery of new satellites and planets is but a -repetition of what was done by Galileo: the determination of their -nodes and apses, the reduction of their motions to the law of the -ellipse, is but a fresh exemplification of the discoveries of -Kepler. Otherwise, the formation of Tables of the satellites of -Jupiter and Saturn, the discovery of the eccentricities of the -orbits, and of the motions of the nodes and apses, by Cassini, -Halley, and others, would rank with the great achievements in -astronomy. Newton's peculiar advance in the _Tables_ of the -celestial motions is the introduction of Perturbations. To these -motions, so affected, we now proceed. {434} - - -_Sect._ 2.--_Application of the Newtonian Theory to the Moon._ - -THE Motions of the Moon may be first spoken of, as the most obvious -and the most important of the applications of the Newtonian Theory. -The verification of such a theory consists, as we have seen in -previous cases, in the construction of Tables derived from the -theory, and the comparison of these with observation. The -advancement of astronomy would alone have been a sufficient motive -for this labor; but there were other reasons which urged it on with -a stronger impulse. A perfect Lunar Theory, if the theory could be -perfected, promised to supply a method of finding the Longitude of -any place on the earth's surface; and thus the verification of a -theory which professed to be complete in its foundations, was -identified with an object of immediate practical use to navigators -and geographers, and of vast acknowledged value. A good method for -the near discovery of the longitude had been estimated by nations -and princes at large sums of money. The Dutch were willing to tempt -Galileo to this task by the offer of a chain of gold: Philip the -Third of Spain had promised a reward for this object still -earlier;[63\7] the parliament of England, in 1714, proposed a -recompense of 20,000_l._ sterling; the Regent Duke of Orléans, two -years afterwards, offered 100,000 francs for the same purpose. These -prizes, added to the love of truth and of fame, kept this object -constantly before the eyes of mathematicians, during the first half -of the last century. - -[Note 63\7: Del. _A. M._ i. 39, 66.] - -If the Tables could be so constructed as to represent the moon's -real place in the heavens with extreme precision, as it would be -seen from a _standard_ observatory, the observation of her apparent -place, as seen from any other point of the earth's surface, would -enable the observer to find his longitude from the standard point. -The motions of the moon had hitherto so ill agreed with the best -Tables, that this method failed altogether. Newton had discovered -the ground of this want of agreement. He had shown that the same -force which produces the Evection, Variation, and Annual Equation, -must produce also a long series of other Inequalities, of various -magnitudes and cycles, which perpetually drag the moon before or -behind the place where she would be sought by an astronomer who knew -only of those principal and notorious inequalities. But to calculate -and apply the new inequalities, was no slight undertaking. {435} - -In the first edition of the _Principia_ in 1687, Newton had not -given any calculations of new inequalities affecting the longitude -of the moon. But in David Gregory's _Elements of Physical and -Geometrical Astronomy_, published in 1702, is inserted[64\7] -"Newton's Lunar Theory as applied by him to Practice;" in which the -great discoverer has given the results of his calculations of eight -of the lunar Equations, their quantities, epochs, and periods. These -calculations were for a long period the basis of new Tables of the -Moon, which were published by various persons;[65\7] as by Delisle -in 1715 or 1716, Grammatici at Ingoldstadt in 1726, Wright in 1732, -Angelo Capelli at Venice in 1733, Dunthorne at Cambridge in 1739. - -[Note 64\7: P. 332.] - -[Note 65\7: Lalande, 1457.] - -Flamsteed had given Tables of the Moon upon Horrox's theory in 1681, -and wished to improve them; and though, as we have seen, he would -not, or could not, accept Newton's doctrines in their whole extent, -Newton communicated his theory to the observer in the shape in which -he could understand it and use it:[66\7] and Flamsteed employed -these directions in constructing new Lunar Tables, which he called -his _Theory_.[67\7] These Tables were not published till long after -his death, by Le Monnier at Paris in 1746. They are said, by -Lalande,[68\7] not to differ much from Halley's. Halley's Tables of -the Moon were printed in 1719 or 1720, but not published till after -his death in 1749. They had been founded on Flamsteed's observations -and his own; and when, in 1720, Halley succeeded Flamsteed in the -post of Astronomer Royal at Greenwich, and conceived that he had the -means of much improving what he had done before, he began by -printing what he had already executed.[69\7] - -[Note 66\7: Baily. _Account of Flamsteed_, p. 72.] - -[Note 67\7: P. 211.] - -[Note 68\7: Lal. 1459.] - -[Note 69\7: Mr. Baily* says that Mayer's _Nouvelles Tables de la -Lune_ in **1753, published upwards of fifty years after Gregory's -_Astronomy_, may be considered as the first lunar tables formed -_solely_ on Newton's principles. Though Wright in 1732 published -_New and Correct Tables of the Lunar Motions according to the -Newtonian Theory_, Newton's rules were in them only partially -adopted. In 1735 Leadbetter published his _Uranoscopia_, in which -those rules were more fully followed. But these _Newtonian Tables_ -did not supersede Flamsteed's Horroxian Tables, till both were -supplanted by those of Mayer. - -* _Supp._ p. 702.] - -But Halley had long proposed a method, different from that of -Newton, but marked by great ingenuity, for amending the Lunar -Tables. He proposed to do this by the use of a cycle, which we have -mentioned as one of the earliest discoveries in astronomy;--the -Period of 223 lunations, or eighteen years and eleven days, the -Chaldean {436} Saros. This period was anciently used for predicting -the eclipses of the sun and moon; for those eclipses which happen -during this period, are repeated again in the same order, and with -nearly the same circumstances, after the expiration of one such -period and the commencement of a second. The reason of this is, that -at the end of such a cycle, the moon is in nearly the same position -with respect to the sun, her nodes, and her apogee, as she was at -first; and is only a few degrees distant from the same part of the -heavens. But on the strength of this consideration, Halley -conjectured that all the irregularities of the moon's motion, -however complex they may be, would recur after such an interval; and -that, therefore, if the requisite corrections were determined by -observation for one such period, we might by means of them give -accuracy to the Tables for all succeeding periods. This idea -occurred to him before he was acquainted with Newton's views.[70\7] -After the lunar theory of the _Principia_ had appeared, he could not -help seeing that the idea was confirmed; for the inequalities of the -moon's motion, which arise from the attraction of the sun, will -depend on her positions with regard to the sun, the apogee, and the -node; and therefore, however numerous, will recur when these -positions recur. - -[Note 70\7: _Phil. Trans._ 1731, p. 188.] - -Halley announced, in 1691,[71\7] his intention of following this -idea into practice; in a paper in which he corrected the text of -three passages in Pliny, in which this period is mentioned, and from -which it is sometimes called the Plinian period. In 1710, in the -preface to a new edition to Street's _Caroline Tables_, he stated -that he had already confirmed it to a considerable extent.[72\7] And -even after Newton's theory had been applied, he still resolved to -use his cycle as a means of obtaining further accuracy. On -succeeding to the Observatory at Greenwich in 1720, he was further -delayed by finding that the instruments had belonged to Flamsteed, -and were removed by his executors. "And this," he says,[73\7] "was -the more grievous to me, on account of my advanced age, being then -in my sixty-fourth year: which put me past all hopes of ever living -to see a complete period of eighteen years' observation. But, thanks -to God, he has been pleased hitherto (in 1731) to afford me -sufficient health and strength to execute my office, in all its -parts, with my own hands and eyes, without any assistance or -interruption, during one whole period of the moon's {437} apogee, -which period is performed in somewhat less than nine years." He -found the agreement very remarkable, and conceived hopes of -attaining the great object, of finding the Longitude with the -requisite degree of exactness; nor did he give up his labors on this -subject till he had completed his Plinian period in 1739. - -[Note 71\7: Ib. p. 536.] - -[Note 72\7: Ib. 1731, p. 187.] - -[Note 73\7: Ib. p. 193.] - -The accuracy with which Halley conceived himself able to predict the -moon's place[74\7] was within two minutes of space, or one fifteenth -of the breadth of the moon herself. The accuracy required for -obtaining the national reward was considerably greater. Le Monnier -pursued the idea of Halley.[75\7] But before Halley's method had -been completed, it was superseded by the more direct prosecution of -Newton's views. - -[Note 74\7: _Phil. Trans._ 1731, p. 195.] - -[Note 75\7: Bailly, _A. M._ c. 131.] - -We have already remarked, in the history of analytical mechanics, that -in the Lunar Theory, considered as one of the cases of the Problem of -Three Bodies, no advance was made beyond what Newton had done, till -mathematicians threw aside the Newtonian artifices, and applied the -newly developed generalizations of the analytical method. The first -great apparent deficiency in the agreement of the law of universal -gravitation with astronomical observation, was removed by Clairaut's -improved approximation to the theoretical Motion of the Moon's Apogee, -in 1750; yet not till it had caused so much disquietude, that Clairaut -himself had suggested a modification of the law of attraction; and it -was only in tracing the consequences of this suggestion, that he found -the Newtonian law of the inverse square to be that which, when rightly -developed, agreed with the facts. Euler solved the problem by the aid -of his analysis in 1745,[76\7] and published Tables of the Moon in -1746. His tables were not very accurate at first;[77\7] but he, -D'Alembert, and Clairaut, continued to labor at this object, and the -two latter published Tables of the Moon in 1754.[78\7] Finally, Tobias -Mayer, an astronomer of Göttingen, having compared Euler's tables with -observations, corrected them so successfully, that in 1753 he -published Tables of the Moon, which really did possess the accuracy -which Halley only flattered himself that he had attained. Mayer's -success in his first Tables encouraged him to make them still more -perfect. He applied himself to the mechanical theory of the moon's -orbit; corrected all the coefficients of the series by a great number -of observations; and in 1755, sent his new Tables to London as worthy -to claim the prize offered for the discovery of longitude. He died -soon after {438} (in 1762), at the early age of thirty-nine, worn out -by his incessant labors; and his widow sent to London a copy of his -Tables with additional corrections. These Tables were committed to -Bradley, then Astronomer Royal, in order to be compared with -observation. Bradley labored at this task with unremitting zeal and -industry, having himself long entertained hopes that the Lunar Method -of finding the Longitude might be brought into general use. He and his -assistant, Gael Morris, introduced corrections into Mayer's Tables of -1755. In his report of 1756, he says,[79\7] that he did not find any -difference so great as a minute and a quarter; and in 1760, he adds, -that this deviation had been further diminished by his corrections. It -is not foreign to our purpose to observe the great labor which this -verification required. Not less than 1220 observations, and long -calculations founded upon each, were employed. The accuracy which -Mayer's Tables possessed was considered to entitle them to a part of -the parliamentary reward; they were printed in 1770, and his widow -received 3000_l._ from the English nation. At the same time, Euler, -whose Tables had been the origin and foundation of Mayer's, also had a -recompense of the same amount. - -[Note 76\7: Lal. 1460.] - -[Note 77\7: Bradley's Correspondence.] - -[Note 78\7: Lal. 1460.] - -[Note 79\7: Bradley's _Mem._ p. xcviii.] - -This public national acknowledgment of the practical accuracy of -these Tables is, it will be observed, also a solemn recognition of -the truth of the Newtonian theory, as far as truth can be judged of -by men acting under the highest official responsibility, and aided -by the most complete command of the resources of the skill and -talents of others. The finding the Longitude is thus the seal of the -moon's gravitation to the sun and earth; and with this occurrence, -therefore, our main concern with the history of the Lunar Theory -ends. Various improvements have been since introduced into this -research; but on these we, with so many other subjects before us, -must forbear to enter. - - -_Sect._ 3.--_Application of the Newtonian Theory to the Planets, -Satellites, and Earth._ - -THE theories of the Planets and Satellites, as affected by the law -of universal gravitation, and therefore by perturbations, were -naturally subjects of interest, after the promulgation of that law. -Some of the effects of the mutual attraction of the planets had, -indeed, already attracted notice. The inequality produced by the -mutual attraction of Jupiter and Saturn cannot be overlooked by a -good observer. In the {439} preface to the second edition of the -_Principia_, Cotes remarks,[80\7] that the perturbation of Jupiter -and Saturn is not unknown to astronomers. In Halley's Tables it was -noticed[81\7] that there are very great deviations from regularity -in these two planets, and these deviations are ascribed to the -perturbing force of the planets on each other; but the correction of -these by a suitable equation is left to succeeding astronomers. - -[Note 80\7: Preface to _Principia_, p. xxi.] - -[Note 81\7: End of Planetary Tables.] - -The motion of the planes and apsides of the planetary orbits was one -of the first results of their mutual perturbation which was -observed. In 1706, La Hire and Maraldi compared Jupiter with the -Rudolphine Tables, and those of Bullialdus: it appeared that his -aphelion had advanced, and that his nodes had regressed. In 1728, J. -Cassini found that Saturn's aphelion had in like manner travelled -forwards. In 1720, when Louville refused to allow in his solar -tables the motion of the aphelion of the earth, Fontenelle observed -that this was a misplaced scrupulousness, since the aphelion of -Mercury certainly advances. Yet this reluctance to admit change and -irregularity was not yet overcome. When astronomers had found an -approximate and apparent constancy and regularity, they were willing -to believe it absolute and exact. In the satellites of Jupiter, for -instance, they were unwilling to admit even the eccentricity of the -orbits; and still more, the variation of the nodes, inclinations, -and apsides. But all the fixedness of these was successively -disproved. Fontenelle in 1732, on the occasion of Maraldi's -discovery of the change of inclination of the fourth satellite, -expresses a suspicion that all the elements might prove liable to -change. "We see," says he, "the constancy of the inclination already -shaken in the three first satellites, and the eccentricity in the -fourth. The immobility of the nodes holds out so far, but there are -strong indications that it will share the same fate." - -The motions of the nodes and apsides of the satellites are a -necessary part of the Newtonian theory; and even the Cartesian -astronomers now required only data, in order to introduce these -changes into their Tables. - -The complete reformation of the Tables of the Sun, Planets, and -Satellites, which followed as a natural consequence from the -revolution which Newton had introduced, was rendered possible by the -labors of the great constellation of mathematicians of whom we have -spoken in the last book, Clairaut, Euler, D'Alembert, and their -successors; and {440} it was carried into effect in the course of -the last century. Thus Lalande applied Clairaut's theory to Mars, as -did Mayer; and the inequalities in this case, says Bailly[82\7] in -1785, may amount to two minutes, and therefore must not be -neglected. Lalande determined the inequalities of Venus, as did -Father Walmesley, an English mathematician; these were found to -reach only to thirty seconds. - -[Note 82\7: _Ast. Mod._ iii. 170.] - -The Planetary Tables[83\7] which were in highest repute, up to the -end of the last century, were those of Lalande. In these, the -perturbations of Jupiter and Saturn were introduced, their magnitude -being such that they cannot be dispensed with; but the Tables of -Mercury, Venus, and Mars, had no perturbations. Hence these latter -Tables might be considered as accurate enough to enable the observer -to find the object, but not to test the theory of perturbations. But -when the calculation of the mutual disturbances of the planets was -applied, it was always found that it enabled mathematicians to bring -the theoretical places to coincide more exactly with those observed. -In improving, as much as possible, this coincidence, it is necessary -to determine the mass of each planet; for upon that, according to -the law of universal gravitation, its disturbing power depends. -Thus, in 1813, Lindenau published Tables of Mercury, and concluded, -from them, that a considerable increase of the supposed mass of -Venus was necessary to reconcile theory with observation.[84\7] He -had published Tables of Venus in 1810, and of Mars in 1811. And, in -proving Bouvard's Tables of Jupiter and Saturn, values were obtained -of the masses of those planets. The form in which the question of -the truth of the doctrine of universal gravitation now offers itself -to the minds of astronomers, is this:--that it is taken for granted -that it will account for the motions of the heavenly bodies, and the -question is, with what supposed masses it will give the _best_ -account.[85\7] The continually increasing accuracy of the table -shows the truth of the fundamental assumption. - -[Note 83\7: Airy, _Report on Ast. to Brit. Ass._ 1832.] - -[Note 84\7: Airy, _Report on Ast. to Brit. **Ass._ 1832.] - -[Note 85\7: Among the most important corrections of the supposed -masses of the planets, we may notice that of Jupiter, by Professor -Airy. This determination of Jupiter's mass was founded, not on the -effect as seen in perturbations, but on a much more direct datum, -the time of revolution of his fourth satellite. It appeared, from -this calculation, that Jupiter's mass required to be increased by -about 1⁄80th. This result agrees with that which has been derived by -German astronomers from the perturbations which the attractions of -Jupiter produce in the four new planets, and has been generally -adopted as an improvement of the elements of our system.] - -The question of perturbation is exemplified in the satellites also. -{441} Thus the satellites of Jupiter are not only disturbed by the -sun, as the moon is, but also by each other, as the planets are. -This mutual action gives rise to some very curious relations among -their motions; which, like most of the other leading inequalities, -were forced upon the notice of astronomers by observation before -they were obtained by mathematical calculation. In Bradley's remarks -upon his own Tables of Jupiter's Satellites, published among -Halley's Tables, he observes that the places of the three interior -satellites are affected by errors which recur in a cycle of 437 -days, answering to the time in which they return to the same -relative position with regard to each other, and to the axis of -Jupiter's shadow. Wargentin, who had noticed the same circumstance -without knowledge of what Bradley had done, applied it, with all -diligence, to the purpose of improving the tables of the satellites -in 1746. But, at a later period, Laplace established, by -mathematical reasoning, the very curious theorem on which this cycle -depends, which he calls the _libration of Jupiter's satellites_; and -Delambre was then able to publish Tables of Jupiter's Satellites -more accurate than those of Wargentin, which he did in 1789.[86\7] - -[Note 86\7: Voiron, _Hist. Ast._ p. 322.] - -The progress of physical astronomy from the time of Euler and -Clairaut, has consisted of a series of calculations and comparisons -of the most abstruse and recondite kind. The formation of Tables of -the Planets and Satellites from the theory, required the solution of -problems much more complex than the original case of the Problem of -Three Bodies. The real motions of the planets and their orbits are -rendered still further intricate by this, that all the lines and -points to which we can refer them, are themselves in motion. The -task of carrying order and law into this mass of apparent confusion, -has required a long series of men of transcendent intellectual -powers; and a perseverance and delicacy of observation, such as we -have not the smallest example of in any other subject. It is -impossible here to give any detailed account of these labors; but we -may mention one instance of the complex considerations which enter -into them. The nodes of Jupiter's fourth satellite do not go -backwards,[87\7] as the Newtonian theory seems to require; they -advance upon Jupiter's orbit. But then, it is to be recollected that -the theory requires the nodes to retrograde upon the orbit of the -perturbing body, which is here the third satellite; and Lalande -showed that, by the necessary relations of space, the latter motion -may be retrograde though the former is direct. {442} - -[Note 87\7: Bailly, iii. 175.] - -Attempts have been made, from the time of the solution of the -Problem of three bodies to the present, to give the greatest -possible accuracy to the Tables of the Sun, by considering the -effect of the various perturbations to which the earth is subject. -Thus, in 1756, Euler calculated the effect of the attractions of the -planets on the earth (the prize-question of the French Academy of -Sciences), and Clairaut soon after. Lacaille, making use of these -results, and of his own numerous observations, published Tables of -the Sun. In 1786, Delambre[88\7] undertook to verify and improve -these tables, by comparing them with 314 observations made by -Maskelyne, at Greenwich, in 1775 and 1784, and in some of the -intermediate years. He corrected most of the elements; but he could -not remove the uncertainty which occurred respecting the amount of -the inequality produced by the reaction of the moon. He admitted -also, in pursuance of Clairaut's theory, a second term of this -inequality depending on the moon's latitude; but irresolutely, and -half disposed to reject it on the authority of the observations. -Succeeding researches of mathematicians have shown, that this term -is not admissible as a result of mechanical principles. Delambre's -Tables, thus improved, were exact to seven or eight seconds;[89\7] -which was thought, and truly, a very close coincidence for the time. -But astronomers were far from resting content with this. In 1806, -the French Board of Longitude published Delambre's improved Solar -Tables; and in the _Connaissance des Tems_ for 1816, Burckhardt gave -the results of a comparison of Delambre's Tables with a great number -of Maskelyne's observations;--far greater than the number on which -they were founded.[90\7] It appeared that the epoch, the perigee, -and the eccentricity, required sensible alterations, and that the -mass of Venus ought to be reduced about one-ninth, and that of the -Moon to be sensibly diminished. In 1827, Professor Airy[91\7] -compared Delambre's tables with 2000 Greenwich observations, made -with the new transit-instrument at Cambridge, and deduced from this -comparison the correction of the elements. These in general agreed -closely with Burckhardt's, excepting that a diminution of Mars -appeared necessary. Some discordances, however, led Professor Airy -to suspect the existence of an inequality which had escaped the -sagacity of Laplace and Burckhardt. And, a few weeks after this -suspicion had been expressed, the same mathematician announced to -the Royal Society that he had {443} detected, in the planetary -theory such an inequality, hitherto unnoticed, arising from the -mutual attraction of Venus and the Earth. Its whole effect on the -earth's longitude, would be to increase or diminish it by nearly -three seconds of space, and its period is about 240 years. "This -term," he adds, "accounts completely for the difference of the -secular motions given by the comparison of the epochs of 1783 and -1821, and by that of the epochs of 1801 and 1821." - -[Note 88\7: Voiron, _Hist._ p. 315.] - -[Note 89\7: Montucla, iv. 42.] - -[Note 90\7: Airy, _Report_, p. 150.] - -[Note 91\7: _Phil. Trans._ 1828.] - -Many excellent Tables of the motions of the sun, moon, and planets, -were published in the latter part of the last century; but the -Bureau des Longitudes which was established in France in 1795, -endeavored to give new or improved tables of most of these motions. -Thus were produced Delambre's Tables of the Sun, Burg's Tables of -the Moon, Bouvard's Tables of Jupiter, Saturn, and Uranus. The -agreement between these and observation is, in general, truly -marvellous. - -We may notice here a difference in the mode of referring to -observation when a theory is first established, and when it is -afterwards to be confirmed and corrected. It was remarked as a merit -in the method of Hipparchus, and an evidence of the mathematical -coherence of his theory, that in order to determine the place of the -sun's apogee, and the eccentricity of his orbit, he required to know -nothing besides the lengths of winter and spring. But if the fewness -of the requisite data is a beauty in the first fixation of a theory, -the multitude of observations to which it applies is its excellence -when it is established; and in correcting Tables, mathematicians -take far more data than would be requisite to determine the -elements. For the theory ought to account for _all_ the facts: and -since it will not do this with mathematical rigor (for observation -is not perfect), the elements are determined, not so as to satisfy -any selected observations, but so as to make the whole mass of error -as small as possible. And thus, in the adaptation of theory to -observation, even in its most advanced state, there is room for -sagacity and skill, prudence and judgment. - -In this manner, by selecting the best mean elements of the motions -of the heavenly bodies, the observed motions deviate from this mean -in the way the theory points out, and constantly return to it. To -this general rule, of the constant return to a mean, there are, -however, some apparent exceptions, of which we shall now speak. {444} - - -_Sect._ 4.--_Application of the Newtonian Theory to Secular -Inequalities._ - -SECULAR Inequalities in the motions of the heavenly bodies occur in -consequence of changes in the elements of the solar system, which go -on progressively from age to age. The example of such changes which -was first studied by astronomers, was the Acceleration of the Moon's -Mean Motion, discovered by Halley. The observed fact was, that the -moon now moves in a very small degree quicker than she did in the -earlier ages of the world. When this was ascertained, the various -hypotheses which appeared likely to account for the fact were -reduced to calculation. The resistance of the medium in which the -heavenly bodies move was the most obvious of these hypotheses. -Another, which was for some time dwelt upon by Laplace, was the -successive transmission of gravity, that is, the hypothesis that the -gravity of the earth takes a certain finite time to reach the moon. -But none of these suppositions gave satisfactory conclusions; and -the strength of Euler, D'Alembert, Lagrange, and Laplace, was for a -time foiled by this difficulty. At length, in 1787, Laplace -announced to the Academy that he had discovered the true cause of -this acceleration, and that it arose from the action of the sun upon -the moon, combined with the secular variation of the eccentricity of -the earth's orbit. It was found that the effects of this combination -would exactly account for the changes which had hitherto so -perplexed mathematicians. A very remarkable result of this -investigation was, that "this Secular Inequality of the motion of -the moon is periodical, but it requires millions of years to -re-establish itself;" so that after an almost inconceivable time, -the acceleration will become a retardation. Laplace some time after -(in 1797), announced other discoveries, relative to the secular -motions of the apogee and the nodes of the moon's orbit. Laplace -collected these researches in his "Theory of the Moon," which he -published in the third volume of the _Mécanique Céleste_ in 1802. - -A similar case occurred with regard to an acceleration of Jupiter's -mean motion, and a retardation of Saturn's, which had been observed -by Cassini, Maraldi, and Horrox. After several imperfect attempts by -other mathematicians, Laplace, in 1787, found that there resulted -from the mutual attraction of these two planets a great Inequality, -of which the period is 929 years and a half, and which has -accelerated Jupiter and retarded Saturn ever since the restoration -of astronomy. {445} - -Thus the secular inequalities of the celestial motions, like all the -others, confirm the law of universal gravitation. They are called -"secular," because ages are requisite to unfold their existence, and -because they are not obviously periodical. They might, in some -measure, be considered as extensions of the Newtonian theory, for -though Newton's law accounts for such facts, he did not, so far as -we know, foresee such a result of it. But on the other hand, they -are exactly of the same nature as those which he did foresee and -calculate. And when we call them _secular_ in opposition to -_periodical_, it is not that there is any real difference, for they, -too, have their cycle; but it is that we have assumed our _mean_ -motion without allowing for these long inequalities. And thus, as -Laplace observes on this very occasion,[92\7] the lot of this great -discovery of gravitation is no less than this, that every apparent -exception becomes a proof, every difficulty a new occasion of a -triumph. And such, as he truly adds, is the character of a true -theory,--of a real representation of nature. - -[Note 92\7: _Syst. du Monde_, 8vo, ii. 37.] - -It is impossible for us here to enumerate even the principal objects -which have thus filled the triumphal march of the Newtonian theory -from its outset up to the present time. But among these secular -changes, we may mention the Diminution of the Obliquity of the -Ecliptic, which has been going on from the earliest times to the -present. This change has been explained by theory, and shown to -have, like all the other changes of the system, a limit, after which -the diminution will be converted into an increase. - -We may mention here some subjects of a kind somewhat different from -those just spoken of. The true theoretical quantity of the -Precession of the Equinoxes, which had been erroneously calculated -by Newton, was shown by D'Alembert to agree with observation. The -constant coincidence of the Nodes of the Moon's Equator with those -of her Orbit, was proved to result from mechanical principles by -Lagrange. The curious circumstance that the Time of the Moon's -rotation on her axis is equal to the Time of her revolution about -the earth, was shown to be consistent with the results of the laws -of motion by Laplace. Laplace also, as we have seen, explained -certain remarkable relations which constantly connect the longitudes -of the three first satellites of Jupiter; Bailly and Lagrange -analyzed and explained the curious librations of the nodes and -inclinations of their orbits; and Laplace traced the effect of -Jupiter's oblate figure on their motions, {446} which masks the -other causes of inequality, by determining the direction of the -motions of the _perijove_ and node of each satellite. - - -_Sect._ 5.--_Application of the Newtonian Theory to the New -Planets._ - -WE are now so accustomed to consider the Newtonian theory as true, -that we can hardly imagine to ourselves the possibility that those -planets which were not discovered when the theory was founded, -should contradict its doctrines. We can scarcely conceive it -possible that Uranus or Ceres should have been found to violate -Kepler's laws, or to move without suffering perturbations from -Jupiter and Saturn. Yet if we can suppose men to have had any doubt -of the exact and universal truth of the doctrine of universal -gravitation, at the period of these discoveries, they must have -scrutinized the motions of these new bodies with an interest far -more lively than that with which we now look for the predicted -return of a comet. The solid establishment of the Newtonian theory -is thus shown by the manner in which we take it for granted not only -in our reasonings, but in our feelings. But though this is so, a -short notice of the process by which the new planets were brought -within the domain of the theory may properly find a place here. - -William Herschel, a man of great energy and ingenuity, who had made -material improvements in reflecting telescopes, observing at Bath on -the 13th of March, 1781, discovered, in the constellation Gemini, a -star larger and less luminous than the fixed stars. On the -application of a more powerful telescope, it was seen magnified, and -two days afterwards he perceived that it had changed its place. The -attention of the astronomical world was directed to this new object, -and the best astronomers in every part of Europe employed themselves -in following it along the sky.[93\7] - -[Note 93\7: Voiron, _Hist. Ast._ p. 12.] - -The admission of an eighth planet into the long-established list, was -a notion so foreign to men's thoughts at that time, that other -suppositions were first tried. The orbit of the new body was at first -calculated as if it had been a comet running in a parabolic path. But -in a few days the star deviated from the course thus assigned it: and -it was in vain that in order to represent the observations, the -perihelion distance of the parabola was increased from fourteen to -eighteen times the earth's distance from the sun. Saron, of the -Academy of Sciences of Paris, is said[94\7] to have been the first -person who perceived that the {447} places were better represented by -a circle than by a parabola: and Lexell, a celebrated mathematician of -Petersburg, found that a motion in a circular orbit, with a radius -double of that of Saturn, would satisfy all the observations. This -made its period about eighty-two years. - -[Note 94\7: Ibid.] - -Lalande soon discovered that the circular motion was subject to a -sensible inequality: the orbit was, in fact, an ellipse, like those -of the other planets. To determine the equation of the centre of a -body which revolves so slowly, would, according to the ancient -methods, have required many years; but Laplace contrived methods by -which the elliptical elements were determined from four -observations, within little more than a year from its first -discovery by Herschel. These calculations were soon followed by -tables of the new planet, published by Nouet. - -In order to obtain additional accuracy, it now became necessary to -take account of the perturbations. The French Academy of Sciences -proposed, in 1789, the construction of new Tables of this Planet as -its prize-question. It is a curious illustration of the constantly -accumulating evidence of the theory, that the calculation of the -perturbations of the planet enabled astronomers to discover that it -had been observed as a star in three different positions in former -times; namely, by Flamsteed in 1690, by Mayer in 1756, and by Le -Monnier in 1769. Delambre, aided by this discovery and by the theory -of Laplace, calculated Tables of the planet, which, being compared -with observation for three years, never deviated from it more than -seven seconds. The Academy awarded its prize to these Tables, they -were adopted by the astronomers of Europe, and the planet of Herschel -now conforms to the laws of attraction, along with those ancient -members of the known system from which the theory was inferred. - -The history of the discovery of the other new planets, Ceres, -Pallas, Juno, and Vesta, is nearly similar to that just related, -except that their planetary character was more readily believed. The -first of these was discovered on the first day of this century by -Piazzi, the astronomer at Palermo; but he had only begun to suspect -its nature, and had not completed his third observation, when his -labors were suspended by a dangerous illness; and on his recovery -the star was invisible, being lost in the rays of the sun. - -He declared it to be a planet with an elliptical orbit; but the path -which it followed, on emerging from the neighborhood of the sun, was -not that which Piazzi had traced out for it. Its extreme smallness -made it difficult to rediscover; and the whole of the year 1801 was -{448} employed in searching the sky for it in vain. At last, after -many trials, Von Zach and Olbers again found it, the one on the last -day of 1801, the other on the first day of 1802. Gauss and Burckhardt -immediately used the new observations in determining the elements of -the orbit; and the former invented a new method for the purpose. Ceres -now moves in a path of which the course and inequalities are known, -and can no more escape the scrutiny of astronomers. - -The second year of the nineteenth century also produced its planet. -This was discovered by Dr. Olbers, a physician of Bremen, while he -was searching for Ceres among the stars of the constellation Virgo. -He found a star which had a perceptible motion even in the space of -two hours. It was soon announced as a new planet, and received from -its discoverer the name of Pallas. As in the case of Ceres, -Burckhardt and Gauss employed themselves in calculating its orbit. -But some peculiar difficulties here occurred. Its eccentricity is -greater than that of any of the old planets, and the inclination of -its orbit to the ecliptic is not less than thirty-five degrees. -These circumstances both made its perturbations large, and rendered -them difficult to calculate. Burckhardt employed the known processes -of analysis, but they were found insufficient: and the Imperial -Institute (as the French Academy was termed during the reign of -Napoleon) proposed the Perturbations of Pallas as a prize-question. - -To these discoveries succeeded others of the same kind. The German -astronomers agreed to examine the whole of the zone in which Ceres -and Pallas move; in the hope of finding other planets, fragments, as -Olbers conceived they might possibly be, of one original mass. In -the course of this research, Mr. Harding of Lilienthal, on the first -of September, 1804, found a new star, which he soon was led to -consider as a planet. Gauss and Burckhardt also calculated the -elements of this orbit, and the planet was named Juno. - -After this discovery, Olbers sought the sky for additional fragments -of his planet with extraordinary perseverance. He conceived that one -of two opposite constellations, the Virgin or the Whale, was the -place where its separation must have taken place; and where, -therefore, all the orbits of all the portions must pass. He resolved -to survey, three times a year, all the small stars in these two -regions. This undertaking, so curious in its nature, was successful. -The 29th of March, 1807, he discovered Vesta, which was soon found -to be a planet. And to show the manner in which Olbers pursued his -labors, we may state that he afterwards published a notification -that he had examined the {449} same parts of the heavens with such -regularity, that he was certain no new planet had passed that way -between 1808 and 1816. Gauss and Burckhardt computed the orbit of -Vesta; and when Gauss compared one of his orbits with twenty-two -observations of M. Bouvard, he found the errors below seventeen -seconds of space in right ascension, and still less in declination. - -The elements of all these orbits have been successively improved, -and this has been done entirely by the German mathematicians.[95\7] -These perturbations are calculated, and the places for some time -before and after opposition are now given in the Berlin Ephemeris. -"I have lately observed," says Professor Airy, "and compared with -the Berlin Ephemeris, the right ascensions of Juno and Vesta, and I -find that they are rather more accurate than those of Venus:" so -complete is the confirmation of the theory by these new bodies; so -exact are the methods of tracing the theory to its consequences. - -[Note 95\7: Airy, _Rep._ 157.] - -We may observe that all these new-discovered bodies have received -names taken from the ancient mythology. In the case of the first of -these, astronomers were originally divided; the discoverer himself -named it the _Georgium Sidus_, in honor of his patron, George the -Third; Lalande and others called it _Herschel_. Nothing can be more -just than this mode of perpetuating the fame of the author of a -discovery; but it was felt to be ungraceful to violate the -homogeneity of the ancient system of names. Astronomers tried to -find for the hitherto neglected denizen of the skies, an appropriate -place among the deities to whose assembly he was at last admitted; -and _Uranus_, the father of Saturn, was fixed upon as best suiting -the order of the course. - -The mythological nomenclature of planets appeared, from this time, -to be generally agreed to. Piazzi termed his _Ceres Ferdinandea_. -The first term, which contains a happy allusion to Sicily, the -country of the discovery in modern, and of the goddess in ancient, -times, has been accepted; the attempt to pay a compliment to royalty -out of the products of science, in this as in most other cases, has -been set aside. Pallas, Juno, and Vesta, were named, without any -peculiar propriety of selection, according to the choice of their -discoverers. - - -_Sect._ 6.--_Application of the Newtonian Theory to Comets._ - -A FEW words must be said upon another class of bodies, which at -first seemed as lawless as the clouds and winds; and which astronomy -{450} has reduced to a regularity as complete as that of the -sun;--upon _Comets_. No part of the Newtonian discoveries excited a -more intense interest than this. These anomalous visitants were -anciently gazed at with wonder and alarm; and might still, as in -former times, be accused of "perplexing nations," though with very -different fears and questionings. The conjecture that they, too, -obeyed the law of universal gravitation, was to be verified by -showing that they described a curve such as that force would -produce. Hevelius, who was a most diligent observer of these -objects, had, without reference to gravitation, satisfied himself -that they moved in parabolas.[96\7] To determine the elements of the -parabola from observations, even Newton called[97\7] "problema longe -difficillimum." Newton determined the orbit of the comet of 1680 by -certain graphical methods. His methods supposed the orbit to be a -parabola, and satisfactorily represented the motion in the visible -part of the comet's path. But this method did not apply to the -possible return of the wandering star. Halley has the glory of -having first detected a periodical comet, in the case of that which -has since borne his name. But this great discovery was not made -without labor. In 1705, Halley[98\7] explained how the parabolic -orbit of a planet may be determined from three observations; and, -joining example to precept, himself calculated the positions and -orbits of twenty-four comets. He found, as the reward of this -industry, that the comets of 1607 and of 1531 had the same orbit as -that of 1682. And here the intervals are also nearly the same, -namely, about seventy-five years. Are the three comets then -identical? In looking back into the history of such appearances, he -found comets recorded in 1456, in 1380, and in 1305; the intervals -are still the same, seventy-five or seventy-six years. It was -impossible now to doubt that they were the periods of a revolving -body; that the comet was a planet; its orbit a long ellipse, not a -parabola.[99\7] - -[Note 96\7: Bailly, ii. 246.] - -[Note 97\7: _Principia_, ed. 1. p. 494.] - -[Note 98\7: Bailly, ii. 646.] - -[Note 99\7: The importance of Halley's labors on Comets has always -been acknowledged. In speaking of Halley's _Synopsis Astronomicæ -Cometicæ_, Delambre says (_Ast._ xviii. _Siècle_, p. 130), "Voilà -bien, depuis Kepler, ce qu'on a fait de plus grand, de plus beau, de -plus neuf en astronomie." Halley, in predicting the comet of 1758, -says, if it returns, "Hoc primum ab homine Anglo iuventum fuisse non -inficiabitur æqua posteritas."] - -But if this were so, the Comet must reappear in 1758 or 1759. Halley -predicted that it would do so; and the fulfilment of this prediction -was naturally looked forwards to, as an additional stamp of the -truths of the theory of gravitation. {451} - -But in all this, the Comet had been supposed to be affected only by -the attraction of the sun. The planets must disturb its motion as -they disturb each other. How would this disturbance affect the time -and circumstances of its reappearance? Halley had proposed, but not -attempted to solve, this question. - -The effect of perturbations upon a comet defeats all known methods -of approximation, and requires immense labor. "Clairaut," says -Bailly,[100\7] "undertook this: with courage enough to dare the -adventure, he had talent enough to obtain a memorable victory;" the -difficulties, the labors, grew upon him as he advanced, but he -fought his way through them, assisted by Lalande, and by a female -calculator, Madame Lepaute. He predicted that the comet would reach -its perihelion April 13, 1759, but claimed the license of a month -for the inevitable inaccuracy of a calculation which, in addition to -all other sources of error, was made in haste, that it might appear -as a prediction. The comet justified his calculations and his caution -together; for it arrived at its perihelion on the 13th of March. - -[Note 100\7: Bailly, _A. M._ iii. 190.] - -Two other Comets, of much shorter period, have been detected of late -years; Encke's, which revolves round the sun in three years and -one-third, and Biela's which describes an ellipse, not extremely -eccentric, in six years and three-quarters. These bodies, apparently -thin and vaporous masses, like other comets, have, since their -orbits were calculated, punctually conformed to the law of -gravitation. If it were still doubtful whether the more conspicuous -comets do so, these bodies would tend to prove the fact, by showing -it to be true in an intermediate case. - -[2d Ed.] [A third Comet of short period was discovered by Faye, at the -Observatory of Paris, Nov. 22, 1843. It is included between the orbits -of Mars and Saturn, and its period is seven years and three-tenths. - -This is commonly called _Faye's Comet_, as the two mentioned in the -text are called _Encke's_ and _Biela's_. In the former edition I had -expressed my assent to the rule proposed by M. Arago, that the latter -ought to be called _Gambart's Comet_, in honor of the astronomer who -first proved it to revolve round the Sun. But astronomers in general -have used the former name, considering that the discovery and -observation of the object are more distinct and conspicuous merits -than a calculation founded upon the observations of others. And in -reality {452} Biela had great merit in the discovery of his Comet's -periodicity, having set about his search of it from an anticipation of -its return founded upon former observations. - -Also a Comet was discovered by De Vico at Rome on Aug. 22, 1844, -which was found to describe an elliptical orbit having its aphelion -near the orbit of Jupiter, which is consequently one of those of -short period. And on Feb. 26, 1846, M. Brorsen of Kiel discovered a -telescopic Comet whose orbit is found to be elliptical.] - -We may add to the history of Comets, that of Lexell's, which, in -1770, appeared to be revolving in a period of about five years, and -whose motion was predicted accordingly. The prediction was -disappointed; but the failure was sufficiently explained by the -comet's having passed close to Jupiter, by which occurrence its -orbit was utterly deranged. - -It results from the theory of universal gravitation, that Comets are -collections of extremely attenuated matter. Lexell's is supposed to -have passed twice (in 1767 and 1779) through the system of Jupiter's -Satellites, without disturbing their motions, though suffering -itself so great a disturbance as to have its orbit entirely altered. -The same result is still more decidedly proved by the last -appearance of Biela's Comet. It appeared double, but the two bodies -did not perceptibly affect each other's motions, as I am informed by -Professor Challis of Cambridge, who observed both of them from Jan. -23 to Mar. 25, 1846. This proves the quantity of matter in each body -to have been exceedingly small. - -Thus, no verification of the Newtonian theory, which was possible in -the motions of the stars, has yet been wanting. The return of -Halley's Comet again in 1835, and the extreme exactitude with which -it conformed to its predicted course, is a testimony of truth, which -must appear striking even to the most incurious respecting such -matters.[101\7] - -[Note 101\7: M. de Humboldt (_Kosmos_, p. 116) speaks of _nine_ -returns of Halley's Comet, the comet observed in China in 1378 being -identified with this. But whether we take 1378 or 1380 for the -appearance in that century, if we begin with that, we have only -_seven_ appearances, namely, in 1378 or 1380, in 1456, in 1531, in -1607, in 1682, in 1759, and in 1835.] - - -_Sect._ 7.--_Application of the Newtonian Theory to the Figure of -the Earth._ - -THE Heavens had thus been consulted respecting the Newtonian -doctrine, and the answer given, over and over again, in a thousand -{453} different forms, had been, that it was true; nor had the most -persevering cross-examination been able to establish any thing of -contradiction or prevarication. The same question was also to be put -to the Earth and the Ocean, and we must briefly notice the result. - -According to the Newtonian principles, the form of the earth must be -a globe somewhat flattened at the poles. This conclusion, or at -least the amount of the flattening, depends not only upon the -existence and law of attraction, but upon its belonging to each -particle of the mass separately; and thus the experimental -confirmation of the form asserted from calculation, would be a -verification of the theory in its widest sense. The application of -such a test was the more necessary to the interests of science, -inasmuch as the French astronomers had collected from their measures, -and had connected with their Cartesian system, the opinion that the -earth was not _oblate_ but _oblong_. Dominic Cassini had measured -seven degrees of latitude from Amiens to Perpignan, in 1701, and -found them to decrease in going from south to north. The prolongation -of this measure to Dunkirk confirmed the same result. But if the -Newtonian doctrine was true, the contrary ought to be the case, and -the degrees ought to increase in proceeding towards the pole. - -The only answer which the Newtonians could at this time make to the -difficulty thus presented, was, that an arc so short as that thus -measured, was not to be depended upon for the determination of such -a question; inasmuch as the inevitable errors of observation might -exceed the differences which were the object of research. It would, -undoubtedly, have become the English to have given a more complete -answer, by executing measurements under circumstances not liable to -this uncertainty. The glory of doing this, however, they for a long -time abandoned to other nations. The French undertook the task with -great spirit.[102\7] In 1733, in one of the meetings of the French -Academy, when this question was discussed, De la Condamine, an -ardent and eager man, proposed to settle this question by sending -members of the Academy to measure a degree of the meridian near the -equator, in order to compare it with the French degrees, and offered -himself for the expedition. Maupertuis, in like manner, urged the -necessity of another expedition to measure a degree in the -neighborhood of the pole. The government received the applications -favorably, and these remarkable scientific missions were sent out at -the national expense. {454} - -[Note 102\7: Bailly, iii. 11.] - -As soon as the result of these measurements was known, there was no -longer any doubt as to the fact of the earth's oblateness, and the -question only turned upon its quantity. Even before the return of -the academicians, the Cassinis and Lacaille had measured the French -arc, and found errors which subverted the former result, making the -earth oblate to the amount of 1⁄168th of its diameter. The -expeditions to Peru and to Lapland had to struggle with difficulties -in the execution of their design, which make their narratives -resemble some romantic history of irregular warfare, rather than the -monotonous records of mere measurements. The equatorial degree -employed the observers not less than eight years. When they did -return, and the results were compared, their discrepancy, as to -quantity, was considerable. The comparison of the Peruvian and -French arcs gave an ellipticity of nearly 1⁄314th, that of the -Peruvian and Swedish arcs gave 1⁄213th for its value. - -Newton had deduced from his theory, by reasonings of singular -ingenuity, an ellipticity of 1⁄230th; but this result had been -obtained by supposing the earth homogeneous. If the earth be, as we -should most readily conjecture it to be, more dense in its interior -than at its exterior, its ellipticity will be less than that of a -homogeneous spheroid revolving in the same time. It does not appear -that Newton was aware of this; but Clairaut, in 1743, in his _Figure -of the Earth_, proved this and many other important results of the -attraction of the particles. Especially he established that, in -proportion as the fraction expressing the Ellipticity becomes -smaller, that expressing the Excess of the polar over the equatorial -gravity becomes larger; and he thus connected the measures of the -ellipticity obtained by means of Degrees, with those obtained by -means of Pendulums in different latitudes. - -The altered rate of a Pendulum when carried towards the equator, had -been long ago observed by Richer and Halley, and had been quoted by -Newton as confirmatory of his theory. Pendulums were swung by the -academicians who measured the degrees, and confirmed the general -character of the results. - -But having reached this point of the verification of the Newtonian -theory, any additional step becomes more difficult. Many excellent -measures, both of Degrees and of Pendulums, have been made since -those just mentioned. The results of the Arcs[103\7] is an -Ellipticity of 1⁄298th;--of the Pendulums, an Ellipticity of about -1⁄285th. This difference {455} is considerable, if compared with the -quantities themselves; but does not throw a shadow of doubt on the -truth of the theory. Indeed, the observations of each kind exhibit -irregularities which we may easily account for, by ascribing them to -the unknown distribution of the denser portions of the earth; but -which preclude the extreme of accuracy and certainty in our result. - -[Note 103\7: Airy, _Fig. Earth_, p. 230.] - -But the near agreement of the determination, from Degrees and from -Pendulums, is not the only coincidence by which the doctrine is -confirmed. We can trace the effect of the earth's Oblateness in -certain minute apparent motions of the stars; for the attraction of -the sun and moon on the protuberant matter of the spheroid produces -the Precession of the equinoxes, and a Nutation of the earth's axis. -The Precession had been known from the time of Hipparchus, and the -existence of Nutation was foreseen by Newton; but the quantity is so -small, that it required consummate skill and great labor in Bradley -to detect it by astronomical observation. Being, however, so -detected, its amount, as well as that of the Precession, gives us -the means of determining the amount of Terrestrial Ellipticity, by -which the effect is produced. But it is found, upon calculation, -that we cannot obtain this determination without assuming some law -of density in the homogeneous strata of which we suppose the earth -to consist[104\7] The density will certainly increase in proceeding -towards the centre, and there is a simple and probable law of this -increase, which will give 1⁄300th for the Ellipticity, from the -amount of two lunar Inequalities (one in latitude and one in -longitude), which are produced by the earth's oblateness. Nearly the -same result follows from the quantity of Nutation. Thus every thing -tends to convince us that the ellipticity cannot deviate much from -this fraction. - -[Note 104\7: Airy, _Fig. Earth_, p. 235.] - -[2d Ed.] [I ought not to omit another class of phenomena in which -the effects of the Earth's Oblateness, acting according to the law -of universal gravitation, have manifested themselves;--I speak of -the Moon's Motion, as affected by the Earth's Ellipticity. In this -case, as in most others, observation anticipated theory. Mason had -inferred from lunar observations a certain Inequality in Longitude, -depending upon the distance of the Moon's Node from the Equinox. -Doubts were entertained by astronomers whether this inequality -really existed; but Laplace showed that such an inequality would -arise from the oblate form of the earth; and that its magnitude -might serve to {456} determine the amount of the oblateness. Laplace -showed, at the same time, that along with this Inequality in -Longitude there must be an Inequality in Latitude; and this -assertion Burg confirmed by the discussion of observations. The two -Inequalities, as shown in the observations, agree in assigning to -the earth's form an Ellipticity of 1⁄305th.] - - -_Sect._ 8.--_Confirmation of the Newtonian Theory by Experiments on -Attraction._ - -THE attraction of all the parts of the earth to one another was thus -proved by experiments, in which the whole mass of the earth is -concerned. But attempts have also been made to measure the -attraction of smaller portions; as mountains, or artificial masses. -This is an experiment of great difficulty; for the attraction of -such masses must be compared with that of the earth, of which it is -a scarcely perceptible fraction; and, moreover, in the case of -mountains, the effect of the mountain will be modified or disguised -by unknown or unappreciable circumstances. In many of the -measurements of degrees, indications of the attraction of mountains -had been perceived; but at the suggestion of Maskelyne, the -experiment was carefully made, in 1774, upon the mountain -Schehallien, in Scotland, the mountain being mineralogically -surveyed by Playfair. The result obtained was, that the attraction -of the mountain drew the plumb-line about six seconds from the -vertical; and it was deduced from this, by Hutton's calculations, -that the density of the earth was about once and four-fifths that of -Schehallien, or four and a half times that of water. - -Cavendish, who had suggested many of the artifices in this -calculation, himself made the experiment in the other form, by using -leaden balls, about nine inches diameter. This observation was -conducted with an extreme degree of ingenuity and delicacy, which -could alone make it valuable; and the result agreed very nearly with -that of the Schehallien experiment, giving for the density of the -earth about five and one-third times that of water. Nearly the same -result was obtained by Carlini, in 1824, from observations of the -pendulum, made at a point of the Alps (the Hospice, on Mount Cenis) at -a considerable elevation above the average surface of the earth. {457} - - -_Sect._ 9.--_Application of the Newtonian Theory to the Tides._ - -WE come, finally, to that result, in which most remains to be done -for the verification of the general law of attraction--the subject -of the Tides. Yet, even here, the verification is striking, as far -as observations have been carried. Newton's theory explained, with -singular felicity, all the prominent circumstances of the tides then -known;--the difference of spring and neap tides; the effect of the -moon's and sun's declination and parallax; even the difference of -morning and evening tides, and the anomalous tides of particular -places. About, and after, this time, attempts were made both by the -Royal Society of England, and by the French Academy, to collect -numerous observations but these were not followed up with -sufficient perseverance. Perhaps, indeed, the theory had not been at -that time sufficiently developed but the admirable prize-essays of -Euler, Bernoulli, and D'Alembert, in 1740, removed, in a great -measure, this deficiency. These dissertations supplied the means of -bringing this subject to the same test to which all the other -consequences of gravitation had been subjected;--namely, the -calculation of tables, and the continued and orderly comparison of -these with observation. Laplace has attempted this verification in -another way, by calculating the results of the theory (which he has -done with an extraordinary command of analysis), and then by -comparing these, in supposed critical cases, with the Brest -observations. This method has confirmed the theory as far as it -could do so; but such a process cannot supersede the necessity of -applying the proper criterion of truth in such cases, the -construction and verification of Tables. Bernoulli's theory, on the -other hand, has been used for the construction of Tide-tables; but -these have not been properly compared with experiment; and when the -comparison has been made, having been executed for purposes of gain -rather than of science, it has not been published, and cannot be -quoted as a verification of the theory. - -Thus we have, as yet, no sufficient comparison of fact with theory, -for Laplace's is far from a complete comparison. In this, as in -other parts of physical astronomy, our theory ought not only to -agree with observations selected and grouped in a particular manner, -but with the whole course of observation, and with every part of the -phenomena. In this, as in other cases, the true theory should be -verified by its giving us the best Tables; but Tide-tables were -never, I believe, {458} calculated upon Laplace's theory, and thus -it was never fairly brought to the test. - -It is, perhaps, remarkable, considering all the experience which -astronomy had furnished, that men should have expected to reach the -completion of this branch of science by improving the mathematical -theory, without, at the same time, ascertaining the laws of the -facts. In all other departments of astronomy, as, for instance, in -the cases of the moon and the planets, the leading features of the -phenomena had been made out empirically, before the theory explained -them. The course which analogy would have recommended for the -cultivation of our knowledge of the tides, would have been, to -ascertain, by an analysis of long series of observations, the effect -of changes in the time of transit, parallax, and declination of the -moon, and thus to obtain the laws of phenomena and then proceed to -investigate the laws of causation. - -Though this was not the course followed by mathematical theorists, -it was really pursued by those who practically calculated -Tide-tables; and the application of knowledge to the useful purposes -of life being thus separated from the promotion of the theory, was -naturally treated as a gainful property, and preserved by secrecy. -Art, in this instance, having cast off her legitimate subordination -to Science, or rather, being deprived of the guidance which it was -the duty of Science to afford, resumed her ancient practices of -exclusiveness and mystery. Liverpool, London, and other places, had -their Tide-tables, constructed by undivulged methods, which methods, -in some instances at least, were handed down from father to son for -several generations as a family possession; and the publication of -new Tables, accompanied by a statement of the mode of calculation, -was resented as an infringement of the rights of property. - -The mode in which these secret methods were invented, was that which -we have pointed out;--the analysis of a considerable series of -observations. Probably the best example of this was afforded by the -Liverpool Tide-tables. These were deduced by a clergyman named -Holden, from observations made at that port by a harbor-master of -the name of Hutchinson; who was led, by a love of such pursuits, to -observe the tides carefully for above twenty years, day and night. -Holden's Tables, founded on four years of these observations, were -remarkably accurate. - -At length men of science began to perceive that such calculations -were part of their business; and that they were called upon, as the -{459} guardians of the established theory of the universe, to -compare it in the greatest possible detail with the facts. Mr. -Lubbock was the first mathematician who undertook the extensive -labors which such a conviction suggested. Finding that regular -tide-observations had been made at the London Docks from 1795, he -took nineteen years of these (purposely selecting the length of a -cycle of the motions of the lunar orbit), and caused them (in 1831) -to be analyzed by Mr. Dessiou, an expert calculator. He thus -obtained[105\7] Tables for the effect of the Moon's Declination, -Parallax, and hour of Transit, on the tides; and was enabled to -produce Tide-tables founded upon the data thus obtained. Some -mistakes in these as first published (mistakes unimportant as to the -theoretical value of the work), served to show the jealousy of the -practical tide-table calculators, by the acrimony with which the -oversights were dwelt upon; but in a very few years, the tables thus -produced by an open and scientific process were more exact than -those which resulted from any of the secrets; and thus practice was -brought into its proper subordination to theory. - -[Note 105\7: _Phil. Trans._ 1831. _British Almanac_, 1832.] - -The theory with which Mr. Lubbock was led to compare his results, was -the Equilibrium-theory of Daniel Bernoulli; and it was found that this -theory, with certain modifications of its elements, represented the -facts to a remarkable degree of precision. Mr. Lubbock pointed out -this agreement especially in the semi-mensual inequality of the times -of high water. The like agreement was afterwards (in 1833) shown by -Mr. Whewell[106\7] to obtain still more accurately at Liverpool, both -for the Times and Heights; for by this time, nineteen years of -Hutchinson's Liverpool Observations had also been discussed by Mr. -Lubbock. The other inequalities of the Times and Heights (depending -upon the Declination and Parallax of the Moon and Sun,) were variously -compared with the Equilibrium-theory by Mr. Lubbock and Mr. Whewell; -and the general result was, that the facts agreed with the condition -of equilibrium at a certain anterior time, but that this anterior time -was different for different phenomena. In like manner it appeared to -follow from these researches, that in order to explain the facts, the -mass of the moon must be supposed different in the calculation at -different places. A result in effect the same was obtained by M. -Daussy,[107\7] an active French Hydrographer; for he found that -observations at various stations could not be reconciled with the -formulæ of Laplace's _Mécanique_ {460} _Céleste_ (in which the ratio -of the heights of spring-tides and neap-tides was computed on an -assumed mass of the moon) without an alteration of level which was, in -fact, equivalent to an alteration of the moon's mass. Thus all things -appeared to tend to show that the Equilibrium-theory would give the -_formulæ_ for the inequalities of the tides, but that the _magnitudes_ -which enter into these formulæ must be sought from observation. - -[Note 106\7: _Phil. Trans._ 1834.] - -[Note 107\7: _Connaissance des Tems_, 1838.] - -Whether this result is consistent with theory, is a question not so -much of Physical Astronomy as of Hydrodynamics, and has not yet been -solved. A Theory of the Tides which should include in its conditions -the phenomena of Derivative Tides, and of their combinations, will -probably require all the resources of the mathematical mechanician. - -As a contribution of empirical materials to the treatment of this -hydrodynamical problem, it may be allowable to mention here Mr. -Whewell's attempts to trace the progress of the tide into all the -seas of the globe, by drawing on maps of the ocean what he calls -_Cotidal Lines_;--lines marking the contemporaneous position of the -various points of the great wave which carries high water from shore -to shore.[108\7] This is necessarily a task of labor and difficulty, -since it requires us to know the time of high water on the same day -in every part of the world; but in proportion as it is completed, it -supplies steps between our general view of the movements of the -ocean and the phenomena of particular ports. - -[Note 108\7: Essay towards a First Approximation to a Map of Cotidal -Lines. _Phil. Trans._ 1833, 1836.] - -Looking at this subject by the light which the example of the -history of astronomy affords, we may venture to repeat, that it will -never have justice done it till it is treated as other parts of -astronomy are treated; that is, till Tables of all the phenomena -which can be observed, are calculated by means of the best knowledge -which we at present possess, and till these tables are constantly -improved by a comparison of the predicted with the observed fact. A -set of Tide-observations and Tide-ephemerides of this kind, would -soon give to this subject that precision which marks the other parts -of astronomy; and would leave an assemblage of unexplained _residual -phenomena_, in which a careful research might find the materials of -other truths as yet unsuspected. - -[2d Ed.] [That there would be, in the tidal movements of the ocean, -inequalities of the heights and times of high and low water {461} -_corresponding_ to those which the equilibrium theory gives, could -be considered only as a conjecture, till the comparison with -observation was made. It was, however, a natural conjecture; since -the waters of the ocean are at every moment _tending_ to acquire the -form assumed in the equilibrium theory: and it may be considered -likely that the causes which prevent their assuming this form -produce an effect nearly constant for each place. Whatever be -thought of this reasoning, the conjecture is confirmed by -observation with curious exactness. The laws of a great number of -the tidal phenomena--namely, of the Semi-mensual Inequality of the -Heights, of the Semi-mensual Inequality of the Times, of the Diurnal -Inequality, of the effect of the Moon's Declination, of the effect -of the Moon's Parallax--are represented very closely by formulæ -derived from the equilibrium theory. The hydrodynamical mode of -treating the subject has not added any thing to the knowledge of the -laws of the phenomena to which the other view had conducted us. - -We may add, that Laplace's assumption, that in the moving fluid the -motions must have a _periodicity_ corresponding to that of the -forces, is also a conjecture. And though this conjecture may, in -some cases of the problem, be verified, by substituting the -resulting expressions in the equations of motion, this cannot be -done in the actual case, where the revolving motion of the ocean is -prevented by the intrusion of tracts of land running nearly from -pole to pole. - -Yet in Mr. Airy's Treatise _On Tides and Waves_ (in the -_Encyclopædia Metropolitana_) much has been done to bring the -hydrodynamical theory of oceanic tides into agreement with -observation. In this admirable work, Mr. Airy has, by peculiar -artifices, solved problems which come so near the actual cases that -they may represent them. He has, in this way, deduced the laws of -the semi-diurnal and the diurnal tide, and the other features of the -tides which the equilibrium theory in some degree imitates; but he -has also, taking into account the effect of friction, shown that the -actual tide may be represented as the tide of an earlier -epoch;--that the relative mass of the moon and sun, as inferred from -the tides, would depend upon the depth of the ocean (Art. -455);--with many other results remarkably explaining the observed -phenomena. He has also shown that the relation of the cotidal lines -to the tide waves really propagated is, in complex cases, very -obscure, because different waves of different magnitudes, travelling -in different directions, may coexist, and the cotidal line is the -compound result of all these. {462} - -With reference to the _Maps of Cotidal Lines_, mentioned in the -text, I may add, that we are as yet destitute of observations which -should supply the means of drawing such lines on a large scale in -the Pacific Ocean. Admiral Lütke has however supplied us with some -valuable materials and remarks on this subject in his _Notice sur -les Marées Périodiques dans le grand Océan Boréal et dans la Mer -Glaciale_; and has drawn them, apparently on sufficient data, in the -White Sea.] - - - - -CHAPTER V. - -DISCOVERIES ADDED TO THE NEWTONIAN THEORY. - - -_Sect._ 1.--_Tables of Astronomical Refraction._ - -WE have travelled over an immense field of astronomical and -mathematical labor in the last few pages, and have yet, at the end -of every step, still found ourselves under the jurisdiction of the -Newtonian laws. We are reminded of the universal monarchies, where a -man could not escape from the empire without quitting the world. We -have now to notice some other discoveries, in which this reference -to the law of universal gravitation is less immediate and obvious; I -mean the astronomical discoveries respecting Light. - -The general truths to which the establishment of the true laws of -Atmospheric Refraction led astronomers, were the law of Deflection -of the rays of light, which applies to all refractions, and the real -structure and size of the Atmosphere, so far as it became known. The -great discoveries of Römer and Bradley, namely, the Velocity of -Light, the Aberration of Light, and the Nutation of the earth's -axis, gave a new distinctness to the conceptions of the propagation -of light in the minds of philosophers, and confirmed the doctrines -of Copernicus, Kepler, and Newton, respecting the motions which -belong to the earth. - -The true laws of Atmospheric Refraction were slowly discovered. -Tycho attributed the apparent displacement of the heavenly bodies to -the low and gross part of the atmosphere only, and hence made it -cease at a point half-way to the zenith; but Kepler rightly extended -it to the zenith itself. Dominic Cassini endeavored to discover the -law of this correction by observation, and gave his result in the -form {463} which, as we have said, sound science prescribes, a Table -to be habitually used for all observations. But great difficulties -at this time embarrassed this investigation, for the parallaxes of -the sun and of the planets were unknown, and very diverse values had -been assigned them by different astronomers. To remove some of these -difficulties, Richer, in 1762, went to observe at the equator; and -on his return, Cassini was able to confirm and amend his former -estimations of parallax and refraction. But there were still -difficulties. According to La Hire, though the phenomena of twilight -give an altitude of 34,000 toises to the atmosphere,[109\7] those of -refraction make it only 2000. John Cassini undertook to support and -improve the calculations of his father Dominic, and took the true -supposition, that the light follows a curvilinear path through the -air. The Royal Society of London had already ascertained -experimentally the refractive power of air.[110\7] Newton calculated -a Table of Refractions, which was published under Halley's name in -the _**Philosophical Transactions_ for 1721, without any indication -of the method by which it was constructed. But M. Biot has recently -shown,[111\7] by means of the published correspondence of Flamsteed, -that Newton had solved the problem in a manner nearly corresponding -to the most improved methods of modern analysis. - -[Note 109\7: Bailly, ii. 612.] - -[Note 110\7: Ibid. ii. 607.] - -[Note 111\7: Biot, _Acad. Sc. Compte Rendu_, Sept. 5, 1836.] - -Dominic Cassini and Picard proved,[112\7] Le Monnier in 1738 -confirmed more fully, the fact that the variations of the -Thermometer affect the Refraction. Mayer, taking into account both -these changes, and the changes indicated by the Barometer, formed a -theory, which Lacaille, with immense labor, applied to the -construction of a Table of Refractions from observation. But -Bradley's Table (published in 1763 by Maskelyne) was more commonly -adopted in England; and his formula, originally obtained -empirically, has been shown by Young to result from the most -probable suppositions we can make respecting the atmosphere. -Bessel's Refraction Tables are now considered the best of those -which have appeared. - -[Note 112\7: Bailly, iii. 92.] - - -_Sect._ 2.--_Discovery of the Velocity of Light.--Römer._ - -THE astronomical history of Refraction is not marked by any great -discoveries, and was, for the most part, a work of labor only. The -progress of the other portions of our knowledge respecting light is -{464} more striking. In 1676, a great number of observations of -eclipses of Jupiter's satellites were accumulated, and could be -compared with Cassini's Tables. Römer, a Danish astronomer, whom -Picard had brought to Paris, perceived that these eclipses happened -constantly later than the calculated time at one season of the year, -and earlier at another season;--a difference for which astronomy -could offer no account. The error was the same for all the -satellites; if it had depended on a defect in the Tables of Jupiter, -it might have affected all, but the effect would have had a -reference to the velocities of the satellites. The cause, then, was -something extraneous to Jupiter. Römer had the happy thought of -comparing the error with the earth's distance from Jupiter, and it -was found that the eclipses happened later in proportion as Jupiter -was further off.[113\7] Thus we see the eclipse later, as it is more -remote; and thus light, the messenger which brings us intelligence -of the occurrence, travels over its course in a measurable time. By -this evidence, light appeared to take about eleven minutes in -describing the diameter of the earth's orbit. - -[Note 113\7: Bailly, ii. 17.] - -This discovery, like so many others, once made, appears easy and -inevitable; yet Dominic Cassini had entertained the idea for a -moment,[114\7] and had rejected it; and Fontenelle had congratulated -himself publicly on having narrowly escaped this seductive error. -The objections to the admission of the truth arose principally from -the inaccuracy of observation, and from the persuasion that the -motions of the satellites were circular and uniform. Their -irregularities disguised the fact in question. As these irregularities -became clearly known, Römer's discovery was finally established, and -the "Equation of Light" took its place in the Tables. - -[Note 114\7: Ib. ii. 419.] - - -_Sect._ 3.--_Discovery of Aberration.--Bradley._ - -IMPROVEMENTS in instruments, and in the art of observing, were -requisite for making the next great step in tracing the effect of -the laws of light. It appears clear, on consideration, that since -light and the spectator on the earth are both in motion, the -apparent direction of an object will be determined by the -composition of these motions. But yet the effect of this composition -of motions was (as is usual in such cases) traced as a fact in -observation, before it was clearly seen as a consequence of -reasoning. This fact, the Aberration of Light, the greatest -astronomical discovery of the eighteenth century, belongs to -Bradley, {465} who was then Professor of Astronomy at Oxford, and -afterwards Astronomer Royal at Greenwich. Molyneux and Bradley, in -1725, began a series of observations for the purpose of -ascertaining, by observations near the zenith, the existence of an -annual parallax of the fixed stars, which Hooke had hoped to detect, -and Flamsteed thought he had discovered. Bradley[115\7] soon found -that the star observed by him had a minute apparent motion different -from that which the annual parallax would produce. He thought of a -nutation of the earth's axis as a mode of accounting for this; but -found, by comparison of a star on the other side of the pole, that -this explanation would not apply. Bradley and Molyneux then -considered for a moment an annual alteration of figure in the -earth's atmosphere, such as might affect the refractions, but this -hypothesis was soon rejected.[116\7] In 1727, Bradley resumed his -observations, with a new instrument, at Wanstead, and obtained -empirical rules for the changes of declination of different stars. -At last, accident turned his thoughts to the direction in which he -was to find the cause of the variations which he had discovered. -Being in a boat on the Thames, he observed that the vane on the top -of the mast gave a different apparent direction to the wind, as the -boat sailed one way or the other. Here was an image of his case: the -boat represented the earth moving in different directions at -different seasons, and the wind represented the light of a star. He -had now to trace the consequences of this idea; he found that it led -to the empirical rules, which he had already discovered, and, in -1729, he gave his discovery to the Royal Society. His paper is a -very happy narrative of his labors and his thoughts. His theory was -so sound that no astronomer ever contested it; and his observations -were so accurate, that the quantity which he assigned as the -greatest amount of the change (one nineteenth of a degree) has -hardly been corrected by more recent astronomers. It must be -noticed, however, that he considered the effects in declination -only; the effects in right ascension required a different mode of -observation, and a consummate goodness in the machinery of clocks, -which at that time was hardly attained. - -[Note 115\7: Rigaud's Bradley.] - -[Note 116\7: Rigaud, p. xxiii.] - - -_Sect._ 4.--_Discovery of Nutation._ - -WHEN Bradley went to Greenwich as Astronomer Royal, he continued -with perseverance observations of the same kind as those by which he -had detected Aberration. The result of these was another {466} -discovery; namely, that very Nutation which he had formerly -rejected. This may appear strange, but it is easily explained. The -aberration is an annual change, and is detected by observing a star -at different seasons of the year: the Nutation is a change of which -the cycle is eighteen years; and which, therefore, though it does -not much change the place of a star in one year, is discoverable in -the alterations of several successive years. A very few years' -observations showed Bradley the effect of this change;[117\7] and -long before the half cycle of nine years had elapsed, he had -connected it in his mind with the true cause, the motion of the -moon's nodes. Machin was then Secretary to the Royal Society,[118\7] -and was "employed in considering the theory of gravity, and its -consequences with regard to the celestial motions:" to him Bradley -communicated his conjectures; from him he soon received a Table -containing the results of his calculations; and the law was found to -be the same in the Table and in observation, though the quantities -were somewhat different. It appeared by both, that the earth's pole, -besides the motion which the precession of the equinoxes gives it, -moves, in eighteen years, through a small circle;--or rather, as was -afterwards found by Bradley, an ellipse, of which the axes are -nineteen and fourteen seconds.[119\7] - -[Note 117\7: Rigaud, lxiv.] - -[Note 118\7: Ib. 25.] - -[Note 119\7: Ib. lxvi.] - -For the rigorous establishment of the mechanical theory of that -effect of the moon's attraction from which the phenomena of Nutation -flow, Bradley rightly and prudently invited the assistance of the -great mathematicians of his time. D'Alembert, Thomas Simpson, Euler, -and others, answered this call, and the result was, as we have -already said in the last chapter (Sect. 7), that this investigation -added another to the recondite and profound evidences of the -doctrine of universal gravitation. - -It has been said[120\7] that Bradley's discoveries "assure him the -most distinguished place among astronomers after Hipparchus and -Kepler." If his discoveries had been made before Newton's, there -could have been no hesitation as to placing him on a level with -those great men. The existence of such suggestions as the Newtonian -theory offered on all astronomical subjects, may perhaps dim, in our -eyes, the brilliance of Bradley's achievements; but this -circumstance cannot place any other person above the author of such -discoveries, and therefore we may consider Delambre's adjudication -of precedence as well warranted, and deserving to be permanent. {467} - -[Note 120\7: Delambre, _Ast. du_ 18 _Sièc._ p. 420. Rigaud, xxxvii.] - - -_Sect._ 5.--_Discovery of the Laws of Double Stars.--The two -Herschels._ - -NO truth, then, can be more certainly established, than that the law -of gravitation prevails to the very boundaries of the solar system. -But does it hold good further? Do the fixed stars also obey this -universal sway? The idea, the question, is an obvious one--but where -are we to find the means of submitting it to the test of observation? - -If the Stars were each insulated from the rest, as our Sun appears -to be from them, we should have been quite unable to answer this -inquiry. But among the stars, there are some which are called -_Double Stars_, and which consist of two stars, so near to each -other that the telescope alone can separate them. The elder Herschel -diligently observed and measured the relative positions of the two -stars in such pairs; and as has so often happened in astronomical -history, pursuing one object he fell in with another. Supposing such -pairs to be really unconnected, he wished to learn, from their -phenomena, something respecting the annual parallax of the earth's -orbit. But in the course of twenty years' observations he made the -discovery (in 1803) that some of these couples were turning round -each other with various angular velocities. These revolutions were -for the most part so slow that he was obliged to leave their -complete determination as an inheritance to the next generation. His -son was not careless of the bequest, and after having added an -enormous mass of observations to those of his father, he applied -himself to determine the laws of these revolutions. A problem so -obvious and so tempting was attacked also by others, as Savary and -Encke, in 1830 and 1832, with the resources of analysis. But a -problem in which the data are so minute and inevitably imperfect, -required the mathematician to employ much judgment, as well as skill -in using and combining these data; and Sir John Herschel, by -employing positions only of the line joining the pair of stars -(which can be observed with comparative exactness), to the exclusion -of their distances (which cannot be measured with much correctness), -and by inventing a method which depended upon the whole body of -observations, and not upon selected ones only, for the determination -of the motion, has made his investigations by far the most -satisfactory of those which have appeared. The result is, that it -has been rendered very probable, that in several of the double stars -the two stars describe ellipses about each other; and therefore that -here also, at an {468} immeasurable distance from our system, the -law of attraction according to the inverse square of the distance, -prevails. And, according to the practice of astronomers when a law -has been established, Tables have been calculated for the future -motions; and we have Ephemerides of the revolutions of suns round -each other, in a region so remote, that the whole circle of our -earth's orbit, if placed there, would be imperceptible by our -strongest telescopes. The permanent comparison of the observed with -the predicted motions, continued for more than one revolution, is -the severe and decisive test of the truth of the theory; and the -result of this test astronomers are now awaiting. - -[2d Ed.] [In calculating the orbits of revolving systems of double -stars, there is a peculiar difficulty, arising from the plane of the -orbit being in a position unknown, but probably oblique, to the -visual ray. Hence it comes to pass that even if the orbit be an -ellipse described about the focus by the laws of planetary motion, -it will appear otherwise; and the true orbit will have to be deduced -from the apparent one. - -With regard to a difficulty which has been mentioned, that the two -stars, if they are governed by gravity, will not revolve the one -about the other, but both about their common centre of -gravity;--this circumstance adds little difficulty to the problem. -Newton has shown (_Princip._ lib. i. Prop. 61) in the _problem of -two bodies_, the relation between the relative orbits and the orbit -about the common centre of gravity. - -_How many of the apparently double stars have orbitual motions?_ Sir -John Herschel in 1833 gave, in his _Astronomy_ (Art. 606), a list of -nine stars, with periods extending from 43 years (η Coronæ) to 1200 -years (γ Leonis), which he presented as the chief results then -obtained in this department. In his work on Double Stars, the fruit -of his labors in both hemispheres, which the astronomical world are -looking for with eager expectation, he will, I believe, have a few -more to add to these. - -_Is it well established that such double stars attract each other -according to the law of the inverse square of the distance?_ The -answer to this question must be determined by ascertaining whether the -above cases are regulated by the laws of elliptical motion. This is a -matter which it must require a long course of careful observation to -determine in such a number of cases as to prove the universality of -the rule. Perhaps the minds of astronomers are still in suspense upon -the subject. When Sir John Herschel's work shall appear, it will -probably {469} be found that with regard to some of these stars, and γ -Virginis in particular, the conformity of the observations with the -laws of elliptical motion amounts to a degree of exactness which must -give astronomers a strong conviction of the truth of the law. For -since Sir W. Herschel's first measures in 1781, the arc described by -one star about the other is above 305 degrees; and during this period -the angular annual motion has been very various, passing through all -gradations from about 20 minutes to 80 degrees. Yet in the whole of -this change, the two curves constructed, the one from the -observations, the other from the elliptical elements, for the purpose -of comparison, having a total ordinate of 305 parts, do not, in any -part of their course, deviate from each other so much as _two_ such -parts.] - -The verification of Newton's discoveries was sufficient employment -for the last century; the first step in the extension of them -belongs to this century. We cannot at present foresee the magnitude -of this task, but every one must feel that the law of gravitation, -before verified in all the particles of our own system, and now -probably extended to the all but infinite distance of the fixed -stars, presses upon our minds with a strong claim to be accepted as -a universal law of the whole material creation. - -Thus, in this and the preceding chapter, I have given a brief sketch -of the history of the verification and extension of Newton's great -discovery. By the mass of labor and of skill which this head of our -subject includes, we may judge of the magnitude of the advance in -our knowledge which that discovery made. A wonderful amount of -talent and industry have been requisite for this purpose; but with -these, external means have co-operated. Wealth, authority, -mechanical skill, the division of labor, the power of associations -and of governments, have been largely and worthily applied in -bringing astronomy to its present high and flourishing condition. We -must consider briefly what has thus been done. {470} - - - - -CHAPTER VI. - -THE INSTRUMENTS AND AIDS OF ASTRONOMY DURING THE NEWTONIAN PERIOD. - - -_Sect._ 1.--_Instruments._ - -SOME instruments or other were employed at all periods of -astronomical observation. But it was only when observation had -attained a considerable degree of delicacy, that the exact -construction of instruments became an object of serious care. -Gradually, as the possibility and the value of increased exactness -became manifest, it was seen that every thing which could improve -the astronomer's instruments was of high importance to him. And -hence in some cases a vast increase of size and of expense was -introduced; in other cases new combinations, or the result of -improvements in other sciences, were brought into play. Extensive -knowledge, intense thought, and great ingenuity, were requisite in -the astronomical instrument maker. Instead of ranking with artisans, -he became a man of science, sharing the honor and dignity of the -astronomer himself. - -1. _Measure of Angles._--Tycho Brahe was the first astronomer who -acted upon a due appreciation of the importance of good instruments. -The collection of such at Uraniburg was by far the finest which had -ever existed. He endeavored to give steadiness to the frame, and -accuracy to the divisions of his instruments. His Mural Quadrant was -well adapted for this purpose; its radius was five cubits: it is -clear, that as we enlarge the instrument we are enabled to measure -smaller arcs. On this principle many large _gnomons_ were erected. -Cassini's celebrated one in the church of St. Petronius at Bologna, -was eighty-three feet (French) high. But this mode of obtaining -accuracy was soon abandoned for better methods. Three great -improvements were introduced about the same time. The application of -the Micrometer to the telescope, by Huyghens, Malvasia, and Auzout; -the application of the Telescope to the astronomical quadrant; and -the fixation of the centre of its field by a Cross of fine wires -placed in the focus by Gascoigne, and afterwards by Picard. We may -judge how great was the improvement which these contrivances -introduced into the art of {471} observing, by finding that Hevelius -refused to adopt them because they would make all the old -observations of no value. He had spent a laborious and active life -in the exercise of the old methods, and could not bear to think that -all the treasures which he had accumulated had lost their worth by -the discovery of a new mine of richer ore. - -[2d Ed.] [Littrow, in his _Die Wunder des Himmels_, Ed. 2, pp. 684, -685, says that Gascoigne invented and used the telescope with wires -in the common focus of the lenses in 1640. He refers to _Phil. -Trans._ xxx. 603. Picard reinvented this arrangement in 1667. I have -already spoken of Gascoigne as the inventor of the micrometer. - -Römer (already mentioned, p. 464) brought into use the Transit -Instrument, and the employment of complete Circles, instead of the -Quadrants used till then; and by these means gave to practical -astronomy a new form, of which the full value was not discovered -till long afterwards.**] - -The apparent place of the object in the instrument being so -precisely determined by the new methods, the exact Division of the -arc into degrees and their subdivisions became a matter of great -consequence. A series of artists, principally English, have acquired -distinguished places in the lists of scientific fame by their -performances in this way; and from that period, particular -instruments have possessed historical interest and individual -reputation. Graham was one of the first of these artists. He -executed a great Mural Arc for Halley at Greenwich; for Bradley he -constructed the Sector which detected aberration. He also made the -Sector which the French academicians carried to Lapland; and -probably the goodness of this instrument, compared with the -imperfection of those which were sent to Peru, was one main cause of -the great difference of duration in the two series of observations. -Bird, somewhat later[121\7] (about 1750), divided several Quadrants -for public observatories. His method of dividing was considered so -perfect, that the knowledge of it was purchased by the English -government, and published in 1767. Ramsden was equally celebrated. -The error of one of his best Quadrants (that at Padua) is said to be -never greater than two seconds. But at a later period, Ramsden -constructed Mural Circles only, holding this to be a kind of -instrument far superior to the quadrant. He made one of five feet -diameter, in 1788, for M. Piazzi at Palermo; and one of eight feet -for the observatory of Dublin. Troughton, a worthy successor of the -{472} artists we have mentioned, has invented a method of dividing -the circle still superior to the former ones; indeed, one which is -theoretically perfect, and practically capable of consummate -accuracy. In this way, circles have been constructed for Greenwich, -Armagh, Cambridge, and many other places; and probably this method, -carefully applied, offers to the astronomer as much exactness as his -other implements allow him to receive; but the slightest casualty -happening to such an instrument, after it has been constructed, or -any doubt whether the method of graduation has been rightly applied, -makes it unfit for the jealous scrupulosity of modern astronomy. - -[Note 121\7: Mont. iv. 337.] - -The English artists sought to attain accurate measurements by -continued bisection and other aliquot subdivision of the limb of -their circle; but Mayer proposed to obtain this end otherwise, by -_repeating_ the measure on different parts of the circumference till -the error of the division becomes unimportant, instead of attempting -to divide an instrument without error. This invention of the -Repeating Circle was zealously adopted by the French, and the -relative superiority of the rival methods is still a matter of -difference of opinion. - -[2d Ed.] [In the series of these great astronomical mechanists, we -must also reckon George Reichenbach. He was born Aug. 24, 1772, at -Durlach; became Lieutenant of Artillery in the Bavarian service in -1794; (Salinenrath) Commissioner of Salt-works in 1811; and in 1820, -First Commissioner of Water-works and Roads. He became, with -Fraunhofer, the ornament of the mechanical and optical Institute -erected in 1805 at Benedictbeuern by Utzschneider; and his -astronomical instruments, meridian circles, transit instruments, -equatorials, heliometers, make an epoch in Observing Astronomy. His -contrivances in the Salt-works at Berchtesgaden and Reichenhall, in -the Arms Manufactory at Amberg, and in the works for boring cannon -at Vienna, are enduring monuments of his rare mechanical talent. He -died May 21, 1826, at Munich.] - -2. _Clocks._--The improvements in the measures of space require -corresponding improvements in the measure of time. The beginning of -any thing which we can call accuracy, in this subject, was the -application of the Pendulum to clocks, by Huyghens, in 1656. That -the successive oscillations of a pendulum occupy equal times, had -been noticed by Galileo; but in order to take advantage of this -property, the pendulum must be connected with machinery by which its -motion is kept from languishing, and by which the number of its -swings is recorded. By inventing such machinery, Huyghens at once -obtained {473} a measure of time more accurate than the sun itself. -Hence astronomers were soon led to obtain the right ascension of a -star, not directly, by measuring a Distance in the heavens, but -indirectly, by observing the Moment of its Transit. This observation -is now made with a degree of accuracy which might, at first sight, -appear beyond the limits of human sense, being noted to a _tenth of -a second of time_: but we may explain this, by remarking that though -the number of the second at which the transit happens is given by -the clock, and is reckoned according to the course of time, the -subdivision of the second of time into smaller fractions is -performed by the eye,--by seeing the space described by the heavenly -body in a whole second, and hence estimating a smaller time, -according to the space which its description occupies. - -But in order to make clocks so accurate as to justify this degree of -precision, their construction was improved by various persons in -succession. Picard soon found that Huyghens' clocks were affected in -their going by temperature, for heat caused expansion of the -metallic pendulum. This cause of error was remedied by combining -different metals, as iron and copper, which expand in a different -degree, in such a way that their effects compensate each other. -Graham afterwards used quicksilver for the same purpose. The -_Escapement_ too (which connects the force which impels the clock -with the pendulum which regulates it), and other parts of the -machinery, had the most refined mechanical skill and ingenuity of -the best artists constantly bestowed upon then. The astronomer of -the present day, constantly testing the going of such a clock by the -motions of the fixed stars, has a scale of time as stable and as -minutely exact as the scales on which he measures distance. - -The construction of good Watches, that is, portable or marine -clocks, was important on another account, namely, because they might -be used in determining the longitude of places. Hence the -improvement of this little machine became an object of national -interest, and was included in the reward of 20,000_l._, which we -have already noticed as offered by the English parliament for the -discovery of the longitude. Harrison,[122\7] originally a carpenter, -turned his mind to this subject with success. After thirty years of -labor, in which he was encouraged by many eminent persons, he -produced, in 1758, a time-keeper, which was sent on a voyage to -Jamaica for trial. After 161 days, the error {474} of the watch was -only one minute five seconds, and the artist received from the -nation 5000_l._ At a later period,[123\7] at the age of seventy-five -years, after a life devoted to this object, having still further -satisfied the commissioners, he received, in 1765, 10,000_l._, at -the same time that Euler and the heirs of Mayer received each -3000_l._ for the lunar tables which they had constructed. - -[Note 122\7: Mont. iv. 554.] - -[Note 123\7: Mont. iv. 560.] - -The two methods of finding the longitude, by Chronometers and by -Lunar Observations, have solved the problem for all practical -purposes; but the latter could not have been employed at sea without -the aid of that invaluable instrument, the Sextant, in which the -distance of two objects is observed, by bringing one to coincide -apparently with the reflected image of the other. This instrument -was invented by Hadley, in 1731. Though the problem of finding the -longitude be, in fact, one of geography rather than astronomy, it is -an application of astronomical science which has so materially -affected the progress of our knowledge, that it deserves the notice -we have bestowed upon it. - -3. _Telescopes._--We have spoken of the application of the telescope -to astronomical measurements, but not of the improvement of the -telescope itself. If we endeavor to augment the optical power of -this instrument, we run, according to the path we take, into various -inconveniences;--distortion, confusion, want of light, or colored -images. Distortion and confusion are produced, if we increase the -magnifying power, retaining the length and the aperture of the -object-glass. If we diminish the aperture we suffer from loss of -light. What remains then is to increase the focal length. This was -done to an extraordinary extent, in telescopes constructed in the -beginning of the last century. Huyghens, in his first attempts, made -them 22 feet long;[124\7] afterwards, Campani, by order of Louis the -Fourteenth, made them of 86, 100, and 136 feet. Huyghens, by new -exertions, made a telescope 210 feet long. Auzout and Hartsoecker -are said to have gone much further, and to have succeeded in making -an object-glass of 600 feet focus. But even such telescopes as those -of Campani are almost unmanageable: in that of Huyghens, the -object-glass was placed on a pole, and the observer was placed at -the focus with an eye-glass. - -[Note 124\7: Bailly, ii. 253.] - -The most serious objection to the increase of the aperture of -object-glasses, was the coloration of the image produced, in -consequence of the unequal refrangibility of differently colored -rays. Newton, who discovered the principle of this defect in lenses, -had maintained that {475} the evil was irremediable, and that a -compound lens could no more refract without producing color, than a -single lens could. Euler and Klingenstierna doubted the exactness of -Newton's proposition; and, in 1755, Dollond disproved it by -experiment. This discovery pointed out a method of making -object-glasses which should give no color;--which should be -_achromatic_. For this purpose Dollond fabricated various kinds of -glass (flint and crown glass); and Clairaut and D'Alembert -calculated formulæ. Dollond and his son[125\7] succeeded in -constructing telescopes of three feet long (with a triple -object-glass) which produced an effect as great as those of -forty-five feet on the ancient principles. At first it was conceived -that these discoveries opened the way to a vast extension of the -astronomer's power of vision; but it was found that the most -material improvement was the compendious size of the new -instruments; for, in increasing the dimensions, the optician was -stopped by the impossibility of obtaining lenses of flint-glass of -very large dimensions. And this branch of art remained long -stationary; but, after a time, its epoch of advance again arrived. -In the present century, Fraunhofer, at Munich, with the help of -Guinand and the pecuniary support of Utzschneider, succeeded in -forming lenses of flint-glass of a magnitude till then unheard of. -Achromatic object-glasses, of a foot in diameter, and twenty feet -focal length, are now no longer impossible; although in such -attempts the artist cannot reckon on certain success. - -[Note 125\7: Bailly, iii. 118.] - -[2d Ed.] [Joseph Fraunhofer was born March 6, 1787, at Straubing in -Bavaria, the son of a poor glazier. He was in his earlier years -employed in his father's trade, so that he was not able to attend -school, and remained ignorant of writing and arithmetic till his -fourteenth year. At a later period he was assisted by Utzschneider, -and tried rapidly to recover his lost ground. In the year 1806 he -entered the establishment of Utzschneider as an optician. In this -establishment (transferred from Benedictbeuern to Munich in 1819) he -soon came to be the greatest Optician of Germany. His excellent -telescopes and microscopes are known throughout Europe. His greatest -telescope, that in the Observatory at Dorpat, has an object-glass of -9 inches diameter, and a focal length of 13⅓ feet. His written -productions are to be found in the _Memoirs_ of the Bavarian -Academy, in Gilbert's _Annalen der Physik_, and in Schumacher's -_Astronomische Nachrichten_. He died the 7th of June, 1826.] {476} - -Such telescopes might be expected to add something to our knowledge -of the heavens, if they had not been anticipated by reflectors of an -equal or greater scale. James Gregory had invented, and Newton had -more efficaciously introduced, reflecting telescopes. But these were -not used with any peculiar effect, till the elder Herschel made them -his especial study. His skill and perseverance in grinding specula, -and in contriving the best apparatus for their use, were rewarded by -a number of curious and striking discoveries, among which, as we -have already related, was the discovery of a new planet beyond -Saturn. In 1789, Herschel surpassed all his former attempts, by -bringing into action a reflecting telescope of forty feet length, -with a speculum of four feet in diameter. The first application of -this magnificent instrument showed a new satellite (the sixth) of -Saturn. He and his son have, with reflectors of twenty feet, made a -complete survey of the heavens, so far as they are visible in this -country; and the latter is now in a distant region completing this -survey, by adding to it the other hemisphere. - -In speaking of the improvements of telescopes we ought to notice, -that they have been pursued in the eye-glasses as well as in the -object-glasses. Instead of the single lens, Huyghens substituted an -eye-piece of two lenses, which, though introduced for another -purpose, attained the object of destroying color.[126\7] Ramsden's -eye-piece is one fit to be used with a micrometer, and others of -more complex construction have been used for various purposes. - -[Note 126\7: Coddington's _Optics_, ii. 21.] - - -_Sect._ 2.--_Observatories._ - -ASTRONOMY, which is thus benefited by the erection of large and -stable instruments, requires also the establishment of permanent -Observatories, supplied with funds for their support, and for that -of the observers. Such observatories have existed at all periods of -the history of the science; but from the commencement of the period -which we are now reviewing, they multiplied to such an extent that -we cannot even enumerate them. Yet we must undoubtedly look upon -such establishments, and the labors of which they have been the -scene, as important and essential parts of the history of the -progress of astronomy. Some of the most distinguished of the -observatories of modern times we may mention. The first of these -were that of Tycho Brahe {477} at Uraniburg, and that of the -Landgrave of Hesse Cassel, at Cassel, where Rothman and Byrgius -observed. But by far the most important observations, at least since -those of Tycho, which were the basis of the discoveries of Kepler -and Newton, have been made at Paris and Greenwich. The Observatory -of Paris was built in 1667. It was there that the first Cassini made -many of his discoveries; three of his descendants have since labored -in the same place, and two others of his family, the -Maraldis;[127\7] besides many other eminent astronomers, as Picard, -La Hire, Lefêvre, Fouchy, Legentil, Chappe, Méchain, Bouvard. -Greenwich Observatory was built a few years later (1675); and ever -since its erection, the observations there made have been the -foundation of the greatest improvements which astronomy, for the -time, received. Flamsteed, Halley, Bradley, Bliss, Maskelyne, Pond, -have occupied the place in succession: on the retirement of the -last-named astronomer in 1835, Professor Airy was removed thither -from the Cambridge Observatory. In every state, and in almost every -principality in Europe, Observatories have been established; but -these have often fallen speedily into inaction, or have contributed -little to the progress of astronomy, because their observations have -not been published. From the same causes, the numerous private -observatories which exist throughout Europe have added little to our -knowledge, except where the attention of the astronomer has been -directed to some definite points; as, for instance, the magnificent -labors of the Herschels, or the skilful observations made by Mr. -Pond with the Westbury circle, which first pointed out the error of -graduation of the Greenwich quadrants. The Observations, now -regularly published,[128\7] are those of Greenwich, begun by -Maskelyne, and continued quarterly by Mr. Pond; those of Königsberg, -published by Bessel since 1814; of Vienna, by Littrow since 1820; of -Speier, by Schwerd since 1826; those of Cambridge, commenced by Airy -in 1828; of Armagh, by Robinson in 1829. Besides these, a number of -useful observations have been published in journals and occasional -forms; as, for instance, those of Zach, made by Seeberg, near Gotha, -since 1788; and others have been employed in forming catalogues, of -which we shall speak shortly. - -[Note 127\7: Mont. iv. 346.] - -[Note 128\7: Airy, _Rep._ p. 128.] - -[2d Ed.] [I have left the statement of published Observations in the -text as it stood originally. I believe that at present (1847) the -twelve places contained in the following list publish their -Observations quite regularly, or nearly so;--Greenwich, Oxford, -Cambridge, Vienna, {478} Berlin, Dorpat, Munich, Geneva, Paris, -Königsberg, Madras, the Cape of Good Hope. - -Littrow, in his translation, adds to the publications noticed in the -text as containing astronomical Observations, Zach's _Monatliche -Correspondenz_, Lindenau and Bohnenberger's _Zeitschrift für -Astronomie_, Bode's _Astronomisches Jahrbuch_, Schumacher's -_Astronomische Nachrichten_.] - -Nor has the establishment of observatories been confined to Europe. -In 1786, M. de Beauchamp, at the expense of Louis the Sixteenth, -erected an observatory at Bagdad, "built to restore the Chaldean and -Arabian observations," as the inscription stated; but, probably, the -restoration once effected, the main intention had been fulfilled, -and little perseverance in observing was thought necessary. In 1828, -the British government completed the building of an observatory at -the Cape of Good Hope, which Lacaille had already made an -astronomical station by his observations there at an earlier period -(1750); and an observatory formed in New South Wales by Sir T. M. -Brisbane in 1822, and presented by him to the government, is also in -activity. The East India Company has founded observatories at -Madras, Bombay, and St. Helena; and observations made at the former -of these places, and at St. Helena, have been published. - -The bearing of the work done at such observatories upon the past -progress of astronomy, has already been seen in the preceding -narrative. Their bearing upon the present condition of the science -will be the subject of a few remarks hereafter. - - -_Sect._ 3.--_Scientific Societies._ - -THE influence of Scientific Societies, or Academical Bodies, has -also been very powerful in the subject before us. In all branches of -knowledge, the use of such associations of studious and inquiring -men is great; the clearness and coherence of a speculator's ideas, -and their agreement with facts (the two main conditions of -scientific truth), are severally but beneficially tested by -collision with other minds. In astronomy, moreover, the vast extent -of the subject makes requisite the division of labor and the support -of sympathy. The Royal Societies of London and of Paris were founded -nearly at the same time as the metropolitan Observatories of the two -countries. We have seen what constellations of philosophers, and -what activity of research, existed at those periods; these -philosophers appear in the lists, their discoveries {479} in the -publications, of the above-mentioned eminent Societies. As the -progress of physical science, and principally of astronomy, -attracted more and more admiration, Academies were created in other -countries. That of Berlin was founded by Leibnitz in 1710; that of -St Petersburg was established by Peter the Great in 1725; and both -these have produced highly valuable Memoirs. In more modern times -these associations have multiplied almost beyond the power of -estimation. They have been formed according to divisions, both of -locality and of subject, conformable to the present extent of -science, and the vast population of its cultivators. It would be -useless to attempt to give a view either of their number or of the -enormous mass of scientific literature which their Transactions -present. But we may notice, as especially connected with our present -subject, the Astronomical Society of London, founded in 1820, which -gave a strong impulse to the pursuit of the science in England. - - -_Sect._ 4.--_Patrons of Astronomy._ - -The advantages which letters and philosophy derive from the -patronage of the great have sometimes been questioned; that love of -knowledge, it has been thought, cannot be genuine which requires -such stimulation, nor those speculations free and true which are -thus forced into being. In the sciences of observation and -calculation, however, in which disputed questions can be -experimentally decided, and in which opinions are not disturbed by -men's practical principles and interests, there is nothing -necessarily operating to poison or neutralize the resources which -wealth and power supply to the investigation of truth. - -Astronomy has, in all ages, flourished under the favor of the rich and -powerful; in the period of which we speak, this was eminently the -case. Louis the Fourteenth gave to the astronomy of France a -distinction which, without him, it could not have attained. No step -perhaps tended more to this than his bringing the celebrated Dominic -Cassini to Paris. This Italian astronomer (for he was born at -Permaldo, in the county of Nice, and was professor at Bologna), was -already in possession of a brilliant reputation, when the French -ambassador, in the name of his sovereign, applied to Pope Clement the -Ninth, and to the senate of Bologna, that he should be allowed to -remove to Paris. The request was granted only so far as an absence of -six years; but at the end of that time, the benefits and honors which -{480} the king had conferred upon him, fixed him in France. The -impulse which his arrival (in 1669) and his residence gave to -astronomy, showed the wisdom of the measure. In the same spirit, the -French government drew to Paris Römer from Denmark, Huyghens from -Holland, and gave a pension to Hevelius, and a large sum when his -observatory at Dantzic had been destroyed by fire in 1679. - -When the sovereigns of Prussia and Russia were exerting themselves to -encourage the sciences in their countries, they followed the same -course which had been so successful in France. Thus, as we have said, -the Czar Peter took Delisle to Petersburg in 1725; the celebrated -Frederick the Great drew to Berlin, Voltaire and Maupertuis, Euler and -Lagrange; and the Empress Catharine obtained in the same way Euler, -two of the Bernoulli's, and other mathematicians. In none of these -instances, however, did it happen that "the generous plant did still -its stock renew," as we have seen was the case at Paris, with the -Cassinis, and their kinsmen the Maraldis. - -[2d Ed.] [I may notice among instances of the patronage of -Astronomy, the reward at present offered by the King of Denmark for -the discovery of a Comet.] - -It is not necessary to mention here the more recent cases in which -sovereigns or statesmen have attempted to patronize individual -astronomers. - - -_Sect._ 5.--_Astronomical Expeditions._ - -BESIDES the pensions thus bestowed upon resident mathematicians and -astronomers, the governments of Europe have wisely and usefully -employed considerable sums upon expeditions and travels undertaken -by men of science for some appropriate object. Thus Picard, in 1671, -was sent to Uraniburg, the scene of Tycho's observations, to -determine its latitude and its longitude. He found that "the City of -the Skies" had utterly disappeared from the earth; and even its -foundations were retraced with difficulty. With the same object, -that of accurately connecting the labors of the places which had -been at different periods the metropolis of astronomy, Chazelles was -sent, in 1693, to Alexandria. We have already mentioned Richer's -astronomical expedition to Cayenne in 1672. Varin and -Deshayes[129\7] were sent a few years later into the same regions -for similar purposes. Halley's expedition to St. {481} Helena in -1677, with the view of observing the southern stars, was at his own -expense; but at a later period (in 1698), he was appointed to the -command of a small vessel by King William the Third, in order that -he might make his magnetical observations in all parts of the world. -Lacaille was maintained by the French government four years at the -Cape of Good Hope (1750-4), for the purpose of observing the stars -of the southern hemisphere. The two transits of Venus in 1761 and -1769, occasioned expeditions to be sent to Kamtschatka and Tobolsk -by the Russians; to the Isle of France, and to Coromandel, by the -French;[130\7] to the isles of St. Helena and Otaheite by the -English; to Lapland and to Drontheim, by the Swedes and Danes. I -shall not here refer to the measures of degrees executed by various -nations, still less the innumerable surveys by land and sea; but I -may just notice the successive English expeditions of Captains Basil -Hall, Sabine, and Foster, for the purpose of determining the length -of the seconds' pendulum in different latitudes; and the voyages of -M. Biot and others, sent by the French government for the same -purpose. Much has been done in this way, but not more than the -progress of astronomy absolutely required; and only a small portion -of that which the completion of the subject calls for. - -[Note 129\7: Bailly, ii. 374.] - -[Note 130\7: Bailly, iii. 107.] - - -_Sect._ 6.--_Present State of Astronomy._ - -ASTRONOMY, in its present condition, is not only much the most -advanced of the sciences, but is also in far more favorable -circumstances than any other science for making any future advance, as -soon as this is possible. The general methods and conditions by which -such an advantage is to be obtained for the various sciences, we shall -endeavor hereafter to throw some light upon; but in the mean time, we -may notice here some of the circumstances in which this peculiar -felicity of the present state of astronomy may be traced. - -The science is cultivated by a number of votaries, with an assiduity -and labor, and with an expenditure of private and public resources, -to which no other subject approaches; and the mode of its -cultivation in all public and most private observatories, has this -character--that it forms, at the same time, a constant process of -verification of existing discoveries, and a strict search for any -new discoverable laws. The observations made are immediately -referred to the best tables, and {482} corrected by the best formulæ -which are known; and if the result of such a reduction leaves any -thing unaccounted for, the astronomer is forthwith curious and -anxious to trace this deviation from the expected numbers to its -rule and its origin; and till the first, at least, of these things -is performed, he is dissatisfied and unquiet. The reference of -observations to the state of the heavens as known by previous -researches, implies a great amount of calculation. The exact places -of the stars at some standard period are recorded in _Catalogues_; -their movements, according to the laws hitherto detected, are -arranged in _Tables_; and if these tables are applied to predict the -numbers which observation on each day ought to give, they form -_Ephemerides_. Thus the catalogues of fixed stars of Flamsteed, of -Piazzi, of Maskelyne, of the Astronomical Society, are the basis of -all observation. To these are applied the Corrections for Refraction -of Bradley or Bessel, and those for Aberration, for Nutation, for -Precession, of the best modern astronomers. The observations so -corrected enable the observer to satisfy himself of the delicacy and -fidelity of his measures of time and space; his Clocks and his Arcs. -But this being done, different stars so observed can be compared -with each other, and the astronomer can then endeavor further to -correct his fundamental Elements;--his Catalogue, or his Tables of -Corrections. In these Tables, though previous discovery has -ascertained the law, yet the exact quantity, the _constant_ or -_coefficient_ of the formula, can be exactly fixed only by numerous -observations and comparisons. This is a labor which is still going -on, and in which there are differences of opinion on almost every -point; but the amount of these differences is the strongest evidence -of the certainty and exactness of those doctrines in which all -agree. Thus Lindenau makes the coefficient of Nutation rather less -than nine seconds, which other astronomers give as about nine -seconds and three-tenths. The Tables of Refraction are still the -subject of much discussion, and of many attempts at improvement. And -after or amid these discussions, arise questions whether there be -not other corrections of which the law has not yet been assigned. -The most remarkable example of such questions is the controversy -concerning the existence of an Annual Parallax of the fixed stars, -which Brinkley asserted, and which Pond denied. Such a dispute -between two of the best modern observers, only proves that the -quantity in question, if it really exist, is of the same order as -the hitherto unsurmounted errors of instruments and corrections. - -[2d Ed.] [The belief in an appreciable parallax of some of the fixed -{483} stars appears to gain ground among astronomers. The parallax -of 61 _Cygni_, as determined by Bessel, is 0"·34; about one-third of -a second, or 1⁄10000 of a degree. That of _α Centauri_, as -determined by Maclear, is 0"·9, or 1⁄4000 of a degree.] - -But besides the fixed stars and their corrections, the astronomer -has the motions of the planets for his field of action. The -established theories have given us tables of these, from which their -daily places are calculated and given in our Ephemerides, as the -_Berliner Jahrbuch_ of Encke, or the _Nautical Almanac_, published -by the government of this country, the _Connaissance des Tems_ which -appears at Paris, or the _Effemeridi di Milano_. The comparison of -the observed with the tabular place, gives us the means of -correcting the coefficients of the tables; and thus of obtaining -greater exactness in the constants of the solar system. But these -constants depend upon the mass and form of the bodies of which the -system is composed; and in this province, as well as in sidereal -astronomy, different determinations, obtained by different paths, -may be compared; and doubts may be raised and may be solved. In this -way, the perturbations produced by Jupiter on different planets gave -rise to a doubt whether his attraction be really proportional to his -mass, as the law of universal gravitation asserts. The doubt has -been solved by Nicolai and Encke in Germany, and by Airy in England. -The mass of Jupiter, as shown by the perturbations of Juno, of -Vesta, and of Encke's Comet, and by the motion of his outermost -Satellite, is found to agree, though different from the mass -previously received on the authority of Laplace. Thus also -Burckhardt, Littrow, and Airy, have corrected the elements of the -Solar Tables. In other cases, the astronomer finds that no change of -the coefficients will bring the Tables and the observations to a -coincidence;--that a new term in the formula is wanting. He obtains, -as far as he can, the law of this unknown term; if possible, he -traces it to some known or probable cause. Thus Mr. Airy, in his -examination of the Solar Tables, not only found that a diminution of -the received mass of Mars was necessary, but perceived discordances -which led him to suspect the existence of a new inequality. Such an -inequality was at length found to result theoretically from the -attraction of Venus. Encke, in his examination of his comet, found a -diminution of the periodic time in the successive revolutions; from -which he inferred the existence of a resisting medium. Uranus still -deviates from his tabular place, and the cause remains yet to be -discovered. (But see the _Additions_ to this volume.) {484} - -Thus it is impossible that an assertion, false to any amount which -the existing state of observation can easily detect, should have any -abiding prevalence in astronomy. Such errors may long keep their -ground in any science which is contained mainly in didactic works, -and studied in the closet, but not acted upon elsewhere;--which is -reasoned upon much, but brought to the test of experiment rarely or -never. Here, on the contrary, an error, if it arise, makes its way -into the Tables, into the Ephemeris, into the observer's nightly -List, or his sheet of Reductions; the evidence of sense flies in its -face in a thousand observatories; the discrepancy is traced to its -source, and soon disappears forever. - -In this favored branch of knowledge, the most recondite and delicate -discoveries can no more suffer doubt or contradiction, than the most -palpable facts of sense which the face of nature offers to our -notice. The last great discovery in astronomy--the motion of the -stars arising from Aberration--is as obvious to the vast population -of astronomical observers in all parts of the world, as the motion -of the stars about the pole is to the casual night wanderer. And -this immunity from the danger of any large error in the received -doctrines, is a firm platform on which the astronomer can stand and -exert himself to reach perpetually further and further into the -region of the unknown. - -The same scrupulous care and diligence in recording all that has -hitherto been ascertained, has been extended to those departments of -astronomy in which we have as yet no general principles which serve -to bind together our acquired treasures. These records may be -considered as constituting a _Descriptive Astronomy_; such are, for -instance, Catalogues of Stars, and Maps of the Heavens, Maps of the -Moon, representations of the appearance of the Sun and Planets as -seen through powerful telescopes, pictures of Nebulæ, of Comets, and -the like. Thus, besides the Catalogue of Fundamental Stars which may -be considered as standard points of reference for all observations -of the Sun, Moon, and Planets, there exist many large catalogues of -smaller stars. Flamsteed's _Historia Celestis_, which much surpassed -any previous catalogue, contained above 3000 stars. But in 1801, the -French _Histoire Céleste_ appeared, comprising observations of -50,000 stars. Catalogues or charts of other special portions of the -sky have been published more recently; and in 1825, the Berlin -Academy proposed to the astronomers of Europe to carry on this work -by portioning out the heavens among them. - -[2d Ed.] [Before Flamsteed, the best Catalogue of the Stars was -{485} Tycho Brahe's, containing the places of about 1000 stars, -determined very roughly with the naked eye. On the occasion of a -project of finding the longitude, which was offered to Charles II., -in 1674, Flamsteed represented that the method was quite useless, in -consequence, among other things, of the inaccuracy of Tycho's places -of the stars. Flamsteed's letters being shown King Charles, he was -startled at the assertion of the fixed stars' places being false in -the Catalogue, and said, with some vehemence, "He must have them -anew observed, examined, and corrected for the use of his seamen." -This was the immediate occasion of building Greenwich Observatory, -and placing Flamsteed there as an observer. Flamsteed's _Historia -Celestis_ contained above 3000 stars, observed with telescopic -sights. It has recently been republished with important improvements -by Mr. Baily. See Baily's _Flamsteed_, p. 38. - -The French _Histoire Céleste_ was published in 1801 by Lalande, -containing 50,000 stars, simply as observed by himself and other -French astronomers. The reduction of the observations contained in -this Catalogue to the mean places at the beginning of the year 1800 -may be effected by means of Tables published by Schumacher for that -purpose in 1825. - -In 1807, Piazzi's Catalogue of 6748 stars, founded on Maskelyne's -Catalogue of 1700, was published; afterwards extended to 7646 stars -in 1814. This is considered as the greatest work undertaken by any -modern astronomer; the observations being well made, reduced, and -compared with those of former astronomers. Piazzi's Catalogue is the -standard and accurate Catalogue, as the _Histoire Céleste_ is the -standard approximate Catalogue for small stars. But the new planets -were discovered mostly by a comparison of the heavens with Bode's -(Berlin) Catalogue. - -I may mention other Catalogues of Stars which have recently been -published. Pond's Catalogue contains 1112 Northern stars; Johnson's, -606; Wrottesley's, 1318 (in Right Ascension only); Airy's First -Cambridge Catalogue, 726; his Greenwich Catalogue, 1439. Pearson's -has 520 zodiacal stars; Groombridge's, 4243 circumpolar stars as far -as 50 degrees of North Polar distance; Santini's, a zone 18 degrees -North of the equator. Besides these, Mr. Taylor has published, by -order of the Madras government, a Catalogue of 11,000 stars observed -by him at Madras; and Rumker, who observed in the Observatory -established by Sir Thomas Brisbane at Paramatta (in Australia), has -commenced a Catalogue which is to contain 12,000. Mr. Baily {486} -published two Standard Catalogues; that of the Royal Astronomical -Society, containing 2881 stars; and that of the British Association, -containing 8377 stars. I omit other Catalogues, as those of -Argelander, &c., and Catalogues of Southern Stars. - -Of the Berlin Maps, fourteen hours in Right Ascension have been -published; and their value may be judged of by this circumstance, that -it was in a great measure by comparing the heavens with these Maps -that the new planet Astræa was discovered. The Zone observations made -at Königsberg, by the late illustrious astronomer Bessel, deserve to -be mentioned, as embracing a vast number of stars. - -The common mode of _designating the Stars_ is founded upon the -ancient constellations as given by Ptolemy; to which Bayer, of -Augsburg, in his _Uranometria_, added the artifice of designating -the brightest stars in each constellation by the Greek letters, α, -β, γ, &c., applied in order of brightness, and when these were -exhausted, the Latin letters. Flamsteed used numbers. As the number -of observed stars increased, various methods were employed for -designating them; and the confusion which has been thus introduced, -both with regard to the boundaries of the constellations and the -nomenclature of the stars in each, has been much complained of -lately. Some attempts have been made to remedy this variety and -disorder. Mr. Argelander has recently recorded stars, according to -their magnitudes as seen by the naked eye, in a _Neue Uranometrie_. - -Among representations of the Moon I may mention Hevelius's -_Selenographia_, a work of former times, and Beer and Madler's Map -of the Moon, recently published.] - -I have already said something of the observations of the two -Herschels on _Double Stars_, which have led to a knowledge of the -law of the revolution of such systems. But besides these, the same -illustrious astronomers have accumulated enormous treasures of -observations of _Nebulæ_; the materials, it may be, hereafter, of -some vast new generalization with respect to the history of the -system of the universe. - -[2d Ed.] [A few measures of Double Stars are to be found in previous -astronomical records. But the epoch of the creation of this part of -the science of astronomy must be placed at the beginning of the -present century, when Sir William Herschel (in 1802) published in -the _Phil. Trans._ a Catalogue of 500 new Nebulæ of various classes, -and in the _Phil. Trans._ 1803, a paper "On the changes in the -relative situation of the Double Stars in 25 years." In succeeding -papers he pursued the subject. In one in 1814 he noticed the -breaking up of the {487} Milky Way in different places, apparently -from some principle of Attraction; and in this, and in one in 1817, -he published those remarkable views on the distribution of the stars -in our own cluster as forming a large stratum, and on the connection -of stars and nebulæ (the stars appearing sometimes to be accompanied -by nebulæ, sometimes to have absorbed a part of the nebula, and -sometimes to have been formed from nebulæ), which have been accepted -and propounded by others as the _Nebular Theory_. Sir William -Herschel's last paper was a Catalogue of 145 new Double Stars -communicated to the Astronomical Society in 1822. In 1827 M. Struve, -of Dorpat (in Russia), published his _Catalogus Novus_, containing -the places of 3112 double stars. While this was going on, Sir John -Herschel and Sir James South published (in the _Phil. Trans._ 1824) -accurate measures of 380 Double and Triple Stars, to which Sir J. -South afterwards added 458. Mr. Dunlop published measures of 253 -Southern Double Stars. Other Observations have been published by -Capt. Smyth, Mr. Dawes, &c. The great work of Struve, _Mensuræ -Micrometricæ_, &c., contains 3134 such objects, including most of -Sir W. Herschel's Double Stars. Sir J. Herschel in 1826, 7, and 8 -presented to the Astronomical Society about 1000 measures of Double -Stars; and in 1830, good measures of 1236, made with his 20-feet -reflector. His paper in vol. v. of the _Ast. Soc. Mem._, besides -measures of 364 such stars, exhibits all the most striking results, -as to the motion of Double Stars, which have yet been obtained. In -1835 he carried his 20-feet reflector to the Cape of Good Hope for -the purpose of completing the survey of Double Stars and Nebulæ in -the southern hemisphere with the same instruments which had explored -the northern skies. He returned from the Cape in 1838, and is now -(1846) about to give the world the results of his labors. Besides -the stars just mentioned, his work will contain from 1500 to 2000 -additional double stars; making a gross number of above 8000; in -which of course are included a number of objects of no great -scientific interest, but in which also are contained the materials -of the most important discoveries which remain to be made by -astronomers. The publication of Sir John Herschel's great work upon -Double Stars and Nebulæ is looked for with eager interest by -astronomers. - -Of the observations of Nebulæ we may say what has just been said of -the observations of Double Stars;--that they probably contain the -materials of important future discoveries. It is impossible not to -regard these phenomena with reference to the _Nebular Hypothesis_, -which has been propounded by Laplace, and much more strongly {488} -insisted upon by other persons;--namely, the hypothesis that systems -of revolving planets, of which the Solar System is an example, arise -from the gradual contraction and separation of vast masses of -nebulous matter. Yet it does not appear that any changes have been -observed in nebulæ which tend to confirm this hypothesis; and the -most powerful telescope in the world, recently erected by the Earl -of Rosse, has given results which militate against the hypothesis; -inasmuch as it has shown that what appeared a diffused nebulous mass -is, by a greater power of vision, resolved, in all cases yet -examined, into separate stars. - -When astronomical phenomena are viewed with reference to the Nebular -Hypothesis, they do not belong so properly to Astronomy, in the view -here taken of it, as to Cosmogony. If such speculations should -acquire any scientific value, we shall have to arrange them among -those which I have called _Palætiological_ Sciences; namely, those -Sciences which contemplate the universe, the earth, and its -inhabitants, with reference to their historical changes and the -causes of those changes.] - - - -{{489}} -ADDITIONS TO THE THIRD EDITION. - - - - -INTRODUCTION. - - -THERE is a difficulty in writing for popular readers a History of the -Inductive Sciences, arising from this;--that the sympathy of such -readers goes most readily and naturally along the course which leads -to false science and to failure. Men, in the outset of their attempts -at knowledge, are prone to rush from a few hasty observations of facts -to some wide and comprehensive principles; and then, to frame a system -on these principles. This is the opposite of the method by which the -Sciences have really and historically been conducted; namely, the -method of a gradual and cautious ascent from observation to principles -of limited generality, and from them to others more general. This -latter, the true Scientific Method, is _Induction_, and has led to the -_Inductive Sciences_. The other, the spontaneous and delusive course, -has been termed by Francis Bacon, who first clearly pointed out the -distinction, and warned men of the error, _Anticipation_. The -hopelessness of this course is the great lesson of his philosophy; but -by this course proceeded all the earlier attempts of the Greek -philosophers to obtain a knowledge of the Universe. - -Laborious observation, narrow and modest inference, caution, slow and -gradual advance, limited knowledge, are all unwelcome efforts and -restraints to the mind of man, when his speculative spirit is once -roused: yet these are the necessary conditions of all advance in the -Inductive Sciences. Hence, as I have said, it is difficult to win the -sympathy of popular readers to the true history of these sciences. The -career of bold systems and fanciful pretences of knowledge is more -entertaining and striking. Not only so, but the bold guesses and -fanciful reasonings of men unchecked by doubt or fear of failure are -often presented as the dictates of _Common Sense_;--as the plain, -unsophisticated, unforced reason of man, acting according to no -artificial rules, but following its own natural course. Such Common -Sense, while it {490} complacently plumes itself on its -clear-sightedness in rejecting arbitrary systems of others, is no less -arbitrary in its own arguments, and often no less fanciful in its -inventions, than those whom it condemns. - -We cannot take a better representative of the Common Sense of the -ancient Greeks than Socrates: and we find that his Common Sense, -judging with such admirable sagacity and acuteness respecting moral -and practical matters, offered, when he applied it to physical -questions, examples of the unconscious assumptions and fanciful -reasonings which, as we have said, Common Sense on such subjects -commonly involves. - -Socrates, Xenophon tells us (_Memorabilia_, iv. 7), recommended his -friends not to study astronomy, so as to pursue it into scientific -details. This was practical advice: but he proceeded further to -speak of the palpable mistakes made by those who had carried such -studies farthest. Anaxagoras, for instance, he said, held that the -Sun was a Fire:--he did not consider that men can look at a fire, -but they cannot look at the Sun; they become dark by the Sun shining -upon them, but not so by the fire. He did not consider that no -plants can grow well except they have sunshine, but if they are -exposed to the fire they are spoiled. Again, when he said that the -Sun was a stone red-hot, he did not consider that a stone heated by -the fire is not luminous, and soon cools, but the Sun is always -luminous and always hot. - -We may easily conceive how a disciple of Anaxagoras would reply to -these arguments. He would say, for example, as we should probably -say at present, that if there were a mass of matter so large and so -hot as Anaxagoras supposed the Sun to be, its light might be as -great and its heat as permanent as the heat and light of the Sun -are, as yet, known to be. In this case the arguments of Socrates are -at any rate no better than the doctrine of Anaxagoras. - - - -{{491}} -BOOK I. - -THE GREEK SCHOOL PHILOSOPHY. - -CHAPTER II. - -THE GREEK SCHOOLS. - - -_The Platonic Doctrine of Ideas._ - -IN speaking of the Foundation of the Greek School Philosophy, I have -referred to the dialogue entitled _Parmenides_, commonly ascribed to -Plato. And the doctrines ascribed to Parmenides, in that and in -other works of ancient authors, are certainly remarkable examples of -the tendency which prevailed among the Greeks to rush at once to the -highest generalizations of which the human mind is capable. The -distinctive dogma of the Eleatic School, of which Parmenides was one -of the most illustrious teachers, was that _All Things are One_. -This indeed was rather a doctrine of metaphysical theology than of -physical science. It tended to, or agreed with, the doctrine that -All things are God:--the doctrine commonly called _Pantheism_. But -the tenet of the Platonists which was commonly put in opposition to -this, that we must seek _The One in the Many_, had a bearing upon -physical science; at least, if we interpret it, as it is generally -interpreted, that we must seek the one Law which pervades a -multiplicity of Phenomena. We may however take the liberty of -remarking, that to speak of a Rule which is exemplified in many -cases, as being "the One in the Many" (a way of speaking by which we -put out of sight the consideration what very different kinds of -things _the One_ and _the Many_ are), is a mode of expression which -makes a very simple matter look very mysterious; and is another -example of the tendency which urges speculative men to aim at -metaphysical generality rather than scientific truth. - -The Dialogue _Parmenides_ is, as I have said, commonly referred to -Plato. Yet it is entirely different in substance, manner, and -tendency {492} from the most characteristic of the Platonic -Dialogues. In these, Socrates is represented as finally successful -in refuting or routing his adversaries, however confident their tone -and however popular their assertions. They are angered or humbled; -he retains his good temper and his air of superiority, and when they -are exhausted, he sums up in his own way. - -In the _Parmenides_, on the contrary, everything is the reverse of -this. Parmenides and Zeno exchange good-humoured smiles at -Socrates's criticism, when the bystanders expect them to grow angry. -They listen to Socrates while he propounds Plato's doctrine of -Ideas; and reply to him with solid arguments which he does not -answer, and which have never yet been answered. Parmenides, in a -patronising way, lets him off; and having done this, being much -entreated, he pronounces a discourse concerning the One and the -Many; which, obscure as it may seem to us, was obviously intended to -be irrefutable: and during the whole of this part of the Dialogue, -the friend of Socrates appears only as a passive respondent, saying -_Yes_ or _No_ as the assertions of Parmenides require him to do; -just in the same way in which the opponents of Socrates are -represented in other Dialogues. - -These circumstances, to which other historical difficulties might be -added, seem to show plainly that the _Parmenides_ must be regarded -as an Eleatic, not as a Platonic Dialogue;--as composed to confute, -not to assert, the Platonic doctrine of Ideas. - -The Platonic doctrine of Ideas has an important bearing upon the -philosophy of Science, and was suggested in a great measure by the -progress which the Greeks had really made in Geometry, Astronomy, -and other Sciences, as I shall elsewhere endeavor to show. This -doctrine has been recommended in our own time,[1\A] as containing "a -mighty substance of imperishable truth." It cannot fail to be -interesting to see in what manner the doctrine is presented by those -who thus judge of it. The following is the statement of its leading -features which they give us. - -[Note 1\A: A. Butler's _Lectures_, Second Series, Lect. viii. p. 132.] - -Man's soul is made to contain not merely a consistent scheme of its -own notions, but a direct apprehension of _real and eternal laws -beyond it_. These real and eternal laws are things _intelligible_, -and not things sensible. The laws, impressed upon creation by its -Creator, and apprehended by man, are something equally distinct from -the Creator {493} and from man; and the whole mass of them may be -termed the World of Things purely Intelligible. - -Further; there are qualities in the Supreme and Ultimate Cause of -all, which are manifested in his creation; and not merely -manifested, but in a manner--after being brought out of his -super-essential nature into the stage of being which is below him, -but next to him--are then, by the causative act of creation, -deposited in things, differencing them one from the other, so that -the things participate of them (μετέχουσι), communicate with them -(κοινωνοῦσι). - -The Intelligence of man, excited to reflection by the impressions of -these objects, thus (though themselves transitory) participant of a -divine quality, may rise to higher conceptions of the perfections -thus faintly exhibited; and inasmuch as the perfections are -unquestionably _real_ existences, and known to be such in the very -act of contemplation, this may be regarded as a distinct -intellectual apprehension of them;--a union of the Reason with the -Ideas in that sphere of being which is common to both. - -Finally, the Reason, in proportion as it learns to contemplate the -Perfect and Eternal, desires the enjoyment of such contemplations in -a more consummate degree, and cannot be fully satisfied except in -the actual fruition of the Perfect itself. - -These propositions taken together constitute the THEORY OF IDEAS. -When we have to treat of the Philosophy of Science, it may be worth -our while to resume the consideration of this subject. - - -In this part of the History, the _Timæus_ of Plato is referred to as -an example of the loose notions of the Greek philosophers in their -physical reasonings. And undoubtedly this Dialogue does remarkably -exemplify the boldness of the early Greek attempts at generalization -on such subjects. Yet in this and in other parts the writings of -Plato contain speculations which may be regarded as containing germs -of true physical science; inasmuch as they assume that the phenomena -of the world are governed by mathematical laws;--by relations of -space and number;--and endeavor, too boldly, no doubt, but not -vaguely or loosely, to assign those laws. The Platonic writings -offer, in this way, so much that forms a Prelude to the Astronomy -and other Physical Sciences of the Greeks, that they will deserve -our notice, as supplying materials for the next two Books of the -History, in which these subjects are treated of. {494} - - - - -CHAPTER III. - -FAILURE OF THE GREEK PHYSICAL PHILOSOPHY. - - -_Francis Bacon's Remarks._ - -THOUGH we do not accept, as authority, even the judgments of Francis -Bacon, and shall have to estimate the strong and the weak parts of -his, no less than of other philosophies, we shall find his remarks -on the Greek philosophers very instructive. Thus he says of -Aristotle, (_Nov. Org._ 1. Aph. lxiii.): - -"He is an example of the kind of philosophy in which much is made -out of little; so that the basis of experience is too narrow. He -corrupted Natural Philosophy by his Logic, and made the world out of -his Categories. He disposed of the distinction of _dense_ and -_rare_, by which bodies occupy more or less dimensions or space, by -the frigid distinction of _act_ and _power_. He assigned to each -kind of body a single proper motion, so that if they have any other -motion they must receive it from some extraneous source; and imposed -many other arbitrary rules upon Nature; being everywhere more -careful how one may give a ready answer, and make a positive -assertion, than how he may apprehend the variety of nature. - -"And this appears most evidently by the comparison of his philosophy -with the other philosophies which had any vogue in Greece. For the -_Homoiomeria_[2\A] of Anaxagoras, the _Atoms_ of Leucippus and -Democritus, the Heaven and Earth of Parmenides, the Love and Hate of -Empedocles, the Fire of Heraclitus, had some trace of the thoughts -of a natural philosopher; some savor of experience, and nature, and -bodily things; while the Physics of Aristotle, in general, sound -only of Logical Terms. - -[Note 2\A: For these technical forms of the Greeks, see Sec. 3 of -this chapter.] - -"Nor let any one be moved by this--that in his books _Of Animals_, -and in his _Problems_, and in others of his tracts, there is often a -quoting of experiments. For he had made up his mind beforehand; and -did not consult experience in order to make right propositions and -axioms, but when he had settled his system to his will, he twisted -experience {495} round, and made her bend to his system: so that in -this way he is even more wrong than his modern followers, the -Schoolmen, who have deserted experience altogether." - -We may note also what Bacon says of the term _Sophist_. (Aph. lxxi.) -"The wisdom of the Greeks was professorial, and prone to run into -disputations: which kind is very adverse to the discovery of Truth. -And the name of _Sophists_, which was cast in the way of contempt, -by those who wished to be reckoned philosophers, upon the old -professors of rhetoric, Gorgias, Protagoras, Hippias, Polus, does, -in fact, fit the whole race of them, Plato,[3\A] Aristotle, Zeno, -Epicurus, Theophrastus; and their successors, Chrysippus, Carneades, -and the rest." - -[Note 3\A: It is curious that the attempt to show that Plato's -opponents were not commonly illusive and immoral reasoners, has been -represented as an attempt to obliterate the distinction of "Sophist" -and "Philosopher."--See A. Butler's _Lectures_, i. 357. Note.] - -That these two classes of teachers, as moralists, were not different -in their kind, has been urged by Mr. Grote in a very striking and -amusing manner. But Bacon speaks of them here as physical -philosophers; in which character he holds that all of them were -_sophists_, that is, illusory reasoners. - - -_Aristotle's Account of the Rainbow._ - -To exemplify the state of physical knowledge among the Greeks, we may -notice briefly Aristotle's account of the _Rainbow_; a phenomenon so -striking and definite, and so completely explained by the optical -science of later times. We shall see that not only the explanations -there offered were of no value, but that even the observation of -facts, so common and so palpable, was inexact. In his _Meteorologica_ -(lib. iii. c. 2) he says, "The Rainbow is never more than a -semicircle. And at sunset and sunrise, the circle is least, but the -arch is greatest; when the sun is high, the circle is larger, but the -arch is less." This is erroneous, for the diameter of the circle of -which the arch of the rainbow forms a part, is always the same, namely -82°. "After the autumnal equinox," he adds, "it appears at every hour -of the day; but in the summer season, it does not appear about noon." -It is curious that he did not see the reason of this. The centre of -the circle of which the rainbow is part, is always opposite to the -sun. And therefore if the sun be more than 41° above the horizon, the -centre of the rainbow will be so much below the horizon, that the -place of the rainbow will {496} be entirely below the horizon. In the -latitude of Athens, which is 38°, the equator is 52° above the -horizon, and the rainbow can be visible only when the sun is 11° lower -than it is at the equinoctial noon. These remarks, however, show a -certain amount of careful observation; and so do those which Aristotle -makes respecting the colors. "Two rainbows at most appear: and of -these, each has three colors; but those in the outer bow are duller; -and their order opposite to those in the inner. For in the inner bow -the first and largest arch is red; but in the outer bow the smallest -arch is red, the nearest to the inner; and the others in order. The -colors are red, green, and purple, such as painters cannot imitate." -It is curious to observe how often modern painters disregard even the -order of the colors, which they could imitate, if they attended to it. - -It may serve to show the loose speculation which we oppose to -science, if we give Aristotle's attempt to explain the phenomenon of -the Rainbow. It is produced, he says (c. iv.), by Reflexion -(ἀνάκλασις) from a cloud opposite to the sun, when the cloud forms -into drops. And as a reason for the red color, he says that a -bright object seen through darkness appears red, as the flame -through the smoke of a fire of green wood. This notion hardly -deserves notice; and yet it was taken up again by Göthe in our own -time, in his speculations concerning colors. - - - -{{497}} -BOOK II. - -THE PHYSICAL SCIENCES IN ANCIENT GREECE. - - -_Plato's Timæus and Republic._ - -ALTHOUGH a great portion of the physical speculations of the Greek -philosophers was fanciful, and consisted of doctrines which were -rejected in the subsequent progress of the Inductive Sciences; still -many of these speculations must be considered as forming a Prelude -to more exact knowledge afterwards attained; and thus, as really -belonging to the Progress of knowledge. These speculations express, -as we have already said, the conviction that the phenomena of nature -are governed by laws of space and number; and commonly, the -mathematical laws which are thus asserted have some foundation in -the facts of nature. This is more especially the case in the -speculations of Plato. It has been justly stated by Professor -Thompson (A. Butler's _Lectures_, Third Series, Lect. i. Note 11), -that it is Plato's merit to have discovered that the laws of the -physical universe are resolvable into numerical relations, and -therefore capable of being represented by mathematical formulæ. Of -this truth, it is there said, Aristotle does not betray the -slightest consciousness. - -The _Timæus_ of Plato contains a scheme of mathematical and physical -doctrines concerning the universe, which make it far more analogous -than any work of Aristotle to Treatises which, in modern times, have -borne the titles of _Principia_, _System of the World_, and the like. -And fortunately the work has recently been well and carefully studied, -with attention, not only to the language, but to the doctrines and -their bearing upon our real knowledge. Stallbaum has published an -edition of the Dialogue, and has compared the opinions of Plato with -those of Aristotle on the like subjects. Professor Archer Butler of -Dublin has devoted to it several of his striking and eloquent -Lectures; and these have been furnished with valuable annotations by -Professor Thompson of Cambridge; and M. The. Henri Martin, then -Professor at Rennes, published in 1841 two volumes of _Etudes sur le -Timée de Platon_, in {498} which the bearings of the work on Science -are very fully discussed. The Dialogue treats not only concerning the -numerical laws of harmonical sounds, of visual appearances, and of the -motions of planets and stars, but also concerning heat, as well as -light; and concerning water, ice, gold, gems, iron, rust, and other -natural objects;--concerning odors, tastes, hearing, sight, light, -colors, and the powers of sense in general:--concerning the parts and -organs of the body, as the bones, the marrow, the brain, the flesh, -muscles, tendons, ligaments, nerves; the skin, the hair, the nails; -the veins and arteries; respiration; generation; and in short every -obvious point of physiology. - -But the opinions delivered in the _Timæus_ upon these latter -subjects have little to do with the progress of real knowledge. The -doctrines, on the other hand, which depend upon geometrical and -arithmetical relations, are portions or preludes of the sciences -which, in the fulness of time, assumed a mathematical form for the -expression of truth. - -Among these may be mentioned the arithmetical relations of -harmonical sounds, to which I have referred in the History. These -occur in various parts of Plato's writings. In the _Timæus_, in -which the numbers are most fully given, the meaning of the numbers -is, at first sight, least obvious. The numbers are given as -representing the proportion of the parts of the Soul (_Tim._ pp. 35, -36), which does not immediately refer us to the relations of Sounds. -But in a subsequent part of the Dialogue (47, D), we are told that -music is a privilege of the hearing given on account of Harmony; and -that Harmony has Cycles corresponding to the movements of the Soul; -(referring plainly to those already asserted.) And the numbers which -are thus given by Plato as elements of harmony, are in a great -measure the same as those which express the musical relations of the -tones of the musical scale at this day in use, as M. Henri Martin -shows (_Et. sur le Timée_, note xxiii.) The intervals C to D, C to -F, C to G, C to C, are expressed by the fractions 9/8, 4/3, 3/2, -2/1, and are now called a Tone, a Fourth, a Fifth, an Octave. They -were expressed by the same fractions among the Greeks, and were -called _Tone_, _Diatessaron_, _Diapente_, _Diapason_. The Major and -Minor Third, and the Major and Minor Sixth, were however wanting, it -is conceived, in the musical scale of Plato. - -The _Timæus_ contains also a kind of theory of vision by reflexion -from a plane, and in a concave mirror; although the theory is in -this case less mathematical and less precise than that of Euclid, -referred to in chap. ii. of this Book. - -One of the most remarkable speculations in the _Timæus_ is that in -{499} which the Regular Solids are assigned as the forms of the -Elements of which the Universe is composed. This curious branch of -mathematics, Solid Geometry, had been pursued with great zeal by -Plato and his friends, and with remarkable success. The five Regular -Solids, the Tetrahedron or regular Triangular Pyramid, the Cube, the -Octahedron, the Dodecahedron, and the Icosahedron, had been -discovered; and the remarkable theorem, that of regular solids there -can be just so many, these and no others, was known. And in the -_Timæus_ it is asserted that the particles of the various elements -have the forms of these solids. Fire has the Pyramid; Earth has the -Cube; Water the Octahedron; Air the Icosahedron; and the -Dodecahedron is the plan of the Universe itself. It was natural that -when Plato had learnt that other mathematical properties had a -bearing upon the constitution of the Universe, he should suppose -that the singular property of space, which the existence of this -limited and varied class of solids implied, should have some -corresponding property in the Universe, which exists in space. - -We find afterwards, in Kepler and others, a recurrence to this -assumption; and we may say perhaps that Crystallography shows us that -there are properties of bodies, of the most intimate kind, which -involve such spatial relations as are exhibited in the Regular Solids. -If the distinctions of Crystalline System in bodies were hereafter to -be found to depend upon the chemical elements which predominate in -their composition, the admirers of Plato might point to his doctrine, -of the different form of the particles of the different elements of -the Universe, as a remote Prelude to such a discovery. - -But the mathematical doctrines concerning the parts and elements of -the Universe are put forwards by Plato, not so much as assertions -concerning physical facts, of which the truth or falsehood is to be -determined by a reference to nature herself. They are rather -propounded as examples of a truth of a higher kind than any -reference to observation can give or can test, and as revelations of -principles such as must have prevailed in the mind of the Creator of -the Universe; or else as contemplations by which the mind of man is -to be raised above the region of sense, and brought nearer to the -Divine Mind. In the _Timæus_ these doctrines appear rather in the -former of the two lights; as an exposition of the necessary scheme -of creation, so far as its leading features are concerned. In the -seventh Book of the _Polity_, the same doctrines are regarded more -as a mental discipline; as the necessary study of the true -philosopher. But in both places these mathematical {500} -propositions are represented as Realities more real than the -Phenomena;--as a Natural Philosophy of a higher kind than the study -of Nature itself can teach. This is no doubt an erroneous -assumption: yet even in this there is a germ of truth; namely, that -the mathematical laws, which prevail in the universe, involve -mathematical truths which being demonstrative, are of a higher and -more cogent kind than mere experimental truths. - -Notions, such as these of Plato, respecting a truth at which science -is to aim, which is of an exact and demonstrative kind, and is -imperfectly manifested in the phenomena of nature, may help or may -mislead inquirers; they may be the impulse and the occasion to great -discoveries; or they may lead to the assertion of false and the loss -of true doctrines. Plato considers the phenomena which nature offers -to the senses as mere suggestions and rude sketches of the objects -which the philosophic mind is to contemplate. The heavenly bodies -and all the splendors of the sky, though the most beautiful of -visible objects, being only visible objects, are far inferior to the -true objects of which they are the representatives. They are merely -diagrams which may assist in the study of the higher truth as we -might study geometry by the aid of diagrams constructed by some -consummate artist. Even then, the true object about which we reason -is the conception which we have in the mind. - -We have, I conceive, an instance of the error as well as of the -truth, to which such views may lead, in the speculations of Plato -concerning Harmony, contained in that part of his writings (the -seventh Book of the _Republic_), in which these views are especially -urged. He there, by way of illustrating the superiority of -philosophical truth over such exactness as the senses can attest, -speaks slightingly of those who take immense pains in measuring -musical notes and intervals by the ear, as the astronomers measure the -heavenly motions by the eye. "They screw their pegs and pinch their -strings, and dispute whether two notes are the same or not." Now, in -truth, the ear is the final and supreme judge whether two notes are -the same or not. But there is a case in which notes which are -nominally the same, are different really and to the ear; and it is -probably to disputes on this subject, which we know did prevail among -the Greek musicians, that Plato here refers. We may ascend from a note -A_{1} to a note C_{3} by two octaves and a third. We may also ascend -from the same note A_{1} to C_{3} by fifths four times repeated. But -the two notes C_{3} thus arrived at are not the same: they differ by a -small interval, which the Greeks called a {501} Comma, of which the -notes are in the ratio of 80 to 81. That the ear really detects this -defect of the musical coincidence of the two notes under the proper -conditions, is a proof of the coincidence of our musical perceptions -with the mathematical relations of the notes; and is therefore an -experimental confirmation of the mathematical principles of harmony. -But it seems to be represented by Plato, that to look out for such -confirmation of mathematical principles, implies a disposition to lean -on the senses, which he regards as very unphilosophical. - - -_Hero of Alexandria._ - -THE other branches of mathematical science which I have spoken of in -the History as cultivated by the Greeks, namely Mechanics and -Hydrostatics, are not treated expressly by Plato; though we know -from Aristotle and others that some of the propositions of those -sciences were known about his time. Machines moved not only by -weights and springs, but by water and air, were constructed at an -early period. Ctesibius, who lived probably about B. C. 250, under -the Ptolemies, is said to have invented a clepsydra or water-clock, -and an hydraulic organ; and to have been the first to discover the -elastic power of air, and to apply it as a moving power. Of his -pupil Hero, the name is to this day familiar, through the little -pneumatic instrument called _Hero's Fountain_. He also described -pumps and hydraulic machines of various kinds; and an instrument -which has been spoken of by some modern writers as a _steam-engine_, -but which was merely a toy made to whirl round by the steam emitted -from holes in its arms. Concerning mechanism, besides descriptions -of _Automatons_, Hero composed two works: the one entitled -_Mechanics_, or _Mechanical Introductions_; the other _Barulcos_, -the _Weight-lifter_. In these works the elementary contrivances by -which weights may be lifted or drawn were spoken of as the _Five -Mechanical Powers_, the same enumeration of such machines as -prevails to this day; namely, the Lever, the Wheel and Axle, the -Pulley, the Wedge, and the Screw. In his Mechanics, it appears that -Hero reduced all these machines to one single machine, namely to the -lever. In the _Barulcos_, Hero proposed and solved the problem which -it was the glory of Archimedes to have solved: To move any object -(however large) by any power (however small). This, as may easily be -conceived by any one acquainted with the elements of Mechanics, is -done by means of a combination of the mechanical powers, and -especially by means of a train of toothed-wheels and axles. {502} - -The remaining writings of Hero of Alexandria have been the subject -of a special, careful, and learned examination by M. Th. H. Martin -(Paris, 1854), in which the works of this writer, Hero the Ancient, -as he is sometimes called, are distinguished from those of another -writer of the same name of later date. - -Hero of Alexandria wrote also, as it appears, a treatise on -_Pneumatics_, in which he described machines, either useful or -amusing, moved by the force of air and vapor. - -He also wrote a work called _Catoptrics_, which contained proofs of -properties of the rays of reflected light. - -And a treatise _On the Dioptra_; which subject however must be -carefully distinguished from the subject entitled _Dioptrics_ by the -moderns. This latter subject treats of the properties of refracted -light; a subject on which the ancients had little exact knowledge -till a later period; as I have shown in the History. The _Dioptra_, -as understood by Hero, was an instrument for taking angles so as to -measure the position and hence to determine the distance of -inaccessible objects; as is done by the _Theodolite_ in our times. - -M. Martin is of opinion that Hero of Alexandria lived at a later -period than is generally supposed; namely, after B. C. 81. - - - -{{503}} -BOOK III. - -THE GREEK ASTRONOMY. - -INTRODUCTION. - - -THE mathematical opinions of Plato respecting the philosophy of -nature, and especially respecting what we commonly call "the -heavenly bodies," the Sun, Moon, and Planets, were founded upon the -view which I have already described: namely, that it is the business -of philosophy to aim at a truth higher than observation can teach; -and to solve problems which the phenomena of the universe only -suggest. And though the students of nature in more recent times have -learnt that this is too presumptuous a notion of human knowledge, -yet the very boldness and hopefulness which it involved impelled men -in the pursuit of truth, with more vigor than a more timorous temper -could have done; and the belief that there must be, in nature, -mathematical laws more exact than experience could discover, -stimulated men often to discover true laws, though often also to -invent false laws. Plato's writings, supplying examples of both -these processes, belong to the Prelude of true Astronomy, as well as -to the errors of false philosophy. We may find specimens of both -kinds in those parts of his Dialogues to which we have referred in -the preceding Book of our History. - -To Plato's merits in preparing the way for the Theory of Epicycles, -I have already referred in Chapter ii. of this Book. I conceive that -he had a great share in that which is an important step in every -discovery, the proposing distinctly the problem to be solved; which -was, in this case, as he states it, To account for the apparent -movements of the planets by a combination of two circular motions -for each:--the motion of identity, and the motion of difference. -(_Tim._ 39, A.) In the tenth Book of the _Republic_, quoted in our -text, the spindle which Destiny or Necessity holds between her -knees, and on which are rings, by means of which the planets revolve -round it as an axis, is a step towards the conception of the -problem, as the construction of a machine. - -It will not be thought surprising that Plato expected that {504} -Astronomy, when further advanced, would be able to render an account -of many things for which she has not accounted even to this day. -Thus, in the passage in the seventh Book of the _Republic_, he says -that the philosopher requires a reason for the proportion of the day -to the month, and the month to the year, deeper and more substantial -than mere observation can give. Yet Astronomy has not yet shown us -any reason why the proportion of the times of the earth's rotation -on its axis, the moon's revolution round the earth, and the earth's -revolution round the sun, might not have been made by the Creator -quite different from what they are. But in thus asking Mathematical -Astronomy for reasons which she cannot give, Plato was only doing -what a great astronomical discoverer, Kepler, did at a later period. -One of the questions which Kepler especially wished to have answered -was, why there are five planets, and why at such particular -distances from the sun? And it is still more curious that he thought -he had found the reason of these things, in the relations of those -Five Regular Solids which, as we have seen, Plato was desirous of -introducing into the philosophy of the universe. We have Kepler's -account of this, his imaginary discovery, in the _Mysterium -Cosmographicum_, published in 1596, as stated in our History, Book -v. Chap. iv. Sect. 2. - -Kepler regards the law which thus determines the number and magnitude -of the planetary orbits by means of the five regular solids as a -discovery no less remarkable and certain than the Three Laws which -give his name its imperishable place in the history of astronomy. - -We are not on this account to think that there is no steady -criterion of the difference between imaginary and real discoveries -in science. As discovery becomes possible by the liberty of -guessing, it becomes real by allowing observation constantly and -authoritatively to determine the value of guesses. Kepler added to -Plato's boldness of fancy his own patient and candid habit of -testing his fancies by a rigorous and laborious comparison with the -phenomena; and thus his discoveries led to those of Newton. {505} - - - - -CHAPTER I. - -EARLIEST STAGES OF ASTRONOMY. - - -_The Globular Form of the Earth._ - -THERE are parts of Plato's writings which have been adduced as bearing -upon the subsequent progress of science; and especially upon the -globular form of the earth, and the other views which led to the -discovery of America. In the _Timæus_ we read of a great continent -lying in the Ocean west of the Pillars of Hercules, which Plato calls -_Atlantis_. He makes the personage in his Dialogue who speaks of this -put it forward as an Egyptian tradition. M. H. Martin, who has -discussed what has been written respecting the Atlantis of Plato, and -has given therein a dissertation rich in erudition and of the most -lively interest, conceives that Plato's notions on this subject arose -from his combining his conviction of the spherical form of the earth, -with interpretations of Homer, and perhaps with traditions which were -current in Egypt (_Etudes sur le Timée_, Note xiii. § ix.). He does -not consider that the belief in Plato's Atlantis had any share in the -discoveries of Columbus. - -It may perhaps surprise modern readers who have a difficulty in -getting rid of the persuasion that there is a natural direction -_upwards_ and a natural direction _downwards_, to learn that both -Plato and Aristotle, and of course other philosophers also, had -completely overcome this difficulty. They were quite ready to allow -and to conceive that _down_ meant nothing but towards some centre, -and _up_, the opposite direction. (Aristotle has, besides, an -ingenious notion that while heavy bodies, as earth and water, tend -to the centre, and light bodies, as fire, tend from the centre, the -fifth element, of which the heavenly bodies are composed, tends to -move _round_ the centre.) - -Plato explains this in the most decided manner in the _Timæus_ (62, -C). "It is quite erroneous to suppose that there are two opposite -regions in the universe, one above and the other below; and that -heavy things naturally tend to the latter place. The heavens are -spherical, and every thing tends to the centre; and thus _above_ and -_below_ have no real meaning. If there be a solid globe in the -middle, {506} and if a person walk round it, he will become the -antipodes to himself, and the direction which is _up_ at one time -will be _down_ at another." - -The notion of _antipodes_, the inhabitants of the part of the globe -of the earth opposite to ourselves, was very familiar. Thus in -Cicero's _Academic Questions_ (ii. 39) one of the speakers says, -"Etiam dicitis esse e regione nobis, e contraria parte terræ, qui -adversis vestigiis stant contra nostra vestigia, quos Antipodas -vocatis." See also _Tusc. Disp._ i. 28 and v. 24. - - -_The Heliocentric System among the Ancients._ - -As the more clear-sighted of the ancients had overcome the natural -prejudice of believing that there is an absolute _up_ and _down_, so -had they also overcome the natural prejudice of believing that the -earth is at rest. Cicero says (_Acad. Quest._ ii. 39), "Hicetas of -Syracuse, as Theophrastus tells us, thinks that the heavens, the -sun, the moon, the stars, do not move; and that nothing does move -but the earth. The earth revolves about her axis with immense -velocity; and thus the same effect is produced as if the earth were -at rest and the heavens moved; and this, he says, Plato teaches in -the _Timæus_, though somewhat obscurely." Of course the assertion -that the moon and planets do not move, was meant of the diurnal -motion only. The passage referred to in the _Timæus_ seems to be -this (40, C)--"As to the Earth, which is our nurse, and which -_clings to_ the axis which stretches through the universe, God made -her the producer and preserver of day and night." The word -εἱλλομένην, which I have translated _clings to_, some translate -_revolves_; and an extensive controversy has prevailed, both in -ancient and modern times (beginning with Aristotle), whether Plato -did or did not believe in the rotation of the earth on her axis. -(See M. Cousin's Note on the _Timæus_, and M. Henri Martin's -Dissertation, Note xxxvii., in his _Etudes sur le Timée_.) The -result of this discussion seems to be that, in the _Timæus_, the -Earth is supposed to be at rest. It is however related by Plutarch -(_Platonic Questions_, viii. 1), that Plato in his old age repented -of having given to the Earth the place in the centre of the universe -which did not belong to it. - -In describing the Prelude to the Epoch of Copernicus (Book v. Chap. -i.), I have spoken of Philolaus, one of the followers of Pythagoras, -who lived at the time of Socrates, as having held the doctrine that -the earth revolves about the sun. This has been a current {507} -opinion;--so current, indeed, that the Abbé Bouillaud, or -Bullialdus, as we more commonly call him, gave the title of -_Philolaus_ to the defence of Copernicus which he published in 1639; -and Chiaramonti, an Aristotelian, published his answer under the -title of _Antiphilolaus_. In 1645 Bullialdus published his -_Astronomia Philolaica_, which was another exposition of the -heliocentric doctrine. - -Yet notwithstanding this general belief, it appears to be tolerably -certain that Philolaus did not hold the doctrine of the earth's -motion round the sun. (M. H. Martin, _Etudes sur le Timée_, 1841, -Note xxxvii. Sect. i.; and Bœckh, _De vera Indole Astronomiæ -Philolaicæ_, 1810.) In the system of Philolaus, the earth revolved -about _the central fire_; but this central fire was not the sun. The -Sun, along with the moon and planets, revolved in circles external -to the earth. The Earth had the _Antichthon_ or _Counter-Earth_ -between it and the centre; and revolving round this centre in one -day, the Antichthon, being always between it and the centre, was, -during a portion of the revolution, interposed between the Earth and -the Sun, and thus made night; while the Sun, by his proper motion, -produced the changes of the year. - -When men were willing to suppose the earth to be in motion, in order -to account for the recurrence of day and night, it is curious that -they did not see that the revolution of a spherical earth about an -axis passing through its centre was a scheme both simple and quite -satisfactory. Yet the illumination of a globular earth by a distant -sun, and the circumstances and phenomena thence resulting, appear to -have been conceived in a very confused manner by many persons. Thus -Tacitus (_Agric._ xii.), after stating that he has heard that in the -northern part of the island of Britain, the night disappears in the -height of summer, says, as his account of this phenomenon, that "the -extreme parts of the earth are low and level, and do not throw their -shadow upwards; so that the shade of night falls below the sky and -the stars." But, as a little consideration will show, it is the -globular form of the earth, and not the level character of the -country, which produces this effect. - -It is not in any degree probable that Pythagoras taught that the Earth -revolves round the Sun, or that it rotates on its own axis. Nor did -Plato hold either of these motions of the Earth. They got so far as to -believe in the Spherical Form of the Earth; and this was apparently -such an effort that the human mind made a pause before going any -further. "It required," says M. H. Martin, "a great struggle for {508} -men to free themselves from the prejudices of the senses, and to -interpret their testimony in such a manner as to conceive the -sphericity of the earth. It is natural that they should have stopped -at this point, before putting the earth in motion in space." - -Some of the expressions which have been understood, as describing a -system in which the Sun is the _centre of motion_, do really imply -merely the Sun is the _middle term_ of the series of heavenly bodies -which revolve round the earth: the series being Moon, Mercury, -Venus, Sun, Mars, Jupiter, Saturn. This is the case, for instance, -in a passage of Cicero's _Vision of Scipio_, which has been supposed -to imply, (as I have stated in the History,) that Mercury and Venus -revolve about the Sun. - -But though the doctrine of the diurnal rotation and annual -revolution of the earth is not the doctrine of Pythagoras, or of -Philolaus, or of Plato, it was nevertheless held by some of the -philosophers of antiquity. The testimony of Archimedes that this -doctrine was held by his contemporary Aristarchus of Samos, is -unquestionable and there is no reason to doubt Plutarch's assertion -that Seleucus further enforced it. - -It is curious that Copernicus appears not to have known anything of -the opinions of Aristarchus and Seleucus, which were really -anticipations of his doctrine; and to have derived his notion from -passages which, as I have been showing, contain no such doctrine. He -says, in his Dedication to Pope Paul III., "I found in Cicero that -Nicetas [or Hicetas] held that the earth was in motion: and in -Plutarch I found that some others had been of that opinion: and his -words I will transcribe that any one may read them: 'Philosophers in -general hold that the earth is at rest. But Philolaus the -Pythagorean teaches that it moves round the central fire in an -oblique circle, in the same direction as the Sun and the Moon. -Heraclides of Pontus and Ecphantus the Pythagorean give the earth a -motion, but not a motion of translation; they make it revolve like a -wheel about its own centre from west to east.'" This last opinion was -a correct assertion of the diurnal motion. - - -_The Eclipse of Thales._ - -"THE Eclipse of Thales" is so remarkable a point in the history of -astronomy, and has been the subject of so much discussion among -astronomers, that it ought to be more especially noticed. The -original {509} record is in the first Book of Herodotus's History -(chap. lxxiv.) He says that there was a war between the Lydians and -the Medes; and after various turns of fortune, "in the sixth year a -conflict took place; and on the battle being joined, it happened -that the day suddenly became night. And this change, Thales of -Miletus had predicted to them, definitely naming this year, in which -the event really took place. The Lydians and the Medes, when they -saw day turned into night, ceased from fighting; and both sides were -desirous of peace." Probably this prediction was founded upon the -Chaldean period of eighteen years, of which I have spoken in Section -11. It is probable, as I have already said, that this period was -discovered by noticing the recurrence of eclipses. It is to be -observed that Thales predicted only the year of the eclipse, not the -day or the month. In fact, the exact prediction of the circumstances -of an eclipse of the sun is a very difficult problem; much more -difficult, it may be remarked, than the prediction of the -circumstance of an eclipse of the moon. - -Now that the Theory of the Moon is brought so far towards -completeness, astronomers are able to calculate backwards the -eclipses of the sun which have taken place in former times; and the -question has been much discussed in what year this Eclipse of Thales -really occurred. The Memoir of Mr. Airy, the Astronomer Royal, on -this subject, in the _Phil. Trans._ for 1853, gives an account of -the modern examinations of this subject. Mr. Airy starts from the -assumption that the eclipse must have been one decidedly total; the -difference between such a one and an eclipse only _nearly_ total -being very marked. A total eclipse alone was likely to produce so -strong an effect on the minds of the combatants. Mr. Airy concludes -from his calculations that the eclipse predicted by Thales took -place B. C. 585. - -Ancient eclipses of the Moon and Sun, if they can be identified, are -of great value for modern astronomy; for in the long interval of -between two and three thousand years which separates them from our -time, those of the _inequalities_, that is, accelerations or -retardations of the Moon's motion, which go on increasing -constantly,[4\A] accumulate to a large amount; so that the actual -time and circumstances of the eclipse give astronomers the means of -determining what the rate of these accelerations or retardations has -been. Accordingly Mr. Airy has discussed, as even more important -than the eclipse of Thales, an eclipse which Diodorus relates to -have happened during an expedition of {510} Agathocles, the ruler of -Sicily, and which is hence known as the Eclipse of Agathocles. He -determines it to have occurred B. C. 310. - -[Note 4\A: Or at least for very long periods.] - -M. H. Martin, in Note xxxvii. to his _Etudes sur le Timée_, -discusses among other astronomical matters, the Eclipse of Thales. -He does not appear to render a very cordial belief to the historical -fact of Thales having delivered the prediction before the event. He -says that even if Thales did make such a prediction of an eclipse of -the sun, as he might do, by means of the Chaldean period of 18 -years, or 223 lunations, he would have to take the chance of its -being visible in Greece, about which he could only guess:--that no -author asserts that Thales, or his successors Anaximander and -Anaxagoras, ever tried their luck in the same way again:--that "en -revanche" we are told that Anaximander predicted an earthquake, and -Anaxagoras the fall of aërolites, which are plainly fabulous -stories, though as well attested as the Eclipse of Thales. He adds -that according to Aristotle, Thales and Anaximenes were so far from -having sound notions of cosmography, that they did not even believe -in the roundness of the earth. - - - -{{511}} -BOOK IV. - -PHYSICAL SCIENCE IN THE MIDDLE AGES. - -GENERAL REMARKS. - - -IN the twelfth Book of the _Philosophy_, in which I have given a -Review of Opinions on the Nature of Knowledge and the method of -seeking it, I have given some account of several of the most important -persons belonging to the ages now under consideration. I have there -(vol. ii. b. xii. p. 146) spoken of the manner in which remarks made -by Aristotle came to be accepted as fundamental maxims in the schools -of the middle ages, and of the manner in which they were discussed by -the greatest of the schoolmen, as Thomas Aquinas, Albertus Magnus, and -the like. I have spoken also (p. 149) of a certain kind of recognition -of the derivation of our knowledge from experience; as shown in -Richard of St. Victor, in the twelfth century. I have considered (p. -152) the plea of the admirers of those ages, that religious authority -was not claimed for physical science. - -I have noticed that the rise of Experimental Philosophy exhibited -two features (chap. vii. p. 155), the Insurrection against -Authority, and the Appeal to Experience: and as exemplifying these -features, I have spoken of Raymond Lully and of Roger Bacon. I have -further noticed the opposition to the prevailing Aristotelian -dogmatism manifested (chap. viii.) by Nicolas of Cus, Marsilius -Ficinus, Francis Patricius, Picus of Mirandula, Cornelius Agrippa, -Theophrastus Paracelsus, Robert Fludd. I have gone on to notice the -Theoretical Reformers of Science (chap. ix.), Bernardinus Telesius, -Thomas Campanella, Andreas Cæsalpinus, Peter Ramus; and the -Protestant Reformers, as Melancthon. After these come the Practical -Reformers of Science, who have their place in the subsequent history -of Inductive Philosophy; Leonardo da Vinci, and the Heralds of the -dawning light of real science, whom Francis Bacon welcomes, as -Heralds are accosted in Homer: - Χαίρετε Κήρυκες Διὸς ἄγγελοι ἠδὲ καὶ ἀνδρῶν. - Hail, Heralds, messengers of Gods and men! {512} - -I have, in the part of the _Philosophy_ referred to, discussed the -merits and defects of Francis Bacon's _Method_, and I shall have -occasion, in the next Book, to speak of his mode of dealing with the -positive science of his time. There is room for much more reflexion on -these subjects, but the references now made may suffice at present. - - - - -CHAPTER V. - -PROGRESS IN THE MIDDLE AGES. - - -_Thomas Aquinas._ - -AQUINAS wrote (besides the _Summa_ mentioned in the text) a -Commentary on the Physics of Aristotle: _Commentaria in Aristotelis -Libros Physicorum_, Venice, 1492. This work is of course of no -scientific value; and the commentary consists of empty permutations -of abstract terms, similar to those which constitute the main -substance of the text in Aristotle's physical speculations. There -is, however, an attempt to give a more technical form to the -propositions and their demonstrations. As specimens of these, I may -mention that in Book vi. c. 2, we have a demonstration that when -bodies move, the time and the magnitude (that is, the space -described), are divided similarly; with many like propositions. And -in Book viii. we have such propositions as this (c. 10): -"Demonstration that a finite mover (_movens_) cannot move anything -in an infinite time." This is illustrated by a diagram in which two -hands are represented as engaged in moving a whole sphere, and one -hand in moving a hemisphere. - -This mode of representing force, in diagrams illustrative of -mechanical reasonings, by human hands pushing, pulling, and the -like, is still employed in elementary books. Probably this is the -first example of such a mode of representation. - - -_Roger Bacon._ - -THIS writer, a contemporary of Thomas Aquinas, exhibits to us a kind -of knowledge, speculation, and opinion, so different from that of any -known person near his time, that he deserves especial notice here; -{513} and I shall transfer to this place the account which I have -given of him in the _Philosophy_. I do this the more willingly because -I regard the existence of such a work as the _Opus Majus_ at that -period as a problem which has never yet been solved. Also I may add, -that the scheme of the Contents of this work which I have given, -deserves, as I conceive, more notice than it has yet received. - -"Roger Bacon was born in 1214, near Ilchester, in Somersetshire, of -an old family. In his youth he was a student at Oxford, and made -extraordinary progress in all branches of learning. He then went to -the University of Paris, as was at that time the custom of learned -Englishmen, and there received the degree of Doctor of Theology. At -the persuasion of Robert Grostête, bishop of Lincoln, he entered the -brotherhood of Franciscans in Oxford, and gave himself up to study -with extraordinary fervor. He was termed by his brother monks -_Doctor Mirabilis_. We know from his own works, as well as from the -traditions concerning him, that he possessed an intimate -acquaintance with all the science of his time which could be -acquired from books; and that he had made many remarkable advances -by means of his own experimental labors. He was acquainted with -Arabic, as well as with the other languages common in his time. In -the title of his works, we find the whole range of science and -philosophy, Mathematics and Mechanics, Optics, Astronomy, Geography, -Chronology, Chemistry, Magic, Music, Medicine, Grammar, Logics, -Metaphysics, Ethics, and Theology; and judging from those which are -published, these works are full of sound and exact knowledge. He is, -with good reason, supposed to have discovered, or to have had some -knowledge of, several of the most remarkable inventions which were -made generally known soon afterwards; as gunpowder, lenses, burning -specula, telescopes, clocks, the correction of the calendar, and the -explanation of the rainbow. - -"Thus possessing, in the acquirements and habits of his own mind, -abundant examples of the nature of knowledge and of the process of -invention, Roger Bacon felt also a deep interest in the growth and -progress of science, a spirit of inquiry respecting the causes which -produced or prevented its advance, and a fervent hope and trust in -its future destinies; and these feelings impelled him to speculate -worthily and wisely respecting a Reform of the Method of -Philosophizing. The manuscripts of his works have existed for nearly -six hundred years in many of the libraries of Europe, and especially -in those of England; and for a long period the very imperfect -portions of them which were {514} generally known, left the -character and attainments of the author shrouded in a kind of -mysterious obscurity. About a century ago, however, his _Opus Majus_ -was published[5\A] by Dr. S. Jebb, principally from a manuscript in -the library of Trinity College, Dublin; and this contained most or -all of the separate works which were previously known to the public, -along with others still more peculiar and characteristic. We are -thus able to judge of Roger Bacon's knowledge and of his views, and -they are in every way well worthy our attention. - -[Note 5\A: _Fratris Rogeri Bacon Ordinis Minorum_ Opus Majus _ad -Clementem Quartum, Pontificem Romanum, ex MS. Codice Dubliniensi cum -aliis quibusdam collato nunc primum edidit_ S. Jebb, M.D. Londini, -1733.] - -"The _Opus Majus_ is addressed to Pope Clement the Fourth, whom -Bacon had known when he was legate in England as Cardinal-bishop of -Sabina, and who admired the talents of the monk, and pitied him for -the persecutions to which he was exposed. On his elevation to the -papal chair, this account of Bacon's labours and views was sent, at -the earnest request of the pontiff. Besides the _Opus Majus_, he -wrote two others, the _Opus Minus_ and _Opus Tertium_; which were -also sent to the pope, as the author says,[6\A] 'on account of the -danger of roads, and the possible loss of the work.' These works -still exist unpublished, in the Cottonian and other libraries. - -[Note 6\A: _Opus Majus_, Præf.] - -"The _Opus Majus_ is a work equally wonderful with regard to its -general scheme, and to the special treatises with which the outlines -of the plan are filled up. The professed object of the work is to -urge the necessity of a reform in the mode of philosophizing, to set -forth the reasons why knowledge had not made a greater progress, to -draw back attention to the sources of knowledge which had been -unwisely neglected, to discover other sources which were yet almost -untouched, and to animate men in the undertaking, by a prospect of -the vast advantages which it offered. In the developement of this -plan, all the leading portions of science are expounded in the most -complete shape which they had at that time assumed; and improvements -of a very wide and striking kind are proposed in some of the -principal of these departments. Even if the work had had no leading -purpose, it would have been highly valuable as a treasure of the -most solid knowledge and soundest speculations of the time; even if -it had contained no such details, it would have been a work most -remarkable for its general views and scope. It may be considered as, -at the same time, the _Encyclopedia_ and the _Novum Organon_ of the -thirteenth century. {515} - -"Since this work is thus so important in the history of Inductive -Philosophy I shall give, in a Note, a view[7\A] of its divisions and -contents. But I must now endeavor to point out more especially the -way in which the various principles, which the reform of scientific -method involved, are here brought into view. - -[Note 7\A: Contents of Roger Bacon's _Opus Majus_: -Part I. On the four causes of human ignorance:--Authority, Custom, - Popular Opinion, and the Pride of supposed Knowledge. -Part II. On the source of perfect wisdom in the Sacred Scripture. -Part III. On the Usefulness of Grammar. -Part IV. On the Usefulness of Mathematics. - (1.) The Necessity of Mathematics in Human Things - (published separately as the _Specula Mathematica_). - (2.) The Necessity of Mathematics in Divine Things.--1°. - This study has occupied holy men: 2°. Geography: 3°. - Chronology: 4°. Cycles; the Golden Number, &c.: 5°. - Natural Phenomena, as the Rainbow: 6°. Arithmetic: - 7°. Music. - (3.) The Necessity of Mathematics in Ecclesiastical - Things. 1°. The Certification of Faith: 2°. The - Correction of the Calendar. - (4.) The Necessity of Mathematics in the State.--1°. Of - Climates: 2°. Hydrography: 3°. Geography: 4°. Astrology. -Part V. On Perspective (published separately as _Perspectiva_). - (1.) The organs of vision. - (2.) Vision in straight lines. - (3.) Vision reflected and refracted. - (4.) De multiplicatione specierum (on the propagation of - the impressions of light, heat, &c.) -Part VI. On Experimental Science.] - -"One of the first points to be noticed for this purpose, is the -resistance to authority; and at the stage of philosophical history -with which we here have to do, this means resistance to the -authority of Aristotle, as adopted and interpreted by the Doctors of -the Schools. Bacon's work[8\A] is divided into Six Parts; and of -these Parts, the First is, Of the four universal Causes of all Human -Ignorance. The causes thus enumerated[9\A] are:--the force of -unworthy authority;--traditionary habit;--the imperfection of the -undisciplined senses;--and the disposition to conceal our ignorance -and to make an ostentatious show of our knowledge. These influences -involve every man, occupy every condition. They prevent our -obtaining the most useful and large and fair doctrines of wisdom, -the secrets of all sciences and arts. He then proceeds to argue, -from the testimony of philosophers themselves, that the authority of -antiquity, and especially of Aristotle, is not infallible. 'We -find[10\A] their books full of doubts, obscurities, and -perplexities. They {516} scarce agree with each other in one empty -question or one worthless sophism, or one operation of science, as -one man agrees with another in the practical operations of medicine, -surgery, and the like arts of secular men. Indeed,' he adds,[11\A] -'not only the philosophers, but the saints have fallen into errors -which they have afterwards retracted,' and this he instances in -Augustin, Jerome, and others. He gives an admirable sketch of the -progress of philosophy from the Ionic School to Aristotle; of whom -he speaks with great applause. 'Yet,' he adds, 'those who came after -him corrected him in some things, and added many things to his -works, and shall go on adding to the end of the world.' Aristotle, -he adds, is now called peculiarly[12\A] the Philosopher, 'yet there -was a time when his philosophy was silent and unregarded, either on -account of the rarity of copies of his works, or their difficulty, -or from envy; till after the time of Mahomet, when Avicenna and -Averroes, and others, recalled this philosophy into the full light -of exposition. And although the Logic and some other works were -translated by Boethius from the Greek, yet the philosophy of -Aristotle first received a quick increase among the Latins at the -time of Michael Scot; who, in the year of our Lord 1230, appeared, -bringing with him portions of the books of Aristotle on Natural -Philosophy and Mathematics. And yet a small part only of the works -of this author is translated, and a still smaller part is in the -hands of common students.' He adds further[13\A] (in the Third Part -of the _Opus Majus_, which is a Dissertation on Language) that the -translations which are current of these writings, are very bad and -imperfect. With these views, he is moved to express himself somewhat -impatiently[14\A] respecting these works: 'If I had,' he says, -'power over the works of Aristotle, I would have them all burnt; for -it is only a loss of time to study in them, and a course of error, -and a multiplication of ignorance beyond expression.' 'The common -herd of students,' he says, 'with their heads, have no principle by -which they can be excited to any worthy employment; and hence they -mope and make asses of themselves over their bad translations, and -lose their time, and trouble, and money.' {517} - -[Note 8\A: _Op. Maj._ p. 1.] - -[Note 9\A: Ib. p. 2.] - -[Note 10\A: Ib. p. 10.] - -[Note 11\A: _Op. Maj._ p. 36.] - -[Note 12\A: _Autonomaticè_.] - -[Note 13\A: _Op. Maj._ p. 46.] - -[Note 14\A: See _Pref._ to Jebb's edition. The passages there quoted, -however, are not extracts from the _Opus Majus_, but (apparently) from -the _Opus Minus_ (_MS. Cott._ Tib. c . 5). "Si haberem potestatem -supra libros Aristotelis, ego facerem omnes cremari; quia non est nisi -temporis amissio studere in illis, et causa erroris, et multiplicatio -ignorantiæ ultra id quod valeat explicari. . . . Vulgus studentum cum -capitibus suis non habet unde excitetur ad aliquid dignum, et ideo -languet et _asininat_ circa male translata, et tempus et studium -amittit in omnibus et expensas."] - -"The remedies which he recommends for these evils, are, in the first -place, the study of that only perfect wisdom which is to be found in -the Sacred Scripture;[15\A] in the next place, the study of -mathematics and the use of experiment.[16\A] By the aid of these -methods, Bacon anticipates the most splendid progress for human -knowledge. He takes up the strain of hope and confidence which we -have noticed as so peculiar in the Roman writers; and quotes some of -the passages of Seneca which we adduced in illustration of -this:--that the attempts in science were at first rude and -imperfect, and were afterwards improved;--that the day will come, -when what is still unknown shall be brought to light by the progress -of time and the labors of a longer period;--that one age does not -suffice for inquiries so wide and various;--that the people of -future times shall know many things unknown to us;--and that the -time shall arrive when posterity will wonder that we overlooked what -was so obvious. Bacon himself adds anticipations more peculiarly in -the spirit of his own time. 'We have seen,' he says, at the end of -the work, 'how Aristotle, by the ways which wisdom teaches, could -give to Alexander the empire of the world. And this the Church ought -to take into consideration against the infidels and rebels, that -there may be a sparing of Christian blood, and especially on account -of the troubles that shall come to pass in the days of Antichrist; -which by the grace of God it would be easy to obviate, if prelates -and princes would encourage study, and join in searching out the -secrets of nature and art.' - -[Note 15\A: Part ii.] - -[Note 16\A: Parts iv. v. and vi.] - -"It may not be improper to observe here that this belief in the -appointed progress of knowledge, is not combined with any -overweening belief in the unbounded and independent power of the -human intellect. On the contrary, one of the lessons which Bacon -draws from the state and prospects of knowledge, is the duty of -faith and humility. 'To him,' he says,[17\A] 'who denies the truth -of the faith because he is unable to understand it, I will propose -in reply the course of nature, and as we have seen it in examples.' -And after giving some instances, he adds, 'These, and the like, -ought to move men and to excite them to the reception of divine -truths. For if, in the vilest objects of creation, truths are found, -before which the inward pride of man must bow, and believe though it -cannot understand, how much more should man humble his mind before -the glorious truths of God!' He had before said:[18\A] 'Man is -incapable of perfect wisdom in this life; it is hard for {518} him -to ascend towards perfection, easy to glide downwards to falsehoods -and vanities: let him then not boast of his wisdom, or extol his -knowledge. What he knows is little and worthless, in respect of that -which he believes without knowing; and still less, in respect of -that which he is ignorant of. He is mad who thinks highly of his -wisdom; he most mad, who exhibits it as something to be wondered -at.' He adds, as another reason for humility, that he has proved by -trial, he could teach in one year, to a poor boy, the marrow of all -that the most diligent person could acquire in forty years' -laborious and expensive study. - -[Note 17\A: _Op. Maj._ p. 476.] - -[Note 18\A: Ib. p. 15.] - -"To proceed somewhat more in detail with regard to Roger Bacon's views -of a Reform in Scientific Inquiry, we may observe that by making -Mathematics and Experiment the two great points of his recommendation, -he directed his improvement to the two essential parts of all -knowledge, Ideas and Facts, and thus took the course which the most -enlightened philosophy would have suggested. He did not urge the -prosecution of experiment, to the comparative neglect of the existing -mathematical sciences and conceptions; a fault which there is some -ground for ascribing to his great namesake and successor Francis -Bacon: still less did he content himself with a mere protest against -the authority of the schools, and a vague demand for change, which was -almost all that was done by those who put themselves forward as -reformers in the intermediate time. Roger Bacon holds his way steadily -between the two poles of human knowledge; which, as we have seen, it -is far from easy to do. 'There are two modes of knowing,' says -he;[19\A] 'by argument, and by experiment. Argument concludes a -question; but it does not make us feel certain, or acquiesce in the -contemplation of truth, except the truth be also found to be so by -experience.' It is not easy to express more decidedly the clearly-seen -union of exact conceptions with certain facts, which, as we have -explained, constitutes real knowledge. - -[Note 19\A: _Op. Maj._ p. 445; see also p. 448. "Scientiæ aliæ -sciunt sua principia invenire per experimenta, sed conclusiones per -argumenta facta ex principiis inventis. Si vero debeant habere -experientiam conclusionum suarum particularem et completam, tunc -oportet quod habeant per adjutorium istius scientiæ nobilis -(experimentalis)."] - -"One large division of the _Opus Majus_ is 'On the Usefulness of -Mathematics,' which is shown by a copious enumeration of existing -branches of knowledge, as Chronology, Geography, the Calendar and -(in a separate Part) Optics. There is a chapter,[20\A] in which it -is proved {519} by reason, that all science requires mathematics. -And the arguments which are used to establish this doctrine, show a -most just appreciation of the office of mathematics in science. They -are such as follows:--That other sciences use examples taken from -mathematics as the most evident:--That mathematical knowledge is, as -it were, innate to us, on which point he refers to the well-known -dialogue of Plato, as quoted by Cicero:--That this science, being -the easiest, offers the best introduction to the more -difficult:--That in mathematics, things as known to us are identical -with things as known to nature:--That we can here entirely avoid -doubt and error, and obtain certainty and truth:--That mathematics -is prior to other sciences in nature, because it takes cognizance of -quantity, which is apprehended by intuition (_intuitu intellectus_). -'Moreover,' he adds,[21\A] 'there have been found famous men, as -Robert, bishop of Lincoln, and Brother Adam Marshman (de Marisco), -and many others, who by the power of mathematics have been able to -explain the causes of things; as may be seen in the writings of -these men, for instance, concerning the Rainbow and Comets, and the -generation of heat, and climates, and the celestial bodies.' - -[Note 20\A: Ib. p. 60.] - -[Note 21\A: _Op. Maj._ p. 64.] - -"But undoubtedly the most remarkable portion of the _Opus Majus_ is -the Sixth and last Part, which is entitled 'De Scientia -experimentali.' It is indeed an extraordinary circumstance to find a -writer of the thirteenth century, not only recognizing experiment as -one source of knowledge, but urging its claims as something far more -important than men had yet been aware of, exemplifying its value by -striking and just examples, and speaking of its authority with a -dignity of diction which sounds like a foremurmur of the Baconian -sentences uttered nearly four hundred years later. Yet this is the -character of what we here find.[22\A] 'Experimental science, the -sole mistress of speculative sciences, has three great Prerogatives -among other parts of knowledge: First she tests by experiment the -noblest conclusions of all other sciences: Next she discovers -respecting the notions which other sciences deal with, magnificent -truths to which these sciences of themselves can by no means attain: -her Third dignity is, that she by her own power and without respect -of other sciences, investigates the secrets of nature.' {520} - -[Note 22\A: "Veritates magnificas in terminis aliarum scientiarum in -quas per nullam viam possunt illæ scientiæ, hæc sola scientiarum -domina speculativarum, potest dare."--_Op. Maj._ p. 465.] - -"The examples which Bacon gives of these 'Prerogatives' are very -curious, exhibiting, among some error and credulity, sound and clear -views. His leading example of the First Prerogative is the Rainbow, of -which the cause, as given by Aristotle, is tested by reference to -experiment with a skill which is, even to us now, truly admirable. The -examples of the Second Prerogative are three--_first_, the art of -making an artificial sphere which shall move with the heavens by -natural influences, which Bacon trusts may be done, though astronomy -herself cannot do it--'et tunc,' he says, 'thesaurum unius regis -valeret hoc instrumentum;'--_secondly_, the art of prolonging life, -which experiment may teach, though medicine has no means of securing -it except by regimen;[23\A]--_thirdly_, the art of making gold finer -than fine gold, which goes beyond the power of alchemy. The Third -Prerogative of experimental science, arts independent of the received -sciences, is exemplified in many curious examples, many of them -whimsical traditions. Thus it is said that the character of a people -may be altered by altering the air.[24\A] Alexander, it seems, applied -to Aristotle to know whether he should exterminate certain nations -which he had discovered, as being irreclaimably barbarous; to which -the philosopher replied, 'If you can alter their air, permit them to -live; if not, put them to death.' In this part, we find the suggestion -that the fire-works made by children, of saltpetre, might lead to the -invention of a formidable military weapon. - -[Note 23\A: One of the ingredients of a preparation here mentioned, -is the flesh of a dragon, which, it appears, is used as food by the -Ethiopians. The mode of preparing this food cannot fail to amuse the -reader. "Where there are good flying dragons, by the art which they -possess, they draw them out of their dens, and have bridles and -saddles in readiness, and they ride upon them, and make them bound -about in the air in a violent manner, that the hardness and -toughness of the flesh may be reduced, as boars are hunted and bulls -are baited before they are killed for eating."--_Op. Maj._ p. 470.] - -[Note 24\A: _Op. Maj._ p. 472.] - -"It could not be expected that Roger Bacon, at a time when -experimental science hardly existed, could give any _precepts_ for -the discovery of truth by experiment. But nothing can be a better -_example_ of the method of such investigation, than his inquiry -concerning the cause of the Rainbow. Neither Aristotle, nor -Avicenna, nor Seneca, he says, have given us any clear knowledge of -this matter, but experimental science can do so. Let the -experimenter (_experimentator_) consider the cases in which he finds -the same colors, as the hexagonal crystals from Ireland and India; -by looking into these he will see colors like those of the rainbow. -Many think that this arises from some {521} special virtue of these -stones and their hexagonal figure; let therefore the experimenter go -on, and he will find the same in other transparent stones, in dark -ones as well as in light-colored. He will find the same effect also -in other forms than the hexagon, if they be furrowed in the surface, -as the Irish crystals are. Let him consider too, that he sees the -same colors in the drops which are dashed from oars in the -sunshine;--and in the spray thrown by a mill wheel;--and in the dew -drops which lie on the grass in a meadow on a summer morning;--and -if a man takes water in his mouth and projects it on one side into a -sunbeam;--and if in an oil lamp hanging in the air, the rays fall in -certain positions upon the surface of the oil;--and in many other -ways, are colors produced. We have here a collection of instances, -which are almost all examples of the same kind as the phenomenon -under consideration; and by the help of a principle collected by -induction from these facts, the colors of the rainbow were -afterwards really explained. - -"With regard to the form and other circumstances of the bow he is -still more precise. He bids us measure the height of the bow and of -the sun, to show that the centre of the bow is exactly opposite to -the sun. He explains the circular form of the bow,--its being -independent of the form of the cloud, its moving when we move, its -flying when we follow,--by its consisting of the reflections from a -vast number of minute drops. He does not, indeed, trace the course -of the rays through the drop, or account for the precise magnitude -which the bow assumes; but he approaches to the verge of this part -of the explanation; and must be considered as having given a most -happy example of experimental inquiry into nature, at a time when -such examples were exceedingly scanty. In this respect, he was more -fortunate than Francis Bacon, as we shall hereafter see. - -"We know but little of the biography of Roger Bacon, but we have -every reason to believe that his influence upon his age was not -great. He was suspected of magic, and is said to have been put into -close confinement in consequence of this charge. In his work he -speaks of Astrology, as a science well worth cultivating. 'But,' -says he, 'Theologians and Decretists, not being learned in such -matters, and seeing that evil as well as good may be done, neglect -and abhor such things, and reckon them among Magic Arts.' We have -already seen, that at the very time when Bacon was thus raising his -voice against the habit of blindly following authority, and seeking -for all science in Aristotle, Thomas Aquinas was employed in -fashioning Aristotle's tenets into that fixed form in which they -became the great impediment to the {522} progress of knowledge. It -would seem, indeed, that something of a struggle between the -progressive and stationary powers of the human mind was going on at -this time. Bacon himself says,[25\A] 'Never was there so great an -appearance of wisdom, nor so much exercise of study in so many -Faculties, in so many regions, as for this last forty years. Doctors -are dispersed everywhere, in every castle, in every burgh, and -especially by the students of two Orders, (he means the Franciscans -and Dominicans, who were almost the only religious orders that -distinguished themselves by an application to study,[26\A]) which -has not happened except for about forty years. And yet there was -never so much ignorance, so much error.' And in the part of his work -which refers to Mathematics, he says of that study,[27\A] that it is -the door and the key of the sciences; and that the neglect of it for -thirty or forty years has entirely ruined the studies of the Latins. -According to these statements, some change, disastrous to the -fortunes of science, must have taken place about 1230, soon after -the foundation of the Dominican and Franciscan Orders.[28\A] Nor can -we doubt that the adoption of the Aristotelian philosophy by these -two Orders, in the form in which the Angelical Doctor had -systematized it, was one of the events which most tended to defer, -for three centuries, the reform which Roger Bacon urged as a matter -of crying necessity in his own time." - -[Note 25\A: Quoted by Jebb, Pref. to _Op. Maj._] - -[Note 26\A: Mosheim, _Hist._ iii. 161.] - -[Note 27\A: _Op. Maj._ p. 57.] - -[Note 28\A: Mosheim, iii. 161.] - -It is worthy of remark that in the _Opus Majus_ of Roger Bacon, as -afterwards in the _Novum Organon_ of Francis Bacon, we have certain -features of experimental research pointed out conspicuously as -_Prærogativæ_: although in the former, this term is employed to -designate the superiority of experimental science in general to the -science of the schools; in the latter work, the term is applied to -certain classes of experiments as superior to others. - - - -{{523}} -BOOK V. - -FORMAL ASTRONOMY. - - - -CHAPTER I. - -PRELUDE TO COPERNICUS. - - -_Nicolas of Cus._ - -I WILL quote the passage, in the writings of this author, which -bears upon the subject in question. I translate it from the edition -of his book _De Docta Ignorantia_, from his works published at Basil -in 1565. He praises _Learned Ignorance_--that is, Acknowledged -Ignorance--as the source of knowledge. His ground for asserting the -motions of the earth is, that there is no such thing as perfect -rest, or an exact centre, or a perfect circle, nor perfect -uniformity of motion. "Neque verus circulus dabilis est, quinetiam -verior dari possit, neque unquam uno tempore sicut alio æqualiter -præcisè, aut movetur, aut circulum veri similem, æqualem describit, -etiamsi nobis hoc non appareat. Et ubicumque quis fuerit, se in -centro esse credit." (Lib. i. cap. xi. p. 39.) He adds, "The -Ancients did not attain to this knowledge, because they were wanting -in Learned Ignorance. Now it is manifest to us that the Earth is -truly in motion, although this do not appear to us; since we do not -apprehend motion except by comparison with something fixed. For if -any one were in a boat in the middle of a river, ignorant that the -water was flowing, and not seeing the banks, how could he apprehend -that the boat was moving? And thus since every one, whether he be in -the Earth, or in the Sun, or in any other star, thinks that he is in -an immovable centre, and that everything else is moving; he would -assign different poles for himself, others as being in the Sun, -others in the Earth, and others in the Moon, and so of the rest. -Whence the machine of the world is as if it had its centre -everywhere and its circumference nowhere." This train of thought -{524} might be a preparation for the reception of the Copernican -system; but it is very different from the doctrine that the Sun is -the centre of the Planetary Motions. - - - - -CHAPTER II. - -THE COPERNICAN THEORY. - - -_The Moon's Rotation._ - -I HAVE said, in page 264, that a confusion of mind produced by the -double reference of motion to absolute space, and to a centre of -revolution, often leads persons to dispute whether the Moon, while -she revolves about the Earth, always turning to it the same face, -revolves about her axis or not. - -This dispute has been revived very lately, and has been conducted in -a manner which shows that popular readers and writers have made -little progress in the clearness of their notions during the last -two or three centuries; and that they have accepted the Newtonian -doctrines in words with a very dim apprehension of their real import. - -If the Moon were carried round the Earth by a rigid arm revolving -about the Earth as a centre, being rigidly fastened to this arm, as -a mimic Moon might be, in a machine constructed to represent her -motions, this contrivance, while it made her revolve round the Earth -would make her also turn the same face to the Earth: and if we were -to make such a machine the standard example of rotation, the Moon -might be said not to rotate on her axis. - -But we are speedily led to endless confusion by taking this case as -the standard of rotation. For the selection of the centre of -rotation in a system which includes several bodies is arbitrary. The -Moon turns all her faces successively to the Sun, and therefore with -regard to the Sun, she does rotate on her axis; and yet she revolves -round the Sun as truly as she revolves round the Earth. And the only -really simple and consistent mode of speaking of rotation, is to -refer the motion not to any relative centre, but to absolute space. - -This is the argument merely on the ground of simplicity and -consistency. But we find physical reasons, as well as mathematical, -for referring the motion to absolute space. If a cup of water be -carried round a centre so as to describe a circle, a straw floating -on the surface {525} of the water, if it point to the centre of the -circle at first, does not continue to do so, but remains parallel to -itself during the whole revolution. Now there is no cause to make -the water (and therefore the straw) rotate on its axis; and -therefore it is not a clear or convenient way of speaking, to say -that the water in this case does revolve on its axis. But if the -water in this case do not revolve on its axis, a body in the case of -the Moon does revolve on its axis. - -The difficulty, as I have said in the text, is of the same nature as -that which the Copernicans at first found in the parallel motion of -the Earth's axis. In order to make the axis of the Earth's rotation -remain parallel to itself while the Earth revolves about the Sun, in -a mechanical representation, some machinery is needed _in addition_ to -the machinery which produces the revolution round the centre (the -Sun): but the simplest way of regarding the parallel motion is, to -conceive that the axis has no motion except that which carries it -round the central Sun. And it was seen, when the science of -Mechanics was established, that no force was needed in nature to -produce this parallelism of the Earth's axis. It was therefore the -only scientific course, to conceive this parallelism as not being a -rotation: and in like manner we are to conceive the parallelism of a -revolving body as not being a rotation. - - -_M. Foucault's Proofs of the Earth's Motion._ - -IT was hardly to be expected that we should discover, in our own -day, a new physical proof of the earth's motion, yet so it has been. -The experiments of M. Foucault have enabled us to see the Rotation -of the Earth on its axis, as taking place, we may say, before our -eyes. These experiments are, in fact, a result of what has been said -in speaking of the Moon's rotation: namely, That the mechanical -causes of motion operate with reference to absolute, not relative, -space; so that where there is no cause operating to change a motion, -it will retain its direction in _absolute_ space; and may on that -account seem to change, if regarded relatively in a _limited_ space. - -In M. Foucault's first experiment, the motion employed was that of a -pendulum. If a pendulum oscillate quite freely, there is no cause -acting to change the vertical plane of oscillation _absolutely_; for -the forces which produce the oscillation are _in_ the vertical -plane. But if the vertical plane remain the same _absolutely_, at a -spot on the surface of the revolving Earth, it will change -_relatively_ to the spectator. He will see the pendulum oscillate in -a vertical plane which gradually {526} turns away from its first -position. Now this is what really happens; and thus the revolution -of the Earth in absolute space is experimentally proved. - -In subsequent experiments, M. Foucault has used the rotation of a -body to prove the same thing. For when a body rotates freely, acted -upon by no power, there is nothing to change the position of the -axis of rotation in absolute space. But if the position of the axis -remain the same in absolute space, it will, in virtue of its -relative motion, change as seen by a spectator at any spot on the -rotating Earth. By taking a heavy disk or globe and making it rotate -on its axis rapidly, the force of absolute permanence (as compared -with the inevitable casual disturbances arising from the machinery -which supports the revolving disk) becomes considerable and hence -the relative motion can, in this way also, be made visible. - -Mr. De Morgan has said (_Comp. to Brit. Alm._ 1836, p. 18) that -astronomy does not supply any argument for the earth's motion which -is absolutely and demonstrably conclusive, till we come to the -Aberration of Light. But we may now venture to say that the -experiments of M. Foucault prove the diurnal motion of the Earth in -the most conclusive manner, by palpable and broad effects, if we -accept the doctrines of the Science of Mechanics: while Aberration -proves the annual motion, if we suppose that we can observe the -places of the fixed stars to the accuracy of a few seconds; and if -we accept, in addition to the doctrines of Mechanics, the doctrine -of the motion of light with a certain great velocity. - - - - -CHAPTER III. - -SEQUEL TO COPERNICUS. - - -_English Copernicans._ - -PROFESSOR DE MORGAN has made numerous and interesting contributions -to the history of the progress and reception of the Copernican -System. These are given mainly in the _Companion to the British -Almanac_; especially in his papers entitled "Old Arguments against -the Motion of the Earth" (1836); "English Mathematical and -Astronomical Writers" (1837); "On the Difficulty of Correct {527} -Description of Books" (1853); "The Progress of the Doctrine of the -Earth's Motion between the Times of Copernicus and Galileo" (1855). -In these papers he insists very rightly upon the distinction between -the _mathematical_ and the _physical_ aspect of the doctrines of -Copernicus: a distinction corresponding very nearly with the -distinction which we have drawn between Formal and Physical -Astronomy; and in accordance with which we have given the history of -the Heliocentric Doctrine as a Formal Theory in Book v., and as a -Physical Theory in Book vii. - -Another interesting part of Mr. De Morgan's researches are the -notices which he has given of the early assertors of the -heliocentric doctrine in England. These make their appearance as -soon as it was well possible they should exist. The work of -Copernicus was published, as we have said, in 1543. In September -1556, John Field published an Ephemeris for 1557, "juxta Copernici -et Reinholdi Canones," in the preface to which he avows his -conviction of the truth of the Copernican hypothesis. Robert -Recorde, the author of various works on Arithmetic, published among -others, "The Pathway to Knowledge" in 1551. In this book, the author -discusses the question of the "quietnes of the earth," and professes -to leave it undecided: but Mr. De Morgan (_Comp. A._ 1837, p. 33) -conceives that it appears from what is said, that he was really a -Copernican, but did not think the world ripe for any such doctrine. - -Mr. Joseph Hunter also has brought to notice[29\A] the claims of -Field, whom he designates as the _Proto-Copernican_ of England. He -quotes the Address to the Reader prefixed to his first _Ephemeris_, -and dated May 31, 1556, in which he says that, since abler men -decline the task, "I have therefore published this Ephemeris of the -year 1557, following in it as my authorities, N. Copernicus and -Erasmus Reinhold, whose writings are established and founded on -true, certain, and authentic demonstrations." I conceive that this -passage, however, only shows that Field had adopted the Copernican -scheme as a basis for the calculation of Ephemerides; which, as Mr. -De Morgan has remarked, is a very different thing from accepting it -as a physical truth. Field, in this same address, makes mention of -the errors "illius turbæ quæ Alphonsi utitur hypothesi;" but the -word _hypothesis_ is still indecisive. - -[Note 29\A: _Ast. Soc. Notices_, vol. iii. p. 3 (1833).] - -As evidence that Field was regarded in his own day as a man who -{528} had rendered good service to science, Mr. Hunter notices that, -in 1558, the Heralds granted to him the right of using, with his -arms, the crest or additional device of a red right arm issuing from -the clouds, and presenting a golden armillary sphere. - -Recorde's claims depend upon a passage in a Dialogue between -_Master_ and _Scholar_, in which the Master expounds the doctrine of -Copernicus, and the authorities against it; to which the Scholar -answers, taking the common view: "Nay, sir, in good faith I desire -not to hear such vaine phantasies, so far against common reason, and -repugnant to all the learned multitude of wryters, and therefore let -it passe for ever and a day longer." The Master, more sagely, warns -him against a hasty judgment, and says, "Another time I will so -declare his supposition, that you shall not only wonder to hear it, -but also peradventure be as earnest then to credit it, as you now -are now to condemne it." I conceive that this passage proves Mr. De -Morgan's assertion, that Recorde was a Copernican, and very likely -the first in England. - -In 1555, also, Leonard Digges published his "Prognostication -Everlasting;" but this is, as Mr. De Morgan says (_Comp. A._ 1837, p. -40) a meteorological work. It was republished in 1592 by his son -Thomas Digges with additions; and as these have been the occasion of -some confusion among those who have written on the history of -astronomy, I am glad to be able, through the kindness of Professor -Walker of Oxford, to give a distinct account of the editions of the -work. - -In the Bodleian Library, besides the editions of 1555 and 1592 of -the "Prognostication Everlasting," there is an edition of 1564. It -is still decidedly Ptolemaic, and contains a Diagram representing a -number of concentric circles, which are marked, in order, as-- -"The Earth, - Moone, - Venus, - Mercury, - Sunne, - Mars, - Jupiter, - Saturne, - The Starrie Firmament, - The Crystalline Heavens, - The First Mover, - The Abode of God and the Elect. Here the Learned do approve." {529} - -The third edition, of 1592, contains an Addition, by the son, of -twenty pages. He there speaks of having found, apparently among his -father's papers, "A description or modile of the world and situation -of Spheres Cœlestiall and elementare according to the doctrine of -Ptolemie, whereunto all universities (led thereunto chiefly by the -authoritie of Aristotle) do consent." He adds: "But in this our age, -one rare witte (seeing the continuall errors that from time to time -more and more continually have been discovered, besides the infinite -absurdities in their Theoricks, which they have been forced to admit -that would not confesse any Mobilitie in the ball of the Earth) hath -by long studye, paynfull practise, and rare invention, delivered a -new Theorick or Model of the world, shewing that the Earth resteth -not in the Center of the whole world or globe of elements, which -encircled and enclosed in the Moone's orbe, and together with the -whole globe of mortalitye is carried yearely round about the Sunne, -which like a king in the middest of all, raygneth and giveth lawes -of motion to all the rest, sphærically dispersing his glorious -beames of light through all this sacred cœlestiall Temple. And the -Earth itselfe to be one of the Planets, having his peculiar and -strange courses, turning every 24 hours rounde upon his owne centre, -whereby the Sunne and great globe of fixed Starres seem to sway -about and turne, albeit indeed they remaine fixed--So many ways is -the sense of mortal man abused." - -This Addition is headed: -"A Perfit Description of the Cœlestiall Orbes, according to the most -ancient doctrine of the Pythagoreans: lately revived by Copernicus, -and by Geometrical Demonstrations approved." Mr. De Morgan, not -having seen this edition, and knowing the title-page only as far as -the word "Pythagoreans," says "their _astrological_ doctrines we -presume, not their reputed _Copernican_ ones." But it now appears -that in this, as in other cases, the authority of the Pythagoreans -was claimed for the Copernican system. Antony a Wood quotes the -latter part of the title thus: "Cui subnectitur _orbium_ -Copernicarum accurata descriptio;" which is inaccurate. Weidler, -still more inaccurately, cites it, "Cui subnectitur _operum_ -Copernici accurata descriptio." Lalande goes still further, -attempting, it would seem, to recover the English title-page from -the Latin: we find in the _Bibl. Astron._ the following: "1592 . . -Leonard Digges, Accurate Description of the Copernican System to the -Astronomical perpetual Prognostication." - -Thomas Digges appears, by others also of his writings, to have been -{530} a clear and decided Copernican. In his "Alæ sive Scalæ -Mathematicæ," 1573, he bestows high praise upon Copernicus and upon -his system: and appears to have been a believer in the real motion -of the Earth, and not merely an admirer of the system of Copernicus -as an explanatory hypothesis. - - -_Giordano Bruno._ - -The complete title of the work referred to is: - -"Jordani Bruni Nolani De Monade Numero et Figura liber consequens -Quinque De Minimo Magno et Mensura, item De Innumerabilibus, Immenso -et Infigurabili; seu De Universo et Mundis libri octo. (Francofurti, -1591.)" - -That the Reader may judge of the value of Bruno's speculations, I -give the following quotations: - -Lib. iv. c. 11 (Index). "Tellurem totam habitabilem esse _intus_ et -extra, et innumerabilia animantium complecti tum nobis sensibilium -tum _occultorum_ genera." - -C. 13. "Ut Mundorum Synodi in Universo et particulares Mundi in -Synodis ordinentur,' &c. - -He says (Lib. v. c. 1, p. 461): "Besides the stars and the great -worlds there are smaller living creatures carried through the -etherial space, in the form of a small sphere which has the aspect -of a bright fire, and is by the vulgar regarded as a fiery beam. -They are below the clouds, and I saw one which seemed to touch the -roofs of the houses. Now this sphere, or beam as they call it, was -really a living creature (_animal_), which I once saw moving in a -straight path, and grazing as it were the roofs of the city of Nola, -as if it were going to impinge on Mount Cicada; which however it -went over." - -There are two recent editions of the works of Giordano Bruno; by -Adolf Wagner, Leipsick, 1830, in two volumes; and by Gfrörer, -Berlin, 1833. Of the latter I do not know that more than one volume -(vol. ii.) has appeared. - - -_Did Francis Bacon reject the Copernican System?_ - -MR. DE MORGAN has very properly remarked (_Comp. B. A._ 1855, p. 11) -that the notice of the heliocentric question in the _Novum Organon_ -must be considered one of the most important passages in his works -upon this point, as being probably the latest written and best {531} -matured. It occurs in Lib. ii. Aphorism xxxvi., in which he is -speaking of _Prerogative Instances_, of which he gives twenty-seven -species. In the passage now referred to, he is speaking of a kind of -Prerogative Instances, better known to ordinary readers than most of -the kinds by name, the _Instantia Crucis_: though probably the -metaphor from which this name is derived is commonly wrongly -apprehended. Bacon's meaning is _Guide-Post Instances_: and the -_Crux_ which he alludes to is not a Cross, but a Guide-Post at -Cross-roads. And among the cases to which such Instances may be -applied, he mentions the diurnal motion of the heavens from east to -west, and the special motion of the particular heavenly bodies from -west to east. And he suggests what he conceives may be an _Instantia -Crucis_ in each case. If, he says, we find any motion from east to -west in the bodies which surround the earth, slow in the ocean, -quicker in the air, quicker still in comets, gradually quicker in -planets according to their greater distance from the earth: _then_ we -may suppose that there is a cosmical diurnal motion, and the motion -of the earth must be denied. - -With regard to the special motions of the heavenly bodies, he first -remarks that each body not coming quite so far westwards as before, -after one revolution of the heavens, and going to the north or the -south, does not imply any special motion; since it may be accounted -for by a modification of the diurnal motion in each, which produces -a defect of the return, and a spiral path; and he says that if we -look at the matter as common people[30\A] and disregard the devices -of astronomers, the motion is really so to the senses; and that he -has made an imitation of it by means of wires. The _instantia -crucis_ which he here suggests is, to see if we can find in any -credible history an account of any comet which did not share in the -diurnal revolution of the skies. - -[Note 30\A: Et certissimum est si paulisper pro plebeiis nos geramus -(missis astronomorum et scholæ commentis, quibus illud in more est, -ut sensui in multis immerito vim faciant et obscuriora malint) talem -esse motum istum ad sensum qualem diximus.] - -On his assertion that the motion of each separate planet is, to -sense, a spiral, we may remark that it is certainly true; but that -the business of science, here, as elsewhere, consists in _resolving_ -the complex phenomenon into simple phenomena; the complex spiral -motion into simple circular motions. - -With regard to the diurnal motion of the earth, it would seem as if -Bacon himself had a leaning to believe it when he wrote this -passage; for neither is he himself, nor are any of the -Anticopernicans, {532} accustomed to assert that the immensely rapid -motion of the sphere of the Fixed Stars graduates by a slower and -slower motion of Planets, Comets, Air, and Ocean, into the -immobility of the Earth. So that the conditions are not satisfied on -which he hypothetically says, "tum abnegandus est motus terræ." - -With regard to the proper motions of the planets, this passage seems -to me to confirm what I have already said of him; that he does not -appear to have seen the full value and meaning of what had been -done, up to his time, in Formal Astronomy. - -We may however fully agree with Mr. De Morgan; that the whole of -what he has said on this subject, when put together, does not -justify Hume's assertion that he rejected the Copernican system -"with the most positive disdain." - -Mr. De Morgan, in order to balance the Copernican argument derived -from the immense velocity of the stars in their diurnal velocity on -the other supposition, has reminded us that those who reject this -great velocity as improbable, accept without scruple the greater -velocity of light. It is curious that Bacon also has made this -comparison, though using it for a different purpose; namely, to show -that the transmission of the visual impression may be instantaneous. -In Aphorism xlvi. of Book ii. of the _Novum Organon_ he is speaking -of what he calls _Instantiæ curriculi_, or _Instantiæ ad aquam_, -which we may call _Instances by the clock_: and he says that the -great velocity of the diurnal sphere makes the marvellous velocity -of the rays of light more credible. - -"Immensa illa velocitas in ipso corpore, quæ cernitur in motu diurno -(quæ etiam viros graves ita obstupefecit ut _mallent credere motum -terræ_), facit motum illum ejaculationis ab ipsis [stellis] (licet -celeritate ut diximus admirabilem) magis credibilem." This passage -shows an inclination towards the opinion of the earth's being at -rest, but not a very strong conviction. - - -_Kepler persecuted._ - -WE have seen (p. 280) that Kepler writes to Galileo in 1597--"Be -trustful and go forwards. If Italy is not a convenient place for the -publication of your views, and if you are likely to meet with any -obstacles, perhaps Germany will grant us the necessary liberty." -Kepler however had soon afterwards occasion to learn that in Germany -also, the cultivators of science were exposed to persecution. It is -true that {533} in his case the persecution went mainly on the broad -ground of his being a Protestant, and extended to great numbers of -persons at that time. The circumstances of this and other portions of -Kepler's life have been brought to light only recently through an -examination of public documents in the Archives of Würtemberg and -unpublished letters of Kepler. (Johann Keppler's Leben und Wirken, -nach neuerlich aufgefundenen Manuscripten bearbeitet von J. L. C. -Freiherrn v. Breitschwart, K. Würtemberg. Staats-Rath. Stuttgart, -1831.) - -Schiller, in his _History of the Thirty Years' War_, says that when -Ferdinand of Austria succeeded to the Archduchy of Stiria, and found -a great number of Protestants among his subjects, he suppressed -their public worship without cruelty and almost without noise. But -it appears now that the Protestants were treated with great -severity. Kepler held a professorship in Stiria, and had married, in -1507, Barbara Müller, who had landed property in that province. On -the 11th of June, 1598, he writes to his friend Mæstlin that the -arrival of the Prince out of Italy is looked forwards to with -terror. In December he writes that the Protestants had irritated the -Catholics by attacks from the pulpit and by caricatures; that -hereupon the Prince, at the prayer of the Estates, had declared the -Letter of License granted by his father to be forfeited, and had -ordered all the Evangelical Teachers to leave the country on pain of -death. They went to the frontiers of Hungary and Croatia; but after -a month, Kepler was allowed to return, on condition of keeping -quiet. His discoveries appear to have operated in his favor. But the -next year he found his situation in Stiria intolerable, and longed -to return to his native country of Würtemberg, and to find some -position there. This he did not obtain. He wrote a circular letter -to his Brother Protestants, to give them consolation and courage; -and this was held to be a violation of the conditions on which his -residence was tolerated. Fortunately, at this time he was invited to -join Tycho Brahe, who had also been driven from his native country, -and was living at Prague. The two astronomers worked together under -the patronage of the Emperor Rudolph II.; and when Tycho died in -1601, Kepler became the Imperial _Mathematicus_. - -We are not to imagine that even among Protestants, astronomical -notions were out of the sphere of religious considerations. When -Kepler was established in Stiria, his first official business was -the calculation of the Calendar for the Evangelical Community. They -protested against the new Calendar, as manifestly calculated for the -furtherance of an impious papistry: and, say they, "We hold the Pope -for a {534} horrible roaring Lion. If we take his Calendar, we must -needs go into the church when he rings us in." Kepler however did -not fail to see, and to say, that the Papal Reformation of the -Calendar was a vast improvement. - -Kepler, as court-astronomer, was of course required to provide such -observations of the heavens as were requisite for the calculations of -the Astrologers. That he considered Astrology to be valuable only as -the nurse of Astronomy, he did not hesitate to reveal. He wrote a work -with a title of which the following is the best translation which I -can give: "_Tertius interveniens_, or: A Warning to certain -_Theologi_, _Medici_, _Philosophi_, that while they reasonably reject -star-gazing superstition, they do not throw away the kernel with the -shell.[31\A] 1610." In this he says, "You over-clever Philosophers -blame this Daughter of Astronomy more than is reasonable. Do you not -know that she must maintain her mother with her charms? How many men -would be able to make Astronomy their business, if men did not cherish -the hope to read the Future in the skies?" - -[Note 31\A: The German passage involves a curious image, borrowed, I -suppose, from some odd story: "dass sie mit billiger Verwerfung des -sternguckerischen Aberglaubens das Kind nicht mit dem Bade -ausschütten." "That they do not throw away the child along with the -dirty water of his bath."] - - -_Were the Papal Edicts against the Copernican System repealed?_ - -ADMIRAL SMYTH, in his _Cycle of Celestial Objects_, vol. i. p. 65, -says--"At length, in 1818, the voice of truth was so prevailing that -Pius VII. repealed the edicts against the Copernican system, and -thus, in the emphatic words of Cardinal Toriozzi, 'wiped off this -scandal from the Church.'" - -A like story is referred to by Sir Francis Palgrave, in his -entertaining and instructive fiction, _The Merchant and the Friar_. - -Having made inquiry of persons most likely to be well informed on -this subject, I have not been able to learn that there is any -further foundation for these statements than this: In 1818, on the -revisal of the _Index Expurgatorius_, Galileo's writings were, after -some opposition, expunged from that Catalogue. - -Monsignor Marino Marini, an eminent Roman Prelate, had addressed to -the _Romana Accademia di Archeologia_, certain historico-critical -Memoirs, which he published in 1850, with the title _Galileo e -l'Inquisizione_. In these, he confirms the conclusion which, I -think, almost {535} all persons who have studied the facts have -arrived at;[32\A] that Galileo trifled with authority to which he -professed to submit, and was punished for obstinate contumacy, not -for heresy. M. Marini renders full justice to Galileo's ability, and -does not at all hesitate to regard his scientific attainments as -among the glories of Italy. He quotes, what Galileo himself quoted, -an expression of Cardinal Baronius, that "the intention of the Holy -Spirit was to teach how to go to heaven, not how heaven goes."[33\A] -He shows that Galileo pleaded (p. 62) that he had not held the -Copernican opinion after it had been intimated to him (by Bellarmine -in 1616), that he was not to hold it; and that his breach of promise -in this respect was the cause of the proceedings against him. - -[Note 32\A: M. Marini (p. 29) mentions Leibnitz, Guizot, Spittler, -Eichhorn, Raumer, Ranke, among the "storici eterodossi" who have at -last done justice to the Roman Church.] - -[Note 33\A: Come si vada al Cielo, e non come vada il Cielo.] - -Those who admire Galileo and regard him as a martyr because, after -escaping punishment by saying "It _does not_ move," he forthwith -said "And yet it _does_ move," will perhaps be interested to know -that the former answer was suggested to him by friends anxious for -his safety. Niccolini writes to Bali Cioli (April 9, 1633) that -Galileo continued to be so persuaded of the truth of his opinions -that "he was resolved (some moments before his sentence) to defend -them stoutly; but I (continues Niccolini) exhorted him to make an -end of this; not to mind defending them; and to submit himself to -that which he sees that they may desire him to believe or to hold -about this matter of the motion of the earth. He was extremely -afflicted." But the Inquisition was satisfied with his answers, and -required no more.[34\A] - -[Note 34\A: Marini, p. 61.] - - - -{{536}} -BOOK VI. - -MECHANICS. - - - - -CHAPTER III. - -PRINCIPLES AND PROBLEMS. - - -_Significance of Analytical Mechanics._ - -IN the text, page 372, I have stated that Lagrange, near the end of -his life, expressed his sorrow that the methods of approximation -employed in Physical Astronomy rested on arbitrary processes, and -not on any insight into the results of mechanical action. From the -recent biography of Gauss, the greatest physical mathematician of -modern times, we learn that he congratulated himself on having -escaped this error. He remarked[35\A] that many of the most -celebrated mathematicians, Euler very often, Lagrange sometimes, had -trusted too much to the symbolical calculation of their problems, -and would not have been able to give an account of the meaning of -each successive step of their investigation. He said that he -himself, on the other hand, could assert that at every step which he -took, he always had the aim and purpose of his operations before his -eyes without ever turning aside from the way. The same, he remarked, -might be said of Newton. - -[Note 35\A: Gauss, _Zum Gedächtniss, von W. Sartorius v. -Waltershausen_, p. 80.] - - -_Engineering Mechanics._ - -The principles of the science of Mechanics were discovered by -observations made upon bodies within the reach of men; as we have -seen in speaking of the discoveries of Stevinus, Galileo, and -others, up to the time of Newton. And when there arose the -controversy about _vis viva_ (Chap. v. Sect. 2 of this -Book);--namely, whether the "living force" of a body is measured by -the product of the weight into the {537} velocity, or of the weight -into the square of the velocity;--still the examples taken were -cases of action in machines and the like terrestrial objects. But -Newton's discoveries identified celestial with terrestrial -mechanics; and from that time the mechanical problems of the heavens -became more important and attractive to mathematicians than the -problems about earthly machines. And thus the generalizations of the -problems, principles, and methods of the mathematical science of -Mechanics from this period are principally those which have -reference to the motions of the heavenly bodies: such as the Problem -of Three Bodies, the Principles of the Conservation of Areas, and of -the Immovable Plane, the Method of Variation of Parameters, and the -like (Chap. vi. Sect. 7 and 14). And the same is the case in the -more recent progress of that subject, in the hands of Gauss, Bessel, -Hansen, and others. - -But yet the science of Mechanics as applied to terrestrial -machines--_Industrial Mechanics_, as it has been termed--has made -some steps which it may be worth while to notice, even in a general -history of science. For the most part, all the most general laws of -mechanical action being already finally established, in the way -which we have had to narrate, the determination of the results and -conditions of any combination of materials and movements becomes -really a mathematical deduction from known principles. But such -deductions may be made much more easy and much more luminous by the -establishment of general terms and general propositions suited to -their special conditions. Among these I may mention a new abstract -term, introduced because a general mechanical principle can be -expressed by means of it, which has lately been much employed by the -mathematical engineers of France, MM. Poncelet, Navier, Morin, &c. -The abstract term is _Travail_, which has been translated _Laboring -Force_; and the principle which gives it its value, and makes it -useful in the solution of problems, is this;--that the _work done_ -(in overcoming resistance or producing any other effect) is equal to -the _Laboring Force_, by whatever contrivances the force be applied. -This is not a new principle, being in fact mathematically equivalent -to the conservation of Vis Viva; but it has been employed by the -mathematicians of whom I have spoken with a fertility and simplicity -which make it the mark of a new school of _The Mechanics of -Engineering_. - -The Laboring Force expended and the work done have been described by -various terms, as _Theoretical Effect_ and _Practical Effect_, and -the like. The usual term among English engineers for the work {538} -which an Engine usually does, is _Duty_; but as this word naturally -signifies what the engine _ought_ to do, rather than what it does, -we should at least distinguish between the Theoretical and the -Actual Duty. - -The difference between the Theoretical and Actual Duty of a Machine -arises from this: that a portion of the Laboring Force is absorbed -in producing effects, that is, in doing work which is not reckoned -as Duty: for instance, overcoming the resistance and waste of the -machine itself. And so long as this resistance and waste are not -rightly estimated, no correspondence can be established between the -theoretical and the practical Duty. Though much had been written -previously upon the theory of the steam-engine, the correspondence -between the Force expended and the Work done was not clearly made -out till Comte De Pambour published his _Treatise on Locomotive -Engines_ in 1835, and his _Theory of the Steam-Engine_ in 1839. - - -_Strength of Materials._ - -Among the subjects which have specially engaged the attention of -those who have applied the science of Mechanics to practical -matters, is the strength of materials: for example, the strength of -a horizontal beam to resist being broken by a weight pressing upon -it. This was one of the problems which Galileo took up. He was led -to his study of it by a visit which he made to the arsenal and -dockyards of Venice, and the conclusions which he drew were -published in his _Dialogues_, in 1633. In his mode of regarding the -problem, he considers the section at which the beam breaks as the -short arm of a bent lever which resists fracture, and the part of -the beam which is broken off as the longer arm of the lever, the -lever turning about the fracture as a hinge. So far this is true; -and from this principle he obtained results which are also true as, -that the strength of a rectangular beam is proportional to the -breadth multiplied into the square of the depth:--that a hollow beam -is stronger than a solid beam of the same mass; and the like. - -But he erred in this, that he supposed the hinge about which the -breaking beam turns, to be exactly at the unrent surface, that -surface resisting all change, and the beam being rent all the way -across. Whereas the fact is, that the unrent surface yields to -compression, while the opposite surface is rent; and the hinge about -which the breaking beam turns is at an intermediate point, where the -extension {539} and rupture end, and the compression and crushing -begin: a point which has been called _the neutral axis_. This was -pointed out by Mariotte; and the notion, once suggested, was so -manifestly true that it was adopted by mathematicians in general. -James Bernoulli,[36\A] in 1705, investigated the strength of beams -on this view; and several eminent mathematicians pursued the -subject; as Varignon, Parent, and Bulfinger; and at a later period, -Dr. Robison in our own country. - -[Note 36\A: _Opera_, ii. p. 976.] - -But along with the fracture of beams, the mathematicians considered -also another subject, the flexure of beams, which they undergo -before they break, in virtue of their elasticity. What is the -_elastic curve_?--the curve into which an elastic line forms itself -under the pressure of a weight--is a problem which had been proposed -by Galileo, and was fully solved, as a mathematical problem, by -Euler and others. - -But beams in practice are not mere lines: they are solids. And their -resistance to flexure, and the amount of it, depends upon the -resistance of their internal parts to extension and compression, and -is different for different substances. To measure these differences, -Dr. Thomas Young introduced the notion of the _Modulus of -Elasticity_:[37\A] meaning thereby a column of the substance of the -same diameter, such as would by its weight produce a compression -equal to the whole length of the beam, the rate of compression being -supposed to continue the same throughout. Thus if a rod of any kind, -100 inches long, were compressed 1 inch by a weight 1000 pounds, the -weight of its modulus of elasticity would be 100,000 pounds. This -notion assumes Hooke's law that the extension of a substance is as -its tension; and extends this law to compression also. - -[Note 37\A: Lecture xiii. The height of the modulus is the same for -the same substance, whatever its breadth and thickness may be; for -atmospheric air it is about five miles, and for steel nearly 1500 -miles.] - -There is this great advantage in introducing the definition of the -Modulus of Elasticity,--that it applies equally to the flexure of a -substance and to the minute vibrations which propagate sound, and -the like. And the notion was applied so as to lead to curious and -important results with regard to the power of beams to resist -flexure, not only when loaded transversely, but when pressed in the -direction of their length, and in any oblique direction. - -But in the fracture of beams, the resistance to extension and to -compression are not practically equal; and it was necessary to -determine {540} the difference of these two forces by experiments. -Several persons pursued researches on this subject; especially Mr. -Barlow, of the Royal Military Academy,[38\A] who investigated the -subject with great labor and skill, so far as wood is concerned. But -the difference between the resistance to tension and to compression -requires more special study in the case of iron; and has been -especially attended to in recent times, in consequence of the vast -increase in the number of iron structures, and in particular, -railways. It appears that wrought iron yields to compressive -somewhat more easily than to tensile force, while cast iron yields -far more easily to tensile than to compressive strains. In all cases -the power of a beam to resist fracture resides mainly in the upper -and the under side, for there the tenacity of the material acts at -the greatest leverage round the hinge of fracture. Hence the -practice was introduced of making iron beams with a broad _flange_ -at the upper and another flange at the under side, connected by a -vertical plate or _web_, of which the office was to keep the two -flanges asunder. Mr. Hodgkinson made many valuable experiments, on a -large scale, to determine the forms and properties of such beams. - -[Note 38\A: _An Essay on the Strength and Shape of Timber_. 3d -edition, 1826.] - -But though engineers were, by such experiments and reasonings, -enabled to calculate the strength of a given iron beam, and the -dimensions of a beam which should bear a given load, it would hardly -have occurred to the boldest speculator, a few years ago, to predict -that there might be constructed beams nearly 500 feet long, resting -merely on their two extremities, of which it could be known -beforehand, that they would sustain, without bending or yielding in -any perceptible degree, the weight of a railroad train, and the jar -of its unchecked motion. Yet of such beams, constructed beforehand -with the most perfect confidence, crowned with the most complete -success, is composed the great tubular bridge which that consummate -engineer, Mr. Robert Stephenson, has thrown across the Menai Strait, -joining Wales with the island of Anglesey. The upper and under -surfaces of this quadrangular tube are the flanges of the beam, and -the two sides are the webs which connect them. In planning this -wonderful structure, the point which required especial care was to -make the upper surface strong enough to resist the compressive force -which it has to sustain; and this was done by constructing the upper -part of the beam of a series of cells, made of iron plate. The -application of the arch, of the dome, and of groined vaulting, to -the widest space over which they have ever been thrown, {541} are -achievements which have, in the ages in which they occurred, been -received with great admiration and applause; but in those cases the -principle of the structure had been tried and verified for ages upon -a smaller scale. Here not only was the space thus spanned wider than -any ever spanned before, but the principle of such a beam with a -cellular structure of its parts, was invented for this very purpose, -experimentally verified with care, and applied with the most exact -calculation of its results. - - -_Roofs--Arches--Vaults._ - -The calculations of the mechanical conditions of structures -consisting of several beams, as for instance, the frames of roofs, -depends upon elementary principles of mechanics; and was a subject -of investigation at an early period of the science. Such frames may -be regarded as assemblages of levers. The parts of which they -consist are rigid beams which sustain and convey force, and _Ties_ -which resist such force by their tension. The former parts must be -made rigid in the way just spoken of with regard to iron beams; but -ties may be rods merely. The wide structures of many of the roofs of -railway stations, compared with the massive wooden roofs of ancient -buildings, may show us how boldly and how successfully this -distinction has been carried out in modern times. The investigation -of the conditions and strength of structures consisting of wooden -beams has been cultivated by Mathematicians and Engineers, and is -often entitled _Carpentry_ in our Mechanical Treatises. In our own -time, Dr. Robison and Dr. Thomas Young have been two of the most -eminent mathematicians who have written upon this subject. - -The properties of the simple machines have been known, as we have -narrated, from the time of the Ancient Greeks. But it is plain that -such machines are prevented from producing their full effect by -various causes. Among the rest, the rubbing of one part of the -machine upon another produces an obstacle to the effectiveness of a -machine: for instance, the rubbing of the axle of a wheel in the -hole in which it rests, the rubbing of a screw against the sides of -its hollow screw; the rubbing of a wedge against the sides of its -notch; the rubbing of a cord against its pulley. In all these cases, -the effect of the machine to produce motion is diminished by the -friction. And this _Friction_ may be measured and its effects -calculated; and thus we have a new branch of mechanics, which has -been much cultivated. {542} - -Among the effects of friction, we may notice the standing of a stone -arch. For each of the vaulting stones of an arch is a truncated -wedge; and though a collection of such stones might be so -proportioned in their weights as to balance exactly, yet this -balance would be a tottering equilibrium, which the slightest shock -would throw down, and which would not practically subsist. But the -friction of the vaulting stones against one another prevents this -instability from being a practical inconvenience; and makes an -equilibrated arch to be an arch strong for practical purposes. The -_Theory of Arches_ is a portion of Mechanics which has been much -cultivated, and which has led to conclusions of practical use, as -well as of theoretical beauty. - -I have already spoken of the invention of the Arch, the Dome, and -Groined Vaulting, as marked steps in building. In all these cases the -invention was devised by practical builders; and mechanical theory, -though it can afterwards justify these structures, did not originally -suggest them. They are not part of the result, nor even of the -application of theory, but only of its exemplification. The authors of -all these inventions are unknown; and the inventions themselves may be -regarded as a part of the Prelude of the science of mechanics, because -they indicate that the ideas of mechanical pressure and support, in -various forms, are acquiring clearness and fixity. - -In this point of view, I spoke (Book iv. chap. v. sect. 5) of the -Architecture of the Middle Ages as indicating a progress of thought -which led men towards the formation of Statics as a science. - -As particular instances of the operation of such ideas, we have the -_Flying Buttresses_ which support stone vaults; and especially, as -already noted, the various contrivances by which stone vaults are -made to intersect one another, so as to cover a complex pillared -space below with _Groined Vaulting_. This invention, executed as it -was by the builders of the twelfth and succeeding centuries, is the -most remarkable advance in the mechanics of building, after the -invention of the _Arch_ itself. - -It is curious that it has been the fortune of our times, among its -many inventions, to have produced one in this department, of which -we may say that it is the most remarkable step in the mechanics of -arches which has been made since the introduction of pointed groined -vaults. I speak of what are called _Skew Arches_, in which the -courses of stone or brick of which the bridge is built run obliquely -to the walls of the bridge. Such bridges have become very common in -the works of railroads; for they save space and material, and the -{543} invention once made, the cost of the ingenuity is nothing. Of -course, the mechanical principles involved in such structures are -obvious to the mathematician, when the problem has been practically -solved. And in this case, as in the previous cardinal inventions in -structure, though the event has taken place within a few years, no -single person, so far as I am aware, can be named as the -inventor.[39\A] - -[Note 39\A: Since this was written, I have been referred to Rees's -_Cyclopædia_, Article _Oblique Arches_, where this invention is -correctly explained, and is claimed for an engineer named Chapman. -It is there said, that the first arch of this kind was erected in -1787 at Naas, near Kildare in Ireland.] - - - -{{544}} -BOOK VII. - -PHYSICAL ASTRONOMY. - - - - -CHAPTER I. - -PRELUDE TO NEWTON. - - -_The Ancients._ - -EXPRESSIONS in ancient writers which may be interpreted as -indicating a notion of gravitation in the Newtonian sense, no doubt -occur. But such a notion, we may be sure, must have been in the -highest degree obscure, wavering, and partial. I have mentioned -(Book i. Chap. 3) an author who has fancied that he traces in the -works of the ancients the origin of most of the vaunted discoveries -of the moderns. But to ascribe much importance to such expressions -would be to give a false representation of the real progress of -science. Yet some of Newton's followers put forward these passages -as well deserving notice; and Newton himself appears to have had -some pleasure in citing such expressions; probably with the feeling -that they relieved him of some of the odium which, he seems to have -apprehended, hung over new discoveries. The Preface to the -_Principia_, begins by quoting[40\A] the authority of the ancients, -as well as the moderns, in favor of applying the science of -Mechanics to Natural Philosophy. In the Preface to David Gregory's -_Astronomiæ Physicæ et Geometricæ Elementa_, published in 1702, is a -large array of names of ancient authors, and of quotations, to prove -the early and wide diffusion of the doctrine of the gravity of the -Heavenly Bodies. And it appears to be now made out, that this -collection of ancient authorities {545} was supplied to Gregory by -Newton himself. The late Professor Rigaud, in his _Historical Essay -on the First Publication of Sir Isaac Newton's Principia_, says (pp. -80 and 101) that having been allowed to examine Gregory's papers, he -found that the quotations given by him in his Preface are copied or -abridged from notes which Newton had supplied to him in his own -handwriting. Some of the most noticeable of the quotations are those -taken from Plutarch's Dialogue _on the Face which appears in the -Moon's Disk_: it is there said, for example, by one of the speakers, -that the Moon is perhaps prevented from falling to the earth by the -rapidity of her revolution round it; as a stone whirled in a sling -keeps it stretched. Lucretius also is quoted, as teaching that all -bodies would descend with an equal celerity in a vacuum: - Omnia quapropter debent per inane quietum - Æque ponderibus non æquis concita ferri. - Lib. ii. v. 238. - -[Note 40\A: Cum veteres _Mechanicam_ (uti author est _Pappus_), in -rerum Naturalium investigatione maximi fecerint, et recentiores, -missis formis substantialibus et qualitatibus occultis, Phenonmena -Naturæ ad leges mathematicas revocare aggressa sunt; visum est in -hoc Tractatu _Mathesin_ excolere quatenus ea ad _Philosophiam_ -spectat.] - -It is asserted in Gregory's Preface that Pythagoras was not -unacquainted with the important law of gravity, the inverse squares -of the distances from the centre. For, it is argued, the seven -strings of Apollo's lyre mean the seven planets; and the proportions -of the notes of strings are reciprocally as the inverse squares of -the weights which stretch them. - -I have attempted, throughout this work, to trace the progress of the -discovery of the great truths which constitute real science, in a -more precise manner than that which these interpretations of ancient -authors exemplify. - - -_Jeremiah Horrox._ - -In describing the Prelude to the Epoch of Newton, I have spoken (p. -395) of a group of philosophers in England who began, in the first -half of the seventeenth century, to knock at the door where Truth -was to be found, although it was left for Newton to force it open; -and I have there noticed the influence of the civil wars on the -progress of philosophical studies. To the persons thus tending -towards the true physical theory of the solar system, I ought to -have added Jeremy Horrox, whom I have mentioned in a former part -(Book v. chap. 5) as one of the earliest admirers of Kepler's -discoveries. He died at the early age of twenty-two, having been the -first person who ever saw Venus pass across the disk of the Sun -according to astronomical prediction, which took place in 1639. His -_Venus in sole visa_, {546} in which this is described, did not -appear till 1661, when it was published by Hevelius of Dantzic. Some -of his papers were destroyed by the soldiers in the English civil -wars; and his remaining works were finally published by Wallis, in -1673. The passage to which I here specially wish to refer is -contained in a letter to his astronomical ally, William Crabtree, -dated 1638. He appears to have been asked by his friend to suggest -some cause for the motion of the aphelion of a planet; and in reply, -he uses an experimental illustration which was afterwards employed -by Hooke in 1666. A ball at the end of a string is made to swing so -that it describes an oval. This contrivance Hooke employed to show -the way in which an orbit results from the combination of a -projectile motion with a central force. But the oval does not keep -its axis constantly in the same position. The apsides, as Horrox -remarked, move in the same direction as the pendulum, though much -slower. And it is true, that this experiment does illustrate, in a -general way, the cause of the motion of the aphelia of the Planetary -Orbits; although the form of the orbit is different in the -experiment and in the solar system; being an ellipse with the centre -of force in the centre of the ellipse, in the former case, and an -ellipse with the centre of force in the focus, in the latter case. -These two forms of orbits correspond to a central force varying -directly as the distance, and a central force varying inversely as -the square of the distance; as Newton proved in the _Principia_. But -the illustration appears to show that Horrox pretty clearly saw how -an orbit arose from a central force. So far, and no further, -Newton's contemporaries could get; and then he had to help them -onwards by showing what was the law of the force, and what larger -truths were now attainable. - - -_Newton's Discovery of Gravitation._ - -[Page 402.] As I have already remarked, men have a willingness to -believe that great discoveries are governed by casual coincidences, -and accompanied by sudden revolutions of feeling. Newton had -entertained the thought of the moon being retained in her orbit by -gravitation as early as 1665 or 1666. He resumed the subject and -worked the thought out into a system in 1684 and 5. What induced him -to return to the question? What led to his success on this last -occasion? With what feelings was the success attended? It is easy to -make an imaginary connection of facts. "His optical discoveries had -recommended him to the Royal Society, and he was now a member. He -{547} _there_ learned the accurate measurement of the Earth by -Picard, differing very much from the estimation by which he had made -his calculation in 1666; and he thought his conjecture now more -likely to be just."[41\A] M. Biot gives his assent to this -guess.[42\A] The English translation of M. Biot's biography[43\A] -converts the guess into an assertion. But, says Professor -Rigaud,[44\A] Picard's measurement of the Earth was well known to -the Fellows of the Royal Society as early as 1675, there being an -account of the results of it given in the _Philosophical -Transactions_ for that year. Moreover, Norwood, in his _Seaman's -Practice_, dated 1636, had given a much more exact measure than -Newton employed in 1666. But Norwood, says Voltaire, had been buried -in oblivion by the civil wars. No, again says the exact and -truth-loving Professor Rigaud, Norwood was in communication with the -Royal Society in 1667 and 1668. So these guesses at the accident -which made the apple of 1665 germinate in 1684, are to be carefully -distinguished from history. - -[Note 41\A: Robison's _Mechanical Philosophy_, vol. iii. p. 94. -(Art. 195.)] - -[Note 42\A: _Biographie Universelle_.] - -[Note 43\A: _Library of Useful Knowledge_.] - -[Note 44\A: _Historical Essay on the First Publication of the -Principia_ (1838).] - -But with what feelings did Newton attain to his success? Here again -we have, I fear, nothing better than conjecture. "He went home, took -out his old papers, and resumed his calculations. As they drew near -to a close, he was so much agitated that he was obliged to desire a -friend to finish them. His former conjecture was now found to agree -with the phænomena with the utmost precision."[45\A] This -conjectural story has been called "a tradition;" but he who relates -it does not call it so. Every one must decide, says Professor -Rigaud, from his view of Newton's character, how far he thinks it -consistent with this statement. Is it likely that Newton, so calm -and so indifferent to fame as he generally showed himself, should be -thus agitated on such an occasion? "No," says Sir David Brewster; -"it is not supported by what we know of Newton's character."[46\A] -To this we may assent; and this conjectural incident we must -therefore, I conceive, separate from history. I had incautiously -admitted it into the text of the first Edition. - -[Note 45\A: Robison, ibid.] - -[Note 46\A: _Life of Newton_, vol. i. p. 292.] - -Newton appears to have discovered the method of demonstrating that a -body might describe an ellipse when acted upon by a force residing -in the focus, and varying inversely as the square of the distance, -in 1669, upon occasion of his correspondence with Hooke. In 1684, -{548} at Halley's request, he returned to the subject; and in -February, 1685 there was inserted in the Register of the Royal -Society a paper of Newton's (_Isaaci Newtoni Propositiones de -Motu_), which contained some of the principal propositions of the -first two Books of the _Principia_. This paper, however, does not -contain the proposition "Lunam gravitare in Terram," nor any of the -propositions of the Third Book. - - - - -CHAPTER III. - -THE PRINCIPIA. - - -_Sect._ 2.--_Reception of the Principia._ - -LORD BROUGHAM has very recently (_Analytical View of Sir Isaac -Newton's Principia_, 1855) shown a strong disposition still to -maintain, what he says has frequently been alleged, that the -reception of the work was not, even in this country, "such as might -have been expected." He says, in explanation of the facts which I -have adduced, showing the high estimation in which Newton was held -immediately after the publication of the _Principia_, that Newton's -previous fame was great by former discoveries. This is true; but the -effect of this was precisely what was most honorable to Newton's -countrymen, that they received with immediate acclamations this new -and greater discovery. Lord Brougham adds, "after its appearance the -_Principia_ was more admired than studied;" which is probably true -of the _Principia_ still, and of all great works of like novelty and -difficulty at all times. But, says Lord Brougham, "there is no -getting over the inference on this head which arises from the dates -of the two first editions. There elapsed an interval of no less than -twenty-seven years between them; and although Cotes [in his Preface] -speaks of the copies having become scarce and in very great demand -when the second edition appeared in 1713, yet had this urgent demand -been of many years' continuance, the reprinting could never have -been so long delayed." But Lord Brougham might have learnt from Sir -David Brewster's _Life of Newton_ (vol. i. p. 312), which he extols -so emphatically, that already in 1691 (only four years after the -publication), a copy of the _Principia_ could hardly be procured, -and that even at that {549} time an improved edition was in -contemplation; that Newton had been pressed by his friends to -undertake it, and had refused. - -When Bentley had induced Newton to consent that a new edition should -be printed, he announces his success with obvious exultation to -Cotes, who was to superintend the work. And in the mean time the -_Astronomy_ of David Gregory, published in 1702, showed in every -page how familiar the Newtonian doctrines were to English -philosophers, and tended to make them more so, as the sermons of -Bentley himself had done in 1692. - -Newton's Cambridge contemporaries were among those who took a part -in bringing the _Principia_ before the world. The manuscript draft -of it was conveyed to the Royal Society (April 28, 1686) by Dr. -Vincent, Fellow of Clare Hall, who was the tutor of Whiston, -Newton's deputy in his professorship; and he, in presenting the -work, spoke of the novelty and dignity of the subject. There exists -in the library of the University of Cambridge a manuscript -containing the early Propositions of the _Principia_ as far as Prop. -xxxiii. (which is a part of Section vii., about Falling Bodies). -This appears to have been a transcript of Newton's Lectures, -delivered as Lucasian Professor: it is dated October, 1684. - - -_Is Gravitation proportional to Quantity of Matter?_ - -It was a portion of Newton's assertion in his great discovery, that -all the bodies of the universe attract each other with forces which -are _as the quantity of matter_ in each: that is, for instance, the -sun attracts the satellites of any planet just as much as he -attracts the planet itself, in proportion to the quantity of matter -in each; and the planets attract one another just as much as they -attract the sun, according to the quantity of matter. - -To prove this part of the law _exactly_ is a matter which requires -careful experiments; and though proved experimentally by Newton, has -been considered in our time worthy of re-examination by the great -astronomer Bessel. There was some ground for doubt; for the mass of -Jupiter, as deduced from the perturbations of Saturn, was only 1/1070 -of the mass of the sun; the mass of the same planet as deduced from -the perturbations of Juno and Pallas was 1/1045 of that of the Sun. If -this difference were to be confirmed by accurate observations and -calculations, it would follow that the attractive power exercised by -Jupiter upon the minor planets was greater than that exercised upon -{550} Saturn. And in the same way, if the attraction of the Earth had -any _specific_ relation to different kinds of matter, the time of -oscillation of a pendulum of equal length composed wholly or in part -of the two substances would be different. If, for instance, it were -more intense for magnetized iron than for stone, the iron pendulum -would oscillate more quickly. Bessel showed[47\A] that it was possible -to assume hypothetically a constitution of the sun, planets, and their -appendages, such that the attraction of the Sun on the Planets and -Satellites should be proportional to the quantity of matter in each; -but that the attraction of the Planets on one another would not be on -the same scale. - -[Note 47\A: _Berlin Mem._ 1824.] - -Newton had made experiments (described in the _Principia_, Book -iii., Prop. vi.) by which it was shown that there could be no -considerable or palpable amount of such specific difference among -terrestrial bodies, but his experiments could not be regarded as -exact enough for the requirements of modern science. Bessel -instituted a laborious series of experiments (presented to the -Berlin Academy in 1832) which completely disproved the conjecture of -such a difference; every substance examined having given exactly the -same coefficient of gravitating intensity as compared with inertia. -Among the substances examined were metallic and stony masses of -meteoric origin, which might be supposed, if any bodies could, to -come from other parts of the solar system. - - - - -CHAPTER IV. - -VERIFICATION AND COMPLETION OF THE NEWTONIAN THEORY. - - -_Tables of the Moon and Planets._ - -THE Newtonian discovery of Universal Gravitation, so remarkable in -other respects, is also remarkable as exemplifying the immense -extent to which the verification of a great truth may be carried, -the amount of human labor which may be requisite to do it justice, -and the striking extension of human knowledge to which it may lead. -I have said that it is remarked as a beauty in the first fixation of -a theory that its measures or elements are established by means of a -few {551} data; but that its excellence when established is in the -number of observations which it explains. The multiplicity of -observations which are explained by astronomy, and which are made -because astronomy explains them, is immense, as I have noted in the -text. And the multitude of observations thus made is employed for -the purpose of correcting the first adopted elements of the theory. -I have mentioned some of the examples of this process: I might -mention many others in order to continue the history of this part of -Astronomy up to the present time. But I will notice only those which -seem to me the most remarkable. - -In 1812, Burckhardt's _Tables de la Lune_ were published by the -French Bureau des Longitudes. A comparison of these and Burg's with -a considerable number of observations, gave 9-100ths of a second as -the mean error of the former in the Moon's longitude, while the mean -error of Burg's was 18-100ths. The preference was therefore accorded -to Burckhardt's. - -Yet the Lunar Tables were still as much as thirty seconds wrong in -single observations. This circumstance, and Laplace's expressed wish, -induced the French Academy to offer a prize for a complete and purely -theoretical determination of the Lunar path, instead of determinations -resting, as hitherto, partly upon theory and partly upon observations. -In 1820, two prize essays appeared, the one by Damoiseau, the other by -Plana and Carlini. And some years afterwards (in 1824, and again in -1828), Damoiseau published _Tables de la Lune formées sur la seule -Théorie d'Attraction_. These agree very closely with observation. That -we may form some notion of the complexity of the problem, I may state -that the longitude of the Moon is in these Tables affected by no fewer -than forty-seven _equations_; and the other quantities which determine -her place are subject to inequalities not much less in number. - -Still I had to state in the second Edition, published in 1847, that -there remained an unexplained discordance between theory and -observation in the motions of the Moon; an inequality of long period -as it seemed, which the theory did not give. - -A careful examination of a long series of the best observations of -the Moon, compared throughout with the theory in its most perfect -form, would afford the means both of correcting the numerical -elements of the theory, and of detecting the nature, and perhaps the -law, of any still remaining discrepancies. Such a work, however, -required vast labor, as well as great skill and profound -mathematical knowledge. {552} Mr. Airy undertook the task; employing -for that purpose, the Observations of the Moon made at Greenwich -from 1750 to 1830. Above 8000 observed places of the Moon were -compared with theory by the computation of the same number of -places, each separately and independently calculated from Plana's -Formulæ. A body of calculators (sometimes sixteen), at the expense -of the British Government, was employed for about eight years in -this work. When we take this in conjunction with the labor which the -observations themselves imply, it may serve to show on what a scale -the verification of the Newtonian theory has been conducted. The -first results of this labor were published in two quarto volumes; -the final deductions as to correction of elements, &c., were given -in the Memoirs of the Astronomical Society in 1848.[48\A] - -[Note 48\A: The total expense of computers, to the end of reading -the proof-sheets, was 4300_l._ - -Mr. Airy's estimate of days' works [made before beginning], for the -heavy part of calculations only, was thirty-six years of one computer. -This was somewhat exceeded, but not very greatly, in that part.] - -Even while the calculations were going on, it became apparent that -there were some differences between the observed places of the Moon, -and the theory so far as it had then been developed. M. Hansen, an -eminent German mathematician who had devised new and powerful -methods for the mathematical determination of the results of the law -of gravitation, was thus led to explore still further the motions of -the Moon in pursuance of this law. The result was that he found -there must exist two lunar inequalities, hitherto not known; the one -of 273, and the other of 239 years, the coefficients of which are -respectively 27 and 23 seconds. Both these originate in the -attraction of Venus; one of them being connected with the long -inequality in the Solar Tables, of which Mr. Airy had already proved -the existence, as stated in Chap. vi. Sect. 6 of this Book. - -These inequalities fell in with the discrepancies between the actual -observations and the previously calculated Tables, which Mr. Airy -had discovered. And again, shortly afterwards, M. Hansen found that -there resulted from the theory two other new equations of the Moon; -one in latitude and one in longitude, agreeing with two which were -found by Mr. Airy in deducing from the observations the correction -of the elements of the Lunar Tables. And again, a little later, -there was detected by these mathematicians a theoretical correction -for the {553} motion of the Node of the Moon's orbit, coinciding -exactly with one which had been found to appear in the observations. - -Nothing can more strikingly exhibit the confirmation which increased -scrutiny brings to light between the Newtonian theory on the one -hand, and the celestial motions on the other. We have here a very -large mass of the best observations which have ever been made, -systematically examined, with immense labor, and with the set -purpose of correcting at once all the elements of the Lunar Tables. -The corrections of the elements thus deduced imply of course some -error in the theory as previously developed. But at the same time, -and with the like determination thoroughly to explore the subject, -the theory is again pressed to yield its most complete results, by -the invention of new and powerful mathematical methods; and the -event is, that residual errors of the old Tables, several in number, -following the most diverse laws, occurring in several detached -parts, agree with the residual results of the Theory thus newly -extracted from it. And thus every additional exactness of scrutiny -into the celestial motions on the one hand and the Newtonian theory -on the other, has ended, sooner or later, in showing the exactness -of their coincidence. - -The comparison of the theory with observation in the case of the -motions of the Planets, the motion of each being disturbed by the -attraction of all the others, is a subject in some respects still -more complicated and laborious. This work also was undertaken by the -same indefatigable astronomer; and here also his materials belonged -to the same period as before; being the admirable observations made -at Greenwich from 1750 to 1830, during the time that Bradley, -Maskelyne, and Pond were the Astronomers Royal.[49\A] These -Planetary observations were deduced, and the observed places were -compared with the tabular places: with Lindenau's Tables of Mercury, -Venus, and Mars; and with Bouvard's Tables of Jupiter, Saturn, and -Uranus; and thus, while the received theory and its elements were -confirmed, the means of testing any improvement which may hereafter -be proposed, either in the form of the theoretical results or in the -constant elements which they involved, was placed within the reach -of the {554} astronomers of all future time. The work appeared in -1845; the expense of the compilations and the publication being -defrayed by the British Government. - -[Note 49\A: The observations of stars made by Bradley, who preceded -Maskelyne at Greenwich, had already been discussed by Bessel, a -great German astronomer; and the results published in 1818, with a -title that well showed the estimation in which he held those -materials: _Fundamenta Astronomiæ pro anno_ 1775, _deducta ex -Ohservationibus viri incomparabilis James Bradley in specula -Astronomica Grenovicensi per annos_ 1750-1762 _institutis_.] - - -_The Discovery of Neptune._ - -The theory of gravitation was destined to receive a confirmation -more striking than any which could arise from any explanation, -however perfect, given by the motions of a known planet; namely, in -revealing the existence of an unknown planet, disclosed to -astronomers by the attraction which it exerted upon a known one. The -story of the discovery of Neptune by the calculations of Mr. Adams -and M. Le Verrier was partly told in the former edition of this -History. I had there stated (vol. ii. p. 306) that "a deviation of -observation from the theory occurs at the very extremity of the -solar system, and that its existence appears to be beyond doubt. -Uranus does not conform to the Tables calculated for him on the -theory of gravitation. In 1821, Bouvard said in the Preface to the -Tables of this Planet, "the formation of these Tables offers to us -this alternative, that we cannot satisfy modern observations to the -requisite degree of precision without making our Tables deviate from -the ancient observations." But when we have done this, there is -still a discordance between the Tables and the more modern -observations, and this discordance goes on increasing. At present -the Tables make the Planet come upon the meridian about eight -seconds later than he really does. This discrepancy has turned the -thoughts of astronomers to the effects which would result from a -planet external to Uranus. It appears that the observed motion would -be explained by applying a planet at twice the distance of Uranus -from the Sun to exercise a disturbing force, and it is found that -the present longitude of this disturbing body must be about 325 -degrees. - -I added, "M. Le Verrier (_Comptes Rendus_, Jan. 1, 1846) and, as I -am informed by the Astronomer Royal, Mr. Adams, of St. John's -College, Cambridge, have both arrived independently at this result." - -To this Edition I added a Postscript, dated, Nov. 7, 1846, in which -I said: - -"The planet exterior to Uranus, of which the existence was inferred -by M. Le Verrier and Mr. Adams from the motions of Uranus (vol. ii. -Note (L.)), has since been discovered. This confirmation of -calculations founded upon the doctrine of universal gravitation, may -be looked upon as the most remarkable event of the kind since the -return of Halley's comet in 1757 and in some respects, as a more -striking event {555} even than that; inasmuch as the new planet had -never been seen at all, and was discovered by mathematicians -entirely by their feeling of its influence, which they perceived -through the organ of mathematical calculation. - -"There can be no doubt that to M. Le Verrier belongs the glory of -having first published a prediction of the place and appearance of the -new planet, and of having thus occasioned its discovery by -astronomical observers. M. Le Verrier's first prediction was published -in the _Comptes Rendus de l'Acad. des Sciences_, for _June_ 1, 1846 -(not _Jan._ 1, as erroneously printed in my Note). A subsequent paper -on the subject was read Aug. 31. The planet was seen by M. Galle, at -the Observatory of Berlin, on September 23, on which day he had -received an express application from M. Le Verrier, recommending him -to endeavor to recognize the stranger by its having a visible disk. -Professor Challis, at the Observatory of Cambridge, was looking out -for the new planet from July 29, and saw it on August 4, and again on -August 12, but without recognizing it, in consequence of his plan of -not comparing his observations till he had accumulated a greater -number of them. On Sept. 29, having read for the first time M. Le -Verrier's second paper, he altered his plan, and paid attention to the -physical appearance rather than the position of the star. On that very -evening, not having then heard of M. Galle's discovery, he singled out -the star by its seeming to have a disk. - -"M. Le Verrier's mode of discussing the circumstances of Uranus's -motion, and inferring the new planet from these circumstances, is in -the highest degree sagacious and masterly. Justice to him cannot -require that the contemporaneous, though unpublished, labors of Mr. -Adams, of St John's College, Cambridge, should not also be recorded. -Mr. Adams made his first calculations to account for the anomalies -in the motion of Uranus, on the hypothesis of a more distant planet, -in 1843. At first he had not taken into account the earlier -Greenwich observations; but these were supplied to him by the -Astronomer Royal, in 1844. In September, 1845, Mr. Adams -communicated to Professor Challis values of the elements of the -supposed disturbing body; namely, its mean distance, mean longitude -at a given epoch, longitude of perihelion, eccentricity of orbit, -and mass. In the next month, he communicated to the Astronomer Royal -values of the same elements, somewhat corrected. The note (L.), vol. -ii., of the present work (2d Ed.), in which the names of MM. Le -Verrier and Adams are mentioned in conjunction, was in the press in -August, 1846, a {556} month before the planet was seen. As I have -stated in the text, Mr. Adams and M. Le Verrier assigned to the -unseen planet nearly the same position; they also assigned to it -nearly the same mass; namely, 2½ times the mass of Uranus. And -hence, supposing the density to be not greater than that of Uranus, -it followed that the visible diameter would be about 3", an apparent -magnitude not much smaller than Uranus himself. - -"M. Le Verrier has mentioned for the new planet the name _Neptunus_; -and probably, deference to his authority as its discoverer, will -obtain general currency for this name." - -Mr. Airy has given a very complete history of the circumstances -attending the discovery of Neptune, in the Memoirs of the -Astronomical Society (read November 13, 1846). In this he shows that -the probability of some disturbing body beyond Uranus had suggested -itself to M. A. Bouvard and Mr. Hussey as early as 1834. Mr. Airy -himself then thought that the time was not ripe for making out the -nature of any external action on the planets. But Mr. Adams soon -afterwards proceeded to work at the problem. As early as 1841 (as he -himself informs me) he conjectured the existence of a planet -exterior to Uranus, and recorded in a memorandum his design of -examining its effect; but deferred the calculations till he had -completed his preparations for the University examination which he -was to undergo in January, 1843, in order to receive the Degree of -Bachelor of Arts. He was the Senior Wrangler of that occasion, and -soon afterwards proceeded to carry his design into effect; applying -to the Astronomer Royal for recorded observations which might aid -him in his task. On one of the last days of October, 1845, Mr. Adams -went to the Observatory at Greenwich; and finding the Astronomer -Royal abroad, he left there a paper containing the elements of the -extra-Uranian Planet: the longitude was in this paper stated as 323½ -degrees. It was, as we have seen, in June, 1846, that M. Le -Verrier's Memoir appeared, in which he assigned to the disturbing -body a longitude of 325 degrees. The coincidence was striking. "I -cannot sufficiently express," says Mr. Airy, "the feeling of delight -and satisfaction which I received from the Memoir of M. Le Verrier." -This feeling communicated itself to others. Sir John Herschel said -in September, 1846, at a meeting of the British Association at -Southampton, "We see it (the probable new planet) as Columbus saw -America from the shores of Spain. Its movements have been felt, -trembling along the far-reaching line of our analysis, with a -certainty hardly inferior to that of ocular demonstration." {557} - -In truth, at the moment when this was uttered, the new Planet had -already been seen by Professor Challis; for, as we have said, he had -seen it in the early part of August. He had included it in the net -which he had cast among the stars for this very purpose; but -employing a slow and cautious process, he had deferred for a time -that examination of his capture which would have enabled him to -detect the object sought. As soon as he received M. Le Verrier's -paper of August 31 on September 29, he was so much impressed with -the sagacity and clearness of the limitations of the field of -observation there laid down, that he instantly changed his plan of -observation, and noted the planet, as an object having a visible -disk, on the evening of the same day. - -In this manner the theory of gravitation predicted and produced the -discovery. Thus to predict unknown facts found afterwards to be -true, is, as I have said, a confirmation of a theory which in -impressiveness and value goes beyond any explanation of known facts. -It is a confirmation which has only occurred a few times in the -history of science; and in the case only of the most refined and -complete theories, such as those of Astronomy and Optics. The -mathematical skill which was requisite in order to arrive at such a -discovery, may in some measure be judged of by the account which we -have had to give of the previous mathematical progress of the theory -of gravitation. It there appeared that the lives of many of the most -acute, clear-sighted, and laborious of mankind, had been employed -for generations in solving the problem. Given the planetary bodies, -to find their mutual perturbations: but here we have the inverse -problem--Given the perturbations, to find the planets.[50\A] - -[Note 50\A: This may be called the _inverse_ problem with reference -to the older and more familiar problem; but we may remark that the -usual phraseology of the Problem of Central Forces differs from this -analogy. In Newton's _Principia_, the earlier Sections, in which the -motion is given to find the force, are spoken of as containing the -Direct Problem of Central Forces: the Eighth Section of the First -Book, where the Force is given to find the orbit, is spoken of as -containing the _Inverse_ Problem of Central Forces.] - - -_The Minor Planets._ - -The discovery of the Minor Planets which revolve between the orbits -of Mars and Jupiter was not a consequence or confirmation of the -Newtonian theory. That theory gives no reason for the distance of -{558} the Planets from the Sun; nor does any theory yet devised give -such reason. But an empirical formula proposed by the Astronomer -Bode of Berlin, gives a law of these distances (_Bode's Law_), -which, to make it coherent, requires a planet between Mars and -Jupiter. With such an addition, the distance of Mercury, Venus, -Earth, Mars, the Missing Planet, Jupiter, Saturn, and Uranus, are -nearly as the numbers 4, 7, 10, 16, 28, 52, 100, 196, in which the -excesses of each number above the preceding are the series 3, 3, 6, -12, 24, 48, 96. On the strength of this law the Germans wrote _on the -long-expected Planet_, and formed themselves into associations for -the discovery of it. - -Not only did this law stimulate the inquiries for the Missing -Planet, and thus lead to the discovery of the Minor Planets, but it -had also a share in the discovery of Neptune. According to the law, -a planet beyond Uranus may be expected to be at the distance -represented by 388. Mr. Adams and M. Le Verrier both of them began -by assuming a distance of nearly this magnitude for the Planet which -they sought; that is, a distance more than 38 times the earth's -distance. It was found afterwards that the distance of Neptune is -only 30 times that of the earth; yet the assumption was of essential -use in obtaining the result and Mr. Airy remarks that the history -of the discovery shows the importance of using any received theory -as far as it will go, even if the theory can claim no higher merit -than that of being plausible.[51\A] - -[Note 51\A: Account of the Discovery of Neptune, &c., _Mem. Ast. -Soc._, vol. xvi. p. 414.] - -The discovery of Minor Planets in a certain region of the interval -between Mars and Jupiter has gone on to such an extent, that their -number makes them assume in a peculiar manner the character of -representatives of a Missing Planet. At first, as I have said in the -text, it was supposed that all these portions must pass through or -near a common node; this opinion being founded on the very bold -doctrine, that the portions must at one time have been united in one -Planet, and must then have separated. At this node, as I have -stated, Olbers lay in wait for them, as for a hostile army at a -defile. Ceres, Pallas, and Juno had been discovered in this way in -the period from 1801 to 1804; and Vesta was caught in 1807. For a -time the chase for new planets in this region seemed to have -exhausted the stock. But after thirty-eight years, to the -astonishment of astronomers, they began to be again detected in -extraordinary numbers. In 1845, M. Hencke of {559} Driessen -discovered a fifth of these planets, which was termed Astræa. In -various quarters the chase was resumed with great ardor. In 1847 -were found Hebe, Iris, and Flora; in 1848, Metis; in 1849, Hygæa; in -1850, Parthenope, Victoria, and Egeria; in 1861, Irene and Eunomia; -in 1852, Psyche, Thetis, Melpomene, Fortuna, Massilia, Lutetia, -Calliope. To these we have now (at the close of 1856) to add -_nineteen_ others; making up the whole number of these Minor Planets -at present known to _forty-two_. - -As their enumeration will show, the ancient practice has been -continued of giving to the Planets mythological names. And for a -time, till the numbers became too great, each of the Minor Planets -was designated in astronomical books by some symbol appropriate to -the character of the mythological person; as from ancient times Mars -has been denoted by a mark indicating a spear, and Venus by one -representing a looking-glass. Thus, when a Minor Planet was -discovered at London in 1851, the year in which the peace of the -world was, in a manner, celebrated by the Great Exhibition of the -Products of All Nations, held at that metropolis, the name _Irene_ -was given to the new star, as a memorial of the auspicious time of -its discovery. And it was agreed, for awhile, that its symbol should -be a dove with an olive-branch. But the vast multitude of the Minor -Planets, as discovery went on, made any mode of designation, except -a numerical one, practically inconvenient. They are now denoted by a -small circle inclosing a figure in the order of their discovery. -Thus, _Ceres_ is (1), _Irene_ is (14), and _Isis_ is (42). - -The rapidity with which these discoveries were made was owing in -part to the formation of star-maps, in which all known fixed stars -being represented, the existence of a new and movable star might be -recognized by comparison of the sky with the map. These maps were -first constructed by astronomers of different countries at the -suggestion of the Academy of Berlin; but they have since been -greatly extended, and now include much smaller stars than were -originally laid down. - -I will mention the number of planets discovered in each year. After -the start was once made, by Hencke's discovery of Astræa in 1845, -the same astronomer discovered Hebe in 1847; and in the same year -Mr. Hind, of London, discovered two others, Iris and Flora. The -years 1848 and 1849 each supplied one; the year 1850, three; 1851, -two; 1852 was marked by the extraordinary discovery of _eight_ new -members of the planetary system. The year 1853 supplied four; 1854, -six; 1855, four; and 1856 has already given us five. {560} - -These discoveries have been distributed among the observatories of -Europe. The bright sky of Naples has revealed seven new planets to -the telescope of Signer Gasparis. Marseilles has given us one; -Germany, four, discovered by M. Luther at Bilk; Paris has furnished -seven; and Mr. Hind, in Mr. Bishop's private observatory in London, -notwithstanding our turbid skies, has discovered no less than ten -planets; and there also Mr. Marth discovered (29) Amphitrite. Mr. -Graham, at the private observatory of Mr. Cooper, in Ireland, -discovered (9) Metis. - -America has supplied its planet, namely (31) Euphrosyne, discovered -by Mr. Ferguson at Washington and the most recent of these -discoveries is that by Mr. Pogson, of Oxford, who has found the -forty-second of these Minor Planets, which has been named -Isis.[52\A] - -[Note 52\A: I take this list from a Memoir of M. Bruhns, Berlin, -1856.] - -I may add that it appears to follow from the best calculations that -the total mass of all these bodies is very small. Herschel reckoned -the diameters of Ceres at 35, and of Pallas at 26 miles. It has -since been calculated[53\A] that some of them are smaller still; -Victoria having a diameter of 9 miles, Lutetia of 8, and Atalanta of -little more than 4. It follows from this that the whole mass would -probably be less than the sixth part of our moon. Hence their -perturbing effects on each other or on other planets are null; but -they are not the less disturbed by the action of the other planets, -and especially of Jupiter. - -[Note 53\A: Bruhns, as above.] - - -_Anomalies in the Action of Gravitation._ - -The complete and exact manner in which the doctrine of gravitation -explains the motions of the Comets as well as of the Planets, has -made astronomers very bold in proposing hypotheses to account for -any deviations from the motion which the theory requires. Thus -Encke's Comet is found to have its motion accelerated by about -one-eighth of a day in every revolution. This result was conceived -to be established by former observations, and is confirmed by the -facts of the appearance of 1852.[54\A] The hypothesis which is -proposed in order to explain this result is, that the Comet moves in -a resisting medium, which makes it fall inwards from its path, -towards the Sun, and thus, by narrowing its orbit, diminishes its -periodic time. On the other hand, M. Le Verrier has found that -Mercury's mean motion has gone on diminishing; {561} as if the -planet were, in the progress of his revolutions, receding further -from the Sun. This is explained, if we suppose that there is, in the -region of Mercury, a resisting medium which moves round the Sun in -the same direction as the Planets move. Evidence of a kind of -nebulous disk surrounding the Sun, and extending beyond the orbits -of Mercury and Venus, appears to be afforded us by the phenomenon -called the _Zodiacal Light_; and as the Sun itself rotates on its -axis, it is most probable that this kind of atmosphere rotates -also.[55\A] On the other hand, M. Le Verrier conceives that the -Comets which now revolve within the ordinary planetary limits have -not always done so, but have been caught and detained by the Planets -among which they move. In this way the action of Jupiter has brought -the Comets of Faye and Vico into their present limited orbits, as it -drew the Comet of Lexell out of its known orbit, when the Comet passed -over the Planet in 1779, since which time it has not been seen. - -[Note 54\A: _Berlin Memoirs_, 1854.] - -[Note 55\A: M. Le Verrier, _Annales de l'Obs. de Paris_, vol. i. -p. 89.] - -Among the examples of the boldness with which astronomers assume the -doctrine of gravitation even beyond the limits of the solar system -to be so entirely established, that hypotheses may and must be -assumed to explain any apparent irregularity of motion, we may -reckon the mode of accounting for certain supposed irregularities in -the proper motion of Sirius, which has been proposed by Bessel, and -which M. Peters thinks is proved to be true by his recent researches -(_Astr. Nach._ xxxi. p. 219, and xxxii. p. 1). The hypothesis is, -that Sirius has a companion star, dark, and therefore invisible to -us; and that the two, revolving round their common centre as the -system moves on, the motion of Sirius is seen to be sometimes -quicker and sometimes slower. - - -_The Earth's Density._ - -"Cavendish's experiment," as it is commonly called--the measure of -the attractions of manageable masses by the torsion balance, in -order to determine the density of the Earth--has been repeated -recently by Professor Reich at Freiberg, and by Mr. Baily in -England, with great attention to the means of attaining accuracy. -Professor Reich's result for the density of the Earth is 5·44; Mr. -Baily's is 5·92. Cavendish's result was 5·48; according to recent -revisions[56\A] it is 5·52. {562} - -[Note 56\A: The calculation has been revised by M. Edward Schmidt. -Humboldt's _Kosmos_, ii. p. 425.] - -But the statical effect of the attraction of manageable masses, or -even of mountains, is very small. The effect of a small change in -gravity may be accumulated by being constantly repeated in the -oscillations of a pendulum, and thus may become perceptible. Mr. -Airy attempted to determine the density of the Earth by a method -depending on this view. A pendulum oscillating at the surface was to -be compared with an equal pendulum at a great depth below the -surface. The difference of their rates would disclose the different -force of gravity at the two positions; and hence, the density of the -Earth. In 1826 and 1828, Mr. Airy attempted this experiment at the -copper mine of Dolcoath in Cornwall, but failed from various causes. -But in 1854, he resumed it at the Harton coal mine in Durham, the -depth of which is 1260 feet; having in this new trial, the advantage -of transmitting the time from one station to the other by the -instantaneous effect of galvanism, instead of by portable watches. -The result was a density of 6·56; which is much larger than the -preceding results, but, as Mr. Airy holds, is entitled to compete -with the others on at least equal terms. - - -_Tides._ - -I should be wanting in the expression of gratitude to those who have -practically assisted me in Researches on the Tides, if I did not -mention the grand series of Tide Observations made on the coast of -Europe and America in June, 1835, through the authority of the Board -of Admiralty, and the interposition of the late Duke of Wellington, at -that time Foreign Secretary. Tide observations were made for a -fortnight at all the Coast-guard stations of Great Britain and Ireland -in June, 1834; and these were repeated in June, 1835, with -corresponding observations on all the coasts of Europe, from the North -Cape of Norway to the Straits of Gibraltar; and from the mouth of the -St. Lawrence to the mouth of the Mississippi. The results of these -observations, which were very complete so far as the coast tides were -concerned, were given in the _Philosophical Transactions_ for 1836. - -Additional accuracy respecting the Tides of the North American coast -may be expected from the survey now going on under the direction of -Superintendent A. Bache. The Tides of the English Channel have been -further investigated, and the phenomena presented under a new point of -view by Admiral Beechey. {563} - -The Tides of the Coast of Ireland have been examined with great care -by Mr. Airy. Numerous and careful observations were made with a view, -in the first instance, of determining what was to be regarded as "the -Level of the Sea;" but the results were discussed so as to bring into -view the laws and progress, on the Irish coast, of the various -inequalities of the Tides mentioned in Chap. iv. Sect. 9 of this Book. - -I may notice as one of the curious results of the Tide Observations -of 1836, that it appeared to me, from a comparison of the -Observations, that there must be a point in the German Ocean, about -midway between Lowestoft on the English coast, and the Brill on the -Dutch coast, where the tide would vanish: and this was ascertained -to be the case by observation; the observations being made by -Captain Hewett, then employed in a survey of that sea. - -_Cotidal Lines_ supply, as I conceive, a good and simple method of -representing the progress and connection of _littoral_ tides. But to -draw cotidal lines across oceans, is a very precarious mode of -representing the facts, except we had much more knowledge on the -subject than we at present possess. In the _Phil. Trans._ for 1848, -I have resumed the subject of the Tides of the Pacific; and I have -there expressed my opinion, that while the littoral tides are -produced by progressive waves, the oceanic tides are more of the -nature of stationary undulations. - -But many points of this kind might be decided, and our knowledge on -this subject might be brought to a condition of completeness, if a -ship or ships were sent expressly to follow the phenomena of the -Tides from point to point, as the observations themselves might -suggest a course. Till this is done, our knowledge cannot be -completed. Detached and casual observations, made _aliud agendo_, -can never carry us much beyond the point where we at present are. - - -_Double Stars._ - -Sir John Herschel's work, referred to in the History (2d Ed.) as -then about to appear, was published in 1847.[57\A] In this work, -besides a vast amount of valuable observations and reasonings on -other subjects {564} (as Nebulæ, the Magnitude of Stars, and the -like), the orbits of several double stars are computed by the aid of -the new observations. But Sir John Herschel's conviction on the -point in question, the operation of the Newtonian law of gravitation -in the region of the stars, is expressed perhaps more clearly in -another work which he published in 1849.[58\A] He there speaks of -Double Stars, and especially of _gamma Virginis_, the one which has -been most assiduously watched, and has offered phenomena of the -greatest interest.[59\A] He then finds that the two components of -this star revolve round each other in a period of 182 years; and -says that the elements of the calculated orbit represent the whole -series of recorded observations, comprising an angular movement of -nearly nine-tenths of a complete circuit, both in angle and -distance, with a degree of exactness fully equal to that of -observation itself. "No doubt can therefore," he adds, "remain as to -the **prevalence in this remote system of the Newtonian Law of -Gravitation." - -[Note 57\A: _Results of Astronomical Observations made during the -years_ 1834, 5, 6, 7, 8, _at the Cape of Good Hope, being the -completion of a Telescopic Survey of the whole Surface of the -visible Heavens commenced in_ 1825.] - -[Note 58\A: _Outlines of Astronomy_.] - -[Note 59\A: _Out._ 844.] - -Yet M. Yvon de Villarceau has endeavored to show[60\A] that this -conclusion, however probable, is not yet proved. He holds, even for -the Double Stars, which have been most observed, the observations are -only equivalent to seven or eight really distinct data, and that seven -data are not sufficient to determine that an ellipse is described -according to the Newtonian law. Without going into the details of this -reasoning, I may remark, that the more rapid relative angular motion -of the components of a Double Star when they are more near each other, -proves, as is allowed on all hands, that they revolve under the -influence of a mutual attractive force, obeying the Keplerian Law of -Areas. But that, whether this force follows the law of the inverse -square or some other law, can hardly have been rigorously proved as -yet, we may easily conceive, when we recollect the manner in which -that law was proved for the Solar System. It was by means of an error -of _eight minutes_, observed by Tycho, that Kepler was enabled, as he -justly boasted, to reform the scheme of the Solar System,--to show, -that is, that the planetary orbits are ellipses with the sun in the -focus. Now, the observations of Double Stars cannot pretend to such -accuracy as this; and therefore the Keplerian theorem cannot, as yet, -have been fully demonstrated from those observations. But when we know -{565} that Double Stars are held together by a central force, to prove -that this force follows a different law from the only law which has -hitherto been found to obtain in the universe, and which obtains -between all the known masses of the universe, would require very clear -and distinct evidence, of which astronomers have as yet seen no trace. - -[Note 60\A: _Connaissance des Temps_, for 1852; published in 1849.] - - - - -CHAPTER VI. - - -_Sect._ 1. _Instruments._--2. _Clocks._ - -IN page 473, I have described the manner in which astronomers are able -to observe the transit of a star, and other astronomical phenomena, to -the exactness of a tenth of a second of time. The mode of observation -there described implies that the observer at the moment of observation -compares the impressions of the eye and of the ear. Now it is found -that the habit which the observer must form of doing this operates -differently in different observers, so that one observer notes the -same fact as happening a fraction of a second earlier or later than -another observer does; and this in every case. Thus, using the term -_equation_, as we use it in Astronomy, to express a correction by -which we get regularity from irregularity, there is a _personal -equation_ belonging to this mode of observation, showing that it is -liable to error. Can this error be got rid of? - -It is at any rate much diminished by a method of observation recently -introduced into observatories, and first practised in America. The -essential feature of this mode of observation consists in combining -the impression of sight with that of touch, instead of with that of -hearing. The observer at the moment of observation presses with his -finger so as to make a mark on a machine which by its motion measures -time with great accuracy and on a large scale; and thus small -intervals of time are made visible. - -A universal, though not a necessary, part of this machinery, as -hitherto adopted, is, that a galvanic circuit has been employed in -conveying the impression from the finger to the part where time is -measured and marked. The facility with which galvanic wires can {566} -thus lead the impression by any path to any distance, and increase its -force in any degree, has led to this combination, and almost -identification, of observation by touch with its record by galvanism. - -The method having been first used by Mr. Bond at Cambridge, in North -America, has been adopted elsewhere, and especially at Greenwich, -where it is used for all the instruments; and consequently a -collection of galvanic batteries is thus as necessary a part of the -apparatus of the establishment as its graduated circles and arcs. - - - - -END OF VOL. I. - - - - -HISTORY -OF THE -INDUCTIVE SCIENCES. - -VOLUME II. - - -HISTORY -OF THE -INDUCTIVE SCIENCES, -FROM -THE EARLIEST TO THE PRESENT TIME. -BY WILLIAM WHEWELL, D. D., -MASTER OF TRINITY COLLEGE, CAMBRIDGE. -_THE THIRD EDITION, WITH ADDITIONS._ -IN TWO VOLUMES. - - -VOLUME II. - - -NEW YORK: -D. APPLETON AND COMPANY, -549 & 551 BROADWAY. -1875. - - - - -CONTENTS - -OF THE SECOND VOLUME. - -_THE SECONDARY MECHANICAL SCIENCES._ - -BOOK VIII. - -HISTORY OF ACOUSTICS. - - PAGE -Introduction. 23 - -CHAPTER I.--PRELUDE TO THE SOLUTION OF PROBLEMS IN ACOUSTICS. 24 - -CHAPTER II.--PROBLEM OF THE VIBRATIONS OF STRINGS. 28 - -CHAPTER III.--PROBLEM OF THE PROPAGATION OF SOUND. 32 - -CHAPTER IV.--PROBLEM OF DIFFERENT SOUNDS OF THE SAME STRING. 36 - -CHAPTER V.--PROBLEM OF THE SOUNDS OF PIPES. 38 - -CHAPTER VI.--PROBLEM OF DIFFERENT MODES OF VIBRATION OF BODIES IN -GENERAL. 41 - -BOOK IX. - -HISTORY OF OPTICS, FORMAL AND PHYSICAL. - -Introduction. 51 -{8} - -_FORMAL OPTICS._ - -CHAPTER I.--PRIMARY INDUCTION OF OPTICS.--RAYS OF LIGHT AND LAWS -OF REFLECTION. 53 - -CHAPTER II.--DISCOVERY OF THE LAW OF REFRACTION. 54 - -CHAPTER III.--DISCOVERY OF THE LAW OF DISPERSION BY REFRACTION. 58 - -CHAPTER IV.--DISCOVERY OF ACHROMATISM. 66 - -CHAPTER V.--DISCOVERY OF THE LAWS OF DOUBLE REFRACTION. 69 - -CHAPTER VI.--DISCOVERY OF THE LAWS OF POLARIZATION. 72 - -CHAPTER VII.--DISCOVERY OF THE LAWS OF THE COLORS OF THIN PLATES. 76 - -CHAPTER VIII.--ATTEMPTS TO DISCOVER THE LAWS OF OTHER PHENOMENA. 78 - -CHAPTER IX.--DISCOVERY OF THE LAWS OF PHENOMENA OF DIPOLARIZED -LIGHT. 80 - -_PHYSICAL OPTICS._ - -CHAPTER X.--PRELUDE TO THE EPOCH OF YOUNG AND FRESNEL. 85 - -CHAPTER XI.--EPOCH OF YOUNG AND FRESNEL. - -_Sect._ 1. Introduction. 92 -_Sect._ 2. Explanation of the Periodical Colors of Thin Plates and -Shadows by the Undulatory Theory. 93 -_Sect._ 3. Explanation of Double Refraction by the Undulatory -Theory. 98 -_Sect._ 4. Explanation of Polarization by the Undulatory Theory. 100 -_Sect._ 5. Explanation of Dipolarization by the Undulatory -Theory. 105 -{9} - -CHAPTER XII.--SEQUEL TO THE EPOCH OF YOUNG AND -FRESNEL.--RECEPTION OF THE UNDULATORY THEORY. 111 - -CHAPTER XIII.--CONFIRMATION AND EXTENSION OF THE UNDULATORY -THEORY. 118 - -1. Double Refraction of Compressed Glass. 119 -2. Circular Polarization. 119 -3. Elliptical Polarization in Quartz. 122 -4. Differential Equations of Elliptical Polarization. 122 -5. Elliptical Polarization of Metals. 123 -6. Newton's Rings by Polarized Light. 124 -7. Conical Refraction. 124 -8. Fringes of Shadows. 126 -9. Objections to the Theory. 126 -10. Dispersion, on the Undulatory Theory. 128 -11. Conclusion. 128 - -BOOK X. - -HISTORY OF THERMOTICS AND ATMOLOGY. - -Introduction. 137 - -_THERMOTICS PROPER._ - -CHAPTER I.--THE DOCTRINES OF CONDUCTION AND RADIATION. - -_Sect._ 1. Introduction of the Doctrine of Conduction. 139 -_Sect._ 2. " " " Radiation. 142 -_Sect._ 3. Verification of the Doctrines of Conduction and -Radiation. 143 -_Sect._ 4. The Geological and Cosmological Application of -Thermotics. 144 - 1. Effect of Solar Heat on the Earth. 145 - 2. Climate. 146 - 3. Temperature of the Interior of the Earth. 147 - 4. Heat of the Planetary Spaces. 148 -_Sect._ 5. Correction of Newton's Law of Cooling. 149 -_Sect._ 6. Other Laws of Phenomena with respect to Radiation. 151 -_Sect._ 7. Fourier's Theory of Radiant Heat. 152 -_Sect._ 8. Discovery of the Polarization of Heat. 153 -{10} - -CHAPTER II.--THE LAWS OF CHANGES OCCASIONED BY HEAT. - -_Sect._ 1. Expansion by Heat.--The Law of Dalton and Gay-Lussac -for Gases. 157 -_Sect._ 2. Specific Heat.--Change of Consistence. 159 -_Sect._ 3. The Doctrine of Latent Heat. 160 - -_ATMOLOGY._ - -CHAPTER III.--THE RELATION OF VAPOR AND AIR. - -_Sect._ 1. The Boylean Law of the Air's Elasticity. 163 -_Sect._ 2. Prelude to Dalton's Doctrine of Evaporation. 165 -_Sect._ 3. Dalton's Doctrine of Evaporation. 170 -_Sect._ 4. Determination of the Laws of the Elastic Force of -Steam. 172 -_Sect._ 5. Consequences of the Doctrine of -Evaporation.--Explanation of Rain, Dew, and Clouds. 176 - -CHAPTER IV.--PHYSICAL THEORIES OF HEAT. - -Thermotical Theories. 181 -Atmological Theories. 184 -Conclusion. 187 - -_THE MECHANICO-CHEMICAL SCIENCES._ - -BOOK XI. - -HISTORY OF ELECTRICITY. - -Introduction. 191 - -CHAPTER I.--DISCOVERY OF LAWS OF ELECTRIC PHENOMENA. 193 - -CHAPTER II.--THE PROGRESS OF ELECTRICAL THEORY. 201 - -Question of One or Two Fluids. 210 -Question of the Material Reality of the Electric Fluid. 212 -{11} - -BOOK XII. - -HISTORY OF MAGNETISM. - -CHAPTER I.--DISCOVERY OF LAWS OF MAGNETIC PHENOMENA. 217 - -CHAPTER II.--PROGRESS OF MAGNETIC THEORY. - -Theory of Magnetic Action. 220 -Theory of Terrestrial Magnetism. 224 -Conclusion. 232 - -BOOK XIII. - -HISTORY OF GALVANISM, OR VOLTAIC ELECTRICITY. - -CHAPTER I.--DISCOVERY OF VOLTAIC ELECTRICITY. 237 - -CHAPTER II.--RECEPTION AND CONFIRMATION OF THE DISCOVERY OF -VOLTAIC ELECTRICITY. 240 - -CHAPTER III.--DISCOVERY OF THE LAWS OF THE MUTUAL ATTRACTION AND -REPULSION OF VOLTAIC CURRENTS.--AMPÈRE. 242 - -CHAPTER IV.--DISCOVERY OF ELECTRO-MAGNETIC ACTION.--OERSTED. 243 - -CHAPTER V.--DISCOVERY OF THE LAWS OF ELECTRO-MAGNETIC ACTION. 245 - -CHAPTER VI.--THEORY OF ELECTRODYNAMICAL ACTION. - -Ampère's Theory. 246 -Reception of Ampère's Theory. 249 - -CHAPTER VII.--CONSEQUENCES OF THE ELECTRODYNAMIC THEORY. 250 - -Discovery of Diamagnetism. 252 -{12} - -CHAPTER VIII.--DISCOVERY OF THE LAWS OF MAGNETO-ELECTRIC -INDUCTION.--FARADAY. 253 - -CHAPTER IX.--TRANSITION TO CHEMICAL SCIENCE. 256 - -_THE ANALYTICAL SCIENCE._ - -BOOK XIV. - -HISTORY OF CHEMISTRY. - -CHAPTER I.--IMPROVEMENT OF THE NOTION OF CHEMICAL ANALYSIS, AND -RECOGNITION OF IT AS THE SPAGIRIC ART. 261 - -CHAPTER II.--DOCTRINE OF ACID AND ALKALI.--SYLVIUS. 262 - -CHAPTER III.--DOCTRINE OF ELECTIVE ATTRACTIONS.--GEOFFROY. -BERGMAN. 265 - -CHAPTER IV.--DOCTRINE OF ACIDIFICATION AND COMBUSTION.--PHLOGISTIC -THEORY. - -Publication of the Theory by Beccher and Stahl. 267 -Reception and Application of the Theory. 271 - -CHAPTER V.--CHEMISTRY OF GASES.--BLACK. CAVENDISH. 272 - -CHAPTER VI.--EPOCH OF THE THEORY OF OXYGEN.--LAVOISIER. - -_Sect._ 1. Prelude to the Theory.--Its Publication. 275 -_Sect._ 2. Reception and Confirmation of the Theory of Oxygen. 278 -_Sect._ 3. Nomenclature of the Oxygen Theory. 281 - -CHAPTER VII.--APPLICATION AND CORRECTION OF THE OXYGEN THEORY. 282 -{13} - -CHAPTER VIII.--THEORY OF DEFINITE, RECIPROCAL, AND MULTIPLE -PROPORTIONS. - -_Sect._ 1. Prelude to the Atomic Theory, and its Publication by -Dalton. 285 -_Sect._ 2. Reception and Confirmation of the Atomic Theory. 288 -_Sect._ 3. The Theory of Volumes.--Gay-Lussac. 290 - -CHAPTER IX.--EPOCH OF DAVY AND FARADAY. - -_Sect._ 1. Promulgation of the Electro-chemical Theory by Davy. 291 -_Sect._ 2. Establishment of the Electro-chemical Theory by -Faraday. 296 -_Sect._ 3. Consequences of Faraday's Discoveries. 302 -_Sect._ 4. Reception of the Electro-chemical Theory. 303 - -CHAPTER X.--TRANSITION FROM THE CHEMICAL TO THE CLASSIFICATORY -SCIENCES. 305 - -_THE ANALYTICO-CLASSIFICATORY SCIENCE._ - -BOOK XV. - -HISTORY OF MINERALOGY. - -INTRODUCTION - -_Sect._ 1. Of the Classificatory Sciences. 313 -_Sect._ 2. Of Mineralogy as the Analytico-classificatory -Science. 314 - -_CRYSTALLOGRAPHY._ - -CHAPTER I.--PRELUDE TO THE EPOCH OF DE LISLE AND HAÜY. 316 - -CHAPTER II.--EPOCH OF ROMÉ DE LISLE AND HAÜY.--ESTABLISHMENT OF -THE FIXITY OF CRYSTALLINE ANGLES, AND THE SIMPLICITY OF THE LAWS -OF DERIVATION. 320 - -CHAPTER III.--RECEPTION AND CORRECTIONS OF THE HAUÏAN -CRYSTALLOGRAPHY. 324 -{14} - -CHAPTER IV.--ESTABLISHMENT OF THE DISTINCTION OF SYSTEMS OF -CRYSTALLIZATION.--WEISS AND MOHS. 326 - -CHAPTER V.--RECEPTION AND CONFIRMATION OF THE DISTINCTION OF -SYSTEMS OF CRYSTALLIZATION. - -Diffusion of the Distinction of Systems. 330 -Confirmation of the Distinction of Systems by the Optical -Properties of Minerals.--Brewster. 331 - -CHAPTER VI.--CORRECTION OF THE LAW OF THE SAME ANGLE FOR THE SAME -SUBSTANCE. - -Discovery of Isomorphism.--Mitscherlich. 334 -Dimorphism. 336 - -CHAPTER VII.--ATTEMPTS TO ESTABLISH THE FIXITY OF OTHER PHYSICAL -PROPERTIES.--WERNER. 336 - -_SYSTEMATIC MINERALOGY._ - -CHAPTER VIII.--ATTEMPTS AT THE CLASSIFICATION OF MINERALS. - -_Sect._ 1. Proper Object of Classification. 339 -_Sect._ 2. Mixed Systems of Classification. 340 - -CHAPTER IX.--ATTEMPTS AT THE REFORM OF MINERALOGICAL -SYSTEMS.--SEPARATION OF THE CHEMICAL AND NATURAL HISTORY METHODS. - -_Sect._ 1. Natural History System of Mohs. 344 -_Sect._ 2. Chemical System of Berzelius and others. 347 -_Sect._ 3. Failure of the Attempts at Systematic Reform. 349 -_Sect._ 4. Return to Mixed Systems with Improvements. 351 - -_CLASSIFICATORY SCIENCES._ - -BOOK XVI. - -HISTORY OF SYSTEMATIC BOTANY AND ZOOLOGY. - -Introduction. 357 -{15} - -CHAPTER I.--IMAGINARY KNOWLEDGE OF PLANTS. 358 - -CHAPTER II.--UNSYSTEMATIC KNOWLEDGE OF PLANTS. 361 - -CHAPTER III.--FORMATION OF A SYSTEM OF ARRANGEMENT OF PLANTS. - -_Sect._ 1. Prelude to the Epoch of Cæsalpinus. 369 -_Sect._ 2. Epoch of Cæsalpinus.--Formation of a System of -Arrangement. 373 -_Sect._ 3. Stationary Interval. 378 -_Sect._ 4. Sequel to the Epoch of Cæsalpinus.--Further Formation -and Adoption of Systematic Arrangement. 382 - -CHAPTER IV.--THE REFORM OF LINNÆUS. - -_Sect._ 1. Introduction of the Reform. 387 -_Sect._ 2. Linnæan Reform of Botanical Terminology. 389 -_Sect._ 3. " " " Nomenclature. 391 -_Sect._ 4. Linnæus's Artificial System, 395 -_Sect._ 5. Linnæus's Views on a Natural Method. 396 -_Sect._ 6. Reception and Diffusion of the Linnæan Reform. 400 - -CHAPTER V.--PROGRESS TOWARDS A NATURAL SYSTEM OF BOTANY. 404 - -CHAPTER VI.--THE PROGRESS OF SYSTEMATIC ZOOLOGY. 412 - -CHAPTER VII.--THE PROGRESS OF ICHTHYOLOGY. 419 - -Period of Unsystematic Knowledge. 420 -Period of Erudition. 421 -Period of Accumulation of Materials.--Exotic Collections. 422 -Epoch of the Fixation of Characters.--Ray and Willoughby. 422 -Improvement of the System.--Artedi. 423 -Separation of the Artificial and Natural Methods in Ichthyology. 426 - -_ORGANICAL SCIENCES._ - -BOOK XVII. - -HISTORY OF PHYSIOLOGY AND COMPARATIVE ANATOMY. - -Introduction. 435 -{16} - -CHAPTER I.--DISCOVERY OF THE ORGANS OF VOLUNTARY MOTION. - -_Sect._ 1. Knowledge of Galen and his Predecessors. 438 -_Sect._ 2. Recognition of Final Causes in Physiology.--Galen. 442 - -CHAPTER II.--DISCOVERY OF THE CIRCULATION OF THE BLOOD. - -_Sect._ 1. Prelude to the Discovery. 444 -_Sect._ 2. The Discovery of the Circulation made by Harvey. 447 -_Sect._ 3. Reception of the Discovery. 448 -_Sect._ 4. Bearing of the Discovery on the Progress of -Physiology. 449 - -CHAPTER III.--DISCOVERY OF THE MOTION OF THE CHYLE, AND CONSEQUENT -SPECULATIONS. - -_Sect._ 1. The Discovery of the Motion of the Chyle. 452 -_Sect._ 2. The Consequent Speculations. Hypotheses of Digestion. 453 - -CHAPTER IV.--EXAMINATION OF THE PROCESS OF REPRODUCTION IN -ANIMALS AND PLANTS, AND CONSEQUENT SPECULATIONS. - -_Sect._ 1. The Examination of the Process of Reproduction in -Animals. 455 -_Sect._ 2. " " " " in -Vegetables. 457 -_Sect._ 3. The Consequent Speculations.--Hypotheses of -Generation. 459 - -CHAPTER V.--EXAMINATION OF THE NERVOUS SYSTEM, AND CONSEQUENT -SPECULATIONS. - -_Sect._ 1. The Examination of the Nervous System. 461 -_Sect._ 2. The Consequent Speculations. Hypotheses respecting -Life, Sensation, and Volition. 464 - -CHAPTER VI.--INTRODUCTION OF THE PRINCIPLE OF DEVELOPED AND -METAMORPHOSED SYMMETRY. - -_Sect._ 1. Vegetable Morphology.--Göthe. De Candolle. 468 -_Sect._ 2. Application of Vegetable Morphology. 474 - -CHAPTER VII.--PROGRESS OF ANIMAL MORPHOLOGY. - -_Sect._ 1. Rise of Comparative Anatomy. 475 -_Sect._ 2. Distinction of the General Types of the Forms of -Animals.--Cuvier. 478 -_Sect._ 3. Attempts to establish the Identity of the Types of -Animal Forms. 480 -{17} - -CHAPTER VIII.--THE DOCTRINE OF FINAL CAUSES IN PHYSIOLOGY. - -_Sect._ 1. Assertion of the Principle of Unity of Plan. 482 -_Sect._ 2. Estimate of the Doctrine of Unity of Plan. 487 -_Sect._ 3. Establishment and Application of the Principle of the -Conditions of Existence of Animals.--Cuvier. 492 - -_THE PALÆTIOLOGICAL SCIENCES._ - -BOOK XVIII. - -HISTORY OF GEOLOGY. - -Introduction. 499 - -_DESCRIPTIVE GEOLOGY._ - -CHAPTER I.--PRELUDE TO SYSTEMATIC DESCRIPTIVE GEOLOGY. - -_Sect._ 1. Ancient Notices of Geological Facts. 505 -_Sect._ 2. Early Descriptions and Collections of Fossils. 506 -_Sect._ 3. First Construction of Geological Maps. 509 - -CHAPTER II.--FORMATION OF SYSTEMATIC DESCRIPTIVE GEOLOGY. - -_Sect._ 1. Discovery of the Order and Stratification of the -Materials of the Earth. 511 -_Sect._ 2. Systematic Form given to Descriptive -Geology.--Werner. 513 -_Sect._ 3. Application of Organic Remains as a Geological -Character.--Smith. 515 -_Sect._ 4. Advances in Palæontology.--Cuvier. 517 -_Sect._ 5. Intellectual Characters of the Founders of Systematic -Descriptive Geology. 520 - -CHAPTER III.--SEQUEL TO THE FORMATION OF SYSTEMATIC DESCRIPTIVE -GEOLOGY. - -_Sect._ 1. Reception and Diffusion of Systematic Geology. 523 -_Sect._ 2. Application of Systematic Geology.--Geological Surveys -and Maps. 526 -_Sect._ 3. Geological Nomenclature. 527 -_Sect._ 4. Geological Synonymy, or Determination of Geological -Equivalents. 531 -{18} - -CHAPTER IV.--ATTEMPTS TO DISCOVER GENERAL LAWS IN GEOLOGY. - -_Sect._ 1. General Geological Phenomena. 537 -_Sect._ 2. Transition to Geological Dynamics. 541 - -_GEOLOGICAL DYNAMICS._ - -CHAPTER V.--INORGANIC GEOLOGICAL DYNAMICS. - -_Sect._ 1. Necessity and Object of a Science of Geological -Dynamics. 542 -_Sect._ 2. Aqueous Causes of Change. 545 -_Sect._ 3. Igneous Causes of Change.--Motions of the Earth's -Surface. 549 -_Sect._ 4. The Doctrine of Central Heat. 554 -_Sect._ 5. Problems respecting Elevations and Crystalline -Forces. 556 -_Sect._ 6. Theories of Changes of Climate. 559 - -CHAPTER VI.--PROGRESS OF THE GEOLOGICAL DYNAMICS OF ORGANIZED -BEINGS. - -_Sect._ 1. Objects of this Science. 561 -_Sect._ 2. Geography of Plants and Animals. 562 -_Sect._ 3. Questions of the Transmutation of Species. 563 -_Sect._ 4. Hypothesis of Progressive Tendencies. 565 -_Sect._ 5. Question of Creation as related to Science. 568 -_Sect._ 6. The Hypothesis of the Regular Creation and Extinction -of Species. 573 - 1. Creation of Species. 573 - 2. Extinction of Species. 576 -_Sect._ 7. The Imbedding of Organic Remains. 577 - -_PHYSICAL GEOLOGY._ - -CHAPTER VII.--PROGRESS OF PHYSICAL GEOLOGY. - -_Sect._ 1. Object and Distinctions of Physical Geology. 579 -_Sect._ 2. Of Fanciful Geological Opinions. 580 -_Sect._ 3. Of Premature Geological Theories. 584 - -CHAPTER VIII.--THE TWO ANTAGONIST DOCTRINES OF GEOLOGY. - -_Sect._ 1. Of the Doctrine of Geological Catastrophes. 586 -_Sect._ 2. " " " Uniformity. 588 -{19} - -_ADDITIONS TO THE THIRD EDITION._ - -BOOK VIII.--ACOUSTICS. - -SOUND. - -The Velocity of Sound in Water. 599 - -BOOK IX.--OPTICS. - -Photography. 601 -Fluorescence. 601 - -UNDULATORY THEORY. - -Direction of the Transverse Vibrations in Polarization. 603 -Final Disproof of the Emission Theory. 604 - -BOOK X.--THERMOTICS.--ATMOLOGY. - -THE RELATION OF VAPOR AND AIR. - -Force of Steam. 606 -Temperature of the Atmosphere. 607 - -THEORIES OF HEAT. - -The Dynamical Theory of Heat. 608 - -BOOK XI.--ELECTRICITY. - -General Remarks. 610 -Dr. Faraday's Views of Statical Electrical Induction. 611 - -BOOK XII.--MAGNETISM. - -Recent Progress of Terrestrial Magnetism. 613 -Correction of Ships' Compasses. 616 -{20} - -BOOK XIII.--VOLTAIC ELECTRICITY. - -MAGNETO-ELECTRIC INDUCTION. - -Diamagnetlc Polarity. 620 -Magneto-optic Effects and Magnecrystallic Polarity. 621 -Magneto-electric Machines. 623 -Applications of Electrodynamic Discoveries. 623 - -BOOK XIV.--CHEMISTRY. - -THE ELECTRO-CHEMICAL THEORY. - -The Number of Elementary Substances. 625 - -BOOK XV.--MINERALOGY. - -Crystallography. 627 -Optical Properties of Minerals. 629 -Classification of Minerals. 630 - -BOOK XVI.--CLASSIFICATORY SCIENCES. - -Recent Views of Botany. 631 - " " Zoology. 634 - -BOOK XVII.--PHYSIOLOGICAL AND COMPARATIVE ANATOMY. - -VEGETABLE MORPHOLOGY. 636 -ANIMAL MORPHOLOGY. 638 -Final Causes. 642 - -BOOK XVIII. - -GEOLOGY. 646 - - - -{{21}} -BOOK VIII. - - -_THE SECONDARY MECHANICAL SCIENCES._ - - -HISTORY OF ACOUSTICS. - - - . . . . . . Go, demand - Of mighty Nature, if 'twas ever meant - That we should pry far off and be unraised, - That we should pore, and dwindle as we pore, - Viewing all objects unremittingly - In disconnexion dead and spiritless; - And still dividing, and dividing still, - Break down all grandeur, still unsatisfied - With the perverse attempt, while littleness - May yet become more little; waging thus - An impious warfare 'gainst the very life - Of our own souls. WORDSWORTH, _Excursion_. - - . . . . . . Ἐσσυμένη δὲ - Ἠερίην ἀψῖδα διεῤῥοίζησε πεδίλῳ - Εἰς δόμον ἉΡΜΟΝIΗΣ παμμητόρος, ὁππόθι νύμφη - Ἴκελον οἶκον ἐναίε τύπῳ τετράζυγι κόσμου - Αὐτοπαγῆ NONNUS. _Dionysiac_. xli. 275. - - Along the skiey arch the goddess trode, - And sought Harmonia's august abode; - The universal plan, the mystic Four, - Defines the figure of the palace-floor. - Solid and square the ancient fabric stands, - Raised by the labors of unnumbered hands. - - - -{{23}} -BOOK VIII. - - - -INTRODUCTION. - - -_The Secondary Mechanical Sciences._ - -IN the sciences of Mechanics and Physical Astronomy, Motion and -Force are the direct and primary objects of our attention. But there -is another class of sciences in which we endeavor to reduce -phenomena, not evidently mechanical, to a known dependence upon -mechanical properties and laws. In the cases to which I refer, the -facts do not present themselves to the senses as modifications of -position and motion, but as _secondary qualities_, which are found -to be in some way derived from those primary attributes. Also, in -these cases the phenomena are reduced to their mechanical laws and -causes in a secondary manner; namely, by treating them as the -operation of a _medium_ interposed between the object and the organ -of sense. These, then, we may call _Secondary Mechanical Sciences_. -The sciences of this kind which require our notice are those which -treat of the sensible qualities, Sound, Light, and Heat; that is. -Acoustics, Optics, and Thermotics. - -It will be recollected that our object is not by any means to give a -full statement of all the additions which have been successively -made to our knowledge on the subjects under review, or a complete -list of the persons by whom such additions have been made; but to -present a view of the progress of each of those branches of -knowledge _as a theoretical science_;--to point out the Epochs of -the discovery of those general principles which reduce many facts to -one theory; and to note all that is most characteristic and -instructive in the circumstances and persons which bear upon such -Epochs. A history of any science, written with such objects, will -not need to be long; but it will fail in its purpose altogether, if -it do not distinctly exhibit some well-marked and prominent -features. {24} - -We begin our account of the Secondary Mechanical Sciences with -Acoustics, because the progress towards right theoretical views, -was, in fact, made much earlier in the science of Sound, than in -those of Light and of Heat; and also, because a clear comprehension -of the theory to which we are led in this case, is the best -preparation for the difficulties (by no means inconsiderable) of the -reasonings of theorists on the other subjects. - - - - -CHAPTER I. - -PRELUDE TO THE SOLUTION OF PROBLEMS IN ACOUSTICS. - - -IN some measure the true theory of sound was guessed by very early -speculators on the subject; though undoubtedly conceived in a very -vague and wavering manner. That sound is caused by some motion of -the sounding body, and conveyed by some motion of the air to the -ear, is an opinion which we trace to the earliest times of physical -philosophy. We may take Aristotle as the best expounder of this -stage of opinion. In his Treatise _On Sound and Hearing_, he says, -"Sound takes place when bodies strike the air, not by the air having -a _form_ impressed upon it (σχηματίζομενον), as some think, but by -its being moved in a corresponding manner; (probably he means in a -manner corresponding to the impulse;) the air being contracted, and -expanded, and overtaken, and again struck by the impulses of the -breath and of the strings. For when the breath falls upon and -strikes the air which is next it, the air is carried forwards with -an impetus, and that which is contiguous to the first is carried -onwards; so that the same voice spreads every way as far as the -motion of the air takes place." - -As is the case with all such specimens of ancient physics, different -persons would find in such a statement very different measures of -truth and distinctness. The admirers of antiquity might easily, by -pressing the language closely, and using the light of modern -discovery, detect in this passage an exact account of the production -and propagation of sound: while others might maintain that in -Aristotle's own mind, there were only vague notions, and verbal -generalizations. This {25} latter opinion is very emphatically -expressed by Bacon.[1\8] "The collision or thrusting of air, which -they will have to be the cause of sound, neither denotes the _form_ -nor the latent process of sound; but is a term of ignorance and of -superficial contemplation." Nor can it be justly denied, that an -exact and distinct apprehension of the kind of motion of the air by -which sound is diffused, was beyond the reach of the ancient -philosophers, and made its way into the world long afterwards. It -was by no means easy to reconcile the nature of such motion with -obvious phenomena. For the process is not evident as motion; since, -as Bacon also observes,[2\8] it does not visibly agitate the flame -of a candle, or a feather, or any light floating substance, by which -the slightest motions of the air are betrayed. Still, the persuasion -that sound is some motion of the air, continued to keep hold of -men's minds, and acquired additional distinctness. The illustration -employed by Vitruvius, in the following passage, is even now one of -the best we can offer.[3\8] "Voice is breath, flowing, and made -sensible to the hearing by striking the air. It moves in infinite -circumferences of circles, as when, by throwing a stone into still -water, you produce innumerable circles of waves, increasing from the -centre and spreading outwards, till the boundary of the space, or -some obstacle, prevents their outlines from going further. In the -same manner the voice makes its motion in circles. But in water the -circle moves breadthways upon a level plain; the voice proceeds in -breadth, and also successively ascends in height." - -[Note 1\8: _Hist. Son. et Aud._ vol. ix. p. 68.] - -[Note 2\8: _Ibid._] - -[Note 3\8: _De Arch._ v. 3.] - -Both the comparison, and the notice of the difference of the two -cases, prove the architect to have had very clear notions on the -subject; which he further shows by comparing the resonance of the -walls of a building to the disturbance of the outline of the waves -of water when they meet with a boundary, and are thrown back. -"Therefore, as in the outlines of waves in water, so in the voice, -if no obstacle interrupt the foremost, it does not disturb the -second and the following ones, so that all come to the ears of -persons, whether high up or low down, without resonance. But when -they strike against obstacles, the foremost, being thrown back, -disturb the lines of those which follow." Similar analogies were -employed by the ancients in order to explain the occurrence of -Echoes. Aristotle says,[4\8] "An Echo takes place, when the air, -being as one body in consequence of the vessel which bounds it, and -being prevented from being thrust forwards, is reflected {26} back -like a ball." Nothing material was added to such views till modern -times. - -[Note 4\8: _De Animâ_, ii. 8.] - -Thus the first conjectures of those who philosophized concerning -sound, led them to an opinion concerning its causes and laws, which -only required to be distinctly understood, and traced to mechanical -principles, in order to form a genuine science of Acoustics. It was, -no doubt, a work which required a long time and sagacious reasoners, -to supply what was thus wanting; but still, in consequence of this -peculiar circumstance in the early condition of the prevalent -doctrine concerning sound, the history of Acoustics assumes a -peculiar form. Instead of containing, like the history of Astronomy -or of Optics, a series of generalizations, each including and rising -above preceding generalizations; in this case, the highest -generalization is in view from the first; and the object of the -philosopher is to determine its precise meaning and circumstances in -each example. Instead of having a series of inductive Truths, -successively dawning on men's minds, we have a series of -Explanations, in which certain experimental facts and laws are -reconciled, as to their mechanical principles and their measures, -with the general doctrine already in our possession. Instead of -having to travel gradually towards a great discovery, like Universal -Gravitation, or Luminiferous Undulations, we take our stand upon -acknowledged truths, the production and propagation of sound by the -motion of bodies and of air; and we connect these with other truths, -the laws of motion and the known properties of bodies, as, for -instance, their elasticity. Instead of _Epochs of Discovery_, we -have _Solutions of Problems_; and to these we must now proceed. - -We must, however, in the first place, notice that these Problems -include other subjects than the mere production and propagation of -sound generally. For such questions as these obviously occur:--what -are the laws and cause of the differences of sounds;--of acute and -grave, loud and low, continued and instantaneous;--and, again, of -the differences of articulate sounds, and of the quality of -different voices and different instruments? The first of these -questions, in particular, the real nature of the difference of acute -and grave sounds, could not help attracting attention; since the -difference of notes in this respect was the foundation of one of the -most remarkable mathematical sciences of antiquity. Accordingly, we -find attempts to explain this difference in the ancient writers on -music. In Ptolemy's _Harmonics_, the third Chapter of the first Book -is entitled, "How the {27} acuteness and graveness of notes is -produced;" and in this, after noting generally the difference of -sounds, and the causes of difference (which he states to be the -force of the striking body, the physical constitution of the body -struck, and other causes), he comes to the conclusion, that "the -things which produce acuteness in sounds, are a greater density and -a smaller size; the things which produce graveness, are a greater -rarity and a bulkier form." He afterwards explains this so as to -include a considerable portion of truth. Thus he says, "That in -strings, and in pipes, other things remaining the same, those which -are stopped at the smaller distance from the bridge give the most -acute note; and in pipes, those notes which come through holes -nearest to the mouth-hole are most acute." He even attempts a -further generalization, and says that the greater acuteness arises, -in fact, from the body being more tense; and that thus "hardness may -counteract the effect of greater density, as we see that brass -produces a more acute sound than lead." But this author's notions of -tension, since they were applied so generally as to include both the -tension of a string, and the tension of a piece of solid brass, must -necessarily have been very vague. And he seems to have been -destitute of any knowledge of the precise nature of the motion or -impulse by which sound is produced; and, of course, still more -ignorant of the mechanical principles by which these motions are -explained. The notion of _vibrations_ of the parts of sounding -bodies, does not appear to have been dwelt upon as an essential -circumstance; though in some cases, as in sounding strings, the fact -is very obvious. And the notion of vibrations of the air does not at -all appear in ancient writers, except so far as it may be conceived -to be implied in the comparison of aërial and watery waves, which we -have quoted from Vitruvius. It is however, very unlikely that, even -in the case of water, the motions of the particles were distinctly -conceived, for such conception is far from obvious. - -The attempts to apprehend distinctly, and to explain mechanically, -the phenomena of sound, gave rise to a series of Problems, of which -we most now give a brief history. The questions which more peculiarly -constitute the Science of Acoustics, are the questions concerning -those motions or affections of the air by which it is the medium of -hearing. But the motions of sounding bodies have both so much -connexion with those of the medium, and so much resemblance to them, -that we shall include in our survey researches on that subject also. -{28} - - - -CHAPTER II. - -PROBLEM OF THE VIBRATIONS OF STRINGS. - - -THAT the continuation of sound depends on a continued minute and -rapid motion, a shaking or trembling, of the parts of the sounding -body, was soon seen. Thus Bacon says,[5\8] "The duration of the -sound of a bell or a string when struck, which appears to be -prolonged and gradually extinguished, does not proceed from the -first percussion; but the trepidation of the body struck perpetually -generates a new sound. For if that trepidation be prevented, and the -bell or string be stopped, the sound soon dies: as in _spinets_, as -soon as the _spine_ is let fall so as to touch the string, the sound -ceases." In the case of a stretched string, it is not difficult to -perceive that the motion is a motion back and forwards across the -straight line which the string occupies when at rest. The further -examination of the quantitative circumstances of this oscillatory -motion was an obvious problem; and especially after oscillations, -though of another kind (those of a pendulous body), had attracted -attention, as they had done in the school of Galileo. Mersenne, one -of the promulgators of Galileo's philosophy in France, is the first -author in whom I find an examination of the details of this case -(_Harmonicorum Liber_, Paris, 1636). He asserts,[6\8] that the -differences and concords of acute and grave sounds depend on the -rapidity of vibrations, and their ratio; and he proves this doctrine -by a series of experimental comparisons. Thus he finds[7\8] that the -note of a string is as its length, by taking a string first twice, -and then four times as long as the original string, other things -remaining the same. This, indeed, was known to the ancients, and was -the basis of that numerical indication of the notes which the -proposition expresses. Mersenne further proceeds to show the effect -of thickness and tension. He finds (Prop. 7) that a string must be -four times as thick as another, to give the octave below; he finds, -also (Prop. 8), that the tension must be about four times as great -in order to produce the octave above. From these proportions various -others are deduced, and the _law of the_ {29} _phenomena_ of this -kind may be considered as determined. Mersenne also undertook to -_measure_ the phenomena numerically, that is to determine the number -of vibrations of the string in each of such cases; which at first -might appear difficult, since it is obviously impossible to count -with the eye the passages of a sounding string backwards and -forwards. But Mersenne rightly assumed, that the number of -vibrations is the same so long as the tone is the same, and that the -ratios of the numbers of vibrations of different strings may be -determined from the numerical relations of their notes. He had, -therefore, only to determine the number of vibrations of one certain -string, or one known note, to know those of all others. He took a -musical string of three-quarters of a foot long, stretched with a -weight of six pounds and five eighths, which he found gave him by -its vibrations a certain standard note in his organ: he found that a -string of the same material and tension, fifteen feet, that is, -twenty times as long, made ten recurrences in a second; and he -inferred that the number of vibrations of the shorter string must -also be twenty times as great; and thus such a string must make in -one second of time two hundred vibrations. - -[Note 5\8: _Hist. Son. et Aud._ vol. ix. p. 71.] - -[Note 6\8: L. i. Prop. 15.] - -[Note 7\8: L. ii. Prop. 6.] - -This determination of Mersenne does not appear to have attracted due -notice; but some time afterwards attempts were made to ascertain the -connexion between the sound and its elementary pulsations in a more -direct manner. Hooke, in 1681, produced sounds by the striking of -the teeth of brass wheels,[8\8] and Stancari, in 1706, by whirling -round a large wheel in air, showed, before the Academy of Bologna, -how the number of vibrations in a given note might be known. -Sauveur, who, though deaf for the first seven years of his life, was -one of the greatest promoters of the science of sound, and gave it -its name of _Acoustics_, endeavored also, about the same time, to -determine the number of vibrations of a standard note, or, as he -called it, Fixed Sound. He employed two methods, both ingenious and -both indirect. The first was the method of _beats_. Two organ-pipes, -which form a discord, are often heard to produce a kind of _howl_, -or _wavy_ noise, the sound swelling and declining at small intervals -of time. This was readily and rightly ascribed to the coincidences -of the pulsations of sound of the two notes after certain cycles. -Thus, if the number of vibrations of the notes were as fifteen to -sixteen in the same time, every fifteenth vibration of the one would -coincide with every {30} sixteenth vibration of the other, while all -the intermediate vibrations of the two tones would, in various -degrees, disagree with each other; and thus every such cycle, of -fifteen and sixteen vibrations, might be heard as a separate beat of -sound. Now, Sauveur wished to take a case in which these beats were -so slow as to be counted,[9\8] and in which the ratio of the -vibrations of the notes was known from a knowledge of their musical -relations. Thus if the two notes form an interval of a semitone, -their ratio will be that above supposed, fifteen to sixteen; and if -the beats be found to be six in a second, we know that, in that -time, the graver note makes ninety and the acuter ninety-six -vibrations. In this manner Sauveur found that an open organ-pipe, -five feet long, gave one hundred vibrations in a second. - -[Note 8\8: _Life_, p. xxiii.] - -[Note 9\8: _Ac. Sc. Hist._ 1700, p. 131.] - -Sauveur's other method is more recondite, and approaches to a -mechanical view of the question.[10\8] He proceeded on this basis; a -string, horizontally stretched, cannot be drawn into a mathematical -straight line, but always hangs in a very flat curve, or _festoon_. -Hence Sauveur assumed that its transverse vibrations may be -conceived to be identical with the lateral swingings of such a -festoon. Observing that the string C, in the middle of a -harpsichord, hangs in such a festoon to the amount of 1⁄323rd of an -inch, he calculates, by the laws of pendulums, the time of -oscillation, and finds it 1⁄122nd of a second. Thus this C, his -_fixed note_, makes one hundred and twenty-two vibrations in a -second. It is curious that this process, seemingly so arbitrary, is -capable of being justified on mechanical principles; though we can -hardly give the author credit for the views which this justification -implies. It is, therefore, easy to understand that it agreed with -other experiments, in the laws which it gave for the dependence of -the tone on the length and tension. - -[Note 10\8: _Ac. Sc. Hist._ 1713.] - -The problem of satisfactorily explaining this dependence, on -mechanical principles, naturally pressed upon the attention of -mathematicians when the law of the phenomena was thus completely -determined by Mersenne and Sauveur. It was desirable to show that -both the circumstances and the measure of the phenomena were such as -known mechanical causes and laws would explain. But this problem, as -might be expected, was not attacked till mechanical principles, and -the modes of applying them, had become tolerably familiar. - -As the vibrations of a string are produced by its tension, it -appeared to be necessary, in the first place, to determine the law -of the tension {31} which is called into action by the motion of the -string; for it is manifest that, when the string is drawn aside from -the straight line into which it is stretched, there arises an -additional tension, which aids in drawing it back to the straight -line as soon as it is let go. Hooke (_On Spring_, 1678) determined -the law of this additional tension, which he expressed in his noted -formula, "Ut tensio sic vis," the Force is as the Tension; or -rather, to express his meaning more clearly, the Force of tension is -as the Extension, or, in a string, as the increase of length. But, -in reality, this principle, which is important in many acoustical -problems, is, in the one now before us, unimportant; the force which -urges the string towards the straight line, depends, with such small -extensions as we have now to consider, not on the extension, but on -the curvature; and the power of treating the mathematical difficulty -of curvature, and its mechanical consequences, was what was -requisite for the solution of this problem. - -The problem, in its proper aspect, was first attacked and mastered -by Brook Taylor, an English mathematician of the school of Newton, -by whom the solution was published in 1715, in his _Methodus -Incrementorum_. Taylor's solution was indeed imperfect, for it only -pointed out a form and a mode of vibration, with which the string -_might_ move consistently with the laws of mechanics; not the mode -in which it _must_ move, supposing its form to be any whatever. It -showed that the curve might be of the nature of that which is called -_the companion to the cycloid_; and, on the supposition of the curve -of the string being of this form, the calculation confirmed the -previously established laws by which the tone, or the time of -vibration, had been discovered to depend on the length, tension, and -bulk of the string. The mathematical incompleteness of Taylor's -reasoning must not prevent us from looking upon his solution of the -problem as the most important step in the progress of this part of -the subject: for the difficulty of applying mechanical principles to -the question being once overcome, the extension and correction of -the application was sure to be undertaken by succeeding -mathematicians; and, accordingly, this soon happened. We may add, -moreover, that the subsequent and more general solutions require to -be considered with reference to Taylor's, in order to apprehend -distinctly their import; and further, that it was almost evident to -a mathematician, even before the general solution had appeared, that -the dependence of the time of vibration on the length and tension, -would be the same in the general case as in the {32} Taylorian -curve; so that, for the ends of physical philosophy, the solution -was not very incomplete. - -John Bernoulli, a few years afterwards,[11\8] solved the problem of -vibrating chords on nearly the same principles and suppositions as -Taylor; but a little later (in 1747), the next generation of great -mathematicians, D'Alembert, Euler, and Daniel Bernoulli, applied the -increased powers of analysis to give generality to the mode of -treating this question; and especially the calculus of partial -differentials, invented for this purpose. But at this epoch, the -discussion, so far as it bore on physics, belonged rather to the -history of another problem, which comes under our notice hereafter, -that of the composition of vibrations; we shall, therefore, defer -the further history of the problem of vibrating strings, till we -have to consider it in connexion with new experimental facts. - -[Note 11\8: _Op._ iii. p. 207.] - - - - -CHAPTER III. - -PROBLEM OF THE PROPAGATION OF SOUND. - - -WE have seen that the ancient philosophers, for the most part, held -that sound was transmitted, as well as produced, by some motion of -the air, without defining what kind of motion this was; that some -writers, however, applied to it a very happy similitude, the -expansive motion of the circular waves produced by throwing a stone -into still water; but that notwithstanding, some rejected this mode -of conception, as, for instance, Bacon, who ascribed the -transmission of sound to certain "spiritual species." - -Though it was an obvious thought to ascribe the motion of sound to -some motion of air; to conceive what kind of motion could and did -produce this effect, must have been a matter of grave perplexity at -the time of which we are speaking; and is far from easy to most -persons even now. We may judge of the difficulty of forming this -conception, when we recollect that John Bernoulli the younger[12\8] -declared, that he could not understand Newton's proposition on this -subject. The difficulty consists in this; that the movement of the -parts of air, in which sound consists, travels along, but that the -parts {33} of air themselves do not so travel. Accordingly Otto -Guericke,[13\8] the inventor of the air-pump, asks, "How can sound -be conveyed by the motion of the air? when we find that it is better -conveyed through air that is still, than when there is a wind." We -may observe, however, that he was partly misled by finding, as he -thought, that a bell could be heard in the vacuum of his air-pump; a -result which arose, probably, from some imperfection in his -apparatus. - -[Note 12\8:_ Prize Dis. on Light_, 1736.] - -[Note 13\8: _De Vac. Spat._ p. 138.] - -Attempts were made to determine, by experiment, the circumstances of -the motion of sound; and especially its velocity. Gassendi[14\8] was -one of the first who did this. He employed fire-arms for the -purpose, and thus found the velocity to be 1473 Paris feet in a -second. Roberval found a velocity so small (560 feet) that it threw -uncertainty upon the rest, and affected Newton's reasonings -subsequently.[15\8] Cassini, Huyghens, Picard, Römer, found a -velocity of 1172 Paris feet, which is more accurate than the former. -Gassendi had been surprised to find that the velocity with which -sounds travel, is the same whether they are loud or gentle. - -[Note 14\8: Fischer, _Gesch. d. Physik_. vol. i. 171.] - -[Note 15\8: Newt. _Prin._ B. ii. P. 50, Schol.] - -The explanation of this constant velocity of sound, and of its -amount, was one of the problems of which a solution was given in the -Great Charter of modern science, Newton's _Principia_ (1687). There, -for the first time, were explained the real nature of the motions -and mutual action of the parts of the air through which sound is -transmitted. It was shown[16\8] that a body vibrating in an elastic -medium, will propagate _pulses_ through the medium; that is, the parts -of the medium will move forwards and backwards, and this motion will -affect successively those parts which are at a greater and greater -distance from the origin of motion. The parts, in going forwards, -produce condensation; in returning to their first places, they allow -extension; and the play of the elasticities developed by these -expansions and contractions, supplies the forces which continue to -propagate the motion. - -[Note 16\8: Newt. _Prin._ B. ii. P. 43.] - -The idea of such a motion as this, is, as we have said, far from -easy to apprehend distinctly: but a distinct apprehension of it is a -step essential to the physical part of the sciences now under -notice; for it is by means of such _pulses_, or _undulations_, that -not only sound, but light, and probably heat, are propagated. We -constantly meet with evidence of the difficulty which men have in -conceiving this undulatory motion, and in separating it from a local -motion of the medium as a {34} mass. For instance, it is not easy at -first to conceive the waters of a great river flowing constantly -_down_ towards the sea, while waves are rolling _up_ the very same -part of the stream; and while the great elevation, which makes the -tide, is travelling from the sea perhaps with a velocity of fifty -miles an hour. The motion of such a wave, or elevation, is distinct -from any stream, and is of the nature of undulations in general. The -parts of the fluid stir for a short time and for a small distance, -so as to accumulate themselves on a neighboring part, and then -retire to their former place; and this movement affects the parts in -the order of their places. Perhaps if the reader looks at a field of -standing corn when gusts of wind are sweeping over it in visible -waves, he will have his conception of this matter aided; for he will -see that here, where each ear of grain is anchored by its stalk, -there can be no permanent local motion of the substance, but only a -successive stooping and rising of the separate straws, producing -hollows and waves, closer and laxer strips of the crowded ears. - -Newton had, moreover, to consider the mechanical consequences which -such condensations and rarefactions of the elastic medium, air, -would produce in the parts of the fluid itself. Employing known laws -of the elasticity of air, he showed, in a very remarkable -proposition,[17\8] the law according to which the particles of air -might vibrate. We may observe, that in this solution, as in that of -the vibrating string already mentioned, a rule was exhibited -according to which the particles _might_ oscillate, but not the law -to which they _must_ conform. It was proved that, by taking the -motion of each particle to be perfectly similar to that of a -pendulum, the forces, developed by contraction and expansion, were -precisely such as the motion required; but it was not shown that no -other type of oscillation would give rise to the same accordance of -force and motion. Newton's reasoning also gave a determination of -the speed of propagation of the pulses: it appeared that sound ought -to travel with the velocity which a body would acquire by falling -freely through half _the height of a homogeneous atmosphere_; "the -height of a homogeneous atmosphere" being the height which the air -must have, in order to produce, at the earth's surface, the actual -atmospheric pressure, supposing no diminution of density to take -place in ascending. This height is about 29,000 feet; and hence it -followed that the velocity was 968 feet. This velocity is really -considerably less than that of sound; but at the time of which {35} -we speak, no accurate measure had been established; and Newton -persuaded himself, by experiments made in the cloister of Trinity -College, his residence, that his calculation was not far from the -fact. When, afterwards, more exact experiments showed the velocity -to be 1142 English feet, Newton attempted to explain the difference -by various considerations, none of which were adequate to the -purpose;--as, the dimensions of the solid particles of which the -fluid air consists;--or the vapors which are mixed with it. Other -writers offered other suggestions; but the true solution of the -difficulty was reserved for a period considerably subsequent. - -[Note 17\8: _Princ._ B. ii. P. 48.] - -Newton's calculation of the motion of sound, though logically -incomplete, was the great step in the solution of the problem; for -mathematicians could not but presume that his result was not -restricted to the hypothesis on which he had obtained it; and the -extension of the solution required only mere ordinary talents. The -logical defect of his solution was assailed, as might have been -expected. Cranmer (professor at Geneva), in 1741, conceived that he -was destroying the conclusiveness of Newton's reasoning, by showing -that it applied equally to other modes of oscillation. This, indeed, -contradicted the enunciation of the 48th Prop. of the Second Book of -the _Principia_; but it confirmed and extended all the general -results of the demonstration; for it left even the velocity of sound -unaltered, and thus showed that the velocity did not depend -mechanically on the type of the oscillation. But the satisfactory -establishment of this physical generalization was to be supplied -from the vast generalizations of analysis, which mathematicians were -now becoming able to deal with. Accordingly this task was performed -by the great master of analytical generalization, Lagrange, in 1759, -when, at the age of twenty-three, he and two friends published the -first volume of the _Turin Memoirs_. Euler, as his manner was, at -once perceived the merit of the new solution, and pursued the -subject on the views thus suggested. Various analytical improvements -and extensions were introduced into the solution by the two great -mathematicians; but none of these at all altered the formula by -which the velocity of sound was expressed; and the discrepancy -between calculation and observation, about one-sixth of the whole, -which had perplexed Newton, remained still unaccounted for. - -The merit of satisfactorily explaining this discrepancy belongs to -Laplace. He was the first to remark[18\8] that the common law of the -{36} changes of elasticity in the air, as dependent on its -compression, cannot be applied to those rapid vibrations in which -sound consists, since the sudden compression produces a degree of -heat which additionally increases the elasticity. The ratio of this -increase depended on the experiments by which the relation of heat -and air is established. Laplace, in 1816, published[19\8] the -theorem on which the correction depends. On applying it, the -calculated velocity of sound agreed very closely with the best -antecedent experiments, and was confirmed by more exact ones -instituted for that purpose. - -[Note 18\8: _Méc. Cél._ t. v. l. xii. p. 96.] - -[Note 19\8: _Ann. Phys. et Chim._ t. iii. p. 288.] - -This step completes the solution of the problem of the propagation -of sound, as a mathematical induction, obtained from, and verified -by, facts. Most of the discussions concerning points of analysis to -which the investigations on this subject gave rise, as, for -instance, the admissibility of _discontinuous functions_ into the -solutions of partial differential equations, belong to the history -of pure mathematics. Those which really concern the physical theory -of sound may be referred to the problem of the motion of air in -tubes, to which we shall soon have to proceed; but we must first -speak of another form which the problem of vibrating strings assumed. - -It deserves to be noticed that the ultimate result of the study of -the undulations of fluids seems to show that the comparison of the -motion of air in the diffusion of sound with the motion of circular -waves from a centre in water, which is mentioned at the beginning of -this chapter, though pertinent in a certain way, is not exact. It -appears by Mr. Scott's recent investigations concerning waves,[20\8] -that the circular waves are oscillating waves of the Second order, -and are _gregarious_. The sound-wave seems rather to resemble the -great solitary Wave of Translation of the First order, of which we -have already spoken in Book vi. chapter vi. - -[Note 20\8: _Brit. Ass. Reports for_ 1844, p. 361.] - - - - -CHAPTER IV. - -PROBLEM OF DIFFERENT SOUNDS OF THE SAME STRING. - - -IT had been observed at an early period of acoustical knowledge, -that one string might give several sounds. Mersenne and others {37} -had noticed[21\8] that when a string vibrates, one which is in -unison with it vibrates without being touched. He was also aware -that this was true if the second string was an octave or a twelfth -below the first. This was observed as a new fact in England in 1674, -and communicated to the Royal Society by Wallis.[22\8] But the later -observers ascertained further, that the longer string divides itself -into two, or into three equal parts, separated by _nodes_, or points -of rest; this they proved by hanging bits of paper on different -parts of the string. The discovery so modified was again made by -Sauveur[23\8] about 1700. The sounds thus produced in one string by -the vibration of another, have been termed _Sympathetic Sounds_. -Similar sounds are often produced by performers on stringed -instruments, by touching the string at one of its aliquot divisions, -and are then called the _Acute harmonics_. Such facts were not -difficult to explain on Taylor's view of the mechanical condition of -the string; but the difficulty was increased when it was noticed -that a sounding body could produce these different notes _at the -same time_. Mersenne had remarked this, and the fact was more -distinctly observed and pursued by Sauveur. The notes thus produced -in addition to the genuine note of the string, have been called -_Secondary Notes_; those usually heard are, the Octave, the Twelfth, -and the Seventeenth above the note itself. To supply a mode of -conceiving distinctly, and explaining mechanically, vibrations which -should allow of such an effect, was therefore a requisite step in -acoustics. - -[Note 21\8: _Harm._ lib. iv. Prop. 28 (1636).] - -[Note 22\8: _Ph. Tr._ 1677, April.] - -[Note 23\8: _A. P._ 1701.] - -This task was performed by Daniel Bernoulli in a memoir published in -1755.[24\8] He there stated and proved the Principle of _the -coexistence of small vibrations_. It was already established, that a -string might vibrate either in a single _swelling_ (if we use this -word to express the curve between two nodes which Bernoulli calls a -_ventre_), or in two or three or any number of equal swellings with -immoveable nodes between. Daniel Bernoulli showed further, that -these nodes might be combined, each taking place as if it were the -only one. This appears sufficient to explain the coexistence of the -harmonic sounds just noticed. D'Alembert, indeed, in the article -_Fundamental_ in the French _Encyclopédie_, and Lagrange in his -_Dissertation on Sound_ in the _Turin Memoirs_,[25\8] offer several -objections to this explanation; and it cannot be denied that the -subject has its difficulties; but {38} still these do not deprive -Bernoulli of the merit of having pointed out the principle of -Coexistent Vibrations, or divest that principle of its value in -physical science. - -[Note 24\8: _Berlin Mem._ 1753, p. 147.] - -[Note 25\8: T. i. pp. 64, 103.] - -Daniel Bernoulli's Memoir, of which we speak, was published at a -period when the clouds which involve the general analytical -treatment of the problem of vibrating strings, were thickening about -Euler and D'Alembert, and darkening into a controversial hue; and as -Bernoulli ventured to interpose his view, as a solution of these -difficulties, which, in a mathematical sense, it is not, we can -hardly be surprised that he met with a rebuff. The further -prosecution of the different modes of vibration of the same body -need not be here considered. - -The sounds which are called _Grave Harmonics_, have no analogy with -the Acute Harmonics above-mentioned; nor do they belong to this -section; for in the case of Grave Harmonics, we have one sound from -the co-operation of two strings, instead of several sounds from one -string. These harmonics are, in fact, connected with beats, of which -we have already spoken; the beats becoming so close as to produce a -note of definite musical quality. The discovery of the Grave -Harmonics is usually ascribed to Tartini, who mentions them in 1754; -but they are first noticed[26\8] in the work of Sorge _On tuning -Organs_, 1744. He there expresses this discovery in a query. "Whence -comes it, that if we tune a fifth (2 : 3), a _third_ sound is -faintly heard, the octave below the lower of the two notes? Nature -shows that with 2 : 3, she still requires the unity, to perfect the -order 1, 2, 3." The truth is, that these numbers express the -frequency of the vibrations, and thus there will be coincidences of -the notes 2 and 3, which are of the frequency 1, and consequently -give the octave below the sound 2. This is the explanation given by -Lagrange,[27\8] and is indeed obvious. - -[Note 26\8: Chladni. _Acoust._ p. 254.] - -[Note 27\8: _Mem. Tur._ i. p. 104.] - - - - -CHAPTER V. - -PROBLEM OF THE SOUNDS OF PIPES. - - -IT was taken for granted by those who reasoned on sounds, that the -sounds of flutes, organ-pipes, and wind-instruments in general, {39} -consisted in vibrations of some kind; but to determine the nature -and laws of these vibrations, and to reconcile them with mechanical -principles, was far from easy. The leading facts which had been -noticed were, that the note of a pipe was proportional to its -length, and that a flute and similar instruments might be made to -produce some of the acute harmonics, as well as the genuine note. It -had further been noticed,[28\8] that pipes closed at the end, -instead of giving the series of harmonics 1, ½, ⅓, ¼, &c., would -give only those notes which answer to the odd numbers 1, ⅓, ⅕, &c. -In this problem also, Newton[29\8] made the first step to the -solution. At the end of the propositions respecting the velocity of -sound, of which we have spoken, he noticed that it appeared by -taking Mersenne's or Sauveur's determination of the number of -vibrations corresponding to a given note, that the pulse of air runs -over twice the length of the pipe in the time of each vibration. He -does not follow out this observation, but it obviously points to the -theory, that the sound of a pipe consists of pulses which travel -back and forwards along its length, and are kept in motion by the -breath of the player. This supposition would account for the -observed dependence of the note on the length of the pipe. The -subject does not appear to have been again taken up in a theoretical -way till about 1760; when Lagrange in the second volume of the -_Turin Memoirs_, and D. Bernoulli in the _Memoirs of the French -Academy_ for 1762, published important essays, in which some of the -leading facts were satisfactorily explained, and which may therefore -be considered as the principal solutions of the problem. - -[Note 28\8: D. Bernoulli, _Berlin. Mem._ 1753, p. 150.] - -[Note 29\8: _Princip._ Schol. Prop. 50.] - -In these solutions there was necessarily something hypothetical. In -the case of vibrating strings, as we have seen, the Form of the -vibrating curve was guessed at only, but the existence and position -of the Nodes could be rendered visible to the eye. In the vibrations -of air, we cannot see either the places of nodes, or the mode of -vibration; but several of the results are independent of these -circumstances. Thus both of the solutions explain the fact, that a -tube closed at one end is in unison with an open tube of double the -length; and, by supposing nodes to occur, they account for the -existence of the odd series of harmonics alone, 1, 3, 5, in closed -tubes, while the whole series, 1, 2, 3, 4, 5, &c., occurs in open -ones. Both views of the nature of the vibration appear to be nearly -the same; though Lagrange's is expressed with an analytical -generality which renders it obscure, and Bernoulli has perhaps {40} -laid down an hypothesis more special than was necessary. -Lagrange[30\8] considers the vibration of open flutes as "the -oscillations of a fibre of air," under the condition that its -elasticity at the two ends is, during the whole oscillation, the -same as that of the surrounding atmosphere. Bernoulli supposes[31\8] -the whole inertia of the air in the flute to be collected into one -particle, and this to be moved by the whole elasticity arising from -this displacement. It may be observed that both these modes of -treating the matter come very near to what we have stated as -Newton's theory; for though Bernoulli supposes all the air in the -flute to be moved at once, and not successively, as by Newton's -pulse, in either case the whole elasticity moves the whole air in -the tube, and requires more time to do this according to its -quantity. Since that time, the subject has received further -mathematical developement from Euler,[32\8] Lambert,[33\8] and -Poisson;[34\8] but no new explanation of facts has arisen. Attempts -have however been made to ascertain experimentally the places of the -nodes. Bernoulli himself had shown that this place was affected by -the amount of the opening, and Lambert[35\8] had examined other -cases with the same view. Savart traced the node in various musical -pipes under different conditions; and very recently Mr. Hopkins, of -Cambridge, has pursued the same experimental inquiry.[36\8] It -appears from these researches, that the early assumptions of -mathematicians with regard to the position of the nodes, are not -exactly verified by the facts. When the air in a pipe is made to -vibrate so as to have several nodes which divide it into equal -parts, it had been supposed by acoustical writers that the part -adjacent to the open end was half of the other parts; the outermost -node, however, is found experimentally to be _displaced_ from the -position thus assigned to it, by a quantity depending on several -collateral circumstances. - -[Note 30\8: _Mém. Turin_, vol. ii. p. 154.] - -[Note 31\8: _Mém. Berlin_, 1753, p. 446.] - -[Note 32\8: _Nov. Act. Petrop._ tom. xvi.] - -[Note 33\8: _Acad. Berlin_, 1775.] - -[Note 34\5: _Journ. Ec. Polyt._ cap. 14.] - -[Note 35\8: _Acad. Berlin_, 1775.] - -[Note 36\8: _Camb. Trans._ vol. v. p. 234.] - -Since our purpose was to consider this problem only so far as it has -tended towards its mathematical solution, we have avoided saying -anything of the dependence of the mode of vibration on the cause by -which the sound is produced; and consequently, the researches on the -effects of reeds, embouchures, and the like, by Chladni, Savart, -Willis, and others, do not belong to our subject. It is easily seen -that the complex effect of the elasticity and other properties of -the reed and of the air together, is a problem of which we can -hardly {41} hope to give a complete solution till our knowledge has -advanced much beyond its present condition. - -Indeed, in the science of Acoustics there is a vast body of facts to -which we might apply what has just been said; but for the sake of -pointing out some of them, we shall consider them as the subjects of -one extensive and yet unsolved problem. - - - - -CHAPTER VI. - -PROBLEM OF DIFFERENT MODES OF VIBRATION OF BODIES IN GENERAL. - - -NOT only the objects of which we have spoken hitherto, strings and -pipes, but almost all bodies are capable of vibration. Bells, gongs, -tuning-forks, are examples of solid bodies; drums and tambourines, -of membranes; if we run a wet finger along the edge of a glass -goblet, we throw the fluid which it contains into a regular -vibration; and the various character which sounds possess according -to the room in which they are uttered, shows that large masses of -air have peculiar modes of vibration. Vibrations are generally -accompanied by sound, and they may, therefore, be considered as -acoustical phenomena, especially as the sound is one of the most -decisive facts in indicating the mode of vibration. Moreover, every -body of this kind can vibrate in many different ways, the vibrating -segments being divided by Nodal Lines and Surfaces of various form -and number. The mode of vibration, selected by the body in each -case, is determined by the way in which it is held, the way in which -it is set in vibration, and the like circumstances. - -The general problem of such vibrations includes the discovery and -classification of the phenomena; the detection of their formal laws; -and, finally, the explanation of these on mechanical principles. We -must speak very briefly of what has been done in these ways. The -facts which indicate Nodal Lines had been remarked by Galileo, on -the sounding board of a musical instrument; and Hooke had proposed -to observe the vibrations of a bell by strewing flour upon it. But -it was Chladni, a German philosopher, who enriched acoustics with -the discovery of the vast variety of symmetrical figures of Nodal -Lines, which are exhibited on plates of regular forms, when {42} -made to sound. His first investigations on this subject, -_Entdeckungen über die Theorie des Klangs_, were published 1787; and -in 1802 and 1817 he added other discoveries. In these works he not -only related a vast number of new and curious facts, but in some -measure reduced some of them to order and law. For instance, he has -traced all the vibrations of square plates to a resemblance with -those forms of vibration in which Nodal Lines are parallel to one -side of the square, and those in which they are parallel to another -side; and he has established a notation for the modes of vibration -founded on this classification. Thus, 5-2 denotes a form in which -there are five nodal lines parallel to one side, and two to another; -or a form which can be traced to a disfigurement of such a standard -type. Savart pursued this subject still further; and traced, by -actual observation, the forms of the Nodal Surfaces which divide -solid bodies, and masses of air, when in a state of vibration. - -The dependence of such vibrations upon their physical cause, namely, -the elasticity of the substance, we can conceive in a general way; -but the mathematical theory of such cases is, as might be supposed, -very difficult, even if we confine ourselves to the obvious question -of the mechanical possibility of these different modes of vibration, -and leave out of consideration their dependence upon the mode of -excitation. The transverse vibrations of elastic rods, plates, and -rings, had been considered by Euler in 1779; but his calculation -concerning plates had foretold only a small part of the curious -phenomena observed by Chladni;[37\8] and the several notes which, -according to his calculation, the same ring ought to give, were not -in agreement with experiment.[38\8] Indeed, researches of this kind, -as conducted by Euler, and other authors,[39\8] rather were, and -were intended for, examples of analytical skill, than explanations -of physical facts. James Bernoulli, after the publication of -Chladni's experiments in 1787, attempted to solve the problem for -plates, by treating a plate as a collection of fibres; but, as -Chladni observes, the justice of this mode of conception is -disproved, by the disagreement of the results with experiment. - -[Note 37\8: Fischer, vi. 587.] - -[Note 38\8: Ib. vi. 596.] - -[Note 39\8: See Chladni, p. 474.] - -The Institute of France, which had approved of Chladni's labours, -proposed, in 1809, the problem now before us as a -prize-question:[40\8]--"To give the mathematical theory of the -vibrations of elastic {43} surfaces, and to compare it with -experiment." Only one memoir was sent in as a candidate for the -prize; and this was not crowned, though honorable mention was made -of it.[41\8] The formulæ of James Bernoulli were, according to M. -Poisson's statement, defective, in consequence of his not taking -into account the normal force which acts at the exterior boundary of -the plate.[42\8] The author of the anonymous memoir corrected this -error, and calculated the note corresponding to various figures of -the nodal lines; and he found an agreement with experiment -sufficient to justify his theory. He had not, however, proved his -fundamental equation, which M. Poisson demonstrated in a Memoir, -read in 1814.[43\8] At a more recent period also, MM. Poisson and -Cauchy (as well as a lady, Mlle. Sophie Germain) have applied to -this problem the artifices of the most improved analysis. M. -Poisson[44\8] determined the relation of the notes given by the -longitudinal and the transverse vibrations of a rod; and solved the -problem of vibrating circular plates when the nodal lines are -concentric circles. In both these cases, the numerical agreement of -his results with experience, seemed to confirm the justice of his -fundamental views.[45\8] He proceeds upon the hypothesis, that -elastic bodies are composed of separate particles held together by -the attractive forces which they exert upon each other, and -distended by the repulsive force of heat. M. Cauchy[46\8] has also -calculated the transverse, longitudinal, and rotatory vibrations of -elastic rods, and has obtained results agreeing closely with -experiment through a considerable list of comparisons. The combined -authority of two profound analysts, as MM. Poisson and Cauchy are, -leads us to believe that, for the simpler cases of the vibrations of -elastic bodies, Mathematics has executed her task; but most of the -more complex cases remain as yet unsubdued. - -[Note 40\8: See Chladni, p. 357.] - -[Note 41\8: Poisson's _Mém. in Ac. Sc._ 1812, p. 169.] - -[Note 42\8: Ib. p. 220.] - -[Note 43\8: Ib. 1812, p. 2.] - -[Note 44\8: Ib. t. viii. 1829.] - -[Note 45\8: _An. Chim._ tom. xxxvi. 1827, p. 90.] - -[Note 46\8: _Exercices de Mathématique_, iii. and iv.] - -The two brothers, Ernest and William Weber, made many curious -observations on undulations, which are contained in their -_Wellenlehre_, (Doctrine of Waves,) published at Leipsig in 1825. -They were led to suppose, (as Young had suggested at an earlier -period,) that Chladni's figures of nodal lines in plates were to be -accounted for by the superposition of undulations.[47\8] Mr. -Wheatstone[48\8] has undertaken to account for Chladni's figures of -vibrating _square_ plates by this {44} superposition of two or more -simple and obviously allowable modes of nodal division, which have -the same time of vibration. He assumes, for this purpose, certain -"primary figures," containing only _parallel_ nodal lines; and by -combining these, first in twos, and then in fours, he obtains most -of Chladni's observed figures, and accounts for their transitions -and deviations from regularity. - -[Note 47\8: _Wellenlehre_, p. 474.] - -[Note 48\8: _Phil. Trans._ 1833, p. 593.] - -The principle of the superposition of vibrations is so solidly -established as a mechanical truth, that we may consider an -acoustical problem as satisfactorily disposed of when it is reduced -to that principle, as well as when it is solved by analytical -mechanics: but at the same time we may recollect, that the right -application and limitation of this law involves no small difficulty; -and in this case, as in all advances in physical science, we cannot -but wish to have the new ground which has been gained, gone over by -some other person in some other manner; and thus secured to us as a -permanent possession. - -_Savart's Laws._--In what has preceded, the vibrations of bodies -have been referred to certain general classes, the separation of -which was suggested by observation; for example, the _transverse_, -_longitudinal_, and _rotatory_,[49\8] vibrations of rods. The -transverse vibrations, in which the rod goes backwards and forwards -across the line of its length, were the only ones noticed by the -earlier acousticians: the others were principally brought into -notice by Chladni. As we have already seen in the preceding pages, -this classification serves to express important laws; as, for -instance, a law obtained by M. Poisson which gives the relation of -the notes produced by the transverse and longitudinal vibrations of -a rod. But this distinction was employed by M. Felix Savart to -express laws of a more general kind; and then, as often happens in -the progress of science, by pursuing these laws to a higher point of -generality, the distinction again seemed to vanish. A very few words -will explain these steps. - -[Note 49\8: Vibrations tournantes.] - -It was long ago known that vibrations may be communicated by -contact. The distinction of transverse and longitudinal vibrations -being established, Savart found that if one rod touched another -perpendicularly, the longitudinal vibrations of the first occasion -transverse vibrations in the second, and _vice versâ_. This is the -more remarkable, since the two sets of vibrations are not equal in -rapidity, and therefore cannot sympathize in any obvious -manner.[50\8] Savart found himself {45} able to generalize this -proposition, and to assert that in any combination of rods, strings, -and laminæ, at right angles to each other, the longitudinal and -transverse vibrations affect respectively the rods in the one and -other direction,[51\8] so that when the horizontal rods, for example, -vibrate in the one way, the vertical rods vibrate in the other. - -[Note 50\8: _An. Chim._ 1819, tom. xiv. p. 138.] - -[Note 51\8: _An. Chim._ p. 152.] - -This law was thus expressed in terms of that classification of -vibrations of which we have spoken. Yet we easily see that we may -express it in a more general manner, without referring to that -classification, by saying, that vibrations are communicated so as -always to be parallel to their original direction. And by following -it out in this shape by means of experiment, M. Savart was led, a -short time afterwards, to deny that there is any essential -distinction in these different kinds of vibration. "We are thus -led," he says[52\8] in 1822, "to consider _normal_ [transverse] -vibrations as only one circumstance in a more general motion common -to all bodies, analogous to _tangential_ [longitudinal and rotatory] -vibrations; that is, as produced by small _molecular oscillations_, -and differently modified according to the direction which it -affects, relatively to the dimensions of the vibrating body." - -[Note 52\8: Ib. t. xxv. p. 33.] - -These "inductions," as he properly calls them, are supported by a -great mass of ingenious experiments; and may be considered as well -established, when they are limited to molecular oscillations, -employing this phrase in the sense in which it is understood in the -above statement; and also when they are confined to bodies in which -the play of elasticity is not interrupted by parts more rigid than -the rest, as the sound-post of a violin.[53\8] And before I quit the -subject, I may notice a consequence which M. Savart has deduced from -his views, and which, at first sight, appears to overturn most of -the earlier doctrines respecting vibrating bodies. It was formerly -held that tense strings and elastic rods could vibrate only in a -determinate series of modes of division, with no intermediate steps. -But M. Savart maintains,[54\8] on the contrary, that they produce -sounds which are gradually transformed into one another, by -indefinite intermediate degrees. The reader may naturally ask, what -is the solution of this apparent {46} contradiction between the -earliest and the latest discoveries in acoustics. And the answer -must be, that these intermediate modes of vibration are complex in -their nature, and difficult to produce; and that those which were -formerly believed to be the only possible vibrating conditions, are -so eminent above all the rest by their features, their simplicity, -and their facility, that we may still, for common purposes, consider -them as a class apart; although for the sake of reaching a general -theorem, we may associate them with the general mass of cases of -molecular vibrations. And thus we have no exception here, as we can -have none in any case, to our maxim, that what formed part of the -early discoveries of science, forms part of its latest systems. - -[Note 53\8: For the suggestion of the necessity of this limitation I -am indebted to Mr. Willis.] - -[Note 54\8: _An. Chim._ 1826, t. xxxii. p. 384.] - -We have thus surveyed the progress of the science of sound up to -recent times, with respect both to the discovery of laws of -phenomena, and the reduction of these to their mechanical causes. -The former branch of the science has necessarily been inductively -pursued; and therefore has been more peculiarly the subject of our -attention. And this consideration will explain why we have not dwelt -more upon the deductive labors of the great analysts who have -treated of this problem. - -To those who are acquainted with the high and deserved fame which -the labors of D'Alembert, Euler, Lagrange, and others, upon this -subject, enjoy among mathematicians, it may seem as if we had not -given them their due prominence in our sketch. But it is to be -recollected here, as we have already observed in the case of -hydrodynamics, that even when the general principles are -uncontested, mere mathematical deductions from them do not belong to -the history of physical science, except when they point out laws -which are intermediate between the general principle and the -individual facts, and which observation may confirm. - -The business of constructing any science may be figured as the task -of forming a road on which our reason can travel through a certain -province of the external world. We have to throw a bridge which may -lead from the chambers of our own thoughts, from our speculative -principles, to the distant shore of material facts. But in all cases -the abyss is too wide to be crossed, except we can find some -intermediate points on which the piers of our structure may rest. -Mere facts, without connexion or law, are only the rude stones hewn -from the opposite bank, of which our arches may, at some time, be -built. But mere hypothetical mathematical calculations are only -plans of projected structures; and those plans which exhibit only -one vast {47} and single arch, or which suppose no support but that -which our own position supplies, will assuredly never become -realities. We must have a firm basis of intermediate generalizations -in order to frame a continuous and stable edifice. - -In the subject before us, we have no want of such points of -intermediate support, although they are in many instances -irregularly distributed and obscurely seen. The number of observed -laws and relations of the phenomena of sound, is already very great; -and though the time may be distant, there seems to be no reason to -despair of one day uniting them by clear ideas of mechanical -causation, and thus of making acoustics a perfect secondary -mechanical science. - -The historical sketch just given includes only such parts of -acoustics as have been in some degree reduced to general laws and -physical causes; and thus excludes much that is usually treated of -under that head. Moreover, many of the numerical calculations -connected with sound belong to its agreeable effect upon the ear; as -the properties of the various systems of _Temperament_. These are -parts of Theoretical Music, not of Acoustics; of the Philosophy of -the Fine Arts, not of Physical Science; and may be referred to in a -future portion of this work, so far as they bear upon our object. - -The science of Acoustics may, however, properly consider other -differences of sound than those of acute and grave,--for instance, -the _articulate_ differences, or those by which the various letters -are formed. Some progress has been made in reducing this part of the -subject to general rules; for though Kempelen's "talking machine" -was only a work of art, Mr. Willis's machine,[55\8] which exhibits -the relation among the vowels, gives us a law such as forms a step -in science. We may, however, consider this instrument as a -_phthongometer_, or measure of vowel quality; and in that point of -view we shall have to refer to it again when we come to speak of -such measures. - -[Note 55\8: On the Vowel Sounds, and on Reed Organ-pipes. _Camb. -Trans._ iii. 237.] - - - -{{49}} -BOOK IX. - - -_SECONDARY MECHANICAL SCIENCES._ - -(CONTINUED) - - -HISTORY OF OPTICS, - -FORMAL AND PHYSICAL. - - - - Ω Διὸς ὑψιμέλαθρον ἔχων κράτος αἰὲν ἀτειρὲς - Ἄστρων, Ἠελίου τε, Σεληναίης τε μέρισμα - Πανδαμάτωρ, πυρίπνου, πᾶσιν ζωοῖσιν ἔναυσμα - **Ὑψιφάνης ἌIϴΗΡ, κόσμου στοιχεῖον, **ἄριστον· - Ἀγλαὸν ὦ βλάστημα, σελασφόρον, ἀστεροφεγγὲς - Κικλήσκων λίτομαι σε, κεκραμένον **εὔδιον εἶναι. - ORPHEUS. HYMN. - - O thou who fillest the palaces of Jove; - Who flowest round moon, and sun, and stars above; - Pervading, bright, life-giving element, - Supernal ETHER, fair and excellent; - Fountain of hope and joy, of light and day, - We own at length thy tranquil, steady sway. - - - -{{51}} -INTRODUCTION. - -_Formal and Physical Optics._ - - -THE history of the science of Optics, written at length, would be -very voluminous; but we shall not need to make our history so; since -our main object is to illustrate the nature of science and the -conditions of its progress. In this way Optics is peculiarly -instructive; the more so, as its history has followed a course in -some respects different from both the sciences previously reviewed. -Astronomy, as we have seen, advanced with a steady and continuous -movement from one generation to another, from the earliest time, -till her career was crowned by the great unforeseen discovery of -Newton; Acoustics had her extreme generalization in view from the -first, and her history consists in the correct application of it to -successive problems; Optics advanced through a scale of -generalizations as remarkable as those of Astronomy; but for a long -period she was almost stationary; and, at last, was rapidly impelled -through all those stages by the energy of two or three discoverers. -The highest point of generality which Optics has reached is little -different from that which Acoustics occupied at once; but in the -older and earlier science we still want that palpable and pointed -confirmation of the general principle, which the undulatory theory -receives from optical phenomena. Astronomy has amassed her vast -fortune by long-continued industry and labor; Optics has obtained -hers in a few years by sagacious and happy speculations; Acoustics, -having early acquired a competence, has since been employed rather -in improving and adorning than in extending her estate. - -The successive inductions by which Optics made her advances, might, -of course, be treated in the same manner as those of Astronomy, each -having its prelude and its sequel. But most of the discoveries in -Optics are of a smaller character, and have less employed the minds -of men, than those of Astronomy; and it will not be necessary to -exhibit them in this detailed manner, till we come to the great -generalization by which the theory was established. I shall, -therefore, now pass rapidly in review the earlier optical -discoveries, without any such division of the series. {52} - -Optics, like Astronomy, has for its object of inquiry, first, the -laws of phenomena, and next, their causes; and we may hence divide -this science, like the other, into _Formal Optics_ and _Physical -Optics_. The distinction is clear and substantive, but it is not -easy to adhere to it in our narrative; for, after the theory had -begun to make its rapid advance, many of the laws of phenomena were -studied and discovered in immediate reference to the theoretical -cause, and do not occupy a separate place in the history of science, -as in Astronomy they do. We may add, that the reason why Formal -Astronomy was almost complete before Physical Astronomy began to -exist, was, that it was necessary to construct the science of -Mechanics in the mean time, in order to be able to go on; whereas, -in Optics, mathematicians were able to calculate the results of the -undulatory theory as soon as it had suggested itself from the earlier -facts, and while the great mass of facts were only becoming known. - -We shall, then, in the first _nine_ chapters of the History of -Optics treat of the Formal Science, that is, the discovery of the -laws of phenomena. The classes of phenomena which will thus pass -under oar notice are numerous; namely, reflection, refraction, -chromatic dispersion, achromatization, double refraction, -polarization, dipolarization, the colors of thin plates, the colors -of thick plates, and the fringes and bands which accompany shadows. -All these cases had been studied, and, in most of them, the laws had -been in a great measure discovered, before the physical theory of -the subject gave to our knowledge a simpler and more solid form. - - - -{{53}} -FORMAL OPTICS. - - - -CHAPTER I. - -PRIMARY INDUCTION OF OPTICS.--RAYS OF LIGHT AND LAWS OF REFLECTION. - - -IN speaking of the Ancient History of Physics, we have already -noticed that the optical philosophers of antiquity had satisfied -themselves that vision is performed in straight lines;--that they -had fixed their attention upon those straight lines, or _rays_, as -the proper object of the science;--they had ascertained that rays -reflected from a bright surface make the _angle of reflection_ equal -to the _angle of incidence_;--and they had drawn several -consequences from these principles. - -We may add to the consequences already mentioned, the art of -_perspective_, which is merely a corollary from the doctrine of -rectilinear visual rays; for if we suppose objects to be referred by -such rays to a plane interposed between them and the eye, all the -rules of perspective follow directly. The ancients practised this -art, as we see in the pictures which remain to us and we learn from -Vitruvius,[1\9] that they also wrote upon it. Agatharchus, who had -been instructed by Eschylus in the art of making decorations for the -theatre, was the first author on this subject, and Anaxagoras, who -was a pupil of Agatharchus, also wrote an _Actinographia_, or -doctrine of drawing by rays: but none of these treatises are come -down to us. The moderns re-invented the art in the flourishing times -of the art of painting, that is, about the end of the fifteenth -century; and, belonging to that period also, we have treatises[2\9] -upon it. - -[Note 1\9: _De Arch._ ix. Mont. i. 707.] - -[Note 2\9: Gauricus, 1504.] - -But these are only deductive applications of the most elementary -optical doctrines; we must proceed to the inductions by which -further discoveries were made. {54} - - - - -CHAPTER II. - -DISCOVERY OF THE LAW OF REFRACTION. - - -WE have seen in the former part of this history that the Greeks had -formed a tolerably clear conception of the refraction as well as the -reflection of the rays of light; and that Ptolemy had measured the -amount of refraction of glass and water at various angles. If we -give the names of the _angle of incidence_ and the _angle of -refraction_ respectively to the angles which a ray of light makes -with the line perpendicular to surface of glass or water (or any -other medium) within and without the medium, Ptolemy had observed -that the angle of refraction is always less than the angle of -incidence. He had supposed it to be less in a given proportion, but -this opinion is false; and was afterwards rightly denied by the -Arabian mathematician Alhazen. The optical views which occur in the -work of Alhazen are far sounder than those of his predecessors; and -the book may be regarded as the most considerable monument which we -have of the scientific genius of the Arabians; for it appears, for -the most part, not to be borrowed from Greek authorities. The author -not only asserts (lib. vii.), that refraction takes place towards -the perpendicular, and refers to experiment for the truth of this: -and that the quantities of the refraction differ according to the -magnitudes of the angles which the directions of the incidental rays -(_primæ lineæ_) make with the perpendiculars to the surface; but he -also says distinctly and decidedly that the angles of refraction do -not follow the proportion of the angles of incidence. - -[2nd Ed.] [There appears to be good ground to assent to the -assertion of Alhazen's originality, made by his editor Risner, who -says, "Euclideum hic vel Ptolemaicum nihil fere est." Besides the -doctrine of reflection and refraction of light, the Arabian author -gives a description of the eye. He distinguishes three fluids, -_humor aqueus_, _crystallinus_, _vitreus_, and four coats of the -eye, _tunica adherens_, _cornea_, _uvea_, _tunica reti similis_. He -distinguishes also three kinds of vision: "Visibile percipitur aut -solo visu, aut visu et syllogismo, aut visu et anticipatâ notione." -He has several propositions relating to what we sometimes call the -Philosophy of Vision: for instance this: "E visibili sæpius viso -remanet in anima generalis notio," &c.] {55} - -The assertion, that the angles of refraction are not proportional to -the angles of incidence, was an important remark; and if it had been -steadily kept in mind, the next thing to be done with regard to -refraction was to go on experimenting and conjecturing till the true -law of refraction was discovered; and in the mean time to apply the -principle as far as it was known. Alhazen, though he gives -directions for making experimental measures of refraction, does not -give any Table of the results of such experiments, as Ptolemy had -done. Vitello, a Pole, who in the 13th century published an -extensive work upon Optics, does give such a table; and asserts it -to be deduced from experiment, as I have already said (vol. i.). But -this assertion is still liable to doubt in consequence of the table -containing impossible observations. - -[2nd Ed.] [As I have already stated, Vitello asserts that his Tables -were derived from his own observations. Their near agreement with -those of Ptolemy does not make this improbable: for where the -observations were only made to half a degree, there was not much -room for observers to differ. It is not unlikely that the -observations of refraction out of air into water and glass, and out -of water into glass, were actually made; while the impossible values -which accompany them, of the refraction out of water and glass into -air, and out of glass into water, were calculated, and calculated -from an erroneous rule.] - -The principle that a ray refracted in glass or water is turned -towards the perpendicular, without knowing the exact law of -refraction, enabled mathematicians to trace the effects of -transparent bodies in various cases. Thus in Roger Bacon's works we -find a tolerably distinct explanation of the effect of a convex -glass; and in the work of Vitello the effect of refraction at the -two surfaces of a glass globe is clearly traceable. - -Notwithstanding Alhazen's assertion of the contrary, the opinion was -still current among mathematicians that the angle of refraction was -proportional to the angle of incidence. But when Kepler's attention -was drawn to the subject, he saw that this was plainly inconsistent -with the observations of Vitello for large angles; and he convinced -himself by his own experiments that the true law was something -different from the one commonly supposed. The discovery of this true -law excited in him an eager curiosity; and this point had the more -interest for him in consequence of the introduction of a correction -for atmospheric refraction into astronomical calculations, which had -been made by Tycho, and of the invention of the telescope. In {56} -his _Supplement to Vitello_, published in 1604, Kepler attempts to -reduce to a rule the measured quantities of refraction. The reader -who recollects what we have already narrated, the manner in which -Kepler attempted to reduce to law the astronomical observations of -Tycho,--devising an almost endless variety of possible formulæ, -tracing their consequences with undaunted industry, and relating, -with a vivacious garrulity, his disappointments and his hopes,--will -not be surprised to find that he proceeded in the same manner with -regard to the Tables of Observed Refractions. He tried a variety of -constructions by triangles, conic sections, &c., without being able -to satisfy himself; and he at last[3\9] is obliged to content -himself with an approximate rule, which makes the refraction partly -proportional to the angle of incidence, and partly, to the secant of -that angle. In this way he satisfies the observed refractions within -a difference of less than half a degree each way. When we consider -how simple the law of refraction is, (that the ratio of the sines of -the angles of incidence and refraction is constant for the same -medium,) it appears strange that a person attempting to discover it, -and drawing triangles for the purpose, should fail; but this lot of -missing what afterwards seems to have been obvious, is a common one -in the pursuit of truth. - -[Note 3\9: L. U. K. _Life of Kepler_, p. 115.] - -The person who did discover the Law of the Sines, was Willebrord -Snell, about 1621; but the law was first published by Descartes, who -had seen Snell's papers.[4\9] Descartes does not acknowledge this -law to have been first detected by another; and after his manner, -instead of establishing its reality by reference to experiment, he -pretends to prove _à priori_ that it must be true,[5\9] comparing, -for this purpose, the particles of light to balls striking a -substance which _accelerates_ them. - -[Note 4\9: Huyghens, _Dioptrica_, p. 2.] - -[Note 5\9: _Diopt._ p. 53.] - -[2nd Ed.] [Huyghens says of Snell's papers, "Quæ et nos vidimus -aliquando, et Cartesium quoque vidisse accepimus, et hinc fortasse -mensuram illam quæ in sinibus consistit elicuerit." Isaac Vossius, -_De Lucis Naturâ et Proprietate_, says that he also had seen this -law in Snell's unpublished optical Treatise. The same writer says, -"Quod itaque (Cartesius) habet, refractionum momenta non exigenda -esse ad angulos sed ad lineas, id tuo Snellio, acceptum ferre -debuisset, cujus nomen _more solito_ dissimulavit." "Cartesius got -his law from Snell, and _in his usual way_, concealed it." {57} - -Huyghens' assertion, that Snell did not _attend to_ the proportion -of the sines, is very captious; and becomes absurdly so, when it is -made to mean that Snell did not _know_ the law of the sines. It is -not denied that Snell knew the true law, or that the true law is the -law of the sines. Snell does not use the trigonometrical term -_sine_, but he expresses the law in a geometrical form more simply. -Even if he _had_ attended to the law of the sines, he might -reasonably have preferred his own way of stating it. - -James Gregory also independently discovered the true law of -refraction; and, in publishing it, states that he had learnt that it -had already been published by Descartes.] - -But though Descartes does not, in this instance, produce any good -claims to the character of an inductive philosopher, he showed -considerable skill in tracing the consequences of the principle when -once adopted. In particular we must consider him as the genuine -author of the explanation of the rainbow. It is true that -Fleischer[6\9] and Kepler had previously ascribed this phenomenon to -the rays of sunlight which, falling on drops of rain, are refracted -into each drop, reflected at its inner surface, and refracted out -again: Antonio de Dominis had found that a glass globe of water, -when placed in a particular position with respect to the eye, -exhibited bright colors; and had hence explained the circular form -of the bow, which, indeed, Aristotle had done before.[7\9] But none -of these writers had shown why there was a narrow bright circle of a -definite diameter; for the drops which send rays to the eye after -two refractions and a reflection, occupy a much wider space in the -heavens. Descartes assigned the reason for this in the most -satisfactory manner,[8\9] by showing that the rays which, after two -refractions and a reflection, come to the eye at an angle of about -forty-one degrees with their original direction, are far more dense -than those in any other position. He showed, in the same manner, -that the existence and position of the _secondary bow_ resulted from -the same laws. This is the complete and adequate account of the -state of things, so far as the brightness of the bows only is -concerned; the explanation of the colors belongs to the next article -of our survey. - -[Note 6\9: Mont. i. 701.] - -[Note 7\9: _Meteorol._ iii. 3.] - -[Note 8\9: _Meteorum_, cap. viii. p. 196.] - -The explanation of the rainbow and of its magnitude, afforded by -Snell's law of sines, was perhaps one of the leading points in the -verification of the law. The principle, being once established, was -applied, by the aid of mathematical reasoning, to atmospheric -refractions, {58} optical instruments, _diacaustic_ curves, (that -is, the curves of intense light produced by refraction,) and to -various other cases; and was, of course, tested and confirmed by -such applications. It was, however, impossible to pursue these -applications far, without a due knowledge of the laws by which, in -such cases, colors are produced. To these we now proceed. - -[2nd Ed.] [I have omitted many interesting parts of the history of -Optics about this period, because I was concerned with the -_inductive_ discovery of laws, rather than with mathematical -_deductions_ from such laws when established, or _applications_ of -them in the form of instruments. I might otherwise have noticed the -discovery of Spectacle Glasses, of the Telescope, of the Microscope, -of the Camera Obscura, and the mathematical explanation of these and -other phenomena, as given by Kepler and others. I might also have -noticed the progress of knowledge respecting the Eye and Vision. We -have seen that Alhazen described the structure of the eye. The -operation of the parts was gradually made out. Baptista Porta -compares the eye to his _Camera Obscura_ (_Magia Naturalis_, 1579). -Scheiner, in his _Oculus_, published 1652, completed the Theory of -the Eye. And Kepler discussed some of the questions even now often -agitated; as the causes and conditions of our seeing objects single -with two eyes, and erect with inverted images.] - - - - -CHAPTER III. - -DISCOVERY OF THE LAW OF DISPERSION BY REFRACTION. - - -EARLY attempts were made to account for the colors of the rainbow, -and various other phenomena in which colors are seen to arise from -transient and unsubstantial combinations of media. Thus Aristotle -explains the colors of the rainbow by supposing[9\9] that it is -light seen through a dark medium: "Now," says he, "the bright seen -through the dark appears red, as, for instance, the fire of green -wood seen through the smoke, and the sun through mist. Also[10\9] -the weaker is the light, or the visual power, and the nearer the -color approaches to the black; becoming first red, then green, then -purple. But[11\9] the {59} vision is strongest in the outer circle, -because the periphery is greater;--thus we shall have a gradation -from red, through green, to purple, in passing from the outer to the -inner circle." This account would hardly have deserved much notice, -if it had not been for a strange attempt to revive it, or something -very like it, in modern times. The same doctrine is found in the -work of De Dominis.[12\9] According to him, light is white: but if -we mix with the light something dark, the colors arise,--first red, -then green, then blue or violet. He applies this to explain the -colors of the rainbow,[13\9] by means of the consideration that, of -the rays which come to the eye from the globes of water, some go -through a larger thickness of the globe than others, whence he -obtains the gradation of colors just described. - -[Note 9\9: _Meteor._ iii. 3, p. 373.] - -[Note 10\9: Ib. p. 374.] - -[Note 11\9: Ib. p. 375.] - -[Note 12\9: Cap. iii. p. 9. See also Göthe, _Farbenl._ vol. ii. -p. 251.] - -[Note 13\9: Göthe, p. 263.] - -Descartes came far nearer the true philosophy of the iridal colors. -He found that a similar series of colors was produced by refraction -of light bounded by shade, through a prism;[14\9] and he rightly -inferred that neither the curvature of the surface of the drops of -water, nor the reflection, nor the repetition of refraction, were -necessary to the generation of such colors. In further examining the -course of the rays, he approaches very near to the true conception -of the case; and we are led to believe that he might have -anticipated Newton in his discovery of the unequal refrangibility of -different colors, if it had been possible for him to reason any -otherwise than in the terms and notions of his preconceived -hypotheses. The conclusion which he draws is,[15\9] that "the -particles of the subtile matter which transmit the action of light, -endeavor to rotate with so great a force and impetus, that they -cannot move in a straight line (whence comes refraction): and that -those particles which endeavor to revolve much more strongly produce -a red color, those which endeavor to move only a little more -strongly produce yellow." Here we have a clear perception that -colors and unequal refraction are connected, though the cause of -refraction is expressed by a gratuitous hypothesis. And we may add, -that he applies this notion rightly, so far as he explains -himself,[16\9] to account for the colors of the rainbow. - -[Note 14\9: _Meteor._ Sect. viii. p. 190.] - -[Note 15\9: Sect. vii. p. 192.] - -[Note 16\9: _Meteor._ Sect. ix.] - -It appears to me that Newton and others have done Descartes -injustice, in ascribing to De Dominis the true theory of the -rainbow. There are two main points of this theory, namely, the -showing that a _bright_ circular band, of a certain definite -diameter, arises from the {60} great intensity of the light returned -at a certain angle; and the referring the different _colors_ to the -_different quantity of the refraction_; and both these steps appear -indubitably to be the discoveries of Descartes. And he informs us -that these discoveries were not made without some exertion of -thought. "At first," he says,[17\9] "I doubted whether the iridal -colors were produced in the same way as those in the prism; but, at -last, taking my pen, and carefully calculating the course of the -rays which fell on each part of the drop, I found that many more -come at an angle of forty-one degrees, than either at a greater or a -less angle. So that there is a bright bow terminated by a shade; and -hence the colors are the same as those produced through a prism." - -[Note 17\9: Sect. ix. p. 193.] - -The subject was left nearly in the same state, in the work of -Grimaldi, _Physico-Mathesis, de Lumine, Coloribus et Iride_, -published at Bologna in 1665. There is in this work a constant -reference to numerous experiments, and a systematic exposition of -the science in an improved state. The author's calculations -concerning the rainbow are put in the same form as those of -Descartes; but he is further from seizing the true principle on -which its coloration depends. He rightly groups together a number of -experiments in which colors arise from refraction;[18\9] and -explains them by saying that the color is brighter where the light -is denser: and the light is denser on the side from which the -refraction turns the ray, because the increments of refraction are -greater in the rays that are more inclined.[19\9] This way of -treating the question might be made to give a sort of explanation of -most of the facts, but is much more erroneous than a developement of -Descartes's view would have been. - -[Note 18\9: Prop. 35, p. 254.] - -[Note 19\9: Ib. p. 256.] - -At length, in 1672, Newton gave[20\9] the true explanation of the -facts; namely, that light consists of rays of different colors and -different refrangibility. This now appears to us so obvious a mode -of interpreting the phenomena, that we can hardly understand how -they can be conceived in any other manner; but yet the impression -which this discovery made, both upon Newton and upon his -contemporaries, shows how remote it was from the then accepted -opinions. There appears to have been a general persuasion that the -coloration was produced, not by any peculiarity in the law of -refraction itself but by some collateral circumstance,--some -dispersion or variation of density of the light, in addition to the -refraction. Newton's discovery consisted in {61} teaching distinctly -that the law of refraction was to be applied, not to the beam of -light in general, but to the colors in particular. - -[Note 20\9: _Phil. Trans._ t. vii. p. 3075.] - -When Newton produced a bright spot on the wall of his chamber, by -admitting the sun's light through a small hole in his -window-shutter, and making it pass through a prism, he expected the -image to be round; which, of course, it would have been, if the -colors had been produced by an equal dispersion in all directions; -but to his surprise he saw the image, or _spectrum_, five times as -long as it was broad. He found that no consideration of the -different thickness of the glass, the possible unevenness of its -surface, or the different angles of rays proceeding from the two -sides of the sun, could be the cause of this shape. He found, also, -that the rays did not go from the prism to the image in curves; he -was then convinced that the different colors were refracted -separately, and at different angles; and he confirmed this opinion -by transmitting and refracting the rays of each color separately. - -The experiments are so easy and common, and Newton's interpretation -of them so simple and evident, that we might have expected it to -receive general assent; indeed, as we have shown, Descartes had -already been led very near the same point. In fact, Newton's -opinions were not long in obtaining general acceptance; but they met -with enough of cavil and misapprehension to annoy extremely the -discoverer, whose clear views and quiet temper made him impatient -alike of stupidity and of contentiousness. - -We need not dwell long on the early objections which were made to -Newton's doctrine. A Jesuit, of the name of Ignatius Pardies, -professor at Clermont, at first attempted to account for the -elongation of the image by the difference of the angles made by the -rays from the two edges of the sun, which would produce a difference -in the amount of refraction of the two borders; but when Newton -pointed out the calculations which showed the insufficiency of this -explanation, he withdrew his opposition. Another more pertinacious -opponent appeared in Francis Linus, a physician of Liege; who -maintained, that having tried the experiment, he found the sun's -image, when the sky was clear, to be round and not oblong; and he -ascribed the elongation noticed by Newton, to the effect of clouds. -Newton for some time refused to reply to this contradiction of his -assertions, though obstinately persisted in; and his answer was at -last sent, just about the time of Linus's death, in 1675. But -Gascoigne, a friend of Linus, still maintained that he and others -had seen what the Dutch physician had described; and Newton, who was -pleased with the candor of {62} Gascoigne's letter, suggested that -the Dutch experimenters might have taken one of the images reflected -from the surfaces of the prism, of which there are several, instead -of the proper refracted one. By the aid of this hint, Lucas of Liege -repeated Newton's experiments, and obtained Newton's result, except -that he never could obtain a spectrum whose length was more than -three and a half times its breadth. Newton, on his side, persisted -in asserting that the image would be five times as long as it was -broad, if the experiment were properly made. It is curious that he -should have been so confident of this, as to conceive himself -certain that such would be the result in all cases. We now know that -the dispersion, and consequently the length, of the spectrum, is -very different for different kinds of glass, and it is very probable -that the Dutch prism was really less dispersive than the English -one.[21\9] The erroneous assumption which Newton made in this -instance, he held by to the last; and was thus prevented from making -the discovery of which we have next to speak. - -[Note 21\9: Brewster's _Newton_, p. 50.] - -Newton was attacked by persons of more importance than those we have -yet mentioned; namely, Hooke and Huyghens. These philosophers, -however, did not object so much to the laws of refraction of -different colors, as to some expressions used by Newton, which, they -conceived, conveyed false notions respecting the composition and -nature of light. Newton had asserted that all the different colors -are of distinct kinds, and that, by their composition, they form -white light. This is true of colors as far as their analysis and -composition by refraction are concerned; but Hooke maintained that -all natural colors are produced by various combinations of two -primary ones, red and violet;[22\9] and Huyghens held a similar -doctrine, taking, however, yellow and blue for his basis. Newton -answers, that such compositions as they speak of are not -compositions of simple colors in his sense of the expressions. These -writers also had both of them adopted an opinion that light -consisted in vibrations; and objected to Newton that his language -was erroneous, as involving the hypothesis that light was a body. -Newton appears to have had a horror of the word _hypothesis_, and -protests against its being supposed that his "theory" rests on such -a foundation. - -[Note 22\9: Brewster's _Newton_, p. 54. _Phil. Trans._ viii. 5084, -6086.] - -The doctrine of the unequal refrangibility of different rays is -clearly exemplified in the effects of lenses, which produce images -more or {63} less bordered with color, in consequence of this -property. The improvement of telescopes was, in Newton's time, the -great practical motive for aiming at the improvement of theoretical -optics. Newton's theory showed why telescopes were imperfect, -namely, in consequence of the different refraction of different -colors, which produces a _chromatic_ aberration: and the theory was -confirmed by the circumstances of such imperfections. The false -opinion of which we have already spoken, that the dispersion must be -the same when the refraction is the same, led him to believe that -the imperfection was insurmountable,--that _achromatic_ refraction -could not be obtained: and this view made him turn his attention to -the construction of reflecting instead of refracting telescopes. But -the rectification of Newton's error was a further confirmation of -the general truth of his principles in other respects; and since -that time, the soundness of the Newtonian law of refraction has -hardly been questioned among physical philosophers. - -It has, however, in modern times, been very vehemently controverted in -a quarter from which we might not readily have expected a detailed -discussion on such a subject. The celebrated Göthe has written a work -on _The Doctrine of Colors_, (_Farbenlehre_; Tübingen, 1810,) one main -purpose of which is, to represent Newton's opinions, and the work in -which they are formally published, (his _Opticks_,) as utterly false -and mistaken, and capable of being assented to only by the most blind -and obstinate prejudice. Those who are acquainted with the extent to -which such an opinion, promulgated by Göthe, was likely to be widely -adopted in Germany, will not be surprised that similar language is -used by other writers of that nation. Thus Schelling[23\9] says: -"Newton's _Opticks_ is the greatest proof of the possibility of a -whole structure of fallacies, which, in all its parts, is founded upon -observation and experiment." Göthe, however, does not concede even so -much to Newton's work. He goes over a large portion of it, page by -page, quarrelling with the experiments, diagrams, reasoning, and -language, without intermission; and holds that it is not reconcileable -with the most simple facts. He declares,[24\9] that the first time he -looked through a prism, he saw the white walls of the room still look -white, "and though alone, I pronounced, as by an instinct, that the -Newtonian doctrine is false." We need not here point out how -inconsistent with the Newtonian doctrine it was, to expect, as Göthe -expected, that the wall should be all over colored various colors. -{64} - -[Note 23\9: _Vorlesungen_, p. 270.] - -[Note 24\9: _Farbenlehre_, vol. ii. p. 678.] - -Göthe not only adopted and strenuously maintained the opinion that -the Newtonian theory was false, but he framed a system of his own to -explain the phenomena of color. As a matter of curiosity, it may be -worth our while to state the nature of this system; although -undoubtedly it forms no part of the _progress_ of physical science. -Göthe's views are, in fact, little different from those of Aristotle -and Antonio de Dominis, though more completely and systematically -developed. According to him, colors arise when we see through a dim -medium ("ein trübes mittel"). Light in itself is colorless; but if -it be seen through a somewhat dim medium, it appears yellow; if the -dimness of the medium increases, or if its depth be augmented, we -see the light gradually assume a yellow-red color, which finally is -heightened to a ruby-red. On the other hand, if darkness is seen -through a dim medium which is illuminated by a light falling on it, -a blue color is seen, which becomes clearer and paler, the more the -dimness of the medium increases, and darker and fuller, as the -medium becomes more transparent; and when we come to "the smallest -degree of the purest dimness," we see the most perfect violet.[25\9] -In addition to this "doctrine of the dim medium," we have a second -principle asserted concerning refraction. In a vast variety of -cases, images are accompanied by "accessory images," as when we see -bright objects in a looking-glass.[26\9] Now, when an image is -displaced by refraction, the displacement is not complete, clear and -sharp, but incomplete, so that there is an accessory image along -with the principal one.[27\9] From these principles, the colors -produced by refraction in the image of a bright object on a dark -ground, are at once derivable. The accessory image is -semitransparent;[28\9] and hence that border of it which is pushed -forwards, is drawn from the dark over the bright, and there the -yellow appears; on the other hand, where the clear border laps over -the dark ground, the blue is seen;[29\9] and hence we easily see -that the image must appear red and yellow at one end, and blue and -violet at the other. - -[Note 25\9: _Farbenlehre_, § 150, p. 151.] - -[Note 26\9: Ib. § 223.] - -[Note 27\9: Ib. § 227.] - -[Note 28\9: Ib. § 238.] - -[Note 29\9: Ib. § 239.] - -We need not explain this system further, or attempt to show how -vague and loose, as well as baseless, are the notions and modes of -conception which it introduces. Perhaps it is not difficult to point -out the peculiarities in Göthe's intellectual character which led to -his singularly unphilosophical views on this subject. One important -{65} circumstance is, that he appears, like many persons in whom the -poetical imagination is very active, to have been destitute of the -talent and the habit of geometrical thought. In all probability, he -never apprehended clearly and steadily those relations of position -on which the Newtonian doctrine depends. Another cause of his -inability to accept the doctrine probably was, that he had conceived -the "composition" of colors in some way altogether different from -that which Newton understands by composition. What Göthe expected to -see, we cannot clearly collect; but we know, from his own statement, -that his intention of experimenting with a prism arose from his -speculations on the roles of coloring in pictures; and we can easily -see that any notion of the composition of colors which such -researches would suggest, would require to be laid aside, before he -could understand Newton's theory of the composition of light. - -Other objections to Newton's theory, of a kind very different, have -been recently made by that eminent master of optical science, Sir -David Brewster. He contests Newton's opinion, that the colored rays -into which light is separated by refraction are altogether simple -and homogeneous, and incapable of being further analysed and -modified. For he finds that by passing such rays through colored -media (as blue glass for instance), they are not only absorbed and -transmitted in very various degrees, but that some of them have -their color altered; which effect he conceives as a further analysis -of the rays, one component color being absorbed and the other -transmitted.[30\9] And on this subject we can only say, as we have -before said, that Newton has incontestably and completely -established his doctrine, so far as analysis and decomposition _by -refraction_ are concerned; but that with regard to any other -analysis, which absorbing media or other agents may produce, we have -no right from his experiments to assert, that the colors of the -spectrum are incapable of _such_ decomposition. The whole subject of -the colors of objects, both opake and transparent, is still in -obscurity. Newton's conjectures concerning the causes of the colors -of natural bodies, appear to help us little; and his opinions on -that subject are to be separated altogether from the important step -which he made in optical science, by the establishment of the true -doctrine of refractive dispersion. - -[Note 30\9: This latter fact has, however, been denied by other -experimenters.] - -[2nd Ed.] [After a careful re-consideration of Sir D. Brewster's -asserted analysis of the solar light into three colors by means of -{66} absorbing media, I cannot consider that he has established his -point as an exception to Newton's doctrine. In the first place, the -analysis of light into _three_ colors appears to be quite arbitrary, -granting all his experimental facts. I do not see why, using other -media, he might not just as well have obtained other elementary -colors. In the next place, this cannot be called an _analysis_ in -the same sense as Newton's analysis, except the relation between the -two is shown. Is it meant that Newton's experiments prove nothing? -Or is Newton's conclusion allowed to be true of light which has not -been analysed by absorption? And where are we to find such light, -since the atmosphere absorbs? But, I must add, in the third place, -that with a very sincere admiration of Sir D. Brewster's skill as an -experimenter, I think his experiment requires, not only limitation, -but confirmation by other experimenters. Mr. Airy repeated the -experiments with about thirty different absorbing substances, and -could not satisfy himself that in any case they changed the color of -a ray of given refractive power. These experiments were described by -him at a meeting of the Cambridge Philosophical Society.] - -We now proceed to the corrections which the next generation -introduced into the details of this doctrine. - - - - -CHAPTER IV. - -DISCOVERY OF ACHROMATISM. - - -THE discovery that the laws of refractive dispersion of different -substances were such as to allow of combinations which neutralised -the dispersion without neutralizing the refraction, is one which has -hitherto been of more value to art than to science. The property has -no definite bearing, which has yet been satisfactorily explained, -upon the _theory_ of light; but it is of the greatest importance in -its application to the construction of telescopes; and it excited -the more notice, in consequence of the prejudices and difficulties -which for a time retarded the discovery. - -Newton conceived that he had proved by experiment,[31\9] that light -{67} is white after refraction, when the emergent rays are parallel -to the incident, and in no other case. If this were so, the -production of colorless images by refracting media would be -impossible; and such, in deference to Newton's great authority, was -for some time the general persuasion. Euler[32\9] observed, that a -combination of lenses which does not color the image must be -possible, since we have an example of such a combination in the -human eye; and he investigated mathematically the conditions -requisite for such a result. Klingenstierna,[33\9] a Swedish -mathematician, also showed that Newton's rule could not be -universally true. Finally, John Dollond,[34\9] in 1757, repeated -Newton's experiment, and obtained an opposite result. He found that -when an object was seen through two prisms, one of glass and one of -water, of such angles that it did not appear displaced by -refraction, it was colored. Hence it followed that, without being -colored, the rays might be made to undergo refraction; and that -thus, substituting lenses for prisms, a combination might be formed, -which should produce an image without coloring it, and make the -construction of an _achromatic_ telescope possible. - -[Note 31\9: _Opticks_, B. i. p. ii. Prop. 3.] - -[Note 32\9: _Ac. Berlin._ 1747.] - -[Note 33\9: _Swedish Trans._ 1754.] - -[Note 34\9: _Phil. Trans._ 1758.] - -Euler at first hesitated to confide in Dollond's experiments; but he -was assured of their correctness by Clairaut, who had throughout -paid great attention to the subject; and those two great -mathematicians, as well as D'Alembert, proceeded to investigate -mathematical formulæ which might be useful in the application of the -discovery. The remainder of the deductions, which were founded upon -the laws of dispersion of various refractive substances, belongs -rather to the history of art than of science. Dollond used at first, -for his achromatic object-glass, a lens of crown-glass, and one of -flint-glass. He afterwards employed two lenses of the former -substance, including between them one of the latter, adjusting the -curvatures of his lenses in such a way as to correct the -imperfections arising from the spherical form of the glasses, as -well as the fault of color. Afterwards, Blair used fluid media along -with glass lenses, in order to produce improved object-glasses. This -has more recently been done in another form by Mr. Barlow. The -inductive laws of refraction being established, their results have -been deduced by various mathematicians, as Sir J. Herschel and -Professor Airy among ourselves, who have simplified and extended the -investigation of the formulæ which determine the best combination of -lenses in the object-glasses and eye-glasses of {68} telescopes, -both with reference to spherical and to _chromatic_ aberrations. - -According to Dollond's discovery, the colored spectra produced by -prisms of two substances, as flint-glass and crown-glass, would be -of the same length when the refraction was different. But a question -then occurred: When the whole distance from the red to the violet in -one spectrum was the same as the whole distance in the other, were -the intermediate colors, yellow, green, &c., in corresponding places -in the two? This point also could not be determined any otherwise -than by experiment. It appeared that such a correspondence did not -exist; and, therefore, when the extreme colors were corrected by -combinations of the different media, there still remained an -uncorrected residue of color arising from the rest of the spectrum. -This defect was a consequence of the property, that the spectra -belonging to different media were not divided in the _same ratio_ by -the same colors, and was hence termed the _irrationality_ of the -spectrum. By using three prisms, or three lenses, three colors may -be made to coincide instead of two, and the effects of this -irrationality greatly diminished. - -For the reasons already mentioned, we do not pursue this subject -further,[35\9] but turn to those optical facts which finally led to -a great and comprehensive theory. - -[Note 35\9: The discovery of the _fixed lines_ in the spectrum, by -Wollaston and Fraunhofer, has more recently supplied the means of -determining, with extreme accuracy, the corresponding portions of -the spectrum in different refracting substances.] - -[2nd Ed.] [Mr. Chester More Hall, of More Hall, in Essex, is said to -have been led by the study of the human eye, which he conceived to -be achromatic, to construct achromatic telescopes as early as 1729. -Mr. Hall, however, kept his invention a secret. David Gregory, in -his _Catoptrics_ (1713), had suggested that it would perhaps be an -improvement of telescopes, if, in imitation of the human eye, the -object-glass were composed of different media. _Encyc. Brit._ art. -_Optics_. - -It is said that Clairaut first discovered the irrationality of the -colored spaces in the spectrum. In consequence of this -irrationality, it follows that when two refracting media are so -combined as to correct each other's extreme dispersion, (the -separation of the red and violet rays,) this first step of -correction still leaves a residue of {69} coloration arising from -the unequal dispersion of the intermediate rays (the green, &c.). -These _outstanding_ colors, as they were termed by Professor -Robison, form the residual, or _secondary_ spectrum. - -Dr. Blair, by very ingenious devices, succeeded in producing an -object-glass, corrected by a fluid lens, in which this aberration of -color was completely corrected, and which performed wonderfully well. - -The dispersion produced by a prism may be corrected by another prism -of the _same substance_ and of a different angle. In this case also -there is an irrationality in the colored spaces, which prevents the -correction of color from being complete; and hence, a new residuary -spectrum, which has been called the _tertiary_ spectrum, by Sir -David Brewster, who first noticed it. - -I have omitted, in the notice of discoveries respecting the -spectrum, many remarkable trains of experimental research, and -especially the investigations respecting the power of various media -to absorb the light of different parts of the spectrum, prosecuted -by Sir David Brewster with extraordinary skill and sagacity. The -observations are referred to in chapter iii. Sir John Herschel, -Prof. Miller, Mr. Daniel, Dr. Faraday, and Mr. Talbot, have also -contributed to this part of our knowledge.] - - - - -CHAPTER V. - -DISCOVERY OF THE LAWS OF DOUBLE REFRACTION. - - -THE laws of refraction which we have hitherto described, were simple -and uniform, and had a symmetrical reference to the surface of the -refracting medium. It appeared strange to men, when their attention -was drawn to a class of phenomena in which this symmetry was -wanting, and in which a refraction took place which was not even in -the plane of incidence. The subject was not unworthy the notice and -admiration it attracted; for the prosecution of it ended in the -discovery of the general laws of light. The phenomena of which I now -speak, are those exhibited by various kinds of crystalline bodies; -but observed for a long time in one kind only, namely, the -rhombohedral calc-spar; or, as it was usually termed, from the -country which supplied the largest and clearest crystals, _Iceland -spar_. These {70} rhombohedral crystals are usually very smooth and -transparent, and often of considerable size; and it was observed, on -looking through them, that all objects appeared double. The -phenomena, even as early as 1669, had been considered so curious, -that Erasmus Bartholin published a work upon them at -Copenhagen,[36\9] (_Experimenta Crystalli Islandici_, Hafniæ, 1669.) -He analysed the phenomena into their laws, so far as to discover -that one of the two images was produced by refraction after the -usual rule, and the other by an unusual refraction. This latter -refraction Bartholin found to vary in different positions; to be -regulated by a line parallel to the sides of the rhombohedron; and -to be greatest in the direction of a line bisecting two of the -angles of the rhombic face of the crystal. - -[Note 36\9: Priestley's _Optics_, p. 550.] - -These rules were exact as far as they went; and when we consider how -geometrically complex the law is, which really regulates the unusual -or extraordinary refraction;--that Newton altogether mistook it, and -that it was not verified till the experiments of Haüy and Wollaston -in our own time;--we might expect that it would not be soon or -easily detected. But Huyghens possessed a key to the secret, in the -theory, which he had devised, of the propagation of light by -undulations, and which he conceived with perfect distinctness and -correctness, so far as its application to these phenomena is -concerned. Hence he was enabled to lay down the law of the phenomena -(the only part of his discovery which we have here to consider), -with a precision and success which excited deserved admiration, when -the subject, at a much later period, regained its due share of -attention. His Treatise was written[37\9] in 1678, but not published -till 1690. - -[Note 37\9: See his _Traité de la Lumière_. Preface.] - -The laws of the _ordinary_ and the _extraordinary_ refraction in -Iceland spar are related to each other; they are, in fact, similar -constructions, made, in the one case, by means of an imaginary -sphere, in the other, by means of a spheroid; the spheroid being of -such oblateness as to suit the rhombohedral form of the crystal, and -the axis of the spheroid being the axis of symmetry of the crystal. -Huyghens followed this general conception into particular positions -and conditions; and thus obtained rules, which he compared with -observation, for cutting the crystal and transmitting the rays in -various manners. "I have examined in detail," says he,[38] "the -properties of the {71} extraordinary refraction of this crystal, to -see if each phenomenon which is deduced from theory, would agree -with what is really observed. And this being so, it is no slight -proof of the truth of our suppositions and principles; but what I am -going to add here confirms them still more wonderfully; that is, the -different modes of cutting this crystal, in which the surfaces -produced give rise to refractions exactly such as they ought to be, -and as I had foreseen them, according to the preceding theory." - -[Note 38\9: See Maseres's _Tracts on Optics_, p. 250; or Huyghens, -_Tr. sur la Lum._ ch. v. Art. 43.] - -Statements of this kind, coming from a philosopher like Huyghens, -were entitled to great confidence; Newton, however, appears not to -have noticed, or to have disregarded them. In his _Opticks_, he -gives a rule for the extraordinary refraction of Iceland spar which -is altogether erroneous, without assigning any reason for rejecting -the law published by Huyghens; and, so far as appears, without -having made any experiments of his own. The Huyghenian doctrine of -double refraction fell, along with his theory of undulations, into -temporary neglect, of which we shall have hereafter to speak. But in -1788, Haüy showed that Huyghens's rule agreed much better than -Newton's with the phenomena: and in 1802, Wollaston, applying a -method of his own for measuring refraction, came to the same result. -"He made," says Young,[39\9] "a number of accurate experiments with -an apparatus singularly well calculated to examine the phenomena, -but could find no general principle to connect them, until the work -of Huyghens was pointed out to him." In 1808, the subject of double -refraction was proposed as a prize-question by the French Institute; -and Malus, whose Memoir obtained the prize, says, "I began by -observing and measuring a long series of phenomena on natural and -artificial faces of Iceland spar. Then, testing by means of these -observations the different laws proposed up to the present time by -physical writers, I was struck with the admirable agreement of the -law of Huyghens with the phenomena, and I was soon convinced that it -is really the law of nature." Pursuing the consequences of the law, -he found that it satisfied phenomena which Huyghens himself had not -observed. From this time, then, the truth of the Huyghenian law was -universally allowed, and soon afterwards, the theory by which it had -been suggested was generally received. - -[Note 39\9: _Quart. Rev._ 1809, Nov. p. 338.] - -The property of double refraction had been first studied only in -Iceland spar, in which it is very obvious. The same property -belongs, {72} though less conspicuously, to many other kinds of -crystals. Huyghens had noticed the same fact in rock-crystal;[40\9] -and Malus found it to belong to a large list of bodies besides; for -instance, arragonite, sulphate of lime, of baryta, of strontia, of -iron; carbonate of lead; zircon, corundum, cymophane, emerald, -euclase, felspar, mesotype, peridote, sulphur, and mellite. Attempts -were made, with imperfect success, to reduce all these to the law -which had been established for Iceland spar. In the first instance, -Malus took for granted that the extraordinary refraction depended -always upon an oblate spheroid; but M. Biot[41\9] pointed out a -distinction between two classes of crystals in which this spheroid -was oblong and oblate respectively, and these he called _attractive_ -and _repulsive_ crystals. With this correction, the law could be -extended to a considerable number of cases; but it was afterwards -proved by Sir D. Brewster's discoveries, that even in this form, it -belonged only to substances of which the crystallization has -relation to a single axis of symmetry, as the rhombohedron, or the -square pyramid. In other cases, as the rhombic prism, in which the -form, considered with reference to its crystalline symmetry, is -_biaxal_, the law is much more complicated. In that case, the sphere -and the spheroid, which are used in the construction for uniaxal -crystals, transform themselves into the two successful convolutions -of a single continuous curve surface; neither of the two rays -follows the law of ordinary refraction; and the formula which -determines their position is very complex. It is, however, capable -of being tested by measures of the refractions of crystals cut in a -peculiar manner for the purpose, and this was done by MM. Fresnel -and Arago. But this complex law of double refraction was only -discovered through the aid of the theory of a luminiferous ether, -and therefore we must now return to the other facts which led to -such a theory. - -[Note 40\9: _ Traité de la Lumière_, ch. v. Art. 20] - -[Note 41\9: Biot, _Traité de Phys._ iii. 330.] - - - - -CHAPTER VI. - -DISCOVERY OF THE LAWS OF POLARIZATION. - - -IF the Extraordinary Refraction of Iceland spar had appeared -strange, another phenomenon was soon noticed in the same {73} -substance, which appeared stranger still, and which in the sequel -was found to be no less important. I speak of the facts which were -afterwards described under the term _Polarization_. Huyghens was the -discoverer of this class of facts. At the end of the treatise which -we have already quoted, he says,[42\9] "Before I quit the subject of -this crystal, I will add one other marvellous phenomenon, which I -have discovered since writing the above; for though hitherto I have -not been able to find out its cause, I will not, on that account, -omit pointing it out, that I may give occasion to others to examine -it." He then states the phenomena; which are, that when two -rhombohedrons of Iceland spar are in parallel positions, a ray -doubly refracted by the first, is not further divided when it falls -on the second: the ordinarily refracted ray is ordinarily refracted -_only_, and the extraordinary ray is only extraordinarily refracted -by the second crystal, neither ray being doubly refracted. The same -is still the case, if the two crystals have their _principal planes_ -parallel, though they themselves are not parallel. But if the -principal plane of the second crystal be perpendicular to that of -the first, the reverse of what has been described takes place; the -ordinarily refracted ray of the first crystal suffers, at the -second, extraordinary refraction _only_, and the extraordinary ray -of the first suffers ordinary refraction only at the second. Thus, -in each of these positions, the double refraction of each ray at the -second crystal is reduced to single refraction, though in a -different manner in the two cases. But in any other position of the -crystals, each ray, produced by the first, is doubly refracted by -the second, so as to produce four rays. - -[Note 42\9: _Tr. Opt._ p. 252.] - -A step in the right conception of these phenomena was made by -Newton, in the second edition of his _Opticks_ (1717). He -represented them as resulting from this;--that the rays of light -have "sides," and that they undergo the ordinary or extraordinary -refraction, according as these sides are parallel to the principal -plane of the crystal, or at right angles to it (Query 26). In this -way, it is clear, that those rays which, in the first crystal, had -been selected for extraordinary refraction, because their sides were -perpendicular to the principal plane, would all suffer extraordinary -refraction at the second crystal for the same reason, if its -principal plane were parallel to that of the first; and would all -suffer ordinary refraction, if the principal plane of the second -crystal were perpendicular to that of the first, and {74} -consequently parallel to the sides of the refracted ray. This view -of the subject includes some of the leading features of the case, -but still leaves several considerable difficulties. - -No material advance was made in the subject till it was taken up by -Malus,[43\9] along with the other circumstances of double refraction, -about a hundred years afterwards. He verified what had been observed -by Huyghens and Newton, on the subject of the variations which light -thus exhibits; but he discovered that this modification, in virtue of -which light undergoes the ordinary, or the extraordinary, refraction, -according to the position of the plane of the crystal, may be -impressed upon it many other ways. One part of this discovery was made -accidentally.[44\9] In 1808, Malus happened to be observing the light -of the setting sun, reflected from the windows of the Luxembourg, -through a rhombohedron of Iceland spar; and he observed that in -turning round the crystal, the two images varied in their intensity. -Neither of the images completely vanished, because the light from the -windows was not properly modified, or, to use the term which Malus -soon adopted, was not completely _polarized_. The complete -polarization of light by reflection from glass, or any other -transparent substance, was found to take place at a certain definite -angle, different for each substance. It was found also that in all -crystals in which double refraction occurred, the separation of the -refracted rays was accompanied by polarization; the two rays, the -ordinary and the extraordinary, being always polarized _oppositely_, -that is, in planes at right angles to each other. The term _poles_, -used by Malus, conveyed nearly the same notion as the term _sides_ -which had been employed by Newton, with the additional conception of a -property which appeared or disappeared according as the _poles_ of the -particles were or were not in a certain direction; a property thus -resembling the _polarity_ of magnetic bodies. When a spot of polarized -light is looked at through a transparent crystal of Iceland spar, each -of the two images produced by the double refraction varies in -brightness as the crystal is turned round. If, for the sake of -example, we suppose the crystal to be turned round in the direction of -the points of the compass, N, E, S, W, and if one image be brightest -when the crystal marks N and S, it will disappear when the crystal -marks E and W: and on the contrary, the second image will vanish when -the crystal marks N and S, {75} and will be brightest when the crystal -marks E and W. The first of these images is polarized _in the plane_ -NS passing through the ray, and the second _in the plane_ EW, -perpendicular to the other. And these rays are _oppositely_ polarized. -It was further found that whether the ray were polarized by reflection -from glass, or from water, or by double refraction, the modification -of light so produced, or the nature of the polarization, was identical -in all these cases;--that the alternatives of ordinary and -extraordinary refraction and non-refraction, were the same, by -whatever crystal they were tested, or in whatever manner the -polarization had been impressed upon the light; in short, that the -property, when once acquired, was independent of everything except the -sides or _poles_ of the ray; and thus, in 1811, the term -"polarization" was introduced.[45\9] - -[Note 43\9: Malus, _Th. de la Doub. Réf._ p. 296.] - -[Note 44\9: Arago, art. _Polarization_, Supp. _Enc. Brit._] - -[Note 45\9: _Mém. Inst._ 1810.] - -This being the state of the subject, it became an obvious question, -by what other means, and according to what laws, this property was -communicated. It was found that some crystals, instead of giving, by -double refraction, two images oppositely polarized, give a single -polarized image. This property was discovered in the agate by Sir D. -Brewster, and in tourmaline by M. Biot and Dr. Seebeck. The latter -mineral became, in consequence, a very convenient part of the -apparatus used in such observations. Various peculiarities bearing -upon this subject, were detected by different experimenters. It was -in a short time discovered, that light might be polarized by -refraction, as well as by reflection, at the surface of -uncrystallized bodies, as glass; the plane of polarization being -perpendicular to the plane of refraction; further, that when a -portion of a ray of light was polarized by reflection, a -corresponding portion was polarized by transmission, the planes of -the two polarizations being at right angles to each other. It was -found also that the polarization which was incomplete with a single -plate, either by reflection or refraction, might be made more and -more complete by increasing the number of plates. - -Among an accumulation of phenomena like this, it is our business to -inquire what general laws were discovered. To make such discoveries -without possessing the general theory of the facts, required no -ordinary sagacity and good fortune. Yet several laws were detected -at this stage of the subject. Malus, in 1811, obtained the important -generalization that, whenever we obtain, by any means, a polarized -ray of light, we produce also another ray, polarized in a contrary -{76} direction; thus when reflection gives a polarized ray, the -companion-ray is refracted polarized oppositely, along with a -quantity of unpolarized light. And we must particularly notice _Sir -D. Brewster's rule_ for the _polarizing angle_ of different bodies. - -Malus[46\9] had said that the angle of reflection from transparent -bodies which most completely polarizes the reflected ray, does not -follow any discoverable rule with regard to the order of refractive -or dispersive powers of the substances. Yet the rule was in reality -very simple. In 1815, Sir D. Brewster stated[47\9] as the law, which -in all cases determines this angle, that "the index of refraction is -the tangent of the angle of polarization." It follows from this, -that the polarization takes place when the reflected and refracted -rays are at right angles to each other. This simple and elegant rule -has been fully confirmed by all subsequent observations, as by those -of MM. Biot and Seebeck; and must be considered one of the happiest -and most important discoveries of the laws of phenomena in Optics. - -[Note 46\9: _Mém. Inst._ 1810.] - -[Note 47\9: _Phil. Trans._ 1815.] - -The rule for polarization by one reflection being thus discovered, -tentative formulæ were proposed by Sir D. Brewster and M. Biot, for -the cases in which several reflections or refractions take place. -Fresnel also in 1817 and 1818, traced the effect of reflection in -modifying the direction of polarization, which Malus had done -inaccurately in 1810. But the complexity of the subject made all -such attempts extremely precarious, till the theory of the phenomena -was understood, a period which now comes under notice. The laws -which we have spoken of were important materials for the -establishment of the theory; but in the mean time, its progress at -first had been more forwarded by some other classes of facts, of a -different kind, and of a longer standing notoriety, to which we must -now turn our attention. - - - - -CHAPTER VII. - -DISCOVERY OF THE LAWS OF THE COLOURS OF THIN PLATES. - - -THE facts which we have now to consider are remarkable, inasmuch as -the colours are produced merely by the smallness of dimensions of -the bodies employed. The light is not analysed by any peculiar {77} -property of the substances, but dissected by the minuteness of their -parts. On this account, these phenomena give very important -indications of the real structure of light; and at an early period, -suggested views which are, in a great measure, just. - -Hooke appears to be the first person who made any progress in -discovering the laws of the colors of thin plates. In his -_Micrographia_, printed by the Royal Society in 1664, he describes, -in a detailed and systematic manner, several phenomena of this kind, -which he calls "fantastical colors." He examined them in _Muscovy -glass_ or mica, a transparent mineral which is capable of being -split into the exceedingly thin films which are requisite for such -colors; he noticed them also in the fissures of the same substance, -in bubbles blown of water, rosin, gum, glass; in the films on the -surface of tempered steel; between two plane pieces of glass; and in -other cases. He perceived also,[48\9] that the production of each -color required a plate of determinate thickness, and he employed -this circumstance as one of the grounds of his theory of light. - -[Note 48\9: _Micrographia_, p. 53.] - -Newton took up the subject where Hooke had left it; and followed it -out with his accustomed skill and clearness, in his _Discourse on -Light and Colors_, communicated to the Royal Society in 1675. He -determined, what Hooke had not ascertained, the thickness of the -film which was requisite for the production of each color; and in -this way explained, in a complete and admirable manner, the colored -rings which occur when two lenses are pressed together, and the -_scale of color_ which the rings follow; a step of the more -consequence, as the same scale occurs in many other optical -phenomena. - -It is not our business here to state the hypothesis with regard to -the properties of light which Newton founded on these facts;--the -"fits of easy transmission and reflection." We shall see hereafter -that his attempted induction was imperfect; and his endeavor to -account, by means of the laws of thin plates, for the colors of -natural bodies, is altogether unsatisfactory. But notwithstanding -these failures in the speculations on this subject, he did make in -it some very important steps; for he clearly ascertained that when -the thickness of the plate was about 1⁄178000th of an inch, or three -times, five times, seven times that magnitude, there was a bright -color produced; but blackness, when the thickness was exactly -intermediate between those magnitudes. He found, also, that the -thicknesses which gave red and {78} violet[49\9] were as fourteen to -nine; and the intermediate colors of course corresponded to -intermediate thicknesses, and therefore, in his apparatus, -consisting of two lenses pressed together, appeared as rings of -intermediate sizes. His mode of confirming the rule, by throwing -upon this apparatus differently colored homogeneous light, is -striking and elegant. "It was very pleasant," he says, "to see the -rings gradually swell and contract as the color of the light was -changed." - -[Note 49\9: _Opticks_, p. 184.] - -It is not necessary to enter further into the detail of these -phenomena, or to notice the rings seen by transmission, and other -circumstances. The important step made by Newton in this matter was, -the showing that the rays of light, in these experiments, as they -pass onwards go periodically through certain cycles of modification, -each period occupying nearly the small fraction of an inch mentioned -above; and this interval being different for different colors. -Although Newton did not correctly disentangle the conditions under -which this periodical character is manifestly disclosed, the -discovery that, under some circumstances, such a periodical -character does exist, was likely to influence, and did influence, -materially and beneficially, the subsequent progress of Optics -towards a connected theory. - -We must now trace this progress; but before we proceed to this task, -we will briefly notice a number of optical phenomena which had been -collected, and which waited for the touch of sound theory to -introduce among them that rule and order which mere observation had -sought for in vain. - - - - -CHAPTER VIII. - -ATTEMPTS TO DISCOVER THE LAWS OF OTHER PHENOMENA. - - -THE phenomena which result from optical combinations, even of a -comparatively simple nature, are extremely complex. The theory which -is now known accounts for these results with the most curious -exactness, and points out the laws which pervade the apparent -confusion; but without this key to the appearances, it was scarcely -possible that any rule or order should be detected. The undertaking -was of {79} the same kind as it would have been, to discover all the -inequalities of the moon's motion without the aid of the doctrine of -gravity. We will enumerate some of the phenomena which thus employed -and perplexed the cultivators of optics. - -The fringes of shadows were one of the most curious and noted of -such classes of facts. These were first remarked by Grimaldi[50\9] -(1665), and referred by him to a property of light which he called -_Diffraction_. When shadows are made in a dark room, by light -admitted through a very small hole, these appearances are very -conspicuous and beautiful. Hooke, in 1672, communicated similar -observations to the Royal Society, as "a new property of light not -mentioned by any optical writer before;" by which we see that he had -not heard of Grimaldi's experiments. Newton, in his _Opticks_, -treats of the same phenomena, which he ascribes to the _inflexion_ -of the rays of light. He asks (Qu. 3), "Are not the rays of light, -in passing by the edges and sides of bodies, bent several times -backward and forward with a motion like that of an eel? And do not -the three fringes of colored light in shadows arise from three such -bendings?" It is remarkable that Newton should not have noticed, -that it is impossible, in this way, to account for the facts, or -even to express their laws; since the light which produces the -fringes must, on this theory, be propagated, even after it leaves -the neighborhood of the opake body, in curves, and not in straight -lines. Accordingly, all who have taken up Newton's notion of -inflexion, have inevitably failed in giving anything like an -intelligible and coherent character to these phenomena. This is, for -example, the case with Mr. (now Lord) Brougham's attempts in the -_Philosophical Transactions_ for 1796. The same may be said of other -experimenters, as Mairan[51\9] and Du Four,[52\9] who attempted to -explain the facts by supposing an atmosphere about the opake body. -Several authors, as Maraldi,[53\9] and Comparetti,[54\9] repeated or -varied these experiments in different ways. - -[Note 50\9: _Physico-Mathesis, de Lumine, Coloribus et Iride._ -Bologna, 1665.] - -[Note 51\9: _Ac. Par._ 1738.] - -[Note 52\9: _Mémoires Présentés_, vol. v.] - -[Note 53\9: _Ac. Par._ 1723.] - -[Note 54\9: _Observationes Opticæ de Luce Inflexâ et Coloribus._ -Padua, 1787.] - -Newton had noticed certain rings of color produced by a glass -speculum, which he called "colors of thick plates," and which he -attempted to connect with the colors of thin plates. His reasoning -is by no means satisfactory; but it was of use, by pointing out this -as a case in which his "fits" (the small periods, or cycles in the -rays of light, of {80} which we have spoken) continued to occur for -a considerable length of the ray. But other persons, attempting to -repeat his experiments, confounded with them extraneous phenomena of -other kinds; as the Duc de Chaulnes, who spread muslin before his -mirror,[55\9] and Dr. Herschel, who scattered hair-powder before -his.[56\9] The colors produced by the muslin were those belonging to -shadows of _gratings_, afterwards examined more successfully by -Fraunhofer, when in possession of the theory. We may mention here -also the colors which appear on finely-striated surfaces, and on -mother-of-pearl, feathers, and similar substances. These had been -examined by various persons (as Boyle, Mazeas, Lord Brougham), but -could still, at this period, be only looked upon as insulated and -lawless facts. - -[Note 55\9: _Ac. Par._ 1755.] - -[Note 56\9: _Phil. Trans._ 1807.] - - - - -CHAPTER IX. - -DISCOVERY OF THE LAWS OF PHENOMENA OF DIPOLARIZED LIGHT. - - -BESIDES the above-mentioned perplexing cases of colors produced by -common light, cases of _periodical colors produced by polarized -light_ began to be discovered, and soon became numerous. In August, -1811, M. Arago communicated to the Institute of France an account of -colors seen by passing polarized light through mica, and -_analysing_[57\9] it with a prism of Iceland spar. It is remarkable -that the light which produced the colors in this case was the light -polarized by the sky, a cause of polarization not previously known. -The effect which the mica thus produced was termed -_depolarization_;--not a very happy term, since the effect is not -the destruction of the polarization, but the combination of a new -polarizing influence with the former. The word _dipolarization_, -which has since been proposed, is a much more appropriate -expression. Several other curious phenomena of the same kind were -observed in quartz, and in flint-glass. M. Arago was not able to -reduce these phenomena to laws, but he had a full conviction of -their value, and ventures to class them with the great steps in {81} -this part of optics. "To Bartholin we owe the knowledge of double -refraction; to Huyghens, that of the accompanying polarization; to -Malus, polarization by reflection; to Arago, depolarization." Sir D. -Brewster was at the same time engaged in a similar train of -research; and made discoveries of the same nature, which, though not -published till some time after those of Arago, were obtained without -a knowledge of what had been done by him. Sir D. Brewster's -_Treatise on New Philosophical Instruments_, published in 1813, -contains many curious experiments on the "depolarizing" properties -of minerals. Both these observers noticed the changes of color which -are produced by changes in the position of the ray, and the -alternations of color in the two oppositely polarized images; and -Sir D. Brewster discovered that, in topaz, the phenomena had a -certain reference to lines which he called the _neutral_ and -_depolarizing_ axes. M. Biot had endeavored to reduce the phenomena -to a law; and had succeeded so far, that he found that in the plates -of sulphate of lime, the place of the tint, estimated in Newton's -_scale_ (see _ante_, chap. vii.), was as the square of the sine of -the inclination. But the laws of these phenomena became much more -obvious when they were observed by Sir D. Brewster with a larger -field of view.[58\9] He found that the colors of topaz, under the -circumstances now described, exhibited themselves in the form of -elliptical rings, crossed by a black bar, "the most brilliant class -of phenomena," as he justly says, "in the whole range of optics." In -1814, also, Wollaston observed the circular rings with a black -cross, produced by similar means in calc-spar; and M. Biot, in 1815, -made the same observation. The rings in several of these cases were -carefully measured by M. Biot and Sir D. Brewster, and a great mass -of similar phenomena was discovered. These were added to by various -persons, as M. Seebeck, and Sir John Herschel. - -[Note 57\9: The prism of Iceland spar produces the colors by -separating the transmitted rays according to the laws of double -refraction. Hence it is said to _analyse_ the light.] - -[Note 58\9: _Phil. Trans._ 1814.] - -Sir D. Brewster, in 1818, discovered a general relation between the -crystalline form and the optical properties, which gave an -incalculable impulse and a new clearness to these researches. He -found that there was a correspondence between the degree of symmetry -of the optical phenomena and the crystalline form; those crystals -which are uniaxal in the crystallographical sense, are also uniaxal -in their optical properties, and give circular rings; those which -are of other forms are, generally speaking, biaxal; they give oval -and knotted _isochromatic_ lines, with two _poles_. He also -discovered a rule for the tint at each point {82} in such cases; and -thus explained, so far as an empirical law of phenomena went, the -curious and various forms of the colored curves. This law, when -simplified by M. Biot,[59\9] made the tint proportional to the -product of the distances of the point from the two poles. In the -following year, Sir J. Herschel confirmed this law by showing, from -actual measurement, that the curve of the isochromatic lines in -these cases was the curve termed the _lemniscata_, which has, for -each point, the product of the distances from two fixed poles equal -to a constant quantity.[60\9] He also reduced to rule some other -apparent anomalies in phenomena of the same class. - -[Note 59\9: _Mém. Inst._ 1818, p. 192.] - -[Note 60\9: _Phil. Trans._ 1819.] - -M. Biot, too, gave a rule for the directions of the planes of -polarization of the two rays produced by double refraction in biaxal -crystals, a circumstance which has a close bearing upon the -phenomena of dipolarization. His rule was, that the one plane of -polarization bisects the dihedral angle formed by the two planes -which pass through the optic axes, and that the other is -perpendicular to such a plane. When, however, Fresnel had discovered -from the theory the true laws of double refraction, it appeared that -the above rule is inaccurate, although in a degree which observation -could hardly detect without the aid of theory.[61\9] - -[Note 61\9: Fresnel, _Mém. Inst._ 1827, p. 162.] - -There were still other classes of optical phenomena which attracted -notice; especially those which are exhibited by plates of quartz cut -perpendicular to the axis. M. Arago had observed, in 1811, that this -substance produced a _twist_ of the plane of polarization to the right -or left hand, the amount of this twist being different for different -colors; a result which was afterwards traced to a modification of -light different both from common and from polarized light, and -subsequently known as _circular polarization_. Sir J. Herschel had -the good fortune and sagacity to discover that this peculiar kind of -polarization in quartz was connected with an equally peculiar -modification of crystallization, the _plagihedral_ faces which are -seen, on some crystals, obliquely disposed, and, as it were, -following each other round the crystal from left to right, or from -right to left. Sir J. Herschel found that the _right-handed_ or -_left-handed_ character of the circular polarization corresponded, -in all cases, to that of the crystal. - -In 1815, M. Biot, in his researches on the subject of circular -polarization, was led to the unexpected and curious discovery, that -this {83} property which seemed to require for its very conception a -crystalline structure in the body, belonged nevertheless to several -fluids, and in different directions for different fluids. Oil of -turpentine, and an essential oil of laurel, gave the plane of -polarization a rotation to the left hand; oil of citron, syrup of -sugar, and a solution of camphor, gave a rotation to the right hand. -Soon after, the like discovery was made independently by Dr. -Seebeck, of Berlin. - -It will easily be supposed that all those brilliant phenomena could -not be observed, and the laws of many of the phenomena discovered, -without attempts on the part of philosophers to combine them all -under the dominion of some wide and profound theory. Endeavors to -ascend from such knowledge as we have spoken of, to the general -theory of light, were, in fact, made at every stage of the subject, -and with a success which at last won almost all suffrages. We are -now arrived at the point at which we are called upon to trace the -history of this theory; to pass from the laws of phenomena to their -causes;--from Formal to Physical Optics. The undulatory theory of -light, the only discovery which can stand by the side of the theory -of universal gravitation, as a doctrine belonging to the same order, -for its generality, its fertility, and its certainty, may properly -be treated of with that ceremony which we have hitherto bestowed -only on the great advances of astronomy; and I shall therefore now -proceed to speak of the Prelude to this epoch, the Epoch itself, and -its Sequel, according to the form of the preceding Book which treats -of astronomy. - -[2nd Ed.] [I ought to have stated, in the beginning of this chapter, -that Malus discovered the depolarization of _white light_ in 1811. -He found that a pencil of light which, being polarized, refused to -be reflected by a surface properly placed, recovered its power of -being reflected after being transmitted through certain crystals and -other transparent bodies. Malus intended to pursue this subject, -when his researches were terminated by his death, Feb. 7, 1812. M. -Arago, about the same time, announced his important discovery of the -depolarization of _colors_ by crystals. - -I may add, to what is above said of M. Biot's discoveries respecting -the circular polarizing power of fluids, that he pursued his -researches so as to bring into view some most curious relations -among the elements of bodies. It appeared that certain substances, -as sugar of canes, had a right-handed effect, and certain other -substances, as gum, a left-handed effect; and that the molecular -value of this effect was not altered by dilution. It appeared also -that a certain element of the {84} substance of fruits, which had -been supposed to be gum, and which is changed into sugar by the -operation of acids, is not gum, and has a very energetic -right-handed effect. This substance M. Biot called _dextrine_, and -he has since traced its effects into many highly curious and -important results.**] - - - -{{85}} -PHYSICAL OPTICS. - - - - -CHAPTER X. - -PRELUDE TO THE EPOCH OF YOUNG AND FRESNEL. - - -BY _Physical_ Optics we mean, as has already been stated, the -theories which explain optical phenomena on mechanical principles. -No such explanation could be given till true mechanical principles -had been obtained; and, accordingly, we must date the commencement -of the essays towards physical optics from Descartes, the founder of -the modern mechanical philosophy. His hypothesis concerning light -is, that it consists of small particles emitted by the luminous -body. He compares these particles to balls, and endeavors to -explain, by means of this comparison, the laws of reflection and -refraction.[62\9] In order to account for the production of colors -by refraction, he ascribes to these balls an alternating rotatory -motion.[63\9] This form of the _emission theory_, was, like most of -the physical speculations of its author, hasty and gratuitous; but -was extensively accepted, like the rest of the Cartesian doctrines, -in consequence of the love which men have for sweeping and simple -dogmas, and deductive reasonings from them. In a short time, -however, the rival optical _theory of undulations_ made its -appearance. Hooke in his _Micrographia_ (1664) propounds it, upon -occasion of his observations, already noticed, (chap. **vii.,) on the -colors of thin plates. He there asserts[64\9] light to consist in a -"quick, short, vibrating motion," and that it is propagated in a -homogeneous medium, in such a way that "every pulse or vibration of -the luminous body will generate a sphere, which will continually -increase and grow bigger, just after the same manner (though -indefinitely swifter) as the waves or rings on the surface of water -do swell into bigger and bigger circles about a point in it."[65\9] -He applies this to the explanation of refraction, {86} by supposing -that the rays in a denser medium move more easily, and hence that -the pulses become oblique; a far less satisfactory and consistent -hypothesis than that of Huyghens, of which we shall next have to -speak. But Hooke has the merit of having also combined with his -theory, though somewhat obscurely, the _Principle of Interferences_, -in the application which he makes of it to the colors of thin -plates. Thus[66\9] he supposes the light to be reflected at the -first surface of such plates; and he adds, "after two refractions -and one reflection (from the second surface) there is propagated a -kind of fainter ray," which comes behind the other reflected pulse; -"so that hereby (the surfaces AB and EF being so near together that -the eye cannot discriminate them from one), this compound or -duplicated pulse does produce on the retina the sensation of a -yellow." The reason for the production of this particular color, in -the case of which he here speaks, depends on his views concerning -the kind of pulses appropriate to each color; and, for the same -reason, when the thickness is different, he finds that the result -will be a red or a green. This is a very remarkable anticipation of -the explanation ultimately given of these colors; and we may observe -that if Hooke could have measured the thickness of his thin plates, -he could hardly have avoided making considerable progress in the -doctrine of interferences. - -[Note 62\9: _Diopt._ c. ii. 4.] - -[Note 63\9: _Meteor._ c. viii. 6.] - -[Note 64\9: _Micrographia_, p. 56.] - -[Note 65\9: _Micrographia_, p. 57.] - -[Note 66\9: _Micrographia_, p. 66.] - -But the person who is generally, and with justice, looked upon as -the great author of the undulatory theory, at the period now under -notice, is Huyghens, whose _Traité de la Lumière_, containing a -developement of his theory, was written in 1678, though not -published till 1690. In this work he maintained, as Hooke had done, -that light consists in undulations, and expands itself spherically, -nearly in the same manner as sound does; and he referred to the -observations of Römer on Jupiter's satellites, both to prove that -this difference takes place successively, and to show its exceeding -swiftness. In order to trace the effect of an undulation, Huyghens -considers that every point of a wave diffuses its motion in all -directions; and hence he draws the conclusion, so long looked upon -as the turning-point of the combat between the rival theories, that -the light will not be _diffused_ beyond the rectilinear space, when -it passes through an aperture; "for," says he,[67\9] "although the -_partial_ waves, produced by the particles comprised in the -aperture, do diffuse themselves beyond the rectilinear space, these -waves do not _concur_ anywhere except in front of the {87} -aperture." He rightly considers this observation as of the most -essential value. "This," he says, "was not known by those who began -to consider the waves of light, among whom are Mr. Hooke in his -_Micrography_, and Father Pardies; who, in a treatise of which he -showed me a part, and which he did not live to finish, had -undertaken to prove, by these waves, the effects of reflection and -refraction. But the principal foundation, which consists in the -remark I have just made, was wanting in his demonstrations." - -[Note 67\9: _Tracts on Optics_, p. 209.] - -By the help of this view, Huyghens gave a perfectly satisfactory and -correct explanation of the laws of reflection and refraction; and he -also applied the same theory, as we have seen, to the double -refraction of Iceland spar with great sagacity and success. He -conceived that in this crystal, besides the spherical waves, there -might be others of a spheroidal form, the axis of the spheroid being -symmetrically disposed with regard to the faces of the rhombohedron, -for to these faces the optical phenomena are symmetrically related. -He found[68\9] that the position of the refracted ray, determined by -such spheroidal undulations, would give an oblique refraction, which -would coincide in its laws with the refraction observed in Iceland -spar; and, as we have stated, this coincidence was long after fully -confirmed by other observers. - -[Note 68\9: _Tracts on Optics_, 237.] - -Since Huyghens, at this early period, expounded the undulatory -theory with so much distinctness, and applied it with so much skill, -it may be asked why we do not hold him up as the great Author of the -induction of undulations of light;--the person who marks the epoch -of the theory? To this we reply, that though Huyghens discovered -strong presumptions in favor of the undulatory theory, it was not -_established_ till a later era, when the fringes of shadows, rightly -understood, made the waves visible, and when the hypothesis which -had been assumed to account for double refraction, was found to -contain also an explanation of polarization. It is _then_ that this -theory of light assumes its commanding form; and the persons who -gave it this form, we must make the great names of our narrative; -without, however, denying the genius and merit of Huyghens, who is, -undoubtedly, the leading character in the prelude to the discovery. - -The undulatory theory, from this time to our own, was unfortunate in -its career. It was by no means destitute of defenders, but these -were not experimenters; and none of them thought of applying it to -{88} Grimaldi's experiments on fringes, of which we have spoken a -little while ago. And the great authority of the period, Newton, -adopted the opposite hypothesis, that of emission, and gave it a -currency among his followers which kept down the sounder theory for -above a century. - -Newton's first disposition appears to have been by no means averse -to the assumption of an ether as the vehicle of luminiferous -undulations. When Hooke brought against his prismatic analysis of -light some objections, founded on his own hypothetical notions, -Newton, in his reply, said,[69\9] "The hypothesis has a much greater -affinity with his own hypothesis than he seems to be aware of; the -vibrations of the ether being as useful and necessary in this as in -his." This was in 1672; and we might produce, from Newton's writing, -passages of the same kind, of a much later date. Indeed it would -seem that, to the last, Newton considered the assumption of an ether -as highly probable, and its vibrations important parts of the -phenomena of light; but he also introduced into his system the -hypothesis of emission, and having followed this hypothesis into -mathematical detail, while he has left all that concerns the ether -in the form of queries and conjectures, the emission theory has -naturally been treated as the leading part of his optical doctrines. - -[Note 69\9: _Phil. Trans._ vii. 5087.] - -The principal propositions of the _Principia_ which bear upon the -question of optical theory are those of the fourteenth Section of -the first Book,[70\9] in which the law of the sines in refraction is -proved on the hypothesis that the particles of bodies act on light -only at very small distances; and the proposition of the eighth -Section of the second Book;[71\9] in which it is pretended to be -demonstrated that the motion propagated in a fluid must diverge when -it has passed through an aperture. The former proposition shows that -the law of refraction, an optical truth which mainly affected the -choice of a theory, (for about reflection there is no difficulty on -any mechanical hypothesis,) follows from the theory of emission: the -latter proposition was intended to prove the inadmissibility of the -rival hypothesis, that of undulations. As to the former point,--the -hypothetical explanation of refraction, on the assumptions there -made,--the conclusion is quite satisfactory; but the reasoning in -the latter case, (respecting the propagation of undulations,) is -certainly inconclusive and vague; and something better might the -more reasonably have been expected, since Huyghens had at least {89} -endeavored to prove the opposite proposition. But supposing we leave -these properties, the rectilinear course, the reflection, and the -refraction of light, as problems in which neither theory has a -decided advantage, what is the next material point? The colors of -thin plates. Now, how does Newton's theory explain these? By a new -and special supposition;--that of _fits of easy transmission and -reflection_: a supposition which, though it truly expresses these -facts, is not borne out by any other phenomena. But, passing over -this, when we come to the peculiar laws of polarization in Iceland -spar, how does Newton's meet this? Again by a special and new -supposition;--that the rays of light have _sides_. Thus we find no -fresh evidence in favor of the emission hypothesis springing out of -the fresh demands made upon it. It may be urged, in reply, that the -same is true of the undulatory theory; and it must be allowed that, -at the time of which we now speak, its superiority in this respect -was not manifested; though Hooke, as we have seen, had caught a -glimpse of the explanation, which this theory supplies, of the -colors of thin plates. - -[Note 70\9: _Principia_, Prop. 94, _et seq._] - -[Note 71\9: Ib. Prop. 42.] - -At a later period, Newton certainly seems to have been strongly -disinclined to believe light to consist in undulations merely. "Are -not," he says, in Question twenty-eight of the _Opticks_, "all -hypotheses erroneous, in which light is supposed to consist in -pression or motion propagated through a fluid medium?" The arguments -which most weighed with him to produce this conviction, appear to -have been the one already mentioned,--that, on the undulatory -hypothesis, undulations passing through an aperture would be -diffused; and again,--his conviction, that the properties of light, -developed in various optical phenomena, "depend not upon new -modifications, but upon the original and unchangeable properties of -the rays." (Question twenty-seven.) - -But yet, even in this state of his views, he was very far from -abandoning the machinery of vibrations altogether. He is disposed to -use such machinery to produce his "fits of easy transmission." In -his seventeenth Query, he says,[72\9] "when a ray of light falls -upon the surface of any pellucid body, and is there refracted or -reflected; may not waves of vibrations or tremors be thereby excited -in the refracting or reflecting medium at the point of incidence? . -. . . and do not these vibrations overtake the rays of light, and by -overtaking them successively, do they not put them into the fits of -easy reflection and easy {90} transmission described above?" Several -of the other queries imply the same persuasion, of the necessity for -the assumption of an ether and its vibrations. And it might have -been asked, whether any good reason could be given for the -hypothesis of an ether as a _part_ of the mechanism of light, which -would not be equally valid in favor of this being the _whole_ of the -mechanism, especially if it could be shown that nothing more was -wanted to produce the results. - -[Note 72\9: _Opticks_, p. 322.] - -The emission theory was, however, embraced in the most strenuous -manner by the disciples of Newton. That propositions existed in the -_Principia_ which proceeded on this hypothesis, was, with many of -these persons, ground enough for adopting the doctrine; and it had -also the advantage of being more ready of conception, for though the -propagation of a wave is not very difficult to conceive, at least by -a mathematician, the motion of a particle is still easier. - -On the other hand, the undulation theory was maintained by no less a -person than Euler; and the war between the two opinions was carried -on with great earnestness. The arguments on one side and on the -other soon became trite and familiar, for no person explained any -new class of facts by either theory. Thus it was urged by Euler -against the system of emission,[73\9]--that the perpetual emanation -of light from the sun must have diminished the mass;--that the -stream of matter thus constantly flowing must affect the motions of -the planets and comets; that the rays must disturb each other;--that -the passage of light through transparent bodies is, on this system, -inconceivable: all such arguments were answered by representations -of the exceeding minuteness and velocity of the matter of light. On -the other hand, there was urged against the theory of waves, the -favorite Newtonian argument, that on this theory the light passing -through an aperture ought to be diffused, as sound is. It is curious -that Euler does not make to this argument the reply which Huyghens -had made before. The fact really was, that he was not aware of the -true ground of the difference of the result in the cases of sound -and light; namely, that any ordinary aperture bears an immense ratio -to the length of an undulation of light, but does not bear a very -great ratio to the length of an undulation of sound. The -demonstrable consequence of this difference is, that light darts -through such an orifice in straight rays, while sound is diffused in -all directions. Euler, not perceiving this difference, rested his -answer mainly upon a circumstance by no means {91} unimportant, that -the partitions usually employed are not impermeable to sound, as -opake bodies are to light. He observes that the sound does not all -come through the aperture; for we hear, though the aperture be -stopped. These were the main original points of attack and defence, -and they continued nearly the same for the whole of the last -century; the same difficulties were over and over again proposed, -and the same solutions given, much in the manner of the disputations -of the schoolmen of the middle ages. - -[Note 73\9: Fischer, iv. 449.] - -The struggle being thus apparently balanced, the scale was naturally -turned by the general ascendancy of the Newtonian doctrines: and the -emission theory was the one most generally adopted. It was still -more firmly established, in consequence of the turn generally taken -by the scientific activity of the latter half of the eighteenth -century: for while nothing was added to our knowledge of optical -laws, the chemical effects of light were studied to a considerable -extent by various inquirers;[74\9] and the opinions at which these -persons arrived, they found that they could express most readily, in -consistency with the reigning chemical views, by assuming the -materiality of light. It is, however, clear, that no reasonings of -the inevitably vague and doubtful character which belong to these -portions of chemistry, ought to be allowed to interfere with the -steady and regular progress of induction and generalization, founded -on relations of space and number, by which procedure the mechanical -sciences are formed. We reject, therefore, all these chemical -speculations, as belonging to other subjects; and consider the -history of optical theory as a blank, till we arrive at some very -different events, of which we have now to speak. {92} - -[Note 74\9: As Scheele, Selle, Lavoisier, De Luc, Richter, -Leonhardi, Gren, Girtanner, Link, Hagen, Voigt, De la Metherie, -Scherer, Dizé, Brugnatelli. See Fischer, vii. p. 20.] - - - - -CHAPTER XI. - -EPOCH OF YOUNG AND FRESNEL. - - -_Sect._ 1.--_Introduction._ - -THE man whose name must occupy the most distinguished place in the -history of Physical Optics, in consequence of what he did in -reviving and establishing the undulatory theory of light, is Dr. -Thomas Young. He was born in 1773, at Milverton in Somersetshire, of -Quaker parents; and after distinguishing himself during youth by the -variety and accuracy of his attainments, he settled in London as a -physician in 1801; but continued to give much of his attention to -general science. His optical theory, for a long time, made few -proselytes; and several years afterwards, Auguste Fresnel, an -eminent French mathematician, an engineer officer, took up similar -views, proved their truth, and traced their consequences, by a -series of labors almost independent of those of Dr. Young. It was -not till the theory was thus re-echoed from another land, that it -was able to take any strong hold on the attention of the countrymen -of its earlier promulgator. - -The theory of undulations, like that of universal gravitation, may -be divided into several successive steps of generalization. In both -cases, all these steps were made by the same persons; but there is -this difference:--all the parts of the law of universal gravitation -were worked out in one burst of inspiration by its author, and -published at one time;--in the doctrine of light, on the other hand, -the different steps of the advance were made and published at -separate times, with intervals between. We see the theory in a -narrower form, and in detached portions, before the widest -generalizations and principles of unity are reached; we see the -authors struggling with the difficulties before we see them -successful. They appear to us as men like ourselves, liable to -perplexity and failure, instead of coming before us, as Newton does -in the history of Physical Astronomy, as the irresistible and almost -supernatural hero of a philosophical romance. {93} - -The main subdivisions of the great advance in physical optics, of -which we have now to give an account, are the following:-- - -1. The explanation of the _periodical colors_ of thin plates, thick -plates, fringed shadows, striated surfaces, and other phenomena of -the same kind, by means of the doctrine of the _interference_ of -undulations. - -2. The explanation of the phenomena of _double refraction_ by the -propagation of undulations in a medium of which the optical -_elasticity_ is different in different directions. - -3. The conception of _polarization_ as the result of the vibrations -being _transverse_; and the consequent explanation of the production -of polarization, and the necessary connexion between polarization -and double refraction, on mechanical principles. - -4. The explanation of the phenomena of _dipolarization_, by means of -the interference of the _resolved parts_ of the vibrations after -double refraction. - -The history of each of these discoveries will be given separately to -a certain extent; by which means the force of proof arising from -their combination will be more apparent. - - -_Sect._ 2.--_Explanation of the Periodical Colors of Thin Plates and -Shadows by the Undulatory Theory._ - -THE explanation of periodical colors by the principle of -interference of vibrations, was the first step which Young made in -his confirmation of the undulatory theory. In a paper on Sound and -Light, dated Emmanuel College, Cambridge, 9th July, 1799, and read -before the Royal Society in January following, he appears to incline -strongly to the Huyghenian theory; not however offering any new -facts or calculations in its favor, but pointing out the great -difficulties of the Newtonian hypothesis. But in a paper read before -the Royal Society, November 12, 1801, he says, "A further -consideration of the colors of thin plates has converted that -prepossession which I before entertained for the undulatory theory -of light, into a very strong conviction of its truth and efficiency; -a conviction which has since been most strikingly confirmed by an -analysis of the colors of _striated surfaces_." He here states the -general principle of interferences in the form of a proposition. -(Prop. viii.) "When two undulations from different origins coincide -either perfectly or very nearly in direction, their joint effect is -a combination of the motions belonging to them." He explains, by the -help of this proposition, the colors which were observed in -Coventry's {94} micrometers, in which instrument lines were drawn on -glass at a distance of 1⁄500th of an inch. The interference of the -undulations of the rays reflected from the two sides of these fine -lines, produced periodical colors. In the same manner, he accounts -for the colors of thin plates, by the interference of the light -partially reflected from the two surfaces of the plates. We have -already seen that Hooke had long before suggested the same -explanation; and Young says at the end of his paper, "It was not -till I had satisfied myself respecting all these phenomena, that I -found in Hooke's _Micrographia_ a passage which might have led me -earlier to a similar opinion." He also quotes from Newton many -passages which assume the existence of an ether; of which, as we -have already seen, Newton suggests the necessity in these very -phenomena, though he would apply it in combination with the emission -of material light. In July, 1802, Young explained, on the same -principle, some facts in indistinct vision, and other similar -appearances. And in 1803,[75\9] he speaks more positively still. "In -making," he says, "some experiments on the fringes of colors -accompanying shadows, I have found so simple and so demonstrative a -proof of the general law of interference of two portions of light, -which I have already endeavored to establish, that I think it right -to lay before the Royal Society a short statement of the facts which -appear to me to be thus decisive." The two papers just mentioned -certainly ought to have convinced all scientific men of the truth of -the doctrine thus urged; for the number and exactness of the -explanations is very remarkable. They include the colored fringes -which are seen with the shadows of fibres; the colors produced by a -dew between two pieces of glass, which, according to the theory, -should appear when the thickness of the plate is _six_ times that of -thin plates, and which do so; the changes resulting from the -employment of other fluids than water; the effect of inclining the -plates; also the fringes and bands which accompany shadows, the -phenomena observed by Grimaldi, Newton, Maraldi, and others, and -hitherto never at all reduced to rule. Young observes, very justly, -"whatever may be thought of the theory, we have got a simple and -general law" of the phenomena. He moreover calculated the length of -an undulation from the measurements of fringes of shadows, as he had -done before from the colors of thin plates; and found a very close -accordance of the results of the various cases with one another. {95} - -[Note 75\9: _Phil. Trans._ Memoir, read Nov. 24.] - -There is one difficulty, and one inaccuracy, in Young's views at -this period, which it may be proper to note. The difficulty was, -that he found it necessary to suppose that light, when reflected at -a rarer medium, is retarded by half an undulation. This assumption, -though often urged at a later period as an argument against the -theory, was fully justified as the mechanical principles of the -subject were unfolded; and the necessity of it was clear to Young -from the first. On the strength of this, says he, "I ventured to -predict, that if the reflections were of the same kind, made at the -surfaces of a thin plate, of a density intermediate between the -densities of the mediums surrounding it, the central spot would be -white; and I have now the pleasure of stating, that I have fully -verified this prediction by interposing a drop of oil of sassafras -between a prism of flint-glass and a lens of crown-glass." - -The inaccuracy of his calculations consisted in his considering the -external fringe of shadows to be produced by the interference of a -ray _reflected_ from the _edge_ of the object, with a ray which -passes clear of it; instead of supposing _all the parts_ of the wave -of light to corroborate or interfere with one another. The -mathematical treatment of the question on the latter hypothesis was -by no means easy. Young was a mathematician of considerable power in -the solution of the problems which came before him: though his -methods possessed none of the analytical elegance which, in his -time, had become general in France. But it does not appear that he -ever solved the problem of undulations as applied to fringes, with -its true conditions. He did, however, rectify his conceptions of the -nature of the interference; and we may add, that the numerical error -of the consequences of the defective hypothesis is not such as to -prevent their confirming the undulatory theory.[76\9] - -[Note 76\9: I may mention, in addition to the applications which -Young made of the principle of interferences, his _Eriometer_, an -instrument invented for the purpose of measuring the thickness of -the fibres of wood; and the explanation of the supernumerary bands -of the rainbow. These explanations involve calculations founded on -the length of an undulation of light, and were confirmed by -experiment, as far as experiment went.] - -But though this theory was thus so powerfully recommended by -experiment and calculation, it met with little favor in the -scientific world. Perhaps this will be in some measure accounted -for, when we come, in the next chapter, to speak of the mode of its -reception by {96} the supposed judges of science and letters. Its -author went on laboring at the completion and application of the -theory in other parts of the subject; but his extraordinary success -in unravelling the complex phenomena of which we have been speaking, -appears to have excited none of the notice and admiration which -properly belonged to it, till Fresnel's Memoir _On Diffraction_ was -delivered to the Institute, in October, 1815. - -MM. Arago and Poinsot were commissioned to make a report upon this -Memoir; and the former of these philosophers threw himself upon the -subject with a zeal and intelligence which peculiarly belonged to -him. He verified the laws announced by Fresnel: "laws," he says, -"which appear to be destined to make an epoch in science." He then -cast a rapid glance at the history of the subject, and recognized, -at once, the place which Young occupied in it. Grimaldi, Newton, -Maraldi, he states, had observed the facts, and tried in vain to -reduce them to rule or cause. "Such[77\9] was the state of our -knowledge on this difficult question, when Dr. Thomas Young made the -very remarkable experiment which is described in the _Philosophical -Transactions_ for 1803;" namely, that to obliterate all the bands -within the shadow, we need only stop the ray which is going to -graze, or has grazed, one border of the object. To this, Arago added -the important observation, that the same obliteration takes place, -if we stop the ray, with a transparent plate; except the plate be -very thin, in which case the bands are displaced, and not -extinguished. "Fresnel," says he, "guessed the effect which a thin -plate would produce, when I had told him of the effect of a thick -glass." Fresnel himself declares[78\9] that he was not, at the time, -aware of Young's previous labors. After stating nearly the same -reasonings concerning fringes which Young had put forward in 1801, -he adds, "it is therefore the meeting, the actual crossing of the -rays, which produces the fringes. This consequence, which is only, -so to speak, the translation of the phenomena, seems to me entirely -opposed to the hypothesis of emission, and confirms the system which -makes light consist in the vibrations of a peculiar fluid." And thus -the Principle of Interferences, and the theory of undulations, so -far as that principle depends upon the theory, was a second time -established by Fresnel in France, fourteen years after it had been -discovered, fully proved, and repeatedly published by Young in -England. {97} - -[Note 77\9: _An. Chim._ 1815, Febr.] - -[Note 78\9: Ib. tom. xvii. p. 402.] - -In this Memoir of Fresnel's, he takes very nearly the same course as -Young had done; considering the interference of the direct light -with that reflected at the edge, as the cause of the external -fringes; and he observes, that in this reflection it is necessary to -suppose half an undulation lost: but a few years later, he -considered the propagation of undulations in a more true and general -manner, and obtained the solution of this difficulty of the -half-undulation. His more complete Memoir on _Diffraction_ was -delivered to the Institute of France, July 29, 1818; and had the -prize awarded it in 1819:[79\9] but by the delays which at that -period occurred in the publication of the _Parisian Academical -Transactions_, it was not published[80\9] till 1826, when the theory -was no longer generally doubtful or unknown in the scientific world. -In this Memoir, Fresnel observes, that we must consider the effect -of _every portion_ of a wave of light upon a distant point, and -must, on this principle, find the illumination produced by any -number of such waves together. Hence, in general, the process of -integration is requisite; and though the integrals which here offer -themselves are of a new and difficult kind, he succeeded in making -the calculation for the cases in which he experimented. His _Table -of the Correspondences of Theory and Observation_,[81\9] is very -remarkable for the closeness of the agreement; the errors being -generally less than one hundredth of the whole, in the distances of -the black bands. He justly adds, "A more striking agreement could -not be expected between experiment and theory. If we compare the -smallness of the differences with the extent of the breadths -measured; and if we remark the great variations which _a_ and _b_ -(the distance of the object from the luminous point and from the -screen) have received in the different observations, we shall find -it difficult not to regard the integral which has led us to these -results as the faithful expression of the law of the phenomena." - -[Note 79\9: _Ann. Chim._ May, 1819.] - -[Note 80\9: _Mém. Inst._ for 1821-2.] - -[Note 81\9: _Mém. Inst._ p. 420-424.] - -A mathematical theory, applied, with this success, to a variety of -cases of very different kinds, could not now fail to take strong -hold of the attention of mathematicians; and accordingly, from this -time, the undulatory doctrine of diffraction has been generally -assented to, and the mathematical difficulties which it involves, -have been duly studied and struggled with. - -Among the remarkable applications of the undulatory doctrine to -diffraction, we may notice those of Joseph Fraunhofer, a {98} -mathematical optician of Munich. He made a great number of -experiments on the shadows produced by small holes, and groups of -small holes, very near each other. These were published[82\9] in his -_New Modifications of Light_, in 1823. The greater part of this -Memoir is employed in tracing the laws of phenomena of the extremely -complex and splendid appearances which he obtained; but at the -conclusion he observes, "It is remarkable that the laws of the -reciprocal influence and of the diffraction of the rays, can be -deduced from the principles of the undulatory theory: knowing the -conditions, we may, by means of an extremely simple equation, -determine the extent of a luminous wave for each of the different -colors; and in every case, the calculation corresponds with -observation." This mention of "an extremely simple equation," -appears to imply that he employed only Young's and Fresnel's earlier -mode of calculating interferences, by considering two portions of -light, and not the method of integration. Both from the late period -at which they were published, and from the absence of mathematical -details, Fraunhofer's labors had not any strong influence on the -establishment of the undulatory theory; although they are excellent -verifications of it, both from the goodness of the observations, and -the complexity and beauty of the phenomena. - -[Note 82\9: In Schumacher's _Astronomische Abhandlungen_, in French; -earlier in German.] - -We have now to consider the progress of the undulatory theory in -another of its departments, according to the division already stated. - - -_Sect._ 3.--_Explanation of Double Refraction by the Undulatory -Theory._ - -WE have traced the history of the undulatory theory applied to -diffraction, into the period when Young came to have Fresnel for his -fellow-laborer. But in the mean time, Young had considered the -theory in its reference to other phenomena, and especially to those -of _double refraction_. - -In this case, indeed, Huyghens's explanation of the facts of Iceland -spar, by means of spheroidal undulations, was so complete, and had -been so fully confirmed by the measurements of Haüy and Wollaston, -that little remained to be done, except to connect the Huyghenian -hypothesis with the mechanical views belonging to the theory, and to -extend his law to other cases. The former part of this task Young -executed, by remarking that we may conceive the _elasticity_ of the -{99} crystal, on which the velocity of propagation of the -luminiferous undulation depends, to be different, in the direction -of the crystallographic axis, and in the direction of the planes at -right angles to this axis; and from such a difference, he deduces -the existence of spheroidal undulations. This suggestion appeared in -the _Quarterly Review_ for November, 1809, in a critique upon an -attempt of Laplace to account for the same phenomena. Laplace had -proposed to reduce the double refraction of such crystals as Iceland -spar, to his favorite machinery of forces which are sensible at -small distances only. The peculiar forces which produce the effect -in this case, he conceives to emanate from the crystallographic -axis: so that the velocity of light within the crystal will depend -only on the situation of the ray with respect to this axis. But the -establishment of this condition is, as Young observes, the main -difficulty of the problem. How are we to conceive refracting forces, -independent of the surface of the refracting medium, and regulated -only by a certain internal line? Moreover, the law of force which -Laplace was obliged to assume, namely, that it varied as the square -of the sine of the angle which the ray made with the axis, could -hardly be reconciled with mechanical principles. In the critique -just mentioned, Young appears to feel that the undulatory theory, -and perhaps he himself, had not received justice at the hands of men -of science; he complains that a person so eminent in the world of -science as Laplace then was, should employ his influence in -propagating error, and should disregard the extraordinary -confirmations which the Huyghenian theory had recently received. - -The extension of this view, of the different elasticity of crystals -in different directions, to other than uniaxal crystals, was a more -complex and difficult problem. The general notion was perhaps -obvious, after what Young had done; but its application and -verification involved mathematical calculations of great generality, -and required also very exact experiments. In fact, this application -was not made till Fresnel, a pupil of the Polytechnic School, -brought the resources of the modern analysis to bear upon the -problem;--till the phenomena of dipolarized light presented the -properties of biaxal crystals in a vast variety of forms;--and till -the theory received its grand impulse by the combination of the -explanation of polarization with the explanation of double -refraction. To the history of this last-mentioned great step we now -proceed. {100} - - -_Sect._ 4.--_Explanation of Polarization by the Undulatory Theory._ - -EVEN while the only phenomena of _polarization_ which were known were -those which affect the two images in Iceland spar, the difficulty -which these facts seemed at first to throw in the way of the -undulatory theory was felt and acknowledged by Young. Malus's -discovery of polarization by reflection increased the difficulty, -and this Young did not attempt to conceal. In his review of the -papers containing this discovery[83\9] he says, "The discovery -related in these papers appears to us to be by far the most -important and interesting which has been made in France concerning -the properties of light, at least since the time of Huyghens; and it -is so much the more deserving of notice, as it greatly influences -the general balance of evidence in the comparison of the undulatory -and projectile theories of the nature of light." He then proceeds to -point out the main features in this comparison, claiming justly a -great advantage for the theory of undulations on the two points we -have been considering, the phenomena of diffraction and of double -refraction. And he adds, with reference to the embarrassment -introduced by polarization, that we are not to expect the course of -scientific discovery to run smooth and uninterrupted; but that we -are to lay our account with partial obscurity and seeming -contradiction, which we may hope that time and enlarged research -will dissipate. And thus he steadfastly held, with no blind -prejudice, but with unshaken confidence, his great philosophical -trust, the fortunes of the undulatory theory. It is here, after the -difficulties of polarization had come into view, and before their -solution had been discovered, that we may place the darkest time of -the history of the theory; and at this period Young was alone in the -field. - -[Note 83\9: _Quart. Rev._ May, 1810.] - -It does not appear that the light dawned upon him for some years. In -the mean time, Young found that his theory would explain dipolarized -colors; and he had the satisfaction to see Fresnel re-discover, and -M. Arago adopt, his views on diffraction. He became engaged in -friendly intercourse with the latter philosopher, who visited him in -England in 1816. On January the 12th, 1817, in writing to this -gentleman, among other remarks on the subject of optics, he says, "I -have also been reflecting on the possibility of giving an imperfect -explanation of the affection of light which constitutes -polarization, {101} without departing from the genuine doctrine of -undulation." He then proceeds to suggest the possibility of "a -_transverse_ vibration, propagated in the direction of the radius, -the motions of the particles being in a certain constant direction -with respect to that radius; and this," he adds, "is -_polarization_." From his further explanation of his views, it -appears that he conceived the motions of the particles to be oblique -to the direction of the ray, and not perpendicular, as the theory -was afterwards framed; but still, here was the essential condition -for the explanation of the facts of polarization,--the transverse -nature of the vibrations. This idea at once made it possible to -conceive how the rays of light could have _sides_; for the direction -in which the vibration was transverse to the ray, might be marked by -peculiar properties. And after the idea was once started, it was -comparatively easy for men like Young and Fresnel to pursue and -modify it till it assumed its true and distinct form. - -We may judge of the difficulty of taking firmly hold of the -conception of transverse vibrations of the ether, as those which -constitute light, by observing how long the great philosophers of -whom we are speaking lingered within reach of it, before they -ventured to grasp it. Fresnel says, in 1821, "When M. Arago and I -had remarked (in 1816) that two rays polarized at right angles -always give the same quantity of light by their union, I thought -this might be explained by supposing the vibrations to be -transverse, and to be at right angles when the rays are polarized at -right angles. But this supposition was so contrary to the received -ideas on the nature of the vibrations of elastic fluids," that -Fresnel hesitated to adopt it till he could reconcile it better to -his mechanical notions. "Mr. Young, more bold in his conjectures, -and less confiding in the views of geometers, published it before -me, though perhaps he thought it after me." And M. Arago was -afterwards wont to relate[84\9] that when he and Fresnel had -obtained their joint experimental results of the non-interference of -oppositely-polarized pencils, and when Fresnel pointed out that -transverse vibrations were the only possible translation of this -fact into the undulatory theory, he himself protested that he had -not courage to publish such a conception; and accordingly, the -second part of the Memoir was published in Fresnel's name alone. -What renders this more remarkable is, that it occurred when M. Arago -had in his possession the very letter of Young, in which he proposed -the same suggestion. {102} - -[Note 84\9: I take the liberty of stating this from personal -knowledge.] - -Young's first published statement of the doctrine of transverse -vibrations was given in the explanation of the phenomena of -dipolarization, of which we shall have to speak in the next Section. -But the primary and immense value of this conception, as a step in -the progress of the undulatory theory, was the connexion which it -established between polarization and double refraction; for it held -forth a promise of accounting for polarization, if any conditions -could be found which might determine what was the direction of the -transverse vibrations. The analysis of these conditions is, in a -great measure, the work of Fresnel; a task performed with profound -philosophical sagacity and great mathematical skill. - -Since the double refraction of uniaxal crystals could be explained -by undulations of the form of a spheroid, it was perhaps not -difficult to conjecture that the undulations of biaxal crystals -would be accounted for by undulations of the form of an ellipsoid, -which differs from the spheroid in having its three axes unequal, -instead of two only; and consequently has that very relation to the -other, in respect of symmetry, which the crystalline and optical -phenomena have. Or, again, instead of supposing two different -degrees of elasticity in different directions, we may suppose three -such different degrees in directions at right angles to each other. -This kind of generalization was tolerably obvious to a practised -mathematician. - -But what shall call into play all these elasticities at once, and -produce waves governed by each of them? And what shall explain the -different polarization of the rays which these separate waves carry -with them? These were difficult questions, to the solution of which -mathematical calculation had hitherto been unable to offer any aid. - -It was here that the conception of transverse vibrations came in, -like a beam of sunlight, to disclose the possibility of a mechanical -connexion of all these facts. If transverse vibrations, travelling -through a uniform medium, come to a medium not uniform, but -constituted so that the elasticity shall be different in different -directions, in the manner we have described, what will be the course -and condition of the waves in the second medium? Will the effects of -such waves agree with the phenomena of doubly-refracted light in -biaxal crystals? Here was a problem, striking to the mathematician -for its generality and difficulty, and of deep interest to the -physical philosopher, because the fate of a great theory depended -upon its solution. - -The solution, obtained by great mathematical skill, was laid before -the French Institute by Fresnel in November, 1821, and was carried -{103} further in two Memoirs presented in 1822. Its import is very -curious. The undulations which, coming from a distant centre, fall -upon such a medium as we have described, are, it appears from the -principles of mechanics, propagated in a manner quite different from -anything which had been anticipated. The "surface of the waves" -(that is, the surface which would bound undulations diverging from a -point), is a very complex, yet symmetrical curve surface; which, in -the case of uniaxal crystals, resolves itself into a sphere and a -spheroid; but which, in general, forms a continuous double envelope -of the central point to which it belongs, intersecting itself and -returning into itself. The directions of the rays are determined by -this curve surface in biaxal crystals, as in uniaxal crystals they -are determined by the sphere and the spheroid; and the result is, -that in biaxal crystals, _both_ rays suffer _extraordinary_ -refraction according to determinate laws. And the positions of the -planes of polarization of the two rays follow from the same -investigation; the plane of polarization in every case being -supposed to be that which is perpendicular to the transverse -vibrations. Now it appeared that the polarization of the two rays, -as determined by Fresnel's theory, would be in directions, not -indeed exactly accordant with the law deduced by M. Biot from -experiment, but deviating so little from those directions, that -there could be small doubt that the empirical formula was wrong, and -the theoretical one right. - -The theory was further confirmed by an experiment showing that, in a -biaxal crystal (topaz), neither of the rays was refracted according -to the ordinary law, though it had hitherto been supposed that one -of them was so; a natural inaccuracy, since the error was -small.[85\9] Thus this beautiful theory corrected, while it -explained, the best of the observations which had previously been -made; and offered itself to mathematicians with an almost -irresistible power of conviction. The explanation of laws so strange -and diverse as those of double refraction and polarization, by the -same general and symmetrical theory, could not result from anything -but the truth of the theory. - -[Note 85\9: _An. Ch._ xxviii. p. 264.] - -"Long," says Fresnel,[86\9] "before I had conceived this theory, I -had convinced myself by a pure contemplation of the facts, that it -was not possible to discover the true explanation of double -refraction, without explaining, at the same time, the phenomena of -polarization, which always goes along with it; and accordingly, it -was after having found {104} what mode of vibration constituted -polarization, that I caught sight of the mechanical causes of double -refraction." - -[Note 86\9: _Sur la Double Réf., Mém. Inst._ 1826, p. 174.] - -Having thus got possession of the principle of the mechanism of -polarization, Fresnel proceeded to apply it to the other cases of -polarized light, with a rapidity and sagacity which reminds us of -the spirit in which Newton traced out the consequences of the -principle of universal gravitation. In the execution of his task, -indeed, Fresnel was forced upon several precarious assumptions, -which make, even yet, a wide difference between the theory of -gravitation and that of light. But the mode in which these were -confirmed by experiment, compels us to admire the happy apparent -boldness of the calculator. - -The subject of _polarization by reflection_ was one of those which -seemed most untractable; but, by means of various artifices and -conjectures, it was broken up and subdued. Fresnel began with the -simplest case, the reflection of light polarized in the plane of -reflection; which he solved by means of the laws of collision of -elastic bodies. He then took the reflection of light polarized -perpendicularly to this plane; and here, adding to the general -mechanical principles a hypothetical assumption, that the -communication of the resolved motion parallel to the refracting -surface, takes place according to the laws of elastic bodies, he -obtains his formula. These results were capable of comparison with -experiment; and the comparison, when made by M. Arago, confirmed the -formulæ. They accounted, too, for Sir D. Brewster's law concerning -the polarizing angle (see Chap. vi.); and this could not but be -looked upon as a striking evidence of their having some real -foundation. Another artifice which MM. Fresnel and Arago employed, -in order to trace the effect of reflection upon common light, was to -use a ray polarized in a plane making half a right angle with the -plane of reflection; for the quantities of the oppositely[87\9] -polarized light in such an incident ray are equal, as they are in -common light; but the relative quantities of the oppositely -polarized light in the reflected ray are indicated by the new plane -of polarization; and thus these relative quantities become known for -the case of common light. The results thus obtained were also -confirmed by facts; and in this manner, all that was doubtful in the -process of Fresnel's reasoning, seemed to be authorized by its -application to real cases. {105} - -[Note 87\9: It will be recollected all along, that _oppositely_ -polarized rays are those which are polarized in two planes -_perpendicular_ to each other. See above, chap. vi.] - -These investigations were published[88\9] in 1821. In succeeding -years, Fresnel undertook to extend the application of his formulæ to -a case in which they ceased to have a meaning, or, in the language -of mathematicians, became _imaginary_; namely, to the case of -internal reflection at the surface of a transparent body. It may -seem strange to those who are not mathematicians, but it is -undoubtedly true, that in many cases in which the solution of a -problem directs impossible arithmetical or algebraical operations to -be performed, these directions may be so interpreted as to point out -a true solution of the question. Such an interpretation Fresnel -attempted[89\9] in the case of which we now speak; and the result at -which he arrived was, that the reflection of light through a rhomb -of glass of a certain form (since called _Fresnel's rhomb_, would -produce a polarization of a kind altogether different from those -which his theory had previously considered, namely, that kind which -we have spoken of as _circular polarization_. The complete -confirmation of this curious and unexpected result by trial, is -another of the extraordinary triumphs which have distinguished the -history of the theory at every step since the commencement of -Fresnel's labors. - -[Note 88\9: _An. Chim._ t. xvii.] - -[Note 89\9: _Bullet. des Sc._ Feb. 1823.] - -But anything further which has been done in this way, may be treated -of more properly in relating the verification of the theory. And we -have still to speak of the most numerous and varied class of facts -to which rival theories of light were applied, and of the -establishment of the undulatory doctrine in reference to that -department; I mean the phenomena of depolarized, or rather, as I -have already said, _di_polarized light. - - -_Sect._ 5.--_Explanation of Dipolarization by the Undulatory Theory._ - -WHEN Arago, in 1811, had discovered the colors produced by polarized -light passing through certain crystals,[90\9] it was natural that -attempts should be made to reduce them to theory. M. Biot, animated -by the success of Malus in detecting the laws of double refraction, -and Young, knowing the resources of his own theory, were the first -persons to enter upon this undertaking. M. Biot's theory, though in -the end displaced by its rival, is well worth notice in the history -of the subject. It was what he called the doctrine of _moveable -polarization_. He conceived that when the molecules of light pass -through {106} thin crystalline plates, the plane of polarization -undergoes an oscillation which carries it backwards and forwards -through a certain angle, namely, twice the angle contained between -the original plane of polarization and the principal section of the -crystal. The intervals which this oscillation occupies are lengths -of the path of the ray, very minute, and different for different -colors, like Newton's fits of easy transmission; on which model, -indeed, the new theory was evidently framed.[91\9] The colors -produced in the phenomena of dipolarization really do depend, in a -periodical manner, on the length of the path of the light through -the crystal, and a theory such as M. Biot's was capable of being -modified, and was modified, so as to include the leading features of -the facts as then known; but many of its conditions being founded on -special circumstances in the experiments, and not on the real -conditions of nature, there were in it several incongruities, as -well as the general defect of its being an arbitrary and unconnected -hypothesis. - -[Note 90\9: See chap. ix.] - -[Note 91\9: See MM. Arago and Biot's Memoirs, _Mém. Inst._ for 1811; -the whole volume for 1812 is a Memoir of M. Biot's (published 1814); -also _Mém. Inst._ for 1817; M. Biot's Mem. read in 1818, published -in 1819 and for 1818.] - -Young's mode of accounting for the brilliant phenomena of -dipolarization appeared in the _Quarterly Review_ for 1814. After -noticing the discoveries of MM. Arago, Brewster, and Biot, he adds, -"We have no doubt that the surprise of these gentlemen will be as -great as our own satisfaction in finding that they are perfectly -reducible, like other causes of recurrent colors, to the general -laws of the interference of light which have been established in -this country;" giving a reference to his former statements. The -results are then explained by the interference of the ordinary and -extraordinary ray. But, as M. Arago properly observes, in his -account of this matter,[92\9] "It must, however, be added that Dr. -Young had not explained either in what circumstances the -interference of the rays can take place, nor why we see no colors -unless the crystallized plates are exposed to light previously -polarized." The explanation of these circumstances depends on the -laws of interference of polarized light which MM. Arago and Fresnel -established in 1816. They then proved, by direct experiment, that -when polarized light was treated so as to bring into view the most -marked phenomena of interference, namely, the bands of shadows; -pencils of light which have a common origin, and which are polarized -in the parallel planes, interfere completely, while those which are -{107} polarized in _opposite_ (that is, perpendicular,) planes do -not interfere at all.[93\9] Taking these principles into the -account, Fresnel explained very completely, by means of the -interference of undulations, all the circumstances of colors -produced by crystallized plates; showing the necessity of the -_polarization_ in the first instance; the _dipolarizing_ effect of -the crystal; and the office of the _analysing plate_, by which -certain portions of each of the two rays in the crystal are made to -interfere and produce color. This he did, as he says,[94\9] without -being aware, till Arago told him, that Young had, to some extent, -anticipated him. - -[Note 92\9: _Enc. Brit._ Supp. art. _Polarization._] - -[Note 93\9: _Ann. Chim._ tom. x.] - -[Note 94\9: Ib. tom. xvii. p. 402.] - -When we look at the history of the emission-theory of light, we see -exactly what we may consider as the natural course of things in the -career of a false theory. Such a theory may, to a certain extent, -explain the phenomena which it was at first contrived to meet; but -every new class of facts requires a new supposition,--an addition to -the machinery; and as observation goes on, these incoherent -appendages accumulate, till they overwhelm and upset the original -frame-work. Such was the history of the hypothesis of solid -epicycles; such has been the history of the hypothesis of the -material emission of light. In its simple form, it explained -reflection and refraction; but the colors of thin plates added to it -the hypothesis of fits of easy transmission and reflection; the -phenomena of diffraction further invested the particles with complex -hypothetical laws of attraction and repulsion; polarization gave -them sides; double refraction subjected them to peculiar forces -emanating from the axes of crystals; finally, dipolarization loaded -them with the complex and unconnected contrivance of moveable -polarization; and even when all this had been assumed, additional -mechanism was wanting. There is here no unexpected success, no happy -coincidence, no convergence of principles from remote quarters; the -philosopher builds the machine, but its parts do not fit; they hold -together only while he presses them: this is not the character of -truth. - -In the undulatory theory, on the other hand, all tends to unity and -simplicity. We explain reflection and refraction by undulations; -when we come to thin plates, the requisite "fits" are already -involved in our fundamental hypothesis, for they are the length of -an undulation; the phenomena of diffraction also require such -intervals; and the intervals thus required agree exactly with the -others in magnitude, {108} so that no new property is needed. -Polarization for a moment checks us; but not long; for the direction -of our vibrations is hitherto arbitrary;--we allow polarization to -decide it. Having done this for the sake of polarization, we find -that it also answers an entirely different purpose, that of giving -the law of double refraction. Truth may give rise to such a -coincidence; falsehood cannot. But the phenomena become more -numerous, more various, more strange; no matter: the Theory is equal -to them all. It makes not a single new physical hypothesis; but out -of its original stock of principles it educes the counterpart of all -that observation shows. It accounts for, explains, simplifies, the -most entangled cases; corrects known laws and facts; predicts and -discloses unknown ones; becomes the guide of its former teacher, -Observation; and, enlightened by mechanical conceptions, acquires an -insight which pierces through shape and color to force and cause. - -We thus reach the philosophical _moral_ of this history, so -important in reference to our purpose; and here we shall close the -account of the discovery and promulgation of the undulatory theory. -Any further steps in its development and extension, may with -propriety be noticed in the ensuing chapters, respecting its -reception and verification. - -[2nd Ed.] [In the _Philosophy of the Inductive Sciences_, B. xi. ch. -iii. Sect. 11, I have spoken of the _Consilience of Inductions_ as -one of the characters of scientific truth. We have several striking -instances of such consilience in the history of the undulatory -theory. The phenomena of fringes of shadows and colored bands in -crystals _jump together_ in the Theory of Vibrations. The phenomena -of polarization and double refraction _jump together_ in the Theory -of Crystalline Vibrations. The phenomena of polarization and of the -interference of polarized rays _jump together_ in the Theory of -Transverse Vibrations. - -The proof of what is above said of the undulatory theory is -contained in the previous history. This theory has "accounted for, -explained, and simplified the most entangled cases;" as the cases of -fringes of shadows; shadows of gratings; colored bands in biaxal -crystals, and in quartz. There are no optical phenomena more -entangled than these. It has "corrected experimental laws," as in -the case of M. Biot's law of the direction of polarization in biaxal -crystals. It has done this, "without making any new physical -hypothesis;" for the transverse direction of vibrations, the -different optical elasticities of crystals in different directions, -and (if it be adopted) the hypothesis of finite {109} intervals of -the particles (see chap. x. and hereafter, chap. xiii.), are only -limitations of what was indefinite in the earlier form of the -hypothesis. And so far as the properties of visible radiant light -are concerned, I do not think it at all too much to say, as M. -Schwerd has said, that "the undulation theory accounts for the -phenomena as completely as the theory of gravitation does for the -facts of the solar system." - -This we might say, even if some facts were not yet fully explained; -for there were till very lately, if there are not still, such -unexplained facts with regard to the theory of gravitation, -presented to us by the solar system. With regard to the undulatory -theory, these exceptions are, I think, disappearing quite as rapidly -and as completely as in the case of gravitation. It is to be -observed that no presumption against the theory can with any show of -reason be collected from the cases in which classes of phenomena -remain unexplained, the theory having never been applied to them by -any mathematician capable of tracing its results correctly. The -history of the theory of gravitation may show us abundantly how -necessary it is to bear in mind this caution; and the results of the -undulatory theory cannot be traced without great mathematical skill -and great labor, any more than those of gravitation. - -This remark applies to such cases as that of the _transverse fringes -of grooved surfaces_. The general phenomena of these cases are -perfectly explained by the theory. But there is an interruption in -the light in an oblique direction, which has not yet been explained; -but looking at what has been done in other cases, it is impossible -to doubt that this phenomenon depends upon the results of certain -integrations, and would be explained if these were rightly performed. - -The phenomena of _crystallized surfaces_, and especially their -effects upon the plane of polarization, were examined by Sir D. -Brewster, and laws of the phenomena made out by him with his usual -skill and sagacity. For a time these were unexplained by the theory. -But recently Mr. Mac Cullagh has traced the consequences of the -theory in this case,[95\9] and obtained a law which represents with -much exactness, Sir D. Brewster's observation. - -[Note 95\9: Prof. Lloyd's _Report, Brit. Assoc._ 1834, p. 374.] - -The phenomena which Sir D. Brewster, in 1837, called a _new property -of light_, (certain appearances of the spectrum when the pupil of -the eye is half covered with a thin glass or crystal,) have been -explained by Mr. Airy in the _Phil. Trans._ for 1840. - -Mr. Airy's explanation of the phenomena termed by Sir D. {110} -Brewster a _new property of light_, is completed in the -_Philosophical Magazine_ for November, 1846. It is there shown that -a dependence of the breadth of the bands upon the aperture of the -pupil, which had been supposed to result from the theory, and which -does not appear in the experiment, did really result from certain -limited conditions of the hypothesis, which conditions do not belong -to the experiment; and that when the problem is solved without those -limitations, the discrepance of theory and observation vanishes; so -that, as Mr. Airy says, "this very remarkable experiment, which long -appeared inexplicable, seems destined to give one of the strongest -confirmations to the Undulatory Theory." - -I may remark also that there is no force in the objection which has -been urged against the admirers of the undulatory theory, that by -the fulness of their assent to it, they discourage further -researches which may contradict or confirm it. We must, in this -point of view also, look at the course of the theory of gravitation -and its results. The acceptance of that theory did not prevent -mathematicians and observers from attending to the apparent -exceptions, but on the contrary, stimulated them to calculate and to -observe with additional zeal, and still does so. The acceleration of -the Moon, the mutual disturbances of Jupiter and Saturn, the motions -of Jupiter's Satellites, the effect of the Earth's oblateness on the -Moon's motion, the motions of the Moon about her own centre, and -many other phenomena, were studied with the greater attention, -_because_ the general theory was deemed so convincing: and the same -cause makes the remaining exceptions objects of intense interest to -astronomers and mathematicians. The mathematicians and optical -experimenters who accept the undulatory theory, will of course -follow out their conviction in the same manner. Accordingly, this -has been done and is still doing, as in Mr. Airy's mathematical -investigation of the effect of an annular aperture; Mr. Earnshaw's, -of the effect of a triangular aperture; Mr. Talbot's explanation of -the effect of interposing a film of mica between a part of the pupil -and the pure spectrum, so nearly approaching to the phenomena which -have been spoken of as a new Polarity of Light; besides other labors -of eminent mathematicians, elsewhere mentioned in these pages. - -The phenomena of the _absorption_ of light have no especial bearing -upon the undulatory theory. There is not much difficulty in -explaining the _possibility_ of absorption upon the theory. When the -light is absorbed, it ceases to belong to the theory. {111} - -For, as I have said, the theory professes only to explain the -phenomena of _radiant visible_ light. We know very well that light -has other bearings and properties. It produces chemical effects. The -optical polarity of crystals is connected with the chemical polarity -of their constitution. The natural colors of bodies, too, are -connected with their chemical constitution. Light is also connected -with heat. The undulatory theory does not undertake to explain these -properties and their connexion. If it did, it would be a Theory of -Heat and of Chemical Composition, as well as a Theory of Light. - -Dr. Faraday's recent experiments have shown that the magnetic -polarity is directly connected with that optical polarity by which -the plane of polarization is affected. When the lines of magnetic -force pass through certain transparent bodies, they communicate to -them a certain kind of circular polarizing power; yet different from -the circular polarizing power of quartz, and certain fluids -mentioned in chapter ix. - -Perhaps I may be allowed to refer to this discovery as a further -illustration of the views I have offered in the _Philosophy of the -Inductive Sciences_ respecting the _Connexion of Co-existent -Polarities_. (B. v. Chap. ii.)] - - - - -CHAPTER XII. - -SEQUEL TO THE EPOCH OF YOUNG AND FRESNEL. RECEPTION OF THE -UNDULATORY THEORY. - - -WHEN Young, in 1800, published his assertion of the Principle of -Interferences, as the true theory of optical phenomena, the -condition of England was not very favorable to a fair appreciation -of the value of the new opinion. The men of science were strongly -pre-occupied in favor of the doctrine of emission, not only from a -national interest in Newton's glory, and a natural reverence for his -authority, but also from deference towards the geometers of France, -who were looked up to as our masters in the application of -mathematics to physics, and who were understood to be Newtonians in -this as in other subjects. A general tendency to an atomic -philosophy, which had begun to appear from the time of Newton, -operated powerfully; and {112} the hypothesis of emission was so -easily conceived, that, when recommended by high authority, it -easily became popular; while the hypothesis of luminiferous -undulations, unavoidably difficult to comprehend, even by the aid of -steady thought, was neglected, and all but forgotten. - -Yet the reception which Young's opinions met with was more harsh -than he might have expected, even taking into account all these -considerations. But there was in England no visible body of men, -fitted by their knowledge and character to pronounce judgment on -such a question, or to give the proper impulse and bias to public -opinion. The Royal Society, for instance, had not, for a long time, -by custom or institution, possessed or aimed at such functions. The -writers of "Reviews" alone, self-constituted and secret tribunals, -claimed this kind of authority. Among these publications, by far the -most distinguished about this period was the _Edinburgh Review_; -and, including among its contributors men of eminent science and -great talents, employing also a robust and poignant style of writing -(often certainly in a very unfair manner), it naturally exercised -great influence. On abstruse doctrines, intelligible to few persons, -more than on other subjects, the opinions and feelings expressed in -a Review must be those of the individual reviewer. The criticism on -some of Young's early papers on optics was written by Mr. -(afterwards Lord) Brougham, who, as we have seen, had experimented -on diffraction, following the Newtonian view, that of inflexion. Mr. -Brougham was perhaps at this time young enough[96\9] to be somewhat -intoxicated with the appearance of judicial authority in matters of -science, which his office of anonymous reviewer gave him: and even -in middle-life, he was sometimes considered to be prone to indulge -himself in severe and sarcastic expressions. In January, 1803, was -published[97\9] his critique on Dr. Young's Bakerian Lecture, _On -the Theory of Light and Colors_, in which lecture the doctrine of -undulations and the law of interferences was maintained. This -critique was an uninterrupted strain of blame and rebuke. "This -paper," the reviewer said, "contains nothing which deserves the name -either of experiment or discovery." He charged the writer with -"dangerous relaxations of the principles of physical logic." "We -wish," he cried, "to recall philosophers to the strict and severe -methods of investigation," describing them as those pointed out by -Bacon, Newton, and the like. Finally, Dr. Young's speculations {113} -were spoken of as a hypothesis, which is a mere work of fancy; and -the critic added, "we cannot conclude our review without entreating -the attention of the Royal Society, which has admitted of late so -many hasty and unsubstantial papers into its _Transactions_;" which -habit he urged them to reform. The same aversion to the undulatory -theory appears soon after in another article by the same reviewer, -on the subject of Wollaston's measures of the refraction of Iceland -spar; he says, "We are much disappointed to find that so acute and -ingenious an experimentalist should have adopted the wild optical -theory of vibrations." The reviewer showed ignorance as well as -prejudice in the course of his remarks; and Young drew up an answer, -which was ably written, but being published separately had little -circulation. We can hardly doubt that these Edinburgh reviews had -their effect in confirming the general disposition to reject the -undulatory theory. - -[Note 96\9: His age was twenty-four.] - -[Note 97\9: _Edin. Review_, vol. i. p. 450.] - -We may add, however, that Young's mode of presenting his opinions -was not the most likely to win them favor; for his mathematical -reasonings placed them out of the reach of popular readers, while -the want of symmetry and system in his symbolical calculations, -deprived them of attractiveness for the mathematician. He himself -gave a very just criticism of his own style of writing, in speaking -on another of his works:[98\9] "The mathematical reasoning, for want -of mathematical symbols, was not understood, even by tolerable -mathematicians. From a dislike of the affectation of algebraical -formality which he had observed in some foreign authors, he was led -into something like an affectation of simplicity, which was equally -inconvenient to a scientific reader." - -[Note 98\9: See _Life of Young_, p. 54.] - -Young appears to have been aware of his own deficiency in the power -of drawing public favor, or even notice, to his discoveries. In -1802, Davy writes to a friend, "Have you seen the theory of my -colleague, Dr. Young, on the undulations of an ethereal medium as -the cause of light? It is not likely to be a popular hypothesis, -after what has been said by Newton concerning it. He would be very -much flattered if you could offer any observations upon it, _whether -for or against it_." Young naturally felt confident in his power of -refuting objections, and wanted only the opportunity of a public -combat. - -Dr. Brewster, who was, at this period, enriching optical knowledge -with so vast a train of new phenomena and laws, shared the general -aversion to the undulatory theory, which, indeed, he hardly overcame -{114} thirty years later. Dr. Wollaston was a person whose character -led him to look long at the laws of phenomena, before he attempted -to determine their causes; and it does not appear that he had -decided the claims of the rival theories in his own mind. Herschel -(I now speak of the son) had at first the general mathematical -prejudice in favor of the emission doctrine. Even when he had -himself studied and extended the laws of dipolarized phenomena, he -translated them into the language of the theory of moveable -polarization. In 1819, he refers to, and corrects, this theory; and -says, it is now "relieved from every difficulty, and entitled to -rank with the fits of easy transmission and reflection as a general -and simple physical law;" a just judgment, but one which now conveys -less of praise than he then intended. At a later period, he remarked -that we cannot be certain that if the theory of emission had been as -much cultivated as that of undulation, it might not have been as -successful; an opinion which was certainly untenable after the fair -trial of the two theories in the case of diffraction, and -extravagant after Fresnel's beautiful explanation of double -refraction and polarization. Even in 1827, in a _Treatise on Light_, -published in the _Encyclopædia Metropolitana_, he gives a section to -the calculations of the Newtonian theory; and appears to consider -the rivalry of the theories as still subsisting. But yet he there -speaks with a proper appreciation of the advantages of the new -doctrine. After tracing the prelude to it, he says, "But the -unpursued speculations of Newton, and the opinions of Hooke, however -distinct, must not be put in competition, and, indeed, ought -scarcely to be mentioned, with the elegant, simple, and -comprehensive theory of Young,--a theory which, if not founded in -nature, is certainly one of the happiest fictions that the genius of -man ever invented to grasp together natural phenomena, which, at -their first discovery, seemed in irreconcileable opposition to it. -It is, in fact, in all its applications and details, one succession -of _felicities_; insomuch, that we may almost be induced to say, if -it be not true, it deserves to be so." - -In France, Young's theory was little noticed or known, except -perhaps by M. Arago, till it was revived by Fresnel. And though -Fresnel's assertion of the undulatory theory was not so rudely -received as Young's had been, it met with no small opposition from -the older mathematicians, and made its way slowly to the notice and -comprehension of men of science. M. Arago would perhaps have at once -adopted the conception of transverse vibrations, when it was -suggested by his fellow-laborer, Fresnel, if it had not been that he -was a member of the {115} Institute, and had to bear the brunt of -the war, in the frequent discussions on the undulatory theory; to -which theory Laplace, and other leading members, were so vehemently -opposed, that they would not even listen with toleration to the -arguments in its favor. I do not know how far influences of this -kind might operate in producing the delays which took place in the -publication of Fresnel's papers. We have seen that he arrived at the -conception of transverse vibrations in 1816, as the true key to the -understanding of polarization. In 1817 and 1818, in a memoir read to -the Institute, he analysed and explained the perplexing phenomena of -quartz, which he ascribed to a _circular polarization_. This memoir -had not been printed, nor any extract from it inserted in the -scientific journals, in 1822, when he confirmed his views by further -experiments.[99\9] His remarkable memoir, which solved the -extraordinary and capital problem of the connexion of double -refraction and crystallization, though written in 1821, was not -published till 1827. He appears by this time to have sought other -channels of publication. In 1822, he gave,[100\9] in the _Annales de -Chimie et de Physique_, an explanation of refraction on the -principles of the undulatory theory; alleging, as the reason for -doing so, that the theory was still little known. And in succeeding -years there appeared in the same work, his theory of reflection. His -memoir on this subject (_Mémoire sur la Loi des Modifications que la -Réflexion imprime à la Lumière Polarisée_,) was read to the Academy -of Sciences in **1823. But the original paper was mislaid, and, for a -time, supposed to be lost; it has since been recovered among the -papers of M. Fourier, and printed in the eleventh volume of the -Memoirs of the Academy.[101\9] Some of the speculations to which he -refers, as communicated to the Academy, have never yet -appeared.[102\9] - -[Note 99\9: Hersch. _Light_, p. 539.] - -[Note 100\9: _Ann. de Chim._ 1822, tom. xxi. p. 235.] - -[Note 101\9: Lloyd. _Report on Optics_, p. 363. (Fourth Rep. of -Brit. Ass.)] - -[Note 102\9: Ib. p. 316, _note._] - -Still Fresnel's labors were, from the first, duly appreciated by -some of the most eminent of his countrymen. His _Memoir on -Diffraction_ was, as we have seen, crowned in 1819: and, in 1822, a -Report upon his _Memoir on Double Refraction_ was drawn up by a -commission consisting of MM. Ampère, Fourier, and Arago. In this -report[103\9] Fresnel's theory is spoken of as confirmed by the most -delicate tests. The reporters add, respecting his "theoretical ideas -on the particular kind of undulations which, according to him, -constitute light," that "it would be impossible for them to -pronounce at present a decided {116} judgment," but that "they have -not thought it right to delay any longer making known a work of -which the difficulty is attested by the fruitless efforts of the -most skilful philosophers, and in which are exhibited in the same -brilliant degree, the talent for experiment and the spirit of -invention." - -[Note 103\9: _Ann. Chim._ tom. xx. p. 343.] - -In the meantime, however, a controversy between the theory of -undulations and the theory of moveable polarization which M. Biot -had proposed with a view of accounting for the colors produced by -dipolarizing crystals, had occurred among the French men of science. -It is clear that in some main features the two theories coincide; -the intervals of interference in the one theory being represented by -the intervals of the oscillations in the other. But these intervals -in M. Biot's explanations were arbitrary hypotheses, suggested by -these very facts themselves; in Fresnel's theory, they were -essential parts of the general scheme. M. Biot, indeed, does not -appear to have been averse from a coalition; for he allowed[104\9] -to Fresnel that "the theory of undulations took the phenomena at a -higher point and carried them further." And M. Biot could hardly -have dissented from M. Arago's account of the matter, that Fresnel's -views "_linked together_"[105\9] the oscillations of moveable -polarization. But Fresnel, whose hypothesis was all of one piece, -could give up no part of it, although he allowed the usefulness of -M. Biot's formulæ. Yet M. Biot's speculations fell in better with -the views of the leading mathematicians of Paris. We may consider as -evidence of the favor with which they were looked upon, the large -space they occupy in the volumes of the Academy for 1811, 1812, -1817, and 1818. In 1812, the entire volume is filled with a memoir -of M. Biot's on the subject of moveable polarization. This doctrine -also had some advantage in coming early before the world in a -didactic form, in his _Traité de Physique_, which was published in -1816, and was the most complete treatise on general physics which -had appeared up to that time. In this and others of this author's -writings, he expresses facts so entirely in the terms of his own -hypothesis, that it is difficult to separate the two. In the sequel -M. Arago was the most prominent of M. Biot's opponents; and in his -report upon Fresnel's memoir on the colors of crystalline plates, he -exposed the weaknesses of the theory of moveable polarization with -some severity. The details of this controversy need not occupy us; -but we may observe that this may be considered as the last struggle -{117} in favor of the theory of emission among mathematicians of -eminence. After this crisis of the war, the theory of moveable -polarization lost its ground; and the explanations of the undulatory -theory, and the calculations belonging to it, being published in the -_Annales de Chimie et de Physique_, of which M. Arago was one of the -conductors, soon diffused it over Europe. - -[Note 104\9: _Ann. Chim._ tom. xvii. p. 251.] - -[Note 105\9: "Nouait".] - -It was probably in consequence of the delays to which we have -referred, in the publication of Fresnel's memoirs, that as late as -December, 1826, the Imperial Academy at St Petersburg proposed, as -one of their prize-questions for the two following years, this,--"To -deliver the optical system of waves from all the objections which -have (as it appears) with justice been urged against it, and to -apply it to the polarization and double refraction of light." In the -programme to this announcement, Fresnel's researches on the subject -are not alluded to, though his memoir on diffraction is noticed; -they were, therefore, probably not known to the Russian Academy. - -Young was always looked upon as a person of marvellous variety of -attainments and extent of knowledge; but during his life he hardly -held that elevated place among great discoverers which posterity -will probably assign him. In 1802, he was constituted Foreign -Secretary of the Royal Society, an office which he held during life; -in 1827 he was elected one of the eight Foreign Members of the -Institute of France; perhaps the greatest honor which men of science -usually receive. The fortune of his life in some other respects was -of a mingled complexion. His profession of a physician occupied, -sufficiently to fetter, without rewarding him; while he was Lecturer -at the Royal Institution, he was, in his lectures, too profound to -be popular; and his office of Superintendent of the _Nautical -Almanac_ subjected him to much minute labor, and many petulant -attacks of pamphleteers. On the other hand, he had a leading part in -the discovery of the long-sought key to the Egyptian hieroglyphics; -and thus the age which was marked by two great discoveries, one in -science and one in literature, owed them both in a great measure to -him. Dr. Young died in 1829, when he had scarcely completed his -fifty-sixth year. Fresnel was snatched from science still more -prematurely, dying, in 1827, at the early age of thirty-nine. - -We need not say that both these great philosophers possessed, in an -eminent degree, the leading characteristics of the discoverer's -mind, perfect clearness of view, rich fertility of invention, and -intense love of knowledge. We cannot read without great interest a -letter of {118} Fresnel to Young,[106\9] in November, 1824: "For a -long time that sensibility, or that vanity, which people call love -of glory, is much blunted in me. I labor much less to catch the -suffrages of the public, than to obtain an inward approval which has -always been the sweetest reward of my efforts. Without doubt I have -often wanted the spur of vanity to excite me to pursue my researches -in moments of disgust and discouragement. But all the compliments -which I have received from MM. Arago, De Laplace, or Biot, never -gave me so much pleasure as the discovery of a theoretical truth, or -the confirmation of a calculation by experiment." - -[Note 106\9: I was able to give this, and some other extracts, from -the then unedited correspondence of Young and Fresnel, by the -kindness of (the Dean of Ely) Professor Peacock, of Trinity College, -Cambridge, whose Life of Dr. Young has since been published.] - -Though Young and Fresnel were in years the contemporaries of many -who are now alive, we must consider ourselves as standing towards -them in the relation of posterity. The Epoch of Induction in Optics -is past; we have now to trace the Verification and Application of -the true theory. - - - - -CHAPTER XIII. - -CONFIRMATION AND EXTENSION OF THE UNDULATORY THEORY. - - -AFTER the undulatory theory had been developed in all its main -features, by its great authors, Young and Fresnel, although it bore -marks of truth that could hardly be fallacious, there was still -here, as in the case of other great theories, a period in which -difficulties were to be removed, objections answered, men's minds -familiarized to the new conceptions thus presented to them; and in -which, also, it might reasonably be expected that the theory would -be extended to facts not at first included in its domain. This -period is, indeed, that in which we are living; and we might, -perhaps with propriety, avoid the task of speaking of our living -contemporaries. But it would be unjust to the theory not to notice -some of the remarkable events, characteristic of such a period, -which have already occurred; and this may be done very simply. {119} - -In the case of this great theory, as in that of gravitation, by far -the most remarkable of these confirmatory researches were conducted -by the authors of the discovery, especially Fresnel. And in looking -at what he conceived and executed for this purpose, we are, it -appears to me, strongly reminded of Newton, by the wonderful -inventiveness and sagacity with which he devised experiments, and -applied to them mathematical reasonings. - -1. _Double Refraction of Compressed Glass._--One of these -confirmatory experiments was the production of double refraction by -the compression of glass. Fresnel observes,[107\9] that though Sir -D. Brewster had shown that glass under compression produced colors -resembling those which are given by doubly-refracting crystals, -"very skilful physicists had not considered those experiments as a -sufficient proof of the bifurcation of the light." In the hypothesis -of moveable polarization, it is added, there is no apparent -connexion between these phenomena of coloration and double -refraction; but on Young's theory, that the colors arise from two -rays which have traversed the crystal with different velocities, it -appears almost unavoidable to admit also a difference of path in the -two rays. - -[Note 107\9: _Ann. de Chim._ 1822, tom. xx. p. 377.] - -"Though," he says, "I had long since adopted this opinion, it did -not appear to me so completely demonstrated, that it was right to -neglect an experimental verification of it;" and therefore, in 1819, -he proceeded to satisfy himself of the fact, by the phenomena of -diffraction. The trial left no doubt on the subject; but he still -thought it would be interesting actually to produce two images in -glass by compression; and by a highly-ingenious combination, -calculated to exaggerate the effect of the double refraction, which -is very feeble, even when the compression is most intense, he -obtained two distinct images. This evidence of the dependence of -dipolarizing structure upon a doubly-refracting state of particles, -thus excogitated out of the general theory, and verified by trial, -may well be considered, as he says, "as a new occasion of proving -the infallibility of the principle of interferences." - -2. _Circular Polarization._--Fresnel then turned his attention to -another set of experiments, related to this indeed, but by a tie so -recondite, that nothing less than his clearness and acuteness of -view could have detected any connexion. The optical properties of -quartz had been perceived to be peculiar, from the period of the -discovery {120} of dipolarized colors by MM. Arago and Biot. At the -end of the Notice just quoted, Fresnel says,[108\9] "As soon as my -occupations permit me, I propose to employ a pile of prisms similar -to that which I have described, in order to study the double -refraction of the rays which traverse crystals of quartz in the -direction of the axis." He then ventures, without hesitation, to -describe beforehand what the phenomena will be. In the _Bulletin des -Sciences_[109\9] for December, 1822, it is stated that experiment -had confirmed what he had thus announced. - -[Note 108\9: _Ann. de Chim._ 1822, tom. xx. p. 382.] - -[Note 109\9: Ib. _Ann. de Chim._ 1822, tom. xx. p. 191.] - -The phenomena are those which have since been spoken of as _circular -polarization_; and the term first occurs in this notice.[110\9] They -are very remarkable, both by their resemblances to, and their -differences from, the phenomena of _plane-polarized_ light. And the -manner in which Fresnel was led to this anticipation of the facts is -still more remarkable than the facts themselves. Having ascertained -by observation that two differently-polarized rays, totally -reflected at the internal surface of glass, suffer different -_retardations_ of their undulations, he applied the formulæ which he -had obtained for the polarizing effect of reflection to this case. -But in this case the formulæ expressed an impossibility; yet as -algebraical formulæ, even in such cases, have often some meaning, "I -interpreted," he says,[111\9] "in the manner which appeared to me -most natural and most probable, what the analysis indicated by this -imaginary form;" and by such an interpretation he collected the law -of the difference of undulation of the two rays. He was thus able to -predict that by two internal reflections in a _rhomb_, or -parallelopiped of glass, of a certain form and position, a polarized -ray would acquire a circular undulation of its particles; and this -constitution of the ray, it appeared, by reasoning further, would -show itself by its possessing peculiar properties, partly the same -as those of polarized light, and partly different. This -extraordinary anticipation was exactly confirmed; and thus the -apparently bold and strange guess of the author was fully justified, -or at least assented to, even by the most cautious philosophers. "As -I cannot appreciate the mathematical evidence for the nature of -circular polarization," says Prof. Airy,[112\9] "I shall mention the -experimental evidence on which I receive it." The conception has -since been universally adopted. - -[Note 110\9: Ib. p. 194.] - -[Note 111\9: _Bullet. des Sc._ 1823, p. 33.] - -[Note 112\9: _Camb. Trans._ vol. iv. p. 81, 1831.] - -But Fresnel, having thus obtained circularly-polarized rays, saw -{121} that he could account for the phenomena of quartz, already -observed by M. Arago, as we have noticed in Chap. ix., by supposing -two circularly-polarized rays to pass, with different velocities, -along the axis. The curious succession of colors, following each -other in right-handed or left-handed circular order, of which we -have already spoken, might thus be hypothetically explained. - -But was this hypothesis of two circularly-polarized rays, travelling -along the axis of such crystals, to be received, merely because it -accounted for the phenomena? Fresnel's ingenuity again enabled him -to avoid such a defect in theorizing. If there were two such rays, -they might be visibly separated[113\9] by the same artifice, of a -pile of prisms properly achromatized, which he had used for -compressed glass. The result was, that he did obtain a visible -separation of the rays; and this result has since been confirmed by -others, for instance. Professor Airy.[114\9] The rays were found to -be in all respects identical with the circularly-polarized rays -produced by the internal reflections in Fresnel's rhomb. This kind -of double refraction gave a hypothetical explanation of the laws -which M. Biot had obtained for the phenomena of this class; for -example,[115\9] the rule, that the deviation of the plane of -polarization of the emergent ray is inversely as the square of the -length of an undulation for each kind of rays. And thus the -phenomena produced by light passing along the axis of quartz were -reduced into complete conformity with the theory. - -[Note 113\9: _Bull. des Sc._ 1822, p. 193.] - -[Note 114\9: _Cambridge Trans._ iv. p. 80.] - -[Note 115\9: _Bull. des Sc._ 1822, p. 197.] - -[2nd Ed.] [I believe, however, Fresnel did not deduce the phenomenon -from the mathematical formula, without the previous suggestion of -experiment. He _observed_ appearances which implied a difference of -retardation in the two differently-polarized rays at total -reflection; as Sir D. Brewster observed in reflection of metals -phenomena having a like character. The general fact being observed, -Fresnel used the theory to discover the law of this retardation, and -to determine a construction in which, one ray being a quarter of an -undulation retarded more than the other, circular polarization would -be produced. And this anticipation was verified by the construction -of his _rhomb_. - -As a still more curious verification of this law, another of -Fresnel's experiments may be mentioned. He found the proper angles -for a circularly-polarizing glass rhomb on the supposition that -there were {122} _four_ internal reflections instead of two; two of -the four taking place when the surface of the glass was dry, and two -when it was wet. The rhomb was made; and when all the points of -reflection were dry, the light was not circularly polarized; when -two points were wet, the light was circularly polarized; and when -all four were wet, it was not circularly polarized.] - -3. _Elliptical Polarization in Quartz._--We now come to one of the -few additions to Fresnel's theory which have been shown to be -necessary. He had accounted fully for the colors produced by the -rays which travel _along the axis_ of quartz crystals; and thus, for -the colors and changes of the central spot which is produced when -polarized light passes through a transverse plate of such crystals. -But this central spot is surrounded by rings of colors. How is the -theory to be extended to these? - -This extension has been successfully made by Professor Airy.[116\9] -His hypothesis is, that as rays passing along the axis of a quartz -crystal are circularly polarized, rays which are oblique to the axis -are elliptically polarized, the amount of ellipticity depending, in -some unknown manner, upon the obliquity; and that each ray is -separated by double refraction into two rays polarized elliptically; -the one right-handed, the other left-handed. By means of these -suppositions, he not only was enabled to account for the simple -phenomena of single plates of quartz; but for many most complex and -intricate appearances which arise from the superposition of two -plates, and which at first sight might appear to defy all attempts -to reduce them to law and symmetry; such as spirals, curves -approaching to a square form, curves broken in four places. "I can -hardly imagine," he says,[117\9] very naturally, "that any other -supposition would represent the phenomena to such extreme accuracy. -I am not so much struck with the accounting for the continued -dilatation of circles, and the general representation of the forms -of spirals, as with the explanations of the minute deviations from -symmetry; as when circles become almost square, and crosses are -inclined to the plane of polarization. And I believe that any one -who shall follow my investigation, and imitate my experiments, will -be surprised at their perfect agreement." - -[Note 116\9: _Camb. Trans._, iv. p. 83, &c.] - -[Note 117\9: _Camb. Trans._, iv. p. 122.] - -4. _Differential Equations of Elliptical Polarization._--Although -circular and elliptical polarization can be clearly conceived, and -their existence, it would seem, irresistibly established by the -phenomena, it {123} is extremely difficult to conceive any -arrangement of the particles of bodies by which such motions can -mechanically be produced; and this difficulty is the greater, -because some fluids and some gases impress a circular polarization -upon light; in which cases we cannot imagine any definite -arrangement of the particles, such as might form the mechanism -requisite for the purpose. Accordingly, it does not appear that any -one has been able to suggest even a plausible hypothesis on that -subject. Yet, even here, something has been done. Professor Mac -Cullagh, of Dublin, has discovered that by slightly modifying the -_analytical expressions_ resulting from the common case of the -propagation of light, we may obtain other expressions which would -give rise to such motions as produce circular and elliptical -polarization. And though we cannot as yet assign the mechanical -interpretation of the language of analysis thus generalized, this -generalization brings together and explains by one common numerical -supposition, two distinct classes of facts;--a circumstance which, -in all cases, entitles an hypothesis to a very favorable -consideration. - -Mr. Mac Cullagh's assumption consists in adding to the two equations -of motion which are expressed by means of second differentials, two -other terms involving third differentials in a simple and -symmetrical manner. In doing this, he introduces a coefficient, of -which the magnitude determines both the amount of rotation of the -polarization of a ray passing along the axis, as observed and -measured by Biot, and the ellipticity of the polarization of a ray -which is oblique to the axis, according to Mr. Airy's theory, of -which ellipticity that philosopher also had obtained certain -measures. The agreement between the two sets of measures[118\9] thus -brought into connexion is such as very strikingly to confirm Mr. Mac -Cullagh's hypothesis. It appears probable, too, that the -confirmation of this hypothesis involves, although in an obscure and -oracular form, a confirmation of the undulatory theory, which is the -starting-point of this curious speculation. - -[Note 118\9: _Royal I. A. Trans._ 1836.] - -5. _Elliptical Polarization of Metals._--The effect of metals upon -the light which they reflect, was known from the first to be -different from that which transparent bodies produce. Sir David -Brewster, who has recently examined this subject very fully,[119\9] -has described the modification thus produced, as _elliptic -polarization_. In employing this term, "he seems to have been led," -it has been observed,[120\9] "by a {124} desire to avoid as much as -possible all reference to theory. The laws which he has obtained, -however, belong to elliptically-polarized light in the sense in -which the term was introduced by Fresnel." And the identity of the -light produced by metallic reflection with the -elliptically-polarized light of the wave-theory, is placed beyond -all doubt, by an observation of Professor Airy, that the rings of -uniaxal crystals, produced by Fresnel's elliptically-polarized -light, are exactly the same as those produced by Brewster's metallic -light. - -[Note 119\9: _Phil. Trans._ 1830.] - -[Note 120\9: Lloyd, _Report on Optics_, p. 372. (Brit. Assoc.)] - -6. _Newton's Rings by Polarized Light._--Other modifications of the -phenomena of thin plates by the use of polarized light, supplied -other striking confirmations of the theory. These were in one case -the more remarkable, since the result was foreseen by means of a -rigorous application of the conception of the vibratory motion of -light, and confirmed by experiment. Professor Airy, of Cambridge, -was led by his reasonings to see, that if Newton's rings are -produced between a lens and a plate of metal, by polarized light, -then, up to the polarizing angle, the central spot will be black, -and instantly beyond this, it will be white. In a note,[121\9] in -which he announced this, he says, "This I anticipated from Fresnel's -expressions; it is confirmatory of them, and defies emission." He -also predicted that when the rings were produced between two -substances of very different refractive powers, the centre would -twice pass from black to white and from white to black, by -increasing the angle; which anticipation was fulfilled by using a -diamond for the higher refraction.[122\9] - -[Note 121\9: Addressed to myself, dated May 28, 1831. I ought, -however, to notice, that this experiment had been made by M. Arago, -fifteen years earlier, and published: though not then recollected by -Mr. Airy.] - -[Note 122\9: _Camb. Trans._ vol. ii. p. 409.] - -7. _Conical Refraction._--In the same manner. Professor Hamilton of -Dublin pointed out that according to the Fresnelian doctrine of double -refraction, there is a certain direction of a crystal in which a -single ray of light will be refracted so as to form a _conical -pencil_. For the direction of the refracted ray is determined by a -plane which touches the wave surface, the rule being that the ray must -pass from the centre of the surface to the point of contact; and -though in general this contact gives a single point only, it so -happens, from the peculiar inflected form of the wave surface, which -has what is called _a cusp_, that in one particular position, the -plane can touch the surface in an entire circle. Thus the general rule -which assigns the path of {125} the refracted ray, would, in this -case, guide it from the centre of the surface to every point in the -circumference of the circle, and thus make it a cone. This very -curious and unexpected result, which Professor Hamilton thus obtained -from the theory, his friend Professor Lloyd verified as an -experimental fact. We may notice, also, that Professor Lloyd found the -light of the conical pencil to be polarized according to a law of an -unusual kind; but one which was easily seen to be in complete -accordance with the theory. - -8. _Fringes of Shadows._--The phenomena of the _fringes of shadows_ -of small holes and groups of holes, which had been the subject of -experiment by Fraunhofer, were at a later period carefully observed -in a vast variety of cases by M. Schwerd of Spires, and published in -a separate work,[123\9] _Beugungs-erscheinungen_ (Phenomena of -Inflection), 1836. In this Treatise, the author has with great -industry and skill calculated the integrals which, as we have seen, -are requisite in order to trace the consequences of the theory; and -the accordance which he finds between these and the varied and -brilliant results of observation is throughout exact. "I shall," -says he, in the preface,[124\9] "prove by the present Treatise, that -all inflection-phenomena, through openings of any form, size, and -arrangement, are not only explained by the undulation-theory, but -that they can be represented by analytical expressions, determining -the intensity of the light in any point whatever." And he justly -adds, that the undulation-theory accounts for the phenomena of -light, as completely as the theory of gravitation does for the facts -of the solar system. - -[Note 123\9: _Die Beugungs-erscheinungen, aus dem Fundamental-gesetz -der Undulations-Theorie analytisch entwickelt und in Bildern -dargestellt_, von F. M. Schwerd. Mannheim, 1835.] - -[Note 124\9: Dated Speyer, Aug. 1835.] - -9. _Objections to the Theory._--We have hitherto mentioned only -cases in which the undulatory theory was either entirely successful -in explaining the facts, or at least hypothetically consistent with -them and with itself. But other objections were started, and some -difficulties were long considered as very embarrassing. Objections -were made to the theory by some English experimenters, as Mr. -Potter, Mr. Barton, and others. These appeared in scientific -journals, and were afterwards answered in similar publications. The -objections depended partly on the measure of the _intensity_ of -light in the different points of the phenomena (a datum which it is -very difficult to obtain with accuracy {126} by experiment), and -partly on misconceptions of the theory; and I believe there are none -of them which would now be insisted on. - -We may mention, also, another difficulty, which it was the habit of -the opponents of the theory to urge as a reproach against it, long -after it had been satisfactorily explained: I mean the -_half-undulation_ which Young and Fresnel had found it necessary, in -some cases, to assume as gained or lost by one of the rays. Though -they and their followers could not analyse the mechanism of -reflection with sufficient exactness to trace out all the -circumstances, it was not difficult to see, upon Fresnel's -principles, that reflection from the interior and exterior surface -of glass must be of opposite kinds, which might be expressed by -supposing one of these rays to lose half an undulation. And thus -there came into view a justification of the step which had -originally been taken upon empirical grounds alone. - -10. _Dispersion, on the Undulatory Theory._--A difficulty of another -kind occasioned a more serious and protracted embarrassment to the -cultivators of this theory. This was the apparent impossibility of -accounting, on the theory, for the prismatic dispersion of color. -For it had been shown by Newton that the amount of refraction is -different for every color; and the amount of refraction depends on -the velocity with which light is propagated. Yet the theory -suggested no reason why the velocity should be different for -different colors: for, by mathematical calculation, vibrations of -all degrees of rapidity (in which alone colors differ) are -propagated with the same speed. Nor does analogy lead us to expect -this variety. There is no such difference between quick and slow -waves of air. The sounds of the deepest and the highest bells of a -peal are heard at any distance in the same order. Here, therefore, -the theory was at fault. - -But this defect was far from being a fatal one. For though the -theory did not explain, it did not contradict, dispersion. The -suppositions on which the calculations had been conducted, and the -analogy of sound, were obviously in no small degree precarious. The -velocity of propagation might differ for different rates of -undulation, in virtue of many causes which would not affect the -general theoretical results. - -Many such hypothetical causes were suggested by various eminent -mathematicians, as solutions of this conspicuous difficulty. But -without dwelling upon these conjectures, it may suffice to notice -that hypothesis upon which the attention of mathematicians was soon -concentrated. This was the _hypothesis of finite intervals_ between -the {127} particles of the ether. The length of one of those -undulations which produce light, is a very small quantity, its mean -value being 1⁄50,000th of an inch; but in the previous -investigations of the consequences of the theory, it had been -assumed that the distance from each other, of the particles of the -ether, which, by their attractions or repulsions, caused the -undulations to be propagated, is indefinitely less than this small -quantity;--so that its amount might be neglected in the cases in -which the length of the undulation was one of the quantities which -determined the result. But this assumption was made arbitrarily, as -a step of simplification, and because it was imagined that, in this -way, a nearer approach was made to the case of a continuous fluid -ether, which the supposition of distinct particles imperfectly -represented. It was still free for mathematicians to proceed upon -the opposite assumption, of particles of which the distances were -finite, either as a mathematical basis of calculation, or as a -physical hypothesis; and it remained to be seen if, when this was -done, the velocity of light would still be the same for different -lengths of undulation, that is, for different colors. M. Cauchy, -calculating, upon the most general principles, the motion of such a -collection of particles as would form an elastic medium, obtained -results which included the new extension of the previous hypothesis. -Professor Powell, of Oxford, applied himself to reduce to -calculation, and to compare with experiment, the result of these -researches. And it appeared that, on M. Cauchy's principles, a -variation in the velocity of light is produced by a variation in the -length of the wave, provided that the interval between the molecules -of the ether bears a sensible ratio to the length of an -undulation.[125\9] Professor Powell obtained also, from the general -expressions, a formula expressing the relation between the -refractive index of a ray, and the length of a wave, or the color of -light.[126\9] It then became his task to ascertain whether this -relation obtained experimentally; and he found a very close -agreement between the numbers which resulted from the formula and -those observed by Fraunhofer, for ten different kinds of media, -namely, certain glasses and fluids.[127\9] To these he afterwards -added ten other cases of crystals observed by M. Rudberg.[128\9] Mr. -Kelland, of Cambridge, also calculated, in a manner somewhat -different, the results of the same hypothesis of finite -intervals;[129\9] and, obtaining {128} formulæ not exactly the same -as Professor Powell, found also an agreement between these and -Fraunhofer's observations. - -[Note 125\9: _Phil. Mag._ vol. vi. p. 266.] - -[Note 126\9: Ib. vol. vii. 1835, p. 266.] - -[Note 127\9: _Phil. Trans._ 1835, p. 249.] - -[Note 128\9: Ib. 1836, p. 17.] - -[Note 129\9: _Camb. Trans._ vol. vi. p. 153.] - -It may be observed, that the refractive indices observed and -employed in these comparisons, were not those determined by the -color of the ray, which is not capable of exact identification, but -those more accurate measures which Fraunhofer was enabled to make, -in consequence of having detected in the spectrum the black lines -which he called B, C, D, E, F, G, H. The agreement between the -theoretical formulæ and the observed numbers is remarkable, -throughout all the series of comparisons of which we have spoken. -Yet we must at present hesitate to pronounce upon the hypothesis of -finite intervals, as proved by these calculations; for though this -hypothesis has given results agreeing so closely with experiment, it -is not yet clear that other hypotheses may not produce an equal -agreement. By the nature of the case, there must be a certain -gradation and continuity in the succession of colors in the -spectrum, and hence, any supposition which will account for the -general fact of the whole dispersion, may possibly account for the -amount of the intermediate dispersions, because these must be -interpolations between the extremes. The result of this hypothetical -calculation, however, shows very satisfactorily that there is not, -in the fact of dispersion, anything which is at all formidable to -the undulatory theory. - -11. _Conclusion._--There are several other of the more recondite -points of the theory which may be considered as, at present, too -undecided to allow us to speak historically of the discussions which -they have occasioned.[130\9] For example, it was conceived, for some -time, that the vibrations of polarized light are perpendicular to -the plane of polarization. But this assumption was not an essential -part of the theory; and all the phenomena would equally allow us to -suppose the vibrations to be in the polarization plane; the main -requisite being, that light polarized in planes at right angles to -each other, should also have the vibrations at right angles. -Accordingly, for some time, this point was left undecided by Young -and Fresnel, and, more recently, some mathematicians have come to -the opinion that ether vibrates in the plane of polarization. The -theory of transverse vibrations is equally stable, whichever -supposition may be finally confirmed. - -[Note 130\9: For on account of these, see Professor Lloyd's _Report -on Physical Optics_. (Brit. Assoc. Report, 1834.)] - -We may speak, in the same manner, of the suppositions which, from -{129} the time of Young and Fresnel, the cultivators of this theory -have been led to make respecting the mechanical constitution of the -ether, and the forces by which transverse vibrations are produced. -It was natural that various difficulties should arise upon such -points, for transverse vibrations had not previously been made the -subject of mechanical calculation, and the forces which occasion -them must act in a different manner from those which were previously -contemplated. Still, we may venture to say, without entering into -these discussions, that it has appeared, from all the mathematical -reasonings which have been pursued, that there is not, in the -conception of transverse vibrations, anything inconsistent either -with the principles of mechanics, or with the best general views -which we can form, of the forces by which the universe is held -together. - -I willingly speak as briefly as the nature of my undertaking allows, -of those points of the undulatory theory which are still under -deliberation among mathematicians. With respect to these, an -intimate acquaintance with mathematics and physics is necessary to -enable any one to understand the steps which are made from day to -day; and still higher philosophical qualifications would be -requisite in order to pronounce a judgment upon them. I shall, -therefore, conclude this survey by remarking the highly promising -condition of this great department of science, in respect to the -character of its cultivators. Nothing less than profound thought and -great mathematical skill can enable any one to deal with this -theory, in any way likely to promote the interests of science. But -there appears, in the horizon of the scientific world, a -considerable class of young mathematicians, who are already bringing -to these investigations the requisite talents and zeal; and who, -having acquired their knowledge of the theory since the time when -its acceptation was doubtful, possess, without effort, that -singleness and decision of view as to its fundamental doctrines, -which it is difficult for those to attain whose minds have had to go -through the hesitation, struggle, and balance of the epoch of the -establishment of the theory. In the hands of this new generation, it -is reasonable to suppose the Analytical Mechanics of light will be -improved as much as the Analytical Mechanics of the solar system was -by the successors of Newton. We have already had to notice many of -this younger race of undulationists. For besides MM. Cauchy, -Poisson, and Ampère, M. Lamé has been more recently following these -researches in France.[131\9] In {130} Belgium, M. Quetelet has given -great attention to them; and, in our own country, Sir William -Hamilton, and Professor Lloyd, of Dublin, have been followed by Mr. -Mac Cullagh. Professor Powell, of Oxford, has continued his -researches with unremitting industry; and, at Cambridge, Professor -Airy, who did much for the establishment and diffusion of the theory -before he was removed to the post of Astronomer Royal, at Greenwich, -has had the satisfaction to see his labors continued by others, even -to the most recent time; for Mr. Kelland,[132\9] whom we have -already mentioned, and Mr. Archibald Smith,[133\9] the two persons -who, in 1834 and 1836, received the highest mathematical honors -which that university can bestow, have both of them published -investigations respecting the undulatory theory. - -[Note 131\9: Prof. Lloyd's _Report_, p. 392.] - -[Note 132\9: _On the Dispersion of Light, as explained by the -Hypothesis of Finite Intervals._ Camb. Trans. vol. vi. p. 153.] - -[Note 133\9: _Investigation of the Equation to Fresnel's Wave -Surface_, ib. p. 85. See also, in the same volume, _Mathematical -Considerations on the Problem of the Rainbow_, showing it to belong -to Physical Optics, by R. Potter, Esq., of Queen's College.] - -We may be permitted to add, as a reflection obviously suggested by -these facts, that the cause of the progress of science is -incalculably benefited by the existence of a body of men, trained -and stimulated to the study of the higher mathematics, such as exist -in the British universities, who are thus prepared, when an abstruse -and sublime theory comes before the world with all the characters of -truth, to appreciate its evidence, to take steady hold of its -principles, to pursue its calculations, and thus to convert into a -portion of the permanent treasure and inheritance of the civilized -world, discoveries which might otherwise expire with the great -geniuses who produced them, and be lost for ages, as, in former -times, great scientific discoveries have sometimes been. - -The reader who is acquainted with the history of recent optical -discovery, will see that we have omitted much which has justly -excited admiration; as, for example, the phenomena produced by glass -under heat or pressure, noticed by MM. Lobeck, and Biot, and -Brewster, and many most curious properties of particular minerals. -We have omitted, too, all notice of the phenomena and laws of the -absorption of light, which hitherto stand unconnected with the -theory. But in this we have not materially deviated from our main -design; for our end, in what we have done, has been to trace the -advances of Optics {131} towards perfection as a theory; and this -task we have now nearly executed as far as our abilities allow. - -We have been desirous of showing that the _type_ of this progress, -in the histories of the two great sciences, Physical Astronomy and -Physical Optics, is the same. In both we have many _Laws of -Phenomena_ detected and accumulated by acute and inventive men; we -have _Preludial_ guesses which touch the true theory, but which -remain for a time imperfect, undeveloped, unconfirmed: finally we -have the _Epoch_ when this true theory, clearly apprehended by great -philosophical geniuses, is recommended by its fully explaining what -it was first meant to explain, and confirmed by its explaining what -it was not meant to explain. We have then its _Progress_ struggling -for a little while with adverse prepossessions and difficulties; -finally overcoming all these, and moving onwards, while its -triumphal procession is joined by all the younger and more vigorous -men of science. - -It would, perhaps, be too fanciful to attempt to establish a -parallelism between the prominent persons who figure in these two -histories. If we were to do this, we must consider Huyghens and -Hooke as standing in the place of Copernicus, since, like him, they -announced the true theory, but left it to a future age to give it -development and mechanical confirmation; Malus and Brewster, -grouping them together, correspond to Tycho Brahe and Kepler, -laborious in accumulating observations, inventive and happy in -discovering laws of phenomena; and Young and Fresnel combined, make -up the Newton of optical science. - -[2nd Ed.] [In the _Report on Physical Optics_, (_Brit. Ass. -Reports_, 1834,) by Prof. Lloyd, the progress of the mathematical -theory after Fresnel's labors is stated more distinctly than I have -stated it, to the following effect. Ampère, in 1828, proved -Fresnel's mathematical results directly, which Fresnel had only -proved indirectly, and derived from his proof Fresnel's beautiful -geometrical construction. Prof. Mac Cullagh not long after gave a -concise demonstration of the same theorem, and of the other -principal points of Fresnel's theory. He represents the elastic -force by means of an ellipsoid whose axes are inversely proportional -to those of Fresnel's generating ellipsoid, and deduces Fresnel's -construction geometrically. In the third Supplement to his _Essay on -the Theory of Systems of Rays_ (_Trans. R. I. Acad._ vol. xvii.), -Sir W. Hamilton has presented that portion of Fresnel's theory which -relates to the fundamental problem of the determination of the -velocity and polarization of a plane wave, in a very elegant and -analytical form. This he does by means of what he calls the {132} -_characteristic function_ of the optical system to which the problem -belongs. From this function is deduced the _surface of -wave-slowness_ of the medium; and by means of this surface, the -direction of the rays refracted into the medium. From this -construction also Sir W. Hamilton was led to the anticipation of -_conical refraction_, mentioned above. - -The investigations of MM. Cauchy and Lamé refer to the laws by which -the particles of the ether act upon each other and upon the -particles of other bodies;--a field of speculation which appears to -me not yet ripe for the final operations of the analyst. - -Among the mathematicians who have supplied defects in Fresnel's -reasoning on this subject, I may mention Mr. Tovey, who treated it -in several papers in the _Philosophical Magazine_ (1837-40). Mr. -Tovey's early death must be deemed a loss to mathematical science. - -Besides investigating the motion of symmetrical systems of particles -which may be supposed to correspond to biaxal crystals, Mr. Tovey -considered the case of unsymmetrical systems, and found that the -undulations propagated would, in the general case, be elliptical; -and that in a particular case, circular undulations would take -place, such as are propagated along the axis of quartz. It appears -to me, however, that he has not given a definite meaning to those -limitations of his general hypothesis which conduct him to this -result. Perhaps if the hypothetical conditions of this result were -traced into detail, they would be found to reside in a _screw-like_ -arrangement of the elementary particles, in some degree such as -crystals of quartz themselves exhibit in their forms, when they have -plagihedral faces at both ends. - -Such crystals of quartz are, some like a right-handed and some like -a left-handed screw; and, as Sir John Herschel discovered, the -circular polarization is right-handed or left-handed according as -the plagihedral form is so. In Mr. Tovey's hypothetical -investigation it does not appear upon what part of the hypothesis -this difference of right and left-handed depends. The definition of -this part of the hypothesis is a very desirable step. - -When crystals of Quartz are right-handed at one end, they are -right-handed at the other end: but there is a different kind of -plagihedral form, which occurs in some other crystals, for instance, -in Apatite: in these the plagihedral faces are right-handed at the -one extremity and left-handed at the other. For the sake of -distinction, we may call the former _homologous_ plagihedral faces, -since, at both ends, they have the same name; and the latter -_heterologous_ plagihedral faces. {133} - -The homologous plagihedral faces of Quartz crystals are accompanied -by homologous circular polarization of the same name. I do not know -that heterologous circular polarization has been observed in any -crystal, but it has been discovered by Dr. Faraday to occur in -glass, &c., when subjected to powerful magnetic action. - -Perhaps it was presumptuous in me to attempt to draw such -comparisons, especially with regard to living persons, as I have -done in the preceding pages of this Book. Having published this -passage, however, I shall not now suppress it. But I may observe -that the immense number and variety of the beautiful optical -discoveries which we owe to Sir David Brewster makes the comparison -in his case a very imperfect representation of his triumphs over -nature; and that, besides his place in the history of the Theory of -Optics, he must hold a most eminent position in the history of -Optical Crystallography, whenever the discovery of a True Optical -Theory of Crystals supplies us with the _Epoch_ to which his labors -in this field form so rich a _Prelude_. I cordially assent to the -expression employed by Mr. Airy in the _Phil. Trans._ for 1840, in -which he speaks of Sir David Brewster as "the Father of Modern -Experimental Optics."] - - - -{{135}} -BOOK X. - -_SECONDARY MECHANICAL SCIENCES._ -(CONTINUED.) - -HISTORY -OF -THERMOTICS AND ATMOLOGY. - - - Et primum faciunt ignem se vortere in auras - Aëris; hinc imbrem gigni terramque creari - Ex imbri; retroque a terrâ cuncta revorti, - Humorem primum, post aëra deinde calorem; - Nec cessare hæc inter se mutare, meare, - De cœlo ad terram de terrâ ad sidera mundi. - LUCRETIUS, i. 783. - - Water, and Air, and Fire, alternate run - Their endless circle, multiform, yet one. - For, moulded by the fervor's latent beams, - Solids flow loose, and fluids flash to steams, - And elemental flame, with secret force, - Pursues through earth, air, sky, its stated course. - - - -{{137}} -INTRODUCTION. - -_Of Thermotics and Atmology._ - - -I EMPLOY the term _Thermotics_ to include all the doctrines -respecting Heat, which have hitherto been established on proper -scientific grounds. Our survey of the history of this branch of -science must be more rapid and less detailed than it has been in -those subjects of which we have hitherto treated: for our knowledge -is, in this case, more vague and uncertain than in the others, and -has made less progress towards a general and certain theory. Still, -the narrative is too important and too instructive to be passed over. - -The distinction of Formal Thermotics and Physical Thermotics,--of -the discovery of the mere Laws of Phenomena, and the discovery of -their causes,--is applicable here, as in other departments of our -knowledge. But we cannot exhibit, in any prominent manner, the -latter division of the science now before us; since no general -theory of heat has yet been propounded, which affords the means of -calculating the circumstances of the phenomena of conduction, -radiation, expansion, and change of solid, liquid, and gaseous form. -Still, on each of these subjects there have been proposed, and -extensively assented to, certain general views, each of which -explains its appropriate class of phenomena; and, in some cases, -these principles have been clothed in precise and mathematical -conditions, and thus made bases of calculation. - -These principles, thus possessing a generality of a limited kind, -connecting several observed laws of phenomena, but yet not -connecting all the observed classes of facts which relate to heat, -will require our separate attention. They may be described as the -Doctrine of Conduction, the Doctrine of Radiation, the Doctrine of -Specific Heat, and the Doctrine of Latent Heat; and these, and -similar doctrines respecting heat, make up the science which we may -call _Thermotics proper_. - -But besides these collections of principles which regard heat by -itself, the relations of heat and moisture give rise to another and -important collection of laws and principles, which I shall treat of -in connexion with Thermotics, and shall term _Atmology_, borrowing -{138} the term from the Greek word (ἄτμος,) which signifies _vapor_. -The _Atmosphere_ was so named by the Greeks, as being a sphere of -vapor; and, undoubtedly, the most general and important of the -phenomena which take place in the air, by which the earth is -surrounded, are those in which water, of one _consistence_ or other -(ice, water, or steam,) is concerned. The knowledge which relates to -what takes place in the atmosphere has been called _Meteorology_, in -its collective form: but such knowledge is, in fact, composed of -parts of many different sciences. And it is useful for our purpose -to consider separately those portions of Meteorology which have -reference to the laws of aqueous vapor, and these we may include -under the term Atmology. - -The instruments which have been invented for the purpose of -measuring the moisture of the air, that is, the quantity of vapor -which exists in it, have been termed _Hygrometers_; and the -doctrines on which these instruments depend, and to which they lead, -have been called _Hygrometry_; but this term has not been used in -quite so extensive a sense as that which we intend to affix to -_Atmology_. - -In treating of Thermotics, we shall first describe the earlier -progress of men's views concerning Conduction, Radiation, and the -like, and shall then speak of the more recent corrections and -extensions, by which they have been brought nearer to theoretical -generality. - - - -{{139}} -THERMOTICS PROPER. - - - - -CHAPTER I. - -THE DOCTRINES OF CONDUCTION AND RADIATION. - -_Section_ 1.--_Introduction of the Doctrine of Conduction._ - - -BY _conduction_ is meant the propagation of heat from one part to -another of a continuous body; or from one body to another in contact -with it; as when one end of a poker stuck in the fire heats the -other end, or when this end heats the hand which takes hold of it. -By _radiation_ is meant the diffusion of heat from the surface of a -body to points not in contact. It is clear in both these cases, -that, in proportion as the hot portion is hotter, it produces a -greater effect in warming the cooler portion; that is, it -_communicates more Heat_ to it, if _Heat_ be the abstract conception -of which this effect is the measure. The simplest rule which can be -proposed is, that the heat thus communicated in a given instant is -proportional to the excess of the heat of the hot body over that of -the contiguous bodies; there are no obvious phenomena which -contradict the supposition that this is the true law; and it was -thence assumed by Newton as the true law for radiation and by other -writers for conduction. This assumption was confirmed approximately, -and afterwards corrected, for the case of Radiation; in its -application to Conduction, it has been made the basis of calculation -up to the present time. We may observe that this statement takes for -granted that we have attained to a measure of heat (or of -_temperature_, as heat thus measured is termed), corresponding to -the law thus assumed; and, in fact, as we shall have occasion to -explain in speaking of the _measures_ of sensible qualities, {140} -the thermometrical scale of heat according to the expansion of -liquids (which is the measure of temperature here adopted), was -constructed with a reference to Newton's law of radiation of heat; -and thus the law is necessarily consistent with the scale. - -In any case in which the parts of a body are unequally hot, the -temperature will vary _continuously_ in passing from one part of the -body to another; thus, a long bar of iron, of which one end is kept -red hot, will exhibit a gradual diminution of temperature at -successive points, proceeding to the other end. The law of -temperature of the parts of such a bar might be expressed by the -ordinates of a _curve_ which should run alongside the bar. And, in -order to trace mathematically the consequences of the assumed law, -some of those processes would be necessary, by which mathematicians -are enabled to deal with the properties of curves; as the method of -infinitesimals, or the differential calculus; and the truth or -falsehood of the law would be determined, according to the usual -rules of inductive science, by a comparison of results so deduced -from the principle, with the observed phenomena. - -It was easily perceived that this comparison was the task which -physical inquirers had to perform; but the execution of it was -delayed for some time; partly, perhaps, because the mathematical -process presented some difficulties. Even in a case so simple as -that above mentioned, of a linear bar with a stationary temperature -at one end, _partial differentials_ entered; for there were three -variable quantities, the time, as well as the place of each point -and its temperature. And at first, another scruple occurred to M. -Biot when, about 1804, he undertook this problem.[1\10] "A -difficulty," says Laplace,[2\10] in 1809, "presents itself, which -has not yet been solved. The quantities of heat received and -communicated in an instant (by any point of the bar) must be -infinitely small quantities of the same order as the excess of the -heat of a slice of the body over that of the contiguous slice; -therefore the _excess_ of the heat received by any slice over the -heat communicated, is an infinitely small quantity of the second -order; and the accumulation in a finite time (which depends on this -excess) cannot be finite." I conceive that this difficulty arises -entirely from an arbitrary and unnecessary assumption concerning the -relation of the infinitesimal parts of the body. Laplace resolved -the difficulty by further reasoning founded upon the same assumption -which occasioned {141} it; but Fourier, who was the most -distinguished of the cultivators of this mathematical doctrine of -conduction, follows a course of reasoning in which the difficulty -does not present itself. Indeed it is stated by Laplace, in the -Memoir above quoted,[3\10] that Fourier had already obtained the -true fundamental equations by views of his own. - -[Note 1\10: Biot, _Traité de Phys._ iv. p. 669.] - -[Note 2\10: Laplace, _Mém. Inst._ for 1809, p. 332.] - -[Note 3\10: Laplace, _Mém. Inst._ for 1809, p. 538.] - -The remaining part of the history of the doctrine of conduction is -principally the history of Fourier's labors. Attention having been -drawn to the subject, as we have mentioned, the French Institute, in -January, 1810, proposed, as their prize question, "To give the -mathematical theory of the laws of the propagation of heat, and to -compare this theory with exact observations." Fourier's Memoir (the -sequel of one delivered in 1807,) was sent in September, 1811; and -the prize (3000 francs) adjudged to it in 1812. In consequence of -the political confusion which prevailed in France, or of other -causes, these important Memoirs were not published by the Academy -till 1824; but extracts had been printed in the _Bulletin des -Sciences_ in 1808, and in the _Annales de Chimie_ in 1816; and -Poisson and M. Cauchy had consulted the manuscript itself. - -It is not my purpose to give, in this place,[4\10] an account of the -analytical processes by which Fourier obtained his results. The -skill displayed in these Memoirs is such as to make them an object -of just admiration to mathematicians; but they consist entirely of -deductions from the fundamental principle which I have -noticed,--that the quantity of heat conducted from a hotter to a -colder point is proportional to the excess of heat, modified by the -_conductivity_, or conducting power of each substance. The equations -which flow from this principle assume nearly the same forms as those -which occur in the most general problems of hydrodynamics. Besides -Fourier's solution, Laplace, Poisson, and M. Cauchy have also -exercised their great analytical skill in the management of these -formulæ. We shall briefly speak of the comparison of the results of -these reasonings with experiment, and notice some other consequences -to which they lead. But before we can do this, we must pay some -attention to the subject of radiation. {142} - -[Note 4\10: I have given an account of Fourier's mathematical -results in the _Reports of the British Association_ for 1835.] - - -_Sect._ 2.--_Introduction of the Doctrine of Radiation._ - -A HOT body, as a mass of incandescent iron, emits heat, as we -perceive by our senses when we approach it; and by this emission of -heat the hot body cools down. The first step in our systematic -knowledge of the subject was made in the _Principia_. "It was in the -destiny of that great work," says Fourier, "to exhibit, or at least -to indicate, the causes of the principal phenomena of the universe." -Newton assumed, as we have already said, that the rate at which a -body cools, that is, parts with its heat to surrounding bodies, is -proportional to its heat; and on this assumption he rested the -verification of his scale of temperatures. It is an easy deduction -from this law, that if times of cooling be taken in arithmetical -progression, the heat will decrease in geometrical progression. -Kraft, and after him Richman, tried to verify this law by direct -experiments on the cooling of vessels of warm water; and from these -experiments, which have since been repeated by others, it appears -that for differences of temperature which do not exceed 50 degrees -(boiling water being 100), this geometrical progression represents, -with tolerable (but not with complete) accuracy, the process of -cooling. - -This principle of radiation, like that of conduction, required to be -followed out by mathematical reasoning. But it required also to be -corrected in the first place, for it was easily seen that the rate -of cooling depended, not on the absolute temperature of the body, -but on the excess of its temperature above the surrounding objects -to which it communicated its heat in cooling. And philosophers were -naturally led to endeavor to explain or illustrate this process by -some physical notions. Lambert in 1765 published[5\10] an _Essay on -the Force of Heat_, in which he assimilates the communication of -heat to the flow of a fluid out of one vessel into another by an -excess of pressure; and mathematically deduces the laws of the -process on this ground. But some additional facts suggested a -different view of the subject. It was found that heat is propagated -by radiation according to straight lines, like light; and that it -is, as light is, capable of being reflected by mirrors, and thus -brought to a focus of intenser action. In this manner the radiative -effect of a body could be more precisely traced. A fact, however, -came under notice, which, at first sight, appeared to {143} offer -some difficulty. It appeared that cold was reflected no less than -heat. A mass of ice, when its effect was concentrated on a -thermometer by a system of mirrors, made the thermometer fall, just -as a vessel of hot water placed in a similar situation made it rise. -Was cold, then, to be supposed a real substance, no less than heat? - -[Note 5\10: _Act. Helvet._ tom. ii. p. 172.] - -The solution of this and similar difficulties was given by Pierre -Prevost, professor at Geneva, whose theory of radiant heat was -proposed about 1790. According to this theory, heat, or _caloric_, -is constantly radiating from every point of the surface of all -bodies in straight lines; and it radiates the more copiously, the -greater is the quantity of heat which the body contains. Hence a -constant exchange of heat is going on among neighboring bodies; and -a body grows hotter or colder, according as it receives more caloric -than it emits, or the contrary. And thus a body is cooled by -rectilinear rays from a cold body, because along these paths it -sends rays of heat in greater abundance than those which return the -same way. This _theory of exchanges_ is simple and satisfactory, and -was soon generally adopted; but we must consider it rather as the -simplest mode of expressing the dependence of the communication of -heat on the excess of temperature, than as a proposition of which -the physical truth is clearly established. - -A number of curious researches on the effect of the different kinds -of surface of the heating and of the heated body, were made by -Leslie and others. On these I shall not dwell; only observing that -the relative amount of this radiative and receptive energy may be -expressed by numbers, for each kind of surface; and that we shall -have occasion to speak of it under the term _exterior conductivity_; -it is thus distinguished from _interior conductivity_, which is the -relative rate at which heat is conducted in the interior of -bodies.[6\10] - -[Note 6\10: The term employed by Fourier, _conductibility_ or -_conducibility_, suggests expressions altogether absurd, as if the -bodies could be called _conductible_, or _conducible_, with respect -to heat: I have therefore ventured upon a slight alteration of the -word, and have used the abstract term which analogy would suggest, -if we suppose bodies to be _conductive_ in this respect.] - - -_Sect._ 3.--_Verifications of the Doctrines of Conduction and -Radiation._ - -THE interior and exterior conductivity of bodies are numbers, which -enter as elements, or _coefficients_, into the mathematical -calculations founded on the doctrines of conduction and radiation. -These {144} coefficients are to be determined for each case by -appropriate experiments: when the experimenters had obtained these -data, as well as the mathematical solutions of the problems, they -could test the truth of their fundamental principles by a comparison -of the theoretical and actual results in properly-selected cases. -This was done for the law of conduction in the simple cases of -metallic bars heated at one end, by M. Biot,[7\10] and the -accordance with experiment was sufficiently close. In the more -complex cases of conduction which Fourier considered, it was less -easy to devise a satisfactory mode of comparison. But some rather -curious relations which he demonstrated to exist among the -temperatures at different points of an _armille_, or ring, afforded -a good criterion of the value of the calculations, and confirmed -their correctness.[8\10] - -[Note 7\10: _Tr. de Phys._ iv. 671.] - -[Note 8\10: _Mém. Inst._ 1819, p. 192, published 1824.] - -We may therefore presume these doctrines of radiation and conduction -to be sufficiently established; and we may consider their -application to any remarkable case to be a portion of the history of -science. We proceed to some such applications. - - -_Sect._ 4.--_The Geological and Cosmological Application of -Thermotics._ - -BY far the most important case to which conclusions from these -doctrines have been applied, is that of the globe of the earth, and -of those laws of climate to which the modifications of temperature -give rise; and in this way we are led to inferences concerning other -parts of the universe. If we had any means of observing these -terrestrial and cosmical phenomena to a sufficient extent, they -would be valuable facts on which we might erect our theories; and -they would thus form part, not of the corollaries, but of the -foundations of our doctrine of heat. In such a case, the laws of the -propagation of heat, as discovered from experiments on smaller -bodies, would serve to explain these phenomena of the universe, just -as the laws of motion explain the celestial movements. But since we -are almost entirely without any definite indications of the -condition of the other bodies in the solar system as to heat; and -since, even with regard to the earth, we know only the temperature -of the parts at or very near the surface, our knowledge of the part -which heat plays in the earth and the heavens must be in a great -measure, not a generalization of observed facts, but a deduction -from theoretical principles. Still, such knowledge, whether obtained -{145} from observation or from theory, must possess great interest -and importance. The doctrines of this kind which we have to notice -refer principally to the effect of the sun's heat on the earth, the -laws of climate,--the thermotical condition of the interior of the -earth,--and that of the planetary spaces. - -1. _Effect of Solar Heat on the Earth._--That the sun's heat passes -into the interior of the earth in a variable manner, depending upon -the succession of days and nights, summers and winters, is an -obvious consequence of our first notions on this subject. The mode -in which it proceeds into the interior, after descending below the -surface, remained to be gathered, either from the phenomena, or from -reasoning. Both methods were employed.[9\10] Saussure endeavored to -trace its course by digging, in 1785, and thus found that at the -depth of about thirty-one feet, the annual variation of temperature -is about 1⁄12th what it is at the surface. Leslie adopted a better -method, sinking the bulbs of thermometers deep in the earth, while -their stems appeared above the surface. In 1813, '16, and '17, he -observed thus the temperatures at the depths of one, two, four, and -eight feet, at Abbotshall, in Fifeshire. The results showed that the -extreme annual oscillations of the temperature diminish as we -descend. At the depth of one foot, the yearly range of oscillation -was twenty-five degrees (Fahrenheit); at two feet it was twenty -degrees; at four feet it was fifteen degrees; at eight feet it was -only nine degrees and a half. And the time at which the heat was -greatest was later and later in proceeding to the lower points. At -one foot, the maximum and minimum were three weeks after the -solstice of summer and of winter; at two feet, they were four or -five weeks; at four feet, they were two months; and at eight feet, -three months. The mean temperature of all the thermometers was -nearly the same. Similar results were obtained by Ott at Zurich in -1762, and by Herrenschneider at Strasburg in 1821, '2, '3.[10\10] - -[Note 9\10: Leslie, art. _Climate_, Supp. _Enc. Brit._ 179.] - -[Note 10\10: Pouillet, _Météorol._ t. ii. p. 643.] - -These results had already been explained by Fourier's theory of -conduction. He had shown[11\10] that when the surface of a sphere is -affected by a periodical heat, certain alternations of heat travel -uniformly into the interior, but that the extent of the alternation -diminishes in geometrical progression in this descent. This -conclusion applies to the effect of days and years on the -temperature of the earth, and shows that such facts as those -observed by Leslie are both exemplifications of {146} the general -circumstances of the earth, and are perfectly in accordance with the -principles on which Fourier's theory rests. - -[Note 11\10: _Mém. Inst._ for 1821 (published 1826), p. 162.] - -2. _Climate._--The term _climate_, which means _inclination_, was -applied by the ancients to denote that inclination of the axis of -the terrestrial sphere from which result the inequalities of days in -different latitudes. This inequality is obviously connected also -with a difference of thermotical condition. Places near the poles -are colder, on the whole, than places near the equator. It was a -natural object of curiosity to determine the law of this variation. - -Such a determination, however, involves many difficulties, and the -settlement of several preliminary points. How is the temperature of -any place to be estimated? and if we reply, by its _mean_ -temperature, how are we to learn this mean? The answers to such -questions require very multiplied observations, exact instruments, -and judicious generalizations; and cannot be given here. But certain -first approximations may be obtained without much difficulty; for -instance, the mean temperature of any place may be taken to be the -temperature of deep springs, which is probably identical with the -temperature of the soil below the reach of the annual oscillations. -Proceeding on such facts, Mayer found that the mean temperature of -any place was nearly proportional to the square of the cosine of the -latitude. This, as a law of phenomena, has since been found to -require considerable correction; and it appears that the mean -temperature does not depend on the latitude alone, but on the -distribution of land and water, and on other causes. M. de Humboldt -has expressed these deviations[12\10] by his map of _isothermal -lines_, and Sir D. Brewster has endeavored to reduce them to a law -by assuming two _poles of maximum cold_. - -[Note 12\10: British Assoc. 1833. Prof. Forbes's _Report on -Meteorology_, p. 215.] - -The expression which Fourier finds[13\10] for the distribution of -heat in a homogeneous sphere, is not immediately comparable with -Mayer's empirical formula, being obtained on a certain hypothesis, -namely, that the equator is kept constantly at a fixed temperature. -But there is still a general agreement; for, according to the -theory, there is a diminution of heat in proceeding from the equator -to the poles in such a case; the heat is propagated from the equator -and the neighboring parts, and radiates out from the poles into the -surrounding space. And thus, in the case of the earth, the solar -heat enters in the tropical {147} parts, and constantly flows -towards the polar regions, by which it is emitted into the planetary -spaces. - -[Note 13\10: Fourier. _Mém. Inst._ tom. v. p. 173.] - -Climate is affected by many thermotic influences, besides the -conduction and radiation of the solid mass of the earth. The -atmosphere, for example, produces upon terrestrial temperatures -effects which it is easy to see are very great; but these it is not -yet in the power of calculation to appreciate;[14\10] and it is -clear that they depend upon other properties of air besides its -power to transmit heat. We must therefore dismiss them, at least for -the present. - -[Note 14\10: _Mém. Inst._ tom. vii. p. 584] - -3. _Temperature of the Interior of the Earth._--The question of the -temperature of the interior of the earth has excited great interest, -in consequence of its bearing on other branches of knowledge. The -various facts which have been supposed to indicate the fluidity of -the central parts of the terrestrial globe, belong, in general, to -geological science; but so far as they require the light of -thermotical calculations in order to be rightly reasoned upon, they -properly come under our notice here. - -The principal problem of this kind which has been treated of is -this:--If in the globe of the earth there be a certain original -heat, resulting from its earlier condition, and independent of the -action of the sun, to what results will this give rise? and how far -do the observed temperatures of points below the surface lead us to -such a supposition? It has, for instance, been asserted, that in -many parts of the world the temperature, as observed in mines and -other excavations, increases in descending, at the rate of one degree -(centesimal) in about forty yards. What inference does this justify? - -The answer to this question was given by Fourier and by Laplace. The -former mathematician had already considered the problem of the -cooling of a large sphere, in his Memoirs of 1807, 1809, and 1811. -These, however, lay unpublished in the archives of the Institute for -many years. But in 1820, when the accumulation of observations which -indicated an increase of the temperature of the earth as we descend, -had drawn observation to the subject, Fourier gave, in the Bulletin -of the Philomathic Society,[15\10] a summary of his results, as far -as they bore on this point. His conclusion was, that such an -increase of temperature in proceeding towards the centre of the -earth, can arise from nothing but the remains of a primitive -heat;--that the heat which the sun's action would communicate, -would, in its final and {148} permanent state, be uniform in the -same vertical line, as soon as we get beyond the influence of the -superficial oscillations of which we have spoken;--and that, before -the distribution of temperature reaches this limit, it will -decrease, not increase, in descending. It appeared also, by the -calculation, that this remaining existence of the primitive heat in -the interior of the earth's mass, was quite consistent with the -absence of all perceptible traces of it at the surface; and that the -same state of things which produces an increase of one degree of -heat in descending forty yards, does not make the surface a quarter -of a degree hotter than it would otherwise be. Fourier was led also -to some conclusions, though necessarily very vague ones, respecting -the time which the earth must have taken to cool from a supposed -original state of incandescence to its present condition, which time -it appeared must have been very great; and respecting the extent of -the future cooling of the surface, which it was shown must be -insensible. Everything tended to prove that, within the period which -the history of the human race embraces, no discoverable change of -temperature had taken place from the progress of this central -cooling. Laplace further calculated the effect[16\10] which any -contraction of the globe of the earth by cooling would produce on -the length of the day. He had already shown, by astronomical -reasoning, that the day had not become shorter by 1⁄200th of a -second, since the time of Hipparchus; and thus his inferences agreed -with those of Fourier. As far as regards the smallness of the -perceptible effect due to the past changes of the earth's -temperature, there can be no doubt that all the curious conclusions -just stated are deduced in a manner quite satisfactory, from the -fact of a general increase of heat in descending below the surface -of the earth; and thus our principles of speculative science have a -bearing upon the history of the past changes of the universe, and -give us information concerning the state of things in portions of -time otherwise quite out of our reach. - -[Note 15\10: _Bullet. des Sc._ 1820, p. 58.] - -[Note 16\10: _Conn. des Tems_, 1823.] - -4. _Heat of the Planetary Spaces._--In the same manner, this portion -of science is appealed to for information concerning parts of space -which are utterly inaccessible to observation. The doctrine of heat -leads to conclusions concerning the temperatures of the spaces which -surround the earth, and in which the planets of the solar system -revolve. In his Memoir, published in 1827,[17\10] Fourier states -that he conceives it to follow from his principles, that these -planetary spaces {149} are not absolutely cold, but have a "proper -heat" independent of the sun and of the planets. If there were not -such a heat, the cold of the polar regions would be much more -intense than it is, and the alternations of cold and warmth, arising -from the influence of the sun, would be far more extreme and sudden -than we find them. As the cause of this heat in the planetary -spaces, he assigns the radiation of the innumerable stars which are -scattered through the universe. - -[Note 17\10: _Mém. Inst._ tom. vii. p. 580.] - -Fourier says,[18\10] "We conclude from these various remarks, and -principally from the mathematical examination of the question," that -this is so. I am not aware that the mathematical calculation which -bears peculiarly upon this point has anywhere been published. But it -is worth notice, that Svanberg has been led[19\10] to the opinion of -the same temperature in these spaces which Fourier had adopted (50 -centigrade below zero), by an entirely different course of -reasoning, founded on the relation of the atmosphere to heat. - -[Note 18\10: _Mém. Inst._ tom. vii. p. 581.] - -[Note 19\10: Berzel. _Jahres Bericht_, xi. p. 50.] - -In speaking of this subject, I have been led to notice incomplete -and perhaps doubtful applications of the mathematical doctrine of -conduction and radiation. But this may at least serve to show that -Thermotics is a science, which, like Mechanics, is to be established -by experiments on masses capable of manipulation, but which, like -that, has for its most important office the solution of geological -and cosmological problems. I now return to the further progress of -our thermotical knowledge. - - -_Sect._ 5.--_Correction of Newton's Law of Cooling._ - -IN speaking of the establishment of Newton's assumption, that the -temperature communicated is proportional to the excess of -temperature, we stated that it was approximately verified, and -afterwards corrected (chap. i., sect. 1.)**. This correction was the -result of the researches of MM. Dulong and Petit in 1817, and the -researches by which they were led to the true law, are an admirable -example both of laborious experiment and sagacious induction. They -experimented through a very great range of temperature (as high as -two hundred and forty degrees centigrade), which was necessary -because the inaccuracy of Newton's law becomes considerable only at -high temperatures. They removed the effect of the surrounding -medium, by making their experiments in a vacuum. They selected with -great {150} judgment the conditions of their experiments and -comparisons, making one quantity vary while the others remained -constant. In this manner they found, that _the quickness of cooling -for a constant excess of temperature, increases in geometrical -progression, when the temperature of the surrounding space increases -in arithmetical progression_; whereas, according to the Newtonian -law, this quickness would not have varied at all. Again, this -variation being left out of the account, it appeared that _the -quickness of cooling, so far as it depends on the excess of -temperature of the hot body, increases as the terms of a geometrical -progression diminished by a constant number, when the temperature of -the hot body increases in arithmetical progression_. These two laws, -with the coefficients requisite for their application to particular -substances, fully determine the conditions of cooling in a vacuum. - -Starting from this determination, MM. Dulong and Petit proceeded to -ascertain the effect of the medium, in which the hot body is placed, -upon its rate of cooling; for this effect became a _residual -phenomenon_,[20\10] when the cooling in the vacuum was taken away. -We shall not here follow this train of research; but we may briefly -state, that they were led to such laws as this;--that the rapidity -of cooling due to any gaseous medium in which the body is placed, is -the same, so long as the excess of the body's temperature is the -same, although the temperature itself vary;--that the cooling power -of a gas varies with the elasticity, according to a determined law; -and other similar rules. - -[Note 20\10: See _Phil. Ind. Sciences_, B. xiii. c. 7, Sect. iv.] - -In reference to the process of their induction, it is worthy of -notice, that they founded their reasonings upon Prevost's law of -exchanges; and that, in this way, the second of their laws above -stated, respecting the quickness of cooling, was a mathematical -consequence of the first. It may be observed also, that their -temperatures are measured by means of the air-thermometer, and that -if they were estimated on another scale, the remarkable simplicity -and symmetry of their results would disappear. This is a strong -argument for believing such a measure of temperature to have a -natural prerogative of simplicity. This belief is confirmed by other -considerations; but these, depending on the laws of _expansion_ by -heat, cannot be here referred to; and we must proceed to finish our -survey of the mathematical theory of heat, as founded on the -phenomena of radiation and conduction, which alone have as yet been -traced up to general principles. - -We may observe, before we quit this subject, that this correction of -{151} Newton's law will materially affect the mathematical -calculations on the subject, which were made to depend on that law -both by Fourier, Laplace, and Poisson. Probably, however, the -general features of the results will be the same as on the old -supposition. M. Libri, an Italian mathematician, has undertaken one -of the problems of this kind, that of the armil, with Dulong and -Petit's law for his basis, in a Memoir read to the Institute of -France in 1825, and since published at Florence.[21\10] - -[Note 21\10: _Mém. de Math. et de Phys._ 1829.] - - -_Sect._ 6.--_Other Laws of Phenomena with respect to Radiation._ - -THE laws of radiation as depending upon the surface of radiating -bodies, and as affecting screens of various kinds interposed between -the hot body and the thermometer, were examined by several -inquirers. I shall not attempt to give an account of the latter -course of research, and of the different laws which luminous and -non-luminous heat have been found to follow in reference to bodies, -whether transparent or opaque, which intercept them. But there are -two or three laws of the phenomena, depending upon the effects of -the surfaces of bodies, which are important. - -1. In the first place, the powers of bodies to _emit_ and to -_absorb_ heat, as far as depends upon their surface, appear to be in -the same proportion. If we blacken the surface of a canister of hot -water, it radiates heat more copiously; and in the same measure, it -is more readily heated by radiation. - -2. In the next place, as the radiative power increases, the power of -reflection diminishes, and the contrary. A bright metal vessel -reflects much heat; on this very account it does not emit much; and -hence a hot fluid which such a vessel contains, remains hot longer -than it does in an unpolished case. - -3. The heat is emitted from every point of the surface of a hot body -in all directions; but by no means in all directions with equal -intensity. The intensity of the heating ray is as the sine of the -angle which it makes with the surface. - -The last law is entirely, the two former in a great measure, due to -the researches of Leslie, whose _Experimental Inquiry into the -Nature and Propagation of Heat_, published in 1804, contains a great -number of curious and striking results and speculations. The laws -now just {152} stated bear, in a very important manner, upon the -formation of the theory; and we must now proceed to consider what -appears to have been done in this respect; taking into account, it -must still be borne in mind, only the phenomena of conduction and -radiation. - - -_Sect._ 7.--_Fourier's Theory of Radiant Heat._ - -THE above laws of phenomena being established, it was natural that -philosophers should seek to acquire some conception of the physical -action by which they might account, both for these laws, and for the -general fundamental facts of Thermotics; as, for instance, the fact -that all bodies placed in an inclosed space assume, in time, the -temperature of the inclosure. Fourier's explanation of this class of -phenomena must be considered as happy and successful; for he has -shown that the supposition to which we are led by the most simple -and general of the facts, will explain, moreover, the less obvious -laws. It is an obvious and general fact, that bodies which are -included in the space tend to acquire the same temperature. And this -identity of temperature of neighboring bodies requires an -hypothesis, which, it is found, also accounts for Leslie's law of -the sine, in radiation. - -This hypothesis is, that the radiation takes place, not from the -surface alone of the hot body, but from all particles situated -within a certain small depth of the surface. It is easy to -see[22\10] that, on this supposition, a ray emitted obliquely from -an internal particle, will be less intense than one sent forth -perpendicular to the surface, because the former will be intercepted -in a greater degree, having a greater length of path within the -body; and Fourier shows, that whatever be the law of this -intercepting power, the result will be, that the radiative intensity -is as the sine of the angle made by the ray with the surface. - -[Note 22\10: _Mém. Inst._ t. v. 1821, p. 204.] - -But this law is, as I have said, likewise necessary, in order that -neighboring bodies may tend to assume the same temperature: for -instance, in order that a small particle placed within a spherical -shell, should finally assume the temperature of the shell. If the -law of the sines did not obtain, the final temperature of such a -particle would depend upon its place in the inclosure;[23\10] and -within a shell of ice we should have, at certain points, the -temperature of boiling water and of melting iron. - -[Note 23\10: _An. Chim._ iv. 1817, p. 129.] - -This proposition may at first appear strange and unlikely; but it -may {153} be shown to be a necessary consequence of the assumed -principle, by very simple reasoning, which I shall give in a general -form in a Note.[24\10] - -[Note 24\10: The following reasoning may show the connexion of the -law of the sines in radiant heat with the general principle of -ultimate identity of neighboring temperatures. The equilibrium and -identity of temperature between an including shell and an included -body, cannot obtain upon the whole, except it obtain between each -pair of parts of the two surfaces of the body and of the shell; that -is, any part of the one surface, in its exchanges with any part of -the other surface, must give and receive the same quantity of heat. -Now the quantity exchanged, so far as it depends on the receiving -surface, will, by geometry, be proportional to the sine of the -obliquity of that surface: and as, in the exchanges, each may be -considered as receiving, the quantity transferred must be -proportional to the sines of the two obliquities; that is, to that -of the giving as well as of the receiving surface. - -Nor is this conclusion disturbed by the consideration, that all the -rays of heat which fall upon a surface are not absorbed, some being -reflected according to the nature of the surface. For, by the other -above-mentioned laws of phenomena, we know that, in the same measure -in which the surface loses the power of admitting, it loses the -power of emitting, heat; and the superficial parts gain, by -absorbing their own radiation, as much as they lose by not absorbing -the incident heat; so that the result of the preceding reasoning -remains unaltered.] - -This reasoning is capable of being presented in a manner quite -satisfactory, by the use of mathematical symbols, and proves that -Leslie's law of the sines is rigorously and mathematically true on -Fourier's hypothesis. And thus Fourier's theory of _molecular -extra-radiation_ acquires great consistency. - - -_Sect._ 8.--_Discovery of the Polarization of Heat._ - -THE laws of which the discovery is stated in the preceding Sections -of this Chapter, and the explanations given of them by the theories -of conduction and radiation, all tended to make the conception of a -material heat, or _caloric_, communicated by an actual flow and -emission, familiar to men's minds; and, till lately, had led the -greater part of thermotical philosophers to entertain such a view, -as the most probable opinion concerning the nature of heat. But some -steps have recently been made in thermotics, which appear to be -likely to overturn this belief, and to make the doctrine of emission -as untenable with regard to heat, as it had been found to be with -regard to light. I speak of the discovery of the polarization of -heat. It being ascertained that rays of heat are polarized in the -same manner as rays of {154} light, we cannot retain the doctrine -that heat radiates by the emanation of material particles, without -supposing those particles of caloric to have poles; an hypothesis -which probably no one would embrace; for, besides that the ill -fortune which attended that hypothesis in the case of light must -deter speculators from it, the intimate connexion of heat and light -would hardly allow us to suppose polarization in the two cases to be -produced by two different kinds of machinery. - -But, without here tracing further the influence which the -polarization of heat must exercise upon the formation of our -theories of heat, we must briefly notice this important discovery, -as a law of phenomena. - -The analogies and connexions between light and heat are so strong, -that when the polarization of light had been discovered, men were -naturally led to endeavor to ascertain whether heat possessed any -corresponding property. But partly from the difficulty of obtaining -any considerable effect of heat separated from light, and partly -from the want of a thermometrical apparatus sufficiently delicate, -these attempts led, for some time, to no decisive result. M. Berard -took up the subject in 1813. He used Malus's apparatus, and -conceived that he found heat to be polarized by reflection at the -surface of glass, in the same manner as light, and with the same -circumstances.[25\10] But when Professor Powell, of Oxford, a few -years later (1830), repeated these experiments with a similar -apparatus, he found[26\10] that though the heat which is conveyed -along with light is, of course, polarizable, "simple radiant heat," -as he terms it, did not offer the smallest difference in the two -rectangular azimuths of the second glass, and thus showed no trace -of polarization. - -[Note 25\10: _Ann. Chim._ March, 1813.] - -[Note 26\10: _Edin. Journ. of Science_, 1830, vol. ii. p. 303.] - -Thus, with the old thermometers, the point remained doubtful. But -soon after this time, MM. Melloni and Nobili invented an apparatus, -depending on certain galvanic laws, of which we shall have to speak -hereafter, which they called a _thermomultiplier_; and which was -much more sensitive to changes of temperature than any -previously-known instrument. Yet even with this instrument, M. -Melloni failed; and did not, at first, detect any perceptible -polarization of heat by the tourmaline;[27\10] nor did M. -Nobili,[28\10] in repeating M. Berard's experiment. But in this -experiment the attempt was made to polarize heat by reflection from -glass, as light is polarized: and the quantity {155} reflected is so -small that the inevitable errors might completely disguise the whole -difference in the two opposite positions. When Prof. Forbes, of -Edinburgh, (in 1834,) employed mica in the like experiments, he -found a very decided polarizing effect; first, when the heat was -transmitted through several films of mica at a certain angle, and -afterwards, when it was reflected from them. In this case, he found -that with non-luminous heat, and even with the heat of water below -the boiling point, the difference of the heating power in the two -positions of opposite polarity (parallel and _crossed_) was -manifest. He also detected by careful experiments,[29\10] the -polarizing effect of tourmaline. This important discovery was soon -confirmed by M. Melloni. Doubts were suggested whether the different -effect in the opposite positions might not be due to other -circumstances; but Professor Forbes easily showed that these -suppositions were inadmissible; and the property of a difference of -_sides_, which at first seemed so strange when ascribed to the rays -of light, also belongs, it seems to be proved, to the rays of heat. -Professor Forbes also found, by interposing a plate of mica to -intercept the ray of heat in an intermediate point, an effect was -produced in certain positions of the mica analogous to what was -called _depolarization_ in the case of light; namely, a partial -destruction of the differences which polarization establishes. - -[Note 27\10: _Ann. de Chimie_, vol. lv.] - -[Note 28\10: _Bibliothèque Universelle_.] - -[Note 29\10: _Ed. R. S. Transactions_, vol. xiv.; and _Phil. Mag._ -1835, vol. v. p. 209. Ib. vol. vii. p. 349.] - -Before this discovery, M. Melloni had already proved by experiment -that heat is _refracted_ by transparent substances as light is. In -the case of light, the _depolarizing_ effect was afterwards found to -be really, as we have seen, a _dipolarizing_ effect, the ray being -divided into two rays by _double refraction_. We are naturally much -tempted to put the same interpretation upon the dipolarizing effect -in the case of heat; but perhaps the assertion of the analogy -between light and heat to this extent is as yet insecure. - -It is the more necessary to be cautious in our attempt to identify -the laws of light and heat, inasmuch as along with all the -resemblances of the two agents, there are very important -differences. The power of transmitting light, _the diaphaneity_ of -bodies, is very distinct from their power of transmitting heat, -which has been called _diathermancy_ by M. Melloni. Thus both a -plate of alum and a plate of rock-salt transmit nearly the whole -light; but while the first stops nearly the whole heat, the second -stops very little of it; and a plate of opake {156} quartz, nearly -impenetrable by light, allows a large portion of the heat to pass. -By passing the rays through various media, the heat may be, as it -were, _sifted_ from the light which accompanies it. - -[2nd Ed.] [The diathermancy of bodies is distinct from their -diaphaneity, in so far that the same bodies do not exercise the same -powers of selection and suppression of certain rays on heat and on -light; but it appears to be proved by the investigations of modern -thermotical philosophers (MM. De la Roche, Powell, Melloni, and -Forbes), that there is a close analogy between the absorption of -certain colors by transparent bodies, and the absorption of certain -kinds of heat by diathermanous bodies. Dark sources of heat emit -rays which are analogous to blue and violet rays of light; and -highly luminous sources emit rays which are analogous to red rays. -And by measuring the angle of total reflection for heat of different -kinds, it has been shown that the former kind of calorific rays are -really less refrangible than the latter.[30\10] - -[Note 30\10: See Prof. Forbes's _Third Series of Researches on -Heat_, _Edinb. R.S. Trans._ vol. xiv.] - -M. Melloni has assumed this analogy as so completely established, -that he has proposed for this part of thermotics the name -_Thermochroology_ (Qu. _Chromothermotics_?); and along with this -term, many others derived from the Greek, and founded on the same -analogy. If it should appear, in the work which he proposes to -publish on this subject, that the doctrines which he has to state -cannot easily be made intelligible without the use of the terms he -suggests, his nomenclature will obtain currency; but so large a mass -of etymological innovations is in general to be avoided in -scientific works. - -M. Melloni's discovery of the extraordinary power of _rock-salt_ to -transmit heat, and Professor Forbes's discovery of the extraordinary -power of _mica_ to polarize and depolarize heat, have supplied -thermotical inquirers with two new and most valuable -instruments.[31\10]] - -[Note 31\10: For an account of many thermotical researches, which I -have been obliged to pass unnoticed here, see two Reports by Prof. -Powell on the present state of our knowledge respecting Radiant -Heat, in the _Reports of the British Association_ for 1832 and 1840.] - -Moreover, besides the laws of conduction and radiation, many other -laws of the phenomena of heat have been discovered by philosophers; -and these must be taken into account in judging any theory of heat. -To these other laws we must now turn our attention. {157} - - - - -CHAPTER II. - -THE LAWS OF CHANGES OCCASIONED BY HEAT. - - -_Sect._ 1.--_Expansion by Heat.--The Law of Dalton and Gay-Lussac -for Gases._ - -ALMOST all bodies expand by heat; solids, as metals, in a small -degree; fluids, as water, oil, alcohol, mercury, in a greater -degree. This was one of the facts first examined by those who -studied the nature of heat, because this property was used for the -measure of heat. In the _Philosophy of the Inductive Sciences_, Book -iv., Chap. iv., I have stated that secondary qualities, such as -Heat, must be measured by their effects: and in Sect. 4 of that -Chapter I have given an account of the successive attempts which -have been made to obtain measures of heat. I have there also spoken -of the results which were obtained by comparing the rate at which -the expansion of different substances went on, under the same -degrees of heat; or as it was called, the different _thermometrical -march_ of each substance. Mercury appears to be the liquid which is -most uniform in its thermometrical march; and it has been taken as -the most common material of our thermometers; but the expansion of -mercury is not proportional to the heat. De Luc was led, by his -experiments, to conclude "that the dilatations of mercury follow an -accelerated march for equal augmentations of heat." Dalton -conjectured that water and mercury both expand as the square of the -_real temperature_ from the point of greatest contraction: the real -temperature being measured so as to lead to such a result. But none -of the rules thus laid down for the expansion of solids and fluids -appear to have led, as yet, to any certain general laws. - -With regard to gases, thermotical inquirers have been more -successful. Gases expand by heat; and their expansion is governed by -a law which applies alike to all degrees of heat, and to all gaseous -fluids. The law is this: that _for equal increments of temperature -they expand by the same fraction of their own bulk_; which fraction -is _three-eights_ {158} in proceeding from freezing to boiling -water. This law was discovered by Dalton and M. Gay-Lussac -independently of each other;[32\10] and is usually called by both -their names, _the law of Dalton and Gay-Lussac_. The latter -says,[33\10] "The experiments which I have described, and which have -been made with great care, prove incontestably that oxygen, -hydrogen, azotic acid, nitrous acid, ammoniacal acid, muriatic acid, -sulphurous acid, carbonic acid, gases, expand equally by equal -increments of heat." "Therefore," he adds with a proper inductive -generalization, "the result does not depend upon physical -properties, and I collect that _all gases expand equally by heat_." -He then extends this to vapors, as ether. This must be one of the -most important foundation-stones of any sound theory of heat. - -[Note 32\10: _Manch. Mem._ vol. v. 1802; and _Ann. Chim._ xliii. -p. 137.] - -[Note 33\10: Ib. p. 272.] - -[2nd Ed.] Yet MM. Magnus and Regnault conceive that they have -overthrown this law of Dalton and Gay-Lussac, and shown that the -different gases do not expand alike for the same increment of heat. -Magnus found the ratio to be for atmospheric air, 1∙366; for -hydrogen, 1∙365; for carbonic acid, 1∙369; for sulphurous-acid gas, -1∙385. But these differences are not greater than the differences -obtained for the same substances by different observers; and as this -law is referred to in Laplace's hypothesis, hereafter to be -discussed, I do not treat the law as disproved. - -Yet that the rate of expansion of gas in certain circumstances is -different for different substances, must be deemed very probable, -after Dr. Faraday's recent investigations _On the Liquefaction and -Solidification of Bodies generally existing as Gases_,[34\10] by -which it appears that the elasticity of vapors _in contact with -their fluids_ increases at different rates in different substances. -"That the force," he says, "of vapor increases in a geometrical -ratio for equal increments of heat is true for all bodies, but the -ratio is not the same for all. . . . For an increase of pressure -from two to six atmospheres, the following number of degrees require -to be added to the bodies named:--water 69°, sulphureous acid 63°, -cyanogen 64°∙5, ammonia 60°, arseniuretted hydrogen 54°, -sulphuretted hydrogen 56°∙5, muriatic acid 43°, carbonic acid 32°∙5, -nitrous oxide 30°."] - -[Note 34\10: _Phil. Trans._ 1845, Pt. 1.] - -We have already seen that the opinion that the air-thermometer is a -true measure of heat, is strongly countenanced by the symmetry -which, by using it, we introduce into the laws of radiation. If we -{159} accept the law of Dalton and Gay-Lussac, it follows that this -result is independent of any peculiar properties in the air -employed; and thus this measure has an additional character of -generality and simplicity which make it still more probable that it -is the true standard. This opinion is further supported by the -attempts to include such facts in a theory; but before we can treat -of such theories, we must speak of some other doctrines which have -been introduced. - - -_Sect._ 2.--_Specific Heat.--Change of Consistence._ - -IN the attempts to obtain measures of heat, it was found that bodies -had different capacities for heat; for the same quantity of heat, -however measured, would raise, in different degrees, the temperature -of different substances. The notion of different capacities for heat -was thus introduced, and each body was thus assumed to have a -specific _capacity for heat_, according to the quantity of heat -which it required to raise it through a given scale of heat.[35\10] -The term "capacity for heat" was introduced by Dr. Irvine, a pupil -of Dr. Black. For this term, Wilcke, the Swedish physicist, -substituted "specific heat;" in analogy with "specific gravity." - -[Note 35\10: See Crawford, _On Heat_, for the History of Specific -Heat.] - -It was found, also, that the capacity of the same substance was -different in the same substance at different temperatures. It -appears from experiments of MM. Dulong and Petit, that, in general, -the capacity of liquids and solids increases as we ascend in the -scale of temperature. - -But one of the most important thermotic facts is, that by the sudden -contraction of any mass, its temperature is increased. This is -peculiarly observable in gases, as, for example, common air. The -amount of the increase of temperature by sudden condensation, or of -the cold produced by sudden rarefaction, is an important datum, -determining the velocity of sound, as we have already seen, and -affecting many points of meteorology. The coefficient which enters -the calculation in the former case depends on the ratio of two -specific heats of air under different conditions; one belonging to -it when, varying in density, the pressure is constant by which the -air is contained; the other, when, varying in density, it is -contained in a constant space. - -A leading fact, also, with regard to the operation of heat on bodies -{160} is, that it changes their _form_, as it is often called, that -is, their condition as solid, liquid, or air. Since the term "form" -is employed in too many and various senses to be immediately -understood when it is intended to convey this peculiar meaning, I -shall use, instead of it, the term _consistence_, and shall hope to -be excused, even when I apply this word to gases, though I must -acknowledge such phraseology to be unusual. Thus there is a change -of consistence when solids become liquid, or liquids gaseous; and -the laws of such changes must be fundamental facts of our -thermotical theories. We are still in the dark as to many of the -laws which belong to this change; but one of them, of great -importance, has been discovered, and to that we must now proceed. - - -_Sect._ 3.--_The Doctrine of Latent Heat._ - -The Doctrine of Latent Heat refers to such changes of consistence as -we have just spoken of. It is to this effect; that during the -conversion of solids into liquids, or of liquids into vapors, there -is communicated to the body heat which is not indicated by the -thermometer. The heat is absorbed, or becomes _latent_; and, on the -other hand, on the condensation of the vapor to a liquid, or the -liquid to a solid consistency, this heat is again given out and -becomes sensible. Thus a pound of ice requires twenty times as long -a time, in a warm room, to raise its temperature seven degrees, as a -pound of ice-cold water does. A kettle placed on a fire, in four -minutes had its temperature raised to the boiling point, 212°: and -this temperature continued stationary for twenty minutes, when the -whole was boiled away. Dr. Black inferred from these facts that a -large quantity of heat is absorbed by the ice in becoming water, and -by the water in becoming steam. He reckoned from the above -experiments, that ice, in melting, absorbs as much heat as would -raise ice-cold water through 140° of temperature: and that water, in -evaporating, absorbs as much heat as would raise it through 940°. - -That snow requires a great quantity of heat to melt it; that water -requires a great quantity of heat to convert it into steam; and that -this heat is not indicated by a rise in the thermometer, are facts -which it is not difficult to observe; but to separate these from all -extraneous conditions, to group the cases together, and to seize -upon the general law by which they are connected, was an effort of -inductive insight, which has been considered, and deservedly, as one -of the most striking {161} events in the modern history of physics. -Of this step the principal merit appears to belong to Black. - -[2nd Ed.] [In the first edition I had mentioned the names of De Luc -and of Wilcke, in connexion with the discovery of Latent Heat, along -with the name of Black. De Luc had observed, in 1755, that ice, in -melting, did not rise above the freezing-point of temperature till -the whole was melted. De Luc has been charged with plagiarizing -Black's discovery, but, I think, without any just ground. In his -_Idées sur la Météorologique_ (1787), he spoke of Dr. Black as "the -first who had attempted the determinations of the quantities of -latent heat." And when Mr. Watt pointed out to him that from this -expression it might be supposed that Black had not discovered the -fact itself, he acquiesced, and redressed the equivocal expression -in an Appendix to the volume.[36\10] - -[Note 36\10: See his _Letter_ to the Editors of the _Edinburgh -Review_, No. xii. p. 502, of the _Review_.] - -Black never published his own account of the doctrine of Latent -Heat: but he delivered it every year after 1760 in his Lectures. In -1770, a surreptitious publication of his Lectures was made by a -London bookseller, and this gave a view of the leading points of Dr. -Black's doctrine. In 1772, Wilcke, of Stockholm, read a paper to the -Royal Society of that city, in which the absorption of heat by -melting ice is described; and in the same year, De Luc of Geneva -published his _Recherches sur les Modifications de l'Atmosphère_, -which has been alleged to contain the doctrine of latent heat, and -which the author asserts to have been written in ignorance of what -Black had done. At a later period, De Luc, adopting, in part. -Black's expression, gave the name of _latent fire_ to the heat -absorbed.[37\10] - -[Note 37\10: See _Ed. Rev._ No. vi. p. 20.] - -It appears that Cavendish determined the amount of heat produced by -condensing steam, and by thawing snow, as early as 1765. He had -perhaps already heard something of Black's investigations, but did -not accept his term "latent heat".**[38\10]] - -[Note 38\10: See Mr. V. Harcourt's _Address_ to the Brit. Assoc. in -1839, and the _Appendix_.] - -The consequences of Black's principle are very important, for upon -it is founded the whole doctrine of evaporation; besides which, the -principle of latent heat has other applications. But the relations -of aqueous vapor to air are so important, and have been so long a -{162} subject of speculation, that we may with advantage dwell a -little upon them. The part of science in which this is done may be -called, as we have said, Atmology; and to that division of Thermotics -the following chapters belong. - - - -{{163}} -ATMOLOGY. - - - - -CHAPTER III. - -THE RELATION OF VAPOR AND AIR. - - -_Sect._ 1.--_The Boylean Law of the Air's Elasticity._ - -IN the Sixth Book (Chap. iv. Sect. 1.) we have already seen how the -conception on the laws of fluid equilibrium was, by Pascal and others, -extended to air, as well as water. But though air presses and is -pressed as water presses and is pressed, pressure produces upon air an -effect which it does not, in any obvious degree, produce upon water. -Air which is pressed is also _compressed_, or made to occupy a smaller -space; and is consequently also made more dense, or _condensed_; and -on the other hand, when the pressure upon a portion of air is -diminished, the air expands or is rarefied. These broad facts are -evident. They are expressed in a general way by saying that air is an -_elastic_ fluid, yielding in a certain degree to pressure, and -recovering its previous dimensions when the pressure is removed. - -But when men had reached this point, the questions obviously offered -themselves, in what degree and according to what law air yields to -pressure; when it is compressed, what relation does the density bear -to the pressure? The use which had been made of tubes containing -columns of mercury, by which the pressure of portions of air was -varied and measured, suggested obvious modes of devising experiments -by which this question might be answered. Such experiments -accordingly were made by Boyle about 1650; and the result at which -he arrived was, that when air is thus compressed, the density is as -the pressure. Thus if the pressure of the atmosphere in its common -state be equivalent to 30 inches of mercury, as shown by the -barometer; if air included in a tube be pressed by 30 additional -inches of {164} mercury, its density will be doubled, the air being -compressed into one half the space. If the pressure be increased -threefold, the density is also trebled; and so on. The same law was -soon afterwards (in 1676) proved experimentally by Mariotte. And -this law of the air's elasticity, that the density is as the -pressure, is sometimes called the _Boylean Law_, and sometimes the -_Law of Boyle and Mariotte_. - -Air retains its aerial character permanently; but there are other -aerial substances which appear as such, and then disappear or change -into some other condition. Such are termed _vapors_. And the -discovery of their true relation to air was the result of a long -course of researches and speculations. - -[2nd Ed.] [It was found by M. Cagniard de la Tour (in 1823), that at -a certain temperature, a liquid, under sufficient pressure, becomes -clear transparent vapor or gas, having the same bulk as the liquid. -This condition Dr. Faraday calls the _Cagniard de la Tour_ state, -(the _Tourian_ state?) It was also discovered by Dr. Faraday that -carbonic-acid gas, and many other gases, which were long conceived -to be permanently elastic, are really reducible to a liquid state by -pressure.[39\10] And in 1835, M. Thilorier found the means of -reducing liquid carbonic acid to a solid form, by means of the cold -produced in evaporation. More recently Dr. Faraday has added several -substances usually gaseous to the list of those which could -previously be shown in the liquid state, and has reduced others, -including ammonia, nitrous oxide, and sulphuretted hydrogen, to a -solid consistency.[40\10] After these discoveries, we may, I think, -reasonably doubt whether all bodies are not capable of existing in -the three _consistencies_ of solid, liquid, and air. - -[Note 39\10: _Phil. Trans._ 1823.] - -[Note 40\10: Ib. Pt. 1. 1845.] - -We may note that the law of Boyle and Mariotte is not exactly true -near the limit at which the air passes to the liquid state in such -cases as that just spoken of. The diminution of bulk is then more -rapid than the increase of pressure. - -The transition of fluids from a liquid to an airy consistence -appears to be accompanied by other curious phenomena. See Prof. -Forbes's papers on the _Color of Steam under certain circumstances_, -and on the _Colors of the Atmosphere_, in the _Edin. Trans._ vol. -xiv.] {165} - - -_Sect._ 2.--_Prelude to Dalton's Doctrine of Evaporation._ - -VISIBLE clouds, smoke, distillation, gave the notion of Vapor; vapor -was at first conceived to be identical with air, as by Bacon.[41\10] -It was easily collected, that by heat, water might be converted into -vapor. It was thought that air was thus produced, in the instrument -called the _æolipile_, in which a powerful blast is caused by a -boiling fluid; but Wolfe showed that the fluid was not converted -into air, by using camphorated spirit of wine, and condensing the -vapor after it had been formed. We need not enumerate the doctrines -(if very vague hypotheses may be so termed) of Descartes, Dechales, -Borelli.[42\10] The latter accounted for the rising of vapor by -supposing it a mixture of fire and water; and thus, fire being much -lighter than air, the mixture also was light. Boyle endeavored to -show that vapors do not permanently float _in vacuo_. He compared -the mixture of vapor with air to that of salt with water. He found -that the pressure of the atmosphere affected the heat of boiling -water; a very important fact. Boyle proved this by means of the -air-pump; and he and his friends were much surprised to find that -when air was removed, water only just warm boiled violently. Huyghens -mentions an experiment of the same kind made by Papin about 1673. - -[Note 41\10: Bacon's _Hist. Nat._ Cent. i. p. 27.] - -[Note 42\10: They may be seen in Fischer, _Geschichte der Physik_, -vol. ii. p. 175.] - -The ascent of vapor was explained in various ways in succession, -according to the changes which physical science underwent. It was a -problem distinctly treated of, at a period when hydrostatics had -accounted for many phenomena; and attempts were naturally made to -reduce this fact to hydrostatical principles. An obvious hypothesis, -which brought it under the dominion of these principles, was, to -suppose that the water, when converted into vapor, was divided into -small hollow globules;--thin pellicles including air or heat. Halley -gave such an explanation of evaporation; Leibnitz calculated the -dimensions of these little bubbles; Derham managed (as he supposed) -to examine them with a magnifying glass: Wolfe also examined and -calculated on the same subject. It is curious to see so much -confidence in so lame a theory; for if water became hollow globules -in order to rise as vapor, we require, in order to explain the -formation of these globules, new laws of nature, which are not even -hinted at by {166} the supporters of the doctrine, though they must -be far more complex than the hydrostatical law by which a hollow -sphere floats. - -Newton's opinion was hardly more satisfactory; he[43\10] explained -evaporation by the repulsive power of heat; the parts of vapors, -according to him, being small, are easily affected by this force, -and thus become lighter than the atmosphere. - -[Note 43\10: _Opticks_, Qu. 31.] - -Muschenbroek still adhered to the theory of globules, as the -explanation of evaporation; but he was manifestly discontented with -it; and reasonably apprehended that the pressure of the air would -destroy the frail texture of these bubbles. He called to his aid a -rotation of the globules (which Descartes also had assumed); and, -not satisfied with this, threw himself on electrical action as a -reserve. Electricity, indeed, was now in favor, as hydrostatics had -been before; and was naturally called in, in all cases of -difficulty. Desaguliers, also, uses this agent to account for the -ascent of vapor, introducing it into a kind of sexual system of -clouds; according to him, the male fire (heat) does a part, and the -female fire (electricity) performs the rest. These are speculations -of small merit and no value. - -In the mean time, Chemistry made great progress in the estimation of -philosophers, and had its turn in the explanation of the important -facts of evaporation. Bouillet, who, in 1742, placed the particles -of water in the interstices of those of air, may be considered as -approaching to the chemical theory. In 1748, the Academy of Sciences -of Bourdeaux proposed the ascent of vapors as the subject of a -prize; which was adjudged in a manner very impartial as to the -choice of a theory; for it was divided between Kratzenstein, who -advocated the bubbles, (the coat of which he determined to be -1⁄50,000th of an inch thick,) and Hamberger, who maintained the -truth to be the adhesion of particles of water to those of air and -fire. The latter doctrine had become much more distinct in the -author's mind when seven years afterwards (1750) he published his -_Elementa Physices_. He then gave the explanation of evaporation in -a phrase which has since been adopted,--the _solution of water in -air_; which he conceived to be of the same kind as other chemical -solutions. - -This theory of solution was further advocated and developed by Le -Roi;[44\10] and in his hands assumed a form which has been -extensively adopted up to our times, and has, in many instances, -tinged the language commonly used. He conceived that air, like other -solvents, {167} might be _saturated_; and that when the water was -beyond the amount required for saturation, it appeared in a visible -form. The saturating quantity was held to depend mainly on warmth -and wind. - -[Note 44\10: _Ac. R. Sc._ Paris, 1750.] - -This theory was by no means devoid of merit; for it brought together -many of the phenomena, and explained a number of the experiments -which Le Roi made. It explained the facts of the transparency of -vapor, (for perfect solutions are transparent,) the precipitation of -water by cooling, the disappearance of the visible moisture by -warming it again, the increased evaporation by rain and wind; and -other observed phenomena. So far, therefore, the introduction of the -notion of the chemical solution of water in air was apparently very -successful. But its defects are of a very fatal kind; for it does -not at all apply to the facts which take place when air is excluded. - -In Sweden, in the mean time,[45\10] the subject had been pursued in -a different, and in a more correct manner. Wallerius Ericsen had, by -various experiments, established the important fact, that water -evaporates in a _vacuum_. His experiments are clear and -satisfactory; and he inferred from them the falsity of the common -explanation of evaporation by the solution of water in _air_. His -conclusions are drawn in a very intelligent manner. He considers the -question whether water can be changed into air, and whether the -atmosphere is, in consequence, a mere collection of vapors; and on -good reasons, decides in the negative, and concludes the existence -of permanently-elastic air different from vapor. He judges, also, -that there are two causes concerned, one acting to produce the first -ascent of vapors, the other to support them afterwards. The first, -which acts in a vacuum, he conceives to be the mutual repulsion of -the particles; and since this force is independent of the presence -of other substances, this seems to be a sound induction. When the -vapors have once ascended into the air, it may readily be granted -that they are carried higher, and driven from side to side by the -currents of the atmosphere. Wallerius conceives that the vapor will -rise till it gets into air of the same density as itself, and being -then in equilibrium, will drift to and fro. - -[Note 45\10: Fischer, _Gesch. Phys._ vol. v. p. 63.] - -The two rival theories of evaporation, that of _chemical solution_ -and that of _independent vapor_, were, in various forms, advocated -by the next generation of philosophers. De Saussure may be -considered as the leader on one side, and De Luc on the other. The -former maintained the solution theory, with some modifications of -his own. De {168} Luc denied all solution, and held vapor to be a -combination of the particles of water with fire, by which they -became lighter than air. According to him, there is always fire -enough present to produce this combination, so that evaporation goes -on at all temperatures. - -This mode of considering independent vapor as a combination of fire -with water, led the attention of those who adopted that opinion to -the thermometrical changes which take place when vapor is formed and -condensed. These changes are important, and their laws curious. The -laws belong to the induction of latent heat, of which we have just -spoken; but a knowledge of them is not absolutely necessary in order -to enable us to understand the manner in which steam exists in air. - -De Luc's views led him[46\10] also to the consideration of the -effect of pressure on vapor. He explains the fact that pressure will -condense vapor, by supposing that it brings the particles within the -distance at which the repulsion arising from fire ceases. In this -way, he also explains the fact, that though external pressure does -thus condense steam, the mixture of a body of air, by which the -pressure is equally increased, will not produce the same effect; and -therefore, vapors can exist in the atmosphere. They make no fixed -proportion of it; but at the same temperature we have the same -pressure arising _from them_, whether they are in air or not. As the -heat increases, vapor becomes capable of supporting a greater and -greater pressure, and at the boiling heat, it can support the -pressure of the atmosphere. - -[Note 46\10: Fischer, vol. vii. p. 453. _Nouvelles Idées sur la -Météorologie_, 1787.] - -De Luc also marked very precisely (as Wallerius had done) the -difference between vapor and air; the former being capable of change -of _consistence_ by cold or pressure, the latter not so. Pictet, in -1786, made a hygrometrical experiment, which appeared to him to -confirm De Luc's views; and De Luc, in 1792, published a concluding -essay on the subject in the _Philosophical Transactions_. Pictet's -_Essay on Fire_, in 1791, also demonstrated that "all the train of -hygrometrical phenomena takes place just as well, indeed rather -quicker, in a vacuum than in air, provided the same quantity of -moisture is present." This essay, and De Luc's paper, gave the -death-blow to the theory of the solution of water in air. - -Yet this theory did not fall without an obstinate struggle. It was -taken up by the new school of French chemists, and connected with -their views of heat. Indeed, it long appears as the prevalent -opinion. {169} Girtanner,[47\10] in his _Grounds of the -Antiphlogistic Theory_, may be considered as one of the principal -expounders of this view of the matter. Hube, of Warsaw, was, -however, the strongest of the defenders of the theory of solution, -and published upon it repeatedly about 1790. Yet he appears to have -been somewhat embarrassed with the increase of the air's elasticity -by vapor. Parrot, in 1801, proposed another theory, maintaining that -De Luc had by no means successfully attacked that of solution, but -only De Saussure's superfluous additions to it. - -[Note 47\10: Fischer, vol. vii. 473.] - -It is difficult to see what prevented the general reception of the -doctrine of independent vapor; since it explained all the facts very -simply, and the agency of air was shown over and over again to be -unnecessary. Yet, even now, the solution of water in air is hardly -exploded. M. Gay Lussac,[48\10] in 1800, talks of the quantity of -water "held in solution" by the air; which, he says, varies -according to its temperature and density by a law which has not yet -been discovered. And Professor Robison, in the article "Steam," in -the _Encyclopædia Britannica_ (published about 1800), says,[49\10] -"Many philosophers imagine that spontaneous evaporation, at low -temperatures, is produced in this way (by elasticity alone). But we -cannot be of this opinion; and must still think that this kind of -evaporation is produced by the dissolving power of the air." He then -gives some reasons for his opinion. "When moist air is suddenly -rarefied, there is always a precipitation of water. But by this new -doctrine the very contrary should happen, because the tendency of -water to appear in the elastic form is promoted by removing the -external pressure." Another main difficulty in the way of the -doctrine of the mere mixture of vapor and air was supposed to be -this; that if they were so mixed, the heavier fluid would take the -lower part, and the lighter the higher part, of the space which they -occupied. - -[Note 48\10: _Ann. Chim._ tom. xliii.] - -[Note 49\10: Robison's _Works_, ii. 37.] - -The former of these arguments was repelled by the consideration that -in the rarefaction of air, its specific heat is changed, and thus -its temperature reduced below the constituent temperature of the -vapor which it contains. The latter argument is answered by a -reference to Dalton's law of the mixture of gases. We must consider -the establishment of this doctrine in a new section, as the most -material step to the true notion of evaporation. {170} - - -_Sect._ 3.--_Dalton's Doctrine of Evaporation._ - -A PORTION of that which appears to be the true notion of evaporation -was known, with greater or less distinctness, to several of the -physical philosophers of whom we have spoken. They were aware that -the vapor which exists in air, in an invisible state, may be -condensed into water by cold: and they had noticed that, in any -state of the atmosphere, there is a certain temperature lower than -that of the atmosphere, to which, if we depress bodies, water forms -upon them in fine drops like dew; this temperature is thence called -the _dew-point_. The vapor of water which exists anywhere may be -reduced below the degree of heat which is necessary to constitute it -vapor, and thus it ceases to be vapor. Hence this temperature is -also called the _constituent temperature_. This was generally known -to the meteorological speculators of the last century, although, in -England, attention was principally called to it by Dr. Wells's -_Essay on Dew_, in 1814. This doctrine readily explains how the cold -produced by rarefaction of air, descending below the constituent -temperature of the contained vapor, may precipitate a dew; and thus, -as we have said, refutes one obvious objection to the theory of -independent vapor. - -The other difficulty was first fully removed by Mr. Dalton. When his -attention was drawn to the subject of vapor, he saw insurmountable -objections to the doctrine of a chemical union of water and air. In -fact, this doctrine was a mere nominal explanation; for, on closer -examination, no chemical analogies supported it. After some -reflection, and in the sequel of other generalizations concerning -gases, he was led to the persuasion, that when air and steam are -mixed together, each follows its separate laws of equilibrium, the -particles of each being elastic with regard to those of their own -kind only: so that steam may be conceived as flowing among the -particles of air[50\10] "like a stream of water among pebbles;" and -the resistance which air offers to evaporation arises, not from its -weight, but from the inertia of its particles. - -[Note 50\10: _Manchester Memoirs_, vol. v. p. 581.] - -It will be found that the theory of independent vapor, understood -with these conditions, will include all the facts of the -case;--gradual evaporation in air; sudden evaporation in a vacuum; -the increase of {171} the air's elasticity by vapor; condensation by -its various causes; and other phenomena. - -But Mr. Dalton also made experiments to prove his fundamental -principle, that if two different gases communicate, they will -diffuse themselves through each other;[51\10]--slowly, if the -opening of communication be small. He observes also, that all the -gases had equal solvent powers for vapor, which could hardly have -happened, had chemical affinity been concerned. Nor does the density -of the air make any difference. - -[Note 51\10: _New System of Chemical Philosophy_, vol. i. p. 151.] - -Taking all these circumstances into the account, Mr. Dalton -abandoned the idea of solution. "In the autumn of 1801," he says, "I -hit upon an idea which seemed to be exactly calculated to explain -the phenomena of vapor: it gave rise to a great variety of -experiments," which ended in fixing it in his mind as a true idea. -"But," he adds, "the theory was almost universally misunderstood, -and consequently reprobated." - -Mr. Dalton answers various objections. Berthollet had urged that we -can hardly conceive the particles of an elastic substance added to -those of another, without increasing its elasticity. To this Mr. -Dalton replies by adducing the instance of magnets, which repel each -other, but do not repel other bodies. One of the most curious and -ingenious objections is that of M. Gough, who argues, that if each -gas is elastic with regard to itself alone, we should hear, produced -by one stroke, four sounds; namely, _first_, the sound through -aqueous vapor; _second_, the sound through azotic gas; _third_, the -sound through oxygen gas; _fourth_, the sound through carbonic acid. -Mr. Dalton's answer is, that the difference of time at which these -sounds would come is very small; and that, in fact, we do hear, -sounds double and treble. - -In his _New System of Chemical Philosophy_, Mr. Dalton considers the -objections of his opponents with singular candor and impartiality. -He there appears disposed to abandon that part of the theory which -negatives the mutual repulsion of the particles of the two gases, -and to attribute their diffusion through one another to the -different size of the particles, which would, he thinks,[52\10] -produce the same effect. - -[Note 52\10: _New System_, vol. i. p. 188.] - -In selecting, as of permanent importance, the really valuable part -of this theory, we must endeavor to leave out all that is doubtful -or unproved. I believe it will be found that in all theories -hitherto {172} promulgated, all assertions respecting the properties -of the particles of bodies, their sizes, distances, attractions, and -the like, are insecure and superfluous. Passing over, then, such -hypotheses, the inductions which remain are these;--that two gases -which are in communication will, by the elasticity of each, diffuse -themselves in one another, quickly or slowly; and--that the quantity -of steam contained in a certain space of air is the same, whatever -be the air, whatever be its density, and even if there be a vacuum. -These propositions may be included together by saying, that one gas -is _mechanically mixed_ with another; and we cannot but assent to -what Mr. Dalton says of the latter fact,--"this is certainly the -touchstone of the mechanical and chemical theories." This _doctrine -of the mechanical mixture of gases_ appears to supply answers to all -the difficulties opposed to it by Berthollet and others, as Mr. -Dalton has shown;[53\10] and we may, therefore, accept it as well -established. - -[Note 53\10: _New System_, vol. i. p. 160, &c.] - -This doctrine, along with the _principle of the constituent -temperature of steam_, is applicable to a large series of -meteorological and other consequences. But before considering the -applications of theory to natural phenomena, which have been made, -it will be proper to speak of researches which were carried on, in a -great measure, in consequence of the use of steam in the arts: I -mean the laws which connect its elastic force with its constituent -temperature. - - -_Sect._ 4.--_Determination of the Laws of the Elastic Force of -Steam._ - -THE expansion of aqueous vapor at different temperatures is -governed, like that of all other vapors, by the law of Dalton and -Gay-Lussac, already mentioned; and from this, its elasticity, when -its expansion is resisted, will be known by the law of Boyle and -Mariotte; namely, by the rule that the pressure of airy fluids is as -the condensation. But it is to be observed, that this process of -calculation goes on the supposition that the steam is cut off from -contact with water, so that no more steam can be generated; a case -quite different from the common one, in which the steam is more -abundant as the heat is greater. The examination of the force of -vapor, when it is in contact with water, must be briefly noticed. - -During the period of which we have been speaking, the progress of -the investigation of the laws of aqueous vapor was much accelerated -{173} by the growing importance of the steam-engine, in which those -laws operated in a practical form. James Watts, the main improver of -that machine, was thus a great contributor to speculative knowledge, -as well as to practical power. Many of his improvements depended on -the laws which regulate the quantity of heat which goes to the -formation or condensation of steam; and the observations which led -to these improvements enter into the induction of latent heat. -Measurements of the force of steam, at all temperatures, were made -with the same view. Watts's attention had been drawn to the -steam-engine in 1759, by Robison, the former being then an -instrument-maker, and the latter a student at the University of -Glasgow.[54\10] In 1761 or 1762, he tried some experiments on the -force of steam in a Papin's Digester;[55\10] and formed a sort of -working model of a steam-engine, feeling already his vocation to -develope the powers of that invention. His knowledge was at that -time principally derived from Desaguliers and Belidor, but his own -experiments added to it rapidly. In 1764 and 1765, he made a more -systematical course of experiments, directed to ascertain the force -of steam. He tried this force, however, only at temperatures above -the boiling-point; and inferred it at lower degrees from the -supposed continuity of the law thus obtained. His friend Robison, -also, was soon after led, by reading the account of some experiments -of Lord Charles Cavendish, and some others of Mr. Nairne, to examine -the same subject. He made out a table of the correspondence of the -elasticity and the temperature of vapor, from thirty-two to two -hundred and eighty degrees of Fahrenheit's thermometer.[56\10] The -thing here to be remarked, is the establishment of a law of the -pressure of steam, down to the freezing-point of water. Ziegler of -Basle, in 1769, and Achard of Berlin, in 1782, made similar -experiments. The latter examined also the elasticity of the vapor of -alcohol. Betancourt, in 1792, published his Memoir on the expansive -force of vapors; and his tables were for some time considered the -most exact. {174} Prony, in his _Architecture Hydraulique_ (1796), -established a mathematical formula,[57\10] on the experiments of -Betancourt, who began his researches in the belief that he was first -in the field, although he afterwards found that he had been -anticipated by Ziegler. Gren compared the experiments of Betancourt -and De Luc with his own. He ascertained an important fact, that when -water _boils_, the elasticity of the steam is equal to that of the -atmosphere. Schmidt at Giessen endeavored to improve the apparatus -used by Betancourt; and Biker, of Rotterdam, in 1800, made new -trials for the same purpose. - -[Note 54\10: Robison's _Works_, vol. ii. p. 113.] - -[Note 55\10: Denis Papin, who made many of Boyle's experiments for -him, had discovered that if the vapor be prevented from rising, the -water becomes hotter than the usual boiling-point; and had hence -invented the instrument called _Papin's Digester_. It is described -in his book, _La manière d'amolir les os et de faire cuire toutes -sorts de viandes en fort peu de temps et à peu de frais_. Paris, -1682.] - -[Note 56\10: These were afterwards published in the _Encyclopædia -Britannica_; in the article "Steam," written by Robison.] - -[Note 57\10: _Architecture Hydraulique_, Seconde Partie, p. 163.] - -In 1801, Mr. Dalton communicated to the Philosophical Society of -Manchester his investigations on this subject; observing truly, that -though the forces at high temperatures are most important when steam -is considered as a mechanical agent, the progress of philosophy is -more immediately interested in accurate observations on the force at -low temperatures. He also found that his elasticities for -equidistant temperatures resembled a _geometrical progression_, but -with a ratio constantly diminishing. Dr. Ure, in 1818, published in -the _Philosophical Transactions_ of London, experiments of the same -kind, valuable from the high temperatures at which they were made, -and for the simplicity of his apparatus. The law which he thus -obtained approached, like Dalton's, to a _geometrical progression_. -Dr. Ure says, that a formula proposed by M. Biot gives an error of -near nine inches out of seventy-five, at a temperature of 266 -degrees. This is very conceivable, for if the formula be wrong at -all, the geometrical progress rapidly inflames the error in the -higher portions of the scale. The elasticity of steam, at high -temperatures, has also been experimentally examined by Mr. Southern, -of Soho, and Mr. Sharpe, of Manchester. Mr. Dalton has attempted to -deduce certain general laws from Mr. Sharpe's experiments; and other -persons have offered other rules, as those which govern the force of -steam with reference to the temperature: but no rule appears yet to -have assumed the character of an established scientific truth. Yet -the law of the expansive force of steam is not only required in -order that the steam-engine may be employed with safety and to the -best advantage; but must also be an important point in every -consistent thermotical theory. - -[2nd Ed.] [To the experiments on steam made by private physicists, -are to be added the experiments made on a grand scale by order of -the governments of France and of America, with a view to {175} -legislation on the subject of steam-engines. The French experiments -were made in 1823, under the direction of a commission consisting of -some of the most distinguished members of the Academy of Sciences; -namely, MM. de Prony, Arago, Girard, and Dulong. The American -experiments were placed in the hands of a committee of the Franklin -Institute of the State of Pennsylvania, consisting of Prof. Bache -and others, in 1830. The French experiments went as high as 435° of -Fahrenheit's thermometer, corresponding to a pressure of 60 feet of -mercury, or 24 atmospheres. The American experiments were made up to -a temperature of 346°, which corresponded to 274 inches of mercury, -more than 9 atmospheres. The extensive range of these experiments -affords great advantages for determining the law of the expansive -force. The French Academy found that their experiments indicated an -increase of the elastic force according to the _fifth_ power of a -binominal 1 + _mt_, where _t_ is the temperature. The American -Institute were led to a _sixth_ power of a like binominal. Other -experimenters have expressed their results, not by powers of the -temperature, but by geometrical ratios. Dr. Dalton had supposed that -the expansion of mercury being as the square of the true temperature -above its freezing-point, the expansive force of steam increases in -geometrical ratio for equal increments of temperature. And the -author of the article _Steam_ in the Seventh Edition of the -_Encyclopædia Britannica_ (Mr. J. S. Russell), has found that the -experiments are best satisfied by supposing mercury, as well as -steam, to expand in a geometrical ratio for equal increments of the -true temperature. - -It appears by such calculation, that while dry gas increases in the -ratio of 8 to 11, by an increase of temperature from freezing to -boiling water; steam in contact with water, by the same increase of -temperature above boiling water, has its expansive force increased -in the proportion of 1 to 12. By an equal increase of temperature, -mercury expands in about the ratio of 8 to 9. - -Recently, MM. Magnus of Berlin, Holzmann and Regnault, have made -series of observations on the relation between temperature and -elasticity of steam.[58\10] - -[Note 58\10: See Taylor's _Scientific Memoirs_, Aug. 1845, vol. iv. -part xiv., and _Ann. de Chimie_.] - -Prof. Magnus measured his temperatures by an air-thermometer; a -process which, I stated in the first edition, seemed to afford the -best promise of simplifying the law of expansion. His result is, -that the {176} elasticity proceeds in a geometric series when the -temperature proceeds in an arithmetical series nearly; the -differences of temperature for equal augmentations of the ratio of -elasticity being somewhat greater for the higher temperatures. - -The forces of the vapors of other liquids in contact with their -liquids, determined by Dr. Faraday, as mentioned in Chap. ii. Sect. -1, are analogous to the elasticity of steam here spoken of.] - - -_Sect._ 5.--_Consequences of the Doctrine of -Evaporation.--Explanation of Rain, Dew, and Clouds._ - -THE discoveries concerning the relations of heat and moisture which -were made during the last century, were principally suggested by -meteorological inquiries, and were applied to meteorology as fast as -they rose. Still there remains, on many points of this subject, so -much doubt and obscurity, that we cannot suppose the doctrines to -have assumed their final form; and therefore we are not here called -upon to trace their progress and connexion. The principles of -atmology are pretty well understood; but the difficulty of observing -the conditions under which they produce their effects in the -atmosphere is so great, that the precise theory of most -meteorological phenomena is still to be determined. - -We have already considered the answers given to the question: -According to what rules does transparent aqueous vapor resume its -form of visible water? This question includes, not only the problems -of Rain and Dew, but also of Clouds; for clouds are not vapor, but -water, vapor being always invisible. An opinion which attracted much -notice in its time, was that of Hutton, who, in 1784, endeavored to -prove that if two masses of air saturated with transparent vapor at -different temperatures are mixed together, the precipitation of -water in the form either of cloud or of drops will take place. The -reason he assigned for the opinion was this: that the temperature of -the mixture is a mean between the two temperatures, but that the -force of the vapor in the mixture, which is the mean of the forces -of the two component vapors, will be greater than that which -corresponds to the mean temperature, since the force increases -faster than the temperature;[59\10] and hence some part of the vapor -will be precipitated. This doctrine, it will be seen, speaks of -vapor as "saturating" air, and is {177} therefore, in this form, -inconsistent with Dalton's principle; but it is not difficult to -modify the expression so as to retain the essential part of the -explanation. - -[Note 59\10: _Edin. Trans._ vol. 1. p. 42.] - -_Dew._--The principle of a "constituent temperature" of steam, and -the explanation of the "dew-point," were known, as we have said -(chap. iii. sect. 3,) to the meteorologists of the last century; but -we perceive how incomplete their knowledge was, by the very gradual -manner in which the consequences of this principle were traced out. -We have already noticed, as one of the books which most drew -attention to the true doctrine, in this country at least, Dr. -Wells's _Essay on Dew_, published in 1814. In this work the author -gives an account of the progress of his opinions;[60\10] "I was -led," he says, "in the autumn of 1784, by the event of a rude -experiment, to think it probable that the formation of dew is -attended with the production of cold." This was confirmed by the -experiments of others. But some years after, "upon considering the -subject more closely, I began to suspect that Mr. Wilson, Mr. Six, -and myself, had all committed an error in regarding the cold which -accompanies the dew, as an _effect_ of the formation of the dew." He -now considered it rather as the _cause_: and soon found that he was -able to account for the circumstances of this formation, many of -them curious and paradoxical, by supposing the bodies on which dew -is deposited, to be cooled down, by radiation into the clear -night-sky, to the proper temperature. The same principle will -obviously explain the formation of mists over streams and lakes when -the air is cooler than the water; which was put forward by Davy, -even in 1810, as a new doctrine, or at least not familiar. - -[Note 60\10: _Essay on Dew_, p. 1.] - -_Hygrometers._--According as air has more or less of vapor in -comparison with that which its temperature and pressure enable it to -contain, it is more or less humid; and an instrument which measures -the degrees of such a gradation is a _hygrometer_. The hygrometers -which were at first invented, were those which measured the moisture -by its effect in producing expansion or contraction in certain -organic substances; thus De Saussure devised a hair-hygrometer, De -Luc a whalebone-hygrometer, and Dalton used a piece of whipcord. All -these contrivances were variable in the amount of their indications -under the same circumstances; and, moreover, it was not easy to know -the physical meaning of the degree indicated. The dew-point, or -constituent temperature of the vapor which exists in the air, is, on -{178} the other hand, both constant and definite. The determination -of this point, as a datum for the moisture of the atmosphere, was -employed by Le Roi, and by Dalton (1802), the condensation being -obtained by cold water:[61\10] and finally, Mr. Daniell (1812) -constructed an instrument, where the condensing temperature was -produced by evaporation of ether, in a very convenient manner. This -invention (_Daniell's Hygrometer_) enables us to determine the -quantity of vapor which exists in a given mass of the atmosphere at -any time of observation. - -[Note 61\10: Daniell, _Met. Ess._ p. 142. _Manch. Mem._ vol. v. -p. 581.] - -[2nd Ed.] [As a happy application of the Atmological Laws which have -been discovered, I may mention the completion of the theory and use -of the _Wet-bulb Hygrometer_; an instrument in which, from the -depression of temperature produced by wetting the bulb of a -thermometer, we infer the further depression which would produce -dew. Of this instrument the history is thus summed up by Prof. -Forbes:--"Hutton invented the method; Leslie revived and extended -it, giving probably the earliest, though an imperfect theory; -Gay-Lussac, by his excellent experiments and reasoning from them, -completed the theory, so far as perfectly dry air is concerned; -Ivory extended the theory; which was reduced to practice by Auguste -and Bohnenberger, who determined the constant with accuracy. English -observers have done little more than confirm the conclusions of our -industrious Germanic neighbors; nevertheless the experiments of -Apjohn and Prinsep must ever be considered as conclusively settling -the value of the coefficient near the one extremity of the scale, as -those of Kæmtz have done for the other."[62\10] - -[Note 62\10: _Second Report on Meteorology_, p. 101.] - -Prof. Forbes's two Reports _On the Recent Progress and Present State -of Meteorology_ given among the _Reports of the British Association_ -for 1832 and 1840, contain a complete and luminous account of recent -researches on this subject. It may perhaps be asked why I have not -given Meteorology a place among the Inductive Sciences; but if the -reader refers to these accounts, or any other adequate view of the -subject, he will see that Meteorology is not a single Inductive -Science, but the application of several sciences to the explanation -of terrestrial and atmospheric phenomena. Of the sciences so -applied, Thermotics and Atmology are the principal ones. But others -also come into play; as Optics, in the explanation of Rainbows, -Halos, {179} Parhelia, Coronæ, Glories, and the like; Electricity, -in the explanation of Thunder and Lightning, Hail, Aurora Borealis; -to which others might be added.] - -_Clouds._--When vapor becomes visible by being cooled below its -constituent temperature, it forms itself into a very fine watery -powder, the diameter of the particles of which this powder consists -being very small: they are estimated by various writers, from -1⁄100,000th to 1⁄20,000th of an inch.[63\10] Such particles, even if -solid, would descend very slowly; and very slight causes would -suffice for their suspension, without recurring to the hypothesis of -vesicles, of which we have already spoken. Indeed that hypothesis -will not explain the fact, except we suppose these vesicles filled -with a rarer air than that of the atmosphere; and, accordingly, -though this hypothesis is still maintained by some,[64\10] it is -asserted as a fact of observation, proved by optical or other -phenomena, and not deduced from the suspension of clouds. Yet the -latter result is still variously explained by different -philosophers: thus, M. Gay-Lussac[65\10] accounts for it by upward -currents of air, and Fresnel explains it by the heat and rarefaction -of air in the interior of the cloud. - -[Note 63\10: Kæmtz, _Met._ i. 393.] - -[Note 64\10: Ib. i. 393. Robison, ii. 13.] - -[Note 65\10: _Ann. Chim._ xxv. 1822.] - -_Classification of Clouds._--A classification of clouds can then -only be consistent and intelligible when it rests upon their -atmological conditions. Such a system was proposed by Mr. Luke -Howard, in 1802-3. His primary modifications are, _Cirrus_, -_Cumulus_, and _Stratus_, which the Germans have translated by terms -equivalent in English to _feather-cloud_, _heap-cloud_, and -_layer-cloud_. The cumulus increases by accumulations on its top, -and floats in the air with a horizontal base; the stratus grows from -below, and spreads along the earth; the cirrus consists of fibres in -the higher regions of the atmosphere, which grow every way. Between -the simple modifications are intermediate ones, _cirro-cumulus_ and -_cirro-stratus_; and, again, compound ones, the _cumulo-stratus_ and -the _nimbus_, or _rain-cloud_. These distinctions have been -generally accepted all over Europe: and have rendered a description -of all the processes which go on in the atmosphere far more definite -and clear than it could be made before their use. - -I omit a mass of facts and opinions, supposed laws of phenomena and -assigned causes, which abound in meteorology more than in any other -science. The slightest consideration will show us what a great {180} -amount of labor, of persevering and combined observation, the -progress of this branch of knowledge requires. I do not even speak -of the condition of the more elevated parts of the atmosphere. The -diminution of temperature as we ascend, one of the most marked of -atmospheric facts, has been variously explained by different -writers. Thus Dalton[66\10] (1808) refers it to a principle "that -each atom of air, in the same perpendicular column, is possessed of -the same degree of heat," which principle he conceives to be -entirely empirical in this case. Fourier says[67\10] (1817), "This -phenomenon results from several causes: one of the principal is the -progressive extinction of the rays of heat in the successive strata -of the atmosphere." - -[Note 66\10: _New Syst. of Chem._ vol. i. p. 125.] - -[Note 67\10: _Ann. Chim._ vi. 285.] - -Leaving, therefore, the application of thermotical and atmological -principles in particular cases, let us consider for a moment the -general views to which they have led philosophers. - - - - -CHAPTER IV. - -PHYSICAL THEORIES OF HEAT. - - -WHEN we look at the condition of that branch of knowledge which, -according to the phraseology already employed, we must call _Physical -Thermotics_, in opposition to Formal Thermotics, which gives us -detached laws of phenomena, we find the prospect very different from -that which was presented to us by physical astronomy, optics, and -acoustics. In these sciences, the maintainers of a distinct and -comprehensive theory have professed at least to show that it -explains and includes the principal laws of phenomena of various -kinds; in Thermotics, we have only attempts to explain a part of the -facts. We have here no example of an hypothesis which, assumed in -order to explain one class of phenomena, has been found also to -account exactly for another; as when central forces led to the -precession of the equinoxes, or when the explanation of polarization -explained also double refraction; or when the pressure of the -atmosphere, as measured by the barometer, gave the true velocity of -sound. Such coincidences, or _consiliences_, as I have elsewhere -called them, are the test of truth; and thermotical theories cannot -yet exhibit credentials of this kind. {181} - -On looking back at our view of this science, it will be seen that it -may be distinguished into two parts; the Doctrines of Conduction and -Radiation, which we call Thermotics proper; and the Doctrines -respecting the relation of Heat, Airs, and Moisture, which we have -termed Atmology. These two subjects differ in their bearing on our -hypothetical views. - -_Thermotical Theories._--The phenomena of radiant heat, like those -of radiant light, obviously admit of general explanation in two -different ways;--by the emission of material particles, or by the -propagation of undulations. Both these opinions have found -supporters. Probably most persons, in adopting Prevost's theory of -exchanges, conceive the radiation of heat to be the radiation of -matter. The undulation hypothesis, on the other hand, appears to be -suggested by the production of heat by friction, and was accordingly -maintained by Rumford and others. Leslie[68\10] appears, in a great -part of his _Inquiry_, to be a supporter of some undulatory -doctrine, but it is extremely difficult to make out what his -undulating medium is; or rather, his opinions wavered during his -progress. In page 31, he asks, "What is this calorific and -frigorific fluid? and after keeping the reader in suspense for a -moment, he replies, - "Quod petis hic est. -It is merely the ambient AIR." But at page 150, he again asks the -question, and, at page 188, he answers, "It is the same subtile -matter that, according to its different modes of existence, -constitutes either heat or light." A person thus vacillating between -two opinions, one of which is palpably false, and the other laden -with exceeding difficulties which he does not even attempt to -remove, had little right to protest against[69\10] "the sportive -freaks of some intangible _aura_;" to rank all other hypotheses than -his own with the "occult qualities of the schools;" and to class the -"prejudices" of his opponents with the tenets of those who -maintained the _fuga vacui_ in opposition to Torricelli. It is worth -while noticing this kind of rhetoric, in order to observe, that it -may be used just as easily on the wrong side as on the right. - -[Note 68\10: _An Experimental Inquiry into the Nature and -Propagation of Heat_, 1804.] - -[Note 69\10: Ib. p. 47.] - -Till recently, the theory of material heat, and of its propagation -by emission, was probably the one most in favor with those who had -studied mathematical thermotics. As we have said, the laws of {182} -conduction, in their ultimate analytical form, were almost identical -with the laws of motion of fluids. Fourier's principle also, that -the radiation of heat takes place from points below the surface, and -is intercepted by the superficial particles, appears to favor the -notion of material emission. - -Accordingly, some of the most eminent modern French mathematicians -have accepted and extended the hypothesis of a material caloric. In -addition to Fourier's doctrine of molecular extra-radiation, Laplace -and Poisson have maintained the hypothesis of _molecular -intra-radiation_, as the mode in which conduction takes place; that -is, they say that the particles of bodies are to be considered as -_discrete_, or as points separated from each other, and acting on -each other at a distance; and the conduction of heat from one part -to another, is performed by radiation between all neighboring -particles. They hold that, without this hypothesis, the differential -equations expressing the conditions of conduction cannot be made -homogeneous: but this assertion rests, I conceive, on an error, as -Fourier has shown, by dispensing with the hypothesis. The necessity -of the hypothesis of discrete molecular action in bodies, is -maintained in all cases by M. Poisson; and he has asserted Laplace's -theory of capillary attraction to be defective on this ground, as -Laplace asserted Fourier's reasoning respecting heat to be so. In -reality, however, this hypothesis of discrete molecules cannot be -maintained as a physical truth; for the law of molecular action, -which is assumed in the reasoning, after answering its purpose in -the progress of calculation, vanishes in the result; the conclusion -is the same, whatever law of the intervals of the molecules be -assumed. The definite integral, which expresses the whole action, no -more proves that this action is actually made of the differential -parts by means of which it was found, than the processes of finding -the weight of a body by integration, prove it to be made up of -differential weights. And therefore, even if we were to adopt the -emission theory of heat, we are by no means bound to take along with -it the hypothesis of discrete molecules. - -But the recent discovery of the refraction, polarization, and -depolarization of heat, has quite altered the theoretical aspect of -the subject, and, almost at a single blow, ruined the emission -theory. Since heat is reflected and refracted like light, analogy -would lead us to conclude that the mechanism of the processes is the -same in the two cases. And when we add to these properties the -property of polarization, it is scarcely possible to believe -otherwise than that heat consists in {183} transverse vibrations; -for no wise philosopher would attempt an explanation by ascribing -poles to the emitted particles, after the experience which Optics -affords, of the utter failure of such machinery. - -But here the question occurs, If heat consists in vibrations, whence -arises the extraordinary identity of the laws of its propagation -with the laws of the flow of matter? How is it that, in conducted -heat, this vibration creeps slowly from one part of the body to -another, the part first heated remaining hottest; instead of leaving -its first place and travelling rapidly to another, as the vibrations -of sound and light do? The answer to these questions has been put in -a very distinct and plausible form by that distinguished -philosopher, M. Ampère, who published a _Note on Heat and Light -considered as the results of Vibratory Motion_,[70\10] in 1834 and -1835; and though this answer is an hypothesis, it at least shows -that there is no fatal force in the difficulty. - -[Note 70\10: _Bibliothèque Universelle de Genève_, vol. xlix. p. -225. _Ann. Chim._ tom. lvii. p. 434.] - -M. Ampère's hypothesis is this; that bodies consist of solid -molecules, which may be considered as arranged at intervals in a -very rare ether; and that the vibrations of the molecules, causing -vibrations of the ether and caused by them, constitute heat. On -these suppositions, we should have the phenomena of conduction -explained; for if the molecules at one end of a bar be hot, and -therefore in a state of vibration, while the others are at rest, the -vibrating molecules propagate vibrations in the ether, but these -vibrations do not produce heat, except in proportion as they put the -quiescent molecules of the bar in vibration; and the ether being -very rare compared with the molecules, it is only by the repeated -impulses of many successive vibrations that the nearest quiescent -molecules are made to vibrate; after which they combine in -communicating the vibration to the more remote molecules. "We then -find necessarily," M. Ampère adds, "the same equations as those -found by Fourier for the distribution of heat, setting out from the -same hypothesis, that the temperature or heat transmitted is -proportional to the difference of the temperatures." - -Since the undulatory hypothesis of heat can thus answer all obvious -objections, we may consider it as upon its trial, to be confirmed or -modified by future discoveries; and especially by an enlarged -knowledge of the laws of the polarization of heat. - -[2nd Ed.] [Since the first edition was written, the analogies -between light and heat have been further extended, as I have already -stated. It {184} has been discovered by MM. Biot and Melloni that -quartz impresses a circular polarization upon heat; and by Prof. -Forbes that mica, of a certain thickness, produces phenomena such as -would be produced by the impression of circular polarization of the -supposed transversal vibrations of radiant heat; and further, a -rhomb of rock-salt, of the shape of the glass rhomb which verified -Fresnel's extraordinary anticipation of the circular polarization of -light, verified the expectation, founded upon other analogies, of -the polarization of heat. By passing polarized heat through various -thicknesses of mica, Prof. Forbes has attempted to calculate the -length of an undulation for heat. - -These analogies cannot fail to produce a strong disposition to -believe that light and heat, essences so closely connected that they -can hardly be separated, and thus shown to have so many curious -properties in common, are propagated by the same machinery; and thus -we are led to an Undulatory Theory of Heat. - -Yet such a Theory has not yet by any means received full -confirmation. It depends upon the analogy and the connexion of the -Theory of Light, and would have little weight if those were removed. -For the separation of the rays in double refraction, and the -phenomena of periodical intensity, the two classes of facts out of -which the Undulatory Theory of Optics principally grew, have neither -of them been detected in thermotical experiments. Prof. Forbes has -assumed alternations of heat for increasing thicknesses of mica, but -in his experiments we find only one _maximum_. The occurrence of -alternate maxima and minima under the like circumstances would -exhibit visible waves of heat, as the fringes of shadows do of -light, and would thus add much to the evidence of the theory. - -Even if I conceived the Undulatory Theory of Heat to be now -established, I should not venture, as yet, to describe its -establishment as an event in the history of the Inductive Sciences. -It is only at an interval of time after such events have taken place -that their history and character can be fully understood, so as to -suggest lessons in the Philosophy of Science.] - -_Atmological Theories._--Hypotheses of the relations of heat and air -almost necessarily involve a reference to the forces by which the -composition of bodies is produced, and thus cannot properly be -treated of, till we have surveyed the condition of chemical -knowledge. But we may say a few words on one such hypothesis; I mean -the hypothesis on the subject of the atmological laws of heat, -proposed by Laplace, in the twelfth Book of the _Mécanique Céléste_, -and published in 1823. {185} It will be recollected that the main -laws of phenomena for which we have to account, by means of such an -hypothesis, are the following:-- - -(1.) The law of Boyle and Mariotte, that the elasticity of an air -varies as its density. See Chap. iii., Sect. 1 of this Book. - -(2.) The Law of Gay-Lussac and Dalton, that all airs expand equally -by heat. See Chap. ii. Sect. 1. - -(3.) The production of heat by sudden compression. See Chap. ii. -Sect. 2. - -(4.) Dalton's principle of the mechanical mixture of airs. See Chap. -iii. Sect. 3. - -(5.) The Law of expansion of solids and fluids by heat. See Chap. -ii. Sect. 1. - -(6.) Changes of consistence by heat, and the doctrine of latent -heat. See Chap. ii. Sect. 3. - -(7.) The Law of the expansive force of steam. See Chap. iii. Sect. 4. - -Besides these, there are laws of which it is doubtful whether they -are or are not included in the preceding, as the low temperature of -the air in the higher parts of the atmosphere. (See Chap. iii. -Sect. 5.) - -Laplace's hypothesis[71\10] is this:--that bodies consist of -particles, each of which gathers round it, by its attraction, a -quantity of caloric: that the particles of the bodies attract each -other, besides attracting the caloric, and that the particles of the -caloric repel each other. - -[Note 71\10: _Méc. Cél._ t. v. p. 89.] - -In gases, the particles of the bodies are so far removed, that their -mutual attraction is insensible, and the matter tends to expand by -the mutual repulsion of the caloric. He conceives this caloric to be -constantly radiating among the particles; the density of this -internal radiation is the _temperature_, and he proves that, on this -supposition, the elasticity of the air will be as the density, and -as this temperature. Hence follow the three first rules above -stated. The same suppositions lead to Dalton's principle of mixtures -(4), though without involving his mode of conception; for Laplace -says that whatever the mutual action of two gases be, the whole -pressure will be equal to the sum of the separate pressures.[72\10] -Expansion (5), and the changes of consistence (6), are explained by -supposing[73\10] that in solids, the mutual attraction of the -particles of the body is the greatest force; in liquids, the -attraction of the particles for the caloric; in airs, the repulsion -of {186} the caloric. But the doctrine of latent heat again -modifies[74\10] the hypothesis, and makes it necessary to include -latent heat in the calculation; yet there is not, as we might -suppose there would be if the theory were the true one, any -confirmation of the hypothesis resulting from the new class of laws -thus referred to. Nor does it appear that the hypothesis accounts -for the relation between the elasticity and the temperature of steam. - -[Note 72\10: Ib. p. 110.] - -[Note 73\10: Ib. p. 92.] - -[Note 74\10: _Méc. Cél._ t. v. p. 93.] - -It will be observed that Laplace's hypothesis goes entirely upon the -materiality of heat, and is inconsistent with any vibratory theory; -for, as Ampère remarks, "It is clear that if we admit heat to -consist in vibrations, it is a contradiction to attribute to heat -(or caloric) a repulsive force of the particles which would be a -cause of vibration." - -An unfavorable judgment of Laplace's Theory of Gases is suggested by -looking for that which, in speaking of Optics, was mentioned as the -great characteristic of a true theory; namely, that the hypotheses, -which were assumed in order to account for one class of facts, are -found to explain another class of a different nature:--the consilience -of inductions. Thus, in thermotics, the law of an intensity of -radiation proportional to the sine of the angle of the ray with the -surface, which is founded on direct experiments of radiation, is found -to be necessary in order to explain the tendency of neighboring bodies -to equality of temperature; and this leads to the higher -generalization, that heat is radiant from points below the surface. -But in the doctrine of the relation of heat to gases, as delivered by -Laplace, there is none of this unexpected confirmation; and though he -explains some of the leading laws, his assumptions bear a large -proportion to the laws explained. Thus, from the assumption that the -repulsion of gases arises from the mutual repulsion of the particles -of caloric, he finds that the pressure in any gas is as the square of -the density and of the quantity of caloric;[75\10] and from the -assumption that the temperature is the internal radiation, he finds -that this temperature is as the density and the square of the -caloric.[76\10] Hence he obtains the law of Boyle and Mariotte, and -that of Dalton and Gay-Lussac. But this view of the subject requires -other assumptions when we come to latent heat; and accordingly, he -introduces, to express the latent heat, a new quantity.[77\10] Yet -this quantity produces no effect on his calculations, nor does he -apply his reasoning to any problem in which latent heat is concerned. -{187} - -[Note 75\10: P = 2 π H K ρ^2_c_^2 (1) p. 107.] - -[Note 76\10: _q_' Π (_a_) = ρ_c_^2 (2) p. 108.] - -[Note 77\10: The quantity _i_, p. 113.] - -Without, then, deciding upon this theory, we may venture to say that -it is wanting in all the prominent and striking characteristics -which we have found in those great theories which we look upon as -clearly and indisputably established. - -_Conclusion._--We may observe, moreover, that heat has other -bearings and effects, which, as soon as they have been analysed into -numerical laws of phenomena, must be attended to in the formation of -thermotical theories. Chemistry will probably supply many such; -those which occur to us, we must examine hereafter. But we may -mention as examples of such, MM. De la Rive and Marcet's law, that -the specific heat of all gases is the same;[78\10] and MM. Dulong -and Petit's law, that single atoms of all simple bodies have the -same capacity for heat.[79\10] Though we have not yet said anything -of the relation of different gases, or explained the meaning of -_atoms_ in the chemical sense, it will easily be conceived that -these are very general and important propositions. - -[Note 78\10: _Ann. Chim._ xxxv. (1827.)] - -[Note 79\10: Ib. x. 397.] - -Thus the science of Thermotics, imperfect as it is, forms a -highly-instructive part of our survey; and is one of the cardinal -points on which the doors of those chambers of physical knowledge -must turn which hitherto have remained closed. For, on the one hand, -this science is related by strong analogies and dependencies to the -most complete portions of our knowledge, our mechanical doctrines -and optical theories; and on the other, it is connected with -properties and laws of a nature altogether different,--those of -chemistry; properties and laws depending upon a new system of -notions and relations, among which clear and substantial general -principles are far more difficult to lay hold of and with which the -future progress of human knowledge appears to be far more concerned. -To these notions and relations we must now proceed; but we shall -find an intermediate stage, in certain subjects which I shall call -the _Mechanico-chemical_ Sciences; viz., those which have to do with -Magnetism, Electricity, and Galvanism. - - - -{{189}} -BOOK XI. - - -_THE MECHANICO-CHEMICAL SCIENCES._ - - -HISTORY OF ELECTRICITY. - - - PARVA metu primo: mox sese extollit in auras, - Ingrediturque solo, et caput inter nubila condit. - _Æn._ iv. 176. - - A timid breath at first, a transient touch, - How soon it swells from little into much! - Runs o'er the ground, and springs into the air, - And fills the tempest's gloom, the lightning's glare; - While denser darkness than the central storm - Conceals the secrets of its inward form. - - - -{{191}} -INTRODUCTION. - -_Of the Mechanico-Chemical Sciences._ - - -UNDER the title of Mechanico-Chemical Sciences, I include the laws -of Magnetism, Electricity, Galvanism, and the other classes of -phenomena closely related to these, as Thermo-electricity. This -group of subjects forms a curious and interesting portion of our -physical knowledge; and not the least of the circumstances which -give them their interest, is that double bearing upon mechanical and -chemical principles, which their name is intended to imply. Indeed, -at first sight they appear to be purely Mechanical Sciences; the -attractions and repulsions, the pressure and motion, which occur in -these cases, are referrible to mechanical conceptions and laws, as -completely as the weight or fall of terrestrial bodies, or the -motion of the moon and planets. And if the phenomena of magnetism -and electricity had directed us only to such laws, the corresponding -sciences must have been arranged as branches of mechanics. But we -find that, on the other side, these phenomena have laws and bearings -of a kind altogether different. Magnetism is associated with -Electricity by its mechanical analogies; and, more recently, has -been discovered to be still more closely connected with it by -physical influence; electric is identified with galvanic agency; but -in galvanism, decomposition, or some action of that kind, -universally appears; and these appearances lead to very general -laws. Now composition and decomposition are the subjects of -Chemistry; and thus we find that we are insensibly but irresistibly -led into the domain of that science. The highest generalizations to -which we can look, in advancing from the elementary facts of -electricity and galvanism, must involve chemical notions; we must -therefore, in laying out the platform of these sciences, make -provision for that convergence of mechanical and chemical theory, -which they are to exhibit as we ascend. - -We must begin, however, with stating the mechanical phenomena of -these sciences, and the reduction of such phenomena to laws. In this -point of view, the phenomena of which we have to speak are those in -which bodies exhibit attractions and repulsions, peculiarly -determined by their nature and circumstances; as the magnet, and a -{192} piece of amber when rubbed. Such results are altogether -different from the universal attraction which, according to Newton's -discovery, prevails among all particles of matter, and to which -cosmical phenomena are owing. But yet the difference of these -special attractions, and of cosmical attraction, was at first so far -from being recognized, that the only way in which men could be led -to conceive or assent to an action of one body upon another at a -distance, in cosmical cases, was by likening it to magnetic -attraction, as we have seen in the history of Physical Astronomy. -And we shall, in the first part of our account, not dwell much upon -the peculiar conditions under which bodies are magnetic or electric, -since these conditions are not readily reducible to mechanical laws; -but, taking the magnetic or electric character for granted, we shall -trace its effects. - -The habit of considering magnetic action as the type or general case -of attractive and repulsive agency, explains the early writers -having spoken of Electricity as a kind of Magnetism. Thus Gilbert, -in his book _De Magnete_ (1600), has a chapter,[1\11] _De coitione -Magniticâ, primumque de Succini attractione, sive verius corporum ad -Succinum applicatione_. The manner in which he speaks, shows us how -mysterious the fact of attraction then appeared; so that, as he -says, "the magnet and amber were called in aid by philosophers as -illustrations, when our sense is in the dark in abstruse inquiries, -and when our reason can go no further. Gilbert speaks of these -phenomena like a genuine inductive philosopher, reproving[2\11] -those who before him had "stuffed the booksellers' shops by copying -from one another extravagant stories concerning the attraction of -magnets and amber, without giving any reason from experiment." He -himself makes some important steps in the subject. He distinguishes -magnetic from _electric_ forces,[3\11] and is the inventor of the -latter name, derived from ἤλεκτρον, _electron_, amber. He observes -rightly, that the electric force attracts all light bodies, while -the magnetic force attracts iron only; and he devises a satisfactory -apparatus by which this is shown. He gives[4\11] a considerable list -of bodies which possess the electric property; "Not only amber and -agate attract small bodies, as some think, but diamond, sapphire, -carbuncle, opal, amethyst, Bristol gem, beryli, crystal, glass, -glass of antimony, spar of various kinds, sulphur, mastic, -sealing-wax," and other substances which he mentions. Even his -speculations on the general laws of these phenomena, though vague -and erroneous, as {193} at that period was unavoidable, do him no -discredit when compared with the doctrines of his successors a -century and a half afterwards. But such speculations belong to a -succeeding part of this history. - -[Note 1\11: Lib. ii. cap. 2.] - -[Note 2\11: _De Magnete_, p. 48.] - -[Note 3\11: Ib. p. 52.] - -[Note 4\11: Ib. p. 48.] - -In treating of these Sciences, I will speak of Electricity in the -first place; although it is thus separated by the interposition of -Magnetism from the succeeding subjects (Galvanism, &c.) with which -its alliance seems, at first sight, the closest, and although some -general notions of the laws of magnets were obtained at an earlier -period than a knowledge of the corresponding relations of electric -phenomena: for the theory of electric attraction and repulsion is -somewhat more simple than of magnetic; was, in fact, the first -obtained; and was of use in suggesting and confirming the -generalization of magnetic laws. - - - - -CHAPTER 1. - -DISCOVERY OF LAWS OF ELECTRIC PHENOMENA. - - -WE have already seen what was the state of this branch of knowledge -at the beginning of the seventeenth century; and the advances made -by Gilbert. We must now notice the additions which it subsequently -received, and especially those which led to the discovery of general -laws, and the establishment of the theory; events of this kind being -those of which we have more peculiarly to trace the conditions and -causes. Among the facts which we have thus especially to attend to, -are the electric attractions of small bodies by amber and other -substances when rubbed. Boyle, who repeated and extended the -experiments of Gilbert, does not appear to have arrived at any new -general notions; but Otto Guericke of Magdeburg, about the same -time, made a very material step, by discovering that there was an -electric force of repulsion as well as of attraction. He found that -when a globe of sulphur had attracted a feather, it afterwards -repelled it, till the feather had been in contact with some other -body. This, when verified under a due generality of circumstances, -forms a capital fact in our present subject. Hawkesbee, who wrote in -1709 (_Physico-Mechanical Experiments_) also observed various of the -effects of attraction and repulsion upon threads hanging loosely. -But the person who appears to have first fully seized the general -law of these facts, is {194} Dufay, whose experiments appear in the -Memoirs of the French Academy, in 1733, 1734, and 1737.[5\11] "I -discovered," he says, "a very simple principle, which accounts for a -great part of the irregularities, and, if I may use the term, the -caprices that seem to accompany most of the experiments in -electricity. This principle is, that electric bodies attract all -those that are not so, and repel them as soon as they are become -electric by the vicinity or contact of the electric body. . . . Upon -applying this principle to various experiments of electricity, any -one will be surprised at the number of obscure and puzzling facts -which it clears up." By the help of this principle, he endeavors to -explain several of Hawkesbee's experiments. - -[Note 5\11: Priestley's _History of Electricity_, p. 45, and the -Memoirs quoted.] - -A little anterior to Dufay's experiments were those of Grey, who, in -1729, discovered the properties of _conductors_. He found that the -attraction and repulsion which appear in electric bodies are -exhibited also by other bodies in contact with the electric. In this -manner he found that an ivory ball, connected with a glass tube by a -stick, a wire, or a packthread, attracted and repelled a feather, as -the glass itself would have done. He was then led to try to extend -this communication to considerable distances, first by ascending to -an upper window and hanging down his ball, and, afterwards, by -carrying the string horizontally supported on loops. As his success -was complete in the former case, he was perplexed by failure in the -latter; but when he supported the string by loops of silk instead of -hempen cords, he found it again become a conductor of electricity. -This he ascribed at first to the smaller thickness of the silk, -which did not carry off so much of the electric virtue; but from -this explanation he was again driven, by finding that wires of brass -still thinner than the silk destroyed the effect. Thus Grey -perceived that the efficacy of the support depended on its being -silk, and he soon found other substances which answered the same -purpose. The difference, in fact, depended on the supporting -substance being electric, and therefore not itself a conductor; for -it soon appeared from such experiments, and especially[6\11] from -those made by Dufay, that substances might be divided into -_electrics per se_, and _non-electrics_, or _conductors_. These -terms were introduced by Desaguliers,[7\11] and gave a permanent -currency to the results of the labors of Grey and others. - -[Note 6\11: _Mém. Acad. Par._ 1734.] - -[Note 7\11: Priestley, p. 66.] - -Another very important discovery belonging to this period is, that -{195} of the two kinds of electricity. This also was made by Dufay. -"Chance," says he, "has thrown in my way another principle more -universal and remarkable than the preceding one, and which casts a new -light upon the subject of electricity. The principle is, that there -are two distinct kinds of electricity, very different from one -another; one of which I call _vitreous_, the other _resinous_, -electricity. The first is that of glass, gems, hair, wool, &c.; the -second is that of amber, gum-lac, silk, &c. The characteristic of -these two electricities is, that they repel themselves and attract -each other." This discovery does not, however, appear to have drawn so -much attention as it deserved. It was published in 1735; (in the -Memoirs of the Academy _for_ 1733;) and yet in 1747, Franklin and his -friends at Philadelphia, who had been supplied with electrical -apparatus and information by persons in England well acquainted with -the then present state of the subject, imagined that they were making -observations unknown to European science, when they were led to assert -two conditions of bodies, which were in fact the opposite -electricities of Dufay, though the American experimenters referred -them to a single element, of which electrized bodies might have either -excess or defect. "Hence," Franklin says, "have arisen some new terms -among us: we say B," who receives a spark from glass, "and bodies in -like circumstances, is electrized _positively_; A," who communicates -his electricity to glass, "_negatively_; or rather B is electrized -_plus_, A _minus_." Dr. (afterwards Sir William) Watson had, about the -same time, arrived at the same conclusions, which he expresses by -saying that the electricity of A was _more rare_, and that of B _more -dense_, than it naturally would have been.[8\11] But that which gave -the main importance to this doctrine was its application to some -remarkable experiments, of which we must now speak. - -[Note 8\11: Priestley, p. 115.] - -Electric action is accompanied, in many cases, by light and a -crackling sound. Otto Guericke[9\11] observes that his -sulphur-globe, when rubbed in a dark place, gave faint flashes, such -as take place when sugar is crushed. And shortly after, a light was -observed at the surface of the mercury in the barometer, when -shaken, which was explained at first by Bernoulli, on the then -prevalent Cartesian principles; but, afterwards, more truly by -Hawkesbee, as an electrical phenomenon. Wall, in 1708, found sparks -produced by rubbing amber, and Hawkesbee observed the light and the -_snapping_, as he calls it, under various modifications. But the -electric spark from a living body, which, as {196} Priestley -says,[10\11] "makes a principal part of the diversion of gentlemen -and ladies who come to see experiments in electricity," was first -observed by Dufay and the Abbé Nollet. Nollet says[11\11] he "shall -never forget the surprise which the first electric spark ever drawn -from the human body excited, both in M. Dufay and in himself." The -drawing of a spark from the human body was practised in various -forms, one of which was familiarly known as the "electrical kiss." -Other exhibitions of electrical light were the electrical star, -electrical rain, and the like. - -[Note 9\11: _Experimenta Magdeburgica_, 1672, lib. iv. cap. 15.] - -[Note 10\11: P. p. 47.] - -[Note 11\11: Priestley, p. 47. Nollet, _Leçons de Physique_, vol. -vi. p. 408.] - -As electricians determined more exactly the conditions of electrical -action, they succeeded in rendering more intense those sudden -actions which the spark accompanies, and thus produced the electric -_shock_. This was especially done in the _Leyden phial_. This -apparatus received its name, while the discovery of its property was -attributed to Cunæus, a native of Leyden, who, in 1746, handling a -vessel containing water in communication with the electrical -machine, and happening thus to bring the inside and the outside into -connexion, received a sudden shock in his arms and breast. It -appears, however,[12\11] that a shock had been received under nearly -the same circumstances in 1746, by Von Kleist, a German prelate, at -Camin, in Pomerania. The strangeness of this occurrence, and the -suddenness of the blow, much exaggerated the estimate which men -formed of its force. Muschenbroek, after taking one shock, declared -he would not take a second for the kingdom of France; though Boze, -with a more magnanimous spirit, wished[13\11] that he might die by -such a stroke, and have the circumstances of the experiment recorded -in the Memoirs of the Academy. But we may easily imagine what a new -fame and interest this discovery gave to the subject of electricity. -It was repeated in all parts of the world, with various -modifications: and the shock was passed through a line of several -persons holding hands; Nollet, in the presence of the king of -France, sent it through a circle of 180 men of the guards, and along -a line of men and wires of 900 toises;[14\11] and experiments of the -same kind were made in England, principally under the direction of -Watson, on a scale so large as to excite the admiration of -Muschenbroek; who says, in a letter to Watson, "Magnificentissimis -tuis experimentis superasti conatus omnium." The result was, that -the transmission of electricity through a length of 12,000 feet was, -to sense, instantaneous. {197} - -[Note 12\11: Fischer, v. 490.] - -[Note 13\11: Fischer, p. 84.] - -[Note 14\11: Ibid. v. 512.] - -The essential circumstances of the electric shock were gradually -unravelled. Watson found that it did not increase in proportion -either to the contents of the phial or the size of the globe by -which the electricity was excited; that the outside coating of the -glass (which, in the first form of the experiment, was only a film -of water), and its contents, might be varied in different ways. To -Franklin is due the merit of clearly pointing out most of the -circumstances on which the efficacy of the Leyden phial depends. He -showed, in 1747,[15\11] that the inside of the bottle is electrized -positively, the outside negatively; and that the shock is produced -by the restoration of the equilibrium, when the outside and inside -are brought into communication suddenly. But in order to complete -this discovery, it remained to be shown that the electric matter was -collected entirely at the surface of the glass, and that the -opposite electricities on the two opposite sides of the glass were -accumulated by their mutual attraction. Monnier the younger -discovered that the electricity which bodies can receive, depends -upon their surface rather than their mass, and Franklin[16\11] soon -found that "the whole force of the bottle, and power of giving a -shock, is in the glass itself." This they proved by decanting the -water out of an electrized into another bottle, when it appeared -that the second bottle did not become electric, but the first -remained so. Thus it was found "that the non-electrics, in contact -with the glass, served only to unite the force of the several parts." - -[Note 15\11: _Letters_, p. 13.] - -[Note 16\11: _Letters_, iv. Sect. 16.] - -So far as the effect of the coating of the Leyden phial is -concerned, this was satisfactory and complete: but Franklin was not -equally successful in tracing the action of the electric matter upon -itself, in virtue of which it is accumulated in the phial; indeed, -he appears to have ascribed the effect to some property of the -glass. The mode of describing this action varied, accordingly as two -electric _fluids_ were supposed (with Dufay,) or one, which was the -view taken by Franklin. On this latter supposition the parts of the -electric fluid repel each other, and the excess in one surface of -the glass expels the fluid from the other surface. This kind of -action, however, came into much clearer view in the experiments of -Canton, Wilcke, and Æpinus. It was principally manifested in the -attractions and repulsions which objects exert when they are in the -neighborhood of electrized bodies; or in the _electrical -atmosphere_, using the phraseology of the time. At present we say -that bodies are electrized _by induction_, when they are {198} thus -made electric by the electric attraction and repulsion of other -bodies. Canton's experiments were communicated to the Royal Society -in 1753, and show that the electricity on each body acts upon the -electricity of another body, at a distance, with a repulsive energy. -Wilcke, in like manner, showed that parts of non-electrics, plunged -in electric atmospheres, acquire an electricity opposite to that of -such atmospheres. And Æpinus devised a method of examining the -nature of the electricity at any part of the surface of a body, by -means of which he ascertained its distribution, and found that it -agreed with such a law of self-repulsion. His attempt to give -mathematical precision to this induction was one of the most -important steps towards electrical theory, and must be spoken of -shortly, in that point of view. But in the mean time we may observe, -that this doctrine was applied to the explanation of the Leyden jar; -and the explanation was confirmed by charging a plate of air, and -obtaining a shock from it, in a manner which the theory pointed out. - -Before we proceed to the history of the theory, we must mention some -other of the laws of phenomena which were noticed, and which theory -was expected to explain. Among the most celebrated of these, were -the effect of sharp points in conductors, and the phenomena of -electricity in the atmosphere. The former of these circumstances was -one of the first which Franklin observed as remarkable. It was found -that the points of needles and the like throw off and draw off the -electric virtue; thus a bodkin, directed towards an electrized ball, -at six or eight inches' distance, destroyed its electric action. The -latter subject, involving the consideration of thunder and -lightning, and of many other meteorological phenomena, excited great -interest. The comparison of the electric spark to lightning had very -early been made; but it was only when the discharge had been -rendered more powerful in the Leyden jar, that the comparison of the -effects became very plausible. Franklin, about 1750, had offered a -few somewhat vague conjectures[17\11] respecting the existence of -electricity in the clouds; but it was not till Wilcke and Æpinus had -obtained clear notions of the effect of electric matter at a -distance, that the real condition of the clouds could be well -understood. In 1752, however,[18\11] D'Alibard, and other French -philosophers, were desirous of verifying Franklin's conjecture of -the analogy of thunder and electricity. This they did by erecting a -pointed iron rod, forty feet high, {199} at Marli: the rod was found -capable of giving out electrical sparks when a thunder-cloud passed -over the place. This was repeated in various parts of Europe, and -Franklin suggested that a communication with the clouds might be -formed by means of a kite. By these, and similar means, the -electricity of the atmosphere was studied by Canton in England, -Mazeas in France, Beccaria in Italy, and others elsewhere. These -essays soon led to a fatal accident, the death of Richman at -Petersburg, while he was, on Aug. 6th, 1753, observing the -electricity collected from an approaching thunder-cloud, by means of -a rod which he called an electrical gnomon: a globe of blue fire was -seen to leap from the rod to the head of the unfortunate professor, -who was thus struck dead. - -[Note 17\11: Letter v.] - -[Note 18\11: Franklin, p. 107.] - -[2nd Ed.] [As an important application of the doctrines of -electricity, I may mention the contrivances employed to protect -ships from the effects of lightning. The use of conductors in such -cases is attended with peculiar difficulties. In 1780 the French -began to turn their attention to this subject, and Le Roi was sent -to Brest and the various sea-ports of France for that purpose. -Chains temporarily applied in the rigging had been previously -suggested, but he endeavored to place, he says, such conductors in -ships as might be fixed and durable. He devised certain long linked -rods, which led from a point in the mast-head along a part of the -rigging, or in divided stages along the masts, and were fixed to -plates of metal in the ship's sides communicating with the sea. But -these were either unable to stand the working of the rigging, or -otherwise inconvenient, and were finally abandoned.[19\11] - -[Note 19\11: See Le Roi's Memoir in the _Hist. Acad. Sc._ for 1790.] - -The conductor commonly used in the English Navy, till recently, -consisted of a flexible copper chain, tied, when occasion required, -to the mast-head, and reaching down into the sea; a contrivance -recommended by Dr. Watson in 1762. But notwithstanding this -precaution, the shipping suffered greatly from the effects of -lightning. - -Mr. Snow Harris (now Sir William Snow Harris), whose electrical -labors are noticed above, proposed to the Admiralty, in 1820, a plan -which combined the conditions of ship-conductors, so desirable, yet -so difficult to secure:--namely, that they should be permanently -fixed, and sufficiently large, and yet should in no way interfere -with the motion of the rigging, or with the sliding masts. The -method which he proposed was to make the masts themselves conductors -of electricity, {200} by incorporating with them, in a peculiar way, -two laminæ of sheet-copper, uniting these with the metallic masses -in the hull by other laminæ, and giving the whole a free -communication with the sea. This method was tried experimentally, -both on models and to a large extent in the navy itself; and a -Commission appointed to examine the result reported themselves -highly satisfied with Mr. Harris's plan, and strongly recommended -that it should be fully carried out in the Navy.[20\11]] - -[Note 20\11: See Mr. Snow Harris's paper in _Phil. Mag._ March, 1841.] - -It is not here necessary to trace the study of atmospheric -electricity any further: and we must now endeavor to see how these -phenomena and laws of phenomena which we have related, were worked -up into consistent theories; for though many experimental -observations and measures were made after this time, they were -guided by the theory, and may be considered as having rather -discharged the office of confirming than of suggesting it. - -We may observe also that we have now described the period of most -extensive activity and interest in electrical researches. These -naturally occurred while the general notions and laws of the -phenomena were becoming, and were not yet become, fixed and clear. -At such a period, a large and popular circle of spectators and -amateurs feel themselves nearly upon a level, in the value of their -trials and speculations, with more profound thinkers: at a later -period, when the subject is become a science, that is, a study in -which all must be left far behind who do not come to it with -disciplined, informed, and logical minds, the cultivators are far -more few, and the shout of applause less tumultuous and less loud. -We may add, too, that the experiments, which are the most striking -to the senses, lose much of their impressiveness with their novelty. -Electricity, to be now studied rightly, must be reasoned upon -mathematically; how slowly such a mode of study makes its way, we -shall see in the progress of the theory, which we must now proceed -to narrate. - -[2nd Ed.] [A new mode of producing electricity has excited much -notice lately. In October, 1840, one of the workmen in attendance -upon a boiler belonging to the Newcastle and Durham Railway, -reported that the boiler was full of fire; the fact being, that -when he placed his hand near it an electrical spark was given out. -This drew the attention of Mr. Armstrong and Mr. Pattinson, who made -the circumstance publicly known.[21\11] Mr. Armstrong pursued the -investigation {201} with great zeal, and after various conjectures -was able to announce[22\11] that the electricity was excited at the -point where the steam is subject to friction in its emission. He -found too that he could produce a like effect by the emission of -condensed air. Following out his views, he was able to construct, -for the Polytechnic Institution in London, a "Hydro-electric -Machine," of greater power than any electrical machine previously -made. Dr. Faraday took up the investigation as the subject of the -Eighteenth Series of his _Researches_, sent to the Royal Society, -Jan. 26, 1842; and in this he illustrated, with his usual command of -copious and luminous experiments, a like view;--that the electricity -is produced by the friction of the particles of the water carried -along by the **steam. And thus this is a new manifestation of that -electricity, which, to distinguish it from voltaic electricity, is -sometimes called _Friction Electricity_ or _Machine Electricity_. -Dr. Faraday has, however, in the course of this investigation, -brought to light several new electrical relations of bodies.] - -[Note 21\11: _Phil. Mag._ Oct 1840.] - -[Note 22\11: _Phil. Mag._ Jan. 1848, dated Dec. 9, 1841.] - - - - -CHAPTER II. - -THE PROGRESS OF ELECTRICAL THEORY. - - -THE cause of electrical phenomena, and the mode of its operation, -were naturally at first spoken of in an indistinct and wavering -manner. It was called the electric _fire_, the electric _fluid_; its -effects were attributed to _virtues_, _effluvia_, _atmospheres_. -When men's mechanical ideas became somewhat more distinct, the -motions and tendencies to motion were ascribed to _currents_, in the -same manner as the cosmical motions had been in the Cartesian -system. This doctrine of currents was maintained by Nollet, who -ascribed all the phenomena of electrized bodies to the -contemporaneous afflux and efflux of electrical matter. It was an -important step towards sound theory, to get rid of this notion of -moving fluids, and to consider attraction and repulsion as statical -forces; and this appears to have been done by others about the same -time. Dufay[23\11] considered that he had proved the existence of -two electricities, the vitreous and the resinous, and conceived each -{202} of these to be a fluid which repelled its own parts and -attracted those of the other: this is, in fact, the outline of the -theory which recently has been considered as the best established; -but from various causes it was not at once, or at least not -generally adopted. The hypothesis of the excess and defect of a -single fluid is capable of being so treated as to give the same -results with the hypothesis of two opposite fluids and happened to -obtain the preference for some time. We have already seen that this -hypothesis, according to which electric phenomena arose from the -excess and defect of a generally diffused fluid, suggested itself to -Watson and Franklin about 1747. Watson found that when an electric -body was excited, the electricity was not created, but collected; -and Franklin held, that when the Leyden jar was charged, the -quantity of electricity was unaltered, though its distribution was -changed. Symmer[24\11] maintained the existence of two fluids; and -Cigna supplied the main defect which belonged to this tenet in the -way in which Dufay held it, by showing that the two opposite -electricities were usually produced at the same time. Still the -apparent simplicity of the hypothesis of one fluid procured it many -supporters. It was that which Franklin adopted, in his explanation -of the Leyden experiment; and though after the first conception of -an electrical charge as a disturbance of equilibrium, there was -nothing in the development or details of Franklin's views which -deserved to win for them any peculiar authority, his reputation, and -his skill as a writer, gave a considerable influence to his -opinions. Indeed, for a time he was considered, over a large part of -Europe, as the creator of the science, and the terms[25\11] -_Franklinism_, _Franklinist_, _Franklinian system_, occur in almost -every page of continental publications on the subject. Yet the -electrical phenomena to the knowledge of which Franklin added least, -those of induction, were those by which the progress of the theory -was most promoted. These, as we have already said, were at first -explained by the hypothesis of electrical atmospheres. Lord Mahon -wrote a treatise, in which this hypothesis was mathematically -treated; yet the hypothesis was very untenable, for it would not -account for the most obvious cases of induction, such as the Leyden -jar, except the atmosphere was supposed to penetrate glass. - -[Note 23\11: _Ac. Par._ 1733, p. 467] - -[Note 24\11: _Phil. Trans._ 1759.] - -[Note 25\11: Priestley, p. 160.] - -The phenomena of electricity by induction, when fairly considered by -a person of clear notions of the relations of space and force, were -seen to accommodate themselves very generally to the conception -{203} introduced by Dufay;[26\11] of two electricities each -repelling itself and attracting the other. If we suppose that there -is only one fluid, which repels itself and attracts all other -matter, we obtain, in many cases, the same general results as if we -suppose two fluids; thus, if an electrized body, overcharged with -the single fluid, act upon a ball, it drives the electric fluid in -the ball to the further side by its repulsion, and then attracts the -ball by attracting the matter of the ball more than it repels the -fluid which is upon the ball. If we suppose two fluids, the -positively electrized body draws the negative fluid to the nearer -side of the ball, repels the positive fluid to the opposite side, -and attracts the ball on the whole, because the attracted fluid is -nearer than that which is repelled. The verification of either of -these hypotheses, and the determination of their details, depended -necessarily upon experiment and calculation. It was under the -hypothesis of a single fluid that this trial was first properly -made. Æpinus of Petersburg published, in 1759, his _Tentamen Theoriæ -Electricitatis et Magnetismi_; in which he traces mathematically the -consequences of the hypothesis of an electric fluid, attracting all -other matter, but repelling itself; the law of force of this -repulsion and attraction he did not pretend to assign precisely, -confining himself to the supposition that the mutual force of the -particles increases as the distance decreases. But it was found, -that in order to make this theory tenable, an additional supposition -was required, namely, that the particles of bodies repel each other -as much as they attract the electric fluid.[27\11] For if two -bodies, A and B, be in their natural electrical condition, they -neither attract nor repel each other. Now, in this case, the fluid -in A attracts the matter in B and repels the fluid in B with equal -energy, and thus no tendency to motion results from the fluid in A; -and if we further suppose that the _matter_ in A attracts the fluid -in B and _repels the matter_ in B with equal energy, we have the -resulting mutual inactivity of the two bodies explained; but without -the latter supposition, there would be a mutual attraction: or we -may put the truth more simply thus; two negatively electrized bodies -repel each other; if negative electrization were merely the -abstraction of the fluid which is the repulsive element, this result -could not follow except there were a repulsion in the bodies -themselves, independent of the fluid. And thus Æpinus found himself -compelled to assume this mutual repulsion of material particles; he -had, in fact, the {204} alternative of this supposition, or that of -two fluids, to choose between, for the mathematical results of both -hypotheses are the same. Wilcke, a Swede, who had at first asserted -and worked out the Æpinian theory in its original form, afterwards -inclined to the opinion of Symmer; and Coulomb, when, at a later -period, he confirmed the theory by his experiments and determined -the law of force, did not hesitate to prefer[28\11] the theory of -two fluids, "because," he says, "it appears to me contradictory to -admit at the same time, in the particles of bodies, an attractive -force in the inverse ratio of the squares of the distances, which is -demonstrated by universal gravitation, and a repulsive force in the -same inverse ratio of the squares of the distances; a force which -would necessarily be infinitely great relatively to the action of -gravitation." We may add, that by forcing us upon this doctrine of -the universal repulsion of matter, the theory of a single fluid -seems quite to lose that superiority in the way of simplicity which -had originally been its principal recommendation. - -[Note 26\11: _Mém. A. P._ 1733, p. 467.] - -[Note 27\11: Robison, vol. iv. p. 18.] - -[Note 28\11: _Mém. Ac. P._ 1788, p. 671.] - -The mathematical results of the supposition of Æpinus, which are, as -Coulomb observes,[29\11] the same as of that of the two fluids, were -traced by the author himself in the work referred to, and shown to -agree, in a great number of cases, with the observed facts of -electrical induction, attraction, and repulsion. Apparently this -work did not make its way very rapidly through Europe; for in 1771, -Henry Cavendish stated[30\11] the same hypothesis in a paper read -before the Royal Society; which he prefaces by saying, "Since I -first wrote the following paper, I find that this way of accounting -for the phenomena of electricity is not new. Æpinus, in his -_Tentamen Theoriæ Electricitatis et Magnetismi_, has made use of the -same, or nearly the same hypothesis that I have; and the conclusions -he draws from it agree nearly with mine as far as he goes." - -[Note 29\11: _Ac. P._ 1788, p. 672.] - -[Note 30\11: _Phil. Trans._ 1771, vol. lxi.] - -The confirmation of the theory was, of course, to be found in the -agreement of its results with experiment; and in particular, in the -facts of electrical induction, attraction, and repulsion, which -suggested the theory. Æpinus showed that such a confirmation -appeared in a number of the most obvious cases; and to these, -Cavendish added others, which, though not obvious, were of such a -nature that the calculations, in general difficult or impossible, -could in these instances be easily performed; as, for example, cases -in which there are plates or globes at the two extremities of a long -wire. In all these cases of {205} electrical action the theory was -justified. But in order to give it full confirmation, it was to be -considered whether any other facts, not immediately assumed in the -foundation of the theory, were explained by it; a circumstance -which, as we have seen, gave the final stamp of truth to the -theories of astronomy and optics. Now we appear to have such -confirmation, in the effect of points, and in the phenomena of the -electrical discharge. The theory of neither of these was fully -understood by Cavendish, but he made an approach to the true view of -them. If one part of a conducting body be a sphere of small radius, -the electric fluid upon the surface of this sphere will, it appears -by calculation, be more dense, and tend to escape more -energetically, in proportion as the radius of the sphere is smaller; -and, therefore, if we consider a point as part of the surface of a -sphere of imperceptible radius, it follows from the theory that the -effort of the fluid to escape at that place will be enormous; so -that it may easily be supposed to overcome the resisting causes. And -the discharge may be explained in nearly the same manner; for when a -conductor is brought nearer and nearer to an electrized body, the -opposite electricity is more and more accumulated by attraction on -the side next to the electrized body; its tension becomes greater by -the increase of its quantity and the diminution of the distance, and -at last it is too strong to be contained, and leaps out in the form -of a spark. - -The light, sound, and mechanical effects produced by the electric -discharge, made the electric _fluid_ to be not merely considered as -a mathematical hypothesis, useful for reducing phenomena to formulæ -(as for a long time the magnetic fluid was), but caused it to be at -once and universally accepted as a physical reality, of which we -learn the existence by the common use of the senses, and of which -measures and calculations are only wanted to teach us the laws. - -The applications of the theory of electricity which I have -principally considered above, are those which belong to conductors, -in which the electric fluid is perfectly moveable, and can take that -distribution which the forces require. In non-conducting or electric -bodies, the conditions to which the fluid is subject are less easy -to determine; but by supposing that the fluid moves with great -difficulty among the particles of such bodies,--that nevertheless it -may be dislodged and accumulated in parts of the surface of such -bodies, by friction and other modes of excitement; and that the -earth is an inexhaustible reservoir of electric matter,--the -principal facts of excitation and the like receive a tolerably -satisfactory explanation. {206} - -The theory of Æpinus, however, still required to have the law of -action of the particles of the fluid determined. If we were to call -to mind how momentous an event in physical astronomy was the -determination of the law of the cosmical forces, the inverse square -of the distance, and were to suppose the importance and difficulty -of the analogous step in this case to be of the same kind, this -would be to mistake the condition of science at that time. The -leading idea, the conception of the possibility of explaining -natural phenomena by means of the action of forces, on rigorously -mechanical principles, had already been promulgated by Newton, and -was, from the first, seen to be peculiarly applicable to electrical -phenomena; so that the very material step of clearly proposing the -problem, often more important than the solution of it, had already -been made. Moreover the confirmation of the truth of the assumed -cause in the astronomical case depended on taking the right law; but -the electrical theory could be confirmed, in a general manner at -least, without this restriction. Still it was an important discovery -that the law of the inverse square prevailed in these as well as in -cosmical attractions. - -It was impossible not to conjecture beforehand that it would be so. -Cavendish had professed in his calculations not to take the exponent -of the inverse power, on which the force depended, to be strictly 2, -but to leave it indeterminate between 1 and 3; but in his -applications of his results, he obviously inclines to the assumption -that it is 2. Experimenters tried to establish this in various ways. -Robison,[31\11] in 1769, had already proved that the law of force is -very nearly or exactly the inverse square; and Meyer[32\11] had -discovered, but not published, the same result. The clear and -satisfactory establishment of this truth is due to Coulomb, and was -one of the first steps in his important series of researches on this -subject. In his first paper[33\11] in the _Memoirs_ of the Academy -for 1785, he proves this law for small globes; in his second Memoir -he shows it to be true for globes one and two feet in diameter. His -invention of the _torsion-balance_, which measures very small forces -with great certainty and exactness, enabled him to set this question -at rest for ever. - -[Note 31\11: _Works_, iv. p. 68.] - -[Note 32\11: _Biog. Univ._ art. _Coulumb_, by Biot.] - -[Note 33\11: _Mém. A. P._ 1785, pp. 569, 578.] - -The law of force being determined for the particles of the electric -fluid, it now came to be the business of the experimenter and the -{207} mathematician to compare the results of the theory in detail -with those of experimental measures. Coulomb undertook both portions -of the task. He examined the electricity of portions of bodies by -means of a little disk (his _tangent plane_) which he applied to -them and then removed, and which thus acted as a sort of electric -_taster_. His numerical results (the intensity being still measured -by the torsion-balance) are the fundamental facts of the theory of -the electrical fluid. Without entering into detail, we may observe -that he found the electricity to be entirely collected at the -surface of conductors (which Beccaria had before shown to be the -case), and that he examined and recorded the electric intensity at -the surface of globes, cylinders, and other conducting bodies, -placed within each other's influence in various ways. - -The mathematical calculation of the distribution of two fluids, all -the particles of which attract and repel each other according to the -above law, was a problem of no ordinary difficulty; as may easily be -imagined, when it is recollected that the attraction and repulsion -determine the distribution, and the distribution reciprocally -determines the attraction and repulsion. The problem was of the same -nature as that of the figure of the earth; and its rigorous solution -was beyond the powers of the analysis of Coulomb's time. He obtained, -however, approximate solutions with much ingenuity; for instance, in a -case in which it was obvious that the electric fluid would be most -accumulated at and near the equator of a certain sphere, he calculated -the action of the sphere on two suppositions: first, that the fluid -was all collected precisely at the equator; and next, that it was -uniformly diffused over the surface; and he then assumed the actual -case to be intermediate between these two. By such artifices he was -able to show that the results of his experiments and of his -calculations gave an agreement sufficiently near to entitle him to -consider the theory as established on a solid basis. - -Thus, at this period, mathematics was behind experiment; and a problem -was proposed, in which theoretical numerical results were wanted for -comparison with observation, but could not be accurately obtained; as -was the case in astronomy also, till the time of the approximate -solution of the Problem of Three Bodies, and the consequent formation -of the Tables of the Moon and Planets on the theory of universal -gravitation. After some time, electrical theory was relieved from this -reproach, mainly in consequence of the progress which astronomy had -occasioned in pure mathematics. About 1801, {208} there appeared in -the _Bulletin des Sciences_,[34\11] an exact solution of the problem -of the distribution of electric fluid on a spheroid, obtained by M. -Biot, by the application of the peculiar methods which Laplace had -invented for the problem of the figure of the planets. And in 1811, M. -Poisson applied Laplace's artifices to the case of two spheres acting -upon one another in contact, a case to which many of Coulomb's -experiments were referrible; and the agreement of the results of -theory and observation, thus extricated from Coulomb's numbers, -obtained above forty years previously, was very striking and -convincing.[35\11] It followed also from Poisson's calculations, that -when two electrized spheres are brought near each other, the -accumulation of the opposite electricities on their nearest points -increases without limit as the spheres approach to contact; so that -before the contact takes place, the external resistance will be -overcome, and a _spark_ will pass. - -[Note 34\11: No. li.] - -[Note 35\11: _Mém. A. P._ 1811.] - -Though the relations of non-conductors to electricity, and various -other circumstances, leave many facts imperfectly explained by the -theory, yet we may venture to say that, as a theory which gives the -laws of the phenomena, and which determines the distribution of -those elementary forces, on the surface of electrized bodies, from -which elementary forces (whether arising from the presence of a -fluid or not,) the total effects result, the doctrine of Dufay and -Coulomb, as developed in the analysis of Poisson, is securely and -permanently established. This part of the subject has been called -_statical electricity_. In the establishment of the theory of this -branch of science, we must, I conceive, allow to Dufay more merit -than is generally ascribed to him; since he saw clearly, and -enunciated in a manner which showed that he duly appreciated their -capital character, the two chief principles,--the conditions of -electrical attraction and repulsion, and the apparent existence of -two kinds of electricity. His views of attraction are, indeed, -partly expressed in terms of the Cartesian hypothesis of vortices, -then prevalent in France; but, at the time when he wrote, these -forms of speech indicated scarcely anything besides the power of -attraction. Franklin's real merit as a discoverer was, that he was -one of the first who distinctly conceived the electrical _charge_ as -a derangement of equilibrium. The great fame which, in his day, he -enjoyed, arose from the clearness and spirit with which he narrated -his discoveries; from his dealing with electricity in the imposing -form of thunder and lightning; and partly, perhaps, from his -character as an {209} American and a politician; for he was already, -in 1736, engaged in public affairs as clerk to the General Assembly -of Pennsylvania, though it was not till a later period of his life -that his admirers had the occasion of saying of him - Eripuit cœlis fulmen sceptrumque tyrannis; - Born to control all lawless force, all fierce and baleful sway, - The thunder's bolt, the tyrant's rod, alike he wrenched away. - -Æpinus and Coulomb were two of the most eminent physical -philosophers of the last century, and labored in the way peculiarly -required by that generation; whose office it was to examine the -results, in particular subjects, of the general conception of -attraction and repulsion, as introduced by Newton. The reasonings of -the Newtonian period had, in some measure, anticipated all possible -theories resembling the electrical doctrine of Æpinus and Coulomb; -and, on that account, this doctrine could not be introduced and -confirmed in a sudden and striking manner, so as to make a great -epoch. Accordingly, Dufay, Symmer, Watson, Franklin, Æpinus and -Coulomb, have all a share in the process of induction. With -reference to these founders of the theory of electricity, Poisson -holds the same place which Laplace holds with reference to Newton. - -The reception of the Coulombian theory (so we most call it, for the -Æpinian theory implies one fluid only,) has hitherto not been so -general as might have been reasonably expected from its very -beautiful accordance with the facts which it contemplates. This has -partly been owing to the extreme abstruseness of the mathematical -reasoning which it employs, and which put it out of the reach of -most experimenters and writers of works of general circulation. The -theory of Æpinus was explained by Robison in the _Encyclopædia -Britannica_; the analysis of Poisson has recently been presented to -the public in the _Encyclopædia Metropolitana_, but is of a kind not -easily mastered even by most mathematicians. On these accounts -probably it is, that in English compilations of science, we find, -even to this day, the two theories of one and of two fluids stated -as if they were nearly on a par in respect of their experimental -evidence. Still we may say that the Coulombian theory is probably -assented to by all who have examined it, at least as giving the laws -of phenomena; and I have not heard of any denial of it from such a -quarter, or of any attempt to show it to be erroneous by detailed -and measured experiments. Mr. Snow Harris {210} has recently[36\11] -described some important experiments and measures; but his apparatus -was of such a kind that the comparison of the results with the -Coulombian theory was not easy; and indeed the mathematical problems -which Mr. Harris's combinations offered, require another Poisson for -their solution. Still the more obvious results are such as agree -with the theory, even in the cases in which their author considered -them to be inexplicable. For example, he found that by doubling the -quantity of electricity of a conductor, it attracted a body with -four times the force; but the body not being insulated, would have -its electricity also doubled by induction, and thus the fact was -what the theory required. - -[Note 36\11: _Phil. Trans._ 1834, p. 2.] - -Though it is thus highly probable that the Coulombian theory of -electricity (or the Æpinian, which is mathematically equivalent) -will stand as a true representation of the law of the elementary -actions, we must yet allow that it has not received that complete -evidence, by means of experiments and calculations added to those of -its founders, which the precedents of other permanent sciences have -led us to look for. The experiments of Coulomb, which he used in the -establishment of the theory, were not very numerous, and they were -limited to a peculiar form of bodies, namely spheres. In order to -form the proper _sequel_ to the promulgation of this theory, to give -a full _confirmation_, and to ensure its general _reception_, we -ought to have experiments more numerous and more varied (such as -those of Mr. Harris are) shown to agree in all respects with results -calculated from the theory. This would, as we have said, be a task -of labor and difficulty; but the person who shall execute it will -deserve to be considered as one of the real founders of the true -doctrine of electricity. To show that the coincidence between theory -and observation, which has already been proved for spherical -conductors, obtains also for bodies of other forms, will be a step -in electricity analogous to what was done in astronomy, when it was -shown that the law of gravitation applied to comets as well as to -planets. - -But although we consider the views of Æpinus or Coulomb in a very -high degree probable as a _formal theory_, the question is very -different when we come to examine them as a _physical theory_;--that -is, when we inquire whether there really is a material electric -fluid or fluids. - -_Question of One or Two Fluids._--In the first place as to the -question whether the fluids are one or two;--Coulomb's introduction -of {211} the hypothesis of two fluids has been spoken of as a reform -of the theory of Æpinus; it would probably have been more safe to -have called his labors an advance in the calculation, and in the -comparison of hypothesis with experiment, than to have used language -which implied that the question, between the rival hypotheses of one -or two fluids, could be treated as settled. For, in reality, if we -assume, as Æpinus does, the mutual repulsion of all the particles of -matter, in addition to the repulsion of the particles of the -electric fluid for one another and their attraction for the -particles of matter, the one fluid of Æpinus will give exactly the -same results as the two fluids of Coulomb. The mathematical formulæ -of Coulomb and of Poisson express the conditions of the one case as -well as of the other; the interpretation only being somewhat -different. The place of the forces of the resinous fluid is supplied -by the excess of the forces ascribed to the matter above the forces -of the fluid, in the parts where the electric fluid is deficient. - -The obvious argument against this hypothesis is, that we ascribe to -the particles of matter a mutual repulsion, in addition to the -mutual attraction of universal gravitation, and that this appears -incongruous. Accordingly, Æpinus says, that when he was first driven -to this proposition it horrified him.[37\11] But we may answer it in -this way very satisfactorily:--If we suppose the mutual repulsion of -matter to be somewhat less than the mutual attraction of matter and -electric fluid, it will follow, as a consequence of the hypothesis, -that besides all obvious electrical action, the particles of matter -would attract each other with forces varying inversely as the square -of the distance. Thus gravitation itself becomes an electrical -phenomenon, arising from the residual excess of attraction over -repulsion; and the fact which is urged against the hypothesis -becomes a confirmation of it. By this consideration the prerogative -of simplicity passes over to the side of the hypothesis of one -fluid; and the rival view appears to lose at least all its -superiority. - -[Note 37\11: Neque diffiteor cum ipsa se mihi offerret . . . . me ad -ipsam quodammodo exhorruisse. _Tentamen Theor. Elect._ p. 39.] - -Very recently, M. Mosotti[38\11] has calculated the results of the -Æpinian theory in a far more complete manner than had previously -been performed; using Laplace's coefficients, as Poisson had done -for the {212} Coulombian theory. He finds that, from the supposition -of a fluid and of particles of matter exercising such forces as that -theory assumes (with the very allowable additional supposition that -the particles are small compared with their distances), it follows -that the particles would exert a force, repulsive at the smallest -distances, a little further on vanishing, afterwards attractive, and -at all sensible distances attracting in proportion to the inverse -square of the distance. Thus there would be a position of stable -equilibrium for the particles at a very small distance from each -other, which may be, M. Mosotti suggests, that equilibrium on which -their physical structure depends. According to this view, the -resistance of bodies to compression and to extension, as well as the -phenomena of statical electricity and the mutual gravitation of -matter, are accounted for by the same hypothesis of a single fluid -or ether. A theory which offers a prospect of such a generalization -is worth attention; but a very clear and comprehensive view of the -doctrines of several sciences is requisite to prepare us to estimate -its value and probable success. - -[Note 38\11: _Sur les Forces qui régissent la Constitution -Intérieure des Corps._ Turin. 1836.] - -_Question of the Material Reality of the Electric Fluid._--At first -sight the beautiful accordance of the experiments with calculations -founded upon the attractions and repulsions of the two hypothetical -fluids, persuade us that the hypotheses must be the real state of -things. But we have already learned that we must not trust to such -evidence too readily. It is a curious instance of the mutual -influence of the histories of two provinces of science, but I think -it will be allowed to be just, to say that the discovery of the -polarization of heat has done much to shake the theory of the -electric fluids as a physical reality. For the doctrine of a -material caloric appeared to be proved (from the laws of conduction -and radiation) by the same kind of mathematical evidence (the -agreement of laws respecting the elementary actions with those of -fluids), which we have for the doctrine of material electricity. Yet -we now seem to see that heat cannot be matter, since its rays have -_sides_, in a manner in which a stream of particles of matter cannot -have sides without inadmissible hypotheses. We see, then, that it -will not be contrary to precedent, if our electrical theory, -representing with perfect accuracy the _laws_ of the actions, in all -their forms, simple and complex, should yet be fallacious as a view -of the _cause_ of the actions. - -Any true view of electricity must include, or at least be consistent -with, the other classes of the phenomena, as well as this statical -electrical action; such as the conditions of excitation and -retention of {213} electricity; to which we may add, the connexion -of electricity with magnetism and with chemistry;--a vast field, as -yet dimly seen. Now, even with regard to the simplest of these -questions, the cause of the retention of electricity at the surface -of bodies, it appears to be impossible to maintain Coulomb's -opinion, that this is effected by the resistance of air to the -passage of electricity. The other questions are such as Coulomb did -not attempt to touch; they refer, indeed, principally to laws not -suspected at his time. How wide and profound a theory must be which -deals worthily with these, we shall obtain some indications in the -succeeding part of our history. - -But it may be said on the other side, that we have the evidence of -our senses for the reality of an electric fluid;--we see it in the -spark; we hear it in the explosion; we feel it in the shock; and it -produces the effects of mechanical violence, piercing and tearing -the bodies through which it passes. And those who are disposed to -assert a real fluid on such grounds, may appear to be justified in -doing so, by one of Newton's "Rules of Philosophizing," in which he -directs the philosopher to assume, in his theories, "causes which -are true." The usual interpretation of a "vera causa," has been, -that it implies causes which, independently of theoretical -calculations, are known to exist by their mechanical effects; as -gravity was familiarly known to exist on the earth, before it was -extended to the heavens. The electric fluid might seem to be such a -_vera causa_. - -To this I should venture to reply, that this reasoning shows how -delusive the Newtonian rule, so interpreted, may be. For a moment's -consideration will satisfy us that none of the circumstances, above -adduced, can really prove material currents, rather than vibrations, -or other modes of agency. The spark and shock are quite insufficient -to supply such a proof. Sound is vibrations,--light is vibrations; -vibrations may affect our nerves, and may rend a body, as when -glasses are broken by sounds. Therefore all these supposed -indications of the reality of the electric fluid are utterly -fallacious. In truth, this mode of applying Newton's rule consists -in elevating our first rude and unscientific impressions into a -supremacy over the results of calculation, generalization, and -systematic induction.[**39\11] {214} - -[Note **39\11: On the subject of this Newtonian Rule of -Philosophizing, see further _Phil. Ind. Sc._ B. xii. c. 13. I have -given an account of the history and evidence of the Theory of -Electricity in the _Reports of the British Association_ for 1835. -I may seem there to have spoken more favorably of the Theory as a -Physical Theory than I have done here. This difference is -principally due to a consideration of the present aspect of the -Theory of Heat.] - -Thus our conclusion with regard to this subject is, that if we wish -to form a stable physical theory of electricity, we must take into -account not only the laws of statical electricity, which we have -been chiefly considering, but the laws of other kinds of agency, -different from the electric, yet connected with it. For the -electricity of which we have hitherto spoken, and which is commonly -excited by friction, is identical with galvanic action, which is a -result of chemical combinations, and belongs to chemical philosophy. -The connexion of these different kinds of electricity with one -another leads us into a new domain; but we must, in the first place, -consider their mechanical laws. We now proceed to another branch of -the same subject, Magnetism. - - - -{{215}} -BOOK XII. - - -_MECHANICO-CHEMICAL SCIENCES._ - -(CONTINUED.) - - -HISTORY OF MAGNETISM. - - - EFFICE, ut interea fera munera militiaï - Per maria ac terras omneis sopita quiescant. - Nam tu sola potes tranquilla pace juvare - Mortales; quoniam belli fera munera Mavors - Armipotens regit, in gremium qui sæpe tuum se - Rejicit, æterno devictus vulnere amoris; - Atque ita suspiciens tereti cervice reposta, - Pascit amore avidos inhians in te, Dea, visus, - Eque tuo pendet resupini spiritus ore. - Hunc tu, Diva, tuo recubantem corpore sancto - Circumfusa super, suaves ex ore loquelas - Funde, petens placidam Romanis, incluta, pacem. - LUCRET. i. 31. - - O charming Goddess, whose mysterious sway - The unseen hosts of earth and sky obey; - To whom, though cold and hard to all besides, - The Iron God by strong affection glides. - Flings himself eager to thy close embrace, - And bends his head to gaze upon thy face; - Do thou, what time thy fondling arms are thrown - Around his form, and he is all thy own, - Do thou, thy Rome to save, thy power to prove, - Beg him to grant a boon for thy dear love; - Beg him no more in battle-fields to deal. - Or crush the nations with his mailed heel. - But, touched and softened by a worthy flame, - Quit sword and spear, and seek a better fame. - Bid him to make all war and slaughter cease, - And ply his genuine task in arts of peace; - And by thee guided o'er the trackless surge, - Bear wealth and joy to ocean's farthest verge. - - - -{{217}} -CHAPTER I. - -DISCOVERY OF LAWS OF MAGNETIC PHENOMENA. - - -THE history of Magnetism is in a great degree similar to that of -Electricity, and many of the same persons were employed in the two -trains of research. The general fact, that the magnet attracts iron, -was nearly all that was known to the ancients, and is frequently -mentioned and referred to; for instance, by Pliny, who wonders and -declaims concerning it, in his usual exaggerated style.[1\12] The -writers of the Stationary Period, in this subject as in others, -employed themselves in collecting and adorning a number of -extravagant tales, which the slightest reference to experiment would -have disproved; as, for example, that a magnet, when it has lost its -virtue, has it restored by goat's blood. Gilbert, whose work _De -Magnete_ we have already mentioned, speaks with becoming indignation -and pity of this bookish folly, and repeatedly asserts the paramount -value of experiments. He himself, no doubt, acted up to his own -precepts; for his work contains all the fundamental facts of the -science, so fully examined indeed, that even at this day we have -little to add to them. Thus, in his first Book, the subjects of the -third, fourth, and fifth Chapters are,--that the magnet has -poles,--that we may call these poles the north and the south -pole,--that in two magnets the north pole of each attracts the south -pole and repels the north pole of the other. This is, indeed, the -cardinal fact on which our generalizations rest; and the reader will -perceive at once its resemblance to the leading phenomena of -statical electricity. - -[Note 1\12: _Hist. Nat._ lib. xxxvi. c. 25.] - -But the doctrines of magnetism, like those of heat, have an -additional claim on our notice from the manner in which they are -exemplified in the globe of the earth. The subject of _terrestrial -magnetism_ forms a very important addition to the general facts of -magnetic attraction and repulsion. The property of the magnet by -which it directs its poles exactly or nearly north and south, when -once discovered, was of immense importance to the mariner. It does -not {218} appear easy to trace with certainty the period of this -discovery. Passing over certain legends of the Chinese, as at any -rate not bearing upon the progress of European science,[2\12] the -earliest notice of this property appears to be contained in the Poem -of Guyot de Provence, who describes the needle as being magnetized, -and then placed in or on a straw, (floating on water, as I presume:) - Puis se torne la pointe toute - Contre l'estoile sans doute; -that is, it turns towards the pole-star. This account would make the -knowledge of this property in Europe anterior to 1200. It was -afterwards found[3\12] that the needle does not point exactly -towards the north. Gilbert was aware of this deviation, which he -calls the _variation_, and also, that it is different in different -places.[4\12] He maintained on theoretical principles also,[5\12] -that at the same place the variation is constant; probably in his -time there were not any recorded observations by which the truth of -this assertion could be tested; it was afterwards found to be false. -The alteration of the variation in proceeding from one place to -another was, it will be recollected, one of the circumstances which -most alarmed the companions of Columbus in 1492. Gilbert says,[6\12] -"Other learned men have, in long navigations, observed the -differences of magnetic variations, as Thomas Hariot, Robert Hues, -Edward Wright, Abraham Kendall, all Englishmen: others have invented -magnetic instruments and convenient modes of observation, such as -are requisite for those who take long voyages, as William Borough in -his Book concerning the variation of the compass, William Barlo in -his supplement, William Norman in his _New Attractive_. This is that -Robert Norman (a good seaman and an ingenious artificer,) who first -discovered the _dip_ of magnetic iron." This important discovery was -made[7\12] in 1576. From the time when the difference of the -variation of the compass in different places became known, it was -important to mariners to register the variation in all parts of the -world. Halley was appointed to the command of a ship in the Royal -Navy by the Government of William and Mary, with orders "to seek by -observation the discovery of the rule for the variation of the -compass." He published Magnetic Charts, which {219} have been since -corrected and improved by various persons. The most recent are those -of Mr. Yates in 1817, and of M. Hansteen. The dip, as well as the -variation, was found to be different in different places. M. -Humboldt, in the course of his travels, collected many such -observations. And both the observations of variation and of dip -seemed to indicate that the earth, as to its effect on the magnetic -needle, may, approximately at least, be considered as a magnet, the -poles of which are not far removed from the earth's poles of -rotation. Thus we have a _magnetic equator_, in which the needle has -no dip, and which does not deviate far from the earth's equator; -although, from the best observations, it appears to be by no means a -regular circle. And the phenomena, both of the dip and of the -variation, in high northern latitudes, appear to indicate the -existence of a pole below the surface of the earth to the north of -Hudson's Bay. In his second remarkable expedition into those -regions, Captain Ross is supposed to have reached the place of this -pole; the dipping-needle there pointing vertically downwards, and -the variation-compass turning towards this point in the adjacent -regions. We shall hereafter have to consider the more complete and -connected views which have been taken of terrestrial magnetism. - -[Note 2\12: _Enc. Met._ art. _Magnetism_, p. 736.] - -[Note 3\12: Before 1269. _Enc. Met._ p. 737.] - -[Note 4\12: _De Magnete_, lib. iv. c. 1.] - -[Note 5\12: c. 3.] - -[Note 6\12: Lib. i. c. 1.] - -[Note 7\12: _Enc. Met._ p. 738.] - -In 1633, Gellibrand discovered that the variation is not constant, -as Gilbert imagined, but that at London it had diminished from -eleven degrees east in 1580, to four degrees in 1633. Since that -time the variation has become more and more westerly; it is now -about twenty-five degrees west, and the needle is supposed to have -begun to travel eastward again. - -The next important fact which appeared with respect to terrestrial -magnetism was, that the position of the needle is subject to a small -_diurnal_ variation: this was discovered in 1722, by Graham, a -philosophical instrument-maker, of London. The daily variation was -established by one thousand observations of Graham, and confirmed by -four thousand more made by Canton, and is now considered to be out -of dispute. It appeared also, by Canton's researches, that the -diurnal variation undergoes an annual inequality, being nearly a -quarter of a degree in June and July, and only half that quantity in -December and January. - -Having thus noticed the principal facts which belong to terrestrial -magnetism, we must return to the consideration of those phenomena -which gradually led to a consistent magnetic theory. Gilbert -observed that both smelted iron and hammered iron have the magnetic -virtue, {220} though in a weaker degree than the magnet -itself,[8\12] and he asserted distinctly that the magnet is merely -an ore of iron, (lib. i. c. 16, Quod magnes et vena ferri idem -sunt.) He also noted the increased energy which magnets acquire by -being _armed_; that is, fitted with a cap of polished iron at each -pole.[9\12] But we do not find till a later period any notice of the -distinction which exists between the magnetical properties of soft -iron and of hard steel;--the latter being susceptible of being -formed into _artificial magnets_, with permanent poles; while soft -iron is only _passively magnetic_, receiving a temporary polarity -from the action of a magnet near it, but losing this property when -the magnet is removed. About the middle of the last century, various -methods were devised of making artificial magnets, which exceeded in -power all magnetic bodies previously known. - -[Note 8\12: Lib. i. c. 9-13.] - -[Note 9\12: Lib. ii. c. 17.] - -The remaining experimental researches had so close an historical -connexion with the theory, that they will be best considered along -with it, and to that, therefore, we now proceed. - - - - -CHAPTER II. - -PROGRESS OF MAGNETIC THEORY. - - -THEORY OF MAGNETIC ACTION.--The assumption of a fluid, as a mode of -explaining the phenomena, was far less obvious in magnetic than in -electric cases, yet it was soon arrived at. After the usual -philosophy of the middle ages, the "forms" of Aquinas, the "efflux" -of Cusanus, the "vapors" of Costæus, and the like, which are -recorded by Gilbert,[10\12] we have his own theory, which he also -expresses by ascribing the effects to a "formal efficiency;"--a -"_form_ of primary globes; the proper entity and existence of their -homogeneous parts, which we may call a primary and radical and -astral _form_;"--of which forms there is one in the sun, one in the -moon, one in the earth, the latter being the magnetic virtue. - -[Note 10\12: Gilb. lib. ii. c. 3, 4] - -Without attempting to analyse the precise import of these expressions, -we may proceed to Descartes's explanation of magnetic phenomena. The -mode in which he presents this subject[11\12] is, perhaps, the {221} -most persuasive of his physical attempts. If a magnet be placed among -iron filings, these arrange themselves in curved lines, which proceed -from one pole of the magnet to the other. It was not difficult to -conceive these to be the traces of currents of ethereal matter which -circulate through the magnet, and which are thus rendered sensible -even to the eye. When phenomena could not be explained by means of one -vortex, several were introduced. Three Memoirs on Magnetism, written -on such principles, had the prize adjudged[12\12] by the French -Academy of Sciences in 1746. - -[Note 11\12: _Prin. Phil._ pars c. iv. 146.] - -[Note 12\12: Coulomb, 1789, p. 482.] - -But the Cartesian philosophy gradually declined; and it was not -difficult to show that the _magnetic curves_, as well as other -phenomena, would, in fact, result from the attraction and repulsion -of two poles. The analogy of magnetism with electricity was so -strong and clear, that similar theories were naturally proposed for -the two sets of facts; the distinction of bodies into conductors and -electrics in the one case, corresponding to the distinction of soft -and hard steel, in their relations to magnetism. Æpinus published a -theory of magnetism and electricity at the same time (1759); and the -former theory, like the latter, explained the phenomena of the -opposite poles as results of the excess and defect of a magnetic -"fluid," which was dislodged and accumulated in the ends of the -body, by the repulsion of its own particles, and by the attraction -of iron or steel, as in the case of induced electricity. The Æpinian -theory of magnetism, as of electricity, was recast by Coulomb, and -presented in a new shape, with two fluids instead of one. But before -this theory was reduced to calculation, it was obviously desirable, -in the first place, to determine the law of force. - -In magnetic, as in electric action, the determination of the law of -attraction of the particles was attended at first with some -difficulty, because the action which a finite magnet exerts is a -compound result of the attractions and repulsions of many points. -Newton had imagined the attractive force of magnetism to be -inversely as the cube of the distance; but Mayer in 1760, and -Lambert a few years later, asserted the law to be, in this as in -other forces, the inverse square. Coulomb has the merit of having -first clearly confirmed this law, by the use of his -torsion-balance.[13\12] He established, at the same time, other very -important facts, for instance, "that the directive magnetic force, -which the earth exerts upon a needle, is a constant quantity, -parallel {222} to the magnetic meridian, and passing through the -same point of the needle whatever be its position." This was the -more important, because it was necessary, in the first place, to -allow for the effect of the terrestrial force, before the mutual -action of the magnets could be extricated from the phenomena.[14\12] -Coulomb then proceeded to correct the theory of magnetism. - -[Note 13\12: _Mem. A. P._ 1784, 2d Mem. p. 593.] - -[Note 14\12: p. 603.] - -Coulomb's reform of the Æpinian theory, in the case of magnetism, as -in that of electricity, substituted two fluids (an _austral_ and a -_boreal_ fluid,) for the single fluid; and in this way removed the -necessity under which Æpinus found himself, of supposing all the -particles of iron and steel and other magnetic bodies to have a -peculiar repulsion for each other, exactly equal to their attraction -for the magnetic fluid. But in the case of magnetism, another -modification was necessary. It was impossible to suppose here, as in -the electrical phenomena, that one of the fluids was accumulated on -one extremity of a body, and the other fluid on the other extremity; -for though this might appear, at first sight, to be the case in a -magnetic needle, it was found that when the needle was cut into two -halves, the half in which the austral fluid had seemed to -predominate, acquired immediately a boreal pole opposite to its -austral pole, and a similar effect followed in the other half. The -same is true, into however many parts the magnetic body be cut. The -way in which Coulomb modified the theory so as to reconcile it with -such facts, is simple and satisfactory. He supposes[15\12] the -magnetic body to be made up of "molecules or integral parts," or, as -they were afterwards called by M. Poisson, "magnetic elements." In -each of these elements, (which are extremely minute,) the fluids can -be separated, so that each element has an austral and a boreal pole; -but the austral pole of an element which is adjacent to the boreal -pole of the next, neutralizes, or nearly neutralizes, its effect; so -that the sensible magnetism appears only towards the extremities of -the body, as it would do if the fluids could permeate the body -freely. We shall have exactly the same result, as to sensible -magnetic force, on the one supposition and on the other, as Coulomb -showed.[16\12] - -[Note 15\12: _Mem. A. P._ 1789, p. 488.] - -[Note 16\12: _Mem. A. P._ p. 492.] - -The theory, thus freed from manifest incongruities, was to be -reduced to calculation, and compared with experiment; this was done -in Coulomb's Seventh Memoir.[17\12] The difficulties of calculation -in this, as in the electric problem, could not be entirely -surmounted by the analysis of Coulomb; but by various artifices, he -obtained theoretically the {223} relative amount of magnetism at -several points of a needle,[18\12] and the proposition that the -directive force of the earth on similar needles saturated with -magnetism, was as the cube of their dimensions; conclusions which -agreed with experiment. - -[Note 17\12: _A. P._ 1789.] - -[Note 18\12: p. 485.] - -The agreement thus obtained was sufficient to give a great -probability to the theory; but an improvement of the methods of -calculation and a repetition of experiments, was, in this as in -other cases, desirable, as a confirmation of the labors of the -original theorist. These requisites, in the course of time, were -supplied. The researches of Laplace and Legendre on the figure of -the earth had (as we have already stated,) introduced some very -peculiar analytical artifices, applicable to the attractions of -spheroids; and these methods were employed by M. Biot in 1811, to -show that on an elliptical spheroid, the thickness of the fluid in -the direction of the radius would be as the distance from the -centre.[19\12] But the subject was taken up in a more complete -manner in 1824 by M. Poisson, who obtained general expressions for -the attractions or repulsions of a body of any form whatever, -magnetized by influence, upon a given point; and in the case of -spherical bodies was able completely to solve the equations which -determine these forces.[20\12] - -[Note 19\12: _Bull. des Sc._ No. li.] - -[Note 20\12: _A. P._ for 1821 and 2, published 1826.] - -Previously to these theoretical investigations, Mr. Barlow had made -a series of experiments on the effect of an iron sphere upon a -compass needle; and had obtained empirical formulæ for the amount of -the deviation of the needle, according to its dependence upon the -position and magnitude of the sphere. He afterwards deduced the same -formulæ from a theory which was, in fact, identical with that of -Coulomb, but which he considered as different, in that it supposed -the magnetic fluids to be entirely collected at the surface of the -sphere. He had indeed found, by experiment, that the surface was the -only part in which there was any sensible magnetism; and that a thin -shell of iron would produce the same effect as a solid ball of the -same diameter. - -But this was, in fact, a most complete verification of Coulomb's -theory. For though that theory did not suppose the magnetism to be -collected solely at the surface, as Mr. Barlow found it, it followed -from the theory, that the _sensible_ magnetic intensity assumed the -same distribution (namely, a surface distribution,) as if the fluids -could permeate the whole body, instead of the "magnetic elements" -only. Coulomb, indeed, had not expressly noticed the result, that -the sensible {224} magnetism would be confined to the surface of -bodies; but he had found that, in a long needle, the magnetic fluid -might be supposed to be concentrated very near the extremities, just -as it is in a long electric body. The theoretical confirmation of -this rule among the other consequences of the theory,--that the -sensible magnetism would be collected at the surface,--was one of -the results of Poisson's analysis. For it appeared that if the sum -of the electric elements of the body was equal to the whole body, -there would be no difference between the action of a solid sphere -and very thin shell. - -We may, then, consider the Coulombian theory to be fully established -and verified, as a representation of the laws of magnetical -phenomena. We may add, as a remarkable and valuable example of an -ulterior step in the course of sciences, the application of the laws -of the distribution of magnetism to the purposes of navigation. It -had been found that the mass of iron which exists in a ship produces -a deviation in the direction of the compass-needle, which was termed -"local attraction," and which rendered the compass an erroneous -guide. Mr. Barlow proposed to correct this by a plate of iron placed -near the compass; the plate being of comparatively small mass, but, -in consequence of its expanded form, and its proximity to the -needle, of equivalent effect to the disturbing cause. - -[2nd Ed.] [This proposed arrangement was not successful, because as -the ship turns into different positions, it may be considered as -revolving round a vertical axis; and as this does not coincide with -the magnetic axis, the relative magnetic position of the disturbing -parts of the ship, and of the correcting plate, will be altered, so -that they will not continue to counteract each other. In high -magnetic latitudes the correcting plate was used with success. - -But when iron ships became common, a correction of the effect of the -iron upon the ship's compass in the general case became necessary. -Mr. Airy devised the means of making this correction. By placing a -magnet and a mass of iron in certain positions relative to the -compass, the effect of the rest of the iron in the ship is -completely counteracted in all positions.[21\12]] - -[Note 21\12: See _Phil. Trans._ 1836.] - -But we have still to trace the progress of the theory of terrestrial -magnetism. - -_Theory of Terrestrial Magnetism._--Gilbert had begun a plausible -course of speculation on this point. "We must reject," he -says,[22\12] "in {225} the first place, that vulgar opinion of -recent writers concerning magnetic mountains, or a certain magnetic -rock, or an imaginary pole at a certain distance from the pole of -the earth." For, he adds, "we learn by experience, that there is no -such fixed pole or term in the earth for the variation." Gilbert -describes the whole earth as a magnetic globe, and attributes the -variation to the irregular form of its protuberances, the solid -parts only being magnetic. It was not easy to confirm or refute this -opinion, but other hypotheses were tried by various writers; for -instance, Halley had imagined, from the forms of the lines of equal -variation, that there must be four magnetic poles; but Euler[23\12] -showed that the "Halleian lines" would, for the most part, result -from the supposition of two magnetic poles, and assigned their -position so as to represent pretty well the known state of the -variation all over the world in 1744. But the variation was not the -only phenomenon which required to be taken into account; the dip at -different places, and also the intensity of the force, were to be -considered. We have already mentioned M. de Humboldt's collection of -observations of the dip. These were examined by M. Biot, with the -view of reducing them to the action of two poles in the supposed -terrestrial magnetic axis. Having, at first, made the distance of -these poles from the centre of the earth indefinite, he found that -his formulæ agreed more and more nearly with the observations, as -the poles were brought nearer; and that fact and theory coincided -tolerably well when both poles were at the centre. In 1809,[24\12] -Krafft simplified this result, by showing that, on this supposition, -the tangent of the dip was twice the tangent of the latitude of the -place as measured from the magnetic equator. But M. Hansteen, who -has devoted to the subject of terrestrial magnetism a great amount -of labor and skill, has shown that, taking together all the -observations which we possess, we are compelled to suppose four -magnetic poles; two near the north pole, and two near the south -pole, of the terrestrial globe; and that these poles, no two of -which are exactly opposite each other, are all in motion, with -different velocities, some moving to the east and some to the west. -This curious collection of facts awaits the hand of future -theorists, when the ripeness of time shall invite them to the task. - -[Note 22\12: Lib. iv. c. 1. _De Variatione._] - -[Note 23\12: _Ac. Berlin_, 1757.] - -[Note 24\12: _Enc. Met._ p. 742.] - -[2nd Ed.] [I had thus written in the first edition. The theorist who -was needed to reduce this accumulation of facts to their laws, {226} -had already laid his powerful hand upon them; namely, M. Gauss, a -mathematician not inferior to any of the great men who completed the -theory of gravitation. And institutions had been established for -extending the collection of the facts pertaining to it, on a scale -which elevates Magnetism into a companionship with Astronomy. M. -Hansteen's _Magnetismus der Erde_ was published in 1819. His -conclusions respecting the position of the four magnetic "poles" -excited so much interest in his own country, that the Norwegian -_Storthing_, or parliament, by a unanimous vote, provided funds for -a magnetic expedition which he was to conduct along the north of -Europe and Asia; and this they did at the very time when they -refused to make a grant to the king for building a palace at -Christiania. The expedition was made in 1828-30, and verified -Hansteen's anticipations as to the existence of a region of magnetic -convergence in Siberia, which he considered as indicating a "pole" -to the north of that country. M. Erman also travelled round the -earth at the same time, making magnetic observations. - -About the same time another magnetical phenomenon attracted -attention. Besides the general motion of the magnetic poles, and the -diurnal movements of the needle, it was found that small and -irregular disturbances take place in its position, which M. de -Humboldt termed _magnetic storms_. And that which excited a strong -interest on this subject was the discovery that these magnetic -storms, seen only by philosophers who watch the needle with -microscopic exactness, rage simultaneously over large tracts of the -surface of our globe. This was detected about 1825 by a comparison -of the observations of M. Arago at Paris with simultaneous -observations of M. Kupffer at Kasan in Russia, distant more than 47 -degrees of longitude. - -At the instance of M. de Humboldt, the Imperial Academy of Russia -adopted with zeal the prosecution of this inquiry, and formed a chain -of magnetic stations across the whole of the Russian empire. Magnetic -observations were established at Petersburg and at Kasan, and -corresponding observations were made at Moscow, at Nicolaieff in the -Crimea, and Barnaoul and Nertchinsk in Siberia, at Sitka in Russian -America, and even at Pekin. To these magnetic stations the Russian -government afterwards added, Catharineburg in Russia Proper, -Helsingfors in Finland, Teflis in Georgia. A comparison of the results -obtained at four of these stations made by MM. de Humboldt and Dove, -in the year 1830, showed that the magnetic disturbances were -simultaneous, and were for the most parallel in their progress. {227} - -Important steps in the prosecution of this subject were soon after -made by M. Gauss, the great mathematician of Göttingen. He contrived -instruments and modes of observation far more perfect than any -before employed, and organized a system of comparative observations -throughout Europe. In 1835, stations for this purpose were -established at Altona, Augsburg, Berlin, Breda, Breslau, Copenhagen, -Dublin, Freiberg, Göttingen, Greenwich, Hanover, Leipsic, Marburg, -Milan, Munich, Petersburg, Stockholm, and Upsala. At these places, -six times in the year, observations were taken simultaneously, at -intervals of five minutes for 24 hours. The _Results of the Magnetic -Association_ (Resultaten des Magnetischen Vereins) were published by -MM. Gauss and Weber, beginning in 1836. - -British physicists did not at first take any leading part in these -plans. But in 1836, Baron Humboldt, who by his long labors and -important discoveries in this subject might be considered as -peculiarly entitled to urge its claims, addressed a letter to the -Duke of Sussex, then President of the Royal Society, asking for the -co-operation of this country in so large and hopeful a scheme for -the promotion of science. The Royal Society willingly entertained -this appeal; and the progress of the cause was still further -promoted when it was zealously taken up by the British Association -for the Advancement of Science, assembled at Newcastle in 1838. The -Association there expressed its strong interest in the German system -of magnetic observations; and at the instigation of this body, and -of the Royal Society, four complete magnetical observatories were -established by the British government, at Toronto, St. Helena, the -Cape of Good Hope, and Van Diemen's Land. The munificence of the -Directors of the East India Company founded and furnished an equal -number at Simla (in the Himalayah), Madras, Bombay, and Sincapore. -Sir Thomas Brisbane added another at his own expense at Kelso, in -Scotland. Besides this, the government sent out a naval expedition -to make discoveries (magnetic among others), in the Antarctic -regions, under the command of Sir James Ross. Other states lent -their assistance also, and founded or reorganized their magnetic -observatories. Besides those already mentioned, one was established -by the French government at Algiers; one by the Belgian, at -Brussels; two by Austria, at Prague and Milan; one by Prussia, at -Breslau; one by Bavaria, at Munich; one by Spain, at Cadiz; there -are two in the United States, at Philadelphia and Cambridge; one at -Cairo, founded by the Pasha of Egypt; and in India, one at -Trevandrum, established by the Rajah of Travancore; and one by {228} -the King of Oude, at Lucknow. At all these distant stations the same -plan was followed out, by observations strictly simultaneous, made -according to the same methods, with the same instrumental means. -Such a scheme, combining world-wide extent with the singleness of -action of an individual mind, is hitherto without parallel. - -At first, the British stations were established for three years -only; but it was thought advisable to extend this period three years -longer, to end in 1845. And when the termination of that period -arrived, a discussion was held among the magneticians themselves, -whether it was better to continue the observations still, or to -examine and compare the vast mass of observations already collected, -so as to see to what results and improvements of methods they -pointed. This question was argued at the meeting of the British -Association at Cambridge in that year; and the conference ended in -the magneticians requesting to have the observations continued, at -some of the observatories for an indefinite period, at others, till -the year 1848. In the mean time the Antarctic expedition had brought -back a rich store of observations, fitted to disclose the magnetic -condition of those regions which it had explored. These were -_discussed_, and their results exhibited, in the _Philosophical -Transactions_ for 1843, by Col. Sabine, who had himself at various -periods, made magnetic observations in the Arctic regions, and in -several remote parts of the globe, and had always been a zealous -laborer in this fruitful field. The general mass of the observations -was placed under the management of Professor Lloyd, of Dublin, who -has enriched the science of magnetism with several valuable -instruments and methods, and who, along with Col. Sabine, made a -magnetic survey of the British Isles in 1835 and 1836. - -I do not dwell upon magnetic surveys of various countries made by -many excellent observers; as MM. Quetelet, Forbes, Fox, Bache and -others. - -The facts observed at each station were, the _intensity_ of the -magnetic force; the _declination_ of the needle from the meridian, -sometimes called the _variation_; and its _inclination_ to the -horizon, _the dip_;--or at least, some elements equivalent to these. -The values of these elements at any given time, if known, can be -expressed by charts of the earth's surface, on which are drawn the -_isodynamic_, _isogonal_, and _isoclinal_ curves. The second of -these kinds of charts contain the "Halleian lines" spoken of in a -previous page. Moreover the magnetic elements at each place are to -be observed in such a {229} manner as to determine both their -_periodical_ variations (the changes which occur in the period of a -day, and of a year), the _secular_ changes, as the gradual increase -or diminution of the declination at the same place for many years; -and the _irregular_ fluctuations which, as we have said, are -simultaneous over a large part, or the whole, of the earth's surface. - -When these Facts have been ascertained over the whole extent of the -earth's surface, we shall still have to inquire what is the Cause of -the changes in the forces which these phenomena disclose. But as a -basis for all speculation on that subject, we must know the law of the -phenomena, and of the forces which immediately produce them. I have -already said that Euler tried to account for the Halleian lines by -means of _two_ magnetic "poles," but that M. Hansteen conceived it -necessary to assume _four_. But an entirely new light has been thrown -upon this subject by the beautiful investigations of Gauss, in his -_Theory of Terrestrial Magnetism_, published in 1839. He remarks that -the term "poles," as used by his predecessors, involves an assumption -arbitrary, and, as it is now found, false; namely, that certain -definite points, two, four, or more, acting according to the laws of -ordinary magnetical poles, will explain the phenomena. He starts from -a more comprehensive assumption, that magnetism is distributed -throughout the mass of the earth in an unknown manner. On this -assumption he obtains a function _V_, by the differentials of which -the elements of the magnetic force at any point will be expressed. -This function _V_ is well known in physical astronomy, and is obtained -by summing all the elements of magnetic force in each particle, each -multiplied by the reciprocal of its distance; or as we may express it, -by taking the sum of each element and its proximity jointly. Hence it -has been proposed[25\12] to term this function the "_integral -proximity_" of the attracting mass.[26\12] By using the most refined -{230} mathematical artifices for deducing the values of _V_ and its -differentials in converging series, he is able to derive the -coefficients of these series from the observed magnetic elements at -certain places, and hence, to calculate them for all places. The -comparison of the calculation with the observed results is, of course, -the test of the truth of the theory. - -[Note 25\12: _Quart. Rev._ No. 131, p. 283.] - -[Note 26\12: The function V is of constant occurrence in -investigations respecting attractions. It is introduced by Laplace -in his investigations respecting the attractions of spheroids, _Méc. -Cél._ Livr. III. Art. 4. Mr. Green and Professor Mac Cullagh have -proposed to term this function the _Potential_ of the system; but -this term (though suggested, I suppose, by analogy with the -substantive _Exponential_), does not appear convenient in its form. -On the other hand, the term _Integral Proximity_ does not indicate -that which gives the function its peculiar claim to distinction; -namely, that its differentials express the power or attraction of -the system. Perhaps _Integral Potentiality_, or _Integral -Attractivity_, would be a term combining the recommendations of both -the others.] - -The degree of convergence of the series depends upon the unknown -distribution of magnetism within the earth. "If we could venture to -assume," says M. Gauss, "that the members have a sensible influence -only as far as the fourth order, complete observations from eight -points would be sufficient, theoretically considered, for the -determination of the coefficients." And under certain limitations, -making this assumption, as the best we can do at present, M. Gauss -obtains from eight places, 24 coefficients (each supplying three -elements), and hence calculates the magnetic elements (intensity, -variation and dip) at 91 places in all parts of the earth. He finds -his calculations approach the observed values with a degree of -exactness which appears to be quite convincing as to the general -truth of his results; especially taking into account how entirely -unlimited is his original hypothesis. - -It is one of the most curious results of this investigation that -according to the most simple meaning which we can give to the term -"pole" the earth has only _two_ magnetic poles; that is, two points -where the direction of the magnetic force is vertical. And thus the -_isogonal curves_ may be looked upon as _deformations_ of the curves -deduced by Euler from the supposition of two poles, the deformation -arising from this, that the earth does not contain a single definite -magnet, but irregularly diffused magnetical elements, which still -have collectively a distinct resemblance to a single magnet. And -instead of Hansteen's Siberian pole, we have a Siberian region in -which the needles converge; but if the apparent convergence be -pursued it nowhere comes to a point; and the like is the case in the -Antarctic region. When the 24 Gaussian elements at any time are -known the magnetic condition of the globe is known, just as the -mechanical condition of the solar system is known, when we know the -elements of the orbits of the satellites and planets and the mass of -each. And the comparison of this magnetic condition of the globe at -distant periods of time cannot fail to supply materials for future -researches and speculations with regard to the agencies by which the -condition of the earth is determined. The condition of which we here -speak must necessarily be its _mechanico-chemical_ condition, being -expressed, as it will be, in terms of the mechanico-chemical -sciences. The {231} investigations I have been describing belong to -the mechanical side of the subject: but when philosophers have to -consider the causes of the secular changes which are found to occur -in this mechanical condition, they cannot fail to be driven to -electrical, that is, chemical agencies and laws. - -I can only allude to Gauss's investigations respecting the _Absolute -Measure_ of the Earth's Magnetic Force. To determine the ratio of the -magnetic force of the earth to that of a known magnet, Poisson -proposed to observe the time of vibration of a second magnet. The -method of Gauss, now universally adopted, consists in observing the -position of equilibrium of the second magnet when deflected by the -first. - -The manner in which the business of magnetic observation has been -taken up by the governments of our time makes this by far the -greatest scientific undertaking which the world has ever seen. The -result will be that we shall obtain in a few years a knowledge of -the magnetic constitution of the earth which otherwise it might have -required centuries to accumulate. The secular magnetic changes must -still require a long time to reduce to their laws of phenomena, -except observation be anticipated or assisted by some happy -discovery as to the cause of these changes. But besides the special -gain to magnetic science by this great plan of joint action among -the nations of the earth, there is thereby a beginning made in the -recognition and execution of the duty of forwarding science in -general by national exertions. For at most of the magnetic -observatories, meteorological observations are also carried on; and -such observations, being far more extensive, systematic, and -permanent than those which have usually been made, can hardly fail -to produce important additions to science. But at any rate they do -for science that which nations can do, and individuals cannot; and -they seek for scientific truths in a manner suitable to the respect -now professed for science and to the progress which its methods have -made. Nor are we to overlook the effect of such observations as -means of training men in the pursuit of science. "There is amongst -us," says one of the magnetic observers, "a growing recognition of -the importance, both for science and for practical life, of forming -exact observers of nature. Hitherto astronomy alone has afforded a -very partial opportunity for the formation of fine observers, of -which few could avail themselves. Experience has shown that magnetic -observations may serve as excellent training schools in this -respect."[27\12]] {232} - -[Note 27\12: _Letter_ of W. Weber. _Brit. Assoc. Rep._ 1845, p. 17.] - -The various other circumstances which terrestrial magnetism -exhibits,--the diurnal and annual changes of the position of the -compass-needle;--the larger secular change which affects it in the -course of years;--the difference of intensity at different places, -and other facts, have naturally occupied philosophers with the -attempt to determine, both the laws of the phenomena and their -causes. But these attempts necessarily depend, not upon laws of -statical magnetism, such as they have been explained above; but upon -the laws by which the production and intensity of magnetism in -different cases are regulated;--laws which belong to a different -province, and are related to a different set of principles. Thus, -for example, we have not attempted to explain the discovery of the -laws by which heat influences magnetism; and therefore we cannot now -give an account of those theories of the facts relating to -terrestrial magnetism, which depend upon the influence of -temperature. The conditions of excitation of magnetism are best -studied by comparing this force with other cases where the same -effects are produced by very different apparent agencies; such as -galvanic and thermo-electricity. To the history of these we shall -presently proceed. - -_Conclusion._--The hypothesis of magnetic fluids, as physical -realities, was never widely or strongly embraced, as that of -electric fluids was. For though the hypothesis accounted, to a -remarkable degree of exactness, for large classes of the phenomena, -the presence of a material fluid was not indicated by facts of a -different kind, such as the spark, the discharge from points, the -shock, and its mechanical effects. Thus the belief of a peculiar -magnetic fluid or fluids was not forced upon men's minds; and the -doctrine above stated was probably entertained by most of its -adherents, chiefly as a means of expressing the laws of phenomena in -their elementary form. - -One other observation occurs here. We have seen that the supposition -of a fluid moveable from one part of bodies to another, and capable -of accumulation in different parts of the surface, appeared at first -to be as distinctly authorized by magnetic as by electric phenomena; -and yet that it afterwards appeared, by calculation, that this must -be considered as a derivative result; no real transfer of fluid -taking place except within the limits of the insensible particles of -the body. Without attempting to found a formula of philosophizing on -this circumstance, we may observe, that this occurrence, like the -disproof of heat as a material fluid, shows the possibility of an -hypothesis which shall very exactly satisfy many phenomena, and yet -be incomplete: it {233} shows, too, the necessity of bringing facts -of all kinds to bear on the hypothesis; thus, in this case it was -requisite to take into account the facts of junction and separation -of magnetic bodies, as well as their attractions and repulsions. - -If we have seen reason to doubt the doctrine of electric fluids as -physical realities, we cannot help pronouncing upon the magnetic -fluids as having still more insecure claims to a material existence, -even on the grounds just stated. But we may add considerations still -more decisive; for at a further stage of discovery, as we shall see, -magnetic and electric action were found to be connected in the -closest manner, so as to lead to the persuasion of their being -different effects of one common cause. After those discoveries, no -philosopher would dream of assuming electric fluids and magnetic -fluids as two distinct material agents. Yet even now the nature of -the dependence of magnetism upon any other cause is extremely -difficult to conceive. But till we have noticed some of the -discoveries to which we have alluded, we cannot even speculate about -that dependence. We now, therefore, proceed to sketch the history of -these discoveries. - - - -{{235}} -BOOK XIII. - -_MECHANICO-CHEMICAL SCIENCES._ - -(CONTINUED.) - - -HISTORY OF GALVANISM, -OR -VOLTAIC ELECTRICITY. - - - Percusssæ gelido trepidant sub pectore fibræ, - Et nova desuetis subrepens vita medullis - Miscetur morti: tunc omnis palpitat artus - Tenduntur nervi; nec se tellure cadaver - Paullatim per membra levat; terrâque repulsum est - Erectumque simul. - LUCAN. vi. 752. - - The form which lay before inert and dead, - Sudden a piercing thrill of change o'erspread; - Returning life gleams in the stony face, - The fibres quiver and the sinews brace, - Move the stiff limbs;--nor did the body rise - With tempered strength which genial life supplies, - But upright starting, its full stature held, - As though the earth the supine corse repelled. - - - -{{237}} -CHAPTER I. - -DISCOVERY OF VOLTAIC ELECTRICITY. - - -WE have given the name of _mechanico-chemical_ to the class of -sciences now under our consideration; for these sciences are -concerned with cases in which mechanical effects, that is, -attractions and repulsions, are produced; while the conditions under -which these effects occur, depend, as we shall hereafter see, on -chemical relations. In that branch of these sciences which we have -just treated of, Magnetism, the mechanical phenomena were obvious, -but their connexion with chemical causes was by no means apparent, -and, indeed, has not yet come under our notice. - -The subject to which we now proceed, Galvanism, belongs to the same -group, but, at first sight, exhibits only the other, the chemical, -portion of the features of the class; for the connexion of galvanic -phenomena with chemical action was soon made out, but the mechanical -effects which accompany them were not examined till the examination -was required by a new train of discovery. It is to be observed, that -I do not include in the class of mechanical effects the convulsive -motions in the limbs of animals which are occasioned by galvanic -action; for these movements are produced, not by attraction and -repulsion, but by muscular irritability; and though they indicate -the existence of a peculiar agency, cannot be used to measure its -intensity and law. - -The various examples of the class of agents which we here -consider,--magnetism, electricity, galvanism, electro-magnetism, -thermo-electricity,--differ from each other principally in the -circumstances by which they are called into action; and these -differences are in reality of a chemical nature, and will have to be -considered when we come to treat of the inductive steps by which the -general principles of chemical theory are established. In the -present part of our task, therefore, we must take for granted the -chemical conditions on which the excitation of these various kinds -of action depends, and trace the history of the discovery of their -mechanical laws only. This rule will much abridge the account we -have here to give of the progress of discovery in the provinces to -which I have just referred. {238} - -The first step in this career of discovery was that made by Galvani, -Professor of Anatomy at Bologna. In 1790, electricity, as an -experimental science, was nearly stationary. The impulse given to -its progress by the splendid phenomena of the Leyden phial had -almost died away; Coulomb was employed in systematizing the theory -of the electric fluid, as shown by its statical effects; but in all -the other parts of the subject, no great principle or new result had -for some time been detected. The first announcement of Galvani's -discovery in 1791 excited great notice, for it was given forth as a -manifestation of electricity under a new and remarkable character; -namely, as residing in the muscles of animals.[1\13] The limbs of a -dissected frog were observed to move, when touched with pieces of -two different metals; the agent which produced these motions was -conceived to be identified with electricity, and was termed _animal -electricity_; and Galvani's experiments were repeated, with various -modifications, in all parts of Europe, exciting much curiosity, and -giving rise to many speculations. - -[Note 1\13: _De Viribus Electricis in Motu Musculari_, Comm. Bonon. -t. vii. 1792.] - -It is our business to determine the character of each great -discovery which appears in the progress of science. Men are fond of -repeating that such discoveries are most commonly the result of -accident; and we have seen reason to reject this opinion, since that -preparation of thought by which the accident produces discovery is -the most important of the conditions on which the successful event -depends. Such accidents are like a spark which discharges a gun -already loaded and pointed. In the case of Galvani, indeed, the -discovery may, with more propriety than usual, be said to have been -casual; but in the form in which it was first noted, it exhibited no -important novelty. His frog was lying on a table near the conductor -of an electrical machine, and the convulsions appeared only when a -spark was taken from the machine. If Galvani had been as good a -physicist as he was an anatomist, he would probably have seen that -the movements so occasioned proved only that the muscles or nerves, -or the two together, formed a very sensitive indicator of electrical -action. It was when he produced such motions by contact of metals -alone, that he obtained an important and fundamental fact in science. - -The analysis of this fact into its real and essential conditions was -the work of Alexander Volta, another Italian professor. Volta, -indeed, possessed that knowledge of the subject of electricity which -made a hint like that of Galvani the basis of a new science. Galvani -appears {239} never to have acquired much general knowledge of -electricity: Volta, on the other hand, had labored at this branch of -knowledge from the age of eighteen, through a period of nearly -thirty years; and had invented an _electrophorus_ and an _electrical -condenser_, which showed great experimental skill. When he turned -his attention to the experiments made by Galvani, he observed that -the author of them had been far more surprised than he needed to be, -at those results in which an electrical spark was produced; and that -it was only in the cases in which no such apparatus was employed, -that the observations could justly be considered as indicating a new -law, or a new kind of electricity.[2\13] He soon satisfied -himself[3\13] (about 1794) that the essential conditions of this -kind of action depended on the metals; that it is brought into play -most decidedly when two different metals touch each other, and are -connected by any moist body;--and that the parts of animals which -had been used discharged the office both of such moist bodies, and -of very sensitive electrometers. The _animal_ electricity of Galvani -might, he observed, be with more propriety called _metallic_ -electricity. - -[Note 2\13: _Phil. Trans._ 1793, p. 21.] - -[Note 3\13: See Fischer, viii. 625.] - -The recognition of this agency as a peculiar kind of _electricity_, -arose in part perhaps, at first, from the confusion made by Galvani -between the cases in which his electrical machine was, and those in -which it was not employed. But the identity was confirmed by its -being found that the known difference of electrical conductors and -non-conductors regulated the conduction of the new influence. The -more exact determination of the new facts to those of electricity -was a succeeding step of the progress of the subject. - -The term "animal electricity" has been superseded by others, of -which _galvanism_ is perhaps the most familiar. I think it will -appear from what has been said, that Volta's office in this -discovery is of a much higher and more philosophical kind than that -of Galvani; and it would, on this account, be more fitting to employ -the term _voltaic electricity_; which, indeed, is very commonly -used, especially by our most recent and comprehensive writers. - -Volta more fully still established his claim as the main originator -of this science by his next step. When some of those who repeated -the experiments of Galvani had expressed a wish that there was some -method of multiplying the effect of _this_ electricity, such as the -Leyden phial supplies for common electricity, they probably thought -their wishes far from a realization. But the _voltaic pile_, which -Volta {240} described in the _Philosophical Transactions_ for 1800, -completely satisfies this aspiration; and was, in fact, a more -important step in the history of electricity than the Leyden jar had -been. It has since undergone various modifications, of which the -most important was that introduced by **Cruickshanks, who[4\13] -substituted a trough for a pile. But in all cases the principle of -the instrument was the same;--a continued repetition of the triple -combination of two metals and a fluid in contact, so as to form a -circuit which returns into itself. - -[Note 4\13: Fischer, viii. p. 683.] - -Such an instrument is capable of causing effects of great intensity; -as seen both in the production of light and heat, and in chemical -changes. But the discovery with which we are here concerned, is not -the details and consequences of the effects, (which belong to -chemistry,) but the analysis of the conditions under which such -effects take place; and this we may consider as completed by Volta -at the epoch of which we speak. - - - - -CHAPTER II. - -RECEPTION AND CONFIRMATION OF THE DISCOVERY OF VOLTAIC ELECTRICITY. - - -GALVANI'S experiments excited a great interest all over Europe, in -consequence partly of a circumstance which, as we have seen, was -unessential, the muscular contractions and various sensations which -they occasioned. Galvani himself had not only considered the animal -element of the circuit as the origin of the electricity, but had -framed a theory,[5\13] in which he compared the muscles to charged -jars, and the nerves to the discharging wires; and a controversy -was, for some time, carried on, in Italy, between the adherents of -Galvani and those of Volta.[6\13] - -[Note 5\13: Ib. viii. 613.] - -[Note 6\13: Ib. viii. 619.] - -The galvanic experiments, and especially those which appeared to -have a physiological bearing, were verified and extended by a number -of the most active philosophers of Europe, and especially William -von Humboldt. A commission of the Institute of France, appointed in -1797, repeated many of the known experiments, but does not seem to -have decided any disputed points. The researches of this {241} -commission referred rather to the discoveries of Galvani than to -those of Volta: the latter were, indeed, hardly known in France till -the conquest of Italy by Bonaparte, in 1801. France was, at the -period of these discoveries, separated from all other countries by -war, and especially from England,[7\13] where Volta's Memoirs were -published. - -[Note 7\13: _Biog. Univ._, art. _Volta_, (by Biot.)] - -The political revolutions of Italy affected, in very different -manners, the two discoverers of whom we speak. Galvani refused to -take an oath of allegiance to the Cisalpine republic, which the -French conqueror established; he was consequently stripped of all -his offices; and deprived, by the calamities of the times, of most -of his relations, he sank into poverty, melancholy, and debility. At -last his scientific reputation induced the republican rulers to -decree his restoration to his professorial chair; but his claims -were recognised too late, and he died without profiting by this -intended favor, in 1798. - -Volta, on the other hand, was called to Paris by Bonaparte as a man -of science, and invested with honors, emoluments, and titles. The -conqueror himself, indeed, was strongly interested by this train of -research.[8\13] He himself founded valuable prizes, expressly with a -view to promote its prosecution. At this period, there was something -in this subject peculiarly attractive to his Italian mind; for the -first glimpses of discoveries of great promise have always excited -an enthusiastic activity of speculation in the philosophers of -Italy, though generally accompanied with a want of precise thought. -It is narrated[9\13] of Bonaparte, that after seeing the -decomposition of the salts by means of the voltaic pile, he turned -to Corvisart, his physician, and said, "Here, doctor, is the image -of life; the vertebral column is the pile, the liver is the -negative, the bladder the positive, pole." The importance of voltaic -researches is not less than it was estimated by Bonaparte; but the -results to which it was to lead were of a kind altogether different -from those which thus suggested themselves to his mind. The -connexion of mechanical and chemical action was the first great -point to be dealt with; and for this purpose the laws of the -mechanical action of voltaic electricity were to be studied. - -[Note 8\13: Becquerel, _Traité d'Electr._ t. i. p. 107.] - -[Note 9\13: Ib. t. i. p. 108.] - -It will readily be supposed that the voltaic researches, thus begun, -opened a number of interesting topics of examination and discussion. -These, however, it does not belong to our place to dwell upon at -present; since they formed parts of the theory of the subject, which -{242} was not completed till light had been thrown upon it from -other quarters. The identity of galvanism with electricity, for -instance, was at first, as we have intimated, rather conjectured -than proved. It was denied by Dr. Fowler, in 1793; was supposed to -be confirmed by Dr. Wells two years later; but was, still later, -questioned by Davy. The nature of the operation of the pile was -variously conceived. Volta himself had obtained a view of it which -succeeding researches confirmed, when he asserted,[10\13] in 1800, -that it resembled an electric battery feebly charged and constantly -renewing its charge. In pursuance of this view, the common -electrical action was, at a later period (for instance by Ampère, in -1820), called _electrical tension_, while the voltaic action was -called the _electrical current_, or _electromotive action_. The -different effects produced, by increasing the size and the number of -the plates in the voltaic trough, were also very remarkable. The -power of producing heat was found to depend on the size of the -plates; the power of producing chemical changes, on the other hand, -was augmented by the number of plates of which the battery -consisted. The former effect was referred to the increased -_quantity_, the latter to the _intensity_, of the electric fluid. We -mention these distinctions at present, rather for the purpose of -explaining the language in which the results of the succeeding -investigations are narrated, than with the intention of representing -the hypotheses and measures which they imply, as clearly -established, at the period of which we speak. For that purpose new -discoveries were requisite, which we have soon to relate. - -[Note 10\13: _Phil. Trans._ p. 403.] - - - - -CHAPTER III. - -DISCOVERY OF THE LAWS OF THE MUTUAL ATTRACTION AND REPULSION OF -VOLTAIC CURRENTS.--AMPÈRE. - - -IN order to show the place of voltaic electricity among the -mechanico-chemical sciences, we must speak of its mechanical laws as -separate from the laws of electro-magnetic action; although, in -fact, it was only in consequence of the forces which conducting -voltaic wires exert upon magnets, that those forces were detected -which they exert upon each {243} other. This latter discovery was -made by M. Ampère; and the extraordinary rapidity and sagacity with -which he caught the suggestion of such forces, from the -electro-magnetic experiments of M. Oersted, (of which we shall speak -in the next chapter,) well entitle him to be considered as a great -and independent discoverer. As he truly says,[11\13] "it by no means -followed, that because a conducting wire exerted a force on a -magnet, two conducting wires must exert a force on each other; for -two pieces of soft iron, both of which affect a magnet, do not -affect each other." But immediately on the promulgation of Oersted's -experiments, in 1820, Ampère leapt forwards to a general theory of -the facts, of which theory the mutual attraction and repulsion of -conducting voltaic wires was a fundamental supposition. The -supposition was immediately verified by direct trial; and the laws -of this attraction and repulsion were soon determined, with great -experimental ingenuity, and a very remarkable command of the -resources of analysis. But the experimental and analytical -investigation of the mutual action of voltaic or electrical -currents, was so mixed up with the examination of the laws of -electro-magnetism, which had given occasion to the investigation, -that we must not treat the two provinces of research as separate. -The mention in this place, premature as it might appear, of the -labors of Ampère, arises inevitably from his being the author of a -beautiful and comprehensive generalization, which not only included -the phenomena exhibited by the new combinations of Oersted, but also -disclosed forces which existed in arrangements already familiar, -although they had never been detected till the theory pointed out -how they were to be looked for. - -[Note 11\13: _Théorie des Phénom. Electrodynamiques_, p. 113.] - - - - -CHAPTER IV. - -DISCOVERY OF ELECTRO-MAGNETIC ACTION.--OERSTED. - - -THE impulse which the discovery of galvanism, in 1791, and that of -the voltaic pile, in 1800, had given to the study of electricity as -a mechanical science, had nearly died away in 1820. It was in that -year that M. Oersted, of Copenhagen, announced that the conducting -{244} wire of a voltaic circuit, acts upon a magnetic needle; and -thus recalled into activity that endeavor to connect magnetism with -electricity, which, though apparently on many accounts so hopeful, -had hitherto been attended with no success. Oersted found that the -needle has a tendency to place itself _at right angles_ to the -wire;--a kind of action altogether different from any which had been -suspected. - -This observation was of vast importance; and the analysis of its -conditions and consequences employed the best philosophers in Europe -immediately on its promulgation. It is impossible, without great -injustice, to refuse great merit to Oersted as the author of the -discovery. We have already said that men appear generally inclined -to believe remarkable discoveries to be accidental, and the -discovery of Oersted has been spoken of as a casual insulated -experiment.[12\13] Yet Oersted had been looking for such an -_accident_ probably more carefully and perseveringly than any other -person in Europe. In 1807, he had published[13\13] a work, in which -he professed that his purpose was "to ascertain whether electricity, -in its most latent state, had any effect on the magnet." And he, as -I know from his own declaration, considered his discovery as the -natural sequel and confirmation of his early researches; as, indeed, -it fell in readily and immediately with speculations on these -subjects then very prevalent in Germany. It was an accident like -that by which a man guesses a riddle on which his mind has long been -employed. - -[Note 12\13: See _Schelling ueber Faraday's Entdeckung_, p. 27.] - -[Note 13\13: Ampère, p. 69.] - -Besides the confirmation of Oersted's observations by many -experimenters, great additions were made to his facts: of these, one -of the most important was due to Ampère. Since the earth is in fact -magnetic, the voltaic wire ought to be affected by terrestrial -magnetism alone, and ought to tend to assume a position depending on -the position of the compass-needle. At first, the attempts to -produce this effect failed, but soon, with a more delicate -apparatus, the result was found to agree with the anticipation. - -It is impossible here to dwell on any of the subsequent researches, -except so far as they are essential to our great object, the progress -towards a general theory of the subject. I proceed, therefore, -immediately to the attempts made towards this object. {245} - - - - -CHAPTER V. - -DISCOVERY OF THE LAWS OF ELECTRO-MAGNETIC ACTION. - - -ON attempting to analyse the electro-magnetic phenomena observed by -Oersted and others into their simplest forms, they appeared, at -least at first sight, to be different from any mechanical actions -which had yet been observed. It seemed as if the conducting wire -exerted on the pole of the magnet a force which was not attractive -or repulsive, but _transverse_;--not tending to draw the point acted -on nearer, or to push it further off, in the line which reached from -the acting point, but urging it to move at right angles to this -line. The forces appeared to be such as Kepler had dreamt of in the -infancy of mechanical conceptions; rather than such as those of -which Newton had established the existence in the solar system, and -such as he, and all his successors, had supposed to be the only -kinds of force which exist in nature. The north pole of the needle -moved as if it were impelled by a vortex revolving round the wire in -one direction, while the south pole seemed to be driven by an -opposite vortex. The case seemed novel, and almost paradoxical. - -It was soon established by experiments, made in a great variety of -forms, that the mechanical action was really of this transverse -kind. And a curious result was obtained, which a little while before -would have been considered as altogether incredible;--that this -force would cause a constant and rapid revolution of either of the -bodies about the other;--of the conducting wire about the magnet, or -of the magnet about the conducting wire. This was effected by Mr. -Faraday in 1821. - -The laws which regulated the intensity of this force, with reference -to the distance and position of the bodies, now naturally came to be -examined. MM. Biot and Savart in France, and Mr. Barlow in England, -instituted such measures; and satisfied themselves that the -elementary force followed the law of magnitude of all known -elementary forces, in being inversely as the square of the distance; -although, in its direction, it was so entirely different from other -forces. But the investigation of the _laws of phenomena_ of the -subject was too closely connected with the choice of a mechanical -theory, to be established {246} previously and independently, as had -been done in astronomy. The experiments gave complex results, and -the analysis of these into their elementary actions was almost an -indispensable step in order to disentangle their laws. We must, -therefore, state the progress of this analysis. - - - - -CHAPTER VI. - -THEORY OF ELECTRODYNAMICAL ACTION. - - -AMPÈRE'S THEORY.--Nothing can show in a more striking manner the -advanced condition of physical speculation in 1820, than the -reduction of the strange and complex phenomena of electromagnetism -to a simple and general theory as soon as they were published. -Instead of a gradual establishment of laws of phenomena, and of -theories more and more perfect, occupying ages, as in the case of -astronomy, or generations, as in the instances of magnetism and -electricity, a few months sufficed for the whole process of -generalization; and the experiments made at Copenhagen were -announced at Paris and London, almost at the same time with the -skilful analysis and comprehensive inductions of Ampère. - -Yet we should err if we should suppose, from the celerity with which -the task was executed, that it was an easy one. There were required -in the author of such a theory, not only those clear conceptions of -the relations of space and force, which are the first conditions of -all sound theory, and a full possession of the experiments; but also -a masterly command of the mathematical arms by which alone the -victory could be gained, and a sagacious selection of proper -experiments which might decide the fate of the proposed hypothesis. - -It is true, that the nature of the requisite hypothesis was not -difficult to see in a certain vague and limited way. The -conducting-wire and the magnetic needle had a tendency to arrange -themselves at right angles to one another. This might be represented -by supposing the wire to be made up of transverse magnetic needles, -or by supposing the needle to be made up of transverse -conducting-wires; for it was easy to conceive forces which should -bring corresponding elements, either magnetic or voltaic, into -parallel positions; and then the {247} general phenomena above -stated would be accounted for. And the choice between the two modes -of conception, appeared at first sight a matter of indifference. The -majority of philosophers at first adopted, or at least employed, the -former method, as Oersted in Germany, Berzelius in Sweden, Wollaston -in England. - -Ampère adopted the other view, according to which the magnet is made -up of conducting-wires in a transverse position. But he did for his -hypothesis what no one did or could do for the other: he showed that -it was the only one which would account, without additional and -arbitrary suppositions, for the facts of _continued_ motion in -electromagnetic cases. And he further elevated his theory to a -higher rank of generality, by showing that it explained,--not only -the action of a conducting-wire upon a magnet, but also two other -classes of facts, already spoken of in this history,--the action of -magnets upon each other,--and the action of conducting-wires upon -each other. - -The deduction of such particular cases from the theory, required, as -may easily be imagined, some complex calculations: but the deduction -being satisfactory, it will be seen that Ampère's theory conformed -to that description which we have repeatedly had to point out as the -usual character of a true and stable theory; namely, that besides -accounting for the class of phenomena which suggested it, it -supplies an unforeseen explanation of other known facts. For the -mutual action of magnets, which was supposed to be already reduced -to a satisfactory theoretical form by Coulomb, was not contemplated -by Ampère in the formation of his hypothesis; and the mutual action -of voltaic currents, though tried only in consequence of the -suggestion of the theory, was clearly a fact distinct from -electromagnetic action; yet all these facts flowed alike from the -theory. And thus Ampère brought into view a class of forces for -which the term "electromagnetic" was too limited, and which he -designated[14\13] by the appropriate term _electrodynamic_; -distinguishing them by this expression, as the forces of an electric -_current_, from the _statical_ effects of electricity which we had -formerly to treat of. This term has passed into common use among -scientific writers, and remains the record and stamp of the success -of the Amperian induction. - -[Note 14\13: _Ann. de Chim._, tom. xx. p. 60 (1822).] - -The first promulgation of Ampère's views was by a communication to -the French Academy of Sciences, September the 18th, 1820; Oersted's -discoveries having reached Paris only in the preceding July. {248} -At almost every meeting of the Academy during the remainder of that -year and the beginning of the following one, he had new -developements or new confirmations of his theory to announce. The -most hypothetical part of his theory,--the proposition that magnets -might be considered in their effects as identical with spiral -voltaic wires,--he asserted from the very first. The mutual -attraction and repulsion of voltaic wires,--the laws of this -action,--the deduction of the observed facts from it by -calculation,--the determination, by new experiments, of the constant -quantities which entered into his formulæ,--followed in rapid -succession. The theory must be briefly stated. It had already been -seen that parallel voltaic currents attracted each other; when, -instead of being parallel, they were situate in any directions, they -still exerted attractive and repulsive forces depending on the -distance, and on the directions of each element of both currents. -Add to this doctrine the hypothetical constitution of magnets, -namely, that a voltaic current runs round the axis of each particle, -and we have the means of calculating a vast variety of results which -may be compared with experiment. But the laws of the elementary -forces required further fixation. What _functions_ are the forces of -the distance and the directions of the elements? - -To extract from experiment an answer to this inquiry was far from -easy, for the elementary forces were mathematically connected with -the observed facts, by a double mathematical integration;--a long, -and, while the constant coefficients remained undefined, hardly a -possible operation. Ampère made some trials in this way, but his -happier genius suggested to him a better path. It occurred to him, -that if his integrals, without being specially found, could be shown -to vanish upon the whole, under certain conditions of the problem, -this circumstance would correspond to arrangements of his apparatus -in which a state of equilibrium was preserved, however the form of -some of the parts might be changed. He found two such cases, which -were of great importance to the theory. The first of these cases -proved that the force exerted by any element of the voltaic wire -might be resolved into other forces by a theorem resembling the -well-known proposition of the parallelogram of forces. This was -proved by showing that the action of a straight wire is the same -with that of another wire which joins the same extremities, but is -bent and contorted in any way whatever. But it still remained -necessary to determine two fundamental quantities; one which -expressed the _power_ of the distance according to which the force -varied; the other, the {249} degree in which the force is affected -by the _obliquity_ of the elements. One of the general causes of -equilibrium, of which we have spoken, gave a relation between these -two quantities;[15\13] and as the power was naturally, and, as it -afterwards appeared, rightly conjectured to be the inverse square, -the other quantity also was determined; and the general problem of -electrodynamical action was fully solved. - -[Note 15\13: Communication to the Acad. Sc., June 10, 1822. See -Ampère, _Recueil_, p. 292.] - -If Ampère had not been an accomplished analyst, he would not have -been able to discover the condition on which the nullity of the -integral in this case depended.[16\13] And throughout his labors, we -find reason to admire, both his mathematical skill, and his -steadiness of thought; although these excellences are by no means -accompanied throughout with corresponding clearness and elegance of -exposition in his writings. - -[Note 16\13: _Recueil_, p. 314.] - -_Reception of Ampère's Theory._--Clear mathematical conceptions, and -some familiarity with mathematical operations, were needed by -readers also, in order to appreciate the evidence of the theory; -and, therefore, we need not feel any surprise if it was, on its -publication and establishment, hailed with far less enthusiasm than -so remarkable a triumph of generalizing power might appear to -deserve. For some time, indeed, the greater portion of the public -were naturally held in suspense by the opposing weight of rival -names. The Amperian theory did not make its way without contention -and competition. The electro-magnetic experiments, from their first -appearance, gave a clear promise of some new and wide -generalization; and held out a prize of honor and fame to him who -should be first in giving the right interpretation of the riddle. In -France, the emulation for such reputation is perhaps more vigilant -and anxious than it is elsewhere; and we see, on this as on other -occasions, the scientific host of Paris springing upon a new subject -with an impetuosity which, in a short time, runs into controversies -for priority or for victory. In this case, M. Biot, as well as -Ampère, endeavored to reduce the electro-magnetic phenomena to -general laws. The discussion between him and Ampère turned on some -points which are curious. M. Biot was disposed to consider as an -elementary action, the force which an element of a voltaic wire -exerts upon a magnetic particle, and which is, as we have seen, at -right angles to their mutual distance; and he conceived that {250} -the equal reaction which necessarily accompanies this action acts -oppositely to the action, not in the same line, but in a parallel -line, at the other extremity of the distance; thus forming a -primitive _couple_, to use a technical expression borrowed from -mechanics. To this Ampère objected,[17\13] that the _direct_ -opposition of all elementary action and reaction was a universal and -necessary mechanical law. He showed too that such a couple as had -been assumed, would follow as a _derivative_ result from his theory. -And in comparing his own theory with that in which the voltaic wire -is assimilated to a collection of transverse magnets, he was also -able to prove that no such assemblage of forces acting to and from -fixed points, as the forces of magnets do act, could produce a -continued motion like that discovered by Faraday. This, indeed, was -only the well-known demonstration of the impossibility of a -perpetual motion. If, instead of a collection of magnets, the -adverse theorists had spoken of a magnetic _current_, they might -probably interpret their expressions so as to explain the facts; -that is, if they considered every element of such a current as a -magnet, and consequently, every point of it as being a north and a -south point at the same instant. But to introduce such a conception -of a magnetic current was to abandon all the laws of magnetic action -hitherto established; and consequently to lose all that gave the -hypothesis its value. The idea of an electric current, on the other -hand, was so far from being a new and hazardous assumption, that it -had already been forced upon philosophers from the time of Volta; -and in this current, the relation of _preceding_ and _succeeding_, -which necessarily existed between the extremities of any element, -introduced that relative polarity on which the success of the -explanations of the facts depended. And thus in this controversy, -the theory of Ampère has a great and undeniable superiority over the -rival hypotheses. - -[Note 17\13: Ampère, _Théorie_, p. 154.] - - - - -CHAPTER VII. - - -CONSEQUENCES OF THE ELECTRODYNAMIC THEORY. - -IT is not necessary to state the various applications which were -soon made of the electro-magnetic discoveries. But we may notice one -{251} of the most important,--the _Galvanometer_, an instrument -which, by enabling the philosopher to detect and to measure -extremely minute electrodynamic actions, gave an impulse to the -subject similar to that which it received from the invention of the -Leyden Phial, or the Voltaic Pile. The strength of the voltaic -current was measured, in this instrument, by the deflection produced -in a compass-needle; and its sensibility was multiplied by making -the wire pass repeatedly above and below the needle. Schweigger, of -Halle, was one of the first devisers of this apparatus. - -The substitution of electro-magnets, that is, of spiral tubes -composed of voltaic wires, for common magnets, gave rise to a -variety of curious apparatus and speculations, some of which I shall -hereafter mention. - -[2nd Ed.] [When a voltaic apparatus is in action, there may be -conceived to be a current of electricity running through its various -elements, as stated in the text. The force of this current in -various parts of the circuit has been made the subject of -mathematical investigation by M. Ohm.[18\13] The problem is in every -respect similar to that of the flow of heat through a body, and -taken generally, leads to complex calculations of the same kind. But -Dr. Ohm, by limiting the problem in the first place by conditions -which the usual nature and form of voltaic apparatus suggest, has -been able to give great simplicity to his reasonings. These -conditions are, the linear form of the conductors (wires) and the -steadiness of the electric state. For this part of the problem Dr. -Ohm's reasonings are as simple and as demonstrative as the -elementary propositions of Mechanics. The formulæ for the electric -force of a voltaic current to which he is led have been -experimentally verified by others, especially Fechner,[19\13] -Gauss,[20\13] Lenz, Jacobi, Poggendorf, and Pouillet. - -[Note 18\13: _Die Galvanische Kette Mathematisch bearbeitet von Dr. -G. S. Ohm_, Berlin, 1827.] - -[Note 19\13: _**Mass-bestimmungen über die Galvanische Kette._ -Leipzig, 1831.] - -[Note 20\13: _Results of the Magnetic Association._] - -Among ourselves, Mr. Wheatstone has confirmed and applied the views -of M. Ohm, in a Memoir[21\13] _On New Instruments and Processes for -determining the Constants of a Voltaic Circuit_. He there remarks -that the clear ideas of electromotive forces and resistances, -substituted by Ohm for the vague notions of quantity and intensity -which have long been prevalent, give satisfactory explanations of -the most important difficulties, and express the laws of a vast -number of phenomena {252} in formulæ of remarkable simplicity and -generality. In this Memoir, Professor Wheatstone describes an -instrument which he terms _Rheostat_, because it brings to a common -standard the voltaic currents which are compared by it. He -generalizes the language of the subject by employing the term -_rheomotor_ for any apparatus which originates an electric current -(whether voltaic or thermoelectric, &c.) and _rheometer_ for any -instrument to measure the force of such a current. It appears that -the idea of constructing an instrument of the nature of the Rheostat -had occurred also to Prof. Jacobi, of St Petersburg.] - -[Note 21\13: _Phil. Trans._ 1843. Pt. 11.] - -The galvanometer led to the discovery of another class of cases in -which the electrodynamical action was called into play, namely, -those in which a circuit, composed of two metals only, became -electro-magnetic by _heating_ one part of it. This discovery of -_thermo-electricity_ was made by Professor Seebeck of Berlin, in -1822, and prosecuted by various persons; especially by Prof. -Cumming[22\13] of Cambridge, who, early in 1823, extended the -examination of this property to most of the metals, and determined -their thermo-electric order. But as these investigations exhibited -no new mechanical effects of electromotive forces, they do not now -further concern us; and we pass on, at present, to a case in which -such forces act in a manner different from any of those already -described. - -[Note 22\13: _Camb. Trans._ vol. ii. p. 62. _On the Development of -Electro-Magnetism by Heat._] - - -DISCOVERY OF DIAMAGNETISM. - -[2nd Ed.] [By the discoveries just related, a cylindrical spiral of -wire through which an electric current is passing is identified with -a magnet; and the effect of such a spiral is increased by placing in -it a core of soft iron. By the use of such a combination under the -influence of a voltaic battery, magnets are constructed far more -powerful than those which depend upon the permanent magnetism of -iron. The electro-magnet employed by Dr. Faraday in some of his -experiments would sustain a hundred-weight at either end. - -By the use of such magnets Dr. Faraday discovered that, besides -iron, nickel and cobalt, which possess magnetism in a high degree, -many bodies are magnetic in a slight degree. And he made the further -very important discovery, that of those substances which are not -magnetic, many, perhaps all, possess an opposite property, in virtue -of which he terms them _diamagnetic_. The opposition is of this -{253} kind;--that magnetic bodies in the form of bars or needles, -if free to move, arrange themselves in the _axial_ line joining the -poles; diamagnetic bodies under the same circumstances arrange -themselves in an _equatorial_ position, perpendicular to the axial -line. And this tendency he conceives to be the result of one more -general; that whereas magnetic bodies are attracted to the poles of -a magnet, diamagnetic bodies are repelled from the poles. The list -of diamagnetic bodies includes all kinds of substances; not only -metals, as antimony, bismuth, gold, silver, lead, tin, zinc, but -many crystals, glass, phosphorus, sulphur, sugar, gum, wood, ivory; -and even flesh and fruit. - -It appears that M. le Bailli had shown, in 1829, that both bismuth -and antimony and bismuth repelled the magnetic needle; and as Dr. -Faraday remarks, it is astonishing that such an experiment should -have remained so long without further results. M. Becquerel in 1827 -observed, and quoted Coulomb as having also observed, that a needle -of wood under certain conditions pointed across the magnetic curves; -and also stated that he had found a needle of wood place itself -parallel to the wires of a galvanometer. This he referred to a -magnetism transverse to the length. But he does not refer the -phenomena to elementary repulsive action, nor show that they are -common to an immense class of bodies, nor distinguish this -diamagnetic from the magnetic class, as Faraday has taught us to do. - -I do not dwell upon the peculiar phenomena of copper which, in the -same series of researches, are traced by Dr. Faraday to the combined -effect of its diamagnetic character, and the electric currents -excited in it by the electro-magnet; nor to the optical phenomena -manifested by certain transparent diamagnetic substances under -electric action; as already stated in Book ix.[23\13]] - -[Note 23\13: See the _Twentieth Series of Experimental Researches in -Electricity_, read to the Royal Society, Dec. 18, 1845.] - - - - -CHAPTER VIII. - -DISCOVERY OF THE LAWS OF MAGNETO-ELECTRIC INDUCTION.--FARADAY. - -IT was clearly established by Ampère, as we have seen, that magnetic -action is a peculiar form of electromotive actions, and that, in -{254} this kind of agency, action and reaction are equal and -opposite. It appeared to follow almost irresistibly from these -considerations, that magnetism might be made to produce electricity, -as electricity could be made to imitate all the effects of -magnetism. Yet for a long time the attempts to obtain such a result -were fruitless. Faraday, in 1825, endeavored to make the -conducting-wire of the voltaic circuit excite electricity in a -neighboring wire by induction, as the conductor charged with common -electricity would have done, but he obtained no such effect. If this -attempt had succeeded, the magnet, which, for all such purposes, is -an assemblage of voltaic circuits, might also have been made to -excite electricity. About the same time, an experiment was made in -France by M. Arago, which really involved the effect thus sought; -though this effect was not extricated from the complex phenomenon, -till Faraday began his splendid career of discovery on this subject -in 1832. Arago's observation was, that the rapid revolution of a -conducting-plate in the neighborhood of a magnet, gave rise to a -force acting on the magnet. In England, Messrs. Barlow and Christie, -Herschel and Babbage, repeated and tried to analyse this experiment; -but referring the forces only to conditions of space and time, and -overlooking the real cause, the electrical currents produced by the -motion, these philosophers were altogether unsuccessful in their -labors. In 1831, Faraday again sought for electro-dynamical -induction, and after some futile trials, at last found it in a form -different from that in which he had looked for it. It was then seen, -that at the precise time of making or breaking the contact which -closed the galvanic circuit, a momentary effect was induced in a -neighboring wire, but disappeared instantly.[24\13] Once in -possession of this fact, Mr. Faraday ran rapidly up the ladder of -discovery, to the general point of view.--Instead of suddenly making -or breaking the contact of the inducing circuit, a similar effect -was produced by removing the inducible wire nearer to or further -from the circuit;[25\13]--the effects were increased by the -proximity of soft iron;[26\13]--when the soft iron was affected by -an ordinary magnet instead of the voltaic wire, the same effect -still recurred;[27\13]--and thus it appeared, that by making and -breaking magnetic contact, a momentary electric current was -produced. It was produced also by moving the magnet;[28\13]--or by -moving the wire with reference to the magnet.[29\13] Finally, it was -found that the earth might supply the place of a magnet {255} in -this as in other experiments;[30\13] and the mere motion of a wire, -under proper circumstances, produced in it, it appeared, a momentary -electric current.[31\13] These facts were curiously confirmed by the -results in special cases. They explained Arago's experiments: for -the momentary effect became permanent by the revolution of the -plate. And without using the magnet, a revolving plate became an -electrical machine;[32\13]--a revolving globe exhibited -electro-magnetic action,[33\13] the circuit being complete in the -globe itself without the addition of any wire;--and a mere motion of -the wire of a galvanometer produced an electro-dynamic effect upon -its needle.[34\13] - -[Note 24\13: _Phil. Trans._ 1832, p. 127, First Series, Art. 10.] - -[Note 25\13: Art. 18.] - -[Note 26\13: Art. 28.] - -[Note 27\13: Art. 37.] - -[Note 28\13: Art. 39.] - -[Note 29\13: Art. 53.] - -[Note 30\13: Second Series, _Phil. Trans._ p. 163.] - -[Note 31\13: Art. 141.] - -[Note 32\13: Art. 150.] - -[Note 33\13: Art. 164.] - -[Note 34\13: Art. 171.] - -But the question occurs, What is the general law which determines -the direction of electric currents thus produced by the joint -effects of motion and magnetism? Nothing but a peculiar steadiness -and clearness in his conceptions of space, could have enabled Mr. -Faraday to detect the law of this phenomenon. For the question -required that he should determine the mutual relations in space -which connect the magnetic poles, the position of the wire, the -direction of the wire's motion, and the electrical current produced -in it. This was no easy problem; indeed, the mere relation of the -magnetic to the electric forces, the one set being perpendicular to -the other, is of itself sufficient to perplex the mind; as we have -seen in the history of the electrodynamical discoveries. But Mr. -Faraday appears to have seized at once the law of the phenomena. -"The relation," he says,[35\13] "which holds between the magnetic -pole, the moving wire or metal, and the direction of the current -evolved, is very simple (so it seemed to him) although rather -difficult to express." He represents it by referring position and -motion to the "magnetic curves," which go from a magnetic pole to -the opposite pole. The current in the wire sets one way or the -other, according to the direction in which the motion of the wire -cuts these curves. And thus he was enabled, at the end of his Second -Series of _Researches_ (December, 1831), to give, in general terms, -the law of nature to which may be referred the extraordinary number -of new and curious experiments which he has stated;[36\13]--namely, -that if a wire move so as to cut a magnetic curve, a power is called -into action which tends to urge a magnetic current through the wire; -and that if a mass move so that its parts do not move in the same -direction across the magnetic curves, {256} and with the same angular -velocity, electrical currents are called into play in the mass. - -[Note 35\13: First Series, Art. 114.] - -[Note 36\13: Art. 256-264.] - -This rule, thus simple from its generality, though inevitably -complex in every special case, may be looked upon as supplying the -first demand of philosophy, _the law of the phenomena_; and -accordingly Dr. Faraday has, in all his subsequent researches on -magneto-electric induction, applied this law to his experiments; and -has thereby unravelled an immense amount of apparent inconsistency -and confusion, for those who have followed him in his mode of -conceiving the subject. - -But yet other philosophers have regarded these phenomena in other -points of view, and have stated the laws of the phenomena in a -manner different from Faraday's, although for the most part -equivalent to his. And these attempts to express, in the most simple -and general form, the law of the phenomena of magneto-electrical -induction, have naturally been combined with the expression of other -laws of electrical and magnetical phenomena. Further, these -endeavors to connect and generalize the Facts have naturally been -clothed in the garb of various Theories:--the _laws of phenomena_ -have been expressed in terms of the supposed _causes of the -phenomena_; as fluids, attractions and repulsions, particles with -currents running through them or round them, physical lines of -force, and the like. Such views, and the conflict of them, are the -natural and hopeful prognostics of a theory which shall harmonize -their discords and include all that each contains of Truth. The -fermentation at present is perhaps too great to allow us to see -clearly the truth which lies at the bottom. But a few of the leading -points of recent discussions on these subjects will be noticed in -the Additions to this volume. - - - - -CHAPTER IX. - -TRANSITION TO CHEMICAL SCIENCE. - - -THE preceding train of generalization may justly appear extensive, -and of itself well worthy of admiration. Yet we are to consider all -that has there been established as only one-half of the science to -which it belongs,--one limb of the colossal form of Chemistry. We -{257} have ascertained, we will suppose, the laws of Electric -Polarity; but we have then to ask, What is the relation of this -Polarity to Chemical Composition? This was the great problem which, -constantly present to the minds of electro-chemical inquirers, drew -them on, with the promise of some deep and comprehensive insight -into the mechanism of nature. Long tasks of research, though only -subsidiary to this, were cheerfully undertaken. Thus Faraday[37\13] -describes himself as compelled to set about satisfying himself of -the identity of common, animal, and voltaic electricity, as "the -decision of a doubtful point which interfered with the extension of -his views, and destroyed the strictness of reasoning." Having -established this identity, he proceeded with his grand undertaking -of electro-chemical research. - -[Note 37\13: Dec. 1832. _Researches_, 266.] - -The connexion of electrical currents with chemical action, though -kept out of sight in the account we have hitherto given, was never -forgotten by the experimenters; for, in fact, the modes in which -electrical currents were excited, were chemical actions;--the action -of acids and metals on each other in the voltaic trough, or in some -other form. The dependence of the electrical effect on these -chemical actions, and still more, the chemical actions produced by -the agency of the poles of the circuit, had been carefully studied; -and we must now relate with what success. - -But in what terms shall we present this narration? We have spoken of -chemical actions,--but what kind of actions are these? -_Decomposition_; the _resolution_ of compounds into their -ingredients; the separation of _acids_ from _bases_; the reduction -of bodies to _simple elements_. These names open to us a new drama; -they are words which belong to a different set of relations of -things, a different train of scientific inductions, a different -system of generalizations, from any with which we have hitherto been -concerned. We must learn to understand these phrases, before we can -advance in our history of human knowledge. - -And how are we to learn the meaning of this collection of words? In -what other language shall it be explained? In what terms shall we -define these new expressions? To this we are compelled to reply, -that we cannot translate these terms into any ordinary -language;--that we cannot define them in any terms already familiar -to us. Here, as in all other branches of knowledge, the meaning of -words is to be sought in the progress of thought; the history of -science is our {258} dictionary; the steps of scientific induction -are our definitions. It is only by going back through the successful -researches of men respecting the composition and elements of bodies, -that we can learn in what sense such terms must be understood, so as -to convey real knowledge. In order that they may have a meaning for -us, we must inquire what meaning they had in the minds of the -authors of our discoveries. - -And thus we cannot advance a step, till we have brought up our -history of Chemistry to the level of our history of -Electricity;--till we have studied the progress of the analytical, -as well as the mechanical sciences. We are compelled to pause and -look backwards here; just as happened in the history of astronomy, -when we arrived at the brink of the great mechanical inductions of -Newton, and found that we must trace the history of Mechanics, -before we could proceed to mechanical Astronomy. The terms "force, -attraction, inertia, momentum," sent us back into preceding -centuries then, just as the terms "composition" and "element" send -us back now. - -Nor is it to a small extent that we have thus to double back upon -our past advance. Next to Astronomy, Chemistry is one of the most -ancient of sciences;--the field of the earliest attempts of man to -command and understand nature. It has held men for centuries by a -kind of fascination; and innumerable and endless are the various -labors, the failures and successes, the speculations and -conclusions, the strange pretences and fantastical dreams, of those -who have pursued it. To exhibit all these, or give any account of -them, would be impossible; and for our design, it would not be -pertinent. To extract from the mass that which is to our purpose, is -difficult; but the attempt must be made. We must endeavor to analyse -the history of Chemistry, so far as it has tended towards the -establishment of general principles. We shall thus obtain a sight of -generalizations of a new kind, and shall prepare ourselves for -others of a higher order. - - - -{{259}} -BOOK XIV. - -_THE ANALYTICAL SCIENCE._ - -HISTORY OF CHEMISTRY. - - - . . . . . . . Soon had his crew - Opened into the hill a spacious wound, - And digged out ribs of gold . . . . - Anon out of the earth a fabric huge - Rose like an exhalation, with the sound - Of dulcet symphonies and voices sweet, - Built like a temple. - MILTON. _Paradise Lost_, i. - - - -{{261}} -CHAPTER I. - -IMPROVEMENT OF THE NOTION OF CHEMICAL ANALYSIS, AND RECOGNITION OF -IT AS THE SPAGIRIC ART. - - -THE doctrine of "the four elements" is one of the oldest monuments -of man's speculative nature; goes back, perhaps, to times anterior -to Greek philosophy; and as the doctrine of Aristotle and Galen, -reigned for fifteen hundred years over the Gentile, Christian, and -Mohammedan world. In medicine, taught as the doctrine of the four -"elementary qualities," of which the human body and all other -substances are compounded, it had a very powerful and extensive -influence upon medical practice. But this doctrine never led to any -attempt actually to analyse bodies into their supposed elements: for -composition was inferred from the resemblance of the qualities, not -from the separate exhibition of the ingredients; the supposed -analysis was, in short, a decomposition of the body into adjectives, -not into substances. - -This doctrine, therefore, may be considered as a negative state, -antecedent to the very beginning of chemistry; and some progress -beyond this mere negation was made, as soon as men began to endeavor -to compound and decompound substances by the use of fire or mixture, -however erroneous might be the opinions and expectations which they -combined with their attempts. Alchemy is a step in chemistry, so far -as it implies the recognition of the work of the cupel and the -retort, as the produce of analysis and synthesis. How perplexed and -perverted were the forms in which this recognition was clothed,--how -mixed up with mythical follies and extravagancies, we have already -seen; and the share which Alchemy had in the formation of any -sounder knowledge, is not such as to justify any further notice of -that pursuit. - -The result of the attempts to analyse bodies by heat, mixture, and -the like processes, was the doctrine that the first principles of -things are _three_, not four; namely, _salt_, _sulphur_, and -_mercury_; and that, of these three, all things are compounded. In -reality, the doctrine, as thus stated, contained no truth which was -of any value; for, though the chemist could extract from most bodies -portions which he called salt, {262} and sulphur, and mercury, these -names were given, rather to save the hypothesis, than because the -substances were really those usually so called: and thus the -supposed analyses proved nothing, as Boyle justly urged against -them.[1\14] - -[Note 1\14: Shaw's Boyle. _Skeptical Chymist_, pp. 312, 313. &c.] - -The only real advance in chemical theory, therefore, which we can -ascribe to the school of _the three principles_, as compared with -those who held the ancient dogma of the four elements, is, the -acknowledgment of the changes produced by the chemist's operations, -as being changes which were to be accounted for by the union and -separation of substantial elements, or, as they were sometimes -called, of _hypostatical principles_. The workmen of this school -acquired, no doubt, a considerable acquaintance with the results of -the kinds of processes which they pursued; they applied their -knowledge to the preparation of new medicines; and some of them, as -Paracelsus and Van Helmont, attained, in this way, to great fame and -distinction: but their merits, as regards theoretical chemistry, -consist only in a truer conception of the problem, and of the mode -of attempting its solution, than their predecessors had entertained. - -This step is well marked by a word which, about the time of which we -speak, was introduced to denote the chemist's employment. It was -called the _Spagiric art_, (often misspelt _Spagyric_,) from two -Greek words, (σπάω, ἀγείρω,) which mean to _separate_ parts, and to -_unite_ them. These two processes, or in more modern language, -_analysis_ and _synthesis_, constitute the whole business of the -chemist. We are not making a fanciful arrangement, therefore, when -we mark the recognition of this object as a step in the progress of -chemistry. I now proceed to consider the manner in which the -conditions of this analysis and synthesis were further developed. - - - - -CHAPTER II. - -DOCTRINE OF ACID AND ALKALI.--SYLVIUS. - - -AMONG the results of mixture observed by chemists, were many -instances in which two ingredients, each in itself pungent or -destructive, being put together, became mild and inoperative; each -{263} counteracting and neutralizing the activity of the other. The -notion of such opposition and neutrality is applicable to a very -wide range of chemical processes. The person who appears first to -have steadily seized and generally applied this notion is Francis de -la Boé Sylvius; who was born in 1614, and practised medicine at -Amsterdam, with a success and reputation which gave great currency -to his opinions on that art.[2\14] His chemical theories were -propounded as subordinate to his medical doctrines; and from being -thus presented under a most important practical aspect, excited far -more attention than mere theoretical opinions on the composition of -bodies could have done. Sylvius is spoken of by historians of -science, as the founder of the _iatro-chemical_ sect among -physicians; that is, the sect which considers the disorders in the -human frame as the effects of chemical relations of the fluids, and -applies to them modes of cure founded upon this doctrine. We have -here to speak, not of his physiological, but of his chemical views. - -[Note 2\14: Sprengel. _Geschichte der Arzneykunde_, vol. iv. -Thomson's _History of Chemistry_ in the corresponding part is -translated from Sprengel.] - -The distinction of _acid_ and _alkaline_ bodies (_acidum_, -_lixivum_) was familiar before the time of Sylvius; but he framed a -system, by considering them both as eminently acrid and yet -opposite, and by applying this notion to the human frame. Thus[3\14] -the lymph contains an acid, the bile an alkaline salt. These two -opposite acrid substances, when they are brought together, -_neutralize_ each other (_infringunt_), and are changed into an -intermediate and milder substance. - -[Note 3\14: _De Methodo Medendi_, Amst. 1679. Lib. ii. cap. 28, -sects. 8 and 53.] - -The progress of this doctrine, as a physiological one, is an -important part of the history of medical science in the seventeenth -century; but with that we are not here concerned. But as a chemical -doctrine, this notion of the opposition of acid and alkali, and of -its very general applicability, struck deep root, and has not been -eradicated up to our own time. Boyle, indeed, whose disposition led -him to suspect all generalities, expressed doubts with regard to -this view;[4\14] and argued that the supposition of acid and -alkaline parts in all bodies was precarious, their offices -arbitrary, and the notion of them unsettled. Indeed it was not -difficult to show, that there was no one certain criterion to which -all supposed acids conformed. Yet the general conception of such a -combination as that of acid and alkali was supposed to {264} be, -served so well to express many chemical facts, that it kept its -ground. It is found, for instance, in Lemery's _Chemistry_, which -was one of those in most general use before the introduction of the -phlogistic theory. In this work (which was translated into English -by Keill, in 1698) we find alkalies defined by their effervescing -with acids.[5\14] They were distinguished as the _mineral_ alkali -(soda), the _vegetable_ alkali (potassa), and the _volatile_ alkali -(ammonia). Again, in Macquer's _Chemistry_, which was long the -text-book in Europe during the reign of phlogiston, we find acids -and alkalies, and their union, in which they rob each other of their -characteristic properties, and form neutral salts, stated among the -leading principles of the science.[6\14] - -[Note 4\14: Shaw's _Boyle_, iii. p. 432.] - -[Note 5\14: Lemery, p. 25.] - -[Note 6\14: Macquer, p. 19.] - -In truth, the mutual relation of acids to alkalies was the most -essential part of the knowledge which chemists possessed concerning -them. The importance of this relation arose from its being the first -distinct form in which the notion of chemical attraction or affinity -appeared. For the acrid or caustic character of acids and alkalies -is, in fact, a tendency to alter the bodies they touch, and thus to -alter themselves; and the neutral character of the compounds **is -the absence of any such proclivity to change. Acids and alkalies -have a strong disposition to unite. They combine, often with -vehemence, and produce neutral salts; they exhibit, in short, a -prominent example of the chemical attraction, or affinity, by which -two ingredients are formed into a compound. The relation of _acid_ -and _base_ in a salt is, to this day, one of the main grounds of all -theoretical reasonings. - -The more distinct development of the notion of such chemical -attraction, gradually made its way among the chemists of the latter -part of the seventeenth and the beginning of the eighteenth century, -as we may see in the writings of Boyle, Newton, and their followers. -Beecher speaks of this attraction as a _magnetism_; but I do not -know that any writer in particular, can be pointed out as the person -who firmly established the general notion of _chemical attraction_. - -But this idea of chemical attraction became both more clear and more -extensively applicable, when it assumed the form of the doctrine of -_elective_ attractions, in which shape we must now speak of it. {265} - - - - -CHAPTER III. - -DOCTRINE OF ELECTIVE ATTRACTIONS. GEOFFROY. BERGMAN. - - -THOUGH the chemical combinations of bodies had already been referred -to attraction, in a vague and general manner, it was impossible to -explain the changes that take place, without supposing the -attraction to be greater or less, according to the nature of the -body. Yet it was some time before the necessity of such a -supposition was clearly seen. In the history of the French Academy -for 1718 (published 1719), the writer of the introductory notice -(probably Fontenelle) says, "That a body which is united to another, -for example, a solvent which has penetrated a metal, should quit it -to go and unite itself with another which we present to it, is a -thing of which the possibility had never been guessed by the most -subtle philosophers, and of which the explanation even now is not -easy." The doctrine had, in fact, been stated by Stahl, but the -assertion just quoted shows, at least, that it was not familiar. The -principle, however, is very clearly stated[7\14] in a memoir in the -same volume, by Geoffroy, a French physician of great talents and -varied knowledge, "We observe in chemistry," he says, "certain -relations amongst different bodies, which cause them to unite. These -relations have their _degrees_ and their _laws_. We observe their -different degrees in this;--that among different matters jumbled -together, which have a certain disposition to unite, we find that -one of these substances always unites constantly with a certain -other, preferably to all the rest." He then states that those which -unite by preference, have "plus de rapport," or, according to a -phrase afterwards used, more _affinity_. "And I have satisfied -myself," he adds, "that we may deduce, from these observations, the -following proposition, which is very extensively true, though I -cannot enunciate it as universal, not having been able to examine -all the possible combinations, to assure myself that I should find -no exception." The proposition which he states in this admirable -spirit of philosophical caution, is this: "In all cases where two -substances, {266} which have any disposition to combine, are united; -if there approaches them a third, which has more affinity with one -of the two, this one unites with the third and lets go the other." -He then states these affinities in the form of a Table; placing a -substance at the head of each column, and other substances in -succession below it, according to the order of their affinities for -the substance which stands at the head. He allows that the -separation is not always complete (an imperfection which he ascribes -to the glutinosity of fluids and other causes), but, with such -exceptions, he defends very resolutely and successfully his Table, -and the notions which it implies. - -[Note 7\14: _Mém. Acad. Par._ 1718, p. 202.] - -The value of such a tabulation was immense at the time, and is even -still very great; it enabled the chemist to trace beforehand the -results of any operation; since, when the ingredients were given, he -could see which were the strongest of the affinities brought into -play, and, consequently, what compounds would be formed. Geoffroy -himself gave several good examples of this use of his table. It was -speedily adopted into works on chemistry. For instance, -Macquer[8\14] places it at the end of his book; "taking it," as he -says, "to be of great use at the end of an elementary tract, as it -collects into one point of view, the most essential and fundamental -doctrines which are dispersed through the work." - -[Note 8\14: Pref., p. 13.] - -The doctrine of _Elective Attraction_, as thus promulgated, -contained so large a mass of truth, that it was never seriously -shaken, though it required further development and correction. In -particular the celebrated work of Torbern Bergman, professor at -Upsala, _On Elective Attractions_, published in 1775, introduced -into it material improvements. Bergman observed, that not only the -order of attractions, but the sum of those attractions which had to -form the new compounds, must be taken account of, in order to judge -of the result. Thus,[9\14] if we have a combination of two elements, -_P_, _s_, (potassa and vitriolic acid), and another combination, -_L_, _m_, (lime and muriatic acid,) though _s_ has a greater -affinity for _P_ than for _L_, yet the sum of the attractions of _P_ -to _m_, and of _L_ to _s_, is greater than that of the original -compounds, and therefore if the two combinations are brought -together, the new compounds, _P_, _m_, and _L_, _s_, are formed. - -[Note 9\14: _Elect. Attract._, p. 19.] - -The Table of Elective Attractions, modified by Bergman in pursuance -of these views, and corrected according to the advanced knowledge of -the time, became still more important than before. The next step -{267} was to take into account the quantities of the elements which -combined; but this leads us into a new train of investigation, which -was, indeed, a natural sequel to the researches of Geoffroy and -Bergman. - -In 1803, however, a chemist of great eminence, Berthollet, published -a work (_Essai de Statique Chimique_), the tendency of which -appeared to be to throw the subject back into the condition in which -it had been before Geoffroy. For Berthollet maintained that the -rules of chemical combination were not definite, and dependent on -the nature of the substances alone, but indefinite, depending on the -quantity present, and other circumstances. Proust answered him, and -as Berzelius says,[10\14] "Berthollet defended himself with an -acuteness which makes the reader hesitate in his judgment; but the -great mass of facts finally decided the point in favor of Proust." -Before, however, we trace the result of these researches, we must -consider Chemistry as extending her inquiries to combustion as well -as mixture, to airs as well as fluids and solids, and to weight as -well as quality. These three steps we shall now briefly treat of. - -[Note 10\14: _Chem._ t. iii. p. 23.] - - - - -CHAPTER IV. - -DOCTRINE OF ACIDIFICATION AND COMBUSTION.--PHLOGISTIC THEORY. - - -PUBLICATION _of the Theory by Beccher and Stahl._--It will be -recollected that we are tracing the history of the _progress_ only -of Chemistry, not of its errors;--that we are concerned with -doctrines only so far as they are true, and have remained part of -the received system of chemical truths. The Phlogistic Theory was -deposed and succeeded by the Theory of Oxygen. But this circumstance -must not lead us to overlook the really sound and permanent part of -the opinions which the founders of the phlogistic theory taught. -They brought together, as processes of the same kind, a number of -changes which at first appeared to have nothing in common; as -acidification, combustion, respiration. Now this classification is -true; and its importance remains undiminished, whatever are the -explanations which we adopt of the processes themselves. - -The two chemists to whom are to be ascribed the merit of this step, -and the establishment of the _phlogistic theory_ which they -connected {268} with it, are John Joachim Beccher and George Ernest -Stahl; the former of whom was professor at Mentz, and physician to -the Elector of Bavaria (born 1625, died 1682); the latter was -professor at Halle, and afterwards royal physician at Berlin (born -1660, died 1734). These two men, who thus contributed to a common -purpose, were very different from each other. The first was a frank -and ardent enthusiast in the pursuit of chemistry, who speaks of -himself and his employments with a communicativeness and affection -both amusing and engaging. The other was a teacher of great talents -and influence, but accused of haughtiness and moroseness; a -character which is well borne out by the manner in which, in his -writings, he anticipates an unfavorable reception, and defies it. -But it is right to add to this that he speaks of Beccher, his -predecessor, with an ungrudging acknowledgment of obligations to -him, and a vehement assertion of his merit as the founder of the -true system, which give a strong impression of Stahl's justice and -magnanimity. - -Beccher's opinions were at first promulgated rather as a correction -than a refutation of the doctrine of the three principles, salt, -sulphur, and mercury. The main peculiarity of his views consists in -the offices which he ascribes to his _sulphur_, these being such as -afterwards induced Stahl to give the name of _Phlogiston_ to this -element. Beccher had the sagacity to see that the reduction of -metals to an earthy form (_calx_), and the formation of sulphuric -acid from sulphur, are operations connected by a general analogy, as -being alike processes of combustion. Hence the metal was supposed to -consist of an earth, and of something which, in the process of -combustion, was separated from it; and, in like manner, sulphur was -supposed to consist of the sulphuric acid, which remained after its -combustion, and of the combustible part or true sulphur, which flew -off in the burning. Beccher insists very distinctly upon this -difference between his element sulphur and the "sulphur" of his -Paracelsian predecessors. - -It must be considered as indicating great knowledge and talent in -Stahl, that he perceived so clearly what part of the views of -Beccher was of general truth and permanent value. Though he[11\14] -everywhere gives to Beccher the credit of the theoretical opinions -which he promulgates, ("Beccheriana sunt quæ profero,") it seems -certain that he had the merit, not only of proving them more -completely, and applying them more widely than his forerunner, but -also of conceiving them {269} with a distinctness which Beccher did -not attain. In 1697, appeared Stahl's _Zymotechnia Fundamentalis_ -(the Doctrine of Fermentation), "simulque _experimentum novum_ -sulphur verum arte producendi." In this work (besides other tenets -which the author considered as very important), the opinion -published by Beccher was now maintained in a very distinct -form;--namely, that the process of forming sulphur from sulphuric -acid, and of restoring the metals from their calces, are analogous, -and consist alike in the addition of some combustible element, which -Stahl termed _phlogiston_ (φλογίστον, _combustible_). The experiment -most insisted on in the work now spoken of,[12\14] was the formation -of sulphur from sulphate of potass (or of soda) by fusing the salt -with an alkali, and throwing in coals to supply phlogiston. This is -the "experimentum novum." Though Stahl published an account of this -process, he seems to have regretted his openness. "He denies not," -he says, "that he should peradventure have dissembled this -experiment as the true foundation of the Beccherian assertion -concerning the nature of sulphur, if he had not been provoked by the -pretending arrogance of some of his contemporaries." - -[Note 11\14: **Stahl, _Præf. ad Specim. Becch._ 1703.] - -[Note 12\14: P. 117.] - -From this time, Stahl's confidence in his theory may be traced -becoming more and more settled in his succeeding publications. It is -hardly necessary to observe here, that the explanations which his -theory gives are easily transformed into those which the more recent -theory supplies. According to modern views, the addition of oxygen -takes place in the formation of acids and of calces, and in -combustion, instead of the subtraction of phlogiston. The coal which -Stahl supposed to supply the combustible in his experiment, does in -fact absorb the liberated oxygen. In like manner, when an acid -corrodes a metal, and, according to existing theory, combines with -and oxidates it, Stahl supposed that the phlogiston separated from -the metal and combined with the acid. That the explanations of the -phlogistic theory are so generally capable of being translated into -the oxygen theory, merely by inverting the supposed transfer of the -combustible element, shows us how important a step towards the -modern doctrines the phlogistic theory really was. - -The question, whether these processes were in fact addition or -subtraction, was decided by the balance, and belongs to a succeeding -period of the science. But we may observe, that both Beccher and -Stahl were aware of the increase of weight which metals undergo in -{270} calcination; although the time had not yet arrived in which -this fact was to be made one of the bases of the theory. - -It has been said,[13\14] that in the adoption of the phlogistic -theory, that is, in supposing the above-mentioned processes to be -addition rather than subtraction, "of two possible roads the wrong -was chosen, as if to prove the perversity of the human mind." But we -must not forget how natural it was to suppose that some part of a -body was _destroyed_ or _removed_ by combustion; and we may observe, -that the merit of Beccher and Stahl did not consist in the selection -of one road or two, but in advancing so far as to reach this point -of separation. That, having done this, they went a little further on -the wrong line, was an error which detracted little from the merit -or value of the progress really made. It would be easy to show, from -the writings of phlogistic chemists, what important and extensive -truths their theory enabled them to express simply and clearly. - -[Note 13\14: Herschel's _Introd. to Nat. Phil._ p. 300.] - -That an enthusiastic temper is favorable to the production of great -discoveries in science, is a rule which suffers no exception in the -character of Beccher. In his preface[14\14] addressed "to the -benevolent reader" of his _Physica Subterranea_, he speaks of the -chemists as a strange class of mortals, impelled by an almost insane -impulse to seek their pleasure among smoke and vapor, soot and -flame, poisons and poverty. "Yet among all these evils," he says, "I -seem to myself to live so sweetly, that, may I die if I would change -places with the Persian king." He is, indeed, well worthy of -admiration, as one of the first who pursued the labors of the -furnace and the laboratory, without the bribe of golden hopes. "My -kingdom," he says, "is not of this world. I trust that I have got -hold of my pitcher by the right handle,--the true method of treating -this study. For the _Pseudochymists_ seek gold; but the _true -philosophers_, science, which is more precious than any gold." - -[Note 14\14: Frankfort, 1681.] - -The _Physica Subterranea_ made no converts. Stahl, in his indignant -manner, says,[15\14] "No one will wonder that it never yet obtained a -physician or a chemist as a disciple, still less as an advocate." And -again, "This work obtained very little reputation or estimation, or, -to speak ingenuously, as far as I know, none whatever." In 1671, -Beccher published a supplement to his work, in which he showed how -metal might be extracted from mud and sand. He offered to execute -{271} this at Vienna; but found that people there cared nothing about -such novelties. He was then induced, by Baron D'Isola, to go to -Holland for similar purposes. After various delays and quarrels, he -was obliged to leave Holland for fear of his creditors; and then, I -suppose, came to Great Britain, where he examined the Scottish and -Cornish mines. He is said to have died in London in 1682. - -[Note 15\14: Præf. _Phys. Sub._ 1703.] - -Stahl's publications appear to have excited more notice, and led to -controversy on the "so-called sulphur." The success of the -experiment had been doubted, which, as he remarks, it was foolish to -make a matter of discussion, when any one might decide the point by -experiment; and finally, it had been questioned whether the -substance obtained by this process were pure sulphur. The -originality of his doctrine was also questioned, which, as he says, -could not with any justice be impugned. He published in defence and -development of his opinion at various intervals, as the _Specimen -Beccherianum_ in 1703, the _Documentum Theoriæ Beecherianæ_, a -Dissertation _De Anatomia Sulphuris Artificialis_; and finally, -_Casual Thoughts on the so-called Sulphur_, in 1718, in which he -gave (in German) both a historical and a systematic view of his -opinions on the nature of salts and of his Phlogiston. - -_Reception and Application of the Theory._--The theory that the -formation of sulphuric acid, and the restoration of metals from -their calces, are analogous processes, and consist in the addition -of _phlogiston_, was soon widely received; and the Phlogistic School -was thus established. From Berlin, its original seat, it was -diffused into all parts of Europe. The general reception of the -theory may be traced, not only in the use of the term "phlogiston," -and of the explanations which it implies; but in the adoption of a -nomenclature founded on those explanations, which, though not very -extensive, is sufficient evidence of the prevalence of the theory. -Thus when Priestley, in 1774, discovered oxygen, and when Scheele, a -little later, discovered chlorine, these gases were termed -_dephlogisticated air_, and _dephlogisticated marine acid_; while -azotic acid gas, having no disposition to combustion, was supposed -to be saturated with phlogiston, and was called _phlogisticated air_. - -This phraseology kept its ground, till it was expelled by the -antiphlogistic, or oxygen theory. For instance. Cavendish's papers -on the chemistry of the airs are expressed in terms of it, although -his researches led him to the confines of the new theory. We must -now give an account of such researches, and of the consequent -revolution in the science. {272} - - - - -CHAPTER V. - -CHEMISTRY OF GASES.--BLACK. CAVENDISH. - - -THE study of the properties of aëriform substances, or Pneumatic -Chemistry, as it was called, occupied the chemists of the eighteenth -century, and was the main occasion of the great advances which the -science made at that period. The most material general truths which -came into view in the course of these researches, were, that gases -were to be numbered among the constituent elements of solid and -fluid bodies; and that, in these, as in all other cases of -composition, the compound was equal to the sum of its elements. The -latter proposition, indeed, cannot be looked upon as a discovery, -for it had been frequently acknowledged, though little applied; in -fact, it could not be referred to with any advantage, till the -aëriform elements, as well as others, were taken into the account. -As soon as this was done, it produced a revolution in chemistry. - -[2nd Ed.] [Though the view of the mode in which gaseous elements -become fixed in bodies and determine their properties, had great -additional light thrown upon it by Dr. Black's discoveries, as we -shall see, the notion that solid bodies involve such gaseous -elements was not new at that period. Mr. Vernon Harcourt has -shown[16\14] that Newton and Boyle admitted into their speculations -airs of various kinds, capable of fixation in bodies. I have, in the -succeeding chapter (chap. vi.), spoken of the views of Rey, Hooke, -and Mayow, connected with the function of airs in chemistry, and -forming a prelude to the Oxygen Theory.] - -[Note 16\14: _Phil. Mag._ 1846.] - -Notwithstanding these preludes, the credit of the first great step -in pneumatic chemistry is, with justice, assigned to Dr. Black, -afterwards professor at Edinburgh, but a young man of the age of -twenty-four at the time when he made his discovery.[17\14] He found -that the difference between caustic lime and common limestone arose -from this, that the latter substance consists of the former, -combined with a certain air, which, being thus fixed in the solid -body, he called _fixed air_ (carbonic {273} acid gas). He found, -too, that magnesia, caustic potash, and caustic soda, would combine -with the same air, with similar results. This discovery consisted, -of course, in a new interpretation of observed changes. Alkalies -appeared to be made caustic by contact with quicklime: at first -Black imagined that they underwent this change by acquiring igneous -matter from the quicklime; but when he perceived that the lime -gained, not lost, in magnitude as it became mild, he rightly -supposed that the alkalies were rendered caustic by imparting their -air to the lime. This discovery was announced in Black's inaugural -dissertation, pronounced in 1755, on the occasion of his taking his -degree of Doctor in the University of Edinburgh. - -[Note 17\14: Thomson's _Hist. Chem._ i. 317.] - -The chemistry of airs was pursued by other experimenters. The -Honorable Henry Cavendish, about 1765, invented an apparatus, in -which aërial fluids are confined by water, so that they can be -managed and examined. This hydro-pneumatic apparatus, or as it is -sometimes called, _the pneumatic trough_, from that time was one of -the most indispensable parts of the chemist's apparatus. -Cavendish,[18\14] in 1766, showed the identity of the properties of -fixed air derived from various sources; and pointed out the peculiar -qualities of _inflammable air_ (afterwards called hydrogen gas), -which, being nine times lighter than common air, soon attracted -general notice by its employment for raising balloons. The promise -of discovery which this subject now offered, attracted the confident -and busy mind of Priestley, whose _Experiments and Observations on -different kinds of Air_ appeared in 1744-79. In these volumes, he -describes an extraordinary number of trials of various kinds; the -results of which were, the discovery of new kinds of air, namely, -_phlogisticated air_ (azotic gas), _nitrous air_ (nitrous gas), and -_dephlogisticated air_ (oxygen gas). - -[Note 18\14: _Phil. Trans._ 1766.] - -But the discovery of new substances, though valuable in supplying -chemistry with materials, was not so important as discoveries -respecting their modes of composition. Among such discoveries, that of -Cavendish, published in the _Philosophical Transactions_ for 1784, and -disclosing the composition of water by the union of two gases, oxygen -and hydrogen, must be considered as holding a most distinguished -place. He states,[19\14] that his "experiments were made principally -with a view to find out the cause of the diminution which common air -is well known to suffer, by all the various ways in which it is -phlogisticated." And, after describing various unsuccessful attempts, -he finds {274} that when inflammable air is used in this -phlogistication (or burning), the diminution of the common air is -accompanied by the formation of a dew in the apparatus.[20\14] And -thus he infers[21\14] that "almost all the inflammable air, and -one-fifth of the common air, are turned into pure water." - -[Note 19\14: _Phil. Trans._ 1784, p. 119.] - -[Note 20\14: _Phil. Trans._ 1784, p. 128.] - -[Note 21\14: Ib. p. 129.] - -Lavoisier, to whose researches this result was, as we shall soon -see, very important, was employed in a similar attempt at the same -time (1783), and had already succeeded,[22\14] when he learned from -Dr. Blagden, who was present at the experiment, that Cavendish had -made the discovery a few months sooner. Monge had, about the same -time, made the same experiments, and communicated the result to -Lavoisier and Laplace immediately afterwards. The synthesis was soon -confirmed by a corresponding analysis. Indeed the discovery -undoubtedly lay in the direct path of chemical research at the time. -It was of great consequence in the view it gave of experiments in -composition; for the small quantity of water produced in many such -processes, had been quite overlooked; though, as it now appeared, -this water offered the key to the whole interpretation of the change. - -[Note 22\14: _A. P._ 1781, p. 472] - -Though some objections to Mr. Cavendish's view were offered by -Kirwan,[23\14] on the whole they were generally received with assent -and admiration. But the bearing of these discoveries upon the new -theory of Lavoisier, who rejected phlogiston, was so close, that we -cannot further trace the history of the subject without proceeding -immediately to that theory. - -[Note 23\14: _P. T._ 1784, p. 154.] - -[2nd Ed.] [I have elsewhere stated,[24\14]--with reference to recent -attempts to deprive Cavendish of the credit of his discovery of the -composition of water, and to transfer it to Watt,--that Watt not -only did not anticipate, but did not fully appreciate the discovery -of Cavendish and Lavoisier; and I have expressed my concurrence with -Mr. Vernon Harcourt's views, when he says,[25\14] that "Cavendish -pared off from the current hypotheses their theory of combustion, -and their affinities of imponderable for ponderable matter, as -complicating chemical with physical considerations; and he then -corrected and adjusted them with admirable skill to the actual -phenomena, not binding the facts to the theory, but adapting the -theory to the facts." - -[Note 24\14: _Philosophy_, b. vi. c. 4.] - -[Note 25\14: _Address to the British Association_, 1839.] - -I conceive that the discussion which the subject has recently -received, has left no doubt on the mind of any one who has perused -the {275} documents, that Cavendish is justly entitled to the honor -of this discovery, which in his own time was never contested. The -publication of his Journals of Experiments[26\14] shows that he -succeeded in establishing the point in question in July, 1781. His -experiments are referred to in an abstract of a paper of -Priestley's, made by Dr. Maty, the secretary of the Royal Society, -in June, 1783. In June, 1783, also, Dr. Blagden communicated the -result of Cavendish's experiments to Lavoisier, at Paris. Watt's -letter, containing his hypothesis that "water is composed of -dephlogisticated air and phlogiston deprived of part of their latent -or elementary heat; and that phlogisticated or pure air is composed -of water deprived of its phlogiston and united to elementary heat -and light," was not read till Nov. 1783; and even if it could have -suggested such an experiment as Cavendish's (which does not appear -likely), is proved, by the dates, to have had no share in doing so. - -[Note 26\14: _Appendix_ to Mr. V. Harcourt's _Address_] - -Mr. Cavendish's experiment was suggested by an experiment in which -Warltire, a lecturer on chemistry at Birmingham, exploded a mixture -of hydrogen and common air in a close vessel, in order to determine -whether heat were ponderable.] - - - - -CHAPTER VI. - -EPOCH OF THE THEORY OF OXYGEN.--LAVOISIER. - - -_Sect._ 1.--_Prelude to the Theory.--Its Publication._ - -WE arrive now at a great epoch in the history of Chemistry. Few -revolutions in science have immediately excited so much general -notice as the introduction of the theory of oxygen. The simplicity -and symmetry of the modes of combination which it assumed; and, -above all, the construction and universal adoption of a nomenclature -which applied to all substances, and which seemed to reveal their -inmost constitution by their name, naturally gave it an almost -irresistible sway over men's minds. We must, however, -dispassionately trace the course of its introduction. {276} - -Antoine Laurent Lavoisier, an accomplished French chemist, had -pursued, with zeal and skill, researches such as those of Black, -Cavendish, and Priestley, which we have described above. In 1774, he -showed that, in the calcination of metals in air, the metal acquires -as much weight as the air loses. It might appear that this discovery -at once overturned the view which supposed the metal to be phlogiston -_added_ to the calx. Lavoisier's contemporaries were, however, far -from allowing this; a greater mass of argument was needed to bring -them to this conclusion. Convincing proofs of the new opinion were, -however, rapidly supplied. Thus, when Priestley had discovered -dephlogisticated air, in 1774, Lavoisier showed, in 1776, that fixed -air consisted of charcoal and the dephlogisticated or pure air; for -the mercurial calx which, heated by itself, gives out pure air, gives -out, when heated with charcoal, fixed air,[27\14] which has, -therefore, since been called _carbonic acid gas_. - -[Note 27\14: _Mém. Ac. Par._ 1775.] - -Again, Lavoisier showed that the atmospheric air consists of pure or -vital air, and of an _unvital_ air, which he thence called _azot_. -The vital air he found to be the agent in combustion, acidification, -calcination, respiration; all of these processes were analogous: all -consisted in a decomposition of the atmospheric air, and a fixation -of the pure or vital portion of it. - -But he thus arrived at the conclusion, that this pure air was added, -in all the cases in which, according to the received theory, -_phlogiston_ was subtracted, and _vice versâ_. He gave the -name[28\14] of _oxygen_ (_principe oxygène_) to "the substance which -thus unites itself with metals to form their calces, and with -combustible substances to form acids." - -[Note 28\14: _Mém. Ac. Par._ 1781, p. 448.] - -A new theory was thus produced, which would account for all the -facts which the old one would explain, and had besides the evidence -of the balance in its favor. But there still remained some apparent -objections to be removed. In the action of dilute acids on metals, -inflammable air was produced. Whence came this element? The -discovery of the decomposition of water sufficiently answered this -question, and converted the objection into an argument on the side -of the theory: and thus the decomposition of water was, in fact, one -of the most critical events for the fortune of the Lavoisierian -doctrine, and one which, more than any other, decided chemists in -its favor. In succeeding years, Lavoisier showed the consistency of -his theory with {277} all that was discovered concerning the -composition of alcohol, oil, animal and vegetable substances, and -many other bodies. - -It is not necessary for us to consider any further the evidence for -this theory, but we must record a few circumstances respecting its -earlier history. Rey, a French physician, had in 1630, published a -book, in which he inquires into the grounds of the increase of the -weight of metals by calcination.[29\14] He says, "To this question, -then, supported on the grounds already mentioned, I answer, and -maintain with confidence, that the increase of weight arises from -the air, which is condensed, rendered heavy and adhesive, by the -heat of the furnace." Hooke and Mayow had entertained the opinion -that the air contains a "nitrous spirit," which is the supporter of -combustion. But Lavoisier disclaimed the charge of having derived -anything from these sources; nor is it difficult to understand how -the received generalizations of the phlogistic theory had thrown all -such narrower explanations into obscurity. The merit of Lavoisier -consisted in his combining the generality of Stahl with the verified -conjectures of Rey and Mayow. - -[Note 29\14: Thomson, _Hist. Chem._ ii. 95.] - -No one could have a better claim, by his early enthusiasm for -science, his extensive knowledge, and his zealous labors, to hope -that a great discovery might fall to his share, than Lavoisier. His -father,[30\14] a man of considerable fortune, had allowed him to -make science his only profession; and the zealous philosopher -collected about him a number of the most active physical inquirers -of his time, who met and experimented at his house one day in the -week. In this school, the new chemistry was gradually formed. A few -years after the publication of Priestley's first experiments, -Lavoisier was struck with the presentiment of the theory which he -was afterwards to produce. In 1772, he deposited[31\14] with the -secretary of the Academy, a note which contained the germ of his -future doctrines. "At that time," he says, in explaining this step, -"there was a kind of rivalry between France and England in science, -which gave importance to new experiments, and which sometimes was -the cause that the writers of the one or other of the nations -disputed the discovery with the real author." In 1777, the editor of -the Memoirs of the Academy speaks of his theory as overturning that -of Stahl; but the general acceptance of the new opinion did not take -place till later. {278} - -[Note 30\14: _Biogr. Univ._ (Cuvier.)] - -[Note 31\14: Thomson, ii. 99.] - - -_Sect._ 2.--_Reception and Confirmation of the Theory of Oxygen._ - -THE Oxygen Theory made its way with extraordinary rapidity among the -best philosophers.[32\14] In 1785, that is, soon after Cavendish's -synthesis of water had removed some of the most formidable -objections to it, Berthollet, already an eminent chemist, declared -himself a convert. Indeed it was so soon generally adopted in -France, that Fourcroy promulgated its doctrines under the name of -"La Chimie Française," a title which Lavoisier did not altogether -relish. The extraordinary eloquence and success of Fourcroy as a -lecturer at the Jardin des Plantes, had no small share in the -diffusion of the oxygen theory; and the name of "the apostle of the -new chemistry" which was at first given him in ridicule, was justly -held by him to be a glorious distinction.[33\14] - -[Note 32\14: Thomson, ii. 130.] - -[Note 33\14: Cuvier, _Eloges_, i. p. 20.] - -Guyton de Morveau, who had at first been a strenuous advocate of the -phlogistic theory, was invited to Paris, and brought over to the -opinions of Lavoisier; and soon joined in the formation of the -nomenclature founded upon the theory. This step, of which we shall -shortly speak, fixed the new doctrine, and diffused it further. -Delametherie alone defended the phlogistic theory with vigor, and -indeed with violence. He was the editor of the _Journal de -Physique_, and to evade the influence which this gave him, the -antiphlogistians[34\14] established, as the vehicle of their -opinions, another periodical, the _Annales de Chimie_. - -[Note 34\14: Thomson, ii. 133.] - -In England, indeed, their success was not so immediate. -Cavendish,[35\14] in his Memoir of 1784, speaks of the question -between the two opinions as doubtful. "There are," he says, "several -Memoirs of M. Lavoisier, in which he entirely discards phlogiston; and -as not only the foregoing experiments, but most other phenomena of -nature, seem explicable as well, or nearly as well, upon this as upon -the commonly believed principle of phlogiston," Cavendish proceeds to -explain his experiments according to the new views, expressing no -decided preference, however, for either system. But Kirwan, another -English chemist, contested the point much more resolutely. His theory -identified inflammable air, or hydrogen, with phlogiston; and in this -view, he wrote a work which was intended as a confutation of {279} the -essential part of the oxygen theory. It is a strong proof of the -steadiness and clearness with which the advocates of the new system -possessed their principles, that they immediately translated this -work, adding, at the end of each chapter, a refutation of the -phlogistic doctrines which it contained. Lavoisier, Berthollet, De -Morveau, Fourcroy, and Monge, were the authors of this curious -specimen of scientific polemics. It is also remarkable evidence of the -candor of Kirwan, that notwithstanding the prominent part he had taken -in the controversy, he allowed himself at last to be convinced. After -a struggle of ten years, he wrote[36\14] to Berthollet in 1796, "I lay -down my arms, and abandon the cause of phlogiston." Black followed the -same course. Priestley alone, of all the chemists of great name, would -never assent to the new doctrines, though his own discoveries had -contributed so much to their establishment. "He saw," says -Cuvier,[37\14] "without flinching, the most skilful defenders of the -ancient theory go over to the enemy in succession; and when Kirwan -had, almost the last of all, abjured phlogiston, Priestley remained -alone on the field of battle, and threw out a new challenge, in a -memoir addressed to the principal French chemists." It happened, -curiously enough, that the challenge was accepted, and the arguments -answered by M. Adet, who was at that time (1798,) the French -ambassador to the United States, in which country Priestley's work was -published. Even in Germany, the birth-place and home of the phlogistic -theory, the struggle was not long protracted. There was, indeed, a -controversy, the older philosophers being, as usual, the defenders of -the established doctrines; but in 1792, Klaproth repeated, before the -Academy of Berlin, all the fundamental experiments; and "the result -was a full conviction on the part of Klaproth and the Academy, that -the Lavoisierian theory was the true one."[38\14] Upon the whole, the -introduction of the Lavoisierian theory in the scientific world, when -compared with the great revolution of opinion to which it comes -nearest in importance, the introduction of the Newtonian theory, -shows, by the rapidity and temper with which it took place, a great -improvement, both in the means of arriving at truth, and in the spirit -with which they were used. - -[Note 35\14: _Phil. Trans._ 1784, p. 150.] - -[Note 36\14: Pref. to Fourcroy's _Chemistry_, xiv.] - -[Note 37\14: Cuvier, _Eloge de Priestley_, p. 208.] - -[Note 38\14: Thomson, vol. ii. p. 136.] - -Some English writers[39\14] have expressed an opinion that there was -{280} little that was original in the new doctrines. But if they -were so obvious, what are we to say of eminent chemists, as Black -and Cavendish, who hesitated when they were presented, or Kirwan and -Priestley, who rejected them? This at least shows that it required -some peculiar insight to see the evidence of these truths. To say -that most of the materials of Lavoisier's theory existed before him, -is only to say that his great merit was, that which must always be -the great merit of a new theory, his generalization. The effect -which the publication of his doctrines produced, shows us that he -was the first person who, possessing clearly the idea of -quantitative composition, applied it steadily to a great range of -well-ascertained facts. This is, as we have often had to observe, -precisely the universal description of an inductive discoverer. It -has been objected, in like manner, to the originality of Newton's -discoveries, that they were contained in those of Kepler. They were -so, but they needed a Newton to find them there. The originality of -the theory of oxygen is proved by the conflict, short as it was, -which accompanied its promulgation; its importance is shown by the -changes which it soon occasioned in every part of the science. - -[Note 39\14: Brande, _Hist. Diss._ in _Enc, Brit._ p. 182. Lunn, -_Chem._ in _Enc. Met._ p. 596.] - -Thus Lavoisier, far more fortunate than most of those who had, in -earlier ages, produced revolutions in science, saw his theory -accepted by all the most eminent men of his time, and established -over a great part of Europe within a few years from its first -promulgation. In the common course of events, it might have been -expected that the later years of his life would have been spent amid -the admiration and reverence which naturally wait upon the patriarch -of a new system of acknowledged truths. But the times in which he -lived allowed no such euthanasia to eminence of any kind. The -democracy which overthrew the ancient political institutions of -France, and swept away the nobles of the land, was not, as might -have been expected, enthusiastic in its admiration of a great -revolution in science, and forward to offer its homage to the -genuine nobility of a great discoverer. Lavoisier was thrown into -prison on some wretched charge of having, in the discharge of a -public office which he had held, adulterated certain tobacco; but in -reality, for the purpose of confiscating his property.[40\14] In his -imprisonment, his philosophy was his resource; and he employed -himself in the preparation of his papers for printing. When he was -brought before the revolutionary tribunal, he begged for a respite -of a few days, in order to complete some researches, the results of -which {281} were, he said, important to the good of humanity. The -brutish idiot, whom the state of the country at that time had placed -in the judgment-seat, told him that the republic wanted no sçavans. -He was dragged to the guillotine, May the 8th, 1794, and beheaded, -in the fifty-second year of his age; a melancholy proof that, in -periods of political ferocity, innocence and merit, private virtues -and public services, amiable manners and the love of friends, -literary fame and exalted genius, are all as nothing to protect -their possessor from the last extremes of violence and wrong, -inflicted under judicial forms. - -[Note 40\14: _Biog. Univ._ (Cuvier.)] - - -_Sect._ 3.--_Nomenclature of the Oxygen Theory._ - -AS we have already said, a powerful instrument in establishing and -diffusing the new chemical theory, was a Systematic Nomenclature -founded upon it, and applicable to all chemical compounds, which was -soon constructed and published by the authors of the theory. Such a -nomenclature made its way into general use the more easily, in that -the want of such a system had already been severely felt; the names -in common use being fantastical, arbitrary, and multiplied beyond -measure. The number of known substances had become so great, that a -list of names with no regulative principle, founded on accident, -caprice, and error, was too cumbrous and inconvenient to be -tolerated. Even before the currency which Lavoisier's theory -obtained, these evils had led to attempts towards a more convenient -set of names. Bergman and Black had constructed such lists; and -Guyton de Morveau, a clever and accomplished lawyer of Dijon, had -formed a system of nomenclature in 1782, before he had become a -convert to Lavoisier's theory, in which task he had been exhorted -and encouraged by Bergman and Macquer. In this system,[41\14] we do -not find most of the characters of the method which was afterwards -adopted. But a few years later, Lavoisier, De Morveau, Berthollet -and Fourcroy, associated themselves for the purpose of producing a -nomenclature which should correspond to the new theoretical views. -This appeared in 1787, and soon made its way into general use. The -main features of this system are, a selection of the simplest -radical words, by which substances are designated, and a systematic -distribution of terminations, to express their relations. Thus, -sulphur, combined with oxygen in two different proportions, forms -two acids, the {282} sulphur_ous_ and the sulphur_ic_; and these -acids form, with earthy or alkaline bases, sulph_ides_ and -sulph_ates_; while sulphur directly combined with another element, -forms a sulph_uret_. The term _oxyd_ (now usually written _oxide_) -expressed a lower degree of combination with oxygen than the acids. -The _Méthode de Nomenclature Chimique_ was published in 1787; and in -1789, Lavoisier published a treatise on chemistry in order further -to explain this method. In the preface to this volume, he apologizes -for the great amount of the changes, and pleads the authority of -Bergman, who had exhorted De Morveau "to spare no improper names; -those who are learned will always be learned, and those who are -ignorant will thus learn sooner." To this maxim they so far -conformed, that their system offers few anomalies; and though the -progress of discovery, and the consequent changes of theoretical -opinion, which have since gone on, appear now to require a further -change of nomenclature, it is no small evidence of the skill with -which this scheme was arranged, that for half a century it was -universally used, and felt to be far more useful and effective than -any nomenclature in any science had ever been before. - -[Note 41\14: _Journal de Physique_, 1782, p. 370.] - - - - -CHAPTER VII. - -APPLICATION AND CORRECTION OF THE OXYGEN THEORY. - - -SINCE a chemical theory, as far as it is true, must enable us to -obtain a true view of the intimate composition of all bodies -whatever, it will readily be supposed that the new chemistry led to -an immense number of analyses and researches of various kinds. These -it is not necessary to dwell upon; nor will I even mention the names -of any of the intelligent and diligent men who have labored in this -field. Perhaps one of the most striking of such analyses was Davy's -decomposition of the earths and alkalies into metallic bases and -oxygen, in 1807 and 1808; thus extending still further that analogy -between the earths and the calces of the metals, which had had so -large a share in the formation of chemical theories. This discovery, -however, both in the means by which it was made, and in the views to -which it led, bears upon subjects hereafter to be treated of. - -The Lavoisierian theory also, wide as was the range of truth which -it embraced, required some limitation and correction. I do not now -{283} speak of some erroneous opinions entertained by the author of -the theory; as, for instance, that the heat produced in combustion, -and even in respiration, arose from the conversion of oxygen gas to -a solid consistence, according to the doctrine of latent heat. Such -opinions not being necessarily connected with the general idea of -the theory, need not here be considered. But the leading -generalization of Lavoisier, that acidification was _always_ -combination with oxygen, was found untenable. The point on which the -contest on this subject took place was the constitution of the -_oxymuriatic_ and _muriatic_ acids;--as they had been termed by -Berthollet, from the belief that muriatic acid contained oxygen, and -oxymuriatic a still larger dose of oxygen. In opposition to this, a -new doctrine was put forward in 1809 by Gay-Lussac and Thenard in -France, and by Davy in England;--namely, that oxymuriatic acid was a -simple substance, which they termed _chlorine_, and that muriatic -acid was a combination of chlorine with hydrogen, which therefore -was called _hydrochloric acid_. It may be observed, that the point -in dispute in the controversy on this subject was nearly the same -which had been debated in the course of the establishment of the -oxygen theory; namely, whether in the formation of muriatic acid -from chlorine, oxygen is subtracted, or hydrogen added, and the -water concealed. - -In the course of this dispute, it was allowed on both sides, that -the combination of dry muriatic acid and ammonia afforded an -_experimentum crucis_; since, if water was produced from these -elements, oxygen must have existed in the acid. Davy being at -Edinburgh in 1812, this experiment was made in the presence of -several eminent philosophers; and the result was found to be, that -though a slight dew appeared in the vessel, there was not more than -might be ascribed to unavoidable imperfection in the process, and -certainly not so much as the old theory of muriatic acid required. -The new theory, after this period, obtained a clear superiority in -the minds of philosophical chemists, and was further supported by -new analogies.[42\14] - -[Note 42\14: Paris, _Life of Davy_, i. 337.] - -For, the existence of one _hydracid_ being thus established, it was -found that other substances gave similar combinations; and thus -chemists obtained the _hydriodic_, _hydrofluoric_, and _hydrobromic_ -acids. These acids, it is to be observed, form salts with bases, in -the same manner as the oxygen acids do. The analogy of the muriatic -and fluoric compounds was first clearly urged by a philosopher who -was {284} not peculiarly engaged in chemical research, but who was -often distinguished by his rapid and happy generalizations, M. -Ampère. He supported this analogy by many ingenious and original -arguments, in letters written to Davy, while that chemist was -engaged in his researches on fluor spar, as Davy himself -declares.[43\14] - -[Note 43\14: Paris, _Life of Davy_, i. 370.] - -Still further changes have been proposed, in that classification of -elementary substances to which the oxygen theory led. It has been -held by Berzelius and others, that other elements, as, for example, -sulphur, form _salts_ with the alkaline and earthy metals, rather -than sulphurets. The character of these _sulpho-salts_, however, is -still questioned among chemists; and therefore it does not become us -to speak as if their place in history were settled. Of course, it -will easily be understood that, in the same manner in which the -oxygen theory introduced its own proper nomenclature, the overthrow -or material transformation of the theory would require a change in -the nomenclature; or rather, the anomalies which tended to disturb -the theory, would, as they were detected, make the theoretical terms -be felt as inappropriate, and would suggest the necessity of a -reformation in that respect. But the discussion of this point -belongs to a step of the science which is to come before us -hereafter. - -It may be observed, that in approaching the limits of this part of -our subject, as we are now doing, the doctrine of the combination of -_acids_ and _bases_, of which we formerly traced the rise and -progress, is still assumed as a fundamental relation by which other -relations are tested. This remark connects the stage of chemistry -now under our notice with its earliest steps. But in order to point -out the chemical bearing of the next subjects of our narrative, we -may further observe, that _metals_, _earths_, _salts_, are spoken of -as known _classes_ of substances; and in like manner the -newly-discovered elements, which form the last trophies of -chemistry, have been distributed into such classes according to -their analogies; thus _potassium_, _sodium_, _barium_, have been -asserted to be metals; _iodine_, _bromine_, _fluorine_, have been -arranged as analogical to _chlorine_. Yet there is something vague -and indefinite in the boundaries of such classifications and -analogies; and it is precisely where this vagueness falls, that the -science is still obscure or doubtful. We are led, therefore, to see -the dependence of Chemistry upon Classification; and it is to -Sciences of Classification which we shall next proceed; as soon as -we have noticed the most general views {285} which have been given -of chemical relations, namely, the views of the electro-chemists. - -But before we do this, we must look back upon a law which obtains in -the combination of elements, and which we have hitherto not stated; -although it appears, more than any other, to reveal to us the -intimate constitution of bodies, and to offer a basis for future -generalizations. I speak of the _Atomic Theory_, as it is usually -termed; or, as we might rather call it, the Doctrine of Definite, -Reciprocal, and Multiple Proportions. - - - - -CHAPTER VIII. - -THEORY OF DEFINITE, RECIPROCAL, AND MULTIPLE PROPORTIONS. - - -_Sect._ 1.--_Prelude to the Atomic Theory, and its Publication by -Dalton._ - -THE general laws of chemical combination announced by Mr. Dalton are -truths of the highest importance in the science, and are now nowhere -contested; but the view of matter as constituted of _atoms_, which -he has employed in conveying those laws, and in expressing his -opinion of their cause, is neither so important nor so certain. In -the place which I here assign to his discovery, as one of the great -events of the history of chemistry, I speak only of the _law of -phenomena_, the rules which govern the quantities in which elements -combine. - -This law may be considered as consisting of three parts, according -to the above description of it;--that elements combine in _definite_ -proportions;--that these determining proportions operate -_reciprocally_;--and that when, between the same elements, several -combining proportions occur, they are related as _multiples_. - -That elements combine in certain definite proportions of quantity, -and in no other, was implied, as soon as it was supposed that -chemical compounds had any definite properties. Those who first -attempted to establish regular formulæ[44\14] for the constitution -of salts, minerals, and {286} other compounds, assumed, as the basis -of this process, that the elements in different specimens had the -same proportion. Wenzel, in 1777, published his _Lehre von der -Verwandschaft der Körper_; or, _Doctrine of the Affinities of -Bodies_; in which he gave many good and accurate analyses. His work, -it is said, never grew into general notice. Berthollet, as we have -already stated, maintained that chemical compounds were not -definite; but this controversy took place at a later period. It -ended in the establishment of the doctrine, that there is, for each -combination, only one proportion of the elements, or at most only -two or three. - -[Note 44\14: Thomson, _Hist. Chem._ vol. ii. p. 279.] - -Not only did Wenzel, by his very attempt, presume the first law of -chemical composition, the definiteness of the proportions, but he -was also led, by his results, to the second rule, that they are -reciprocal. For he found that when two _neutral_ salts decompose -each other, the resulting salts are also neutral. The neutral -character of the salts shows that they are definite compounds; and -when the two elements of the one salt, _P_ and _s_, are presented to -those of the other, _B_ and _n_, if _P_ be in such quantity as to -combine definitely with _n_, _B_ will also combine definitely with -_s_.[45\14] - -[Note 45\14: I am told that Wenzel (whose book I have not seen), -though he adduces many cases in which double decomposition gives -neutral salts, does not express the proposition in a general form, -nor use letters in expressing it.] - -Views similar to those of Wenzel were also published by Jeremiah -Benjamin Richter[46\14] in 1792, in his _Anfangsgründe der -Stöchyometrie, oder Messkunst Chymischer Elemente_, (_Principles of -the Measure of Chemical Elements_) in which he took the law, just -stated, of reciprocal proportions, as the basis of his researches, -and determined the numerical quantities of the common bases and -acids which would saturate each other. It is clear that, by these -steps, the two first of our three rules may be considered as fully -developed. The change of general views which was at this time going -on, probably prevented chemists from feeling so much interest as -they might have done otherwise, in these details; the French and -English chemists, in particular, were fully employed with their own -researches and controversies. - -[Note 46\14: Thomson, _Hist. Chem._ vol. ii. p. 283.] - -Thus the rules which had already been published by Wenzel and -Richter had attracted so little notice, that we can hardly consider -Mr. Dalton as having been anticipated by those writers, when, in -1803, he began to communicate his views on the chemical constitution -of {287} bodies; these views being such as to include both these two -rules in their most general form, and further, the rule, at that -time still more new to chemists, of _multiple_ proportions. He -conceived bodies as composed of atoms of their constituent elements, -grouped, either one and one, or one and two, or one and three, and -so on. Thus, if _C_ represent an atom of carbon and _O_ one of -oxygen, _O C_ will be an atom of _carbonic oxide_, and _O C O_ an -atom of _carbonic acid_; and hence it follows, that while both these -bodies have a definite quantity of oxygen to a given quantity of -carbon, in the latter substance this quantity is _double_ of what it -is in the former. - -The consideration of bodies as consisting of compound atoms, each of -these being composed of elementary atoms, naturally led to this law -of multiple proportions. In this mode of viewing bodies, Mr. Dalton -had been preceded (unknown to himself) by Mr. Higgins, who, in 1789, -published[47\14] his _Comparative View of the Phlogistic and -Antiphlogistic Theories_. He there says,[48\14] "That in volatile -vitriolic acid, a single ultimate particle of sulphur is united only -to a single particle of dephlogisticated air; and that in perfect -vitriolic acid, every single particle of sulphur is united to two of -dephlogisticated air, being the quantity necessary to saturation;" -and he reasons in the same manner concerning the constitution of -water, and the compounds of nitrogen and oxygen. These observations -of Higgins were, however, made casually, and not followed out, and -cannot affect Dalton's claim to original merit. - -[Note 47\14: Turner's _Chem._ p. 217.] - -[Note 48\14: P. 36 and 37.] - -Mr. Dalton's generalization was first suggested[49\14] during his -examination of olefiant gas and carburetted hydrogen gas; and was -asserted generally, on the strength of a few facts, being, as it -were, irresistibly recommended by the clearness and simplicity which -the notion possessed. Mr. Dalton himself represented the compound -atoms of bodies by symbols, which professed to exhibit the -arrangement of the elementary atoms in space as well as their -numerical proportion; and he attached great importance to this part -of his scheme. It is clear, however, that this part of his doctrine -is not essential to that numerical comparison of the law with facts, -on which its establishment rests. These hypothetical configurations -of atoms have no value till they are confirmed by corresponding -facts, such as the optical or crystalline properties of bodies may -perhaps one day furnish. {288} - -[Note 49\14: Thomson, vol. ii. p. 291.] - - -_Sect._ 2.--_Reception and Confirmation of the Atomic Theory._ - -IN order to give a sketch of the progress of the Atomic Theory into -general reception, we cannot do better than borrow our information -mainly from Dr. Thomson, who was one of the earliest converts and -most effective promulgators of the doctrine. Mr. Dalton, at the time -when he conceived his theory, was a teacher of mathematics at -Manchester, in circumstances which might have been considered -narrow, if he himself had been less simple in his manner of life, -and less moderate in his worldly views. His experiments were -generally made with apparatus of which the simplicity and cheapness -corresponded to the rest of his habits. In 1804, he was already in -possession of his atomic theory, and explained it to Dr. Thomson, -who visited him at that time. It was made known to the chemical -world in Dr. Thomson's _Chemistry_, in 1807; and in Dalton's own -_System of Chemistry_ (1808) the leading ideas of it were very -briefly stated. Dr. Wollaston's memoir, "on superacid and subacid -salts," which appeared in the _Philosophical Transactions_ for 1808, -did much to secure this theory a place in the estimation of -chemists. Here the author states, that he had observed, in various -salts, the quantities of acid combined with the base in the neutral -and in the superacid salts to be as one to two: and he says that, -thinking it likely this law might obtain generally in such -compounds, it was his design to have pursued this subject, with the -hope of discovering the cause to which so regular a relation may be -ascribed. But he adds, that this appears to be superfluous after the -publication of Dalton's theory by Dr. Thomson, since all such facts -are but special cases of the general law. We cannot but remark here, -that the scrupulous timidity of Wollaston was probably the only -impediment to his anticipating Dalton in the publication of the rule -of multiple proportions; and the forwardness to generalize, which -belongs to the character of the latter, justly secured him, in this -instance, the name of the discoverer of this law. The rest of the -English chemists soon followed Wollaston and Thomson, though Davy -for some time resisted. They objected, indeed, to Dalton's -assumption of atoms, and, to avoid this hypothetical step, Wollaston -used the phrase _chemical equivalents_, and Davy the word -_proportions_, for the numbers which expressed Dalton's atomic -weights. We may, however, venture to say that the term "atom" is the -most convenient, and it need not be understood as claiming our -assent to the hypothesis of indivisible molecules. {289} - -As Wollaston and Dalton were thus arriving independently at the same -result in England, other chemists, in other countries, were, unknown -to each other, travelling towards the same point. - -In 1807, Berzelius,[50\14] intending to publish a system of -chemistry, went through several works little read, and among others -the treatises of Richter. He was astonished, he tells us, at the -light which was there thrown upon composition and decomposition, and -which had never been turned to profit. He was led to a long train of -experimental research, and, when he received information of Dalton's -ideas concerning multiple proportions, he found, in his own -collection of analyses, a full confirmation of this theory. - -[Note 50\14: Berz. _Chem._ B. iii. p. 27.] - -Some of the Germans, indeed, appear discontented with the partition -of reputation which has taken place with respect to the Theory of -Definite Proportions. One[51\14] of them says, "Dalton has only done -this;--he has wrapt up the good Richter (whom he knew; compare -Schweigger, T, older series, vol. x., p. 381;) in a ragged suit, -patched together of atoms; and now poor Richter comes back to his -own country in such a garb, like Ulysses, and is not recognized." It -is to be recollected, however, that Richter says nothing of multiple -proportions. - -[Note 51\14: Marx. _Gesch. der Cryst._ p. 202.] - -The general doctrine of the atomic theory is now firmly established -over the whole of the chemical world. There remain still several -controverted points, as, for instance, whether the atomic weights of -all elements are exact multiples of the atomic weight of hydrogen. -Dr. Prout advanced several instances in which this appeared to be -true, and Dr. Thomson has asserted the law to be of universal -application. But, on the other hand, Berzelius and Dr. Turner -declare that this hypothesis is at variance with the results of the -best analyses. Such controverted points do not belong to our -history, which treats only of the progress of scientific truths -already recognized by all competent judges. - -Though Dalton's discovery was soon generally employed, and -universally spoken of with admiration, it did not bring to him -anything but barren praise, and he continued in the humble -employment of which we have spoken, when his fame had filled Europe, -and his name become a household word in the laboratory. After some -years he was appointed a corresponding member of the Institute of -France; which may be considered as a European recognition of the -importance {290} of what he had done; and, in 1826, two medals for -the encouragement of science having been placed at the disposal of -the Royal Society by the King of England, one of them was assigned -to Dalton, "for his development of the atomic theory." In 1833, at -the meeting of the British Association for the Advancement of -Science, which was held in Cambridge, it was announced that the King -had bestowed upon him a pension of 150_l._; at the preceding meeting -at Oxford, that university had conferred upon him the degree of -Doctor of Laws, a step the more remarkable, since he belonged to the -sect of Quakers. At all the meetings of the British Association he -has been present, and has always been surrounded by the reverence -and admiration of all who feel any sympathy with the progress of -science. May he long remain among us thus to remind us of the vast -advance which Chemistry owes to him! - -[2nd Ed.] [Soon after I wrote these expressions of hope, the period -of Dalton's sojourn among us terminated. He died on the 27th of -July, 1844, aged 78. - -His fellow-townsmen, the inhabitants of Manchester, who had so long -taken a pride in his residence among them, soon after his death came -to a determination to perpetuate his memory by establishing in his -honor a Professor of Chemistry at Manchester.] - - -_Sect._ 3.--_The Theory of Volumes.--Gay-Lussac._ - -THE atomic theory, at the very epoch of its introduction into -France, received a modification in virtue of a curious discovery -then made. Soon after the publication of Dalton's system, Gay-Lussac -and Humboldt found a rule for the combination of substances, which -includes that of Dalton as far as it goes, but extends to -combinations of gases only. This law is the _theory of volumes_; -namely, that gases unite together _by volume_ in very simple and -definite proportions. Thus water is composed exactly of 100 measures -of oxygen and 200 measures of hydrogen. And since these simple -ratios 1 and 1, 1 and 2, 1 and 3, alone prevail in such -combinations, it may easily be shown that laws like Dalton's law of -multiple proportions, must obtain in such cases as he considered. - -[2nd Ed.] [M. Schröder, of Mannheim, has endeavored to extend to -solids a law in some degree resembling Gay-Lussac's law of the -volumes of gases. According to him, the volumes of the chemical -equivalents {291} of simple substances and their compounds are as -whole numbers.[52\14] MM. Kopp, Playfair, and Joule have labored in -the same field.] - -[Note 52\14: _Die molecular-volume der Chemischen Verbindungen in -festen und flüssingen Zustande_, 1843.] - -I cannot now attempt to trace other bearings and developments of -this remarkable discovery. I hasten on to the last generalization of -chemistry; which presents to us chemical forces under a new aspect, -and brings us back to the point from which we departed in commencing -the history of this science. - - - - -CHAPTER IX. - -EPOCH OF DAVY AND FARADAY. - - -_Sect._ 1.--_Promulgation of the Electro-chemical Theory by Davy._ - -THE reader will recollect that the History of Chemistry, though -highly important and instructive in itself, has been an interruption -of the History of Electro-dynamic Research:--a necessary -interruption, however; for till we became acquainted with Chemistry -in general, we could not follow the course of Electro-chemistry: we -could not estimate its vast yet philosophical theories, nor even -express its simplest facts. We have now to endeavor to show what has -thus been done, and by what steps;--to give a fitting view of the -Epoch of Davy and Faraday. - -This is, doubtless, a task of difficulty and delicacy. We cannot -execute it at all, except we suppose that the great truths, of which -the discovery marks this epoch, have already assumed their definite -and permanent form. For we do not learn the just value and right -place of imperfect attempts and partial advances in science, except -by seeing to what they lead. We judge properly of our trials and -guesses only when we have gained our point and guessed rightly. We -might personify philosophical theories, and might represent them to -ourselves as figures, all pressing eagerly onwards in the same {292} -direction, whom we have to pursue: and it is only in proportion as -we ourselves overtake those figures in the race, and pass beyond -them, that we are enabled to look back upon their faces; to discern -their real aspects, and to catch the true character of their -countenances. Except, therefore, I were of opinion that the great -truths which Davy brought into sight have been firmly established -and clearly developed by Faraday, I could not pretend to give the -history of this striking portion of science. But I trust, by the -view I have to offer of these beautiful trains of research and their -result, to justify the assumption on which I thus proceed. - -I must, however, state, as a further appeal to the reader's -indulgence, that, even if the great principles of electro-chemistry -have now been brought out in their due form and extent, the -discovery is but a very few years, I might rather say a few months, -old, and that this novelty adds materially to the difficulty of -estimating previous attempts from the point of view to which we are -thus led. It is only slowly and by degrees that the mind becomes -sufficiently imbued with those new truths, of which the office is, -to change the face of a science. We have to consider familiar -appearances under a new aspect; to refer old facts to new -principles; and it is not till after some time, that the struggle -and hesitation which this employment occasions, subsides into a -tranquil equilibrium. In the newly acquired provinces of man's -intellectual empire, the din and confusion of conquest pass only -gradually into quiet and security. We have seen, in the history of -all capital discoveries, how hardly they have made their way, even -among the most intelligent and candid philosophers of the antecedent -schools: we must, therefore, not expect that the metamorphosis of -the theoretical views of chemistry which is now going on, will be -effected without some trouble and delay. - -I shall endeavor to diminish the difficulties of my undertaking, by -presenting the earlier investigations in the department of which I -have now to speak, as much as possible according to the most -deliberate view taken of them by the great discoverers themselves, -Davy and Faraday; since these philosophers are they who have taught -us the true import of such investigations. - -There is a further difficulty in my task, to which I might -refer;--the difficulty of speaking, without error and without -offence, of men now alive, or who were lately members of social -circles which exist still around us. But the scientific history in -which such persons play a part, is so important to my purpose, that -I do not hesitate to incur {293} the responsibility which the -narration involves; and I have endeavored earnestly, and I hope not -in vain, to speak as if I were removed by centuries from the -personages of my story. - -The phenomena observed in the Voltaic apparatus were naturally the -subject of many speculations as to their cause, and thus gave rise -to "Theories of the Pile." Among these phenomena there was one class -which led to most important results: it was discovered by Nicholson -and Carlisle, in 1800, that water was _decomposed_ by the pile of -Volta; that is, it was found that when the wires of the pile were -placed with their ends near each other in the fluid, a stream of -bubbles of air arose from each wire, and these airs were found on -examination to be oxygen and hydrogen: which, as we have had to -narrate, had already been found to be the constituents of water. -This was, as Davy says,[53\14] the true origin of all that has been -done in electro-chemical science. It was found that other substances -also suffered a like decomposition under the same circumstances. -Certain metallic solutions were decomposed, and an alkali was -separated on the negative plates of the apparatus. Cruickshank, in -pursuing these experiments, added to them many important new -results; such as the decomposition of muriates of magnesia, soda, -and ammonia by the pile; and the general observation that the -alkaline matter always appeared at the _negative_, and the acid at -the _positive_, pole. - -[Note 53\14: _Phil. Trans._ 1826, p. 386.] - -Such was the state of the subject when one who was destined to do so -much for its advance, first contributed his labors to it. Humphry -Davy was a young man who had been apprenticed to a surgeon at -Penzance, and having shown an ardent love and a strong aptitude for -chemical research, was, in 1798, made the superintendent of a -"Pneumatic Institution," established at Bristol by Dr. Beddoes, for -the purpose of discovering medical powers of factitious airs.[54\14] -But his main attention was soon drawn to galvanism; and when, in -consequence of the reputation he had acquired, he was, in 1801, -appointed lecturer at the Royal Institution in London (then recently -established), he was soon put in possession of a galvanic apparatus -of great power; and with this he was not long in obtaining the most -striking results. - -[Note 54\14: Paris, _Life of Davy_, i. 58.] - -His first paper on the subject[55\14] is sent from Bristol, in -September, 1800; and describes experiments, in which he had found -that the decompositions observed by Nicholson and Carlisle go on, -although the {294} water, or other substance in which the two wires -are plunged, be separated into two portions, provided these portions -are connected by muscular or other fibres. This use of muscular -fibres was, probably, a remnant of the original disposition, or -accident, by which galvanism had been connected with physiology, as -much as with chemistry. Davy, however, soon went on towards the -conclusion, that the phenomena were altogether chemical in their -nature. He had already conjectured,[56\14] in 1802, that all -decompositions might be _polar_; that is, that in all cases of -chemical decomposition, the elements might be related to each other -as electrically _positive_ and _negative_; a thought which it was -the peculiar glory of his school to confirm and place in a distinct -light. At this period such a view was far from obvious; and it was -contended by many, on the contrary, that the elements which the -voltaic apparatus brought to view, were not liberated from -combinations, but generated. In 1806, Davy attempted the solution of -this question; he showed that the ingredients which had been -supposed to be produced by electricity, were due to impurities in -the water, or to the decomposition of the vessel; and thus removed -all preliminary difficulties. And then he says,[57\14] "referring to -my experiments of 1800, 1801, and 1802, and to a number of new -facts, which showed that inflammable substances and oxygen, alkalies -and acids, and oxidable and noble metals, were in electrical -relations of positive and negative, I drew the conclusion, _that the -combinations and decompositions by electricity were referrible to -the law of electrical attractions and repulsions_," and advanced the -hypothesis, "_that chemical and electrical attractions were produced -by the same cause, acting in the one case on particles, in the other -on masses; . . . and that the same property, under different -modifications, was the cause of all the phenomena exhibited by -different voltaic combinations._" - -[Note 55\14: Nicholson's _Journal_, 4to. iv. 275.] - -[Note 56\14: _Phil. Trans._ 1826.] - -[Note 57\14: Ib. 1826, p. 389.] - -Although this is the enunciation, in tolerably precise terms, of the -great discovery of his epoch, it was, at the period of which we -speak, conjectured rather than proved; and we shall find that -neither Davy nor his followers, for a considerable period, -apprehended it with that distinctness which makes a discovery -complete. But in a very short time afterwards, Davy drew great -additional notice to his researches by effecting, in pursuance, as -it appeared, of his theoretical views, the decomposition of potassa -into a metallic base and oxygen. This was, as he truly said, in the -memorandum written in his journal at the {295} instant, "a capital -experiment." This discovery was soon followed by that of the -decomposition of soda; and shortly after, of other bodies of the -same kind; and the interest and activity of the whole chemical world -were turned to the subject in an intense degree. - -At this period, there might be noticed three great branches of -speculation on this subject; _the theory of the pile_, _the theory -of electrical decomposition_, and **_the theory of the identity of -chemical and electrical forces_; which last doctrine, however, was -found to include the other two, as might have been anticipated from -the time of its first suggestion. - -It will not be necessary to say much on the theories of the voltaic -pile, as separate from other parts of the subject. The -_contact-theory_, which ascribed the action to the contact of -different metals, was maintained by Volta himself; but gradually -disappeared, as it was proved (by Wollaston[58\14] especially,) that -the effect of the pile was inseparably connected with oxidation or -other chemical changes. The theories of electro-chemical -decomposition were numerous, and especially after the promulgation -of Davy's _Memoir_ in 1806; and, whatever might be the defects under -which these speculations for a long time labored, the subject was -powerfully urged on in the direction in which truth lay, by Davy's -discoveries and views. That there remained something still to be -done, in order to give full evidence and consistency to the theory, -appears from this;--that some of the most important parts of Davy's -results struck his followers as extraordinary paradoxes;--for -instance, the fact that the decomposed elements are transferred from -one part of the circuit to another, in a form which escapes the -cognizance of our senses, through intervening substances for which -they have a strong affinity. It was found afterwards that the -circumstance which appeared to make the process so wonderful, was, -in fact, the condition of its going on at all. Davy's expressions -often seem to indicate the most exact notions: for instance, he -says, "It is very natural to suppose that the repellent and -attractive energies are communicated from one particle to another of -the same kind, so as to establish a conducting _chain_ in the fluid; -and that the locomotion takes place in consequence;"[59\14] and yet -at other times he speaks of the element as _attracted_ and -_repelled_ by the metallic surfaces which form the _poles_;--a -different, and, as it appeared afterwards, an untenable view. Mr. -Faraday, who supplied what was wanting, justly notices this -vagueness. {296} He says,[60\14] that though, in Davy's celebrated -Memoir of 1806, the points established are of the utmost value, the -mode of action by which the effects take place is stated very -generally; so generally, indeed, that probably a dozen precise -schemes of electro-chemical action might be drawn up, differing -essentially from each other, yet all agreeing with the statement -there given." And at a period a little later, being reproached by -Davy's brother with injustice in this expression, he substantiated -his assertion by an enumeration of twelve such schemes which had -been published. - -[Note 58\14: _Phil. Trans._ 1801, p. 427.] - -[Note 59\14: Paris, i. 154.] - -[Note 60\14: _Researches_, 482.] - -But yet we cannot look upon this Memoir of 1806, otherwise than as a -great event, perhaps the most important event of the epoch now under -review. And as such it was recognized at once all over Europe. In -particular, it received the distinguished honor of being crowned by -the Institute of France, although that country and England were then -engaged in fierce hostility. Buonaparte had proposed a prize of -sixty thousand francs "to the person who by his experiments and -discoveries should advance the knowledge of electricity and -galvanism, as much as Franklin and Volta did;" and "of three -thousand francs for the best experiment which should be made in the -course of each year on the galvanic fluid;" the latter prize was, by -the First Class of the Institute, awarded to Davy. - -From this period he rose rapidly to honors and distinctions, and -reached a height of scientific fame as great as has ever fallen to -the lot of a discoverer in so short a time. I shall not, however, -dwell on such circumstances, but confine myself to the progress of -my subject. - - -_Sect._ 2.--_Establishment of the Electro-chemical Theory by Faraday._ - -THE defects of Davy's theoretical views will be seen most clearly by -explaining what Faraday added to them. Michael Faraday was in every -way fitted and led to become Davy's successor in his great career of -discovery. In 1812, being then a bookseller's apprentice, he -attended the lectures of Davy, which at that period excited the -highest admiration.[61\14] "My desire to escape from trade," Mr. -Faraday says, "which I thought vicious and selfish, and to enter -into the service of science, which I imagined made its pursuers -amiable and liberal, induced me at last to take the bold and simple -step of writing to Sir H. Davy." He was favorably received, and, in -the next year, became {297} Davy's assistant at the Institution; and -afterwards his successor. The Institution which produced such -researches as those of these two men, may well be considered as a -great school of exact and philosophical chemistry. Mr. Faraday, from -the beginning of his course of inquiry, appears to have had the -consciousness that he was engaged on a great connected work. His -_Experimental Researches_, which appeared in a series of Memoirs in -the _Philosophical Transactions_, are divided into short paragraphs, -numbered into a continued order from 1 up to 1160, at the time at -which I write;[62\14] and destined, probably, to extend much -further. These paragraphs are connected by a very rigorous method of -investigation and reasoning which runs through the whole body of -them. Yet this unity of purpose was not at first obvious. His first -two Memoirs were upon subjects which we have already treated of (B. -xiii. c. 5 and c. 8), Voltaic Induction, and the evolution of -Electricity from Magnetism. His "Third Series" has also been already -referred to. Its object was, as a preparatory step towards further -investigation, to show the identity of voltaic and animal -electricity with that of the electrical machine; and as machine -electricity differs from other kinds in being successively in a -state of tension and explosion, instead of a continued current, Mr. -Faraday succeeded in identifying it with them, by causing the -electrical discharge to pass through a bad conductor into a -discharging-train of vast extent; nothing less, indeed, than the -whole fabric of the metallic gas-pipes and water-pipes of London. In -this Memoir[63\14] it is easy to see already traces of the general -theoretical views at which he had arrived; but these are not -expressly stated till his "Fifth Series;" his intermediate Fourth -Series being occupied by another subsidiary labor on the conditions -of conduction. At length, however, in the Fifth Series, which was -read to the Royal Society in June, 1833, he approaches the theory of -electro-chemical decomposition. Most preceding theorists, and Davy -amongst the number, had referred this result to _attractive powers_ -residing in the _poles_ of the apparatus; and had even pretended to -compare the intensity of this attraction at different distances from -the poles. By a number of singularly beautiful and skilful -experiments, Mr. Faraday shows that the phenomena can with no -propriety be {298} ascribed to the attraction of the poles.[64\14] -"As the substances evolved in cases of electro-chemical -decomposition may be made to appear against air,[65\14] which, -according to common language, is not a conductor, nor is decomposed; -or against water,[66\14] which is a conductor, and can be -decomposed; as well as against the metal poles, which are excellent -conductors, but undecomposable; there appears but little reason to -consider this phenomenon generally as due to the attraction or -attractive powers of the latter, when used in the ordinary way, -since similar attractions can hardly be imagined in the former -instances." - -[Note 61\14: Paris, ii. 3.] - -[Note 62\14: December, 1835. (At present, when I am revising the -second edition, September, 1846, Dr. Faraday has recently published -the "Twenty-first Series" of his _Researches_ ending with paragraph -2453.)] - -[Note 63\14: _Phil. Trans._ 1833.] - -[Note 64\14: _Researches_, Art. 497] - -[Note 65\14: _Researches_, Arts. 465, 469.] - -[Note 66\14: 495.] - -Faraday's opinion, and, indeed, the only way of expressing the -results of his experiments, was, that the chemical elements, in -obedience to the direction of the voltaic currents established in -the decomposing substance, were evolved, or, as he prefers to say, -_ejected_ at its extremities.[67\14] He afterwards states that the -influence which is present in the electric current may be -described[68\14] as _an axis of power, having_ [at each point] -_contrary forces exactly equal in amount in contrary directions_. - -[Note 67\14: 493.] - -[Note 68\14: 517.] - -Having arrived at this point, Faraday rightly wished to reject the -term _poles_, and other words which could hardly be used without -suggesting doctrines now proved to be erroneous. He considered, in -the case of bodies electrically decomposed, or, as he termed them, -_electrolytes_, the elements as travelling in two opposite -directions; which, with reference to the direction of terrestrial -magnetism, might be considered as naturally east and west; and he -conceived elements as, in this way, arriving at the doors or outlets -at which they finally made their separate appearance. The doors he -called _electrodes_, and, separately, the _anode_ and the -_cathode_;[69\14] and the elements which thus travel he termed the -_anïon_ and the _catïon_ (or _cathïon_).[70\14] By means of this -nomenclature he was able to express his general results with much -more distinctness and facility. - -[Note 69\14: 663.] - -[Note 70\14: The analogy of the Greek derivation requires _catïon_; -but to make the relation to _cathode_ obvious to the English reader, -and to avoid a violation of the habits of English pronunciation, I -should prefer _cathïon_.] - -But this general view of the electrolytical process required to be -pursued further, in order to explain the nature of the action. The -identity of electrical and chemical forces, which had been hazarded -as {299} a conjecture by Davy, and adopted as the basis of chemistry -by Berzelius, could only be established by exact measures and -rigorous proofs. Faraday had, in his proof of the identity of -voltaic and electric agency, attempted also to devise such a measure -as should give him a comparison of their quantity; and in this way -he proved that[71\14] a voltaic group of two small wires of platinum -and zinc, placed near each other, and immersed in dilute acid for -three seconds, yields as much electricity as the electrical battery, -charged by ten turns of a large machine; and this was established -both by its momentary electro-magnetic effect, and by the amount of -its chemical action.[72\14] - -[Note 71\14: _Researches_, Art. 371.] - -[Note 72\14: 537.] - -It was in his "Seventh Series," that he finally established a -principle of definite measurement of the amount of electrolytical -action, and described an instrument which he termed[73\14] a -_volta-electrometer_. In this instrument the amount of action was -measured by the quantity of water decomposed: and it was necessary, -in order to give validity to the mensuration, to show (as Faraday -did show) that neither the size of the electrodes, nor the intensity -of the current, nor the strength of the acid solution which acted on -the plates of the pile, disturbed the accuracy of this measure. He -proved, by experiments upon a great variety of substances, of the -most different kinds, that the electro-chemical action is definite -in amount according to the measurement of the new instrument.[74\14] -He had already, at an earlier period,[75\14] asserted, that _the -chemical power of a current of electricity is in direct proportion -to the absolute quantity of electricity which passes_; but the -volta-electrometer enabled him to fix with more precision the -meaning of this general proposition, as well as to place it beyond -doubt. - -[Note 73\14: 739.] - -[Note 74\14: Arts. 758, 814.] - -[Note 75\14: 377.] - -The vast importance of this step in chemistry soon came into view. -By the use of the volta-electrometer, Faraday obtained, for each -elementary substance, a number which represented the relative amount -of its decomposition, and which might properly[76\14] be called its -"electro-chemical equivalent." And the question naturally occurs, -whether these numbers bore any relation to any previously -established chemical measures. The answer is remarkable. _They were -no other than the atomic weights of the Daltonian theory_, which -formed the climax of the previous ascent of chemistry; and thus -here, as everywhere in {300} the progress of science, the -generalizations of one generation are absorbed in the wider -generalizations of the next. - -[Note 76\14: 792.] - -But in order to reach securely this wider generalization, Faraday -combined the two branches of the subject which we have already -noticed;--the _theory of electrical decomposition_ with the _theory -of the pile_. For his researches on the origin of activity of the -voltaic circuit (his Eighth Series), led him to see more clearly -than any one before him, what, as we have said, the most sagacious -of preceding philosophers had maintained, that the current in the -pile was due to the mutual chemical action of its elements. He was -led to consider the processes which go on in the _exciting-cell_ and -in the decomposing place as of the same kind, but opposite in -direction. The chemical _composition_ of the fluid with the zinc, in -the common apparatus, produces, when the circuit is completed, a -current of electric influence in the wire; and this current, if it -pass through an electrolyte, manifests itself by _decomposition_, -overcoming the chemical affinity which there resists it. An -electrolyte cannot conduct without being decomposed. The forces at -the point of composition and the point of decomposition are of the -same kind, and are opposed to each other by means of the -conducting-wire; the wire may properly be spoken of[77\14] as -_conducting chemical affinity_: it allows two forces of the same -kind to oppose one another;[78\14] electricity is only another mode -of the exertion of chemical forces;[79\14] and we might express all -the circumstances of the voltaic pile without using any other term -than chemical affinity, though that of electricity may be very -convenient.[80\14] Bodies are held together by a definite power, -which, when it ceases to discharge that office, may be thrown into -the condition of an electric current.[81\14] - -[Note 77\14: Researches Art. 918.] - -[Note 78\14: 910.] - -[Note 79\14: 915.] - -[Note 80\14: 917.] - -[Note 81\14: 855.] - -Thus the great principle of the identity of electrical and chemical -action was completely established. It was, as Faraday with great -candor says,[82\14] a confirmation of the general views put forth by -Davy, in 1806, and might be expressed in his terms, that "chemical -and electrical attractions are produced by the same cause;" but it -is easy to see that neither was the full import of these expressions -understood nor were the quantities to which they refer conceived as -measurable quantities, nor was the assertion anything but a -sagacious conjecture, till Faraday gave the interpretation, measure, -and proof, of which we have spoken. The evidence of the -incompleteness of the views of his predecessor we have already -adduced, in speaking of his vague and {301} inconsistent theoretical -account of decomposition. The confirmation of Davy's discoveries by -Faraday is of the nature of Newton's confirmation of the views of -Borelli and Hooke respecting gravity, or like Young's confirmation -of the undulatory theory of Huyghens. - -[Note 82\14: 965.] - -We must not omit to repeat here the moral which we wish to draw from -all great discoveries, that they depend upon the combination of -_exact facts_ with _clear ideas_. The former of these conditions is -easily illustrated in the case of Davy and Faraday, both admirable -and delicate experimenters. Davy's rapidity and resource in -experimenting were extraordinary,[83\14] and extreme elegance and -ingenuity distinguish almost every process of Faraday. He had -published, in 1829, a work on _Chemical Manipulation_, in which -directions are given for performing in the neatest manner all -chemical processes. Manipulation, as he there truly says, is to the -chemist like the external senses to the mind;[84\14] and without the -supply of fit materials which such senses only can give, the mind -can acquire no real knowledge. - -[Note 83\14: Paris, i. 145.] - -[Note 84\14: _Pref._ p. ii.] - -But still the operations of the mind as well as the information of the -senses, ideas as well as facts, are requisite for the attainment of -any knowledge; and all great steps in science require a peculiar -distinctness and vividness of thought in the discoverer. This it is -difficult to exemplify in any better way than by the discoveries -themselves. Both Davy and Faraday possessed this vividness of mind; -and it was a consequence of this endowment, that Davy's **lectures -upon chemistry, and Faraday's upon almost any subject of physical -philosophy, were of the most brilliant and captivating character. In -discovering the nature of voltaic action, the essential intellectual -requisite was to have a distinct conception of that which Faraday -expressed by the remarkable phrase,[85\14] "_an axis of power having -equal and opposite forces_;" and the distinctness of this idea in -Faraday's mind shines forth in every part of his writings. Thus he -says, the force which determines the decomposition of a body is _in_ -the body, not in the poles.[86\14] But for the most part he can of -course only convey this fundamental idea by illustrations. Thus[87\14] -he represents the voltaic circuit by a double circle, studded with the -elements of the circuit, and shows how the _anïons_ travel round it in -one direction, and the _cathïons_ in the opposite. He considers[88\14] -the powers at the two places of action as balancing against each other -through the medium of the conductors, in a manner {302} analogous to -that in which mechanical forces are balanced against each other by the -intervention of the lever. It is impossible to him[89\14] to resist -the idea, that the voltaic current must be preceded by a state of -tension in its interrupted condition, which is relieved when the -circuit is completed. He appears to possess the idea of this kind of -force with the same eminent distinctness with which Archimedes in the -ancient, and Stevinus in the modern history of science, possessed the -idea of pressure, and were thus able to found the science of -mechanics.[90\14] And when he cannot obtain these distinct modes of -conception, he is dissatisfied, and conscious of defect. Thus in the -relation between magnetism and electricity,[91\14] "there appears to -be a link in the chain of effects, a wheel in the physical mechanism -of the action, as yet unrecognized." All this variety of expression -shows how deeply seated is the thought. This conception of Chemical -Affinity as a peculiar influence of force, which, acting in opposite -directions, combines and resolves bodies;--which may be liberated and -thrown into the form of a voltaic current, and thus be transferred to -remote points, and applied in various ways; is essential to the -understanding, as it was to the making, of these discoveries. - -[Note 85\14: Art. 517.] - -[Note 86\14: Art. 661.] - -[Note 87\14: **963.] - -[Note 88\14: 917.] - -[Note 89\14: Art. 950.] - -[Note 90\14: 990.] - -[Note 91\14: 1114.] - -By those to whom this conception has been conveyed, I venture to -trust that I shall be held to have given a faithful account of this -important event in the history of science. We may, before we quit -the subject, notice one or two of the remarkable subordinate -features of Faraday's discoveries. - - -_Sect._ 3.--_Consequences of Faraday's Discoveries._ - -FARADAY'S volta-electrometer, in conjunction with the method he had -already employed, as we have seen, for the comparison of voltaic and -common electricity, enabled him to measure the actual quantity of -electricity which is exhibited, in given cases, in the form of -chemical affinity. His results appeared in numbers of that enormous -amount which so often comes before us in the expression of natural -laws. One grain of water[92\14] will require for its decomposition -as much electricity as would make a powerful flash of lightning. By -further calculation, he finds this quantity to be not less than -800,000 charges of his Leyden battery;[93\14] and this is, by his -theory of the identity of the combining with the decomposing force, -the quantity of electricity {303} which is naturally associated with -the elements of the grain of water, endowing them with their mutual -affinity. - -[Note 92\14: **853.] - -[Note 93\14: 861.] - -Many of the subordinate facts and laws which were brought to light -by these researches, clearly point to generalizations, not included -in that which we have had to consider, and not yet discovered: such -laws do not properly belong to our main plan, which is to make our -way _up to_ the generalizations. But there is one which so evidently -promises to have an important bearing on future chemical theories, -that I will briefly mention it. The class of bodies which are -capable of electrical decomposition is limited by a very remarkable -law: they are such binary compounds only as consist of _single_ -proportionals of their elementary principles. It does not belong to -us here to speculate on the possible import of this curious law; -which, if not fully established, Faraday has rendered, at least, -highly probable:[94\14] but it is impossible not to see how closely -it connects the Atomic with the Electro-chemical Theory; and in the -connexion of these two great members of Chemistry, is involved the -prospect of its reaching wider generalizations, and principles more -profound than we have yet caught sight of. - -[Note 94\14: Art. 697.] - -As another example of this connexion, I will, finally, notice that -Faraday has employed his discoveries in order to decide, in some -doubtful cases, what is the true chemical equivalent;[95\14] "I have -such conviction," he says, "that the power which governs -electro-decomposition and ordinary chemical attractions is the same; -and such confidence in the overruling influence of those natural -laws which render the former definite, as to feel no hesitation in -believing that the latter must submit to them too. Such being the -case, I can have no doubt that, assuming hydrogen as 1, and -dismissing small fractions for the simplicity of expression, the -equivalent number or atomic weight of oxygen is 8, of chlorine 36, -of bromine 78·4, of lead 103·5, of tin 59, &c.; notwithstanding that -a very high authority doubles several of these numbers." - -[Note 95\14: 851.] - - -_Sect._ 4.--_Reception of the Electro-chemical Theory._ - -THE epoch of establishment of the electro-chemical theory, like -other great scientific epochs, must have its sequel, the period of -its reception and confirmation, application and extension. In that -period we {304} are living, and it must be the task of future -historians to trace its course. - -We may, however, say a word on the reception which the theory met -with, in the forms which it assumed, anterior to the labors of -Faraday. Even before the great discovery of Davy, Grotthuss, in -1805, had written upon the theory of electro-chemical decomposition; -but he and, as we have seen, Davy, and afterwards other writers, as -Riffault and Chompré, in 1807, referred the effects to the -poles.[96\14] But the most important attempt to appropriate and -employ the generalization which these discoveries suggested, was -that of Berzelius; who adopted at once the view of the identity, or -at least the universal connexion, of electrical relations with -chemical affinity. He considered,[97\14] that in all chemical -combinations the elements may be considered as electro-positive and -electro-negative; and made this opposition the basis of his chemical -doctrines; in which he was followed by a large body of the chemists -of Germany. He held too that the heat and light, evolved during -cases of powerful combination, are the consequence of the electric -discharge which is at that moment taking place: a conjecture which -Faraday at first spoke of with praise.[98\14] But at a later period -he more sagely says,[99\14] that the flame which is produced in such -cases exhibits but a small portion of the electric power which -really acts. "These therefore may not, cannot, be taken as evidences -of the nature of the action; but are merely incidental results, -incomparably small in relation to the forces concerned, and -supplying no information of the way in which the particles are -active on each other, or in which their forces are finally -arranged." And comparing the evidence which he himself had given of -the principle on which Berzelius's speculations rested, with the -speculations themselves, Faraday justly conceived, that he had -transferred the doctrine from the domain of what he calls _doubtful -knowledge_, to that of inductive certainty. - -[Note 96\14: Faraday (_Researches_, Art. 481, 492).] - -[Note 97\14: _Ann. Chim._ lxxxvi. 146, for 1813.] - -[Note 98\14: _Researches_, Art. 870] - -[Note 99\14: 960.] - -Now that we are arrived at the starting-place, from which this -well-proved truth, the identity of electric and chemical forces, -must make its future advances, it would be trifling to dwell longer -on the details of the diffusion of that doubtful knowledge which -preceded this more certain science. Our history of chemistry is, -therefore, here at an end. I have, as far as I could, executed my -task; which was, to mark all the {305} great steps of its advance, -from the most unconnected facts and the most imperfect speculations, -to the highest generalization at which chemical philosophers have -yet arrived. - -Yet it will appear to our purpose to say a few words on the -connexion of this science with those of which we are next to treat; -and that I now proceed to do. - - - - -CHAPTER X. - -TRANSITION FROM THE CHEMICAL TO THE CLASSIFICATORY SCIENCES. - - -IT is the object and the boast of chemistry to acquire a knowledge -of bodies which is more exact and constant than any knowledge -borrowed from their sensible qualities can be; since it penetrates -into their intimate constitution, and discloses to us the invariable -laws of their composition. But yet it will be seen, on a little -reflection, that such knowledge could not have any existence, if we -were not also attentive to their sensible qualities. - -The whole fabric of chemistry rests, even at the present day, upon -the opposition of acids and bases: an acid was certainly at first -known by its sensible qualities, and how otherwise, even now, do we -perceive its quality? It was a great discovery of modern times that -earths and alkalies have for their bases metals: but what are -_metals_? or how, except from lustre, hardness, weight, and the -like, do we recognize a body as a metal? And how, except by such -characters, even before its analysis, was it known to be an earth or -an alkali? We must suppose some classification established, before -we can make any advance by experiment or observation. - -It is easy to see that all attempts to avoid this difficulty by -referring to processes and analogies, as well as to substances, -bring us back to the same point in a circle of fallacies. If we say -that an acid and alkali are known by combining with each other, we -still must ask, What is the criterion that they have _combined_? If -we say that the distinctive qualities of metals and earths are, that -metals become earths by oxidation, we must still inquire how we -recognize the process of _oxidation_? We have seen how important a -part combustion plays in the history of chemical speculation; and we -may usefully form such classes of {306} bodies as _combustibles_ and -_supporters of combustion_. But even _combustion_ is not capable of -being infallibly known, for it passes by insensible shades into -oxidation. We can find no basis for our reasonings, which does not -assume a classification of obvious facts and qualities. - -But any classification of substances on such grounds, appears, at -first sight, to involve us in vagueness, ambiguity, and -contradiction. Do we really take the sensible qualities of an acid -as the criterion of its being an acid?--for instance, its sourness? -Prussic acid, arsenious acid, are not sour. "I remember," says Dr. -Paris,[100\14] "a chemist having been exposed to much ridicule from -speaking of a _sweet_ acid,--why not?" When Davy had discovered -potassium, it was disputed whether it was a metal; for though its -lustre and texture are metallic, it is so light as to swim on water. -And if potassium be allowed to be a metal, is silicium one, a body -which wants the metallic lustre, and is a non-conductor of -electricity? It is clear that, at least, the _obvious_ application -of a classification by physical characters, is attended with endless -perplexity. - -[Note 100\14: _Life of Davy_, i. 263.] - -But since we cannot even begin our researches without assuming a -classification, and since the forms of such a classification which -first occur, end in apparent confusion, it is clear that we must -look to our philosophy for a solution of this difficulty; and must -avoid the embarrassments and contradictions of casual and -unreflective classification, by obtaining a consistent and -philosophical arrangement. We must employ external characters and -analogies in a connected and systematic manner; we must have -_Classificatory Sciences_, and these must have a bearing even on -Chemistry. - -Accordingly, the most philosophical chemists now proceed upon this -principle. "The method which I have followed," says M. Thenard, in -his _Traité de Chimie_, published in 1824, "is, to unite in one -group all analogous bodies; and the advantage of this method, which -is that employed by naturalists, is very great, especially in the -study of the metals and their compounds."[101\14] In this, as in all -good systems of chemistry, which have appeared since the -establishment of the phlogistic theory, combustion, and the -analogous processes, are one great element in the arrangement, while -the difference of metallic and non-metallic, is another element. -Thus Thenard, in the first place, speaks of Oxygen; in the next -place, of the Non-metallic Combustibles, as Hydrogen, Carbon, -Sulphur, Chlorine; and in the next place, of Metals. But the Metals -are again divided into six Sections, with reference, {307} -principally, to their facility of combination with oxygen. Thus, the -First Section is the Metals of the Earths; the Second, the Metals of -the Alkalies; the Third, the Easily Oxidable Metals, as Iron; the -Fourth, Metals Less Oxidable, as Copper and Lead; the Fifth Section -contains only Mercury and Osmium; and the Sixth, what were at an -earlier period termed the _Noble_ Metals, Gold, Silver, Platinum, -and others. - -[Note 101\14: Pref., p. viii.] - -How such principles are to be applied, so as to produce a definite -and consistent arrangement, will be explained in speaking of the -philosophy of the Classificatory Sciences; but there are one or two -peculiarities in the classes of bodies thus recognized by modern -chemistry, which it may be useful to notice. - -1. The distinction of Metallic and Non-metallic is still employed, -as of fundamental importance. The discovery of new metals is so much -connected with the inquiries concerning chemical elements, that we -may notice the general progress of such discoveries. _Gold_, -_Silver_, _Iron_, _Copper_, _Quicksilver_, _Lead_, _Tin_, were known -from the earliest antiquity. In the beginning of the sixteenth -century, mine-directors, like George Agricola, had advanced so far -in practical metallurgy, that they had discovered the means of -extracting three additional metals, _Zinc_, _Bismuth_, _Antimony_. -After this, there was no new metal discovered for a century, and -then such discoveries were made by the theoretical chemists, a race -of men who had not existed before Beccher and Stahl. Thus _Arsenic_ -and _Cobalt_ were made known by Brandt, in the middle of the -eighteenth century, and we have a long list of similar discoveries -belonging to the same period; _Nickel_, _Manganese_, and _Tungsten_, -which were detected by Cronstedt, Gahn, and Scheele, and Delhuyart, -respectively; metals of a very different kind, _Tellurium_ and -_Molybdenum_, which were brought to light by Müller, Scheele, -Bergman, and Hielm; _Platinum_, which was known as early as 1741, -but with the ore of which, in 1802 and 1803, the English chemists, -Wollaston and Tennant, found that no less than four other new metals -(_Palladium_, _Rhodium_, _Iridium_ and _Osmium_) were associated. -Finally, (omitting some other new metals,) we have another period of -discovery, opened in 1807, by Davy's discovery of _Potassium_, and -including the resolution of all, or almost all, the alkalies and -earths into metallic bases. - -[2nd Ed.] [The next few years made some, at least some conjectural, -additions to the list of simple substances, detected by a more -minute scrutiny of known substances. _Thorium_ was discovered by -Berzelius in 1828; and _Vanadium_ by Professor Sefström in 1830. A -{308} metal named _Cerium_, was discovered in 1803, by Hisinger and -Berzelius, in a rare Swedish mineral known by the name of Cerit. -Mosander more recently has found combined with Cerium, other new -metals which he has called _Lanthanium_, _Didymium_, _Erbium_, and -_Terbium_: M. Klaus has found a new metal, _Ruthenium_, in the ore -of Platinum; and Rose has discovered in Tantalite two other new -metals, which he has announced under the names of _Pelopium_ and -_Niobium_. Svanberg is said to have discovered a new earth in -Eudialyt, which is supposed to have, like the rest, a new radical. -If these last discoveries be confirmed, the number of simple -substances will be raised to _sixty-two_.] - -2. Attempts have been made to indicate the classification of -chemical substances by some peculiarity in the Name; and the Metals, -for example, have been designated generally by names in _um_, like -the Latin names of the ancient metals, _aurum_, _ferrum_. This -artifice is a convenient nomenclature for the purpose of marking a -recognized difference; and it would be worth the while of chemists -to agree to make it universal, by writing molybden_um_ and -platin_um_; which is sometimes done, but not always. - -3. I am not now to attempt to determine how far this -class,--Metals,--extends; but where the analogies of the class cease -to hold there the nomenclature must also change. Thus, some -chemists, as Dr. Thomson, have conceived that the base of Silica is -more analogous to Carbon and Boron, which form acids with oxygen, -than it is to the metals: and he has accordingly associated this -base with these substances, and has given it the same termination, -_Silicon_. But on the validity of this analogy chemists appear not -to be generally agreed. - -4. There is another class of bodies which have attracted much notice -among modern chemists, and which have also been assimilated to each -other in the form of their names; the English writers calling them -_Chlorine_, _Fluorine_, _Iodine_, _Bromine_, while the French use -the terms _Chlore_, _Phtore_, _Iode_, _Brome_. We have already -noticed the establishment of the doctrine--that muriatic acid is -formed of a base, chlorine, and of hydrogen,--as a great reform in -the oxygen theory; with regard to which rival claims were advanced -by Davy, and by MM. Gay-Lussac and Thenard in 1800. Iodine, a -remarkable body which, from a dark powder, is converted into a -violet-colored gas by the application of heat, was also, in 1813, -the subject of a similar rivalry between the same English and French -chemists. Bromine {309} was only discovered as late as 1826; and -Fluorine, or _Phtore_, as, from its destructive nature, it has been -proposed to term it, has not been obtained as a separate substance, -and is inferred to exist by analogy only. The analogies of these -bodies (Chlore, Phtore, &c.) are very peculiar; for instance, by -combination with metals they form salts; by combination with -hydrogen they form very strong acids; and all, at the common -temperature of the atmosphere, operate on other bodies in the most -energetic manner. Berzelius[102\14] proposes to call them -_halogenous_ bodies, or _halogenes_. - -[Note 102\14: _Chem._ i. 262.] - -5. The number of Elementary Substances which are at present -presented in our treatises of chemistry[103\14] is _fifty-three_, [or -rather, as we have said above, _sixty-two_.] It is naturally often -asked what evidence we have, that all these are _elementary_, and -what evidence that they are _all_ the elementary bodies;--how we -know that new elements may not hereafter be discovered, or these -supposed simple bodies resolved into simpler still? To these -questions we can only answer, by referring to the history of -chemistry;--by pointing out what chemists have understood by -analysis, according to the preceding narrative. They have -considered, as the analysis of a substance, that elementary -constitution of it which gives the only intelligible explanation of -the results of chemical manipulation, and which is proved to be -complete as to quantity, by the balance, since the whole can only be -equal to all its parts. It is impossible to maintain that new -substances may not hereafter be discovered; for they may lurk, even -in familiar substances, in doses so minute that they have not yet -been missed amid the inevitable slight inaccuracies of all analysis; -in the way in which iodine and bromine remained so long undetected -in sea-water; and new minerals, or old ones not yet sufficiently -examined, can hardly fail to add something to our list. As to the -possibility of a further analysis of our supposed simple bodies, we -may venture to say that, in regard to such supposed simple bodies as -compose a numerous and well-characterized class, no such step can be -made, except through some great change in chemical theory, which -gives us a new view of all the general relations which chemistry has -yet discovered. The proper evidence of the reality of any supposed -new analysis is, that it is more consistent with the known analogies -of chemistry, to suppose the process analytical than synthetical. -Thus, as has already been said, chemists admit the existence of -fluorine, from the analogy of chlorine; and Davy, when it was found -{310} that ammonia formed an amalgam with mercury, was tempted to -assign to it a metallic basis. But then he again hesitates,[104\14] -and doubts whether the analogies of our knowledge are not better -preserved by supposing that ammonia, as a compound of hydrogen and -another principle, is "a type of the composition of the metals." - -[Note 103\14: Turner, p. 971.] - -[Note 104\14: _Elem. Chem. Phil._ 1812, p. 481.] - -Our history, which is the history of what we know, has little to do -with such conjectures. There are, however, some not unimportant -principles which bear upon them, and which, as they are usually -employed, belong to the science which next comes under our review, -Mineralogy. - - - -{{311}} -BOOK XV. - -_THE ANALYTICO-CLASSIFICATORY SCIENCE._ - -HISTORY OF MINERALOGY. - - - Κρύσταλλον φαέθοντα διαυγέα λάζεο χερσὶ, - Λᾶαν ἀπόῤῥοιαν περιφεγγέος ἀμβρότου αἴγλης, - Αἰθέρι δ' ἀθανάτων μέγα τέρπεται ἄφθιτον ἦτορ. - Τόν κ' εἴπερ μετὰ χειρὰς ἔχων, περὶ νηὸν ἵκηαι, - Οὔτις τοι μακάρων ἀρνήσεται εὐχωλῆσι. - ORPHEUS. _Lithica._ - - Now, if the bold but pious thought be thine, - To reach our spacious temple's inner shrine, - Take in thy reverent hands the crystal stone, - Where heavenly light in earthy shroud is shown:-- - Where, moulded into measured form, with rays - Complex yet clear, the eternal Ether plays; - This if thou firmly hold and rightly use, - Not long the gods thy ardent wish refuse. - - - -{{313}} -INTRODUCTION. - - -_Sect._ 1.--_Of the Classificatory Sciences._ - -THE horizon of the sciences spreads wider and wider before us, as we -advance in our task of taking a survey of the vast domain. We have -seen that the existence of Chemistry as a science which declares the -ingredients and essential constitution of all kinds of bodies, -implies the existence of another corresponding science, which shall -divide bodies into kinds, and point out steadily and precisely what -bodies they are which we have analysed. But a science thus dividing -and defining bodies, is but one member of an order of sciences, -different from those which we have hitherto described; namely, of -the _classificatory sciences_. Such sciences there must be, not only -having reference to the bodies with which chemistry deals, but also -to all things respecting which we aspire to obtain any general -knowledge, as, for instance, plants and animals. Indeed it will be -found, that it is with regard to these latter objects, to organized -beings, that the process of scientific classification has been most -successfully exercised; while with regard to inorganic substances, -the formation of a satisfactory system of arrangement has been found -extremely difficult; nor has the necessity of such a system been -recognised by chemists so distinctly and constantly as it ought to -be. The best exemplification of these branches of knowledge, of -which we now have to speak, will, therefore, be found in the organic -world, in Botany and Zoology; but we will, in the first place, take -a brief view of the science which classifies inorganic bodies, and -of which Mineralogy is hitherto the very imperfect representative. - -The principles and rules of the Classificatory Sciences, as well as -of those of the other orders of sciences, must be fully explained -when we come to treat of the Philosophy of the Sciences; and cannot -be introduced here, where we have to do with history only. But I may -observe very briefly, that with the process of _classing_, is joined -the process of _naming_;--that names imply classification;--and that -even the rudest and earliest application of language presupposes a -distribution of objects according to their kinds;--but that such a -spontaneous {314} and unsystematic distribution cannot, in the cases -we now have to consider, answer the purposes of exact and general -knowledge. Our classification of objects must be made consistent and -systematic, in order to be scientific; we must discover marks and -characters, properties and conditions, which are constant in their -occurrence and relations; we must form our classes, we must impose -our names, according to such marks. We can thus, and thus alone, -arrive at that precise, certain, and systematic knowledge, which we -seek; that is, at science. The object, then, of the classificatory -sciences is to obtain FIXED CHARACTERS of the kinds of things; and -the criterion of the fitness of names is, that THEY MAKE GENERAL -PROPOSITIONS POSSIBLE. - -I proceed to review the progress of certain sciences on these -principles, and first, though briefly, the science of Mineralogy. - - -_Sect._ 2.--_Mineralogy as the Analytico-classificatory Science._ - -MINERALOGY, as it has hitherto been cultivated, is, as I have -already said, an imperfect representative of the department of human -knowledge to which it belongs. The attempts at the science have -generally been made by collecting various kinds of information -respecting mineral bodies; but the science which we require is a -complete and consistent classified system of all inorganic bodies. -For chemistry proceeds upon the principle that the constitution of a -body invariably determines its properties; and, consequently, its -kind: but we cannot apply this principle, except we can speak with -precision of the _kind_ of a body, as well as of its composition. We -cannot attach any sense to the assertion, that "soda or baryta has a -metal for its base," except we know what _a metal_ is, or at least -what properties it implies. It may not be, indeed it is not, -possible, to define the kinds of bodies by words only; but the -classification must proceed by some constant and generally -applicable process; and the knowledge which has reference to the -classification will be precise as far as this process is precise, -and vague as far as this is vague. - -There must be, then, as a necessary supplement to Chemistry, a -Science of those properties of bodies by which we divide them into -_kinds_. Mineralogy is the branch of knowledge which has discharged -the office of such a science, so far as it has been discharged; and, -indeed, Mineralogy has been gradually approaching to a clear -consciousness of her real place, and of her whole task; I shall give -the history of some of the advances which have thus been made. They -are, principally, {315} the establishment and use of External -Characters, especially of _Crystalline Form_, as a fixed character -of definite substances; and the attempts to bring into view the -connexion of Chemical Constitution and External Properties, made in -the shape of mineralogical _Systems_; both those in which _chemical -methods of arrangement_ are adopted, and those which profess to -classify by the _natural-history method_. - - - -{{316}} -CRYSTALLOGRAPHY. - - - - -CHAPTER I. - -PRELUDE TO THE EPOCH OF DE LISLE AND HAÜY. - - -OF all the physical properties of bodies, there is none so fixed, -and in every way so remarkable, as this;--that the same chemical -compound always assumes, with the utmost precision, the same -geometrical form. This identity, however, is not immediately -obvious; it is often obscured by various mixtures and imperfections -in the substance; and even when it is complete, it is not -immediately recognized by a common eye, since it consists, not in -the equality of the sides or faces of the figures, but in the -equality of their angles. Hence it is not surprising that the -constancy of form was not detected by the early observers. Pliny -says,[1\15] "Why crystal is generated in a hexagonal form, it is -difficult to assign a reason; and the more so, since, while its -faces are smoother than any art can make them, the pyramidal points -are _not all of the same kind_." The quartz crystals of the Alps, to -which he refers, are, in some specimens, very regular, while in -others, one side of the pyramid becomes much the largest; yet the -angles remain constantly the same. But when the whole shape varied -so much, the angles also seemed to vary. Thus Conrad Gessner, a very -learned naturalist, who, in 1564, published at Zurich his work, _De -rerum Fossilium, Lapidum et Gemmarum maxime, Figuris_, says,[2\15] -"One crystal differs from another in its angles, and consequently in -its figure." And Cæsalpinus, who, as we shall find, did so much in -establishing fixed characters in botany, was led by some of his -general views to disbelieve the fixity of the form of crystals. In -his work _De Metallicis_, published at Nuremberg in 1602, he -says,[3\15] "To ascribe to inanimate bodies a definite form, does -not appear consentaneous to reason; for it is the office of -organization to produce a definite form;" {317} an opinion very -natural in one who had been immersed in the study of the general -analogies of the forms of plants. But though this is excusable in -Cæsalpinus, the rejection of this definiteness of form a hundred -years later, when its existence had been proved, and its laws -developed by numerous observers, cannot be ascribed to anything but -strong prejudice; yet this was the course taken by no less a person -than Buffon. "The form of crystallization," says he,[4\15] "is _not -a constant character_, but is more equivocal and more variable than -any other of the characters by which minerals are to be -distinguished." And accordingly, he makes no use of this most -important feature in his history of minerals. This strange -perverseness may perhaps be ascribed to the dislike which Buffon is -said to have entertained for Linnæus, who had made crystalline form -a leading character of minerals. - -[Note 1\15: _Nat. Hist._ xxvii. 2.] - -[Note 2\15: p. 25.] - -[Note 3\15: p. 97.] - -[Note 4\15: _Hist. des Min._ p. 343.] - -It is not necessary to mark all the minute steps by which -mineralogists were gradually led to see clearly the nature and laws -of the fixity of crystalline forms. These forms were at first -noticed in that substance which is peculiarly called rock-crystal or -quartz; and afterwards in various stones and gems, in salts obtained -from various solutions, and in snow. But those who observed the -remarkable regular figures which these substances assume, were at -first impelled onwards in their speculations by the natural tendency -of the human mind to generalize and guess, rather than to examine -and measure. They attempted to snatch at once the general laws of -geometrical regularity of these occurrences, or to connect them with -some doctrine concerning formative causes. Thus Kepler,[5\15] in his -_Harmonics of the World_, asserts a "_formatrix facultas_, which has -its seat in the entrails of the earth, and, after the manner of a -pregnant woman, expresses the five regular geometrical solids in the -forms of gems." But Philosophers, in the course of time, came to -build more upon observation, and less upon abstract reasonings. -Nicolas Steno, a Dane, published, in 1669, a dissertation _De Solido -intra Solidum Naturaliter contento_, in which he says,[6\15] that -though the sides of the hexagonal crystal may vary, _the angles are -not changed_. And Dominic Gulielmini, in a _Dissertation on Salts_, -published in 1707, says,[7\15] in a true inductive spirit, "Nature -does not employ all figures, but only certain ones of those which -are possible; and of these, the determination is not to be fetched -from the brain, or proved _à priori_, but obtained by experiments -and observations." And {318} he speaks[8\15] with entire decision on -this subject: "Nevertheless since there is here a principle of -crystallization, the inclination of the planes and of the angles is -always constant." He even anticipates, very nearly, the views of -later crystallographers as to the mode in which crystals are formed -from elementary molecules. From this time, many persons labored and -speculated on this subject; as Cappeller, whose _Prodromus -Crystallographiæ_ appeared at Lucern in 1723; Bourguet, who -published _Lettres Philosophiques sur la Formation de Sels et de -Cristaux_, at Amsterdam, in 1792; and Henckel, the "Physicus" of the -Elector of Saxony, whose _Pyritologia_ came forth in 1725. In this -last work we have an example of the description of the various forms -of special classes of minerals, (iron pyrites, copper pyrites, and -arsenic pyrites;) and an example of the enthusiasm which this -apparently dry and laborious study can excite: "Neither tongue nor -stone," he exclaims,[9\15] "can express the satisfaction which I -received on setting eyes upon this sinter covered with galena; and -thus it constantly happens, that one must have more pleasure in what -seems worthless rubbish, than in the purest and most precious ores, -if we know aught of minerals." - -[Note 5\15: Linz. 1619, p. 161.] - -[Note 6\15: p. 69.] - -[Note 7\15: p. 19.] - -[Note 8\15: p. 83.] - -[Note 9\15: p. 343.] - -Still, however, Henckel[10\15] disclaims the intention of arranging -minerals according to their mathematical forms; and this, which may -be considered as the first decided step in the formation of -crystallographic mineralogy, appears to have been first attempted by -Linnæus. In this attempt, however, he was by no means happy; nor -does he himself appear to have been satisfied. He begins his preface -by saying, "Lithology is not what I plume myself upon." (_Lithologia -mihi cristas non eriget_.) Though his sagacity, as a natural -historian, led him to see that crystalline form was one of the most -definite, and therefore most important, characters of minerals, he -failed in profiting by this thought, because, in applying it, he did -not employ the light of geometry, but was regulated by what appeared -to him resemblances, arbitrarily selected, and often -delusive.[11\15] Thus he derived the form of pyrites from that of -vitriol;[12\15] and brought together alum and diamond on account of -their common octohedral form. But he had the great merit of -animating to this study one to whom, more perhaps than to any other -person, it owes its subsequent progress; I mean Romé de Lisle. -"Instructed," this writer says, in his preface to his _Essais de -Crystallographie_, "by the works of the celebrated Von Linnée, how -{319} greatly the study of the angular form of crystals might become -interesting, and fitted to extend the sphere of our mineralogical -knowledge, I have followed them in all their metamorphoses with the -most scrupulous attention." The views of Linnæus, as to the -importance of this character, had indeed been adopted by several -others; as John Hill, the King's gardener at Kew, who, in 1777, -published his _Spathogenesia_; and Grignon, who, in 1775, says, -"These crystallizations may give the means of finding a new theory -of the generation of crystalline gems." - -[Note 10\15: p. 167.] - -[Note 11\15: Marx. _Gesch._ p. 97.] - -[Note 12\15: _Syst. Nat._ vi. p. 220.] - -The circumstance which threw so much difficulty in the way of those -who tried to follow out his thought was, that in consequence of the -apparent irregularity of crystals, arising from the extension or -contraction of particular sides of the figure, each kind of -substance may really appear under many different forms, connected -with each other by certain geometrical relations. These may be -conceived by considering a certain fundamental form to be cut into -new forms in particular ways. Thus if we take a cube, and cut off -all the eight corners, till the original faces disappear, we make it -an octohedron; and if we stop short of this, we have a figure of -fourteen faces, which has been called a _cubo-octohedron_. The first -person who appears distinctly to have conceived this _truncation_ of -angles and edges, and to have introduced the word, is -Démeste;[13\15] although Wallerius[14\15] had already said, in -speaking of the various crystalline forms of calcspar, "I conceive -it would be better not to attend to all differences, lest we be -overwhelmed by the number." And Werner, in his celebrated work _On -the External Characters of Minerals_,[15\15] had formally spoken of -_truncation_, _acuation_, and _acumination_, or replacement by a -plane, an edge, a point respectively, (_abstumpfung_, _zuschärfung_, -_zuspitzung_,) as ways in which the forms of crystals are modified -and often disguised. He applied this process in particular to show -the connexion of the various forms which are related to the cube. -But still the extension of the process to the whole range of minerals -and other crystalline bodies, was due to Romé de Lisle. {320} - -[Note 13\15: _Lettres_, 1779, i. 48.] - -[Note 14\15: _Systema Mineralogicum_, 1772-5, i. 143.] - -[Note 15\15: Leipzig, 1774.] - - - - -CHAPTER II. - -EPOCH OF ROMÉ DE LISLE AND HAÜY.--ESTABLISHMENT OF THE FIXITY OF -CRYSTALLINE ANGLES, AND THE SIMPLICITY OF THE LAWS OF DERIVATION. - - -WE have already seen that, before 1780, several mineralogists had -recognized the constancy of the angles of crystals, and had seen (as -Démeste and Werner,) that the forms were subject to modifications of -a definite kind. But neither of these two thoughts was so -apprehended and so developed, as to supersede the occasion for a -discoverer who should put forward these principles as what they -really were, the materials of a new and complete science. The merit -of this step belongs jointly to Romé de Lisle and to Haüy. The -former of these two men had already, in 1772, published an _Essai de -Crystallographie_, in which he had described a number of crystals. -But in this work his views are still rude and vague; he does not -establish any connected sequence of transitions in each kind of -substance, and lays little or no stress on the angles. But in 1783, -his ideas[16\15] had reached a maturity which, by comparison, -excites our admiration. In this he asserts, in the most distinct -manner, the _invariability_ of the angles of crystals of each kind, -under all the changes of relative dimension which the faces may -undergo;[17\15] and he points out that this invariability applies -only to the _primitive forms_, from each of which many secondary -forms are derived by various changes.[18\15] Thus we cannot deny him -the merit of having taken steady hold on both the handles of this -discovery, though something still remained for another to do. Romé -pursues his general ideas into detail with great labor and skill. He -gives drawings of more than five hundred regular forms (in his first -work he had inserted only one hundred and ten; Linnæus only knew -forty); and assigns them to their proper substances; for instance, -thirty to calcspar, and sixteen to felspar. He also invented and -used a goniometer. We cannot doubt that he would have been {321} -looked upon as a great discoverer, if his fame had not been dimmed -by the more brilliant success of his contemporary Haüy. - -[Note 16\15: _Cristallographie, ou Description de Formes propres à -tous les Corps du Règne Minéral._ 3 vols. and 1 vol. of plates.] - -[Note 17\15: p. 68.] - -[Note 18\15: p. 73.] - -Réné-Just Haüy is rightly looked upon as the founder of the modern -school of crystallography; for all those who have, since him, -pursued the study with success, have taken his views for their -basis. Besides publishing a system of crystallography and of -mineralogy, far more complete than any which had yet appeared, the -peculiar steps in the advance which belong to him are, the discovery -of the importance of _cleavage_, and the consequent expression of -the laws of derivation of secondary from primary forms, by means of -the _decrements_ of the successive layers of _integrant molecules_. - -The latter of these discoveries had already been, in some measure, -anticipated by Bergman, who had, in 1773, conceived a hexagonal -prism to be built up by the juxtaposition of solid rhombs on the -planes of a rhombic nucleus.[19\15] It is not clear[20\15] whether -Haüy was acquainted with Bergman's Memoir, at the time when the -cleavage of a hexagonal prism of calcspar, accidentally obtained, -led him to the same conception of its structure. But however this -might be, he had the indisputable credit of following out this -conception with all the vigor of originality, and with the most -laborious and persevering earnestness; indeed he made it the -business of his life. The hypothesis of a solid, built up of small -solids, had this peculiar advantage in reference to crystallography; -it rendered a reason of this curious fact;--that a certain series of -forms occur in crystals of the same kind, while other forms, -apparently intermediate between those which actually occur, are -rigorously excluded. The doctrine of decrements explained this; for -by placing a number of regularly-decreasing rows of equal solids, -as, for instance, of bricks, upon one another, we might form a -regular equal-sided triangle, as the gable of a house; and if the -breadth of the gable were one hundred bricks, the height of the -triangle might be one hundred, or fifty, or twenty-five; but it -would be found that if the height were an intermediate number, as -fifty-seven, or forty-three, the edge of the wall would become -irregular; and such irregularity is assumed to be inadmissible in -the regular structure of crystals. Thus this mode of conceiving -crystals allows of certain definite secondary forms, and no others. - -[Note 19\15: _De Formis Crystallorum._ Nov. Act. Reg. Soc. Sc. Ups. -1773.] - -[Note 20\15: _Traité de Minér._ 1822, i. 15.] - -The mathematical deduction of the dimensions and proportions {322} -of these secondary forms;--the invention of a notation to express -them;--the examination of the whole mineral kingdom in accordance -with these views;--the production of a work[21\15] in which they are -explained with singular clearness and vivacity;--are services by -which Haüy richly earned the admiration which has been bestowed upon -him. The wonderful copiousness and variety of the forms and laws to -which he was led, thoroughly exercised and nourished the spirit of -deduction and calculation which his discoveries excited in him. The -reader may form some conception of the extent of his labors, by -being told--that the mere geometrical propositions which he found it -necessary to premise to his special descriptions, occupy a volume -and a half of his work;--that his diagrams are nearly a thousand in -number;--that in one single substance (calcspar) he has described -forty-seven varieties of form;--and that he has described one kind -of crystal (called by him _fer sulfuré parallélique_) which has one -hundred and thirty-four faces. - -[Note 21\15: _Traité de Minéralogie_, 1801, 5 vols.] - -In the course of a long life, he examined, with considerable care, -all the forms he could procure of all kinds of mineral; and the -interpretation which he gave of the laws of those forms was, in many -cases, fixed, by means of a name applied to the mineral in which the -form occurred; thus, he introduced such names as _équiaxe_, -_métastatique_, _unibinaire_, _perihexahèdre_, _bisalterne_, and -others. It is not now desirable to apply separate names to the -different forms of the same mineral species, but these terms -answered the purpose, at the time, of making the subjects of study -more definite. A symbolical notation is the more convenient mode of -designating such forms, and such a notation Haüy invented; but the -symbols devised by him had many inconveniences, and have since been -superseded by the systems of other crystallographers. - -Another of Haüy's leading merits was, as we have already intimated, -to have shown, more clearly than his predecessors had done, that the -crystalline angles of substances are a criterion of the substances; -and that this is peculiarly true of the _angles of cleavage_;--that -is, the angles of those edges which are obtained by cleaving a -crystal in two different directions;--a mode of division which the -structure of many kinds of crystals allowed him to execute in the -most complete manner. As an instance of the employment of this -criterion, I may mention his separation of the sulphates of baryta -and strontia, which had {323} previously been confounded. Among -crystals which in the collections were ranked together as "heavy -spar," and which were so perfect as to admit of accurate -measurement, he found that those which were brought from Sicily, and -those of Derbyshire, differed in their cleavage angle by three -degrees and a half. "I could not suppose," he says,[22\15] "that -this difference was the effect of any law of decrement; for it would -have been necessary to suppose so rapid and complex a law, that such -an hypothesis might have been justly regarded as an abuse of the -theory." He was, therefore, in great perplexity. But a little while -previous to this, Klaproth had discovered that there is an earth -which, though in many respects it resembles baryta, is different -from it in other respects; and this earth, from the place where it -was found (in Scotland), had been named _Strontia_. The French -chemists had ascertained that the two earths had, in some cases, -been mixed or confounded; and Vauquelin, on examining the Sicilian -crystals, found that their base was strontia, and not, as in the -Derbyshire ones, baryta. The riddle was now read; all the crystals -with the larger angle belong to the one, all those with the smaller, -to the other, of these two sulphates; and crystallometry was clearly -recognized as an authorized test of the difference of substances -which nearly resemble each other. - -[Note 22\15: _Traité_, ii. 320.] - -Enough has been said, probably, to enable the reader to judge how -much each of the two persons, now under review, contributed to -crystallography. It would be unwise to compare such contributions to -science with the great discoveries of astronomy and chemistry; and -we have seen how nearly the predecessors of Romé and Haüy had -reached the point of knowledge on which these two crystallographers -took their stand. But yet it is impossible not to allow, that in -these discoveries, which thus gave form and substance to the science -of crystallography, we have a manifestation of no common sagacity -and skill. Here, as in other discoveries, were required ideas and -facts;--clearness of geometrical conception which could deal with -most complex relations of form; a minute and extensive acquaintance -with actual crystals; and the talent and habit of referring these -facts to the general ideas. Haüy, in particular, was happily endowed -for his task. Without being a great mathematician, he was -sufficiently a geometer to solve all the problems which his -undertaking demanded; and though the mathematical reasoning might -have been made more compendious {324} by one who was more at home in -mathematical generalization, probably this could hardly have been -done without making the subject less accessible and less attractive -to persons moderately disciplined in mathematics. In all his -reasonings upon particular cases, Haüy is acute and clear; while his -general views appear to be suggested rather by a lively fancy than -by a sage inductive spirit: and though he thus misses the character -of a great philosopher, the vivacity of style, and felicity and -happiness of illustration, which grace his book, and which agree -well with the character of an Abbé of the old French monarchy, had a -great and useful influence on the progress of the subject. - -Unfortunately Romé de Lisle and Haüy were not only rivals, but in -some measure enemies. The former might naturally feel some vexation -at finding himself, in his later years (he died in 1790), thrown -into shade by his more brilliant successor. In reference to Haüy's -use of cleavage, he speaks[23\15] of "innovators in crystallography, -who may properly be called _crystalloclasts_." Yet he adopted, in -great measure, the same views of the formation of crystals by -laminæ,[24\15] which Haüy illustrated by the destructive process at -which he thus sneers. His sensitiveness was kept alive by the -conduct of the Academy of Sciences, which took no notice of him and -his labors;[25\15] probably because it was led by Buffon, who -disliked Linnæus, and might dislike Romé as his follower; and who, -as we have seen, despised crystallography. Haüy revenged himself by -rarely mentioning Romé in his works, though it was manifest that his -obligations to him were immense; and by recording his errors while -he corrected them. More fortunate than his rival, Haüy was, from the -first, received with favor and applause. His lectures at Paris were -eagerly listened to by persons from all quarters of the world. His -views were, in this manner, speedily diffused; and the subject was -soon pursued, in various ways, by mathematicians and mineralogists -in every country of Europe. - -[Note 23\15: Pref. p. xxvii.] - -[Note 24\15: T. ii. p. 21.] - -[Note 25\15: Marx. _Gesch. d. Cryst._ 130.] - - - - -CHAPTER III. - -RECEPTION AND CORRECTIONS OF THE HAUÏAN CRYSTALLOGRAPHY. - - -I HAVE not hitherto noticed the imperfections of the -crystallographic views and methods of Haüy, because my business in -the last section {325} was to mark the permanent additions he made -to the science. His system did, however, require completion and -rectification in various points; and in speaking of the -crystallographers of the subsequent time, who may all be considered -as the cultivators of the Hauïan doctrines, we must also consider -what they did in correcting them. - -The three main points in which this improvement was needed were;--a -better determination of the crystalline forms of the special -substances;--a more general and less arbitrary method of considering -crystalline forms according to their symmetry; and a detection of -more general conditions by which the crystalline angle is regulated. -The first of these processes may be considered as the natural sequel -of the Hauïan epoch: the other two must be treated as separate steps -of discovery. - -When it appeared that the angle of natural or of cleavage faces -could be used to determine the differences of minerals, it became -important to measure this angle with accuracy. Haüy's measurements -were found very inaccurate by many succeeding crystallographers: -Mohs says[26\15] that they are so generally inaccurate, that no -confidence can be placed in them. This was said, of course, -according to the more rigorous notions of accuracy to which the -establishment of Haüy's system led. Among the persons who -principally labored in ascertaining, with precision, the crystalline -angles of minerals, were several Englishmen, especially Wollaston, -Phillips, and Brooke. Wollaston, by the invention of his Reflecting -Goniometer, placed an entirely new degree of accuracy within the -reach of the crystallographer; the angle of two faces being, in this -instrument, measured by means of the reflected images of bright -objects seen in them, so that the measure is the more accurate the -more minute the faces are. In the use of this instrument, no one was -more laborious and successful than William Phillips, whose power of -apprehending the most complex forms with steadiness and clearness, -led Wollaston to say that he had "a geometrical sense." Phillips -published a Treatise on Mineralogy, containing a great collection of -such determinations; and Mr. Brooke, a crystallographer of the same -exact and careful school, has also published several works of the -same kind. The precise measurement of crystalline angles must be the -familiar employment of all who study crystallography; and, -therefore, any further enumeration of those {326} who have added in -this way to the stock of knowledge, would be superfluous. - -[Note 26\15: Marx. p. 153.] - -Nor need I dwell long on those who added to the knowledge which Haüy -left, of derived forms. The most remarkable work of this kind was -that of Count Bournon, who published a work on a single mineral -(calcspar) in three quarto volumes.[27\15] He has here given -representations of seven hundred forms of crystals, of which, -however, only fifty-six are essentially different. From this example -the reader may judge what a length of time, and what a number of -observers and calculators, were requisite to exhaust the subject. - -[Note 27\15: _Traité complet de la Chaux Carbonatée et d'Aragonite_, -par M. le Comte de Bournon. London, 1808.] - -If the calculations, thus occasioned, had been conducted upon the -basis of Haüy's system, without any further generalization, they -would have belonged to that process, the natural sequel of inductive -discoveries, which we call _deduction_; and would have needed only a -very brief notice here. But some additional steps were made in the -upward road to scientific truth, and of these we must now give an -account. - - - - -CHAPTER IV. - -ESTABLISHMENT OF THE DISTINCTION OF SYSTEMS OF -CRYSTALLIZATION.--WEISS AND MOHS. - - -IN Haüy's views, as generally happens in new systems, however true, -there was involved something that was arbitrary, something that was -false or doubtful, something that was unnecessarily limited. The -principal points of this kind were;--his having made the laws of -crystalline derivation depend so much upon cleavage;--his having -assumed an atomic constitution of bodies as an essential part of his -system; and his having taken a set of primary forms, which, being -selected by no general view, were partly superfluous, and partly -defective. - -How far evidence, such as has been referred to by various -philosophers, has proved, or can prove, that bodies are constituted -of indivisible atoms, will be more fully examined in the work which -treats of the Philosophy of this subject. There can be little doubt -that the {327} portion of Haüy's doctrine which most riveted popular -attention and applause, was his dissection of crystals, in a manner -which was supposed to lead actually to their ultimate material -elements. Yet it is clear, that since the solids given by cleavage -are, in many cases, such as cannot make up a solid space, the -primary conception of a necessary geometrical identity between the -results of division and the elements of composition, which is the -sole foundation of the supposition that crystallography points out -the actual elements, disappears on being scrutinized: and when Haüy, -pressed by this difficulty, as in the case of fluor-spar, put his -integrant octohedral molecules together, touching by the edges only, -his method became an empty geometrical diagram, with no physical -meaning. - -The real fact, divested of the hypothesis which was contained in the -fiction of decrements, was, that when the relation of the derivative -to the primary faces is expressed by means of numerical indices, -these numbers are integers, and generally very small ones; and this -was the form which the law gradually assumed, as the method of -derivation was made more general and simple by Weiss and others. - -"When, in 1809, I published my Dissertation," says Weiss,[28\15] "I -shared the common opinion as to the necessity of the assumption and -the reality of the existence of a primitive form, at least in a -sense not very different from the usual sense of the expression. -While I sought," he adds, referring to certain doctrines of general -philosophy which he and others entertained, "a _dynamical_ ground -for this, instead of the untenable atomistic view, I found that, out -of my primitive forms, there was gradually unfolded to my hands, -that which really governs them, and is not affected by their casual -fluctuations, the fundamental relations of those Dimensions -according to which a multiplicity of internal oppositions, -necessarily and mutually interdependent, are developed in the mass, -each having its own polarity; so that the crystalline character is -co-extensive with these polarities." - -[Note 28\15: _Mem. Acad. Berl._ 1816, p. 307.] - -The "Dimensions" of which Weiss here speaks, are the _Axes of -Symmetry_ of the crystal; that is, those lines in reference to -which, every face is accompanied by other faces, having like -positions and properties. Thus a rhomb, or more properly a -_rhombohedron_,[29\15] of {328} calcspar may be placed with one of -its obtuse corners uppermost, so that all the three faces which meet -there are equally inclined to the vertical line. In this position, -every derivative face, which is obtained by any modification of the -faces or edges of the rhombohedron, implies either three or six such -derivative faces; for no one of the three upper faces of the -rhombohedron has any character or property different from the other -two; and, therefore, there is no reason for the existence of a -derivative from one of these primitive faces, which does not equally -hold for the other primitive faces. Hence the derivative forms will, -in all cases, contain none but faces connected by this kind of -correspondence. The axis thus made vertical will be an Axis of -Symmetry, and the crystal will consist of three divisions, ranged -round this axis, and exactly resembling each other. According to -Weiss's nomenclature, such a crystal is "three-and-three-membered." - -[Note 29\15: I use this name for the solid figure, since _rhomb_ has -always been used for a plane figure.] - -But this is only one of the kinds of symmetry which crystalline -forms may exhibit. They may have _three axes_ of complete and -_equal_ symmetry at right angles to each other, as the cube and the -regular octohedron;--or, _two axes_ of equal symmetry, perpendicular -to each other and to a _third axis_, which is not affected with the -same symmetry with which they are; such a figure is a square -pyramid;--or they may have _three_ rectangular _axes_, all of -_unequal_ symmetry, the modifications referring to each axis -separately from the other two. - -These are essential and necessary distinctions of crystalline form; -and the introduction of a classification of forms founded on such -relations, or, as they were called, _Systems of Crystallization_, -was a great improvement upon the divisions of the earlier -crystallographers, for those divisions were separated according to -certain arbitrarily-assumed primary forms. Thus Romé de Lisle's -fundamental forms were, the tetrahedron, the cube, the octohedron, -the rhombic prism, the rhombic octohedron, the dodecahedron with -triangular faces: Haüy's primary forms are the cube, the -rhombohedron, the oblique rhombic prism, the right rhombic prism, -the rhombic dodecahedron, the regular octohedron, tetrahedron, and -six-sided prism, and the bipyramidal dodecahedron. This division, as -I have already said, errs both by excess and defect, for some of -these primary forms might be made derivatives from others; and no -solid reason could be assigned why they were not. Thus the cube may -be derived from the tetrahedron, by truncating the edges; and the -rhombic dodecahedron again from the cube, by truncating its edges; -while the square pyramid could not be legitimately identified with -the derivative of any of these forms; for if we were to {329} derive -it from the rhombic prism, why should the acute angles always suffer -decrements corresponding in a certain way to those of the obtuse -angles, as they must do in order to give rise to a square pyramid? - -The introduction of the method of reference to Systems of -Crystallization has been a subject of controversy, some ascribing -this valuable step to Weiss, and some to Mohs.[30\15] It appears, I -think, on the whole, that Weiss first published works in which the -method is employed; but that Mohs, by applying it to all the known -species of minerals, has had the merit of making it the basis of -real crystallography. Weiss, in 1809, published a Dissertation _On -the mode of investigating the principal geometrical character of -crystalline forms_, in which he says,[31\15] "No part, line, or -quantity, is so important as the axis; no consideration is more -essential or of a higher order than the relation of a crystalline -plane to the axis;" and again, "An axis is any line governing the -figure, about which all parts are similarly disposed, and with -reference to which they correspond mutually." This he soon followed -out by examination of some difficult cases, as Felspar and Epidote. -In the Memoirs of the Berlin Academy,[32\15] for 1814-15, he -published _An Exhibition of the natural Divisions of Systems of -Crystallization_. In this Memoir, his divisions are as follows:--The -_regular_ system, the _four-membered_, the _two-and-two-membered_, -the _three-and-three-membered_, and some others of inferior degrees -of symmetry. These divisions are by Mohs (_Outlines of Mineralogy_, -1822), termed the _tessular_, _pyramidal_, _prismatic_, and -_rhombohedral_ systems respectively. Hausmann, in his -_Investigations concerning the Forms of Inanimate Nature_,[33\15] -makes a nearly corresponding arrangement;--the _isometric_, -_monodimetric_, _trimetric_, and _monotrimetic_; and one or other of -these sets of terms have been adopted by most succeeding writers. - -[Note 30\15: _Edin. Phil. Trans._ 1823, vols. xv. and xvi.] - -[Note 31\15: pp. 16, 42.] - -[Note 32\15: Ibid.] - -[Note 33\15: Göttingen, 1821.] - -In order to make the distinctions more apparent, I have purposely -omitted to speak of the systems which arise when the _prismatic_ -system loses some part of its symmetry;--when it has only half or a -quarter its complete number of faces;--or, according to Mohs's -phraseology, when it is _hemihedral_ or _tetartohedral_. Such -systems are represented by the singly-oblique or doubly-oblique -prism; they are termed by Weiss _two-and-one-membered_, and -_one-and-one-membered_; by other writers, _Monoklinometric_, and -_Triklinometric_ Systems. There are also other {330} peculiarities -of Symmetry, such, for instance, as that of the _plagihedral_ faces -of quartz, and other minerals. - -The introduction of an arrangement of crystalline forms into -systems, according to their degree of symmetry, was a step which was -rather founded on a distinct and comprehensive perception of -mathematical relations, than on an acquaintance with experimental -facts, beyond what earlier mineralogists had possessed. This -arrangement was, however, remarkably confirmed by some of the -properties of minerals which attracted notice about the time now -spoken of, as we shall see in the next chapter. - - - - -CHAPTER V. - -RECEPTION AND CONFIRMATION OF THE DISTINCTION OF SYSTEMS OF -CRYSTALLIZATION. - - -DIFFUSION OF THE DISTINCTION OF SYSTEMS.--The distinction of systems -of crystallization was so far founded on obviously true views, that -it was speedily adopted by most mineralogists. I need not dwell on -the steps by which this took place. Mr. Haidinger's translation of -Mohs was a principal occasion of its introduction in England. As an -indication of dates, bearing on this subject, perhaps I may be -allowed to notice, that there appeared in the _Philosophical -Transactions for_ 1825, _A General Method of Calculating the -**Angles of Crystals_, which I had written, and in which I referred -only to Haüy's views; but that in 1826,[34\15] I published a Memoir -_On the Classification of Crystalline Combinations_, founded on the -methods of Weiss and Mohs, especially the latter; with which I had -in the mean time become acquainted, and which appeared to me to -contain their own evidence and recommendation. General methods, such -as was attempted in the Memoir just quoted, are part of that process -in the history of sciences, by which, when the principles are once -established, the mathematical operation of deducing their -consequences is made more and more general and symmetrical: which we -have seen already exemplified in the history of celestial mechanics -after the time of Newton. It does not enter into our plan, to dwell -upon the various steps in this way {331} made by Levy, Naumann, -Grassmann, Kupffer, Hessel, and by Professor Miller among ourselves. -I may notice that one great improvement was, the method introduced -by Monteiro and Levy, of determining the laws of derivation of -forces by means of the _parallelisms of edges_; which was afterwards -extended so that faces were considered as belonging to _zones_. Nor -need I attempt to enumerate (what indeed it would be difficult to -describe in words) the various methods of _notation_ by which it has -been proposed to represent the faces of crystals, and to facilitate -the calculations which have reference to them. - -[Note 34\15: _Camb. Trans._ vol. ii. p. 391.] - -[2nd Ed.] [My Memoir of 1825 depended on the views of Haüy in so far -as that I started from his "primitive forms;" but being a general -method of expressing all forms by co-ordinates, it was very little -governed by these views. The mode of representing crystalline forms -which I proposed seemed to contain its own evidence of being more -true to nature than Haüy's theory of decrements, inasmuch as my -method expressed the faces at much lower numbers. I determine a face -by means of the dimensions of the primary form _divided_ by certain -numbers; Haüy had expressed the face virtually by the same -dimensions _multiplied_ by numbers. In cases where my notation gives -such numbers as (3, 4, 1), (1, 3, 7), (5, 1, 19), his method -involves the higher numbers (4, 3, 12), (21, 7, 3), (19, 95, 5). My -method however has, I believe, little value as a method of -"_calculating_ the angles of crystals." - -M. Neumann, of Königsberg, introduced a very convenient and elegant -mode of representing the position of faces of crystals by -corresponding points on the surface of a circumscribing sphere. He -gave (in 1823) the laws of the derivation of crystalline faces, -expressed geometrically by the intersection of zones, (_Beiträge zur -Krystallonomie_.) The same method of indicating the position of -faces of crystals was afterwards, together with the notation, -re-invented by M. Grassmann, (_Zur Krystallonomie und Geometrischen -Combinationslehre_, 1829.) Aiding himself by the suggestions of -these writers, and partly adopting my method, Prof. Miller has -produced a work on Crystallography remarkable for mathematical -elegance and symmetry; and has given expressions really useful for -calculating the angles of crystalline faces, (_A Treatise on -Crystallography_. Cambridge, 1839.)] - -_Confirmation of the Distinction of Systems by the Optical -Properties of Minerals.--Brewster._--I must not omit to notice the -striking confirmation which the distinction of systems of -crystallization received from optical discoveries, especially those -of Sir D. Brewster. Of the {332} history of this very rich and -beautiful department of science, we have already given some account, -in speaking of Optics. The first facts which were noticed, those -relating to double refraction, belonged exclusively to crystals of -the rhombohedral system. The splendid phenomena of the rings and -lemniscates produced by dipolarizing crystals, were afterwards -discovered; and these were, in 1817, classified by Sir David -Brewster, according to the crystalline forms to which they belong. -This classification, on comparison with the distinction of Systems -of Crystallization, resolved itself into a necessary relation of -mathematical symmetry: all crystals of the pyramidal and -rhombohedral systems, which from their geometrical character have a -single axis of symmetry, are also optically uniaxal, and produce by -dipolarization circular rings; while the prismatic system, which has -no such single axis, but three unequal axes of symmetry, is optically -biaxal, gives lemniscates by dipolarized light, and according to -Fresnel's theory, has three rectangular axes of unequal elasticity. - -[2nd Ed.] [I have placed Sir David Brewster's arrangement of -crystalline forms in this chapter, as an event belonging to the -_confirmation_ of the distinctions of forms introduced by Weiss and -Mohs; because that arrangement was established, not on -crystallographical, but on optical grounds. But Sir David Brewster's -optical discovery was a much greater step in science than the -systems of the two German crystallographers; and even in respect to -the crystallographical principle, Sir D. Brewster had an independent -share in the discovery. He divided crystalline forms into three -classes, enumerating the Hauïan "primitive forms" which belonged to -each; and as he found some exceptions to this classification, (such -as idocrase, &c.,) he ventured to pronounce that in those substances -the received primitive forms were probably erroneous; a judgment -which was soon confirmed by a closer crystallographical scrutiny. He -also showed his perception of the mineralogical importance of his -discovery by publishing it, not only in the _Phil. Trans._ (1818), -but also in the _Transactions of the Wernerian Society of Natural -History_. In a second paper inserted in this later series, read in -1820, he further notices Mohs's System of Crystallography, which had -then recently appeared, and points out its agreement with his own. - -Another reason why I do not make his great optical discovery a -cardinal point in the history of crystallography is, that as a -crystallographical system it is incomplete. Although we are thus led -to distinguish the _tessular_ and the _prismatic_ systems (using -Mohs's terms) {333} from the _rhombohedral_ and the _square -prismatic_, we are not led to distinguish the latter two from each -other; inasmuch as they have no optical difference of character. But -this distinction is quite essential in crystallography; for these -two systems have faces formed by laws as different as those of the -other two systems. - -Moreover, Weiss and Mohs not only divided crystalline forms into -certain classes, but showed that by doing this, the derivation of -all the existing forms from the fundamental ones assumed a new -aspect of simplicity and generality; and this was the essential part -of what they did. - -On the other hand, I do not think it is too much to say as I have -elsewhere said[35\15] that "Sir D. Brewster's optical experiments -must have led to a classification of crystals into the above -systems, or something nearly equivalent, even if crystals had not -been so arranged by attention to their forms."] - -[Note 35\15: _Philosophy of the Inductive Sciences_, B. viii. C. -iii. Art. 3.] - -Many other most curious trains of research have confirmed the -general truth, that the degree and kind of geometrical symmetry -corresponds exactly with the symmetry of the optical properties. As -an instance of this, eminently striking for its singularity, we may -notice the discovery of Sir John Herschel, that the _plagihedral_ -crystallization of quartz, by which it exhibits faces _twisted_ to -the right or the left, is accompanied by right-handed or left-handed -circular polarization respectively. No one acquainted with the -subject can now doubt, that the correspondence of geometrical and -optical symmetry is of the most complete and fundamental kind. - -[2nd Ed.] [Our knowledge with respect to the positions of the -optical axes of the oblique prismatic crystals is still imperfect. -It appears to be ascertained that, in singly oblique crystals, one -of the axes of optical elasticity coincides with the rectangular -crystallographic axis. In doubly oblique crystals, one of the axes -of optical elasticity is, in many cases, coincident with the axis of -a principal zone. I believe no more determinate laws have been -discovered.] - -Thus the highest generalization at which mathematical -crystallographers have yet arrived, may be considered as fully -established; and the science of Crystallography, in the condition in -which these place it, is fit to be employed as one of the members of -Mineralogy, and thus to fill its appropriate place and office. {334} - - - - -CHAPTER VI. - -CORRECTION OF THE LAW OF THE SAME ANGLE FOR THE SAME SUBSTANCE. - - -DISCOVERY OF ISOMORPHISM. MITSCHERLICH.--The discovery of which we -now have to speak may appear at first sight too large to be included -in the history of crystallography, and may seem to belong rather to -chemistry. But it is to be recollected that crystallography, from -the time of its first assuming importance in the hands of Haüy, -founded its claim to notice entirely upon its connexion with -chemistry; crystalline forms were properties of _something_; but -_what_ that something was, and how it might be modified without -becoming something else, no crystallographer could venture to -decide, without the aid of chemical analysis. Haüy had assumed, as -the general result of his researches, that the same chemical -elements, combined in the same proportions, would always exhibit the -same crystalline form; and reciprocally, that the same form and -angles (except in the obvious case of the tessular system, in which -the angles are determined by its _being_ the tessular system,) -implied the same chemical constitution. But this dogma could only be -considered as an approximate conjecture; for there were many glaring -and unexplained exceptions to it. The explanation of several of -these was beautifully described by the discovery that there are -various elements which are _isomorphous_ to each other; that is, -such that one may take the place of another without altering the -crystalline form; and thus the chemical composition may be much -changed, while the crystallographic character is undisturbed. - -This truth had been caught sight of, probably as a guess only, by -Fuchs as early as 1815. In speaking of a mineral which had been -called Gehlenite, he says, "I hold the oxide of iron, not for an -essential component part of this genus, but only as a _vicarious_ -element, replacing so much lime. We shall find it necessary to -consider the results of several analyses of mineral bodies in this -point of view, if we wish, on the one hand, to bring them into -agreement with the doctrine of chemical proportions, and on the -other, to avoid unnecessarily splitting up genera." In a lecture _On -the Mutual Influence of_ {335} _Chemistry and Mineralogy_,[36\15] he -again draws attention to his term _vicarious_ (_vicarirende_), which -undoubtedly expresses the nature of the general law afterwards -established by Mitscherlich in 1822. - -[Note 36\15: Munich, 1820.] - -But Fuchs's conjectural expression was only a prelude to -Mitscherlich's experimental discovery of isomorphism. Till many -careful analyses had given substance and signification to this -conception of vicarious elements, it was of small value. Perhaps no -one was more capable than Berzelius of turning to the best advantage -any ideas which were current in the chemical world; yet we find -him,[37\15] in 1820, dwelling upon a certain vague view of these -cases,--that "oxides which contain equal doses of oxygen must have -their general properties common;" without tracing it to any definite -conclusions. But his scholar, Mitscherlich, gave this proposition a -real crystallographical import. Thus he found that the carbonates of -lime (calcspar,) of magnesia, of protoxide of iron, and of protoxide -of manganese, agree in many respects of form, while the homologous -angles vary through one or two degrees only; so again the carbonates -of baryta, strontia, lead, and lime (arragonite), agree nearly; the -different kinds of felspar vary only by the substitution of one -alkali for another; the phosphates are almost identical with the -arseniates of several bases. These, and similar results, were -expressed by saying that, in such cases, the bases, lime, protoxide -of iron, and the rest, are _isomorphous_; or in the latter instance, -that the arsenic and phosphoric acids are isomorphous. - -[Note 37\15: _Essay on the Theory of Chemical Proportions_, p. 122.] - -Since, in some of these cases, the substitution of one element of -the isomorphous group for another does alter the angle, though -slightly, it has since been proposed to call such groups -_plesiomorphous_. - -This discovery of isomorphism was of great importance, and excited -much attention among the chemists of Europe. The history of its -reception, however, belongs, in part, to the classification of -minerals; for its effect was immediately to metamorphose the -existing chemical systems of arrangement. But even those -crystallographers and chemists who cared little for general systems -of classification, received a powerful impulse by the expectation, -which was now excited, of discovering definite laws connecting -chemical constitution with crystalline form. Such investigations -were soon carried on with great activity. Thus, at a recent period, -Abich analysed a number of tessular minerals, spinelle, pleonaste, -gahnite, franklinite, and chromic iron oxide; and {336} seems to -have had some success in **giving a common type to their chemical -formulæ, as there is a common type in their crystallization. - -[2nd Ed.] [It will be seen by the above account that Prof. -Mitscherlich's merit in the great discovery of Isomorphism is not at -all narrowed by the previous conjectures of M. Fuchs. I am informed, -moreover, that M. Fuchs afterwards (in Schweigger's _Journal_) -retracted the opinions he had put forward on this subject.] - -_Dimorphism._--My business is, to point out the connected truths -which have been obtained by philosophers, rather than insulated -difficulties which still stand out to perplex them. I need not, -therefore, dwell on the curious cases of _dimorphism_; cases in -which the same definite chemical compound of the same elements -appears to have two different forms; thus the carbonate of lime has -two forms, _calcspar_ and _arragonite_, which belong to different -systems of crystallization. Such facts may puzzle us; but they -hardly interfere with any received general truths, because we have -as yet no truths of very high order respecting the connexion of -chemical constitution and crystalline form. Dimorphism does not -interfere with isomorphism; the two classes of facts stand at the -same stage of inductive generalization, and we wait for some higher -truth which shall include both, and rise above them. - -[2nd Ed.] [For additions to our knowledge of the Dimorphism of -Bodies, see Professor Johnstone's valuable _Report_ on that subject -in the _Reports of the British Association_ for 1837. Substances -have also been found which are _trimorphous_. We owe to Professor -Mitscherlich the discovery of dimorphism, as well as of isomorphism: -and to him also we owe the greater part of the knowledge to which -these discoveries have led.] - - - - -CHAPTER VII. - -ATTEMPTS TO ESTABLISH THE FIXITY OF OTHER PHYSICAL -PROPERTIES.--WERNER. - - -THE reflections from which it appeared, (at the end of the last -Book,) that in order to obtain general knowledge respecting bodies, -we must give scientific fixity to our appreciation of their -properties, applies to their other properties as well as to their -crystalline {337} form. And though none of the other properties have -yet been referred to standards so definite as that which geometry -supplies for crystals, a system has been introduced which makes -their measures far more constant and precise than they are to a -common undisciplined sense. - -The author of this system was Abraham Gottlob Werner, who had been -educated in the institutions which the Elector of Saxony had -established at the mines of Freiberg. Of an exact and methodical -intellect, and of great acuteness of the senses, Werner was well -fitted for the task of giving fixity to the appreciation of outward -impressions; and this he attempted in his _Dissertation on the -external Characters of Fossils_, which was published at Leipzig in -1774. Of the precision of his estimation of such characters, we may -judge from the following story, told by his biographer -Frisch.[38\15] One of his companions had received a quantity of -pieces of amber, and was relating to Werner, then very young, that -he had found in the lot one piece from which he could extract no -signs of electricity. Werner requested to be allowed to put his hand -in the bag which contained these pieces, and immediately drew out -the unelectrical piece. It was yellow chalcedony, which is -distinguishable from amber by its weight and coldness. - -[Note 38\15: _Werner's Leben_, p. 26.] - -The principal external characters which were subjected by Werner to -a systematic examination were color, lustre, hardness, and specific -gravity. His subdivisions of the first character (_Color_), were -very numerous; yet it cannot be doubted that if we recollect them by -the eye, and not by their names, they are definite and valuable -characters, and especially the metallic colors. Breithaupt, merely -by the aid of this character, distinguished two new compounds among -the small grains found along with the grains of platinum, and -usually confounded with them. The kinds of _Lustre_, namely, -_glassy_, _fatty_, _adamantine_, _metallic_, are, when used in the -same manner, equally valuable. _Specific Gravity_ obviously admits -of a numerical measure; and the _Hardness_ of a mineral was pretty -exactly defined by the substances which it would scratch, and by -which it was capable of being scratched. - -Werner soon acquired a reputation as a mineralogist, which drew -persons from every part of Europe to Freiberg in order to hear his -lectures; and thus diffused very widely his mode of employing -external characters. It was, indeed, impossible to attend so closely -to {338} these characters as the Wernerian method required, without -finding that they were more distinctive than might at first sight be -imagined; and the analogy which this mode of studying Mineralogy -established between that and other branches of Natural History, -recommended the method to those in whom a general inclination to -such studies was excited. Thus Professor Jameson of Edinburgh, who -had been one of the pupils of Werner at Freiberg, not only published -works in which he promulgated the mineralogical doctrines of his -master, but established in Edinburgh a "Wernerian Society," having -for its object the general cultivation of Natural History. - -Werner's standards and nomenclature of external characters were -somewhat modified by Mohs, who, with the same kinds of talents and -views, succeeded him at Freiberg. Mohs reduced hardness to numerical -measure by selecting ten known minerals, each harder than the other -in order, from _talc_ to _corundum_ and _diamond_, and by making the -place which these minerals occupy in the list, the numerical measure -of the hardness of those which are compared with them. The result of -the application of this fixed measurement and nomenclature of -external characters will appear in the History of Classification, to -which we now proceed. - - - -{{339}} -SYSTEMATIC MINERALOGY. - - - - -CHAPTER VIII. - -ATTEMPTS AT THE CLASSIFICATION OF MINERALS. - - -_Sect._ 1.--_Proper object of Classification._ - -THE fixity of the crystalline and other physical properties of -minerals is turned to account by being made the means of classifying -such objects. To use the language of Aristotle,[39\15] -Classification is the _architectonic_ science, to which -Crystallography and the Doctrine of External Characters are -subordinate and ministerial, as the art of the bricklayer and -carpenter are to that of the architect. But classification itself is -useful only as subservient to an ulterior science, which shall -furnish us with knowledge concerning things so classified. To -classify is to divide and to name; and the value of the Divisions -which we thus make, and of the names which we give them, is -this;--that they render exact knowledge and general propositions -possible. Now the knowledge which we principally seek concerning -minerals is a knowledge of their chemical composition; the general -propositions to which we hope to be led are such as assert relations -between their intimate constitution and their external attributes. -Thus our Mineralogical Classification must always have an eye turned -towards Chemistry. We cannot get rid of the fundamental conviction, -that the elementary composition of bodies, since it fixes their -essence, must determine their properties. Hence all mineralogical -arrangements, whether they profess it or not, must be, in effect, -chemical; they must have it for their object to bring into view a -set of relations, which, whatever else they may be, are at least -chemical relations. We may begin with the outside, but it is only in -order to reach the inner {340} structure. We may classify without -reference to chemistry; but if we do so, it is only that we may -assert chemical propositions with reference to our classification. - -[Note 39\15: _Eth. Nicom._ i. 2.] - -But, as we have already attempted to show, we not only may, but we -_must_ classify, by other than chemical characters, in order to be -able to make our classification the basis of chemical knowledge. In -order to assert chemical truths concerning bodies, we must have the -bodies known by some tests not chemical. The chemist cannot assert -that Arragonite does or does not contain Strontia, except the -mineralogist can tell him whether any given specimen is or is not -_Arragonite_. If chemistry be called upon to supply the -_definitions_ as well as the _doctrines_ of mineralogy, the science -can only consist of identical propositions. - -Yet chemistry has been much employed in mineralogical -classifications, and, it is generally believed, with advantage to -the science: How is this consistent with what has been said? - -To this the answer is, that when this _has_ been done with -advantage, the authority of external characters, as well as of -chemical constitution, has really been brought into play. We have -two sets of properties to compare, chemical and physical; to exhibit -the connexion of these is the object of scientific mineralogy. And -though this connexion would be most distinctly asserted, if we could -keep the two sets of properties distinct, yet it may be brought into -view in a great degree, by classifications in which both are -referred to as guides. Since the governing principle of the attempts -at classification is the conviction that the chemical constitution -and the physical properties have a definite relation to each other, -we appear entitled to use both kinds of evidence, in proportion as -we can best obtain each; and then the general consistency and -convenience of our system will be the security for its containing -substantial knowledge, though this be not presented in a rigorously -logical or systematic form. - -Such _mixed systems_ of classification, resting partly on chemical -and partly on physical characters, naturally appeared as the -earliest attempts in this way, before the two members of the subject -had been clearly separated in men's minds; and these systems, -therefore, we must first give an account of. - - -_Sect._ 2.--_Mixed Systems of Classification._ - -_Early Systems._--The first attempts at classifying minerals went -upon the ground of those differences of general aspect which had -been {341} recognized in the formation of common language; as -_earths_, _stones_, _metals_. But such arrangements were manifestly -vague and confused; and when chemistry had advanced to power and -honor, her aid was naturally called in to introduce a better order. -"Hiarne and Bromell were, as far as I know," says[40\15] Cronstedt, -"the first who founded any mineral system upon chemical principles; -to them we owe the three known divisions of the most simple mineral -bodies; viz., the _calcarei_, _vitrescentes_, and _apyri_." But -Cronstedt's own _Essay towards a System of Mineralogy_, published in -Swedish in 1758, had perhaps more influence than any other, upon -succeeding systems. In this, the distinction of earths and stones, -and also of vitrescent and non-vitrescent earths (_apyri_), is -rejected. The earths are classed as _calcareous_, _siliceous_, -_argillaceous_, and the like. Again, calcareous earth is pure (_calc -spar_), or united with acid of vitriol (_gypsum_), or united with -the muriatic add (_sal ammoniac_), and the like. It is easy to see -that this is the method, which, in its general principle, has been -continued to our own time. In such methods, it is supposed that we -can recognize the substance by its general appearance, and on this -assumption, its place in the system conveys to us chemical knowledge -concerning it. - -[Note 40\15: _Mineralogy_, Pref. p. viii.] - -But as the other branches of Natural History, and especially Botany, -assumed a systematic form, many mineralogists became dissatisfied -with this casual and superficial mode of taking account of external -characters; they became convinced, that in Mineralogy as in other -sciences, classification must have its system and its rules. The -views which Werner ascribes to his teacher, Pabst van Ohain,[41\15] -show the rise of those opinions which led through Werner to Mohs: -"He was of opinion that a natural mineral system must be constructed -by chemical determinations, and external characters at the same time -(_methodus mixta_); but that along with this, mineralogists ought -also to construct and employ what he called an _artificial system_, -which might serve us as a guide (_loco indicis_) how to introduce -newly-discovered fossils into the system, and how to find easily and -quickly those already known and introduced." Such an artificial -system, containing not the grounds of classification, but marks for -recognition, was afterwards attempted by Mohs, and termed by him the -_Characteristic_ of his system. - -[Note 41\15: Frisch. _Werner's Leben_, p. 15.] - -_Werner's System._--But, in the mean time, Werner's classification -had an extensive reign, and this was still a mixed system. Werner -himself, indeed, never published a system of mineralogy. "We might -{342} almost imagine," Cuvier says,[42\15] "that when he had -produced his nomenclature of external characters, he was affrighted -with his own creation; and that the reason of his writing so little -after his first essay, was to avoid the shackles which he had -imposed upon others." His system was, indeed, made known both in and -out of Germany, by his pupils; but in consequence of Werner's -unwillingness to give it on his own authority, it assumed, in its -published forms, the appearance of an extorted secret imperfectly -told. A _Notice of the Mineralogical Cabinet of Mine-Director Pabst -von Ohain_, was, in 1792, published by Karsten and Hoffman, under -Werner's direction; and conveyed by example, his views of -mineralogical arrangement; and[43\15] in 1816 his _Doctrine of -Classification_ was surreptitiously copied from his manuscript, and -published in a German Journal, termed _The Hesperus_. But it was -only in 1817, after his death, that there appeared _Werner's Last -Mineral System_, edited from his papers by Breithaupt and Köhler: -and by this time, as we shall soon see, other systems were coming -forwards on the stage. - -[Note 42\15: Cuv. _El._ ii. 314.] - -[Note 43\15: Frisch. p. 52.] - -A very slight notice of Werner's arrangement will suffice to show -that it was, as we have termed it, a Mixed System. He makes four -great Classes of fossils, _Earthy_, _Saline_, _Combustible_, -_Metallic_: the earthy fossils are in eight Genera--Diamond, Zircon, -Silica, Alumina, Talc, Lime, Baryta, Hallites. It is clear that -these genera are in the main chemical, for chemistry alone can -definitely distinguish the different Earths which characterize them. -Yet the Wernerian arrangement supposed the distinctions to be -practically made by reference to those external characters which the -teacher himself could employ with such surpassing skill. And though -it cannot be doubted, that the chemical views which prevailed around -him had a latent influence on his classification in some cases, he -resolutely refused to bend his system to the authority of chemistry. -Thus,[44\15] when he was blamed for having, in opposition to the -chemists, placed diamond among the earthy fossils, he persisted in -declaring that, mineralogically considered, it was a stone, and -could not be treated as anything else. - -[Note 44\15: Frisch. p. 62.] - -This was an indication to that tendency, which, under his successor, -led to a complete separation of the two grounds of classification. -But before we proceed to this, we must notice what was doing at this -period in other parts of Europe. - -_Haüy's System._--Though Werner, on his own principles, ought to -{343} have been the first person to see the immense value of the -most marked of external characters, crystalline form, he did not, in -fact, attach much importance to it. Perhaps he was in some measure -fascinated by a fondness for those characters which he had himself -systematized, and the study of which did not direct him to look for -geometrical relations. However this may be, the glory of giving to -Crystallography its just importance in Mineralogy is due to France: -and the Treatise of Haüy, published in 1801, is the basis of the -best succeeding works of mineralogy. In this work, the arrangement -is professedly chemical; and the classification thus established is -employed as the means of enunciating crystallographic and other -properties. "The principal object of this Treatise," says the -author,[45\15] "is the exposition and development of a method -founded on certain principles, which may serve as a frame-work for -all the knowledge which Mineralogy can supply, aided by the -different sciences which can join hands with her and march on the -same line.**" It is worthy of notice, as characteristic of this -period of Mixed Systems, that the classification of Haüy, though -founded on principles so different from the Wernerian ones, deviates -little from it in the general character of the divisions. Thus, the -first Order of the first Class of Haüy is _Acidiferous Earthy -Substances_; the first genus is _Lime_; the species are, _Carbonate -of Lime_, _Phosphate of Lime_, _Fluate of Lime_, _Sulphate of Lime_, -and so on. - -[Note 45\15: Disc. Prél. p. xvii.] - -_Other Systems._--Such mixed methods were introduced also into this -country, and have prevailed, we may say, up to the present time. The -_Mineralogy_ of William Phillips, which was published in 1824, and -which was an extraordinary treasure of crystallographic facts, was -arranged by such a mixed system; that is, by a system professedly -chemical; but, inasmuch as a rigid chemical system is impossible, -and the assumption of such a one leads into glaring absurdities, the -system was, in this and other attempts of the same kind, corrected -by the most arbitrary and lax application of other considerations. - -It is a curious example of the difference of national intellectual -character, that the manifest inconsistencies of the prevalent -systems, which led in Germany, as we shall see, to bold and sweeping -attempts at reform, produced in England a sort of contemptuous -despair with regard to systems in general;--a belief that no system -could be consistent or useful;--and a persuasion that the only -valuable knowledge is the accumulation of particular facts. This is -not the place to {344} explain how erroneous and unphilosophical -such an opinion is. But we may notice that while such a temper -prevails among us, our place in this science can never be found in -advance of that position which we are now considering as exemplified -in the period of Werner and Haüy. So long as we entertain such views -respecting the objects of Mineralogy, we can have no share in the -fortunes of the succeeding period of its history, to which I now -proceed. - - - - -CHAPTER IX. - -ATTEMPTS AT THE REFORM OF MINERALOGICAL SYSTEMS.--SEPARATION OF THE -CHEMICAL AND NATURAL HISTORY METHODS. - - -_Sect._ 1.--_Natural History System of Mohs._ - -THE chemical principle of classification, if pursued at random, as -in the cases just spoken of leads to results at which a -philosophical spirit revolts; it separates widely substances which -are not distinguishable; joins together bodies the most dissimilar; -and in hardly any instance does it bring any truth into view. The -vices of classifications like that of Haüy could not long be -concealed; but even before time had exposed the weakness of his -system, Haüy himself had pointed out, clearly and without -reserve,[46\15] that a chemical system is only one side of the -subject, and supposes, as its counterpart, a science of external -characters. In the mean time, the Wernerians were becoming more and -more in love with the form which they had given to such a science. -Indeed, the expertness which Werner and his scholars acquired in the -use of external characters, justified some partiality for them. It -is related of him,[47\15] that, by looking at a piece of iron-ore, -and poising it in his hand, he was able to tell, almost precisely, -the proportion of pure metal which it contained. And in the last -year of his life,[48\15] he had marked out, as the employment of the -ensuing winter, the study of the system of Berzelius, with a view to -find out the laws of combination as disclosed by external -characters. In the same spirit, his pupil {345} Breithaupt[49\15] -attempted to discover the ingredients of minerals by their -peculiarities of crystallization. The persuasion that there must be -_some_ connexion between composition and properties, transformed -itself, in their minds, into a belief that they could seize the -nature of the connexion by a sort of instinct. - -[Note 46\15: See his Disc. Prél.] - -[Note 47\15: Frisch. _Werner's Leben_, p. 78.] - -[Note 48\15: Frisch. 3.] - -[Note 49\15: _Dresdn. Auswahl_, vol. ii. p. 97.] - -This opinion of the independency of the science of external -characters, and of its sufficiency for its own object, at last -assumed its complete form in the bold attempt to construct a system -which should borrow nothing from chemistry. This attempt was made by -Frederick Mohs, who had been the pupil of Werner, and was afterwards -his successor in the school of Freiberg; and who, by the acute and -methodical character of his intellect, and by his intimate knowledge -of minerals, was worthy of his predecessor. Rejecting altogether all -divisions of which the import was chemical, Mohs turned for -guidance, or at least for the light of analogy, to botany. His -object was to construct a _Natural System_ of mineralogy. What the -conditions and advantages of a natural system of any province of -nature are, we must delay to explain till we have before us, in -botany, a more luminous example of such a scheme. But further; in -mineralogy, as in botany, besides the Natural System, by which we -_form_ our classes, it is necessary to have an _Artificial System_ -by which we _recognize_ them;--a principle which, we have seen, had -already taken root in the school of Freiberg. Such an artificial -system Mohs produced in his _Characteristic of the Mineral Kingdom_, -which was published at Dresden in 1820; and which, though extending -only to a few pages, excited a strong interest in Germany, where -men's minds were prepared to interpret the full import of such a -work. Some of the traits of such a "Characteristic" had, indeed, -been previously drawn by others; as for example, by Haüy, who -notices that each of his Classes has peculiar characters. For -instance, his First Class (acidiferous substances,) alone possesses -these combinations of properties; "division into a regular -octohedron, without being able to scratch glass; specific gravity -above 3·5, without being able to scratch glass." The extension of -such characters into a scheme which should exhaust the whole mineral -kingdom, was the undertaking of Mohs. - -Such a collection of marks of classes, implied a classification -previously established, and accordingly, Mohs had created his own -mineral system. His aim was to construct it, as we shall hereafter -see that other natural systems are constructed, by taking into -account _all_ the {346} resemblances and differences of the objects -classified. It is obvious that to execute such a work, implied a -most intimate and universal acquaintance with minerals;--a power of -combining in one vivid survey the whole mineral kingdom. To -illustrate the spirit in which Professor Mohs performed his task, I -hope I may be allowed to refer to my own intercourse with him. At an -early period of my mineralogical studies, when the very conception -of a Natural System was new to me, he, with great kindliness of -temper, allowed me habitually to propose to him the scruples which -arose in my mind, before I could admit principles which appeared to -me then so vague and indefinite; and answered my objections with -great patience and most instructive clearness. Among other -difficulties, I one day propounded to him this;--"You have published -a Treatise on Mineralogy, in which you have described _all_ the -important properties of all known minerals. On your principles, -then, it ought to be possible, merely by knowing the descriptions in -your book, and without seeing any minerals, to construct a natural -system; and this natural system ought to turn out identical with -that which you have produced, by so careful an examination of the -minerals themselves." He pondered a moment, and then he answered, -"It is true; but what an enormous _imagination_ (_einbildungskraft_, -_power of inward imagining_), a man must have for such a work!" -Vividness of conception of sensible properties, and the steady -intuition (_anschauung_) of objects, were deemed by him, and by the -Wernerian school in general, to be the most essential conditions of -complete knowledge. - -It is not necessary to describe Mohs's system in detail; it may -sufficiently indicate its form to state that the following -substances, such as I before gave as examples of other arrangements, -calcspar, gypsum, fluor spar, apatite, heavy spar, are by Mohs -termed respectively, _Rhombohedral Lime Haloide_, _Gyps Haloide_, -_Octohedral Fluor Haloide_, _Rhombohedral Fluor Haloide_, _Prismatic -Hal Baryte_. These substances are thus referred to the _Orders_ -Haloide, and Baryte; to _Genera_ Lime Haloide, Fluor Haloide, Hal -Baryte; and the _Species_ is an additional particularization. - -Mohs not only aimed at framing such a system, but was also ambitious -of giving to all minerals _Names_ which should accord with the -system. This design was too bold to succeed. It is true, that a new -nomenclature was much needed in mineralogy: it is true, too, that it -was reasonable to expect, from an improved classification, an -improved nomenclature, such as had been so happily obtained in -botany by the {347} reform of Linnæus. But besides the defects of -Mohs's system, he had not prepared his verbal novelties with the -temperance and skill of the great botanical reformer. He called upon -mineralogists to change the name of almost every mineral with which -they were acquainted; and the proposed appellations were mostly of a -cumbrous form, as the above example may serve to show. Such names -could have obtained general currency, only after a general and -complete acceptance of the system; and the system did not possess, -in a sufficient degree, that evidence which alone could gain it a -home in the belief of philosophers,--the coincidence of its results -with those of Chemistry. But before I speak finally of the fortunes -of the Natural-history System, I will say something of the other -attempt which was made about the same time to introduce a Reform -into Mineralogy from the opposite extremity of the science. - - -_Sect._ 2.--_Chemical System of Berzelius and others._ - -IF the students of external characters were satisfied of the -independence of their method, the chemical analysts were naturally -no less confident of the legitimate supremacy of their principles: -and when the beginning of the present century had been distinguished -by the establishment of the theory of definite proportions, and by -discoveries which pointed to the electro-chemical theory, it could -not appear presumption to suppose, that the classification of -bodies, so far as it depended on chemistry, might be presented in a -form more complete and scientific than at any previous time. - -The attempt to do this was made by the great Swedish chemist Jacob -Berzelius. In 1816, he published his _Essay to establish a purely -Scientific System of Mineralogy, by means of the Application of the -Electro-chemical Theory and the Chemical Doctrine of Definite -Proportions_. It is manifest that, for minerals which are -constituted by the law of Definite Proportions, this constitution -must be a most essential part of their character. The -electro-chemical theory was called in aid, in addition to the -composition, because, distinguishing the elements of all compounds -as electro-positive and electro-negative, and giving to every -element a place in a series, and a place defined by the degree of -these relations, it seemed to afford a rigorous and complete -principle of arrangement. Accordingly, Berzelius, in his First -System, arranged minerals according to their electro-positive -element, and the elements according to their electro-positive rank; -{348} and supposed that he had thus removed all that was arbitrary -and vague in the previous chemical systems of mineralogy. - -Though the attempt appeared so well justified by the state of -chemical science, and was so plausible in its principle, it was not -long before events showed that there was some fallacy in these -specious appearances. In 1820, Mitscherlich discovered Isomorphism: -by that discovery it appeared that bodies containing very different -electro-positive elements could not be distinguished from each -other; it was impossible, therefore, to put them in distant portions -of the classification;--and thus the first system of Berzelius -crumbled to pieces. - -But Berzelius did not so easily resign his project. With the most -unhesitating confession of his first failure, but with undaunted -courage, he again girded himself to the task of rebuilding his -edifice. Defeated at the electro-positive position, he now resolved -to make a stand at the electro-negative element. In 1824, he -published in the Transactions of the Swedish Academy, a Memoir _On -the Alterations in the Chemical Mineral System, which necessarily -follow from the Property exhibited by Isomorphous Bodies, of -replacing each other in given Proportions_. The alteration was, in -fact, an inversion of the system, with an attempt still to preserve -the electro-chemical principle of arrangement. Thus, instead of -arranging metallic minerals according to the _metal_, under iron, -copper, &c., all the _sulphurets_ were classed together, all the -_oxides_ together, all the _sulphates_ together, and so in other -respects. That such an order was a great improvement on the -preceding one, cannot be doubted; but we shall see, I think, that as -a strict scientific system it was not successful. The discovery of -isomorphism, however, naturally led to such attempts. Thus Gmelin -also, in 1825, published a mineral system,[50\15] which, like that -of Berzelius, founded its leading distinctions on the -electro-negative, or, as it was sometimes termed, the _formative_ -element of bodies; and, besides this, took account of the _numbers_ -of atoms or proportions which appear in the composition of the body; -distinguishing, for instance, Silicates, as simple silicates, double -silicates, and so on, to _quintuple_ silicate (_Pechstein_) and -_sextuple_ silicate (_Perlstein_). In like manner, Nordenskiöld -devised a system resting on the same bases, taking into account also -the crystalline form. In 1824, Beudant published his _Traité -Elémentaire de Minéralogie_, in which he professes to found his -arrangement on the electro-negative element, and on Ampère's -circular {349} arrangement of elementary substances. Such schemes -exhibit rather a play of the mere logical faculty, exercising itself -on assumed principles, than any attempt at the real interpretation -of nature. Other such pure chemical systems may have been published, -but it is not necessary to accumulate instances. I proceed to -consider their result. - -[Note 50\15: _Zeitsch. der Min._ 1825, p. 435.] - - -_Sect._ 3.--_Failure of the Attempts at Systematic Reform._ - -IT may appear presumptuous to speak of the failure of those whom, -like Berzelius and Mohs, we acknowledge as our masters, at a period -when, probably, they and some of their admirers still hold them to -have succeeded in their attempt to construct a consistent system. -But I conceive that my office as an historian requires me to exhibit -the fortunes of this science in the most distinct form of which they -admit, and that I cannot evade the duty of attempting to seize the -true aspect of recent occurrences in the world of science. Hence I -venture to speak of the failure of both the attempts at framing a -pure scientific system of mineralogy,--that founded on the chemical, -and that founded on the natural-history principle; because it is -clear that they have not obtained that which alone we could, -according to the views here presented, consider as success,--a -coincidence of each with the other. A Chemical System of -arrangement, which should bring together, in all cases, the -substances which come nearest each other in external properties;--a -Natural-history System, which should be found to arrange bodies in -complete accordance with their chemical constitution:--if such -systems existed, they might, with justice, claim to have succeeded. -Their agreement would be their verification. The interior and -exterior system are the type and the antitype, and their entire -correspondence would establish the mode of interpretation beyond -doubt. But nothing less than this will satisfy the requisitions of -science. And when, therefore, the chemical and the natural-history -system, though evidently, as I conceive, tending towards each other, -are still far from coming together, it is impossible to allow that -either method has been successful in regard to its proper object. - -But we may, I think, point out the fallacy of the principles, as well -as the imperfection of the results, of both of those methods. With -regard to that of Berzelius, indeed, the history of the subject -obviously betrays its unsoundness. The electro-positive principle was, -in a very short time after its adoption, proved and acknowledged to be -utterly untenable: what security have we that the electro-negative -element is {350} more trustworthy? Was not the necessity of an entire -change of system, a proof that the ground, whatever that was, on which -the electro-chemical principle was adopted, was an unfounded -assumption? And, in fact, do we not find that the same argument which -was allowed to be fatal to the First System of Berzelius, applies in -exactly the same manner against the Second? If the electro-positive -elements be often isomorphous, are not the electro-negative elements -sometimes isomorphous also? for instance, the arsenic and phosphoric -acids. But to go further, what _is_ the ground on which the -electro-chemical arrangement is adopted? Granted that the electrical -relations of bodies are important; but how do we come to know that -these relations have anything to do with mineralogy? How does it -appear that on them, principally, depend those external properties -which mineralogy must study? How does it appear that because sulphur -is the electro-negative part of one body, and an acid the -electro-negative part of another, these two elements similarly affect -the compounds? How does it appear that there is any analogy whatever -in their functions? We allow that the composition must, in _some way_, -determine the classified place of the mineral,--but why in _this_ way? - -I do not dwell on the remark which Berzelius himself[51\15] makes on -Nordenskiöld's system;--that it assumes a perfect knowledge of the -composition in every case; although, considering the usual -discrepancies of analyses of minerals, this objection must make all -pure chemical systems useless. But I may observe, that mineralogists -have not yet determined what characters are sufficiently affixed to -determine a species of minerals. We have seen that the ancient -notion of the composition of a species, has been unsettled by the -discovery of isomorphism. The tenet of the constancy of the angle is -rendered doubtful by cases of plesiomorphism. The optical -properties, which are so closely connected with the crystalline, are -still so imperfectly known, that they are subject to changes which -appear capricious and arbitrary. Both the chemical and the optical -mineralogists have constantly, of late, found occasion to separate -species which had been united, and to bring together those which had -been divided. Everything shows that, in this science, we have our -classification still to begin. The detection of that fixity of -characters, on which a right establishment of species must rest, is -not yet complete, great as the progress is which we have made, by -acquiring a knowledge of the laws of crystallization and of {351} -definite chemical constitution. Our ignorance may surprise us; but -it may diminish our surprise to recollect, that the knowledge which -we seek is that of the laws of the physical constitution of all -bodies whatever; for to us, as mineralogists, all chemical compounds -are minerals. - -[Note 51\15: _Jahres Bericht._ viii. 188.] - -The defect of the principle of the natural-history classifiers may be -thus stated:--in studying the external characters of bodies, they take -for granted that they can, without any other light, discover the -relative value and importance of those characters. The grouping of -Species into a Genus, of Genera into an Order, according to the method -of this school, proceeds by no definite rules, but by a latent talent -of appreciation,--a sort of classifying instinct. But this course -cannot reasonably be expected to lead to scientific truth; for it can -hardly be hoped, by any one who looks at the general course of -science, that we shall discover the relation between external -characters and chemical composition, otherwise than by tracing their -association in cases where both are known. It is urged that in other -classificatory sciences, in botany, for example, we obtain a natural -classification from external characters without having recourse to any -other source of knowledge. But this is not true in the sense here -meant. In framing a natural system of botany, we have constantly -before our eyes the principles of physiology; and we estimate the -value of the characters of a plant by their bearing on its -functions,--by their place in its organization. In an unorganic body, -the chemical constitution is the law of its being; and we shall never -succeed in framing a science of such bodies but by studiously -directing our efforts to the interpretation of that law. - -On these grounds, then, I conceive, that the bold attempts of Mohs -and of Berzelius to give new forms to mineralogy, cannot be deemed -successful in the manner in which their authors aspired to succeed. -Neither of them can be marked as a permanent reformation of the -science. I shall not inquire how far they have been accepted by men -of science, for I conceive that their greatest effect has been to -point out improvements which might be made in mineralogy without -going the whole length either of the _pure_ chemical, or of the -_pure_ natural-history system. - - -_Sect._ 4.--_Return to Mixed Systems with Improvements._ - -IN spite of the efforts of the purists, mineralogists returned to -mixed systems of classification; but these systems are much better -than they were before such efforts were made. {352} - -The Second System of Berzelius, though not tenable in its rigorous -form, approaches far nearer than any previous system to a complete -character, bringing together like substances in a large portion of -its extent. The System of Mohs also, whether or not unconsciously -swayed by chemical doctrines, forms orders which have a community of -chemical character; thus, the minerals of the order _Haloide_ are -salts of oxides, and those of the order _Pyrites_ are sulphurets of -metals. Thus the two methods appear to be converging to a common -centre; and though we are unable to follow either of them to this -point of union, we may learn from both in what direction we are to -look for it. If we regard the best of the pure systems hitherto -devised as indications of the nature of that system, perfect both as -a chemical and as a natural-history system, to which a more complete -condition of mineralogical knowledge may lead us, we may obtain, -even at present, a tolerably good approximation to a complete -classification; and such a one, if we recollect that it must be -imperfect, and is to be held as provisional only, may be of no small -value and use to us. - -The best of the mixed systems produced by this compromise again -comes from Freiberg, and was published by Professor Naumann in 1828. -Most of his orders have both a chemical character and great external -resemblances. Thus his _Haloides_, divided into _Unmetallic_ and -_Metallic_, and these again into _Hydrous_ and _Anhydrous_, give -good natural groups. The most difficult minerals to arrange in all -systems are the siliceous ones. These M. Naumann calls _Silicides_, -and subdivides them into _Metallic_, _Unmetallic_, and _Amphoteric_ -or mixed; and again, into _Hydrous_ and _Anhydrous_. Such a system -is at least a good basis for future researches; and this is, as we -have said, all that we can at present hope for. And when we -recollect that the natural-history principle of classification has -begun, as we have already seen, to make its appearance in our -treatises of chemistry, we cannot doubt that some progress is making -towards the object which I have pointed out. But we know not yet how -far we are from the end. The combination of chemical, -crystallographical, physical and optical properties into some lofty -generalization, is probably a triumph reserved for future and -distant years. - -_Conclusion._--The history of Mineralogy, both in its successes and -by its failures, teaches us this lesson;--that in the sciences of -classification, the establishment of the fixity of characters, and -the discovery of such characters as are fixed, are steps of the -first importance in the progress of these sciences. The recollection -of this maxim may aid us in {353} shaping our course through the -history of other sciences of this kind; in which, from the extent of -the subject, and the mass of literature belonging to it, we might at -first almost despair of casting the history into distinct epochs and -periods. To the most prominent of such sciences, Botany, I now -proceed. - - - -{{355}} -BOOK XVI. - - -_CLASSIFICATORY SCIENCES._ - - -HISTORY -OF -SYSTEMATIC BOTANY AND ZOOLOGY. - - - . . . . . Vatem aspicies quæ rupe sub altâ - Fata canit, foliisque notas et nomina mandat. - Quæcunque in foliis descripsit carmina virgo - Digerit in numerum atque antro seclusa relinquit - Illa manent immorta locis neque ab ordine cedunt. - VIRGIL. _Æn._ iii. 443. - - Behold the Sibyl!--Her who weaves a long, - A tangled, full, yet sweetly flowing song. - Wondrous her skill; for leaf on leaf she frames - Unerring symbols and enduring names; - And as her nicely measured line she binds, - For leaf on leaf a fitting place she finds; - Their place once found, no more the leaves depart, - But fixed rest:--such is her magic art. - - - -{{357}} -INTRODUCTION. - - -WE now arrive at that study which offers the most copious and -complete example of the sciences of classification, I mean Botany. -And in this case, we have before us a branch of knowledge of which -we may say, more properly than of any of the sciences which we have -reviewed since Astronomy, that it has been constantly advancing, -more or less rapidly, from the infancy of the human race to the -present day. One of the reasons of this resemblance in the fortunes -of two studies so widely dissimilar, is to be found in a simplicity -of principle which they have in common; the ideas of Likeness and -Difference, on which the knowledge of plants depends, are, like the -ideas of Space and Time, which are the foundation of astronomy, -readily apprehended with clearness and precision, even without any -peculiar culture of the intellect. But another reason why, in the -history of Botany, as in that of Astronomy, the progress of -knowledge forms an unbroken line from the earliest times, is -precisely the great difference of the kind of knowledge which has -been attained in the two cases. In Astronomy, the discovery of -general truths began at an early period of civilization; in Botany, -it has hardly yet begun; and thus, in each of these departments of -study, the lore of the ancient is homogeneous with that of the -modern times, though in the one case it is science, in the other, -the absence of science, which pervades all ages. The resemblance of -the form of their history arises from the diversity of their -materials. - -I shall not here dwell further upon this subject, but proceed to -trace rapidly the progress of _Systematic Botany_, as the -classificatory science is usually denominated, when it is requisite -to distinguish between that and Physiological Botany. My own -imperfect acquaintance with this study admonishes me not to venture -into its details, further than my purpose absolutely requires. I -trust that, by taking my views principally from writers who are -generally allowed to possess the best insight into the science, I -may be able to draw the larger features of its history with -tolerable correctness; and if I succeed in this, I shall attain an -object of great importance in my general scheme. {358} - - - -CHAPTER I. - -IMAGINARY KNOWLEDGE OF PLANTS. - - -THE apprehension of such differences and resemblances as those by -which we group together and discriminate the various kinds of plants -and animals, and the appropriation of words to mark and convey the -resulting notions, must be presupposed, as essential to the very -beginning of human knowledge. In whatever manner we imagine man to -be placed on the earth by his Creator, these processes must be -conceived to be, as our Scriptures represent them, contemporaneous -with the first exertion of reason, and the first use of speech. If -we were to indulge ourselves in framing a hypothetical account of -the origin of language, we should probably assume as the -first-formed words, those which depend on the visible likeness or -unlikeness of objects; and should arrange as of subsequent -formation, those terms which imply, in the mind, acts of wider -combination and higher abstraction. At any rate, it is certain that -the names of the kinds of vegetables and animals are very abundant -even in the most uncivilized stages of man's career. Thus we are -informed[1\16] that the inhabitants of New Zealand have a distinct -name of every tree and plant in their island, of which there are six -or seven hundred or more different kinds. In the accounts of the -rudest tribes, in the earliest legends, poetry, and literature of -nations, pines and oaks, roses and violets, the olive and the vine, -and the thousand other productions of the earth, have a place, and -are spoken of in a manner which assumes, that in such kinds of -natural objects, permanent and infallible distinctions had been -observed and universally recognized. - -[Note 1\16: Yate's _New Zealand_, p. 238.] - -For a long period, it was not suspected that any ambiguity or -confusion could arise from the use of such terms; and when such -inconveniences did occur, (as even in early times they did,) men -were far from divining that the proper remedy was the construction -of a science of classification. The loose and insecure terms of the -language of common life retained their place in botany, long after -their {359} defects were severely felt: for instance, the vague and -unscientific distinction of vegetables into _trees_, _shrubs_, and -_herbs_, kept its ground till the time of Linnæus. - -While it was thus imagined that the identification of a plant, by -means of its name, might properly be trusted to the common -uncultured faculties of the mind, and to what we may call the -instinct of language, all the attention and study which were -bestowed on such objects, were naturally employed in learning and -thinking upon such circumstances respecting them as were supplied by -any of the common channels through which knowledge and opinion flow -into men's minds. - -The reader need hardly be reminded that in the earlier periods of -man's mental culture, he acquires those opinions on which he loves -to dwell, not by the exercise of observation subordinate to reason; -but, far more, by his fancy and his emotions, his love of the -marvellous, his hopes and fears. It cannot surprise us, therefore, -that the earliest lore concerning plants which we discover in the -records of the past, consists of mythological legends, marvellous -relations, and extraordinary medicinal qualities. To the lively -fancy of the Greeks, the Narcissus, which bends its head over the -stream, was originally a youth who in such an attitude became -enamored of his own beauty: the hyacinth,[2\16] on whose petals the -notes of grief were traced (A I, A I), recorded the sorrow of Apollo -for the death of his favorite Hyacinthus: the beautiful lotus of -India,[3\16] which floats with its splendid flower on the surface of -the water, is the chosen seat of the goddess Lackshmi, the daughter -of Ocean.[4\16] In Egypt, too,[5\16] Osiris swam on a lotus-leaf and -Harpocrates was cradled in one. The lotus-eaters of Homer lost -immediately their love of home. Every one knows how easy it would be -to accumulate such tales of wonder or religion. - -[Note 2\16: Lilium martagon. - Ipse suos gemitus foliis inscribit et A I, A I, - Flos habet inscriptum funestaque litera ducta est.--OVID.] - -[Note 3\16: Nelumbium speciosum.] - -[Note 4\16: Sprengel, _Geschichte der Botanik_, i. 27.] - -[Note 5\16: Ib. i. 28.] - -Those who attended to the effects of plants, might discover in them -some medicinal properties, and might easily imagine more; and when -the love of the marvellous was added to the hope of health, it is -easy to believe that men would be very credulous. We need not dwell -upon the examples of this. In Pliny's Introduction to that book of -his {360} Natural History which treats of the medicinal virtues of -plants, he says,[6\16] "Antiquity was so much struck with the -properties of herbs, that it affirmed things incredible. Xanthus, -the historian, says, that a man killed by a dragon, will be restored -to life by an herb which he calls _balin_; and that Thylo, when -killed by a dragon, was recovered by the same plant. Democritus -asserted, and Theophrastus believed, that there was an herb, at the -touch of which, the wedge which the woodman had driven into a tree -would leap out again. Though we cannot credit these stories, most -persons believe that almost anything might be effected by means of -herbs, if their virtues were fully known." How far from a reasonable -estimate of the reality of such virtues were the persons who -entertained this belief we may judge from the many superstitious -observances which they associated with the gathering and using of -medicinal plants. Theophrastus speaks of these;[7\16] "The -drug-sellers and the rhizotomists (root-cutters) tell us," he says, -"some things which may be true, but other things which are merely -solemn quackery;[8\16] thus they direct us to gather some plants, -standing from the wind, and with our bodies anointed; some by night, -some by day, some before the sun falls on them. So far there may be -something in their rules. But others are too fantastical and far -fetched. It is, perhaps, not absurd to use a prayer in plucking a -plant; but they go further than this. We are to draw a sword three -times round the mandragora, and to cut it looking to the west: -again, to dance round it, and to use obscene language, as they say -those who sow cumin should utter blasphemies. Again, we are to draw -a line round the black hellebore, standing to the east and praying; -and to avoid an eagle either on the right or on the left; for, say -they, 'if an eagle be near, the cutter will die in a year.'" - -[Note 6\16: Lib. xxv. 5.] - -[Note 7\16: _De Plantis_, ix. 9.] - -[Note 8\16: Ἐπιτραγῳδοῦντες.] - -This extract may serve to show the extent to which these -imaginations were prevalent, and the manner in which they were -looked upon by Theophrastus, our first great botanical author. And -we may now consider that we have given sufficient attention to these -fables and superstitions, which have no place in the history of the -progress of real knowledge, except to show the strange chaos of wild -fancies and legends out of which it had to emerge. We proceed to -trace the history of the knowledge of plants. {361} - - - - -CHAPTER II. - -UNSYSTEMATIC KNOWLEDGE OF PLANTS. - - -A STEP was made towards the formation of the Science of Plants, -although undoubtedly a slight one, as soon as men began to collect -information concerning them and their properties, from a love and -reverence for knowledge, independent of the passion for the -marvellous and the impulse of practical utility. This step was very -early made. The "wisdom" of Solomon, and the admiration which was -bestowed upon it, prove, even at that period, such a working of the -speculative faculty: and we are told, that among other evidences of -his being "wiser than all men," "he spake of trees, from the -cedar-tree that is in Lebanon even unto the hyssop that springeth -out of the wall."[9\16] The father of history, Herodotus, shows us -that a taste for natural history had, in his time, found a place in -the minds of the Greeks. In speaking of the luxuriant vegetation of -the Babylonian plain,[10\16] he is so far from desiring to astonish -merely, that he says, "the blades of wheat and barley are full four -fingers wide; but as to the size of the trees which grow from millet -and sesame, though I could mention it, I will not; knowing well that -those who have not been in that country will hardly believe what I -have said already." He then proceeds to describe some remarkable -circumstances respecting the fertilization of the date-palms in -Assyria. - -[Note 9\16: 1 Kings iv. 33.] - -[Note 10\16: Herod. i. 193.] - -This curious and active spirit of the Greeks led rapidly, as we have -seen in other instances, to attempts at collecting and systematizing -knowledge on almost every subject: and in this, as in almost every -other department, Aristotle may be fixed upon, as the representative -of the highest stage of knowledge and system which they ever -attained. The vegetable kingdom, like every other province of -nature, was one of the fields of the labors of this universal -philosopher. But though his other works on natural history have come -down to us, and are a most valuable monument of the state of such -knowledge in his time, his Treatise on Plants is lost. The book _De -Plantis_ {362} which appears with his name, is an imposture of the -middle ages, full of errors and absurdities.[11\16] - -[Note 11\16: Mirbel, _Botanique_, ii. 505.] - -His disciple, friend, and successor, Theophrastus of Eresos, is, as -we have said already, the first great writer on botany whose works -we possess; and, as may be said in most cases of the first great -writer, he offers to us a richer store of genuine knowledge and good -sense than all his successors. But we find in him that the Greeks of -his time, who aspired, as we have said, to collect and _systematize_ -a body of information on every subject, failed in one half of their -object, as far as related to the vegetable world. Their attempts at -a systematic distribution of plants were altogether futile. Although -Aristotle's divisions of the animal kingdom are, even at this day, -looked upon with admiration by the best naturalists, the -arrangements and comparisons of plants which were contrived by -Theophrastus and his successors, have not left the slightest trace -in the modern form of the science; and, therefore, according to our -plan, are of no importance in our history. And thus we can treat all -the miscellaneous information concerning vegetables which was -accumulated by the whole of this school of writers, in no other way -than as something antecedent to the first progress towards -systematic knowledge. - -The information thus collected by the unsystematic writers is of -various kinds; and relates to the economical and medicinal uses of -plants, their habits, mode of cultivation, and many other -circumstances: it frequently includes some description; but this is -always extremely imperfect, because the essential conditions of -description had not been discovered. Of works composed of materials -so heterogeneous, it can be of little use to produce specimens; but -I may quote a few words from Theophrastus, which may serve to -connect him with the future history of the science, as bearing upon -one of the many problems respecting the identification of ancient -and modern plants. It has been made a question whether the following -description does not refer to the potato.[12\16] He is speaking of -the differences of roots: "Some roots," he says, "are still -different from those which have been described; as that of the -_arachidna_[13\16] plant: for this bears fruit underground as well -as above: the fleshy part sends one thick root deep into the ground, -but the others, which bear the fruit, are more slender {363} and -higher up, and ramified. It loves a sandy soil, and has no leaf -whatever." - -[Note 12\16: Theoph. i. 11.] - -[Note 13\16: Most probably the _Arachnis hypogæa_, or ground-nut.] - -The books of Aristotle and Theophrastus soon took the place of the -Book of Nature in the attention of the degenerate philosophers who -succeeded them. A story is told by Strabo[14\16] concerning the fate -of the works of these great naturalists. In the case of the wars and -changes which occurred among the successors of Alexander, the heirs -of Theophrastus tried to secure to themselves his books, and those -of his master, by burying them in the ground. There the manuscripts -suffered much from damp and worms; till Apollonicon, a -book-collector of those days, purchased them, and attempted, in his -own way, to supply what time had obliterated. When Sylla marched the -Roman troops into Athens, he took possession of the library of -Apollonicon; and the works which it contained were soon circulated -among the learned of Rome and Alexandria, who were thus enabled to -_Aristotelize_[15\16] on botany as on other subjects. - -[Note 14\16: Strabo, lib. xiii. c. i. § 54.] - -[Note 15\16: Ἀριστοτλίζειν.] - -The library collected by the Attalic kings of Pergamus, and the -Alexandrian Museum, founded and supported by the Ptolemies of Egypt, -rather fostered the commentatorial spirit than promoted the increase -of any real knowledge of nature. The Romans, in this as in other -subjects, were practical, not speculative. They had, in the times of -their national vigor, several writers on agriculture, who were -highly esteemed; but no author, till we come to Pliny, who dwells on -the mere knowledge of plants. And even in Pliny, it is easy to -perceive that we have before us a writer who extracted his -information principally from books. This remarkable man,[16\16] in -the middle of a public and active life, of campaigns and voyages, -contrived to accumulate, by reading and study, an extraordinary -store of knowledge of all kinds. So unwilling was he to have his -reading and note-making interrupted, that, even before day-break in -winter, and from his litter as he travelled, he was wont to dictate -to his amanuensis, who was obliged to preserve his hand from the -numbness which the cold occasioned, by the use of gloves.[17\16] - -[Note 16\16: Sprengel, i. 163.] - -[Note 17\16: Plin. Jun. Epist. 3, 5.] - -It has been ingeniously observed, that we may find traces in the -botanical part of his Natural History, of the errors which this -hurried and broken habit of study produced; and that he appears -frequently to have had books read to him and to have heard them -amiss.[18\16] Thus, {364} among several other instances, -Theophrastus having said that the plane-tree is in Italy -rare,[19\16] Pliny, misled by the similarity of the Greek word -(_spanian_, rare), says that the tree occurs in Italy and -Spain.[20\16] His work has, with great propriety, been called the -Encyclopædia of Antiquity; and, in truth, there are few portions of -the learning of the times to which it does not refer. Of the -thirty-seven Books of which it consists, no less than sixteen (from -the twelfth to the twenty-seventh) relate to plants. The information -which is collected in these books, is of the most miscellaneous -kind; and the author admits, with little distinction, truth and -error, useful knowledge and absurd fables. The declamatory style, -and the comprehensive and lofty tone of thought which we have -already spoken of as characteristic of the Roman writers, are -peculiarly observable in him. The manner of his death is well known: -it was occasioned by the eruption of Vesuvius, A.D. 79, to which, in -his curiosity, he ventured so near as to be suffocated. - -[Note 18\16: Sprengel, i. 163.] - -[Note 19\16: Theoph. iv. 7. Ἔν μὲν γὰρ τῷ Ἀδρίᾳ πλάτανον οὐ φασὶν -εἶναι πλῆν περὶ το Διομήδους ἱερόν, _σπανίαν_ δὲ καὶ ἐν Ἰταλίᾳ πάσῃ] - -[Note 20\16: Plin. Nat. Hist. xii. 3. Et alias (platanos) fuisse in -Italia, ac nominatim _Hispania_, apud auctores invenitur.] - -Pliny's work acquired an almost unlimited authority, as one of the -standards of botanical knowledge, in the middle ages; but even more -than his, that of his contemporary, Pedanius Dioscorides, of -Anazarbus in Cilicia. This work, written in Greek, is held by the -best judges[21\16] to offer no evidence that the author observed for -himself. Yet he says expressly in his Preface, that his love of -natural history, and his military life, have led him into many -countries, in which he has had opportunity to become acquainted with -the nature of herbs and trees.[22\16] He speaks of six hundred -plants, but often indicates only their names and properties, giving -no description by which they can be identified. The main cause of -his great reputation in subsequent times was, that he says much of -the medicinal virtues of vegetables. - -[Note 21\16: Mirbel, 510.] - -[Note 22\16: Sprengel, i. 136.] - -We come now to the ages of darkness and lethargy, when the habit of -original thought seems to die away, as the talent of original -observation had done before. Commentators and mystics succeed to the -philosophical naturalists of better times. And though a new race, -altogether distinct in blood and character from the Greek, -appropriates to itself the stores of Grecian learning, this movement -does not, as might be expected, break the chains of literary -slavery. The Arabs {365} bring, to the cultivation of the science of -the Greeks, their own oriental habit of submission, their oriental -love of wonder; and thus, while they swell the herd of commentators -and mystics, they produce no philosopher. - -Yet the Arabs discharged an important function in the history of -human knowledge,[23\16] by preserving, and transmitting to more -enlightened times, the intellectual treasures of antiquity. The -unhappy dissensions which took place in the Christian church had -scattered these treasures over the East, at a period much antecedent -to the rise of the Saracen power. In the fifth century, the -adherents of Nestorius, bishop of Constantinople, were declared -heretical by the Council of Ephesus (A.D. 431), and driven into -exile. In this manner, many of the most learned and ingenious men of -the Christian world were removed to the Euphrates, where they formed -the _Chaldean_ church, erected the celebrated Nestorian school of -Edessa, and gave rise to many offsets from this in various regions. -Already, in the fifth century, Hibas, Cumas, and Probus, translated -the writings of Aristotle into Syriac. But the learned Nestorians -paid an especial attention to the art of medicine, and were the most -zealous students of the works of the Greek physicians. At -Djondisabor, in Khusistan, they became an ostensible medical school, -who distributed academical honors as the result of public -disputations. The califs of Bagdad heard of the fame and the wisdom -of the doctors of Djondisabor, summoned some of them to Bagdad, and -took measures for the foundation of a school of learning in that -city. The value of the skill, the learning, and the virtues of the -Nestorians, was so strongly felt, that they were allowed by the -Mohammedans the free exercise of the Christian religion, and -intrusted with the conduct of the studies of those of the Moslemin, -whose education was most cared for. The affinity of the Syriac and -Arabic languages made the task of instruction more easy. The -Nestorians translated the works of the ancients out of the former -into the latter language: hence there are still found Arabic -manuscripts of Dioscorides, with Syriac words in the margin. Pliny -and Aristotle likewise assumed an Arabic dress; and were, as well as -Dioscorides, the foundation of instruction in all the Arabian -academies; of which a great number were established throughout the -Saracen empire, from Bokhara in the remotest east, to Marocco and -Cordova in the west. After some time, the Mohammedans themselves -began to translate and {366} extract from their Syriac sources; and -at length to write works of their own. And thus arose vast -libraries, such as that of Cordova, which contained 250,000 volumes. - -[Note 23\16: Sprengel, i. 203.] - -The Nestorians are stated[24\16] to have first established among the -Arabs those collections of medicinal substances (_Apothecæ_), from -which our term _Apothecary_ is taken; and to have written books -(_Dispensatoria_) containing systematic instructions for the -employment of these medicaments; a word which long continued to be -implied in the same sense, and which we also retain, though in a -modified application (_Dispensary_). - -[Note 24\16: Sprengel, i. 205.] - -The directors of these collections were supposed to be intimately -acquainted with plants; and yet, in truth, the knowledge of plants -owed but little to them; for the Arabic Dioscorides was the source -and standard of their knowledge. The flourishing commerce of the -Arabians, their numerous and distant journeys, made them, no doubt, -practically acquainted with the productions of lands unknown to the -Greeks and Romans. Their Nestorian teachers had established -Christianity even as far as China and Malabar; and their travellers -mention[25\16] the camphor of Sumatra, the aloe-wood of Socotra near -Java, the tea of China. But they never learned the art of converting -their practical into speculative knowledge. They treat of plants -only in so far as their use in medicine is concerned,[26\16] and -followed Dioscorides in the description, and even in the order of -the plants, except when they arrange them according to the Arabic -alphabet. With little clearness of view, they often mistake what -they read:[27\16] thus when Dioscorides says that _ligusticon_ grows -on the _Apennine_, a mountain not far from the _Alps_; Avicenna, -misled by a resemblance of the Arabic letters, quotes him as saying -that the plant grows on _Akabis_, a mountain near _Egypt_. - -[Note 25\16: Sprengel, i. 206.] - -[Note 26\16: Ib. i. 207.] - -[Note 27\16: Ib. i. 211.] - -It is of little use to enumerate such writers. One of the most noted -of them was Mesuë, physician of the Calif of Kahirah. His work, -which was translated into Latin at a later period, was entitled, _On -Simple Medicines_; a title which was common to many medical -treatises, from the time of Galen in the second century. Indeed, of -this opposition of _simple_ and _compound_ medicines, we still have -traces in our language: {367} - He would ope his leathern scrip, - And show me _simples_ of a thousand names, - Telling their strange and vigorous faculties. - MILTON, _Comus_. - -Where the subject of our history is so entirely at a stand, it is -unprofitable to dwell on a list of names. The Arabians, small as -their science was, were able to instruct the Christians. Their -writings were translated by learned Europeans, for instance Michael -Scot, and Constantine of Africa, a Carthaginian who had lived forty -years among the Saracens[28\16] and who died A.D. 1087. Among his -works, is a Treatise, _De Gradibus_, which contains the Arabian -medicinal lore. In the thirteenth century occur Encyclopædias, as -that of Albertus Magnus, and of Vincent of Beauvais; but these -contain no natural history except traditions and fables. Even the -ancient writers were altogether perverted and disfigured. The -Dioscorides of the middle ages varied materially from ours.[29\16] -Monks, merchants, and adventurers travelled far, but knowledge was -little increased. Simon of Genoa,[30\16] a writer on plants in the -fourteenth century, boasts that he perambulated the East in order to -collect plants. "Yet in his _Clavis Sanationis_," says a modern -botanical writer,[31\16] "we discover no trace of an acquaintance -with nature. He merely compares the Greek, Arabic, and Latin names -of plants, and gives their medicinal effect after his -predecessors:"--so little true is it, that the use of the senses -alone necessarily leads to real knowledge. - -[Note 28\16: Sprengel, i. 230.] - -[Note 29\16: Ib. i. 239.] - -[Note 30\16: Ib. i. 241.] - -[Note 31\16: Ib. ib.] - -Though the growing activity of thought in Europe, and the revived -acquaintance with the authors of Greece in their genuine form, were -gradually dispelling the intellectual clouds of the middle ages, yet -during the fifteenth century, botany makes no approach to a -scientific form. The greater part of the literature of this subject -consisted of Herbals, all of which were formed on the same plan, and -appeared under titles such as _Hortus_, or _Ortus Sanitatis_. There -are, for example, three[32\16] such German Herbals, with woodcuts, -which date about 1490. But an important peculiarity in these works -is that they contain some indigenous species placed side by side -with the old ones. In 1516, _The Grete Herbal_ was published in -England, also with woodcuts. It contains an account of more than -four hundred vegetables, and their {368} products; of which one -hundred and fifty are English, and are no way distinguished from the -exotics by the mode in which they are inserted in the work. - -[Note 32\16: Augsburg, 1488. Mainz, 1491. Lubec, 1492.] - -We shall see, in the next chapter, that when the intellect of Europe -began really to apply itself to the observation of nature, the -progress towards genuine science soon began to be visible, in this -as in other subjects; but before this tendency could operate freely, -the history of botany was destined to show, in another instance, how -much more grateful to man, even when roused to intelligence and -activity, is the study of tradition than the study of nature. When -the scholars of Europe had become acquainted with the genuine works -of the ancients in the original languages, the pleasure and -admiration which they felt, led them to the most zealous endeavors -to illustrate and apply what they read. They fell into the error of -supposing that the plants described by Theophrastus, Dioscorides, -Pliny, must be those which grew in their own fields. And thus -Ruellius,[33\16] a French physician, who only travelled in the -environs of Paris and Picardy, imagined that he found there the -plants of Italy and Greece. The originators of genuine botany in -Germany, Brunfels and Tragus (Bock), committed the same mistake; and -hence arose the misapplication of classical names to many genera. -The labors of many other learned men took the same direction, of -treating the ancient writers as if they alone were the sources of -knowledge and truth. - -[Note 33\16: _De Natura Stirpium_, 1536.] - -But the philosophical spirit of Europe was already too vigorous to -allow this superstitious erudition to exercise a lasting sway. -Leonicenus, who taught at Ferrara till he was almost a hundred years -old, and died in 1524,[34\16] disputed, with great freedom, the -authority of the Arabian writers, and even of Pliny. He saw, and -showed by many examples, how little Pliny himself knew of nature, -and how many errors he had made or transmitted. The same -independence of thought with regard to other ancient writers, was -manifested by other scholars. Yet the power of ancient authority -melted away but gradually. Thus Antonius Brassavola, who established -on the banks of the Po the first botanical garden of modern times, -published in 1536, his _Examen omnium Simplicium Medicamentorum_; -and, as Cuvier says,[35\16] though he studied plants in nature, his -book (written in the {369} Platonic form of dialogue), has still the -character of a commentary on the ancients. - -[Note 34\16: Sprengel, i. 252.] - -[Note 35\16: _Hist. des Sc. Nat._ partie ii. 169.] - -The Germans appear to have been the first to liberate themselves -from this thraldom, and to publish works founded mainly on actual -observation. The first of the botanists who had this great merit is -Otho Brunfels of Mentz, whose work, _Herbarum Vivæ Icones_, appeared -in 1530. It consists of two volumes in folio, with wood-cuts; and in -1532, a German edition was published. The plants which it contains -are given without any arrangement, and thus he belongs to the period -of unsystematic knowledge. Yet the progress towards the formation of -a system manifested itself so immediately in the series of German -botanists to which he belongs, that we might with almost equal -propriety transfer him to the history of that progress; to which we -now proceed. - - - - -CHAPTER III. - -FORMATION OF A SYSTEM OF ARRANGEMENT OF PLANTS. - - -_Sect._ 1.--_Prelude to the Epoch of Cæsalpinus._ - -THE arrangement of plants in the earliest works was either -arbitrary, or according to their use, or some other extraneous -circumstance, as in Pliny. This and the division of vegetables by -Dioscorides into _aromatic_, _alimentary_, _medicinal_, _vinous_, -is, as will be easily seen, a merely casual distribution. The -Arabian writers, and those of the middle ages, showed still more -clearly their insensibility to the nature of system, by adopting an -alphabetical arrangement; which was employed also in the Herbals of -the sixteenth century. Brunfels, as we have said, adopted no -principle of order; nor did his successor, Fuchs. Yet the latter -writer urged his countrymen to put aside their Arabian and barbarous -Latin doctors, and to observe the vegetable kingdom for themselves; -and he himself set the example of doing this, examined plants with -zeal and accuracy, and made above fifteen hundred drawings of -them.[36\16] {370} - -[Note 36\16: His _Historia Stirpium_ was published at Basil in 1542.] - -The difficulty of representing plants in any useful way by means of -drawings, is greater, perhaps, than it at first appears. So long as -no distinction was made of the importance of different organs of the -plant, a picture representing merely the obvious general appearance -and larger parts, was of comparatively small value. Hence we are not -to wonder at the slighting manner in which Pliny speaks of such -records. "Those who gave such pictures of plants," he says, -"Crateuas, Dionysius, Metrodorus, have shown nothing clearly, except -the difficulty of their undertaking. A picture may be mistaken, and -is changed and disfigured by copyists; and, without these -imperfections, it is not enough to represent the plant in one state, -since it has four different aspects in the four seasons of the year." - -The diffusion of the habit of exact drawing, especially among the -countrymen of Albert Durer and Lucas Cranach, and the invention of -wood-cuts and copper-plates, remedied some of these defects. -Moreover, the conviction gradually arose in men's minds that the -structure of the flower and the fruit are the most important -circumstances in fixing the identity of the plant. Theophrastus -speaks with precision of the organs which he describes, but these -are principally the leaves, roots, and stems. Fuchs uses the term -_apices_ for the anthers, and _gluma_ for the blossom of grasses, -thus showing that he had noticed these parts as generally present. - -In the next writer whom we have to mention, we find some traces of a -perception of the real resemblances of plants beginning to appear. -It is impossible to explain the progress of such views without -assuming in the reader some acquaintance with plants; but a very few -words may suffice to convey the requisite notions. Even in plants -which most commonly come in our way, we may perceive instances of -the resemblances of which we speak. Thus, Mint, Marjoram, Basil, -Sage, Lavender, Thyme, Dead-nettle, and many other plants, have a -tubular flower, of which the mouth is divided into two lips; hence -they are formed into a family, and termed _Labiatæ_. Again, the -Stock, the Wall-flower, the Mustard, the Cress, the Lady-smock, the -Shepherd's purse, have, among other similarities, their blossoms -with four petals arranged crosswise; these are all of the order -_Cruciferæ_. Other flowers, apparently more complex, still resemble -each other, as Daisy. Marigold, Aster, and Chamomile; these belong -to the order _Compositæ_. And though the members of each such family -may differ widely in their larger parts, their stems and leaves, the -close study of nature leads the botanist irresistibly to consider -their resemblances as {371} occupying a far more important place -than their differences. It is the general establishment of this -conviction and its consequences which we have now to follow. - -The first writer in whom we find the traces of an arrangement -depending upon these natural resemblances, is Hieronymus Tragus, -(Jerom Bock,) a laborious German botanist, who, in 1551, published a -herbal. In this work, several of the species included in those -natural families to which we have alluded,[37\16] as for instance -the Labiatæ, the Cruciferæ, the Compositæ, are for the most part -brought together; and thus, although with many mistakes as to such -connexions, a new principle of order is introduced into the subject. - -[Note 37\16: Sprengel, i. 270.] - -In pursuing the development of such principles of natural order, it -is necessary to recollect that the principles lead to an assemblage -of divisions and groups, successively subordinate, the lower to the -higher, like the brigades, regiments, and companies of an army, or -the provinces, towns, and parishes of a kingdom. Species are -included in Genera, Genera in Families or Orders, and orders in -Classes. The perception that there is some connexion among the -species of plants, was the first essential step; the detection of -different marks and characters which should give, on the one hand, -limited groups, on the other, comprehensive divisions, were other -highly important parts of this advance. To point out every -successive movement in this progress would be a task of extreme -difficulty, but we may note, as the most prominent portions of it, -the establishment of the groups which immediately include Species, -that is, _the formation of Genera_; and the invention of a method -which should distribute into consistent and distinct divisions the -whole vegetable kingdom, that is, _the construction of a System_. - -To the second of these two steps we have no difficulty in assigning -its proper author. It belongs to Cæsalpinus, and marks the first -great epoch of this science. It is less easy to state to what -botanist is due the establishment of Genera; yet we may justly -assign the greater part of the merit of this invention, as is -usually done, to Conrad Gessner of Zurich. This eminent naturalist, -after publishing his great work on animals, died[38\16] of the -plague in 1565, at the age of forty-nine, while he was preparing to -publish a History of Plants, a sequel to his History of Animals. The -fate of the work thus left {372} unfinished was remarkable. It fell -into the hands of his pupil, Gaspard Wolf, who was to have published -it, but wanting leisure for the office, sold it to Joachim -Camerarius, a physician and botanist of Nuremberg, who made use of -the engravings prepared by Gessner, in an Epitome which he published -in 1586. The text of Gessner's work, after passing through various -hands, was published in 1754 under the title of _Gessneri Opera -Botanica per duo Sæcula desiderata, &c._, but is very incomplete. - -[Note 38\16: Cuvier, _Leçons sur l'Hist. des Sciences Naturelles_, -partie ii. p. 193.] - -The imperfect state in which Gessner left his botanical labors, -makes it necessary to seek the evidence of his peculiar views in -scattered passages of his correspondence and other works. One of his -great merits was, that he saw the peculiar importance of the flower -and fruit as affording the characters by which the affinities of -plants were to be detected; and that he urged this view upon his -contemporaries. His plates present to us, by the side of each plant, -its flower and its fruit, carefully engraved. And in his -communications with his botanical correspondents, he repeatedly -insists on these parts. Thus[39\16] in 1565 he writes to Zuinger -concerning some foreign plants which the latter possessed: "Tell me -if your plants have fruit and flower, as well as stalk and leaves, -for those are of much the greater consequence. By these three -marks,--flower, fruit, and seed,--I find that Saxifraga and -Consolida Regalis are related to Aconite." These characters, derived -from the _fructification_ (as the assemblage of flower and fruit is -called), are the means by which genera are established, and hence, -by the best botanists, Gessner is declared to be the inventor of -genera.[40\16] {373} - -[Note 39\16: _Epistolæ_, fol. 113 a; see also fol. 65 b.] - -[Note 40\16: Haller, _Biblio Botanica_, i. 284. Methodi Botanicæ -rationem primus pervidit;--dari nempe et genera quæ plures species -comprehenderent et classes quæ multa genera. Varias etiam classes -naturales expressit. Characterem in flore inque semine posuit, -&c.--_Rauwolfio Socio Epist._ Wolf, p. 39. - -Linnæus, _Genera Plantarum_, Pref. xiii. "A fructificatione plantas -distinguere in genera, infinitæ sapientiæ placuisse, detexit -posterior ætas, et quidem primus, sæculi sui ornamentum, Conradus -Gessnerus, uti patet ex Epistolis ejus postremis, et Tabulis per -Carmerarium editis." - -Cuvier says (_Hist. des Sc. Nat._ 2^e p^e, p. 193), after speaking to -the same effect, "Il fit voir encore que toutes les plantes qui ont -des fleurs et des fruits semblables se ressemblent par leurs -propriétés, et que quand on rapproche ces plantes on obtient ainsi une -classification naturelle." I do not know if he here refers to any -particular passages of Gessner's work.] - -The labors of Gessner in botany, both on account of the unfinished -state in which he left the application of his principles, and on -account of the absence of any principles manifestly applicable to -the whole extent of the vegetable kingdom, can only be considered as -a prelude to the epoch in which those defects were supplied. To that -epoch we now proceed. - - -_Sect._ 2.--_Epoch of Cæsalpinus.--Formation of a System of -Arrangement._ - -IF any one were disposed to question whether Natural History truly -belongs to the domain of Inductive Science;--whether it is to be -prosecuted by the same methods, and requires the same endowments of -mind as those which lead to the successful cultivation of the -Physical Sciences,--the circumstances under which Botany has made -its advance appear fitted to remove such doubts. The first decided -step in this study was merely the construction of a classification -of its subjects. We shall, I trust, be able to show that such a -classification includes, in reality, the establishment of one -general principle, and leads to more. But without here dwelling on -this point, it is worth notice that the person to whom we owe this -classification, Andreas Cæsalpinus of Arezzo, was one of the most -philosophical men of his time, profoundly skilled in the -Aristotelian lore which was then esteemed, yet gifted with courage -and sagacity which enabled him to weigh the value of the Peripatetic -doctrines, to reject what seemed error, and to look onwards to a -better philosophy. "How are we to understand," he inquires, "that we -must proceed from universals to particulars (as Aristotle directs), -when particulars are better known?"[41\16] Yet he treats the Master -with deference, and, as has been observed,[42\16] we see in his -great botanical work deep traces of the best features of the -Aristotelian school, logic and method; and, indeed, in this work he -frequently refers to his _Quæstiones Peripateticæ_. His book, -entitled _De Plantis libri_ xvi. appeared at Florence in 1583. The -aspect under which his task presented itself to his mind appears to -me to possess so much interest, that I will transcribe a few of his -reflections. After speaking of the splendid multiplicity of the -productions of nature, and the confusion which has hitherto -prevailed among writers on plants, {374} the growing treasures of -the botanical world; he adds,[43\16] "In this immense multitude of -plants, I see that want which is most felt in any other unordered -crowd: if such an assemblage be not arranged into brigades like an -army, all must be tumult and fluctuation. And this accordingly -happens in the treatment of plants: for the mind is overwhelmed by -the confused accumulation of things, and thus arise endless mistake -and angry altercation." He then states his general view, which, as -we shall see, was adopted by his successors. "_Since all science -consists in the collection of similar, and the distinction of -dissimilar things_, and since the consequence of this is a -distribution into genera and species, which are to be natural -classes governed by real differences, I have attempted to execute -this task in the whole range of plants;--ut si quid pro ingenii mei -tenuitate in hujusmodi studio profecerim, ad communem utilitatem -proferam." We see here how clearly he claims for himself the credit -of being the first to execute this task of arrangement. - -[Note 41\16: _Quæstiones Peripateticæ_, (1569,) lib. i. quæst. i.] - -[Note 42\16: Cuvier, p. 198.] - -[Note 43\16: Dedicatio, a 2.] - -After certain preparatory speculations, he says,[44\16] "Let us now -endeavor to mark the kinds of plants by essential circumstances in -the fructification." He then observes, "In the constitution of -organs three things are mainly important--the number, the position, -the figure." And he then proceeds to exemplify this: "Some have -under one flower, ONE _seed_, as _Amygdala_, or ONE -seed-_receptacle_, as _Rosa_; or TWO _seeds_, as _Ferularia_, or TWO -seed-_receptacles_, as _Nasturtium_; or three, as the _Tithymalum_ -kind have THREE _seeds_, the _Bulbaceæ_ THREE _receptacles_; or -four, as _Marrubium_, FOUR _seeds_, _Siler_ FOUR _receptacles_; or -more, as _Cicoraceæ_, and _Acanaceæ_ have MORE _seeds_, _Pinus_, -MORE _receptacles_." - -[Note 44\16: Lib. i. c. 13, 14.] - -It will be observed that we have here ten classes made out by means -of number alone, added to the consideration of whether the seed is -alone in its covering, as in a cherry, or contained in a receptacle -with several others, as in a berry, pod, or capsule. Several of -these divisions are, however, further subdivided according to other -circumstances, and especially according as the vital part of the -seed, which he called the heart (_cor_[45\16]), is situated in the -upper or lower part of the seed. As our object here is only to -indicate the principle of the method of Cæsalpinus, I need not -further dwell on the details, and still less on the defects by which -it is disfigured, as, for instance, the retention of the old -distinction of Trees, Shrubs, and Herbs. {375} - -[Note 45\16: _Corculum_, of Linnæus.] - -To some persons it may appear that this arbitrary distribution of -the vegetable kingdom, according to the number of parts of a -particular kind, cannot deserve to be spoken of as a great -discovery. And if, indeed, the distribution had been arbitrary, this -would have been true; the real merit of this and of every other -system is, that while it is artificial in its form, it is natural in -its results. The plants which are associated by the arrangement of -Cæsalpinus, are those which have the closest resemblances in the -most essential points. Thus, as Linnæus says, though the first in -attempting to form natural orders, he observed as many as the most -successful of later writers. Thus his _Legumina_[46\16] correspond -to the natural order _Leguminosæ_; his _genus Ferulaceum_[47\16] to -the _Umbellatæ_; his _Bulbaceæ_[48\16] to _Liliaceæ_; his -_Anthemides_[49\16] to the _Compositæ_; in like manner, the -_Boragineæ_ are brought together,[50\16] and the _Labiatæ_. That -such assemblages are produced by the application of his principles, -is a sufficient evidence that they have their foundation in the -general laws of the vegetable world. If this had not been the case, -the mere application of number or figure alone as a standard of -arrangement, would have produced only intolerable anomalies. If, for -instance, Cæsalpinus had arranged plants by the number of flowers on -the same stalk, he would have separated individuals of the same -species; if he had distributed them according to the number of -leaflets which compose the leaves, he would have had to place far -asunder different species of the same genus. Or, as he himself -says,[51\16] "If we make one genus of those which have a round root, -as Rapum, Aristolochia, Cyclaminus, Aton, we shall separate from -this genus those which most agree with it, as Napum and Raphanum, -which resemble Rapum, and the long Aristolochia, which resembles the -round; while we shall join the most remote kinds, for the nature of -Cyclaminus and Rapum is altogether diverse in all other respects. Or -if we attend to the differences of stalk, so as to make one genus of -those which have a naked stalk, as the Junci, Cæpe, Aphacæ, along -with Cicoraceæ, Violæ, we shall still connect the most unlike -things, and disjoin the closest affinities. And if we note the -differences of leaves, or even flowers, we fall into the same -difficulty; for many plants very different in kind have leaves very -similar, as Polygonum and Hypericum, Ernea and Sesamois, Apium and -Ranunculus; and plants of the same genus have sometimes very -different {376} leaves, as the several species of Ranunculus and of -Lactuca. Nor will color or shape of the flowers help us better; for -what has Vitis in common with Œnanthe, except the resemblance of the -flower?" He then goes on to say, that if we seek a too close -coincidence of all the characters we shall have no Species; and thus -shows us that he had clearly before his view the difficulty, which -he had to attack, and which it is his glory to have overcome, that -of constructing Natural Orders. - -[Note 46\16: Lib. vi.] - -[Note 47\16: Lib. vii.] - -[Note 48\16: Lib. x.] - -[Note 49\16: Lib. xii.] - -[Note 50\16: Lib. xi.] - -[Note 51\16: Lib. i. cap. xii. p. 25.] - -But as the principles of Cæsalpinus are justified, on the one hand, -by their leading to _Natural Orders_, they are recommended on the -other by their producing a _System_ which applies through the whole -extent of the vegetable kingdom. The parts from which he takes his -characters must occur in all flowering-plants, for all such plants -have seeds. And these seeds, if not very numerous for each flower, -will be of a certain definite number and orderly distribution. And -thus every plant will fall into one part or other of the same system. - -It is not difficult to point out, in this induction of Cæsalpinus, -the two elements which we have so often declared must occur in all -inductive processes; the exact acquaintance with _facts_, and the -general and applicable _ideas_ by which these facts are brought -together. Cæsalpinus was no mere dealer in intellectual relations or -learned traditions, but a laborious and persevering collector of -plants and of botanical knowledge. "For many years," he says in his -Dedication, "I have been pursuing my researches in various regions, -habitually visiting the places in which grew the various kinds of -herbs, shrubs, and trees; I have been assisted by the labors of many -friends, and by gardens established for the public benefit, and -containing foreign plants collected from the most remote regions." -He here refers to the first garden directed to the public study of -Botany, which was that of Pisa,[52\16] instituted in 1543, by order -of the Grand Duke Cosmo the First. The management of it was confided -first to Lucas Ghini, and afterwards to Cæsalpinus. He had collected -also a herbarium of dried plants, which he calls the rudiment of his -work. "Tibi enim," he says, in his dedication to Francis Medici, -Grand Duke of Etruria, "apud quem extat ejus rudimentum ex plantis -libro agglutinatis a me compositum." And, throughout, he speaks with -the most familiar and vivid acquaintance of the various vegetables -which he describes. - -[Note 52\16: Cuv. 187.] - -But Cæsalpinus also possessed fixed and general views concerning the -relation and functions of the parts of plants, and ideas of symmetry -{377} and system; without which, as we see in other botanists of his -and succeeding times, the mere accumulation of a knowledge of -details does not lead to any advance in science. We have already -mentioned his reference to general philosophical principles, both of -the Peripatetics and of his own. The first twelve chapters of his -work are employed in explaining the general structure of plants, and -especially that point to which he justly attaches so much -importance, the results of the different situation of the _cor_ or -_corculum_ of the seed. He shows[53\16] that if we take the root, or -stem, or leaves, or blossom, as our guide in classification, we -shall separate plants obviously alike, and approximate those which -have merely superficial resemblances. And thus we see that he had in -his mind ideas of fixed resemblance and symmetrical distribution, -which he sedulously endeavored to apply to plants; while his -acquaintance with the vegetable kingdom enabled him to see in what -manner these ideas were not, and in what manner they were, really -applicable. - -[Note 53\16: Lib. i. cap. xii.] - -The great merit and originality of Cæsalpinus have been generally -allowed, by the best of the more modern writers on Botany. Linnæus -calls him one of the founders of the science; "Primus verus -systematicus;"[54\16] and, as if not satisfied with the expression -of his admiration in prose, hangs a poetical garland on the tomb of -his hero. The following distich concludes his remarks on this -writer: - Quisquis hic extiterit primos concedet honores - Cæsalpine tibi; primaque serta dabit: -and similar language of praise has been applied to him by the best -botanists up to Cuvier,[55\16] who justly terms his book "a work of -genius." - -[Note 54\16: _Philosoph. Bot._ p. 19.] - -[Note 55\16: Cuv. _Hist._ 193.] - -Perhaps the great advance made in this science by Cæsalpinus, is -most strongly shown by this; that no one appeared, to follow the -path which he had opened to system and symmetry, for nearly a -century. Moreover, when the progress of this branch of knowledge was -resumed, his next successor, Morison, did not choose to acknowledge -that he had borrowed so much from so old a writer; and thus, hardly -mentions his name, although he takes advantage of his labors, and -even transcribes his words without acknowledgement, as I shall show. -The pause between the great invention of Cæsalpinus, and its natural -sequel, the developement and improvement of his method, is so -marked, that I {378} will, in order to avoid too great an -interruption of chronological order, record some of its -circumstances in a separate section. - - -_Sect._ 3.--_Stationary Interval._ - -THE method of Cæsalpinus was not, at first, generally adopted. It -had, indeed, some disadvantages. Employed in drawing the -boundary-lines of the larger divisions of the vegetable kingdom, he -had omitted those smaller groups, Genera, which were both most -obvious to common botanists, and most convenient in the description -and comparison of plants. He had also neglected to give the Synonyms -of other authors for the plants spoken of by him; an appendage to -botanical descriptions, which the increase of botanical information -and botanical books had now rendered indispensable. And thus it -happened, that a work, which must always be considered as forming a -great epoch in the science to which it refers, was probably little -read, and in a short time could be treated as if it were quite -forgotten. - -In the mean time, the science was gradually improved in its details. -Clusius, or Charles de l'Ecluse, first taught botanists to describe -well. "Before him," says Mirbel,[56\16] "the descriptions were -diffuse, obscure, indistinct; or else concise, incomplete, vague. -Clusius introduced exactitude, precision, neatness, elegance, -method: he says nothing superfluous; he omits nothing necessary." He -travelled over great part of Europe, and published various works on -the more rare of the plants which he had seen. Among such plants, we -may note now one well known, the potato; which he describes as being -commonly used in Italy in 1586;[57\16] thus throwing doubt, at -least, on the opinion which ascribes the first introduction of it -into Europe to Sir Walter Raleigh, on his return from Virginia, -about the same period. As serving to illustrate, both this point, -and the descriptive style of Clusius, I quote, in a note, his -description of the flower of this plant.[58\16] {379} - -[Note 56\16: _Physiol. Veg._ p. 525.] - -[Note 57\16: Clusius. _Exotic_. iv. c. 52, p. lxxix.] - -[Note 58\16: "Papas Peruanorum. Arachidna, Theoph. forte. Flores -elegantes, uncialis amplitudinis aut majores, angulosi, singulari -folio constantes, sed ita complicato ut quinque folia discreta -videantur, coloris exterius ex purpura candicantis, interius -purpurascentis, radiis quinque herbaceis ex umbilico stellæ instar -prodeuntibus, et totidem staminibus flavis in umbonem coeuntibus." - -He says that the Italians do not know whence they had the plant, and -that they call it _Taratouffli_. The name _Potato_ was, in England, -previously applied to the Sweet Potato (_Convolvulus batatas_), -which was the _common_ Potato, in distinction to the _Virginian -_Potato, at the time of Gerard's Herbal. (1597?) Gerard's figures of -both plants are copied from those of Clusius. - -It may be seen by the description of Arachidna, already quoted from -Theophrastus, (above,) that there is little plausibility in -Clusius's conjecture of the plant being known to the ancients. I -need not inform the botanist that this opinion is untenable.] - -The addition of exotic species to the number of known plants was -indeed going on rapidly during the interval which we are now -considering. Francis Hernandez, a Spaniard, who visited America -towards the end of the sixteenth century, collected and described -many plants of that country, some of which were afterwards published -by Recchi.[59\16] Barnabas Cobo, who went as a missionary to America -in 1596, also described plants.[60\16] The Dutch, among other -exertions which they made in their struggle with the tyranny of -Spain, sent out an expedition which, for a time, conquered the -Brazils; and among other fruits of this conquest, they published an -account of the natural history of the country.[61\16] To avoid -interrupting the connexion of such labors, I will here carry them on -a little further in the order of time. Paul Herman, of Halle, in -Saxony, went to the Cape of Good Hope and to Ceylon; and on his -return, astonished the botanists of Europe by the vast quantity of -remarkable plants which he introduced to their knowledge.[62\16] -Rheede, the Dutch governor of Malabar, ordered descriptions and -drawings to be made of many curious species, which were published in -a large work in twelve folio volumes.[63\16] Rumphe, another Dutch -consul at Amboyna,[64\16] labored with zeal and success upon the -plants of the Moluccas. Some species which occur in Madagascar -figured in a description of that island composed by the French -Commandant Flacourt.[65\16] Shortly afterwards, Engelbert -Kæmpfer,[66\16] a Westphalian of great acquirements and undaunted -courage, visited Persia, Arabia Felix, the Mogul Empire, Ceylon, -Bengal, Sumatra, Java, Siam, Japan; Wheler travelled in Greece and -Asia Minor; and Sherard, the English consul, published an account of -the plants of the neighborhood of Smyrna. {380} - -[Note 59\16: _Nova Plantarum Regni Mexicana Historia_, Rom. 1651, -fol.] - -[Note 60\16: Sprengel, _Gesch. der Botanik_, ii. 62.] - -[Note 61\16: _Historia Naturalis Brasiliæ_, L. B. 1648, fol. (Piso -and Maregraf).] - -[Note 62\16: _Museum Zeylanicum_, L. B. 1726.] - -[Note 63\16: _Hortus Malabaricus_, 1670-1703.] - -[Note 64\16: _Herbarium Amboinense_, Amsterdam, 1741-51, fol.] - -[Note 65\16: _Histoire de la grande Isle Madagascar_, Paris, 1661.] - -[Note 66\16: _Amœnitates Exoticæ_, Lemgov. 1712. 4to.] - -At the same time, the New World excited also the curiosity of -botanists. Hans Sloane collected the plants of Jamaica; John -Banister those of Virginia; William Vernon, also an Englishman, and -David Kriege, a Saxon, those of Maryland; two Frenchmen, Surian and -Father Plumier, those of Saint Domingo. - -We may add that public botanical gardens were about this time -established all over Europe. We have already noticed the institution -of that of Pisa in 1543; the second was that of Padua in 1545; the -next, that of Florence in 1556; the fourth, that of Bologna, 1568; -that of Rome, in the Vatican, dates also from 1568. - -The first transalpine garden of this kind arose at Leyden in 1577; -that of Leipzig in 1580. Henry the Fourth of France established one -at Montpellier in 1597. Several others were instituted in Germany; -but that of Paris did not begin to exist till 1626; that of Upsal, -afterwards so celebrated, took its rise in 1657, that of Amsterdam -in 1684. Morison, whom we shall soon have to mention, calls himself, -in 1680, the first Director of the Botanical Garden at Oxford. - -[2nd Ed.] [To what is above said of Botanical Gardens and Botanical -Writers, between the times of Cæsalpinus and Morison, I may add a -few circumstances. The first academical garden in France was that at -Montpellier, which was established by Peter Richier de Belleval, at -the end of the sixteenth century. About the same period, rare -flowers were cultivated at Paris, and pictures of them made, in -order to supply the embroiderers of the court-robes with new -patterns. Thus figures of the most beautiful flowers in the garden -of Peter Robins were published by the court-embroiderer Peter -Vallet, in 1608, under the title of _Le Jardin du Roi Henry IV_. But -Robins' works were of great service to botany; and his garden -assisted the studies of Renealmus (Paul Reneaulme), whose _Specimen -Historiæ Plantarum_ (Paris, 1611), is highly spoken of by the best -botanists. Recently, Mr. Robert Brown has named after him a new -genus of _Irideæ_ (RENEALMIA); adding, "Dixi in memoriam PAULI -RENEALMI, botanici sui ævi accuratissimi, atque staminum primi -scrutatoris; qui non modo eorum numerum et situm, sed etiam -filamentorum proportionem passim descripsit, et characterem -tetradynamicum siliquosarum perspexit." (_Prodromus Floræ Novæ -Hollandiæ_, p. 448.) - -The oldest Botanical Garden in England is that at Hampton Court, -founded by Queen Elizabeth, and much enriched by Charles II. and -William III. (Sprengel, _Gesch. d. Bot._ vol. ii. p. 96.)] - -In the mean time, although there appeared no new system which {381} -commanded the attention of the botanical world, the feeling of the -importance of the affinities of plants became continually more -strong and distinct. - -Lobel, who was botanist to James the First, and who published his -_Stirpium Adversaria Nova_ in 1571, brings together the natural -families of plants more distinctly than his predecessors, and even -distinguishes (as Cuvier states,[67\16]) monocotyledonous from -dicotyledonous plants; one of the most comprehensive division-lines -of botany, of which succeeding times discovered the value more -completely. Fabius Columna,[68\16] in 1616, gave figures of the -fructification of plants on copper, as Gessner had before done on -wood. But the elder Bauhin (John), notwithstanding all that -Cæsalpinus had done, retrograded, in a work published in 1619, into -the less precise and scientific distinctions of--trees with nuts; -with berries; with acorns; with pods; creeping plants, gourds, &c.: -and no clear progress towards a system was anywhere visible among -the authors of this period. - -[Note 67\16: Cuv. _Leçons, &c._ 198.] - -[Note 68\16: Ib. 206.] - -While this continued to be the case, and while the materials, thus -destitute of order, went on accumulating, it was inevitable that the -evils which Cæsalpinus had endeavored to remedy, should become more -and more grievous. "The nomenclature of the subject[69\16] was in -such disorder, it was so impossible to determine with certainty the -plants spoken of by preceding writers, that thirty or forty -different botanists had given to the same plant almost as many -different names. Bauhin called by one appellation, a species which -Lobel or Matheoli designated by another. There was an actual chaos, -a universal confusion, in which it was impossible for men to find -their way." We can the better understand such a state of things, -from having, in our own time, seen another classificatory science, -Mineralogy, in the very condition thus described. For such a state -of confusion there is no remedy but the establishment of a true -system of classification; which by its real foundation renders a -reason for the place of each species; and which, by the fixity of -its classes, affords a basis for a standard nomenclature, as finally -took place in Botany. But before such a remedy is obtained, men -naturally try to alleviate the evil by tabulating the synonyms of -different writers, as far as they are able to do so. The task of -constructing such a _Synonymy_ of botany at the period of which we -speak, was undertaken by Gaspard Bauhin, the brother of John, but -nineteen years younger. This work, the _Pinax Theatri Botanici_, was -printed {382} at Basil in 1623. It was a useful undertaking at the -time; but the want of any genuine order in the _Pinax_ itself, -rendered it impossible that it should be of great permanent utility. - -[Note 69\16: Ib. 212.] - -After this period, the progress of almost all the sciences became -languid for a while; and one reason of this interruption was, the -wars and troubles which prevailed over almost the whole of Europe. -The quarrels of Charles the First and his parliament, the civil wars -and the usurpation, in England; in France, the war of the League, -the stormy reign of Henry the Fourth, the civil wars of the minority -of Louis the Thirteenth, the war against the Protestants and the war -of the Fronde in the minority of Louis the Fourteenth; the bloody -and destructive Thirty Years' War in Germany; the war of Spain with -the United Provinces and with Portugal;--all these dire agitations -left men neither leisure nor disposition to direct their best -thoughts to the promotion of science. The baser spirits were -brutalized; the better were occupied by high practical aims and -struggles of their moral nature. Amid such storms, the intellectual -powers of man could not work with their due calmness, nor his -intellectual objects shine with their proper lustre. - -At length a period of greater tranquillity gleamed forth, and the -sciences soon expanded in the sunshine. Botany was not inert amid -this activity, and rapidly advanced in a new direction, that of -physiology; but before we speak of this portion of our subject, we -must complete what we have to say of it as a classificatory science. - - -_Sect._ 4.--_Sequel to the Epoch of Cæsalpinus. Further Formation -and Adoption of Systematic Arrangement._ - -SOON after the period of which we now speak, that of the restoration -of the Stuarts to the throne of England, systematic arrangements of -plants appeared in great numbers; and in a manner such as to show -that the minds of botanists had gradually been ripening for this -improvement, through the influence of preceding writers, and the -growing acquaintance with plants. The person whose name is usually -placed first on this list, Robert Morison, appears to me to be much -less meritorious than many of those who published very shortly after -him; but I will give him the precedence in my narrative. He was a -Scotchman, who was wounded fighting on the royalist side in the -civil wars of England. On the triumph of the republicans, he -withdrew to France, when he became director of the garden of Gaston, -Duke of Orléans at Blois; and there he came under the notice of our -Charles {383} the Second; who, on his restoration, summoned Morison -to England, where he became Superintendent of the Royal Gardens, and -also of the Botanic Garden at Oxford. In 1669, he published _Remarks -on the Mistakes of the two Bauhins_, in which he proves that many -plants in the _Pinax_ are erroneously placed, and shows considerable -talent for appreciating natural families and genera. His great -systematic work appeared from the University press at Oxford in -1680. It contains a system, but a system, Cuvier says,[70\16] which -approaches rather to a natural method than to a rigorous -distribution, like that of his predecessor Cæsalpinus, or that of -his successor Ray. Thus the herbaceous plants are divided into -_climbers_, _leguminous_, _siliquose_, _unicapsalar_, _bicapsular_, -_tricapsular_, _quadricapsular_, _quinquecapsular_; this division -being combined with characters derived from the number of petals. -But along with these numerical elements, are introduced others of a -loose and heterogeneous kind, for instance, the classification of -herbs as _lactescent_ and _emollient_. It is not unreasonable to -say, that such a scheme shows no talent for constructing a complete -system; and that the most distinct part of it, that dependent on the -fruit, was probably borrowed from Cæsalpinus. That this is so, we -have, I think, strong proof; for though Morison nowhere, I believe, -mentions Cæsalpinus, except in one place in a loose enumeration of -botanical writers,[71\16] he must have made considerable use of his -work. For he has introduced into his own preface a passage copied -literally[72\16] from the dedication of Cæsalpinus; which passage we -have already quoted (p. 374,) beginning, "Since all science consists -in the collection of similar, and the distinction of dissimilar -things." And that the mention of the original is not omitted by -accident, appears from this; that Morison appropriates also the -conclusion of the passage, which has a personal reference, "_Conatus -sum id præstare in universa plantarum historia, ut si quid pro -ingenii mei tenuitate in hujusmodi studio profecerim, ad communem -utilitatem proferrem._" That Morison, thus, at so long an interval -after the publication of the work of Cæsalpinus, borrowed from him -without acknowledgement, and adopted his system so as to mutilate -it, proves that he had neither the temper nor the talent of a -discoverer; and justifies us withholding from him the credit which -belongs to those, who, in his time, resumed the great undertaking of -constructing a vegetable system. - -[Note 70\16: Cuv. _Leçons_, &c. p. 486.] - -[Note 71\16: Pref. p. i.] - -[Note 72\16: Ib. p. ii.] - -Among those whose efforts in this way had the greatest and earliest -{384} influence, was undoubtedly our countryman, John Ray, who was -Fellow of Trinity College, Cambridge, at the same time with Isaac -Newton. But though Cuvier states[73\16] that Ray was the model of -the systematists during the whole of the eighteenth century, the -Germans claim a part of his merit for one of their countrymen, -Joachim Jung, of Lubeck, professor at Hamburg.[74\16] Concerning the -principles of this botanist, little was known during his life. But a -manuscript of his book was communicated[75\16] to Ray in 1660, and -from this time forwards, says Sprengel, there might be noticed in -the writings of Englishmen, those better and clearer views to which -Jung's principles gave birth. Five years after the death of Jung, -his _Doxoscopia Physica_ was published, in 1662; and in 1678, his -_Isagoge Phytoscopica_. But neither of these works was ever much -read; and even Linnæus, whom few things escaped which concerned -botany, had, in 1771, seen none of Jung's works. - -[Note 73\16: _Leçons Hist. Sc._ p. 487.] - -[Note 74\16: Sprengel, ii. 27.] - -[Note 75\16: Ray acknowledges this in his _Index Plant. Agri -Cantab._ p. 87, and quotes from it the definition of _caulis_.] - -I here pass over Jung's improvements of botanical language, and -speak only of those which he is asserted to have suggested in the -arrangement of plants. He examines, says Sprengel,[76\16] the value -of characters of species, which, he holds, must not be taken from -the thorns, nor from color, taste, smell, medicinal effects, time -and place of blossoming. He shows, in numerous examples, what plants -must be separated, though called by a common name, and what most be -united, though their names are several. - -[Note 76\16: Sprengel, ii. 29.] - -I do not see in this much that interferes with the originality of -Ray's method,[77\16] of which, in consequence of the importance -ascribed to it by Cuvier, as we have already seen, I shall give an -account, following that great naturalist.[78\16] I confine myself to -the ordinary plants, and omit the more obscure vegetables, as -mushrooms, mosses, ferns, and the like. - -[Note 77\16: _Methodus Plantarum Nova_, 1682. _Historia Plantarum_, -1686.] - -[Note 78\16: Cuv. _Leçons Hist. Sc._ 488.] - -Such plants are _composite_ or _simple_. The _composite_ flowers are -those which contain many florets in the same _calyx_.[79\16] These -are subdivided according as they are composed altogether of complete -florets, {385} or of half florets, or of a centre of complete -florets, surrounded by a circumference or ray of demi-florets. Such -are the divisions of the _corymbiferæ_, or _compositæ_. - -[Note 79\16: _Involucrum_, in modern terminology.] - -In the _simple_ flowers, the seeds are _naked_, or in a _pericarp_. -Those with _naked_ seeds are arranged according to the number of the -seeds, which may be one, two, three, four, or more. If there is only -one, no subdivision is requisite: if there are two, Ray makes a -subdivision, according as the flower has five petals, or a continuous -corolla. Here we come to several natural families. Thus, the flowers -with two seeds and five petals are the _Umbelliferous_ plants; the -monopetalous flowers with two seeds are the _Stellatæ_. He founds the -division of four-seeded flowers on the circumstance of the leaves -being opposite, or alternate; and thus again, we have the natural -families of _Asperifoliæ_, as _Echium_, &c., which have the leaves -alternate, and the _Verticillatæ_, as _Salvia_, in which the leaves -are opposite. When the flower has more than four seeds, he makes no -subdivision. - -So much for simple flowers with naked seeds. In those where the -seeds are surrounded by a _pericarp_, or fruit, this fruit is large, -soft, and fleshy, and the plants are _pomiferous_; or it is small -and juicy, and the fruit is a berry, as a Gooseberry. - -If the fruit is not juicy, but _dry_, it is multiple or simple. If -it be simple, we have the _leguminose_ plants. If it be multiple, -the form of the flower is to be attended to. The flower may be -_monopetalous_, or _tetrapetalous_, or _pentapetalous_, or with -still _more_ divisions. The monopetalous may be _regular_ or -_irregular_; so may the tetrapetalous. The regular tetrapetalous -flowers are, for example, the _Cruciferæ_, as Stock and Cauliflower; -the irregular, are the _papilionaceous_ plants, Peas, Beans, and -Vetches; and thus we again come to natural families. The remaining -plants are divided in the same way, into those with _imperfect_, and -those with _perfect_, flowers. Those with _imperfect_ flowers are -the _Grasses_, the _Rushes_ (_Junci_), and the like; among those -with _perfect_ flowers, are the _Palmaceæ_, and the _Liliaceæ_. - -We see that the division of plants is complete as a system; all -flowers must belong to one or other of the divisions. Fully to -explain the characters and further subdivisions of these families, -would be to write a treatise on botany; but it is easily seen that -they exhaust the subject as far as they go. - -Thus Ray constructed his system partly on the fruit and partly on -the flower; or more properly, according to the expression of -Linnæus, {386} comparing his earlier with his later system, he began -by being a _fructicist_, and ended by being a _corollist_.[80\16] - -[Note 80\16: Ray was a most industrious herbalizer, and I cannot -understand on what ground Mirbel asserts (_Physiol. Veg._, tom. ii. -p. 531,) that he was better acquainted with books than with plants.] - -As we have said, a number of systems of arrangement of plants were -published about this time, some founded on the fruit, some on the -corolla, some on the calyx, and these employed in various ways. -Rivinus[81\16] (whose real name was Bachman,) classified by the -flower alone; instead of combining it with the fruit, as Ray had -done.[82\16] He had the further merit of being the first who -rejected the old division, of _woody_ and _herbaceous_ plants; a -division which, though at variance with any system founded upon the -structure of the plants was employed even by Tournefort, and only -finally expelled by Linnæus. - -[Note 81\16: Cuv. _Leçons_, 491.] - -[Note 82\16: _Historia Generalis ad rem Herbariam_, 1690.] - -It would throw little light upon the history of botany, especially -for our purpose, to dwell on the peculiarities of these transitory -systems. Linnæus,[83\16] after his manner, has given a -classification of them. Rivinus, as we have just seen, was a -_corollist_, according to the regularity and number of the petals; -Hermann was a _fructicist_. Christopher Knaut[84\16] adopted the -system of Ray, but inverted the order of its parts; Christian Knaut -did nearly the same with regard to that of Rivinus, taking number -before regularity in the flower.[85\16] - -[Note 83\16: _Philos. Bot._ p. 21.] - -[Note 84\16: _Enumeratio Plantarum_, &c., 1687.] - -[Note 85\16: Linn.] - -Of the systems which prevailed previous to that of Linnæus, -Tournefort's was by far the most generally accepted. Joseph Pitton -de Tournefort was of a noble family in Provence, and was appointed -professor at the Jardin du Roi in 1683. His well-known travels in -the Levant are interesting on other subjects, as well as botany. His -_Institutio Rei Herbariæ_, published in 1700, contains his method, -which is that of a _corollist_. He is guided by the regularity or -irregularity of the flowers, by their form, and by the situation of -the receptacle of the seeds below the calyx, or within it. Thus his -classes are--those in which the flowers are _campaniform_, or -bell-shaped; those in which they are _infundibuliform_, or -funnel-shaped, as Tobacco; then the irregular flowers, as the -_Personatæ_, which resemble an ancient mask; the _Labiatæ_, with -their two lips; the _Cruciform_; the _Rosaceæ_, with flowers like a -rose; the _Umbelliferæ_; the _Caryophylleæ_, as the {387} Pink; the -_Liliaceæ_, with six petals, as the Tulip, Narcissus, Hyacinth, -Lily; the _Papilionaceæ_, which are leguminous plants, the flower of -which resembles a butterfly, as Peas and Beans; and finally, the -_Anomalous_, as Violet, Nasturtium, and others. - -Though this system was found to be attractive, as depending, in an -evident way, on the most conspicuous part of the plant, the flower, -it is easy to see that it was much less definite than systems like -that of Rivinus, Hermann, and Ray, which were governed by number. -But Tournefort succeeded in giving to the characters of genera a -degree of rigor never before attained, and abstracted them in a -separate form. We have already seen that the reception of botanical -Systems has depended much on their arrangement into Genera. - -Tournefort's success was also much promoted by the author inserting -in his work a figure of a flower and fruit belonging to each genus; -and the figures, drawn by Aubriet, were of great merit. The study of -botany was thus rendered easy, for it could be learned by turning -over the leaves of a book. In spite of various defects, these -advantages gave this writer an ascendancy which lasted, from 1700, -when his book appeared, for more than half a century. For though -Linnæus began to publish in 1735, his method and his nomenclature -were not generally adopted till 1760. - - - - -CHAPTER IV. - -THE REFORM OF LINNÆUS. - - -_Sect._ 1.--_Introduction of the Reform._ - -ALTHOUGH, perhaps, no man of science ever exercised a greater sway -than Linnæus, or had more enthusiastic admirers, the most -intelligent botanists always speak of him, not as a great -discoverer, but as a judicious and strenuous _Reformer_. Indeed, in -his own lists of botanical writers, he places himself among the -"Reformatores;" and it is apparent that this is the nature of his -real claim to admiration; for the doctrine of the sexes of plants, -even if he had been the first to establish it, was a point of -botanical physiology, a province of the {388} science which no one -would select as the peculiar field of Linnæus's glory; and the -formation of a system of arrangement on the basis of this doctrine, -though attended with many advantages, was not an improvement of any -higher order than those introduced by Ray and Tournefort. But as a -Reformer of the state of Natural History in his time, Linnæus was -admirable for his skill, and unparalleled in his success. And we -have already seen, in the instance of the reform of mineralogy, as -attempted by Mohs and Berzelius, that men of great talents and -knowledge may fail in such an undertaking. - -It is, however, only by means of the knowledge which he displays, -and of the beauty and convenience of the improvements which he -proposes, that any one can acquire such an influence as to procure -his suggestions to be adopted. And even if original circumstances of -birth or position could invest any one with peculiar prerogatives -and powers in the republic of science, Karl Linné began his career -with no such advantages. His father was a poor curate in Smaland, a -province of Sweden; his boyhood was spent in poverty and privation; -it was with great difficulty that, at the age of twenty-one, he -contrived to subsist at the University of Upsal, whither a strong -passion for natural history had urged him. Here, however, he was so -far fortunate, that Olaus Rudbeck, the professor of botany, -committed to him the care of the Botanic Garden.[86\16] The perusal -of the works of Vaillant and Patrick Blair suggested to him the idea -of an arrangement of plants, formed upon the sexual organs, the -stamens and pistils; and of such an arrangement he published a -sketch in 1731, at the age of twenty-four. - -[Note 86\16: Sprengel, ii. 232.] - -But we must go forwards a few years in his life, to come to the -period to which his most important works belong. University and -family quarrels induced him to travel; and, after various changes of -scene, he was settled in Holland, as the curator of the splendid -botanical garden of George Clifford, an opulent banker. Here it -was[87\16] that he laid the foundation of his future greatness. In -the two years of his residence at Harlecamp, he published nine -works. The first, the _Systema Naturæ_, which contained a -comprehensive sketch of the whole domain of Natural History, excited -general astonishment, by the acuteness of the observations, the -happy talent of combination, and the clearness of the systematic -views. Such a work could not fail to procure considerable respect -for its author. His _Hortus Cliffortiana_ {389} and _Musa -Cliffortiana_ added to this impression. The weight which he had thus -acquired, he proceeded to use for the improvement of botany. His -_Fundamenta Botanica_ and _Bibliotheca Botanica_ appeared in 1736; -his _Critica Botanica_ and _Genera Plantarum_ in 1737; his _Classes -Plantarum_ in 1738; his _Species Plantarum_ was not published till -1753; and all these works appeared in many successive editions, -materially modified. - -[Note 87\16: Ibid. 234.] - -This circulation of his works showed that his labors were producing -their effect. His reputation grew; and he was soon enabled to exert -a personal, as well as a literary, influence, on students of natural -history. He became Botanist Royal, President of the Academy of -Sciences at Stockholm, and Professor in the University of Upsal; and -this office he held for thirty-six years with unrivalled credit; -exercising, by means of his lectures, his constant publications, and -his conversation, an extraordinary power over a multitude of zealous -naturalists, belonging to every part of the world. - -In order to understand more clearly the nature and effect of the -reforms introduced by Linnæus into botany, I shall consider them -under the four following heads;--_Terminology_, _Nomenclature_, -_Artificial System_, and _Natural System_. - - -_Sect._ 2.--_Linnæan Reform of Botanical Terminology._ - -IT must be recollected that I designate as _Terminology_, the system -of _terms_ employed in the _description_ of objects of natural -history; while by _Nomenclature_, I mean the collection of the -_names_ of _species_. The reform of the descriptive part of botany -was one of the tasks first attempted by Linnæus; and his terminology -was the instrument by which his other improvements were effected. - -Though most readers, probably, entertain, at first, a persuasion -that a writer ought to content himself with the use of common words -in their common sense, and feel a repugnance to technical terms and -arbitrary rules of phraseology, as pedantic and troublesome; it is -soon found, by the student of any branch of science that, without -technical terms and fixed rules, there can be no certain or -progressive knowledge. The loose and infantine grasp of common -language cannot hold objects steadily enough for scientific -examination, or lift them from one stage of generalization to -another. They must be secured by the rigid mechanism of a scientific -phraseology. This necessity had been felt in all the sciences, from -the earliest periods of their progress. But the {390} conviction had -never been acted upon so as to produce a distinct and adequate -descriptive botanical language. Jung, indeed,[88\16] had already -attempted to give rules and precepts which should answer this -purpose; but it was not till the _Fundamenta Botanica_ appeared, -that the science could be said to possess a fixed and complete -terminology. - -[Note 88\16: _Isagoge Phytoscopica_, 1679.] - -To give an account of such a terminology, is, in fact, to give a -description of a dictionary and grammar, and is therefore what -cannot here be done in detail. Linnæus's work contains about a -thousand terms of which the meaning and application are distinctly -explained; and rules are given, by which, in the use of such terms, -the botanist may avoid all obscurity, ambiguity, unnecessary -prolixity and complexity, and even inelegance and barbarism. Of -course the greater part of the words which Linnæus thus recognized -had previously existed in botanical writers; and many of them had -been defined with technical precision. Thus Jung[89\16] had already -explained what was a _composite_, what a _pinnate_ leaf; what kind -of a bunch of flowers is a _spike_, a _panicle_, an _umbel_, a -_corymb_, respectively. Linnæus extended such distinctions, -retaining complete clearness in their separation. Thus, with him, -composite leaves are further distinguished as _digitate_, _pinnate_, -_bipinnate_, _pedate_, and so on; pinnate leaves are _abruptly_ so, -or _with an odd_ one, or _with a tendril_; they are pinnate -_oppositely_, _alternately_, _interruptedly_, _articulately_, -_decursively_. Again, the _inflorescence_, as the mode of assemblage -of the flowers is called, may be a _tuft_ (fasciculus), a _head_ -(capitulum), a _cluster_ (racemus), a _bunch_ (thyrsus), a -_panicle_, a _spike_, a _catkin_ (amentum), a _corymb_, an _umbel_, -a _cyme_, a _whorl_ (verticillus). And the rules which he gives, -though often apparently arbitrary and needless, are found, in -practice, to be of great service by their fixity and connexion. By -the good fortune of having had a teacher with so much delicacy of -taste as Linnæus, in a situation of so much influence, Botany -possesses a descriptive language which will long stand as a model -for all other subjects. - -[Note 89\16: Sprengel, ii. 28.] - -It may, perhaps, appear to some persons, that such a terminology as -we have here described must be enormously cumbrous; and that, since -the terms are arbitrarily invested with their meaning, the invention -of them requires no knowledge of nature. With respect to the former -doubt, we may observe, that technical description is, in reality, -the only description which is clearly intelligible; but that -technical language cannot be understood without being learnt as any -other {391} language is learnt; that is, the reader must connect the -terms immediately with his own sensations and notions, and not -mediately, through a verbal explanation; he must not have to guess -their meaning, or to discover it by a separate act of interpretation -into more familiar language as often as they occur. The language of -botany must be the botanist's most familiar tongue. When the student -has thus learnt to _think_ in botanical language, it is no idle -distinction to tell him that a _bunch_ of grapes is not a _cluster_; -that is, a _thyrsus_ not a _raceme_. And the terminology of botany -is then felt to be a useful implement, not an oppressive burden. It -is only the schoolboy that complains of the irksomeness of his -grammar and vocabulary. The accomplished student possesses them -without effort or inconvenience. - -As to the other question, whether the construction of such a botanical -grammar and vocabulary implies an extensive and accurate acquaintance -with the facts of nature, no one can doubt who is familiar with any -descriptive science. It is true, that a person might construct an -arbitrary scheme of distinctions and appellations, with no attention -to natural objects; and this is what shallow and self-confident -persons often set about doing, in some branch of knowledge with which -they are imperfectly acquainted. But the slightest attempt to use such -a phraseology leads to confusion; and any continued use of it leads to -its demolition. Like a garment which does not fit us, if we attempt to -work in it we tear it in pieces. - -The formation of a good descriptive language is, in fact, an -inductive process of the same kind as those which we have already -noticed in the progress of natural history. It requires the -_discovery of fixed characters_, which discovery is to be marked and -fixed, like other inductive steps, by appropriate _technical terms_. -The characters must be so far fixed, that the things which they -connect must have a more permanent and real association than the -things which they leave unconnected. If one bunch of grapes were -really a racemus, and another a thyrsus, according to the definition -of these terms, this part of the Linnæan language would lose its -value; because it would no longer enable us to assert a general -proposition with respect to one kind of plants. - - -_Sect._ 3.--_Linnæan Reform of Botanical Nomenclature._ - -IN the ancient writers each recognized kind of plants had a distinct -name. The establishment of Genera led to the practice of designating -{392} Species by the name of the genus, with the addition of a -"phrase" to distinguish the species. These phrases, (expressed in -Latin in the ablative case,) were such as not only to mark, but to -describe the species, and were intended to contain such features of -the plant as were sufficient to distinguish it from others of the -same genus. But in this way the designation of a plant often became -a long and inconvenient assemblage of words. Thus different kinds of -Rose were described as, - Rosa campestris, spinis carens, biflora (_Rosa alpina_.) - Rosa aculeata, foliis odoratis subtus rubiginosis (_R. eglanteria_.) - Rosa carolina fragrans, foliis medio tenus serratis (_R. carolina_.) - Rosa sylvestris vulgaris, flore odorato incarnato (_R. canina_.) -And several others. The prolixity of these appellations, their -variety in every different author, the insufficiency and confusion -of the distinctions which they contained, were felt as extreme -inconveniences. The attempt of Bauhin to remedy this evil by a -Synonymy, had, as we have seen, failed at the time, for want of any -directing principle; and was become still more defective by the -lapse of years and the accumulation of fresh knowledge and new -books. Haller had proposed to distinguish the species of each genus -by the numbers 1, 2, 3, and so on; but botanists found that their -memory could not deal with such arbitrary abstractions. The need of -some better nomenclature was severely felt. - -The remedy which Linnæus finally introduced was the use of _trivial_ -names; that is, the designation of each species by the name of the -genus along with a _single_ conventional word, imposed without any -general rule. Such names are added above in parentheses, to the -specimens of the names previously in use. But though this remedy was -found to be complete and satisfactory, and is now universally -adopted in every branch of natural history, it was not one of the -reforms which Linnæus at first proposed. Perhaps he did not at first -see its full value; or, if he did, we may suppose that it required -more self-confidence than he possessed, to set himself to introduce -and establish ten thousand new names in the botanical world. -Accordingly, the first attempts of Linnæus at the improvement of the -nomenclature of botany were, the proposal of fixed and careful rules -for the generic name, and for the descriptive phrase. Thus, in his -_Critica Botanica_, he gives many precepts concerning the selection -of the names of {393} genera, intended to secure convenience or -elegance. For instance, that they are to be single words;[90\16] he -substitutes _atropa_ for _bella donna_, and _leontodon_ for _dens -leonis_; that they are not to depend upon the name of another -genus,[91\16] as _acriviola_, _agrimonoides_; that they are -not[92\16] to be "sesquipedalia;" and, says he, any word is -sesquipedalian to me, which has more than twelve letters, as -_kalophyllodendron_, for which he substitutes _calophyllon_. Though -some of these rules may seem pedantic, there is no doubt that, taken -altogether, they tend exceedingly, like the labors of purists in -other languages, to exclude extravagance, caprice, and barbarism in -botanical speech. - -[Note 90\16: _Phil. Bot._ 224.] - -[Note 91\16: Ib. 228, 229.] - -[Note 92\16: Ib. 252.] - -The precepts which he gives for the matter of the "descriptive -phrase," or, as it is termed in the language of the Aristotelian -logicians, the "differentia," are, for the most part, results of the -general rule, that the most fixed characters which can be found are -to be used; this rule being interpreted according to all the -knowledge of plants which had then been acquired. The language of -the rules was, of course, to be regulated by the terminology, of -which we have already spoken. - -Thus, in the _Critica Botanica_, the name of a plant is considered -as consisting of a generic word and a specific phrase; and these -are, he says,[93\16] the right and left hands of the plant. But he -then speaks of another kind of name; the _trivial_ name, which is -opposed to the scientific. Such names were, he says,[94\16] those of -his predecessors, and especially of the most ancient of them. -Hitherto[95\16] no rules had been given for their use. He -manifestly, at this period, has small regard for them. "Yet," he -says, "trivial names may, perhaps, be used on this account,--that -the _differentia_ often turns out too long to be convenient in -common use, and may require change as new species are discovered. -However," he continues, "in this work we set such names aside -altogether, and attend only to the _differentiæ_." - -[Note 93\16: Ib. 266.] - -[Note 94\16: Ib. 261.] - -[Note 95\16: Ib. 260.] - -Even in the _Species Plantarum_, the work which gave general -currency to these trivial names, he does not seem to have yet dared -to propose so great a novelty. They only stand in the margin of the -work. "I have placed them there," he says in his Preface, "that, -without circumlocution, we may call every herb by a single name; I -have done this without selection, which would require more time. And -I beseech all sane botanists to avoid most religiously ever {394} -proposing a trivial name without a sufficient specific distinction, -lest the science should fall into its former barbarism." - -It cannot be doubted, that the general reception of these trivial -names of Linnæus, as the current language among botanists, was due, in -a very great degree, to the knowledge, care, and skill with which his -characters, both of genera and of species, were constructed. The -rigorous rules of selection and expression which are proposed in the -_Fundamenta Botanica_ and _Critica Botanica_, he himself conformed to; -and this scrupulosity was employed upon the results of immense labor. -"In order that I might make myself acquainted with the species of -plants," he says, in the preface to his work upon them, "I have -explored the Alps of Lapland, the whole of Sweden, a part of Norway, -Denmark, Germany, Belgium, England, France: I have examined the -Botanical Gardens of Paris, Oxford, Chelsea, Harlecamp, Leyden, -Utrecht, Amsterdam, Upsal, and others: I have turned over the Herbals -of Burser, Hermann, Clifford, Burmann, Oldenland, Gronovius, Royer, -Sloane, Sherard, Bobart, Miller, Tournefort, Vaillant, Jussieu, -**Surian, Beck, Brown, &c.: my dear disciples have gone to distant -lands, and sent me plants from thence; Kerlen to Canada, Hasselquist -to Egypt, Asbech to China, Toren to Surat, Solander to England, -Alstrœmer to Southern Europe, Martin to Spitzbergen, Pontin to -Malabar, Kœhler to Italy, Forskähl to the East, Lœfling to Spain, -Montin to Lapland: my botanical friends have sent me many seeds and -dried plants from various countries: Lagerström many from the East -Indies; Gronovius most of the Virginian; Gmelin all the Siberian; -Burmann those of the Cape." And in consistency with this habit of -immense collection of materials, is his maxim,[96\16] that "a person -is a better botanist in proportion as he knows more species." It will -easily be seen that this maxim, like Newton's declaration that -discovery requires patient thought alone, refers only to the exertions -of which the man of genius is conscious; and leaves out of sight his -peculiar endowments, which he does not see because they are part of -his power of vision. With the taste for symmetry which dictated the -_Critica Botanica_, and the talent for classification which appears in -the _Genera Plantarum_, and the _Systema Naturæ_, a person must -undoubtedly rise to higher steps of classificatory knowledge and -skill, as he became acquainted with a greater number of facts. - -[Note 96\16: _Phil. Bot._ 259.] - -The acknowledged superiority of Linnæus in the knowledge of the -{395} matter of his science, induced other persons to defer to him -in what concerned its form; especially when his precepts were, for -the most part, recommended strongly both by convenience and -elegance. The trivial names of the _Species Plantarum_ were -generally received; and though some of the details may have been -altered, the immense advantage of the scheme ensures its permanence. - - -_Sect._ 4.--_Linnæus's Artificial System._ - -WE have already seen, that, from the time of Cæsalpinus, botanists -had been endeavoring to frame a systematic arrangement of plants. -All such arrangements were necessarily both artificial and natural: -they were _artificial_, inasmuch as they depended upon assumed -principles, the number, form, and position of certain parts, by the -application of which the whole vegetable kingdom was imperatively -subdivided; they were _natural_, inasmuch as the justification of -this division was, that it brought together those plants which were -naturally related. No system of arrangement, for instance, would -have been tolerated which, in a great proportion of cases, separated -into distant parts of the plan the different species of the same -genus. As far as the main body of the genera, at least, all systems -are natural. - -But beginning from this line, we may construct our systems with two -opposite purposes, according as we endeavor to carry our assumed -principle of division rigorously and consistently through the -system, or as we wish to associate natural families of a wider kind -than genera. The former propensity leads to an artificial, the -latter to a natural method. Each is a _System of Plants_; but in the -first, the emphasis is thrown on the former word of the title, in -the other, on the latter. - -The strongest recommendation of an artificial system, (besides its -approaching to a natural method,) is, that it shall be capable of -easy use; for which purpose, the facts on which it depends must be -apparent in their relations, and universal in their occurrence. The -system of Linnæus, founded upon the number, position, and other -circumstances of the stamina and pistils, the reproductive organs of -the plants, possessed this merit in an eminent degree, as far as -these characters are concerned; that is, as far as the classes and -orders. In its further subdivision into genera, its superiority was -mainly due to the exact observation and description, which we have -already had to notice as talents which Linnæus peculiarly possessed. - -The Linnæan system of plants was more definite than that of {396} -Tournefort, which was governed by the corolla; for number is more -definite than irregular form. It was more readily employed than any -of those which depend on the fruit, for the flower is a more obvious -object, and more easily examined. Still, it can hardly be doubted, -that the circumstance which gave the main currency to the system of -Linnæus was its physiological signification: it was the _Sexual -System_. The relation of the parts to which it directed the -attention, interested both the philosophical faculty and the -imagination. And when, soon after the system had become familiar in -our own country, the poet of _The Botanic Garden_ peopled the bell -of every flower with "Nymphs" and "Swains," his imagery was felt to -be by no means forced and far-fetched. - -The history of the doctrine of the sexes of plants, as a point of -physiology, does not belong to this place; and the Linnæan system of -classification need not be longer dwelt upon for our present -purpose. I will only explain a little further what has been said, -that it is, up to a certain point, a natural system. Several of -Linnæus's classes are, in a great measure, natural associations, -kept together in violation of his own artificial rules. Thus the -class _Diadelphia_, in which, by the system, the filaments of the -stamina should be bound together in two parcels, does, in fact, -contain many genera which are_ monadelphous_, the filaments of the -stamina all cohering so as to form one bundle only; as in _Genista_, -_Spartium_, _Anthyllis_, _Lupinus_, &c. And why is this violation of -rule? Precisely because these genera all belong to the natural tribe -of Papilionaceous plants, which the author of the system could not -prevail upon himself to tear asunder. Yet in other cases Linnæus was -true to his system, to the injury of natural alliances, as he was, -for instance, in another portion of this very tribe of -_Papilionaceæ_; for there are plants which undoubtedly belong to the -tribe, but which have ten separate stamens; and these he placed in -the order _Decandria_. Upon the whole, however, he inclines rather -to admit transgression of art than of nature. - -The reason of this inclination was, that he rightly considered an -artificial method as instrumental to the investigation of a natural -one; and to this part of his views we now proceed. - - -_Sect._ 5.--_Linnæus's Views on a Natural Method._ - -THE admirers of Linnæus, the English especially, were for some time -in the habit of putting his Sexual System in opposition to the -Natural Method, which about the same time was attempted in France. -And {397} as they often appear to have imagined that the ultimate -object of botanical methods was to know the name of plants, they -naturally preferred the Swedish method, which is excellent as a -_finder_. No person, however, who wishes to know botany as a -science, that is, as a body of general truths, can be content with -making names his ultimate object. Such a person will be constantly -and irresistibly led on to attempt to catch sight of the natural -arrangement of plants, even before he discovers, as he will discover -by pursuing such a course of study, that the knowledge of the -natural arrangement is the knowledge of the essential construction -and vital mechanism of plants. He will consider an artificial method -as a means of arriving at a natural method. Accordingly, however -much some of his followers may have overlooked this, it is what -Linnæus himself always held and taught. And though what he executed -with regard to this object was but little,[97\16] the distinct -manner in which he presented the relations of an artificial and -natural method, may justly be looked upon as one of the great -improvements which he introduced into the study of his science. - -[Note 97\16: The natural orders which he proposed are a bare -enumeration of genera, and have not been generally followed.] - -Thus in the _Classes Plantarum_ (1747), he speaks of the difficulty of -the task of discovering the natural orders, and of the attempts made -by others. "Yet," he adds, "I too have labored at this, have done -something, have much still to do, and shall labor at the object as -long as I live." He afterwards proposed sixty-seven orders, as the -fragments of a natural method, always professing their -imperfection.[98\16] And in others of his works[99\16] he lays down -some antitheses on the subject after his manner. "The natural orders -teach us the nature of plants; the artificial orders enable us to -recognize plants. The natural orders, without a key, do not constitute -a Method; the Method ought to be available without a master." - -[Note 98\16: _Phil. Bot._ p. 80.] - -[Note 99\16: _Genera Plantarum_, 1764. See _Prælect. in Ord. Nat._ -p. xlviii.] - -That extreme difficulty must attend the formation of a Natural Method, -may be seen from the very indefinite nature of the Aphorisms upon this -subject which Linnæus has delivered, and which the best botanists of -succeeding times have assented to. Such are these;--the Natural Orders -must be formed by attention, not to one or two, but to _all_ the parts -of plants;--the same organs are of great importance in regulating the -divisions of one part of the system, and {398} of small importance in -another part;[100\16]--the Character does not constitute the Genus, -but the Genus the Character;--the Character is necessary, not to make -the Genus, but to recognize it. The vagueness of these maxims is -easily seen; the rule of attending to all the parts, implies, that we -are to estimate their relative importance, either by physiological -considerations (and these again lead to arbitrary rules, as, for -instance, the superiority of the function of nutrition to that of -reproduction), or by a sort of latent naturalist instinct, which -Linnæus in some passages seems to recognize. "The Habit of a plant," -he says,[101\16] "must be secretly consulted. A practised botanist -will distinguish, at the first glance, the plants of different -quarters of the globe, and yet will be at a loss to tell by what mark -he detects them. There is, I know not what look,--sinister, dry, -obscure in African plants; superb and elevated, in the Asiatic; smooth -and cheerful, in the American; stunted and indurated, in the Alpine." - -[Note 100\16: _Phil. Bot._ p. 172.] - -[Note 101\16: Ib. p. 171.] - -Again, the rule that the same parts are of very different value in -different Orders, not only leaves us in want of rules or reasons -which may enable us to compare the marks of different Orders, but -destroys the systematic completeness of the natural arrangement. If -some of the Orders be regulated by the flower and others by the -fruit, we may have plants, of which the flower would place them in -one Order, and the fruit in another. The answer to this difficulty -is the maxim already stated;--that no Character _makes_ the Order; -and that if a Character do not enable us to recognize the Order, it -does not answer its purpose, and ought to be changed for another. - -This doctrine, that the Character is to be employed as a servant and -not as a master, was a stumbling-block in the way of those disciples -who looked only for dogmatical and universal rules. One of Linnæus's -pupils, Paul Dietrich Giseke, has given us a very lively account of -his own perplexity on having this view propounded to him, and of the -way in which he struggled with it. He had complained of the want of -intelligible grounds, in the collection of natural orders given by -Linnæus. Linnæus[102\16] wrote in answer, "You ask me for the -characters of the Natural Orders: I confess I cannot give them." -Such a reply naturally increased Giseke's difficulties. But -afterwards, in 1771, he had the good fortune to spend some time at -Upsal; and he narrates a conversation which he held with the great -{399} teacher on this subject, and which I think may serve to show -the nature of the difficulty;--one by no means easily removed, and -by the general reader, not even readily comprehended with -distinctness. Giseke began by conceiving that an Order _must_ have -that attribute from which its name is derived;--that the _Umbellatæ_ -must have their flower disposed in an umbel. The "mighty master" -smiled,[103\16] and told him not to look at names, but at nature. -"But" (said the pupil) "what is the use of the name, if it does not -mean what it professes to mean?" "It is of small import" (replied -Linnæus) "_what_ you _call_ the Order, if you take a proper series -of plants and give it some name, which is clearly understood to -apply to the plants which you have associated. In such cases as you -refer to, I followed the logical rule, of borrowing a name _a -potiori_, from the principal member. Can you" (he added) "give me -the character of any single Order?" _Giseke._ "Surely, the character -of the _Umbellatæ_ is, that they have an umbel?" _Linnæus._ "Good; -but there are plants which have an umbel, and are not of the -_Umbellatæ_." _G._ "I remember. We must therefore add, that they -have two naked seeds." _L._ "Then, _Echinophora_, which has only one -seed, and _Eryngium_, which has not an umbel, will not be -_Umbellatæ_; and yet they are of the Order." _G._ "I would place -_Eryngium_ among the _Aggregatæ_. _L._ "No; both are beyond dispute -_Umbellatæ_. _Eryngium_ has an involucrum, five stamina, two -pistils, &c. Try again for your Character." _G._ "I would transfer -such plants to the end of the Order, and make them form the -transition to the next Order. _Eryngium_ would connect the -_Umbellatæ_ with the _Aggregatæ_." _L._ "Ah! my good friend, the -_Transition_ from Order to Order is one thing; the _Character_ of an -Order is another. The Transitions I could indicate; but a Character -of a Natural Order is impossible. I will not give my reasons for the -distribution of Natural Orders which I have published. You or some -other person, after twenty or after fifty years, will discover them, -and see I was in the right." - -[Note 102\16: _Linnæi Prælectiones_, Pref. p. xv.] - -[Note 103\16: "Subrisit ὁ πανυ."] - -I have given a portion of this curious conversation in order to show -that the attempt to establish Natural Orders leads to convictions -which are out of the domain of the systematic grounds on which they -profess to proceed. I believe the real state of the case to be that -the systematist, in such instances, is guided by an unformed and -undeveloped apprehension of physiological functions. The ideas of -the form, {400} number, and figure of parts are, in some measure, -overshadowed and superseded by the rising perception of organic and -vital relations; and the philosopher who aims at a Natural Method, -while he is endeavoring merely to explore the apartment in which he -had placed himself, that of Arrangement, is led beyond it, to a -point where another light begins, though dimly, to be seen; he is -brought within the influence of the ideas of Organization and Life. - -The sciences which depend on these ideas will be the subject of our -consideration hereafter. But what has been said may perhaps serve to -explain the acknowledged and inevitable imperfection of the -unphysiological Linnæan attempts towards a natural method. -"Artificial Glasses are," Linnæus says, "a substitute for Natural, -till Natural are detected." But we have not yet a Natural Method. -"Nor," he says, in the conversation above cited, "can we have a -Natural Method; for a Natural Method implies Natural Classes and -Orders; and these Orders must have Characters." "And they," he adds -in another place,[104\16] "who, though they cannot obtain a complete -Natural Method, arrange plants according to the fragments of such a -method, to the rejection of the Artificial, seem to me like persons -who pull down a convenient vaulted room, and set about building -another, though they cannot turn the vault which is to cover it." - -[Note 104\16: _Gen. Plant. in Prælect._ p. xii.] - -How far these considerations deterred other persons from turning -their main attention to a natural method, we shall shortly see; but -in the mean time, we must complete the history of the Linnæan Reform. - - -_Sect._ 6.--_Reception and Diffusion of the Linnæan Reform._ - -WE have already seen that Linnæus received, from his own country, -honors and emoluments which mark his reputation as established, as -early as 1740; and by his publications, his lectures, and his -personal communications, he soon drew round him many disciples, whom -he impressed strongly with his own doctrines and methods. It would -seem that the sciences of classification tend, at least in modern -times more than other sciences, to collect about the chair of the -teacher a large body of zealous and obedient pupils; Linnæus and -Werner were by far the most powerful heads of schools of any men who -appeared in the course of the last century. Perhaps one reason of -this is, that in these sciences, consisting of such an enormous -multitude of species, of descriptive {401} particulars, and of -previous classifications, the learner is dependent upon the teacher -more completely, and for a longer time than in other subjects of -speculation: he cannot so soon or so easily cast off the aid and -influence of the master, to pursue reasonings and hypotheses of his -own. Whatever the cause may be, the fact is, that the reputation and -authority of Linnæus, in the latter part of his life, were immense. -He enjoyed also royal favor, for the King and Queen of Sweden were -both fond of natural history. In 1753, Linnæus received from the -hand of his sovereign the knighthood of the Polar Star, an honor -which had never before been conferred for literary merit; and in -1756, was raised to the rank of Swedish nobility by the title of Von -Linné; and this distinction was confirmed by the Diet in 1762. He -lived, honored and courted, to the age of seventy-one; and in 1778 -was buried in the cathedral of Upsal, with many testimonials of -public respect and veneration. - -De Candolle[105\16] assigns, as the causes of the successes of the -Linnæan system,--the specific names,--the characteristic -phrase,--the fixation of descriptive language,--the distinction of -varieties and species,--the extension of the method to all the -kingdoms of nature,--and the practice of introducing into it the -species most recently discovered. This last course Linnæus -constantly pursued; thus making his works the most valuable for -matter, as they were the most convenient in form. The general -diffusion of his methods over Europe may be dated, perhaps, a few -years after 1760, when the tenth and the succeeding editions of the -_Systema Naturæ_ were in circulation, professing to include every -species of organized beings. But his pupils and correspondents -effected no less than his books, in giving currency to his system. -In Germany,[106\16] it was defended by Ludwig, Gesner, Fabricius. -But Haller, whose reputation in physiology was as great as that of -Linnæus in methodology, rejected it as too merely artificial. In -France, it did not make any rapid or extensive progress: the best -French botanists were at this time occupied with the solution of the -great problem of the construction of a Natural Method. And though -the rhetorician Rousseau charmed, we may suppose, with the elegant -precision of the _Philosophia Botanica_, declared it to be the most -philosophical work he had ever read in his life, Buffon and -Andanson, describers and philosophers of a more ambitious school, -felt a repugnance to the rigorous rules, and limited, but finished, -undertakings of the Swedish naturalist. To resist his {402} criticism -and his influence, they armed themselves with dislike and contempt. - -[Note 105\16: _Théor. Elém._ p. 40.] - -[Note 106\16: Sprengel, ii. 244.] - -In England the Linnæan system was very favorably received:--perhaps -the more favorably, for being a strictly artificial system. For the -indefinite and unfinished form which almost inevitably clings to a -natural method, appears to be peculiarly distasteful to our -countrymen. It might seem as if the suspense and craving which comes -with knowledge confessedly incomplete were so disagreeable to them, -that they were willing to avoid it, at any rate whatever; either by -rejecting system altogether, or by accepting a dogmatical system -without reserve. The former has been their course in recent times with -regard to Mineralogy; the latter was their proceeding with respect to -the Linnæan Botany. It is in this country alone, I believe, that -_Wernerian_ and _Linnæan_ Societies have been instituted. Such -appellations somewhat remind us of the Aristotelian and Platonic -schools of ancient Greece. In the same spirit it was, that the -Artificial System was at one time here considered, not as subsidiary -and preparatory to the Natural Orders, but as opposed to them. This -was much as if the disposition of an army in a review should be -considered as inconsistent with another arrangement of it in a battle. - -When Linnæus visited England in 1736, Sloane, then the patron of -natural history in this country, is said to have given him a cool -reception, such as was perhaps most natural from an old man to a -young innovator; and Dillenius, the Professor at Oxford, did not -accept the sexual system. But as Pulteney, the historian of English -Botany, says, when his works became known, "the simplicity of the -classical characters, the uniformity of the generic notes, all -confined to the parts of the fructification, and the precision which -marked the specific distinctions, merits so new, soon commanded the -assent of the unprejudiced." - -Perhaps the progress of the introduction of the Linnæan System into -England will be best understood from the statement of T. Martyn, who -was Professor of Botany in the University of Cambridge, from 1761 to -1825. "About the year 1750," he says,[107\16] "I was a pupil of the -school of our great countryman Ray; but the rich vein of knowledge, -the profoundness and precision, which I remarked everywhere in the -_Philosophia Botanica_, (published in 1751,) withdrew me from my -first master, and I became a decided convert to that system of -botany which has since been generally received. In 1753, the -_Species_ {403} _Plantarum_, which first introduced the specific -names, made me a Linnæan completely." In 1763, he introduced the -system in his lectures at Cambridge, and these were the first -Linnæan lectures in England. Stillingfleet had already, in 1757, and -Lee, in 1760, called the attention of English readers to Linnæus. -Sir J. Hill, (the king's gardener at Kew,) in his _Flora -Britannica_, published in 1760, had employed the classes and generic -characters, but not the nomenclature; but the latter was adopted by -Hudson, in 1762, in the _Flora Anglica_. - -[Note 107\16: Pref. to _Language of Botany_, 3rd edit. 1807.] - -Two young Swedes, pupils of Linnæus, Dryander and Solander, settled in -England, and were in intimate intercourse with the most active -naturalists, especially with Sir Joseph Banks, of whom the former was -librarian, and the latter a fellow-traveller in Cook's celebrated -voyage. James Edward Smith was also one of the most zealous disciples -of the Linnæan school; and, after the death of Linnæus, purchased his -Herbariums and Collections. It is related,[108\16] as a curious proof -of the high estimation in which Linnæus was held, that when the -Swedish government heard of this bargain, they tried, though too late, -to prevent these monuments of their countryman's labor and glory being -carried from his native land, and even went so far as to send a -frigate in pursuit of the ship which conveyed them to England. Smith -had, however, the triumph of bringing them home in safety. On his -death they were purchased by the Linnæan Society. Such relics serve, -as will easily be imagined, not only to warm the reverence of his -admirers, but to illustrate his writings: and since they have been in -this country, they have been the object of the pilgrimage of many a -botanist, from every part of Europe. - -[Note 108\16: Trapp's _Transl. of Stower's Life of Linnæus_, p. 314.] - -I have purposely confined myself to the history of the Linnæan system -in the cases in which it is most easily applicable, omitting all -consideration of more obscure and disputed kinds of vegetables, as -ferns, mosses, fungi, lichens, sea-weeds, and the like. The nature and -progress of a classificatory science, which it is our main purpose to -bring into view, will best be understood by attending, in the first -place, to the cases in which such a science has been pursued with the -most decided success; and the advances which have been made in the -knowledge of the more obscure vegetables, are, in fact, advances in -artificial classification, only in as far as they are advances in -natural classification, and in physiology. - -To these subjects we now proceed. {404} - - - - -CHAPTER V. - -PROGRESS TOWARDS A NATURAL SYSTEM OF BOTANY. - -WE have already said, that the formation of a Natural System of -classification must result from a comparison of _all_ the -resemblances and differences of the things classed; but that, in -acting upon this maxim, the naturalist is necessarily either guided -by an obscure and instinctive feeling, which is, in fact, an -undeveloped recognition of physiological relations, or else -acknowledges physiology for his guide, though he is obliged to -assume arbitrary rules in order to interpret its indications. Thus -all Natural Classification of organized beings, either begins or -soon ends in Physiology; and can never advance far without the aid -of that science. Still, the progress of the Natural Method in botany -went to such a length before it was grounded entirely on the anatomy -of plants, that it will be proper, and I hope instructive, to -attempt a sketch of it here. - -As I have already had occasion to remark, the earlier systems of -plants were natural; and they only ceased to be so, when it appeared -that the problem of constructing a _system_ admitted of a very -useful solution, while the problem of devising a _natural system_ -remained insoluble. But many botanists did not so easily renounce -the highest object of their science. In France, especially, a -succession of extraordinary men labored at it with no inconsiderable -success: and they were seconded by worthy fellow-laborers in Germany -and elsewhere. - -The precept of taking into account all the parts of plants according -to their importance, may be applied according to arbitrary rules. We -may, for instance, assume that the fruit is the most important part; -or we may make a long list of parts, and look for agreement in the -greatest possible number of these, in order to construct our natural -orders. The former course was followed by Gærtner;[109\16] the -latter by Adanson. Gærtner's principles, deduced from the dissection -of more than a thousand kinds of fruits,[110\16] exercised, in the -sequel, a great and {405} permanent influence on the formation of -natural classes. Adanson's attempt, bold and ingenious, belonged, -both in time and character, to a somewhat earlier stage of the -subject.[111\16] Enthusiastic and laborious beyond belief but -self-confident, and contemptuous of the labors of others, Michael -Adanson had collected, during five years spent in Senegal, an -enormous mass of knowledge and materials; and had formed plans for -the systems which he conceived himself thus empowered to reach, far -beyond the strength and the lot of man.[112\16] In his _Families of -Plants_, however, all agree that his labors were of real value to -the science. The method which he followed is thus described by his -eloquent and philosophical eulogist.[113\16] - -[Note 109\16: _De Fructibus et Seminibus Plantarum_. Stuttg. -1788-1791.] - -[Note 110\16: Sprengel, ii. 290.] - -[Note 111\16: _Familles des Plantes_, 1763.] - -[Note 112\16: Cuvier's _Eloge_.] - -[Note 113\16: Cuv. _Eloges_, tom. i. p. 282.] - -Considering each organ by itself, he formed, by pursuing its various -modifications, a system of division, in which he arranged all known -species according to that organ alone. Doing the same for another -organ, and another, and so for many, he constructed a collection of -systems of arrangement, each artificial,--each founded upon one -assumed organ. The species which come together in all these systems -are, of all, naturally the nearest to each other; those which are -separated in a few of the systems, but contiguous in the greatest -number, are naturally near to each other, though less near than the -former; those which are separated in a greater number, are further -removed from each other in nature; and they are the more removed, -the fewer are the systems in which they are associated. - -Thus, by this method, we obtain the means of estimating precisely -the degree of natural affinity of all the species which our systems -include, independent of a physiological knowledge of the influence -of the organs. But the method has, Cuvier adds, the inconvenience of -presupposing another kind of knowledge, which, though it belongs -only to descriptive natural history, is no less difficult to -obtain;--the knowledge, namely, of all species, and of all the -organs of each. A single one neglected, may lead to relations the -most false; and Adanson himself, in spite of the immense number of -his observations, exemplifies this in some instances. - -We may add, that in the division of the structure into organs, and -in the estimation of the gradations of these in each artificial -system, there is still room for arbitrary assumption. - -In the mean time, the two Jussieus had presented to the world a -"Natural Method," which produced a stronger impression than the -{406} "Universal Method" of Adanson. The first author of the system -was Bernard de Jussieu, who applied it in the arrangement of the -garden of the Trianon, in 1759, though he never published upon it. -His nephew, Antoine Laurent de Jussieu, in his _Treatise of the -Arrangement of the Trianon_,[114\16] gave an account of the -principles and orders of his uncle, which he adopted when he -succeeded him; and, at a later period, published his _Genera -Plantarum secundum Ordines Naturales disposita_; a work, says -Cuvier, which perhaps forms as important an epoch in the sciences of -observation, as the _Chimie_ of Lavoisier does in the sciences of -experiment. The object of the Jussieus was to obtain a system which -should be governed by the natural affinities of the plants, while, -at the same time, the characters by which the orders were ostensibly -determined, should be as clear, simple, and precise, as those of the -best artificial system. The main points in these characters were the -number of the cotyledons, and the structure of the seed: and -subordinate to this, the insertion of the stamina, which they -distinguished as _epigynous_, _perigynous_, and _hypogynous_, -according as they were inserted over, about, or under, the germen. -And the classes which were formed by the Jussieus, though they have -since been modified by succeeding writers, have been so far retained -by the most profound botanists, notwithstanding all the new care and -new light which have been bestowed upon the subject, as to show that -what was done at first, was a real and important step in the -solution of the problem. - -[Note 114\16: _Mém. Ac. P._ 1774.] - -The merit of the formation of this natural method of plants must be -divided between the two Jussieus. It has been common to speak of the -nephew, Antoine Laurent, as only the publisher of his uncle's -work.[115\16] But this appears, from a recent statement,[116\16] to -be highly unjust. Bernard left nothing in writing but the catalogues -of the garden of the Trianon, which he had arranged according to his -own views; but these catalogues consist merely of a series of names -without explanation or reason added. The nephew, in 1773, undertook -and executed for himself the examination of a natural family, the -_Ranunculaceæ_; and he was wont to relate (as his son informs us) -that it {407} was this employment which first opened his eyes and -rendered him a botanist. In the memoir which he wrote, he explained -fully the relative importance of the characters of plants, and the -subordination of some to others;--an essential consideration, which -Adanson's scheme had failed to take account of. The uncle died in -1777; and his nephew, in speaking of him, compares his arrangement -to the _Ordines Naturales_ of Linnæus: "Both these authors," he -says, "have satisfied themselves with giving a catalogue of genera -which approach each other in different points, without explaining -the motives which induced them to place one order before another, or -to arrange a genus under a certain order. These two arrangements may -be conceived as problems which their authors have left for botanists -to solve. Linnæus published his; that of M. de Jussieu is only known -by the manuscript catalogues of the garden of the Trianon." - -[Note 115\16: _Prodromus Floræ Penins. Ind. Orient._ Wight and -Walker-Arnott, Introd. p. xxxv.] - -[Note 116\16: By Adrien de Jussieu, son of Antoine Laurent, in the -_Annales des Sc. Nat._, Nov. 1834.] - -It was not till the younger Jussieu had employed himself for -nineteen years upon botany, that he published, in 1789, his _Genera -Plantarum_; and by this time he had so entirely formed his scheme in -his head, that he began the impression without having written the -book, and the manuscript was never more than two pages in advance of -the printer's type. - -When this work appeared, it was not received with any enthusiasm; -indeed, at that time, the revolution of states absorbed the thoughts -of all Europe, and left men little leisure to attend to the -revolutions of science. The author himself was drawn into the vortex -of public affairs, and for some years forgot his book. The method -made its way slowly and with difficulty: it was a long time before -it was comprehended and adopted in France, although the botanists of -that country had, a little while before, been so eager in pursuit of -a natural system. In England and Germany, which had readily received -the Linnæan method, its progress was still more tardy. - -There is only one point, on which it appears necessary further to -dwell. A main and fundamental distinction in all natural systems, is -that of the Monocotyledonous and Dicotyledonous plants; that is, -plants which unfold themselves from an embryo with two little -leaves, or with one leaf only. This distinction produces its effects -in the systems which are regulated by numbers; for the flowers and -fruit of the monocotyledons are generally referrible to some law in -which the number _three_ prevails; a type which rarely occurs in -dicotyledons, these affecting most commonly an arrangement founded -on the number _five_. But it appears, when we attempt to rise -towards a natural {408} method, that this division according to the -cotyledons is of a higher order than the other divisions according -to number; and corresponds to a distinction in the general structure -and organization of the plant. The apprehension of the due rank of -this distinction has gradually grown clearer. Cuvier[117\16] -conceives that he finds such a division clearly marked in Lobel, in -1581, and employed by Ray as the basis of his classification a -century later. This difference has had its due place assigned it in -more recent systems of arrangement; but it is only later still that -its full import has been distinctly brought into view. Desfontaines -discovered[118\16] that the ligneous fibre is developed in an -opposite manner in vegetables with one and with two -cotyledons;--towards the inside in the former case, and towards the -outside in the latter; and hence these two great classes have been -since termed _endogenous_ and _exogenous_. - -[Note 117\16: _Hist. Sc. Nat._ ii. 197.] - -[Note 118\16: _Hist. Sc. Nat._ i. pp. 196, 290.] - -Thus this division, according to the cotyledons, appears to have the -stamp of reality put upon it, by acquiring a physiological meaning. -Yet we are not allowed to forget, even at this elevated point of -generalization, that _no one_ character can be imperative in a natural -method. Lamarck, who employed his great talents on botany, before he -devoted himself exclusively to other branches of natural history, -published his views concerning methods, systems,[119\16] and -characters. His main principle is, that no single part of a plant, -however essential, can be an absolute rule for classification; and -hence he blames the Jussieuian method, as giving this inadmissible -authority to the cotyledons. Roscoe[120\16] further urges that some -plants, as _Orchis morio_, and _Limodorum verecundum_, have no visible -cotyledons. Yet De Candolle, who labored along with Lamarck, in the -new edition of the _Flore Française_, has, as we have already -intimated, been led, by the most careful application of the wisest -principles, to a system of Natural Orders, of which Jussieu's may be -looked upon as the basis; and we shall find the greatest botanists, up -to the most recent period, recognizing, and employing themselves in -improving, Jussieu's Natural Families; so that in the progress of this -part of our knowledge, vague and perplexing as it is, we have no -exception to our general aphorism, that no real acquisition in science -is ever discarded. {409} - -[Note 119\16: Sprengel, ii. 296; and, there quoted, _Flore -Française_, t. i. 3, 1778. _Mém. Ac. P._ 1785. _Journ. Hist. Nat._ -t. i. For Lamarck's _Méthode Analytique_, see Dumeril, _Sc. Nat._ i. -Art. 390.] - -[Note 120\16: Roscoe, _Linn. Tr._ vol. xi. _Cuscuta_ also has no -cotyledons.] - -The reception of the system of Jussieu in this country was not so -ready and cordial as that of Linnæus. As we have already noticed, -the two systems were looked upon as rivals. Thus Roscoe, in -1810,[121\16] endeavored to show that Jussieu's system was not more -natural than the Linnæan, and was inferior as an artificial system: -but he argues his points as if Jussieu's characters were the grounds -of his distribution; which, as we have said, is to mistake the -construction of a natural system. In 1803, Salisbury[122\16] had -already assailed the machinery of the system, maintaining that there -are no cases of perigynous stamens, as Jussieu assumes; but this he -urges with great expressions of respect for the author of the -method. And the more profound botanists of England soon showed that -they could appreciate and extend the natural method. Robert Brown, -who had accompanied Captain Flinders to New Holland in 1801, and -who, after examining that country, brought home, in 1805, nearly -four thousand species of plants, was the most distinguished example -of this. In his preface to the _Prodromus Floræ Novæ Hollandiæ_, he -says, that he found himself under the necessity of employing the -natural method, as the only way of avoiding serious error, when he -had to deal with so many new genera as occur in New Holland; and -that he has, therefore, followed the method of Jussieu; the greater -part of whose orders are truly natural, "although their arrangement -in classes, as is," he says, "conceded by their author, no less -candid than learned, is often artificial, and, as appears to me, -rests on doubtful grounds." - -[Note 121\16: _Linn. Tr._ vol. xi. p. 50.] - -[Note 122\16: Ibid. vol. viii.] - -From what has already been said, the reader will, I trust, see what -an extensive and exact knowledge of the vegetable world, and what -comprehensive views of affinity, must be requisite in a person who -has to modify the natural system so as to make it suited to receive -and arrange a great number of new plants, extremely different from -the genera on which the arrangement was first formed, as the New -Holland genera for the most part were. He will also see how -impossible it must be to convey by extract or description any notion -of the nature of these modifications: it is enough to say, that they -have excited the applause of botanists wherever the science is -studied, and that they have induced M. de Humboldt and his -fellow-laborers, themselves botanists of the first rank, to dedicate -one of their works to him in terms of the strongest -admiration.[123\16] Mr. Brown has also published {410} special -disquisitions on parts of the Natural System; as on Jussieu's -_Proteaceæ_;[124\16] on the _Asclepiadeæ_, a natural family of -plants which must be separated from Jussieu's _Apocyneæ_;[125\16] -and other similar labors. - -[Note 123\16: Roberto Brown, Britanniarum gloriæ atque ornamento, -totam Botanices scientiam ingenio mirifico complectenti. &c.] - -[Note 124\16: _Linn. Tr._ vol. x. 1809.] - -[Note 125\16: _Mem. of Wernerian N. H. Soc._ vol. i. 1809.] - -We have, I think, been led, by our survey of the history of Botany, -to this point;--that a Natural Method directs us to the study of -Physiology, as the only means by which we can reach the object. This -conviction, which in botany comes at the end of a long series of -attempts at classification, offers itself at once in the natural -history of animals, where the physiological signification of the -resemblances and differences is so much more obvious. I shall not, -therefore, consider any of these branches of natural history in -detail as examples of mere classification. They will come before us, -if at all, more properly when we consider the classifications which -depend on the functions of organs, and on the corresponding -modifications which they necessarily undergo; that is, when we trace -the results of Physiology. But before we proceed to sketch the -history of that part of our knowledge, there are a few points in the -progress of Zoology, understood as a mere classificatory science, -which appear to me sufficiently instructive to make it worth our -while to dwell upon them. - -[2nd Ed.] [Mr. Lindley's recent work, _The Vegetable Kingdom_ (1846), -may be looked upon as containing the best view of the recent history -of Systematic Botany. In the Introduction to this work, Mr. Lindley -has given an account of various recent works on the subject; as -Agardh's _Classes Plantarum_ (1826); Perleb's _Lehrbuch der -Naturgeschichte der Pflanzenreich_ (1826); Dumortier's _Florula -Belgica_ (1827); Bartling's _Ordines Naturales Plantarum_ (1830); -Hess's _Uebersicht der Phanerogenischen Natürlichen Pflanzenfamilien_ -(1832); Schulz's _Natürliches System des Pflanzenreich's_ (1832); -Horaninow's _Primæ Lineæ Systematis Naturæ_ (1834); Fries's _Corpus -Florarum provincialium Sueciæ_ (1835); Martins's _Conspectus Regni -Vegetablis secundum Characteres Morphologicos_ (1835); Sir Edward F. -Bromhead's System, as published in the _Edinburgh Journal_ and other -Journals (1836-1840); Endlicher's _Genera Plantarum secundum Ordines -Naturales disposita_ (1836-1840); Perleb's _Clavis Classicum Ordinum -et Familiarum_ (1838); Adolphe Brongniart's _Enumération des Genres de -Plantes_ (1843); Meisner's _Plantarum vascularium Genera secundum -Ordines Naturales digesta_ (1843); Horaninow's _Tetractys Naturæ, seu -Systema quinquemembre omnium Naturalium_ {411} (1843); Adrien de -Jussieu's _**Cours Elémentaire d'Histoire Naturelle. Botanique_ -(1844). - -Mr. Lindley, in this as in all his works, urges strongly the -superior value of natural as compared with artificial systems; his -principles being, I think, nearly such as I have attempted to -establish in the _Philosophy of the Sciences_, Book viii., Chapter -ii. He states that the leading idea which has been kept in view in -the compilation of his work is this maxim of Fries: "Singula sphæra -(sectio) _ideam quandam_ exponit, indeque ejus character notione -simplici optime exprimitur;" and he is hence led to think that the -true characters of all natural assemblages are extremely simple. - -One of the leading features in Mr. Lindley's system is that he has -thrown the Natural Orders into groups subordinate to the higher -divisions of Classes and Sub-classes. He had already attempted this, -in imitation of Agardh and Bartling, in his _Nixus Plantarum_ -(1838). The groups of Natural Orders were there called _Nixus_ -(tendencies); and they were denoted by names ending in _ales_; but -these groups were further subordinated to _Cohorts_. Thus the first -member of the arrangement was Class 1. EXOGENÆ. Sub-class 1. -POLYPETALÆ. Cohort 1. ALBUMINOSÆ. _Nixus_ 1. _Ranales_. Natural -Orders included in this _Nixus_, Ranunculaceæ, Saraceniceæ, -Papaveraceæ, &c. In the _Vegetable Kingdom_, the groups of Natural -Orders are termed _Alliances_. In this work, the Sub-classes of the -EXOGENS are four: I. DICLINOUS; II. HYPOGYNOUS; III. PERIGYNOUS; IV. -EPIGYNOUS; and the Alliances are subordinated to these without the -intervention of _Cohorts_. - -Mr. Lindley has also, in this as in other works, given English names -for the Natural Orders. Thus for _Nymphaceæ_, _Ranunculaceæ_, -_Tamaricaceæ_, _Zygophyllaceæ_, _Eleatrinaceæ_, he substitutes -Water-Lilies, Crowfoots, Tamarisks, Bean-Capers, and Water-Peppers; -for _Malvaceæ_, _Aurantiaceæ_, _Gentianaceæ_, _Primulaceæ_, -_Urtiaceæ_, _Euphorbiaceæ_, he employs Mallow-worts, Citron-worts, -Gentian-worts, Prim-worts, Nettle-worts, Spurge-worts; and the terms -Orchids, Hippurids, Amaryllids, Irids, Typhads, Arads, Cucurbits, -are taken as English equivalents for _Orchidaceæ_, _Haloragaceæ_, -_Amaryllidaceæ_, _Iridaceæ_, _Typhaceæ_, _Araceæ_, _Cucurbitaceæ_. -All persons who wish success to the study of botany in England must -rejoice to see it tend to assume this idiomatic shape.] {412} - - - - -CHAPTER VI. - -THE PROGRESS OF SYSTEMATIC ZOOLOGY. - - -THE history of Systematic Botany, as we have presented it, may be -considered as a sufficient type of the general order of progression -in the sciences of classification. It has appeared, in the survey -which we have had to give, that this science, no less than those -which we first considered, has been formed by a series of inductive -processes, and has, in its history, Epochs at which, by such -processes, decided advances were made. The important step in such -cases is, the seizing upon some artificial mark which conforms to -natural resemblances;--some basis of arrangement and nomenclature by -means of which true propositions of considerable generality can be -enunciated. The advance of other classificatory sciences, as well as -botany, must consist of such steps; and their course, like that of -botany, must (if we attend only to the real additions made to -knowledge,) be gradual and progressive, from the earliest times to -the present. - -To exemplify this continued and constant progression in the whole -range of Zoology, would require vast knowledge and great labor; and -is, perhaps, the less necessary, after we have dwelt so long on the -history of Botany, considered in the same point of view. But there -are a few observations respecting Zoology in general which we are -led to make in consequence of statements recently promulgated; for -these statements seem to represent the history of Zoology as having -followed a course very different from that which we have just -ascribed to the classificatory sciences in general. It is held by -some naturalists, that not only the formation of a systematic -classification in Zoology dates as far back as Aristotle; but that -his classification is, in many respects, superior to some of the -most admired and recent attempts of modern times. - -If this were really the case, it would show that at least the idea -of a Systematic Classification had been formed and developed long -previous to the period to which we have assigned such a step; and it -would be difficult to reconcile such an early maturity of Zoology -with the conviction, which we have had impressed upon us by the -other {413} parts of our history, that not only labor but time, not -only one man of genius but several, and those succeeding each other, -are requisite to the formation of any considerable science. - -But, in reality, the statements to which we refer, respecting the -scientific character of Aristotle's Zoological system, are -altogether without foundation; and this science confirms the lessons -taught us by all the others. The misstatements respecting -Aristotle's doctrines are on this account so important, and are so -curious in themselves, that I must dwell upon them a little. - -Aristotle's nine Books _On Animals_ are a work enumerating the -differences of animals in almost all conceivable respects;--in the -organs of sense, of motion, of nutrition, the interior anatomy, the -exterior covering, the manner of life, growth, generation, and many -other circumstances. These differences are very philosophically -estimated. "The corresponding parts of animals," he says,[126\16] -"besides the differences of quality and circumstance, differ in -being more or fewer, greater or smaller, and, speaking generally, in -excess and defect. Thus some animals have crustaceous coverings, -others hard shells; some have long beaks, some short; some have many -wings, some have few; Some again have parts which others want, as -crests and spurs." He then makes the following important remark: -"Some animals have parts which correspond to those of others, not as -being the same in species, nor by excess and defect, but by -_analogy_; thus a claw is analogous to a thorn, and a nail to a -hoof, and a hand to the nipper of a lobster, and a feather to a -scale; for what a feather is in a bird, that is a scale in a fish." - -[Note 126\16: Lib. i. c. i.] - -It will not, however, be necessary, in order to understand Aristotle -for our present purpose, that we should discuss his notion of -Analogy. He proceeds to state his object,[127\16] which is, as we -have said, to describe the differences of animals in their structure -and habits. He then observes, that for structure, we may take Man -for our type,[128\16] as being best known to us; and the remainder -of the first Book is occupied with a description of man's body, -beginning from the head, and proceeding to the extremities. - -[Note 127\16: Lib. i. c. ii.] - -[Note 128\16: c. iii.] - -In the next Book, (from which are taken the principal passages in -which his modern commentators detect his system,) he proceeds to -compare the differences of parts in different animals, according to -the order which he had observed in man. In the first chapter he -speaks {414} of the head and neck of animals; in the second, of the -parts analogous to arms and hands; in the third, of the breast and -paps, and so on; and thus he comes, in the seventh chapter, to the -legs, feet, and toes: and in the eleventh, to the teeth, and so to -other parts. - -The construction of a classification consists in the selection of -certain parts, as those which shall eminently and peculiarly -determine the place of each species in our arrangement. It is clear, -therefore, that such an enumeration of differences as we have -described, supposing it complete, contains the materials of all -possible classifications. But we can with no more propriety say that -the author of such an enumeration of differences is the author of -any classification which can be made by means of them, than we can -say that a man who writes down the whole alphabet writes down the -solution of a given riddle or the answer to a particular question. - -Yet it is on no other ground than this enumeration, so far as I can -discover, that Aristotle's "System" has been so decidedly spoken -of,[129\16] and exhibited in the most formal tabular shape. The -authors of this _Systema Aristotelicum_, have selected, I presume, -the following passages from the work _On Animals_, as they might -have selected any other; and by arranging them according to a -subordination unknown to Aristotle himself have made for him a -scheme which undoubtedly bears a great resemblance to the most -complete systems of modern times. - -[Note 129\16: _Linnæan Transactions_, vol. xvi. p. 24.] - -Book I., chap. v.--"Some animals are viviparous, some oviparous, -some vermiparous. The viviparous are such as man, and the horse, and -all those animals which have hair; and of aquatic animals, the whale -kind, as the dolphin and cartilaginous fishes." - -Book II., chap. vii.--"Of quadrupeds which have blood and are -viviparous, some are (as to their extremities,) many-cloven, as the -hands and feet of man. For some are many-toed, as the lion, the dog, -the panther; some are bifid, and have hoofs instead of nails, as the -sheep, the goat, the elephant, the hippopotamus; and some have -undivided feet, as the solid-hoofed animals, the horse and ass. The -swine kind share both characters." - -Chap. ii.--"Animals have also great differences in the teeth, both -when compared with each other and with man. For all quadrupeds which -have blood and are viviparous, have teeth. And in the first place, -some are ambidental,[130\16] (having teeth in both jaws;) and some -{415} are not so, wanting the front teeth in the upper jaw. Some -have neither front teeth nor horns, as the camel; some have -tusks,[131\16] as the boar, some have not. Some have -serrated[132\16] teeth, as the lion, the panther, the dog; some have -the teeth unvaried,[133\16] as the horse and the ox; for the animals -which vary their cutting-teeth have all serrated teeth. No animal -has both tusks and horns; nor has any animal with serrated teeth -either of those weapons. The greater part have the front teeth -cutting, and those within broad." - -[Note 130\16: Ἀμφόδοντα.] - -[Note 131\16: Χαυλιόδοντα.] - -[Note 132\16: Καρχαρόδοντα.] - -[Note 133\16: Ἀνεπάλλακτα.] - -These passages undoubtedly contain most of the differences on which -the asserted Aristotelian classification rests; but the -classification is formed by using the characters drawn from the -teeth, in order to subdivide those taken from the feet; whereas in -Aristotle these two sets of characters stand side by side, along -with dozens of others; any selection of which, employed according to -any arbitrary method of subordination, might with equal justice be -called Aristotle's system. - -Why, for instance, in order to form subdivisions of animals, should -we not go on with Aristotle's continuation of the second of the -above quoted passages, instead of capriciously leaping to the third? -"Of these some have horns, some have none . . . Some have a -fetlock-joint,[134\16] some have none . . . Of those which have -horns, some have them solid throughout, as the stag; others, for the -most part, hollow . . . Some cast their horns, some do not." If it -be replied, that we could not, by means of such characters, form a -tenable zoological system; we again ask by what right we assume -Aristotle to have made or attempted a systematic arrangement, when -what he has written, taken in its natural order, does not admit of -being construed into a system. - -[Note 134\16: Ἀστράγαλον.] - -Again, what is the object of any classification? This, at least, -among others. To enable the person who uses it to study and describe -more conveniently the objects thus classified. If, therefore, -Aristotle had formed or adopted any system of arrangement, we should -see it in the order of the subjects in his work. Accordingly, so far -as he has a system, he professes to make this use of it. At the -beginning of the fifth Book, where he is proceeding to treat of the -different modes of generation of animals, he says, "As we formerly -made a Division of animals according to their kinds, we must now, in -the same manner, give a general survey of their History (θεωρίαν). -Except, indeed, that in the former case we made our commencement by -a description {416} of man, but in the present instance we must -speak of him last, because he requires most study. We must begin -then with those animals which have shells; we must go on to those -which have softer coverings, as crustacea, soft animals, and -insects; after these, fishes, both viviparous and oviparous; then -birds; then land animals, both viviparous and oviparous." - -It is clear from this passage that Aristotle had certain wide and -indefinite views of classification, which though not very exact, are -still highly creditable to him; but it is equally clear that he was -quite unconscious of the classification that has been ascribed to -him. If he had adopted that or any other system, this was precisely -the place in which he must have referred to and employed it. - -The honor due to the stupendous accumulation of zoological knowledge -which Aristotle's works contain, cannot be tarnished by our denying -him the credit of a system which he never dreamt of and which, from -the nature of the progress of science, could not possibly be -constructed at that period. But, in reality, we may exchange the -mistaken claims which we have been contesting for a better, because -a truer praise. Aristotle does show, as far as could be done at his -time, a perception of the need of groups, and of names of groups, in -the study of the animal kingdom; and thus may justly be held up as -the great figure in the Prelude to the Formation of Systems which -took place in more advanced scientific times. - -This appears, in some measure, from the passage last quoted. For not -only is there, in that, a clear recognition of the value and object -of a method in natural history; but the general arrangement of the -animal kingdom there proposed has considerable scientific merit, and -is, for the time, very philosophical. But there are passages in his -work in which he shows a wish to carry the principle of arrangement -more into detail. Thus, in the first Book, before proceeding to his -survey of the differences of animals,[135\16] after speaking of such -classes as Quadrupeds. Birds, Fishes, Cetaceous, Testaceous, -Crustaceous Animals, Mollusks, Insects, he says, (chap. vii.) -"Animals cannot be divided into large genera, in which one kind -includes many kinds. For some kinds are unique, and have no -difference of species, as _man_. Some have such kinds, but have no -names for them. Thus all quadrupeds which have not wings, have -blood. But of these, some are viviparous, some oviparous. Those -which are {417} viviparous have not all hair; those which are -oviparous have scales." We have here a manifestly intentional -subordination of characters: and a kind of regret that we have not -names for the classes here indicated; such, for instance, as -viviparous quadrupeds having hair. But he follows the subject into -further detail. "Of the class of viviparous quadrupeds," he -continues, "there are many genera,[136\16] but these again are -without names, except specific names, such as _man_, _lion_, _stag_, -_horse_, _dog_, and the like. Yet there is a genus of animals that -have names, as the horse, the ass, the _oreus_, the _ginnus_, the -_innus_, and the animal which in Syria is called _heminus_ (mule); -for these are called _mules_, from their resemblance only; not being -mules, for they breed of their own kind. Wherefore," he adds, that -is, because we do not possess recognized genera and generic names of -this kind, "we must take the species separately, and study the -nature of each." - -[Note 135\16: Γένη.] - -[Note 136\16: **Εἴδη.] - -These passages afford us sufficient ground for placing Aristotle at -the head of those naturalists to whom the first views of the -necessity of a zoological system are due. It was, however, very long -before any worthy successor appeared, for no additional step was -made till modern times. When Natural History again came to be -studied in Nature, the business of Classification, as we have seen, -forced itself upon men's attention, and was pursued with interest in -animals, as in plants. The steps of its advance were similar in the -two cases;--by successive naturalists, various systems of artificial -marks were selected with a view to precision and convenience;--and -these artificial systems assumed the existence of certain natural -groups, and of a natural system to which they gradually tended. But -there was this difference between botany and zoology:--the reference -to physiological principles, which, as we have remarked, influenced -the natural systems of vegetables in a latent and obscure manner, -botanists being guided by its light, but hardly aware that they were -so, affected the study of systematic zoology more directly and -evidently. For men can neither overlook the general physiological -features of animals, nor avoid being swayed by them in their -judgments of the affinities of different species. Thus the -classifications of zoology tended more and more to a union with -comparative anatomy, as the science was more and more -improved.[137\16] But comparative anatomy belongs to the subject of -the next Book; and anything it may be proper to say respecting its -influence upon zoological arrangements, will properly find a place -there. {418} - -[Note 137\16: Cuvier, _Leç. d'Anat. Comp._ vol. i. p. 17.] - -It will appear, and indeed it hardly requires to be proved, that -those steps in systematic zoology which are due to the light thrown -upon the subject by physiology, are the result of a long series of -labors by various naturalists, and have been, like other advances in -science, led to and produced by the general progress of such -knowledge. We can hardly expect that the classificatory sciences can -undergo any material improvement which is not of this kind. Very -recently, however, some authors have attempted to introduce into -these sciences certain principles which do not, at first sight, -appear as a continuation and extension of the previous researches of -comparative anatomists. I speak, in particular, of the doctrines of -a _Circular Progression_ in the series of affinity; of a _Quinary -Division_ of such circular groups; and of a relation of _Analogy_ -between the members of such groups, entirely distinct from the -relation of _Affinity_. - -The doctrine of Circular Progression has been propounded principally -by Mr. Macleay; although, as he has shown,[138\16] there are -suggestions of the same kind to be found in other writers. So far as -this view negatives the doctrine of a mere linear progression in -nature, which would place each genus in contact only with the -preceding and succeeding ones, and so far as it requires us to -attend to more varied and ramified resemblances, there can be no -doubt that it is supported by the result of all the attempts to form -natural systems. But whether that assemblage of circles of -arrangement which is now offered to naturalists, be the true and -only way of exhibiting the natural relations of organized bodies, is -a much more difficult question, and one which I shall not here -attempt to examine; although it will be found, I think, that those -analogies of science which we have had to study, would not fail to -throw some light upon such an inquiry. The prevalence of an -invariable numerical law in the divisions of natural groups, (as the -number _five_ is asserted to prevail by Mr. Macleay, the number -_ten_ by Fries, and other numbers by other writers), would be a -curious fact, if established; but it is easy to see that nothing -short of the most consummate knowledge of natural history, joined -with extreme clearness of view and calmness of judgment, could -enable any one to pronounce on the attempts which have been made to -establish such a principle. But the doctrine of a relation of -_Analogy_ distinct from Affinity, in the manner which has recently -been taught, seems to be obviously at variance with that gradual -approximation of the classificatory to the {419} physiological -sciences, which has appeared to us to be the general tendency of -real knowledge. It seems difficult to understand how a reference to -such relations as those which are offered as examples of -analogy[139\16] can be otherwise than a retrograde step in science. - -[Note 138\16: _Linn. Trans._ vol. xvi. p. 9.] - -[Note 139\16: For example, the goatsucker has an _affinity_ with the -swallow; but it has an _analogy_ with the bat, because both fly at -the same hour of the day, and feed in the same manner.--Swainson, -_Geography and Classification of Animals_, p. 129.] - -Without, however, now dwelling upon these points, I will treat a -little more in detail of one of the branches of Zoology. - -[2nd Ed.] [For the more recent progress of Systematic Zoology, see -in the _Reports_ of the British Association, in 1834, Mr. L. -Jenyns's _Report an the Recent Progress and Present State of -Zoology_, and in 1844, Mr. Strickland's _Report on the Recent -Progress and Present State of Ornithology_. In these Reports, the -questions of the Circular Arrangement, the Quinary System, and the -relation of Analogy and Affinity are discussed.] - - - - -CHAPTER VII. - -THE PROGRESS OF ICHTHYOLOGY. - - -IF it had been already observed and admitted that sciences of the -same kind follow, and must follow, the same course in the order of -their development, it would be unnecessary to give a history of any -special branch of Systematic Zoology; since botany has already -afforded us a sufficient example of the progress of the -classificatory sciences. But we may be excused for introducing a -sketch of the advance of one department of zoology, since we are led -to the attempt by the peculiar advantage we possess in having a -complete history of the subject written with great care, and brought -up to the present time, by a naturalist of unequalled talents and -knowledge. I speak of Cuvier's _Historical View of Ichthyology_, -which forms the first chapter of his great work on that part of -natural history. The place and office in the progress of this -science, which is assigned to each person by Cuvier, will probably -not be lightly contested. It will, therefore, be no small -confirmation of the justice of the views on which the {420} -distribution of the events in the history of botany was founded, if -Cuvier's representation of the history of ichthyology offers to us -obviously a distribution almost identical. - -We shall find that this is so;--that we have, in zoology as in botany, -a period of unsystematic knowledge; a period of misapplied erudition; -an epoch of the discovery of fixed characters; a period in which many -systems were put forward; a struggle of an artificial and a natural -method; and a gradual tendency of the natural method to a manifestly -physiological character. A few references to Cuvier's history will -enable us to illustrate these and other analogies. - -_Period of Unsystematic Knowledge._--It would be easy to collect a -number of the fabulous stories of early times, which formed a -portion of the imaginary knowledge of men concerning animals as well -as plants. But passing over these, we come to a long period and a -great collection of writers, who, in various ways, and with various -degrees of merit, contributed to augment the knowledge which existed -concerning fish, while as yet there was hardly ever any attempt at a -classification of that province of the animal kingdom. Among these -writers, Aristotle is by far the most important. Indeed he carried -on his zoological researches under advantages which rarely fall to -the lot of the naturalist; if it be true, as Athenæus and Pliny -state,[140\16] that Alexander gave him sums which amounted to nine -hundred talents, to enable him to collect materials for his history -of animals, and put at his disposal several thousands of men to be -employed in hunting, fishing, and procuring information for him. The -works of his on Natural History which remain to us are, nine Books -_Of the History of Animals_; four, _On the Parts of Animals_; five, -_On the Generation of Animals_; one, _On the Going of Animals_; one, -_Of the Sensations, and the Organs of them_; one, _On Sleeping and -Waking_; one, _On the Motion of Animals_; one, _On the Length and -Shortness of Life_; one, _On Youth and Old Age_; one, _On Life and -Death_; one, _On Respiration_. The knowledge of the external and -internal conformation of animals, their habits, instincts, and uses, -which Aristotle displays in these works, is spoken of as something -wonderful even to the naturalists of our own time. And he may be -taken as a sufficient representative of the whole of the period of -which we speak; for he is, says Cuvier,[141\16] not only the first, -but the only one of the ancients who has treated of the natural -history of fishes (the province to which {421} we now confine -ourselves,) in a scientific point of view, and in a way which shows -genius. - -[Note 140\16: Cuv. _Hist. Nat. des Poissons_, i. 13.] - -[Note 141\16: Cuv. p. 18.] - -We may pass over, therefore, the other ancient authors from whose -writings Cuvier, with great learning and sagacity, has levied -contributions to the history of ichthyology; as Theophrastus, Ovid, -Pliny, Oppian, Athenæus, Ælian, Ausonius, Galen. We may, too, leave -unnoticed the compilers of the middle ages, who did little but -abstract and disfigure the portions of natural history which they -found in the ancients. Ichthyological, like other knowledge, was -scarcely sought except in books, and on that very account was not -understood when it was found. - -_Period of Erudition._--Better times at length came, and men began to -observe nature for themselves. The three great authors who are held to -be the founders of modern ichthyology, appeared in the middle of the -sixteenth century; these were Bélon, Rondelet, and Salviani, who all -published about 1555. All the three, very different from the compilers -who filled the interval from Aristotle to them, themselves saw and -examined the fishes which they describe, and have given faithful -representations of them. But, resembling in that respect the founders -of modern botany, Briassavola, Ruellius, Tragus, and others, they -resembled them in this also, that they attempted to make their own -observations a commentary upon the ancient writers. Faithful to the -spirit of their time, they are far more careful to make out the names -which each fish bore in the ancient world, and to bring together -scraps of their history from the authors in whom these names occur, -than to describe them in a lucid manner; so that without their -figures, says Cuvier, it would be almost as difficult to discover -their species as those of the ancients. - -The difficulty of describing and naming species so that they can be -recognized, is little appreciated at first, although it is in -reality the main-spring of the progress of the sciences of -classification. Aristotle never dreamt that the nomenclature which -was in use in his time could ever become obscure;[142\16] hence he -has taken no precaution to enable his readers to recognize the -species of which he speaks; and in him and in other ancient authors, -it requires much labor and great felicity of divination to determine -what the names mean. The perception of this difficulty among modern -naturalists led to systems, and to nomenclature founded upon system; -but these did not come into {422} being immediately at the time of -which we speak; nor till the evil had grown to a more inconvenient -magnitude. - -[Note 142\16: Cuvier, p. 17.] - -_Period of Accumulation of Materials. Exotic Collections._--The -fishes of Europe were for some time the principal objects of study; -but those of distant regions soon came into notice.[143\16] In the -seventeenth century the Dutch conquered Brazil, and George Margrave, -employed by them, described the natural productions of the country, -and especially the fishes. Bontius, in like manner, described some -of those of Batavia. Thus these writers correspond to Romphius and -Rheede in the history of botany. Many others might be mentioned; but -we must hasten to the formation of systems, which is our main object -of attention. - -[Note 143\16: Cuv. p. 43.] - -_Epoch of the Fixation of Characters. Ray and Willoughby._--In -botany, as we have seen, though Ray was one of the first who -invented a connected system, he was preceded at a considerable -interval by Cæsalpinus, who had given a genuine solution of the same -problem. It is not difficult to assign reasons why a sound -classification should be discovered for plants at an earlier period -than for fishes. The vastly greater number of the known species, and -the facilities which belong to the study of vegetables, give the -botanist a great advantage; and there are numerical relations of a -most definite kind (for instance, the number of parts of the -seed-vessel employed by Cæsalpinus as one of the bases of his -system), which are tolerably obvious in plants, but which are not -easily discovered in animals. And thus we find that in ichthyology, -Ray, with his pupil and friend Willoughby, appears as the first -founder of a tenable system.[144\16] - -[Note 144\16: Francisci Willoughbeii, Armigeri, _de Historia -Piscium_, libri iv. jussu et sumptibus Societatis Regiæ Londinensis -editi, &c. Totum opus recognovit, coaptavit, supplevit, librum etiam -primum et secundum adjecit Joh. Raius. Oxford, 1668.] - -The first great division in this system is into _cartilaginous_ and -_bony_ fishes; a primary division, which had been recognized by -Aristotle, and is retained by Cuvier in his latest labors. The -subdivisions are determined by the general form of the fish (as long -or flat), by the teeth, the presence or absence of ventral fins, the -number of dorsal fins, and the nature of the spines of the fins, as -soft or prickly. Most of these characters have preserved their -importance in later systems; especially the last, which, under the -terms _malacopterygian_ and _acanthopterygian_, holds a place in the -best recent arrangements. {423} - -That this system was a true first approximation to a solution of the -problem, appears to be allowed by naturalists. Although, says -Cuvier,[145\16] there are in it no genera well defined and well -limited, still in many places the species are brought together very -naturally, and in such a way that a few words of explanation would -suffice to form, from the groups thus presented to us, several of -the genera which have since been received. Even in botany, as we -have seen, genera were hardly maintained with any degree of -precision, till the binary nomenclature of Linnæus made this -division a matter of such immense convenience. - -[Note 145\16: Cuvier, p. 57.] - -The amount of this convenience, the value of a brief and sure -nomenclature, had not yet been duly estimated. The work of Willoughby -forms an epoch,[146\16] and a happy epoch, in the history of -ichthyology; for the science, once systematized, could distinguish the -new from the old, arrange methodically, describe clearly. Yet, because -Willoughby had no nomenclature of his own, and no fixed names for his -genera, his immediate influence was not great. I will not attempt to -trace this influence in succeeding authors, but proceed to the next -important step in the progress of system. - -[Note 146\16: p. 58.] - -_Improvement of the System. Artedi._--Peter Artedi was a countryman -and intimate friend of Linnæus; and rendered to ichthyology nearly -the same services which Linnæus rendered to botany. In his -_Philosophia Ichthyologica_, he analysed[147\16] all the interior -and exterior parts of animals; he created a precise terminology for -the different forms of which these parts are susceptible; he laid -down rules for the nomenclature of genera and species; besides his -improvements of the subdivisions of the class. It is impossible not -to be struck with the close resemblance between these steps, and -those which are due to the _Fundamenta Botanica_. The latter work -appeared in 1736, the former was published by Linnæus, after the -death of the author, in 1738; but Linnæus had already, as early as -1735, made use of Artedi's manuscripts in the ichthyological part of -his _Systema Naturæ_. We cannot doubt that the two young naturalists -(they were nearly of the same age), must have had a great influence -upon each other's views and labors; and it would be difficult now to -ascertain what portion of the peculiar merits of the Linnæan reform -was derived from Artedi. But we may remark that, in ichthyology at -least, Artedi appears to have been a naturalist of more original -views and profounder philosophy than his friend and editor, who -afterwards himself took up the subject. {424} The reforms of -Linnæus, in all parts of natural history, appear as if they were -mainly dictated by a love of elegance, symmetry, clearness, and -definiteness; but the improvement of the ichthyological system by -Artedi seems to have been a step in the progress to a natural -arrangement. His genera,[148\16] which are forty-five in number, are -so well constituted, that they have almost all been preserved; and -the subdivisions which the constantly-increasing number of species -has compelled his successors to introduce, have very rarely been -such that they have led to the transposition of his genera. - -[Note 147\16: p. 20.] - -[Note 148\16: Cuvier, p. 71.] - -In its bases, however, Artedi's was an artificial system. His -characters were positive and decisive, founded in general upon the -number of rays of the membrane of the gills, of which he was the -first to mark the importance;--upon the relative position of the -fins, upon their number, upon the part of the mouth where the teeth -are found, upon the conformation of the scales. Yet, in some cases, -he has recourse to the interior anatomy. - -Linnæus himself at first did not venture to deviate from the -footsteps of a friend, who, in this science, had been his master. -But in 1758, in the tenth edition of the _Systema Naturæ_, he chose -to depend upon himself and devised a new ichthyological method. He -divided some genera, united others, gave to the species trivial -names and characteristic phrases, and added many species to those of -Artedi. Yet his innovations are for the most part disapproved of by -Cuvier; as his transferring the _chondropterygian_ fishes of Artedi -to the class of reptiles, under the title of _Amphybia nantes_; and -his rejecting the distinction of acanthopterygian and -malacopterygian, which, as we have seen, had prevailed from the time -of Willoughby, and introducing in its stead a distribution founded -on the presence or absence of the ventral fins, and on their -situation with regard to the pectoral fins. "Nothing," says Cuvier, -"more breaks the true connexions of genera than these orders of -_apodes_, _jugulares_, _thoracici_, and _abdominales_." - -Thus Linnæus, though acknowledging the value and importance of -natural orders, was not happy in his attempts to construct a system -which should lead to them. In his detection of good characters for -an artificial system he was more fortunate. He was always attentive -to number, as a character; and he had the very great merit[149\16] -of introducing into the classification the number of rays of the -fins of each species. This mark is one of great importance and use. -And this, as well as {425} other branches of natural history, -derived incalculable advantages from the more general merits of the -illustrious Swede;[150\16]--the precision of the characters, the -convenience of a well-settled terminology, the facility afforded by -the binary nomenclature. These recommendations gave him a -pre-eminence which was acknowledged by almost all the naturalists of -his time, and displayed by the almost universal adoption of his -nomenclature, in zoology, as well as in botany; and by the almost -exclusive employment of his distributions of classes, however -imperfect and artificial they might be. - -[Note 149\16: p. 74.] - -[Note 150\16: Cuvier, p. 85.] - -And even[151\16] if Linnæus had had no other merit than the impulse -he gave to the pursuit of natural science, this alone would suffice -to immortalize his name. In rendering natural history easy, or at -least in making it appear so, he diffused a general taste for it. -The great took it up with interest; the young, full of ardor, rushed -forwards in all directions, with the sole intention of completing -his system. The civilized world was eager to build the edifice which -Linnæus had planned. - -[Note 151\16: Ib. p. 88.] - -This spirit, among other results, produced voyages of natural -historical research, sent forth by nations and sovereigns. George -the Third of England had the honor of setting the example in this -noble career, by sending out the expeditions of Byron, Wallis, and -Carteret, in 1765. These were followed by those of Bougainville, -Cook, Forster, and others. Russia also scattered several scientific -expeditions through her vast dominions; and pupils of Linnæus sought -the icy shores of Greenland and Iceland, in order to apply his -nomenclature to the productions of those climes. But we need not -attempt to convey any idea of the vast stores of natural historical -treasures which were thus collected from every part of the globe. - -I shall not endeavor to follow Cuvier in giving an account of the -great works of natural history to which this accumulation of materials -gave rise; such as the magnificent work of Bloch on Fishes, which -appeared in 1782-1785; nor need I attempt, by his assistance, to -characterize or place in their due position the several systems of -classification proposed about this time. But in the course of these -various essays, the distinction of the artificial and natural methods -of classification came more clearly into view than before; and this is -a point so important to the philosophy of the subject, that we must -devote a few words to it. {426} - -_Separation of the Artificial and Natural Methods in Ichthyology._--It -has already been said that all so-called _artificial methods_ of -classification must be natural, at least as to the narrowest members -of the system; thus the artificial Linnæan method is natural as to -species, and even as to genera. And on the other hand, all proposed -natural methods, so long as they remain unmodified, are artificial as -to their characteristic marks. Thus a Natural Method is an attempt to -provide positive and distinct _characters_ for the _wider_ as well as -for the narrower _natural groups_. These considerations are applicable -to zoology as well as to botany. But the question, how we know natural -groups before we find marks for them, was, in botany, as we have seen, -susceptible only of vague and obscure answers:--the mind forms them, -it was said, by taking the aggregate of all the characters; or by -establishing a subordination of characters. And each of these answers -had its difficulty, of which the solution appeared to be, that in -attempting to form natural orders we are really guided by a latent -undeveloped estimate of physiological relations. Now this principle, -which was so dimly seen in the study of vegetables, shines out with -much greater clearness when we come to the study of animals, in which -the physiological relations of the parts are so manifest that they -cannot be overlooked, and have so strong an attraction for our -curiosity that we cannot help having our judgments influenced by them. -Hence the superiority of natural systems in zoology would probably be -far more generally allowed than in botany; and no arrangement of -animals which, in a large number of instances, violated strong and -clear natural affinities, would be tolerated because it answered the -purpose of enabling us easily to find the name and place of the animal -in the artificial system. Every system of zoological arrangement may -be supposed to aspire to be a natural system. But according to the -various habits of the minds of systematizers, this object was pursued -more or less steadily and successfully; and these differences came -more and more into view with the increase of knowledge and the -multiplication of attempts. - -Bloch, whose ichthyological labors have been mentioned, followed in -his great work the method of Linnæus. But towards the end of his -life he had prepared a general system, founded upon one single -numerical principle;--the number of fins; just as the sexual system -of Linnæus is founded upon the number of stamina; and he made his -subdivisions according to the position of the ventral and pectoral -fins; the same character which Linnæus had employed for his primary -{427} division. He could not have done better, says Cuvier,[152\16] -if his object had been to turn into ridicule all artificial methods, -and to show to what absurd combinations they may lead. - -[Note 152\16: p. 108.] - -Cuvier himself who always pursued natural systems with a singularly -wise and sagacious consistency, attempted to improve the -ichthyological arrangements which had been proposed before him. In -his _Règne Animal_, published in 1817, he attempts the problem of -arranging this class; and the views suggested to him, both by his -successes and his failures, are so instructive and philosophical, -that I cannot illustrate the subject better than by citing some of -them. - -"The class of fishes," he says,[153\16] "is, of all, that which -offers the greatest difficulties, when we wish to subdivide it into -orders, according to fixed and obvious characters. After many -trials, I have determined on the following distribution, which in -some instances is wanting in precision, but which possesses the -advantage of keeping the natural families entire. - -[Note 153\16: _Règne Animal_, vol. ii. p. 110.] - -"Fish form two distinct series;--that of _chondropterygians_ or -_cartilaginous fish_, and that of _fish_ properly so called. - -"The _first_ of these series has for its character, that the -palatine bones replace, in it, the bones of the upper jaw: moreover -the whole of its structure has evident analogies, which we shall -explain. - -"It divides itself into three ORDERS: -"The CYCLOSTOMES, in which the jaws are soldered (_soudées_) into an -immovable ring, and the bronchiæ are open in numerous holes. - -"The SELACIANS, which have the bronchiæ like the preceding, but not -the jaws. - -"The STURONIANS, in which the bronchiæ are open as usual by a slit -furnished with an operculum. - -"The second series, or that of _ordinary fishes_, offers me, in the -first place, a primary division, into those of which the maxillary -bone and the palatine arch are dovetailed (_engrenés_) to the skull. -Of these I make an order of PECTOGNATHS, divided into two families; -the _gymnodonts_ and the _scleroderms_. - -"After these I have the fishes with complete jaws, but with bronchiæ -which, instead of having the form of combs, as in all the others, -have the form of a series of little tufts (_houppes_). Of these I -again form an order, which I call LOPHOBRANCHS, which only includes -one family. {428} - -"There then remains an innumerable quantity of fishes, to which we -can no longer apply any characters except those of the exterior -organs of motion. After long examination, I have found that the -least bad of these characters is, after all, that employed by Ray -and Artedi, taken from the nature of the first rays of the dorsal -and of the anal fin. Thus ordinary fishes are divided into -MALACOPTERYGIANS, of which all the rays are soft, except sometimes -the first of the dorsal fin or the pectorals;--and -ACANTHOPTERYGIANS, which have always the first portion of the -dorsal, or of the first dorsal when there are two, supported by -spinous rays, and in which the anal has also some such rays, and the -ventrals, at least, each one. - -"The former may be subdivided without inconvenience, according to -their ventral fins, which are sometimes situate behind the abdomen, -sometimes adherent to the apparatus of the shoulder, or, finally, -are sometimes wanting altogether. - -"We thus arrive at the three orders of ABDOMINAL MALACOPTERYGIANS, -of SUBBRACHIANS, and of APODES; each of which includes some natural -families which we shall explain: the first, especially, is very -numerous. - -"But this basis of division is absolutely impracticable with the -Acanthopterygians; and the problem of establishing among these any -other subdivision than that of the natural families has hitherto -remained for me insoluble. Fortunately several of these families -offer characters almost as precise as those which we could give to -true orders. - -"In truth, we cannot assign to the families of fishes, ranks as -marked, as for example, to those of mammifers. Thus the -Chondropterygians on the one hand hold to reptiles by the organs of -the senses, and by those of generation in some; and they are related -to mollusks and worms by the imperfection of the skeleton in others. - -"As to Ordinary Fishes, if any part of the organization is found -more developed in some than in others, there does not result from -this any pre-eminence sufficiently marked, or of sufficient -influence upon their whole system, to oblige us to consult it in the -methodical arrangement. - -"We shall place them, therefore, nearly in the order in which we -have just explained their characters." - -I have extracted the whole of this passage, because, though it is -too technical to be understood in detail by the general reader, -those who have followed with any interest the history of the -attempts at a natural classification in any department in nature, -will see here a fine example of the problems which such attempts -propose, of the {429} difficulties which it may present, and of the -reasonings, labors, cautions, and varied resources, by means of -which its solution is sought, when a great philosophical naturalist -girds himself to the task. We see here, most instructively, how -different the endeavor to frame such a natural system, is from the -procedure of an artificial system, which carries imperatively -through the whole of a class of organized beings, a system of marks -either arbitrary, or conformable to natural affinities in a partial -degree. And we have not often the advantage of having the reasons -for a systematic arrangement so clearly and fully indicated, as is -done here, and in the descriptions of the separate orders. - -This arrangement Cuvier adhered to in all its main points, both in -the second edition of the _Règne Animal_, published in 1821, and in -his _Histoire Naturelle des Poissons_, of which the first volume was -published in 1828, but which unfortunately was not completed at the -time of his death. It may be supposed, therefore, to be in -accordance with those views of zoological philosophy, which it was -the business of his life to form and to apply; and in a work like -the present, where, upon so large a question of natural history, we -must be directed in a great measure by the analogy of the history of -science, and by the judgments which seem most to have the character -of wisdom, we appear to be justified in taking Cuvier's -ichthyological system as the nearest approach which has yet been -made to a natural method in that department. - -The true natural method is only one: artificial methods, and even -good ones, there may be many, as we have seen in botany; and each of -these may have its advantages for some particular use. On some -methods of this kind, on which naturalists themselves have hardly -yet had time to form a stable and distinct opinion, it is not our -office to decide. But judging, as I have already said, from the -general analogy of the natural sciences, I find it difficult to -conceive that the ichthyological method of M. Agassiz, recently -propounded with an especial reference to fossil fishes, can be -otherwise than an artificial method. It is founded entirely on one -part of the animal, its scaly covering, and even on a single scale. -It does not conform to that which almost all systematic -ichthyologists hitherto have considered as a permanent natural -distinction of a high order; the distinction of bony and -cartilaginous fishes; for it is stated that each order contains -examples of both.[154\16] I do not know what general anatomical or -physiological {430} truths it brings into view; but they ought to be -very important and striking ones, to entitle them to supersede those -which led Cuvier to his system. To this I may add, that the new -ichthyological classification does not seem to form, as we should -expect that any great advance towards a natural system would form, a -connected sequel to the past history of ichthyology;--a step to -which anterior discoveries and improvements have led, and in which -they are retained. - -[Note 154\16: Dr. Buckland's _Bridgewater Treatise_, p. 270.] - -But notwithstanding these considerations, the method of M. Agassiz -has probably very great advantages for his purpose; for in the case -of fossil fish, the parts which are the basis of his system often -remain, when even the skeleton is gone. And we may here again refer -to a principle of the classificatory sciences which we cannot make -too prominent;--all arrangements and nomenclatures are good, which -enable us to assert general propositions. Tried by this test, we -cannot fail to set a high value on the arrangement of M. Agassiz; -for propositions of the most striking generality respecting fossil -remains of fish, of which geologists before had never dreamt, are -enunciated by means of his groups and names. Thus only the two first -orders, the _Placoïdians_ and _Ganoïdians_, existed before the -commencement of the cretaceous formation: the third and fourth -orders, the _Ctenoïdians_ and _Cycloïdians_, which contain -three-fourths of the eight thousand known species of living Fishes, -appear for the first time in the cretaceous formation: and other -geological relations of these orders, no less remarkable, have been -ascertained by M. Agassiz. - -But we have now, I trust, pursued these sciences of classification -sufficiently far; and it is time for us to enter upon that higher -domain of Physiology to which, as we have said. Zoology so -irresistibly directs us. - -[2nd Ed.] [I have retained the remarks which I ventured at first to -make on the System of M. Agassiz; but I believe the opinion of the -most philosophical ichthyologists to be that Cuvier's System was too -exclusively based on the internal skeleton, as Agassiz's was on the -external skeleton. In some degree both systems have been superseded, -while all that was true in each has been retained. Mr. Owen, in his -_Lectures on Vertebrata_ (1846), takes Cuvierian characters from the -endo-skeleton, Agassizian ones from the exo-skeleton, Linnæan ones -from the ventral fins, Müllerian ones from the air-bladder, and -combines them by the light of his own researches, with the view of -forming a system more truly natural than any preceding one. - -As I have said above, naturalists, in their progress towards a -Natural {431} System, are guided by physiological relations, -latently in Botany, but conspicuously in Zoology. From the epoch of -Cuvier's _Règne Animal_, the progress of Systematic Zoology is -inseparably dependent on the progress of Comparative Anatomy. Hence -I have placed Cuvier's Classification of animal forms in the next -Book, which treats of Physiology.] - - - -{{433}} -BOOK XVII. - - -_ORGANICAL SCIENCES._ - - -HISTORY OF PHYSIOLOGY -AND -COMPARATIVE ANATOMY. - - - Fearful and wondrous is the skill which moulds - Our body's vital plan, - And from the first dim hidden germ unfolds - The perfect limbs of man. - Who, who can pierce the secret? tell us how - Something is drawn from naught, - Life from the inert mass? Who, Lord! but thou, - Whose hand the whole has wrought? - Of this corporeal substance, still to be, - Thine eye a survey took; - And all my members, yet unformed by thee, - Were written in thy book. - PSALM cxxxix. 13-16. - - - -{{435}} -INTRODUCTION. - - -_Of the Organical Sciences_ - -THOUGH the general notion of _life_ is acknowledged by the most -profound philosophers to be dim and mysterious, even up to the -present time; and must, in the early stages of human speculation, -have been still more obscure and confused; it was sufficient, even -then, to give interest and connexion to men's observations upon -their own bodies and those of other animals. It was seen, that in -living things, certain peculiar processes were constantly repeated, -as those of breathing and of taking food, for example; and that a -certain conformation of the parts of the animal was subservient to -these processes; and thus were gradually formed the notions of -_Function_ and of _Organization_. And the sciences of which these -notions formed the basis are clearly distinguishable from all those -which we have hitherto considered. We conceive an _organized_ body -to be one in which the parts are there for the sake of the whole, in -a manner different from any mechanical or chemical connexion; we -conceive a _function_ to be not merely a process of change, but of -change connected with the general vital process. When mechanical or -chemical processes occur in the living body, they are instrumental -to, and directed by, the peculiar powers of life. The sciences which -thus consider organization and vital functions may be termed -_organical_ sciences. - -When men began to speculate concerning such subjects, the general -mode of apprehending the process in the cases of some functions, -appeared to be almost obvious; thus it was conceived that the growth -of animals arose from their frame appropriating to itself a part of -the substance of the food through the various passages of the body. -Under the influence of such general conceptions, speculative men -were naturally led to endeavor to obtain more clear and definite -views of the course of each of such processes, and of the mode in -which the separate parts contributed to it. Along with the -observation of the living person, the more searching examination -which could be carried on in the dead body, and the comparison of -various kinds of animals, soon showed that this pursuit was rich in -knowledge and in interest. {436} Moreover, besides the interest -which the mere speculative faculty gave to this study, the Art of -Healing added to it a great practical value; and the effects of -diseases and of medicines supplied new materials and new motives for -the reasonings of the philosopher. - -In this manner anatomy or physiology may be considered as a science -which began to be cultivated in the earliest periods of civilization. -Like most other ancient sciences, its career has been one of perpetual -though variable progress; and as in others, so in this, each step has -implied those which had been previously made, and cannot be understood -aright except we understand them. Moreover, the steps of this advance -have been very many and diverse; the cultivators of anatomy have in -all ages been numerous and laborious; the subject is one of vast -extent and complexity; almost every generation had added something to -the current knowledge of its details; and the general speculations of -physiologists have been subtle, bold, and learned. It must, therefore, -be difficult or impossible for a person who has not studied the -science with professional diligence and professional advantages, to -form just judgments of the value of the discoveries of various ages -and persons, and to arrange them in their due relation to each other. -To this we may add, that though all the discoveries which have been -made with respect to particular functions or organizations are -understood to be subordinate to one general science, the Philosophy of -Life, yet the principles and doctrines of this science nowhere exist -in a shape generally received and assented to among physiologists; and -thus we have not, in this science, the advantage which in some others -we have possessed;--of discerning the true direction of its first -movements, by knowing the point to which they ultimately tend;--of -running on beyond the earlier discoveries, and thus looking them in -the face, and reading their true features. With these disadvantages, -all that we can have to say respecting the history of Physiology must -need great indulgence on the part of the reader. - -Yet here, as in other cases, we may, by guiding our views by those -of the greatest and most philosophical men who have made the subject -their study, hope to avoid material errors. Nor can we well evade -making the attempt. To obtain some simple and consistent view of the -progress of physiological science, is in the highest degree -important to the completion of our views of the progress of physical -science. For the physiological or organical sciences form a class to -which the classes already treated of, the mechanical, chemical, and -classificatory sciences, are subordinate and auxiliary. Again, -another {437} circumstance which makes physiology an important part -of our survey of human knowledge is, that we have here a science -which is concerned, indeed, about material combinations, but in -which we are led almost beyond the borders of the material world, -into the region of sensation and perception, thought and will. Such -a contemplation may offer some suggestions which may prepare us for -the transition from physical to metaphysical speculations. - -In the survey which we must, for such purposes, take of the progress -of physiology, it is by no means necessary that we should exhaust -the subject, and attempt to give the history of every branch of the -knowledge of the phenomena and laws of living creatures. It will be -sufficient, if we follow a few of the lines of such researches, -which may be considered as examples of the whole. We see that life -is accompanied and sustained by many processes, which at first offer -themselves to our notice as separate functions, however they may -afterwards be found to be connected and identified; such are -feeling, digestion, respiration, the action of the heart and pulse, -generation, perception, voluntary motion. The analysis of any one of -these functions may be pursued separately. And since in this, as in -all genuine sciences, our knowledge becomes real and scientific, -only in so far as it is verified in particular facts, and thus -established in general propositions, such an original separation of -the subjects of research is requisite to a true representation of -the growth of real knowledge. The loose hypotheses and systems, -concerning the connexion of different vital faculties and the -general nature of living things, which have often been promulgated, -must be excluded from this part of our plan. We do not deny all -value and merit to such speculations; but they cannot be admitted in -the earlier stages of the history of physiology, treated of as an -inductive science. If the doctrine so propounded have a solid and -permanent truth, they will again come before us when we have -travelled through the range of more limited truths, and are prepared -to ascend with security and certainty into the higher region of -general physiological principles. If they cannot be arrived at by -such a road, they are then, however plausible and pleasing, no -portion of that real and progressive science with which alone our -history is concerned. - -We proceed, therefore, to trace the establishment of some of the -more limited but certain doctrines of physiology. {438} - - - - -CHAPTER I. - -DISCOVERY OF THE ORGANS OF VOLUNTARY MOTION. - - -_Sect._ 1.--_Knowledge of Galen and his Predecessors._ - -IN the earliest conceptions which men entertained of their power of -moving their own members, they probably had no thought of any -mechanism or organization by which this was effected. The foot and -the hand, no less than the head, were seen to be endowed with life; -and this pervading life seemed sufficiently to explain the power of -motion in each part of the frame, without its being held necessary -to seek out a special seat of the will, or instruments by which its -impulses were made effective. But the slightest inspection of -dissected animals showed that their limbs were formed of a curious -and complex collection of cordage, and communications of various -kinds, running along and connecting the bones of the skeleton. These -cords and communications we now distinguish as muscles, nerves, -veins, arteries, &c.; and among these, we assign to the muscles the -office of moving the parts to which they are attached, as cords move -the parts of a machine. Though this action of the muscles on the -bones may now appear very obvious, it was, probably, not at first -discerned. It is observed that Homer, who describes the wounds which -are inflicted in his battles with so much apparent anatomical -precision, nowhere employs the word _muscle_. And even Hippocrates -of Cos, the most celebrated physician of antiquity, is held to have -had no distinct conception of such an organ.[1\17] He always employs -the word _flesh_ when he means _muscle_, and the first explanation -of the latter word (μῦς) occurs in a spurious work ascribed to him. -For nerves, sinews, ligaments,[2\17] he used indiscriminately the -same terms; (τόνος or νεῦρον;) and of these nerves (νεῦρα) he -asserts that they contract the limbs. Nor do we find much more -distinctness on this subject even in Aristotle, a generation or two -later. "The origin of the νεῦρα," he says,[3\17] "is from the heart; -they connect {439} the bones, and surround the joints." It is clear -that he means here the muscles, and therefore it is with injustice -that he has been accused of the gross error of deriving the nerves -from the heart. And he is held to have really had the merit[4\17] of -discovering the nerves of sensation, which he calls the "canals of -the brain" (πόροι τοῦ ἐγκεφάλου); but the analysis of the mechanism -of motion is left by him almost untouched. Perhaps his want of sound -mechanical notions, and his constant straining after verbal -generalities, and systematic classifications of the widest kind, -supply the true account of his thus missing the solution of one of -the simplest problems of Anatomy. - -[Note 1\17: Sprengel, _Geschichte der Arzneikunde_, i. 382.] - -[Note 2\17: Sprengel, _Gesch. Arz._ i. 385.] - -[Note 3\17: _Hist. Anim._ iii. 5.] - -[Note 4\17: Ib. i. 456.] - -In this, however, as in other subjects, his immediate predecessors -were far from remedying the deficiencies of his doctrines. Those who -professed to study physiology and medicine were, for the most part, -studious only to frame some general system of abstract principles, -which might give an appearance of connexion and profundity to their -tenets. In this manner the successors of Hippocrates became a -medical school, of great note in its day, designated as the -_Dogmatic_ school;[5\17] in opposition to which arose an _Empiric_ -sect, who professed to deduce their modes of cure, not from -theoretical dogmas, but from experience. These rival parties -prevailed principally in Asia Minor and Egypt, during the time of -Alexander's successors,--a period rich in names, but poor in -discoveries; and we find no clear evidence of any decided advance in -anatomy, such as we are here attempting to trace. - -[Note 5\17: Sprengel, _Gesch. Arz._ i. 583.] - -The victories of Lucullus and Pompeius, in Greece and Asia, made the -Romans acquainted with the Greek philosophy; and the consequence -soon was, that shoals of philosophers, rhetoricians, poets, and -physicians[6\17] streamed from Greece, Asia Minor, and Egypt, to -Rome and Italy, to traffic their knowledge and their arts for Roman -wealth. Among these, was one person whose name makes a great figure -in the history of medicine, Asclepiades of Prusa in Bithynia. This -man appears to have been a quack, with the usual endowments of his -class;--boldness, singularity, a contemptuous rejection of all -previously esteemed opinions, a new classification of diseases, a -new list of medicines, and the assertion of some wonderful cures. He -would not, on such accounts, deserve a place in the history of -science, but that he became the founder of a new school, the -_Methodic_, which professed to hold itself separate both from the -Dogmatics and the Empirics. {440} - -[Note 6\17: Sprengel, _Gesch. Arz._ ii. 5.] - -I have noticed these schools of medicine, because, though I am not -able to state distinctly their respective merits in the cultivation -of anatomy, a great progress in that science was undoubtedly made -during their domination, of which the praise must, I conceive, be in -some way divided among them. The amount of this progress we are able -to estimate, when we come to the works of Galen, who flourished -under the Antonines, and died about A.D. 203. The following passage -from his works will show that this progress in knowledge was not -made without the usual condition of laborious and careful -experiment, while it implies the curious fact of such experiment -being conducted by means of family tradition and instruction, so as -to give rise to a _caste_ of dissectors. In the opening of his -Second Book _On Anatomical Manipulations_, he speaks thus of his -predecessors: "I do not blame the ancients, who did not write books -on anatomical manipulation; though I praise Marinus, who did. For it -was superfluous for them to compose such records for themselves or -others, while they were, from their childhood, exercised by their -parents in dissecting, just as familiarly as in writing and reading; -so that there was no more fear of their forgetting their anatomy, -than of forgetting their alphabet. But when grown men, as well as -children, were taught, this thorough discipline fell off; and, the -art being carried out of the family of the Asclepiads, and declining -by repeated transmission, books became necessary for the student." - -That the general structure of the animal frame, as composed of bones -and muscles, was known with great accuracy before the time of Galen, -is manifest from the nature of the mistakes and deficiencies of his -predecessors which he finds it necessary to notice. Thus he -observes, that some anatomists have made one muscle into two, from -its having two heads;--that they have overlooked some of the muscles -in the face of an ape, in consequence of not skinning the animal -with their own hands;--and the like. Such remarks imply that the -current knowledge of this kind was tolerably complete. Galen's own -views of the general mechanical structure of an animal are very -clear and sound. The skeleton, he observes, discharges[7\17] the -office of the pole of a tent, or the walls of a house. With respect -to the action of the muscles, his views were anatomically and -mechanically correct; in some instances, he showed what this action -was, by severing the muscle.[8\17] He himself added considerably to -the existing knowledge of {441} this subject; and his discoveries -and descriptions, even of very minute parts of the muscular system, -are spoken of with praise by modern anatomists.[9\17] - -[Note 7\17: _De Anatom. Administ._ i. 2.] - -[Note 8\17: Sprengel, ii. 157.] - -[Note 9\17: Sprengel, ii. 150.] - -We may consider, therefore, that the doctrine of the muscular -system, as a collection of cords and sheets, by the contraction of -which the parts of the body are moved and supported, was firmly -established, and completely followed into detail, by Galen and his -predecessors. But there is another class of organs connected with -voluntary motion, the nerves, and we must for a moment trace the -opinions which prevailed respecting these. Aristotle, as we have -said, noticed some of the nerves of sensation. But Herophilus, who -lived in Egypt in the time of the first Ptolemy, distinguished -nerves as the organs of the will,[10\17] and Rufus, who lived in the -time of Trajan,[11\17] divides the nerves into sensitive and motive, -and derives them all from the brain. But this did not imply that men -had yet distinguished the nerves from the muscles. Even Galen -maintained that every muscle consists of a bundle of nerves and -sinews.[12\17] But the important points, the necessity of the nerve, -and the origination of all this apparatus of motion from the brain, -he insists upon with great clearness and force. Thus he proved the -necessity experimentally, by cutting through some of the bundles of -nerves,[13\17] and thus preventing the corresponding motions. And it -is, he says,[14\17] allowed by all, both physicians and -philosophers, that where the origin of the nerve is, there the seat -of the soul (ἡγημονικὸν τῆς ψυχῆς) must be: now this, he adds, is in -the brain, and not in the heart. - -[Note 10\17: Ib. i. 534.] - -[Note 11\17: Ib. ii. 67.] - -[Note 12\17: Ibid. ii. 152. Galen, _De Motu Musc._, p. 553.] - -[Note 13\17: Ib. 157.] - -[Note 14\17: _De Hippocr. et Plat. Dog._ viii. 1.] - -Thus the general construction and arrangement of the organization by -which voluntary motion is effected, was well made out at the time of -Galen, and is found distinctly delivered in his works. We cannot, -perhaps, justly ascribe any large portion of the general discovery -to him: indeed, the conception of the mechanism of the skeleton and -muscles was probably so gradually unfolded in the minds of -anatomical students, that it would be difficult, even if we knew the -labors of each person, to select one, as peculiarly the author of -the discovery. But it is clear that all those who did materially -contribute to the establishment of this doctrine, must have -possessed the qualifications which we find in Galen for such a task; -namely, clear mechanical views of what the {442} tensions of -collections of strings could do, and an exact practical acquaintance -with the muscular cordage which exists in the animal frame;--in -short, in this as in other instances of real advance in science, -there must have been clear ideas and real facts, unity of thought -and extent of observation, brought into contact. - - -_Sect._ 2.--_Recognition of Final Causes in Physiology. Galen._ - -THERE is one idea which the researches of the physiologist and the -anatomist so constantly force upon him, that he cannot help assuming -it as one of the guides of his speculations; I mean, the idea of a -_purpose_, or, as it is called in Aristotelian phrase, a _final -cause_, in the arrangements of the animal frame. It is impossible to -doubt that the motive nerves run along the limbs, _in order that_ -they may convey to the muscles the impulses of the will; and that -the muscles are attached to the bones, _in order that_ they may move -and support them. This conviction prevails so steadily among -anatomists, that even when the use of any part is altogether -unknown, it is still taken for granted that it has some use. The -developement of this conviction,--of a purpose in the parts of -animals,--of a function to which each portion of the organization is -subservient,--contributed greatly to the progress of physiology; for -it constantly urged men forwards in their researches respecting each -organ, till some definite view of its purpose was obtained. The -assumption of hypothetical final causes in Physics may have been, as -Bacon asserts it to have been, prejudicial to science; but the -assumption of unknown final causes in Physiology, has given rise to -the science. The two branches of speculation, Physics and -Physiology, were equally led, by every new phenomenon, to ask their -question, "Why?" But, in the former case, "why" meant "through what -cause?" in the latter, "for what end?" And though it may be possible -to introduce into physiology the doctrine of efficient causes, such -a step can never obliterate the obligations which the science owes -to the pervading conception of a purpose contained in all -organization. - -This conception makes its appearance very early. Indeed, without any -special study of our structure, the thought, that we are fearfully and -wonderfully made, forces itself upon men, with a mysterious -impressiveness, as a suggestion of our Maker. In this bearing, the -thought is developed to a considerable extent in the well-known -passage in Xenophon's _Conversations of Socrates_. Nor did it ever -lose its hold on sober-minded and instructed men. The Epicureans, -indeed, {443} held that the eye was not made for seeing, nor the ear -for hearing; and Asclepiades, whom we have already mentioned as an -impudent pretender, adopted this wild dogma.[15\17] Such assertions -required no labor. "It is easy," says Galen,[16\17] "for people like -Asclepiades, when they come to any difficulty, to say that Nature has -worked to no purpose." The great anatomist himself pursues his subject -in a very different temper. In a well-known passage, he breaks out -into an enthusiastic scorn of the folly of the atheistical -notions.[17\17] "Try," he says, "if you can imagine a shoe made with -half the skill which appears in the skin of the foot." Some one had -spoken of a structure of the human body which he would have preferred -to that which it now has. "See," Galen exclaims, after pointing out -the absurdity of the imaginary scheme, "see what brutishness there is -in this wish. But if I were to spend more words on such cattle, -reasonable men might blame me for desecrating my work, which I regard -as a religious hymn in honor of the Creator." - -[Note 15\17: Sprengel, ii. 15.] - -[Note 16\17: _De Usu Part._ v. 5, (on the kidneys.)] - -[Note 17\17: _De Usu Part._ iii. 10.] - -Galen was from the first highly esteemed as an anatomist. He was -originally of Pergamus; and after receiving the instructions of many -medical and philosophical professors, and especially of those of -Alexandria, which was then the metropolis of the learned and -scientific world, he came to Rome, where his reputation was soon so -great as to excite the envy and hatred of the Roman physicians. The -emperors Marcus Aurelius and Lucius Verus would have retained him -near them; but he preferred pursuing his travels, directed -principally by curiosity. When he died, he left behind him numerous -works, all of them of great value for the light they throw on the -history of anatomy and medicine; and these were for a long period -the storehouse of all the most important anatomical knowledge which -the world possessed. In the time of intellectual barrenness and -servility, among the Arabians and the Europeans of the dark ages, -the writings of Galen had almost unquestioned authority;[18\17] and -it was only by an uncommon effort of independent thinking that -Abdollatif ventured to assert, that even Galen's assertions must -give way to the evidence of the senses. In more modern times, when -Vesalius, in the sixteenth century, accused Galen of mistakes, he -drew upon himself the hostility of the whole body of physicians. Yet -the mistakes were such as might have {444} been pointed out and -confessed[19\17] without acrimony, if, in times of revolution, -mildness and moderation were possible; but an impatience of the -superstition of tradition on the part of the innovators, and an -alarm of the subversion of all recognized truths on the part of the -established teachers, inflame and pervert all such discussions. -Vesalius's main charge against Galen is, that his dissections were -performed upon animals, and not upon the human body. Galen himself -speaks of the dissection of apes as a very familiar employment, and -states that he killed them by drowning. The natural difficulties -which, in various ages, have prevented the unlimited prosecution of -human dissection, operated strongly among the ancients, and it would -have been difficult, under such circumstances, to proceed more -judiciously than Galen did. - -[Note 18\17: Sprengel, ii. 359.] - -[Note 19\17: Cuv. _Leçons sur l'Hist. des Sc. Nat._ p. 25.] - -I shall now proceed to the history of the discovery of another and -less obvious function, the circulation of the blood, which belongs -to modern times. - - - - -CHAPTER II. - -DISCOVERY OF THE CIRCULATION OF THE BLOOD. - - -_Sect._ 1.--_Prelude to the Discovery._ - -THE blood-vessels, the veins and arteries, are as evident and -peculiar in their appearance as the muscles; but their function is -by no means so obvious. Hippocrates[20\17] did not discriminate -Veins and Arteries; both are called by the same name (φλέβες) and -the word from which artery comes (ἀρτηρίη) means, in his works, the -windpipe. Aristotle, scanty as was his knowledge of the vessels of -the body, has yet the merit of having traced the origin of all the -veins to the heart. He expressly contradicts those of his -predecessors who had derived the veins from the head;[21\17] and -refers to dissection for the proof. If the book _On the Breath_ be -genuine (which is doubted), Aristotle was aware of the distinction -between veins and arteries. "Every artery," {445} it is there -asserted, "is accompanied by a vein; the former are filled only with -breath or air."[22\17] But whether or no this passage be -Aristotle's, he held opinions equally erroneous; as, that the -windpipe conveys air into the heart.[23\17] Galen[24\17] was far -from having views respecting the blood-vessels, as sound as those -which he entertained concerning the muscles. He held the liver to be -the origin of the veins, and the heart of the arteries. He was, -however, acquainted with their junctions, or _anastomoses_. But we -find no material advance in the knowledge of this subject, till we -overleap the blank of the middle ages, and reach the dawn of modern -science. - -[Note 20\17: Sprengel, i. 383.] - -[Note 21\17: _Hist. Animal._ iii. 3.] - -[Note 22\17: _De Spiritu_, v. 1078.] - -[Note 23\17: Spr. i. 501.] - -[Note 24\17: Ib. ii. 152.] - -The father of modern anatomy is held to be Mondino,[25\17] who -dissected and taught at Bologna in 1315. Some writers have traced in -him the rudiments of the doctrine of the circulation of the blood; -for he says that the heart transmits blood to the lungs. But it is -allowed, that he afterwards destroys the merit of his remark, by -repeating the old assertion that the left ventricle ought to contain -spirit or air, which it generates from the blood. - -[Note 25\17: _Encyc. Brit._ 692. Anatomy.] - -Anatomy was cultivated with great diligence and talent in Italy by -Achillini, Carpa, and Messa, and in France by Sylvius and Stephanus -(Dubois and Etienne). Yet still these empty assumptions respecting -the heart and blood-vessels kept their ground. Vesalius, a native of -Brussels, has been termed the founder of human anatomy, and his -great work _De Humani Corporis Fabricâ_ is, even yet, a splendid -monument of art, as well as science. It is said that his figures -were designed by Titian; and if this be not exactly true, says -Cuvier,[26\17] they must, at least, be from the pencil of one of the -most distinguished pupils of the great painter; for to this day, -though we have more finished drawings, we have no designs that are -more artist-like. Fallopius, who succeeded Vesalius at Padua, made -some additions to the researches of his predecessor; but in his -treatise _De Principio Venarum_, it is clearly seen[27\17] that the -circulation of the blood was unknown to him. Eustachius also, whom -Cuvier groups with Vesalius and Fallopius, as the three great -founders of modern anatomy, wrote a treatise on the vein -_azygos_[28\17] which is a little treatise on comparative anatomy; -but the discovery of the functions of the veins came from a -different quarter. {446} - -[Note 26\17: _Leçons sur l'Hist. des Sc. Nat._ p. 21.] - -[Note 27\17: Cuv. _Sc. Nat._ p. 32.] - -[Note 28\17: Ib. p. 34.] - -The unfortunate Servetus, who was burnt at Geneva as a heretic in -1553, is the first person who speaks distinctly of the small -circulation, or that which carries the blood from the heart to the -lungs, and back again to the heart. His work entitled _Christianismi -Restitutio_ was also burnt; and only two copies are known to have -escaped the flames. It is in this work that he asserts the doctrine -in question, as a collateral argument or illustration of his -subject. "The communication between the right and left ventricle of -the heart, is made," he says, "not as is commonly believed, through -the partition of the heart, but by a remarkable artifice (_magno -artificio_) the blood is carried from the right ventricle by a long -circuit through the lungs; is elaborated by the lungs, made yellow, -and transfused from the _vena arteriosa_ into the _arteria venosa_." -This truth is, however, mixed with various of the traditional -fancies concerning the "_vital spirit_, which has its origin in the -left ventricle." It may be doubted, also, how far Servetus formed -his opinion upon conjecture, and on a hypothetical view of the -formation of this vital spirit. And we may, perhaps, more justly -ascribe the real establishment of the pulmonary circulation as an -inductive truth, to Realdus Columbus, a pupil and successor of -Vesalius at Padua, who published a work _De Re Anatomicâ_ in 1559, -in which he claims this discovery as his own.[29\17] - -[Note 29\17: _Encyc. Brit._] - -Andrew Cæsalpinus, who has already come under our notice as one of -the fathers of modern inductive science, both by his metaphysical -and his physical speculations, described the pulmonary circulation -still more completely in his _Quæstiones Peripateticæ_, and even -seemed to be on the eve of discovering the great circulation; for he -remarked the swelling of veins below ligatures, and inferred from it -a refluent motion of blood in these vessels.[30\17] But another -discovery of structure was needed, to prepare the way for this -discovery of function; and this was made by Fabricius of -Acquapendente, who succeeded in the grand list of great professors -at Padua, and taught there for fifty years.[31\17] Sylvius had -discovered the existence of the valves of the veins; but Fabricius -remarked that they are all turned towards the heart. Combining this -disposition with that of the valves of the heart, and with the -absence of valves in the arteries, he might have come to the -conclusion[32\17] that the blood moves in a different direction in -the arteries and in the veins, and might thus have discovered the -circulation: but this glory was reserved for William Harvey: so true -{447} is it, observes Cuvier, that we are often on the brink of a -discovery without suspecting that we are so;--so true is it, we may -add, that a certain succession of time and of persons is generally -necessary to familiarize men with one thought, before they can -advance to that which is the next in order. - -[Note 30\17: Ib.] - -[Note 31\17: Cuv. p. 44.] - -[Note 32\17: p. 45.] - - -_Sect._ 2.--_The Discovery of the Circulation made by Harvey._ - -WILLIAM HARVEY was born in 1578, at Folkestone in Kent.[33\17] He -first studied at Cambridge: he afterwards went to Padua, where the -celebrity of Fabricius of Acquapendente attracted from all parts -those who wished to be instructed in anatomy and physiology. In this -city, excited by the discovery of the valves of the veins, which his -master had recently made, and reflecting on the direction of the -valves which are at the entrance of the veins into the heart, and at -the exit of the arteries from it, he conceived the idea of making -experiments, in order to determine what is the course of the blood -in its vessels. He found that when he tied up veins in various -animals, they swelled below the ligature, or in the part furthest -from the heart; while arteries, with a like ligature, swelled on the -side next the heart. Combining these facts with the direction of the -valves, he came to the conclusion that the blood is impelled, by the -left side of the heart, in the arteries to the extremities, and -thence returns by the veins into the right side of the heart. He -showed, too, how this was confirmed by the phenomena of the pulse, -and by the results of opening the vessels. He proved, also, that the -circulation of the lungs is a continuation of the larger -circulation; and thus the whole doctrine of the double circulation -was established. - -[Note 33\17: Cuv. p. 51.] - -Harvey's experiments had been made in 1616 and 1618; it is commonly -said that he first promulgated his opinion in 1619; but the -manuscript of the lectures, delivered by him as lecturer to the -College of Physicians, is extant in the British Museum, and, -containing the propositions on which the doctrine is founded, refers -them to April, 1616. It was not till 1628 that he published, at -Frankfort, his _Exercitatio Anatomica de Motu Cordis et Sanguinis_; -but he there observes that he had for above nine years confirmed and -illustrated his opinion in his lectures, by arguments grounded upon -ocular demonstrations. {448} - - -_Sect._ 3.--_Reception of the Discovery._ - -WITHOUT dwelling long upon the circumstances of the general reception -of this doctrine, we may observe that it was, for the most part, -readily accepted by his countrymen, but that abroad it had to -encounter considerable opposition. Although, as we have seen, his -predecessors had approached so near to the discovery, men's minds were -by no means as yet prepared to receive it. Several physicians denied -the truth of the opinion, among whom the most eminent was Riolan, -professor at the Collège de France. Other writers, as usually happens -in the case of great discoveries, asserted that the doctrine was -ancient, and even that it was known to Hippocrates. Harvey defended -his opinion with spirit and temper; yet he appears to have retained a -lively recollection of the disagreeable nature of the struggles in -which he was thus involved. At a later period of his life, Ent,[34\17] -one of his admirers, who visited him, and urged him to publish the -researches on generation, on which he had long been engaged, gives -this account of the manner in which he received the proposal: "And -would you then advise me, (smilingly replies the doctor,) to quit the -tranquillity of this haven, wherein I now calmly spend my days, and -again commit myself to the unfaithful ocean? You are not ignorant how -great troubles my lucubrations, formerly published, have raised. -Better it is, certainly, at some time, to endeavor to grow wise at -home in private, than by the hasty divulgation of such things to the -knowledge whereof you have attained with vast labor, to stir up -tempests that may deprive you of your leisure and quiet for the -future." - -[Note 34\17: Epist. Dedic. to _Anatom. Exercit._] - -His merits were, however, soon generally recognized. He was[35\17] -made physician to James the First, and afterwards to Charles the -First, and attended that unfortunate monarch in the civil war. He -had the permission of the parliament to accompany the king on his -leaving London; but this did not protect him from having his house -plundered in his absence, not only of its furniture, but, which he -felt more, of the records of his experiments. In 1652, his brethren -of the College of Physicians placed a marble bust of him in their -hall, with an inscription recording his discoveries; and two years -later, he was nominated to the office of President of the College, -which however he {449} declined in consequence of his age and -infirmities. His doctrine soon acquired popular currency; it was, -for instance, taken by Descartes[36\17] as the basis of his -physiology in his work _On Man_; and Harvey had the pleasure, which -is often denied to discoverers, of seeing his discovery generally -adopted during his lifetime. - -[Note 35\17: _Biog. Brit._] - -[Note 36\17: Cuv. 53.] - - -_Sect._ 4.--_Bearing of the Discovery on the Progress of Physiology._ - -IN considering the intellectual processes by which Harvey's -discoveries were made, it is impossible not to notice, that the -recognition of a creative purpose, which, as we have said, appears -in all sound physiological reasonings, prevails eminently here. "I -remember," says Boyle, "that when I asked our famous Harvey what -were the things that induced him to think of a circulation of the -blood, he answered me, that when he took notice that the valves in -the veins of so many parts of the body were so placed, that they -gave a free passage to the blood towards the heart, but opposed the -passage of the venal blood the contrary way; he was incited to -imagine that so provident a cause as Nature had not placed so many -valves without design; and no design seemed more probable than that -the blood should be sent through the arteries, and return through -the veins, whose valves did not oppose its course that way." - -We may notice further, that this discovery implied the usual -conditions, distinct general notions, careful observation of many -facts, and the mental act of bringing together these elements of -truth. Harvey must have possessed clear views of the motions and -pressures of a fluid circulating in ramifying tubes, to enable him -to see how the position of valves, the pulsation of the heart, the -effects of ligatures, of bleeding, and of other circumstances, ought -to manifest themselves in order to confirm his view. That he -referred to a multiplied and varied experience for the evidence that -it was so confirmed, we have already said. Like all the best -philosophers of his time, he insists rigidly upon the necessity of -such experience. "In every science," he says,[37\17] "be it what it -will, a diligent observation is requisite, and sense itself must be -frequently consulted. We must not rely upon other men's experience, -but our own, without which no man is a proper disciple of any part -of natural knowledge." And by publishing his experiments, he trusts, -he adds, that he has enabled his reader "to be an equitable {450} -umpire between Aristotle and Galen;" or rather, he might have said, -to see how, in the promotion of science, sense and reason, -observation and invention, have a mutual need of each other. - -[Note 37\17: _Generation of Animals_, Pref.] - -We may observe further, that though Harvey's glory, in the case now -before us, rested upon his having proved the reality of certain -mechanical movements and actions in the blood, this discovery, and -all other physiological truths, necessarily involved the assumption -of some peculiar agency belonging to living things, different both -from mechanical agency, and from chemical; and in short, something -_vital_, and not physical merely. For when it was seen that the -pulsation of the heart, its _systole_ and _diastole_, caused the -circulation of the blood, it might still be asked, what force caused -this constantly-recurring contraction and expansion. And again, -circulation is closely connected with respiration; the blood is, by -the circulation, carried to the lungs, and is there, according to -the expression of Columbus and Harvey, mixed with air. But by what -mechanism does this _mixture_ take place, and what is the real -nature of it? And when succeeding researches had enabled -physiologists to give an answer to this question, as far as chemical -relations go, and to say, that the change consists in the -abstraction of the carbon from the blood by means of the oxygen of -the atmosphere; they were still only led to ask further, how this -chemical change was effected, and how such a change of the blood -fitted it for its uses. Every function of which we explain the -course, the mechanism, or the chemistry, is connected with other -functions,--is subservient to them, and they to it; and all together -are parts of the general vital system of the animal, ministering to -its life, but deriving their activity from the life. Life is not a -collection of forces, or polarities, or affinities, such as any of -the physical or chemical sciences contemplate; it has powers of its -own, which often supersede those subordinate relations; and in the -cases where men have traced such agents in the animal frame, they -have always seen, and usually acknowledged, that these agents were -ministerial to some higher agency, more difficult to trace than -these, but more truly the cause of the phenomena. - -The discovery of the mechanical and chemical conditions of the vital -functions, as a step in physiology, may be compared to the discovery -of the laws of phenomena in the heavens by Kepler and his -predecessors, while the discovery of the force by which they were -produced was still reserved in mystery for Newton to bring to light. -The subordinate relation of the facts, their **dependence on space -and time, their reduction to order and cycle, had been fully -performed; but the {451} reference of them to distinct ideas of -causation, their interpretation as the results of mechanical force, -was omitted or attempted in vain. The very notion of such Force, and -of the manner in which motions were determined by it, was in the -highest degree vague and vacillating; and a century was requisite, -as we have seen, to give to the notion that clearness and fixity -which made the Mechanics of the Heavens a possible science. In like -manner, the notion of Life, and of Vital Forces, is still too -obscure to be steadily held. We cannot connect it distinctly with -severe inductions from facts. We can trace the motions of the animal -fluids as Kepler traced the motions of the planets; but when we seek -to render a reason for these motions, like him, we recur to terms of -a wide and profound, but mysterious import; to Virtues, Influences, -undefined Powers. Yet we are not on this account to despair. The -very instance to which I am referring shows us how rich is the -promise of the future. Why, says Cuvier,[38\17] may not Natural -History one day have its Newton? The idea of the vital forces may -gradually become so clear and definite as to be available in -science; and future generations may include, in their physiology, -propositions elevated as far above the circulation of the blood, as -the doctrine of universal gravitation goes beyond the explanation of -the heavenly motions by epicycles. - -[Note 38\17: _Ossem. Foss._ Introd.] - -If, by what has been said, I have exemplified sufficiently the -nature of those steps in physiology, which, like the discovery of -the Circulation, give an explanation of the process of some of the -animal functions, it is not necessary for me to dwell longer on the -subject; for to write a history, or even a sketch of the history of -Physiology, would suit neither my powers nor my purpose. Some -further analysis of the general views which have been promulgated by -the most eminent physiologists, may perhaps be attempted in treating -of the Philosophy of Inductive Science; but the estimation of the -value of recent speculations and investigations must be left to -those who have made this vast subject the study of their lives. A -few brief notices may, however, be here introduced. {452} - - - - -CHAPTER III. - -DISCOVERY OF THE MOTION OF THE CHYLE, AND CONSEQUENT SPECULATIONS. - - -_Sect._ 1.--_The Discovery of the Motion of the Chyle._ - -IT may have been observed in the previous course of this History of -the Sciences, that the discoveries in each science have a peculiar -physiognomy: something of a common type may be traced in the -progress of each of the theories belonging to the same department of -knowledge. We may notice something of this common form in the -various branches of physiological speculation. In most, or all of -them, we have, as we have noticed the case to be with respect to the -circulation of the blood, clear and certain discoveries of -mechanical and chemical processes, succeeded by speculations far -more obscure, doubtful, and vague, respecting the relation of these -changes to the laws of life. This feature in the history of -physiology may be further instanced, (it shall be done very -briefly), in one or two other cases. And we may observe, that the -lesson which we are to collect from this narrative, is by no means -that we are to confine ourselves to the positive discovery, and -reject all the less clear and certain speculations. To do this, -would be to lose most of the chances of ulterior progress; for -though it may be, that our conceptions of the nature of organic life -are not yet sufficiently precise and steady to become the guides to -positive inductive truths, still the only way in which these -peculiar physiological ideas can be made more distinct and precise, -and thus brought more nearly into a scientific form, is by this -struggle with our ignorance or imperfect knowledge. This is the -lesson we have learnt from the history of physical astronomy and -other sciences. We must strive to refer facts which are known and -understood, to higher principles, of which we cannot doubt the -existence, and of which, in some degree, we can see the place; -however dim and shadowy may be the glimpses we have hitherto been -able to obtain of their forms. We may often fail in such attempts, -but without the attempt we can never succeed. {453} - -That the food is received into the stomach, there undergoes a change -of its consistence, and is then propelled along the intestines, are -obvious facts in the animal economy. But a discovery made in the -course of the seventeenth century brought into clearer light the -sequel of this series of processes, and its connexion with other -functions. In the year 1622, Asellius or Aselli[39\17] discovered -certain minute vessels, termed _lacteals_, which absorb a white -liquid (the _chyle_) from the bowels, and pour it into the blood. -These vessels had, in fact, been discovered by Eristratus, in the -ancient world,[40\17] in the time of Ptolemy; but Aselli was the -first modern who attended to them. He described them in a treatise -entitled _De Venis Lacteis, cum figuris elegantissimis_, printed at -Milan in 1627, the year after the death of the author. The work is -remarkable as the first which exhibits _colored_ anatomical figures; -the arteries and veins are represented in red, the lacteals in black. - -[Note 39\17: Mayo, _Physiology_, p. 156.] - -[Note 40\17: Cuv. _Hist. Sc._ p. 50.] - -Eustachius,[41\17] at an earlier period, had described (in the -horse) the thoracic duct by which the chyle is poured into the -subclavian vein, on the right side of the neck. But this description -did not excite so much notice as to prevent its being forgotten, and -rediscovered in 1550, after the knowledge of the circulation of the -blood had given more importance to such a discovery. Up to this -time,[42\17] it had been supposed that the lacteals carried the -chyle to the liver, and that the blood was manufactured there. This -opinion had prevailed in all the works of the ancients and moderns; -its falsity was discovered by Pecquet, a French physician, and -published in 1651, in his _New Anatomical Experiments_; in which are -discovered a receptacle of the chyle, unknown till then, and the -vessel which conveys it to the subclavian vein. Pecquet himself and -other anatomists, soon connected this discovery with the doctrine, -then recently promulgated, of the circulation of the blood. In 1665, -these vessels, and the _lymphatics_ which are connected with them, -were further illustrated by Ruysch in his exhibition of their -valves. (_Dilucidatio valvularum in vasis lymphaticis et lacteis_.) - -[Note 41\17: Cuv. _Hist._ p. 34.] - -[Note 42\17: Ib. p. 365.] - - -_Sect._ 2.--_The Consequent Speculations. Hypotheses of Digestion._ - -THUS it was shown that aliments taken into the stomach are, by its -action, made to produce _chyme_; from the chyme, gradually changed -{454} in its progress through the intestines, _chyle_ is absorbed by -the lacteals; and this, poured into the blood by the thoracic duct, -repairs the waste and nourishes the growth of the animal. But by -what powers is the food made to undergo these transformations? Can -we explain them on mechanical or on chemical principles? Here we -come to a part of physiology less certain than the discovery of -vessels, or of the motion of fluids. We have a number of opinions on -this subject, but no universally acknowledged truth. We have a -collection of _Hypotheses of Digestion_ and _Nutrition_. - -I shall confine myself to the former class; and without dwelling -long upon these, I shall mention some of them. The philosophers of -the Academy _del Cimento_, and several others, having experimented -on the stomach of gallinaceous birds, and observed the astonishing -force with which it breaks and grinds substances, were led to -consider the digestion which takes place in the stomach as a kind of -_trituration_.[43\17] Other writers thought it was more properly -described as _fermentation_; others again spoke of it as a -_putrefaction_. Varignon gave a merely physical account of the first -part of the process, maintaining that the division of the aliments -was the effect of the disengagement of the air introduced into the -stomach, and dilated by the heat of the body. The opinion that -digestion is a _solution_ of the food by the gastric juice has been -more extensively entertained. - -[Note 43\17: Bourdon, _Physiol. Comp._ p. 514.] - -Spallanzani and others made many experiments on this subject. Yet it -is denied by the best physiologists, that the changes of digestion -can be adequately represented as chemical changes only. The nerves -of the stomach (the _pneumo-gastric_) are said to be essential to -digestion. Dr. Wilson Philip has asserted that the influence of -these nerves, when they are destroyed, may be replaced by a galvanic -current.[44\17] This might give rise to a supposition that digestion -depends on galvanism. Yet we cannot doubt that all these -hypotheses,--mechanical, physical, chemical, galvanic--are -altogether insufficient. "The stomach must have," as Dr. Prout -says,[45\17] "the power of {455} organizing and vitalizing the -different elementary substances. It is impossible to imagine that -this organizing agency of the stomach can be chemical. This agency -is _vital_, and its nature completely unknown." - -[Note 44\17: Müller (_Manual of Physiology_, B. iii. Sect. 1, Chap. -iii.) speaks of Dr. Wilson Philip's assertion that the nerves of the -stomach being cut, and a galvanic current kept up in them, digestion -is still accomplished. He states that he and other physiologists -have repeated such experiments on an extensive scale, and have found -no effect of this kind.] - -[Note 45\17: _Bridgewater Tr._ p. 493.] - - - - -CHAPTER IV. - -EXAMINATION OF THE PROCESS OF REPRODUCTION IN ANIMALS AND PLANTS, -AND CONSEQUENT SPECULATIONS. - - -_Sect._ 1.--_The Examination of the Process of Reproduction in -Animals._ - -IT would not, perhaps, be necessary to give any more examples of -what has hitherto been the general process of investigations on each -branch of physiology; or to illustrate further the combination which -such researches present, of certain with uncertain knowledge;--of -solid discoveries of organs and processes, succeeded by indefinite -and doubtful speculation concerning vital forces. But the -reproduction of organized beings is not only a subject of so much -interest as to require some notice, but also offers to us laws and -principles which include both the vegetable and the animal kingdom; -and which, therefore, are requisite to render intelligible the most -general views to which we can attain, respecting the world of -organization. - -The facts and laws of reproduction were first studied in detail in -animals. The subject appears to have attracted the attention of some -of the philosophers of antiquity in an extraordinary degree: and -indeed we may easily imagine that they hoped, by following this -path, if any, to solve the mystery of creation. Aristotle appears to -have pursued it with peculiar complacency; and his great work _On -animals_ contains[46\17] an extraordinary collection of curious -observations relative to this subject. He had learnt the modes of -reproduction of most of the animals with which he was acquainted; -and his work is still, as a writer of our own times has said,[47\17] -"original after so many copies, and young after two thousand years." -His observations referred principally to the external circumstances -of generation: the anatomical examination was {456} left to his -successors. Without dwelling on the intermediate labors, we come to -modern times, and find that this examination owes its greatest -advance to those who had the greatest share in the discovery of the -circulation of the blood;--Fabricius of Acquapendente, and Harvey. -The former[48\17] published a valuable work on the Egg and the -Chick. In this are given, for the first time, figures representing -the developement of the chick, from its almost imperceptible -beginning, to the moment when it breaks the shell. Harvey pursued -the researches of his teacher. Charles[49\17] the First had supplied -him with the means of making the experiments which his purpose -required, by sacrificing a great number of the deer in Windsor Park -in the state of gestation: but his principal researches were those -respecting the egg, in which he followed out the views of Fabricius. -In the troubles which succeeded the death of the unfortunate Charles -the house of Harvey was pillaged; and he lost the whole of the -labors he had bestowed on the generation of insects. His work, -_Exercitationes de Generatione Animalium_, was published at London -in 1651; it is more detailed and perfect than that of Fabricius; but -the author was prevented by the unsettled condition of the country -from getting figures engraved to accompany his descriptions. - -[Note 46\17: Bourdon, p. 161.] - -[Note 47\17: Ib. p. 101.] - -[Note 48\17: Cuv. _Hist. Sc. Nat._ p. 46.] - -[Note 49\17: Ib. p. 53.] - -Many succeeding anatomists pursued the examination of the series of -changes in generation, and of the organs which are concerned in -them, especially Malpighi, who employed the microscope in this -investigation, and whose work on the Chick was published in 1673. It -is impossible to give here any general view of the result of these -laborious series of researches: but we may observe, that they led to -an extremely minute and exact survey of all the parts of the fœtus, -its envelopes and appendages, and, of course, to a designation of -these by appropriate names. These names afterwards served to mark -the attempts which were made to carry the analogy of animal -generation into the vegetable kingdom. - -There is one generalization of Harvey which deserves notice.[50\17] -He was led by his researches to the conclusion, that all living -things may be properly said to come from eggs: "Omne vivum ex ovo." -Thus not only do oviparous animals produce by means of eggs, but in -those which are viviparous, the process of generation begins with -the developement of a small vesicle, which comes from the ovary, and -which exists before the embryo: and thus viviparous or -suckling-beasts, {457} notwithstanding their name, are born from -eggs, as well as birds, fishes, and reptiles.[51\17] This principle -also excludes that supposed production of organized beings without -parents (of worms in corrupted matter, for instance,) which was -formerly called _spontaneous generation_; and the best physiologists -of modern times agree in denying the reality of such a mode of -generation.[52\17] - -[Note 50\17: Exerc. lxiii.] - -[Note 51\17: Bourdon, p. 221.] - -[Note 52\17: Ib. p. 49.] - - -_Sect._ 2.--_The Examination of the Process of Reproduction in -Vegetables._ - -THE extension of the analogies of animal generation to the vegetable -world was far from obvious. This extension was however made;--with -reference to the embryo plant, principally by the microscopic -observers, Nehemiah Grew, Marcello Malpighi, and Antony -Leeuwenhoek;--with respect to the existence of the sexes, by Linnæus -and his predecessors. - -The microscopic labors of Grew and Malpighi were patronized by the -Royal Society of London in its earliest youth. Grew's book, _The -Anatomy of Plants_, was ordered to be printed in 1670. It contains -plates representing extremely well the process of germination in -various seeds, and the author's observations exhibit a very clear -conception of the relation and analogies of different portions of -the seed. On the day on which the copy of this work was laid before -the Society, a communication from Malpighi of Bologna, _Anatomes -Plantarum Idea_, stated his researches, and promised figures which -should illustrate them. Both authors afterwards went on with a long -train of valuable observations, which they published at various -times, and which contain much that has since become a permanent -portion of the science. - -Both Grew and Malpighi were, as we have remarked, led to apply to -vegetable generation many terms which imply an analogy with the -generation of animals. Thus, Grew terms the innermost coat of the -seed, the _secundine_; speaks of the _navel-fibres_, &c. Many more -such terms have been added by other writers. And, as has been -observed by a modern physiologist,[53\17] the resemblance is -striking. Both in the vegetable seed and in the fertilized animal -egg, we have an _embryo_, _chalazæ_, a _placenta_, an _umbilical -cord_, a _cicatricula_, an _amnios_, _membranes_, _nourishing -vessels_. The _cotyledons_ of the seed are the equivalent of the -_vitellus_ of birds, or of the _umbilical vesicle_ of -**suckling-beasts: {458} the _albumen_ or _perisperm_ of the grain is -analogous to the _white of the egg_ of birds, or the _allantoid_ of -viviparous animals. - -[Note 53\17: Ib. p. 384.] - -_Sexes of Plants._--The attribution of sexes to plants, is a notion -which was very early adopted; but only gradually unfolded into -distinctness and generality.[54\17] The ancients were acquainted -with the fecundation of vegetables. Empedocles, Aristotle, -Theophrastus, Pliny, and some of the poets, make mention of it; but -their notions were very incomplete, and the conception was again -lost in the general shipwreck of human knowledge. A Latin poem, -composed in the fifteenth century by Jovianus Pontanus, the -preceptor of Alphonso, King of Naples, is the first modern work in -which mention is made of the sex of plants. Pontanus sings the loves -of two date-palms, which grew at the distance of fifteen leagues -from each other: the male at Brundusium, the female at Otranto. The -distance did not prevent the female from becoming fruitful, as soon -as the palms had raised their heads above the surrounding trees, so -that nothing intervened directly between them, or, to speak with the -poet, so that they were able to see each other. - -[Note 54\17: Mirbel, _El._ ii. 538.] - -Zaluzian, a botanist who lived at the end of the fifteenth century, -says that the greater part of the species of plants are -_androgynes_, that is, have the properties of the male and of the -female united in the same plant; but that some species have the two -sexes in separate individuals; and he adduces a passage of Pliny -relative to the fecundation of the date-palm. John Bauhin, in the -middle of the seventeenth century, cites the expressions of -Zaluzian; and forty years later, a professor of Tübingen, Rudolph -Jacob Camerarius, pointed out clearly the organs of generation, and -proved by experiments on the mulberry, on maize, and on the plant -called Mercury (_mercurialis_), that when by any means the action of -the stamina upon the pistils is intercepted, the seeds are barren. -Camerarius, therefore, a philosopher in other respects of little -note, has the honor assigned him of being the author of the -discovery of the sexes of plants in modern times.[55\17] - -[Note 55\17: Mirbel, ii. 539.] - -The merit of this discovery will, perhaps, appear more considerable -when it is recollected that it was rejected at first by very eminent -botanists. Thus Tournefort, misled by insufficient experiments, -maintained that the stamina are excretory organs; and Reaumur, at -the beginning of the eighteenth century, inclined to the same -doctrine. {459} Upon this, Geoffroy, an apothecary at Paris, -scrutinized afresh the sexual organs; he examined the various forms -of the pollen, already observed by Grew and Malpighi; he pointed out -the excretory canal, which descends through the style, and the -_micropyle_, or minute orifice in the coats of the ovule, which is -opposite to the extremity of this canal; though he committed some -mistakes with regard to the nature of the pollen. Soon afterwards, -Sebastian Vaillant, the pupil of Tournefort, but the corrector of -his error on this subject, explained in his public lectures the -phenomenon of the fecundation of plants, described the explosion of -the anthers, and showed that the _florets_ of composite flowers, -though formed on the type of an _androgynous_ flower, are sometimes -male, sometimes female, and sometimes neuter. - -But though the sexes of plants had thus been noticed, the subject -drew far more attention when Linnæus made the sexual parts the basis -of his classification. Camerarius and Burkard had already -entertained such a thought, but it was Linnæus who carried into -effect, and thus made the notion of the sexes of vegetables almost -as familiar to us as that of the sexes of animals. - - -_Sect._ 3.--_The Consequent Speculations.--Hypotheses of Generation._ - -THE views of the processes of generation, and of their analogies -throughout the whole of the organic world, which were thus -established and diffused, form an important and substantial part of -our physiological knowledge. That a number of curious but doubtful -hypotheses should be put forward, for the purpose of giving further -significance and connexion to these discoveries, was to be expected. -We must content ourselves with speaking of these very briefly. We -have such hypotheses in the earliest antiquity of Greece; for as we -have already said, the speculations of cosmogony were the source of -the Greek philosophy; and the laws of generation appeared to offer -the best promise of knowledge respecting the mystery of creation. -Hippocrates explained the production of a new animal by the _mixture -of seed_ of the parents; and the offspring was male or female as the -seminal principle of the father or of the mother was the more -powerful. According to Aristotle, the mother supplied the _matter_, -and the father the _form_. Harvey's doctrine was, that the ovary of -the female is fertilized by a _seminal contagion_ produced by the -seed of the male. But an opinion which obtained far more general -reception was, that {460} the _embryo pre-existed_ in the mother, -before any union of the sexes.[56\17] It is easy to see that this -doctrine is accompanied with great difficulties;[57\17] for if the -mother, at the beginning of life, contain in her the embryos of all -her future children; these embryos again must contain the children -which they are capable of producing; and so on indefinitely; and -thus each female of each species contains in herself the germs of -infinite future generations. The perplexity which is involved in -this notion of an endless series of creatures, thus encased one -within another, has naturally driven inquirers to attempt other -suppositions. The microscopic researches of Leeuwenhoek and others -led them to the belief that there are certain animalcules contained -in the seed of the male, which are the main agents in the work of -reproduction. This system ascribes almost everything to the male, as -the one last mentioned does to the female. Finally, we have the -system of Buffon;--the famous hypothesis of _organic molecules_. -That philosopher asserted that he found, by the aid of the -microscope, all nature full of moving globules, which he conceived -to be, not animals as Leeuwenhoek imagined, but bodies capable of -producing, by their combination, either animals or vegetables, in -short, all organized bodies. These globules he called _organic -molecules_.[58\17] And if we inquire how these organic molecules, -proceeding from all parts of the two parents, unite into a whole, as -perfect as either of the progenitors, Buffon answers, that this is -the effect of the _interior mould_; that is, of a system of internal -laws and tendencies which determine the form of the result as an -external mould determines the shape of the cast. - -[Note 56\17: Bourdon, p. 204.] - -[Note 57\17: Ib. p. 209.] - -[Note 58\17: Ib. p. 219.] - -An admirer of Buffon, who has well shown the untenable character of -this system, has urged, as a kind of apology for the promulgation of -the hypothesis,[59\17] that at the period when its author wrote, he -could not present his facts with any hope of being attended to, if he -did not connect them by some common tie, some dominant idea which -might gratify the mind; and that, acting under this necessity, he did -well to substitute for the extant theories, already superannuated and -confessedly imperfect, conjectures more original and more probable. -Without dissenting from this view, we may observe, that Buffon's -theory, like those which preceded it, is excusable, and even deserving -of admiration, so far as it groups the facts consistently; because in -doing this, it exhibits the necessity, which the physiological -speculator ought to feel, of aspiring to definite and solid general -principles; and that thus, though {461} the theory may not be -established as true, it may be useful by bringing into view the real -nature and application of such principles. - -[Note 59\17: Ib. p. 221.] - -It is, therefore, according to our views, unphilosophical to derive -despair, instead of hope, from the imperfect success of Buffon and -his predecessors. Yet this is what is done by the writer to whom we -refer. "For me," says he,[60\17] "I vow that, after having long -meditated on the system of Buffon,--a system so remarkable, so -ingenious, so well matured, so wonderfully connected in all its -parts, at first sight so probable;--I confess that, after this long -study, and the researches which it requires, I have conceived in -consequence, a distrust of myself a skepticism, a disdain of -hypothetical systems, a decided predilection and exclusive taste for -pure and rational observation, in short, a disheartening, which I -had never felt before." - -[Note 60\17: Bourdon, p. 274.] - -The best remedy of such feelings is to be found in the history of -science. Kepler, when he had been driven to reject the solid -epicycles of the ancients, or a person who had admired Kepler as M. -Bourdon admires Buffon, but who saw that his magnetic virtue was an -untenable fiction, might, in the same manner, have thrown up all -hope of a sound theory of the causes of the celestial motions. But -astronomers were too wise and too fortunate to yield to such -despondency. The predecessors of Newton substituted a solid science -of Mechanics for the vague notions of Kepler; and the time soon came -when Newton himself reduced the motions of the heavens to a Law as -distinctly conceived as the Motions had been before. - - - - -CHAPTER V. - -EXAMINATION OF THE NERVOUS SYSTEM, AND CONSEQUENT SPECULATIONS. - - -_Sect._ 1.--_The Examination of the Nervous System._ - -IT is hardly necessary to illustrate by further examples the manner -in which anatomical observation has produced conjectural and -hypothetical attempts to connect structure and action with some -{462} higher principle, of a more peculiarly physiological kind. But -it may still be instructive to notice a case in which the principle, -which is thus brought into view, is far more completely elevated -above the domain of matter and mechanism than in those we have yet -considered;--a case where we have not only Irritation, but -Sensation;--not only Life, but Consciousness and Will. A part of -science in which suggestions present themselves, brings us, in a -very striking manner, to the passage from the physical to the -hyperphysical sciences. - -We have seen already (chap. i.) that Galen and his predecessors had -satisfied themselves that the nerves are the channels of perception; a -doctrine which had been distinctly taught by Herophilus[61\17] in the -Alexandrian school. Herophilus, however, still combined, under the -common name of Nerves, the Tendons; though he distinguished such -Nerves from those which arise from the brain and the spinal marrow, -and which are subservient to the will. In Galen's time this subject -had been prosecuted more into detail. That anatomist has left a -Treatise expressly upon _The Anatomy of the Nerves_; in which he -describes the successive _Pairs_ of Nerves: thus, the First Pair are -the visual nerves: and we see, in the language which Galen uses, the -evidence of the care and interest with which he had himself examined -them. "These nerves," he says, "are not resolved into many fibres, -like all the other nerves, when they reach the organs to which they -belong; but spread out in a different and very remarkable manner, -which it is not easy to describe or to believe, without actually -seeing it." He then gives a description of the retina. In like manner -he describes the Second Pair, which is distributed to the muscles of -the eyes; the Third and Fourth Pairs, which go to the tongue and -palate; and so on to the Seventh Pair. This division into Seven Pairs -was established by Marinus,[62\17] but Vesalius found it to be -incomplete. The examination which is the basis of the anatomical -enumeration of the Nerves at present recognized was that of Willis. -His book, entitled _Cerebri Anatome, cui accessit Nervorum descriptio -et usus_, appeared at London in 1664. He made important additions to -the knowledge of this subject.[63\17] Thus he is the first who -describes in a distinct manner what has been called the _Nervous -Centre_,[64\17] the pyramidal eminences which, according to more -recent anatomists, are the communication of the brain with the spinal -marrow: and of which the _Decussation_, described by Santorini, -affords the explanation of the action of a part {463} of the brain -upon the nerves of the opposite side. Willis proved also that the -_Rete Mirabile_, the remarkable net-work of arteries at the base of -the brain, observed by the ancients in ruminating animals, does not -exist in man. He described the different Pairs of Nerves with more -care than his predecessors; and his mode of numbering them is employed -up to the present time. He calls the Olfactory Nerves the First Pair; -previously to him, these were not reckoned a Pair: and thus the optic -nerves were, as we have seen, called the first. He added the Sixth and -the Ninth Pairs, which the anatomists who preceded him did not reckon. -Willis also examined carefully the different _Ganglions_, or knots -which occur upon the nerves. He traced them wherever they were to be -found, and he gave a general figure of what Cuvier calls the _nervous -skeleton_, very superior to that of Vesalius, which was coarse and -inexact. Willis also made various efforts to show the connexion of the -parts of the brain. In the earlier periods of anatomy, the brain had -been examined by slicing it, so as to obtain a section. Varolius -endeavored to unravel it, and was followed by Willis. Vicq d'Azyr, in -modern times, has carried the method of section to greater perfection -than had before been given it;[65\17] as Vieussens and Gall have done -with respect to the method of Varolius and Willis. Recently Professor -Chaussier[66\17] makes three kinds of Nerves:--the _Encephalic_, which -proceed from the head, and are twelve on each side;--the _Rachidian_, -which proceed from the spinal marrow, and are thirty on each -side;--and _Compound Nerves_, among which is the _Great Sympathetic_ -Nerve. - -[Note 61\17: Spr. i. 534.] - -[Note 62\17: _Dic. Sc. Med._ xxxv. 467.] - -[Note 63\17: Cuv. _Sc. Nat._ p. 385.] - -[Note 64\17: Ibid.] - -[Note 65\17: Cuv. p. 40.] - -[Note 66\17: _Dict. Sc. Nat._ xxxv. 467.] - -One of the most important steps ever made in our knowledge of the -nerves is, the distinction which Bichat is supposed to have -established, of a _ganglionic system_, and a _cerebral system_. And -we may add, to the discoveries in nervous anatomy, the remarkable -one, made in our own time, that the two offices--of conducting the -motive impressions from the central seat of the will to the muscles, -and of propagating sensations from the surface of the body and the -external organs of sense to the sentient mind--reside in two -distinct portions of the nervous substance:--a discovery which has -been declared[67\17] to be "doubtless the most important accession -to physiological (anatomical) knowledge since the time of Harvey." -This doctrine was first published and taught by Sir Charles Bell: -after an interval of some {464} years, it was more distinctly -delivered in the publications of Mr. John Shaw, Sir C. Bell's pupil. -Soon afterwards it was further confirmed, and some part of the -evidence corrected, by Mr. Mayo, another pupil of Sir C. Bell, and -by M. Majendie.[68\17] - -[Note 67\17: Dr. Charles Henry's _Report of Brit. Assoc._ iii. -p. 62.] - -[Note 68\17: As authority for the expressions which I have now used -in the text, I will mention Müller's _Manual of Physiology_ (4th -edition, 1844). In Book iii. Section 2, Chap. i., "On the Nerves of -Sensation and Motion," Müller says, "Charles Bell was the first who -had the ingenious thought that the posterior roots of the nerves of -the spine--those which are furnished with a ganglion--govern -sensation only; that the anterior roots are appointed for motion; -and that the primitive fibres of these roots, after being united in -a single nervous cord, are mingled together in order to supply the -wants of the skin and muscles. He developed this idea in a little -work (_An Idea of a new Anatomy of the Brain_, London, 1811), which -was not intended to travel beyond the circle of his friends." Müller -goes on to say, that eleven years later, Majendie prosecuted the -same theory. But Mr. Alexander Shaw, in 1839, published _A Narrative -of the Discoveries of Sir Charles Bell in the Nervous System_, in -which it appears that Sir Charles Bell had further expounded his -views in his lectures to his pupils (p. 89), and that one of these, -Mr. John Shaw, had in various publications, in 1821 and 1822, -further insisted upon the same views; especially in a Memoir _On -Partial Paralysis_ (p. 75). MM. Mayo and Majendie both published -Memoirs in August, 1822; and these and subsequent works confirmed -the doctrine of Bell. Mr. Alexander Shaw states (p. 97), that a -mistake of Sir Charles Bell's, in an experiment which he had made to -prove his doctrine, was discovered through the joint labors of M. -Majendie and Mr. Mayo.] - - -_Sect._ 2.--_The Consequent Speculations. Hypotheses respecting -Life, Sensation, and Volition._ - -I SHALL not attempt to explain the details of these anatomical -investigations; and I shall speak very briefly of the speculations -which have been suggested by the obvious subservience of the nerves -to life, sensation, and volition. Some general inferences from their -distribution were sufficiently obvious; as, that the seat of -sensation and volition is in the brain. Galen begins his work, _On -the Anatomy of the Nerves_, thus: "That none of the members of the -animal either exercises voluntary motion, or receives sensation, and -that if the nerve be cut, the part immediately becomes inert and -insensible, is acknowledged by all physicians. But that the origin -of the nerves is partly from the brain, and partly from the spinal -marrow, I proceed to explain." And in his work _On the Doctrines of -Plato and Hippocrates_, he proves at {465} great length[69\17] that -the brain is the origin of sensation and motion, refuting the -opinions of earlier days, as that of Chrysippus,[70\17] who placed -the _hegemonic_ or master-principle of the soul, in the heart. But -though Galen thought that the rational soul resides in the brain, he -was disposed to agree with the poets and philosophers, according to -whom the heart is the seat of courage and anger, and the liver the -seat of love.[71\17] The faculties of the soul were by succeeding -physiologists confined to the brain; but the disposition still -showed itself, to attribute to them distinct localities. Thus -Willis[72\17] places the imagination in the _corpus callosum_, the -memory in the folds of the _hemispheres_, the perception in the -_corpus striatum_. In more recent times, a system founded upon a -similar view has been further developed by Gall and his followers. -The germ of Gall's system may be considered as contained in that of -Willis; for Gall represents the hemispheres as the folds of a great -membrane which is capable of being unwrapped and spread out, and -places the different faculties of man in the different regions of -this membrane. The chasm which intervenes between matter and motion -on the one side, and thought and feeling on the other, is brought -into view by all such systems; but none of the hypotheses which they -involve can effectually bridge it over. - -[Note 69\17: Lib. vii.] - -[Note 70\17: Lib. iii. c. 1.] - -[Note 71\17: Lib. vi. c. 8.] - -[Note 72\17: Cuv. _Sc. Nat._ p. 384.] - -The same observation may be made respecting the attempts to explain -the manner in which the nerves operate as the instruments of -sensation and volition. Perhaps a real step was made by -Glisson,[73\17] professor of medicine in the University of -Cambridge, who distinguished in the fibres of the muscles of motion -a peculiar property, different from any merely mechanical or -physical action. His work _On the Nature of the Energetic Substance, -or on the Life of Nature and of its Three First Faculties, The -Perceptive, Appetitive, and Motive_, which was published in 1672, is -rather metaphysical than physiological. But the principles which he -establishes in this treatise he applies more specially to physiology -in a treatise _On the Stomach and Intestines_ (Amsterdam, 1677). In -this he ascribes to the fibres of the animal body a peculiar power -which he calls _Irritability_. He divides _irritation_ into natural, -vital, and animal; and he points out, though briefly, the gradual -differences of irritability in different organs. "It is hardly -comprehensible," says Sprengel,[74\17] "how this {466} lucid and -excellent notion of the Cambridge teacher was not accepted with -greater alacrity, and further unfolded by his contemporaries." It -has, however, since been universally adopted. - -[Note 73\17: Cuv. _Sc. Nat._ p. 434.] - -[Note 74\17: Spr. iv. 47.] - -But though the discrimination of muscular irritability as a peculiar -power might be a useful step in physiological research, the -explanations hitherto offered, of the way in which the nerves -operate on this irritability, and discharge their other offices, -present only a series of hypotheses. Glisson[75\17] assumed the -existence of certain vital spirits, which, according to him, are a -mild, sweet fluid, resembling the spirituous part of white of egg, -and residing in the nerves.--This hypothesis, of a very subtle humor -or spirit existing in the nerves, was indeed very early taken -up.[76\17] This nervous spirit had been compared to air by -Erasistratus, Asclepiades, Galen, and others. The chemical -tendencies of the seventeenth century led to its being described as -acid, sulphureous or nitrous. At the end of that century, the -hypothesis of an _ether_ attracted much notice as a means of -accounting for many phenomena; and this ether was identified with -the nervous fluid. Newton himself inclines to this view, in the -remarkable Queries which are annexed to his _Opticks_. After -ascribing many physical effects to his ether, he adds (Query 23), -"Is not vision performed chiefly by the vibrations of this medium, -excited in the bottom of the eye by the rays of light, and -propagated through the solid, pellucid, and uniform capillamenta of -the nerves into the place of sensation?" And (Query 24), "Is not -animal motion performed by the vibrations of this medium, excited in -the brain by the power of the will, and propagated from thence -through the capillamenta of the nerves into the muscles for -contracting and dilating them?" And an opinion approaching this has -been adopted by some of the greatest of modern physiologists; as -Haller, who says,[77\17] that, though it is more easy to find what -this nervous spirit is not than what it is, he conceives that, while -it must be far too fine to be perceived by the sense, it must yet be -more gross than fire, magnetism, or electricity; so that it may be -contained in vessels, and confined by boundaries. And Cuvier speaks -to the same effect:[78\17] "There is a great probability that it is -by an imponderable fluid that the nerve acts on the fibre, and that -this nervous fluid is drawn from the blood, and secreted by the -medullary matter." - -[Note 75\17: Spr. iv. 38.] - -[Note 76\17: Haller, _Physiol._ iv. 365.] - -[Note 77\17: _Physiol._ iv. 381, lib. x. sect. viii. § 15.] - -[Note 78\17: _Règne Animal_, Introd. p. 30.] - -Without presuming to dissent from such authorities on a point of -{467} anatomical probability, we may venture to observe, that these -hypotheses do not tend at all to elucidate the physiological -principle which is here involved; for this principle cannot be -mechanical, chemical, or physical, and therefore cannot be better -understood by embodying it in a fluid; the difficulty we have in -conceiving what the moving force _is_, is not got rid of by explaining -the machinery by which it is merely _transferred_. In tracing the -phenomena of sensation and volition to their cause, it is clear that -we must call in some peculiar and hyperphysical principle. The -hypothesis of a fluid is not made more satisfactory by attenuating -the fluid; it becomes subtle, spirituous, ethereal, imponderable, to -no purpose; it must cease to be a fluid, before its motions can -become sensation and volition. This, indeed, is acknowledged by most -physiologists; and strongly stated by Cuvier.[79\17] "The impression -of external objects upon the ME, the production of a sensation, of -an image, is a mystery impenetrable for our thoughts." And in -several places, by the use of this peculiar phrase, "_the me_," (_le -moi_) for the sentient and volent faculty, he marks, with peculiar -appropriateness and force, that phraseology borrowed from the world -of matter will, in this subject, no longer answer our purpose. We -have here to go from Nouns to Pronouns, from Things to Persons. We -pass from the Body to the Soul, from Physics to Metaphysics. We are -come to the borders of material philosophy; the next step is into -the domain of Thought and Mind. Here, therefore, we begin to feel -that we have reached the boundaries of our present subject. The -examination of that which lies beyond them must be reserved for a -philosophy of another kind, and for the labors of the future; if we -are ever enabled to make the attempt to extend into that loftier and -wider scene, the principles which we gather on the ground we are now -laboriously treading. - -[Note 79\17: _Règne Animal_, Introd. p. 47.] - -Such speculations as I have quoted respecting the nervous fluid, -proceeding from some of the greatest philosophers who ever lived, -prove only that hitherto the endeavor to comprehend the mystery of -perception and will, of life and thought, have been fruitless and -vain. Many anatomical truths have been discovered, but, so far as -our survey has yet gone, no genuine physiological principle. All the -trains of physiological research which we have followed have begun -in exact examination of organization and function, and have ended in -wide conjectures and arbitrary hypotheses. The stream of knowledge -in all such cases is {468} clear and lively at its outset; but, -instead of reaching the great ocean of the general truths of -science, it is gradually spread abroad among sands and deserts till -its course can be traced no longer. - -Hitherto, therefore, we must consider that we have had to tell the -story of the _failures_ of physiological speculation. But of late -there have come into view and use among physiologists certain -principles which may be considered as peculiar to organized -subjects; and of which the introduction forms a real advance in -organical science. Though these have hitherto been very imperfectly -developed, we must endeavor to exhibit, in some measure, their -history and bearing. - -[2nd Ed.] [In order to show that I am not unaware how imperfect the -sketch given in this work is, as a History of Physiology, I may -refer to the further discussions on these subjects contained in the -_Philosophy of the Inductive Sciences_, Book ix. I have there (Chap. -ii.) noticed the successive _Biological Hypotheses_ of the Mystical, -the Iatrochemical, and Iatromathematical Schools, the Vital-Fluid -School, and the Psychical School. I have (Chaps. iii., iv., v.) -examined several of the attempts which have been made to analyze the -Idea of Life, to classify Vital Functions, and to form Ideas of -Separate Vital Forces. I have considered in particular, the attempts -to form a distinct conception of Assimilation and Secretion, of -Generation, and of Voluntary Motion; and I have (Chap. vi.) further -discussed the Idea of Final Causes as employed in Biology.] - - - - -CHAPTER VI. - -INTRODUCTION OF THE PRINCIPLE OF DEVELOPED AND METAMORPHOSED -SYMMETRY. - - -_Sect._ 1.--_Vegetable Morphology. Göthe. De Candolle._ - -BEFORE we proceed to consider the progress of principles which -belong to animal and human life, such as have just been pointed at, -we must look round for such doctrines, if any such there be, as -apply alike to all organized beings, conscious or unconscious, fixed -or locomotive;--to the laws which regulate vegetable as well as -animal forms and functions. Though we are very far from being able -to present a {469} clear and connected code of such laws, we may -refer to one law, at least, which appears to be of genuine authority -and validity; and which is worthy our attention as an example of a -properly organical or physiological principle, distinct from all -mechanical, chemical, or other physical forces; and such as cannot -even be conceived to be resolvable into those. I speak of the -tendency which produces such results as have been brought together -in recent speculations upon _Morphology_. - -It may perhaps be regarded as indicating how peculiar are the -principles of organic life, and how far removed from any mere -mechanical action, that the leading idea in these speculations was -first strongly and effectively apprehended, not by a laborious -experimenter and reasoner, but by a man of singularly brilliant and -creative fancy; not by a mathematician or chemist, but by a poet. -And we may add further, that this poet had already shown himself -incapable of rightly apprehending the relation of physical facts to -their principles; and had, in trying his powers on such subjects, -exhibited a signal instance of the ineffectual and perverse -operation of the method of philosophizing to which the constitution -of his mind led him. The person of whom we speak, is John Wolfgang -Göthe, who is held, by the unanimous voice of Europe, to have been -one of the greatest poets of our own, or of any time, and whose -_Doctrine of Colors_ we have already had to describe, in the History -of Optics, as an entire failure. Yet his views on the laws which -connect the forms of plants into one simple system, have been -generally accepted and followed up. We might almost be led to think -that this writer's poetical endowments had contributed to this -scientific discovery;--the love of beauty of form, by fixing the -attention upon the symmetry of plants; and the creative habit of -thought, by making constant developement of a familiar -process.[80\17] {470} - -[Note 80\17: We may quote some of the poet's own verses as an -illustration of his feelings on this subject. They are addressed to -a lady. - - Dich verwirret, geliebte, die tausendfältige mischung - Dieses blumengewühls über dem garten umher; - Viele namen hörest du an, und immer verdränget, - Mit barbarischem klang, einer den andern im ohr. - Alle gestalten sind **ähnlich und keine gleichet der andern; - Und so deutet das chor auf ein geheimes gesetz, - Auf ein heiliges räthsel. O! könnte ich dich, liebliche freundinn, - Ueberliefern so gleich glücklich das lösende wort. - - Thou, my love, art perplext with the endless seeming confusion - Of the luxuriant wealth which in the garden is spread; - Name upon name thou hearest, and in thy dissatisfied hearing, - With a barbarian noise one drives another along. - All the forms resemble, yet none is the same as another; - Thus the whole of the throng points at a deep hidden law. - Points at a sacred riddle. Oh! could I to thee, my beloved friend, - Whisper the fortunate word by which the riddle is read!] - -But though we cannot but remark the peculiarity of our being -indebted to a poet for the discovery of a scientific principle, we -must not forget that he himself held, that in making this step, he -had been guided, not by his invention, but by observation. He -repelled, with extreme repugnance, the notion that he had -substituted fancy for fact, or imposed ideal laws on actual things. -While he was earnestly pursuing his morphological speculations, he -attempted to impress them upon Schiller. "I expounded to him, in as -lively a manner as possible, the metamorphosis of plants, drawing on -paper, with many characteristic strokes, a symbolic plant before his -eyes. He heard me," Göthe says,[81\17] "with much interest and -distinct comprehension; but when I had done, he shook his head, and -said, 'That is not Experience; that is an Idea:' I stopt with some -degree of irritation; for the point which separated us was marked -most luminously by this expression." And in the same work he relates -his botanical studies and his habit of observation, from which it is -easily seen that no common amount of knowledge and notice of -details, were involved in the course of thought which led him to the -principle of the Metamorphosis of Plants. - -[Note 81\17:_ Zur Morphologie_, p. 24.] - -Before I state the history of this principle, I may be allowed to -endeavor to communicate to the reader, to whom this subject is new, -some conception of the principle itself. This will not be difficult, -if he will imagine to himself a flower, for instance, a common -wild-rose, or the blossom of an apple-tree, as consisting of a -series of parts disposed in _whorls_, placed one over another on an -_axis_. The lowest whorl is the calyx with its five sepals; above -this is the corolla with its five petals; above this are a multitude -of stamens, which may be considered as separate whorls of five each, -often repeated; above these is a whorl composed of the ovaries, or -what become the seed-vessels in the fruit, which are five united -together in the apple, but indefinite in number and separate in the -rose. Now the morphological view is {471} this;--that the members of -each of these whorls are in their nature identical, and the same as -if they were whorls of ordinary leaves, brought together by the -shortening their common axis, and modified in form by the successive -elaboration of their nutriment. Further, according to this view, a -whorl of leaves itself is to be considered as identical with several -detached leaves dispersed spirally along the axis, and brought -together because the axis is shortened. Thus all the parts of a -plant are, or at least represent, the successive metamorphoses of -the same elementary member. The root-leaves thus pass into the -common leaves;--these into bracteæ;--these into the sepals;--these -into the petals;--these into the stamens with their anthers;--these -into the ovaries with their styles and stigmas;--these ultimately -become the fruit; and thus we are finally led to the seed of a new -plant. - -Moreover the same notion of metamorphosis may be applied to explain -the existence of flowers which are not symmetrical like those we -have just referred to, but which have an irregular corolla or calyx. -The papilionaceous flower of the pea tribe, which is so markedly -irregular, may be deduced by easy gradations from the regular -flower, (through the _mimoseæ_,) by expanding one petal, joining one -or two others, and modifying the form of the intermediate ones. - -Without attempting to go into detail respecting the proofs of that -identity of all the different organs, and all the different forms of -plants, which is thus asserted, we may observe, that it rests on -such grounds as these;--the transformations which the parts of -flowers undergo by accidents of nutriment or exposure. Such changes, -considered as monstrosities where they are very remarkable, show the -tendencies and possibilities belonging to the organization in which -they occur. For instance, the single wild-rose, by culture, -transforms many of its numerous stamens into petals, and thus -acquires the deeply folded flower of the double garden-rose. We -cannot doubt of the reality of this change, for we often see stamens -in which it is incomplete. In other cases we find petals becoming -leaves, and a branch growing out of the centre of the flower. Some -pear-trees, when in blossom, are remarkable for their tendencies to -such monstrosities.[82\17] Again, we find that flowers which are -usually irregular, occasionally become regular, and conversely. The -common snap-dragon (_Linaria vulgaris_) affords a curious instance -of this.[83\17] The usual form of this plant is "personate," the -corolla being divided into two lobes, which differ in form, and -{472} together present somewhat the appearance of an animal's face; -and the upper portion of the corolla is prolonged backwards into a -tube-like "spur." No flower can be more irregular; but there is a -singular variety of this plants termed _Peloria_, in which the -corolla is strictly symmetrical, consisting of a conical tube, -narrowed in front, elongated behind into five equal spurs, and -containing five stamens of equal length, instead of the two unequal -pairs of the didynamous Linaria. These and the like appearances show -that there is in nature a capacity for, and tendency to, such -changes as the doctrine of metamorphosis asserts. - -[Note 82\17: Lindley, _Nat. Syst._ p. 84.] - -[Note 83\17: Henslow, _Principles of Botany_, p. 116.] - -Göthe's _Metamorphosis of Plants_ was published 1790: and his system -was the result of his own independent course of thoughts. The view -which it involved was not, however, absolutely new, though it had -never before been unfolded in so distinct and persuasive a manner. -Linnæus considered the leaves, calyx, corolla, stamens, each as -evolved in succession from the other; and spoke of it as _prolepsis_ -or _anticipation_,[84\17] when the leaves changed accidentally into -bracteæ, these into a calyx, this into a corolla, the corolla into -stamens, or these into the pistil. And Caspar Wolf apprehended in a -more general manner the same principle. "In the whole plant," says -he,[85\17] "we see nothing but leaves and stalk;" and in order to -prove what is the situation of the leaves in all their later forms, -he adduces the cotyledons as the first leaves. - -[Note 84\17: Sprengel, _Bot._ ii. 302. _Amœn. Acad._ vi. 324, 365.] - -[Note 85\17: _Nov. Con. Ac. Petrop._ xii. 403, xiii. 478.] - -Göthe was led to his system on this subject by his general views of -nature. He saw, he says,[86\17] that a whole life of talent and -labor was requisite to enable any one to arrange the infinitely -copious organic forms of a single kingdom of nature. "Yet I felt," -he adds, "that for me there must be another way, analogous to the -rest of my habits. The appearance of the changes, round and round, -of organic creatures had taken strong hold on my mind. Imagination -and Nature appeared to me to vie with each other which could go on -most boldly yet most consistently." His observation of nature, -directed by such a thought, led him to the doctrine of the -metamorphosis. - -[Note 86\17: _Zur Morph._ i. 30.] - -In a later republication of his work (_Zur Morphologie_, 1817,) he -gives a very agreeable account of the various circumstances which -affected the reception and progress of his doctrine. -Willdenow[87\17] quoted {473} him thus:--"The life of plants is, as -Mr. Göthe very prettily says, an expansion and contraction, and -these alternations make the various periods of life." "This -'_prettily_,'" says Göthe, "I can be well content with, but the -'_egregie_,' of Usteri is much more pretty and obliging." Usteri had -used this term respecting Göthe in an edition of Jussieu. - -[Note 87\17: _Zur Morph._ i. 121.] - -The application of the notion of metamorphosis to the explanation of -double and monstrous flowers had been made previously by Jussieu. -Göthe's merit was, to have referred to it the _regular_ formation of -the flower. And as Sprengel justly says,[88\17] his view had so -profound a meaning, made so strong an appeal by its simplicity, and -was so fruitful in the most valuable consequences, that it was not -to be wondered at if it occasioned further examination of the -subject; although many persons pretend to slight it. The task of -confirming and verifying the doctrine by a general application of it -to all cases,--a labor so important and necessary after the -promulgation of any great principle,--Göthe himself did not execute. -At first he collected specimens and made drawings with some such -view,[89\17] but he was interrupted and diverted to other matters. -"And now," says he, in his later publication, "when I look back on -this undertaking, it is easy to see that the object which I had -before my eyes was, for me, in my position, with my habits and mode -of thinking, unattainable. For it was no less than this: that I was -to take that which I had stated in general, and presented to the -conception, to the mental intuition, in words; and that I should, in -a particularly visible, orderly, and gradual manner, present it to -the eye; so as to show to the outward sense that out of the germ of -this idea might grow a tree of physiology fit to overshadow the -world." - -[Note 88\17: _Gesch. Botan._ ii. 304.] - -[Note 89\17: _Zur Morph._ i. **129.] - -Voigt, professor at Jena, was one of the first who adopted Göthe's -view into an elementary work, which he did in 1808. Other botanists -labored in the direction which had thus been pointed out. Of those -who have thus contributed to the establishment and developement of -the metamorphic doctrine. Professor De Candolle, of Geneva, is -perhaps the most important. His Theory of Developement rests upon -two main principles, _abortion_ and _adhesion_. By considering some -parts as degenerated or absent through the abortion of the buds -which might have formed them, and other parts as adhering together, -he holds that all plants may be reduced to perfect symmetry: and the -actual and constant occurrence of such incidents is shown beyond -{474} all doubt. And thus the snap-dragon, of which we have spoken -above, is derived from the Peloria, which is the normal condition of -the flower, by the abortion of one stamen, and the degeneration of -two others. Such examples are too numerous to need to be dwelt on. - - -_Sect._ 2.--_Application of Vegetable Morphology._ - -THE doctrine, being thus fully established, has been applied to -solve different problems in botany; for instance, to explain the -structure of flowers which appear at first sight to deviate widely -from the usual forms of the vegetable world. We have an instance of -such an application in Mr. Robert Brown's explanation of the real -structure of various plants which had been entirely misunderstood: -as, for example, the genus _Euphorbia_. In this plant he showed that -what had been held to be a jointed filament, was a pedicel with a -filament above it, the intermediate corolla having evanesced. In -_Orchideæ_ (the orchis tribe), he showed that the peculiar structure -of the plant arose from its having six stamens (two sets of three -each), of which five are usually abortive. In _Coniferæ_ (the -cone-bearing trees), it was made to appear that the seed was naked, -while the accompanying appendage, corresponding to a seed-vessel, -assumed all forms, from a complete leaf to a mere scale. In like -manner it was proved that the _pappus_, or down of _composite_ -plants (as thistles), is a transformed calyx. - -Along with this successful application of a profound principle, it -was natural that other botanists should make similar attempts. Thus -Mr. Lindley was led to take a view[90\17] of the structure of -_Reseda_ (mignonette) different from that usually entertained; -which, when published, attracted a good deal of attention, and -gained some converts among the botanists of Germany and France. But -in 1833, Mr. Lindley says, with great candor, "Lately, Professor -Henslow has satisfactorily proved, in part by the aid of a -monstrosity in the common _Mignonette_, in part by a severe -application of morphological rules, that my hypothesis must -necessarily be false." Such an agreement of different botanists -respecting the consequences of morphological rules, proves the -reality and universality of the rules. - -[Note 90\17: Lindley, _Brit. Assoc. Report_, iii. 50.] - -We find, therefore, that a principle which we may call the -_Principle of Developed and Metamorphosed Symmetry_, is firmly -established {475} and recognized, and familiarly and successfully -applied by botanists. And it will be apparent, on reflection, that -though _symmetry_ is a notion which applies to inorganic as well as -to organic things, and is, in fact, a conception of certain -relations of space and position, such _developement_ and -_metamorphosis_ as are here spoken of, are ideas entirely different -from any of those to which the physical sciences have led us in our -previous survey; and are, in short, genuine _organical_ or -_physiological_ ideas;--real elements of the philosophy of _life_. - -We must, however imperfectly, endeavor to trace the application of -this idea in the other great department of the world of life; we -must follow the history of Animal Morphology. - - - - -CHAPTER VII. - -PROGRESS OF ANIMAL MORPHOLOGY. - - -_Sect._ 1.--_Rise of Comparative Anatomy._ - -THE most general and constant relations of the form of the organs, -both in plants and animals, are the most natural grounds of -classification. Hence the first scientific classifications of -animals are the first steps in animal morphology. At first, a -_zoology_ was constructed by arranging animals, as plants were at -first arranged, according to their external parts. But in the course -of the researches of the anatomists of the seventeenth century, it -was seen that the internal structure of animals offered resemblances -and transitions of a far more coherent and philosophical kind, and -the Science of _Comparative Anatomy_ rose into favor and importance. -Among the main cultivators of this science[91\17] at the period just -mentioned, we find Francis Redi, of Arezzo; Guichard-Joseph -Duvernay, who was for sixty years Professor of Anatomy at the Jardin -du Roi at Paris, and during this lapse of time had for his pupils -almost all the greatest anatomists of the greater part of the -eighteenth century; Nehemiah Grew, secretary to the Royal Society of -London, whose _Anatomy of Plants_ we have already noticed. - -[Note 91\17: Cuv. _Leçons sur l'Hist. des Sc. Nat._ 414, 420.] - -But Comparative Anatomy, which had been cultivated with ardor {476} -to the end of the seventeenth century, was, in some measure, -neglected during the first two-thirds of the eighteenth. The -progress of botany was, Cuvier sagaciously suggests,[92\17] one -cause of this; for that science had made its advances by confining -itself to external characters, and rejecting anatomy; and though -Linnæus acknowledged the dependence of zoology upon anatomy[93\17] -so far as to make the number of teeth his characters, even this was -felt, in his method, as a bold step. But his influence was soon -opposed by that of Buffon, Daubenton, and Pallas; who again brought -into view the importance of comparative anatomy in Zoology; at the -same time that Haller proved how much might be learnt from it in -Physiology. John Hunter in England, the two Monros in Scotland, -Camper in Holland, and Vicq d'Azyr in France, were the first to -follow the path thus pointed out. Camper threw the glance of genius -on a host of interesting objects, but almost all that he produced -was a number of sketches; Vicq d'Azyr, more assiduous, was stopt in -the midst of a most brilliant career by a premature death. - -[Note 92\17: Cuv. _Hist. Sc. Nat._ i. 301.] - -[Note 93\17: Ib.] - -Such is Cuvier's outline of the earlier history of comparative -anatomy. We shall not go into detail upon this subject; but we may -observe that such studies had fixed in the minds of naturalists the -conviction of the possibility and the propriety of considering large -divisions of the animal kingdom as modifications of one common -_type_. Belon, as early as 1555, had placed the skeleton of a man -and a bird side by side, and shown the correspondence of parts. So -far as the case of vertebrated animals extends, this correspondence -is generally allowed; although it required some ingenuity to detect -its details in some cases; for instance, to see the analogy of parts -between the head of a man and a fish. - -In tracing these less obvious correspondencies, some curious steps -have been made in recent times. And here we must, I conceive, again -ascribe no small merit to the same remarkable man who, as we have -already had to point out, gave so great an impulse to vegetable -morphology. Göthe, whose talent and disposition for speculating on -all parts of nature were truly admirable, was excited to the study -of anatomy by his propinquity to the Duke of Weimar's cabinet of -natural history. In 1786, he published a little essay, the object of -which was to show that in man, as well as in beasts, the upper jaw -contains an intermaxillary bone, although the sutures are -obliterated. After 1790,[94\17] animated and impelled by the same -passion for natural {477} observation and for general views, which -had produced his Metamorphosis of Plants, he pursued his -speculations on these subjects eagerly and successfully. And in -1795, he published a _Sketch of a Universal Introduction into -Comparative Anatomy, beginning with Osteology_; in which he attempts -to establish an "osteological type," to which skeletons of all -animals may be referred. I do not pretend that Göthe's anatomical -works have had any influence on the progress of the science -comparable with that which has been exercised by the labors of -professional anatomists; but the ingenuity and value of the views -which they contained was acknowledged by the best authorities; and -the clearer introduction and application of the principle of -developed and metamorphosed symmetry may be dated from about this -time. Göthe declares that, at an early period of these speculations, -he was convinced[95\17] that the bony head of beasts is to be -derived from six vertebræ. In 1807, Oken published a "Program" _On -the Signification of the Bones of the Skull_, in which he maintained -that these bones are equivalent to four vertebræ); and Meckel, in -his _Comparative Anatomy_, in 1811, also resolved the skull into -vertebræ. But Spix, in his elaborate work _Cephalogenesis_, in 1815, -reduced the vertebræ of the head to three. "Oken," he says,[96\17] -"published opinions merely theoretical, and consequently contrary to -those maintained in this work, which are drawn from observation." -This resolution of the head into vertebræ is assented to by many of -the best physiologists, as explaining the distribution of the -nerves, and other phenomena. Spix further extended the application -of the vertebral theory to the heads of all classes of vertebrate -animals; and Bojanus published a Memoir expressly on the vertebral -structure of the skulls of fishes in Oken's _Isis_ for 1818. -Geoffroy Saint-Hilaire presented a lithographic plate to the French -Academy in February 1824, entitled _Composition de la Tête **osseuse -chez l'Homme et les Animaux_, and developed his views of the -vertebral composition of the skull in two Memoirs published in the -_Annales des Sciences Naturelles_ for 1824. We cannot fail to -recognize here the attempt to apply to the skeleton of animals the -principle which leads botanists to consider all the parts of a -flower as transformations of the same organs. How far the -application of the principle, as here proposed, is just, I must -leave philosophical physiologists to decide. - -[Note 94\17: _Zur Morphologie_, i. 234.] - -[Note 95\17: _Zur Morphologie_, 250.] - -[Note 96\17: Spix, _Cephalogenesis_.] - -By these and similar researches, it is held by the best -physiologists {478} that the skull of all vertebrate animals is -pretty well reduced to a uniform structure, and the laws of its -variations nearly determined.[97\17] - -[Note 97\17: Cuv. _Hist. Sc. Nat._ iii. 442.] - -The vertebrate animals being thus reduced to a single type, the -question arises how far this can be done with regard to other -animals, and how many such types there are. And here we come to one -of the important services which Cuvier rendered to natural history. - - -_Sect._ 2.--_Distinction of the General Types of the Forms of -Animals.--Cuvier._ - -ANIMALS were divided by Lamarck into vertebrate and invertebrate; -and the general analogies of all vertebrate animals are easily made -manifest. But with regard to other animals, the point is far from -clear. Cuvier was the first to give a really philosophical view of -the animal world in reference to the plan on which each animal is -constructed. There are,[98\17] he says, four such plans;--four forms -on which animals appear to have been modelled; and of which the -ulterior divisions, with whatever titles naturalists have decorated -them, are only very slight modifications, founded on the development -or addition of some parts which do not produce any essential change -in the plan. - -[Note 98\17: _Règne Animal_, p. 57.] - -These four great branches of the animal world are the _vertebrata_, -_mollusca_, _articulata_, _radiata_; and the differences of these -are so important that a slight explanation of them may be permitted. - -The _vertebrata_ are those animals which (as man and other sucklers, -birds, fishes, lizards, frogs, serpents) have a backbone and a skull -with lateral appendages, within which the viscera are included, and -to which the muscles are attached. - -The _mollusca_, or soft animals, have no bony skeleton; the muscles -are attached to the skin, which often includes stony plates called -_shells_; such molluscs are shell-fish; others are cuttle-fish, and -many pulpy sea-animals. - -The _articulata_ consist of _crustacea_ (lobsters, &c.), _insects_, -_spiders_, and _annulose worms_, which consist of a head and a -number of successive annular portions of the body _jointed_ together -(to the interior of which the muscles are attached), whence the name. - -Finally, the _radiata_ include the animals known under the name of -_zoophytes_. In the preceding three branches the organs of motion -and of sense were distributed symmetrically on the two sides of an -axis, {479} so that the animal has a right and a left side. In the -radiata the similar members radiate from the axis in a circular -manner, like the petals of a regular flower. - -The whole value of such a classification cannot be understood -without explaining its use in enabling us to give general -descriptions, and general laws of the animal functions of the -classes which it includes; but in the present part of our work our -business is to exhibit it as an exemplification of the reduction of -animals to laws of Symmetry. The bipartite Symmetry of the form of -vertebrate and articulate animals is obvious; and the reduction of -the various forms of such animals to a common type has been -effected, by attention to their anatomy, in a manner which has -satisfied those who have best studied the subject. The molluscs, -especially those in which the head disappears, as oysters, or those -which are rolled into a spiral, as snails, have a less obvious -Symmetry, but here also we can apply certain general types. And the -Symmetry of the radiated zoophytes is of a nature quite different -from all the rest, and approaching, as we have suggested, to the -kind of Symmetry found in plants. Some naturalists have doubted -whether[99\17] these zoophytes are not referrible to two types -(_acrita_ or polypes, and true _radiata_,) rather than to one. - -[Note 99\17: _Brit. Assoc. Rep._ iv. 227.] - -This fourfold division was introduced by Cuvier.[100\17] Before him, -naturalists followed Linnæus, and divided non-vertebrate animals -into two classes, insects and worms. "I began," says Cuvier, "to -attack this view of the subject, and offered another division, in a -Memoir read at the Society of Natural History of Paris, the 21st of -Floreal, in the year III. of the Republic (May 10, 1795,) printed in -the _Décade Philosophique_: in this, I mark the characters and the -limits of molluscs, insects, worms, echinoderms, and zoophytes. I -distinguish the red-blooded worms or annelides, in a Memoir read to -the Institute, the 11th Nivose, year X. (December 31, 1801.) I -afterwards distributed these different classes into three branches, -each co-ordinate to the branch formed by the vertebrate animals, in -a Memoir read to the Institute in July, 1812, printed in the -_Annales du Muséum d'Histoire Naturelle_, tom. xix." His great -systematic work, the _Règne Animal_, founded on this distribution, -was published in 1817; and since that time the division has been -commonly accepted among naturalists. - -[Note 100\17: _Règne A._ 61.] - -[2nd Ed.] [The question of the Classification of Animals is -discussed in the first of Prof. Owen's _Lectures on the -Invertebrate_ {480} _Animals_ (1843). Mr. Owen observes that the -arrangement of animals into _Vertebrate_ and _Invertebrate_ which -prevailed before Cuvier, was necessarily bad, inasmuch as no -_negative_ character in Zoology gives true natural groups. Hence the -establishment of the _sub-kingdoms_, _Mollusca_, _Articulata_, -_Radiata_, as co-ordinate with _Vertebrata_, according to the -arrangement of the nervous system, was a most important advance. But -Mr. Owen has seen reason to separate the _Radiata_ of Cuvier into -two divisions; the _Nematoneura_, in which the nervous system can be -traced in a filamentary form (including _Echinoderma_, -_Ciliobrachiata_, _Cœlelmintha_, _Rotifera_,) and the _Acrita_ or -lowest division of the animal kingdom, including _Acalepha_, -_Nudibrachiata_, _Sterelmintha_, _Polygastria_.] - - -_Sect._ 3.--_Attempts to establish the Identity of the Types of -Animal Forms._ - -SUPPOSING this great step in Zoology, of which we have given an -account,--the reduction of all animals to four types or plans,--to -be quite secure, we are then led to ask whether any further advance -is possible;--whether several of these types can be referred to one -common form by any wider effort of generalization. On this question -there has been a considerable difference of opinion. Geoffroy -Saint-Hilaire,[101\17] who had previously endeavored to show that -all vertebrate animals were constructed so exactly upon the same -plan as to preserve the strictest analogy of parts in respect to -their osteology, thought to extend this unity of plan by -demonstrating, that the hard parts of crustaceans and insects are -still only modifications of the skeleton of higher animals, and that -therefore the type of vertebrata must be made to include them -also:--the segments of the articulata are held to be strictly -analogous to the vertebras of the higher animals, and thus the -former live _within_ their vertebral column in the same manner as -the latter live _without_ it. Attempts have even been made to reduce -molluscous and vertebrate animals to a community of type, as we -shall see shortly. - -[Note 101\17: Mr. Jenyns, _Brit. Assoc. Rep._ iv. 150.] - -Another application of the principle, according to which creatures -the most different are developments of the same original type, may -be discerned[102\17] in the doctrine, that the embryo of the higher -forms of animal life passes by gradations through those forms which -are {481} permanent in inferior animals. Thus, according to this -view, the human fœtus assumes successively the plan of the zoophyte, -the worm, the fish, the turtle, the bird, the beast. But it has been -well observed, that "in these analogies we look in vain for the -precision which can alone support the inference that has been -deduced;"[103\17] and that at each step, the higher embryo and the -lower animal which it is supposed to resemble, differ in having each -different organs suited to their respective destinations. - -[Note 102\17: Dr. Clark, _Report_, Ib. iv. 113.] - -[Note 103\17: Dr. Clark, p. 114.] - -Cuvier[104\17] never assented to this view, nor to the attempts to -refer the different divisions of his system to a common type. "He -could not admit," says his biographer, "that the lungs or gills of -the vertebrates are in the same connexion as the branchiæ of -molluscs and crustaceans, which in the one are situated at the base -of the feet, or fixed on the feet themselves, and in the other often -on the back or about the arms. He did not admit the analogy between -the skeleton of the vertebrates and the skin of the articulates; he -could not believe that the tænia and the sepia were constructed on -the same plan; that there was a similarity of composition between -the bird and the echinus, the whale and the snail; in spite of the -skill with which some persons sought gradually to efface their -discrepancies." - -[Note 104\17: Laurillard, _Elog. de Cuvier_, p. 66.] - -Whether it may be possible to establish, among the four great -divisions of the "Animal Kingdom," some analogies of a higher order -than those which prevail within each division, I do not pretend to -conjecture. If this can be done, it is clear that it must be by -comparing the types of these divisions under their most general -forms: and thus Cuvier's arrangement, so far as it is itself rightly -founded on the unity of composition of each branch, is the surest -step to the discovery of a unity pervading and uniting these -branches. But those who generalize surely, and those who generalize -rapidly, may travel in the same direction, they soon separate so -widely, that they appear to move from each other. The partisans of a -universal "unity of composition" of animals, accused Cuvier of being -too inert in following the progress of physiological and zoological -science. Borrowing their illustration from the political parties of -the times, they asserted that he belonged to the science of -_resistance_, not to the science of the _movement_. Such a charge -was highly honorable to him; for no one acquainted with the history -of zoology can doubt that he had a great share in the impulse by -which the "movement" was occasioned; or that he {482} himself made a -large advance with it; and it was because he was so poised by the -vast mass of his knowledge, so temperate in his love of doubtful -generalizations, that he was not swept on in the wilder part of the -stream. To such a charge, moderate reformers, who appreciate the -value of the good which exists, though they try to make it better, -and who know the knowledge, thoughtfulness, and caution, which are -needful in such a task, are naturally exposed. For us, who can only -decide on such a subject by the general analogies of the history of -science, it may suffice to say, that it appears doubtful whether the -fundamental conceptions of affinity, analogy, transition, and -developement, have yet been fixed in the minds of physiologists with -sufficient firmness and clearness, or unfolded with sufficient -consistency and generality, to make it likely that any great -additional step of this kind can for some time be made. - -We have here considered the doctrine of the identity of the -seemingly various types of animal structure, as an attempt to extend -the correspondencies which were the basis of Cuvier's division of -the animal kingdom. But this doctrine has been put forward in -another point of view, as the antithesis to the doctrine of final -causes. This question is so important a one, that we cannot help -attempting to give some view of its state and bearings. - - - - -CHAPTER VIII. - -THE DOCTRINE OF FINAL CAUSES IN PHYSIOLOGY. - - -_Sect._ 1.--_Assertion of the Principle of Unity of Plan._ - -WE have repeatedly seen, in the course of our historical view of -Physiology, that those who have studied the structure of animals and -plants, have had a conviction forced upon them, that the organs are -constructed and combined in subservience to the life and functions -of the whole. The parts have a _purpose_, as well as a _law_;--we -can trace Final Causes, as well as Laws of Causation. This principle -is peculiar to physiology; and it might naturally be expected that, -in the progress of the science, it would come under special -consideration. This accordingly has happened; and the principle has -been drawn {483} into a prominent position by the struggle of two -antagonistic schools of physiologists. On the one hand, it has been -maintained that this doctrine of final causes is altogether -unphilosophical, and requires to be replaced by a more comprehensive -and profound principle: on the other hand, it is asserted that the -doctrine is not only true, but that, in our own time, it has been -fixed and developed so as to become the instrument of some of the -most important discoveries which have been made. Of the views of -these two schools we must endeavor to give some account. - -The disciples of the former of the two schools express their tenets -by the phrases _unity_ of _plan_, _unity_ of _composition_; and the -more detailed developement of these doctrines has been termed the -_Theory of Analogies_, by Geoffroy Saint-Hilaire, who claims this -theory as his own creation. According to this theory, the structure -and functions of animals are to be studied by the guidance of their -analogy only; our attention is to be turned, not to the fitness of -the organization for any end of life or action, but to its -resemblance to other organizations by which it is gradually derived -from the original type. - -According to the rival view of this subject, we must not assume, and -cannot establish, that the plan of all animals is the same, or their -composition similar. The existence of a single and universal system -of analogies in the construction of all animals is entirely -unproved, and therefore cannot be made our guide in the study of -their properties. On the other hand, the plan of the animal, the -purpose of its organization in the support of its life, the -necessity of the functions to its existence, are truths which are -irresistibly apparent, and which may therefore be safely taken as -the bases of our reasonings. This view has been put forward as the -doctrine of the _conditions of existence_: it may also be described -as the principle of _a purpose in organization_; the structure being -considered as having the function for its end. We must say a few -words on each of these views. - -It had been pointed out by Cuvier, as we have seen in the last -chapter, that the animal kingdom may be divided into four great -branches; in each of which the _plan_ of the animal is different, -namely, _vertebrata_, _articulata_, _mollusca_, _radiata_. Now the -question naturally occurs, is there really no resemblance of -construction in these different classes? It was maintained by some, -that there is such a resemblance. In 1820,[105\17] M. Audouin, a -young naturalist of Paris, {484} endeavored to fill up the chasm -which separates insects from other animals; and by examining -carefully the portions which compose the solid frame-work of -insects, and following them through their various transformations in -different classes, he conceived that he found relations of position -and function, and often of number and form, which might be compared -with the relations of the parts of the skeleton in vertebrate -animals. He thought that the first segment of an insect, the -head,[106\17] represents one of the three vertebræ which, according -to Spix and others, compose the vertebrate head: the second segment -of the insects, (the _prothorax_ of Audouin,) is, according to M. -Geoffroy, the second vertebra of the head of the vertebrata, and so -on. Upon this speculation Cuvier[107\17] does not give any decided -opinion; observing only, that even if false, it leads to active -thought and useful research. - -[Note 105\17: Cuv. _Hist. Sc. Nat._ iii. 422.] - -[Note 106\17: Ib. 437.] - -[Note 107\17: Cuv. _Hist. Sc. Nat._ iii. 441.] - -But when an attempt was further made to identify the plan of another -branch of the animal world, the mollusca, with that of the -vertebrata, the radical opposition between such views and those of -Cuvier, broke out into an animated controversy. - -Two French anatomists, MM. Laurencet and Meyranx, presented to the -Academy of Sciences, in 1830, a Memoir containing their views on the -organization of molluscous animals; and on the sepia or cuttle-fish -in particular, as one of the most complete examples of such animals. -These creatures, indeed, though thus placed in the same division -with shell-fish of the most defective organization and obscure -structure, are far from being scantily organized. They have a -brain,[108\17] often eyes, and these, in the animals of this class, -(_cephalopoda_) are more complicated than in any -vertebrates;[109\17] they have sometimes ears, salivary glands, -multiple stomachs, a considerable liver, a bile, a complete double -circulation, provided with auricles and ventricles; in short, their -vital activity is vigorous, and their senses are distinct. - -[Note 108\17: Geoffroy Saint-Hilaire denies this. _Principes de -Phil. Zoologique discutés en_ 1830, p. 68.] - -[Note 109\17: Geoffroy Saint-Hilaire, _Principes de Phil. Zoologique -discutés en_ 1830, p. 55.] - -But still, though this organization, in the abundance and diversity -of its parts, approaches that of vertebrate animals, it had not been -considered as composed in the same manner, or arranged in the same -order, Cuvier had always maintained that the plan of molluscs is not -a continuation of the plan of vertebrates. {485} - -MM. Laurencet and Meyranx, on the contrary, conceived that the sepia -might be reduced to the type of a vertebrate creature, by -considering the back-bone of the latter bent double backwards, so as -to bring the root of the tail to the nape of the neck; the parts -thus brought into contact being supposed to coalesce. By this mode -of conception, these anatomists held that the viscera were placed in -the same connexion as in the vertebrate type, and the functions -exercised in an analogous manner. - -To decide on the reality of the analogy thus asserted, clearly -belonged to the jurisdiction of the most eminent anatomists and -physiologists. The Memoir was committed to Geoffroy Saint-Hilaire -and Latreille, two eminent zoologists, in order to be reported on. -Their report was extremely favorable; and went almost to the length -of adopting the views of the authors. - -Cuvier expressed some dissatisfaction with this report on its being -read;[110\17] and a short time afterwards,[111\17] represented -Geoffroy Saint-Hilaire as having asserted that the new views of -Laurencet and Meyranx refuted completely the notion of the great -interval which exists between molluscous and vertebrate animals. -Geoffroy protested against such an interpretation of his -expressions; but it soon appeared, by the controversial character -which the discussions on this and several other subjects assumed, -that a real opposition of opinions was in action. - -[Note 110\17: _Princ. de Phil. Zool. discutés en_ 1830, p. 36.] - -[Note 111\17: p. 50.] - -Without attempting to explain the exact views of Geoffroy, (we may, -perhaps, venture to say that they are hardly yet generally -understood with sufficient distinctness to justify the mere -historian of science in attempting such an explanation,) their -general tendency may be sufficiently collected from what has been -said; and from the phrases in which his views are conveyed.[112\17] -_The principle of connexions, the elective affinities of organic -elements, the equilibrization of organs_;--such are the designations -of the leading doctrines which are unfolded in the preliminary -discourse of his _Anatomical Philosophy_. Elective affinities of -organic elements are the forces by which the vital structures and -varied forms of living things are produced; and the principles of -connexion and equilibrium of these forces in the various parts of -the organization prescribe limits and conditions to the variety and -developement of such forms. - -[Note 112\17: _Phil. Zool._ 15.] - -The character and tendency of this philosophy will be, I think, -{486} much more clear, if we consider what it excludes and denies. -It rejects altogether all conception of a plan and purpose in the -organs of animals, as a principle which has determined their forms, -or can be of use in directing our reasonings. "I take care," says -Geoffroy, "not to ascribe to God any intention."[113\17] And when -Cuvier speaks of the combination of organs in such order that they -may be in consistence with the part which the animal _has to play_ -in nature; his rival rejoins,[114\17] I "know nothing of animals -which _have to play_ a part in nature." Such a notion is, he holds, -unphilosophical and dangerous. It is an abuse of final causes which -makes the cause to be engendered by the effect. And to illustrate -still further his own view, he says, "I have read concerning -fishes, that because they live in a medium which resists more than -air, their motive forces are calculated so as to give them the power -of progression under those circumstances. By this mode of reasoning, -you would say of a man who makes use of crutches, that he was -originally destined to the misfortune of having a leg paralysed or -amputated." - -[Note 113\17: "Je me garde de prêter à Dieu aucune intention." -_Phil. Zool._ 10.] - -[Note 114\17: "Je ne connais point d'animal qui DOIVE jouer un rôle -dans la nature." p. 65.] - -How far this doctrine of unity in the plan in animals, is admissible -or probable in physiology when kept within proper limits, that is, -when not put in opposition to the doctrine of a purpose involved in -the plan of animals, I do not pretend even to conjecture. The -question is one which appears to be at present deeply occupying the -minds of the most learned and profound physiologists; and such -persons alone, adding to their knowledge and zeal, judicial sagacity -and impartiality, can tell us what is the general tendency of the -best researches on this subject.[115\17] But when the anatomist -expresses such opinions, and defends them by such illustrations as -those which I have just quoted,[116\17] we perceive that he quits -the entrenchments of his superior science, in which he might {487} -have remained unassailable so long as the question was a -professional one; and the discussion is open to those who possess no -peculiar knowledge of anatomy. We shall, therefore, venture to say a -few words upon it. - -[Note 115\17: So far as this doctrine is generally accepted among -the best physiologists, we cannot doubt the propriety of Meckel's -remark, (_Comparative Anatomy_, 1821, Pref. p. xi.) that it cannot -be truly asserted either to be new, or to be peculiarly due to -Geoffroy Saint-Hilaire.] - -[Note 116\17: It is hardly worth while answering such illustrations, -but I may remark, that the one quoted above, irrelevant and -unbecoming as it is, tells altogether against its author. The fact -that the wooden leg is of the same length as the other, proves, and -would satisfy the most incredulous man, that it was _intended_ for -walking.] - - -_Sect._ 2.--_Estimate of the Doctrine of Unity of Plan._ - -IT has been so often repeated, and so generally allowed in modern -times, that Final Causes ought not to be made our guides in natural -philosophy, that a prejudice has been established against the -introduction of any views to which this designation can be applied, -into physical speculations. Yet, in fact, the assumption of an end -or purpose in the structure of organized beings, appears to be an -intellectual habit which no efforts can cast off. It has prevailed -from the earliest to the latest ages of zoological research; appears -to be fastened upon us alike by our ignorance and our knowledge; and -has been formally accepted by so many great anatomists, that we -cannot feel any scruple in believing the rejection of it to be the -superstition of a false philosophy, and a result of the exaggeration -of other principles which are supposed capable of superseding its -use. And the doctrine of unity of plan of all animals, and the other -principles associated with this doctrine, so far as they exclude the -conviction of an intelligible scheme and a discoverable end, in the -organization of animals, appear to be utterly erroneous. I will -offer a few reasons for an opinion which may appear presumptuous in -a writer who has only a general knowledge of the subject. - -1. In the first place, it appears to me that the argumentation on -the case in question, the Sepia, does by no means turn out to the -advantage of the new hypothesis. The arguments in support of the -hypothetical view of the structure of this mollusc were, that by -this view the relative position of the parts was explained, and -confirmations which had appeared altogether anomalous, were reduced -to rule; for example, the beak, which had been supposed to be in a -position the reverse of all other beaks, was shown, by the assumed -posture, to have its upper mandible longer than the lower, and thus -to be regularly placed. "But," says Cuvier,[117\17] "supposing the -posture, in order that the side on which the funnel of the sepia is -folded should be the back of the animal, considered as similar to a -vertebrate, the brain with {488} regard to the beak, and the -œsophagus with regard to the liver, should have positions -corresponding to those in vertebrates; but the positions of these -organs are exactly contrary to the hypothesis. How, then, can you -say," he asks, "that the cephalopods and vertebrates have _identity -of composition_, _unity of composition_, without using words in a -sense entirely different from their common meaning?" - -[Note 117\17: _G. S. H. Phil. Zool._ p. 70.] - -This argument appears to be exactly of the kind on which the value -of the hypothesis must depend.[118\17] It is, therefore, interesting -to see the reply made to it by the theorist. It is this: "I admit -the facts here stated, but I deny that they lead to the notion of a -different sort of animal composition. Molluscous animals had been -placed too high in the zoological scale; but if they are only the -embryos of its lower stages, if they are only beings in which far -fewer organs come into play, it does not follow that the organs are -destitute of the relations which the power of successive generations -may demand. The organ A will be in an unusual relation with the -organ C, if B has not been produced;--if a stoppage of the -developement has fallen upon this latter organ, and has thus -prevented its production. And thus," he says, "we see how we may -have different arrangements, and divers constructions as they appear -to the eye." - -[Note 118\17: I do not dwell on other arguments which were employed. -It was given as a circumstance suggesting the supposed posture of -the type, that in this way the back was colored, and the belly was -white. On this Cuvier observes (_Phil. Zool._ pp. 93, 68), "I must -say, that I do not know any naturalist so ignorant as to suppose -that the back is determined by its dark color, or even by its -position when the animal is in motion; they all know that the badger -has a black belly and a white back; that an infinity of other -animals, especially among insects, are in the same case; and that -many fishes swim on their side, or with their belly upwards."] - -It seems to me that such a concession as this entirely destroys the -theory which it attempts to defend; for what arrangement does the -principle of unity of composition _exclude_, if it admits unusual, -that is, various arrangements of some organs, accompanied by the -total absence of others? Or how does this differ from Cuvier's mode -of stating the conclusion, except in the introduction of certain -arbitrary hypotheses of developement and stoppage? "I reduce the -facts," Cuvier says, "to their true expression, by saying that -Cephalopods have several organs which are common to them and -vertebrates, and which discharge the same offices; but that these -organs are in them differently distributed, and often constructed in -a different manner; {489} and they are accompanied by several other -organs which vertebrates have not; while these on the other hand -have several which are wanting in cephalopods." - -We shall see afterwards the general principles which Cuvier himself -considered as the best guides in these reasonings. But I will first -add a few words on the disposition of the school now under -consideration, to reject all assumption of an end. - -2. That the parts of the bodies of animals are made in order to -discharge their respective offices, is a conviction which we cannot -believe to be otherwise than an irremovable principle of the -philosophy of organization, when we see the manner in which it has -constantly forced itself upon the minds of zoologists and anatomists -in all ages; not only as an inference, but as a guide whose -indications they could not help following. I have already noticed -expressions of this conviction in some of the principal persons who -occur in the history of physiology, as Galen and Harvey. I might add -many more, but I will content myself with adducing a contemporary of -Geoffroy's whose testimony is the more remarkable, because he -obviously shares with his countryman in the common prejudice against -the use of final causes. "I consider," he says, in speaking of the -provisions for the reproduction of animals,[119\17] "with the great -Bacon, the philosophy of final causes as sterile; but I have -elsewhere acknowledged that it was very difficult for the most -cautious man never to have recourse to them in his explanations." -After the survey which we have had to take of the history of -physiology, we cannot but see that the assumption of final causes in -this branch of science is so far from being sterile, that it has had -a large share in every discovery which is included in the existing -mass of real knowledge. The use of every organ has been discovered -by starting from the assumption that it must have _some_ use. The -doctrine of the circulation of the blood was, as we have seen, -clearly and professedly due to the persuasion of a purpose in the -circulatory apparatus. The study of comparative anatomy is the study -of the adaption of animal structures to their purposes. And we shall -soon have to show that this conception of final causes has, in our -own times, been so far from barren, that it has, in the hands of -Cuvier and others, enabled us to become intimately acquainted with -vast departments of zoology to which we have no other mode of -access. It has placed before us in a complete state, {490} animals, -of which, for thousands of years, only a few fragments have existed, -and which differ widely from all existing animals; and it has given -birth, or at least has given the greatest part of its importance and -interest, to a science which forms one of the brightest parts of the -modern progress of knowledge. It is, therefore, very far from being -a vague and empty assertion, when we say that final causes are a -real and indestructible element in zoological philosophy; and that -the exclusion of them, as attempted by the school of which we speak, -is a fundamental and most mischievous error. - -[Note 119\17: Cabanis, _Rapports du Physique et du Morale de -l'Homme_, i. **299.] - -3. Thus, though the physiologist may persuade himself that he ought -not to refer to final causes, we find that, practically, he cannot -help doing this; and that the event shows that his practical habit -is right and well-founded. But he may still cling to the speculative -difficulties and doubts in which such subjects may be involved by _à -priori_ considerations. He may say, as Saint-Hilaire does -say,[120\17] "I ascribe no intention to God, for I mistrust the -feeble powers of my reason. I observe facts merely, and go no -further. I only pretend to the character of the historian of _what -is_." "I cannot make Nature an intelligent being who does nothing in -vain, who acts by the shortest mode, who does all for the best." - -[Note 120\17: _Phil. Zool._ p. 10.] - -I am not going to enter at any length into this subject, which, thus -considered, is metaphysical and theological, rather than -physiological. If any one maintain, as some have maintained, that no -manifestation of means apparently used for ends in nature, can prove -the existence of design in the Author of nature, this is not the -place to refute such an opinion in its general form. But I think it -may be worth while to show, that even those who incline to such an -opinion, still cannot resist the necessity which compels men to -assume, in organized beings, the existence of an end. - -Among the philosophers who have referred our conviction of the being -of God to our moral nature, and have denied the possibility of -demonstration on mere physical grounds, Kant is perhaps the most -eminent. Yet he has asserted the reality of such a principle of -physiology as we are now maintaining in the most emphatic manner. -Indeed, this assumption of an end makes his very definition of an -organized being. "An organized product of nature is that in which -all the parts are mutually ends and means."[121\17] And this, he -says, is a universal and necessary maxim. He adds, "It is well known -that the {491} anatomizers of plants and animals, in order to -investigate their structure, and to obtain an insight into the -grounds why and to what end such parts, why such a situation and -connexion of the parts, and exactly such an internal form, come -before them, assume, as indispensably necessary, this maxim, that in -such a creature nothing is _in vain_, and proceed upon it in the -same way in which in general natural philosophy we proceed upon the -principle that _nothing happens by chance_. In fact, they can as -little free themselves from this _teleological_ principle as from -the general physical one; for as, on omitting the latter, no -experience would be possible, so on omitting the former principle, -no clue could exist for the observation of a kind of natural objects -which can be considered teleologically under the conception of -natural ends." - -[Note 121\17: _Urtheilskraft_, p. 296.] - -Even if the reader should not follow the reasoning of this -celebrated philosopher, he will still have no difficulty in seeing -that he asserts, in the most distinct manner, that which is denied -by the author whom we have before quoted, the propriety and -necessity of assuming the existence of an end as our guide in the -study of animal organization. - -4. It appears to me, therefore, that whether we judge from the -arguments, the results, the practice of physiologists, their -speculative opinions, or those of the philosophers of a wider field, -we are led to the same conviction, that in the organized world we -may and must adopt the belief that organization exists for its -purpose, and that the apprehension of the purpose may guide us in -seeing the meaning of the organization. And I now proceed to show -how this principle has been brought into additional clearness and -use by Cuvier. - -In doing this, I may, perhaps, be allowed to make a reflection of a -kind somewhat different from the preceding remarks, though suggested -by them. In another work,[122\17] I endeavored to show that those -who have been discoverers in science have generally had minds, the -disposition of which was to believe in an intelligent Maker of the -universe; and that the scientific speculations which produced an -opposite tendency, were generally those which, though they might -deal familiarly with known physical truths, and conjecture boldly -with regard to the unknown, did not add to the number of solid -generalizations. In order to judge whether this remark is distinctly -applicable in the case now considered, I should have to estimate -Cuvier in comparison with other physiologists of his time, which I -do not presume to do. But I may {492} observe, that he is allowed by -all to have established, on an indestructible basis, many of the -most important generalizations which zoology now contains; and the -principal defect which his critics have pointed out, has been, that -he did not generalize still more widely and boldly. It appears, -therefore, that he cannot but be placed among the great discoverers -in the studies which he pursued; and this being the case, those who -look with pleasure on the tendency of the thoughts of the greatest -men to an Intelligence far higher than their own, most be gratified -to find that he was an example of this tendency; and that the -acknowledgement of a creative purpose, as well as a creative power, -not only entered into his belief but made an indispensable and -prominent part of his philosophy. - -[Note 122\17: _Bridgewater Treatise_, B. iii. c. vii. and viii. On -Inductive Habits of Thought, and on Deductive Habits of Thought.] - - -_Sect._ 3.--_Establishment and Application of the Principle of the -Conditions of Existence of Animals.--Cuvier._ - -WE have now to describe more in detail the doctrine which Cuvier -maintained in opposition to such opinions as we have been speaking -of; and which, in his way of applying it, we look upon as a material -advance in physiological knowledge, and therefore give to it a -distinct place in our history. "Zoology has," he says,[123\17] in -the outset of his _Règne Animal_, "a principle of reasoning which is -peculiar to it, and which it employs with advantage on many -occasions: this is the principle of _the Conditions of Existence_, -vulgarly the principle of _Final Causes_. As nothing can exist if it -do not combine all the conditions which render its existence -possible, the different parts of each being must be co-ordinated in -such a manner as to render the total being possible, not only in -itself, but in its relations to those which surround it; and the -analysis of these conditions often leads to general laws, as clearly -demonstrated as those which result from calculation or from -experience." - -[Note 123\17: _Règne An._ p. 6.] - -This is the enunciation of his leading principle in general terms. -To our ascribing it to him, some may object on the ground of its -being self-evident in its nature,[124\17] and having been very -anciently applied. But to this we reply, that the principle must be -considered as a real discovery in the hands of him who first shows -how to make it an instrument of other discoveries. It is true, in -other cases as well as in this, that some vague apprehension, of -true general principles, such as _à_ {493} _priori_ considerations -can supply, has long preceded the knowledge of them as real and -verified laws. In such a way it was seen, before Newton, that the -motions of the planets must result from attraction; and so, before -Dufay and Franklin, it was held that electrical actions must result -from a fluid. Cuvier's merit consisted, not in seeing that an animal -cannot exist without combining all the conditions of its existence; -but in perceiving that this truth may be taken as a guide in our -researches concerning animals;--that the mode of their existence may -be collected from one part of their structure, and then applied to -interpret or detect another part. He went on the supposition not -only that animal forms have _some_ plan, _some_ purpose, but that -they have an intelligible plan, a discoverable purpose. He proceeded -in his investigations like the decipherer of a manuscript, who makes -out his alphabet from one part of the context, and then applies it -to read the rest. The proof that his principle was something very -different from an identical proposition, is to be found in the fact, -that it enabled him to understand and arrange the structures of -animals with unprecedented clearness and completeness of order; and -to restore the forms of the extinct animals which are found in the -rocks of the earth, in a manner which has been universally assented -to as irresistibly convincing. These results cannot flow from a -trifling or barren principle; and they show us that if we are -disposed to form such a judgment of Cuvier's doctrine, it must be -because we do not fully apprehend its import. - -[Note 124\17: Swainson. _Study of Nat. Hist._ p. 85.] - -To illustrate this, we need only quote the statement which he makes, -and the uses to which he applies it. Thus in the Introduction to his -great work on _Fossil Remains_ he says, "Every organized being forms -an entire system of its own, all the parts of which mutually -correspond, and concur to produce a certain definite purpose by -reciprocal reaction, or by combining to the same end. Hence none of -these separate parts can change their forms without a corresponding -change in the other parts of the same animal; and consequently each of -these parts, taken separately, indicates all the other parts to which -it has belonged. Thus, if the viscera of an animal are so organized as -only to be fitted for the digestion of recent flesh, it is also -requisite that the jaws should be so constructed as to fit them for -devouring prey; the claws must be constructed for seizing it and -tearing it to pieces; the teeth for cutting and dividing its flesh; -the entire system of the limbs or organs of motion for pursuing and -overtaking it; and the organs of sense for discovering it at a -distance. Nature must also have endowed the brain of the animal with -instincts sufficient for concealing itself and for laying plans to -{494} catch its necessary victims."[125\17] By such considerations he -has been able to reconstruct the whole of many animals of which parts -only were given;--a positive result, which shows both the reality and -the value of the truth on which he wrought. - -[Note 125\17: _Theory of the Earth_, p. 90.] - -Another great example, equally showing the immense importance of -this principle in Cuvier's hands, is the reform which, by means of -it, he introduced into the classification of animals. Here again we -may quote the view he himself has given[126\17] of the character of -his own improvements. In studying the physiology of the natural -classes of vertebrate animals, he found, he says, "in the respective -quantity of their respiration, the reason of the quantity of their -motion, and consequently of the kind of locomotion. This, again, -furnishes the reason for the forms of their skeletons and muscles; -and the energy of their senses, and the force of their digestion, -are in a necessary proportion to the same quantity. Thus a division -which had till then been established, like that of vegetables, only -upon observation, was found to rest upon causes appreciable, and -applicable to other cases." Accordingly, he applied this view to -invertebrates;--examined the modifications which take place in their -organs of circulation, respiration, and sensation; and having -calculated the necessary results of these modifications, he deduced -from it a new division of those animals, in which they are arranged -according to their true relations. - -[Note 126\17: _Hist. Sc. Nat._ i. 293.] - -Such have been some of the results of the principle of the -Conditions of Existence, as applied by its great assertor. - -It is clear, indeed, that such a principle could acquire its -practical value only in the hands of a person intimately acquainted -with anatomical details, with the functions of the organs, and with -their variety in different animals. It is only by means of such -nutriment that the embryo truth could be developed into a vast tree -of science. But it is not the less clear, that Cuvier's immense -knowledge and great powers of thought led to their results, only by -being employed under the guidance of this master-principle: and, -therefore, we may justly consider it as the distinctive feature of -his speculations, and follow it with a gratified eye, as the thread -of gold which runs through, connects, and enriches his zoological -researches:--gives them a deeper interest and a higher value than -can belong to any view of the organical sciences, in which the very -essence of organization is kept out of sight. {495} - -The real philosopher, who knows that all the kinds of truth are -intimately connected, and that all the best hopes and encouragements -which are granted to our nature must be consistent with truth, will be -satisfied and confirmed, rather than surprised and disturbed, thus to -find the Natural Sciences leading him to the borders of a higher -region. To him it will appear natural and reasonable, that after -journeying so long among the beautiful and orderly laws by which the -universe is governed, we find ourselves at last approaching to a -Source of order and law, and intellectual beauty:--that, after -venturing into the region of life and feeling and will, we are led to -believe the Fountain of life and will not to be itself unintelligent -and dead, but to be a living Mind, a Power which aims as well as acts. -To us this doctrine appears like the natural cadence of the tones to -which we have so long been listening; and without such a final strain -our ears would have been left craving and unsatisfied. We have been -lingering long amid the harmonies of law and symmetry, constancy and -development; and these notes, though their music was sweet and deep, -must too often have sounded to the ear of our moral nature, as vague -and unmeaning melodies, floating in the air around us, but conveying -no definite thought, moulded into no intelligible announcement. But -one passage which we have again and again caught by snatches, though -sometimes interrupted and lost, at last swells in our ears full, -clear, and decided; and the religious "Hymn in honor of the Creator," -to which Galen so gladly lent his voice, and in which the best -physiologists of succeeding times have ever joined, is filled into a -richer and deeper harmony by the greatest philosophers of these later -days, and will roll on hereafter the "perpetual song" of the temple of -science. - - - -{{497}} -BOOK XVIII. - - -_THE PALÆTIOLOGICAL SCIENCES._ - - -HISTORY OF GEOLOGY. - - - Di quibus imperium est animarum, Umbræque silentes, - Et Chaos, et Phlegethon, loca nocte silentia late, - Sit mihi fas audita loqui; sit, numine vestro - Pandere res alta terrâ et caligine mersas. - VIRGIL. _Æn._ vi. 264. - - Ye Mighty Ones, who sway the Souls that go - Amid the marvels of the world below! - Ye, silent Shades, who sit and hear around! - Chaos! and Streams that burn beneath the ground! - All, all forgive, if by your converse stirred, - My lips shall utter what my ears have heard; - If I shall speak of things of doubtful birth, - Deep sunk in darkness, as deep sunk in earth. - - - -{{499}} -INTRODUCTION. - - -_Of the Palætiological Sciences._ - -WE now approach the last Class of Sciences which enter into the -design of the present work; and of these, Geology is the -representative, whose history we shall therefore briefly follow. By -the Class of Sciences to which I have referred it, I mean to point -out those researches in which the object is, to ascend from the -present state of things to a more ancient condition, from which the -present is derived by intelligible causes. - -The sciences which treat of causes have sometimes been termed -_ætiological_, from αἰτία, _a cause_: but this term would not -sufficiently describe the speculations of which we now speak; since -it might include sciences which treat of Permanent Causality, like -Mechanics, as well as inquiries concerning Progressive Causation. -The investigations which I now wish to group together, deal, not -only with the possible, but with the actual past; and a portion of -that science on which we are about to enter, Geology, has properly -been termed _Palæontology_, since it treats of beings which formerly -existed.[1\18] Hence, combining these two notions,[2\18] -_Palætiology_ appears to be a term not inappropriate, to describe -those speculations which thus refer to actual past events, and -attempt to explain them by laws of causation. - -[Note 1\18: Πάλαι, ὄντα] - -[Note 2\18: Πάλαι, αἰτία] - -Such speculations are not confined to the world of inert matter; we -have examples of them in inquiries concerning the monuments of the -art and labor of distant ages; in examinations into the origin and -early progress of states and cities, customs and languages; as well -as in researches concerning the causes and formations of mountains -and rocks, the imbedding of fossils in strata, and their elevation -from the bottom of the ocean. All these speculations are connected -by this bond,--that they endeavor to ascend to a past state of -things, by the aid of the evidence of the present. In asserting, -with Cuvier, that {500} "The geologist is an antiquary of a new -order," we do not mark a fanciful and superficial resemblance of -employment merely, but a real and philosophical connexion of the -principles of investigation. The organic fossils which occur in the -rock, and the medals which we find in the ruins of ancient cities, -are to be studied in a similar spirit and for a similar purpose. -Indeed, it is not always easy to know where the task of the -geologist ends, and that of the antiquary begins. The study of -ancient geography may involve us in the examination of the causes by -which the forms of coasts and plains are changed; the ancient mound -or scarped rock may force upon us the problem, whether its form is -the work of nature or of man; the ruined temple may exhibit the -traces of time in its changed level, and sea-worn columns; and thus -the antiquarian of the earth may be brought into the very middle of -the domain belonging to the antiquarian of art. - -Such a union of these different kinds of archæological -investigations has, in fact, repeatedly occurred. The changes which -have taken place in the temple of Jupiter Serapis, near Puzzuoli, -are of the sort which have just been described; and this is only one -example of a large class of objects;--the monuments of art converted -into records of natural events. And on a wider scale, we find -Cuvier, in his inquiries into geological changes, bringing together -historical and physical evidence. Dr. Prichard, in his _Researches -into the Physical History of Man_, has shown that to execute such a -design as his, we must combine the knowledge of the physiological -laws of nature with the traditions of history and the philosophical -comparison of languages. And even if we refuse to admit, as part of -the business of geology, inquiries concerning the origin and -physical history of the present population of the globe; still the -geologist is compelled to take an interest in such inquiries, in -order to understand matters which rigorously belong to his proper -domain; for the ascertained history of the present state of things -offers the best means of throwing light upon the causes of _past_ -changes. Mr. Lyell quotes Dr. Prichard's book more frequently than -any geological work of the same extent. - -Again, we may notice another common circumstance in the studies -which we are grouping together as palætiological, diverse as they -are in their subjects. In all of them we have the same kind of -manifestations of a number of successive changes, each springing out -of a preceding state; and in all, the phenomena at each step become -more and more complicated, by involving the results of all that has -preceded, modified by supervening agencies. The general aspect of -all these {501} trains of change is similar, and offers the same -features for description. The relics and ruins of the earlier states -are preserved, mutilated and dead, in the products of later times. -The analogical figures by which we are tempted to express this -relation are philosophically true. It is more than a mere fanciful -description, to say that in languages, customs, forms of Society, -political institutions, we see a number of formations super-imposed -upon one another, each of which is, for the most part, an assemblage -of fragments and results of the preceding condition. Though our -comparison might be bold, it would be just, if we were to assert, -that the English language is a conglomerate of Latin words, bound -together in a Saxon cement; the fragments of the Latin being partly -portions introduced directly from the parent quarry, with all their -sharp edges, and partly pebbles of the same material, obscured and -shaped by long rolling in a Norman or some other channel. Thus the -study of palætiology in the materials of the earth, is only a type -of similar studies with respect to all the elements, which, in the -history of the earth's inhabitants, have been constantly undergoing -a series of connected changes. - -But, wide as is the view which such considerations give us of the -class of sciences to which geology belongs, they extend still -further. "The science of the changes which have taken place in the -organic kingdoms of nature," (such is the description which has been -given of Geology,[3\18]) may, by following another set of -connexions, be extended beyond "the modifications of the surface of -our own planet." For we cannot doubt that some resemblance of a -closer or looser kind, has obtained between the changes and causes -of change, on other bodies of the universe, and on our own. The -appearances of something of the kind of volcanic action on the -surface of the moon, are not to be mistaken. And the inquiries -concerning the origin of our planet and of our solar system, -inquiries to which Geology irresistibly impels her students, direct -us to ask what information the rest of the universe can supply, -bearing upon this subject. It has been thought by some, that we can -trace systems, more or less like our solar system, in the process of -formation; the nebulous matter, which is at first expansive and -attenuated, condensing gradually into suns and planets. Whether this -_Nebular Hypothesis_ be tenable or not, I shall not here inquire; -but the discussion of such a question would be closely connected -with {502} geology, both in its interests and in its methods. If men -are ever able to frame a science of the past changes by which the -universe has been brought into its present condition, this science -will be properly described as _Cosmical Palætiology_. - -[Note 3\18: Lyell, _Principles of Geology_, p. 1.] - -These palætiological sciences might properly be called _historical_, -if that term were sufficiently precise: for they are all of the -nature of history, being concerned with the succession of events: -and the part of history which deals with the past causes of events, -is, in fact, a moral palætiology. But the phrase _Natural History_ -has so accustomed us to a use of the word _history_ in which we have -nothing to do with time, that, if we were to employ the word -_historical_ to describe the palætiological sciences, it would be in -constant danger of being misunderstood. The fact is, as Mohs has -said, that Natural History, when systematically treated, rigorously -excludes all that is _historical_; for it classes objects by their -permanent and universal properties, and has nothing to do with the -narration of particular and casual facts. And this is an -inconsistency which we shall not attempt to rectify. - -All palætiological sciences, since they undertake to refer changes -to their causes, assume a certain classification of the phenomena -which change brings forth, and a knowledge of the operation of the -causes of change. These phenomena, these causes, are very different, -in the branches of knowledge which I have thus classed together. The -natural features of the earth's surface, the works of art, the -institutions of society, the forms of language, taken together, are -undoubtedly a very wide collection of subjects of speculation; and -the kinds of causation which apply to them are no less varied. Of -the causes of change in the inorganic and organic world,--the -peculiar principles of Geology--we shall hereafter have to speak. As -these must be studied by the geologist, so, in like manner, the -tendencies, instincts, faculties, principles, which direct man to -architecture and sculpture, to civil government, to rational and -grammatical speech, and which have determined the circumstances of -his progress in these paths, must be in a great degree known to the -Palætiologist of Art, of Society, and of Language, respectively, in -order that he may speculate soundly upon his peculiar subject. With -these matters we shall not here meddle, confining ourselves, in our -exemplification of the conditions and progress of such sciences, to -the case of Geology. - -The journey of survey which we have attempted to perform over the -field of human knowledge, although carefully directed according to -the paths and divisions of the physical sciences, has already {503} -conducted us to the boundaries of physical science, and gives us a -glimpse of the region beyond. In following the history of Life, we -found ourselves led to notice the perceptive and active faculties of -man; it appeared that there was a ready passage from physiology to -psychology, from physics to metaphysics. In the class of sciences -now under notice, we are, at a different point, carried from the -world of matter to the world of thought and feeling,--from things to -men. For, as we have already said, the science of the causes of -change includes the productions of Man as well as of Nature. The -history of the earth, and the history of the earth's inhabitants, as -collected from phenomena, are governed by the same principles. Thus -the portions of knowledge which seek to travel back towards the -origin, whether of inert things or of the works of man, resemble -each other. Both of them treat of events as connected by the thread -of time and causation. In both we endeavor to learn accurately what -the present is, and hence what the past has been. Both are -_historical_ sciences in the same sense. - -It must be recollected that I am now speaking of history as -ætiological;--as it investigates causes, and as it does this in a -scientific, that is, in a rigorous and systematic, manner. And I may -observe here, though I cannot now dwell on the subject, that all -ætiological sciences will consist of three portions; the Description -of the facts and phenomena;--the general Theory of the causes of -change appropriate to the case;--and the Application of the theory -to the facts. Thus, taking Geology for our example, we must have, -first _Descriptive_ or _Phenomenal_ Geology; next, the exposition of -the general principles by which such phenomena can be produced, -which we may term _Geological Dynamics_; and, lastly, doctrines -hence derived, as to what have been the causes of the existing state -of things, which we may call _Physical Geology_. - -These three branches of geology may be found frequently or -constantly combined in the works of writers on the subject, and it -may not always be easy to discriminate exactly what belongs to each -subject.[4\18] But the analogy of this science with others, its -present {504} condition and future fortunes, will derive great -illustration from such a distribution of its history; and in this -point of view, therefore, we shall briefly treat of it; dividing the -history of Geological Dynamics, for the sake of convenience, into -two Chapters, one referring to inorganic, and one to organic, -phenomena. - -[Note 4\18: The Wernerians, in distinguishing their study from -_Geology_, and designating it as _Geognosy_, the _knowledge_ of the -earth, appear to have intended to select Descriptive Geology for -their peculiar field. In like manner, the original aim of the -Geological Society of London, which was formed (1807) "with a view -to record and multiply observations," recognized the possibility of -a Descriptive Geology separate from the other portions of the -science.] - - - -{{505}} -DESCRIPTIVE GEOLOGY. - - - - -CHAPTER I. - -PRELUDE TO SYSTEMATIC DESCRIPTIVE GEOLOGY. - - -_Sect._ 1.--_Ancient Notices of Geological Facts._ - -THE recent history of Geology, as to its most important points, is -bound up with what is doing at present from day to day; and that -portion of the history of the science which belongs to the past, has -been amply treated by other writers.[5\18] I shall, therefore, pass -rapidly over the series of events of which this history consists; -and shall only attempt to mention what may seem to illustrate and -confirm my own view of its state and principles. - -[Note 5\18: As MM. Lyell, Fitton, Conybeare, in our own country.] - -Agreeably to the order already pointed out, I shall notice, in the -first place, Phenomenal Geology, or the description of the facts, as -distinct from the inquiry into their causes. It is manifest that -such a merely descriptive kind of knowledge may exist; and it -probably will not be contested, that such knowledge ought to be -collected, before we attempt to frame theories concerning the causes -of the phenomena. But it must be observed, that we are here speaking -of the formation of a _science_; and that it is not a collection of -miscellaneous, unconnected, unarranged knowledge that can be -considered as constituting science; but a methodical, coherent, and, -as far as possible, complete body of facts, exhibiting fully the -condition of the earth as regards those circumstances which are the -subject matter of geological speculation. Such a Descriptive Geology -is a pre-requisite to Physical Geology, just as Phenomenal Astronomy -necessarily preceded Physical Astronomy, or as Classificatory Botany -is a necessary accompaniment to Botanical Physiology. We may observe -also that Descriptive Geology, such as we now speak of, is one of -the classificatory sciences, like {506} Mineralogy or Botany: and -will be found to exhibit some of the features of that class of -sciences. - -Since, then, our History of Descriptive Geology is to include only -systematic and scientific descriptions of the earth or portions of -it, we pass over, at once, all the casual and insulated statements -of facts, though they may be geological facts, which occur in early -writers; such, for instance, as the remark of Herodotus,[6\18] that -there are shells in the mountains of Egypt; or the general -statements which Ovid puts in the mouth of Pythagoras:[7\18] - Vidi ego quod fuerat solidissima tellus, - Esse fretum; vidi factas ex æquore terras, - Et procul a pelago conchæ jacuere marinæ. - -[Note 6\18: ii. 12.] - -[Note 7\18: Met. xv. 262.] - -We may remark here already how generally there are mingled with -descriptive notices of such geological facts, speculations -concerning their causes. Herodotus refers to the circumstance just -quoted, for the purpose of showing that Egypt was formerly a gulf of -the sea; and the passage of the Roman poet is part of a series of -exemplifications which he gives of the philosophical tenet, that -nothing perishes but everything changes. It will be only by constant -attention that we shall be able to keep our provinces of geology -distinct. - - -_Sect._ 2.--_Early Descriptions and Collections of Fossils._ - -IF we look, as we have proposed to do, for systematic and exact -knowledge of geological facts, we find nothing which we can properly -adduce till we come to modern times. But when facts such as those -already mentioned, (that sea-shells and other marine objects are -found imbedded in rocks,) and other circumstances in the structure -of the Earth, had attracted considerable attention, the exact -examination, collection, and record of these circumstances began to -be attempted. Among such steps in Descriptive Geology, we may notice -descriptions and pictures of fossils, descriptions of veins and -mines, collections of organic and inorganic fossils, maps of the -mineral structure of countries, and finally, the discoveries -concerning the superposition of strata, the constancy of their -organic contents, their correspondence in different countries, and -such great general relations of the materials and features of the -earth as have been discovered up to the present time. {507} Without -attempting to assign to every important advance its author, I shall -briefly exemplify each of the modes of contributing to descriptive -geology which I have just enumerated. - -The study of organic fossils was first pursued with connexion and -system in Italy. The hills which on each side skirt the -mountain-range of the Apennines are singularly rich in remains of -marine animals. When these remarkable objects drew the attention of -thoughtful men, controversies soon arose whether they really were -the remains of living creatures, or the productions of some -capricious or mysterious power by which the forms of such creatures -were mimicked; and again, if the shells were really the spoils of -the sea, whether they had been carried to the hills by the deluge of -which the Scripture speaks, or whether they indicated revolutions of -the earth of a different kind. The earlier works which contain the -descriptions of the phenomena have, in almost all instances, by far -the greater part of their pages occupied with these speculations; -indeed, the facts could not be studied without leading to such -inferences, and would not have been collected but for the interest -which such reasonings possessed. As one of the first persons who -applied a sound and vigorous intellect to these subjects, we may -notice the celebrated painter Leonardo da Vinci, whom we have -already had to refer to as one of the founders of the modern -mechanical sciences. He strenuously asserts the contents of the -rocks to be real shells, and maintains the reality of the changes of -the domain of land and sea which these spoils of the ocean imply. -"You will tell me," he says, "that nature and the influence of the -stars have formed these shelly forms in the mountains; then show me -a place in the mountains where the stars at the present day make -shelly forms of different ages, and of different species in the same -place. And how, with that, will you explain the gravel which is -hardened in stages at different heights in the mountains?" He then -mentions several other particulars respecting these evidences that -the existing mountains were formerly in the bed of the sea. Leonardo -died in 1519. At present we refer to geological essays like his, -only so far as they are descriptive. Going onwards with this view, -we may notice Fracastoro, who wrote concerning the petrifactions -which were brought to light in the mountains of Verona, when, in -1517, they were excavated for the purpose of repairing the city. -Little was done in the way of collection of facts for some time -after this. In 1669, Steno, a Dane resident in Italy, put forth his -treatise, _De Solido intra Solidum naturaliter contento_; and the -{508} following year, Augustino Scilla, a Sicilian painter, -published a Latin epistle, _De Corporibus Marinis Lapidescentibus_, -illustrated by good engravings of fossil-shells, teeth, and -corals.[8\18] After another interval of speculative controversy, we -come to Antonio Vallisneri, whose letters, _De' Corpi Marini che su' -Monti si trovano_, appeared at Venice in 1721. In these letters he -describes the fossils of Monte Bolca, and attempts to trace the -extent of the marine deposits of Italy,[9\18] and to distinguish the -most important of the fossils. Similar descriptions and figures were -published with reference to our own country at a later period. In -1766, Brander's _Fossilia Hantoniensia_, or Hampshire Fossils, -appeared; containing excellent figures of fossil shells from a part -of the south coast of England; and similar works came forth in other -parts of Europe. - -[Note 8\18: Augustine Scilla's original drawings of fossil shells, -teeth, and corals, from which the engravings mentioned in the text -were executed, as well as the natural objects from which the -drawings were made, were bought by Woodward, and are now in the -Woodwardian Museum at Cambridge.] - -[Note 9\18: p. 20.] - -However exact might be the descriptions and figures thus produced, -they could not give such complete information as the objects -themselves, collected and permanently preserved in museums. -Vallisneri says,[10\18] that having begun to collect fossils for the -purpose of forming a grotto, he selected the best, and preserved -them "as a noble diversion for the more curious." The museum of -Calceolarius at Verona contained a celebrated collection of such -remains. A copious description of it appeared in 1622. Such -collections had been made from an earlier period, and catalogues of -them published. Thus Gessner's work, _De Rerum Fossilium, Lapidum et -Gemmarum Figuris_ (1565), contains a catalogue of the cabinet of -petrifactions collected by John Kentman; many catalogues of the same -kind appeared in the seventeenth century.[11\18] Lhwyd's -_**Lythophylacii Britannici Iconographia_, published at Oxford in -1669, and exhibiting a very ample catalogue of English Fossils -contained in the Ashmolean Museum, may be noticed as one of these. - -[Note 10\18: p. 1.] - -[Note 11\18: Parkinson, _Organic Remains_, vol. i. p. 20.] - -One of the most remarkable occurrences in the progress of -descriptive geology in England, was the formation of a geological -museum by William Woodward as early as 1695. This collection, formed -with great labor, systematically arranged, and carefully catalogued, -he bequeathed to the University of Cambridge; founding and endowing -{509} at the same time a professorship of the study of geology. The -Woodwardian Museum still subsists, a monument of the sagacity with -which its author so early saw the importance of such a collection. - -Collections and descriptions of fossils, including in the term -specimens of minerals of all kinds, as well as organic remains, were -frequently made, and especially in places where mining was -cultivated; but under such circumstances, they scarcely tended at -all to that general and complete knowledge of the earth of which we -are now tracing the progress. - -In more modern times, collections may be said to be the most -important books of the geologist, at least next to the strata -themselves. The identifications and arrangements of our best -geologists, the immense studies of fossil anatomy by Cuvier and -others, have been conducted mainly by means of collections of -specimens. They are more important in this study than in botany, -because specimens which contain important geological information are -both more rare and more permanent. Plants, though each individual is -perishable, perpetuate and diffuse their kind; while the organic -impression on a stone, if lost, may never occur in a second -instance; but, on the other hand, if it be preserved in the museum, -the individual is almost as permanent in this case, as the species -in the other. - -I shall proceed to notice another mode in which such information was -conveyed. - - -_Sect._ 3.--_First Construction of Geological Maps._ - -DR. LISTER, a learned physician, sent to the Royal Society, in 1683, -a proposal for maps of soils or minerals; in which he suggested that -in the map of England, for example, each soil and its boundaries -might be distinguished by color, or in some other way. Such a mode -of expressing and connecting our knowledge of the materials of the -earth was, perhaps, obvious, when the mass of knowledge became -considerable. In 1720, Fontenelle, in his observations on a paper of -De Reaumur's, which contained an account of a deposit of -fossil-shells in Touraine, says, that in order to reason on such -cases, "we must have a kind of geographical charts, constructed -according to the collection of shells found in the earth." But he -justly adds, "What a quantity of observations, and what time would -it not require to form such maps!" - -The execution of such projects required, not merely great labor, but -{510} several steps in generalization and classification, before it -could take place. Still such attempts were made. In 1743, was -published, _A new Philosophico-chorographical Chart of East Kent, -invented and delineated_ by Christopher Packe, M.D.; in which, -however, the main object is rather to express the course of the -valleys than the materials of the country. Guettard formed the -project of a mineralogical map of France, and Monnet carried this -scheme into effect in 1780,[12\18] "by order of the king." In these -maps, however, the country is not considered as divided into soils, -still less strata; but each part is marked with its predominant -mineral only. The spirit of generalization which constitutes the -main value of such a work is wanting. - -[Note 12\18: _Atlas et Description Minéralogique de la France, -entrepris par ordre du Roi_, par MM. Guettard et Monnet, Paris, -1780, pp. 212, with 31 maps.] - -Geological maps belong strictly to Descriptive Geology; they are -free from those wide and doubtful speculations which form so large a -portion of the earlier geological books. Yet even geological maps -cannot be usefully or consistently constructed without considerable -steps of classification and generalization. When, in our own time, -geologists were become weary of controversies respecting theory, -they applied themselves with extraordinary zeal to the construction -of stratigraphical maps of various countries; flattering themselves -that in this way they were merely recording incontestable facts and -differences. Nor do I mean to intimate that their facts were -doubtful, or their distinctions arbitrary. But still they were facts -interpreted, associated, and represented, by means of the -classifications and general laws which earlier geologists had -established; and thus even Descriptive Geology has been brought into -existence as a science by the formation of systems and the discovery -of principles. At this we cannot be surprized, when we recollect the -many steps which the formation of Classificatory Botany required. We -must now notice some of the discoveries which tended to the -formation of Systematic Descriptive Geology. {511} - - - - -CHAPTER II. - -FORMATION OF SYSTEMATIC DESCRIPTIVE GEOLOGY. - - -_Sect._ 1.--_Discovery of the Order and Stratification of the -Materials of the Earth._ - -THAT the substances of which the earth is framed are not scattered -and mixed at random, but possess identity and continuity to a -considerable extent, Lister was aware, when he proposed his map. But -there is, in his suggestions, nothing relating to stratification; -nor any order of position, still less of time, assigned to these -materials. Woodward, however, appears to have been fully aware of -the general law of stratification. On collecting information from -all parts, "the result was," he says, "that in time I was abundantly -assured that the circumstances of these things in remoter countries -were much the same with those of ours here: that the stone, and -other terrestrial matter in France, Flanders, Holland, Spain, Italy, -Germany, Denmark, and Sweden, was distinguished into _strata or -layers_, as it is in England; that these strata were divided by -parallel fissures; that there were enclosed in the stone and all the -other denser kinds of terrestrial matter, great numbers of the -shells, and other productions of the sea, in the same manner as in -that of this island."[13\18] So remarkable a truth, thus collected -from a copious collection of particulars by a patient induction, was -an important step in the science. - -[Note 13\18: _Natural History of the Earth_, 1723.] - -These general facts now began to be commonly recognized, and followed -into detail. **Stukeley the antiquary[14\18] (1724), remarked an -important feature in the strata of England, that their _escarpments_, -or steepest sides, are turned towards the west and north-west; and -Strachey[15\18] (1719), gave a stratigraphical description of certain -coal-mines near Bath.[16\18] Michell, appointed Woodwardian Professor -at Cambridge {512} in 1762, described this stratified structure of the -earth far more distinctly than his predecessors, and pointed out, as -the consequence of it, that "the same kinds of earths, stones, and -minerals, will appear at the surface of the earth in long parallel -slips, parallel to the long ridges of mountains; and so, in fact, we -find them."[17\18] - -[Note 14\18: _Itinerarium Curiosum_, 1724.] - -[Note 15\18: _Phil. Trans._ 1719, and _Observations on Strata, &c._ -1729.] - -[Note 16\18: Fitton, _Annals of Philosophy_, N. S. vol. i. and ii. -(1832, '3), p. 157.] - -[Note 17\18: _Phil. Trans._ 1760.] - -Michell (as appeared by papers of his which were examined after his -death) had made himself acquainted with the series of English strata -which thus occur from Cambridge to York;--that is, from the chalk to -the coal. These relations of position required that geological maps, -to complete the information they conveyed, should be accompanied by -geological _Sections_, or imaginary representations of the order and -mode of superpositions, as well as of the superficial extent of the -strata, as in more recent times has usually been done. The strata, -as we travel from the higher to the lower, come from under each -other into view; and this _out-cropping_, _basseting_, or by -whatever other term it is described, is an important feature in -their description. - -It was further noticed that these relations of position were -combined with other important facts, which irresistibly suggested -the notion of a relation in time. This, indeed, was implied in all -theories of the earth; but observations of the facts most require -our notice. Steno is asserted by Humboldt[18\18] to be the first who -(in 1669) distinguished between rocks anterior to the existence of -plants and animals upon the globe, containing therefore no organic -remains; and rocks super-imposed on these, and full of such remains; -"turbidi maris sedimenta sibi invicem imposita". - -[Note 18\18: _Essai **Géognostique_.] - -Rouelle is stated, by his pupil Desmarest, to have made some -additional and important observations. "He saw," it is said, "that -the shells which occur in rocks were not the same in all countries; -that certain species occur together, while others do not occur in -the same beds; that there is a constant order in the arrangement of -these shells, certain species lying in distinct bands."[19\18] - -[Note 19\18: _Encycl. Méthod. Geogr. Phys._ tom. i. p. 416, as -quoted by Fitton as above, p. 159.] - -Such divisions as these required to be marked by technical names. A -distinction was made of _l'ancienne terre_ and _la nouvelle terre_, -to which Rouelle added a _travaille intermédiaire_. Rouelle died in -1770, having been known by lectures, not by books. Lehman, in 1756, -claims for himself the credit of being the first to observe and -describe correctly the structure of stratified countries; being -ignorant, {513} probably, of the labors of Strachey in England. He -divided mountains into three classes;[20\18] _primitive_, which were -formed with the world;--those which resulted from a partial -destruction of the primitive rocks;--and a third class resulting -from local or universal deluges. In 1759, also, Arduine,[21\18] in -his Memoirs on the mountains of Padua, Vicenza, and Verona, deduced, -from original observations, the distinction of rocks into _primary_, -_secondary_, and _tertiary_. - -[Note 20\18: Lyell, i. 70.] - -[Note 21\18: Ib. 72.] - -The relations of position and fossils were, from this period, -inseparably connected with opinions concerning succession in time. -Odoardi remarked,[22\18] that the strata of the **Sub-Apennine hills -are _unconformable_ to those of the Apennine, (as Strachey had -observed, that the strata above the coal were unconformable to the -coal;[23\18]) and his work contained a clear argument respecting the -different ages of these two classes of hills. Fuchsel was, in 1762, -aware of the distinctness of strata of different ages in Germany. -Pallas and Saussure were guided by general views of the same kind in -observing the countries which they visited: but, perhaps, the -general circulation of such notions was most due to Werner. - -[Note 22\18: Ib. 74.] - -[Note 23\18: Fitton, p. 157.] - - -_Sect._ 2.--_Systematic form given to Descriptive Geology.--Werner._ - -WERNER expressed the general relations of the strata of the earth by -means of classifications which, so far as general applicability is -concerned, are extremely imperfect and arbitrary; he promulgated a -theory which almost entirely neglected all the facts previously -discovered respecting the grouping of fossils,--which was founded -upon observations made in a very limited district of Germany,--and -which was contradicted even by the facts of this district. Yet the -acuteness of his discrimination in the subjects which he studied, -the generality of the tenets he asserted, and the charm which he -threw about his speculations, gave to Geology, or, as he termed it, -_Geognosy_, a popularity and reputation which it had never before -possessed. His system had asserted certain universal formations, -which followed each other in a constant order;--granite the -lowest,--then mica-slate and clay-slate;--upon these _primitive_ -rocks, generally highly inclined, rest other _transition_ -strata;--upon these, lie _secondary_ ones, which being more nearly -horizontal, are called _flötz_ or flat. The term _formation_, {514} -which we have thus introduced, indicating groups which, by evidence -of all kinds,--of their materials, their position, and their organic -contents,--are judged to belong to the same period, implies no small -amount of theory: yet this term, from this time forth, is to be -looked upon as a term of classification solely, so far as -classification can be separately attended to. - -Werner's distinctions of strata were for the most part drawn from -mineralogical constitution. Doubtless, he could not fail to perceive -the great importance of organic fossils. "I was witness," says M. de -Humboldt, one of his most philosophical followers, "of the lively -satisfaction which he felt when, in 1792, M. de **Schlottheim, one of -the most distinguished geologists of the school of Freiberg, began -to make the relations of fossils to strata the principal object of -his studies." But Werner and the disciples of his school, even the -most enlightened of them, never employed the characters derived from -organic remains with the same boldness and perseverance as those who -had from the first considered them as the leading phenomena: thus M. -de Humboldt expresses doubts which perhaps many other geologists do -not feel when, in 1823, he says, "Are we justified in concluding -that all formations are characterized by particular species? that -the fossil-shells of the chalk, the muschelkalk, the Jura limestone, -and the Alpine limestone, are all different? I think this would be -pushing the induction much too far."[24\18] In Prof. Jamieson's -_Geognosy_, which may be taken as a representation of the Wernerian -doctrines, organic fossils are in no instance referred to as -characters of formations or strata. After the curious and important -evidence, contained in organic fossils, which had been brought into -view by the labors of Italian, English, and German writers, the -promulgation of a system of Descriptive Geology, in which all this -evidence was neglected, cannot be considered otherwise than as a -retrograde step in science. - -[Note 24\18: _Gissement des Roches_, p. 41.] - -Werner maintained the aqueous deposition of all strata above the -primitive rocks; even of those _trap_ rocks, to which, from their -resemblance to lava and other phenomena, Raspe, Arduino, and others, -had already assigned a volcanic origin. The fierce and long -controversy between the _Vulcanists_ and _Neptunists_, which this -dogma excited, does not belong to this part of our history; but the -discovery of veins of granite penetrating the superincumbent slate, -to which the controversy led, was an important event in descriptive -geology. Hutton, the {515} author of the theory of igneous causation -which was in this country opposed to that of Werner, sought and -found this phenomenon in the Grampian hills, in 1785. This supposed -verification of his system "filled him with delight, and called -forth such marks of joy and exultation, that the guides who -accompanied him were persuaded, says his biographer,[25\18] that he -must have discovered a vein of silver or gold."[26\18] - -[Note 25\18: Playfair's _Works_, vol. iv. p. 75.] - -[Note 26\18: Lyell, i. 90.] - -Desmarest's examination of Auvergne (1768) showed that there was -there an instance of a country which could not even be described -without terms implying that the basalt, which covered so large a -portion of it, had flowed from the craters of extinct volcanoes. His -map of Auvergne was an excellent example of a survey of such a -country, thus exhibiting features quite different from those of -common stratified countries.[27\18] - -[Note 27\18: Lyell, i. 86.] - -The facts connected with metalliferous veins were also objects of -Werner's attention. A knowledge of such facts is valuable to the -geologist as well as to the miner, although even yet much difficulty -attends all attempts to theorize concerning them. The facts of this -nature have been collected in great abundance in all mining -districts; and form a prominent part of the descriptive geology of -such districts; as, for example, the Hartz, and Cornwall. - -Without further pursuing the history of the knowledge of the -inorganic phenomena of the earth, I turn to a still richer -department of geology, which is concerned with organic fossils. - - -_Sect._ 3.--_Application of Organic Remains as a Geological -Character.--Smith._ - -ROUELLE and Odoardi had perceived, as we have seen, that fossils -were grouped in bands: but from this general observation to the -execution of a survey of a large kingdom, founded upon this -principle, would have been a vast stride, even if the author of it -had been aware of the doctrines thus asserted by these writers. In -fact, however, William Smith executed such a survey of England, with -no other guide or help than his own sagacity and perseverance. In -his employments as a civil engineer, he noticed the remarkable -continuity and constant order of the strata in the neighborhood of -Bath, as discriminated by their fossils; and about the year 1793, -he[28\18] drew up a Tabular View of the {516} strata of that -district, which contained the germ of his subsequent discoveries. -Finding in the north of England the same strata and associations of -strata with which he had become acquainted in the west, he was led -to name them and to represent them by means of maps, according to -their occurrence over the whole face of England. These maps -appeared[29\18] in 1815; and a work by the same author, entitled -_The English Strata identified by Organic Remains_, came forth -later. But the views on which this identification of strata rests, -belong to a considerably earlier date; and had not only been acted -upon, but freely imparted in conversation many years before. - -[Note 28\18: Fitton, p. 148.] - -[Note 29\18: Brit. Assoc. 1832. Conybeare, p. 373.] - -In the meantime the study of fossils was pursued with zeal in -various countries. Lamarck and Defrance employed themselves in -determining the fossil shells of the neighborhood of Paris;[30\18] -and the interest inspired by this subject was strongly nourished and -stimulated by the memorable work of Cuvier and Brongniart, _On the -Environs of Paris_, published in 1811, and by Cuvier's subsequent -researches on the subjects thus brought under notice. For now, not -only the distinction, succession, and arrangement, but many other -relations among fossil strata, irresistibly arrested the attention -of the philosopher. Brongniart[31\18] showed that very striking -resemblances occurred in their fossil remains, between certain -strata of Europe and of North America; and proved that a rock may be -so much disguised, that the identity of the stratum can only be -recognized by geological characters.[32\18] - -[Note 30\18: Humboldt, _Giss. d. R._ p. 35.] - -[Note 31\18: _Hist. Nat. des Crustacés Fossiles_, pp. 57, 62.] - -[Note 32\18: Humboldt, _Giss. d. R._ p. 45.] - -The Italian geologists had found in their hills, for the most part, -the same species of shells which existed in their seas; but the -German and English writers, as Gesner,[33\18] Raspe,[34\18] and -Brander,[35\18] had perceived that the fossil-shells were either of -unknown species, or of such as lived in distant latitudes. To decide -that the animals and plants, of which we find the remains in a -fossil state, were of species now extinct, obviously required an -exact and extensive knowledge of natural history. And if this were -so, to assign the relations of the past to the existing tribes of -beings, and the peculiarities of their vital processes and habits, -were tasks which could not be performed without the most consummate -physiological skill and talent. Such tasks, however, have been the -familiar employments of geologists, and naturalists incited and -{517} appealed to by geologists, ever since Cuvier published his -examination of the fossil inhabitants of the Paris basin. Without -attempting a history of such labors, I may notice a few -circumstances connected with them. - -[Note 33\18: Lyell, i. 70.] - -[Note 34\18: Ib. 74.] - -[Note 35\18: Ib. 76.] - - -_Sect._ 4.--_Advances in Palæontology.--Cuvier._ - -SO long as the organic fossils which were found in the strata of the -earth were the remains of marine animals, it was very difficult for -geologists to be assured that the animals were such as did not exist -in any part or clime of the existing ocean. But when large land and -river animals were discovered, different from any known species, the -persuasion that they were of extinct races was forced upon the -naturalist. Yet this opinion was not taken up slightly, nor -acquiesced in without many struggles. - -Bones supposed to belong to fossil elephants, were some of the first -with regard to which this conclusion was established. Such remains -occur in vast numbers in the soil and gravel of almost every part of -the world; especially in Siberia, where they are called the bones of -the _mammoth_. They had been noticed by the ancients, as we learn -from Pliny;[36\18] and had been ascribed to human giants, to -elephants imported by the Romans, and to many other origins. But in -1796, Cuvier had examined these opinions with a more profound -knowledge than his predecessors; and he thus stated the result of -his researches.[37\18] "With regard to what have been called the -fossil remains of elephants, from Tentzelius to Pallas, I believe -that I am in the condition to prove, that they belong to animals -which were very clearly different in species from our existing -elephants, although they resembled them sufficiently to be -considered as belonging to the same genera." He had founded this -conclusion principally on the structure of the teeth, which he found -to differ in the Asiatic and African elephant; while, in the fossil -animal, it was different from both. But he also reasoned in part on -the form of the skull, of which the best-known example had been -described in the _Philosophical Transactions_ as early as -1737.[38\18] "As soon," says Cuvier, at a later period, "as I became -acquainted with Messerschmidt's drawing, and joined to the -differences which it presented, those which I had myself observed in -the inferior jaw and the {518} molar teeth, I no longer doubted that -the fossil elephants were of a species different from the Indian -elephant. This idea, which I announced to the Institute in the month -of January, 1796, opened to me views entirely new respecting the -theory of the earth; and determined me to devote myself to the long -researches and to the assiduous labors which have now occupied me -for twenty-five years."[39\18] - -[Note 36\18: _Hist. Nat._ lib. xxxvi. 18.] - -[Note 37\18: _Mém. Inst. Math. et Phys._ tom. ii. p. 4.] - -[Note 38\18: Described by Breyne from a specimen found in Siberia by -Messerschmidt in 1722. _Phil. Trans._ xl. 446.] - -[Note 39\18: _Ossemens Fossiles_, second edit. i. 178.] - -We have here, then, the starting-point of those researches -concerning extinct animals, which, ever since that time, have -attracted so large a share of notice from geologists and from the -world. Cuvier could hardly have anticipated the vast storehouse of -materials which lay under his feet, ready to supply him occupation -of the most intense interest in the career on which he had thus -entered. The examination of the strata on which Paris stands, and of -which its buildings consist, supplied him with animals, not only -different from existing ones, but some of them of great size and -curious peculiarities. A careful examination of the remains which -these strata contain was undertaken soon after the period we have -referred to. In 1802, Defrance had collected several hundreds of -undescribed species of shells; and Lamarck[40\18] began a series of -Memoirs upon them; remodelling the whole of Conchology, in order -that they might be included in its classifications. And two years -afterwards (1804) appears the first of Cuvier's grand series of -Memoirs containing the restoration of the vertebrate animals of -these strata. In this vast natural museum, and in contributions from -other parts of the globe, he discovered the most extraordinary -creatures:--the Palæotherium,[41\18] which is intermediate between -the horse and the pig; the Anoplotherium, which stands nearest to -the rhinoceros and the tapir; the Megalonix and Megatherium, animals -of the sloth tribe, but of the size of the ox and the rhinoceros. -The Memoirs which contained these and many other discoveries, set -the naturalists to work in every part of Europe. - -[Note 40\18: _Annales du Muséum d'Hist. Nat._ tom. i. p. 308, and -the following volumes.] - -[Note 41\18: Daubuisson, ii. 411.] - -Another very curious class of animals was brought to light -principally by the geologists of England; animals of which the -bones, found in the _lias_ stratum, were at first supposed to be -those of crocodiles. But in 1816,[42\18] Sir Everard Home says, "In -truth, on a consideration of this skeleton, we cannot but be -inclined to believe, that among the animals destroyed by the -catastrophes of remote antiquity, there had {519} been some at least -that differ so entirely in their structure from any which now exist -as to make it impossible to arrange their fossil remains with any -known class of animals." The animal thus referred to, being clearly -intermediate between fishes and lizards, was named by Mr. König, -_Ichthyosaurus_; and its structure and constitution were more -precisely determined by Mr. Conybeare in 1821, when he had occasion -to compare with it another extinct animal of which he and Mr. de la -Beche had collected the remains. This animal, still more nearly -approaching the lizard tribe, was by Mr. Conybeare called -_Plesiosaurus_.[43\18] Of each of these two genera several species -were afterwards found. - -[Note 42\18: _Phil. Trans._ 1816, p. 20.] - -[Note 43\18: _Geol. Trans._ vol. v.] - -Before this time, the differences of the races of animals and plants -belonging to the past and the present periods of the earth's -history, had become a leading subject of speculation among -geological naturalists. The science produced by this study of the -natural history of former states of the earth has been termed -_Palæontology_; and there is no branch of human knowledge more -fitted to stir men's wonder, or to excite them to the widest -physiological speculations. But in the present part of our history -this science requires our notice, only so far as it aims at the -restoration of the types of ancient animals, on clear and undoubted -principles of comparative anatomy. To show how extensive and how -conclusive is the science when thus directed, we need only refer to -Cuvier's _Ossemens Fossiles_;[44\18] a work of vast labor and -profound knowledge, which has opened wide the doors of this part of -geology. I do not here attempt even to mention the labors of the -many other eminent contributors to Palæontology; as Brocchi, Des -Hayes, Sowerby, Goldfuss, Agassiz, who have employed themselves on -animals, and Schlottheim, Brongniart, Hutton, Lindley, on plants. - -[Note 44\18: The first edition appeared in 1812, consisting -principally of the Memoirs to which reference has already been made.] - -[2nd Ed.] [Among the many valuable contributions to Palæontology in -more recent times, I may especially mention Mr. Owen's _Reports on -British Fossil Reptiles_, _on British Fossil Mammalia_, and _on the -Extinct Animals of Australia_, with descriptions of certain Fossils -indicative of large Marsupial Pachydermata: and M. Agassiz's _Report -on the Fossil Fishes of the Devonian System_, his _Synoptical Table -of British Fossil Fishes_, and his _Report on the Fishes of the -London Clay_. All these are contained in the volumes produced by the -British Association from 1839 to 1845. {520} - -A new and most important instrument of palæontological investigation -has been put in the geologist's hand by Prof. Owen's discovery, that -the internal structure of teeth, as disclosed by the microscope, is -a means of determining the kind of the animal. He has carried into -every part of the animal kingdom an examination founded upon this -discovery, and has published the results of this in his -_Odontography_. As an example of the application of this character -of animals, I may mention that a tooth brought from Riga by Sir R. -Murchison was in this way ascertained by Mr. Owen to belong to a -fish of the genus _Dendrodus_. (_Geology of Russia_, i. 67.)] - -When it had thus been established, that the strata of the earth are -characterized by innumerable remains of the organized beings which -formerly inhabited it, and that anatomical and physiological -considerations must be carefully and skilfully applied in order -rightly to interpret these characters, the geologist and the -palæontologist obviously had, brought before them, many very wide -and striking questions. Of these we may give some instances; but, in -the first place, we may add a few words concerning those eminent -philosophers to whom the science owed the basis on which succeeding -speculations were to be built. - - -_Sect._ 5.--_Intellectual Characters of the Founders of Systematic -Descriptive Geology._ - -IT would be in accordance with the course we have pursued in -treating of other subjects, that we should attempt to point out in -the founders of the science now under consideration, those -intellectual qualities and habits to which we ascribe their success. -The very recent date of the generalizations of geology, which has -hardly allowed us time to distinguish the calm expression of the -opinion of the wisest judges, might, in this instance, relieve us -from such a duty; but since our plan appears to suggest it, we will, -at least, endeavor to mark the characters of the founders of -geology, by a few of their prominent lines. - -The three persons who must be looked upon as the main authors of -geological classification are, Werner, Smith, and Cuvier. These -three men were of very different mental constitution; and it will, -perhaps, not be difficult to compare them, in reference to those -qualities which we have all along represented as the main features -of the discoverer's genius, clearness of ideas, the possession of -numerous facts, and the power of bringing these two elements into -contact. {521} - -In the German, considering him as a geologist, the ideal element -predominated. That Werner's powers of external discrimination were -extremely acute, we have seen in speaking of him as a mineralogist; -and his talent and tendency for classifying were, in his -mineralogical studies, fully fed by an abundant store of -observation; but when he came to apply this methodizing power to -geology, the love of system, so fostered, appears to have been too -strong for the collection of facts he had to deal with. As we have -already said, he promulgated, as representing the world, a scheme -collected from a province, and even too hastily gathered from that -narrow field. Yet his intense spirit of method in some measure -compensated for other deficiencies, and enabled him to give the -character of a science to what had been before a collection of -miscellaneous phenomena. The ardor of system-making produced a sort -of fusion, which, however superficial, served to bind together the -mass of incoherent and mixed materials, and thus to form, though by -strange and anomalous means, a structure of no small strength and -durability, like the ancient vitrified structures which we find in -some of our mountain regions. - -Of a very different temper and character was William Smith. No -literary cultivation of his youth awoke in him the speculative love -of symmetry and system; but a singular clearness and precision of -the classifying power, which he possessed as a native talent, was -exercised and developed by exactly those geological facts among -which his philosophical task lay. Some of the advances which he -made, had, as we have seen, been at least entered upon by others who -preceded him: but of all this he was ignorant; and, perhaps, went on -more steadily and eagerly to work out his own ideas, from the -persuasion that they were entirely his own. At a later period of his -life, he himself published an account of the views which had -animated him in his earlier progress. In this account[45\18] he -dates his attempts to discriminate and connect strata from the year -1790, at which time he was twenty years old. In 1792, he "had -considered how he could best represent the order of -superposition--continuity of course--and general eastern declination -of the strata." Soon after, doubts which had arisen were removed by -the "discovery of a mode of identifying the strata by the organized -fossils respectively imbedded therein." And "thus stored with -ideas," as he expresses himself, he began to communicate them to his -friends. In all this, we see great vividness {522} of thought and -activity of mind, unfolding itself exactly in proportion to the -facts with which it had to deal. We are reminded of that cyclopean -architecture in which each stone, as it occurs, is, with wonderful -ingenuity, and with the least possible alteration of its form, -shaped so as to fit its place in a solid and lasting edifice. - -[Note 45\18: _Phil. Mag._ 1833, vol. i. p. 38.] - -Different yet again was the character (as a geological discoverer) -of the great naturalist of the beginning of the nineteenth century. -In that part of his labors of which we have now to speak, Cuvier's -dominant ideas were rather physiological than geological. In his -views of past physical changes, he did not seek to include any -ranges of facts which lay much beyond the narrow field of the Paris -basin. But his sagacity in applying his own great principle of the -Conditions of Existence, gave him a peculiar and unparalleled power -in interpreting the most imperfect fossil records of extinct -anatomy. In the constitution of his mind, all philosophical -endowments were so admirably developed and disciplined, that it was -difficult to say, whether more of his power was due to genius or to -culture. The talent of classifying which he exercised in geology, -was the result of the most complete knowledge and skill in zoology; -while his views concerning the revolutions which had taken place in -the organic and inorganic world, were in no small degree aided by an -extraordinary command of historical and other literature. His -guiding ideas had been formed, his facts had been studied, by the -assistance of all the sciences which could be made to bear upon -them. In his geological labors we seem to see some beautiful temple, -not only firm and fair in itself, but decorated with sculpture and -painting, and rich in all that art and labor, memory and -imagination, can contribute to its beauty. - -[2nd Ed.] [Sir Charles Lyell (B. i. c. iv.) has quoted with approval -what I have elsewhere said, that the advancement of three of the -main divisions of geology in the beginning of the present century -was promoted principally by the three great nations of Europe,--the -German, the English, and the French:--Mineralogical Geology by the -German school of Werner:--Secondary Geology by Smith and his English -successors;--Tertiary Geology by Cuvier and his fellow-laborers in -France.] {523} - - - - -CHAPTER III. - -SEQUEL TO THE FORMATION OF SYSTEMATIC DESCRIPTIVE GEOLOGY. - - -_Sect._ 1.--_Reception and Diffusion of Systematic Geology._ - -IF our nearness to the time of the discoveries to which we have just -referred, embarrasses us in speaking of their authors, it makes it -still more difficult to narrate the reception with which these -discoveries met. Yet here we may notice a few facts which may not be -without their interest. - -The impression which Werner made upon his hearers was very strong; -and, as we have already said, disciples were gathered to his school -from every country, and then went forward into all parts of the -world, animated by the views which they had caught from him. We may -say of him, as has been so wisely said of a philosopher of a very -different kind,[46\18] "He owed his influence to various causes; at -the head of which may be placed that genius for system, which, -though it cramps the growth of knowledge, perhaps finally atones for -that mischief by the zeal and activity which it rouses among -followers and opponents, who discover truth by accident, when in -pursuit of weapons for their warfare." The list of Werner's pupils -for a considerable period included most of the principal geologists -of Europe; Freisleben, Mohs, Esmark, d'Andrada, Raumer, Engelhart, -Charpentier, Brocchi. Alexander von Humboldt and Leopold von Buch -went forth from his school to observe America and Siberia, the Isles -of the Atlantic, and the coast of Norway. Professor Jameson -established at Edinburgh a Wernerian Society; and his lecture-room -became a second centre of Wernerian doctrines, whence proceeded many -zealous geological observers; among these we may mention as one of -the most distinguished, M. Ami Boué, though, like several others, he -soon cast away the peculiar opinions of the Wernerian school. The -classifications of this school were, however, diffused over the -civilized world with {524} extraordinary success; and were looked -upon with great respect, till the study of organic fossils threw -them into the shade. - -[Note 46\18: Mackintosh _on Hobbes_, Dissert. p. 177.] - -Smith, on the other hand, long pursued his own thoughts without aid -and without sympathy. About 1799 he became acquainted with a few -gentlemen (Dr. Anderson, Mr. Richardson, Mr. Townsend, and Mr. -Davies), who had already given some attention to organic fossils, -and who were astonished to find his knowledge so much more exact and -extensive than their own. From this time he conceived the intention -of publishing his discoveries; but the want of literary leisure and -habits long prevented him. His knowledge was orally communicated -without reserve to many persons; and thus gradually and insensibly -became part of the public stock. When this diffusion of his views -had gone on for some time, his friends began to complain that the -author of them was deprived of his well-merited share of fame. His -delay in publication made it difficult to remedy this wrong; for -soon after he published his Geological Map of England, another -appeared, founded upon separate observations; and though, perhaps, -not quite independent of his, yet in many respects much more -detailed and correct. Thus, though his general ideas obtained -universal currency, he did not assume his due prominence as a -geologist. In 1818, a generous attempt was made to direct a proper -degree of public gratitude to him, in an article in the _Edinburgh -Review_, the production of Dr. Fitton, a distinguished English -geologist. And when the eminent philosopher, Wollaston, had -bequeathed to the Geological Society of London a fund from which a -gold medal was to be awarded to geological services, the first of -such medals was, in 1831, "given to Mr. William Smith, in -consideration of his being a great original discoverer in English -geology; and especially for his having been the first in this -country to discover and to teach the identification of strata, and -to determine their succession by means of their imbedded fossils." - -Cuvier's discoveries, on the other hand, both from the high -philosophic fame of their author, and from their intrinsic -importance, arrested at once the attention of scientific Europe; -and, notwithstanding the undoubted priority of Smith's labors, for a -long time were looked upon as the starting-point of our knowledge of -organic fossils. And, in reality, although Cuvier's memoirs derived -the greatest part of their value from his zoological conclusions, -they reflected back no small portion of interest on the -classifications of strata which were involved in his inferences. And -the views which he presented gave to geology an attractive and -striking character, and a connexion with {525} large physiological -as well as physical principles, which added incomparably to its -dignity and charm. - -In tracing the reception and diffusion of doctrines such as those of -Smith and Cuvier, we ought not to omit to notice more especially the -formation and history of the Geological Society of London, just -mentioned. It was established in 1807, with a view to multiply and -record observations, and patiently to await the result of some -future period; that is, its founders resolved to apply themselves to -Descriptive Geology, thinking the time not come for that theoretical -geology which had then long fired the controversial ardor of -Neptunists and Plutonists. The first volume of the Transactions of -this society was published in 1811. The greater part of the contents -of this volume[47\18] savor of the notions of the Wernerian school; -and there are papers on some of the districts in England most rich -in fossils, which Mr. Conybeare says, well exhibit the low state of -secondary geology at that period. But a paper by Mr. Parkinson -refers to the discoveries both of Smith and of Cuvier; and in the -next volume, Mr. Webster gives an account of the Isle of Wight, -following the admirable model of Cuvier and Brongniart's account of -the Paris basin. "If we compare this memoir of Mr. Webster with the -preceding one of Dr. Berger (also of the Isle of Wight), they at -once show themselves to belong to two very distinct eras of science; -and it is difficult to believe that the interval which elapsed -between their respective publication was only three or four -years."[48\18] - -[Note 47\18: Conybeare, _Report. Brit. Assoc._ p. 372.] - -[Note 48\18: Conybeare, _Report_, p. 372.] - -Among the events belonging to the diffusion of sound geological -views in this country, we may notice the publication of a little -volume entitled, _The Geology of England and Wales_, by Mr. -Conybeare and Mr. Phillips, in 1821; an event far more important -than, from the modest form and character of the work, it might at -first sight appear. By describing in detail the geological structure -and circumstances of England (at least as far downwards as the -coal), it enabled a very wide class of readers to understand and -verify the classifications which geology had then very recently -established; while the extensive knowledge and philosophical spirit -of Mr. Conybeare rendered it, under the guise of a topographical -enumeration, in reality a profound and instructive scientific -treatise. The vast impulse which it gave to the study of sound -descriptive geology was felt and acknowledged in other countries, as -well as in Britain. {526} - -Since that period, Descriptive Geology in England has constantly -advanced. The advance has been due mainly to the labors of the members -of the Geological Society; on whose merits as cultivators of their -science, none but those who are themselves masters of the subject, -have a right to dwell. Yet some parts of the scientific character of -these men may be appreciated by the general speculator; for they have -shown that there are no talents and no endowments which may not find -their fitting employment in this science. Besides that they have -united laborious research and comprehensive views, acuteness and -learning, zeal and knowledge; the philosophical eloquence with which -they have conducted their discussions has had a most beneficial -influence on the tone of their speculations; and their researches in -the field, which have carried them into every country and every class -of society, have given them that prompt and liberal spirit, and that -open and cordial bearing, which results from intercourse with the -world on a large and unfettered scale. It is not too much to say, that -in our time, Practical Geology has been one of the best schools of -philosophical and general culture of mind. - - -_Sect._ 2.--_Application of Systematic Geology. Geological Surveys -and Maps._ - -SUCH surveys as that which Conybeare and Phillips's book presented -with respect to England, were not only a means of disseminating the -knowledge implied in the classifications of such a work, but they -were also an essential part of the Application and Extension of the -principles established by the founders of Systematic Geology. As -soon as the truth of such a system was generally acknowledged, the -persuasion of the propriety of geological surveys and maps of each -country could not but impress itself on men's minds. - -When the earlier writers, as Lister and Fontenelle, spoke of -mineralogical and fossilological maps, they could hardly be said to -know the meaning of the terms which they thus used. But when -subsequent classifications had shown how such a suggestion might be -carried into effect, and to what important consequences it might -lead, the task was undertaken in various countries in a vigorous and -consistent manner. In England, besides Smith's map, another, drawn -up by Mr. Greenough, was published by the Geological Society in -1819; and, being founded on very numerous observations of the author -and his friends, made with great labor and cost, was not only an -important {527} correction and confirmation of Smith's labors, but a -valuable storehouse and standard of what had then been done in -English geology. Leopold von Buch had constructed a geological map -of a large portion of Germany, about the same period; but, aware of -the difficulty of the task he had thus attempted, he still forbore -to publish it. At a later period, and as materials accumulated, more -detailed maps of parts of Germany were produced by Hoffmann and -others. The French government entrusted to a distinguished Professor -of the School of Mines (M. Brochant de Villiers), the task of -constructing a map of France on the model of Mr. Greenough's; -associating with him two younger persons, selected for their energy -and talents, MM. Beaumont and Dufrénoy. We shall have occasion -hereafter to speak of the execution of this survey. By various -persons, geological maps of almost every country and province of -Europe, and of many parts of Asia and America, have been published. -I need not enumerate these, but I may refer to the account given of -them by Mr. Conybeare, in the _Reports of the British Association -for_ 1832, p. 384. These various essays may be considered as -contributions, though hitherto undoubtedly very imperfect ones, to -that at which Descriptive Geology ought to aim, and which is -requisite as a foundation for sound theory;--a complete geological -survey of the whole earth. But we must say a few words respecting -the language in which such a survey must be written. - -As we have already said, that condition which made such maps and the -accompanying descriptions possible, was that the strata and their -contents had previously undergone classification and arrangement at -the hands of the fathers of geology. Classification, in this as in -other cases, implied names which should give to the classes -distinctness and permanence; and when the series of strata belonging -to one country were referred to in the description of another, in -which they appeared, as was usually the case, under an aspect at -least somewhat different, the supposed identification required a -peculiar study of each case; and thus Geology had arrived at the -point, which we have before had to notice as one of the stages of -the progress of Classificatory Botany, at which a technical -_nomenclature_ and a well-understood _synonymy_ were essential parts -of the science. - - -_Sect._ 3.--_Geological Nomenclature._ - -BY Nomenclature we mean a _system_ of names; and hence we can {528} -not speak of a Geological Nomenclature till we come to Werner and -Smith. The earlier mineralogists had employed names, often -artificial and arbitrary, for special minerals, but no technical and -constant names for strata. The elements of Werner's names for the -members of his geological series were words in use among miners, as -_Gneiss_, _Grauwacke_, _Thonschiefer_, _Rothe todte liegende_, -_Zechstein_; or arbitrary names of the mineralogists, as Syenite, -Serpentine, Porphyry, Granite. But the more technical part of his -phraseology was taken from that which is the worst kind of name, -arbitrary numeration. Thus he had his _first_ sandstone formation, -_second_ sandstone, _third_ sandstone; _first_ flötz limestone, -_second_ flötz limestone, _third_ flötz limestone. Such names are, -beyond all others, liable to mistake in their application, and -likely to be expelled by the progress of knowledge; and accordingly, -though the Wernerian names for rocks mineralogically distinguished, -have still some currency, his sandstones and limestones, after -creating endless confusion while his authority had any sway, have -utterly disappeared from good geological works. - -The nomenclature of Smith was founded upon English provincial terms -of very barbarous aspect, as _Cornbrash_, _Lias_, _Gault_, _Clunch -Clay_, _Coral Rag_. Yet these terms were widely diffused when his -classification was generally accepted; they kept their place, -precisely because they had no systematic signification; and many of -them are at present part of the geological language of the whole -civilized world. - -Another kind of names which has been very prevalent among geologists -are those borrowed from places. Thus the Wernerians spoke of Alpine -Limestone and Jura Limestone; the English, of Kimmeridge Clay and -Oxford Clay, Purbeck Marble, and Portland Rock. These names, -referring to the stratum of a known locality as a type, were good, -as far as an identity with that type had been traced; but when this -had been incompletely done, they were liable to great ambiguity. If -the Alps or the Jura contain several formations of limestone, such -terms as we have noticed, borrowed from those mountains, cease to be -necessarily definite, and may give rise to much confusion. - -Descriptive names, although they might be supposed to be the best, -have, in fact, rarely been fortunate. The reason of this is -obvious;--the mark which has been selected for description may -easily fail to be essential; and the obvious connexions of natural -facts may overleap the arbitrary definition. As we have already -stated in the history of botany, the establishment of descriptive -marks of real classes presupposes the important but difficult step, -of the discovery of such marks. {529} Hence those descriptive names -only have been really useful in geology which had been used without -any scrupulous regard to the appropriateness of the description. The -_Green Sand_ may be white, brown, or red; the _Mountain Limestone_ -may occur only in valleys; the _Oolite_ may have no roe-like -structure; and yet these may be excellent geological names, if they -be applied to formations geologically identical with those which the -phrases originally designated. The signification may assist the -memory, but must not be allowed to subjugate the faculty of natural -classification. - -The terms which have been formed by geologists in recent times have -been drawn from sources similar to those of the older ones, and will -have their fortune determined by the same conditions. Thus Mr. Lyell -has given to the divisions of the tertiary strata the appellations -_Pleiocene_, _Meiocene_, _Eocene_, accordingly as they contain a -_majority_ of recent species of shells, a _minority_ of such -species, or a small proportion of living species, which may be -looked upon as indicating the _dawn_ of the existing state of the -animate creation. But in this case, he wisely treats his -distinctions, not as definitions, but as the marks of natural -groups. "The plurality of species indicated by the name _pleiocene_ -must not," he says,[49\18] "be understood to imply an absolute -majority of recent fossil shells in all cases, but a comparative -preponderance wherever the pleiocene are contrasted with strata of -the period immediately preceding." - -[Note 49\18: _Geol._ iii. 392.] - -Mr. Lyell might have added, that no precise percentage of recent -species, nor any numerical criterion whatever, can be allowed to -overbear the closer natural relations of strata, proved by evidence -of a superior kind, if such can be found. And this would be the -proper answer to the objection made by De la Beche to these names; -namely, that it may happen that the _meiocene_ rocks of one country -may be of the same date as the _pleiocene_ of another; the same -formation having in one place a majority, in another a minority, of -existing species. We are not to run into this incongruity, for we -are not so to apply the names. The formation which has been called -pleiocene, must continue to be so called, even where the majority of -recent species fails; and all rocks that agree with that in date, -without further reference to the numerical relations of their -fossils, must also share in the name. - -To invent good names for these large divisions of the series of -strata is indeed extremely difficult. The term _Oolite_ is an -instance in which {530} a descriptive word has become permanent in a -case of this kind; and, in imitation of it, _Pœcilite_ (from -ποικίλος, various,**) has been proposed by Mr. Conybeare[50\18] as -a name for the group of strata inferior to the oolites, of which the -_Variegated_ Sandstone (Bunter Sandstein, Grès Bigarré,) is a -conspicuous member. For the series of formations which lies -immediately over the rocks in which no organic remains are found, -the term _Transition_ was long used, but with extreme ambiguity and -vagueness. When this series, or rather the upper part of it, was -well examined in South Wales, where it consists of many well-marked -members, and may be probably taken as a type for a large portion of -the rest of the world, it became necessary to give to the group thus -explored a name not necessarily leading to assumption or -controversy. Mr. Murchison selected the term _Silurian_, borrowed -from the former inhabitants of the country in which his types were -found; and this is a term excellent in many respects; but one which -will probably not quite supersede "Transition," because, in other -places, transition rocks occur which correspond to none of the -members of the Silurian region. - -[Note 50\18: _Report_, p. 379.] - -Though new names are inevitable accompaniments of new views of -classification, and though, therefore, the geological discoverer -must be allowed a right to coin them, this is a privilege which, for -the sake of his own credit, and the circulation of his tokens, he -must exercise with great temperance and judgment. M. Brongniart may -be taken as an example of the neglect of this caution. Acting upon -the principle, in itself a sound one, that inconveniences arise from -geological terms which have a mineralogical signification, he has -given an entirely new list of names of the members of the geological -series. Thus the primitive unstratified rocks are _terrains -agalysiens_; the transition semi-compact are _hemilysiens_; the -sedimentary strata are _yzemiens_; the diluvial deposits are -_clysmiens_; and these divisions are subdivided by designations -equally novel; thus of the "terrains yzemiens," members are--the -terrains _clastiques_, _tritoniens_, _protéïques_, _palæotheriens_, -_epilymniques_, _thalassiques_.[51\18] Such a nomenclature appears -to labor under great inconveniences, since the terms are descriptive -in their derivation, yet are not generally intelligible, and refer -to theoretical views yet have not the recommendation of systematic -connexion. {531} - -[Note 51\18: Brongniart, _Tableau des Terrains_, 1829.] - - -_Sect._ 4.--_Geological Synonymy, or Determination of Geological -Equivalents._ - -IT will easily be supposed that with so many different sources of -names as we have mentioned, the same stratum may be called by -different designations; and thus a synonymy may be necessary for -geology; as it was for botany in the time of Bauhin, when the same -plants had been spoken of by so many different appellations in -different authors. But in reality, the synonymy of geology is a -still more important part of the subject than the analogy of botany -would lead us to suppose. For in plants, the species are really -fixed, and easily known when seen; and the ambiguity is only in the -imperfect communication or confused ideas of the observers. But in -geology, the identity of a stratum or formation in different places, -though not an arbitrary, may be a very doubtful matter, even to him -who has seen and examined. To assign its right character and place -to a stratum in a new country, is, in a great degree, to establish -the whole geological history of the country. To assume that the same -names may rightly be applied to the strata of different countries, -is to take for granted, not indeed the Wernerian dogma of universal -formations, but a considerable degree of generality and uniformity -in the known formations. And how far this generality and uniformity -prevail, observation alone can teach. The search for geological -synonyms in different countries brings before us two -questions;--first, _are_ there such synonyms? and only in the second -place, and as far as they occur, _what_ are they? - -In fact, it is found that although formations which must be considered -as geologically identical (because otherwise no classification is -possible,) do extend over large regions, and pass from country to -country, their identity includes certain modifications; and the -determination of the identity and of the modifications are inseparably -involved with each other, and almost necessarily entangled with -theoretical considerations. And in two countries, in which we find -this modified coincidence, instead of saying that the strata are -identical, and that their designations are synonyms, we may, with more -propriety, consider them as two corresponding series; of which the -members of the one may be treated as the _Representatives_ or -_Equivalents_ of the members of the other. - -This doctrine of Representatives or Equivalents supposes that the -geological phenomena in the two countries have been the results of -{532} similar series of events, which have, in some measure, coincided -in time and order; and thus, as we have said, refers us to a theory. -But yet, considered merely as a step in classification, the comparison -of the geological series of strata in different countries is, in the -highest degree, important and interesting. Indeed in the same manner -in which the separation of Classificatory from Chemical Mineralogy is -necessary for the completion of mineralogical science, the comparative -Classification of the strata of different countries according to their -resemblances and differences alone, is requisite as a basis for a -Theory of their causes. But, as will easily be imagined from its -nature, this part of descriptive geology deals with the most difficult -and the most elevated problems; and requires a rare union of laborious -observation with a comprehensive spirit of philosophical -classification. - -In order to give instances of this process (for of the vast labor -and great talents which have been thus employed in England, France, -and Germany, it is only instances that we can give,) I may refer to -the geological survey of France, which was executed, as we have -already stated, by order of the government. In this undertaking it -was intended to obtain a knowledge of the whole mineral structure of -France; but no small portion of this knowledge was brought into -view, when a synonymy had been established between the Secondary -Rocks of France and the corresponding members of the English and -German series, which had been so well studied as to have become -classical points of standard reference. For the purpose of doing -this, the principal directors of the survey, MM. Brochant de -Villiers, De Beaumont, and Dufrénoy, came to England in 1822, and -following the steps of the best English geologists, in a few months -made themselves acquainted with the English series. They then -returned to France, and, starting from the chalk of Paris in various -directions, travelled on the lines which carried them over the edges -of the strata which emerge from beneath the chalk, identifying, as -they could, the strata with their foreign analogues. They thus -recognized almost all of the principal beds of the oolitic series of -England.[52\18] At the same time they found differences as well as -resemblances. Thus the Portland and Kimmeridge beds of France were -found to contain in abundance a certain shell, the _gryphæa -virgula_, which had not before been much remarked in those beds in -England. With regard to the synonyms in Germany, on the other hand, -a difference of opinion {538} arose between M. Elie de Beaumont and -M. Voltz,[53\18] the former considering the _Grès de Vosges_ as the -equivalent of the _Rothe todte liegende_, which occurs beneath the -Zechstein, while M. Voltz held that it was the lower portion of the -Red or _Variegated Sandstone_ which rests on the Zechstein. - -[Note 52\18: De la Beche, _Manual_, 305.] - -[Note 53\18: De la Beche, _Manual_, 381.] - -In the same manner, from the first promulgation of the Wernerian -system, attempts were made to identify the English with the German -members of the geological alphabet; but it was long before this -alphabet was rightly read. Thus the English geologists who first -tried to apply the Wernerian series to this country, conceived the -Old and New Red Sandstone of England to be the same with the Old and -New Red Sandstone of Werner; whereas Werner's Old Red, the Rothe -todte liegende, is above the coal, while the English Old Red is -below it. This mistake led to a further erroneous identification of -our Mountain Limestone with Werner's First Flötz Limestone; and -caused an almost inextricable confusion, which, even at a recent -period, has perplexed the views of German geologists respecting this -country. Again, the Lias of England was, at first, supposed to be -the equivalent of the Muschelkalk of Germany. But the error of this -identification was brought into view by examinations and discussions -in which MM. Œyenhausen and Dechen took the lead; and at a later -period, Professor Sedgwick, by a laborious examination of the strata -of England, was enabled to show the true relation of this part of -the geology of the two countries. According to him, the New Red -Sandstone of England, considered as one great complex formation, may -be divided into seven members, composed of sandstones, limestones, -and marls; five of which represent respectively the _Rothe todte -liegende_; the _Kupfer schiefer_; the _Zechstein_, (with the -_Rauchwacké_, _Asche_, and _Stinkstein_ of the Thuringenwald;) the -_Bunter sandstein_; and the _Keuper_: while the _Muschelkalk_, which -lies between the two last members of the German list, has not yet -been discovered in our geological series. "Such a coincidence," he -observes,[54\18] "in the subdivisions of two distant mechanical -deposits, even upon the supposition of their being strictly -contemporaneous, is truly astonishing. It has not been assumed -hypothetically, but is the fair result of the facts which are -recorded in this paper." - -[Note 54\18: _Geol. Trans._ Second Series, iii. 121.] - -As an example in which the study of geological equivalents becomes -still more difficult, we may notice the attempts to refer the strata -of {534} the Alps to those of the north-west of Europe. The -dark-colored marbles and schists resembling mica slate[55\18] were, -during the prevalence of the Wernerian theory, referred, as was -natural, to the transition class. The striking physical characters -of this mountain region, and its long-standing celebrity as a -subject of mineralogical examination, made a complete subversion of -the received opinion respecting its place in the geological series, -an event of great importance in the history of the science. Yet this -was what occurred when Dr. Buckland, in 1820, threw his piercing -glance upon this district. He immediately pointed out that these -masses, by their fossils, approach to the Oolitic Series of this -country. From this view it followed, that the geological equivalents -of that series were to be found among rocks in which the -mineralogical characters were altogether different, and that the -loose limestones of England represent some of the highly-compact and -crystalline marbles of Italy and Greece. This view was confirmed by -subsequent investigations; and the correspondence was traced, not -only in the general body of the formations, but in the occurrence of -the Red Marl at its bottom, and the Green Sand and Chalk at its top. - -[Note 55\18: De la Beche, _Manual_, 313.] - -The talents and the knowledge which such tasks require are of no -ordinary kind; nor, even with a consummate acquaintance with the -well-ascertained formations, can the place of problematical strata -be decided without immense labor. Thus the examination and -delineation of hundreds of shells by the most skilful conchologists, -has been thought necessary in order to determine whether the -calcareous beds of Maestricht and of Gosau are or are not -intermediate, as to their organic contents, between the chalk and -the tertiary formations. And scarcely any point of geological -classification can be settled without a similar union of the -accomplished naturalist with the laborious geological collector. - -It follows from the views already presented, of this part of geology, -that no attempt to apply to distant countries the names by which the -well-known European strata have been described, can be of any value, -if not accompanied by a corresponding attempt to show how far the -European series is really applicable. This must be borne in mind in -estimating the import of the geological accounts which have been given -of various parts of Asia, Africa, and America. For instance, when the -carboniferous group and the new red sandstone are stated to {535} be -found in India, we require to be assured that these formations are, in -some way, the equivalents of their synonyms in countries better -explored. Till this is done, the results of observation in such places -would be better conveyed by a nomenclature implying only those facts -of resemblance, difference, and order, which have been ascertained in -the country so described. We know that serious errors were incurred by -the attempts made to identify the Tertiary strata of other countries -with those first studied in the Paris basin. Fancied points of -resemblance, Mr. Lyell observes, were magnified into undue importance, -and essential differences in mineral character and organic contents -were slurred over. - -[2nd Ed.] [The extension of geological surveys, the construction of -geological maps, and the determination of the geological equivalents -which replace each other in various countries, have been carried on -in continuation of the labors mentioned above, with enlarged -activity, range, and means. It is estimated that one-third of the -land of each hemisphere has been geologically explored; and that -thus Descriptive Geology has now been prosecuted so far, that it is -not likely that even the extension of it to the whole globe would -give any material novelty of aspect to Theoretical Geology. The -recent literature of the subject is so voluminous that it is -impossible for me to give any account of it here; very imperfectly -acquainted, as I am, even with the English portion, and still more, -with what has been produced in other countries. - -While I admire the energetic and enlightened labors by which the -philosophers of France, Belgium, Germany, Italy, Russia, and -America, have promoted scientific geology, I may be allowed to -rejoice to see in the very phraseology of the subject, the evidence -that English geologists have not failed to contribute their share to -the latest advances in the science. The following order of strata -proceeding upwards is now, I think, recognized throughout Europe. -The _Silurian_; the _Devonian_ (Old Red Sandstone;) the -_Carboniferous_; the _Permian_, (Lower part of the new Red Sandstone -series;) the _Trias_, (Upper three members of the New Red Sandstone -series;) the _Lias_; the _Oolite_, (in which are reckoned by M. -D'Orbigny the Etages _Bathonien_, _Oxonien_, _Kimmeridgien_, and -_Portlandien_;) the _Neocomien_, (Lower Green Sand,) the Chalk; and -above these, Tertiary and Supra-Tertiary beds. Of these, the -Silurian, described by Sir R. Murchison from its types in South -Wales, has been traced by European Geologists through the Ardennes, -Servia, Turkey, the shores of the Gulf of Finland, the valley {536} -of the Mississippi, the west coast of North America, and the -mountains of South America. Again, the labors of Prof. Sedgwick and -Sir R. Murchison, in 1836, '7, and '8, aided by the sagacity of Mr. -Lonsdale, led to their placing certain rocks of Devon and Cornwall -as a formation intermediate between the Silurian and Carboniferous -Series; and the Devonian System thus established has been accepted -by geologists in general, and has been traced, not only in various -parts of Europe, but in Australia and Tasmania, and in the -neighborhood of the Alleganies. - -Above the Carboniferous Series, Sir R. Murchison and his fellow -laborers, M. de Verneuil and Count Keyserling, have found in Russia -a well-developed series of rocks occupying the ancient kingdom of -Permia, which they have hence called the _Permian formation_; and -this term also has found general acceptance. The next group, the -Keuper, Muschelkalk, and Bunter Sandstein of Germany, has been -termed _Trias_ by the continental geologists. The _Neocomien_ is -called from Neuchatel, where it is largely developed. Below all -these rocks come, in England, the _Cambrian_ on which Prof. Sedgwick -has expended so many years of valuable labor. The comparison of the -Protozoic and Hypozoic rocks of different countries is probably -still incomplete. - -The geologists of North America have made great progress in -decyphering and describing the structure of their own country; and -they have wisely gone, in a great measure, upon the plan which I -have commended at the end of the third Chapter;--they have compared -the rocks of their own country with each other, and given to the -different beds and formations names borrowed from their own -localities. This course will facilitate rather than impede the -redaction of their classification to its synonyms and equivalents in -the old world. - -Of course it is not to be expected nor desired that books belonging -to Descriptive Geology shall exclude the other two branches of the -subject, Geological Dynamics and Physical Geology. On the contrary, -among the most valuable contributions to both these departments have -been speculations appended to descriptive works. And this is -naturally and rightly more and more the case as the description -embraces a wider field. The noble work _On the Geology of Russia and -the Urals_, by Sir Roderick Murchison and his companions, is a great -example of this, as of other merits in a geological book. The author -introduces into his pages the various portions of geological -dynamics of which I shall have to speak afterwards; and thus -endeavors to make out the {537} physical history of the region, the -boundaries of its raised sea bottoms, the shores of the great -continent on which the mammoths lived, the period when the gold ore -was formed, and when the watershed of the Ural chain was elevated.] - - - - -CHAPTER IV. - -ATTEMPTS TO DISCOVER GENERAL LAWS IN GEOLOGY. - - -_Sect._ 1.--_General Geological Phenomena._ - -BESIDES thus noticing such features in the rocks of each country as -were necessary to the identification of the strata, geologists have -had many other phenomena of the earth's surface and materials -presented to their notice; and these they have, to a certain extent, -attempted to generalize, so as to obtain on this subject what we -have elsewhere termed the Laws of Phenomena, which are the best -materials for physical theory. Without dwelling long upon these, we -may briefly note some of the most obvious. Thus it has been observed -that mountain ranges often consist of a ridge of subjacent rock, on -which lie, on each side, strata sloping from the ridge. Such a ridge -is an _Anticlinal Line_, a _Mineralogical Axis_. The sloping strata -present their _Escarpements_, or steep edges, to this axis. Again, -in mining countries, the _Veins_ which contain the ore are usually a -system of _parallel_ and nearly vertical partitions in the rock; and -these are, in very many cases, intersected by another system of -veins parallel to each other and nearly _perpendicular_ to the -former. Rocky regions are often intersected by _Faults_, or fissures -interrupting the strata, in which the rock on one side the fissure -appears to have been at first continuous with that on the other, and -shoved aside or up or down after the fracture. Again, besides these -larger fractures, rocks have _Joints_,--separations, or tendencies -to separate in some directions rather than in others; and a _slaty -Cleavage_, in which the parallel subdivisions may be carried on, so -as to produce laminæ of indefinite thinness. As an example of those -laws of phenomena of which we have spoken, we may instance the -general law asserted by Prof. {538} Sedgwick (not, however, as free -from exception), that in one particular class of rocks the slaty -Cleavage _never_ coincides with the Direction of the strata. - -The phenomena of metalliferous veins may be referred to, as another -large class of facts which demand the notice of the geologist. It -would be difficult to point out briefly any general laws which -prevail in such cases; but in order to show the curious and complex -nature of the facts, it may be sufficient to refer to the -description of the metallic veins of Cornwall by Mr. Carne;[56\18] -in which the author maintains that their various contents, and the -manner in which they cut across, and _stop_, or _shift_, each other, -leads naturally to the assumption of veins of no less than six or -eight different ages in one kind of rock. - -[Note 56\18: _Transactions of the Geol. Soc. of Cornwall_, vol. ii.] - -Again, as important characters belonging to the physical history of -the earth, and therefore to geology, we may notice all the general -laws which refer to its temperature;--both the laws of climate, as -determined by the _isothermal lines_, which Humboldt has drawn, by -the aid of very numerous observations made in all parts of the -world; and also those still more curious facts, of the increase of -temperature which takes place as we descend in the solid mass. The -latter circumstance, after being for a while rejected as a fable, or -explained away as an accident, is now generally acknowledged to be -the true state of things in many distant parts of the globe, and -probably in all. - -Again, to turn to cases of another kind: some writers have -endeavored to state in a general manner laws according to which the -members of the geological series succeed each other; and to reduce -apparent anomalies to order of a wider kind. Among those who have -written with such views, we may notice Alexander von Humboldt, -always, and in all sciences, foremost in the race of generalization. -In his attempt to extend the doctrine of geological equivalents from -the rocks of Europe[57\18] to those of the Andes, he has marked by -appropriate terms the general modes of geological succession. "I -have insisted," he says[58\18] "principally upon the phenomena of -_alternation_, _oscillation_, and _local suppression_, and on those -presented by the _passages_ of formations from one to another, by -the effect of an _interior developement_." - -[Note 57\18: _Gissement des Roches dans les deux Hemisphères_, 1823.] - -[Note 58\18: Pref. p. vi.] - -The phenomena of alternation to which M. de Humboldt here refers -are, in fact, very curious: as exhibiting a mode in which the -transitions from one formation to another may become gradual and -insensible, {539} instead of sudden and abrupt. Thus the coal -measures in the south of England are above the mountain limestone; -and the distinction of the formations is of the most marked kind. -But as we advance northward into the coal-field of Yorkshire and -Durham, the subjacent limestone begins to be subdivided by thick -masses of sandstone and carbonaceous strata, and passes into a -complex deposit, not distinguishable from the overlying coal -measures; and in this manner the transition from the limestone to -the coal is made by alternation. Thus, to use another expression of -M. de Humboldt's in ascending from the limestone, the coal, before -we quit the subjacent stratum, _preludes_ to its fuller exhibition -in the superior beds. - -Again, as to another point: geologists have gone on up to the -present time endeavoring to discover general laws and facts, with -regard to the position of mountain and mineral masses upon the -surface of the earth. Thus M. Von Buch, in his physical description -of the Canaries, has given a masterly description of the lines of -volcanic action and volcanic products, all over the globe. And, more -recently, M. Elie de Beaumont has offered some generalizations of a -still wider kind. In this new doctrine, those mountain ranges, even -in distant parts of the world, which are of the same age, according -to the classifications already spoken of, are asserted to be -parallel[59\18] to each other, while those ranges which are of -different ages lie in different directions. This very wide and -striking proposition may be considered as being at present upon its -trial among the geologists of Europe.[60\18] - -[Note 59\18: We may observe that the notion of parallelism, when -applied to lines drawn on _remote_ portions of a globular surface, -requires to be interpreted in so arbitrary a manner, that we can -hardly imagine it to express a physical law.] - -[Note 60\18: Mr. Lyell, in the sixth edition of his _Principles_, B. -i. c. xii., has combated the hypothesis of M. Elie de Beaumont, -stated in the text. He has argued both against the catastrophic -character of the elevation of mountain chains, and the parallelism -of the contemporaneous ridges. It is evident that the former -doctrine may be true, though the latter be shown to be false.] - -Among the organic phenomena, also, which have been the subject of -geological study, general laws of a very wide and comprehensive kind -have been suggested, and in a greater or less degree confirmed by -adequate assemblages of facts. Thus M. Adolphe Brongniart has not -only, in his _Fossil Flora_, represented and skilfully restored a -vast number of the plants of the ancient world; but he has also, in -the _Prodromus_ of the work, presented various important and -striking views of the general character of the vegetation of former -periods, as {540} insular or continental, tropical or temperate. And -M. Agassiz, by the examination of an incredible number of specimens -and collections of fossil fish, has been led to results which, -expressed in terms of his own ichthyological classification, form -remarkable general laws. Thus, according to him,[61\18] when we go -below the lias, we lose all traces of two of the four orders under -which he comprehends all known kinds of fish; namely, the -_Cycloïdean_ and the _Ctenoïdean_; while the other two orders, the -_Ganoïdean_ and _Placoïdean_, rare in our days, suddenly appear in -great numbers, together with large sauroid and carnivorous fishes. -Cuvier, in constructing his great work on ichthyology, transferred -to M. Agassiz the whole subject of fossil fishes, thus showing how -highly he esteemed his talents as a naturalist. And M. Agassiz has -shown himself worthy of his great predecessor in geological natural -history, not only by his acuteness and activity, but by the -comprehensive character of his zoological philosophy, and by the -courage with which he has addressed himself to the vast labors which -lie before him. In his _Report on the Fossil Fish discovered in -England_, published in 1835, he briefly sketches some of the large -questions which his researches have suggested; and then adds,[62\18] -"Such is the meagre outline of a history of the highest interest, -full of curious episodes, but most difficult to relate. To unfold -the details which it contains will be the business of my life." - -[Note 61\18: Greenough, _Address to Geol. Soc._ 1835, p. 19.] - -[Note 62\18: _Brit. Assoc. Report_, p. 72.] - -[2nd Ed.] [In proceeding downwards through the series of formations -into which geologists have distributed the rocks of the earth, one -class of organic forms after another is found to disappear. In the -Tertiary Period we find all the classes of the present world: -Mammals, Birds, Reptiles, Fishes, Crustaceans, Mollusks, Zoophytes. -In the Secondary Period, from the Chalk down to the New Red -Sandstone, Mammals are not found, with the minute exception of the -marsupial _amphitherium_ and _phascolotherium_ in the Stonesfield -slate. In the Carboniferous and Devonian period we have no large -Reptiles, with, again, a minute amount of exception. In the lower -part of the Silurian rocks, Fishes vanish, and we have no animal -forms but Mollusks, Crustaceans and Zoophytes. - -The Carboniferous, Devonian and Silurian formations, thus containing -the oldest forms of life, have been termed _palæozoic_. The -boundaries of the life-bearing series have not yet been determined; -but the series in which vertebrated animals do not appear has been -{541} provisionally termed _protozoic_, and the lower Silurian rocks -may probably be looked upon as its upper members. Below this, -geologists place a _hypozoic_ or _azoic_ series of rocks. - -Geologists differ as to the question whether these changes in the -inhabitants of the globe were made by determinate steps or by -insensible gradations. M. Agassiz has been led to the conviction -that the organized population of the globe was renewed in the -interval of each principal member of its formations.[63\18] Mr. -Lyell, on the other hand, conceives that the change in the -collection of organized beings was gradual, and has proposed on this -subject an hypothesis which I shall hereafter consider.] - -[Note 63\18: _Brit. Assoc. Report_ 1842, p. 83.] - - -_Sect._ 2.--_Transition to Geological Dynamics._ - -WHILE we have been giving this account of the objects with which -Descriptive Geology is occupied, it must have been felt how -difficult it is, in contemplating such facts, to confine ourselves -to description and classification. Conjectures and reasonings -respecting the causes of the phenomena force themselves upon us at -every step; and even influence our classification and nomenclature. -Our Descriptive Geology impels us to endeavor to construct a -Physical Geology. This close connexion of the two branches of the -subject by no means invalidates the necessity of distinguishing -them: as in Botany, although the formation of a Natural System -necessarily brings us to physiological relations, we still -distinguish Systematic from Physiological Botany. - -Supposing, however, our Descriptive Geology to be completed, as far -as can be done without considering closely the causes by which the -strata have been produced, we have now to enter upon the other -province of the science, which treats of those causes, and of which -we have already spoken, as _Physical Geology_. But before we can -treat this department of speculation in a manner suitable to the -conditions of science, and to the analogy of other parts of our -knowledge, a certain intermediate and preparatory science must be -formed, of which we shall now consider the origin and progress. - - - -{{542}} -GEOLOGICAL DYNAMICS. - - - - -CHAPTER V. - -INORGANIC GEOLOGICAL DYNAMICS. - - -_Sect._ 1.--_Necessity and Object of a Science of Geological -Dynamics._ - -WHEN the structure and arrangement which men observed in the -materials of the earth instigated them to speculate concerning the -past changes and revolutions by which such results had been -produced, they at first supposed themselves sufficiently able to -judge what would be the effects of any of the obvious agents of -change, as water or volcanic fire. It did not at once occur to them -to suspect, that their common and extemporaneous judgment on such -points was far from sufficient for sound knowledge;--they did not -foresee that they must create a special science, whose object should -be to estimate the general laws and effects of assumed causes, -before they could pronounce whether such causes had actually -produced the particular facts which their survey of the earth had -disclosed to them. - -Yet the analogy of the progress of knowledge on other subjects -points out very clearly the necessity of such a science. When -phenomenal astronomy had arrived at a high point of completeness, by -the labors of ages, and especially by the discovery of Kepler's -laws, astronomers were vehemently desirous of knowing the causes of -these motions; and sanguine men, such as Kepler, readily conjectured -that the motions were the effects of certain virtues and influences, -by which the heavenly bodies acted upon each other. But it did not -at first occur to him and his fellow-speculators, that they had not -ascertained what motions the influences of one body upon another -could produce: and that, therefore, they were not prepared to judge -whether such causes as they spoke of, did really regulate the -motions of the planets. Yet such was found to be the necessary -course of sound inference. Men needed a science of motion, in order -to arrive at a science of the {543} heavenly motions: they could not -advance in the study of the Mechanics of the heavens, till they had -learned the Mechanics of terrestrial bodies. And thus they were, in -such speculations, at a stand for nearly a century, from the time of -Kepler to the time of Newton, while the science of Mechanics was -formed by Galileo and his successors. Till that task was executed, -all the attempts to assign the causes of cosmical phenomena were -fanciful guesses and vague assertions; after that was done, they -became demonstrations. The science of _Dynamics_ enabled -philosophers to pass securely and completely from _Phenomenal -Astronomy_ to _Physical Astronomy_. - -In like manner, in order that we may advance from Phenomenal Geology -to Physical Geology, we need a science of _Geological -Dynamics_;--that is, a science which shall investigate and determine -the laws and consequences of the known causes of changes such as -those which Geology considers:--and which shall do this, not in an -occasional, imperfect, and unconnected manner, but by systematic, -complete, and conclusive methods;--shall, in short, be a Science, -and not a promiscuous assemblage of desultory essays. - -The necessity of such a study, as a distinct branch of geology, is -perhaps hardly yet formally recognized, although the researches -which belong to it have, of late years, assumed a much more -methodical and scientific character than they before possessed. Mr. -Lyell's work (_Principles of Geology_), in particular, has eminently -contributed to place Geological Dynamics in its proper prominent -position. Of the four books of his Treatise, the second and third -are upon this division of the subject; the second book treating of -aqueous and igneous causes of change, and the third, of changes in -the organic world. - -There is no difficulty in separating this auxiliary geological -science from theoretical Geology itself, in which we apply our -principles to the explanation of the actual facts of the earth's -surface. The former, if perfected, would be a demonstrative science -dealing with general cases; the latter is an ætiological view having -reference to special facts; the one attempts to determine what -always must be under given conditions; the other is satisfied with -knowing what is and has been, and why it has been; the first study -has a strong resemblance to Mechanics, the other to philosophical -Archæology. - -Since this portion of science is still so new, it is scarcely -possible to give any historical account of its progress, or any -complete survey of its shape and component parts. I can only attempt -a few notices, {544} which may enable us in some measure to judge to -what point this division of our subject is tending. - -We may remark, in this as in former cases, that since we have here -to consider the formation and progress of a _science_, we must treat -as unimportant preludes to its history, the detached and casual -observations of the effects of causes of change which we find in -older writers. It is only when we come to systematic collections of -information, such as may afford the means of drawing general -conclusions; or to rigorous deductions from known laws of -nature;--that we can recognise the separate existence of geological -dynamics, as a path of scientific research. - -The following may perhaps suffice, for the present, as a sketch of -the subjects of which this science treats:--the aqueous causes of -change, or those in which water adds to, takes from, or transfers, -the materials of the land:--the igneous causes; volcanoes, and, -closely connected with them, earthquakes, and the forces by which -they are produced;--the calculations which determine, on physical -principles, the effects of assumed mechanical causes acting upon -large portions of the crust of the earth;--the effect of the forces, -whatever they be, which produce the crystalline texture of rocks, -their fissile structure, and the separation of materials, of which -we see the results in metalliferous veins. Again, the estimation of -the results of changes of temperature in the earth, whether -operating by pressure, expansion, or in any other way;--the effects -of assumed changes in the superficial condition, extent, and -elevation, of terrestrial continents upon the climates of the -earth;--the effect of assumed cosmical changes upon the temperature -of this planet;--and researches of the same nature as these. - -These researches are concerned with the causes of change in the -inorganic world; but the subject requires no less that we should -investigate the causes which may modify the forms and conditions of -organic things; and in the large sense in which we have to use the -phrase, we may include researches on such subjects also as parts of -Geological Dynamics; although, in truth, this department of -physiology has been cultivated, as it well deserves to be, -independently of its bearing upon geological theories. The great -problem which offers itself here, in reference to Geology, is, to -examine the value of any hypotheses by which it may be attempted to -explain the succession of different races of animals and plants in -different strata; and though it may be difficult, in this inquiry, -to arrive at any positive result, we {545} may at least be able to -show the improbability of some conjectures which have been -propounded. - -I shall now give a very brief account of some of the attempts made -in these various departments of this province of our knowledge; and -in the present chapter, of Inorganic Changes. - - -_Sect._ 2.--_Aqueous Causes of Change._ - -THE controversies to which the various theories of geologists gave -rise, proceeding in various ways upon the effects of the existing -causes of change, led men to observe, with some attention and -perseverance, the actual operation of such causes. In this way, the -known effect of the Rhine, in filling up the Lake of Geneva at its -upper extremity, was referred to by De Luc, Kirwan, and others, in -their dispute with the Huttonians; and attempts were even made to -calculate how distant the period was, when this alluvial deposit -first began. Other modern observers have attended to similar facts -in the natural history of rivers and seas. But the subject may be -considered as having first assumed its proper form, when taken up by -Mr. Von Hoff; of whose _History of the Natural Changes of the -Earth's surface which are proved by Tradition_, the first part, -treating of aqueous changes, appeared in 1822. This work was -occasioned by a Prize Question of the Royal Society of Göttingen, -promulgated in 1818; in which these changes were proposed as the -subject of inquiry, with a special reference to geology. Although -Von Hoff does not attempt to establish any general inductions upon -the facts which his book contains, the collection of such a body of -facts gave almost a new aspect to the subject, by showing that -changes in the relative extent of land and water were going on at -every time, and almost at every place; and that mutability and -fluctuation in the form of the solid parts of the earth, which had -been supposed by most persons to be a rare exception to the common -course of events, was, in fact, the universal rule. But it was Mr. -Lyell's _Principles of Geology, being an attempt to explain the -former Changes of the Earth's Surface by the Causes now in action_ -(of which the first volume was published in 1830), which disclosed -the full effect of such researches on geology; and which attempted -to present such assemblages of special facts, as examples of general -laws. Thus this work may, as we have said, be looked upon as the -beginning of Geological Dynamics, at least among us. Such -generalizations and applications as it contains give the most lively -{546} interest to a thousand observations respecting rivers and -floods, mountains and morasses, which otherwise appear without aim -or meaning; and thus this department of science cannot fail to be -constantly augmented by contributions from every side. At the same -time it is clear, that these contributions, voluminous as they must -become, must, from time to time, be resolved into laws of greater -and greater generality; and that thus alone the progress of this, as -of all other sciences, can be furthered. - -I need not attempt any detailed enumeration of the modes of aqueous -action which are here to be considered. Some are destructive, as -when the rivers erode the channels in which they flow; or when the -waves, by their perpetual assault, shatter the shores, and carry the -ruins of them into the abyss of the ocean. Some operations of the -water, on the other hand, add to the land; as when _deltas_ are -formed at the mouths of rivers or when calcareous springs form -deposits of _travertin_. Even when bound in icy fetters, water is by -no mean deprived of its active power; the _glacier_ carries into the -valley masses of its native mountain, and often, becoming ice-bergs, -float with a lading of such materials far into the seas of the -temperate zone. It is indisputable that vast beds of worn down -fragments of the existing land are now forming into strata at the -bottom of the ocean; and that many other effects are constantly -produced by existing aqueous causes, which resemble some, at least, -of the facts which geology has to explain. - -[2nd Ed.] [The effects of glaciers above mentioned are obvious; but -the mechanism of these bodies,--the mechanical cause of their -motions,--was an unsolved problem till within a very few years. That -they slide as rigid masses;--that they advance by the expansion of -their mass;--that they advance as a collection of rigid fragments; -were doctrines which were held by eminent physicists; though a very -slight attention to the subject shows these opinions to be -untenable. In Professor James Forbes's theory on the subject -(published in his _Travels through the Alps_, 1843,) we find a -solution of the problem, so simple, and yet so exact, as to produce -the most entire conviction. In this theory, the ice of a glacier is, -on a great scale, supposed to be a plastic or viscous mass, though -small portions of it are sensibly rigid. It advances down the slope -of the valley in which it lies as a plastic mass would do, -accommodating itself to the varying shape and size of its bed, and -showing by its crevasses its mixed character between fluid and -rigid. It shows this character still more curiously by a _ribboned_ -{547} _structure_ on a small scale, which is common in the solid ice -of the glacier. The planes of these _ribbons_ are, for the most -part, at right angles to the crevasses, near the sides of the -glacier, while, near its central line, they _dip_ towards the upper -part of the glacier. This structure appears to arise from the -difference of velocities of contiguous moving filaments of the icy -mass, as the crevasses themselves arise from the tension of larger -portions. Mr. Forbes has, in successive publications, removed the -objections which have been urged against this theory. In the last of -them, a Memoir in the _Phil. Trans._, 1846, (_Illustrations of the -Viscous Theory of Glacier Motion_,) he very naturally expresses -astonishment at the opposition which has been made to the theory on -the ground of the rigidity of small pieces of ice. He has himself -shown that the ice of glaciers has a plastic flexibility, by marking -forty-five points in a transverse straight line upon the Mer de -Glace, and observing them for several days. The straight line in -that time not only became oblique to the side, but also became -visibly curved. - -Both Mr. Forbes and other philosophers have made it in the highest -degree probable that glaciers have existed in many places in which -they now exist no longer, and have exercised great powers in -transporting large blocks of rock, furrowing and polishing the rocks -along which they slide, and leaving lines and masses of detritus or -_moraine_ which they had carried along with them or pushed before -them. It cannot be doubted that extinct glaciers have produced some -of the effects which the geologist has to endeavor to explain. But -this part of the machinery of nature has been worked by some -theorists into an exaggerated form, in which it cannot, as I -conceive, have any place in an account of Geological Dynamics which -aims at being permanent. - -The great problem of the diffusion of drift and erratic blocks from -their parent rocks to great distances, has driven geologists to the -consideration of other hypothetical machinery by which the effects -may be accounted for: especially the great _northern drift_ and -_boulders_,--the rocks from the Scandinavian chain which cover the -north of Europe on a vast area, having a length of 2000 and breadth -of from 400 to 800 miles. The diffusion of these blocks has been -accounted for by supposing them to be imbedded in icebergs, detached -from the shore, and floated into oceanic spaces, where they have -grounded and been deposited by the melting of the ice. And this mode -of action may to some extent be safely admitted into geological -speculation. For it is a matter of fact, that our navigators in -arctic and antarctic regions have {548} repeatedly seen icebergs and -icefloes sailing along laden with such materials. - -The above explanation of the phenomena of drift supposes the land on -which the travelled materials are found to have been the bottom of a -sea where they were deposited. But it does not, even granting the -conditions, account for some of the facts observed;--that the drift -and the boulders are deposited in "trainées" or streaks, which, in -direction, diverge from the parent rock;--and that the boulders are -of smaller and smaller size, as they are found more remote from that -centre. These phenomena rather suggest the notion of currents of -water as the cause of the distribution of the materials into their -present situations. And though the supposition that the whole area -occupied by drift and boulders was a sea-bottom when they were -scattered over it much reduces the amount of violence which it is -necessary to assume in order to distribute the loose masses, yet -still the work appears to be beyond the possible effect of ordinary -marine currents, or any movements which would be occasioned by a -slow and gradual rising of the centre of distribution. - -It has been suggested that a _sudden_ rise of the centre of -distribution would cause a motion in the surrounding ocean sufficient -to produce such an effect: and in confirmation of this reference has -been made to Mr. Scott Russell's investigations with respect to waves, -already referred to. (Book VIII.) The wave in this case would be the -_wave of translation_, in which the motion of the water is as great at -the bottom as at the top; and it has hence been asserted that by -paroxysmal elevations of 100 or 200 feet, a current of 25 or 30 miles -an hour might be accounted for. But I think it has not been -sufficiently noted that at each point this "current" is transient: it -lasts only while the wave is passing over the point, and therefore it -would only either carry a single mass the whole way with its own -velocity, or move through a short distance a series of masses over -which it successively passed. It does not appear, therefore, that we -have here a complete account of the transport of a collection of -materials, in which each part is transferred through great -distances:--except, indeed, we were to suppose a numerous succession -of paroxysmal elevations. Such a _battery_ might, by successive -shocks, transmitting their force through the water, diffuse the -fragments of the central mass over any area, however wide. - -The fact that the erratic blocks are found to rest on the lower -drift, is well explained by supposing the latter to have been spread -on the {549} sea bottom while rock-bearing ice-masses floated on the -surface till they deposited their lading. - -Sir R. Murchison has pointed out another operation of ice in -producing mounds of rocky masses; namely, the effects of rivers and -lakes, in climates where, as in Russia, the waters carry rocky -fragments entangled in the winter ice, and leave them in heaps at -the highest level which the waters attain. - -The extent to which the effects of glaciers, now vanished, are -apparent in many places, especially in Switzerland and in England, -and other phenomena of the like tendency, have led some of the most -eminent geologists to the conviction that, interior to the period of -our present temperature, there was a _Glacial Period_, at which the -temperature of Europe was lower than it now is.] - -Although the study of the common operations of water may give the -geologist such an acquaintance with the laws of his subject as may -much aid his judgment respecting the extent to which such effects -may proceed, a long course of observation and thought must be -requisite before such operations can be analysed into their -fundamental principles, and become the subjects of calculation, or -of rigorous reasoning in any manner which is as precise and certain -as calculation. Various portions of Hydraulics have an important -bearing upon these subjects, including some researches which have -been pursued with no small labor by engineers and mathematicians; as -the effects of currents and waves, the laws of tides and of rivers, -and many similar problems. In truth, however, such subjects have not -hitherto been treated by mathematicians with much success; and -probably several generations must elapse before this portion of -geological dynamics can become an exact science. - - -_Sect._ 3.--_Igneous Causes of Change.--Motions of the Earth's -Surface._ - -THE effects of volcanoes have long been noted as important and -striking features in the physical history of our globe; and the -probability of their connexion with many geological phenomena, had -not escaped notice at an early period. But it was not till more -recent times, that the full import of these phenomena was -apprehended. The person who first looked at such operations with -that commanding general view which showed their extensive connexion -with physical geology, was Alexander von Humboldt, who explored the -volcanic phenomena {550} of the New World, from 1799 to 1804. He -remarked[64\18] the linear distribution of volcanic domes, -considering them as vents placed along the edge of vast fissures -communicating with reservoirs of igneous matter, and extending -across whole continents. He observed, also, the frequent sympathy of -volcanic and terremotive action in remote districts of the earth's -surface, thus showing how deeply seated must be the cause of these -convulsions. These views strongly excited and influenced the -speculations of geologists; and since then, phenomena of this kind -have been collected into a general view as parts of a -natural-historical science. Von Hoff, in the second volume of the -work already mentioned, was one of the first who did this; "At -least," he himself says,[65\18] (1824,) "it was not known to him -that any one before him had endeavored to combine so large a mass of -facts with the general ideas of the natural philosopher, so as to -form a whole." Other attempts were, however, soon made. In 1825, M. -von Ungern-Sternberg published his book _On the Nature and Origin of -Volcanoes_,[66\18] in which, he says, his object is, to give an -empirical representation of these phenomena. In the same year, Mr. -Poulett Scrope published a work in which he described the known -facts of volcanic action; not, however, confining himself to -description; his purpose being, as his title states, to consider -"the probable causes of their phenomena, the laws which determine -their march, the disposition of their products, and their connexion -with the present state and past history of the globe; leading to the -establishment of a new theory of the earth." And in 1826, Dr. -Daubeny, of Oxford, produced _A Description of Active_ and Extinct -_Volcanoes_, including in the latter phrase the volcanic rocks of -central France, of the Rhine, of northern and central Italy, and -many other countries. Indeed, the near connexion between the -volcanic effects now going on, and those by which the basaltic rocks -of Auvergne and many other places had been produced, was, by this -time, no longer doubted by any; and therefore the line which here -separates the study of existing causes from that of past effects may -seem to melt away. But yet it is manifest that the assumption of an -identity of scale and mechanism between volcanoes now active, and -the igneous catastrophes of which the products have {551} survived -great revolutions on the earth's surface, is hypothetical; and all -which depends on this assumption belongs to theoretical geology. - -[Note 64\18: Humboldt, _Relation Historique_; and his other works.] - -[Note 65\18: Vol. ii. Prop. 5.] - -[Note 66\18: _Werden und Seyn des Vulkanischen Gebirges_. Carlsruhe, -1825.] - -Confining ourselves, then, to volcanic effects, which have been -produced, certainly or probably, since the earth's surface assumed -its present form, we have still an ample exhibition of powerful -causes of change, in the streams of lava and other materials emitted -in eruptions; and still more in the earthquakes which, as men easily -satisfied themselves, are produced by the same causes as the -eruptions of volcanic fire. - -Mr. Lyell's work was important in this as in other portions of this -subject. He extended the conceptions previously entertained of the -effects which such causes may produce, not only by showing how great -these operations are historically known to have been, and how -constantly they are going on, if we take into our survey the whole -surface of the earth; but still more, by urging the consequences -which would follow in a long course of time from the constant -repetition of operations in themselves of no extraordinary amount. A -lava-stream many miles long and wide, and several yards deep, a -subsidence or elevation of a portion of the earth's surface of a few -feet, are by no means extraordinary facts. Let these operations, -said Mr. Lyell, be repeated thousands of times; and we have results -of the same order with the changes which geology discloses. - -The most mitigated earthquakes have, however, a character of -violence. But it has been thought by many philosophers that there is -evidence of a change of level of the land in cases where none of -these violent operations are going on. The most celebrated of these -cases is Sweden; the whole of the land from Gottenburg to the north -of the Gulf of Bothnia has been supposed in the act of rising, -slowly and insensibly, from the surrounding waters. The opinion of -such a change of level has long been the belief of the inhabitants; -and was maintained by Celsius in the beginning of the eighteenth -century. It has since been conceived to be confirmed by various -observations of marks cut on the face of the rock; beds of shells, -such as now live in the neighboring seas, raised to a considerable -height; and other indications. Some of these proofs appear doubtful; -but Mr. Lyell, after examining the facts upon the spot in 1834, -says, "In regard to the proposition that the land, in certain parts -of Sweden, is gradually rising, I have no hesitation in assenting to -it, after my visit to the districts above alluded to."[67\18] If -this conclusion be generally accepted by {552} geologists, we have -here a daily example of the operation of some powerful agent which -belongs to geological dynamics; and which, for the purposes of the -geological theorist, does the work of the earthquake upon a very -large scale, without assuming its terrors. - -[Note 67\18: _Phil. Trans._ 1835, p. 32.] - -[2nd Ed.] [Examples of changes of level of large districts occurring -at periods when the country has been agitated by earthquakes are -well ascertained, as the rising of the coast of Chili in 1822, and -the subsidence of the district of Cutch, in the delta of the Indus, -in 1819. (Lyell, B. II. c. xv.) But the cases of more slow and -tranquil movement seem also to be established. The gradual secular -rise of the shore of the Baltic, mentioned in the text, has been -confirmed by subsequent investigation. It appears that the rate of -elevation increases from Stockholm, where it is only a few inches in -a century, to the North Cape, where it is several feet. It appears -also that several other regions are in a like state of secular -change. The coast of Greenland is sinking. (Lyell, B. II. c. xviii.) -And the existence of "raised beaches" along various coasts is now -generally accepted among geologists. Such beaches, anciently forming -the margin of the sea, but now far above it, exist in many places; -for instance, along a great part of the Scotch coast; and among the -raised beaches of that country we ought probably, with Mr. Darwin, -to include the "parallel roads" of Glenroy, the subject, in former -days, of so much controversy among geologists and antiquaries. - -Connected with the secular rise and fall of large portions of the -earth's surface, another agency which plays an important part in -Geological dynamics has been the subject of some bold yet singularly -persuasive speculations by Mr. Darwin. I speak of the formation of -Coral, and Coral Reefs. He says that the coral-building animal works -only at small and definite distances below the surface. How then are -we to account for the vast number of coral islands, rings, and -reefs, which are scattered over the Pacific and Indian Oceans! Can -we suppose that there are so many mountains, craters, and ridges, -all exactly within a few feet of the same height through this vast -portion of the globe's surface? This is incredible. How then are we -to explain the facts? Mr. Darwin replies, that if we suppose the -land to subside slowly beneath the sea, and at the same time suppose -the coralline zoophytes to go on building, so that their structure -constantly rises nearly to the surface of the water, we shall have -the facts explained. A submerged island will produce a ring; a long -coast, a barrier reef; and so on. Mr. Darwin also notes other -phenomena, as {553} elevated beds of coral, which, occurring in -other places, indicate a recent rising of the land; and on such -grounds as these he divides the surface of those parts of the ocean -into regions of elevation and of depression. - -The labors of coralline zoophytes, as thus observed, form masses of -coral, such as are found fossilized in the strata of the earth. But -our knowledge of the laws of life which have probably affected the -distribution of marine remains in strata, has received other very -striking accessions by the labors of Prof. Edward Forbes in -observing the marine animals of the Ægean Sea. He found that, even -in their living state, the mollusks and zoophytes are already -distributed into strata. Dividing the depth into eight regions, from -2 to 230 fathoms, he found that each region had its peculiar -inhabitants, which disappeared speedily either in ascending or in -descending. The zero of animal life appeared to occur at about 300 -fathoms. This curious result bears in various ways upon geology. Mr. -Forbes himself has given an example of the mode in which it may be -applied, by determining the depth at which the submarine eruption -took place which produced the volcanic isle of Neokaimeni in 1707. -By an examination of the fossils embedded in the pumice, he showed -that it came from the fourth region.[68\18] - -[Note 68\18: _British Assoc. Reports_, 1843, p. 177.] - -To the modes in which organized beings operate in producing the -materials of the earth, we must add those pointed out by the -extraordinary microscopic discoveries of Professor Ehrenberg. It -appears that whole beds of earthy matter consist of the cases of -certain infusoria, the remains of these creatures being accumulated -in numbers which it confounds our thoughts to contemplate.] - -Speculations concerning the _causes_ of volcanoes and earthquakes, -and of the rising and sinking of land, are a highly important -portion of this science, at least as far as the calculation of the -possible results of definite causes is concerned. But the various -hypotheses which have been propounded on this subject can hardly be -considered as sufficiently matured for such calculation. A mass of -matter in a state of igneous fusion, extending to the centre of the -earth, even if we make such an hypothesis, requires some additional -cause to produce eruption. The supposition that this fire may be -produced by intense chemical action between combining elements, -requires further, not only some agency to bring together such -elements, but some reason why {554} they should be originally -separate. And if any other causes have been suggested, as -electricity or magnetism, this has been done so vaguely as to elude -all possibility of rigorous deduction from the hypothesis. The -doctrine of a Central Heat, however, has occupied so considerable a -place in theoretical geology, that it ought undoubtedly to form an -article in geological dynamics. - - -_Sect._ 4.--_The Doctrine of Central Heat._ - -THE early geological theorists who, like Leibnitz and Buffon, -assumed that the earth was originally a mass in a state of igneous -fusion, naturally went on to deduce from this hypothesis, that the -crust consolidated and cooled before the interior, and that there -might still remain a central heat, capable of producing many -important effects. But it is in more recent times that we have -measures of such effects, and calculations which we can compare with -measures. It was found, as we have said, that in descending below -the surface of the earth, the temperature of its materials -increased. Now it followed from Fourier's mathematical -investigations of the distribution of heat in the earth, that if -there be no primitive heat (_chaleur d'origine_), the temperature, -when we descend below the crust, will be constant in each vertical -line. Hence an observed increase of temperature in descending, -appeared to point out a central heat resulting from some cause now -no longer in action. - -The doctrine of a central heat has usually been combined with the -supposition of a central igneous fluidity; for the heat in the -neighborhood of the centre must be very intense, according to any -law of its increase in descending which is consistent with known -principles. But to this central fluidity it has been objected that -such a fluid must be in constant circulation by the cooling of its -exterior. Mr. Daniell found this to be the case in all fused metals. -It has also been objected that there must be, in such a central -fluid, _tides_ produced by the moon and sun; but this inference -would require several additional suppositions and calculations to -give it a precise form. - -Again, the supposition of a central heat of the earth, considered as -the effect of a more ancient state of its mass, appeared to indicate -that its cooling must still be going on. But if this were so, the -earth might contract, as most bodies do when they cool; and this -contraction might lead to mechanical results, as the shortening of -the day. Laplace satisfied himself, by reference to ancient -astronomical records, that no such {555} alteration in the length of -the day had taken place, even to the amount of one two-hundredth of -a second; and thus, there was here no confirmation of the hypothesis -of a primitive heat of the earth. - -Though we find no evidence of the secular contraction of the earth -in the observations with which astronomy deals, there are some -geological facts which at first appear to point to the reality of a -refrigeration within geological periods; as the existence of the -remains of plants and shells of tropical climates, in the strata of -countries which are now near to or within the frigid zones. These -facts, however, have given rise to theories of the changes of -climate, which we must consider separately. - -But we may notice, as connected with the doctrine of central heat, -the manner in which this hypothesis has been applied to explain -volcanic and geological phenomena. It does not enter into my plan, -to consider explanations in which this central heat is supposed to -give rise to an expansive force,[69\18] without any distinct -reference to known physical laws. But we may notice; as more likely -to become useful materials of the science now before us, such -speculations as those of Mr. Babbage; in which he combines the -doctrine of central heat with other physical laws;[70\18] as, that -solid rocks _expand_ by being heated, but that clay contracts; that -different rocks and strata _conduct_ heat differently; that the -earth _radiates_ heat differently, or at different parts of its -surface, according as it is covered with forests, with mountains, -with deserts, or with water. These principles, applied to large -masses, such as those which constitute the crust of the earth, might -give rise to changes as great as any which geology discloses. For -example: when the bed of a sea is covered by a thick deposit of new -matter worn from the shores, the strata below the bed, being -protected by a bad conductor of heat, will be heated, and, being -heated, maybe expanded; or, as Sir J. Herschel has observed, may -produce explosion by the conversion of their moisture into steam. -Such speculations, when founded on real data and sound calculations, -may hereafter be of material use in geology. - -[Note 69\18: Scrope _On Volcanoes_, p. 192.] - -[Note 70\18: _On the Temple of Serapis_, 1834. See also _Journal of -the Royal Inst._ vol. ii., quoted in Conyb. and Ph. p. xv. Lyell, -B. ii. c. xix. p. 383, (4th ed.) on Expansion of Stone.] - -The doctrine of central heat and fluidity has been rejected by some -eminent philosophers. Mr. Lyell's reasons for this rejection belong -{556} rather to Theoretical Geology; but I may here notice M. -**Poisson's opinion. He does not assent to the conclusion of Fourier, -that once the temperature increases in descending, there must be some -primitive central heat. On the contrary, he considers that such an -increase may arise from this;--that the earth, at some former period, -passed (by the motion of the solar system in the universe,) **through -a portion of space which was warmer than the space in which it now -revolves (by reason, it may be, of the heat of other stars to which it -was then nearer). He supposes that, since such a period, the surface -has cooled down by the influence of the surrounding circumstances; -while the interior, for a certain unknown depth, retains the trace of -the former elevation of temperature. But this assumption is not likely -to expel the belief is the terrestrial origin of the subterraneous -heat. For the supposition of such an inequality in the temperature of -the different regions in which the solar system is placed at different -times, is altogether arbitrary; and, if pushed to the amount to which -it must be carried, in order to account for the phenomenon, is highly -improbable.[71\18] The doctrine of central heat, on the other hand, -(which need not be conceived as implying the _universal_ fluidity of -the mass,) is not only naturally suggested by the subterraneous -increase of temperatures, but explains the spheroidal figure of the -earth; and falls in with almost any theory which can be devised, of -volcanoes, earthquakes, and great geological changes. - -[Note 71\18: For this hypothesis would make it necessary to suppose -that the earth has, at some former period, derived from some other -star or stars more heat than she now derives from the sun. But this -would imply, as highly probable, that at some period some other star -or stars must have produced also a _mechanical_ effect upon the -solar system, greater than the effect of the sun. Now such a past -operation of forces, fitted to obliterate all order and symmetry, is -quite inconsistent with the simple, regular, and symmetrical -relation which the whole solar system, as far as Uranus, bears to -the present central body.] - - -_Sect._ 5.--_Problems respecting Elevations and Crystalline Forces._ - -OTHER problems respecting the forces by which great masses of the -earth's crust have been displaced, have also been solved by various -mathematicians. It has been maintained by Von Buch that there occur, -in various places, _craters of elevation_; that is, mountain-masses -resembling the craters of volcanoes, but really produced by an -expansive force from below, bursting an aperture through horizontal -strata, {557} and elevating them in a conical form. Against this -doctrine, as exemplified in the most noted instances, strong -arguments have been adduced by other geologists. Yet the protrusion -of fused rock by subterraneous forces upon a large scale is not -denied: and how far the examples of such operations may, in any -cases, be termed craters of elevation, must be considered as a -question not yet decided. On the supposition of the truth of Von -Buch's doctrine, M. de Beaumont has calculated the relations of -position, the fissures, &c., which would arise. And Mr. -Hopkins,[72\18] of Cambridge, has investigated in a much more -general manner, upon mechanical principles, the laws of the -elevations, fissures, faults, veins, and other phenomena which would -result from an elevatory force, acting simultaneously at every point -beneath extensive portions of the crust of the earth. An application -of mathematical reasoning to the illustration of the phenomena of -veins had before been made in Germany by Schmidt and -Zimmerman.[73\18] The conclusion which Mr. Hopkins has obtained, -respecting the two sets of fissures, at right angles to each other, -which would in general be produced by such forces as he supposes, -may suggest interesting points of examination respecting the -geological phenomena of fissured districts. - -[Note 72\18: _Trans. Camb. Phil. Soc._ vol. vi. 1836.] - -[Note 73\18: _Phil. Mag._ July, 1836, p. 2.] - -[2nd Ed.] [The theory of craters of elevation probably errs rather -by making the elevation of a point into a particular class of -volcanic agency, than by giving volcanic agency too great a power of -elevation. - -A mature consideration of the subject will make us hesitate to -ascribe much value to the labors of those writers who have applied -mathematical reasoning to geological questions. Such reasoning, when -it is carried to the extent which requires symbolical processes, has -always been, I conceive, a source, not of knowledge, but of error, -and confusion; for in such applications the real questions are -slurred over in the hypothetical assumptions of the mathematician, -while the calculation misleads its followers by a false aspect of -demonstration. All symbolical reasonings concerning the fissures of -a semi-rigid mass produced by elevatory or other forces, appear to -me to have turned out valueless. At the same time it cannot be too -strongly borne in mind, that mathematical and mechanical habits of -thought are requisite to all clear thinking on such subjects.] - -Other forces, still more secure in their nature and laws, have -played a very important part in the formation of the earth's crust. -I speak of the forces by which the crystalline, slaty, and jointed -structure of {558} mineral masses has been produced. These forces -are probably identical, on the one hand, with the cohesive forces -from which rocks derive their solidity and their physical -properties; while, on the other hand, they are closely connected -with the forces of chemical attraction. No attempts, of any lucid -and hopeful kind, have yet been made to bring such forces under -definite mechanical conceptions: and perhaps mineralogy, to which -science, as the point of junction of chemistry and crystallography, -such attempts would belong, is hardly yet ripe for such -speculations. But when we look at the universal prevalence of -crystalline forms and cleavages, at the extent of the phenomena of -slaty cleavage, and at the _segregation_ of special minerals into -veins and nodules, which has taken place in some unknown manner, we -cannot doubt that the forces of which we now speak have acted very -widely and energetically. Any elucidation of their nature would be -an important step in Geological Dynamics. - -[2nd Ed.] [A point of Geological Dynamics of great importance is, the -change which rocks undergo in structure after they are deposited, -either by the action of subterraneous heat, or by the influence of -crystalline or other corpuscular forces. By such agencies, sedimentary -rocks may be converted into crystalline, the traces of organic fossils -may be obliterated, a slaty cleavage may be produced, and other like -effects. The possibility of such changes was urged by Dr. Hutton in -his Theory; and Sir James Hall's very instructive and striking -experiments were made for the purpose of illustrating this theory. In -these experiments, powdered chalk was, by the application of heat -under pressure, converted into crystalline calcspar. Afterwards Dr. -McCulloch's labors had an important influence in satisfying geologists -of the reality of corresponding changes in nature. Dr. McCulloch, by -his very lively and copious descriptions of volcanic regions, by his -representations of them, by his classification of igneous rocks, and -his comprehensive views of the phenomena which they exhibit, probably -was the means of converting many geologists from the Wernerian -opinions. - -Rocks which have undergone changes since they were deposited are -termed by Mr. Lyell _metamorphic_. The great extent of metamorphic -rock changed by heat is now uncontested. The internal changes which -are produced by the crystalline forces of mountain masses have been -the subjects of important and comprehensive speculations by -Professor Sedgwick.] {559} - - -_Sect._ 6.--_Theories of Changes of Climate._ - -AS we have already stated, Geology offers to us strong evidence that -the climate of the ancient periods of the earth's history was hotter -than that which now exists in the same countries. This, and other -circumstances, have led geologists to the investigation of the -effects of any hypothetical causes of such changes of condition in -respect of heat. - -The love of the contemplation of geometrical symmetry, as well as -other reasons, suggested the hypothesis that the earth's axis had -originally no obliquity, but was perpendicular to the equator. Such -a construction of the world had been thought of before the time of -Milton,[74\18] as what might be supposed to have existed when man -was expelled from Paradise; and Burnet, in his _Sacred Theory of the -Earth_ (1690), adopted this notion of the paradisiacal condition of -the globe: - The spring - Perpetual smiled on earth with verdant flowers, - Equal in days and nights. - -[Note 74\18: Some said he bade his angels turn askance - The poles of earth twice ten degrees and more - From the sun's axle, &c.--_Paradise Lost_, x. 214.] - -In modern times, too, some persons have been disposed to adopt this -hypothesis, because they have conceived that the present polar -distribution of light is inconsistent with the production of the -fossil plants which are found in those regions,[75\18] even if we -could, in some other way, account for the change of temperature. But -this alteration in the axes of a revolution could not take place -without a subversion of the equilibrium of the surface, such as does -not appear to have occurred; and the change has of late been -generally declared impossible by physical astronomers. - -[Note 75\18: Lyell, i. 155. Lindley, _Fossil Flora_.] - -The effects of other astronomical changes have been calculated by -Sir John Herschel. He has examined, for instance, the thermotical -consequences of the diminution of the eccentricity of the earth's -orbit, which has been going on for ages beyond the records of -history. He finds[76\18] that, on this account, the annual effect of -solar radiation would increase as we go back to remoter periods of -the past; but (probably at least) not in a degree sufficient to -account for the apparent past {560} changes of climate. He finds, -however, that though the effect of this change on the mean -temperature of the year may be small, the effect on the extreme -temperature of the seasons will be much more considerable; "so as to -produce alternately, in the same latitude of either hemisphere, a -perpetual spring, or the extreme vicissitudes of a burning summer -and a rigorous winter."[77\18] - -[Note 76\18: _Geol. Trans._ vol. iii. p. 295.] - -[Note 77\18: _Geol. Trans._ vol. iii. p. 298.] - -Mr. Lyell has traced the consequences of another hypothesis on this -subject, which appears at first sight to promise no very striking -results, but which yet is found, upon examination, to involve -adequate causes of very great changes: I refer to the supposed -various distribution of land and water at different periods of the -earth's history. If the land were all gathered into the neighborhood -of the poles, it would become the seat of constant ice and snow, and -would thus very greatly reduce the temperature of the whole surface -of the globe. If, on the other hand, the polar regions were -principally water, while the tropics were occupied with a belt of -land, there would be no part of the earth's surface on which the -frost could fasten a firm hold, while the torrid zone would act like -a furnace to heat the whole. And, supposing a cycle of terrestrial -changes in which these conditions should succeed each other, the -winter and summer of this "great year" might differ much more than -the elevated temperature which we are led to ascribe to former -periods of the globe, can be judged to have differed from the -present state of things. - -The ingenuity and plausibility of this theory cannot be doubted: and -perhaps its results may hereafter be found not quite out of the -reach of calculation. Some progress has already been made in -calculating the movement of heat into, through, and out of the -earth; but when we add to this the effects of the currents of the -ocean and the atmosphere, the problem, thus involving so many -thermotical and atmological laws, operating under complex -conditions, is undoubtedly one of extreme difficulty. Still, it is -something, in this as in all cases, to have the problem even stated; -and none of the elements of the solution appears to be of such a -nature that we need allow ourselves to yield to despair, respecting -the possibility of dealing with it in a useful manner, as our -knowledge becomes more complete and definite. {561} - - - - -CHAPTER VI. - -PROGRESS OF THE GEOLOGICAL DYNAMICS OF ORGANIZED BEINGS. - - -_Sect._ 1.--_Objects of this Science._ - -PERHAPS in extending the term _Geological Dynamics_ to the causes of -changes in organized beings, I shall be thought to be employing a -forced and inconvenient phraseology. But it will be found that, in -order to treat geology in a truly scientific manner, we must bring -together all the classes of speculations concerning known causes of -change; and the Organic Dynamics of Geology, or of Geography, if the -reader prefers the word, appears not an inappropriate phrase for one -part of this body of researches. - -As has already been said, the species of plants and animals which -are found embedded in the strata of the earth, are not only -different from those which now live in the same regions, but, for -the most part, different from any now existing on the face of the -earth. The remains which we discover imply a past state of things -different from that which now prevails; they imply also that the -whole organic creation has been renewed, and that this renewal has -taken place several times. Such extraordinary general facts have -naturally put in activity very bold speculations. - -But it has already been said, we cannot speculate upon such facts in -the past history of the globe, without taking a large survey of its -present condition. Does the present animal and vegetable population -differ from the past, in the same way in which the products of one -region of the existing earth differ from those of another? Can the -creation and diffusion of the fossil species be explained in the -same manner as the creation and diffusion of the creatures among -which we live? And these questions lead us onwards another step, to -ask,--What _are_ the laws by which the plants and animals of -different parts of the earth differ? What was the manner in which -they were originally diffused?--Thus we have to include, as portions -of our subject, {562} the _Geography of Plants_, and _of Animals_, -and the _History of their change and diffusion_; intending by the -latter subject, of course, _palætiological_ history,--the -examination of the causes of what has occurred, and the inference of -past events, from what we know of causes. - -It is unnecessary for me to give at any length a statement of the -problems which are included in these branches of science, or of the -progress which has been made in them; since Mr. Lyell, in his -_Principles of Geology_, has treated these subjects in a very able -manner, and in the same point of view in which I am thus led to -consider them. I will only briefly refer to some points, availing -myself of his labors and his ideas. - - -_Sect._ 2.--_Geography of Plants and Animals._ - -WITH regard both to plants and animals, it appears,[78\18] that -besides such differences in the products of different regions as we -may naturally suppose to be occasioned by climate and other external -causes; an examination of the whole organic population of the globe -leads us to consider the earth as divided into _provinces_, each -province being occupied by its own group of species, and these -groups not being mixed or interfused among each other to any great -extent. And thus, as the earth is occupied by various nations of -men, each appearing at first sight to be of a different stock, so -each other tribe of living things is scattered over the ground in a -similar manner, and distributed into its separate _nations_ in -distant countries. The places where species are thus peculiarly -found, are, in the case of plants, called their _stations_. Yet each -species in its own region loves and selects some peculiar conditions -of shade or exposure, soil or moisture: its place, defined by the -general description of such conditions, is called its _habitation_. - -[Note 78\18: Lyell, _Principles_, B. iii. c. v.] - -Not only each species thus placed in its own province, has its -position further fixed by its own habits, but more general groups -and assemblages are found to be determined in their situation by -more general conditions. Thus it is the character of the _flora_ of -a collection of islands, scattered through a wide ocean in a -tropical and humid climate, to contain an immense preponderance of -tree-ferns. In the same way, the situation and depth at which -certain genera of shells are found have been tabulated[79\18] by Mr. -Broderip. Such general inferences, if {563} they can be securely -made, are of extreme interest in their bearing on geological -speculations. - -[Note 79\18: Greenough, _Add._ 1835, p. 20.] - -The means by which plants and animals are now diffused from one -place to another, have been well described by Mr. Lyell.[80\18] And -he has considered also, with due attention, the manner in which they -become imbedded in mineral deposits of various kinds.[81\18] He has -thus followed the history of organized bodies, from the germ to the -tomb, and thence to the cabinet of the geologist. - -[Note 80\18: Lyell, B. iii. c. v. vi. vii.] - -[Note 81\18: B. iii. c. xiii. xiv. xv. xvi.] - -But, besides the fortunes of individual plants and animals, there is -another class of questions, of great interest, but of great -difficulty;--the fortunes of each species. In what manner do species -which were not, begin to be? as geology teaches us that they many -times have done; and, as even our own reasonings convince us they must -have done, at least in the case of the species among which we live. - -We here obviously place before us, as a subject of research, the -Creation of Living Things;--a subject shrouded in mystery, and not -to be approached without reverence. But though we may conceive, -that, on this subject, we are not to seek our belief from science -alone, we shall find, it is asserted, within the limits of allowable -and unavoidable speculation, many curious and important problems -which may well employ our physiological skill. For example, we may -ask:--how we are to recognize the species which were originally -created distinct?--whether the population of the earth at one -geological epoch could pass to the form which it has at a succeeding -period, by the agency of natural causes alone?--and if not, what -other account we can give of the succession which we find to have -taken place? - -The most remarkable point in the attempts to answer these and the -like questions, is the controversy between the advocates and the -opponents of the doctrine of the _transmutation of species_. This -question is, even from its mere physiological import, one of great -interest; and the interest is much enhanced by our geological -researches, which again bring the question before us in a striking -form, and on a gigantic scale. We shall, therefore, briefly state -the point at issue. - - -_Sect._ 3.--_Question of the Transmutation of Species._ - -WE see that animals and plants may, by the influence of breeding, -and of external agents operating upon their constitution, be greatly -{564} modified, so as to give rise to varieties and races different -from what before existed. How different, for instance, is one kind -and breed of dog from another! The question, then, is, whether -organized beings can, by the mere working of natural causes, pass -from the type of one species to that of another? whether the wolf -may, by domestication, become the dog? whether the ourang-outang -may, by the power of external circumstances, be brought within the -circle of the human species? And the dilemma in which we are placed -is this;--that if species are not thus interchangeable, we must -suppose the fluctuations of which each species is capable, and which -are apparently indefinite, to be bounded by rigorous limits; -whereas, if we allow such a _transmutation of species_, we abandon -that belief in the adaptation of the structure of every creature to -its destined mode of being, which not only most persons would give -up with repugnance, but which, as we have seen, has constantly and -irresistibly impressed itself on the minds of the best naturalists, -as the true view of the order of the world. - -But the study of Geology opens to us the spectacle of many groups of -species which have, in the course of the earth's history, succeeded -each other at vast intervals of time; one set of animals and plants -disappearing, as it would seem, from the face of our planet, and -others, which did not before exist, becoming the only occupants of -the globe. And the dilemma then presents itself to us anew:--either -we must accept the doctrine of the transmutation of species, and -must suppose that the organized species of one geological epoch were -transmuted into those of another by some long-continued agency of -natural causes; or else, we must believe in many successive acts of -creation and extinction of species, out of the common course of -nature; acts which, therefore, we may properly call miraculous. - -This latter dilemma, however, is a question concerning the facts -which have happened in the history of the world; the deliberation -respecting it belongs to physical geology itself, and not to that -subsidiary science which we are now describing, and which is -concerned only with such causes as we know to be in constant and -orderly action. - -The former question, of the limited or unlimited extent of the -modifications of animals and plants, has received full and careful -consideration from eminent physiologists; and in their opinions we -find, I think, an indisputable preponderance to that decision which -rejects the transmutation of species, and which accepts the former -side of the dilemma; namely, that the changes of which each species -is {565} susceptible, though difficult to define in words, are -limited in fact. It is extremely interesting and satisfactory thus -to receive an answer in which we can confide, to inquiries seemingly -so wide and bold as those which this subject involves. I refer to -Mr. Lyell, Dr. Prichard, Mr. Lawrence, and others, for the history -of the discussion, and for the grounds of the decision; and I shall -quote very briefly the main points and conclusions to which the -inquiry has led.[82\18] - -[Note 82\18: Lyell, B. iii. c. iv.] - -It may be considered, then, as determined by the over-balance of -physiological authority, that there is a capacity in all species to -accommodate themselves, to a certain extent, to a change of external -circumstances; this extent varying greatly according to the species. -There may thus arise changes of appearance or structure, and some of -these changes are transmissible to the offspring: but the mutations -thus superinduced are governed by constant laws, and confined within -certain limits. Indefinite divergence from the original type is not -possible; and the extreme limit of possible variation may usually be -reached in a brief period of time: in short, _species have a real -existence in nature_, and a transmutation from one to another does -not exist. - -Thus, for example, Cuvier remarks, that notwithstanding all the -differences of size, appearance, and habits, which we find in the dogs -of various races and countries, and though we have (in the Egyptian -mummies) skeletons of this animal as it existed three thousand years -ago, the relation of the bones to each other remains essentially the -same; and, with all the varieties of their shape[83\18] and size, -there are characters which resist all the influences both of external -nature, of human intercourse, and of time. - -[Note 83\18: _Ossem. Foss._ Disc. Prél. p. 61.] - - -_Sect._ 4.--_Hypothesis of Progressive Tendencies._ - -WITHIN certain limits, however, as we have said, external -circumstances produce changes in the forms of organized beings. The -causes of change, and the laws and limits of their effects, as they -obtain in the existing state of the organic creation, are in the -highest degree interesting. And, as has been already intimated, the -knowledge thus obtained, has been applied with a view to explain the -origin of the existing population of the world, and the succession -of its past conditions. But those who have attempted such an -explanation, have found it necessary to assume certain additional -laws, in order to enable themselves to {566} deduce, from the tenet -of the transmutability of the species of organized beings, such a -state of things as we see about us, and such a succession of states -as is evidenced by geological researches. And here, again, we are -brought to questions of which we must seek the answers from the most -profound physiologists. Now referring, as before, to those which -appear to be the best authorities, it is found that these additional -positive laws are still more inadmissible than the primary -assumption of indefinite capacity of change. For example, in order -to account, on this hypothesis, for the seeming adaptation of the -endowments of animals to their wants, it is held that the endowments -are the result of the wants; that the swiftness of the antelope, the -claws and teeth of the lion, the trunk of the elephant, the long -neck of the giraffe have been produced by a certain plastic -character in the constitution of animals, operated upon, for a long -course of ages, by the attempts which these animals made to attain -objects which their previous organization did not place within their -reach. In this way, it is maintained that the most striking -attributes of animals, those which apparently imply most clearly the -providing skill of their Creator, have been brought forth by the -long-repeated efforts of the creatures to attain the object of their -desire; thus animals with the highest endowments have been gradually -developed from ancestral forms of the most limited organization; -thus fish, bird, and beast, have grown from _small gelatinous -bodies_, "petits corps gelatineux," possessing some obscure -principle of life, and the capacity of development; and thus man -himself with all his intellectual and moral, as well as physical -privileges, has been derived from some creature of the ape or baboon -tribe, urged by a constant tendency to improve, or at least to alter -his condition. - -As we have said, in order to arrive even hypothetically at this -result, it is necessary to assume besides a mere capacity for -change, other positive and active principles, some of which we may -notice. Thus, we must have as the direct productions of nature on -this hypothesis, certain monads or rough draughts, the primary -_rudiments_ of plants and animals. We must have, in these, a -constant _tendency to progressive improvement_, to the attainment of -higher powers and faculties than they possess; which tendency is -again perpetually modified and controlled by the _force of external -circumstances_. And in order to account for the simultaneous -existence of animals in every stage of this imaginary progress, we -must suppose that nature is compelled to be _constantly_ producing -those elementary beings, from which all animals are successively -developed. {567} - -I need not stay to point out how extremely arbitrary every part of -this scheme is; and how complex its machinery would be, even if it -did account for the facts. It may be sufficient to observe, as -others have done,[84\18] that the capacity of change, and of being -influenced by external circumstances, such as we really find it in -nature, and therefore such as in science we must represent it, is a -tendency, not to improve, but to deteriorate. When species are -modified by external causes, they usually degenerate, and do not -advance. And there is no instance of a species acquiring an entirely -new sense, faculty, or organ, in addition to, or in the place of, -what it had before. - -[Note 84\18: Lyell, B. III. c. iv.] - -Not only, then, is the doctrine of the transmutation of species in -itself disproved by the best physiological reasonings, but the -additional assumptions which are requisite, to enable its advocates -to apply it to the explanation of the geological and other phenomena -of the earth, are altogether gratuitous and fantastical. - -Such is the judgment to which we are led by the examination of the -discussions which have taken place on this subject. Yet in certain -speculations, occasioned by the discovery of the _Sivatherium_, a -new fossil animal from the Sub-Himalaya mountains of India, M. -Geoffroy Saint-Hilaire speaks of the belief in the immutability of -species as a conviction which is fading away from men's minds. He -speaks too of the termination of the age of Cuvier, "la clôture du -siècle de Cuvier," and of the commencement of a better zoological -philosophy.[85\18] But though he expresses himself with great -animation, I do not perceive that he adduces, in support of his -peculiar opinions, any arguments in addition to those which he urged -during the lifetime of Cuvier. And the reader[86\18] may recollect -that the consideration of that controversy led us to very different -anticipations from his, respecting the probable future progress of -physiology. The discovery of the Sivatherium supplies no particle of -proof to the hypothesis, that the existing species of animals are -descended from extinct creatures which are specifically distinct: -and we cannot act more wisely than in listening to the advice of -that eminent naturalist, M. de Blainville.[87\18] "Against this -hypothesis, which, up to the present time, I regard as purely -gratuitous, and likely to turn geologists out of the sound and -excellent road in which they now are, I willingly raise my voice, -with the most absolute conviction of being in the right." {568} - -[Note 85\18: _Compte Rendu de l'Acad. des Sc._ 1837, No. 3, p. 81.] - -[Note 86\18: See B. XVII. c. vii.] - -[Note 87\18: _Compte Rendu_, 1837, No. 5, p. 168.] - -[2nd Ed.] [The hypothesis of the progressive developement of species -has been urged recently, in connexion with the physiological tenet -of Tiedemann and De Serres, noticed in B. XVII. c. vii. sect. -3;--namely, that the embryo of the higher forms of animals passes by -gradations through those forms which are permanent in inferior -animals. Assuming this tenet as exact, it has been maintained that -the higher animals which are found in the more recent strata may -have been produced by an ulterior development of the lower forms in -the embryo state; the circumstances being such as to favor such a -developement. But all the best physiologists agree in declaring that -such an extraordinary developement of the embryo is inconsistent -with physiological possibility. Even if the progression of the -embryo in time have a general correspondence with the order of -animal forms as more or less perfectly organized (which is true in -an extremely incomplete and inexact degree), this correspondence -must be considered, not as any indication of causality, but as one -of those marks of universal analogy and symmetry which are stamped -upon every part of the creation. - -Mr. Lyell[88\18] notices this doctrine of Tiedemann and De Serres; -and observes, that though nature presents us with cases of animal -forms degraded by incomplete developement, she offers none of forms -exalted by extraordinary developement. Mr. Lyell's own hypothesis of -the introduction of new species upon the earth, not having any -physiological basis, hardly belongs to this chapter.] - -[Note 88\18: _Principles_, B. III. c. iv.] - - -_Sect._ 5.--_Question of Creation as related to Science._ - -BUT since we reject the production of new species by means of -external influence, do we then, it may be asked, accept the other -side of the dilemma which we have stated; and admit a series of -creations of species, by some power beyond that which we trace in -the ordinary course of nature? - -To this question, the history and analogy of science, I conceive, -teach us to reply as follows:--All palætiological sciences, all -speculations which attempt to ascend from the present to the remote -past, by the chain of causation, do also, by an inevitable -consequence, urge us to look for the beginning of the state of -things which we thus contemplate; but in none of these cases have -men been able, by the aid of science, to arrive at a beginning which -is homogeneous with the {569} known course of events. The first -origin of language, of civilization, of law and government, cannot -be clearly made out by reasoning and research; just as little, we -may expect, will a knowledge of the origin of the existing and -extinct species of plants and animals, be the result of -physiological and geological investigation. - -But, though philosophers have never yet demonstrated, and perhaps -never will be able to demonstrate, what was that primitive state of -things in the social and material worlds, from which the progressive -state took its first departure; they can still, in all the lines of -research to which we have referred, go very far back;--determine many -of the remote circumstances of the past sequence of events;--ascend to -a point which, from our position at least, seems to be near the -origin;--and exclude many suppositions respecting the origin itself. -Whether, by the light of reason alone, men will ever be able to do -more than this, it is difficult to say. It is, I think, no irrational -opinion, even on grounds of philosophical analogy alone, that in all -those sciences which look back and seek a beginning of things, we may -be unable to arrive at a consistent and definite belief, without -having recourse to other grounds of truth, as well as to historical -research and scientific reasoning. When our thoughts would apprehend -steadily the creation of things, we find that we are obliged to summon -up other ideas than those which regulate the pursuit of scientific -truths;--to call in other powers than those to which we refer natural -events: it cannot, then, be considered as very surprizing, if, in this -part of our inquiry, we are compelled to look for other than the -ordinary evidence of science. - -Geology, forming one of the palætiological class of sciences, which -trace back the history of the earth and its inhabitants on -philosophical grounds, is thus associated with a number of other -kinds of research, which are concerned about language, law, art, and -consequently about the internal faculties of man, his thoughts, his -social habits, his conception of right, his love of beauty. Geology -being thus brought into the atmosphere of moral and mental -speculations, it may be expected that her investigations of the -probable past will share an influence common to them; and that she -will not be allowed to point to an origin of her own, a merely -physical beginning of things; but that, as she approaches towards -such a goal, she will be led to see that it is the origin of many -trains of events, the point of convergence of many lines. It may be, -that instead of being allowed to travel up to this focus of being, -we are only able to estimate its place and nature, and {570} to form -of it such a judgment as this;--that it is not only the source of -mere vegetable and animal life, but also of rational and social -life, language and arts, law and order; in short, of all the -progressive tendencies by which the highest principles of the -intellectual and moral world have been and are developed, as well as -of the succession of organic forms, which we find scattered, dead or -living, over the earth. - -This reflection concerning the natural scientific view of creation, -it will be observed, has not been sought for, from a wish to arrive -at such conclusions; but it has flowed spontaneously from the manner -in which we have had to introduce geology into our classification of -the sciences; and this classification was framed from an unbiassed -consideration of the general analogies and guiding ideas of the -various portions of our knowledge. Such remarks as we have made may -on this account be considered more worthy of attention. - -But such a train of thought must be pursued with caution. Although -it may not be possible to arrive at a right conviction respecting -the origin of the world, without having recourse to other than -physical considerations, and to other than geological evidence: yet -extraneous considerations, and extraneous evidence, respecting the -nature of the beginning of things, must never be allowed to -influence our physics or our geology. Our geological dynamics, like -our astronomical dynamics, may be inadequate to carry us back to an -origin of that state of things, of which it explains the progress: -but this deficiency must be supplied, not by adding supernatural to -natural geological dynamics, but by accepting, in their proper -place, the views supplied by a portion of knowledge of a different -character and order. If we include in our Theology the speculations -to which we have recourse for this purpose, we must exclude from -them our Geology. The two sciences may conspire, not by having any -part in common: but because, though widely diverse in their lines, -both point to a mysterious and invisible origin of the world. - -All that which claims our assent on those higher grounds of which -theology takes cognizance, must claim such assent as is consistent -with those grounds; that is, it must require belief in respect of -all that bears upon the highest relations of our being, those on -which depend our duties and our hopes. Doctrines of this kind may -and must be conveyed and maintained, by means of information -concerning the past history of man, and his social and material, as -well as moral and spiritual fortunes. He who believes that a -Providence has {571} ruled the affairs of mankind, will also believe -that a Providence has governed the material world. But any language -in which the narrative of this government of the material world can -be conveyed, must necessarily be very imperfect and inappropriate; -being expressed in terms of those ideas which have been selected by -men, in order to describe appearances and relations of created -things as they affect one another. In all cases, therefore, where we -have to attempt to interpret such a narrative, we must feel that we -are extremely liable to err; and most of all, when our -interpretation refers to those material objects and operations which -are most foreign to the main purpose of a history of providence. If -we have to consider a communication containing a view of such a -government of the world, imparted to us, as we may suppose, in order -to point out the right direction for our feelings of trust, and -reverence, and hope, towards the Governor of the world, we may -expect that we shall be in no danger of collecting from our -authority erroneous notions with regard to the power, and wisdom, -and goodness of His government; or with respect to our own place, -duties, and prospects, and the history of our race so far as our -duties and prospects are concerned. But that we shall rightly -understand the detail of all events in the history of man, or of the -skies, or of the earth, which are narrated for the purpose of thus -giving a right direction to our minds, is by no means equally -certain; and I do not think it would be too much to say, that an -immunity from perplexity and error, in such matters, is, on general -grounds, very improbable. It cannot then surprise us to find, that -parts of such narrations which seem to refer to occurrences like -those of which astronomers and geologists have attempted to -determine the laws, have given rise to many interpretations, all -inconsistent with one another, and most of them at variance with the -best established principles of astronomy and geology. - -It may be urged, that all truths must be consistent with all other -truths, and that therefore the results of true geology or astronomy -cannot be irreconcileable with the statements of true theology. And -this universal consistency of truth with itself must be assented to; -but it by no means follows that we must be able to obtain a full -insight into the nature and manner of such a consistency. Such an -insight would only be possible if we could obtain a clear view of -that central body of truth, the source of the principles which -appear in the separate lines of speculation. To expect that we -should see clearly how the providential government of the world is -consistent with the unvarying laws {572} by which its motions and -developements are regulated, is to expect to understand thoroughly -the laws of motion, of developement, and of providence; it is to -expect that we may ascend from geology and astronomy to the creative -and legislative centre, from which proceeded earth and stars; and -then descend again into the moral and spiritual world, because its -source and centre are the same as those of the material creation. It -is to say that reason, whether finite or infinite, must be -consistent with itself; and that, therefore, the finite must be able -to comprehend the infinite, to travel from any one province of the -moral and material universe to any other, to trace their bearing, -and to connect their boundaries. - -One of the advantages of the study of the history and nature of -science in which we are now engaged is, that it warns us of the -hopeless and presumptuous character of such attempts to understand -the government of the world by the aid of science, without throwing -any discredit upon the reality of our knowledge;--that while it -shows how solid and certain each science is, so long as it refers -its own facts to its own ideas, it confines each science within its -own limits, and condemns it as empty and helpless, when it -pronounces upon those subjects which are extraneous to it. The error -of persons who should seek a geological narrative in theological -records, would be rather in the search itself than in their -interpretation of what they might find; and in like manner the error -of those who would conclude against a supernatural beginning, or a -providential direction of the world, upon geological or -physiological reasonings, would be, that they had expected those -sciences alone to place the origin or the government of the world in -its proper light. - -Though these observations apply generally to all the palætiological -sciences, they may be permitted here, because they have an especial -bearing upon some of the difficulties which have embarrassed the -progress of geological speculation; and though such difficulties -are, I trust, nearly gone by, it is important for us to see them in -their true bearing. - -From what has been said, it follows that geology and astronomy are, -of themselves, incapable of giving us any distinct and satisfactory -account of the origin of the universe, or of its parts. We need not -wonder, then, at any particular instance of this incapacity; as, for -example, that of which we have been speaking, the impossibility of -accounting by any natural means for the production of all the -successive tribes of plants and animals which have peopled the world -in the {573} various stages of its progress, as geology teaches us. -That they were, like our own animal and vegetable contemporaries, -profoundly adapted to the condition in which they were placed, we -have ample reason to believe; but when we inquire whence they came -into this our world, geology is silent. The mystery of creation is -not within the range of her legitimate territory; she says nothing, -but she points upwards. - - -_Sect._ 6.--_The Hypothesis of the regular Creation and Extinction -of Species._ - -1. _Creation of Species._--We have already seen, how untenable, as a -physiological doctrine, is the principle of the transmutability and -progressive tendency of species; and therefore, when we come to -apply to theoretical geology the principles of the present chapter, -this portion of the subject will easily be disposed of. I hardly -know whether I can state that there is any other principle which has -been applied to the solution of the geological problem, and which, -therefore, as a general truth, ought to be considered here. Mr. -Lyell, indeed, has spoken[89\18] of an hypothesis that "the -successive creation of species may constitute a regular part of the -economy of nature:" but he has nowhere, I think, so described this -process as to make it appear in what department of science we are to -place the hypothesis. Are these new species created by the -production, at long intervals, of an offspring different in species -from the parents? Or are the species so created produced without -parents? Are they gradually evolved from some embryo substance? or -do they suddenly start from the ground, as in the creation of the -poet? - . . . . . . . Perfect forms - Limbed and full-grown: out of the ground up rose - As from his lair, the wild beast where he wons - In forest wild, in thicket, brake, or den; . . . - The grassy clods now calved; now half appeared - The tawny lion, pawing to get free - His hinder parts; then springs as broke from bounds, - And rampant shakes his brinded mane; &c. &c. - _Paradise Lost_, B. vii. - -[Note 89\18: B. III. c. xi. p. 234.] - -Some selection of one of these forms of the hypothesis, rather than -the others, with evidence for the selection, is requisite to entitle -us to {574} place it among the known causes of change which in this -chapter we are considering. The bare conviction that a creation of -species has taken place, whether once or many times, so long as it -is unconnected with our organical sciences, is a tenet of Natural -Theology rather than of Physical Philosophy. - -[2nd Ed.] [Mr. Lyell has explained his theory[90\18] by supposing -man to people a great desert, introducing into it living plants and -animals: and he has traced, in a very interesting manner, the -results of such a hypothesis on the distribution of vegetable and -animal species. But he supposes the agents who do this, before they -import species into particular localities, to study attentively the -climate and other physical conditions of each spot, and to use -various precautions. It is on account of the notion of design thus -introduced that I have, above, described this opinion as rather a -tenet of Natural Theology than of Physical Philosophy. - -[Note 90\18: B. III. c. viii. p. 166.] - -Mr. Edward Forbes has published some highly interesting speculations -on the distribution of existing species of animals and plants. It -appears that the manner in which animal and vegetable forms are now -diffused requires us to assume centres from which the diffusion took -place by no means limited by the present divisions of continents and -islands. The changes of land and water which have thus occurred -since the existing species were placed on the earth must have been -very extensive, and perhaps reach into the glacial period of which I -have spoken above.[91\18] - -[Note 91\18: See, in _Memoirs of the Geological Survey of Great -Britain_, vol. i. p. 336, Professor Forbes's Memoir "On the -Connection between the Distribution of the existing Fauna and Flora -of the British Isles, and the Geological Changes which have affected -their area, especially during the epoch of the Northern Drift."] - -According to Mr. Forbes's views, for which he has offered a great -body of very striking and converging reasons, the present vegetable -and animal population of the British Isles is to be accounted for by -the following series of events. The marine deposits of the -_meiocine_ formation were elevated into a great Atlantic continent, -yet separate from what is now America, and having its western shore -where now the great semi-circular belt of gulf-weed ranges from the -15th to the 45th parallel of latitude. This continent then became -stocked with life, and of its vegetable population, the flora of the -west of Ireland, which has many points in common with the flora of -Spain and the {575} Atlantic islands (the _Asturian_ flora), is the -record. The region between Spain and Ireland, and the rest of this -meiocene continent, was destroyed by some geological movement, but -there were left traces of the connexion which still remain. -Eastwards of the flora just mentioned, there is a flora common to -Devon and Cornwall, to the south-east part of Ireland, the Channel -Isles, and the adjacent provinces of France;--a flora passing to a -southern character; and having its course marked by the remains of a -great rocky barrier, the destruction of which probably took place -anterior to the formation of the narrower part of the channel. -Eastward from this _Devon_ or _Norman_ flora, again, we have the -_Kentish_ flora, which is an extension of the flora of North-western -France, insulated by the breach which formed the straits of Dover. -Then came the _Glacial period_, when the east of England and the -north of Europe were submerged, the northern drift was distributed, -and England was reduced to a chain of islands or ridges, formed by -the mountains of Wales, Cumberland, and Scotland, which were -connected with the land of Scandinavia. This was the period of -glaciers, of the dispersion of boulders, of the grooving and -scratching of rocks as they are now found. The climate being then -much colder than it now is, the flora, even down to the water's -edge, consisted of what are now Alpine plants; and this _Alpine_ -flora is common to Scandinavia and to our mountain-summits. And -these plants kept their places, when, by the elevation of the land, -the whole of the present German Ocean became a continent connecting -Britain with central Europe. For the increased elevation of their -stations counterbalanced the diminished cold of the succeeding -period. Along the dry bed of the German Sea, thus elevated, the -principal part of the existing flora of England, the _Germanic_ -flora, migrated. A large portion of our existing animal population -also came over through the same region; and along with those, came -hyenas, tigers, rhinoceros, aurochs, elk, wolves, beavers, which are -extinct in Britain, and other animals which are extinct altogether, -as the primigenian elephant or mammoth. But then, again, the German -Ocean and the Irish Channel were scooped out; and the climate again -changed. In our islands, so detached, many of the larger beasts -perished, and their bones were covered up in peat-mosses and caves, -where we find them. This distinguished naturalist has further shown -that the population of the sea lends itself to the same view. Mr. -Forbes says that the writings of Mr. Smith, of Jordan-hill, "On the -last Changes in the relative Levels of the Land and Sea in the -British Islands," published in the _Memoirs of the_ {576} _Wernerian -Society for_ 1837-8, must be esteemed the foundation of a critical -investigation of this subject in Britain.] - -2. _Extinction of Species._--With regard to the extinction of -species Mr. Lyell has propounded a doctrine which is deserving of -great attention here. Brocchi, when he had satisfied himself, by -examination of the Sub-Apennines, that about half the species which -had lived at the period of their deposition, had since become -extinct, suggested as a possible cause for this occurrence, that the -vital energies of a species, like that of an individual, might -gradually decay in the progress of time and of generations, till at -last the prolific power might fail, and the species wither away. -Such a property would be conceivable as a physiological fact; for we -see something of the kind in fruit-trees propagated by cuttings: -after some time, the stock appears to wear out, and loses its -peculiar qualities. But we have no sufficient evidence that this is -the case in generations of creatures continued by the reproductive -powers. Mr. Lyell conceives, that, without admitting any inherent -constitutional tendency to deteriorate, the misfortunes to which -plants and animals are exposed by the change of the physical -circumstances of the earth, by the alteration of land and water, and -by the changes of climate, must very frequently occasion the loss of -several species. We have historical evidence of the extinction of -one conspicuous species, the Dodo, a bird of large size and singular -form, which inhabited the Isle of France when that island was first -discovered, and which now no longer exists. Several other species of -animals and plants seem to be in the course of vanishing from the -face of the earth, even under our own observation. And taking into -account the greater changes of the surface of the globe which -geology compels us to assume, we may imagine many or all the -existing species of living things to be extirpated. If, for -instance, that reduction of the climate of the earth which appears, -from geological evidence, to have taken place already, be supposed -to go on much further, the advancing snow and cold of the polar -regions may destroy the greater part of our plants and animals, and -drive the remainder, or those of them which possess the requisite -faculties of migration and accommodation, to seek an asylum near the -equator. And if we suppose the temperature of the earth to be still -further reduced, this zone of now-existing life, having no further -place of refuge, will perish, and the whole earth will be tenanted, -if at all, by a new creation. Other causes might produce the same -effect as a change of climate; and, without supposing such causes to -affect the whole globe, it is easy to {577} imagine circumstances -such as might entirely disturb the equilibrium which the powers of -diffusion of different species have produced;--might give to some -the opportunity of invading and conquering the domain of others; and -in the end, the means of entirely suppressing them, and establishing -themselves in their place. - -That this extirpation of certain species, which, as we have seen, -happens in a few cases under common circumstances, might happen upon -a greater scale, if the range of external changes were to be much -enlarged, cannot be doubted. The extent, therefore, to which natural -causes may account for the extinction of species, will depend upon -the amount of change which we suppose in the physical conditions of -the earth. It must be a task of extreme difficulty to estimate the -effect upon the organic world, even if the physical circumstances -were given. To determine the physical condition to which a given -state of the earth would give rise, I have already noted as another -very difficult problem. Yet these two problems must be solved, in -order to enable us to judge of the sufficiency of any hypothesis of -the extinction of species; and in the mean time, for the mode in -which new species come into the places of those which are -extinguished, we have (as we have seen) no hypothesis which -physiology can, for a moment, sanction. - - -_Sect._ 7.--_The Imbedding of Organic Remains._ - -THERE is still one portion of the Dynamics of Geology, a branch of -great and manifest importance, which I have to notice, but upon -which I need only speak very briefly. The mode in which the spoils -of existing plants and animals are imbedded in the deposits now -forming, is a subject which has naturally attracted the attention of -geologists. During the controversy which took place in Italy -respecting the fossils of the Sub-Apennine hills, Vitaliano -Donati,[92\18] in 1750, undertook an examination of the Adriatic, -and found that deposits containing shells and corals, extremely -resembling the strata of the hills, were there in the act of -formation. But without dwelling on other observations of like kind, -I may state that Mr. Lyell has treated this subject, and all the -topics connected with it, in a very full and satisfactory manner. He -has explained,[93\18] by an excellent collection of illustrative -facts, how deposits of various substance and contents are formed; -how plants and animals become fossil in peat, in blown sand, in -volcanic matter, in {578} alluvial soil, in caves, and in the beds -of lakes and seas. This exposition is of the most instructive -character, as a means of obtaining right conclusions concerning the -causes of geological phenomena. Indeed, in many cases, the -similarity of past effects with operations now going on, is so -complete, that they may be considered as identical; and the -discussion of such cases belongs, at the same time, to Geological -Dynamics and to Physical Geology; just as the problem of the fall of -meteorolites may be considered as belonging alike to mechanics and -to physical astronomy. The growth of modern peat-mosses, for -example, fully explains the formation of the most ancient: objects -are buried in the same manner in the ejections of active and of -extinct volcanoes; within the limits of history, many estuaries have -been filled up; and in the deposits which have occupied these -places, are strata containing shells,[94\18] as in the older -formations. - -[Note 92\18: Lyell, B. I. c. iii. p. 67. (4th ed.)] - -[Note 93\18: B. III. c. xiii. xiv. xv. xvi. xvii.] - -[Note 94\18: Lyell, B. III. c. xvii. p. 286. See also his Address to -the Geological Society in 1837, for an account of the Researches of -Mr. Stokes and of Professor Göppert, on the lapidification of -vegetables.] - - - -{{579}} -PHYSICAL GEOLOGY. - - - - -CHAPTER VII. - -PROGRESS OF PHYSICAL GEOLOGY. - - -_Sect._ 1.--_Object and Distinctions of Physical Geology._ - -BEING, in consequence of the steps which we have attempted to -describe, in possession of two sciences, one of which traces the -laws of action of known causes, and the other describes the -phenomena which the earth's surface presents, we are now prepared to -examine how far the attempts to refer the facts to their causes have -been successful: we are ready to enter upon the consideration of -Theoretical or _Physical_ Geology, as, by analogy with Physical -Astronomy, we may term this branch of speculation. - -The distinction of this from other portions of our knowledge is -sufficiently evident. In former times, Geology was always associated -with Mineralogy, and sometimes confounded with it; but the mistake -of such an arrangement must be clear, from what has been said. -Geology is connected with Mineralogy, only so far as the latter -science classifies a large portion of the objects which Geology -employs as evidence of its statements. To confound the two is the -same error as it would be to treat philosophical history as -identical with the knowledge of medals. Geology procures evidence of -her conclusions wherever she can; from minerals or from seas; from -inorganic or from organic bodies; from the ground or from the skies. -The geologist's business is to learn the past history of the earth; -and he is no more limited to one or a few kinds of documents, as his -sources of information, than is the historian of man, in the -execution of a similar task. - -Physical Geology, of which I now speak, may not be always easily -separable from Descriptive Geology: in fact, they have generally -been combined, for few have been content to describe, without -attempting in some measure to explain. Indeed, if they had done so, -it is {580} probable that their labors would have been far less -zealous, and their expositions far less impressive. We by no means -regret, therefore, the mixture of these two kinds of knowledge, -which has so often occurred; but still, it is our business to -separate them. The works of astronomers before the rise of sound -physical astronomy, were full of theories, but these were -advantageous, not prejudicial, to the progress of the science. - -Geological theories have been abundant and various; but yet our -history of them must be brief. For our object is, as must be borne in -mind, to exhibit these, only so far as they are steps discoverably -tending to the _true_ theory of the earth: and in most of them we do -not trace this character. Or rather, the portions of the labors of -geologists which do merit this praise, belong to the two preceding -divisions of the subject, and have been treated of there. - -The history of Physical Geology, considered as the advance towards a -science as real and stable as those which we have already treated of -(and this is the form in which we ought to trace it), hitherto -consists of few steps. We hardly know whether the progress is begun. -The history of Physical Astronomy almost commences with Newton, and -few persons will venture to assert that the Newton of Geology has -yet appeared. - -Still, some examination of the attempts which have been made is -requisite, in order to explain and justify the view which the -analogy of scientific history leads us to take, of the state of the -subject. Though far from intending to give even a sketch of all past -geological speculations, I must notice some of the forms such -speculations have at different times assumed. - - -_Sect._ 2.--_Of Fanciful Geological Opinions._ - -REAL and permanent geological knowledge, like all other physical -knowledge, can be obtained only by inductions of classification and -law from many clearly seen phenomena. The labor of the most active, -the talent of the most intelligent, are requisite for such a -purpose. But far less than this is sufficient to put in busy -operation the inventive and capricious fancy. A few appearances -hastily seen, and arbitrarily interpreted, are enough to give rise -to a wondrous tale of the past, full of strange events and -supernatural agencies. The mythology and early poetry of nations -afford sufficient evidence of man's love of the wonderful, and of -his inventive powers, in early stages of intellectual development. -The scientific faculty, on the other hand, {581} and especially that -part of it which is requisite for the induction of laws from facts, -emerges slowly and with difficulty from the crowd of adverse -influences, even under the most favorable circumstances. We have -seen that in the ancient world, the Greeks alone showed themselves -to possess this talent; and what they thus attained to, amounted -only to a few sound doctrines in astronomy, and one or two extremely -imperfect truths in mechanics, optics, and music, which their -successors were unable to retain. No other nation, till we come to -the dawn of a better day in modern Europe, made any positive step at -all in sound physical speculation. Empty dreams or useless -exhibitions of ingenuity, formed the whole of their essays at such -knowledge. - -It must, therefore, independently of positive evidence, be -considered as extremely improbable, that any of these nations -should, at an early period, have arrived, by observation and -induction, at wide general truths, such as the philosophers of -modern times have only satisfied themselves of by long and patient -labor and thought. If resemblances should be discovered between the -assertions of ancient writers and the discoveries of modern science, -the probability in all cases, the certainty in most, is that these -are accidental coincidences;--that the ancient opinion is no -anticipation of the modern discovery, but is one guess among many, -not a whit the more valuable because its expression agrees with a -truth. The author of the guess could not intend the truth, because -his mind was not prepared to comprehend it. Those of the ancients -who spoke of the _harmony_ which binds all things together, could -not mean the Newtonian gravitation, because they had never been led -to conceive an attractive force, governed by definite mathematical -laws in its quantity and operation. - -In agreement with these views, we must, I conceive, estimate the -opinions which we find among the ancients, respecting the changes -which the earth's surface has undergone. These opinions, when they -are at all of a general kind, are arbitrary fictions of the fancy, -showing man's love of generality indeed, but indulging it without -that expense of labor and thought which alone can render it -legitimate. - -We might, therefore, pass by all the traditions and speculations of -Oriental, Egyptian, and Greek cosmogony, as extraneous to our -subject. But since these have recently been spoken of, as -conclusions collected, however vaguely, from observed facts,[95\18] -we may make a remark or two upon them. {582} - -[Note 95\18: Lyell, B. i. c. ii. p. 8. (4th ed.)] - -The notion of a series of creations and destructions of worlds, -which appears in the sacred volume of the Hindoos, which formed part -of the traditionary lore of Egypt, and which was afterwards adopted -into the poetry and philosophy of Greece, must be considered as a -mythological, not a physical, doctrine. When this doctrine was dwelt -upon, men's thoughts were directed, not to the terrestrial facts -which it seemed to explain, but to the attributes of the deities -which it illustrated. The conception of a Supreme power, impelling -and guiding the progress of events, which is permanent among all -perpetual change, and regular among all seeming chance, was readily -entertained by contemplative and enthusiastic minds; and when -natural phenomena were referred to this doctrine, it was rather for -the purpose of fastening its impressiveness upon the senses, than in -the way of giving to it authority and support. Hence we perceive -that in the exposition of this doctrine, an attempt was always made -to fill and elevate the mind with the notions of marvellous events, -and of infinite times, in which vast cycles of order recurred. The -"great year," in which all celestial phenomena come round, offered -itself as capable of being calculated; and a similar great year was -readily assumed for terrestrial and human events. Hence there were -to be brought round by great cycles, not only deluges and -conflagrations which were to destroy and renovate the earth, but -also the series of historical occurrences. Not only the sea and land -were to recommence their alternations, but there was to be another -Argo, which should carry warriors on the first sea-foray,[96\18] and -another succession of heroic wars. Looking at the passages of -ancient authors which refer to terrestrial changes in this view, we -shall see that they are addressed almost entirely to the love of the -marvellous and the infinite, and cannot with propriety be taken as -indications of a spirit of physical philosophy. For example, if we -turn to the celebrated passage in Ovid,[97\18] where Pythagoras is -represented as asserting that land becomes sea, and sea land, and -many other changes which geologists have verified, we find that -these observations are associated with many fables, as being matter -of exactly the same kind;--the fountain of Ammon which was cold by -day and warm by night;[98\18]--the waters of Salmacis which -effeminate men;--the Clitorian spring which makes them loathe -wine;--the Simplegades islands which were once moveable;--the -Tritonian lake which covered men's bodies with feathers;--and many -similar marvels. And the general purport of {583} the whole is, to -countenance the doctrine of the metempsychosis, and the Pythagorean -injunction of not eating animal food. It is clear, I think, that -facts so introduced must be considered as having been contemplated -rather in the spirit of poetry than of science. - -[Note 96\18: Virg. _Eclog._ 4.] - -[Note 97\18: _Met._ Lib. xv.] - -[Note 98\18: V. 309, &c.] - -We must estimate in the same manner, the very remarkable passage -brought to light by M. Elie de Beaumont,[99\18] from the Arabian -writer, Kazwiri; in which we have a representation of the same spot -of ground, as being, at successive intervals of five hundred years, -a city, a sea, a desert, and again a city. This invention is -adduced, I conceive, rather to feed the appetite of wonder, than to -fix it upon any reality: as the title of his book, _The Marvels of -Nature_ obviously intimates. - -[Note 99\18: _Ann. des Sc. Nat._ xxv. 380.] - -The speculations of Aristotle, concerning the exchanges of land and -sea which take place in long periods, are not formed in exactly the -same spirit, but they are hardly more substantial; and seem to be -quite as arbitrary, since they are not confirmed by any examples and -proofs. After stating,[100\18] that the same spots of the earth are -not always land and always water, he gives the reason. "The -principle and cause of this is," he says, "that the inner parts of -the earth, like the bodies of plants and animals, have their ages of -vigor and of decline; but in plants and animals all the parts are in -vigor, and all grow old, at once: in the earth different parts -arrive at maturity at different times by the operation of cold and -heat: they grow and decay on account of the sun and the revolution -of the stars, and thus the parts of the earth acquire different -power, so that for a certain time they remain moist, and then become -dry and old: and then other places are revivified, and become -partially watery." We are, I conceive, doing no injustice to such -speculations by classing them among _fanciful_ geological opinions. - -[Note 100\18: _Meteorol._ i. 14.] - -We must also, I conceive, range in the same division another class -of writers of much more modern times;--I mean those who have trained -their geology by interpretations of Scripture. I have already -endeavored to show that such an attempt is a perversion of the -purpose of a divine communication, and cannot lead to any physical -truth. I do not here speak of geological speculations in which the -Mosaic account of the deluge has been referred to; for whatever -errors may have been committed on that subject, it would be as -absurd to disregard the most ancient historical record, in -attempting to trace back the history of the earth, as it would be, -gratuitously to reject any other {584} source of information. But -the interpretations of the account of the creation have gone further -beyond the limits of sound philosophy: and when we look at the -arbitrary and fantastical inventions by which a few phrases of the -writings of Moses have been moulded into complete systems, we cannot -doubt that these interpretations belong to the present Section. - -I shall not attempt to criticize, nor even to enumerate, these -Scriptural Geologies,--_Sacred Theories of the Earth_, as Burnet -termed his. Ray, Woodward, Whiston, and many other persons to whom -science has considerable obligations, were involved, by the -speculative habits of their times, in these essays; and they have -been resumed by persons of considerable talent and some knowledge, -on various occasions up to the present day; but the more geology has -been studied on its own proper evidence, the more have geologists -seen the unprofitable character of such labors. - -I proceed now to the next step in the progress of Theoretical -Geology. - - -_Sect._ 3.--_Of Premature Geological Theories._ - -WHILE we were giving our account of Descriptive Geology, the -attentive reader would perceive that we did, in fact, state several -steps in the advance towards general knowledge; but when, in those -cases, the theoretical aspect of such discoveries softened into an -appearance of mere classification, the occurrence was assigned to -the history of Descriptive rather than of Theoretical Geology. Of -such a kind was the establishment, by a long and vehement -controversy, of the fact, that the impressions in rocks are really -the traces of ancient living things; such, again, were the division -of rocks into Primitive, Secondary, Tertiary; the ascertainment of -the orderly succession of organic remains: the consequent fixation -of a standard series of formations and strata; the establishment of -the igneous nature of trap rocks; and the like. These are geological -truths which are assumed and implied in the very language which -geology uses; thus showing how in this, as in all other sciences, -the succeeding steps involve the preceding. But in the history of -geological theory, we have to consider the wider attempts to combine -the facts, and to assign them to their causes. - -The close of the last century produced two antagonist theories of -this kind, which long maintained a fierce and doubtful -struggle;--that of Werner and that of Hutton: the one termed -_Neptunian_, from its {585} ascribing the phenomena of the earth's -surface mainly to aqueous agency; the other _Plutonian_ or -_Vulcanian_, because it employed the force of subterraneous fire as -its principal machinery. The circumstance which is most worthy of -notice in these remarkable essays is, the endeavor to give, by means -of such materials as the authors possessed, a complete and simple -account of all the facts of the earth's history. The Saxon -professor, proceeding on the examination of a small district in -Germany, maintained the existence of a chaotic fluid, from which a -series of universal formations had been precipitated, the position -of the strata being broken up by the falling in of subterraneous -cavities, in the intervals between these depositions. The Scotch -philosopher, who had observed in England and Scotland, thought -himself justified in declaring that the existing causes were -sufficient to spread new strata on the bottom of the ocean, and that -they are consolidated, elevated, and fractured by volcanic heat, so -as to give rise to new continents. - -It will hardly be now denied that all that is to remain as permanent -science in each of these systems must be proved by the examination -of many cases and limited by many conditions and circumstances. -Theories so wide and simple, were consistent only with a -comparatively scanty collection of facts, and belong to the early -stage of geological knowledge. In the progress of the science, the -"theory" of each part of the earth must come out of the examination -of that part, combined with all that is well established, concerning -all the rest; and a general theory must result from the comparison -of all such partial theoretical views. Any attempt to snatch it -before its time must fail; and therefore we may venture at present -to designate general theories, like those of Hutton and Werner, as -_premature_. - -This, indeed, is the sentiment of most of the good geologists of the -present day. The time for such general systems, and for the fierce -wars to which the opposition of such generalities gives rise, is -probably now past for ever; and geology will not again witness such -a controversy as that of the Wernerian and Huttonian schools. - . . . . . . As when two black clouds - With heaven's artillery fraught, come rattling on - Over the Caspian: then stand front to front, - Hovering a space, till winds the signal blow - To join their dark encounter in mid-air. - So frowned the mighty combatants, that hell - Grew darker at their frown; so matched they stood: - For never but once more was either like - To meet so great a foe. {586} - -The main points really affecting the progress of sound theoretical -geology, will find a place in one of the two next Sections. - -[2nd Ed.] [I think I do no injustice to Dr. Hutton in describing his -theory of the earth as _premature_. Prof. Playfair's elegant work, -_Illustrations of the Huttonian Theory_ (1802,) so justly admired, -contains many doctrines which the more mature geology of modern -times rejects; such as the igneous origin of chalk-flints, siliceous -pudding stone, and the like; the universal formation of river-beds -by the rivers themselves; and other points. With regard to this -last-mentioned question, I think all who have read Deluc's -_Geologie_ (1810) will deem his refutation of Playfair complete. - -But though Hutton's theory was premature, as well as Werner's, the -former had a far greater value as an important step on the road to -truth. Many of its boldest hypotheses and generalizations have -become a part of the general creed of geologists; and its -publication is perhaps the greatest event which has yet occurred in -the progress of Physical Geology.] - - - - -CHAPTER VIII. - -THE TWO ANTAGONIST DOCTRINES OF GEOLOGY. - - -_Sect._ 1.--_Of the Doctrine of Geological Catastrophes._ - -THAT great changes, of a kind and intensity quite different from the -common course of events, and which may therefore properly be called -_catastrophes_, have taken place upon the earth's surface, was an -opinion which appeared to be forced upon men by obvious facts. -Rejecting, as a mere play of fancy, the notions of the destruction -of the earth by cataclysms or conflagrations, of which we have -already spoken, we find that the first really scientific examination -of the materials of the earth, that of the Sub-Apennine hills, led -men to draw this inference. Leonardo da Vinci, whom we have already -noticed for his early and strenuous assertion of the real marine -origin of fossil impressions of shells, also maintained that the -bottom of the sea had become the top of the mountain; yet his mode -of explaining this may perhaps be claimed by the modern advocates of -uniform causes as more allied to their {587} opinion, than to the -doctrine of catastrophes.[101\18] But Steno, in 1669, approached -nearer to this doctrine; for he asserted that Tuscany must have -changed its face at intervals, so as to acquire six different -configurations, by the successive breaking down of the older strata -into inclined positions, and the horizontal deposit of new ones upon -them. Strabo, indeed, at an earlier period had recourse to -earthquakes, to explain the occurrence of shells in mountains; and -Hooke published the same opinion later. But the Italian geologists -prosecuted their researches under the advantage of having, close at -hand, large collections of conspicuous and consistent phenomena. -Lazzaro Moro, in 1740, attempted to apply the theory of earthquakes -to the Italian strata; but both he and his expositor, Cirillo -Generelli, inclined rather to reduce the violence of these -operations within the ordinary course of nature,[102\18] and thus -leant to the doctrine of uniformity, of which we have afterwards to -speak. Moro was encouraged in this line of speculation by the -extraordinary occurrence, as it was deemed by most persons, of the -rise of a new volcanic island from a deep part of the Mediterranean, -near Santorino, in 1707.[103\18] But in other countries, as the -geological facts were studied, the doctrine of catastrophes appeared -to gain ground. Thus in England, where, through a large part of the -country, the coal-measures are extremely inclined and contorted, and -covered over by more horizontal fragmentary beds, the opinion that -some violent catastrophe had occurred to dislocate them, before the -superincumbent strata were deposited, was strongly held. It was -conceived that a period of violent and destructive action must have -succeeded to one of repose; and that, for a time, some unusual and -paroxysmal forces must have been employed in elevating and breaking -the pre-existing strata, and wearing their fragments into smooth -pebbles, before nature subsided into a new age of tranquillity and -vitality. In like manner Cuvier, from the alternations of -fresh-water and salt-water species in the strata of Paris, collected -the opinion of a series of great revolutions, in which "the thread -of induction was broken." Deluc and others, to whom we owe the first -steps in geological dynamics, attempted carefully to distinguish -between causes now in action, and those which have ceased to act; in -which latter class they reckoned the causes which have {588} -elevated the existing continents. This distinction was assented to -by many succeeding geologists. The forces which have raised into the -clouds the vast chains of the Pyrenees, the Alps, the Andes, must -have been, it was deemed, something very different from any agencies -now operating. - -[Note 101\18: "Here is a part of the earth which has become more -light, and which rises, while the opposite part approaches nearer to -the centre, and what was the bottom of the sea is become the top of -the mountain."--Venturi's _Léonardo da Vinci_.] - -[Note 102\18: Lyell, i. 3. p. 64. (4th ed.)] - -[Note 103\18: Ib. p. 60.] - -This opinion was further confirmed by the appearance of a complete -change in the forms of animal and vegetable life, in passing from -one formation to another. The species of which the remains occurred, -were entirely different, it was said, in two successive epochs: a -new creation appears to have intervened; and it was readily believed -that a transition, so entirely out of the common course of the -world, might be accompanied by paroxysms of mechanical energy. Such -views prevail extensively among geologists up to the present time: -for instance, in the comprehensive theoretical generalizations of -Elie de Beaumont and others, respecting mountain-chains, it is -supposed that, at certain vast intervals, systems of mountains, -which may be recognized by the parallelism of course of their -inclined beds, have been disturbed and elevated, lifting up with -them the aqueous strata which had been deposited among them in the -intervening periods of tranquillity, and which are recognized and -identified by means of their organic remains: and according to the -adherents of this hypothesis, these sudden elevations of -mountain-chains have been followed, again and again, by mighty -waves, desolating whole regions of the earth. - -The peculiar bearing of such opinions upon the progress of physical -geology will be better understood by attending to the _doctrine of -uniformity_, which is opposed to them, and with the consideration of -which we shall close our survey of this science, the last branch of -our present task. - - -_Sect._ 2.--_Of the Doctrine of Geological Uniformity._ - -THE opinion that the history of the earth had involved a serious of -catastrophes, confirmed by the two great classes of facts, the -symptoms of mechanical violence on a very large scale, and of -complete changes in the living things by which the earth had been -tenanted, took strong hold of the geologists of England, France, and -Germany. Hutton, though he denied that there was evidence of a -beginning of the present state of things, and referred many -processes in the formation of strata to existing causes, did not -assert that the elevatory forces which raise continents from the -bottom of the ocean, were of the same order, {589} as well as of the -same kind, with the volcanoes and earthquakes which now shake the -surface. His doctrine of uniformity was founded rather on the -supposed analogy of other lines of speculation, than on the -examination of the amount of changes now going on. "The Author of -nature," it was said, "has not permitted in His works any symptom of -infancy or of old age, or any sign by which we may estimate either -their future or their past duration:" and the example of the -planetary system was referred to in illustration of this.[104\18] -And a general persuasion that the champions of this theory were not -disposed to accept the usual opinions on the subject of creation, -was allowed, perhaps very unjustly, to weigh strongly against them -in the public opinion. - -[Note 104\18: Lyell, i. 4, p. 94.] - -While the rest of Europe had a decided bias towards the doctrine of -geological catastrophes, the phenomena of Italy, which, as we have -seen, had already tended to soften the rigor of that doctrine, in the -progress of speculation from Steno to Generelli, were destined to -mitigate it still more, by converting to the belief of uniformity -transalpine geologists who had been bred up in the catastrophist -creed. This effect was, indeed, gradual. For a time the distinction of -the _recent_ and the _tertiary_ period was held to be marked and -strong. Brocchi asserted that a large portion of the Sub-Apennine -fossil shells belonged to a living species of the Mediterranean Sea: -but the geologists of the rest of Europe turned an incredulous ear to -this Italian tenet; and the persuasion of the distinction of the -tertiary and the recent period was deeply impressed on most geologists -by the memorable labors of Cuvier and Brongniart on the Paris basin. -Still, as other tertiary deposits were examined, it was found that -they could by no means be considered as contemporaneous, but that they -formed a chain of posts, advancing nearer and nearer to the recent -period. Above the strata of the basins of London and Paris,[105\18] -lie the newer strata of Touraine, of Bourdeaux, of the valley of the -Bormida and the Superga near Turin, and of the basin of Vienna, -explored by M. Constant Prevost. Newer and higher still than these, -are found the Sub-Apennine formations of Northern Italy, and probably -of the same period, the English "crag" of Norfolk and Suffolk. And -most of these marine formations are associated with volcanic products -and fresh-water deposits, so as to imply apparently a long train of -alternations of corresponding processes. It may easily be supposed -that, when the subject had assumed this form, the boundary of the -present and past condition of the earth {590} was in some measure -obscured. But it was not long before a very able attempt was made to -obliterate it altogether. In 1828, Mr. Lyell set out on a geological -tour through France and Italy.[106\18] He had already conceived the -idea of classing the tertiary groups by reference to the number of -recent species which were found in a fossil state. But as he passed -from the north to the south of Italy, he found, by communication with -the best fossil conchologists, Borelli at Turin, Guidotti at Parma, -Costa at Naples, that the number of extinct species decreased; so that -the last-mentioned naturalist, from an examination of the fossil -shells of Otranto and Calabria, and of the neighboring seas, was of -opinion that few of the tertiary shells were of extinct species. To -complete the series of proof, Mr. Lyell himself explored the strata of -Ischia, and found, 2000 feet above the level of the sea, shells, which -were all pronounced to be of species now inhabiting the Mediterranean; -and soon after, he made collections of a similar description on the -flanks of Etna, in the Val di Noto, and in other places. - -[Note 105\18: Lyell, 1st ed. vol. iii. p. 61.] - -[Note 106\18: 1st ed. vol. iii. Pref.] - -The impression produced by these researches is described by -himself.[107\18] "In the course of my tour I had been frequently led -to reflect on the precept of Descartes, that a philosopher should -once in his life doubt everything he had been taught; but I still -retained so much faith in my early geological creed as to feel the -most lively surprize on visiting Sortino, Pentalica, Syracuse, and -other parts of the Val di Noto, at beholding a limestone of enormous -thickness, filled with recent shells, or sometimes with mere casts -of shells, resting on marl in which shells of Mediterranean species -were imbedded in a high state of preservation. All idea of -[necessarily] attaching a high antiquity to a regularly-stratified -limestone, in which the casts and impressions of shells alone were -visible, vanished at once from my mind. At the same time, I was -struck with the identity of the associated igneous rocks of the Val -di Noto with well-known varieties of 'trap' in Scotland and other -parts of Europe; varieties which I had also seen entering largely -into the structure of Etna. - -[Note 107\18: Lyell, 1st ed. Pref. x.] - -"I occasionally amused myself," Mr. Lyell adds, "with speculating on -the different rate of progress which geology might have made, had it -been first cultivated with success at Catania, where the phenomena -above alluded to, and the great elevation of the modern tertiary beds -in the Val di Noto, and the changes produced in the historical era by -the Calabrian earthquakes, would have been familiarly known." {591} - -Before Mr. Lyell entered upon his journey, he had put into the hands -of the printer the first volume of his "Principles of Geology, being -an attempt to explain the former Changes of the Earth's Surface _by -reference to the Causes now in Operation_." And after viewing such -phenomena as we have spoken of, he, no doubt, judged that the -doctrine of catastrophes of a kind entirely different from the -existing course of events, would never have been generally received, -if geologists had at first formed their opinions upon the Sicilian -strata. The boundary separating the present from the anterior state -of things crumbled away; the difference of fossil and recent species -had disappeared, and, at the same time, the changes of position -which marine strata had undergone, although not inferior to those of -earlier geological periods, might be ascribed, it was thought, to -the same kind of earthquakes as those which still agitate that -region. Both the supposed proofs of catastrophic transition, the -organical and the mechanical changes, failed at the same time; the -one by the removal of the fact, the other by the exhibition of the -cause. The powers of earthquakes, even such as they now exist, were, -it was supposed, if allowed to operate for an illimitable time, -adequate to produce all the mechanical effects which the strata of -all ages display. And it was declared that all evidence of a -beginning of the present state of the earth, or of any material -alteration in the energy of the forces by which it has been modified -at various epochs, was entirely wanting. - -Other circumstances in the progress of geology tended the same way. -Thus, in cases where there had appeared in one country a sudden and -violent transition from one stratum to the next, it was found, that -by tracing the formations into other countries, the chasm between -them was filled up by intermediate strata; so that the passage -became as gradual and gentle as any other step in the series. For -example, though the conglomerates, which in some parts of England -overlie the coal-measures, appear to have been produced by a -complete discontinuity in the series of changes; yet in the -coal-fields of Yorkshire, Durham, and Cumberland, the transition is -smoothed down in such a way that the two formations pass into each -other. A similar passage is observed in Central-Germany, and in -Thuringia is so complete, that the coal-measures have sometimes been -considered as subordinate to the _todtliegendes_.[108\18] - -[Note 108\18: De la Beche, p. 414, _Manual_.] - -Upon such evidence and such arguments, the doctrine of {592} -catastrophes was rejected with some contempt and ridicule; and it -was maintained, that the operation of the causes of geological -change may properly and philosophically be held to have been uniform -through all ages and periods. On this opinion, and the grounds on -which it he been urged, we shall make a few concluding remarks. - -It must be granted at once, to the advocates of this geological -uniformity, that we are not arbitrarily to assume the existence of -catastrophes. The degree of uniformity and continuity with which -terremotive forces have acted, must be collected, not from any -gratuitous hypothesis, but from the facts of the case. We must -suppose the causes which have produced geological phenomena, to have -been as similar to existing causes, and as dissimilar, as the -effects teach us. We are to avoid all bias in favor of powers -deviating in kind and degree from those which act at present; a bias -which, Mr. Lyell asserts, has extensively prevailed among -geologists. - -But when Mr. Lyell goes further, and considers it a merit in a -course of geological speculation that it _rejects_ any difference -between the intensity of existing and of past causes, we conceive -that he errs no less than those whom he censures. "An _earnest and -patient endeavor to reconcile_ the former indication of -change,"[109\18] with _any_ restricted class of causes,--a habit -which he enjoins,--is not, we may suggest, the temper in which -science ought to be pursued. The effects must themselves teach us -the nature and intensity of the causes which have operated; and we -are in danger of error, if we seek for slow and shun violent -agencies further than the facts naturally direct us, no less than if -we were parsimonious of time and prodigal of violence. _Time_, -inexhaustible and ever accumulating his efficacy, can undoubtedly do -much for the theorist in geology; but _Force_, whose limits we -cannot measure, and whose nature we cannot fathom, is also a power -never to be slighted: and to call in the one to protect us from the -other, is equally presumptuous, to whichever of the two our -superstition leans. To invoke Time, with ten thousand earthquakes, -to overturn and set on edge a mountain-chain, should the phenomena -indicate the change to have been sudden and not successive, would be -ill excused by pleading the obligation of first appealing to known -causes.[110\18] {593} - -[Note 109\18: Lyell, B. iv. c. i. p. 328, 4th ed.] - -[Note 110\18: [2nd Ed.] [I have, in the text, quoted the fourth -edition of Mr. Lyell's _Principles_, in which he recommends "an -earnest and patient endeavor to reconcile the former indications of -change with the evidence of gradual mutation now in progress." In -the sixth edition, in that which is, I presume, the corresponding -passage, although it is transferred from the fourth to the first -Book (B. i. c. xiii. p. 325) he recommends, instead, "an earnest and -patient inquiry how far geological appearances are reconcileable -with the effect of changes now in progress." But while Mr. Lyell has -thus softened the advocate's character in his language in this -passage, the transposition which I have noticed appears to me to -have an opposite tendency. For in the former edition, the causes now -in action were first described in the second and third Books, and -the great problem of Geology, stated in the first Book, was -attempted to be solved in the fourth. But by incorporating this -fourth Book with the first, and thus prefixing to the study of -existing causes arguments against the belief of their geological -insufficiency, there is an appearance as if the author wished his -reader to be prepared by a previous pleading against the doctrine of -catastrophes, before he went to the study of existing causes. The -Doctrines of Catastrophes and of Uniformity, and the other leading -questions of the Palætiological Sciences, are further discussed in -the _Philosophy of the Inductive Sciences_, Book x.]] - -In truth, we know causes only by their effects; and in order to -learn the nature of the causes which modify the earth, we must study -them through all ages of their action, and not select arbitrarily -the period in which we live as the standard for all other epochs. -The forces which have produced the Alps and Andes are known to us by -experience, no less than the forces which have raised Etna to its -present height; for we learn their amount in both cases by their -results. Why, then, do we make a merit of using the latter case as a -measure for the former? Or how can we know the true scale of such -force, except by comprehending in our view all the facts which we -can bring together? - -In reality when we speak of the _uniformity_ of nature, are we not -obliged to use the term in a very large sense, in order to make the -doctrine at all tenable? It includes catastrophes and convulsions of -a very extensive and intense kind; what is the limit to the violence -which we must allow to these changes? In order to enable ourselves -to represent geological causes as operating with uniform energy -through all time, we must measure our time by long cycles, in which -repose and violence alternate; how long may we extend this cycle of -change, the repetition of which we express by the word _uniformity_? - -And why must we suppose that all our experience, geological as well -as historical, includes more than _one_ such cycle? Why must we -insist upon it, that man has been long enough an observer to obtain -the _average_ of forces which are changing through immeasurable -time? {594} - -The analogy of other sciences has been referred to, as sanctioning -this attempt to refer the whole train of facts to known causes. To -have done this, it has been said, is the glory of Astronomy: she -seeks no hidden virtues, but explains all by the force of -gravitation, which we witness operating at every moment. But let us -ask, whether it would really have been a merit in the founders of -Physical Astronomy, to assume that the celestial revolutions -resulted from any selected class of known causes? When Newton first -attempted to explain the motions of the moon by the force of -gravity, and failed because the measures to which he referred were -erroneous, would it have been philosophical in him, to insist that -the difference which he found ought to be overlooked, since -otherwise we should be compelled to go to causes other than those -which we usually witness in action? Or was there any praise due to -those who assumed the celestial forces to be the same with gravity, -rather than to those who assimilated them with any other known -force, as magnetism, till the calculation of the laws and amount of -these forces, from the celestial phenomena, had clearly sanctioned -such an identification? We are not to select a conclusion now well -proved, to persuade ourselves that it would have been wise to assume -it anterior to proof, and to attempt to philosophize in the method -thus recommended. - -Again, the analogy of Astronomy has been referred to, as confirming -the assumption of perpetual uniformity. The analysis of the heavenly -motions, it has been said, supplies no trace of a beginning, no -promise of an end. But here, also, this analogy is erroneously -applied. Astronomy, as the science of cyclical motions, has nothing -in common with Geology. But look at Astronomy where she has an -analogy with Geology; consider our knowledge of the heavens as a -palætiological science;--as the study of a past condition, from -which the present is derived by causes acting in time. Is there then -no evidence of a beginning, or of a progress? What is the import of -the Nebular Hypothesis? A luminous matter is condensing, solid -bodies are forming, are arranging themselves into systems of -cyclical motion; in short, we have exactly what we are told, on this -analogy, we ought not to have;--the beginning of a world. I will -not, to justify this argument, maintain the truth of the nebular -hypothesis; but if geologists wish to borrow maxims of -philosophizing from astronomy, such speculations as have led to that -hypothesis must be their model. - -Or, let them look at any of the other provinces of palætiological -speculation; at the history of states, of civilization, of -languages. We {595} may assume some _resemblance_ or connexion -between the principles which determined the progress of government, -or of society, or of literature, in the earliest ages, and those -which now operate; but who has speculated successfully, assuming an -_identity_ of such causes? Where do we now find a language in the -process of formation, unfolding itself in inflexions, terminations, -changes of vowels by grammatical relations, such as characterize the -oldest known languages? Where do we see a nation, by its natural -faculties, inventing writing, or the arts of life, as we find them -in the most ancient civilized nations? We may assume hypothetically, -that man's faculties develop themselves in these ways; but we see no -such effects produced by these faculties, in our own time, and now -in progress, without the influence of foreigners. - -Is it not clear, in all these cases, that history does not exhibit a -series of cycles, the aggregate of which may be represented as a -uniform state, without indication of origin or termination? Does it -not rather seem evident that, in reality, the whole course of the -world, from the earliest to the present times, is but one cycle, yet -unfinished;--offering, indeed, no clear evidence of the mode of its -beginning; but still less entitling us to consider it as a -repetition or series of repetitions of what had gone before? - -Thus we find, in the analogy of the sciences, no confirmation of the -doctrine of uniformity, as it has been maintained in Geology. Yet we -discern, in this analogy, no ground for resigning our hope, that -future researches, both in Geology and in other palætiological -sciences, may throw much additional light on the question of the -uniform or catastrophic progress of things, and on the earliest -history of the earth and of man. But when we see how wide and -complex is the range of speculation to which our analogy has -referred us, we may well be disposed to pause in our review of -science;--to survey from our present position the ground that we -have passed over;--and thus to collect, so far as we may, guidance -and encouragement to enable us to advance in the track which lies -before us. - -Before we quit the subject now under consideration, we may, however, -observe, that what the analogy of science really teaches us, as the -most promising means of promoting this science, is the strenuous -cultivation of the two subordinate sciences, Geological Knowledge of -Facts, and Geological Dynamics. These are the two provinces of -knowledge--corresponding to Phenomenal Astronomy, and Mathematical -Mechanics--which may lead on to the epoch of the Newton of {596} -geology. We may, indeed, readily believe that we have much to do in -both these departments. While so large a portion of the globe is -geologically unexplored;--while all the general views which are to -extend our classifications satisfactorily from one hemisphere to -another, from one zone to another, are still unformed; while the -organic fossils of the tropics are almost unknown, and their general -relation to the existing state of things has not even been -conjectured;--how can we expect to speculate rightly and securely, -respecting the history of the whole of our globe? And if Geological -Classification and Description are thus imperfect, the knowledge of -Geological Causes is still more so. As we have seen, the necessity -and the method of constructing a science of such causes, are only -just beginning to be perceived. Here, then, is the point where the -labors of geologists may be usefully applied; and not in premature -attempts to decide the widest and abstrusest questions which the -human mind can propose to itself. - -It has been stated,[111\18] that when the Geological Society of -London was formed, their professed object was to multiply and record -observations, and patiently to await the result at some future time; -and their favorite maxim was, it is added, that the time was not yet -come for a General System of Geology. This was a wise and -philosophical temper, and a due appreciation of their position. And -even now, their task is not yet finished; their mission is not yet -accomplished. They have still much to do, in the way of collecting -Facts; and in entering upon the exact estimation of Causes, they -have only just thrown open the door of a vast Labyrinth, which it -may employ many generations to traverse, but which they must needs -explore, before they can penetrate to the Oracular Chamber of Truth. - -[Note 111\18: Lyell, B. i. c. iv. p. 103.] - -I REJOICE, on many accounts, to find myself arriving at the -termination of the task which I have attempted. One reason why I am -glad to close my history is, that in it I have been compelled, -especially in the latter part of my labors, to speak as a judge -respecting eminent philosophers whom I reverence as my Teachers in -those very sciences on which I have had to pronounce a -judgment;--if, indeed, even the appellation of Pupil be not too -presumptuous. But I doubt not that such men are as full of candor -and tolerance, as they are of knowledge and thought. And if they -deem, as I did, that such a history of {597} science ought to be -attempted, they will know that it was not only the historian's -privilege, but his duty, to estimate the import and amount of the -advances which he had to narrate; and if they judge, as I trust they -will, that the attempt has been made with full integrity of -intention and no want of labor, they will look upon the inevitable -imperfections of the execution of my work with indulgence and hope. - -There is another source of satisfaction in arriving at this point of -my labors. If, after our long wandering through the region of -physical science, we were left with minds unsatisfied and unraised, -to ask, "Whether this be all?"--our employment might well be deemed -weary and idle. If it appeared that all the vast labor and intense -thought which has passed under our review had produced nothing but a -barren Knowledge of the external world, or a few Arts ministering -merely to our gratification; or if it seemed that the methods of -arriving at truth, so successfully applied in these cases, aid us -not when we come to the higher aims and prospects of our -being;--this History might well be estimated as no less melancholy -and unprofitable than those which narrate the wars of states and the -wiles of statesmen. But such, I trust, is not the impression which -our survey has tended to produce. At various points, the researches -which we have followed out, have offered to lead us from matter to -mind, from the external to the internal world; and it was not -because the thread of investigation snapped in our hands, but rather -because we were resolved to confine ourselves, for the present, to -the material sciences, that we did not proceed onwards to subjects -of a closer interest. It will appear, also, I trust, that the most -perfect method of obtaining speculative truth,--that of which I have -had to relate the result,--is by no means confined to the least -worthy subjects; but that the Methods of learning what is really -true, though they must assume different aspects in cases where a -mere contemplation of external objects is concerned, and where our -own internal world of thought, feeling, and will, supplies the -matter of our speculations, have yet a unity and harmony throughout -all the possible employments of our minds. To be able to trace such -connexions as this, is the proper sequel, and would be the high -reward, of the labor which has been bestowed on the present work. -And if a persuasion of the reality of such connexions, and a -preparation for studying them, have been conveyed to the reader's -mind while he has been accompanying me through our long survey, his -time may not have been employed on {598} these pages in vain. -However vague and hesitating and obscure may be such a persuasion, -it belongs, I doubt not, to the dawning of a better Philosophy, -which it may be my lot, perhaps, to develop more fully hereafter, if -permitted by that Superior Power to whom all sound philosophy -directs our thoughts. - - - -{{599}} -ADDITIONS TO THE THIRD EDITION. - - - - -BOOK VIII. - -ACOUSTICS. - -CHAPTER III. - -SOUND. - - -_The Velocity of Sound in Water._ - -THE Science of which the history is narrated in this Book has for -its objects, the minute Vibrations of the parts of bodies such as -those by which Sounds are produced, and the properties of Sounds. -The Vibrations of bodies are the result of a certain tension of -their structure which we term _Elasticity_. The Elasticity -determines the rate of Vibration: the rate of Vibration determines -the audible note: the Elasticity determines also the velocity with -which the vibration travels through the substance. These points of -the subject, Elasticity, Rate of Vibration, Velocity of Propagation, -Audible Note, are connected in each substance, and are different in -different substances. - -In the history of this Science, considered as tending to a -satisfactory general theory, the Problems which have obviously -offered themselves were, to explain the properties of Sounds by the -relations of their constituent vibrations; and to explain the -existence of vibrations by the elasticity of the substances in which -they occurred: as in Optics, philosophers have explained the -phenomenon of light and colors by the Undulatory Theory, and are -still engaged in explaining the requisite modulations by means of -the elasticity of the Ether. But the _Undulatory Theory of Sound_ -was seen to be true at an early period of the Science: and the -explanation, in a general way at least, of all kinds of such -undulations by means of the elasticity of the vibrating substances -has been performed by a series of mathematicians of whom I have -given an account in this Book. Hence the points of the subject -already mentioned (Elasticity, Vibrations and their Propagations, -{600} and Note), have a known material dependence, and each may be -employed in determining the other: for instance, the Note may be -employed in determining the velocity of sound and the elasticity of -the vibrating substance. - -Chladni,[1\B] and the Webers,[2\B] had made valuable experimental -inquiries on such subjects. But more complete investigations of this -kind have been conducted with care and skill by M. Wertheim.[3\B] -For instance, he has determined the velocity with which sound -travels in water, by making an organ-pipe to sound by the passage of -water through it. This is a matter of some difficulty; for the -mouthpiece of an organ-pipe, if it be not properly and carefully -constructed, produces sounds of its own, which are not the genuine -musical note of the pipe. And though the note depends mainly upon -the length of the pipe, it depends also, in a small degree, on the -breadth of the pipe and the size of the mouthpiece. - -[Note 1\B: _Traité d'Acoustique_, 1809.] - -[Note 2\B: _Wellenlehre_, 1852.] - -[Note 3\B: _Mémoires de Physique Mécanique_. Paris, 1848.] - -If the pipe were a mere line, the time of a vibration would be the -time in which a vibration travels from one end of the pipe to the -other; and thus the note for a given length (which is determined by -the time of vibration), is connected with the velocity of vibration. -He thus found that the velocity of a vibration along the pipe in -sea-water is 1157 _mètres_ per second. - -But M. Wertheim conceived that he had previously shown, by general -mathematical reasoning, that the velocity with which sound travels -in an unlimited expanse of any substance, is to the velocity with -which it travels along a pipe or linear strip of the same substance -as the square root of 3 to the square root of 2. Hence the velocity -of sound in sea-water would be 1454 _mètres_ a second. The velocity -of sound in air is 332 _mètres_. - -M. Wertheim also employed the vibrations of rods of steel and other -metals in order to determine their _modulus of elasticity_--that is, -the quantity which determines for each substance, the extent to -which, in virtue of its elasticity, it is compressed and expanded by -given pressures or tensions. For this purpose he caused the rod to -vibrate near to a tuning-fork of given pitch, so that both the rod -and the tuning-fork by their vibrations traced undulating curves on -a revolving disk. The curves traced by the two could be compared so -as to give their relative rate, and thus to determine the elasticity -of the substance. - - - -{{601}} -BOOK IX. - -PHYSICAL OPTICS. - - -_Photography._ - -I HAVE, at the end of Chapter xi., stated that the theory of which I -have endeavored to sketch the history professes to explain only the -phenomena of radiant visible light; and that though we know that -light has other properties--for instance, that it produces chemical -effects--these are not contemplated as included within the domain of -the theory. The chemical effects of light cannot as yet be included -in exact and general truths, such as those which constitute the -undulatory theory of radiant visible light. But though the present -age has not yet attained to a _Science_ of the chemistry of Light, -it has been enriched with a most exquisite _Art_, which involves the -principles of such a science, and may hereafter be made the -instrument of bringing them into the view of the philosopher. I -speak of the Art of _Photography_, in which chemistry has discovered -the means of producing surfaces almost as sensitive to the -modifications of light as the most sensitive of organic textures, -the retina of the eye: and has given permanence to images which in -the eye are only momentary impressions. Hereafter, when the laws -shall have been theoretically established, which connect the -chemical constitution of bodies with the action of light upon them, -the prominent names in the Prelude to such an Epoch must be those -who by their insight, invention, and perseverance, discovered and -carried to their present marvellous perfection the processes of -photographic Art:--Niepce and Daguerre in France, and our own -accomplished countryman, Mr. Fox Talbot. - - -_Fluorescence._ - -As already remarked, it is not within the province of the undulatory -theory to explain the phenomena of the absorption of light which -take place in various ways when the light is transmitted through -various {602} mediums. I have, at the end of Chapter iii., given the -reasons which prevent my assenting to the assertion of a special -analysis of light by absorption. In the same manner, with regard to -other effects produced by media upon light, it is sufficient for the -defence of the theory that it should be consistent with the -possibility of the laws of phenomena which are observed, not that it -should explain those laws; for they belong, apparently, to another -province of philosophy. - -Some of the optical properties of bodies which have recently -attracted notice appear to be of this kind. It was noticed by Sir -John Herschel,[4\B] that a certain liquid, sulphate of quinine, -which is under common circumstances colorless, exhibits in certain -aspects and under certain incidences of light, a beautiful celestial -blue color. It appeared that this color proceeded from the surface -on which the light first fell; and color thus produced Sir J. -Herschel called _epipolic_ colors, and spoke of the light as -_epipolized_. Sir David Brewster had previously noted effects of -color in transparent bodies which he ascribed to internal -dispersion:[5\B] and he conceived that the colors observed by Sir J. -Herschel were of the same class. Professor Stokes[6\B] of Cambridge -applied himself to the examination of these phenomena, and was led -to the conviction that they arise from a power which certain bodies -possess, of changing the color, and with it, the refrangibility of -the rays of light which fall upon them: and he traced this property -in various substances, into various remarkable consequences. As this -change of refrangibility always makes the rays _less_ refrangible, -it was proposed to call it a _degradation_ of the light; or again, -_dependent emission_, because the light is emitted in the manner of -self-luminous bodies, but only in dependence upon the active rays, -and so long as the body is under their influence. In this respect it -differs from _phosphorescence_, in which light is emitted without -such dependence. The phenomenon occurs in a conspicuous and -beautiful manner in certain kinds of fluor spar: and the term -_fluorescence_, suggested by Professor Stokes, has the advantage of -inserting no hypothesis, and will probably be found the most -generally acceptable.[7\B] - -[Note 4\B: _Phil. Trans._ 1845.] - -[Note 5\B: _Edinb. Trans._ 1833.] - -[Note 6\B: _Phil. Trans._ 1852 and 1854.] - -[Note 7\B: _Phil. Trans._ 1852.] - -It may be remarked that Professor Stokes rejects altogether the -doctrine that light of definite refrangibility may still be -compound, and maybe analysed by absorption. He says, "I have not -overlooked the remarkable effect of absorbing media in causing -apparent changes {603} of color in a pure spectrum; but this I -believe to be a subjective phenomenon depending upon contrast." - - - - -CHAPTER XIII. - -UNDULATORY THEORY. - - -_Direction of the Transverse Vibrations in Polarization._ - -IN the conclusion of Chapter xiii. I have stated that there is a -point in the undulatory theory which was regarded as left undecided -by Young and Fresnel, and on which the two different opinions have -been maintained by different mathematicians; namely, whether the -vibrations of polarized light are perpendicular to the plane of -polarization or in that plane. Professor Stokes of Cambridge has -attempted to solve this question in a manner which is, -theoretically, exceedingly ingenious, though it is difficult to make -the requisite experiments in a decisive manner. The method may be -briefly described. - -If polarized light be _diffracted_ (see Chap. xi. sect. 2), each ray -will be bent from its position, but will still be polarized. The -original ray and the diffracted ray, thus forming a broken line, may -be supposed to be connected at the angle by a universal joint -(called a _Hooke's Joint_), such that when the original ray turns -about its axis, the diffracted ray also turns about its axis; as in -the case of the long handle of a telescope and the screw which is -turned by it. Now if the motion of the original ray round its axis -be uniform, the motion of the diffracted ray round its axis is not -uniform: and hence if, in a series of cases, the planes of -polarization of the original ray differ by equal angles, in the -diffracted ray the planes of polarization will differ by unequal -angles. Then if vibrations be perpendicular to the plane of -polarization, the planes of polarization in the diffracted rays will -be crowded together in the neighborhood of the plane in which the -diffraction takes place, and will be more rarely distributed in the -neighborhood of the plane perpendicular to this, in which is the -diffracting thread or groove. - -On making the experiment, Prof. Stokes conceived that he found, in -his experiments, such a crowding of the planes of diffracted -polarization towards the plane of diffraction; and thus he held that -the {604} hypothesis that the transverse vibrations which constitute -polarization are perpendicularly transverse to the plane of -polarization was confirmed.[8\B] - -[Note 8\B: _Camb. Trans._, vol. ix. part i. 1849.] - -But Mr. Holtzmann,[9\B] who, assenting to the reasoning, has made -the experiment in a somewhat different manner, has obtained an -opposite result; so that the point may be regarded as still -doubtful. - -[Note 9\B: _Phil. Mag._, Feb. 1857.] - - -_Final Disproof of the Emission Theory._ - -As I have stated in the History, we cannot properly say that there -ever was an Emission Theory of Light which was the _rival_ of the -Undulatory Theory: for while the undulatory theory provided -explanations of new classes of phenomena as fast as they arose, and -exhibited a _consilience_ of theories in these explanations, the -hypothesis of emitted particles required new machinery for every new -set of facts, and soon ceased to be capable even of expressing the -facts. The simple cases of the ordinary reflexion and refraction of -light were explained by Newton on the supposition that the -transmission of light is the motion of particles: and though his -explanation includes a somewhat harsh assumption (that a refracting -surface exercises an attractive force through a _fixed finite_ -space), the authority of his great name gave it a sort of permanent -notoriety, and made it to be regarded as a standard point of -comparison between a supposed "Emission Theory" and the undulation -theory. And the way in which the theories were to be tested in this -case was obvious: in the Newtonian theory, the velocity of light is -increased by the refracting medium; in the undulatory theory, it is -diminished. On the former hypothesis the velocity of light in air -and in water is as 3 to 4; in the latter, as 4 to 3. - -But the immense velocity of light made it appear impossible to -measure it, within the limits of any finite space which we can -occupy with refracting matter. The velocity of light is known from -astronomical phenomena;--from the eclipses of Jupiter's satellites, -by which it appears that light occupies 8 minutes in coming from the -sun to the earth; and from the aberration of light, by which its -velocity is shown to be 10,000 times the velocity of the earth in -its orbit. Is it, then, possible to make apparent so small a -difference as that between its passing through a few yards of air -and of water? - -Mr. Wheatstone, in 1831, invented a machine by which this could -{605} be done. His object was to determine the velocity of the -electric shock. His apparatus consisted in a small mirror, turning -with great velocity about an axis which is in its own plane, like a -coin spinning on its edge. The velocity of spinning may be made so -great, that an object reflected shall change its place perceptibly -after an almost inconceivably small fraction of a second. The -application of this contrivance to measure the velocity of light, -was, at the suggestion of Arago, who had seen the times of the rival -theories of light, undertaken by younger men at Paris, his eyesight -not allowing him to prosecute such a task himself. It was necessary -that the mirrors should turn more than 1000 times in a second, in -order that the two images, produced, one by light coming through -air, and the other by light coming through an equal length of water, -should have places perceptibly different. The mechanical -difficulties of the experiment consisted in keeping up this great -velocity by the machinery without destroying the machinery, and in -transmitting the light without too much enfeebling it. These -difficulties were overcome in 1850, by M. Fizeau and M. Léon -Foucault separately: and the result was, that the velocity of light -was found to be less in water than in air. And thus the Newtonian -explanation of refraction, the last remnant of the Emission Theory, -was proved to be false. - - - -{{606}} -BOOK X. - -THERMOTICS.--ATMOLOGY. - -CHAPTER III. - -THE RELATION OF VAPOUR AND AIR. - - -_Sect._ 4.--_Force of Steam._ - -THE experiments on the elastic force of steam made by the French -Academy are fitted in an especial manner to decide the question -between rival formulæ, in consequence of the great amount of force -to which they extend; namely, 60 feet of mercury, or 24 atmospheres: -for formulæ which give results almost indistinguishable in the lower -part of the scale diverge widely at those elevated points. Mr. -Waterston[10\B] has reduced both these and other experiments to a -rule in the following manner:--He takes the zero of gaseous tension, -determined by other experimenters (Rudberg, Magnus, and Regnault,) -to be 461° below the zero of Fahrenheit, or 274° below the zero of -the centigrade scale: and temperatures reckoned from this zero he -calls "G temperatures." The square root of the G temperatures is the -element to which the elastic force is referred (for certain -theoretical reasons), and it is found that the density of steam is -as the _sixth power_ of this element. The agreement of this rule -with the special results is strikingly close. A like rule was found -by him to apply generally to many other gases in contact with their -liquids. - -[Note 10\B: _Phil. Trans._ 1852.] - -But M. Regnault has recently investigated the subject in the most -complete and ample manner, and has obtained results somewhat -different.[11\B] He is led to the conclusion that no formula -proceeding by {607} a power of the temperature can represent the -experiments. He also finds that the rule of Dalton (that as the -temperatures increase in arithmetical progression, the elastic force -increases in geometric progression) deviates from the observations, -especially at high temperatures. Dalton's rule would be expressed by -saying that the variable part of the elastic force is as _a^t_, where -_t_ is the temperature. This failing, M. Regnault makes trial of a -formula suggested by M. Biot, consisting of a sum of two terms, one of -which is as _a^t_, and the other is _b^t_: and in this way satisfies -the experiments very closely. But this can only be considered as a -formula of interpolation, and has no theoretical basis. M. Roche had -proposed a formula in which the force is as _a^z_, _z_ depending upon -the temperature by an equation[12\B] to which he had been led by -theoretical considerations. This agrees better with observation than -any other formula which includes only the same number of coefficients. - -[Note 11\B: _Mém. de l'Institut_, vol. xxi. (1847). M. Regnault's -Memoir occupies 767 pages.] - -[Note 12\B: The equation _z_ = _t_ ⁄ (1 + _mt_).] - -Among the experimental thermotical laws referred to by M. Regnault -are, the Law of Watt,[13\B] that "the quantity of heat which is -required to convert a pint of water at a temperature of zero into -steam, is the same whatever be the pressure." Also, the Law of -Southern, that "the latent heat of vaporization, that is the heat -absorbed in the passage from the liquid to the gaseous consistence, -is constant for all purposes: and that we obtain the total heat in -adding to the constant latent heat the number which represents the -latent heat of steam." Southern found the latent heat of the steam -of water to be represented by about 950 degrees of Fahrenheit.[14\B] - -[Note 13\B: See Robison's _Mechanical Philosophy_, vol. ii. p. 8.] - -[Note 14\B: Ib. p. 160.] - - -_Sect._ 5.--_Temperature of the Atmosphere._ - -I MAY notice, as important additions to our knowledge on this -subject, the results of four balloon ascents made in 1852,[15\B] by -the Committee of the Meteorological Observatory established at Kew -by the British Association for the Advancement of Science. In these -ascents the observers mounted to more than 13,000, 18,000, and -19,000 feet, and in the last to 22,370; by which ascent the -temperature fell from 49 degrees to nearly 10 degrees below zero; -and the dew-point fell from 37° to 12°. Perhaps the most marked -result of these observations is the {608} following:--The temperature -of the air decreases uniformly as we ascend above the earth's -surface; but this decrease does not go on continuously. At a certain -elevation, varying on different days, the decrease is arrested: and -for a depth of two or three thousand feet of air, the temperature -decreases little, or even increases in ascending. Above this, the -diminution again takes place at nearly the same rate as in the lower -regions. This intermediate region of undecreasing temperature -extended in the various ascents, from about altitude 4000 to 6000 -feet, 6500 to 10,000, 2000 to 4500, and 4000 to 8000. This -interruption in the decrease of temperature is accompanied by a -large and abrupt fall in the temperature of the dew-point, or by an -actual condensation of vapor. Thus, this region is the _region of -the clouds_, and the increase of heat appears to arise from the -latent heat liberated when aqueous vapor is formed into clouds. - -[Note 15\B: _Phil. Trans._ 1853.] - - - - -CHAPTER IV. - -THEORIES OF HEAT. - - -_The Dynamical Theory of Heat._ - -THAT the transmission of _radiant_ Heat takes place by means of the -vibrations of a medium, as the transmission of Sound certainly does, -and the transmission of Light most probably, is a theory which, as I -have endeavored to explain, has strong arguments and analogies in -its favor. But that Heat itself, in its essence and quantity, is -Motion is a hypothesis of quite another kind. This hypothesis has -been recently asserted and maintained with great ability. The -doctrine thus asserted is, that Motion may be converted into Heat, -and Heat into Motion; that Heat and Motion may produce each other, -as we see in the rarefaction and condensation of air, in -steam-engines, and the like: and that in all such cases the Motion -produced and the Heat expended exactly measure each other. The -foundation of this theory is conceived to have been laid by Mr. -Joule of Manchester, in 1844: and it has since been prosecuted by -him and by Professor Thomson of Glasgow, by experimental -investigations of various kinds. It is difficult to make these -experiments so as to be quite satisfactory; for it is {609} -difficult to measure _all_ the heat gained or lost in any of the -changes here contemplated. That friction, agitation of fluids, -condensation of gases, conversion of gases into fluids and liquids -into solids, produce heat, is undoubted: and that the quantity of -such heat may be measured by the mechanical force which produces it, -or which it produces, is a generalization which will very likely be -found a fertile source of new propositions, and probably of -important consequences. - -As an example of the conclusions which Professor Thomson draws from -this doctrine of the mutual conversion of motion and heat, I may -mention his speculations concerning the cause which produces and -sustains the heat of the sun.[16\B] He conceives that the support of -the solar heat must be meteoric matter which is perpetually falling -towards the globe of the sun, and has its motion converted into -heat. He inclines to think that the meteors containing the stores of -energy for future Sun-light must be principally within the earth's -orbit; and that we actually see them there as the "Zodiacal Light," -an illuminated shower, or rather tornado, of stones. The inner parts -of this tornado are always getting caught in the Sun's atmosphere, -and drawn to his mass by gravitation. - -[Note 16\B: On the Mechanical Energies of the Solar System. _Edinb. -Trans._ vol. XXI. part i. (1854), p. 67.] - - - -{{610}} -BOOK XI. - -ELECTRICITY. - - -GENERAL REMARKS. - - -ELECTRICITY in the form in which it was originally -studied--Franklinic, frictional, or statical electricity--has been -so completely identified with electricity in its more comprehensive -form--Voltaic, chemical, or dynamical electricity--that any -additions we might have to make to the history of the earlier form -of the subject are included in the later science. - -There are, however, several subjects which may still be regarded -rather as branches of Electricity than of the Cognate Sciences. Such -are, for instance, Atmospheric Electricity, with all that belongs to -Thunderstorms and Lightning Conductors. The observation of -Atmospheric Electricity has been prosecuted with great zeal at -various meteorological observatories; and especially at the -Observatory established by the British Association at Kew. The -Aurora Borealis, again, is plainly an electrical phenomenon; but -probably belonging rather to dynamical than to statical electricity. -For it strongly affects the magnetic needle, and its position has -reference to the direction of magnetism; but it has not been -observed to affect the electroscope. The general features of this -phenomenon have been described by M. de Humboldt, and more recently -by M. de Bravais; and theories of the mode of its production have -been propounded by MM. Biot, De la Rive, Kaemtz, and others. - -Again, there are several fishes which have the power of giving an -electrical shock:--the torpedo, the gymnotus, and the silurus. The -agency of these creatures has been identified with electricity in -the most general sense. The peculiar energy of the animal has been -made to produce the effects which are produced by an electrical -discharge or a voltaic current:--not only to destroy life in small -animals, but to {611} deflect a magnet, to make a magnet, to -decompose water, and to produce a spark. - - -_Dr. Faraday's Views of Statical Electric Induction._ - -According to the theories of electricity of Æpinus and Coulomb, -which in this Book of our History are regarded as constituting a -main part of the progress of this portion of science, the particles -of the electric fluid or fluids exert forces, attractive and -repulsive, upon each other in straight lines at a distance, in the -same way in which, in the Newtonian theory of the universe, the -particles of matter are conceived as exerting attractive forces upon -each other. An electrized body presented a conducting body of any -form, determines a new arrangement of the electric fluids in the -conductor, attracting the like fluid to its own side, and repelling -the opposite fluid to the opposite side. This is Electrical -_Induction_. And as, by the theory, the attraction is greater at the -smaller distances, the distribution of the fluid upon the conductor -in virtue of this Induction will not be symmetrical, but will be -governed by laws which it will require a complex and difficult -calculation to determine--as we have seen was the case in the -investigations of Coulomb, Poisson, and others. - -Instead of this action at a distance. Dr. Faraday has been led to -conceive Electrical Induction to be the result of an action taking -place between the electrized body and the conductor through lines of -contiguous particles in the mass of the intermediate body, which he -calls the _Dielectric_. And the irregularities of the distribution -of the electricity in these cases of Induction, and indeed the -existence of an action in points protected from direct action by the -protuberant sides of the conductor, are the causes, I conceive, -which lead him to the conclusion that Induction takes place in -_curved lines_[17\B] of such contiguous particles. - -[Note 17\B: _Researches_, 1165, &c.] - -With reference to this, I may remark that, as I have said, the -distribution of electricity on a conductor in the presence of an -electrized body is so complex a mathematical problem that I do not -conceive any merely popular way of regarding the result can entitle -us to say, that the distribution which we find cannot be explained -by the Coulombian theory, and must force us upon the assumption of -an action in curved lines:--which is, indeed, itself a theory, and -so vague a one {612} that it requires to be made much more precise -before we can say what consequences it does or does not lead to. -Professor W. Thomson has arrived at a mathematical proof that the -effect of induction on the view of Coulomb and of Faraday must, -under certain conditions, be necessarily and universally the same. - -With regard to the influence of different _Dielectrics_ upon -Induction, the inquiry appears to be of the highest importance; and -may certainly necessitate some addition to the theory. - - - -{{613}} -BOOK XII. - -MAGNETISM. - - -_Recent Progress of Terrestrial Magnetism._ - -IN Chapter II., I have noticed the history of Terrestrial Magnetism; -Hansteen's map published in 1819; the discovery of "magnetic storms" -about 1825; the chain of associated magnetic observations, suggested -by M. de Humboldt, and promoted by the British Association and the -Royal Society; the demand for the continuation of these till 1848; -the magnetic observations made in several voyages; the magnetic -surveys of various countries. And I have spoken also of Gauss's -theory of Terrestrial Magnetism, and his directions and requirements -concerning the observations to be made. I may add a few words with -regard to the more recent progress of the subject. - -The magnetic observations made over large portions of the Earth's -surface by various persons, and on the Ocean by British officers, -have been transmitted to Woolwich, where they have been employed by -General Sabine in constructing magnetic maps of the Earth for the -year 1840.[18\B] Following the course of inquiry described in the -part of the history referred to, these maps exhibit the declination, -inclination, and intensity of the magnetic force at every point of -the earth's surface. The curves which mark equal amounts of each of -these three elements (the _lines of equal declination_, -_inclination_, and _force_:--the _isogonal_, the _isoclinal_, and -the _isodynamic_ lines,) are, in their general form, complex and -irregular; and it has been made a matter of question (the facts -being agreed upon) whether it be more proper to say that they -indicate four poles, as Halley and as Hansteen said, or only two -poles, as Gauss asserts. The matter appears to become more clear if -we draw magnetic _meridians_; that is, lines obtained by following -the directions, or pointings, of the magnetic needle to the north or -to {614} the south, till we arrive at the points of convergence of -all their directions; for there are only two such poles, one in the -Arctic and one in the Antarctic region. But in consequence of the -irregularity of the magnetic constitution of the earth, if we follow -the inclination of the magnetic force round the earth on any -parallel of latitude, we find that it has two _maxima_ and two -_minima_, as if there were four magnetic poles. The isodynamic map -is a new presentation of the facts of this subject; the first having -been constructed by Colonel Sabine in 1837. - -[Note 18\B: These maps are published in Mr. Keith Johnstone's -_Physical Atlas_.] - -I have stated also that the magnetic elements at each place are to -be observed in such a manner as to bring into view both their -_periodical_, their _secular_, and their _irregular_ or _occasional_ -changes. The observations made at Toronto in Canada, and at Hobart -Town in Van Diemen's Land, two stations at equal distances from the -two poles of the earth, and also at St Helena, a station within the -tropics, have been discussed by General Sabine with great care, and -with an amount of labor approaching to that employed upon reductions -of astronomical observations. And the results have been curious and -unexpected. - -The declination was first examined.[19\B] This magnetical element is, -as we have already seen (p. 232), liable both to a diurnal and to an -annual inequality; and also to irregular perturbations which have been -termed magnetic storms. Now it was found that all these inequalities -went on increasing gradually and steadily from 1843 to 1848, so as to -become, at the end of that time, above twice as large as they were at -the beginning of it. A new periodical change in all these elements -appeared to be clearly established by this examination. M. Lamont, of -Munich, had already remarked indications of a decennial period in the -diurnal variation of the declination of the needle. The duration of -the period from minimum to maximum being about five years, and -therefore the whole period about ten years. The same conclusion was -found to follow still more decidedly from the observations of the dip -and intensity. - -[Note 19\B: _Phil. Trans._ 1852 and 1856.] - -This period of ten years had no familiar meaning in astronomy; and -if none such had been found for it, its occurrence as a magnetic -period must have been regarded, as General Sabine says,[20\B] in the -light of a fragmentary fact. But it happened about this time that -the scientific world was made aware of the existence of a like -period in a {615} phenomenon which no one would have guessed to be -connected with terrestrial magnetism, namely, the spots in the Sun. -M. Schwabe, of Dessau, had observed the Sun's disk with immense -perseverance for 24 years:--often examining it more than 300 days in -the year; and had found that the spots had, as to their quantity and -frequency, a periodical character. The years of maximum are 1828, -1838, 1848, in which there were respectively 225,[21\B] 282, 330 -groups of spots. The minimum years, 1833, 1843, had only 33 and 34 -such groups. This curious fact[22\B] was first made public by M. de -Humboldt, in the third volume of his _Kosmos_ (1850). The -coincidence of the periods and epochs of these two classes of facts -was pointed out by General Sabine in a Memoir presented to the Royal -Society in March, 1852. - -[Note 20\B: _Phil. Trans._ 1856, p. 382.] - -[Note 21\B: In 1837 there were 333.] - -[Note 22\B: The observations up to 1844 were published in -Poggendorf's _Annalen_.] - -Of course it was natural to suppose, even before this discovery, -that the diurnal and annual inequalities of the magnetic element at -each place depend upon the action of the sun, in some way or other. - -Dr. Faraday had endeavored to point out how the effect of the solar -heat upon the atmosphere would, according to the known relations of -heat and magnetism, explain many of the phenomena. But this new -feature of the phenomena, their quinquennial increase and decrease, -makes us doubt whether such an explanation can really be the true one. - -Of the _secular_ changes in the magnetic elements, not much more is -known than was known some years ago. These changes go on, but their -laws are imperfectly known, and their causes not even conjectured. -M. Hansteen, in a recent memoir,[23\B] says that the decrease of the -inclination goes on progressively diminishing. With us this rate of -decrease appears to be at present nearly uniform. We cannot help -conjecturing that the sun, which has so plain a connexion with the -diurnal, annual, and occasional movements of the needle, must also -have some connexion with its secular movements. - -[Note 23\B: See K. Johnstone's _Physical Atlas_.] - -In 1840 the observations made at various places had to a great -extent enabled Gauss, in connexion with W. Weber, to apply his -Theory to the actual condition of the Earth;[24\B] and he -calculated the Declination, Inclination, and Intensity at above 100 -places, and found {616} the agreement, as he says, far beyond his -hopes. They show, he says, that the Theory comes near to the Truth. - -[Note 24\B: _Atlas des Erdmagnetismus nach den Elementen der Theorie -Entworfen_. See Preface.] - - -_Correction of Ship's Compasses._ - -The magnetic needle had become of importance when it was found that -it always pointed to the North. Since that time the history of -magnetism has had its events reflected in the history of navigation. -The change of the declination arising from a change of place -terrified the companions of Columbus. The determination of the laws -of this change was the object of the voyage of Halley; and has been -pursued with the utmost energy in the Arctic and Antarctic regions -by navigators up to the present time. Probably the dependence of the -magnetic declination upon place is now known well enough for the -purposes of navigation. But a new source of difficulty has in the -meantime come into view; the effect of the iron in the ship upon the -Compass. And this has gone on increasing as guns, cables, stays, -knees, have been made of iron; then steam-engines with funnels, -wheels, and screws, have been added; and finally the whole ship has -been made of iron. How can the compass be trusted in such cases? - -I have already said in the history that Mr. Barlow proposed to -correct the error of the compass by placing near to the compass an -iron plate, which from its proximity to the compass might -counterbalance magnetically the whole effect of the ship's iron upon -the compass. This correction was not effectual, because the magnetic -forces of the plate and of the ship do not change their direction -and value according to the same law, with the change of position. I -have further stated that Mr. Airy devised other means of correcting -the error. I may add a few words on the subject; for the subject has -been further examined by Mr. Airy[25\B] and by others. - -[Note 25\B: _Phil. Trans._ 1856.] - -It appears, by mathematical reasoning, that the magnetic effect of -the iron in a ship may be regarded as producing two kinds of -deviation which are added together;--a "polar-magnet deviation," -which changes from positive to negative as the direction of the -ship's keel, in a horizontal revolution, passes from semicircle to -semicircle; and a "quadrantal deviation," which changes from -positive to negative as the keel turns from quadrant to quadrant. -The latter deviation may be remedied completely by a mass of -unmagnetized iron placed on a level {617} with the compass, either -in the athwartship line or in the fore-and-aft line, according to -circumstances. "The polar-magnet-deviation" may be corrected at _any -given place_ by a magnet or magnets, but the magnets thus applied at -one place will not always correct the deviation in another magnetic -latitude. For it appears that this deviation arises partly from a -magnetism inherent in the materials of the ship, not changing with -the change of magnetic position, and partly from the effect of -terrestrial magnetism upon the ship's iron. But the errors arising -from both sources may be remedied by adjusting, at a new locality, -the positions of the corrective magnets. - -The inherent magnetism of the ship, of which I have spoken, may be -much affected by the position in which the ship was built; and may -change from time to time; for instance, by the effect of the -battering of the waves, and other causes. Hence it is called by Mr. -Airy "sub-permanent magnetism." - -Another method of correcting the errors of a ship's compass has been -proposed, and is used to some extent; namely, by _swinging_ the ship -round (in harbor) to all points of azimuth, and thus constructing a -_Table of Compass Errors_ for that particular ship. But to this -method it is objected that the Table loses its value in a new -magnetic latitude much more than the correction by magnets does; -besides the inconveniences of steering a ship by a Table. - - - -{{618}} -BOOK XIII. - -VOLTAIC ELECTRICITY. - -CHAPTER VII. - -MAGNETO-ELECTRIC INDUCTION. - - -FARADAY'S discovery that, in combinations like those in which a -voltaic current was known to produce motion, motion would produce a -voltaic current, naturally excited great attention among the -scientific men of Europe. The general nature of his discovery was -communicated by letter[26\B] to M. Hachette at Paris, in December, -1831; and experiments having the like results were forthwith made by -MM. Becquerel and Ampère at Paris, and MM. Nobili and Antinori at -Florence. - -[Note 26\B: _Ann. de Chimie_, vol. xlviii. (1831), p. 402.] - -It was natural also that in a case in which the relations of space -which determine the results are so complicated, different -philosophers should look at them in different ways. There had been, -from the first discovery by Oersted of the effect of a voltaic -current upon a magnet, two rival methods of regarding the facts. -Electric and magnetic lines exert an effort to place themselves -transverse to each other (see chapter iv. of this Book), and (as I -have already said) two ways offered themselves of simplifying this -general truth:--to suppose an electric current made up of transverse -magnetic lines; or to suppose magnetic lines made up of transverse -electric currents. On either of these assumptions, the result was -expressed by saying that _like_ currents or lines (electric or -magnetic) tend to place themselves parallel; which is a law more -generally intelligible than the law of transverse position. Faraday -had adopted the former view; had taken the lines of magnetic force -for the fundamental lines of his system, and defined the direction -of the magneto-electric current of induction by the relation {619} -of the motion to these lines. Ampère, on the other hand, supposed -the magnet to be made up of transverse electric currents (chap. -vi.); and had deduced all the facts of electro-dynamical action, -with great felicity, from this conception. The question naturally -arose, in what manner, on this view, were the new facts of -magneto-electric induction by motion to be explained, or even -expressed? - -Various philosophers attempted to answer this question. Perhaps the -form in which the answer has obtained most general acceptance is -that in which it was put by Lenz, who discoursed on the subject to -the Academy of St. Petersburg in 1833.[27\B] His general rule is to -this effect: when a wire moves in the neighborhood of an electric -current or a magnet, a current takes place in it, such as, existing -independently, would have produced a motion opposite to the actual -motion. Thus two parallel _forward_ currents move towards each -other:--hence if a current move towards a parallel wire, it produces -in it a _backward_ current. A moveable wire conducting a current -_downwards_ will move round the north pole of a magnet in the -direction N., W., S., E.:--hence if, when the wire have in it no -current, we move it in the direction N., W., S., E., we produce in -the wire an _upward_ current. And thus, as M. de la Rive -remarks,[28\B] in cases in which the mutual action of two currents -produces a limited motion, as attraction or repulsion, or a -deviation right or left, the corresponding magneto-electric -induction produces an instantaneous current only; but when the -electrodynamic action produces a continued motion, the corresponding -motion produces, by induction, a continued current. - -[Note 27\B: _Acad. Petrop._ Nov. 29, 1833. _Pogg. Ann._ vol. xxxi. -p. 483.] - -[Note 28\B: _Traité de l'Electricité_, vol. i. p. 441 (1854).] - -Looking at this mode of stating the law, it is impossible not to -regard this effect as a sort of reaction; and accordingly, this view -was at once taken of it. Professor Ritchie said, in 1833, "The law -is founded on the universal principle that action and reaction are -equal." Thus, if voltaic electricity induce magnetism under certain -arrangements, magnetism will, by similar arrangements, react on a -conductor and induce voltaic electricity.[29\B] - -[Note 29\B: On the Reduction of Mr. Faraday's discoveries in -Magneto-electric Induction to a General Law. _Trans._ of R. S. in -_Phil. Mag._ N.S. vol. iii. 37, and vol. iv. p. 11. In the second -edition of this history I used the like expressions.] - -There are still other ways of looking at this matter. I have -elsewhere pointed out that where polar properties co-exist, they are -{620} generally found to be connected,[30\B] and have illustrated -this law in the case of electrical, magnetical, and chemical -polarities. If we regard motion backwards and forwards, to the right -and the left, and the like, as _polar_ relations, we see that -magneto-electric induction gives us a new manifestation of connected -polarities. - -[Note 30\B: _Phil. Ind. Sc._ B. v. c. ii.] - - -_Diamagnetic Polarity_. - -But the manifestation of co-existent polarities which are brought into -view in this most curious department of nature is not yet exhausted by -those which we have described. I have already spoken (chap. **vii.) of -Dr. Faraday's discovery that there are diamagnetic as well as magnetic -bodies; bodies which are repelled by the pole of a magnet, as well as -bodies which are attracted. Here is a new opposition of properties. -What is the exact definition of this opposition in connexion with -other polarities? To this, at present, different philosophers give -different answers. Some say that diamagnetism is completely the -opposite of ordinary magnetism, or, as Dr. Faraday has termed it for -the sake of distinction, of _paramagnetism_. They say that as a north -pole of a magnet gives to the neighboring extremity of a piece of soft -iron a south pole, so it gives to the neighboring extremity of a piece -of bismuth a north pole, and that the bismuth becomes for a time an -inverted magnet; and hence, arranges itself across the line of -magnetised force, instead of along it. Dr. Faraday himself at first -adopted this view;[31\B] but he now conceives that the bismuth is not -made polar, but is simply repelled by the magnet; and that the -transverse position which it assumes, arises merely from its elongated -form, each end trying to recede as far as possible from the repulsive -pole of the magnet. - -[Note 31\B: Faraday's _Researches_, Art. 2429, 2430.] - -Several philosophers of great eminence, however, who have examined -the subject with great care, adhere to Dr. Faraday's first view of -the nature of Diamagnetism--as W. Weber,[32\B] Plücker, and Mr. -Tyndall among ourselves. If we translate this view into the language -of Ampère's theory, it comes to this:--that as currents are induced -in iron and magnetics parallel to those existing in the inducing -magnet or battery wire; so in bismuth, heavy glass, and other -diamagnetic bodies, the currents induced are in the contrary {621} -directions:--these hypothetical currents being in non-conducting -diamagnetic, as in magnetic bodies, not in the mass, but round the -particles of the matter. - -[Note 32\B: Poggendorf's _Ann. Jou._ 1848.] - - -_Magneto-optic Effects and Magnecrystallic Polarity._ - -Not even yet have we terminated the enumeration of the co-existent -polarities which in this province of nature have been brought into -view. Light has polar properties; the very term _polarization_ is -the record of the discovery of these. The forces which determine the -crystalline forms of bodies are of a polar nature: crystalline -forms, when complete, may be defined as those forms which have a -certain degree of symmetry in reference to opposite poles. Now has -this optical and crystalline polarity any relation to the electrical -polarity of which we have been speaking? - -However much we might be disposed beforehand to conjecture that -there is some relation between these two groups of polar properties, -yet in this as in the other parts of this history of discoveries -respecting polarities, no conjecture hits the nature of the -relation, such as experiment showed it to be. In November, 1846, -Faraday announced the discovery of what he then called "the action -of magnets on light." But this action was manifested, not on light -directly, but on light passing through certain kinds of glass.[33\B] -When this glass, subjected to the action of the powerful magnets -which he used, transmitted a ray of light parallel to the line of -magnetic force, an effect was produced upon the light. But of what -nature was this effect? When light was ordinary light, no change in -its condition was discoverable. But if the light were light -polarized in any plane, the plane of polarization was turned round -through a certain angle while the ray passed through the glass:--a -greater angle, in proportion as the magnetic force was greater, and -the thickness of the glass greater. - -[Note 33\B: Silicated borate of lead. See _Researches_, § 2151, &c. -Also flint glass, rock salt, water (2215).] - -A power in some respects of this kind, namely, a power to rotate the -plane of polarization of a ray passing through them, is possessed by -some bodies in their natural state; for instance, quartz crystals, -and oil of turpentine. But yet, as Dr. Faraday remarks,[34\B] there -is a great difference in the two cases. When polarized rays pass -through oil of turpentine, in whatever direction they pass, they all -of them have their {622} plane of polarization rotated in the same -direction; that is, all to the right or all to the left; but when a -ray passes through the heavy glass, the power of rotation exists -only in a plane perpendicular to the magnetic line, and its -direction as right or left-handed is reversed by reversing the -magnetic polarity. - -[Note 34\B: _Researches_, Art. 2231.] - -In this case, we have optical properties, which do not depend on -crystalline form, affected by the magnetic force. But it has also been -found that crystalline form, which is so fertile a source of optical -properties, affords indications of magnetic forces. In 1847, M. -Plücker,[35\B] of the University of Bonn, using a powerful magnetic -apparatus, similar to Faraday's, found that crystals in general are -magnetic, in this sense, that the axes of crystalline form tend to -assume a certain position with reference to the magnetic lines of -force. The possession of one optic axis or of two is one of the broad -distinctions of the different crystalline forms: and using this -distinction, M. Plücker found that a crystal having a single optic -axis tends to place itself with this axis transverse to the magnetic -line of force, as if its optic axis were repelled by each magnetic -pole; and crystals with two axes act as if each of these axes were -repelled by the magnetic poles. This force is independent of the -magnetic or diamagnetic character of the crystal; and is a directive, -more properly than an attractive or repulsive force. - -[Note 35\B: Taylor's _Scientific Memoirs_, vol. v.] - -Soon afterwards (in 1848) Faraday also discovered[36\B] an effect of -magnetism depending on crystalline form, which at first sight appeared -to be different from the effects observed by M. Plücker. He found that -a crystal of bismuth, of which the form is nearly a cube, but more -truly a rhombohedron with one diagonal a little longer than the -others, tends to place itself with this diagonal in the direction of -the lines of magnetic force. At first he conceived[37\B] the -properties thus detected to be different from those observed by M. -Plücker; since in this case the force of a crystalline axis is axial, -whereas in those, it was equatorial. But a further consideration of -the subject, led him[38\B] to a conviction that these forces must be -fundamentally identical: for it was easy to conceive a combination of -bismuth crystals which would behave in the magnetic field as a crystal -of calcspar does; or a combination of calcspar crystals which would -behave as a crystal of bismuth does. - -[Note 36\B: _Researches_, Art. 2454, &c.] - -[Note 37\B: Art. 2469.] - -[Note 38\B: Art 2593, 2601.] - -And thus we have fresh examples to show that the Connexion of -coexistent Polarities is a thought deeply seated in the minds of the -{623} profoundest and most sagacious philosophers, and perpetually -verified and illustrated, by unforeseen discoveries in unguessed -forms, through the labors of the most skilful experimenters. - - -_Magneto-electric Machines._ - -The discovery that a voltaic wire moved in presence of a magnet, has -a current generated in it, was employed as the ground of the -construction of machines to produce electrical effects. In Saxton's -machine two coils of wire including a core of soft iron revolved -opposite to the ends of a horseshoe magnet, and thus, as the two -coils came opposite to the N. and S. and to the S. and N. poles of -the magnet, currents were generated alternately in the wires in -opposite directions. But by arranging the connexions of the ends of -the wires, the successive currents might be made to pass in -corresponding directions. The alternations or successions of -currents in such machines are governed by a contrivance which -alternately interrupts and permits the action; this contrivance has -been called a _rheotome_. Clarke gave a new form to a machine of the -same nature as Saxton's. But the like effect may be produced by -using an electro-magnet instead of a common magnet. When this is -done, a current is produced which by induction produces a current in -another wire, and the action is alternately excited and interrupted. -When the inducing current is interrupted, a momentary current _in an -opposite direction_ is produced in the induced wire; and when this -current stops, it produces in the inducing wire a current _in the -original direction_, which may be adjusted so as to reinforce the -resumed action of the original current. This was pointed out by M. -De la Rive in 1843.[39\B] Machines have been constructed on such -principles by him and others. Of such machines the most powerful -hitherto known is that constructed by M. Ruhmkorff. The effects of -this instrument are exceedingly energetic. - -[Note 39\B: _Traité de l'Elect._ i. 391.] - - -_Applications of Electrodynamic Discoveries._ - -The great series of discoveries of which I have had to speak have -been applied in many important ways to the uses of life. The -_Electric Telegraph_ is one of the most remarkable of these. By -wires extended to the most distant places, the electric current is -transmitted {624} thither in an imperceptible time; and by means of -well-devised systems of operation, is made to convey from man to man -words, which are now most emphatically "winged words." In the most -civilised states such wires now form a net-work across the land, -which is familiar to our thoughts as the highway is to our feet; and -wide seas have such pathways of human thought buried deep in their -waves from shore to shore. Again, by using the chemical effects of -electrodynamic action, of which we shall have to speak in the next -Book, a new means has been obtained of copying, with an exactness -unattainable before, any forms which art or nature has produced, and -of covering them with a surface of metal. The _Electrotype Process_ -is now one of the great powers which manufacturing art employs. - -But these discoveries have also been employed in explaining natural -phenomena, the causes of which had before been altogether -inscrutable. This is the case with regard to the diurnal variation -of the magnetic needle; a fact which as to its existence is -universal in all places, and which yet is so curiously diverse in -its course at different places. Dr. Faraday has shown that some of -the most remarkable of these diversities, and probably all, seem to -be accounted for by the different magnetic effects of air at -different temperatures: although, as I have already said, **(Book -xii.) the discovery of a decennial period in the diurnal changes of -magnetic declination shows that any explanation of those changes -which refers them to causes existing in the atmosphere must be very -incomplete.[40\B] - -[Note 40\B: _Researches_, Art. 2892.] - - - -{{625}} -BOOK XIV. - -CHEMISTRY. - -CHAPTER IX. - -THE ELECTRO-CHEMICAL THEORY. - - -AMONG the consequences of the Electro-chemical Theory, must be -ranged the various improvements which have been made in the voltaic -battery. Daniel introduced between the two metals a partition -permeable by chemical action, but such as to allow of two different -acid solutions being in contact with the two metals. Mr. Grove's -battery, in which the partition is of porous porcelain, and the -metals are platinum and amalgamated zinc, is one of the most -powerful hitherto known. Another has been constructed by Dr. Callan, -in which the negative or conducting plate is a cylinder of cast -iron, and the positive element a cylinder of amalgamated zinc placed -in a porous cell. This also has great energy. - - -_The Number of Elementary Substances._ - -There have not been, I believe, any well-established additions to -the list of the simple substances recognized by chemists. Indeed the -tendency at present appears to be rather to deny the separate -elementary character of some already announced as such substances. -Pelopium and Niobium were, as I have said, two of the new metals. -But Naumann, in his _Elemente der Mineralogie_ (4th ed. 1855), says, -in a foot note (page 25): "_Pelopium_ is happily again got rid of; -for Pelopic Acid and Niobic Acid possess the same Radical. -_Donarium_ had a still shorter existence." - -In the same way, when Hermann imagined that he had discovered a new -simple metallic substance in the mineral Samarskite from Miask, the -discovery was disproved by H. Rose (_Pogg. Ann._ B. 73, s. 449). {626} - -In general the insulation of the new simple substances, the metallic -bases of the earths, and the like,--their separation from their -combinations, and the exhibition of them in a metallic form--has been -a difficult chemical process, and has rarely been executed on any -considerable scale. But in the case of _Aluminium_, the basis of the -earth Alumina, the process of its extraction has recently been so much -facilitated, that the metal can be produced in abundance. This being -the case, it will probably soon be applied to special economical uses, -for which it is fitted by possessing special properties. - - - -{{626}} -BOOK XV. - -MINERALOGY. - - -BY the kindness of W. H. Miller, Esq., Professor of Mineralogy in -the University of Cambridge, I am able to add to this part the -following notices of books and memoirs. - -1. _Crystallography._ - -_Elemente der Krystallographie, nebst einer tabellarischen -Uebersicht der Mineralien nach der Krystallformen_, von Gustav Rose. -2. Auflage. Berlin, 1838. The crystallographic method here adopted -is, for the most part, that of Weiss. The method of this work has -been followed in - -_A System of Crystallography, with its Applications to Mineralogy_. -By John Joseph Griffin. Glasgow, 1841. Mr. Griffin has, however, -modified the notation of Rose. He has constructed a series of models -of crystalline forms. - -Frankenheim's _System der Krystalle_. 1842. This work adopts nearly -the Mohsian systems of crystallization. It contains Tables of the -chemical constitution, inclinations of the axis, and magnitude of -the axes of all the crystals of which a description was to be found, -including those formed in the laboratory, as well as those usually -called minerals; 713 in all. - -Fr. Aug. Quenstedt, _Methode der Krystallographie_, 1840, employs a -fanciful method of representing a crystal by projecting upon one -face of the crystal all the other faces. This invention appears to -be more curious than useful. - -Dr. Karl Naumann, who is spoken of in Chap. ix. of this Book, as the -author of the best of the Mixed Systems of Classification, published -also _Grundriss der Krystallographie_, Leipzig, 1826. In this and -other works he modifies the notation of Mohs in a very advantageous -manner. {628} - -Professor Dana, in his _System of Mineralogy_, New Haven (U.S.), -1837, follows Naumann for the most part, both in crystallography and -in mineral classification. In the latter part of the subject, he has -made the attempt, which in all cases is a source of confusion and of -failure, to introduce a whole system of new names of the members of -his classification. - -The geometry of crystallography has been investigated in a very -original manner by M. Bravais, in papers published in the Journal of -the Ecole Polytechnique, entitled _Mémoires sur les Systèmes formés -par des Points_. 1850. _Etudes Crystallographiques_. 1851. - -Hermann Kopp (_Einleitung in die Krystallographie_, Braunschweig. -1849) has given the description and measurement of the angles of a -large number of laboratory crystals. - -Rammelsberg (_Krystallographische Chemie_, Berlin, 1855) has -collected an account of the systems, simple forms and angles of all -the laboratory crystals of which he could obtain descriptions. - -Schabus of Vienna (_Bestimmung der Krystallgestalten **in Chemischen -Laboratorien erzeugten Producte_, Wien, 1855; a successful Prize -Essay) has given a description, accompanied by measurements, of 90 -crystalline species from his own observations. - -To these attempts made in other countries to simplify and improve -crystallography, I may add a remarkable Essay very recently made -here by Mr. Brooke, and suggested to him by his exact and familiar -knowledge of Mineralogy. It is to this effect. All the crystalline -forms of any given mineral species are derived from the _primitive -form_ of that species; and the degree of symmetry, and the -_parameters_, of this form determine the angles of all derivative -forms. But how is this primitive form selected and its parameters -determined? The selection of the kind of the primitive form depends -upon the _degree of symmetry_ which appears in all the derivative -forms; according to which they belong to the _rhombohedral_, -_prismatic_, _square pyramidal_, or some other _system_: and this -determination is commonly clear. But the parameters, or the angles, -of the primitive form, are commonly determined by the _cleavage_ of -the mineral. Is this a sufficient and necessary ground of such -determination? May not a simplification be effected, in some cases, -by taking some other parameters? by taking a primitive form which -belongs to the proper system, but which has some other angles than -those given by cleavage? Mr. Brooke has tried whether, for instance, -crystals of the rhombohedral system may not be referred with -advantage to primitive rhombohedrons which have, in all {629} the -species, nearly the same angles. The advantage to be obtained by -such a change would be the simplification of the laws of derivation -in the derivative forms: and therefore we have to ask, whether the -indices of derivation are smaller numbers in this way or with the -hitherto accepted fundamental angles. It appears to me, from the -examples given, that the advantage of simplicity in the indices is -on the side of the old system: but whether this be so or not, it was -a great benefit to crystallography to have the two methods compared. -Mr. Brooke's Essay is a Memoir presented to the Royal Society in 1856. - - -2. _Optical Properties of Minerals._ - -The _Handbuch der Optik_, von F. W. G. Radicke, Berlin, 1839, -contains a chapter on the optical properties of crystals. The -author's chief authority is Sir D. Brewster, as might be expected. - -M. Haidinger has devoted much attention to experiments on the -_pleochroism_ of minerals. He has invented an instrument which makes -the dichroism of minerals more evident by exhibiting the two colors -side by side. - -The pleochroism of minerals, and especially the remarkable clouds -that in the cases of Iolite, Andalusite, Augite, Epidote, and -Axinite, border the positions of either optical axis, have been most -successfully imitated by M. de Senarmont by means of artificial -crystallizations. (_Ann. de Chim._ 3 _Ser._ xli. p. 319.) - -M. Pasteur has found that Racemic Acid consists of two different -acids, having the same density and composition. The salts of these -acids, with bases of Ammonia and of Potassa, are hemihedral, the -hemihedral faces which occur in the one being wanting in the other. -The acids of these different crystals have circular polarization of -opposite kinds. (_Ann. de Chim._ 3 _Ser._ xxviii. 56, 99.) This -discovery was marked by the assignation of the Rumford Medal to M. -Pasteur in 1856. - -M. Marbach has discovered that crystals of chlorate of soda, which -apparently belongs to the cubic or tessular system, exhibit hemihedral -faces of a peculiar character; and that the crystals have circular -polarization of opposite kinds in accordance with the differences of -the plagihedral faces. (_Poggendorf's Annalen_, xci. 482.) - -M. Seybolt of Vienna has found a means of detecting plagihedral -faces in quartz crystals which do not reveal them externally. -(_Akad. d. Wissenschaft zu Wien_, B. xv. s. 59.) {630} - - -3. _Classification of Minerals._ - -In the _Philosophy of the Inductive Sciences_, B. VIII. C. iii., I -have treated of the Application of the Natural-history Method of -Classification to Mineralogy, and have spoken of the Systems of this -kind which have been proposed. I have there especially discussed the -system proposed in the treatise of M. Necker, _Le Règne Minéral -ramené aux Méthodes d'Histoire Naturelle_ (Paris, 1835). More -recently have been published M. Beudant's _Cours élémentaire -d'Histoire Naturelle, Minéralogie_ (Paris, 1841); and M. A. -Dufresnoy's _Traité de Minéralogie_ (Paris, 1845). Both these works -are so far governed by mere chemical views that they lapse into the -inconveniences and defects which are avoided in the best systems of -German mineralogists. - -The last mineral system of Berzelius has been developed by M. -Rammelsberg (Nürnberg, 1847). It is in principle such as we have -described it in the history. - -M. **Nordenskiöld's system (3rd Ed. 1849,) has been criticised by G. -Rose, who observes that it removes the defects of the system of -Berzelius only in part. He himself proposes what he calls a -"Krystallo-Chemisches System," in which the crystalline form -determines the genus and the chemical composition the species. His -classes are-- -1. Simple Substances. -2. Combinations of Sulphur, Selenium, Titanium, Arsenic, Antimony. -3. Chlorides, Fluorides, Bromides, Iodides. -4. Combinations with Oxygen. - -We have already said that for us, all chemical compounds are -_minerals_, in so far that they are included in our classifications. -The propriety of this mode of dealing with the subject is confirmed -by our finding that there is really no tenable distinction between -native minerals and the products of the laboratory. A great number -of eminent chemists have been employed in producing, by artificial -means, crystals which had before been known only as native products. - - - -{{631}} -BOOK XVI. - -CLASSIFICATORY SCIENCES. - -BOTANY. - - -FOR the purpose of giving to my reader some indication of the -present tendency of Botanical Science, I conceive that I cannot do -better than direct his attention to the reflections, procedure, and -reasonings which have been suggested by the most recent extensions -of man's knowledge of the vegetable world. And as a specimen of -these, I may take the labors of Dr. Joseph Hooker, on the Flora of -the Antarctic Regions,[41\B] and especially of New Zealand. Dr. -Hooker was the Botanist to an expedition commanded by Sir James -Ross, sent out mainly for the purpose of investigating the phenomena -of Terrestrial Magnetism near the South Pole; but directed also to -the improvement of Natural History. The extension of botanical -descriptions and classifications to a large mass of new objects -necessarily suggests wider views of the value of classes (genera, -species, &c.,) and the conclusions to be drawn from their constancy -or inconstancy. A few of Dr. Hooker's remarks may show the nature of -the views taken under such circumstances. - -[Note 41\B: _The Botany of the Antarctic Voyage of H. M. Discovery -Ships Erebus and Terror, in the years_ 1839-40. Published 1847. -_Flora Novæ Zelandiæ_. 1853.] - -I may notice, in the first place, (since this work is intended for -general rather than for scientific readers,) Dr. Hooker's testimony -to the value of a technical descriptive language for a -classificatory science--a Terminology, as it is called. He says, "It -is impossible to write Botanical descriptions which a person -ignorant of Botany can understand, although it is supposed by many -unacquainted with science that this can and should be done." And -hence, he says, the state of botanical science demands Latin -descriptions of the plants; and this is a lesson which he especially -urges upon the Colonists who study the indigenous plants. {632} - -Dr. Hooker's remarks on the limits of species, their dispersion and -variation, are striking and instructive. He is of opinion that -species vary more, and are more widely diffused, than is usually -supposed. Hence he conceives that the number of species has been -needlessly and erroneously multiplied, by distinguishing the -specimens which occur in different places, and vary in unessential -features. He says that though, according to the lowest estimate of -compilers, 100,000 is the commonly received number of known plants, -he thinks that half that number is much nearer the truth. "This," he -says, "may be well conceived, when it is notorious that nineteen -species have been made of the Common Potatoe, and many more of -_Solanum nigrum_ alone. _Pteris aquilina_ has given rise to numerous -book species; _Vernonia cinerea_ of India to fifteen at least. . . . -. . . Many more plants are common to most countries than is -supposed; I have found 60 New Zealand flowering plants and 9 Ferns -to be European ones, besides inhabiting numerous intermediate -countries. . . . . . So long ago as 1814, Mr. Brown drew attention -to the importance of such considerations, and gave a list of 150 -European plants common to Australia." - -As an example of the extent to which unessential differences may go, -he says (p. xvii.,) "The few remaining native Cedars of Lebanon may -be abnormal states of the tree which was once spread over the whole -of the Lebanon; for there are now growing in England varieties of it -which have no existence in a wild state. Some of them closely -resemble the Cedars of Atlas and of the Himalayas (_Deodar_;) and -the absence of any valid botanical differences tends to prove that -all, though generally supposed to be different species, are one." - -Still the great majority of the species of plants in those Southern -regions are peculiar. "There are upwards of 100 genera, subgenera, -or other well marked groups of plants, entirely or nearly confined -to New Zealand, Australia, and extra-tropical South America. They -are represented by one or more species in two or more of those -countries, and thus effect a botanical relationship or affinity -between them all which every botanist appreciates." - -In reference to the History of Botany, I have received corrections -and remarks from Dr. Hooker, with which I am allowed to enrich my -pages. - -"P. 359. Note ^3. ~= Note 3\16~ _Nelumbium speciosum_, the Lotus of -India. The _Nelumbium_ does not float, but raises both leaf and flower -several feet above the water: the _Nymphæa Lotus_ has floating leaves. -Both enter largely into the symbolism of the Hindoos, and are often -confounded. {633} - -"P. 362. Note ^5. ~= Note 13\16~ For _Arachnis_ read _Arachis_. The -_Arachidna_ of Theophrastus cannot, however, be the _Arachis_ or -ground-nut. - -"Pp. 388 and 394. For _Harlecamp_ read _Hartecamp_. - -"P. 394. For _Kerlen_ read _Kalm_. - -"P. 394. For _Asbech_ read _Osbeck_. - -"P. 386. _John Ray_. Ray was further the author of the present -Natural System in its most comprehensive sense. He first divided -plants into Flowerless and Flowering; and the latter into -Monocotyledonous and Dicotyledonous:--'Floriferas dividemus in -DICOTYLEDONES, quarum semina sata binis foliis, seminalibus dictis, -quæ cotyledonorum usum præstant, e terra exeunt, vel in binos saltem -lobos dividuntur, quamvis eos supra terram foliorum specie non -efferant; et MONOCOTYLEDONES, quæ nec folia bina seminalia efferunt -nec lobos binos condunt. Hæc divisio ad arbores etiam extendi -potest; siquidem Palmæ et congeneres hoc respectu eodem modo a -reliquis arboribus differunt quo Monocotyledones a reliquis herbis.' - -"P. 408. _Endogenous and Exogenous Growth._ The exact course of the -wood fibres which traverse the stems of both Monocotyledonous and -Dicotyledonous plants has been only lately discovered. In the -Monocotyledons, those fibres are collected in bundles, which follow -a very peculiar course:--from the base of each leaf they may be -followed downwards and inwards, towards the axis of the trunk, when -they form an arch with the convexity to the centre; and curving -outwards again reach the circumference, where they are lost amongst -the previously deposited fibres. The intrusion of the bases of these -bundles amongst those already deposited, causes the circumference of -the stem to be harder than the centre; and as all these arcs have a -short course (their chords being nearly equal), the trunk does not -increase in girth, and grows at the apex only. The wood-bundles are -here definite. In the Dicotyledonous trunks, the layers of wood run -in parallel courses from the base to the top of the trunk, each -externally to that last formed, and the trunk increases both in -height and girth; the wood-bundles are here indefinite. - -"With regard to the Cotyledons, though it is often difficult to -distinguish a Monocotyledonous Embryo from a Dicotyledonous, they -may always be discriminated when germinating. The Cotyledons, when -two or more, and primordial leaves (when no Cotyledons are visible) -of a Monocotyledon, are alternate; those of a Dicotyledon are -opposite. - -"A further physiological distinction between Monocotyledons and -{634} Dicotyledons is observed in germination, when the -Dicotyledonous radicle elongates and forms the root of the young -plant; the Monocotyledonous radicle does not elongate, but pushes -out rootlets from itself at once. Hence the not very good terms, -_exorhizal_ for Dicotyledonous, and _endorhizal_ for -Monocotyledonous. - -"The highest physiological generalization in the vegetable kingdom -is between _Phænogama_ and _Cryptogama_. In the former, -fertilization is effected by a pollen-tube touching the nucleus of -an ovule; in Cryptogams, the same process is effected by the contact -of a sperm-cell, usually ciliated (_antherozoid_), upon another kind -of cell called a germ-cell. In Phænogams, further, the organs of -fructification are all modified leaves; those of Cryptogams are not -homologous." (J. D. H.) - - -ZOOLOGY. - -I have exemplified the considerations which govern zoological -classification by quoting the reflexions which Cuvier gives us, as -having led him to his own classification of Fishes. Since the -varieties of Quadrupeds, or _Mammals_ (omitting whales, &c.), are -more familiar to the common reader than those of Fishes, I may -notice some of the steps in their classification; the more so as -some curious questions have recently arisen thereupon. - -Linnæus first divides Mammals into two groups, as they have Claws, -or Hoofs (_unguiculata_, _ungulata_.) But he then again divides them -into six orders (omitting whales, &c.), according to their number of -_incisor_, _laniary_, and _molar_ teeth; namely:-- -_Primates_. (Man, Monkey, &c.) -_Bruta_. (Rhinoceros, Elephant, &c.) -_Feræ_. (Dog, Cat, Bear, Mole, &c.) -_Glires_. (Mouse, Squirrel, Hare, &c.) -_Pecora_. (Camel, Giraffe, Stag, Goat, Sheep, Ox, &c.) -_Belluæ_. (Horse, Hippopotamus, Tapir, Sow, &c.) - -In the place of these, Cuvier, as I have stated in the _Philosophy_ -(_On the Language of Sciences_, Aphorism xvi.), introduced the -following orders: _Bimanes_, _Quadrumanes_, _Carnassiers_, -_Rongeurs_, _Edentés_, _Pachyderms_, _Ruminans_. Of these, the -_Carnassiers_ correspond to the _Feræ_ of Linnæus; the _Rongeurs_ to -his _Glires_; the _Edentés_ are a new order, taking the Sloths, -Ant-eaters, &c., from the _Bruta_ of Linnæus, the Megatherium from -extinct animals, and the Ornithorhynchus, &c., from the new animals -of Australia; the _Ruminans_ agree with the {635} _Pecora_; the -_Pachyderms_ include some of the _Bruta_ and the _Belluæ_, -comprehending also extinct animals, as _Anoplotherium_ and -_Palæotherium_. - -But the two orders of Hoofed Animals, the Pachyderms and the -Ruminants, form a group which is held by Mr. Owen to admit of a -better separation, on the ground of a character already pointed out -by Cuvier; namely, as to whether they are _two-toed_ or -_three-toed_. According to this view, the Horse is connected with -the Tapir, the Palæotherium, and the Rhinoceros, not only by his -teeth, but by his feet, for he has really three digits. And Cuvier -notices that in the two-toed or even-toed Pachyderms, the astragalus -bone has its face divided into two equal parts by a ridge; while in -the uneven-toed pachyderms it has a narrow cuboid face. Mr. Owen has -adopted this division of Pachyderms and Ruminants, giving the names -_artiodactyla_ and _perissodactyla_ to the two groups; the former -including the Ox, Hog, Peccary, Hippopotamus, &c.; the latter -comprehending the Horse, Tapir, Rhinoceros, Hyrax, &c. And thus the -Ruminants take their place as a subordinate group of the great -natural even-toed Division of the Hoofed Section of Mammals; and the -Horse is widely separated from them, inasmuch as he belongs to the -odd-toed division.[42\B] - -[Note 42\B: Owen, _Odontography_.] - -As we have seen, these modern classifications are so constructed as -to include extinct as well as living species of animals; and indeed -the species which have been discovered in a fossil state have tended -to fill up the gaps in the series of zoological forms which had -marred the systems of modern zoologists. This has been the case with -the division of which we are speaking. - -Mr. Owen had established two genera of extinct Herbivorous Animals, -on the strength of fossil remains brought from South -America:--_Toxodon_, and _Nesodon_. In a recent communication to the -Royal Society[43\B] he has considered the bearing of these genera -upon the divisions of odd-toed and even-toed animals. He had already -been led to the opinion that the three sections, _Proboscidea_, -_Perissodactyla_, and _Artiodactyla_, formed a natural division of -Ungulata; and he is now led to think that this division implies -another group, "a distinct division of the _Ungulata_, of equal -value, if not with the _Perissodactyla_ and _Artiodactyla_ at least -with the _Proboscidea_. This group he proposes to call _Toxodonta_. - -[Note 43\B: _Phil. Trans._, 1853.] - - - -{{636}} -BOOK XVII. - -PHYSIOLOGY AND COMPARATIVE ANATOMY. - -VEGETABLE MORPHOLOGY. - - -_Morphology in Linnæus._ - -I HAVE stated that Linnæus had some views on this subject. Dr. -Hooker conceives these views to be more complete and correct than is -generally allowed, though unhappily clothed in metaphorical language -and mixed with speculative matter. By his permission I insert some -remarks which I have received from him. - -The fundamental passage on this subject is in the _Systema Naturæ_; -in the Introduction to which work the following passage occurs:-- - -"Prolepsis (Anticipation) exhibits the mystery of the metamorphosis -of plants, by which the herb, which is the _larva_ or imperfect -condition, is changed into the declared fructification: for the -plant is capable of producing either a leafy herb or a -fructification. . . . . . - -"When a tree produces a flower, nature anticipates the produce of -five years where these come out all at once; forming of the -bud-leaves of the next year _bracts_; of those of the following -year, the _calyx_; of the following, the _corolla_; of the next, the -_stamina_; of the subsequent, the _pistils_, filled with the -granulated marrow of the seed, the terminus of the life of a -vegetable." - -Dr. Hooker says, "I derive my idea of his having a better knowledge -of the subject than most Botanists admit, not only from the -Prolepsis, but from his paper called _Reformatio Botanices_ (_Amœn. -Acad._ vol. vi.); a remarkable work, in respect of his candor in -speaking of his predecessors' labors, and the sagacity he shows in -indicating researches to be undertaken or completed. Amongst the -latter is V. 'Prolepsis plantarum, ulterius extendenda per earum -metamorphoses.' The last word occurs rarely in his _Prolepsis_; but -when it does it seems to me that he uses it as indicating a normal -change and not an accidental one. {637} - -"In the _Prolepsis_ the speculative matter, which Linnæus himself -carefully distinguishes as such, must be separated from the rest, -and this may I think be done in most of the sections. He starts with -explaining clearly and well the origin and position of buds, and -their constant presence, whether developed or not, in the axil of -the leaf: adding abundance of acute observations and experiments to -prove his statements. The leaf he declares to be the first effort of -the plant in spring: he proceeds to show, successively, that bracts, -calyx, corolla, stamens, and pistil are each of them metamorphosed -leaves, in every case giving MANY EXAMPLES, both from monsters and -from characters presented by those organs in their normal condition. - -"The (to me) obscure and critical part of the _Prolepsis_ was that -relating to the change of the style of _Carduus_ into two leaves. Mr. -Brown has explained this. He says it was a puzzle to him, till he went -to Upsala and consulted Fries and Wahlenberg, who informed him that -such monstrous _Cardui_ grew in the neighborhood, and procured him -some. Considering how minute and masked the organs of _Compositæ_ are, -it shows no little skill in Linnæus, and a very clear view of the -whole matter, to have traced the metamorphosis of all their floral -organs into leaves, except their stamens, of which he says, 'Sexti -anni folia e staminibus me non in compositis vidisse fateor, sed -illorum loco folia pistillacea, quæ in compositis aut plenis sunt -frequentissima.' I must say that nothing could well be clearer to my -mind than the full and accurate appreciation which Linnæus shows of -the whole series of phenomena, and their _rationale_. He over and over -again asserts that these organs are leaves, every one of them,--I do -not understand him to say that the prolepsis is an accidental change -of leaves into bracts, of bracts into calyx, and so forth. Even were -the language more obscure, much might be inferred from the wide range -and accuracy of the observations he details so scientifically. It is -inconceivable that a man should have traced the sequence of the -phenomena under so many varied aspects, and shown such skill, -knowledge, ingenuity, and accuracy in his methods of observing and -describing, and yet missed the _rationale_ of the whole. Eliminate the -speculative parts and there is not a single error of observation or -judgment; whilst his history of the developement of buds, leaves, and -floral organs, and of various other obscure matters of equal interest -and importance, are of a very high order of merit, are, in fact, for -the time profound. - -"There is nothing in all this that detracts from the merit of -Goethe's {638} re-discovery. With Goethe it was, I think, a -deductive process,--with Linnæus an inductive. Analyse Linnæus's -observations and method, and I think it will prove a good example of -inductive reasoning. - -"P. 473. Perhaps Professor Auguste St Hilaire of Montpellier should -share with De Candolle the honor of contributing largely to -establish the metamorphic doctrine;--their labors were -cotemporaneous. - -"P. **474. Linnæus pointed out that the pappus was calyx: 'Et -_pappum_ gigni ex quarti anni foliis, in jam nominatis -Carduis.'--_Prol. Plant._ 338." (_J. D. H._) - - - - -CHAPTER VII. - -ANIMAL MORPHOLOGY. - - -THE subject of Animal Morphology has recently been expanded into a -form strikingly comprehensive and systematic by Mr. Owen; and -supplied by him with a copious and carefully-chosen language; which -in his hands facilitates vastly the comparison and appreciation of -the previous labors of physiologists, and opens the way to new -truths and philosophical generalizations. Though the steps which -have been made had been prepared by previous anatomists, I will -borrow my view of them mainly from him; with the less scruple, -inasmuch as he has brought into full view the labors of his -predecessors. - -I have stated in the History that the skeletons of all vertebrate -animals are conceived to be reducible to a single Type, and the -skull reducible to a series of vertebræ. But inasmuch as this -reduction includes not only a detailed correspondence of the bones -of man with those of beasts, but also with those of birds, fishes, -and reptiles, it may easily be conceived that the similarities and -connexions are of a various and often remote kind. The views of such -relations, held by previous Comparative Anatomists, have led to the -designations of the bones of animals which have been employed in -anatomical descriptions; and these designations having been framed -and adopted by anatomists looking at the subject from different -sides, and having different views of analogies and relations, have -been very various and unstable; besides being often of cumbrous -length and inconvenient form. - -The corresponding parts in different animals are called _homologues_, -{639} a term first applied to anatomy by the philosophers of Germany; -and this term Mr. Owen adopts, to the exclusion of terms more loosely -denoting identity or similarity. And the Homology of the various bones -of vertebrates having been in a great degree determined by the labors -of previous anatomists, Mr. Owen has proposed names for each of the -bones: the condition of such names being, that the homologues in all -vertebrates shall be called by the same name, and that these names -shall be founded upon the terms and phrases in which the great -anatomists of the 16th, 17th, and 18th centuries expressed the results -of their researches respecting the human skeleton. These names, thus -selected, so far as concerned the bones of the Head of Fishes, one of -the most difficult cases of this Special Homology, he published in a -Table,[44\B] in which they were compared, in parallel columns, with -the names or phrases used for the like purpose by Cuvier, Agassiz, -Geoffroy, Hallman, Sœmmering, Meckel, and Wagner. As an example of the -considerations by which this selection of names was determined, I may -quote what he says with regard to one of these bones of the skull. - -[Note 44\B: _Lectures on Vertebrates_. 1846, p. 158. And _On the -Archetype and Homologies of the Vertebrate Skeleton_. 1848, p. 172.] - -"With regard to the 'squamosal' (_squamosum_. Lat. pars squamosa -ossis temporis.--Sœmmering), it might be asked why the term -'temporal' might not be retained for this bone. I reply, because -that term has long been, and is now universally, understood in human -anatomy to signify a peculiarly anthropotomical coalesced congeries -of bones, which includes the 'squamosal' together with the -'petrosal,' the 'tympanic,' the 'mastoid,' and the 'stylohyal.' It -seems preferable, therefore, to restrict the signification of the -term 'temporal' to the whole (in Man) of which the 'squamosal' is a -part. To this part Cuvier has unfortunately applied the term -'temporal' in one class, and 'jugal' in another; and he has also -transferred the term 'temporal' to a third equally distinct bone in -fishes; while to increase the confusion M. Agassiz has shifted the -name to a fourth different bone in the skull of fishes. Whatever, -therefore, may be the value assigned to the arguments which will be -presently set forth, as to the special homologies of the 'pars -squamosa ossis temporis,' I have felt compelled to express the -conclusion by a definite term, and in the present instance, have -selected that which recalls the best accepted anthropomorphical -designation of the part; although 'squamosal' must be understood and -applied in an arbitrary sense; and not as descriptive of a -scale-like {640} form; which in reference to the bone so called, is -rather its exceptional than normal figure in the vertebrate series." - -The principles which Mr. Owen here adopts in the selection of names -for the parts of the skeleton are wise and temperate. They agree -with the aphorisms concerning the language of science which I -published in the _Philosophy of the Inductive Sciences_; and Mr. -Owen does me the great honor of quoting with approval some of those -Aphorisms. I may perhaps take the liberty of remarking that the -system of terms which he has constructed, may, according to our -principles, be called rather a _Terminology_ **than a -_Nomenclature_: that is, they are analogous more nearly to the -_terms_ by which botanists describe the parts and organs of plants, -than to the _names_ by which they denote genera and species. As we -have seen in the History, plants as well as animals are subject to -morphological laws; and the names which are given to organs in -consequence of those laws are a part of the Terminology of the -science. Nor is this distinction between Terminology and -Nomenclature without its use; for the rules of prudence and -propriety in the selection of words in the two cases are different. -The Nomenclature of genera and species may be arbitrary and casual, -as is the case to a great extent in Botany and in Zoology, -especially of fossil remains; names being given, for instance, -simply as marks of honor to individuals. But in a Terminology, such -a mode of derivation is not admissible: some significant analogy or -idea must be adopted, at least as the origin of the name, though not -necessarily true in all its applications, as we have seen in the -case of the "squamosal" just quoted. This difference in the rules -respecting two classes of scientific words is stated in the -_Aphorisms_ xiii. and xiv. _concerning the Language of Science_. - -Such a Terminology of the bones of the skeletons of all vertebrates -as Mr. Owen has thus propounded, cannot be otherwise than an immense -acquisition to science, and a means of ascending from what we know -already to wider truths and new morphological doctrines. - -With regard to one of these doctrines, the resolution of the human -head into vertebræ, Mr. Owen now regards it as a great truth, and -replies to the objections of Cuvier and M. Agassiz, in detail.[45\B] -He gives a Table in which the Bones of the Head are resolved into -four vertebræ, which he terms the Occipital, Parietal, Frontal, and -Nasal Vertebra, respectively. These four vertebræ agree in general -with what Oken called the Ear-vertebra, the Jaw-vertebra, the -Eye-vertebra, and {641} the Nose-vertebra, in his work _On the -Signification of the Bones of the Skull_, published in 1807: and in -various degrees, with similar views promulgated by Spix (1815), -Bojanus (1818), Geoffroy (1824), Carus **(1828). And I believe that -these views, bold and fanciful as they at first appeared, have now -been accepted by most of the principal physiologists of our time. - -[Note 45\B: _Archetype and Homologies of the Vertebrate Skeleton_. -1848, p. 141.] - -But another aspect of this generalization has been propounded among -physiologists; and has, like the others, been extended, -systematized, and provided with a convenient language by Mr. Owen. -Since animal skeletons are thus made up of vertebræ and their parts -are to be understood as developements of the parts of vertebræ, -Geoffroy (1822), Carus (1828), Müller (1834), Cuvier (1836), had -employed certain terms while speaking of such developements; Mr. -Owen in the _Geological Transactions_ in 1838, while discussing the -osteology of certain fossil Saurians, used terms of this kind, which -are more systematic than those of his predecessors, and to which he -has given currency by the quantity of valuable knowledge and thought -which he has embodied in them. - -According to his Terminology,[46\B] a vertebra, in its typical -completeness, consists of a central part or _centrum_; at the back -of this, two plates (the _neural apophyses_) and a third outward -projecting piece (the _neural spine_), which three, with the -centrum, form a canal for the spinal marrow; at the front of the -centrum two other plates (the _hæmal apophyses_) and a projecting -piece, forming a canal for a vascular trunk. Further lateral -elements (_pleuro-apophyses_) and other projections, are in a -certain sense dependent on these principal bones; besides which the -vertebra may support _diverging appendages_. These parts of the -vertebra are fixed together, so that a vertebra is by some -anatomists described as a single bone; but the parts now mentioned -are usually developed from distinct and independent centres, and are -therefore called by Mr. Owen "autogenous" elements. - -[Note 46\B: _Archetype and Homologies of the Vertebrate Skeleton_. -1848, p. 81.] - -The _General_ Homology of the vertebral skeleton is the reference of -all the parts of a skeleton to their true types in a series of -vertebræ: and thus, as _special_ homology refers all the parts of -skeletons to a given type of skeleton, say that of Man, _general_ -homology refers all the parts of every skeleton, say that of Man, to -the parts of a series of Vertebræ. And thus as Oken propounded his -views of the Head as a resolution of the Problem of _the -Signification of the Bones of the Head_, {642} so have we in like -manner, for the purposes of General Homology, to solve the Problem -of _the Signification of Limbs_. The whole of the animal being a -string of vertebræ, what are arms and legs, hands and paws, claws -and fingers, wings and fins, and the like? This inquiry Mr. Owen has -pursued as a necessary part of his inquiries. In giving a public -lecture upon the subject in 1849,[47\B] he conceived that the phrase -which I have just employed would not be clearly apprehended by an -English Audience, and entitled his Discourse "On the _Nature_ of -Limbs:" and in this discourse he explained the modifications by -which the various kinds of limbs are derived from their rudiments in -an archetypal skeleton, that is, a mere series of vertebræ without -head, arms, legs, wings, or fins. - -[Note 47\B: _On the Nature of Limbs_, a discourse delivered at a -Meeting of the Royal Institution, 1849.] - - -_Final Causes_ - -It has been mentioned in the History that in the discussions which -took place concerning the Unity of Plan of animal structure, this -principle was in some measure put in opposition to the principle of -Final Causes: Morphology was opposed to Teleology. It is natural to -ask whether the recent study of Morphology has affected this -antithesis. - -If there be advocates of Final Causes in Physiology who would push -their doctrines so far as to assert that every feature and every -relation in the structure of animals have a purpose discoverable by -man, such reasoners are liable to be perpetually thwarted and -embarrassed by the progress of anatomical knowledge; for this -progress often shows that an arrangement which had been explained -and admired with reference to some purpose, exists also in cases -where the purpose disappears; and again, that what had been noted as -a special teleological arrangement is the result of a general -morphological law. Thus to take an example given by Mr. Owen: that -the ossification of the head originates in several centres, and thus -in its early stages admits of compression, has been pointed out as a -provision to facilitate the birth of viviparous animals; but our -view of this provision is disturbed, when we find that the same mode -of the formation of the bony framework takes place in animals which -are born from an egg. And the number of points from which -ossification begins, depends in a wider sense on the general -homology of the animal frame, according to which each part is -composed of a certain number of autogenous vertebral elements. In -this {643} way, the admission of a new view as to Unity of Plan will -almost necessarily displace or modify some of the old views -respecting Final Causes. - -But though the view of Final Causes is displaced, it is not -obliterated; and especially if the advocate of Purpose is also ready -to admit visible correspondences which have not a discoverable -object, as well as contrivances which have. And in truth, how is it -possible for the student of anatomy to shut his eyes to either of -these two evident aspects of nature? The arm and hand of man are -made for taking and holding, the wing of the sparrow is made for -flying; and each is adapted to its end with subtle and manifest -contrivance. There is plainly Design. But the arm of man and the -wing of the sparrow correspond to each other in the most exact -manner, bone for bone. Where is the Use or the Purpose of this -correspondence? If it be said that there may be a purpose though we -do not see it, that is granted. But Final Causes _for us_ are -contrivances of which _we see_ the end; and nothing is added to the -evidence of Design by the perception of a unity of plan which in no -way tends to promote the design. - -It may be said that the design appears in the modification of the -plan in special ways for special purposes;--that the vertebral plan -of an animal being given, the fore limbs are modified in Man and in -Sparrow, as the nature and life of each require. And this is truly -said; and is indeed the truth which we are endeavoring to bring into -view:--that there are in such speculations, two elements; one given, -the other to be worked out from our examination of the case; the -_datum_ and the _problem_; the homology and the teleology. - -Mr. Owen, who has done so much for the former of these portions of -our knowledge, has also been constantly at the same time -contributing to the other. While he has been aiding our advances -towards the Unity of Nature, he has been ever alive to the -perception of an Intelligence which pervades Nature. While his -morphological doctrines have moved the point of view from which he -sees Design, they have never obscured his view of it, but, on the -contrary, have led him to present it to his readers in new and -striking aspects. Thus he has pointed out the final purposes in the -different centres of ossification of the long bones of the limbs of -mammals, and shown how and why they differ in this respect from -reptiles (_Archetype_, p. 104). And in this way he has been able to -point out the insufficiency of the rule laid down both by Geoffroy -St. Hilaire and Cuvier, for ascertaining the true number of bones in -each species. {644} - -Final Causes, or Evidences of Design, appear, as we have said, not -merely as contrivances for evident purposes, but as modifications of -a given general Plan for special given ends. If the general Plan be -discovered after the contrivance has been noticed, the discovery may -at first seem to obscure our perception of Purpose; but it will soon -be found that it merely transfers us to a higher point of view. The -adaptation of the Means to the End remains, though the Means are -parts of a more general scheme than we were aware of. No -generalization of the Means can or ought permanently to shake our -conviction of the End; because we must needs suppose that the -Intelligence which contemplates the End is an intelligence which can -see at a glance along a vista of Means, however long and complex. -And on the other hand, no special contrivance, however clear be its -arrangement, can be unconnected with the general correspondences and -harmonies by which all parts of nature are pervaded and bound -together. And thus no luminous teleological point can be -extinguished by homology; nor, on the other hand, can it be detached -from the general expanse of homological light. - -The reference to Final Causes is sometimes spoken of as -unphilosophical, in consequence of Francis Bacon's comparison of -Final Causes in Physics to Vestal Virgins devoted to God, and -barren. I have repeatedly shown that, in Physiology, almost all the -great discoveries which have been made, have been made by the -assumption of a purpose in animal structures. With reference to -Bacon's simile, I have elsewhere said that if he had had occasion to -develope its bearings, full of latent meaning as his similes so -often are, he would probably have said that to those Final Causes -barrenness was no reproach, seeing they ought to be not the Mothers -but the Daughters of our Natural Sciences; and that they were -barren, not by imperfection of their nature, but in order that they -might be kept pure and undefiled, and so fit ministers in the temple -of God. I might add that in Physiology, if they are not Mothers, -they are admirable Nurses; skilful and sagacious in perceiving the -signs of pregnancy, and helpful in bringing the Infant Truth into -the light of day. - -There is another aspect of the doctrine of the Archetypal Unity of -Composition of Animals, by which it points to an Intelligence from -which the frame of nature proceeds; namely this:--that the Archetype -of the Animal Structure being of the nature of an _Idea_, implies a -mind in which this Idea existed; and that thus Homology itself -points the way to the Divine Mind. But while we acknowledge the full -{645} value of this view of theological bearing of physiology, we -may venture to say that it is a view quite different from that which -is described by speaking of "Final Causes," and one much more -difficult to present in a lucid manner to ordinary minds. - - - -{{646}} -BOOK XVIII. - -GEOLOGY. - - -WITH regard to Geology, as a Palætiological Science, I do not know -that any new light of an important kind has been thrown upon the -general doctrines of the science. Surveys and examinations of -special phenomena and special districts have been carried on with -activity and intelligence; and the animals of which the remains -people the strata, have been reconstructed by the skill and -knowledge of zoologists:--of such reconstructions we have, for -instance, a fine assemblage in the publications of the -Palæontological Society. But the great questions of the manner of -the creation and succession of animal and vegetable species upon the -earth remain, I think, at the point at which they were when I -published the last edition of the History. - -I may notice the views propounded by some chemists of certain -bearings of Mineralogy upon Geology. As we have, in mineral masses, -organic remains of former organized beings, so have we crystalline -remains of former crystals; namely, what are commonly called -_pseudomorphoses_--the shape of one crystal in the substance of -another. M. G. Bischoff[48\B] considers the study of pseudomorphs as -important in geology, and as frequently the only means of tracing -processes which have taken place and are still going on in the -mineral kingdom. - -[Note 48\B: _Chemical and Physical Geology_.] - -I may notice also Professor Breithaupt's researches on the order of -succession of different minerals, by observing the mode in which -they occur and the order in which different crystals have been -deposited, promise to be of great use in following out the -geological changes which the crust of the globe has undergone. (_Die -Paragenesis der Mineralien_. Freiberg. 1849.) - -In conjunction with these may be taken M. de Senarmont's experiments -on the formation of minerals in veins; and besides Bischoff's {647} -_Chemical Geology_, Sartorius von Walterhausen's Observations on the -occurrence of minerals in Amygdaloid. - -As a recent example of speculations concerning Botanical -Palætiology, I may give Dr. Hooker's views of the probable history -of the Flora of the Pacific. - -In speculating upon this question, Dr. Hooker is led to the -discussion of geological doctrines concerning the former continuity -of tracts of land which are now separate, the elevation of low lands -into mountain ranges in the course of ages, and the like. We have -already seen, in the speculations of the late lamented Edward -Forbes, (see Book xviii. chap. vi. of this History,) an example of a -hypothesis propounded to account for the existing Flora of England: -a hypothesis, namely, of a former Connexion of the West of the -British Isles with Portugal, of the Alps of Scotland with those of -Scandinavia, and of the plains of East Anglia with those of Holland. -In like manner Dr. Hooker says (p. xxi.) that he was led to -speculate on the possibility of the plants of the Southern Ocean -being the remains of a Flora that had once spread over a larger and -more continuous tract of land than now exists in the ocean; and that -the peculiar Antarctic genera and species may be the vestiges of a -Flora characterized by the predominance of plants which are now -scattered throughout the Southern islands. He conceives this -hypothesis to be greatly supported by the observations and -reasonings of Mr. Darwin, tending to show that such risings and -sinkings are in active progress over large portions of the -continents and islands of the Southern hemisphere: and by the -speculations of Sir C. Lyell respecting the influence of climate on -the migrations of plants and animals, and the influence of -geological changes upon climate. - -In Zoology I may notice (following Mr. Owen)[49\B] recent -discoveries of the remains of the animals which come nearest to man -in their structure. At the time of Cuvier's death, in 1832, no -evidence had been obtained of fossil Quadrumana; and he supposed -that these, as well as Bimana, were of very recent introduction. -Soon after, in the oldest (eocene) tertiary deposits of Suffolk, -remains were found proving the existence of a monkey of the genus -Macacus. In the Himalayan tertiaries were found petrified bones of a -Semnopithecus; in Brazil, remains of an extinct platyrhine monkey of -great size; and lastly, in the middle tertiary series of the South -of France, was discovered a fragment of the jaw of the long-armed -ape (_Hylobates_). But no fossil human {648} remains have been -discovered in the regularly deposited layers of any divisions (not -even the pleiocene) of the tertiary series; and thus we have evidence -that the placing of man on the earth was the last and peculiar act -of Creation. - -[Note 49\B: _Brit. Asso._ 1854, p. 112.] - - -THE END. - - - - -Transcriber's Notes - -Whewell's book was originally published in 3 volumes in London in -1837. A second edition appeared in 1847, and a third in 1857. A -2-volume version of the 3rd edition was published in New York in 1858, -reprinted 1875. This Project Gutenberg text, combining both volumes -in sequence, was derived from the 1875 version, relying upon resources -kindly provided by the Internet Archive. - -Three items have been added to the Contents of the First Volume; -they are marked off by ~ ~, as are any other additions to the text. - -Printed page numbers have been transcribed in { }; pages without a -printed number have been indicated by {{ }}. Where words were -hyphenated across pages, the number has been placed before the word. - -Fractions have been transcribed as numerator/denominator, occasionally -using parentheses to disambiguate. The original sometimes has -numerator over a line with denominator below, at other times numerator -hyphen denominator. Superscripted characters are marked by a ^ before -the character. - -Footnotes in the original text were numbered by chapter; here they -have been numbered by Book (the number of which is given after a \, -for the two appendices to the 3rd edition A has been used for volume -1, B for volume 2). They are placed after the paragraph in which -they occur, and are transcribed [Note m\n: ...]. Footnote anchors -are transcribed [m\n]. All other square brackets are in the original -text. - -One difficult item is the use of numbers within a ring as names of -asteroids; here the numbers are in ( ). - -Corrections to the text have been marked with **. They are listed -below, and were usually confirmed by reference to English printings -of the text. Inconsistencies, especially with respect to accents and -formatting, are numerous and have in general not been adjusted, though -Greek quotations have been checked against other versions where -available. Nor have Whewell's unbalanced quotation marks been -modernised. The English versions have been used to restore Whewell's -"gesperrt" emphases in some Greek passages. - -Location 1875 Text Correction -Vol. 1 -p. 25 Cruikshanks Cruickshank -p. 30 19 65 -p. 30 : ; -p. 33 (thrice) 184 182 -p. 36 184 182 -p. 71 Arisotelians Aristotelians -p. 75 " -p. 79 σερματικοὶ σπερματικοὶ -p. 101 " -note 1\2 6 7 -p. 175 ecliptical elliptical -note 1\4 iv. vi. -note 75\4 Summæ Summa -note 10\5 iii. iv. -p. 271 (twice) Mastlin Mæstlin -p. 282 _Dialogo "_Dialogo -p. 284 semil semel -p. 287 endeaver endeavor -note 7\6 1. i. -note 8\6 Dial. i. p. 40. p. 141. -note 9\6 _Speculutionum _Speculationum -p. 325 Gualtier Gualter -p. 341 and 342 Marsenne Mersenne -p. 374 of -p. 377 prependicularity perpendicularity -p. 403 " -note 30\7 Cosmotheros Cosmotheoros -p. 415 _casual_ _causal_ -p. 416 ) -p. 419 ] -p. 431 _a_ a -note 69\7 1453 1753 -note 84\7 Ast. Ass. -p. 463 Philosphical Philosophical -p. 471 ] -p. 564 prevalance prevalence -Vol. 2 -p. 50 Ὑφιφάνη Ὑψιφάνη - ἄρισπον ἄριστον - οὔδιον εὔδιον -p. 84 ] -p. 85 viii. vii. -p. 115 1853 1823 -p. 149 , . -p. 162 Footnote number missing in text -p. 201 stream steam -p. 213 and note 39\11 same number as the preceding note -p. 240 Cruikshanks Cruickshank -note 18\13 Mass-bestimmengen Mass-bestimmungen -p. 264 in is -note 11\14 _Stahl Stahl -p. 295 the _the -note 78\14 the entire text of this note is missing -p. 301 lecture lectures -note 87\14 96. 963. -note 92\14 153 853 -p. 330 Angels Angles -p. 336 given giving -p. 343 " -p. 394 Surien Surian -p. 411 _Couérs Elmentaire_ _Cours Elémentaire_ -note 136\16 Εἴδην Εἴδη -p. 450 dependance dependence -p. 457 sucking-beasts suckling-beasts -note 80\17 ählich ähnlich -note 89\17 229 129 -p. 477 osseuze osseuse -note 119\17 229 299* -p. 508 Lythophylaccii Lythophylacii -p. 511 Stukely Stukeley -note 18\18 Géognastique Géognostique -p. 513 Sabapennine Sub-Apennine -p. 514 Schlotheim Schlottheim -p. 530 , ( ,) -p. 556 Poissons Poisson's -p. 620 iv. vii. -p. 624 [ ( -p. 628 in (not italicised in text) -p. 630 Nordenskiold's Nordenskiöld's -p. 638 390 474 -p. 640 then than -p. 641 1828 (1828) - -* This is the page number given in the English edition. 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