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+The Project Gutenberg EBook of Popular scientific lectures, by Ernst Mach
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Popular scientific lectures
+
+Author: Ernst Mach
+
+Translator: Thomas Joseph McCormack
+
+Release Date: April 22, 2012 [EBook #39508]
+
+Language: English
+
+Character set encoding: UTF-8
+
+*** START OF THIS PROJECT GUTENBERG EBOOK POPULAR SCIENTIFIC LECTURES ***
+
+
+
+
+Produced by Anna Hall, Albert László and the Online
+Distributed Proofreading Team at http://www.pgdp.net (This
+file was produced from images generously made available
+by The Internet Archive)
+
+
+
+
+
+
+
+
+
+POPULAR SCIENTIFIC LECTURES.
+
+
+
+
+BY THE SAME AUTHOR.
+
+
+THE SCIENCE OF MECHANICS. Translated from the Second German Edition
+    by T. J. McCormack. 250 Cuts and Illustrations. 534 Pages. Half
+    Morocco, Gilt Top. Price, $2.50.
+
+CONTRIBUTIONS TO THE ANALYSIS OF THE SENSATIONS. Translated by C. M.
+    Williams. With Notes and New Additions by the Author. 200 Pages.
+    36 Cuts. Price, $1.00.
+
+POPULAR SCIENTIFIC LECTURES. Translated by T. J. McCormack. Third
+    Revised and Enlarged Edition. 411 Pages. 59 Cuts. Cloth, $1.50;
+    Paper, 50 cents.
+
+THE OPEN COURT PUBLISHING CO.,
+324 DEARBORN ST., CHICAGO.
+
+
+
+
+  POPULAR SCIENTIFIC LECTURES
+
+  BY ERNST MACH
+
+  FORMERLY PROFESSOR OF PHYSICS IN THE UNIVERSITY OF PRAGUE, NOW
+  PROFESSOR OF THE HISTORY AND THEORY OF INDUCTIVE SCIENCE IN THE
+  UNIVERSITY OF VIENNA
+
+  TRANSLATED BY THOMAS J. McCORMACK
+
+  THIRD EDITION, REVISED AND ENLARGED
+
+  WITH FIFTY-NINE CUTS AND DIAGRAMS
+
+  CHICAGO THE OPEN COURT PUBLISHING COMPANY
+
+  FOR SALE BY
+
+  KEGAN PAUL, TRENCH, TRUEBNER & CO., LONDON
+
+  1898
+
+
+
+
+  COPYRIGHT
+
+  BY THE OPEN COURT PUBLISHING CO.
+
+  Pages   1-258 }
+                } in 1894.
+  Pages 338-374 }
+  Pages 259-281 in 1896.
+  Pages 282-308 in 1897.
+  Pages 309-337 in 1898.
+
+
+
+
+AUTHOR'S PREFACE TO THE FIRST EDITION.
+
+
+Popular lectures, owing to the knowledge they presuppose, and the time
+they occupy, can afford only a _modicum_ of instruction. They must
+select for this purpose easy subjects, and restrict themselves to the
+exposition of the simplest and the most essential points. Nevertheless,
+by an appropriate choice of the matter, the _charm_ and the _poetry_ of
+research can be conveyed by them. It is only necessary to set forth the
+attractive and the alluring features of a problem, and to show what
+broad domains of fact can be illuminated by the light radiating from the
+solution of a single and ofttimes unobtrusive point.
+
+Furthermore, such lectures can exercise a favorable influence by showing
+the substantial sameness of scientific and every-day thought. The
+public, in this way, loses its shyness towards scientific questions, and
+acquires an interest in scientific work which is a great help to the
+inquirer. The latter, in his turn, is brought to understand that his
+work is a small part only of the universal process of life, and that the
+results of his labors must redound to the benefit not only of himself
+and a few of his associates, but to that of the collective whole.
+
+I sincerely hope that these lectures, in the present excellent
+translation, will be productive of good in the direction indicated.
+
+    E. MACH.
+
+PRAGUE, December, 1894.
+
+
+
+
+TRANSLATOR'S NOTE TO THE THIRD EDITION.
+
+
+The present third edition of this work has been enlarged by the addition
+of a new lecture, "On Some Phenomena Attending the Flight of
+Projectiles." The additions to the second consisted of the following
+four lectures and articles: Professor Mach's Vienna Inaugural Lecture,
+"The Part Played by Accident in Invention and Discovery," the lecture on
+"Sensations of Orientation," recently delivered and summing up the
+results of an important psychological investigation, and two historical
+articles (see Appendix) on Acoustics and Sight.
+
+The lectures extend over a long period, from 1864 to 1898, and differ
+greatly in style, contents, and purpose. They were first published in
+collected form in English; afterwards two German editions were called
+for.
+
+As the dates of the first five lectures are not given in the footnotes
+they are here appended. The first lecture, "On the Forms of Liquids,"
+was delivered in 1868 and published with that "On Symmetry" in 1872
+(Prague). The second and third lectures, on acoustics, were first
+published in 1865 (Graz); the fourth and fifth, on optics, in 1867
+(Graz). They belong to the earliest period of Professor Mach's
+scientific activity, and with the lectures on electrostatics and
+education will more than realise the hope expressed in the author's
+Preface.
+
+The eighth, ninth, tenth, eleventh, and twelfth lectures are of a more
+philosophical character and deal principally with the methods and nature
+of scientific inquiry. In the ideas summarised in them will be found one
+of the most important contributions to the theory of knowledge made in
+the last quarter of a century. Significant hints in psychological
+method, and exemplary specimen-researches in psychology and physics, are
+also presented; while in physics many ideas find their first discussion
+that afterwards, under other names and other authorship, became
+rallying-cries in this department of inquiry.
+
+All the proofs of this translation have been read by Professor Mach
+himself.
+
+    T. J. MCCORMACK.
+
+LA SALLE, ILL., May, 1898.
+
+
+
+
+TABLE OF CONTENTS.
+
+
+  The Forms of Liquids                                             1
+  The Fibres of Corti                                             17
+  On the Causes of Harmony                                        32
+  The Velocity of Light                                           48
+  Why Has Man Two Eyes?                                           66
+  On Symmetry                                                     89
+  On the Fundamental Concepts of Electrostatics                  107
+  On the Principle of the Conservation of Energy                 137
+  On the Economical Nature of Physical Inquiry                   186
+  On Transformation and Adaptation in Scientific Thought         214
+  On the Principle of Comparison in Physics                      236
+  On the Part Played by Accident in Invention and Discovery      259
+  On Sensations of Orientation                                   282
+  On Some Phenomena Attending the Flight of Projectiles          309
+  On Instruction in the Classics and the Mathematico-Physical
+      Sciences                                                   338
+  Appendixes.
+      I. A Contribution to the History of Acoustics              375
+      II. Remarks on the Theory of Spatial Vision                386
+  Index                                                          393
+
+
+
+
+THE FORMS OF LIQUIDS.
+
+
+What thinkest thou, dear Euthyphron, that the holy is, and the just, and
+the good? Is the holy holy because the gods love it, or are the gods
+holy because they love the holy? By such easy questions did the wise
+Socrates make the market-place of Athens unsafe and relieve presumptuous
+young statesmen of the burden of imaginary knowledge, by showing them
+how confused, unclear, and self-contradictory their ideas were.
+
+You know the fate of the importunate questioner. So called good society
+avoided him on the promenade. Only the ignorant accompanied him. And
+finally he drank the cup of hemlock--a lot which we ofttimes wish would
+fall to modern critics of his stamp.
+
+What we have learned from Socrates, however,--our inheritance from
+him,--is scientific criticism. Every one who busies himself with science
+recognises how unsettled and indefinite the notions are which he has
+brought with him from common life, and how, on a minute examination of
+things, old differences are effaced and new ones introduced. The
+history of science is full of examples of this constant change,
+development, and clarification of ideas.
+
+But we will not linger by this general consideration of the fluctuating
+character of ideas, which becomes a source of real uncomfortableness,
+when we reflect that it applies to almost every notion of life. Rather
+shall we observe by the study of a physical example how much a thing
+changes when it is closely examined, and how it assumes, when thus
+considered, increasing definiteness of form.
+
+The majority of you think, perhaps, you know quite well the distinction
+between a liquid and a solid. And precisely persons who have never
+busied themselves with physics will consider this question one of the
+easiest that can be put. But the physicist knows that it is one of the
+most difficult. I shall mention here only the experiments of Tresca,
+which show that solids subjected to high pressures behave exactly as
+liquids do; for example, may be made to flow out in the form of jets
+from orifices in the bottoms of vessels. The supposed difference of kind
+between liquids and solids is thus shown to be a mere difference of
+degree.
+
+The common inference that because the earth is oblate in form, it was
+originally fluid, is an error, in the light of these facts. True, a
+rotating sphere, a few inches in diameter will assume an oblate form
+only if it is very soft, for example, is composed of freshly kneaded
+clay or some viscous stuff. But the earth, even if it consisted of the
+rigidest stone, could not help being crushed by its tremendous weight,
+and must perforce behave as a fluid. Even our mountains could not extend
+beyond a certain height without crumbling. The earth _may_ once have
+been fluid, but this by no means follows from its oblateness.
+
+The particles of a liquid are displaced on the application of the
+slightest pressure; a liquid conforms exactly to the shapes of the
+vessels in which it is contained; it possesses no form of its own, as
+you have all learned in the schools. Accommodating itself in the most
+trifling respects to the conditions of the vessel in which it is placed,
+and showing, even on its surface, where one would suppose it had the
+freest play, nothing but a polished, smiling, expressionless
+countenance, it is the courtier _par excellence_ of the natural bodies.
+
+Liquids have no form of their own! No, not for the superficial observer.
+But persons who have observed that a raindrop is round and never
+angular, will not be disposed to accept this dogma so unconditionally.
+
+It is fair to suppose that every man, even the weakest, would possess a
+character, if it were not too difficult in this world to keep it. So,
+too, we must suppose that liquids would possess forms of their own, if
+the pressure of the circumstances permitted it,--if they were not
+crushed by their own weights.
+
+An astronomer once calculated that human beings could not exist on the
+sun, apart from its great heat, because they would be crushed to pieces
+there by their own weight. The greater mass of this body would also
+make the weight of the human body there much greater. But on the moon,
+because here we should be much lighter, we could jump as high as the
+church-steeples without any difficulty, with the same muscular power
+which we now possess. Statues and "plaster" casts of syrup are
+undoubtedly things of fancy, even on the moon, but maple-syrup would
+flow so slowly there that we could easily build a maple-syrup man on the
+moon, for the fun of the thing, just as our children here build
+snow-men.
+
+Accordingly, if liquids have no form of their own with us on earth, they
+have, perhaps, a form of their own on the moon, or on some smaller and
+lighter heavenly body. The problem, then, simply is to get rid of the
+effects of gravity; and, this done, we shall be able to find out what
+the peculiar forms of liquids are.
+
+The problem was solved by Plateau of Ghent, whose method was to immerse
+the liquid in another of the same specific gravity.[1] He employed for
+his experiments oil and a mixture of alcohol and water. By Archimedes's
+well-known principle, the oil in this mixture loses its entire weight.
+It no longer sinks beneath its weight; its formative forces, be they
+ever so weak, are now in full play.
+
+As a fact, we now see, to our surprise, that the oil, instead of
+spreading out into a layer, or lying in a formless mass, assumes the
+shape of a beautiful and perfect sphere, freely suspended in the
+mixture, as the moon is in space. We can construct in this way a sphere
+of oil several inches in diameter.
+
+If, now, we affix a thin plate to a wire and insert the plate in the oil
+sphere, we can, by twisting the wire between our fingers, set the whole
+ball in rotation. Doing this, the ball assumes an oblate shape, and we
+can, if we are skilful enough, separate by such rotation a ring from the
+ball, like that which surrounds Saturn. This ring is finally rent
+asunder, and, breaking up into a number of smaller balls, exhibits to us
+a kind of model of the origin of the planetary system according to the
+hypothesis of Kant and Laplace.
+
+[Illustration: Fig. 1.]
+
+Still more curious are the phenomena exhibited when the formative forces
+of the liquid are partly disturbed by putting in contact with the
+liquid's surface some rigid body. If we immerse, for example, the wire
+framework of a cube in our mass of oil, the oil will everywhere stick to
+the wire framework. If the quantity of oil is exactly sufficient we
+shall obtain an oil cube with perfectly smooth walls. If there is too
+much or too little oil, the walls of the cube will bulge out or cave in.
+In this manner we can produce all kinds of geometrical figures of oil,
+for example, a three-sided pyramid, a cylinder (by bringing the oil
+between two wire rings), and so on. Interesting is the change of form
+that occurs when we gradually suck out the oil by means of a glass tube
+from the cube or pyramid. The wire holds the oil fast. The figure grows
+smaller and smaller, until it is at last quite thin. Ultimately it
+consists simply of a number of thin, smooth plates of oil, which extend
+from the edges of the cube to the centre, where they meet in a small
+drop. The same is true of the pyramid.
+
+[Illustration: Fig. 2.]
+
+The idea now suggests itself that liquid figures as thin as this, and
+possessing, therefore, so slight a weight, cannot be crushed or deformed
+by their weight; just as a small, soft ball of clay is not affected in
+this respect by its weight. This being the case, we no longer need our
+mixture of alcohol and water for the production of figures, but can
+construct them in the open air. And Plateau, in fact, found that these
+thin figures, or at least very similar ones, could be produced in the
+air, by dipping the wire nets described in a solution of soap and water
+and quickly drawing them out again. The experiment is not difficult. The
+figure is formed of itself. The preceding drawing represents to the eye
+the forms obtained with cubical and pyramidal nets. In the cube, thin,
+smooth films of soap-suds proceed from the edges to a small, quadratic
+film in the centre. In the pyramid, a film proceeds from each edge to
+the centre.
+
+These figures are so beautiful that they hardly admit of appropriate
+description. Their great regularity and geometrical exactness evokes
+surprise from all who see them for the first time. Unfortunately, they
+are of only short duration. They burst, on the drying of the solution in
+the air, but only after exhibiting to us the most brilliant play of
+colors, such as is often seen in soap-bubbles. Partly their beauty of
+form and partly our desire to examine them more minutely induces us to
+conceive of methods of endowing them with permanent form. This is very
+simply done.[2] Instead of dipping the wire nets in solutions of soap,
+we dip them in pure melted colophonium (resin). When drawn out the
+figure at once forms and solidifies by contact with the air.
+
+It is to be remarked that also solid fluid-figures can be constructed
+in the open air, if their weight be light enough, or the wire nets of
+very small dimensions. If we make, for example, of very fine wire a
+cubical net whose sides measure about one-eighth of an inch in length,
+we need simply to dip this net in water to obtain a small solid cube of
+water. With a piece of blotting paper the superfluous water may be
+easily removed and the sides of the cube made smooth.
+
+Yet another simple method may be devised for observing these figures. A
+drop of water on a greased glass plate will not run if it is small
+enough, but will be flattened by its weight, which presses it against
+its support. The smaller the drop the less the flattening. The smaller
+the drop the nearer it approaches the form of a sphere. On the other
+hand, a drop suspended from a stick is elongated by its weight. The
+undermost parts of a drop of water on a support are pressed against the
+support, and the upper parts are pressed against the lower parts because
+the latter cannot yield. But when a drop falls freely downward all its
+parts move equally fast; no part is impeded by another; no part presses
+against another. A freely falling drop, accordingly, is not affected by
+its weight; it acts as if it were weightless; it assumes a spherical
+form.
+
+A moment's glance at the soap-film figures produced by our various wire
+models, reveals to us a great multiplicity of form. But great as this
+multiplicity is, the common features of the figures also are easily
+discernible.
+
+    "All forms of Nature are allied, though none is the same as the other;
+    Thus, their common chorus points to a hidden law."
+
+This hidden law Plateau discovered. It may be expressed, somewhat
+prosily, as follows:
+
+1) If several plane liquid films meet in a figure they are always three
+in number, and, taken in pairs, form, each with another, nearly equal
+angles.
+
+2) If several liquid edges meet in a figure they are always four in
+number, and, taken in pairs, form, each with another, nearly equal
+angles.
+
+This is a strange law, and its reason is not evident. But we might apply
+this criticism to almost all laws. It is not always that the motives of
+a law-maker are discernible in the form of the law he constructs. But
+our law admits of analysis into very simple elements or reasons. If we
+closely examine the paragraphs which state it, we shall find that their
+meaning is simply this, that the surface of the liquid assumes the shape
+of smallest area that is possible under the circumstances.
+
+If, therefore, some extraordinarily intelligent tailor, possessing a
+knowledge of all the artifices of the higher mathematics, should set
+himself the task of so covering the wire frame of a cube with cloth that
+every piece of cloth should be connected with the wire and joined with
+the remaining cloth, and should seek to accomplish this feat with the
+greatest saving of material, he would construct no other figure than
+that which is here formed on the wire frame in our solution of soap and
+water. Nature acts in the construction of liquid figures on the
+principle of a covetous tailor, and gives no thought in her work to the
+fashions. But, strange to say, in this work, the most beautiful fashions
+are of themselves produced.
+
+The two paragraphs which state our law apply primarily only to soap-film
+figures, and are not applicable, of course, to solid oil-figures. But
+the principle that the superficial area of the liquid shall be the least
+possible under the circumstances, is applicable to all fluid figures. He
+who understands not only the letter but also the reason of the law will
+not be at a loss when confronted with cases to which the letter does not
+accurately apply. And this is the case with the principle of least
+superficial area. It is a sure guide for us even in cases in which the
+above-stated paragraphs are not applicable.
+
+Our first task will now be, to show by a palpable illustration the mode
+of formation of liquid figures by the principle of least superficial
+area. The oil on the wire pyramid in our mixture of alcohol and water,
+being unable to leave the wire edges, clings to them, and the given mass
+of oil strives so to shape itself that its surface shall have the least
+possible area. Suppose we attempt to imitate this phenomenon. We take a
+wire pyramid, draw over it a stout film of rubber, and in place of the
+wire handle insert a small tube leading into the interior of the space
+enclosed by the rubber (Fig. 3). Through this tube we can blow in or
+suck out air. The quantity of air in the enclosure represents the
+quantity of oil. The stretched rubber film, which, clinging to the wire
+edges, does its utmost to contract, represents the surface of the oil
+endeavoring to decrease its area. By blowing in, and drawing out the
+air, now, we actually obtain all the oil pyramidal figures, from those
+bulged out to those hollowed in. Finally, when all the air is pumped or
+sucked out, the soap-film figure is exhibited. The rubber films strike
+together, assume the form of planes, and meet at four sharp edges in the
+centre of the pyramid.
+
+[Illustration: Fig. 3.]
+
+[Illustration: Fig. 4.]
+
+The tendency of soap-films to assume smaller forms may be directly
+demonstrated by a method of Van der Mensbrugghe. If we dip a square wire
+frame to which a handle is attached into a solution of soap and water,
+we shall obtain on the frame a beautiful, plane film of soap-suds. (Fig.
+4.) On this we lay a thread having its two ends tied together. If, now,
+we puncture the part enclosed by the thread, we shall obtain a soap-film
+having a circular hole in it, whose circumference is the thread. The
+remainder of the film decreasing in area as much as it can, the hole
+assumes the largest area that it can. But the figure of largest area,
+with a given periphery, is the circle.
+
+[Illustration: Fig. 5.]
+
+Similarly, by the principle of least superficial area, a freely
+suspended mass of oil assumes the shape of a sphere. The sphere is the
+form of least surface for a given content. This is evident. The more we
+put into a travelling-bag, the nearer its shape approaches the spherical
+form.
+
+The connexion of the two above-mentioned paragraphs with the principle
+of least superficial area may be shown by a yet simpler example. Picture
+to yourselves four fixed pulleys, _a_, _b_, _c_, _d_, and two movable
+rings _f_, _g_ (Fig. 5); about the pulleys and through the rings imagine
+a smooth cord passed, fastened at one extremity to a nail _e_, and
+loaded at the other with a weight _h_. Now this weight always tends to
+sink, or, what is the same thing, always tends to make the portion of
+the string _e h_ as long as possible, and consequently the remainder of
+the string, wound round the pulleys, as short as possible. The strings
+must remain connected with the pulleys, and on account of the rings also
+with each other. The conditions of the case, accordingly, are similar to
+those of the liquid figures discussed. The result also is a similar one.
+When, as in the right hand figure of the cut, four pairs of strings
+meet, a different configuration must be established. The consequence of
+the endeavor of the string to shorten itself is that the rings separate
+from each other, and that now at all points only three pairs of strings
+meet, every two at equal angles of one hundred and twenty degrees. As a
+fact, by this arrangement the greatest possible shortening of the string
+is attained; as can be easily proved by geometry.
+
+This will help us to some extent to understand the creation of beautiful
+and complicated figures by the simple tendency of liquids to assume
+surfaces of least superficial area. But the question arises, _Why_ do
+liquids seek surfaces of least superficial area?
+
+The particles of a liquid cling together. Drops brought into contact
+coalesce. We can say, liquid particles attract each other. If so, they
+seek to come as close as they can to each other. The particles at the
+surface will endeavor to penetrate as far as they can into the interior.
+This process will not stop, cannot stop, until the surface has become as
+small as under the circumstances it possibly can become, until as few
+particles as possible remain at the surface, until as many particles as
+possible have penetrated into the interior, until the forces of
+attraction have no more work to perform.[3]
+
+The root of the principle of least surface is to be sought, accordingly,
+in another and much simpler principle, which may be illustrated by some
+such analogy as this. We can _conceive_ of the natural forces of
+attraction and repulsion as purposes or intentions of nature. As a
+matter of fact, that interior pressure which we feel before an act and
+which we call an intention or purpose, is not, in a final analysis, so
+essentially different from the pressure of a stone on its support, or
+the pressure of a magnet on another, that it is necessarily unallowable
+to use for both the same term--at least for well-defined purposes.[4] It
+is the purpose of nature, accordingly, to bring the iron nearer the
+magnet, the stone nearer the centre of the earth, and so forth. If such
+a purpose can be realised, it is carried out. But where she cannot
+realise her purposes, nature does nothing. In this respect she acts
+exactly as a good man of business does.
+
+It is a constant purpose of nature to bring weights lower. We can raise
+a weight by causing another, larger weight to sink; that is, by
+satisfying another, more powerful, purpose of nature. If we fancy we are
+making nature serve our purposes in this, it will be found, upon closer
+examination, that the contrary is true, and that nature has employed us
+to attain her purposes.
+
+Equilibrium, rest, exists only, but then always, when nature is brought
+to a halt in her purposes, when the forces of nature are as fully
+satisfied as, under the circumstances, they can be. Thus, for example,
+heavy bodies are in equilibrium, when their so-called centre of gravity
+lies as low as it possibly can, or when as much weight as the
+circumstances admit of has sunk as low as it can.
+
+The idea forcibly suggests itself that perhaps this principle also holds
+good in other realms. Equilibrium exists also in the state when the
+purposes of the parties are as fully satisfied as for the time being
+they can be, or, as we may say, jestingly, in the language of physics,
+when the social potential is a maximum.[5]
+
+You see, our miserly mercantile principle is replete with
+consequences.[6] The result of sober research, it has become as fruitful
+for physics as the dry questions of Socrates for science generally. If
+the principle seems to lack in ideality, the more ideal are the fruits
+which it bears.
+
+But why, tell me, should science be ashamed of such a principle? Is
+science[7] itself anything more than--a business? Is not its task to
+acquire with the least possible work, in the least possible time, with
+the least possible thought, the greatest possible part of eternal truth?
+
+
+  FOOTNOTES:
+
+  [Footnote 1: _Statique expérimentale et théorique des liquids_,
+  1873. See also _The Science of Mechanics_, p. 384 et seqq., The Open
+  Court Publishing Co., Chicago, 1893.]
+
+  [Footnote 2: Compare Mach, _Ueber die Molecularwirkung der
+  Flüssigkeiten_, Reports of the Vienna Academy, 1862.]
+
+  [Footnote 3: In almost all branches of physics that are well worked
+  out such maximal and minimal problems play an important part.]
+
+  [Footnote 4: Compare Mach, _Vorträge über Psychophysik_, Vienna,
+  1863, page 41; _Compendium der Physik für Mediciner_, Vienna, 1863,
+  page 234; and also _The Science of Mechanics_, Chicago, 1893, pp. 84
+  and 464.]
+
+  [Footnote 5: Like reflexions are found in Quételet, _Du système
+  sociale_.]
+
+  [Footnote 6: For the full development of this idea see the essay "On
+  the Economical Nature of Physical Inquiry," p. 186, and the chapter
+  on "The Economy of Science," in my _Mechanics_ (Chicago: The Open
+  Court Publishing Company, 1893), p. 481.]
+
+  [Footnote 7: Science may be regarded as a maximum or minimum
+  problem, exactly as the business of the merchant. In fact, the
+  intellectual activity of natural inquiry is not so greatly different
+  from that exercised in ordinary life as is usually supposed.]
+
+
+
+
+THE FIBRES OF CORTI.
+
+
+Whoever has roamed through a beautiful country knows that the tourist's
+delights increase with his progress. How pretty that wooded dell must
+look from yonder hill! Whither does that clear brook flow, that hides
+itself in yonder sedge? If I only knew how the landscape looked behind
+that mountain! Thus even the child thinks in his first rambles. It is
+also true of the natural philosopher.
+
+The first questions are forced upon the attention of the inquirer by
+practical considerations; the subsequent ones are not. An irresistible
+attraction draws him to these; a nobler interest which far transcends
+the mere needs of life. Let us look at a special case.
+
+For a long time the structure of the organ of hearing has actively
+engaged the attention of anatomists. A considerable number of brilliant
+discoveries has been brought to light by their labors, and a splendid
+array of facts and truths established. But with these facts a host of
+new enigmas has been presented.
+
+Whilst in the theory of the organisation and functions of the eye
+comparative clearness has been attained; whilst, hand in hand with this,
+ophthalmology has reached a degree of perfection which the preceding
+century could hardly have dreamed of, and by the help of the
+ophthalmoscope the observing physician penetrates into the profoundest
+recesses of the eye, the theory of the ear is still much shrouded in
+mysterious darkness, full of attraction for the investigator.
+
+Look at this model of the ear. Even at that familiar part by whose
+extent we measure the quantity of people's intelligence, even at the
+external ear, the problems begin. You see here a succession of helixes
+or spiral windings, at times very pretty, whose significance we cannot
+accurately state, yet for which there must certainly be some reason.
+
+[Illustration: Fig. 6.]
+
+The shell or concha of the ear, _a_ in the annexed diagram, conducts the
+sound into the curved auditory passage _b_, which is terminated by a
+thin membrane, the so-called tympanic membrane, _e_. This membrane is
+set in motion by the sound, and in its turn sets in motion a series of
+little bones of very peculiar formation, _c_. At the end of all is the
+labyrinth _d_. The labyrinth consists of a group of cavities filled with
+a liquid, in which the innumerable fibres of the nerve of hearing are
+imbedded. By the vibration of the chain of bones _c_, the liquid of the
+labyrinth is shaken, and the auditory nerve excited. Here the process of
+hearing begins. So much is certain. But the details of the process are
+one and all unanswered questions.
+
+To these old puzzles, the Marchese Corti, as late as 1851, added a new
+enigma. And, strange to say, it is this last enigma, which, perhaps, has
+first received its correct solution. This will be the subject of our
+remarks to-day.
+
+Corti found in the cochlea, or snail-shell of the labyrinth, a large
+number of microscopic fibres placed side by side in geometrically
+graduated order. According to Kölliker their number is three thousand.
+They were also the subject of investigation at the hands of Max Schultze
+and Deiters.
+
+A description of the details of this organ would only weary you, besides
+not rendering the matter much clearer. I prefer, therefore, to state
+briefly what in the opinion of prominent investigators like Helmholtz
+and Fechner is the peculiar function of Corti's fibres. The cochlea, it
+seems, contains a large number of elastic fibres of graduated lengths
+(Fig. 7), to which the branches of the auditory nerve are attached.
+These fibres, called the fibres, pillars, or rods of Corti, being of
+unequal length, must also be of unequal elasticity, and, consequently,
+pitched to different notes. The cochlea, therefore, is a species of
+pianoforte.
+
+[Illustration: Fig. 7.]
+
+What, now, may be the office of this structure, which is found in no
+other organ of sense? May it not be connected with some special
+property of the ear? It is quite probable; for the ear possesses a very
+similar power. You know that it is possible to follow the individual
+voices of a symphony. Indeed, the feat is possible even in a fugue of
+Bach, where it is certainly no inconsiderable achievement. The ear can
+pick out the single constituent tonal parts, not only of a harmony, but
+of the wildest clash of music imaginable. The musical ear analyses every
+agglomeration of tones.
+
+The eye does not possess this ability. Who, for example, could tell from
+the mere sight of white, without a previous experimental knowledge of
+the fact, that white is composed of a mixture of other colors? Could it
+be, now, that these two facts, the property of the ear just mentioned,
+and the structure discovered by Corti, are really connected? It is very
+probable. The enigma is solved if we assume that every note of definite
+pitch has its special string in this pianoforte of Corti, and,
+therefore, its special branch of the auditory nerve attached to that
+string. But before I can make this point perfectly plain to you, I must
+ask you to follow me a few steps into the dry domain of physics.
+
+Look at this pendulum. Forced from its position of equilibrium by an
+impulse, it begins to swing with a definite time of oscillation,
+dependent upon its length. Longer pendulums swing more slowly, shorter
+ones more quickly. We will suppose our pendulum to execute one
+to-and-fro movement in a second.
+
+This pendulum, now, can be thrown into violent vibration in two ways;
+either by a _single_ heavy impulse, or by a _number_ of properly
+communicated slight impulses. For example, we impart to the pendulum,
+while at rest in its position of equilibrium, a very slight impulse. It
+will execute a very small vibration. As it passes a third time its
+position of equilibrium, a second having elapsed, we impart to it again
+a slight shock, in the same direction with the first. Again after the
+lapse of a second, on its fifth passage through the position of
+equilibrium, we strike it again in the same manner; and so continue. You
+see, by this process the shocks imparted augment continually the motion
+of the pendulum. After each slight impulse, the pendulum reaches out a
+little further in its swing, and finally acquires a considerable
+motion.[8]
+
+But this is not the case under all circumstances. It is possible only
+when the impulses imparted synchronise with the swings of the pendulum.
+If we should communicate the second impulse at the end of half a second
+and in the same direction with the first impulse, its effects would
+counteract the motion of the pendulum. It is easily seen that our little
+impulses help the motion of the pendulum more and more, according as
+their time accords with the time of the pendulum. If we strike the
+pendulum in any other time than in that of its vibration, in some
+instances, it is true, we shall augment its vibration, but in others
+again, we shall obstruct it. Our impulses will be less effective the
+more the motion of our own hand departs from the motion of the pendulum.
+
+What is true of the pendulum holds true of every vibrating body. A
+tuning-fork when it sounds, also vibrates. It vibrates more rapidly when
+its sound is higher; more slowly when it is deeper. The standard _A_ of
+our musical scale is produced by about four hundred and fifty vibrations
+in a second.
+
+I place by the side of each other on this table two tuning-forks,
+exactly alike, resting on resonant cases. I strike the first one a sharp
+blow, so that it emits a loud note, and immediately grasp it again with
+my hand to quench its note. Nevertheless, you still hear the note
+distinctly sounded, and by feeling it you may convince yourselves that
+the other fork which was not struck now vibrates.
+
+I now attach a small bit of wax to one of the forks. It is thrown thus
+out of tune; its note is made a little deeper. I now repeat the same
+experiment with the two forks, now of unequal pitch, by striking one of
+them and again grasping it with my hand; but in the present case the
+note ceases the very instant I touch the fork.
+
+What has happened here in these two experiments? Simply this. The
+vibrating fork imparts to the air and to the table four hundred and
+fifty shocks a second, which are carried over to the other fork. If the
+other fork is pitched to the same note, that is to say, if it vibrates
+when struck in the same time with the first, then the shocks first
+emitted, no matter how slight they may be, are sufficient to throw the
+second fork into rapid sympathetic vibration. But when the time of
+vibration of the two forks is slightly different, this does not take
+place. We may strike as many forks as we will, the fork tuned to _A_ is
+perfectly indifferent to their notes; is deaf, in fact, to all except
+its own; and if you strike three, or four, or five, or any number
+whatsoever, of forks all at the same time, so as to make the shocks
+which come from them ever so great, the _A_ fork will not join in with
+their vibrations unless another fork _A_ is found in the collection
+struck. It picks out, in other words, from all the notes sounded, that
+which accords with it.
+
+The same is true of all bodies which can yield notes. Tumblers resound
+when a piano is played, on the striking of certain notes, and so do
+window panes. Nor is the phenomenon without analogy in other provinces.
+Take a dog that answers to the name "Nero." He lies under your table.
+You speak of Domitian, Vespasian, and Marcus Aurelius Antoninus, you
+call upon all the names of the Roman Emperors that occur to you, but the
+dog does not stir, although a slight tremor of his ear tells you of a
+faint response of his consciousness. But the moment you call "Nero" he
+jumps joyfully towards you. The tuning-fork is like your dog. It answers
+to the name _A_.
+
+You smile, ladies. You shake your heads. The simile does not catch your
+fancy. But I have another, which is very near to you: and for punishment
+you shall hear it. You, too, are like tuning-forks. Many are the hearts
+that throb with ardor for you, of which you take no notice, but are
+cold. Yet what does it profit you! Soon the heart will come that beats
+in just the proper rhythm, and then your knell, too, has struck. Then
+your heart, too, will beat in unison, whether you will or no.
+
+The law of sympathetic vibration, here propounded for sounding bodies,
+suffers some modification for bodies incompetent to yield notes. Bodies
+of this kind vibrate to almost every note. A high silk hat, we know,
+will not sound; but if you will hold your hat in your hand when
+attending your next concert you will not only hear the pieces played,
+but also feel them with your fingers. It is exactly so with men. People
+who are themselves able to give tone to their surroundings, bother
+little about the prattle of others. But the person without character
+tarries everywhere: in the temperance hall, and at the bar of the
+public-house--everywhere where a committee is formed. The high silk hat
+is among bells what the weakling is among men of conviction.
+
+A sonorous body, therefore, always sounds when its special note, either
+alone or in company with others, is struck. We may now go a step
+further. What will be the behaviour of a group of sonorous bodies which
+in the pitch of their notes form a scale? Let us picture to ourselves,
+for example (Fig. 8), a series of rods or strings pitched to the notes
+_c d e f g_.... On a musical instrument the accord _c e g_ is struck.
+Every one of the rods of Fig. 8 will see if its special note is
+contained in the accord, and if it finds it, it will respond. The rod
+_c_ will give at once the note _c_, the rod _e_ the note _e_, the rod
+_g_ the note _g_. All the other rods will remain at rest, will not
+sound.
+
+[Illustration: Fig. 8.]
+
+We need not look about us long for such an instrument. Every piano is an
+instrument of this kind, with which the experiment mentioned may be
+executed with splendid success. Two pianos stand here by the side of
+each other, both tuned alike. We will employ the first for exciting the
+notes, while we will allow the second to respond; after having first
+pressed upon the loud pedal, so as to render all the strings capable of
+motion.
+
+Every harmony struck with vigor on the first piano is distinctly
+repeated on the second. To prove that it is the same strings that are
+sounded in both pianos, we repeat the experiment in a slightly changed
+form. We let go the loud pedal of the second piano and pressing on the
+keys _c e g_ of that instrument vigorously strike the harmony _c e g_ on
+the first piano. The harmony _c e g_ is now also sounded on the second
+piano. But if we press only on one key _g_ of one piano, while we strike
+_c e g_ on the other, only _g_ will be sounded on the second. It is
+thus always the like strings of the two pianos that excite each other.
+
+The piano can reproduce any sound that is composed of its musical notes.
+It will reproduce, for example, very distinctly, a vowel sound that is
+sung into it. And in truth physics has proved that the vowels may be
+regarded as composed of simple musical notes.
+
+You see that by the exciting of definite tones in the air quite definite
+motions are set up with mechanical necessity in the piano. The idea
+might be made use of for the performance of some pretty pieces of
+wizardry. Imagine a box in which is a stretched string of definite
+pitch. This is thrown into motion as often as its note is sung or
+whistled. Now it would not be a very difficult task for a skilful
+mechanic to so construct the box that the vibrating cord would close a
+galvanic circuit and open the lock. And it would not be a much more
+difficult task to construct a box which would open at the whistling of a
+certain melody. Sesame! and the bolts fall. Truly, we should have here a
+veritable puzzle-lock. Still another fragment rescued from that old
+kingdom of fables, of which our day has realised so much, that world of
+fairy-stories to which the latest contributions are Casselli's
+telegraph, by which one can write at a distance in one's own hand, and
+Prof. Elisha Gray's telautograph. What would the good old Herodotus have
+said to these things who even in Egypt shook his head at much that he
+saw? [Greek: emoi men ou pista], just as simple-heartedly as then, when
+he heard of the circumnavigation of Africa.
+
+A new puzzle-lock! But why invent one? Are not we human beings ourselves
+puzzle-locks? Think of the stupendous groups of thoughts, feelings, and
+emotions that can be aroused in us by a word! Are there not moments in
+all our lives when a mere name drives the blood to our hearts? Who that
+has attended a large mass-meeting has not experienced what tremendous
+quantities of energy and motion can be evolved by the innocent words,
+"Liberty, Equality, Fraternity."
+
+But let us return to the subject proper of our discourse. Let us look
+again at our piano, or what will do just as well, at some other
+contrivance of the same character. What does this instrument do?
+Plainly, it decomposes, it analyses every agglomeration of sounds set up
+in the air into its individual component parts, each tone being taken up
+by a different string; it performs a real spectral analysis of sound. A
+person completely deaf, with the help of a piano, simply by touching the
+strings or examining their vibrations with a microscope, might
+investigate the sonorous motion of the air, and pick out the separate
+tones excited in it.
+
+The ear has the same capacity as this piano. The ear performs for the
+mind what the piano performs for a person who is deaf. The mind without
+the ear is deaf. But a deaf person, with the piano, does hear after a
+fashion, though much less vividly, and more clumsily, than with the
+ear. The ear, thus, also decomposes sound into its component tonal
+parts. I shall now not be deceived, I think, if I assume that you
+already have a presentiment of what the function of Corti's fibres is.
+We can make the matter very plain to ourselves. We will use the one
+piano for exciting the sounds, and we shall imagine the second one in
+the ear of the observer in the place of Corti's fibres, which is a model
+of such an instrument. To every string of the piano in the ear we will
+suppose a special fibre of the auditory nerve attached, so that this
+fibre and this alone, is irritated when the string is thrown into
+vibration. If we strike now an accord on the external piano, for every
+tone of that accord a definite string of the internal piano will sound
+and as many different nervous fibres will be irritated as there are
+notes in the accord. The simultaneous sense-impressions due to different
+notes can thus be preserved unmingled and be separated by the attention.
+It is the same as with the five fingers of the hand. With each finger I
+can touch something different. Now the ear has three thousand such
+fingers, and each one is designed for the touching of a different
+tone.[9] Our ear is a puzzle-lock of the kind mentioned. It opens at the
+magic melody of a sound. But it is a stupendously ingenious lock. Not
+only one tone, but every tone makes it open; but each one differently.
+To each tone it replies with a different sensation.
+
+More than once it has happened in the history of science that a
+phenomenon predicted by theory, has not been brought within the range of
+actual observation until long afterwards. Leverrier predicted the
+existence and the place of the planet Neptune, but it was not until
+sometime later that Galle actually found the planet at the predicted
+spot. Hamilton unfolded theoretically the phenomenon of the so-called
+conical refraction of light, but it was reserved for Lloyd some time
+subsequently to observe the fact. The fortunes of Helmholtz's theory of
+Corti's fibres have been somewhat similar. This theory, too, received
+its substantial confirmation from the subsequent observations of V.
+Hensen. On the free surface of the bodies of Crustacea, connected with
+the auditory nerves, rows of little hairy filaments of varying lengths
+and thicknesses are found, which to some extent are the analogues of
+Corti's fibres. Hensen saw these hairs vibrate when sounds were excited,
+and when different notes were struck different hairs were set in
+vibration.
+
+I have compared the work of the physical inquirer to the journey of the
+tourist. When the tourist ascends a new hill he obtains of the whole
+district a different view. When the inquirer has found the solution of
+one enigma, the solution of a host of others falls into his hands.
+
+Surely you have often felt the strange impression experienced when in
+singing through the scale the octave is reached, and nearly the same
+sensation is produced as by the fundamental tone. The phenomenon finds
+its explanation in the view here laid down of the ear. And not only this
+phenomenon but all the laws of the theory of harmony may be grasped and
+verified from this point of view with a clearness before undreamt of.
+Unfortunately, I must content myself to-day with the simple indication
+of these beautiful prospects. Their consideration would lead us too far
+aside into the fields of other sciences.
+
+The searcher of nature, too, must restrain himself in his path. He also
+is drawn along from one beauty to another as the tourist from dale to
+dale, and as circumstances generally draw men from one condition of life
+into others. It is not he so much that makes the quests, as that the
+quests are made of him. Yet let him profit by his time, and let not his
+glance rove aimlessly hither and thither. For soon the evening sun will
+shine, and ere he has caught a full glimpse of the wonders close by, a
+mighty hand will seize him and lead him away into a different world of
+puzzles.
+
+Respected hearers, science once stood in an entirely different relation
+to poetry. The old Hindu mathematicians wrote their theorems in verses,
+and lotus-flowers, roses, and lilies, beautiful sceneries, lakes, and
+mountains figured in their problems.
+
+"Thou goest forth on this lake in a boat. A lily juts forth, one palm
+above the water. A breeze bends it downwards, and it vanishes two palms
+from its previous spot beneath the surface. Quick, mathematician, tell
+me how deep is the lake!"
+
+Thus spoke an ancient Hindu scholar. This poetry, and rightly, has
+disappeared from science, but from its dry leaves another poetry is
+wafted aloft which cannot be described to him who has never felt it.
+Whoever will fully enjoy this poetry must put his hand to the plough,
+must himself investigate. Therefore, enough of this! I shall reckon
+myself fortunate if you do not repent of this brief excursion into the
+flowered dale of physiology, and if you take with yourselves the belief
+that we can say of science what we say of poetry,
+
+    "Who the song would understand,
+    Needs must seek the song's own land;
+    Who the minstrel understand
+    Needs must seek the minstrel's land."
+
+  FOOTNOTES:
+
+  [Footnote 8: This experiment, with its associated reflexions, is due
+  to Galileo.]
+
+  [Footnote 9: A development of the theory of musical audition
+  differing in many points from the theory of Helmholtz here
+  expounded, will be found in my _Contributions to the Analysis of the
+  Sensations_ (English translation by C. M. Williams), Chicago, The
+  Open Court Publishing Company, 1897.]
+
+
+
+
+ON THE CAUSES OF HARMONY.
+
+
+We are to speak to-day of a theme which is perhaps of somewhat more
+general interest--_the causes of the harmony of musical sounds_. The
+first and simplest experiences relative to harmony are very ancient. Not
+so the explanation of its laws. These were first supplied by the
+investigators of a recent epoch. Allow me an historical retrospect.
+
+Pythagoras (586 B. C.) knew that the note yielded by a string of steady
+tension was converted into its octave when the length of the string was
+reduced one-half, and into its fifth when reduced two-thirds; and that
+then the first fundamental tone was consonant with the two others. He
+knew generally that the same string under fixed tension gives consonant
+tones when successively divided into lengths that are in the proportions
+of the simplest natural numbers; that is, in the proportions of 1:2,
+2:3, 3:4, 4:5.
+
+Pythagoras failed to reveal the causes of these laws. What have
+consonant tones to do with the simple natural numbers? That is the
+question we should ask to-day. But this circumstance must have appeared
+less strange than inexplicable to Pythagoras. This philosopher sought
+for the causes of harmony in the occult, miraculous powers of numbers.
+His procedure was largely the cause of the upgrowth of a numerical
+mysticism, of which the traces may still be detected in our
+oneirocritical books and among some scientists, to whom marvels are more
+attractive than lucidity.
+
+Euclid (300 B. C.) gives a definition of consonance and dissonance that
+could hardly be improved upon, in point of verbal accuracy. The
+consonance ([Greek: symphônia]) of two tones, he says, is the mixture,
+the blending ([Greek: krasis]) of those two tones; dissonance ([Greek:
+diaphônia]), on the other hand, is the incapacity of the tones to blend
+([Greek: amixia]), whereby they are made harsh for the ear. The person
+who knows the correct explanation of the phenomenon hears it, so to
+speak, reverberated in these words of Euclid. Still, Euclid did not know
+the true cause of harmony. He had unwittingly come very near to the
+truth, but without really grasping it.
+
+Leibnitz (1646-1716 A. D.) resumed the question which his predecessors
+had left unsolved. He, of course, knew that musical notes were produced
+by vibrations, that twice as many vibrations corresponded to the octave
+as to the fundamental tone, etc. A passionate lover of mathematics, he
+sought for the cause of harmony in the secret computation and comparison
+of the simple numbers of vibrations and in the secret satisfaction of
+the soul at this occupation. But how, we ask, if one does not know that
+musical notes are vibrations? The computation and the satisfaction at
+the computation must indeed be pretty secret if it is unknown. What
+queer ideas philosophers have! Could anything more wearisome be imagined
+than computation as a principle of æsthetics? Yes, you are not utterly
+wrong in your conjecture, yet you may be sure that Leibnitz's theory is
+not wholly nonsense, although it is difficult to make out precisely what
+he meant by his secret computation.
+
+The great Euler (1707-1783) sought the cause of harmony, almost as
+Leibnitz did, in the pleasure which the soul derives from the
+contemplation of order in the numbers of the vibrations.[10]
+
+Rameau and D'Alembert (1717-1783) approached nearer to the truth. They
+knew that in every sound available in music besides the fundamental note
+also the twelfth and the next higher third could be heard; and further
+that the resemblance between a fundamental tone and its octave was
+always strongly marked. Accordingly, the combination of the octave,
+fifth, third, etc., with the fundamental tone appeared to them
+"natural." They possessed, we must admit, the correct point of view; but
+with the simple naturalness of a phenomenon no inquirer can rest
+content; for it is precisely this naturalness for which he seeks his
+explanations.
+
+Rameau's remark dragged along through the whole modern period, but
+without leading to the full discovery of the truth. Marx places it at
+the head of his theory of composition, but makes no further application
+of it. Also Goethe and Zelter in their correspondence were, so to speak,
+on the brink of the truth. Zelter knew of Rameau's view. Finally, you
+will be appalled at the difficulty of the problem, when I tell you that
+till very recent times even professors of physics were dumb when asked
+what were the causes of harmony.
+
+Not till quite recently did Helmholtz find the solution of the question.
+But to make this solution clear to you I must first speak of some
+experimental principles of physics and psychology.
+
+1) In every process of perception, in every observation, the attention
+plays a highly important part. We need not look about us long for proofs
+of this. You receive, for example, a letter written in a very poor hand.
+Do your best, you cannot make it out. You put together now these, now
+those lines, yet you cannot construct from them a single intelligible
+character. Not until you direct your attention to groups of lines which
+really belong together, is the reading of the letter possible.
+Manuscripts, the letters of which are formed of minute figures and
+scrolls, can only be read at a considerable distance, where the
+attention is no longer diverted from the significant outlines to the
+details. A beautiful example of this class is furnished by the famous
+iconographs of Giuseppe Arcimboldo in the basement of the Belvedere
+gallery at Vienna. These are symbolic representations of water, fire,
+etc.: human heads composed of aquatic animals and of combustibles. At a
+short distance one sees only the details, at a greater distance only the
+whole figure. Yet a point can be easily found at which, by a simple
+voluntary movement of the attention, there is no difficulty in seeing
+now the whole figure and now the smaller forms of which it is composed.
+A picture is often seen representing the tomb of Napoleon. The tomb is
+surrounded by dark trees between which the bright heavens are visible as
+background. One can look a long time at this picture without noticing
+anything except the trees, but suddenly, on the attention being
+accidentally directed to the bright background, one sees the figure of
+Napoleon between the trees. This case shows us very distinctly the
+important part which attention plays. The same sensuous object can,
+solely by the interposition of attention, give rise to wholly different
+perceptions.
+
+If I strike a harmony, or chord, on this piano, by a mere effort of
+attention you can fix every tone of that harmony. You then hear most
+distinctly the fixed tone, and all the rest appear as a mere addition,
+altering only the quality, or acoustic color, of the primary tone. The
+effect of the same harmony is essentially modified if we direct our
+attention to different tones.
+
+Strike in succession two harmonies, for example, the two represented in
+the annexed diagram, and first fix by the attention the upper note _e_,
+afterwards the base _e_-_a_; in the two cases you will hear the same
+sequence of harmonies differently. In the first case, you have the
+impression as if the fixed tone remained unchanged and simply altered
+its _timbre_; in the second case, the whole acoustic agglomeration seems
+to fall sensibly in depth. There is an art of composition to guide the
+attention of the hearer. But there is also an art of hearing, which is
+not the gift of every person.
+
+[Music: Fig. 9.]
+
+The piano-player knows the remarkable effects obtained when one of the
+keys of a chord that is struck is let loose. Bar 1 played on the piano
+sounds almost like bar 2. The note which lies next to the key let loose
+resounds after its release as if it were freshly struck. The attention
+no longer occupied with the upper note is by that very fact insensibly
+led to the upper note.
+
+[Music: Fig. 10.]
+
+Any tolerably cultivated musical ear can perform the resolution of a
+harmony into its component parts. By much practice we can go even
+further. Then, every musical sound heretofore regarded as simple can be
+resolved into a subordinate succession of musical tones. For example, if
+I strike on the piano the note 1, (annexed diagram,) we shall hear, if
+we make the requisite effort of attention, besides the loud fundamental
+note the feebler, higher overtones, or harmonics, 2 ... 7, that is, the
+octave, the twelfth, the double octave, and the third, the fifth, and
+the seventh of the double octave.
+
+[Music: Fig. 11.]
+
+The same is true of every musically available sound. Each yields, with
+varying degrees of intensity, besides its fundamental note, also the
+octave, the twelfth, the double octave, etc. The phenomenon is
+observable with special facility on the open and closed flue-pipes of
+organs. According, now, as certain overtones are more or less distinctly
+emphasised in a sound, the _timbre_ of the sound changes--that peculiar
+quality of the sound by which we distinguish the music of the piano from
+that of the violin, the clarinet, etc.
+
+On the piano these overtones can be very easily rendered audible. If I
+strike, for example, sharply note 1 of the foregoing series, whilst I
+simply press down upon, one after another, the keys 2, 3, ... 7, the
+notes 2, 3, ... 7 will continue to sound after the striking of 1,
+because the strings corresponding to these notes, now freed from their
+dampers, are thrown into sympathetic vibration.
+
+As you know, this sympathetic vibration of the like-pitched strings with
+the overtones is really not to be conceived as sympathy, but rather as
+lifeless mechanical necessity. We must not think of this sympathetic
+vibration as an ingenious journalist pictured it, who tells a gruesome
+story of Beethoven's F minor sonata, Op. 2, that I cannot withhold from
+you. "At the last London Industrial Exhibition nineteen virtuosos played
+the F minor sonata on the same piano. When the twentieth stepped up to
+the instrument to play by way of variation the same production, to the
+terror of all present the piano began to render the sonata of its own
+accord. The Archbishop of Canterbury, who happened to be present, was
+set to work and forthwith expelled the F minor devil."
+
+Although, now, the overtones or harmonics which we have discussed are
+heard only upon a special effort of the attention, nevertheless they
+play a highly important part in the formation of musical _timbre_, as
+also in the production of the consonance and dissonance of sounds. This
+may strike you as singular. How can a thing which is heard only under
+exceptional circumstances be of importance generally for audition?
+
+But consider some familiar incidents of your every-day life. Think of
+how many things you see which you do not notice, which never strike your
+attention until they are missing. A friend calls upon you; you cannot
+understand why he looks so changed. Not until you make a close
+examination do you discover that his hair has been cut. It is not
+difficult to tell the publisher of a work from its letter-press, and yet
+no one can state precisely the points by which this style of type is so
+strikingly different from that style. I have often recognised a book
+which I was in search of from a simple piece of unprinted white paper
+that peeped out from underneath the heap of books covering it, and yet I
+had never carefully examined the paper, nor could I have stated its
+difference from other papers.
+
+What we must remember, therefore, is that every sound that is musically
+available yields, besides its fundamental note, its octave, its twelfth,
+its double octave, etc., as overtones or harmonics, and that these are
+important for the agreeable combination of several musical sounds.
+
+2) One other fact still remains to be dealt with. Look at this
+tuning-fork. It yields, when struck, a perfectly smooth tone. But if you
+strike in company with it a second fork which is of slightly different
+pitch, and which alone also gives a perfectly smooth tone, you will
+hear, if you set both forks on the table, or hold both before your ear,
+a uniform tone no longer, but a number of shocks of tones. The rapidity
+of the shocks increases with the difference of the pitch of the forks.
+These shocks, which become very disagreeable for the ear when they
+amount to thirty-three in a second, are called "beats."
+
+Always, when one of two like musical sounds is thrown out of unison with
+the other, beats arise. Their number increases with the divergence from
+unison, and simultaneously they grow more unpleasant. Their roughness
+reaches its maximum at about thirty-three beats in a second. On a still
+further departure from unison, and a consequent increase of the number
+of beats, the unpleasant effect is diminished, so that tones which are
+widely apart in pitch no longer produce offensive beats.
+
+To give yourselves a clear idea of the production of beats, take two
+metronomes and set them almost alike. You can, for that matter, set the
+two exactly alike. You need not fear that they will strike alike. The
+metronomes usually for sale in the shops are poor enough to yield, when
+set alike, appreciably unequal strokes. Set, now, these two metronomes,
+which strike at unequal intervals, in motion; you will readily see that
+their strokes alternately coincide and conflict with each other. The
+alternation is quicker the greater the difference of time of the two
+metronomes.
+
+If metronomes are not to be had, the experiment may be performed with
+two watches.
+
+Beats arise in the same way. The rhythmical shocks of two sounding
+bodies, of unequal pitch, sometimes coincide, sometimes interfere,
+whereby they alternately augment and enfeeble each other's effects.
+Hence the shock-like, unpleasant swelling of the tone.
+
+Now that we have made ourselves acquainted with overtones and beats, we
+may proceed to the answer of our main question, Why do certain relations
+of pitch produce pleasant sounds, consonances, others unpleasant sounds,
+dissonances? It will be readily seen that all the unpleasant effects of
+simultaneous sound-combinations are the result of beats produced by
+those combinations. Beats are the only sin, the sole evil of music.
+Consonance is the coalescence of sounds without appreciable beats.
+
+[Illustration: Fig. 12.]
+
+To make this perfectly clear to you I have constructed the model which
+you see in Fig. 12. It represents a claviatur. At its top a movable
+strip of wood _aa_ with the marks 1, 2 ... 6 is placed. By setting this
+strip in any position, for example, in that where the mark 1 is over the
+note _c_ of the claviatur, the marks 2, 3 ... 6, as you see, stand over
+the overtones of _c_. The same happens when the strip is placed in any
+other position. A second, exactly similar strip, _bb_, possesses the
+same properties. Thus, together, the two strips, in any two positions,
+point out by their marks all the tones brought into play upon the
+simultaneous sounding of the notes indicated by the marks 1.
+
+The two strips, placed over the same fundamental note, show that also
+all the overtones of those notes coincide. The first note is simply
+intensified by the other. The single overtones of a sound lie too far
+apart to permit appreciable beats. The second sound supplies nothing
+new, consequently, also, no new beats. Unison is the most perfect
+consonance.
+
+Moving one of the two strips along the other is equivalent to a
+departure from unison. All the overtones of the one sound now fall
+alongside those of the other; beats are at once produced; the
+combination of the tones becomes unpleasant: we obtain a dissonance. If
+we move the strip further and further along, we shall find that as a
+general rule the overtones always fall alongside each other, that is,
+always produce beats and dissonances. Only in a few quite definite
+positions do the overtones partially coincide. Such positions,
+therefore, signify higher degrees of euphony--they point out _the
+consonant intervals_.
+
+These consonant intervals can be readily found experimentally by cutting
+Fig. 12 out of paper and moving _bb_ lengthwise along _aa_. The most
+perfect consonances are the octave and the twelfth, since in these two
+cases the overtones of the one sound coincide absolutely with those of
+the other. In the octave, for example, 1_b_ falls on 2_a_, 2_b_ on 4_a_,
+3_b_ on 6_a_. Consonances, therefore, are simultaneous
+sound-combinations not accompanied by disagreeable beats. This, by the
+way, is, expressed in English, what Euclid said in Greek.
+
+Only such sounds are consonant as possess in common some portion of
+their partial tones. Plainly we must recognise between such sounds, also
+when struck one after another, a certain affinity. For the second sound,
+by virtue of the common overtones, will produce partly the same
+sensation as the first. The octave is the most striking exemplification
+of this. When we reach the octave in the ascent of the scale we actually
+fancy we hear the fundamental tone repeated. The foundations of harmony,
+therefore, are the foundations of melody.
+
+Consonance is the coalescence of sounds without appreciable beats! This
+principle is competent to introduce wonderful order and logic into the
+doctrines of the fundamental bass. The compendiums of the theory of
+harmony which (Heaven be witness!) have stood hitherto little behind the
+cook-books in subtlety of logic, are rendered extraordinarily clear and
+simple. And what is more, all that the great masters, such as
+Palestrina, Mozart, Beethoven, unconsciously got right, and of which
+heretofore no text-book could render just account, receives from the
+preceding principle its perfect verification.
+
+But the beauty of the theory is, that it bears upon its face the stamp
+of truth. It is no phantom of the brain. Every musician can hear for
+himself the beats which the overtones of his musical sounds produce.
+Every musician can satisfy himself that for any given case the number
+and the harshness of the beats can be calculated beforehand, and that
+they occur in exactly the measure that theory determines.
+
+This is the answer which Helmholtz gave to the question of Pythagoras,
+so far as it can be explained with the means now at my command. A long
+period of time lies between the raising and the solving of this
+question. More than once were eminent inquirers nearer to the answer
+than they dreamed of.
+
+The inquirer seeks the truth. I do not know if the truth seeks the
+inquirer. But were that so, then the history of science would vividly
+remind us of that classical rendezvous, so often immortalised by
+painters and poets. A high garden wall. At the right a youth, at the
+left a maiden. The youth sighs, the maiden sighs! Both wait. Neither
+dreams how near the other is.
+
+I like this simile. Truth suffers herself to be courted, but she has
+evidently no desire to be won. She flirts at times disgracefully. Above
+all, she is determined to be merited, and has naught but contempt for
+the man who will win her too quickly. And if, forsooth, one breaks his
+head in his efforts of conquest, what matter is it, another will come,
+and truth is always young. At times, indeed, it really seems as if she
+were well disposed towards her admirer, but that admitted--never! Only
+when Truth is in exceptionally good spirits does she bestow upon her
+wooer a glance of encouragement. For, thinks Truth, if I do not do
+something, in the end the fellow will not seek me at all.
+
+This one fragment of truth, then, we have, and it shall never escape us.
+But when I reflect what it has cost in labor and in the lives of
+thinking men, how it painfully groped its way through centuries, a
+half-matured thought, before it became complete; when I reflect that it
+is the toil of more than two thousand years that speaks out of this
+unobtrusive model of mine, then, without dissimulation, I almost repent
+me of the jest I have made.
+
+And think of how much we still lack! When, several thousand years hence,
+boots, top-hats, hoops, pianos, and bass-viols are dug out of the earth,
+out of the newest alluvium as fossils of the nineteenth century; when
+the scientists of that time shall pursue their studies both upon these
+wonderful structures and upon our modern Broadways, as we to-day make
+studies of the implements of the stone age and of the prehistoric
+lake-dwellings--then, too, perhaps, people will be unable to comprehend
+how we could come so near to many great truths without grasping them.
+And thus it is for all time the unsolved dissonance, for all time the
+troublesome seventh, that everywhere resounds in our ears; we feel,
+perhaps, that it will find its solution, but we shall never live to see
+the day of the pure triple accord, nor shall our remotest descendants.
+
+Ladies, if it is the sweet purpose of your life to sow confusion, it is
+the purpose of mine to be clear; and so I must confess to you a slight
+transgression that I have been guilty of. On one point I have told you
+an untruth. But you will pardon me this falsehood, if in full repentance
+I make it good. The model represented in Fig. 12 does not tell the whole
+truth, for it is based upon the so-called "even temperament" system of
+tuning. The overtones, however, of musical sounds are not tempered, but
+purely tuned. By means of this slight inexactness the model is made
+considerably simpler. In this form it is fully adequate for ordinary
+purposes, and no one who makes use of it in his studies need be in fear
+of appreciable error.
+
+If you should demand of me, however, the full truth, I could give you
+that only by the help of a mathematical formula. I should have to take
+the chalk into my hands and--think of it!--reckon in your presence. This
+you might take amiss. Nor shall it happen. I have resolved to do no more
+reckoning for to-day. I shall reckon now only upon your forbearance, and
+this you will surely not gainsay me when you reflect that I have made
+only a limited use of my privilege to weary you. I could have taken up
+much more of your time, and may, therefore, justly close with Lessing's
+epigram:
+
+    "If thou hast found in all these pages naught that's worth the thanks,
+    At least have gratitude for what I've spared thee."
+
+  FOOTNOTES:
+
+  [Footnote 10: Sauveur also set out from Leibnitz's idea, but arrived
+  by independent researches at a different theory, which was very near
+  to that of Helmholtz. Compare on this point Sauveur, _Mémoires de
+  l'Académie des Sciences_, Paris, 1700-1705, and R. Smith,
+  _Harmonics_, Cambridge, 1749. (See _Appendix_, p. 346.)]
+
+
+
+
+THE VELOCITY OF LIGHT.
+
+
+When a criminal judge has a right crafty knave before him, one well
+versed in the arts of prevarication, his main object is to wring a
+confession from the culprit by a few skilful questions. In almost a
+similar position the natural philosopher seems to be placed with respect
+to nature. True, his functions here are more those of the spy than the
+judge; but his object remains pretty much the same. Her hidden motives
+and laws of action is what nature must be made to confess. Whether a
+confession will be extracted depends upon the shrewdness of the
+inquirer. Not without reason, therefore, did Lord Bacon call the
+experimental method a questioning of nature. The art consists in so
+putting our questions that they may not remain unanswered without a
+breach of etiquette.
+
+Look, too, at the countless tools, engines, and instruments of torture
+with which man conducts his inquisitions of nature, and which mock the
+poet's words:
+
+    "Mysterious even in open day,
+    Nature retains her veil, despite our clamors;
+    That which she doth not willingly display
+    Cannot be wrenched from her with levers, screws, and hammers."
+
+Look at these instruments and you will see that the comparison with
+torture also is admissible.[11]
+
+This view of nature, as of something designedly concealed from man, that
+can be unveiled only by force or dishonesty, chimed in better with the
+conceptions of the ancients than with modern notions. A Grecian
+philosopher once said, in offering his opinion of the natural science of
+his time, that it could only be displeasing to the gods to see men
+endeavoring to spy out what the gods were not minded to reveal to
+them.[12] Of course all the contemporaries of the speaker were not of
+his opinion.
+
+Traces of this view may still be found to-day, but upon the whole we are
+now not so narrow-minded. We believe no longer that nature designedly
+hides herself. We know now from the history of science that our
+questions are sometimes meaningless, and that, therefore, no answer can
+be forthcoming. Soon we shall see how man, with all his thoughts and
+quests, is only a fragment of nature's life.
+
+Picture, then, as your fancy dictates, the tools of the physicist as
+instruments of torture or as engines of endearment, at all events a
+chapter from the history of those implements will be of interest to you,
+and it will not be unpleasant to learn what were the peculiar
+difficulties that led to the invention of such strange apparatus.
+
+Galileo (born at Pisa in 1564, died at Arcetri in 1642) was the first
+who asked what was the velocity of light, that is, what time it would
+take for a light struck at one place to become visible at another, a
+certain distance away.[13]
+
+The method which Galileo devised was as simple as it was natural. Two
+practised observers, with muffled lanterns, were to take up positions in
+a dark night at a considerable distance from each other, one at _A_ and
+one at _B_. At a moment previously fixed upon, _A_ was instructed to
+unmask his lantern; while as soon as _B_ saw the light of _A_'s lantern
+he was to unmask his. Now it is clear that the time which _A_ counted
+from the uncovering of his lantern until he caught sight of the light of
+_B_'s would be the time which it would take light to travel from _A_ to
+_B_ and from _B_ back to _A_.
+
+[Illustration: Fig. 13.]
+
+The experiment was not executed, nor could it, in the nature of the
+case, have been a success. As we now know, light travels too rapidly to
+be thus noted. The time elapsing between the arrival of the light at _B_
+and its perception by the observer, with that between the decision to
+uncover and the uncovering of the lantern, is, as we now know,
+incomparably greater than the time which it takes light to travel the
+greatest earthly distances. The great velocity of light will be made
+apparent, if we reflect that a flash of lightning in the night
+illuminates instantaneously a very extensive region, whilst the single
+reflected claps of thunder arrive at the observer's ear very gradually
+and in appreciable succession.
+
+During his life, then, the efforts of Galileo to determine the velocity
+of light remained uncrowned with success. But the subsequent history of
+the measurement of the velocity of light is intimately associated with
+his name, for with the telescope which he constructed he discovered the
+four satellites of Jupiter, and these furnished the next occasion for
+the determination of the velocity of light.
+
+The terrestrial spaces were too small for Galileo's experiment. The
+measurement was first executed when the spaces of the planetary system
+were employed. Olaf Römer, (born at Aarhuus in 1644, died at Copenhagen
+in 1710) accomplished the feat (1675-1676), while watching with Cassini
+at the observatory of Paris the revolutions of Jupiter's moons.
+
+[Illustration: Fig. 14.]
+
+Let _AB_ (Fig. 14) be Jupiter's orbit. Let _S_ stand for the sun, _E_
+for the earth, _J_ for Jupiter, and _T_ for Jupiter's first satellite.
+When the earth is at _E₁_ we see the satellite enter regularly into
+Jupiter's shadow, and by watching the time between two successive
+eclipses, can calculate its time of revolution. The time which Römer
+noted was forty-two hours, twenty-eight minutes, and thirty-five
+seconds. Now, as the earth passes along in its orbit towards E₂, the
+revolutions of the satellite grow apparently longer and longer: the
+eclipses take place later and later. The greatest retardation of the
+eclipse, which occurs when the earth is at _E₂_, amounts to sixteen
+minutes and twenty-six seconds. As the earth passes back again to _E₁_,
+the revolutions grow apparently shorter, and they occur in exactly the
+time that they first did when the earth arrives at _E₁_. It is to be
+remarked that Jupiter changes only very slightly its position during one
+revolution of the earth. Römer guessed at once that these periodical
+changes of the time of revolution of Jupiter's satellite were not
+actual, but apparent changes, which were in some way connected with the
+velocity of light.
+
+Let us make this matter clear to ourselves by a simile. We receive
+regularly by the post, news of the political status at our capital.
+However far away we may be from the capital, we hear the news of every
+event, later it is true, but of all equally late. The events reach us in
+the same succession of time as that in which they took place. But if we
+are travelling away from the capital, every successive post will have a
+greater distance to pass over, and the events will reach us more slowly
+than they took place. The reverse will be the case if we are approaching
+the capital.
+
+At rest, we hear a piece of music played in the same _tempo_ at all
+distances. But the _tempo_ will be seemingly accelerated if we are
+carried rapidly towards the band, or retarded if we are carried rapidly
+away from it.[14]
+
+[Illustration: Fig. 15.]
+
+Picture to yourself a cross, say the sails of a wind-mill (Fig. 15), in
+uniform rotation about its centre. Clearly, the rotation of the cross
+will appear to you more slowly executed if you are carried very rapidly
+away from it. For the post which in this case conveys to you the light
+and brings to you the news of the successive positions of the cross will
+have to travel in each successive instant over a longer path.
+
+Now this must also be the case with the rotation (the revolution) of the
+satellite of Jupiter. The greatest retardation of the eclipse (16½
+minutes), due to the passage of the earth from _E₁_ to _E₂_, or to its
+removal from Jupiter by a distance equal to the diameter of the orbit of
+the earth, plainly corresponds to the time which it takes light to
+traverse a distance equal to the diameter of the earth's orbit. The
+velocity of light, that is, the distance described by light in a second,
+as determined by this calculation, is 311,000 kilometres,[15] or 193,000
+miles. A subsequent correction of the diameter of the earth's orbit,
+gives, by the same method, the velocity of light as approximately
+186,000 miles a second.
+
+The method is exactly that of Galileo; only better conditions are
+selected. Instead of a short terrestrial distance we have the diameter
+of the earth's orbit, three hundred and seven million kilometres; in
+place of the uncovered and covered lanterns we have the satellite of
+Jupiter, which alternately appears and disappears. Galileo, therefore,
+although he could not carry out himself the proposed measurement, found
+the lantern by which it was ultimately executed.
+
+Physicists did not long remain satisfied with this beautiful discovery.
+They sought after easier methods of measuring the velocity of light,
+such as might be performed on the earth. This was possible after the
+difficulties of the problem were clearly exposed. A measurement of the
+kind referred to was executed in 1849 by Fizeau (born at Paris in 1819).
+
+I shall endeavor to make the principle of Fizeau's apparatus clear to
+you. Let _s_ (Fig. 16) be a disk free to rotate about its centre, and
+perforated at its rim with a series of holes. Let _l_ be a luminous
+point casting its light on an unsilvered glass, _a_, inclined at an
+angle of forty-five degrees to the axis of the disk. The ray of light,
+reflected at this point, passes through one of the holes of the disk and
+falls at right angles upon a mirror _b_, erected at a point about five
+miles distant. From the mirror _b_ the light is again reflected, passes
+once more through the hole in _s_, and, penetrating the glass plate,
+finally strikes the eye, _o_, of the observer. The eye, _o_, thus, sees
+the image of the luminous point _l_ through the glass plate and the hole
+of the disk in the mirror _b_.
+
+[Illustration: Fig. 16.]
+
+If, now, the disk be set in rotation, the unpierced spaces between the
+apertures will alternately take the place of the apertures, and the eye
+o will now see the image of the luminous point in _b_ only at
+interrupted intervals. On increasing the rapidity of the rotation,
+however, the interruptions for the eye become again unnoticeable, and
+the eye sees the mirror _b_ uniformly illuminated.
+
+But all this holds true only for relatively small velocities of the
+disk, when the light sent through an aperture in _s_ to _b_ on its
+return strikes the aperture at almost the same place and passes through
+it a second time. Conceive, now, the speed of the disk to be so
+increased that the light on its return finds before it an unpierced
+space instead of an aperture, it will then no longer be able to reach
+the eye. We then see the mirror _b_ only when no light is emitted from
+it, but only when light is sent to it; it is covered when light comes
+from it. In this case, accordingly, the mirror will always appear dark.
+
+If the velocity of rotation at this point were still further increased,
+the light sent through one aperture could not, of course, on its return
+pass through the same aperture but might strike the next and reach the
+eye by that. Hence, by constantly increasing the velocity of the
+rotation, the mirror _b_ may be made to appear alternately bright and
+dark. Plainly, now, if we know the number of apertures of the disk, the
+number of rotations per second, and the distance _sb_, we can calculate
+the velocity of light. The result agrees with that obtained by Römer.
+
+The experiment is not quite as simple as my exposition might lead you to
+believe. Care must be taken that the light shall travel back and forth
+over the miles of distance _sb_ and _bs_ undispersed. This difficulty
+is obviated by means of telescopes.
+
+If we examine Fizeau's apparatus closely, we shall recognise in it an
+old acquaintance: the arrangement of Galileo's experiment. The luminous
+point _l_ is the lantern _A_, while the rotation of the perforated disk
+performs mechanically the uncovering and covering of the lantern.
+Instead of the unskilful observer _B_ we have the mirror _b_, which is
+unfailingly illuminated the instant the light arrives from _s_. The disk
+_s_, by alternately transmitting and intercepting the reflected light,
+assists the observer _o_. Galileo's experiment is here executed, so to
+speak, countless times in a second, yet the total result admits of
+actual observation. If I might be pardoned the use of a phrase of
+Darwin's in this field, I should say that Fizeau's apparatus was the
+descendant of Galileo's lantern.
+
+A still more refined and delicate method for the measurement of the
+velocity of light was employed by Foucault, but a description of it here
+would lead us too far from our subject.
+
+The measurement of the velocity of sound is easily executed by the
+method of Galileo. It was unnecessary, therefore, for physicists to rack
+their brains further about the matter; but the idea which with light
+grew out of necessity was applied also in this field. Koenig of Paris
+constructs an apparatus for the measurement of the velocity of sound
+which is closely allied to the method of Fizeau.
+
+The apparatus is very simple. It consists of two electrical clock-works
+which strike simultaneously, with perfect precision, tenths of seconds.
+If we place the two clock-works directly side by side, we hear their
+strokes simultaneously, wherever we stand. But if we take our stand by
+the side of one of the works and place the other at some distance from
+us, in general a coincidence of the strokes will now not be heard. The
+companion strokes of the remote clock-work arrive, as sound, later. The
+first stroke of the remote work is heard, for example, immediately after
+the first of the adjacent work, and so on. But by increasing the
+distance we may produce again a coincidence of the strokes. For example,
+the first stroke of the remote work coincides with the second of the
+near work, the second of the remote work with the third of the near
+work, and so on. If, now, the works strike tenths of seconds and the
+distance between them is increased until the first coincidence is noted,
+plainly that distance is travelled over by the sound in a tenth of a
+second.
+
+We meet frequently the phenomenon here presented, that a thought which
+centuries of slow and painful endeavor are necessary to produce, when
+once developed, fairly thrives. It spreads and runs everywhere, even
+entering minds in which it could never have arisen. It simply cannot be
+eradicated.
+
+The determination of the velocity of light is not the only case in which
+the direct perception of the senses is too slow and clumsy for use. The
+usual method of studying events too fleet for direct observation
+consists in putting into reciprocal action with them other events
+already known, the velocities of all of which are capable of comparison.
+The result is usually unmistakable, and susceptible of direct inference
+respecting the character of the event which is unknown. The velocity of
+electricity cannot be determined by direct observation. But it was
+ascertained by Wheatstone, simply by the expedient of watching an
+electric spark in a mirror rotating with tremendous known velocity.
+
+[Illustration: Fig. 17.]
+
+[Illustration: Fig. 18.]
+
+If we wave a staff irregularly hither and thither, simple observation
+cannot determine how quickly it moves at each point of its course. But
+let us look at the staff through holes in the rim of a rapidly rotating
+disk (Fig. 17). We shall then see the moving staff only in certain
+positions, namely, when a hole passes in front of the eye. The single
+pictures of the staff remain for a time impressed upon the eye; we think
+we see several staffs, having some such disposition as that represented
+in Fig. 18. If, now, the holes of the disk are equally far apart, and
+the disk is rotated with uniform velocity, we see clearly that the staff
+has moved slowly from _a_ to _b_, more quickly from _b_ to _c_, still
+more quickly from _c_ to _d_, and with its greatest velocity from _d_ to
+_e_.
+
+A jet of water flowing from an orifice in the bottom of a vessel has the
+appearance of perfect quiet and uniformity, but if we illuminate it for
+a second, in a dark room, by means of an electric flash we shall see
+that the jet is composed of separate drops. By their quick descent the
+images of the drops are obliterated and the jet appears uniform. Let us
+look at the jet through the rotating disk. The disk is supposed to be
+rotated so rapidly that while the second aperture passes into the place
+of the first, drop 1 falls into the place of 2, 2 into the place of 3,
+and so on. We see drops then always in the same places. The jet appears
+to be at rest. If we turn the disk a trifle more slowly, then while the
+second aperture passes into the place of the first, drop 1 will have
+fallen somewhat lower than 2, 2 somewhat lower than 3, etc. Through
+every successive aperture we shall see drops in successively lower
+positions. The jet will appear to be flowing slowly downwards.
+
+[Illustration: Fig. 19.]
+
+Now let us turn the disk more rapidly. Then while the second aperture is
+passing into the place of the first, drop 1 will not quite have reached
+the place of 2, but will be found slightly above 2, 2 slightly above 3,
+etc. Through the successive apertures we shall see the drops at
+successively higher places. It will now look as if the jet were flowing
+upwards, as if the drops were rising from the lower vessel into the
+higher.
+
+You see, physics grows gradually more and more terrible. The physicist
+will soon have it in his power to play the part of the famous lobster
+chained to the bottom of the Lake of Mohrin, whose direful mission, if
+ever liberated, the poet Kopisch humorously describes as that of a
+reversal of all the events of the world; the rafters of houses become
+trees again, cows calves, honey flowers, chickens eggs, and the poet's
+own poem flows back into his inkstand.
+
+       *       *       *       *       *
+
+You will now allow me the privilege of a few general remarks. You have
+seen that the same principle often lies at the basis of large classes of
+apparatus designed for different purposes. Frequently it is some very
+unobtrusive idea which is productive of so much fruit and of such
+extensive transformations in physical technics. It is not otherwise here
+than in practical life.
+
+The wheel of a waggon appears to us a very simple and insignificant
+creation. But its inventor was certainly a man of genius. The round
+trunk of a tree perhaps first accidentally led to the observation of the
+ease with which a load can be moved on a roller. Now, the step from a
+simple supporting roller to a fixed roller, or wheel, appears a very
+easy one. At least it appears very easy to us who are accustomed from
+childhood up to the action of the wheel. But if we put ourselves vividly
+into the position of a man who never saw a wheel, but had to invent one,
+we shall begin to have some idea of its difficulties. Indeed, it is
+even doubtful whether a single man could have accomplished this feat,
+whether perhaps centuries were not necessary to form the first wheel
+from the primitive roller.[16]
+
+History does not name the progressive minds who constructed the first
+wheel; their time lies far back of the historic period. No scientific
+academy crowned their efforts, no society of engineers elected them
+honorary members. They still live only in the stupendous results which
+they called forth. Take from us the wheel, and little will remain of the
+arts and industries of modern life. All disappears. From the
+spinning-wheel to the spinning-mill, from the turning-lathe to the
+rolling-mill, from the wheelbarrow to the railway train, all vanishes.
+
+In science the wheel is equally important. Whirling machines, as the
+simplest means of obtaining quick motions with inconsiderable changes of
+place, play a part in all branches of physics. You know Wheatstone's
+rotating mirror, Fizeau's wheel, Plateau's perforated rotating disks,
+etc. Almost the same principle lies at the basis of all these apparatus.
+They differ from one another no more than the pen-knife differs, in the
+purposes it serves, from the knife of the anatomist or the knife of the
+vine-dresser. Almost the same might be said of the screw.
+
+It will now perhaps be clear to you that new thoughts do not spring up
+suddenly. Thoughts need their time to ripen, grow, and develop in, like
+every natural product; for man, with his thoughts, is also a part of
+nature.
+
+Slowly, gradually, and laboriously one thought is transformed into a
+different thought, as in all likelihood one animal species is gradually
+transformed into new species. Many ideas arise simultaneously. They
+fight the battle for existence not otherwise than do the Ichthyosaurus,
+the Brahman, and the horse.
+
+A few remain to spread rapidly over all fields of knowledge, to be
+redeveloped, to be again split up, to begin again the struggle from the
+start. As many animal species long since conquered, the relicts of ages
+past, still live in remote regions where their enemies cannot reach
+them, so also we find conquered ideas still living on in the minds of
+many men. Whoever will look carefully into his own soul will acknowledge
+that thoughts battle as obstinately for existence as animals. Who will
+gainsay that many vanquished modes of thought still haunt obscure
+crannies of his brain, too faint-hearted to step out into the clear
+light of reason? What inquirer does not know that the hardest battle, in
+the transformation of his ideas, is fought with himself.
+
+Similar phenomena meet the natural inquirer in all paths and in the most
+trifling matters. The true inquirer seeks the truth everywhere, in his
+country-walks and on the streets of the great city. If he is not too
+learned, he will observe that certain things, like ladies' hats, are
+constantly subject to change. I have not pursued special studies on this
+subject, but as long as I can remember, one form has always gradually
+changed into another. First, they wore hats with long projecting rims,
+within which, scarcely accessible with a telescope, lay concealed the
+face of the beautiful wearer. The rim grew smaller and smaller; the
+bonnet shrank to the irony of a hat. Now a tremendous superstructure is
+beginning to grow up in its place, and the gods only know what its
+limits will be. It is not otherwise with ladies' hats than with
+butterflies, whose multiplicity of form often simply comes from a slight
+excrescence on the wing of one species developing in a cognate species
+to a tremendous fold. Nature, too, has its fashions, but they last
+thousands of years. I could elucidate this idea by many additional
+examples; for instance, by the history of the evolution of the coat, if
+I were not fearful that my gossip might prove irksome to you.
+
+       *       *       *       *       *
+
+We have now wandered through an odd corner of the history of science.
+What have we learned? The solution of a small, I might almost say
+insignificant, problem--the measurement of the velocity of light. And
+more than two centuries have worked at its solution! Three of the most
+eminent natural philosophers, Galileo, an Italian, Römer, a Dane, and
+Fizeau, a Frenchman, have fairly shared its labors. And so it is with
+countless other questions. When we contemplate thus the many blossoms of
+thought that must wither and fall before one shall bloom, then shall we
+first truly appreciate Christ's weighty but little consolatory words:
+"Many be called but few are chosen."
+
+Such is the testimony of every page of history. But is history right?
+Are really only those chosen whom she names? Have those lived and
+battled in vain, who have won no prize?
+
+I doubt it. And so will every one who has felt the pangs of sleepless
+nights spent in thought, at first fruitless, but in the end successful.
+No thought in such struggles was thought in vain; each one, even the
+most insignificant, nay, even the erroneous thought, that which
+apparently was the least productive, served to prepare the way for those
+that afterwards bore fruit. And as in the thought of the individual
+naught is in vain, so, also, it is in that of humanity.
+
+Galileo wished to measure the velocity of light. He had to close his
+eyes before his wish was realised. But he at least found the lantern by
+which his successor could accomplish the task.
+
+And so I may maintain that we all, so far as inclination goes, are
+working at the civilisation of the future. If only we all strive for the
+right, then are we _all_ called and _all_ chosen!
+
+  FOOTNOTES:
+
+  [Footnote 11: According to Mr. Jules Andrieu, the idea that nature
+  must be tortured to reveal her secrets is preserved in the name
+  _crucible_--from the Latin _crux_, a cross. But, more probably,
+  _crucible_ is derived from some Old French or Teutonic form, as
+  _cruche_, _kroes_, _krus_, etc., a pot or jug (cf. Modern English
+  _crock_, _cruse_, and German _Krug_).--_Trans._]
+
+  [Footnote 12: Xenophon, Memorabilia iv, 7, puts into the mouth of
+  Socrates these words: [Greek: oute gar heureta anthrôpois auta
+  enomizen einai, oute chaoizesthai theois an hêgeito ton zêtounta ha
+  ekeinoi saphênisai ouk eboulêthêsan].]
+
+  [Footnote 13: Galilei, _Discorsi e dimostrazione matematiche_.
+  Leyden, 1638. _Dialogo Primo._]
+
+  [Footnote 14: In the same way, the pitch of a locomotive-whistle is
+  higher as the locomotive rapidly approaches an observer, and lower
+  when rapidly leaving him than if the locomotive were at
+  rest.--_Trans._]
+
+  [Footnote 15: A kilometre is 0.621 or nearly five-eighths of a
+  statute mile.]
+
+  [Footnote 16: Observe, also, the respect in which the wheel is held
+  in India, Japan and other Buddhistic countries, as the emblem of
+  power, order, and law, and of the superiority of mind over matter.
+  The consciousness of the importance of this invention seems to have
+  lingered long in the minds of these nations.--_Tr._]
+
+
+
+
+WHY HAS MAN TWO EYES?
+
+
+Why has man two eyes? That the pretty symmetry of his face may not be
+disturbed, the artist answers. That his second eye may furnish a
+substitute for his first if that be lost, says the far-sighted
+economist. That we may weep with two eyes at the sins of the world,
+replies the religious enthusiast.
+
+Odd opinions! Yet if you should approach a modern scientist with this
+question you might consider yourself fortunate if you escaped with less
+than a rebuff. "Pardon me, madam, or my dear sir," he would say, with
+stern expression, "man fulfils no purpose in the possession of his eyes;
+nature is not a person, and consequently not so vulgar as to pursue
+purposes of any kind."
+
+Still an unsatisfactory answer! I once knew a professor who would shut
+with horror the mouths of his pupils if they put to him such an
+unscientific question.
+
+But ask a more tolerant person, ask me. I, I candidly confess, do not
+know exactly why man has two eyes, but the reason partly is, I think,
+that I may see you here before me to-night and talk with you upon this
+delightful subject.
+
+Again you smile incredulously. Now this is one of those questions that a
+hundred wise men together could not answer. You have heard, so far, only
+five of these wise men. You will certainly want to be spared the
+opinions of the other ninety-five. To the first you will reply that we
+should look just as pretty if we were born with only one eye, like the
+Cyclops; to the second we should be much better off, according to his
+principle, if we had four or eight eyes, and that in this respect we are
+vastly inferior to spiders; to the third, that you are not just in the
+mood to weep; to the fourth, that the unqualified interdiction of the
+question excites rather than satisfies your curiosity; while of me you
+will dispose by saying that my pleasure is not as intense as I think,
+and certainly not great enough to justify the existence of a double eye
+in man since the fall of Adam.
+
+But since you are not satisfied with my brief and obvious answer, you
+have only yourselves to blame for the consequences. You must now listen
+to a longer and more learned explanation, such as it is in my power to
+give.
+
+As the church of science, however, debars the question "Why?" let us put
+the matter in a purely orthodox way: Man has two eyes, what _more_ can
+he see with two than with one?
+
+I will invite you to take a walk with me? We see before us a wood. What
+is it that makes this real wood contrast so favorably with a painted
+wood, no matter how perfect the painting may be? What makes the one so
+much more lovely than the other? Is it the vividness of the coloring,
+the distribution of the lights and the shadows? I think not. On the
+contrary, it seems to me that in this respect painting can accomplish
+very much.
+
+The cunning hand of the painter can conjure up with a few strokes of his
+brush forms of wonderful plasticity. By the help of other means even
+more can be attained. Photographs of reliefs are so plastic that we
+often imagine we can actually lay hold of the elevations and
+depressions.
+
+[Illustration: Fig. 20.]
+
+But one thing the painter never can give with the vividness that nature
+does--the difference of near and far. In the real woods you see plainly
+that you can lay hold of some trees, but that others are inaccessibly
+far. The picture of the painter is rigid. The picture of the real woods
+changes on the slightest movement. Now this branch is hidden behind
+that; now that behind this. The trees are alternately visible and
+invisible.
+
+Let us look at this matter a little more closely. For convenience sake
+we shall remain upon the highway, I, II. (Fig. 20.) To the right and the
+left lies the forest. Standing at I, we see, let us say, three trees (1,
+2, 3) in a line, so that the two remote ones are covered by the nearest.
+Moving further along, this changes. At II we shall not have to look
+round so far to see the remotest tree 3 as to see the nearer tree 2, nor
+so far to see this as to see 1. _Hence, as we move onward, objects that
+are near to us seem to lag behind as compared with objects that are
+remote from us, the lagging increasing with the proximity of the
+objects._ Very remote objects, towards which we must always look in the
+same direction as we proceed, appear to travel along with us.
+
+If we should see, therefore, jutting above the brow of yonder hill the
+tops of two trees whose distance from us we were in doubt about, we
+should have in our hands a very easy means of deciding the question. We
+should take a few steps forward, say to the right, and the tree-top
+which receded most to the left would be the one nearer to us. In truth,
+from the amount of the recession a geometer could actually determine the
+distance of the trees from us without ever going near them. It is simply
+the scientific development of this perception that enables us to
+measure the distances of the stars.
+
+_Hence, from change of view in forward motion the distances of objects
+in our field of vision can be measured._
+
+Rigorously, however, even forward motion is not necessary. For every
+observer is composed really of _two_ observers. Man has _two_ eyes. The
+right eye is a short step ahead of the left eye in the right-hand
+direction. Hence, the two eyes receive _different_ pictures of the same
+woods. The right eye will see the near trees displaced to the left, and
+the left eye will see them displaced to the right, the displacement
+being greater, the greater the proximity. This difference is sufficient
+for forming ideas of distance.
+
+We may now readily convince ourselves of the following facts:
+
+1. With one eye, the other being shut, you have a very uncertain
+judgment of distances. You will find it, for example, no easy task, with
+one eye shut, to thrust a stick through a ring hung up before you; you
+will miss the ring in almost every instance.
+
+2. You see the same object differently with the right eye from what you
+do with the left.
+
+Place a lamp-shade on the table in front of you with its broad opening
+turned downwards, and look at it from above. (Fig. 21.) You will see
+with your right eye the image 2, with your left eye the image 1. Again,
+place the shade with its wide opening turned upwards; you will receive
+with your right eye the image 4, with your left eye the image 3. Euclid
+mentions phenomena of this character.
+
+3. Finally, you know that it is easy to judge of distances with both
+eyes. Accordingly your judgment must spring in some way from a
+co-operation of the two eyes. In the preceding example the openings in
+the different images received by the two eyes seem displaced with
+respect to one another, and this displacement is sufficient for the
+inference that the one opening is nearer than the other.
+
+[Illustration: Fig. 21.]
+
+I have no doubt that you, ladies, have frequently received delicate
+compliments upon your eyes, but I feel sure that no one has ever told
+you, and I know not whether it will flatter you, that you have in your
+eyes, be they blue or black, little geometricians. You say you know
+nothing of them? Well, for that matter, neither do I. But the facts are
+as I tell you.
+
+You understand little of geometry? I shall accept that confession. Yet
+with the help of your two eyes you judge of distances? Surely that is a
+geometrical problem. And what is more, you know the solution of this
+problem: for you estimate distances correctly. If, then, _you_ do not
+solve the problem, the little geometricians in your eyes must do it
+clandestinely and whisper the solution to you. I doubt not they are
+fleet little fellows.
+
+What amazes me most here is, that you know nothing about these little
+geometricians. But perhaps they also know nothing about you. Perhaps
+they are models of punctuality, routine clerks who bother about nothing
+but their fixed work. In that case we may be able to deceive the
+gentlemen.
+
+If we present to our right eye an image which looks exactly like the
+lamp-shade for the right eye, and to our left eye an image which looks
+exactly like a lamp-shade for the left eye, we shall imagine that we see
+the whole lamp-shade bodily before us.
+
+You know the experiment. If you are practised in squinting, you can
+perform it directly with the figure, looking with your right eye at the
+right image, and with your left eye at the left image. In this way the
+experiment was first performed by Elliott. Improved and perfected, its
+form is Wheatstone's stereoscope, made so popular and useful by
+Brewster.
+
+By taking two photographs of the same object from two different points,
+corresponding to the two eyes, a very clear three-dimensional picture of
+distant places or buildings can be produced by the stereoscope.
+
+But the stereoscope accomplishes still more than this. It can visualise
+things for us which we never see with equal clearness in real objects.
+You know that if you move much while your photograph is being taken,
+your picture will come out like that of a Hindu deity, with several
+heads or several arms, which, at the spaces where they overlap, show
+forth with equal distinctness, so that we seem to see the one picture
+_through_ the other. If a person moves quickly away from the camera
+before the impression is completed, the objects behind him will also be
+imprinted upon the photograph; the person will look transparent.
+Photographic ghosts are made in this way.
+
+Some very useful applications may be made of this discovery. For
+example, if we photograph a machine stereoscopically, successively
+removing during the operation the single parts (where of course the
+impression suffers interruptions), we obtain a transparent view, endowed
+with all the marks of spatial solidity, in which is distinctly
+visualised the interaction of parts normally concealed. I have employed
+this method for obtaining transparent stereoscopic views of anatomical
+structures.
+
+You see, photography is making stupendous advances, and there is great
+danger that in time some malicious artist will photograph his innocent
+patrons with solid views of their most secret thoughts and emotions. How
+tranquil politics will then be! What rich harvests our detective force
+will reap!
+
+       *       *       *       *       *
+
+By the joint action of the two eyes, therefore, we arrive at our
+judgments of distances, as also of the forms of bodies.
+
+Permit me to mention here a few additional facts connected with this
+subject, which will assist us in the comprehension of certain phenomena
+in the history of civilisation.
+
+You have often heard, and know from personal experience, that remote
+objects appear perspectively dwarfed. In fact, it is easy to satisfy
+yourself that you can cover the image of a man a few feet away from you
+simply by holding up your finger a short distance in front of your eye.
+Still, as a general rule, you do not notice this shrinkage of objects.
+On the contrary, you imagine you see a man at the end of a large hall,
+as large as you see him near by you. For your eye, in its measurement of
+the distances, makes remote objects correspondingly larger. The eye, so
+to speak, is aware of this perspective contraction and is not deceived
+by it, although its possessor is unconscious of the fact. All persons
+who have attempted to draw from nature have vividly felt the difficulty
+which this superior dexterity of the eye causes the perspective
+conception. Not until one's judgment of distances is made uncertain, by
+their size, or from lack of points of reference, or from being too
+quickly changed, is the perspective rendered very prominent.
+
+On sweeping round a curve on a rapidly moving railway train, where a
+wide prospect is suddenly opened up, the men upon distant hills appear
+like dolls.[17] You have at the moment, here, no known references for
+the measurement of distances. The stones at the entrance of a tunnel
+grow visibly larger as we ride towards it; they shrink visibly in size
+as we ride from it.
+
+Usually both eyes work together. As certain views are frequently
+repeated, and lead always to substantially the same judgments of
+distances, the eyes in time must acquire a special skill in geometrical
+constructions. In the end, undoubtedly, this skill is so increased that
+a single eye alone is often tempted to exercise that office.
+
+Permit me to elucidate this point by an example. Is any sight more
+familiar to you than that of a vista down a long street? Who has not
+looked with hopeful eyes time and again into a street and measured its
+depth. I will take you now into an art-gallery where I will suppose you
+to see a picture representing a vista into a street. The artist has not
+spared his rulers to get his perspective perfect. The geometrician in
+your left eye thinks, "Ah ha! I have computed that case a hundred times
+or more. I know it by heart. It is a vista into a street," he continues;
+"where the houses are lower is the remote end." The geometrician in the
+right eye, too much at his ease to question his possibly peevish comrade
+in the matter, answers the same. But the sense of duty of these punctual
+little fellows is at once rearoused. They set to work at their
+calculations and immediately find that all the points of the picture are
+equally distant from them, that is, lie all upon a plane surface.
+
+What opinion will you now accept, the first or the second? If you accept
+the first you will see distinctly the vista. If you accept the second
+you will see nothing but a painted sheet of distorted images.
+
+It seems to you a trifling matter to look at a picture and understand
+its perspective. Yet centuries elapsed before humanity came fully to
+appreciate this trifle, and even the majority of you first learned it
+from education.
+
+I can remember very distinctly that at three years of age all
+perspective drawings appeared to me as gross caricatures of objects. I
+could not understand why artists made tables so broad at one end and so
+narrow at the other. Real tables seemed to me just as broad at one end
+as at the other, because my eye made and interpreted its calculations
+without my intervention. But that the picture of the table on the plane
+surface was not to be conceived as a plane painted surface but stood for
+a table and so was to be imaged with all the attributes of extension was
+a joke that I did not understand. But I have the consolation that whole
+nations have not understood it.
+
+Ingenuous people there are who take the mock murders of the stage for
+real murders, the dissembled actions of the players for real actions,
+and who can scarcely restrain themselves, when the characters of the
+play are sorely pressed, from running in deep indignation to their
+assistance. Others, again, can never forget that the beautiful
+landscapes of the stage are painted, that Richard III. is only the
+actor, Mr. Booth, whom they have met time and again at the clubs.
+
+Both points of view are equally mistaken. To look at a drama or a
+picture properly one must understand that both are _shows_, simply
+_denoting_ something real. A certain preponderance of the intellectual
+life over the sensuous life is requisite for such an achievement, where
+the intellectual elements are safe from destruction by the direct
+sensuous impressions. A certain liberty in choosing one's point of view
+is necessary, a sort of humor, I might say, which is strongly wanting in
+children and in childlike peoples.
+
+Let us look at a few historical facts. I shall not take you as far back
+as the stone age, although we possess sketches from this epoch which
+show very original ideas of perspective. But let us begin our
+sight-seeing in the tombs and ruined temples of ancient Egypt, where the
+numberless reliefs and gorgeous colorings have defied the ravages of
+thousands of years.
+
+A rich and motley life is here opened to us. We find the Egyptians
+represented in all conditions of life. What at once strikes our
+attention in these pictures is the delicacy of their technical
+execution. The contours are extremely exact and distinct. But on the
+other hand only a few bright colors are found, unblended and without
+trace of transition. Shadows are totally wanting. The paint is laid on
+the surfaces in equal thicknesses.
+
+Shocking for the modern eye is the perspective. All the figures are
+equally large, with the exception of the king, whose form is unduly
+exaggerated. Near and far appear equally large. Perspective contraction
+is nowhere employed. A pond with water-fowl is represented flat, as if
+its surface were vertical.
+
+Human figures are portrayed as they are never seen, the legs from the
+side, the face in profile. The breast lies in its full breadth across
+the plane of representation. The heads of cattle appear in profile,
+while the horns lie in the plane of the drawing. The principle which the
+Egyptians followed might be best expressed by saying that their figures
+are pressed in the plane of the drawing as plants are pressed in a
+herbarium.
+
+The matter is simply explained. If the Egyptians were accustomed to
+looking at things ingenuously with both eyes at once, the construction
+of perspective pictures in space could not be familiar to them. They saw
+all arms, all legs on real men in their natural lengths. The figures
+pressed into the planes resembled more closely, of course, in their eyes
+the originals than perspective pictures could.
+
+This will be better understood if we reflect that painting was developed
+from relief. The minor dissimilarities between the pressed figures and
+the originals must gradually have compelled men to the adoption of
+perspective drawing. But physiologically the painting of the Egyptians
+is just as much justified as the drawings of our children are.
+
+A slight advance beyond the Egyptians is shown by the Assyrians. The
+reliefs rescued from the ruined mounds of Nimrod at Mossul are, upon the
+whole, similar to the Egyptian reliefs. They were made known to us
+principally by Layard.
+
+Painting enters on a new phase among the Chinese. This people have a
+marked feeling for perspective and correct shading, yet without being
+very logical in the application of their principles. Here, too, it
+seems, they took the first step but did not go far. In harmony with this
+immobility is their constitution, in which the muzzle and the bamboo-rod
+play significant functions. In accord with it, too, is their language,
+which like the language of children has not yet developed into a
+grammar, or, rather, according to the modern conception, has not yet
+degenerated into a grammar. It is the same also with their music which
+is satisfied with the five-toned scale.
+
+The mural paintings at Herculaneum and Pompeii are distinguished by
+grace of representation, as also by a pronounced sense for perspective
+and correct illumination, yet they are not at all scrupulous in
+construction. Here still we find abbreviations avoided. But to offset
+this defect, the members of the body are brought into unnatural
+positions, in which they appear in their full lengths. Abridgements are
+more frequently observed in clothed than in unclothed figures.
+
+A satisfactory explanation of these phenomena first occurred to me on
+the making of a few simple experiments which show how differently one
+may see the same object, after some mastery of one's senses has been
+attained, simply by the arbitrary movement of the attention.
+
+[Illustration: Fig. 22.]
+
+Look at the annexed drawing (Fig. 22). It represents a folded sheet of
+paper with either its depressed or its elevated side turned towards you,
+as you wish. You can conceive the drawing in either sense, and in either
+case it will appear to you differently.
+
+If, now, you have a real folded sheet of paper on the table before you,
+with its sharp edges turned towards you, you can, on looking at it with
+one eye, see the sheet alternately elevated, as it really is, or
+depressed. Here, however, a remarkable phenomenon is presented. When you
+see the sheet properly, neither illumination nor form presents anything
+conspicuous. When you see it bent back you see it perspectively
+distorted. Light and shadow appear much brighter or darker, or as if
+overlaid thickly with bright colors. Light and shadow now appear devoid
+of all cause. They no longer harmonise with the body's form, and are
+thus rendered much more prominent.
+
+In common life we employ the perspective and illumination of objects to
+determine their forms and position. Hence we do not notice the lights,
+the shadows, and the distortions. They first powerfully enter
+consciousness when we employ a different construction from the usual
+spatial one. In looking at the planar image of a camera obscura we are
+amazed at the plenitude of the light and the profundity of the shadows,
+both of which we do not notice in real objects.
+
+In my earliest youth the shadows and lights on pictures appeared to me
+as spots void of meaning. When I began to draw I regarded shading as a
+mere custom of artists. I once drew the portrait of our pastor, a friend
+of the family, and shaded, from no necessity, but simply from having
+seen something similar in other pictures, the whole half of his face
+black. I was subjected for this to a severe criticism on the part of my
+mother, and my deeply offended artist's pride is probably the reason
+that these facts remained so strongly impressed upon my memory.
+
+You see, then, that many strange things, not only in the life of
+individuals, but also in that of humanity, and in the history of general
+civilisation, may be explained from the simple fact that man has two
+eyes.
+
+Change man's eye and you change his conception of the world. We have
+observed the truth of this fact among our nearest kin, the Egyptians,
+the Chinese, and the lake-dwellers; how must it be among some of our
+remoter relatives,--with monkeys and other animals? Nature must appear
+totally different to animals equipped with substantially different eyes
+from those of men, as, for example, to insects. But for the present
+science must forego the pleasure of portraying this appearance, as we
+know very little as yet of the mode of operation of these organs.
+
+It is an enigma even how nature appears to animals closely related to
+man; as to birds, who see scarcely anything with two eyes at once, but
+since their eyes are placed on opposite sides of their heads, have a
+separate field of vision for each.[18]
+
+The soul of man is pent up in the prison-house of his head; it looks at
+nature through its two windows, the eyes. It would also fain know how
+nature looks through other windows. A desire apparently never to be
+fulfilled. But our love for nature is inventive, and here, too, much has
+been accomplished.
+
+Placing before me an angular mirror, consisting of two plane mirrors
+slightly inclined to each other, I see my face twice reflected. In the
+right-hand mirror I obtain a view of the right side, and in the
+left-hand mirror a view of the left side, of my face. Also I shall see
+the face of a person standing in front of me, more to the right with my
+right eye, more to the left with my left. But in order to obtain such
+widely different views of a face as those shown in the angular mirror,
+my two eyes would have to be set much further apart from each other than
+they actually are.
+
+[Illustration: Fig. 23.]
+
+Squinting with my right eye at the image in the right-hand mirror, with
+my left eye at the image in the left-hand mirror, my vision will be the
+vision of a giant having an enormous head with his two eyes set far
+apart. This, also, is the impression which my own face makes upon me. I
+see it now, single and solid. Fixing my gaze, the relief from second to
+second is magnified, the eyebrows start forth prominently from above the
+eyes, the nose seems to grow a foot in length, my mustache shoots forth
+like a fountain from my lip, the teeth seem to retreat immeasurably. But
+by far the most horrible aspect of the phenomenon is the nose.
+
+Interesting in this connexion is the telestereoscope of Helmholtz. In
+the telestereoscope we view a landscape by looking with our right eye
+(Fig. 24) through the mirror _a_ into the mirror _A_, and with our left
+eye through the mirror _b_ into the mirror _B_. The mirrors _A_ and _B_
+stand far apart. Again we see with the widely separated eyes of a giant.
+Everything appears dwarfed and near us. The distant mountains look like
+moss-covered stones at our feet. Between, you see the reduced model of a
+city, a veritable Liliput. You are tempted almost to stroke with your
+hand the soft forest and city, did you not fear that you might prick
+your fingers on the sharp, needle-shaped steeples, or that they might
+crackle and break off.
+
+[Illustration: Fig. 24.]
+
+Liliput is no fable. We need only Swift's eyes, the telestereoscope, to
+see it.
+
+Picture to yourself the reverse case. Let us suppose ourselves so small
+that we could take long walks in a forest of moss, and that our eyes
+were correspondingly near each other. The moss-fibres would appear like
+trees. On them we should see strange, unshapely monsters creeping about.
+Branches of the oak-tree, at whose base our moss-forest lay, would seem
+to us dark, immovable, myriad-branched clouds, painted high on the vault
+of heaven; just as the inhabitants of Saturn, forsooth, might see their
+enormous ring. On the tree-trunks of our mossy woodland we should find
+colossal globes several feet in diameter, brilliantly transparent,
+swayed by the winds with slow, peculiar motions. We should approach
+inquisitively and should find that these globes, in which here and there
+animals were gaily sporting, were liquid globes, in fact that they were
+water. A short, incautious step, the slightest contact, and woe betide
+us, our arm is irresistibly drawn by an invisible power into the
+interior of the sphere and held there unrelentingly fast! A drop of dew
+has engulfed in its capillary maw a manikin, in revenge for the
+thousands of drops that its big human counterparts have quaffed at
+breakfast. Thou shouldst have known, thou pygmy natural scientist, that
+with thy present puny bulk thou shouldst not joke with capillarity!
+
+My terror at the accident brings me back to my senses. I see I have
+turned idyllic. You must pardon me. A patch of greensward, a moss or
+heather forest with its tiny inhabitants have incomparably more charms
+for me than many a bit of literature with its apotheosis of human
+character. If I had the gift of writing novels I should certainly not
+make John and Mary my characters. Nor should I transfer my loving pair
+to the Nile, nor to the age of the old Egyptian Pharaohs, although
+perhaps I should choose that time in preference to the present. For I
+must candidly confess that I hate the rubbish of history, interesting
+though it may be as a mere phenomenon, because we cannot simply observe
+it but must also _feel_ it, because it comes to us mostly with
+supercilious arrogance, mostly unvanquished. The hero of my novel would
+be a cockchafer, venturing forth in his fifth year for the first time
+with his newly grown wings into the light, free air. Truly it could do
+no harm if man would thus throw off his inherited and acquired
+narrowness of mind by making himself acquainted with the world-view of
+allied creatures. He could not help gaining incomparably more in this
+way than the inhabitant of a small town would in circumnavigating the
+globe and getting acquainted with the views of strange peoples.
+
+       *       *       *       *       *
+
+I have now conducted you, by many paths and by-ways, rapidly over hedge
+and ditch, to show you what wide vistas we may reach in every field by
+the rigorous pursuit of a single scientific fact. A close examination of
+the two eyes of man has conducted us not only into the dim recesses of
+humanity's childhood, but has also carried us far beyond the bourne of
+human life.
+
+It has surely often struck you as strange that the sciences are divided
+into two great groups; that the so-called humanistic sciences, belonging
+to the so-called "higher education," are placed in almost a hostile
+attitude to the natural sciences.
+
+I must confess I do not overmuch believe in this partition of the
+sciences. I believe that this view will appear as childlike and
+ingenuous to a matured age as the want of perspective in the old
+paintings of Egypt does to us. Can it really be that "higher culture" is
+to be gotten only from a few old pots and palimpsests, which are at best
+mere scraps of nature, or that more is to be learned from them alone
+than from all the rest of nature? I believe that both these sciences are
+simply parts of the same science, which have begun at different ends. If
+these two ends still act towards each other as the Montagues and
+Capulets, if their retainers still indulge in lively tilts, I believe
+that after all they are not in earnest. On the one side there is surely
+a Romeo, and on the other a Juliet, who, some day, it is hoped, will
+unite the two houses with a less tragic sequel than that of the play.
+
+Philology began with the unqualified reverence and apotheosis of the
+Greeks. Now it has begun to draw other languages, other peoples and
+their histories, into its sphere; it has, through the mediation of
+comparative linguistics, already struck up, though as yet somewhat
+cautiously, a friendship with physiology.
+
+Physical science began in the witch's kitchen. It now embraces the
+organic and inorganic worlds, and with the physiology of articulation
+and the theory of the senses, has even pushed its researches, at times
+impertinently, into the province of mental phenomena.
+
+In short, we come to the understanding of much within us solely by
+directing our glance without, and _vice versa_. Every object belongs to
+both sciences. You, ladies, are very interesting and difficult problems
+for the psychologist, but you are also extremely pretty phenomena of
+nature. Church and State are objects of the historian's research, but
+not less phenomena of nature, and in part, indeed, very curious
+phenomena. If the historical sciences have inaugurated wide extensions
+of view by presenting to us the thoughts of new and strange peoples, the
+physical sciences in a certain sense do this in a still greater degree.
+In making man disappear in the All, in annihilating him, so to speak,
+they force him to take an unprejudiced position without himself, and to
+form his judgments by a different standard from that of the petty human.
+
+But if you should ask me now why man has two eyes, I should answer:
+
+That he may look at nature justly and accurately; that he may come to
+understand that he himself, with all his views, correct and incorrect,
+with all his _haute politique_, is simply an evanescent shred of nature;
+that, to speak with Mephistopheles, he is a part of the part, and that
+it is absolutely unjustified,
+
+    "For man, the microcosmic fool, to see
+    Himself a whole so frequently."
+
+  FOOTNOTES:
+
+  [Footnote 17: This effect is particularly noticeable in the size of
+  workmen on high chimneys and church-steeples--"steeple Jacks." When
+  the cables were slung from the towers of the Brooklyn bridge (277
+  feet high), the men sent out in baskets to paint them, appeared,
+  against the broad background of heaven and water, like
+  flies.--_Trans._]
+
+  [Footnote 18: See Joh. Müller, _Vergleichende Physiologie des
+  Gesichtssinnes_, Leipsic, 1826.]
+
+
+
+
+ON SYMMETRY.[19]
+
+
+An ancient philosopher once remarked that people who cudgelled their
+brains about the nature of the moon reminded him of men who discussed
+the laws and institutions of a distant city of which they had heard no
+more than the name. The true philosopher, he said, should turn his
+glance within, should study himself and his notions of right and wrong;
+only thence could he derive real profit.
+
+This ancient formula for happiness might be restated in the familiar
+words of the Psalm:
+
+    "Dwell in the land, and verily thou shalt be fed."
+
+To-day, if he could rise from the dead and walk about among us, this
+philosopher would marvel much at the different turn which matters have
+taken.
+
+The motions of the moon and the other heavenly bodies are accurately
+known. Our knowledge of the motions of our own body is by far not so
+complete. The mountains and natural divisions of the moon have been
+accurately outlined on maps, but physiologists are just beginning to
+find their way in the geography of the brain. The chemical constitution
+of many fixed stars has already been investigated. The chemical
+processes of the animal body are questions of much greater difficulty
+and complexity. We have our _Mécanique céleste_. But a _Mécanique
+sociale_ or a _Mécanique morale_ of equal trustworthiness remains to be
+written.
+
+Our philosopher would indeed admit that we have made great progress. But
+we have not followed his advice. The patient has recovered, but he took
+for his recovery exactly the opposite of what the doctor prescribed.
+
+Humanity is now returned, much wiser, from its journey in celestial
+space, against which it was so solemnly warned. Men, after having become
+acquainted with the great and simple facts of the world without, are now
+beginning to examine critically the world within. It sounds absurd, but
+it is true, that only after we have thought about the moon are we able
+to take up ourselves. It was necessary that we should acquire simple and
+clear ideas in a less complicated domain, before we entered the more
+intricate one of psychology, and with these ideas astronomy principally
+furnished us.
+
+To attempt any description of that stupendous movement, which,
+originally springing out of the physical sciences, went beyond the
+domain of physics and is now occupied with the problems of psychology,
+would be presumptuous in this place. I shall only attempt here, to
+illustrate to you by a few simple examples the methods by which the
+province of psychology can be reached from the facts of the physical
+world--especially the adjacent province of sense-perception. And I wish
+it to be remembered that my brief attempt is not to be taken as a
+measure of the present state of such scientific questions.
+
+       *       *       *       *       *
+
+It is a well-known fact that some objects please us, while others do
+not. Generally speaking, anything that is constructed according to fixed
+and logically followed rules, is a product of tolerable beauty. We see
+thus nature herself, who always acts according to fixed rules,
+constantly producing such pretty things. Every day the physicist is
+confronted in his workshop with the most beautiful vibration-figures,
+tone-figures, phenomena of polarisation, and forms of diffraction.
+
+A rule always presupposes a repetition. Repetitions, therefore, will
+probably be found to play some important part in the production of
+agreeable effects. Of course, the nature of agreeable effects is not
+exhausted by this. Furthermore, the repetition of a physical event
+becomes the source of agreeable effects only when it is connected with
+a repetition of sensations.
+
+An excellent example that repetition of sensations is a source of
+agreeable effects is furnished by the copy-book of every schoolboy,
+which is usually a treasure-house of such things, and only in need of an
+Abbé Domenech to become celebrated. Any figure, no matter how crude or
+poor, if several times repeated, with the repetitions placed in line,
+will produce a tolerable frieze.
+
+[Illustration: Fig. 25.]
+
+Also the pleasant effect of symmetry is due to the repetition of
+sensations. Let us abandon ourselves a moment to this thought, yet not
+imagine when we have developed it, that we have fully exhausted the
+nature of the agreeable, much less of the beautiful.
+
+First, let us get a clear conception of what symmetry is. And in
+preference to a definition let us take a living picture. You know that
+the reflexion of an object in a mirror has a great likeness to the
+object itself. All its proportions and outlines are the same. Yet there
+is a difference between the object and its reflexion in the mirror,
+which you will readily observe.
+
+Hold your right hand before a mirror, and you will see in the mirror a
+left hand. Your right glove will produce its mate in the glass. For you
+could never use the reflexion of your right glove, if it were present to
+you as a real thing, for covering your right hand, but only for covering
+your left. Similarly, your right ear will give as its reflexion a left
+ear; and you will at once perceive that the left half of your body could
+very easily be substituted for the reflexion of your right half. Now
+just as in the place of a missing right ear a left ear cannot be put,
+unless the lobule of the ear be turned upwards, or the opening into the
+concha backwards, so, despite all similarity of form, the reflexion of
+an object can never take the place of the object itself.[20]
+
+The reason of this difference between the object and its reflexion is
+simple. The reflexion appears as far behind the mirror as the object is
+in front of it. The parts of the object, accordingly, which are nearest
+the mirror will also be nearest the mirror in the reflexion.
+Consequently, the succession of the parts in the reflexion will be
+reversed, as may best be seen in the reflexion of the face of a watch or
+of a manuscript.
+
+It will also be readily seen, that if a point of the object be joined
+with its reflexion in the image, the line of junction will cut the
+mirror at right angles and be bisected by it. This holds true of all
+corresponding points of object and image.
+
+If, now, we can divide an object by a plane into two halves so that each
+half, as seen in the reflecting plane of division, is a reproduction of
+the other half, such an object is termed symmetrical, and the plane of
+division is called the plane of symmetry.
+
+If the plane of symmetry is vertical, we can say that the body is
+vertically symmetrical. An example of vertical symmetry is a Gothic
+cathedral.
+
+If the plane of symmetry is horizontal, we can say that the object is
+horizontally symmetrical. A landscape on the shores of a lake with its
+reflexion in the water, is a system of horizontal symmetry.
+
+Exactly here is a noticeable difference. The vertical symmetry of a
+Gothic cathedral strikes us at once, whereas we can travel up and down
+the whole length of the Rhine or the Hudson without becoming aware of
+the symmetry between objects and their reflexions in the water. Vertical
+symmetry pleases us, whilst horizontal symmetry is indifferent, and is
+noticed only by the experienced eye.
+
+Whence arises this difference? I say from the fact that vertical
+symmetry produces a repetition of the same sensation, while horizontal
+symmetry does not. I shall now show that this is so.
+
+Let us look at the following letters:
+
+  d b
+  q p
+
+It is a fact known to all mothers and teachers, that children in their
+first attempts to read and write, constantly confound d and b, and q and
+p, but never d and q, or b and p. Now d and b and q and p are the two
+halves of a _vertically_ symmetrical figure, while d and q, and b and p
+are two halves of a _horizontally_ symmetrical figure. The first two are
+confounded; but confusion is only possible of things that excite in us
+the same or similar sensations.
+
+Figures of two flower-girls are frequently seen on the decorations of
+gardens and of drawing-rooms, one of whom carries a flower-basket in her
+right hand and the other a flower-basket in her left. All know how apt
+we are, unless we are very careful, to confound these figures with one
+another.
+
+While turning a thing round from right to left is scarcely noticed, the
+eye is not at all indifferent to the turning of a thing upside down. A
+human face which has been turned upside down is scarcely recognisable as
+a face, and makes an impression which is altogether strange. The reason
+of this is not to be sought in the unwontedness of the sight, for it is
+just as difficult to recognise an arabesque that has been inverted,
+where there can be no question of a habit. This curious fact is the
+foundation of the familiar jokes played with the portraits of unpopular
+personages, which are so drawn that in the upright position of the page
+an exact picture of the person is presented, but on being inverted some
+popular animal is shown.
+
+It is a fact, then, that the two halves of a vertically symmetrical
+figure are easily confounded and that they therefore probably produce
+very nearly the same sensations. The question, accordingly, arises,
+_why_ do the two halves of a vertically symmetrical figure produce the
+same or similar sensations? The answer is: Because our apparatus of
+vision, which consists of our eyes and of the accompanying muscular
+apparatus is itself vertically symmetrical.[21]
+
+Whatever external resemblances one eye may have with another they are
+still not alike. The right eye of a man cannot take the place of a left
+eye any more than a left ear or left hand can take the place of a right
+one. By artificial means, we can change the part which each of our eyes
+plays. (Wheatstone's pseudoscope.) But we then find ourselves in an
+entirely new and strange world. What is convex appears concave; what is
+concave, convex. What is distant appears near, and what is near appears
+far.
+
+The left eye is the reflexion of the right. And the light-feeling retina
+of the left eye is a reflexion of the light-feeling retina of the right,
+in all its functions.
+
+The lense of the eye, like a magic lantern, casts images of objects on
+the retina. And you may picture to yourself the light-feeling retina of
+the eye, with its countless nerves, as a hand with innumerable fingers,
+adapted to feeling light. The ends of the visual nerves, like our
+fingers, are endowed with varying degrees of sensitiveness. The two
+retinæ act like a right and a left hand; the sensation of touch and the
+sensation of light in the two instances are similar.
+
+Examine the right-hand portion of this letter T: namely, T. Instead of
+the two retinæ on which this image falls, imagine feeling the object, my
+two hands. The T, grasped with the right hand, gives a different
+sensation from that which it gives when grasped with the left. But if we
+turn our character about from right to left, thus: T, it will give the
+same sensation in the left hand that it gave before in the right. The
+sensation is repeated.
+
+If we take a whole T, the right half will produce in the right hand the
+same sensation that the left half produces in the left, and _vice
+versa_.
+
+The symmetrical figure gives the same sensation twice.
+
+If we turn the T over thus: T, or invert the half T thus: L, so long as
+we do not change the position of our hands we can make no use of the
+foregoing reasoning.
+
+The retinæ, in fact, are exactly like our two hands. They, too, have
+their thumbs and index fingers, though they are thousands in number; and
+we may say the thumbs are on the side of the eye near the nose, and the
+remaining fingers on the side away from the nose.
+
+With this I hope to have made perfectly clear that the pleasing effect
+of symmetry is chiefly due to the repetition of sensations, and that
+the effect in question takes place in symmetrical figures, only where
+there is a repetition of sensation. The pleasing effect of regular
+figures, the preference which straight lines, especially vertical and
+horizontal straight lines, enjoy, is founded on a similar reason. A
+straight line, both in a horizontal and in a vertical position, can cast
+on the two retinæ the same image, which falls moreover on symmetrically
+corresponding spots. This also, it would appear, is the reason of our
+psychological preference of straight to curved lines, and not their
+property of being the shortest distance between two points. The straight
+line is felt, to put the matter briefly, as symmetrical to itself, which
+is the case also with the plane. Curved lines are felt as deviations
+from straight lines, that is, as deviations from symmetry.[22] The
+presence of a sense for symmetry in people possessing only one eye from
+birth, is indeed a riddle. Of course, the sense of symmetry, although
+primarily acquired by means of the eyes, cannot be wholly limited to the
+visual organs. It must also be deeply rooted in other parts of the
+organism by ages of practice and can thus not be eliminated forthwith by
+the loss of one eye. Also, when an eye is lost, the symmetrical muscular
+apparatus is left, as is also the symmetrical apparatus of innervation.
+
+
+It appears, however, unquestionable that the phenomena mentioned have,
+in the main, their origin in the peculiar structure of our eyes. It will
+therefore be seen at once that our notions of what is beautiful and ugly
+would undergo a change if our eyes were different. Also, if this view is
+correct, the theory of the so-called eternally beautiful is somewhat
+mistaken. It can scarcely be doubted that our culture, or form of
+civilisation, which stamps upon the human body its unmistakable traces,
+should not also modify our conceptions of the beautiful. Was not
+formerly the development of all musical beauty restricted to the narrow
+limits of a five-toned scale?
+
+The fact that a repetition of sensations is productive of pleasant
+effects is not restricted to the realm of the visible. To-day, both the
+musician and the physicist know that the harmonic or the melodic
+addition of one tone to another affects us agreeably only when the added
+tone reproduces a part of the sensation which the first one excited.
+When I add an octave to a fundamental tone, I hear in the octave a part
+of what was heard in the fundamental tone. (Helmholtz.) But it is not my
+purpose to develop this idea fully here.[23] We shall only ask to-day,
+whether there is anything similar to the symmetry of figures in the
+province of sounds.
+
+Look at the reflexion of your piano in the mirror.
+
+You will at once remark that you have never seen such a piano in the
+actual world, for it has its high keys to the left and its low ones to
+the right. Such pianos are not manufactured.
+
+If you could sit down at such a piano and play in your usual manner,
+plainly every step which you imagined you were performing in the upward
+scale would be executed as a corresponding step in the downward scale.
+The effect would be not a little surprising.
+
+For the practised musician who is always accustomed to hearing certain
+sounds produced when certain keys are struck, it is quite an anomalous
+spectacle to watch a player in the glass and to observe that he always
+does the opposite of what we hear.
+
+But still more remarkable would be the effect of attempting to strike a
+harmony on such a piano. For a melody it is not indifferent whether we
+execute a step in an upward or a downward scale. But for a harmony, so
+great a difference is not produced by reversal. I always retain the same
+consonance whether I add to a fundamental note an upper or a lower
+third. Only the order of the intervals of the harmony is reversed. In
+point of fact, when we execute a movement in a major key on our
+reflected piano, we hear a sound in a minor key, and _vice versa_.
+
+It now remains to execute the experiments indicated. Instead of playing
+upon the piano in the mirror, which is impossible, or of having a piano
+of this kind built, which would be somewhat expensive, we may perform
+our experiments in a simpler manner, as follows:
+
+1) We play on our own piano in our usual manner, look into the mirror,
+and then repeat on our real piano what we see in the mirror. In this way
+we transform all steps upwards into corresponding steps downwards. We
+play a movement, and then another movement, which, with respect to the
+key-board, is symmetrical to the first.
+
+2) We place a mirror beneath the music in which the notes are reflected
+as in a body of water, and play according to the notes in the mirror. In
+this way also, all steps upwards are changed into corresponding, equal
+steps downwards.
+
+3) We turn the music upside down and read the notes from right to left
+and from below upwards. In doing this, we must regard all sharps as
+flats and all flats as sharps, because they correspond to half lines and
+spaces. Besides, in this use of the music we can only employ the bass
+clef, as only in this clef are the notes not changed by symmetrical
+reversal.
+
+You can judge of the effect of these experiments from the examples which
+appear in the annexed musical cut. (Page 102.) The movement which
+appears in the upper lines is symmetrically reversed in the lower.
+
+The effect of the experiments may be briefly formulated. The melody is
+rendered unrecognisable. The harmony suffers a transposition from a
+major into a minor key and _vice versa_. The study of these pretty
+effects, which have long been familiar to physicists and musicians, was
+revived some years ago by Von Oettingen.[24]
+
+[Music: Fig. 26.
+
+(See pages 101 and 103.)]
+
+Now, although in all the preceding examples I have transposed steps
+upward into equal and similar steps downward, that is, as we may justly
+say, have played for every movement the movement which is symmetrical to
+it, yet the ear notices either little or nothing of symmetry. The
+transposition from a major to a minor key is the sole indication of
+symmetry remaining. The symmetry is there for the mind, but is wanting
+for sensation. No symmetry exists for the ear, because a reversal of
+musical sounds conditions no repetition of sensations. If we had an ear
+for height and an ear for depth, just as we have an eye for the right
+and an eye for the left, we should also find that symmetrical
+sound-structures existed for our auditory organs. The contrast of major
+and minor for the ear corresponds to inversion for the eye, which is
+also only symmetry for the mind, but not for sensation.
+
+By way of supplement to what I have said, I will add a brief remark for
+my mathematical readers.
+
+Our musical notation is essentially a graphical representation of a
+piece of music in the form of curves, where the time is the abscissæ,
+and the logarithms of the number of vibrations the ordinates. The
+deviations of musical notation from this principle are only such as
+facilitate interpretation, or are due to historical accidents.
+
+If, now, it be further observed that the sensation of pitch also is
+proportional to the logarithm of the number of vibrations, and that the
+intervals between the notes correspond to the differences of the
+logarithms of the numbers of vibrations, the justification will be found
+in these facts of calling the harmonies and melodies which appear in the
+mirror, symmetrical to the original ones.
+
+       *       *       *       *       *
+
+I simply wish to bring home to your minds by these fragmentary remarks
+that the progress of the physical sciences has been of great help to
+those branches of psychology that have not scorned to consider the
+results of physical research. On the other hand, psychology is beginning
+to return, as it were, in a spirit of thankfulness, the powerful
+stimulus which it received from physics.
+
+The theories of physics which reduce all phenomena to the motion and
+equilibrium of smallest particles, the so-called molecular theories,
+have been gravely threatened by the progress of the theory of the senses
+and of space, and we may say that their days are numbered.
+
+I have shown elsewhere[25] that the musical scale is simply a species of
+space--a space, however, of only one dimension, and that, a one-sided
+one. If, now, a person who could only hear, should attempt to develop a
+conception of the world in this, his linear space, he would become
+involved in many difficulties, as his space would be incompetent to
+comprehend the many sides of the relations of reality. But is it any
+more justifiable for us, to attempt to force the whole world into the
+space of our eye, in aspects in which it is not accessible to the eye?
+Yet this is the dilemma of all molecular theories.
+
+We possess, however, a sense, which, with respect to the scope of the
+relations which it can comprehend, is richer than any other. It is our
+reason. This stands above the senses. It alone is competent to found a
+permanent and sufficient view of the world. The mechanical conception of
+the world has performed wonders since Galileo's time. But it must now
+yield to a broader view of things. A further development of this idea is
+beyond the limits of my present purpose.
+
+One more point and I have done. The advice of our philosopher to
+restrict ourselves to what is near at hand and useful in our researches,
+which finds a kind of exemplification in the present cry of inquirers
+for limitation and division of labor, must not be too slavishly
+followed. In the seclusion of our closets, we often rack our brains in
+vain to fulfil a work, the means of accomplishing which lies before our
+very doors. If the inquirer must be perforce a shoemaker, tapping
+constantly at his last, it may perhaps be permitted him to be a
+shoemaker of the type of Hans Sachs, who did not deem it beneath him to
+take a look now and then at his neighbor's work and to comment on the
+latter's doings.
+
+Let this be my apology, therefore, if I have forsaken for a moment
+to-day the last of my specialty.
+
+  FOOTNOTES:
+
+  [Footnote 19: Delivered before the German Casino of Prague, in the
+  winter of 1871.
+
+  A fuller treatment of the problems of this lecture will be found in
+  my _Contributions to the Analysis of the Sensations_ (Jena, 1886),
+  English Translation, Chicago, 1895. J. P. Soret, _Sur la perception
+  du beau_ (Geneva, 1892), also regards repetition as a principle of
+  æsthetics. His discussions of the _æsthetical_ side of the subject
+  are much more detailed than mine. But with respect to the
+  psychological and physiological foundation of the principle, I am
+  convinced that the _Contributions to the Analysis of the Sensations_
+  go deeper.--MACH (1894).]
+
+  [Footnote 20: Kant, in his _Prolegomena zu jeder künftigen
+  Metaphysik_, also refers to this fact, but for a different purpose.]
+
+  [Footnote 21: Compare Mach, _Fichte's Zeitschrift für Philosophie_,
+  1864, p. 1.]
+
+  [Footnote 22: The fact that the first and second differential
+  coefficients of a curve are directly seen, but the higher
+  coefficients not, is very simply explained. The first gives the
+  position of the tangent, the declination of the straight line from
+  the position of symmetry, the second the declination of the curve
+  from the straight line. It is, perhaps, not unprofitable to remark
+  here that the ordinary method of testing rulers and plane surfaces
+  (by reversed applications) ascertains the deviation of the object
+  from symmetry to itself.]
+
+  [Footnote 23: See the lecture _On the Causes of Harmony_.]
+
+  [Footnote 24: A. von Oettingen, _Harmoniesystem in dualer
+  Entwicklung_. Leipsic and Dorpat, 1866.]
+
+  [Footnote 25: Compare Mach's _Zur Theorie des Gehörorgans_, Vienna
+  Academy, 1863.]
+
+
+
+
+ON THE FUNDAMENTAL CONCEPTS OF ELECTROSTATICS.[26]
+
+
+The task has been assigned me to develop before you in a
+popular manner the fundamental quantitative concepts of
+electrostatics--"quantity of electricity," "potential," "capacity,"
+and so forth. It would not be difficult, even within the brief
+limits of an hour, to delight the eye with hosts of beautiful
+experiments and to fill the imagination with numerous and varied
+conceptions. But we should, in such a case, be still far from a
+lucid and easy grasp of the phenomena. The means would still fail us
+for reproducing the facts accurately in thought--a procedure which
+for the theoretical and practical man is of equal importance. These
+means are the _metrical concepts_ of electricity.
+
+As long as the pursuit of the facts of a given province of phenomena
+is in the hands of a few isolated investigators, as long as every
+experiment can be easily repeated, the fixing of the collected facts
+by provisional description is ordinarily sufficient. But the case
+is different when the whole world must make use of the results
+reached by many, as happens when the science acquires broader
+foundations and scope, and particularly so when it begins to supply
+intellectual nourishment to an important branch of the practical
+arts, and to draw from that province in return stupendous empirical
+results. Then the facts must be so described that individuals in all
+places and at all times can, from a few easily obtained elements,
+put the facts accurately together in thought, and reproduce them
+from the description. This is done with the help of the metrical
+concepts and the international measures.
+
+The work which was begun in this direction in the period of the
+purely scientific development of the science, especially by Coulomb
+(1784), Gauss (1833), and Weber (1846), was powerfully stimulated by
+the requirements of the great technical undertakings manifested
+since the laying of the first transatlantic cable, and brought to a
+brilliant conclusion by the labors of the British Association, 1861,
+and of the Paris Congress, 1881, chiefly through the exertions of
+Sir William Thomson.
+
+It is plain, that in the time allotted to me I cannot conduct you
+over all the long and tortuous paths which the science has actually
+pursued, that it will not be possible at every step to remind you of
+all the little precautions for the avoidance of error which the
+early steps have taught us. On the contrary, I must make shift with
+the simplest and rudest tools. I shall conduct you by the shortest
+paths from the facts to the ideas, in doing which, of course, it
+will not be possible to anticipate all the stray and chance ideas
+which may and must arise from prospects into the by-paths which we
+leave untrodden.
+
+     *       *       *       *       *
+
+Here are two small, light bodies (Fig. 27) of equal size, freely
+suspended, which we "electrify" either by friction with a third body
+or by contact with a body already electrified. At once a repulsive
+force is set up which drives the two bodies away from each other in
+opposition to the action of gravity. This force could accomplish
+anew the same mechanical work which was expended to produce it.[27]
+
+[Illustration: Fig. 27.]
+
+[Illustration: Fig. 28.]
+
+Coulomb, now, by means of delicate experiments with the
+torsion-balance, satisfied himself that if the bodies in question,
+say at a distance of two centimetres, repelled each other with the
+same force with which a milligramme-weight strives to fall to the
+ground, at half that distance, or at one centimetre, they would
+repel each other with the force of four milligrammes, and at double
+that distance, or at four centimetres, they would repel each other
+with the force of only one-fourth of a milligramme. He found that
+the electrical force acts inversely as the square of the distance.
+
+Let us imagine, now, that we possessed some means of measuring
+electrical repulsion by weights, a means which would be supplied,
+for example, by our electrical pendulums; then we could make the
+following observation.
+
+The body _A_ (Fig. 28) is repelled by the body _K_ at a distance of
+two centimetres with a force of one milligramme. If we touch _A_,
+now, with an equal body _B_, the half of this force of repulsion
+will pass to the body _B_; both _A_ and _B_, now, at a distance of
+two centimetres from _K_, are repelled only with the force of
+one-half a milligramme. But both together are repelled still with
+the force of one milligramme. Hence, _the divisibility of electrical
+force_ among bodies in contact _is a fact_. It is a useful, but by
+no means a necessary supplement to this fact, to imagine an
+electrical fluid present in the body _A_, with the quantity of which
+the electrical force varies, and half of which flows over to _B_.
+For, in the place of the new physical picture, thus, an old,
+familiar one is substituted, which moves spontaneously in its wonted
+courses.
+
+Adhering to this idea, we define the _unit_ of electrical
+quantity, according to the now almost universally adopted
+centimetre-gramme-second (C. G. S.) system, as that quantity which
+at a distance of one centimetre repels an equal quantity with unit
+of force, that is, with a force which in one second would impart to
+a mass of one gramme a velocity-increment of a centimetre.
+As a gramme mass acquires through the action of gravity a
+velocity-increment of about 981 centimetres in a second,
+accordingly, a gramme is attracted to the earth with 981, or, in
+round numbers, 1000 units of force of the centimetre-gramme-second
+system, while a milligramme-weight would strive to fall to the earth
+with approximately the unit force of this system.
+
+We may easily obtain by this means a clear idea of what the unit
+quantity of electricity is. Two small bodies, _K_, weighing each a
+gramme, are hung up by vertical threads, five metres in length and
+almost weightless, so as to touch each other. If the two bodies be
+equally electrified and move apart upon electrification to a
+distance of one centimetre, their charge is approximately equivalent
+to the electrostatic unit of electric quantity, for the repulsion
+then holds in equilibrium a gravitational force-component of
+approximately one milligramme, which strives to bring the bodies
+together.
+
+Vertically beneath a small sphere suspended from the equilibrated
+beam of a balance a second sphere is placed at a distance of a
+centimetre. If both be equally electrified the sphere suspended
+from the balance will be rendered apparently lighter by the
+repulsion. If by adding a weight of one milligramme equilibrium is
+restored, each of the spheres contains in round numbers the
+electrostatic unit of electrical quantity.
+
+In view of the fact that the same electrical bodies exert at
+different distances different forces upon one another, exception
+might be taken to the measure of quantity here developed. What kind
+of a quantity is that which now weighs more, and now weighs less, so
+to speak? But this apparent deviation from the method of
+determination commonly used in practical life, that by weight, is,
+closely considered, an agreement. On a high mountain a heavy mass
+also is less powerfully attracted to the earth than at the level of
+the sea, and if it is permitted us in our determinations to neglect
+the consideration of level, it is only because the comparison of a
+body with fixed conventional weights is invariably effected at the
+same level. In fact, if we were to make one of the two weights
+equilibrated on our balance approach sensibly to the centre of the
+earth, by suspending it from a very long thread, as Prof. von Jolly
+of Munich suggested, we should make the gravity of that weight, its
+heaviness, proportionately greater.
+
+Let us picture to ourselves, now, two different electrical fluids, a
+positive and a negative fluid, of such nature that the particles of
+the one attract the particles of the other according to the law of
+the inverse squares, but the particles of the same fluid repel each
+other by the same law; in non-electrical bodies let us imagine the
+two fluids uniformly distributed in equal quantities, in electric
+bodies one of the two in excess; in conductors, further, let us
+imagine the fluids mobile, in non-conductors immobile; having formed
+such pictures, we possess the conception which Coulomb developed and
+to which he gave mathematical precision. We have only to give this
+conception free play in our minds and we shall see as in a clear
+picture the fluid particles, say of a positively charged conductor,
+receding from one another as far as they can, all making for the
+surface of the conductor and there seeking out the prominent parts
+and points until the greatest possible amount of work has been
+performed. On increasing the size of the surface, we see a
+dispersion, on decreasing its size we see a condensation of the
+particles. In a second, non-electrified conductor brought into the
+vicinity of the first, we see the two fluids immediately separate,
+the positive collecting itself on the remote and the negative on the
+adjacent side of its surface. In the fact that this conception
+reproduces, lucidly and spontaneously, all the data which arduous
+research only slowly and gradually discovered, is contained its
+advantage and scientific value. With this, too, its value is
+exhausted. We must not seek in nature for the two hypothetical
+fluids which we have added as simple mental adjuncts, if we would
+not go astray. Coulomb's view may be replaced by a totally
+different one, for example, by that of Faraday, and the most proper
+course is always, after the general survey is obtained, to go back
+to the actual facts, to the electrical forces.
+
+[Illustration: Fig. 29.]
+
+[Illustration: Fig. 30.]
+
+We will now make ourselves familiar with the concept of electrical
+quantity, and with the method of measuring or estimating it. Imagine
+a common Leyden jar (Fig. 29), the inner and outer coatings of which
+are connected together by means of two common metallic knobs placed
+about a centimetre apart. If the inside coating be charged with the
+quantity of electricity +_q_, on the outer coating a distribution of
+the electricities will take place. A positive quantity almost
+equal[28] to the quantity +_q_ flows off to the earth, while a
+corresponding quantity-_q_ is still left on the outer coating. The
+knobs of the jar receive their portion of these quantities and when
+the quantity _q_ is sufficiently great a rupture of the insulating
+air between the knobs, accompanied by the self-discharge of the
+jar, takes place. For any given distance and size of the knobs, a
+charge of a definite electric quantity _q_ is always necessary for
+the spontaneous discharge of the jar.
+
+Let us insulate, now, the outer coating of a Lane's unit jar _L_,
+the jar just described, and put in connexion with it the inner
+coating of a jar _F_ exteriorly connected with the earth (Fig. 30).
+Every time that _L_ is charged with +_q_, a like quantity +_q_ is
+collected on the inner coating of _F_, and the spontaneous discharge
+of the jar _L_, which is now again empty, takes place. The number of
+the discharges of the jar _L_ furnishes us, thus, with a measure of
+the quantity collected in the jar _F_, and if after 1, 2, 3, ...
+spontaneous discharges of _L_ the jar _F_ is discharged, it is
+evident that the charge of _F_ has been proportionately augmented.
+
+[Illustration: Fig. 31.]
+
+Let us supply now, to effect the spontaneous discharge, the jar _F_
+with knobs of the same size and at the same distance apart as those
+of the jar _L_ (Fig. 31). If we find, then, that five discharges of
+the unit jar take place before one spontaneous discharge of the jar
+_F_ occurs, plainly the jar _F_, for equal distances between the
+knobs of the two jars, equal striking distances, is able to hold
+five times the quantity of electricity that _L_ can, that is, has
+five times the _capacity_ of _L_.[29]
+
+[Illustration: Fig. 32.]
+
+We will now replace the unit jar _L_, with which we measure
+electricity, so to speak, _into_ the jar _F_, by a Franklin's pane,
+consisting of two parallel flat metal plates (Fig. 32), separated
+only by air. If here, for example, thirty spontaneous discharges of
+the pane are sufficient to fill the jar, ten discharges will be
+found sufficient if the air-space between the two plates be filled
+with a cake of sulphur. Hence, the capacity of a Franklin's pane of
+sulphur is about three times greater than that of one of the same
+shape and size made of air, or, as it is the custom to say, the
+specific inductive capacity of sulphur (that of air being taken as
+the unit) is about 3.[30] We are here arrived at a very simple fact,
+which clearly shows us the significance of the number called
+_dielectric constant_, or _specific inductive capacity_, the
+knowledge of which is so important for the theory of submarine
+cables.
+
+Let us consider a jar _A_, which is charged with a certain quantity
+of electricity. We can discharge the jar directly. But we can also
+discharge the jar _A_ (Fig. 33) partly into a jar _B_, by connecting
+the two outer coatings with each other. In this operation a portion
+of the quantity of electricity passes, accompanied by sparks, into
+the jar _B_, and we now find both jars charged.
+
+[Illustration: Fig. 33.]
+
+[Illustration: Fig. 34.]
+
+It may be shown as follows that the conception of a constant
+quantity of electricity can be regarded as the expression of a pure
+fact. Picture to yourself any sort of electrical conductor (Fig.
+34); cut it up into a large number of small pieces, and place these
+pieces by means of an insulated rod at a distance of one centimetre
+from an electrical body which acts with unit of force on an equal
+and like-constituted body at the same distance. Take the sum of the
+forces which this last body exerts on the single pieces of the
+conductor. The sum of these forces will be the quantity of
+electricity on the whole conductor. It remains the same, whether we
+change the form and the size of the conductor, or whether we bring
+it near or move it away from a second electrical conductor, so long
+as we keep it insulated, that is, do not discharge it.
+
+A basis of reality for the notion of electric quantity seems also to
+present itself from another quarter. If a current, that is, in the
+usual view, a definite quantity of electricity per second, is sent
+through a column of acidulated water; in the direction of the
+positive stream, hydrogen, but in the opposite direction, oxygen is
+liberated at the extremities of the column. For a given quantity of
+electricity a given quantity of oxygen appears. You may picture the
+column of water as a column of hydrogen and a column of oxygen,
+fitted into each other, and may say the electric current is a
+chemical current and _vice versa_. Although this notion is more
+difficult to adhere to in the field of statical electricity and with
+non-decomposable conductors, its further development is by no means
+hopeless.
+
+The concept quantity of electricity, thus, is not so aerial as might
+appear, but is able to conduct us with certainty through a multitude
+of varied phenomena, and is suggested to us by the facts in almost
+palpable form. We can collect electrical force in a body, measure it
+out with one body into another, carry it over from one body into
+another, just as we can collect a liquid in a vessel, measure it out
+with one vessel into another, or pour it from one into another.
+
+For the analysis of mechanical phenomena, a metrical notion, derived
+from experience, and bearing the designation _work_, has proved
+itself useful. A machine can be set in motion only when the forces
+acting on it can perform work.
+
+[Illustration: Fig. 35.]
+
+Let us consider, for example, a wheel and axle (Fig. 35) having the
+radii 1 and 2 metres, loaded respectively with the weights 2 and 1
+kilogrammes. On turning the wheel and axle, the 1 kilogramme-weight,
+let us say, sinks two metres, while the 2 kilogramme-weight rises
+one metre. On both sides the product
+
+KGR. M. KGR. M.
+
+1 × 2 = 2 × 1.
+
+is equal. So long as this is so, the wheel and axle will not move of
+itself. But if we take such loads, or so change the radii of the
+wheels, that this product (kgr. × metre) on displacement is in
+excess on one side, that side will sink. As we see, this product is
+characteristic for mechanical events, and for this reason has been
+invested with a special name, _work_.
+
+In all mechanical processes, and as all physical processes present a
+mechanical side, in all physical processes, work plays a
+determinative part. Electrical forces, also, produce only changes in
+which work is performed. To the extent that forces come into play in
+electrical phenomena, electrical phenomena, be they what they may,
+extend into the domain of mechanics and are subject to the laws
+which hold in this domain. The universally adopted measure of work,
+now, is the product of the force into the distance through which it
+acts, and in the C. G. S. system, the unit of work is the action
+through one centimetre of a force which would impart in one second
+to a gramme-mass a velocity-increment of one centimetre, that is, in
+round numbers, the action through a centimetre of a pressure equal
+to the weight of a milligramme. From a positively charged body,
+electricity, yielding to the force of repulsion and performing work,
+flows off to the earth, providing conducting connexions exist. To a
+negatively charged body, on the other hand, the earth under the
+same circumstances gives off positive electricity. The electrical
+work possible in the interaction of a body with the earth,
+characterises the electrical condition of that body. We will call
+the work which must be expended on the unit quantity of positive
+electricity to raise it from the earth to the body _K_ the
+_potential_ of the body _K_.[31]
+
+We ascribe to the body _K_ in the C. G. S. system the potential +1,
+if we must expend the unit of work to raise the positive
+electrostatic unit of electric quantity from the earth to that body;
+the potential -1, if we gain in this procedure the unit of work; the
+potential 0, if no work at all is performed in the operation.
+
+The different parts of one and the same electrical conductor in
+electrical equilibrium have the same potential, for otherwise the
+electricity would perform work and move about upon the conductor,
+and equilibrium would not have existed. Different conductors of
+equal potential, put in connexion with one another, do not exchange
+electricity any more than bodies of equal temperature in contact
+exchange heat, or in connected vessels, in which the same pressures
+exist, liquids flow from one vessel to the other. Exchange of
+electricity takes place only between conductors of different
+potentials, but in conductors of given form and position a definite
+difference of potential is necessary for a spark, which pierces the
+insulating air, to pass between them.
+
+On being connected, every two conductors assume at once the same
+potential. With this the means is given of determining the potential
+of a conductor through the agency of a second conductor expressly
+adapted to the purpose called an electrometer, just as we determine
+the temperature of a body with a thermometer. The values of the
+potentials of bodies obtained in this way simplify vastly our
+analysis of their electrical behavior, as will be evident from what
+has been said.
+
+Think of a positively charged conductor. Double all the electrical
+forces exerted by this conductor on a point charged with unit
+quantity, that is, double the quantity at each point, or what is the
+same thing, double the total charge. Plainly, equilibrium still
+subsists. But carry, now, the positive electrostatic unit towards
+the conductor. Everywhere we shall have to overcome double the force
+of repulsion we did before, everywhere we shall have to expend
+double the work. By doubling the charge of the conductor a double
+potential has been produced. Charge and potential go hand in hand,
+are proportional. Consequently, calling the total quantity of
+electricity of a conductor _Q_ and its potential _V_, we can write:
+_Q = CV_, where _C_ stands for a constant, the import of which will
+be understood simply from noting that _C = Q/V_.[32] But the
+division of a number representing the units of quantity of a
+conductor by the number representing its units of potential tells us
+the quantity which falls to the share of the unit of potential. Now
+the number _C_ here we call the capacity of a conductor, and have
+substituted, thus, in the place of the old relative determination of
+capacity, an absolute determination.[33]
+
+In simple cases the connexion between charge, potential, and
+capacity is easily ascertained. Our conductor, let us say, is a
+sphere of radius _r_, suspended free in a large body of air. There
+being no other conductors in the vicinity, the charge _q_ will then
+distribute itself uniformly upon the surface of the sphere, and
+simple geometrical considerations yield for its potential the
+expression _V = q/r_. Hence, _q/V = r_; that is, the capacity of a
+sphere is measured by its radius, and in the C. G. S. system in
+centimetres.[34] It is clear also, since a potential is a quantity
+divided by a length, that a quantity divided by a potential must be
+a length.
+
+Imagine (Fig. 36) a jar composed of two concentric conductive
+spherical shells of the radii _r_ and _r₁_, having only air between
+them. Connecting the outside sphere with the earth, and charging the
+inside sphere by means of a thin, insulated wire passing through the
+first, with the quantity _Q_, we shall have _V = (r₁-r)/(r₁r)Q_, and
+for the capacity in this case _(r₁r)/(r₁-r)_, or, to take a specific
+example, if _r = 16_ and _r₁ = 19_, a capacity of about 100
+centimetres.
+
+[Illustration: Fig. 36.]
+
+We shall now use these simple cases for illustrating the principle
+by which capacity and potential are determined. First, it is clear
+that we can use the jar composed of concentric spheres with its
+known capacity as our unit jar and by means of this ascertain, in
+the manner above laid down, the capacity of any given jar _F_. We
+find, for example, that 37 discharges of this unit jar of the
+capacity 100, just charges the jar investigated at the same
+striking distance, that is, at the same potential. Hence, the
+capacity of the jar investigated is 3700 centimetres. The large
+battery of the Prague physical laboratory, which consists of sixteen
+such jars, all of nearly equal size, has a capacity, therefore, of
+something like 50,000 centimetres, or the capacity of a sphere, a
+kilometre in diameter, freely suspended in atmospheric space. This
+remark distinctly shows us the great superiority which Leyden jars
+possess for the storage of electricity as compared with common
+conductors. In fact, as Faraday pointed out, jars differ from simple
+conductors mainly by their great capacity.
+
+[Illustration: Fig. 37.]
+
+For determining potential, imagine the inner coating of a jar _F_,
+the outer coating of which communicates with the ground, connected
+by a long, thin wire with a conductive sphere _K_ placed free in a
+large atmospheric space, compared with whose dimensions the radius
+of the sphere vanishes. (Fig. 37.) The jar and the sphere assume at
+once the same potential. But on the surface of the sphere, if that
+be sufficiently far removed from all other conductors, a uniform
+layer of electricity will be found. If the sphere, having the radius
+_r_, contains the charge _q_, its potential is _V = q/r_. If the
+upper half of the sphere be severed from the lower half and
+equilibrated on a balance with one of whose beams it is connected by
+silk threads, the upper half will be repelled from the lower half
+with the force _P = q²/8r² = 1/8V²_. This repulsion _P_ may be
+counter-balanced by additional weights placed on the beam-end, and
+so ascertained. The potential is then _V = [sqrt](8P)_.[35]
+
+That the potential is proportional to the square root of the force
+is not difficult to see. A doubling or trebling of the potential
+means that the charge of all the parts is doubled or trebled; hence
+their combined power of repulsion quadrupled or nonupled.
+
+Let us consider a special case. I wish to produce the potential 40
+on the sphere. What additional weight must I give to the half sphere
+in grammes that the force of repulsion shall maintain the balance in
+exact equilibrium? As a gramme weight is approximately equivalent
+to 1000 units of force, we have only the following simple example to
+work out: _40×40 = 8× 1000.x_, where _x_ stands for the number of
+grammes. In round numbers we get _x_ = 0.2 gramme. I charge the jar.
+The balance is deflected; I have reached, or rather passed, the
+potential 40, and you see when I discharge the jar the associated
+spark.[36]
+
+The striking distance between the knobs of a machine increases with
+the difference of the potential, although not proportionately to
+that difference. The striking distance increases faster than the
+potential difference. For a distance between the knobs of one
+centimetre on this machine the difference of potential is 110. It
+can easily be increased tenfold. Of the tremendous differences of
+potential which occur in nature some idea may be obtained from the
+fact that the striking distances of lightning in thunder-storms is
+counted by miles. The differences of potential in galvanic batteries
+are considerably smaller than those of our machine, for it takes
+fully one hundred elements to give a spark of microscopic striking
+distance.
+
+     *       *       *       *       *
+
+We shall now employ the ideas reached to shed some light upon
+another important relation between electrical and mechanical
+phenomena. We shall investigate what is the potential _energy_, or
+the _store of work_, contained in a charged conductor, for example,
+in a jar.
+
+If we bring a quantity of electricity up to a conductor, or, to
+speak less pictorially, if we generate by work electrical force in a
+conductor, this force is able to produce anew the work by which it
+was generated. How great, now, is the energy or capacity for work of
+a conductor of known charge _Q_ and known potential _V_?
+
+Imagine the given charge _Q_ divided into very small parts _q_,
+_q₁_, _q₂_ ..., and these little parts successively carried up to
+the conductor. The first very small quantity _q_ is brought up
+without any appreciable work and produces by its presence a small
+potential _V__{'}. To bring up the second quantity, accordingly, we
+must do the work _q__{'}_V__{'}, and similarly for the quantities
+which follow the work _q__{''}_V__{''}, _q__{'''}_V__{'''}, and so
+forth. Now, as the potential rises proportionately to the quantities
+added until the value _V_ is reached, we have, agreeably to the
+graphical representation of Fig. 38, for the total work performed,
+
+_W = 1/2QV_,
+
+which corresponds to the total energy of the charged conductor.
+Using the equation _Q_ = _CV_, where _C_ stands for capacity, we
+also have,
+
+_W = 1/2CV²_, or _W = Q²/2C_.
+
+It will be helpful, perhaps, to elucidate this idea by an analogy
+from the province of mechanics. If we pump a quantity of liquid,
+_Q_, gradually into a cylindrical vessel (Fig. 39), the level of the
+liquid in the vessel will gradually rise. The more we have pumped
+in, the greater the pressure we must overcome, or the higher the
+level to which we must lift the liquid. The stored-up work is
+rendered again available when the heavy liquid _Q_, which reaches up
+to the level _h_, flows out. This work _W_ corresponds to the fall
+of the whole liquid weight _Q_, through the distance _h_/2 or
+through the altitude of its centre of gravity. We have
+
+_W = 1/2Qh_.
+
+Further, since _Q_ = _Kh_, or since the weight of the liquid and the
+height _h_ are proportional, we get also
+
+_W = 1/2Kh²_ and _W = Q²/2K_.
+
+[Illustration: Fig. 38.]
+
+[Illustration: Fig. 39.]
+
+As a special case let us consider our jar. Its capacity is _C_ =
+3700, its potential _V_ = 110; accordingly, its quantity _Q = CV_ =
+407,000 electrostatic units and its energy _W = 1/2QV_ = 22,385,000
+C. G. S. units of work.
+
+The unit of work of the C. G. S. system is not readily appreciable
+by the senses, nor does it well admit of representation, as we are
+accustomed to work with weights. Let us adopt, therefore, as our
+unit of work the gramme-centimetre, or the gravitational pressure of
+a gramme-weight through the distance of a centimetre, which in round
+numbers is 1000 times greater than the unit assumed above; in this
+case, our numerical result will be approximately 1000 times smaller.
+Again, if we pass, as more familiar in practice, to the
+kilogramme-metre as our unit of work, our unit, the distance being
+increased a hundred fold, and the weight a thousand fold, will be
+100,000 times larger. The numerical result expressing the work done
+is in this case 100,000 times less, being in round numbers 0.22
+kilogramme-metre. We can obtain a clear idea of the work done here
+by letting a kilogramme-weight fall 22 centimetres.
+
+This amount of work, accordingly, is performed on the charging of
+the jar, and on its discharge appears again, according to the
+circumstances, partly as sound, partly as a mechanical disruption of
+insulators, partly as light and heat, and so forth.
+
+The large battery of the Prague physical laboratory, with its
+sixteen jars charged to equal potentials, furnishes, although the
+effect of the discharge is imposing, a total amount of work of only
+three kilogramme-metres.
+
+In the development of the ideas above laid down we are not
+restricted to the method there pursued; in fact, that method was
+selected only as one especially fitted to familiarise us with the
+phenomena. On the contrary, the connexion of the physical processes
+is so multifarious that we can come at the same event from very
+different directions. Particularly are electrical phenomena
+connected with all other physical events; and so intimate is this
+connexion that we might justly call the study of electricity the
+theory of the general connexion of physical processes.
+
+With respect to the principle of the conservation of energy which
+unites electrical with mechanical phenomena, I should like to point
+out briefly two ways of following up the study of this connexion.
+
+A few years ago Professor Rosetti, taking an influence-machine,
+which he set in motion by means of weights alternately in the
+electrical and non-electrical condition with the same velocities,
+determined the mechanical work expended in the two cases and was
+thus enabled, after deducting the work of friction, to ascertain the
+mechanical work consumed in the development of the electricity.
+
+I myself have made this experiment in a modified, and, as I think,
+more advantageous form. Instead of determining the work of friction
+by special trial, I arranged my apparatus so that it was eliminated
+of itself in the measurement and could consequently be neglected.
+The so-called fixed disk of the machine, the axis of which is
+placed vertically, is suspended somewhat like a chandelier by three
+vertical threads of equal lengths _l_ at a distance _r_ from the
+axis. Only when the machine is excited does this fixed disk, which
+represents a Prony's brake, receive, through its reciprocal action
+with the rotating disk, a deflexion _[alpha]_ and a moment of
+torsion which is expressed by _D = (Pr²/l)[alpha]_, where _P_ is the
+weight of the disk.[37] The angle _[alpha]_ is determined by a
+mirror set in the disk. The work expended in _n_ rotations is given
+by _2n[pi]D_.
+
+If we close the machine, as Rosetti did, we obtain a continuous
+current which has all the properties of a very weak galvanic
+current; for example, it produces a deflexion in a multiplier which
+we interpose, and so forth. We can directly ascertain, now, the
+mechanical work expended in the maintenance of this current.
+
+If we charge a jar by means of a machine, the energy of the jar
+employed in the production of sparks, in the disruption of the
+insulators, etc., corresponds to a part only of the mechanical work
+expended, a second part of it being consumed in the arc which forms
+the circuit.[38] This machine, with the interposed jar, affords in
+miniature a picture of the transference of force, or more properly
+of work. And in fact nearly the same laws hold here for the
+economical coefficient as obtain for large dynamo-machines.
+
+Another means of investigating electrical energy is by its
+transformation into heat. A long time ago (1838), before the
+mechanical theory of heat had attained its present popularity, Riess
+performed experiments in this field with the help of his electrical
+air-thermometer or thermo-electrometer.
+
+[Illustration: Fig. 40.]
+
+If the discharge be conducted through a fine wire passing through
+the globe of the air-thermometer, a development of heat is observed
+proportional to the expression above-discussed _W = 1/2QV_. Although
+the total energy has not yet been transformed into measurable heat
+by this means, in as much as a portion is left behind in the spark
+in the air outside the thermometer, still everything tends to show
+that the total heat developed in all parts of the conductor and
+along all the paths of discharge is the equivalent of the work
+1/2_QV_.
+
+It is not important here whether the electrical energy is
+transformed all at once or partly, by degrees. For example, if of
+two equal jars one is charged with the quantity _Q_ at the potential
+_V_ the energy present is 1/2_QV_. If the first jar be discharged
+into the second, _V_, since the capacity is now doubled, falls to
+_V_/2. Accordingly, the energy 1/4_QV_ remains, while 1/4_QV_ is
+transformed in the spark of discharge into heat. The remainder,
+however, is equally distributed between the two jars so that each on
+discharge is still able to transform 1/8_QV_ into heat.
+
+     *       *       *       *       *
+
+We have here discussed electricity in the limited phenomenal form in
+which it was known to the inquirers before Volta, and which has been
+called, perhaps not very felicitously, "statical electricity." It is
+evident, however, that the nature of electricity is everywhere one
+and the same; that a substantial difference between statical and
+galvanic electricity does not exist. Only the quantitative
+circumstances in the two provinces are so widely different that
+totally new aspects of phenomena may appear in the second, for
+example, magnetic effects, which in the first remained unnoticed,
+whilst, _vice versa_, in the second field statical attractions and
+repulsions are scarcely appreciable. As a fact, we can easily
+show the magnetic effect of the current of discharge of an
+influence-machine on the galvanoscope although we could hardly have
+made the original discovery of the magnetic effects with this
+current. The statical distant action of the wire poles of a galvanic
+element also would hardly have been noticed had not the phenomenon
+been known from a different quarter in a striking form.
+
+If we wished to characterise the two fields in their chief and most
+general features, we should say that in the first, high potentials
+and small quantities come into play, in the second small potentials
+and large quantities. A jar which is discharging and a galvanic
+element deport themselves somewhat like an air-gun and the bellows
+of an organ. The first gives forth suddenly under a very high
+pressure a small quantity of air; the latter liberates gradually
+under a very slight pressure a large quantity of air.
+
+In point of principle, too, nothing prevents our retaining the
+electrostatical units in the domain of galvanic electricity and in
+measuring, for example, the strength of a current by the number of
+electrostatic units which flow per second through its cross-section.
+But this would be in a double aspect impractical. In the first
+place, we should totally neglect the magnetic facilities for
+measurement so conveniently offered by the current, and substitute
+for this easy means a method which can be applied only with
+difficulty and is not capable of great exactness. In the second
+place our units would be much too small, and we should find
+ourselves in the predicament of the astronomer who attempted to
+measure celestial distances in metres instead of in radii of the
+earth and the earth's orbit; for the current which by the magnetic
+C. G. S. standard represents the unit, would require a flow of some
+30,000,000,000 electrostatic units per second through its
+cross-section. Accordingly, different units must be adopted here.
+The development of this point, however, lies beyond my present
+task.
+
+  FOOTNOTES:
+
+  [Footnote 26: A lecture delivered at the International Electrical
+  Exhibition, in Vienna, on September 4, 1883.]
+
+  [Footnote 27: If the two bodies were oppositely electrified they
+  would exert attractions upon each other.]
+
+  [Footnote 28: The quantity which flows off is in point of fact less
+  than _q_. It would be equal to the quantity _q_ only if the inner
+  coating of the jar were wholly encompassed by the outer coating.]
+
+  [Footnote 29: Rigorously, of course, this is not correct. First, it
+  is to be noted that the jar _L_ is discharged simultaneously with
+  the electrode of the machine. The jar _F_, on the other hand, is
+  always discharged simultaneously with the outer coating of the jar
+  _L_. Hence, if we call the capacity of the electrode of the machine
+  _E_, that of the unit jar _L_, that of the outer coating of _L_,
+  _A_, and that of the principal jar _F_, then this equation would
+  exist for the example in the text: _(F + A)/(L + E) = 5_. A cause of
+  further departure from absolute exactness is the residual charge.]
+
+  [Footnote 30: Making allowance for the corrections indicated in the
+  preceding footnote, I have obtained for the dielectric constant of
+  sulphur the number 3.2, which agrees practically with the results
+  obtained by more delicate methods. For the highest attainable
+  precision one should by rights immerse the two plates of the
+  condenser first wholly in air and then wholly in sulphur, if the
+  ratio of the capacities is to correspond to the dielectric constant.
+  In point of fact, however, the error which arises from inserting
+  simply a plate of sulphur that exactly fills the space between the
+  two plates, is of no consequence.]
+
+  [Footnote 31: As this definition in its simple form is apt to give
+  rise to misunderstandings, elucidations are usually added to it. It
+  is clear that we cannot lift a quantity of electricity to _K_,
+  without changing the distribution on _K_ and the potential on _K_.
+  Hence, the charges on _K_ must be conceived as fixed, and so small a
+  quantity raised that no appreciable change is produced by it. Taking
+  the work thus expended as many times as the small quantity in
+  question is contained in the unit of quantity, we shall obtain the
+  potential. The potential of a body _K_ may be briefly and precisely
+  defined as follows: If we expend the element of work _dW_ to raise
+  the element of positive quantity _dQ_ from the earth to the
+  conductor, the potential of a conductor _K_ will be given by _V =
+  dW/dQ_.]
+
+  [Footnote 32: In this article the solidus or slant stroke is used
+  for the usual fractional sign of division. Where plus or minus signs
+  occur in the numerator or denominator, brackets or a vinculum is
+  used.--_Tr._]
+
+  [Footnote 33: A sort of agreement exists between the notions of
+  thermal and electrical capacity, but the difference between the two
+  ideas also should be carefully borne in mind. The thermal capacity
+  of a body depends solely upon that body itself. The electrical
+  capacity of a body _K_ is influenced by all bodies in its vicinity,
+  inasmuch as the charge of these bodies is able to alter the
+  potential of _K_. To give, therefore, an unequivocal significance to
+  the notion of the capacity (_C_) of a body _K_, _C_ is defined as
+  the relation _Q_/_V_ for the body _K_ in a certain given position of
+  all neighboring bodies, and during connexion of all neighboring
+  conductors with the earth. In practice the situation is much
+  simpler. The capacity, for example, of a jar, the inner coating of
+  which is almost enveloped by its outer coating, communicating with
+  the ground, is not sensibly affected by charged or uncharged
+  adjacent conductors.]
+
+  [Footnote 34: These formulæ easily follow from Newton's theorem that
+  a homogeneous spherical shell, whose elements obey the law of the
+  inverse squares, exerts no force whatever on points within it but
+  acts on points without as if the whole mass were concentrated at its
+  centre. The formulæ next adduced also flow from this proposition.]
+
+  [Footnote 35: The energy of a sphere of radius _r_ charged with the
+  quantity _q_ is 1/2(_q_²/_r_). If the radius increase by the space
+  _dr_ a loss of energy occurs, and the work done is
+  1/2(_q_²/_r_²)_dr_. Letting _p_ denote the uniform electrical
+  pressure on unit of surface of the sphere, the work done is also
+  4_r_²[pi]_pdr_. Hence _p = (1/8r²[pi])(q²/r²)_. Subjected to the
+  same superficial pressure on all sides, say in a fluid, our half
+  sphere would be an equilibrium. Hence we must make the pressure _p_
+  act on the surface of the great circle to obtain the effect on the
+  balance, which is _r²[pi]p = 1/8(q²/r²) = 1/8V²_.]
+
+  [Footnote 36: The arrangement described is for several reasons not
+  fitted for the actual measurement of potential. Thomson's absolute
+  electrometer is based upon an ingenious modification of the
+  electrical balance of Harris and Volta. Of two large plane parallel
+  plates, one communicates with the earth, while the other is brought
+  to the potential to be measured. A small movable superficial portion
+  _f_ of this last hangs from the balance for the determination of the
+  attraction _P_. The distance of the plates from each other being _D_
+  we get _V = D[sqrt](8[pi]P/f)_.]
+
+  [Footnote 37: This moment of torsion needs a supplementary
+  correction, on account of the vertical electric attraction of the
+  excited disks. This is done by changing the weight of the disk by
+  means of additional weights and by making a second reading of the
+  angles of deflexion.]
+
+  [Footnote 38: The jar in our experiment acts like an accumulator,
+  being charged by a dynamo machine. The relation which obtains
+  between the expended and the available work may be gathered from the
+  following simple exposition. A Holtz machine _H_ (Fig. 40) is
+  charging a unit jar _L_, which after _n_ discharges of quantity _q_
+  and potential _v_, charges the jar _F_ with the quantity _Q_ at the
+  potential _V_. The energy of the unit-jar discharges is lost and
+  that of the jar _F_ alone is left. Hence the ratio of the available
+  work to the total work expended is
+
+_½QV/[½QV + (n/2)qv]_ and as _Q = nq_, also _V/(V + v)_.
+
+  If, now, we interpose no unit jar, still the parts of the machine
+  and the wires of conduction are themselves virtually such unit jars
+  and the formula still subsists _V/(V + [sum]v)_, in which [sum]_v_
+  represents the sum of all the successively introduced differences of
+  potential in the circuit of connexion.]
+
+
+
+
+ON THE PRINCIPLE OF THE CONSERVATION OF ENERGY.[39]
+
+
+In a popular lecture, distinguished for its charming simplicity and
+clearness, which Joule delivered in the year 1847,[40] that famous
+physicist declares that the living force which a heavy body has acquired
+by its descent through a certain height and which it carries with it in
+the form of the velocity with which it is impressed, is the _equivalent_
+of the attraction of gravity through the space fallen through, and that
+it would be "absurd" to assume that this living force could be destroyed
+without some restitution of that equivalent. He then adds: "You will
+therefore be surprised to hear that until very _recently_ the universal
+opinion has been that living force could be absolutely and irrevocably
+destroyed at any one's option." Let us add that to-day, after
+forty-seven years, the _law of the conservation of energy_, wherever
+civilisation exists, is accepted as a fully established truth and
+receives the widest applications in all domains of natural science.
+
+The fate of all momentous discoveries is similar. On their first
+appearance they are regarded by the majority of men as errors. J. R.
+Mayer's work on the principle of energy (1842) was rejected by the first
+physical journal of Germany; Helmholtz's treatise (1847) met with no
+better success; and even Joule, to judge from an intimation of Playfair,
+seems to have encountered difficulties with his first publication
+(1843). Gradually, however, people are led to see that the new view was
+long prepared for and ready for enunciation, only that a few favored
+minds had perceived it much earlier than the rest, and in this way the
+opposition of the majority is overcome. With proofs of the fruitfulness
+of the new view, with its success, confidence in it increases. The
+majority of the men who employ it cannot enter into a deep-going
+analysis of it; for them, its success is its proof. It can thus happen
+that a view which has led to the greatest discoveries, like Black's
+theory of caloric, in a subsequent period in a province where it does
+not apply may actually become an obstacle to progress by its blinding
+our eyes to facts which do not fit in with our favorite conceptions. If
+a theory is to be protected from this dubious rôle, the grounds and
+motives of its evolution and existence must be examined from time to
+time with the utmost care.
+
+The most multifarious physical changes, thermal, electrical, chemical,
+and so forth, can be brought about by mechanical work. When such
+alterations are reversed they yield anew the mechanical work in exactly
+the quantity which was required for the production of the part reversed.
+This is the _principle of the conservation of energy_; "energy" being
+the term which has gradually come into use for that "indestructible
+something" of which the measure is mechanical _work_.
+
+How did we acquire this idea? What are the sources from which we have
+drawn it? This question is not only of interest in itself, but also for
+the important reason above touched upon. The opinions which are held
+concerning the foundations of the law of energy still diverge very
+widely from one another. Many trace the principle to the impossibility
+of a perpetual motion, which they regard either as sufficiently proved
+by experience, or as self-evident. In the province of pure mechanics the
+impossibility of a perpetual motion, or the continuous production of
+_work_ without some _permanent_ alteration, is easily demonstrated.
+Accordingly, if we start from the theory that all physical processes are
+purely _mechanical_ processes, motions of molecules and atoms, we
+embrace also, by this _mechanical_ conception of physics, the
+impossibility of a perpetual motion in the _whole_ physical domain. At
+present this view probably counts the most adherents. Other inquirers,
+however, are for accepting only a purely _experimental_ establishment of
+the law of energy.
+
+It will appear, from the discussion to follow, that _all_ the factors
+mentioned have co-operated in the development of the view in question;
+but that in addition to them a logical and purely formal factor,
+hitherto little considered, has also played a very important part.
+
+
+I. THE PRINCIPLE OF THE EXCLUDED PERPETUAL MOTION.
+
+The law of energy in its modern form is not identical with the principle
+of the excluded perpetual motion, but it is very closely related to it.
+The latter principle, however, is by no means new, for in the province
+of mechanics it has controlled for centuries the thoughts and
+investigations of the greatest thinkers. Let us convince ourselves of
+this by the study of a few historical examples.
+
+[Illustration: Fig. 41.]
+
+S. Stevinus, in his famous work _Hypomnemata mathematica_, Tom. IV, _De
+statica_, (Leyden, 1605, p. 34), treats of the equilibrium of bodies on
+inclined planes.
+
+Over a triangular prism _ABC_, one side of which, _AC_, is horizontal,
+an endless cord or chain is slung, to which at equal distances apart
+fourteen balls of equal weight are attached, as represented in
+cross-section in Figure 41. Since we can imagine the lower symmetrical
+part of the cord _ABC_ taken away, Stevinus concludes that the four
+balls on _AB_ hold in equilibrium the two balls on _BC_. For if the
+equilibrium were for a moment disturbed, it could never subsist: the
+cord would keep moving round forever in the same direction,--we should
+have a perpetual motion. He says:
+
+     "But if this took place, our row or ring of balls would come once
+     more into their original position, and from the same cause the
+     eight globes to the left would again be heavier than the six to the
+     right, and therefore those eight would sink a second time and these
+     six rise, and all the globes would keep up, of themselves, _a
+     continuous and unending motion, which is false_."[41]
+
+Stevinus, now, easily derives from this principle the laws of
+equilibrium on the inclined plane and numerous other fruitful
+consequences.
+
+In the chapter "Hydrostatics" of the same work, page 114, Stevinus sets
+up the following principle: "Aquam datam, datum sibi intra aquam locum
+servare,"--a given mass of water preserves within water its given place.
+
+[Illustration: Fig. 42.]
+
+This principle is demonstrated as follows (see Fig. 42):
+
+     "For, assuming it to be possible by natural means, let us suppose
+     that A does not preserve the place assigned to it, but sinks down
+     to D. This being posited, the water which succeeds A will, for the
+     same reason, also flow down to _D_; _A_ will be forced out of its
+     place in _D_; and thus this body of water, for the conditions in it
+     are everywhere the same, _will set up a perpetual motion, which is
+     absurd_."[42]
+
+From this all the principles of hydrostatics are deduced. On this
+occasion Stevinus also first develops the thought so fruitful for modern
+analytical mechanics that the equilibrium of a system is not destroyed
+by the addition of rigid connexions. As we know, the principle of the
+conservation of the centre of gravity is now sometimes deduced from
+D'Alembert's principle with the help of that remark. If we were to
+reproduce Stevinus's demonstration to-day, we should have to change it
+slightly. We find no difficulty in imagining the cord on the prism
+possessed of unending uniform motion if all hindrances are thought away,
+but we should protest against the assumption of an accelerated motion or
+even against that of a uniform motion, if the resistances were not
+removed. Moreover, for greater precision of proof, the string of balls
+might be replaced by a heavy homogeneous cord of infinite flexibility.
+But all this does not affect in the least the historical value of
+Stevinus's thoughts. It is a fact, Stevinus deduces apparently much
+simpler truths from the principle of an impossible perpetual motion.
+
+In the process of thought which conducted Galileo to his discoveries at
+the end of the sixteenth century, the following principle plays an
+important part, that a body in virtue of the velocity acquired in its
+descent can rise exactly as high as it fell. This principle, which
+appears frequently and with much clearness in Galileo's thought, is
+simply another form of the principle of excluded perpetual motion, as we
+shall see it is also in Huygens.
+
+Galileo, as we know, arrived at the law of uniformly accelerated motion
+by _a priori_ considerations, as that law which was the "simplest and
+most natural," after having first assumed a different law which he was
+compelled to reject. To verify his law he executed experiments with
+falling bodies on inclined planes, measuring the times of descent by the
+weights of the water which flowed out of a small orifice in a large
+vessel. In this experiment he assumes as a fundamental principle, that
+the velocity acquired in descent down an inclined plane always
+corresponds to the vertical height descended through, a conclusion which
+for him is the immediate outcome of the fact that a body which has
+fallen down one inclined plane can, with the velocity it has acquired,
+rise on another plane of any inclination only to the same vertical
+height. This principle of the height of ascent also led him, as it
+seems, to the law of inertia. Let us hear his own masterful words in the
+_Dialogo terzo_ (_Opere_, Padova, 1744, Tom. III). On page 96 we read:
+
+     "I take it for granted that the velocities acquired by a body in
+     descent down planes of different inclinations are equal if the
+     heights of those planes are equal."[43]
+
+Then he makes Salviati say in the dialogue:[44]
+
+     "What you say seems very probable, but I wish to go further and by
+     an experiment so to increase the probability of it that it shall
+     amount almost to absolute demonstration. Suppose this sheet of
+     paper to be a vertical wall, and from a nail driven in it a ball of
+     lead weighing two or three ounces to hang by a very fine thread
+     _AB_ four or five feet long. (Fig. 43.) On the wall mark a
+     horizontal line _DC_ perpendicular to the vertical _AB_, which
+     latter ought to hang about two inches from the wall. If now the
+     thread _AB_ with the ball attached take the position _AC_ and the
+     ball be let go, you will see the ball first descend through the arc
+     _CB_ and passing beyond _B_ rise through the arc _BD_ almost to the
+     level of the line _CD_, being prevented from reaching it exactly by
+     the resistance of the air and of the thread. From this we may truly
+     conclude that its impetus at the point _B_, acquired by its descent
+     through the arc _CB_, is sufficient to urge it through a similar
+     arc _BD_ to the same height. Having performed this experiment and
+     repeated it several times, let us drive in the wall, in the
+     projection of the vertical _AB_, as at _E_ or at _F_, a nail five
+     or six inches long, so that the thread _AC_, carrying as before the
+     ball through the arc _CB_, at the moment it reaches the position
+     _AB_, shall strike the nail _E_, and the ball be thus compelled to
+     move up the arc _BG_ described about _E_ as centre. Then we shall
+     see what the same impetus will here accomplish, acquired now as
+     before at the same point _B_, which then drove the same moving body
+     through the arc _BD_ to the height of the horizontal _CD_. Now
+     gentlemen, you will be pleased to see the ball rise to the
+     horizontal line at the point _G_, and the same thing also happen if
+     the nail be placed lower as at _F_, in which case the ball would
+     describe the arc _BJ_, always terminating its ascent precisely at
+     the line _CD_. If the nail be placed so low that the length of
+     thread below it does not reach to the height of _CD_ (which would
+     happen if _F_ were nearer _B_ than to the intersection of _AB_ with
+     the horizontal _CD_), then the thread will wind itself about the
+     nail. This experiment leaves no room for doubt as to the truth of
+     the supposition. For as the two arcs _CB_, _DB_ are equal and
+     similarly situated, the momentum acquired in the descent of the arc
+     _CB_ is the same as that acquired in the descent of the arc _DB_;
+     but the momentum acquired at _B_ by the descent through the arc
+     _CB_ is capable of driving up the same moving body through the arc
+     _BD_; hence also the momentum acquired in the descent _DB_ is equal
+     to that which drives the same moving body through the same arc from
+     _B_ to _D_, so that in general every momentum acquired in the
+     descent of an arc is equal to that which causes the same moving
+     body to ascend through the same arc; but all the momenta which
+     cause the ascent of all the arcs _BD_, _BG_, _BJ_, are equal since
+     they are made by the same momentum acquired in the descent _CB_, as
+     the experiment shows: therefore all the momenta acquired in the
+     descent of the arcs _DB_, _GB_, _JB_ are equal."
+
+[Illustration: Fig. 43.]
+
+The remark relative to the pendulum may be applied to the inclined plane
+and leads to the law of inertia. We read on page 124:[45]
+
+     "It is plain now that a movable body, starting from rest at _A_ and
+     descending down the inclined plane _AB_, acquires a velocity
+     proportional to the increment of its time: the velocity possessed
+     at _B_ is the greatest of the velocities acquired, and by its
+     nature immutably impressed, provided all causes of new acceleration
+     or retardation are taken away: I say acceleration, having in view
+     its possible further progress along the plane extended;
+     retardation, in view of the possibility of its being reversed and
+     made to mount the ascending plane _BC_. But in the horizontal plane
+     _GH_ its equable motion, according to its velocity as acquired in
+     the descent from _A_ to _B_, will be continued _ad infinitum_."
+     (Fig. 44.)
+
+[Illustration: Fig. 44.]
+
+Huygens, upon whose shoulders the mantel of Galileo fell, forms a
+sharper conception of the law of inertia and generalises the principle
+respecting the heights of ascent which was so fruitful in Galileo's
+hands. He employs the latter principle in the solution of the problem of
+the centre of oscillation and is perfectly clear in the statement that
+the principle respecting the heights of ascent is identical with the
+principle of the excluded perpetual motion.
+
+The following important passages then occur (Hugenii, _Horologium
+oscillatorium, pars secunda_). _Hypotheses_:
+
+     "If gravity did not exist, nor the atmosphere obstruct the motions
+     of bodies, a body would keep up forever the motion once impressed
+     upon it, with equable velocity, in a straight line."[46]
+
+In part four of the _Horologium de centro oscillationis_ we read:
+
+     "If any number of weights be set in motion by the force of gravity,
+     the common centre of gravity of the weights as a whole cannot
+     possibly rise higher than the place which it occupied when the
+     motion began.
+
+     "That this hypothesis of ours may arouse no scruples, we will state
+     that it simply imports, what no one has ever denied, that heavy
+     bodies do not move _upwards_.--And truly if the devisers of the new
+     machines who make such futile attempts to construct a perpetual
+     motion would acquaint themselves with this principle, they could
+     easily be brought to see their errors and to understand that the
+     thing is utterly impossible by mechanical means."[47]
+
+There is possibly a Jesuitical mental reservation contained in the words
+"mechanical means." One might be led to believe from them that Huygens
+held a non-mechanical perpetual motion for possible.
+
+The generalisation of Galileo's principle is still more clearly put in
+Prop. IV of the same chapter:
+
+     "If a pendulum, composed of several weights, set in motion from
+     rest, complete any part of its full oscillation, and from that
+     point onwards, the individual weights, with their common connexions
+     dissolved, change their acquired velocities upwards and ascend as
+     far as they can, the common centre of gravity of all will be
+     carried up to the same altitude with that which it occupied before
+     the beginning of the oscillation."[48]
+
+On this last principle now, which is a generalisation, applied to a
+system of masses, of one of Galileo's ideas respecting a single mass and
+which from Huygens's explanation we recognise as the principle of
+excluded perpetual motion, Huygens grounds his theory of the centre of
+oscillation. Lagrange characterises this principle as precarious and is
+rejoiced at James Bernoulli's successful attempt, in 1681, to reduce the
+theory of the centre of oscillation to the laws of the lever, which
+appeared to him clearer. All the great inquirers of the seventeenth and
+eighteenth centuries broke a lance on this problem, and it led
+ultimately, in conjunction with the principle of virtual velocities, to
+the principle enunciated by D'Alembert in 1743 in his _Traité de
+dynamique_, though previously employed in a somewhat different form by
+Euler and Hermann.
+
+Furthermore, the Huygenian principle respecting the heights of ascent
+became the foundation of the "law of the conservation of living force,"
+as that was enunciated by John and Daniel Bernoulli and employed with
+such signal success by the latter in his _Hydrodynamics_. The theorems
+of the Bernoullis differ in form only from Lagrange's expression in the
+_Analytical Mechanics_.
+
+The manner in which Torricelli reached his famous law of efflux for
+liquids leads again to our principle. Torricelli assumed that the liquid
+which flows out of the basal orifice of a vessel cannot by its velocity
+of efflux ascend to a greater height than its level in the vessel.
+
+Let us next consider a point which belongs to pure mechanics, the
+history of the principle of _virtual motions_ or _virtual velocities_.
+This principle was not first enunciated, as is usually stated, and as
+Lagrange also asserts, by Galileo, but earlier, by Stevinus. In his
+_Trochleostatica_ of the above-cited work, page 72, he says:
+
+     "Observe that this axiom of statics holds good here:
+
+     "As the space of the body acting is to the space of the body acted
+     upon, so is the power of the body acted upon to the power of the
+     body acting."[49]
+
+Galileo, as we know, recognised the truth of the principle in the
+consideration of the simple machines, and also deduced the laws of the
+equilibrium of liquids from it.
+
+Torricelli carries the principle back to the properties of the centre of
+gravity. The condition controlling equilibrium in a simple machine, in
+which power and load are represented by weights, is that the common
+centre of gravity of the weights shall not sink. Conversely, if the
+centre of gravity cannot sink equilibrium obtains, because heavy bodies
+of themselves do not move upwards. In this form the principle of virtual
+velocities is identical with Huygens's principle of the impossibility of
+a perpetual motion.
+
+John Bernoulli, in 1717, first perceived the universal import of the
+principle of virtual movements for all systems; a discovery stated in a
+letter to Varignon. Finally, Lagrange gives a general demonstration of
+the principle and founds upon it his whole _Analytical Mechanics_. But
+this general demonstration is based after all upon Huygens and
+Torricelli's remarks. Lagrange, as is known, conceives simple pulleys
+arranged in the directions of the forces of the system, passes a cord
+through these pulleys, and appends to its free extremity a weight which
+is a common measure of all the forces of the system. With no difficulty,
+now, the number of elements of each pulley may be so chosen that the
+forces in question shall be replaced by them. It is then clear that if
+the weight at the extremity cannot sink, equilibrium subsists, because
+heavy bodies cannot of themselves move upwards. If we do not go so far,
+but wish to abide by Torricelli's idea, we may conceive every individual
+force of the system replaced by a special weight suspended from a cord
+passing over a pulley in the direction of the force and attached at its
+point of application. Equilibrium subsists then when the common centre
+of gravity of all the weights together cannot sink. The fundamental
+supposition of this demonstration is plainly the impossibility of a
+perpetual motion.
+
+Lagrange tried in every way to supply a proof free from extraneous
+elements and fully satisfactory, but without complete success. Nor were
+his successors more fortunate.
+
+The whole of mechanics, thus, is based upon an idea, which, though
+unequivocal, is yet unwonted and not coequal with the other principles
+and axioms of mechanics. Every student of mechanics, at some stage of
+his progress, feels the uncomfortableness of this state of affairs;
+every one wishes it removed; but seldom is the difficulty stated in
+words. Accordingly, the zealous pupil of the science is highly rejoiced
+when he reads in a master like Poinsot (_Théorie générale de l'équilibre
+et du mouvement des systèmes_) the following passage, in which that
+author is giving his opinion of the _Analytical Mechanics_:
+
+     "In the meantime, because our attention in that work was first
+     wholly engrossed with the consideration of its beautiful
+     development of mechanics, which seemed to spring complete from a
+     single formula, we naturally believed that the science was
+     completed or that it only remained to seek the demonstration of the
+     principle of virtual velocities. But that quest brought back all
+     the difficulties that we had overcome by the principle itself. That
+     law so general, wherein are mingled the vague and unfamiliar ideas
+     of infinitely small movements and of perturbations of equilibrium,
+     only grew obscure upon examination; and the work of Lagrange
+     supplying nothing clearer than the march of analysis, we saw
+     plainly that the clouds had only appeared lifted from the course of
+     mechanics because they had, so to speak, been gathered at the very
+     origin of that science.
+
+     "At bottom, a general demonstration of the principle of virtual
+     velocities would be equivalent to the establishment of the whole of
+     mechanics upon a different basis: for the demonstration of a law
+     which embraces a whole science is neither more nor less than the
+     reduction of that science to another law just as general, but
+     evident, or at least more simple than the first, and which,
+     consequently, would render that useless."[50]
+
+According to Poinsot, therefore, a proof of the principle of virtual
+movements is tantamount to a total rehabilitation of mechanics.
+
+Another circumstance of discomfort to the mathematician is, that in the
+historical form in which mechanics at present exists, dynamics is
+founded on statics, whereas it is desirable that in a science which
+pretends to deductive completeness the more special statical theorems
+should be deducible from the more general dynamical principles.
+
+In fact, a great master, Gauss, gave expression to this desire in his
+presentment of the principle of least constraint (Crelle's _Journal für
+reine und angewandte Mathematik_, Vol. IV, p. 233) in the following
+words: "Proper as it is that in the gradual development of a science,
+and in the instruction of individuals, the easy should precede the
+difficult, the simple the complex, the special the general, yet the
+mind, when once it has reached a higher point of view, demands the
+contrary course, in which all statics shall appear simply as a special
+case of mechanics." Gauss's own principle, now, possesses all the
+requisites of universality, but its difficulty is that it is not
+immediately intelligible and that Gauss deduced it with the help of
+D'Alembert's principle, a procedure which left matters where they were
+before.
+
+Whence, now, is derived this strange part which the principle of virtual
+motion plays in mechanics? For the present I shall only make this reply.
+It would be difficult for me to tell the difference of impression which
+Lagrange's proof of the principle made on me when I first took it up as
+a student and when I subsequently resumed it after having made
+historical researches. It first appeared to me insipid, chiefly on
+account of the pulleys and the cords which did not fit in with the
+mathematical view, and whose action I would much rather have discovered
+from the principle itself than have taken for granted. But now that I
+have studied the history of the science I cannot imagine a more
+beautiful demonstration.
+
+In fact, through all mechanics it is this self-same principle of
+excluded perpetual motion which accomplishes almost all, which
+displeased Lagrange, but which he still had to employ, at least tacitly,
+in his own demonstration. If we give this principle its proper place and
+setting, the paradox is explained.
+
+The principle of excluded perpetual motion is thus no new discovery; it
+has been the guiding idea, for three hundred years, of all the great
+inquirers. But the principle cannot properly be _based_ upon mechanical
+perceptions. For long before the development of mechanics the conviction
+of its truth existed and even contributed to that development. Its power
+of conviction, therefore, must have more universal and deeper roots. We
+shall revert to this point.
+
+
+II. MECHANICAL PHYSICS.
+
+It cannot be denied that an unmistakable tendency has prevailed, from
+Democritus to the present day, to explain _all_ physical events
+_mechanically_. Not to mention earlier obscure expressions of that
+tendency we read in Huygens the following:[51]
+
+     "There can be no doubt that light consists of the _motion_ of a
+     certain substance. For if we examine its production, we find that
+     here on earth it is principally fire and flame which engender it,
+     both of which contain beyond doubt bodies which are in rapid
+     movement, since they dissolve and destroy many other bodies more
+     solid than they: while if we regard its effects, we see that when
+     light is accumulated, say by concave mirrors, it has the property
+     of combustion just as fire has, that is to say, it disunites the
+     parts of bodies, which is assuredly a proof of _motion_, at least
+     in the _true philosophy_, in which the causes of all natural
+     effects are conceived as _mechanical_ causes. Which in my judgment
+     must be accomplished or all hope of ever understanding physics
+     renounced."[52]
+
+S. Carnot,[53] in introducing the principle of excluded perpetual motion
+into the theory of heat, makes the following apology:
+
+     "It will be objected here, perhaps, that a perpetual motion proved
+     impossible for _purely mechanical actions_, is perhaps not so when
+     the influence of _heat_ or of electricity is employed. But can
+     phenomena of heat or electricity be thought of as due to anything
+     else than to _certain motions of bodies_, and as such must they not
+     be subject to the general laws of mechanics?"[54]
+
+These examples, which might be multiplied by quotations from recent
+literature indefinitely, show that a tendency to explain all things
+mechanically actually exists. This tendency is also intelligible.
+Mechanical events as simple motions in space and time best admit of
+observation and pursuit by the help of our highly organised senses. We
+reproduce mechanical processes almost without effort in our imagination.
+Pressure as a circumstance that produces motion is very familiar to us
+from daily experience. All changes which the individual personally
+produces in his environment, or humanity brings about by means of the
+arts in the world, are effected through the instrumentality of
+_motions_. Almost of necessity, therefore, motion appears to us as the
+most important physical factor. Moreover, mechanical properties may be
+discovered in all physical events. The sounding bell trembles, the
+heated body expands, the electrified body attracts other bodies. Why,
+therefore, should we not attempt to grasp all events under their
+mechanical aspect, since that is so easily apprehended and most
+accessible to observation and measurement? In fact, no objection _is_ to
+be made to the attempt to elucidate the properties of physical events by
+mechanical _analogies_.
+
+But modern physics has proceeded _very far_ in this direction. The point
+of view which Wundt represents in his excellent treatise _On the
+Physical Axioms_ is probably shared by the majority of physicists. The
+axioms of physics which Wundt sets up are as follows:
+
+1. All natural causes are motional causes.
+
+2. Every motional cause lies outside the object moved.
+
+3. All motional causes act in the direction of the straight line of
+junction, and so forth.
+
+4. The effect of every cause persists.
+
+5. Every effect involves an equal countereffect.
+
+6. Every effect is equivalent to its cause.
+
+These principles might be studied properly enough as fundamental
+principles of mechanics. But when they are set up as axioms of physics,
+their enunciation is simply tantamount to a negation of all events
+except motion.
+
+According to Wundt, all changes of nature are mere changes of place. All
+causes are motional causes (page 26). Any discussion of the
+philosophical grounds on which Wundt supports his theory would lead us
+deep into the speculations of the Eleatics and the Herbartians. Change
+of place, Wundt holds, is the _only_ change of a thing in which a thing
+remains identical with itself. If a thing changed _qualitatively_, we
+should be obliged to imagine that something was annihilated and
+something else created in its place, which is not to be reconciled with
+our idea of the identity of the object observed and of the
+indestructibility of matter. But we have only to remember that the
+Eleatics encountered difficulties of exactly the same sort in motion.
+Can we not also imagine that a thing is destroyed in _one_ place and in
+_another_ an exactly similar thing created? After all, do we really know
+_more_ why a body leaves one place and appears in another, than why a
+_cold_ body grows _warm_? Granted that we had a perfect knowledge of the
+mechanical processes of nature, could we and should we, for that reason,
+_put out of the world_ all other processes that we do not understand? On
+this principle it would really be the simplest course to deny the
+existence of the whole world. This is the point at which the Eleatics
+ultimately arrived, and the school of Herbart stopped little short of
+the same goal.
+
+Physics treated in this sense supplies us simply with a diagram of the
+world, in which we do not know reality again. It happens, in fact, to
+men who give themselves up to this view for many years, that the world
+of sense from which they start as a province of the greatest
+familiarity, suddenly becomes, in their eyes, the supreme
+"world-riddle."
+
+Intelligible as it is, therefore, that the efforts of thinkers have
+always been bent upon the "reduction of all physical processes to the
+motions of atoms," it must yet be affirmed that this is a chimerical
+ideal. This ideal has often played an effective part in popular
+lectures, but in the workshop of the serious inquirer it has discharged
+scarcely the least function. What has really been achieved in mechanical
+physics is either the _elucidation_ of physical processes by more
+familiar _mechanical analogies_, (for example, the theories of light and
+of electricity,) or the exact _quantitative_ ascertainment of the
+connexion of mechanical processes with other physical processes, for
+example, the results of thermodynamics.
+
+
+III. THE PRINCIPLE OF ENERGY IN PHYSICS.
+
+We can know only from _experience_ that mechanical processes produce
+other physical transformations, or _vice versa_. The attention was first
+directed to the connexion of mechanical processes, especially the
+performance of work, with changes of thermal conditions by the invention
+of the steam-engine, and by its great technical importance. Technical
+interests and the need of scientific lucidity meeting in the mind of S.
+Carnot led to the remarkable development from which thermodynamics
+flowed. It is simply _an accident of history_ that the development in
+question was not connected with the practical applications of
+_electricity_.
+
+In the determination of the maximum quantity of _work_ that, generally,
+a heat-machine, or, to take a special case, a steam-engine, can perform
+with the expenditure of a _given_ amount of heat of combustion, Carnot
+is guided by mechanical analogies. A body can do work on being heated,
+by expanding under pressure. But to do this the body must receive heat
+from a _hotter_ body. Heat, therefore, to do work, must pass from a
+hotter body to a colder body, just as water must fall from a higher
+level to a lower level to put a mill-wheel in motion. Differences of
+temperature, accordingly, represent forces able to do work exactly as do
+differences of height in heavy bodies. Carnot pictures to himself an
+ideal process in which no heat flows away unused, that is, without doing
+work. With a given expenditure of heat, accordingly, this process
+furnishes the maximum of work. An analogue of the process would be a
+mill-wheel which scooping its water out of a higher level would slowly
+carry it to a lower level without the loss of a drop. A peculiar
+property of the process is, that with the expenditure of the same work
+the water can be raised again exactly to its original level. This
+property of _reversibility_ is also shared by the process of Carnot. His
+process also can be reversed by the expenditure of the same amount of
+work, and the heat again brought back to its original temperature level.
+
+Suppose, now, we had _two_ different reversible processes _A_, _B_, such
+that in _A_ a quantity of heat, _Q_, flowing off from the temperature
+_t₁_ to the lower temperature _t₂_ should perform the work _W_, but in
+_B_ under the same circumstances it should perform a greater quantity of
+work _W_ + _W'_; then, we could join _B_ in the sense assigned and _A_
+in the reverse sense into a _single_ process. Here _A_ would reverse the
+transformation of heat produced by _B_ and would leave a surplus of work
+_W'_, produced, so to speak, from nothing. The combination would present
+a perpetual motion.
+
+With the feeling, now, that it makes little difference whether the
+mechanical laws are broken directly or indirectly (by processes of
+heat), and convinced of the existence of a _universal_ law-ruled
+connexion of nature, Carnot here excludes for the first time from the
+province of _general_ physics the possibility of a perpetual motion.
+_But it follows, then, that the quantity of work W, produced by the
+passage of a quantity of heat Q from a temperature t₁ to a temperature
+t₂, is independent of the nature of the substances as also of the
+character of the process, so far as that is unaccompanied by loss, but
+is wholly dependent upon the temperature t₁, t₂.
+
+This important principle has been fully confirmed by the special
+researches of Carnot himself (1824), of Clapeyron (1834), and of Sir
+William Thomson (1849), now Lord Kelvin. The principle was reached
+_without any assumption whatever_ concerning the nature of heat, simply
+by the exclusion of a perpetual motion. Carnot, it is true, was an
+adherent of the theory of Black, according to which the sum-total of the
+quantity of heat in the world is constant, but so far as his
+investigations have been hitherto considered the decision on this point
+is of no consequence. Carnot's principle led to the most remarkable
+results. W. Thomson (1848) founded upon it the ingenious idea of an
+"absolute" scale of temperature. James Thomson (1849) conceived a Carnot
+process to take place with water freezing under pressure and, therefore,
+performing work. He discovered, thus, that the freezing point is lowered
+0·0075° Celsius by every additional atmosphere of pressure. This is
+mentioned merely as an example.
+
+About twenty years after the publication of Carnot's book a further
+advance was made by J. R. Mayer and J. P. Joule. Mayer, while engaged as
+a physician in the service of the Dutch, observed, during a process of
+bleeding in Java, an unusual redness of the venous blood. In agreement
+with Liebig's theory of animal heat he connected this fact with the
+diminished loss of heat in warmer climates, and with the diminished
+expenditure of organic combustibles. The total expenditure of heat of a
+man at rest must be equal to the total heat of combustion. But since
+_all_ organic actions, even the mechanical actions, must be set down to
+the credit of the heat of combustion, some connexion must exist between
+mechanical work and expenditure of heat.
+
+Joule started from quite similar convictions concerning the galvanic
+battery. A heat of association equivalent to the consumption of the zinc
+can be made to appear in the galvanic cell. If a current is set up, a
+part of this heat appears in the conductor of the current. The
+interposition of an apparatus for the decomposition of water causes a
+part of this heat to disappear, which on the burning of the explosive
+gas formed, is reproduced. If the current runs an electromotor, a
+portion of the heat again disappears, which, on the consumption of the
+work by friction, again makes its appearance. Accordingly, both the
+heat produced and the work produced, appeared to Joule also as
+connected with the consumption of material. The thought was therefore
+present, both to Mayer and to Joule, of regarding heat and work as
+equivalent quantities, so connected with each other that what is lost in
+one form universally appears in another. The result of this was a
+_substantial_ conception of heat and of work, and _ultimately a
+substantial conception of energy_. Here every physical change of
+condition is regarded as energy, the destruction of which generates work
+or equivalent heat. An electric charge, for example, is energy.
+
+In 1842 Mayer had calculated from the physical constants then
+universally accepted that by the disappearance of one kilogramme-calorie
+365 kilogramme-metres of work could be performed, and _vice versa_.
+Joule, on the other hand, by a long series of delicate and varied
+experiments beginning in 1843 ultimately determined the mechanical
+equivalent of the kilogramme-calorie, more exactly, as 425
+kilogramme-metres.
+
+If we estimate every change of physical condition by the _mechanical
+work_ which can be performed upon the _disappearance_ of that condition,
+and call this measure _energy_, then we can measure all physical changes
+of condition, no matter how different they may be, with the same common
+measure, and say: _the sum-total of all energy remains constant_. This
+is the form that the principle of excluded perpetual motion received at
+the hands of Mayer, Joule, Helmholtz, and W. Thomson in its extension to
+the whole domain of physics.
+
+After it had been proved that heat must _disappear_ if mechanical work
+was to be done at its expense, Carnot's principle could no longer be
+regarded as a complete expression of the facts. Its improved form was
+first given, in 1850, by Clausius, whom Thomson followed in 1851. It
+runs thus: "If a quantity of heat _Q'_ is transformed into work in a
+reversible process, _another_ quantity of heat _Q_ of the absolute[55]
+temperature _T₁_ is lowered to the absolute temperature _T₂_." Here
+_Q'_ is dependent only on _Q_, _T₁_, _T₂_, but is independent of the
+substances used and of the character of the process, so far as that is
+unaccompanied by loss. Owing to this last fact, it is sufficient to find
+the relation which obtains for some one well-known physical substance,
+say a gas, and some definite simple process. The relation found will be
+the one that holds generally. We get, thus,
+
+_Q'/(Q' + Q) = (T₁-T₂)/T₁_ (1)
+
+that is, the quotient of the available heat _Q'_ transformed into work
+divided by the sum of the transformed and transferred heats (the total
+sum used), the so-called _economical coefficient_ of the process, is,
+
+_(T₁-T₂)/T₁_.
+
+
+IV. THE CONCEPTIONS OF HEAT.
+
+When a cold body is put in contact with a warm body it is observed that
+the first body is warmed and that the second body is cooled. We may say
+that the first body is warmed _at the expense of_ the second body. This
+suggests the notion of a thing, or heat-substance, which passes from the
+one body to the other. If two masses of water _m_, _m'_, of unequal
+temperatures, be put together, it will be found, upon the rapid
+equalisation of the temperatures, that the respective changes of
+temperatures _u_ and _u'_ are inversely proportional to the masses and
+of opposite signs, so that the algebraical sum of the products is,
+
+_mu + m'u' = 0_.
+
+Black called the products _mu_, _m'u'_, which are decisive for our
+knowledge of the process, _quantities of heat_. We may form a very clear
+_picture_ of these products by conceiving them with Black as measures of
+the quantities of some substance. But the essential thing is not this
+picture but the _constancy_ of the sum of these products in simple
+processes of conduction. If a quantity of heat disappears at one point,
+an equally large quantity will make its appearance at some other point.
+The retention of this idea leads to the discovery of specific heat.
+Black, finally, perceives that also something else may appear for a
+vanished quantity of heat, namely: the fusion or vaporisation of a
+definite quantity of matter. He adheres here still to this favorite
+view, though with some freedom, and considers the vanished quantity of
+heat as still present, but as _latent_.
+
+The generally accepted notion of a caloric, or heat-stuff, was strongly
+shaken by the work of Mayer and Joule. If the quantity of heat can be
+increased and diminished, people said, heat cannot be a substance, but
+must be a _motion_. The subordinate part of this statement has become
+much more popular than all the rest of the doctrine of energy. But we
+may convince ourselves that the motional conception of heat is now as
+unessential as was formerly its conception as a substance. Both ideas
+were favored or impeded solely by accidental historical circumstances.
+It does not follow that heat is not a substance from the fact that a
+mechanical equivalent exists for quantity of heat. We will make this
+clear by the following question which bright students have sometimes put
+to me. Is there a mechanical equivalent of electricity as there is a
+mechanical equivalent of heat? Yes, and no. There is no mechanical
+equivalent of _quantity_ of electricity as there is an equivalent of
+_quantity_ of heat, because the same quantity of electricity has a very
+different capacity for work, according to the circumstances in which it
+is placed; but there _is_ a mechanical equivalent of electrical energy.
+
+Let us ask another question. Is there a mechanical equivalent of water?
+No, there is no mechanical equivalent of quantity of water, but there is
+a mechanical equivalent of weight of water multiplied by its distance
+of descent.
+
+When a Leyden jar is discharged and work thereby performed, we do not
+picture to ourselves that the quantity of electricity disappears as work
+is done, but we simply assume that the electricities come into different
+positions, equal quantities of positive and negative electricity being
+united with one another.
+
+What, now, is the reason of this difference of view in our treatment of
+heat and of electricity? The reason is purely historical, wholly
+conventional, and, what is still more important, is wholly indifferent.
+I may be allowed to establish this assertion.
+
+In 1785 Coulomb constructed his torsion balance, by which he was enabled
+to measure the repulsion of electrified bodies. Suppose we have two
+small balls, _A_, _B_, which over their whole extent are similarly
+electrified. These two balls will exert on one another, at a certain
+distance _r_ of their centres, a certain repulsion _p_. We bring into
+contact with _B_ now a ball _C_, suffer both to be equally electrified,
+and then measure the repulsion of _B_ from _A_ and of _C_ from _A_ at
+the same distance _r_. The sum of these repulsions is again _p_.
+Accordingly something has remained constant. If we ascribe this effect
+to a substance, then we infer naturally its constancy. But the essential
+point of the exposition is the divisibility of the electric force _p_
+and not the simile of substance.
+
+In 1838 Riess constructed his electrical air-thermometer (the
+thermoelectrometer). This gives a measure of the quantity of heat
+produced by the discharge of jars. This quantity of heat is not
+proportional to the quantity of electricity contained in the jar by
+Coulomb's measure, but if _Q_ be this quantity and _C_ be the capacity,
+is proportional to _Q_²/2_C_, or, more simply still, to the energy of
+the charged jar. If, now, we discharge the jar completely through the
+thermometer, we obtain a certain quantity of heat, _W_. But if we make
+the discharge through the thermometer into a second jar, we obtain a
+quantity less than _W_. But we may obtain the remainder by completely
+discharging both jars through the air-thermometer, when it will again be
+proportional to the energy of the two jars. On the first, incomplete
+discharge, accordingly, a part of the electricity's capacity for work
+was lost.
+
+When the charge of a jar produces heat its energy is changed and its
+value by Riess's thermometer is decreased. But by Coulomb's measure the
+quantity remains unaltered.
+
+Now let us imagine that Riess's thermometer had been invented before
+Coulomb's torsion balance, which is not a difficult feat, since both
+inventions are independent of each other; what would be more natural
+than that the "quantity" of electricity contained in a jar should be
+measured by the heat produced in the thermometer? But then, this
+so-called quantity of electricity would decrease on the production of
+heat or on the performance of work, whereas it now remains unchanged;
+in that case, therefore, electricity would not be a _substance_ but a
+_motion_, whereas now it is still a substance. The reason, therefore,
+why we have other notions of electricity than we have of heat, is purely
+historical, accidental, and conventional.
+
+This is also the case with other physical things. Water does not
+disappear when work is done. Why? Because we measure quantity of water
+with scales, just as we do electricity. But suppose the capacity of
+water for work were called quantity, and had to be measured, therefore,
+by a mill instead of by scales; then this quantity also would disappear
+as it performed the work. It may, now, be easily conceived that many
+substances are not so easily got at as water. In that case we should be
+unable to carry out the one kind of measurement with the scales whilst
+many other modes of measurement would still be left us.
+
+In the case of heat, now, the historically established measure of
+"quantity" is accidentally the work-value of the heat. Accordingly, its
+quantity disappears when work is done. But that heat is not a substance
+follows from this as little as does the opposite conclusion that it is a
+substance. In Black's case the quantity of heat remains constant because
+the heat passes into no _other_ form of energy.
+
+If any one to-day should still wish to think of heat as a substance, we
+might allow that person this liberty with little ado. He would only have
+to assume that that which we call quantity of heat was the energy of a
+substance whose quantity remained unaltered, but whose energy changed.
+In point of fact we might much better say, in analogy with the other
+terms of physics, energy of heat, instead of quantity of heat.
+
+When we wonder, therefore, at the discovery that heat is motion, we
+wonder at something that was never discovered. It is perfectly
+indifferent and possesses not the slightest scientific value, whether we
+think of heat as a substance or not. The fact is, heat behaves in some
+connexions like a substance, in others not. Heat is latent in steam as
+oxygen is latent in water.
+
+
+V. THE CONFORMITY IN THE DEPORTMENT OF THE ENERGIES.
+
+The foregoing reflexions will gain in lucidity from a consideration of
+the conformity which obtains in the behavior of all energies, a point to
+which I called attention long ago.[56]
+
+A weight _P_ at a height _H₁_ represents an energy _W₁ = PH₁_. If we
+suffer the weight to sink to a lower height _H₂_, during which work is
+done, and the work done is employed in the production of living force,
+heat, or an electric charge, in short, is transformed, then the energy
+_W₂ = PH₂_ is still _left_. The equation subsists
+
+_W₁/H₁ = W₂/H₂_, (2)
+
+or, denoting the _transformed_ energy by _W' = W₁-W₂_ and the
+_transferred_ energy, that transported to the lower level, by _W = W₂_,
+
+_W'/(W' + W) = (H₁-H₂)/H₁_, (3)
+
+an equation in all respects analogous to equation (1) at page 165. The
+property in question, therefore, is by no means peculiar to heat.
+Equation (2) gives the relation between the energy taken from the higher
+level and that deposited on the lower level (the energy left behind); it
+says that these _energies_ are proportional to the _heights of the
+levels_. An equation analogous to equation (2) may be set up for _every_
+form of energy; hence the equation which corresponds to equation (3),
+and so to equation (1), may be regarded as valid for every form. For
+electricity, for example, _H₁_, _H₂_ signify the potentials.
+
+When we observe for the first time the agreement here indicated in the
+transformative law of the energies, it appears surprising and
+unexpected, for we do not perceive at once its reason. But to him who
+pursues the comparative historical method that reason will not long
+remain a secret.
+
+Since Galileo, mechanical work, though long under a different name, has
+been a _fundamental concept_ of mechanics, as also a very important
+notion in the applied sciences. The transformation of work into living
+force, and of living force into work, suggests directly the notion of
+energy--the idea having been first fruitfully employed by Huygens,
+although Thomas Young first called it by the _name_ of "energy." Let us
+add to this the constancy of weight (really the constancy of mass) and
+we shall see that with respect to mechanical energy it is involved in
+the very definition of the term that the capacity for work or the
+potential energy of a weight is proportional to the height of the level
+at which it is, in the geometrical sense, and that it decreases on the
+lowering of the weight, on transformation, proportionally to the height
+of the level. The zero level here is wholly arbitrary. With this,
+equation (2) is given, from which all the other forms follow.
+
+When we reflect on the tremendous start which mechanics had over the
+other branches of physics, it is not to be wondered at that the attempt
+was always made to apply the notions of that science wherever this was
+possible. Thus the notion of mass, for example, was imitated by Coulomb
+in the notion of quantity of electricity. In the further development of
+the theory of electricity, the notion of work was likewise immediately
+introduced in the theory of potential, and heights of electrical level
+were measured by the work of unit of quantity raised to that level. But
+with this the preceding equation with all its consequences is given for
+electrical energy. The case with the other energies was similar.
+
+_Thermal_ energy, however, appears as a special case. Only by the
+peculiar experiments mentioned could it be discovered that heat is an
+energy. But the measure of this energy by Black's quantity of heat is
+the outcome of fortuitous circumstances. In the first place, the
+accidental slight variability of the capacity for heat _c_ with the
+temperature, and the accidental slight deviation of the usual
+thermometrical scales from the scale derived from _the tensions of
+gases_, brings it about that the notion "quantity of heat" can be set up
+and that the quantity of heat _ct_ corresponding to a difference of
+temperature _t_ is nearly proportional to the energy of the heat. It is
+a quite accidental historical circumstance that Amontons hit upon the
+idea of measuring temperature by the tension of a gas. It is certain in
+this that he did not think of the work of the heat.[57] But the numbers
+standing for temperature, thus, are made proportional to the tensions of
+gases, that is, to the work done by gases, with otherwise equal changes
+of volume. It thus happens that _temperature heights_ and _level heights
+of work_ are proportional to one another.
+
+If properties of the thermal condition varying greatly from the tensions
+of gases had been chosen, this relation would have assumed very
+complicated forms, and the agreement between heat and the other energies
+above considered would not subsist. It is very instructive to reflect
+upon this point. A _natural law_, therefore, is not implied in the
+conformity of the behavior of the energies, but this conformity is
+rather conditioned by the uniformity of our modes of conception and is
+also partly a matter of good fortune.
+
+
+VI. THE DIFFERENCES OF THE ENERGIES AND THE LIMITS OF THE PRINCIPLE OF
+ENERGY.
+
+Of every quantity of heat _Q_ which does work in a reversible process
+(one unaccompanied by loss) between the absolute temperatures _T₁_,
+_T₂_, only the portion
+
+_(T₁-T₂)/T₁_
+
+is transformed into work, while the remainder is transferred to the
+lower temperature-level _T₂_. This transferred portion can, upon the
+reversal of the process, with the same expenditure of work, again be
+brought back to the level _T₁_. But if the process is not reversible,
+then more heat than in the foregoing case flows to the lower level, and
+the surplus can no longer be brought back to the higher level _T₂_
+without some _special_ expenditure. W. Thomson (1852), accordingly, drew
+attention to the fact, that in all non-reversible, that is, in all real
+thermal processes, quantities of heat are lost for mechanical work, and
+that accordingly a dissipation or waste of mechanical energy is taking
+place. In all cases, heat is only partially transformed into work, but
+frequently work is wholly transformed into heat. Hence, a tendency
+exists towards a diminution of the _mechanical_ energy and towards an
+increase of the _thermal_ energy of the world.
+
+For a simple, closed cyclical process, accompanied by no loss, in which
+the quantity of heat _Q₁_ is taken from the level _T₁_, and the quantity
+_Q₂_ is deposited upon the level _T₂_, the following relation, agreeably
+to equation (2), exists,
+
+_-(Q₁/T₁) + (Q₂/T₂) = 0_.
+
+Similarly, for any number of compound reversible cycles Clausius finds
+the algebraical sum
+
+_[sum]Q/T = 0_,
+
+and supposing the temperature to change continuously,
+
+_[integral]dQ/T = 0_ (4)
+
+Here the elements of the quantities of heat deducted from a given level
+are reckoned negative, and the elements imparted to it, positive. If the
+process is not reversible, then expression (4), which Clausius calls
+_entropy_, increases. In actual practice this is always the case, and
+Clausius finds himself led to the statement:
+
+1. That the energy of the world remains constant.
+
+2. That the entropy of the world tends toward a maximum.
+
+Once we have noted the above-indicated conformity in the behavior of
+different energies, the _peculiarity_ of thermal energy here mentioned
+must strike us. Whence is this peculiarity derived, for, generally every
+energy passes only partly into another form, which is also true of
+thermal energy? The explanation will be found in the following.
+
+Every transformation of a special kind of energy _A_ is accompanied with
+a fall of potential of that particular kind of energy, including heat.
+But whilst for the other kinds of energy a transformation and therefore
+a loss of energy on the part of the kind sinking in potential is
+connected with the fall of the potential, with heat the case is
+different. Heat can suffer a fall of potential without sustaining a loss
+of energy, at least according to the customary mode of estimation. If a
+weight sinks, it must create perforce kinetic energy, or heat, or some
+other form of energy. Also, an electrical charge cannot suffer a fall of
+potential without loss of energy, i. e., without transformation. But
+heat can pass with a fall of temperature to a body of greater capacity
+and the same thermal energy still be preserved, so long as we regard
+_every quantity_ of heat as energy. This it is that gives to heat,
+besides its property of energy, in many cases the character of a
+material _substance_, or quantity.
+
+If we look at the matter in an unprejudiced light, we must ask if there
+is any scientific sense or purpose in still considering as energy a
+quantity of heat that can no longer be transformed into mechanical work,
+(for example, the heat of a closed equably warmed material system). The
+principle of energy certainly plays in this case a wholly superfluous
+rôle, which is assigned to it only from habit.[58] To maintain the
+principle of energy in the face of a knowledge of the dissipation or
+waste of mechanical energy, in the face of the increase of entropy is
+equivalent almost to the liberty which Black took when he regarded the
+heat of liquefaction as still present but latent.[59] It is to be
+remarked further, that the expressions "energy of the world" and
+"entropy of the world" are slightly permeated with scholasticism. Energy
+and entropy are _metrical_ notions. What meaning can there be in
+applying these notions to a case in which they are not applicable, in
+which their values are not determinable?
+
+If we could really determine the entropy of the world it would represent
+a true, absolute measure of time. In this way is best seen the utter
+tautology of a statement that the entropy of the world increases with
+the time. Time, and the fact that certain changes take place only in a
+definite sense, are one and the same thing.
+
+
+
+VII. THE SOURCES OF THE PRINCIPLE OF ENERGY.
+
+We are now prepared to answer the question, What are the sources of the
+principle of energy? All knowledge of nature is derived in the last
+instance from experience. In this sense they are right who look upon the
+principle of energy as a result of experience.
+
+Experience teaches that the sense-elements [alpha beta gamma delta ...]
+into which the world may be decomposed, are subject to change. It tells
+us further, that certain of these elements are _connected_ with other
+elements, so that they appear and disappear together; or, that the
+appearance of the elements of one class is connected with the
+disappearance of the elements of the other class. We will avoid here the
+notions of cause and effect because of their obscurity and
+equivocalness. The result of experience may be expressed as follows:
+_The sensuous elements of the world ([alpha beta gamma delta ...]) show
+themselves to be interdependent._ This interdependence is best
+represented by some such conception as is in geometry that of the mutual
+dependence of the sides and angles of a triangle, only much more varied
+and complex.
+
+As an example, we may take a mass of gas enclosed in a cylinder and
+possessed of a definite volume ([alpha]), which we change by a pressure
+([beta]) on the piston, at the same time feeling the cylinder with our
+hand and receiving a sensation of heat ([gamma]). Increase of pressure
+diminishes the volume and increases the sensation of heat.
+
+The various facts of experience are not in all respects alike. Their
+common sensuous elements are placed in relief by a process of
+abstraction and thus impressed upon the memory. In this way the
+expression is obtained of the features of _agreement_ of extensive
+groups of facts. The simplest sentence which we can utter is, by the
+very nature of language, an abstraction of this kind. But account must
+also be taken of the _differences_ of related facts. Facts may be so
+nearly related as to contain the same kind of a [alpha beta gamma ...],
+but the relation be such that the [alpha beta gamma ...] of the one
+differ from the [alpha beta gamma ...] of the other only by the number
+of equal parts into which they can be divided. Such being the case, if
+rules can be given for deducing _from one another_ the numbers which are
+the measures of these [alpha beta gamma ...], then we possess in such
+rules the _most general_ expression of a group of facts, as also that
+expression which corresponds to all its differences. This is the goal of
+quantitative investigation.
+
+If this goal be reached what we have found is that between the [alpha
+beta gamma ...] of a group of facts, or better, between the numbers
+which are their measures, a number of equations exists. The simple fact
+of change brings it about that the number of these equations must be
+smaller than the number of the [alpha beta gamma ...]. If the former be
+smaller by one than the latter, then one portion of the [alpha beta
+gamma ...] is _uniquely_ determined by the other portion.
+
+The quest of relations of this last kind is the most important function
+of special experimental research, because we are enabled by it to
+complete in thought facts that are only partly given. It is self-evident
+that only experience can ascertain that between the [alpha beta gamma
+...] relations exist and of what kind they are. Further, only experience
+can tell that the relations that exist between the [alpha beta gamma
+...] are such that changes of them can be reversed. If this were not the
+fact all occasion for the enunciation of the principle of energy, as is
+easily seen, would be wanting. In experience, therefore, is buried the
+ultimate well-spring of all knowledge of nature, and consequently, in
+this sense, also the ultimate source of the principle of energy.
+
+But this does not exclude the fact that the principle of energy has also
+a logical root, as will now be shown. Let us assume on the basis of
+experience that one group of sensuous elements [alpha beta gamma ...]
+determines _uniquely_ another group [lambda mu nu ...]. Experience
+further teaches that changes of [alpha beta gamma ...] can be
+_reversed_. It is then a logical consequence of this observation, that
+every time that [alpha beta gamma ...] assume the same values this is
+also the case with [lambda mu nu ...]. Or, that purely _periodical_
+changes of [alpha beta gamma ...] can produce no _permanent_ changes of
+[lambda mu nu ...]. If the group [lambda mu nu ...] is a mechanical
+group, then a perpetual motion is excluded.
+
+It will be said that this is a vicious circle, which we will grant. But
+psychologically, the situation is essentially different, whether I think
+simply of the unique determination and reversibility of events, or
+whether I exclude a perpetual motion. The attention takes in the two
+cases different directions and diffuses light over different sides of
+the question, which logically of course are necessarily connected.
+
+Surely that firm, logical setting of the thoughts noticeable in the
+great inquirers, Stevinus, Galileo, and the rest, which, consciously or
+instinctively, was supported by a fine feeling for the slightest
+contradictions, has no other purpose than to limit the bounds of thought
+and so exempt it from the possibility of error. In this, therefore, the
+logical root of the principle of excluded perpetual motion is given,
+namely, in that universal conviction which existed even before the
+development of mechanics and co-operated in that development.
+
+It is perfectly natural that the principle of excluded perpetual motion
+should have been first developed in the simple domain of pure mechanics.
+Towards the transference of that principle into the domain of general
+physics the idea contributed much that all physical phenomena are
+mechanical phenomena. But the foregoing discussion shows how little
+essential this notion is. The issue really involved is the recognition
+of a general interconnexion of nature. This once established, we see
+with Carnot that it is indifferent whether the mechanical laws are
+broken directly or circuitously.
+
+The principle of the excluded perpetual motion is very closely related
+to the modern principle of energy, but it is not identical with it, for
+the latter is to be deduced from the former only by means of a definite
+_formal conception_. As may be seen from the preceding exposition, the
+perpetual motion can be excluded without our employing or possessing the
+notion of _work_. The modern principle of energy results primarily from
+a _substantial_ conception of work and of every change of physical
+condition which by being reversed produces work. The strong need of such
+a conception, which is by no means necessary, but in a formal sense is
+very convenient and lucid, is exhibited in the case of J. R. Mayer and
+Joule. It was before remarked that this conception was suggested to both
+inquirers by the observation that both the production of heat and the
+production of mechanical work were connected with an expenditure of
+substance. Mayer says: "Ex nihilo nil fit," and in another place, "The
+creation or destruction of a force (work) lies without the province of
+human activity." In Joule we find this passage: "It is manifestly
+_absurd_ to suppose that the powers with which God has endowed matter
+can be destroyed."
+
+Some writers have observed in such statements the attempt at a
+_metaphysical_ establishment of the doctrine of energy. But we see in
+them simply the formal need of a simple, clear, and living grasp of the
+facts, which receives its development in practical and technical life,
+and which we carry over, as best we can, into the province of science.
+As a fact, Mayer writes to Griesinger: "If, finally, you ask me how I
+became involved in the whole affair, my answer is simply this: Engaged
+during a sea voyage almost exclusively with the study of physiology, I
+discovered the new theory for the sufficient reason that I _vividly felt
+the need of it_."
+
+The substantial conception of work (energy) is by no means a necessary
+one. And it is far from true that the problem is solved with the
+recognition of the need of such a conception. Rather let us see how
+Mayer gradually endeavored to satisfy that need. He first regards
+quantity of motion, or momentum, _mv_, as the equivalent of work, and
+did not light, until later, on the notion of living force (_mv²/2_). In
+the province of electricity he was unable to assign the expression which
+is the equivalent of work. This was done later by Helmholtz. The formal
+need, therefore, is _first_ present, and our conception of nature is
+subsequently gradually _adapted_ to it.
+
+The laying bare of the experimental, logical, and formal root of the
+present principle of energy will perhaps contribute much to the removal
+of the mysticism which still clings to this principle. With respect to
+our formal need of a very simple, palpable, substantial conception of
+the processes in our environment, it remains an open question how far
+nature corresponds to that need, or how far we can satisfy it. In one
+phase of the preceding discussions it would seem as if the substantial
+notion of the principle of energy, like Black's material conception of
+heat, has its natural limits in facts, beyond which it can only be
+artificially adhered to.
+
+  FOOTNOTES:
+
+  [Footnote 39: Published in Vol. 5, No. I, of _The Monist_, October,
+  1894, being in part a re-elaboration of the treatise _Ueber die
+  Erhaltung der Arbeit_, Prague, 1872.]
+
+  [Footnote 40: _On Matter, Living Force, and Heat_, Joule:
+  _Scientific Papers_, London, 1884, I, p. 265.]
+
+  [Footnote 41: "Atqui hoc si sit, globorum series sive corona eundem
+  situm cum priore habebit, eademque de causa octo globi sinistri
+  ponderosiores erunt sex dextris, ideoque rursus octo illi
+  descendent, sex illi ascendent, istique globi ex sese _continuum et
+  aeternum motum efficient, quod est falsum_."]
+
+  [Footnote 42: "A igitur, (si ullo modo per naturam fieri possit)
+  locum sibi tributum non servato, ac delabatur in _D_; quibus positis
+  aqua quae ipsi _A_ succedit eandem ob causam deffluet in _D_, eademque
+  ab alia istinc expelletur, atque adeo aqua haec (cum ubique eadem
+  ratio sit) _motum instituet perpetuum, quod absurdum fuerit_."]
+
+  [Footnote 43: "Accipio, gradus velocitatis ejusdem mobilis super
+  diversas planorum inclinationes acquisitos tunc esse aequales, cum
+  eorundum planorum elevationes aequales sint."]
+
+  [Footnote 44: "Voi molto probabilmente discorrete, ma oltre al veri
+  simile voglio con una esperienza crescer tanto la probabilità, che
+  poco gli manchi all'agguagliarsi ad una ben necessaria
+  dimostrazione. Figuratevi questo foglio essere una parete eretta
+  all'orizzonte, e da un chiodo fitto in essa pendere una palla di
+  piombo d'un'oncia, o due, sospesa dal sottil filo _AB_ lungo due, o
+  tre braccia perpendicolare all'orizzonte, e nella parete segnate una
+  linea orizontale _DC_ segante a squadra il perpendicolo _AB_, il
+  quale sia lontano dalla parete due dita in circa, trasferendo poi il
+  filo _AB_ colla palla in _AC_, lasciata essa palla in libertà, la
+  quale primieramente vedrete scendere descrivendo l'arco _CBD_, e di
+  tanto trapassare il termine _B_, che scorrendo per l'arco _BD_
+  sormonterà fino quasi alla segnata parallela _CD_, restando di per
+  vernirvi per piccolissimo intervallo, toltogli il precisamente
+  arrivarvi dall'impedimento dell'aria, e del filo. Dal che possiamo
+  veracemente concludere, che l'impeto acquistato nel punto _B_ dalla
+  palla nello scendere per l'arco _CB_, fu tanto, che bastò a
+  risospingersi per un simile arco _BD_ alla medesima altezza; fatta,
+  e più volte reiterata cotale esperienza, voglio, che fiechiamo nella
+  parete rasente al perpendicolo _AB_ un chiodo come in _E_, ovvero in
+  _F_, che sporga in fuori cinque, o sei dita, e questo acciocchè il
+  filo _AC_ tornando come prima a riportar la palla _C_ per l'arco
+  _CB_, giunta che ella sia in _B_, inoppando il filo nel chiodo _E_,
+  sia costretta a camminare per la circonferenza _BG_ descritta in
+  torno al centro _E_, dal che vedremo quello, che potrà far quel
+  medesimo impeto, che dianzi concepizo nel medesimo termine _B_,
+  sospinse l'istesso mobile per l'arco _ED_ all'altezza
+  dell'orizzonale _CD_. Ora, Signori, voi vedrete con gusto condursi
+  la palla all'orizzontale nel punto _G_, e l'istesso accadere,
+  l'intoppo si metesse più basso, come in _F_, dove la palla
+  descriverebbe l'arco _BJ_, terminando sempre la sua salita
+  precisamente nella linea _CD_, e quando l'intoppe del chiodo fusse
+  tanto basso, che l'avanzo del filo sotto di lui non arivasse
+  all'altezza di _CD_ (il che accaderebbe, quando fusse più vicino al
+  punto _B_, che al segamento dell' _AB_ coll'orizzontale _CD_),
+  allora il filo cavalcherebbe il chiodo, e segli avolgerebbe intorno.
+  Questa esperienza non lascia luogo di dubitare della verità del
+  supposto: imperocchè essendo li due archi _CB_, _DB_ equali e
+  similmento posti, l'acquisto di momento fatto per la scesa nell'arco
+  _CB_, è il medesimo, che il fatto per la scesa dell'arco _DB_; ma il
+  momento acquistato in _B_ per l'arco _CB_ è potente a risospingere
+  in su il medesimo mobile per l'arco _BD_; adunque anco il momento
+  acquistato nella scesa _DB_ è eguale a quello, che sospigne
+  l'istesso mobile pel medesimo arco da _B_ in _D_, sicche
+  universal-mente ogni memento acquistato per la scesa d'un arco è
+  eguale a quello, che può far risalire l'istesso mobile pel medesimo
+  arco: ma i momenti tutti che fanno resalire per tutti gli archi
+  _BD_, _BG_, _BJ_ sono eguali, poichè son fatti dal istesso medesimo
+  momento acquistato per la scesa _CB_, come mostra l'esperienza:
+  adunque tutti i momenti, che si acquistano per le scese negli archi
+  _DB_, _GB_, _JB_ sono eguali."]
+
+  [Footnote 45: "Constat jam, quod mobile ex quiete in _A_ descendens
+  per _AB_, gradus acquirit velocitatis juxta temporis ipsius
+  incrementum: gradum vero in _B_ esse maximum acquisitorum, et suapte
+  natura immutabiliter impressum, sublatis scilicet causis
+  accelerationis novae, aut retardationis: accelerationis inquam, si
+  adhuc super extenso plano ulterius progrederetur; retardationis
+  vero, dum super planum acclive _BC_ fit reflexio: in horizontali
+  autem _GH_ aequabilis motus juxta gradum velocitatis ex _A_ in _B_
+  acquisitae in infinitum extenderetur."]
+
+  [Footnote 46: "Si gravitas non esset, neque aër motui corporum
+  officeret, unumquodque eorum, acceptum semel motum continuaturum
+  velocitate aequabili, secundum lineam rectam."]
+
+  [Footnote 47: "Si pondera quotlibet, vi gravitatis suae, moveri
+  incipiant; non posse centrum gravitatis ex ipsis compositae altius,
+  quam ubi incipiente motu reperiebatur, ascendere.
+
+  "Ipsa vero hypothesis nostra quominus scrupulum moveat, nihil aliud
+  sibi velle ostendemus, quam, quod nemo unquam negavit, gravia nempe
+  sursum non ferri.--Et sane, si hac eadem uti scirent novorum operum
+  machinatores, qui motum perpetuum irrito conatu moliuntur, facile
+  suos ipsi errores deprehenderent, intelligerentque rem eam mechanica
+  ratione haud quaquam possibilem esse."]
+
+  [Footnote 48: "Si pendulum e pluribus ponderibus compositum, atque e
+  quiete dimissum, partem quamcunque oscillationis integrae
+  confecerit, atque inde porro intelligantur pondera ejus singula,
+  relicto communi vinculo, celeritates acquisitas sursum convertere,
+  ac quousque possunt ascendere; hoc facto centrum gravitatis ex
+  omnibus compositae, ad eandem altitudinem reversum erit, quam ante
+  inceptam oscillationem obtinebat."]
+
+  [Footnote 49: "Notato autem hic illud staticum axioma etiam locum
+  habere:
+
+    "Ut spatium agentis ad spatium patientis
+    Sic potentia patientis ad potentiam agentis."]
+
+  [Footnote 50: "Cependant, comme dans cet ouvrage on ne fut d'abord
+  attentif qu'à considérer ce beau développement de la mécanique qui
+  semblait sortir tout entière d'une seule et même formule, on crut
+  naturellement que la science etait faite, et qu'il ne restait plus
+  qu'à chercher la démonstration du principe des vitesses virtuelles.
+  Mais cette recherche ramena toutes les difficultés qu'on avait
+  franchies par le principe même. Cette loi si générale, où se mêlent
+  des idées vagues et étrangères de mouvements infinement petits et de
+  perturbation d'équilibre, ne fit en quelque sorte que s'obsurcir à
+  l'examen; et le livre de Lagrange n'offrant plus alors rien de clair
+  que la marche des calculs, on vit bien que les nuages n'avaient paru
+  levé sur le cours de la mécanique que parcequ'ils étaient, pour
+  ainsi dire, rassemblés à l'origine même do cette science.
+
+  "Une démonstration générale du principe des vitesses virtuelles
+  devait au fond revenir a établir le mécanique entière sur une autre
+  base: car la demonstration d'une loi qui embrasse toute une science
+  ne peut être autre chose qua la reduction de cette science à une
+  autre loi aussi générale, mais évidente, ou du moins plus simple que
+  la première, et qui partant la rende inutile."]
+
+  [Footnote 51: _Traité de la lumière_, Leyden, 1690, p. 2.]
+
+  [Footnote 52: "L'on ne sçaurait douter que la lumière ne consiste
+  dans le _mouvement_ de certaine matière. Car soit qu'on regarde sa
+  production, on trouve qu'içy sur la terre c'est principalement le
+  feu et la flamme qui l'engendrent, lesquels contient sans doute des
+  corps qui sont dans un mouvement rapide, puis qu'ils dissolvent et
+  fondent plusieurs autres corps des plus solides: soit qu'on regarde
+  ses effets, on voit que quand la lumière est ramasseé, comme par des
+  miroires concaves, elle a la vertu de brûler comme le feu.
+  c-est-à-dire qu'elle desunit les parties des corps; ce qui marque
+  assurément du _mouvement_, au moins dans la _vraye Philosophie_,
+  dans laquelle on conçoit la cause de tous les effets naturels par
+  des raisons de _mechanique_. Ce qu'il faut faire à mon avis, ou bien
+  renoncer à tout espérance de jamais rien comprendre dans la
+  Physique."]
+
+  [Footnote 53: _Sur la puissance motrice du feu_. (Paris, 1824.)]
+
+  [Footnote 54: "On objectra peut-être ici que le mouvement perpétuel,
+  démontré impossible par les _seules actions mécaniques_, ne l'est
+  peut-être pas lorsqu'on emploie l'influence soit de la _chaleur_,
+  soit de l'électricité; mais pent-on concevoir les phénomènes de la
+  chaleur et de l'électricité comme dus à autre chose qu'à des
+  _mouvements quelconques des corps_ et comme tels ne doivent-ils pas
+  être soumis aux lois générales de la mécanique?"]
+
+  [Footnote 55: By this is meant the temperature of a Celsius scale,
+  the zero of which is 273° below the melting-point of ice.]
+
+  [Footnote 56: I first drew attention to this fact in my treatise
+  _Ueber die Erhaltung der Arbeit_, Prague, 1872. Before this, Zeuner
+  had pointed out the analogy between mechanical and thermal energy. I
+  have given a more extensive development of this idea in a
+  communication to the _Sitzungsberichte der Wiener_ _Akademie_,
+  December, 1892, entitled _Geschichte und Kritik des Carnot'schen
+  Wärmegesetzes_. Compare also the works of Popper (1884), Helm
+  (1887), Wronsky (1888), and Ostwald (1892).]
+
+  [Footnote 57: Sir William Thomson first consciously and
+  intentionally introduced (1848, 1851) a _mechanical_ measure of
+  temperature similar to the electric measure of potential.]
+
+  [Footnote 58: Compare my _Analysis of the Sensations_, Jena, 1886:
+  English translation, Chicago, 1897.]
+
+  [Footnote 59: A better terminology appears highly desirable in the
+  place of the usual misleading one. Sir William Thomson (1852)
+  appears to have felt this need, and it has been clearly expressed by
+  F. Wald (1889). We should call the work which corresponds to a
+  vanished quantity of heat its mechanical substitution-value; while
+  that work which can be _actually_ performed in the passage of a
+  thermal condition _A_ to a condition _B_, alone deserves the name of
+  the _energy-value_ of this change of condition. In this way the
+  _arbitrary_ substantial conception of the processes would be
+  preserved and misapprehensions forestalled.]
+
+
+
+
+THE ECONOMICAL NATURE OF PHYSICAL INQUIRY.[60]
+
+
+When the human mind, with its limited powers, attempts to mirror in
+itself the rich life of the world, of which it is itself only a small
+part, and which it can never hope to exhaust, it has every reason for
+proceeding economically. Hence that tendency, expressed in the
+philosophy of all times, to compass by a few organic thoughts the
+fundamental features of reality. "Life understands not death, nor death
+life." So spake an old Chinese philosopher. Yet in his unceasing desire
+to diminish the boundaries of the incomprehensible, man has always been
+engaged in attempts to understand death by life and life by death.
+
+Among the ancient civilised peoples, nature was filled with demons and
+spirits having the feelings and desires of men. In all essential
+features, this animistic view of nature, as Tylor[61] has aptly termed
+it, is shared in common by the fetish-worshipper of modern Africa and
+the most advanced nations of antiquity. As a theory of the world it has
+never completely disappeared. The monotheism of the Christians never
+fully overcame it, no more than did that of the Jews. In the belief in
+witchcraft and in the superstitions of the sixteenth and seventeenth
+centuries, the centuries of the rise of natural science, it assumed
+frightful pathological dimensions. Whilst Stevinus, Kepler, and Galileo
+were slowly rearing the fabric of modern physical science, a cruel and
+relentless war was waged with firebrand and rack against the devils that
+glowered from every corner. To-day even, apart from all survivals of
+that period, apart from the traces of fetishism which still inhere in
+our physical concepts,[62] those very ideas still covertly lurk in the
+practices of modern spiritualism.
+
+
+By the side of this animistic conception of the world, we meet from time
+to time, in different forms, from Democritus to the present day, another
+view, which likewise claims exclusive competency to comprehend the
+universe. This view may be characterised as the _physico-mechanical_
+view of the world. To-day, that view holds, indisputably, the first
+place in the thoughts of men, and determines the ideals and the
+character of our times. The coming of the mind of man into the full
+consciousness of its powers, in the eighteenth century, was a period of
+genuine disillusionment. It produced the splendid precedent of a life
+really worthy of man, competent to overcome the old barbarism in the
+practical fields of life; it created the _Critique of Pure Reason_,
+which banished into the realm of shadows the sham-ideas of the old
+metaphysics; it pressed into the hands of the mechanical philosophy the
+reins which it now holds.
+
+The oft-quoted words of the great Laplace,[63] which I will now give,
+have the ring of a jubilant toast to the scientific achievements of the
+eighteenth century: "A mind to which were given for a single instant all
+the forces of nature and the mutual positions of all its masses, if it
+were otherwise powerful enough to subject these problems to analysis,
+could grasp, with a single formula, the motions of the largest masses as
+well as of the smallest atoms; nothing would be uncertain for it; the
+future and the past would lie revealed before its eyes." In writing
+these words, Laplace, as we know, had also in mind the atoms of the
+brain. That idea has been expressed more forcibly still by some of his
+followers, and it is not too much to say that Laplace's ideal is
+substantially that of the great majority of modern scientists.
+
+Gladly do we accord to the creator of the _Mécanique céleste_ the sense
+of lofty pleasure awakened in him by the great success of the
+Enlightenment, to which we too owe our intellectual freedom. But to-day,
+with minds undisturbed and before _new_ tasks, it becomes physical
+science to secure itself against self-deception by a careful study of
+its character, so that it can pursue with greater sureness its true
+objects. If I step, therefore, beyond the narrow precincts of my
+specialty in this discussion, to trespass on friendly neighboring
+domains, I may plead in my excuse that the subject-matter of knowledge
+is common to all domains of research, and that fixed, sharp lines of
+demarcation cannot be drawn.
+
+The belief in occult magic powers of nature has gradually died away, but
+in its place a new belief has arisen, the belief in the magical power of
+science. Science throws her treasures, not like a capricious fairy into
+the laps of a favored few, but into the laps of all humanity, with a
+lavish extravagance that no legend ever dreamt of! Not without apparent
+justice, therefore, do her distant admirers impute to her the power of
+opening up unfathomable abysses of nature, to which the senses cannot
+penetrate. Yet she who came to bring light into the world, can well
+dispense with the darkness of mystery, and with pompous show, which she
+needs neither for the justification of her aims nor for the adornment of
+her plain achievements.
+
+The homely beginnings of science will best reveal to us its simple,
+unchangeable character. Man acquires his first knowledge of nature
+half-consciously and automatically, from an instinctive habit of
+mimicking and forecasting facts in thought, of supplementing sluggish
+experience with the swift wings of thought, at first only for his
+material welfare. When he hears a noise in the underbrush he constructs
+there, just as the animal does, the enemy which he fears; when he sees a
+certain rind he forms mentally the image of the fruit which he is in
+search of; just as we mentally associate a certain kind of matter with a
+certain line in the spectrum or an electric spark with the friction of a
+piece of glass. A knowledge of causality in this form certainly reaches
+far below the level of Schopenhauer's pet dog, to whom it was ascribed.
+It probably exists in the whole animal world, and confirms that great
+thinker's statement regarding the will which created the intellect for
+its purposes. These primitive psychical functions are rooted in the
+economy of our organism not less firmly than are motion and digestion.
+Who would deny that we feel in them, too, the elemental power of a long
+practised logical and physiological activity, bequeathed to us as an
+heirloom from our forefathers?
+
+Such primitive acts of knowledge constitute to-day the solidest
+foundation of scientific thought. Our instinctive knowledge, as we shall
+briefly call it, by virtue of the conviction that we have consciously
+and intentionally contributed nothing to its formation, confronts us
+with an authority and logical power which consciously acquired knowledge
+even from familiar sources and of easily tested fallibility can never
+possess. All so-called axioms are such instinctive knowledge. Not
+consciously gained knowledge alone, but powerful intellectual instinct,
+joined with vast conceptive powers, constitute the great inquirer. The
+greatest advances of science have always consisted in some successful
+formulation, in clear, abstract, and communicable terms, of what was
+instinctively known long before, and of thus making it the permanent
+property of humanity. By Newton's principle of the equality of pressure
+and counterpressure, whose truth all before him had felt, but which no
+predecessor had abstractly formulated, mechanics was placed by a single
+stroke on a higher level. Our statement might also be historically
+justified by examples from the scientific labors of Stevinus, S. Carnot,
+Faraday, J. R. Mayer, and others.
+
+All this, however, is merely the soil from which science starts. The
+first real beginnings of science appear in society, particularly in the
+manual arts, where the necessity for the communication of experience
+arises. Here, where some new discovery is to be described and related,
+the compulsion is first felt of clearly defining in consciousness the
+important and essential features of that discovery, as many writers can
+testify. The aim of instruction is simply the saving of experience; the
+labor of one man is made to take the place of that of another.
+
+The most wonderful economy of communication is found in language. Words
+are comparable to type, which spare the repetition of written signs and
+thus serve a multitude of purposes; or to the few sounds of which our
+numberless different words are composed. Language, with its helpmate,
+conceptual thought, by fixing the essential and rejecting the
+unessential, constructs its rigid pictures of the fluid world on the
+plan of a mosaic, at a sacrifice of exactness and fidelity but with a
+saving of tools and labor. Like a piano-player with previously prepared
+sounds, a speaker excites in his listener thoughts previously prepared,
+but fitting many cases, which respond to the speaker's summons with
+alacrity and little effort.
+
+The principles which a prominent political economist, E. Hermann,[64]
+has formulated for the economy of the industrial arts, are also
+applicable to the ideas of common life and of science. The economy of
+language is augmented, of course, in the terminology of science. With
+respect to the economy of written intercourse there is scarcely a doubt
+that science itself will realise that grand old dream of the
+philosophers of a Universal Real Character. That time is not far
+distant. Our numeral characters, the symbols of mathematical analysis,
+chemical symbols, and musical notes, which might easily be supplemented
+by a system of color-signs, together with some phonetic alphabets now in
+use, are all beginnings in this direction. The logical extension of what
+we have, joined with a use of the ideas which the Chinese ideography
+furnishes us, will render the special invention and promulgation of a
+Universal Character wholly superfluous.
+
+The communication of scientific knowledge always involves description,
+that is, a mimetic reproduction of facts in thought, the object of which
+is to replace and save the trouble of new experience. Again, to save the
+labor of instruction and of acquisition, concise, abridged description
+is sought. This is really all that natural laws are. Knowing the value
+of the acceleration of gravity, and Galileo's laws of descent, we
+possess simple and compendious directions for reproducing in thought all
+possible motions of falling bodies. A formula of this kind is a complete
+substitute for a full table of motions of descent, because by means of
+the formula the data of such a table can be easily constructed at a
+moment's notice without the least burdening of the memory.
+
+No human mind could comprehend all the individual cases of refraction.
+But knowing the index of refraction for the two media presented, and the
+familiar law of the sines, we can easily reproduce or fill out in
+thought every conceivable case of refraction. The advantage here
+consists in the disburdening of the memory; an end immensely furthered
+by the written preservation of the natural constants. More than this
+comprehensive and condensed report about facts is not contained in a
+natural law of this sort. In reality, the law always contains less than
+the fact itself, because it does not reproduce the fact as a whole but
+only in that aspect of it which is important for us, the rest being
+either intentionally or from necessity omitted. Natural laws may be
+likened to intellectual type of a higher order, partly movable, partly
+stereotyped, which last on new editions of experience may become
+downright impediments.
+
+When we look over a province of facts for the first time, it appears to
+us diversified, irregular, confused, full of contradictions. We first
+succeed in grasping only single facts, unrelated with the others. The
+province, as we are wont to say, is not _clear_. By and by we discover
+the simple, permanent elements of the mosaic, out of which we can
+mentally construct the whole province. When we have reached a point
+where we can discover everywhere the same facts, we no longer feel lost
+in this province; we comprehend it without effort; it is _explained_ for
+us.
+
+Let me illustrate this by an example. As soon as we have grasped the
+fact of the rectilinear propagation of light, the regular course of our
+thoughts stumbles at the phenomena of refraction and diffraction. As
+soon as we have cleared matters up by our index of refraction we
+discover that a special index is necessary for each color. Soon after we
+have accustomed ourselves to the fact that light added to light
+increases its intensity, we suddenly come across a case of total
+darkness produced by this cause. Ultimately, however, we see everywhere
+in the overwhelming multifariousness of optical phenomena the fact of
+the spatial and temporal periodicity of light, with its velocity of
+propagation dependent on the medium and the period. This tendency of
+obtaining a survey of a given province with the least expenditure of
+thought, and of representing all its facts by some one single mental
+process, may be justly termed an economical one.
+
+The greatest perfection of mental economy is attained in that science
+which has reached the highest formal development, and which is widely
+employed in physical inquiry, namely, in mathematics. Strange as it
+may sound, the power of mathematics rests upon its evasion of
+all unnecessary thought and on its wonderful saving of mental
+operations. Even those arrangement-signs which we call numbers are a
+system of marvellous simplicity and economy. When we employ the
+multiplication-table in multiplying numbers of several places, and so
+use the results of old operations of counting instead of performing the
+whole of each operation anew; when we consult our table of logarithms,
+replacing and saving thus new calculations by old ones already
+performed; when we employ determinants instead of always beginning
+afresh the solution of a system of equations; when we resolve new
+integral expressions into familiar old integrals; we see in this simply
+a feeble reflexion of the intellectual activity of a Lagrange or a
+Cauchy, who, with the keen discernment of a great military commander,
+substituted for new operations whole hosts of old ones. No one will
+dispute me when I say that the most elementary as well as the highest
+mathematics are economically-ordered experiences of counting, put in
+forms ready for use.
+
+In algebra we perform, as far as possible, all numerical operations
+which are identical in form once for all, so that only a remnant of work
+is left for the individual case. The use of the signs of algebra and
+analysis, which are merely symbols of operations to be performed, is due
+to the observation that we can materially disburden the mind in this way
+and spare its powers for more important and more difficult duties, by
+imposing all mechanical operations upon the hand. One result of this
+method, which attests its economical character, is the construction of
+calculating machines. The mathematician Babbage, the inventor of the
+difference-engine, was probably the first who clearly perceived this
+fact, and he touched upon it, although only cursorily, in his work, _The
+Economy of Manufactures and Machinery_.
+
+The student of mathematics often finds it hard to throw off the
+uncomfortable feeling that his science, in the person of his pencil,
+surpasses him in intelligence,--an impression which the great Euler
+confessed he often could not get rid of. This feeling finds a sort of
+justification when we reflect that the majority of the ideas we deal
+with were conceived by others, often centuries ago. In great measure it
+is really the intelligence of other people that confronts us in science.
+The moment we look at matters in this light, the uncanniness and magical
+character of our impressions cease, especially when we remember that we
+can think over again at will any one of those alien thoughts.
+
+Physics is experience, arranged in economical order. By this order not
+only is a broad and comprehensive view of what we have rendered
+possible, but also the defects and the needful alterations are made
+manifest, exactly as in a well-kept household. Physics shares with
+mathematics the advantages of succinct description and of brief,
+compendious definition, which precludes confusion, even in ideas where,
+with no apparent burdening of the brain, hosts of others are contained.
+Of these ideas the rich contents can be produced at any moment and
+displayed in their full perceptual light. Think of the swarm of
+well-ordered notions pent up in the idea of the potential. Is it
+wonderful that ideas containing so much finished labor should be easy to
+work with?
+
+Our first knowledge, thus, is a product of the economy of
+self-preservation. By communication, the experience of _many_ persons,
+individually acquired at first, is collected in _one_. The communication
+of knowledge and the necessity which every one feels of managing his
+stock of experience with the least expenditure of thought, compel us to
+put our knowledge in economical forms. But here we have a clue which
+strips science of all its mystery, and shows us what its power really
+is. With respect to specific results it yields us nothing that we could
+not reach in a sufficiently long time without methods. There is no
+problem in all mathematics that cannot be solved by direct counting. But
+with the present implements of mathematics many operations of counting
+can be performed in a few minutes which without mathematical methods
+would take a lifetime. Just as a single human being, restricted wholly
+to the fruits of his own labor, could never amass a fortune, but on the
+contrary the accumulation of the labor of many men in the hands of one
+is the foundation of wealth and power, so, also, no knowledge worthy of
+the name can be gathered up in a single human mind limited to the span
+of a human life and gifted only with finite powers, except by the most
+exquisite economy of thought and by the careful amassment of the
+economically ordered experience of thousands of co-workers. What strikes
+us here as the fruits of sorcery are simply the rewards of excellent
+housekeeping, as are the like results in civil life. But the business of
+science has this advantage over every other enterprise, that from _its_
+amassment of wealth no one suffers the least loss. This, too, is its
+blessing, its freeing and saving power.
+
+The recognition of the economical character of science will now help us,
+perhaps, to understand better certain physical notions.
+
+Those elements of an event which we call "cause and effect" are certain
+salient features of it, which are important for its mental reproduction.
+Their importance wanes and the attention is transferred to fresh
+characters the moment the event or experience in question becomes
+familiar. If the connexion of such features strikes us as a necessary
+one, it is simply because the interpolation of certain intermediate
+links with which we are very familiar, and which possess, therefore,
+higher authority for us, is often attended with success in our
+explanations. That _ready_ experience fixed in the mosaic of the mind
+with which we meet new events, Kant calls an innate concept of the
+understanding (_Verstandesbegriff_).
+
+The grandest principles of physics, resolved into their elements, differ
+in no wise from the descriptive principles of the natural historian. The
+question, "Why?" which is always appropriate where the explanation of a
+contradiction is concerned, like all proper habitudes of thought, can
+overreach itself and be asked where nothing remains to be understood.
+Suppose we were to attribute to nature the property of producing like
+effects in like circumstances; just these like circumstances we should
+not know how to find. Nature exists once only. Our schematic mental
+imitation alone produces like events. Only in the mind, therefore, does
+the mutual dependence of certain features exist.
+
+All our efforts to mirror the world in thought would be futile if we
+found nothing permanent in the varied changes of things. It is this that
+impels us to form the notion of substance, the source of which is not
+different from that of the modern ideas relative to the conservation of
+energy. The history of physics furnishes numerous examples of this
+impulse in almost all fields, and pretty examples of it may be traced
+back to the nursery. "Where does the light go to when it is put out?"
+asks the child. The sudden shrivelling up of a hydrogen balloon is
+inexplicable to a child; it looks everywhere for the large body which
+was just there but is now gone.
+
+Where does heat come from? Where does heat go to? Such childish
+questions in the mouths of mature men shape the character of a century.
+
+In mentally separating a body from the changeable environment in which
+it moves, what we really do is to extricate a group of sensations on
+which our thoughts are fastened and which is of relatively greater
+stability than the others, from the stream of all our sensations.
+Absolutely unalterable this group is not. Now this, now that member of
+it appears and disappears, or is altered. In its full identity it never
+recurs. Yet the sum of its constant elements as compared with the sum of
+its changeable ones, especially if we consider the continuous character
+of the transition, is always so great that for the purpose in hand the
+former usually appear sufficient to determine the body's identity. But
+because we can separate from the group every single member without the
+body's ceasing to be for us the same, we are easily led to believe that
+after abstracting all the members something additional would remain. It
+thus comes to pass that we form the notion of a substance distinct from
+its attributes, of a thing-in-itself, whilst our sensations are regarded
+merely as symbols or indications of the properties of this
+thing-in-itself. But it would be much better to say that bodies or
+things are compendious mental symbols for groups of sensations--symbols
+that do not exist outside of thought. Thus, the merchant regards the
+labels of his boxes merely as indexes of their contents, and not the
+contrary. He invests their contents, not their labels, with real value.
+The same economy which induces us to analyse a group and to establish
+special signs for its component parts, parts which also go to make up
+other groups, may likewise induce us to mark out by some single symbol a
+whole group.
+
+On the old Egyptian monuments we see objects represented which do not
+reproduce a single visual impression, but are composed of various
+impressions. The heads and the legs of the figures appear in profile,
+the head-dress and the breast are seen from the front, and so on. We
+have here, so to speak, a mean view of the objects, in forming which the
+sculptor has retained what he deemed essential, and neglected what he
+thought indifferent. We have living exemplifications of the processes
+put into stone on the walls of these old temples, in the drawings of our
+children, and we also observe a faithful analogue of them in the
+formation of ideas in our own minds. Only in virtue of some such
+facility of view as that indicated, are we allowed to speak of a body.
+When we speak of a cube with trimmed corners--a figure which is not a
+cube--we do so from a natural instinct of economy, which prefers to add
+to an old familiar conception a correction instead of forming an
+entirely new one. This is the process of all judgment.
+
+The crude notion of "body" can no more stand the test of analysis than
+can the art of the Egyptians or that of our little children. The
+physicist who sees a body flexed, stretched, melted, and vaporised, cuts
+up this body into smaller permanent parts; the chemist splits it up into
+elements. Yet even an element is not unalterable. Take sodium. When
+warmed, the white, silvery mass becomes a liquid, which, when the heat
+is increased and the air shut out, is transformed into a violet vapor,
+and on the heat being still more increased glows with a yellow light. If
+the name sodium is still retained, it is because of the continuous
+character of the transitions and from a necessary instinct of economy.
+By condensing the vapor, the white metal may be made to reappear.
+Indeed, even after the metal is thrown into water and has passed into
+sodium hydroxide, the vanished properties may by skilful treatment still
+be made to appear; just as a moving body which has passed behind a
+column and is lost to view for a moment may make its appearance after a
+time. It is unquestionably very convenient always to have ready the name
+and thought for a group of properties wherever that group by any
+possibility can appear. But more than a compendious economical symbol
+for these phenomena, that name and thought is not. It would be a mere
+empty word for one in whom it did not awaken a large group of
+well-ordered sense-impressions. And the same is true of the molecules
+and atoms into which the chemical element is still further analysed.
+
+True, it is customary to regard the conservation of weight, or, more
+precisely, the conservation of mass, as a direct proof of the constancy
+of matter. But this proof is dissolved, when we go to the bottom of it,
+into such a multitude of instrumental and intellectual operations, that
+in a sense it will be found to constitute simply an equation which our
+ideas in imitating facts have to satisfy. That obscure, mysterious lump
+which we involuntarily add in thought, we seek for in vain outside the
+mind.
+
+It is always, thus, the crude notion of substance that is slipping
+unnoticed into science, proving itself constantly insufficient, and ever
+under the necessity of being reduced to smaller and smaller
+world-particles. Here, as elsewhere, the lower stage is not rendered
+indispensable by the higher which is built upon it, no more than the
+simplest mode of locomotion, walking, is rendered superfluous by the
+most elaborate means of transportation. Body, as a compound of light and
+touch sensations, knit together by sensations of space, must be as
+familiar to the physicist who seeks it, as to the animal who hunts its
+prey. But the student of the theory of knowledge, like the geologist and
+the astronomer, must be permitted to reason back from the forms which
+are created before his eyes to others which he finds ready made for
+him.
+
+All physical ideas and principles are succinct directions, frequently
+involving subordinate directions, for the employment of economically
+classified experiences, ready for use. Their conciseness, as also the
+fact that their contents are rarely exhibited in full, often invests
+them with the semblance of independent existence. Poetical myths
+regarding such ideas,--for example, that of Time, the producer and
+devourer of all things,--do not concern us here. We need only remind the
+reader that even Newton speaks of an _absolute_ time independent of all
+phenomena, and of an absolute space--views which even Kant did not shake
+off, and which are often seriously entertained to-day. For the natural
+inquirer, determinations of time are merely abbreviated statements of
+the dependence of one event upon another, and nothing more. When we say
+the acceleration of a freely falling body is 9·810 metres per second, we
+mean the velocity of the body with respect to the centre of the earth is
+9·810 metres greater when the earth has performed an additional 86400th
+part of its rotation--a fact which itself can be determined only by the
+earth's relation to other heavenly bodies. Again, in velocity is
+contained simply a relation of the position of a body to the position of
+the earth.[65] Instead of referring events to the earth we may refer
+them to a clock, or even to our internal sensation of time. Now, because
+all are connected, and each may be made the measure of the rest, the
+illusion easily arises that time has significance independently of
+all.[66]
+
+The aim of research is the discovery of the equations which subsist
+between the elements of phenomena. The equation of an ellipse expresses
+the universal _conceivable_ relation between its co-ordinates, of which
+only the real values have _geometrical_ significance. Similarly, the
+equations between the elements of _phenomena_ express a universal,
+mathematically conceivable relation. Here, however, for many values only
+certain directions of change are _physically_ admissible. As in the
+ellipse only certain _values_ satisfying the equation are realised, so
+in the physical world only certain _changes_ of value occur. Bodies are
+always accelerated towards the earth. Differences of temperature, left
+to themselves, always grow less; and so on. Similarly, with respect to
+space, mathematical and physiological researches have shown that the
+space of experience is simply an _actual_ case of many conceivable
+cases, about whose peculiar properties experience alone can instruct us.
+The elucidation which this idea diffuses cannot be questioned, despite
+the absurd uses to which it has been put.
+
+Let us endeavor now to summarise the results of our survey. In the
+economical schematism of science lie both its strength and its weakness.
+Facts are always represented at a sacrifice of completeness and never
+with greater precision than fits the needs of the moment. The
+incongruence between thought and experience, therefore, will continue to
+subsist as long as the two pursue their course side by side; but it will
+be continually diminished.
+
+In reality, the point involved is always the completion of some partial
+experience; the derivation of one portion of a phenomenon from some
+other. In this act our ideas must be based directly upon sensations. We
+call this measuring.[67] The condition of science, both in its origin
+and in its application, is a _great relative stability_ of our
+environment. What it teaches us is interdependence. Absolute forecasts,
+consequently, have no significance in science. With great changes in
+celestial space we should lose our co-ordinate systems of space and
+time.
+
+When a geometer wishes to understand the form of a curve, he first
+resolves it into small rectilinear elements. In doing this, however, he
+is fully aware that these elements are only provisional and arbitrary
+devices for comprehending in parts what he cannot comprehend as a whole.
+When the law of the curve is found he no longer thinks of the elements.
+Similarly, it would not become physical science to see in its
+self-created, changeable, economical tools, molecules and atoms,
+realities behind phenomena, forgetful of the lately acquired sapience of
+her older sister, philosophy, in substituting a mechanical mythology for
+the old animistic or metaphysical scheme, and thus creating no end of
+suppositious problems. The atom must remain a tool for representing
+phenomena, like the functions of mathematics. Gradually, however, as the
+intellect, by contact with its subject-matter, grows in discipline,
+physical science will give up its mosaic play with stones and will seek
+out the boundaries and forms of the bed in which the living stream of
+phenomena flows. The goal which it has set itself is the _simplest_ and
+_most economical_ abstract expression of facts.
+
+       *       *       *       *       *
+
+The question now remains, whether the same method of research which till
+now we have tacitly restricted to physics, is also applicable in the
+psychical domain. This question will appear superfluous to the physical
+inquirer. Our physical and psychical views spring in exactly the same
+manner from instinctive knowledge. We read the thoughts of men in their
+acts and facial expressions without knowing how. Just as we predict the
+behavior of a magnetic needle placed near a current by imagining
+Ampère's swimmer in the current, similarly we predict in thought the
+acts and behavior of men by assuming sensations, feelings, and wills
+similar to our own connected with their bodies. What we here
+instinctively perform would appear to us as one of the subtlest
+achievements of science, far outstripping in significance and ingenuity
+Ampère's rule of the swimmer, were it not that every child unconsciously
+accomplished it. The question simply is, therefore, to grasp
+scientifically, that is, by conceptional thought, what we are already
+familiar with from other sources. And here much is to be accomplished. A
+long sequence of facts is to be disclosed between the physics of
+expression and movement and feeling and thought.
+
+We hear the question, "But how is it possible to explain feeling by the
+motions of the atoms of the brain?" Certainly this will never be done,
+no more than light or heat will ever be deduced from the law of
+refraction. We need not deplore, therefore, the lack of ingenious
+solutions of this question. The problem is not a problem. A child
+looking over the walls of a city or of a fort into the moat below sees
+with astonishment living people in it, and not knowing of the portal
+which connects the wall with the moat, cannot understand how they could
+have got down from the high ramparts. So it is with the notions of
+physics. We cannot climb up into the province of psychology by the
+ladder of our abstractions, but we can climb down into it.
+
+Let us look at the matter without bias. The world consists of colors,
+sounds, temperatures, pressures, spaces, times, and so forth, which now
+we shall not call sensations, nor phenomena, because in either term an
+arbitrary, one-sided theory is embodied, but simply _elements_. The
+fixing of the flux of these elements, whether mediately or immediately,
+is the real object of physical research. As long as, neglecting our own
+body, we employ ourselves with the interdependence of those groups of
+elements which, including men and animals, make up _foreign_ bodies, we
+are physicists. For example, we investigate the change of the red color
+of a body as produced by a change of illumination. But the moment we
+consider the special influence on the red of the elements constituting
+our body, outlined by the well-known perspective with head invisible, we
+are at work in the domain of physiological psychology. We close our
+eyes, and the red together with the whole visible world disappears.
+There exists, thus, in the perspective field of every sense a portion
+which exercises on all the rest a different and more powerful influence
+than the rest upon one another. With this, however, all is said. In the
+light of this remark, we call _all_ elements, in so far as we regard
+them as dependent on this special part (our body), _sensations_. That
+the world is our sensation, in this sense, cannot be questioned. But to
+make a system of conduct out of this provisional conception, and to
+abide its slaves, is as unnecessary for us as would be a similar course
+for a mathematician who, in varying a series of variables of a function
+which were previously assumed to be constant, or in interchanging the
+independent variables, finds his method to be the source of some very
+surprising ideas for him.[68]
+
+If we look at the matter in this unbiassed light it will appear
+indubitable that the method of physiological psychology is none other
+than that of physics; what is more, that this science is a part of
+physics. Its subject-matter is not different from that of physics. It
+will unquestionably determine the relations the sensations bear to the
+physics of our body. We have already learned from a member of this
+academy (Hering) that in all probability a sixfold manifoldness of the
+chemical processes of the visual substance corresponds to the sixfold
+manifoldness of color-sensation, and a threefold manifoldness of the
+physiological processes to the threefold manifoldness of
+space-sensations. The paths of reflex actions and of the will are
+followed up and disclosed; it is ascertained what region of the brain
+subserves the function of speech, what region the function of
+locomotion, etc. That which still clings to our body, namely, our
+thoughts, will, when those investigations are finished, present no
+difficulties new in principle. When experience has once clearly
+exhibited these facts and science has marshalled them in economic and
+perspicuous order, there is no doubt that we shall _understand_ them.
+For other "understanding" than a mental mastery of facts never existed.
+Science does not create facts from facts, but simply _orders_ known
+facts.
+
+Let us look, now, a little more closely into the modes of research of
+physiological psychology. We have a very clear idea of how a body moves
+in the space encompassing it. With our optical field of sight we are
+very familiar. But we are unable to state, as a rule, how we have come
+by an idea, from what corner of our intellectual field of sight it has
+entered, or by what region the impulse to a motion is sent forth.
+Moreover, we shall never get acquainted with this mental field of view
+from self-observation alone. Self-observation, in conjunction with
+physiological research, which seeks out physical connexions, can put
+this field of vision in a clear light before us, and will thus first
+really reveal to us our inner man.
+
+Primarily, natural science, or physics, in its widest sense, makes us
+acquainted with only the firmest connexions of groups of elements.
+Provisorily, we may not bestow too much attention on the single
+constituents of those groups, if we are desirous of retaining a
+comprehensible whole. Instead of equations between the primitive
+variables, physics gives us, as much the easiest course, equations
+between _functions_ of those variables. Physiological psychology teaches
+us how to separate the visible, the tangible, and the audible from
+bodies--a labor which is subsequently richly requited, as the division
+of the subjects of physics well shows. Physiology further analyses the
+visible into light and space sensations; the first into colors, the last
+also into their component parts; it resolves noises into sounds, these
+into tones, and so on. Unquestionably this analysis can be carried much
+further than it has been. It will be possible in the end to exhibit the
+common elements at the basis of very abstract but definite logical acts
+of like form,--elements which the acute jurist and mathematician, as it
+were, _feels_ out, with absolute certainty, where the uninitiated hears
+only empty words. Physiology, in a word, will reveal to us the true real
+elements of the world. Physiological psychology bears to physics in its
+widest sense a relation similar to that which chemistry bears to physics
+in its narrowest sense. But far greater than the mutual support of
+physics and chemistry will be that which natural science and psychology
+will render each other. And the results that shall spring from this
+union will, in all likelihood, far outstrip those of the modern
+mechanical physics.
+
+What those ideas are with which we shall comprehend the world when the
+closed circuit of physical and psychological facts shall lie complete
+before us, (that circuit of which we now see only two disjoined parts,)
+cannot be foreseen at the outset of the work. The men will be found who
+will see what is right and will have the courage, instead of wandering
+in the intricate paths of logical and historical accident, to enter on
+the straight ways to the heights from which the mighty stream of facts
+can be surveyed. Whether the notion which we now call matter will
+continue to have a scientific significance beyond the crude purposes of
+common life, we do not know. But we certainly shall wonder how colors
+and tones which were such innermost parts of us could suddenly get lost
+in our physical world of atoms; how we could be suddenly surprised that
+something which outside us simply clicked and beat, in our heads should
+make light and music; and how we could ask whether matter can feel, that
+is to say, whether a mental symbol for a group of sensations can feel?
+
+We cannot mark out in hard and fast lines the science of the future, but
+we can foresee that the rigid walls which now divide man from the world
+will gradually disappear; that human beings will not only confront each
+other, but also the entire organic and so-called lifeless world, with
+less selfishness and with livelier sympathy. Just such a presentiment as
+this perhaps possessed the great Chinese philosopher Licius some two
+thousand years ago when, pointing to a heap of mouldering human bones,
+he said to his scholars in the rigid, lapidary style of his tongue:
+"These and I alone have the knowledge that we neither live nor are
+dead."
+
+  FOOTNOTES:
+
+  [Footnote 60: An address delivered before the anniversary meeting of
+  the Imperial Academy of Sciences, at Vienna, May 25, 1882.]
+
+  [Footnote 61: _Primitive Culture._]
+
+  [Footnote 62: Tylor, _loc. cit._]
+
+  [Footnote 63: _Essai philosophique sur les probabilités_. 6th Ed.
+  Paris, 1840, p. 4. The necessary consideration of the initial
+  velocities is lacking in this formulation.]
+
+  [Footnote 64: _Principien der Wirthschaftslehre_, Vienna, 1873.]
+
+  [Footnote 65: It is clear from this that all so-called elementary
+  (differential) laws involve a relation to the whole.]
+
+  [Footnote 66: If it be objected, that in the case of perturbations
+  of the velocity of rotation of the earth, we could be sensible of
+  such perturbations, and being obliged to have some measure of time,
+  we should resort to the period of vibration of the waves of sodium
+  light,--all that this would show is that for practical reasons we
+  should select that event which best served us as the _simplest_
+  common measure of the others.]
+
+  [Footnote 67: Measurement, in fact, is the definition of one
+  phenomenon by another (standard) phenomenon.]
+
+  [Footnote 68: I have represented the point of view here taken for
+  more than thirty years and developed it in various writings
+  (_Erhaltung der Arbeit_, 1872, parts of which are published in the
+  article on _The Conservation of Energy_ in this collection; _The
+  Forms of Liquids_, 1872, also published in this collection; and the
+  _Bewegungsempfindungen_, 1875). The idea, though known to
+  philosophers, is unfamiliar to the majority of physicists. It is a
+  matter of deep regret to me, therefore, that the title and author of
+  a small tract which accorded with my views in numerous details and
+  which I remember having caught a glance of in a very busy period
+  (1879-1880), have so completely disappeared from my memory that all
+  efforts to obtain a clue to them have hitherto been fruitless.]
+
+
+
+
+ON TRANSFORMATION AND ADAPTATION IN SCIENTIFIC THOUGHT.[69]
+
+
+It was towards the close of the sixteenth century that Galileo with a
+superb indifference to the dialectic arts and sophistic subtleties of
+the Schoolmen of his time, turned the attention of his brilliant mind to
+nature. By nature his ideas were transformed and released from the
+fetters of inherited prejudice. At once the mighty revolution was felt,
+that was therewith effected in the realm of human thought--felt indeed
+in circles far remote and wholly unrelated to the sphere of science,
+felt in strata of society that hitherto had only indirectly recognised
+the influence of scientific thought.
+
+And how great and how far-reaching that revolution was! From the
+beginning of the seventeenth century till its close we see arising, at
+least in embryo, almost all that plays a part in the natural and
+technical science of to-day, almost all that in the two centuries
+following so wonderfully transformed the facial appearance of the earth,
+and all that is moving onward in process of such mighty evolution
+to-day. And all this, the direct result of Galilean ideas, the direct
+outcome of that freshly awakened sense for the investigation of natural
+phenomena which taught the Tuscan philosopher to form the concept and
+the law of falling bodies from the _observation_ of a falling stone!
+Galileo began his investigations without an implement worthy of the
+name; he measured time in the most primitive way, by the efflux of
+water. Yet soon afterwards the telescope, the microscope, the barometer,
+the thermometer, the air-pump, the steam engine, the pendulum, and the
+electrical machine were invented in rapid succession. The fundamental
+theorems of dynamical science, of optics, of heat, and of electricity
+were all disclosed in the century that followed Galileo.
+
+Of scarcely less importance, it seems, was that movement which was
+prepared for by the illustrious biologists of the hundred years just
+past, and formally begun by the late Mr. Darwin. Galileo quickened the
+sense for the simpler phenomena of _inorganic_ nature. And with the same
+simplicity and frankness that marked the efforts of Galileo, and without
+the aid of technical or scientific instruments, without physical or
+chemical experiment, but solely by the power of thought and observation,
+Darwin grasps a new property of _organic_ nature--which we may briefly
+call its _plasticity_.[70] With the same directness of purpose, Darwin,
+too, pursues his way. With the same candor and love of truth, he points
+out the strength and the weakness of his demonstrations. With masterly
+equanimity he holds aloof from the discussion of irrelevant subjects and
+wins alike the admiration of his adherents and of his adversaries.
+
+Scarcely thirty years have elapsed[71] since Darwin first propounded the
+principles of his theory of evolution. Yet, already we see his ideas
+firmly rooted in every branch of human thought, however remote.
+Everywhere, in history, in philosophy, even in the physical sciences, we
+hear the watchwords: heredity, adaptation, selection. We speak of the
+struggle for existence among the heavenly bodies and of the struggle for
+existence in the world of molecules.[72]
+
+The impetus given by Galileo to scientific thought was marked in every
+direction; thus, his pupil, Borelli, founded the school of exact
+medicine, from whence proceeded even distinguished mathematicians. And
+now Darwinian ideas, in the same way, are animating all provinces of
+research. It is true, nature is not made up of two distinct parts, the
+inorganic and the organic; nor must these two divisions be treated
+perforce by totally distinct methods. Many _sides_, however, nature has.
+Nature is like a thread in an intricate tangle, which must be followed
+and traced, now from this point, now from that. But we must never
+imagine,--and this physicists have learned from Faraday and J. R.
+Mayer,--that progress along paths once entered upon is the _only_ means
+of reaching the truth.
+
+It will devolve upon the specialists of the future to determine the
+relative tenability and fruitfulness of the Darwinian ideas in the
+different provinces. Here I wish simply to consider the growth of
+natural _knowledge_ in the light of the theory of evolution. For
+knowledge, too, is a product of organic nature. And although ideas, as
+such, do not comport themselves in all respects like independent organic
+individuals, and although violent comparisons should be avoided, still,
+if Darwin reasoned rightly, the general imprint of evolution and
+transformation must be noticeable in ideas also.
+
+I shall waive here the consideration of the fruitful topic of the
+transmission of ideas or rather of the transmission of the aptitude for
+certain ideas.[73] Nor would it come within my province to discuss
+psychical evolution in any form, as Spencer[74] and many other modern
+psychologists have done, with varying success. Neither shall I enter
+upon a discussion of the struggle for existence and of natural selection
+among scientific theories.[75] We shall consider here only such
+processes of transformation as every student can easily observe in his
+own mind.
+
+       *       *       *       *       *
+
+The child of the forest picks out and pursues with marvellous acuteness
+the trails of animals. He outwits and overreaches his foes with
+surpassing cunning. He is perfectly at home in the sphere of his
+peculiar experience. But confront him with an unwonted phenomenon; place
+him face to face with a technical product of modern civilisation, and he
+will lapse into impotency and helplessness. Here are facts which he
+does not comprehend. If he endeavors to grasp their meaning, he
+misinterprets them. He fancies the moon, when eclipsed, to be tormented
+by an evil spirit. To his mind a puffing locomotive is a living monster.
+The letter accompanying a commission with which he is entrusted, having
+once revealed his thievishness, is in his imagination a conscious being,
+which he must hide beneath a stone, before venturing to commit a fresh
+trespass. Arithmetic to him is like the art of the geomancers in the
+Arabian Nights,--an art which is able to accomplish every imaginable
+impossibility. And, like Voltaire's _ingénu_, when placed in our social
+world, he plays, as we think, the maddest pranks.
+
+With the man who has made the achievements of modern science and
+civilisation his own, the case is quite different. He sees the moon pass
+temporarily into the shadow of the earth. He feels in his thoughts the
+water growing hot in the boiler of the locomotive; he feels also the
+increase of the tension which pushes the piston forward. Where he is not
+able to trace the direct relation of things he has recourse to his
+yard-stick and table of logarithms, which aid and facilitate his thought
+without predominating over it. Such opinions as he cannot concur in, are
+at least known to him, and he knows how to meet them in argument.
+
+Now, wherein does the difference between these two men consist? The
+train of thought habitually employed by the first one does not
+correspond to the facts that he sees. He is surprised and nonplussed at
+every step. But the thoughts of the second man follow and anticipate
+events, his thoughts have become adapted or accommodated to the larger
+field of observation and activity in which he is located; he conceives
+things as they are. The Indian's sphere of experience, however, is quite
+different; his bodily organs of sense are in constant activity; he is
+ever intensely alert and on the watch for his foes; or, his entire
+attention and energy are engaged in procuring sustenance. Now, how can
+such a creature project his mind into futurity, foresee or prophesy?
+This is not possible until our fellow-beings have, in a measure,
+relieved us of our concern for existence. It is then that we acquire
+freedom for observation, and not infrequently too that narrowness of
+thought which society helps and teaches us to disregard.
+
+If we move for a time within a fixed circle of phenomena which recur
+with unvarying uniformity, our thoughts gradually adapt themselves to
+our environment; our ideas reflect unconsciously our surroundings. The
+stone we hold in our hand, when dropped, not only falls to the ground in
+reality; it also falls in our thoughts. Iron-filings dart towards a
+magnet in imagination as well as in fact, and, when thrown into a fire,
+they grew hot in conception as well.
+
+The impulse to complete mentally a phenomenon that has been only
+partially observed, has not its origin in the phenomenon itself; of this
+fact, we are fully sensible. And we well know that it does not lie
+within the sphere of our volition. It seems to confront us rather as a
+power and a law imposed from without and controlling both thought and
+facts.
+
+The fact that we are able by the help of this law to prophesy and
+forecast, merely proves a sameness or uniformity of environment
+sufficient to effect a mental adaptation of this kind. A necessity of
+fulfilment, however, is not contained in this compulsory principle which
+controls our thoughts; nor is it in any way determined by the
+possibility of prediction. We are always obliged, in fact, to await the
+completion of what has been predicted. Errors and departures are
+constantly discernible, and are slight only in provinces of great rigid
+constancy, as in astronomy.
+
+In cases where our thoughts follow the connexion of events with ease,
+and in instances where we positively forefeel the course of a
+phenomenon, it is natural to fancy that the latter is determined by and
+must conform to our thoughts. But the belief in that mysterious agency
+called _causality_, which holds thought and event in unison, is
+violently shaken when a person first enters a province of inquiry in
+which he has previously had no experience. Take for instance the strange
+interaction of electric currents and magnets, or the reciprocal action
+of currents, which seem to defy all the resources of mechanical science.
+Let him be confronted with such phenomena and he will immediately feel
+himself forsaken by his power of prediction; he will bring nothing with
+him into this strange field of events but the hope of soon being able
+to adapt his ideas to the new conditions there presented.
+
+A person constructs from a bone the remaining anatomy of an animal; or
+from the visible part of a half-concealed wing of a butterfly he infers
+and reconstructs the part concealed. He does so with a feeling of
+highest confidence in the accuracy of his results; and in these
+processes we find nothing preternatural or transcendent. But when
+physicists adapt their thoughts to conform to the dynamical course of
+events in time, we invariably surround their investigations with a
+metaphysical halo; yet these latter adaptations bear quite the same
+character as the former, and our only reason for investing them with a
+metaphysical garb, perhaps, is their high practical value.[76]
+
+Let us consider for a moment what takes place when the field of
+observation to which our ideas have been adapted and now conform,
+becomes enlarged. We had, let us say, always seen heavy bodies sink when
+their support was taken away; we had also seen, perhaps, that the
+sinking of heavier bodies forced lighter bodies upwards. But now we see
+a lever in action, and we are suddenly struck with the fact that a
+lighter body is lifting another of much greater weight. Our customary
+train of thought demands its rights; the new and unwonted event likewise
+demands its rights. From this conflict between thought and fact the
+_problem_ arises; out of this partial contrariety springs the question,
+"Why?" With the new adaptation to the enlarged field of observation, the
+problem disappears, or, in other words, is solved. In the instance
+cited, we must adopt the habit of always considering the mechanical work
+performed.
+
+The child just awakening into consciousness of the world, knows no
+problem. The bright flower, the ringing bell, are all new to it; yet it
+is surprised at nothing. The out and out Philistine, whose only thoughts
+lie in the beaten path of his every-day pursuits, likewise has no
+problems. Everything goes its wonted course, and if perchance a thing go
+wrong at times, it is at most a mere object of curiosity and not worth
+serious consideration. In fact, the question "Why?" loses all warrant in
+relations where we are familiar with every aspect of events. But the
+capable and talented young man has his head full of problems; he has
+acquired, to a greater or less degree, certain habitudes of thought, and
+at the same time he is constantly observing what is new and unwonted,
+and in his case there is no end to the questions, "Why?"
+
+Thus, the factor which most promotes scientific thought is the gradual
+widening of the field of experience. We scarcely notice events we are
+accustomed to; the latter do not really develop their intellectual
+significance until placed in contrast with something to which we are
+unaccustomed. Things that at home are passed by unnoticed, delight us
+when abroad, though they may appear in only slightly different forms.
+The sun shines with heightened radiance, the flowers bloom in brighter
+colors, our fellow-men accost us with lighter and happier looks. And,
+returning home, we find even the old familiar scenes more inspiring and
+suggestive than before.
+
+Every motive that prompts and stimulates us to modify and transform our
+thoughts, proceeds from what is new, uncommon, and not understood.
+Novelty excites wonder in persons whose fixed habits of thought are
+shaken and disarranged by what they see. But the element of wonder never
+lies in the phenomenon or event observed; its place is in the person
+observing. People of more vigorous mental type aim at once at an
+_adaptation of thought_ that will conform to what they have observed.
+Thus does science eventually become the natural foe of the wonderful.
+The sources of the marvellous are unveiled, and surprise gives way to
+calm interpretation.
+
+Let us consider such a mental transformative process in detail. The
+circumstance that heavy bodies fall to the earth appears perfectly
+natural and regular. But when a person observes that wood floats upon
+water, and that flames and smoke rise in the air, then the contrary of
+the first phenomenon is presented. An olden theory endeavors to explain
+these facts by imputing to substances the power of volition, as that
+attribute which is most familiar to man. It asserted that every
+substance seeks its proper place, heavy bodies tending downwards and
+light ones upwards. It soon turned out, however, that even smoke had
+weight, that it, too, sought its place below, and that it was forced
+upwards only because of the downward tendency of the air, as wood is
+forced to the surface of water because the water exerts the greater
+downward pressure.
+
+Again, we see a body thrown into the air. It ascends. How is it that it
+does not seek its proper place? Why does the velocity of its "violent"
+motion decrease as it rises, while that of its "natural" fall increases
+as it descends. If we mark closely the relation between these two facts,
+the problem will solve itself. We shall see, as Galileo did, that the
+decrease of velocity in rising and the increase of velocity in falling
+are one and the same phenomenon, viz., an increase of velocity towards
+the earth. Accordingly, it is not a place that is assigned to the body,
+but an increase of velocity towards the earth.
+
+By this idea the movements of heavy bodies are rendered perfectly
+familiar. Newton, now, firmly grasping this new way of thinking, sees
+the moon and the planets moving in their paths upon principles similar
+to those which determine the motion of a projectile thrown into the air.
+Yet the movements of the planets were marked by peculiarities which
+compelled him once more to modify slightly his customary mode of
+thought. The heavenly bodies, or rather the parts composing them, do not
+move with constant accelerations towards each other, but "attract each
+other," directly as the mass and inversely as the square of the
+distance.
+
+This latter notion, which includes the one applying to terrestrial
+bodies as a special case, is, as we see, quite different from the
+conception from which we started. How limited in scope was the original
+idea and to what a multitude of phenomena is not the present one
+applicable! Yet there is a trace, after all, of the "search for place"
+in the expression "attraction." And it would be folly, indeed, for us to
+avoid, with punctilious dread, this conception of "attraction" as
+bearing marks of its pedigree. It is the historical base of the
+Newtonian conception and it still continues to direct our thoughts in
+the paths so long familiar to us. Thus, the happiest ideas do not fall
+from heaven, but spring from notions already existing.
+
+Similarly, a ray of light was first regarded as a continuous and
+homogeneous straight line. It then became the path of projection for
+minute missiles; then an aggregate of the paths of countless different
+kinds of missiles. It became periodic; it acquired various sides; and
+ultimately it even lost its motion in a straight line.
+
+The electric current was conceived originally as the flow of a
+hypothetical fluid. To this conception was soon added the notion of a
+chemical current, the notion of an electric, magnetic, and anisotropic
+optical field, intimately connected with the path of the current. And
+the richer a conception becomes in following and keeping pace with
+facts, the better adapted it is to anticipate them.
+
+Adaptive processes of this kind have no assignable beginning, inasmuch
+as every problem that incites to new adaptation, presupposes a fixed
+habitude of thought. Moreover, they have no visible end; in so far as
+experience never ceases. Science, accordingly, stands midway in the
+evolutionary process; and science may advantageously direct and promote
+this process, but it can never take its place. That science is
+inconceivable the principles of which would enable a person with no
+experience to construct the world of experience, without a knowledge of
+it. One might just as well expect to become a great musician, solely by
+the aid of theory, and without musical experience; or to become a
+painter by following the directions of a text-book.
+
+In glancing over the history of an idea with which we have become
+perfectly familiar, we are no longer able to appreciate the full
+significance of its growth. The deep and vital changes that have been
+effected in the course of its evolution, are recognisable only from the
+astounding narrowness of view with which great contemporary scientists
+have occasionally opposed each other. Huygens's wave-theory of light was
+incomprehensible to Newton, and Newton's idea of universal gravity was
+unintelligible to Huygens. But a century afterwards both notions were
+reconcilable, even in ordinary minds.
+
+On the other hand, the original creations of pioneer intellects,
+unconsciously formed, do not assume a foreign garb; their form is their
+own. In them, childlike simplicity is joined to the maturity of manhood,
+and they are not to be compared with processes of thought in the average
+mind. The latter are carried on as are the acts of persons in the state
+of mesmerism, where actions involuntarily follow the images which the
+words of other persons suggest to their minds.
+
+The ideas that have become most familiar through long experience, are
+the very ones that intrude themselves into the conception of every new
+fact observed. In every instance, thus, they become involved in a
+struggle for self-preservation, and it is just they that are seized by
+the inevitable process of transformation.
+
+Upon this process rests substantially the method of explaining by
+hypothesis new and uncomprehended phenomena. Thus, instead of forming
+entirely new notions to explain the movements of the heavenly bodies and
+the phenomena of the tides, we imagine the material particles composing
+the bodies of the universe to possess weight or gravity with respect to
+one another. Similarly, we imagine electrified bodies to be freighted
+with fluids that attract and repel, or we conceive the space between
+them to be in a state of elastic tension. In so doing, we substitute
+for new ideas distinct and more familiar notions of old
+experience--notions which to a great extent run unimpeded in their
+courses, although they too must suffer partial transformation.
+
+The animal cannot construct new members to perform every new function
+that circumstances and fate demand of it. On the contrary it is obliged
+to make use of those it already possesses. When a vertebrate animal
+chances into an environment where it must learn to fly or swim, an
+additional pair of extremities is not grown for the purpose. On the
+contrary, the animal must adapt and transform a pair that it already
+has.
+
+The construction of hypotheses, therefore, is not the product of
+artificial scientific methods. This process is unconsciously carried on
+in the very infancy of science. Even later, hypotheses do not become
+detrimental and dangerous to progress except when more reliance is
+placed on them than on the facts themselves; when the contents of the
+former are more highly valued than the latter, and when, rigidly
+adhering to hypothetical notions, we overestimate the ideas we possess
+as compared with those we have to acquire.
+
+The extension of our sphere of experience always involves a
+transformation of our ideas. It matters not whether the face of nature
+becomes actually altered, presenting new and strange phenomena, or
+whether these phenomena are brought to light by an intentional or
+accidental turn of observation. In fact, all the varied methods of
+scientific inquiry and of purposive mental adaptation enumerated by John
+Stuart Mill, those of observation as well as those of experiment, are
+ultimately recognisable as forms of one fundamental method, the method
+of change, or variation. It is through change of circumstances that the
+natural philosopher learns. This process, however, is by no means
+confined to the investigator of nature. The historian, the philosopher,
+the jurist, the mathematician, the artist, the æsthetician,[77] all
+illuminate and unfold their ideas by producing from the rich treasures
+of memory similar, but different, cases; thus, they observe and
+experiment in their thoughts. Even if all sense-experience should
+suddenly cease, the events of the days past would meet in different
+attitudes in the mind and the process of adaptation would still
+continue--a process which, in contradistinction to the adaptation of
+thoughts to facts in practical spheres, would be strictly theoretical,
+being an adaptation of thoughts to thoughts.
+
+The method of change or variation brings before us like cases of
+phenomena, having partly the same and partly different elements. It is
+only by comparing different cases of refracted light at changing angles
+of incidence that the common factor, the constancy of the refractive
+index, is disclosed. And only by comparing the refractions of light of
+different colors, does the difference, the inequality of the indices of
+refraction, arrest the attention. Comparison based upon change leads the
+mind simultaneously to the highest abstractions and to the finest
+distinctions.
+
+Undoubtedly, the animal also is able to distinguish between the similar
+and dissimilar of two cases. Its consciousness is aroused by a noise or
+a rustling, and its motor centre is put in readiness. The sight of the
+creature causing the disturbance, will, according to its size, provoke
+flight or prompt pursuit; and in the latter case, the more exact
+distinctions will determine the mode of attack. But man alone attains to
+the faculty of voluntary and conscious comparison. Man alone can, by his
+power of abstraction, rise, in one moment, to the comprehension of
+principles like the conservation of mass or the conservation of energy,
+and in the next observe and mark the arrangement of the iron lines in
+the spectrum. In thus dealing with the objects of his conceptual life,
+his ideas unfold and expand, like his nervous system, into a widely
+ramified and organically articulated tree, on which he may follow every
+limb to its farthermost branches, and, when occasion demands, return to
+the trunk from which he started.
+
+The English philosopher Whewell has remarked that two things are
+requisite to the formation of science: facts and ideas. Ideas alone lead
+to empty speculation; mere facts can yield no organic knowledge. We see
+that all depends upon the capacity of adapting existing notions to fresh
+facts.
+
+Over-readiness to yield to every new fact prevents fixed habits of
+thought from arising. Excessively rigid habits of thought impede freedom
+of observation. In the struggle, in the compromise between judgment and
+prejudgment (prejudice), if we may use the term, our understanding of
+things broadens.
+
+Habitual judgment, applied to a new case without antecedent tests, we
+call prejudgment or prejudice. Who does not know its terrible power! But
+we think less often of the importance and utility of prejudice.
+Physically, no one could exist, if he had to guide and regulate the
+circulation, respiration, and digestion of his body by conscious and
+purposive acts. So, too, no one could exist intellectually if he had to
+form judgments on every passing experience, instead of allowing himself
+to be controlled by the judgments he has already formed. Prejudice is a
+sort of reflex motion in the province of intelligence.
+
+On prejudices, that is, on habitual judgments not tested in every case
+to which they are applied, reposes a goodly portion of the thought and
+work of the natural scientist. On prejudices reposes most of the conduct
+of society. With the sudden disappearance of prejudice society would
+hopelessly dissolve. That prince displayed a deep insight into the power
+of intellectual habit, who quelled the loud menaces and demands of his
+body-guard for arrears of pay and compelled them to turn about and
+march, by simply pronouncing the regular word of command; he well knew
+that they would be unable to resist that.
+
+Not until the discrepancy between habitual judgments and facts becomes
+great is the investigator implicated in appreciable illusion. Then
+tragic complications and catastrophes occur in the practical life of
+individuals and nations--crises where man, placing custom above life,
+instead of pressing it into the service of life, becomes the victim of
+his error. The very power which in intellectual life advances, fosters,
+and sustains us, may in other circumstances delude and destroy us.
+
+       *       *       *       *       *
+
+Ideas are not all of life. They are only momentary efflorescences of
+light, designed to illuminate the paths of the will. But as delicate
+reagents on our organic evolution our ideas are of paramount importance.
+No theory can gainsay the vital transformation which we feel taking
+place within us through their agency. Nor is it necessary that we should
+have a proof of this process. We are immediately assured of it.
+
+The transformation of ideas thus appears as a part of the general
+evolution of life, as a part of its adaptation to a constantly widening
+sphere of action. A granite boulder on a mountain-side tends towards the
+earth below. It must abide in its resting-place for thousands of years
+before its support gives way. The shrub that grows at its base is
+farther advanced; it accommodates itself to summer and winter. The fox
+which, overcoming the force of gravity, creeps to the summit where he
+has scented his prey, is freer in his movements than either. The arm of
+man reaches further still; and scarcely anything of note happens in
+Africa or Asia that does not leave an imprint upon his life. What an
+immense portion of the life of other men is reflected in ourselves;
+their joys, their affections, their happiness and misery! And this too,
+when we survey only our immediate surroundings, and confine our
+attention to modern literature. How much more do we experience when we
+travel through ancient Egypt with Herodotus, when we stroll through the
+streets of Pompeii, when we carry ourselves back to the gloomy period of
+the crusades or to the golden age of Italian art, now making the
+acquaintance of a physician of Molière, and now that of a Diderot or of
+a D'Alembert. What a great part of the life of others, of their
+character and their purpose, do we not absorb through poetry and music!
+And although they only gently touch the chords of our emotions, like the
+memory of youth softly breathing upon the spirit of an aged man, we have
+nevertheless lived them over again in part. How great and comprehensive
+does self become in this conception; and how insignificant the person!
+Egoistical systems both of optimism and pessimism perish with their
+narrow standard of the import of intellectual life. We feel that the
+real pearls of life lie in the ever changing contents of consciousness,
+and that the person is merely an indifferent symbolical thread on which
+they are strung.[78]
+
+We are prepared, thus, to regard ourselves and every one of our ideas as
+a product and a subject of universal evolution; and in this way we shall
+advance sturdily and unimpeded along the paths which the future will
+throw open to us.[79]
+
+  FOOTNOTES:
+
+  [Footnote 69: Inaugural Address, delivered on assuming the Rectorate
+  of the University of Prague, October 18, 1883.
+
+  The idea presented in this essay is neither new nor remote. I have
+  touched upon it myself on several occasions (first in 1867), but
+  have never made it the subject of a formal disquisition. Doubtless,
+  others, too, have treated it; it lies, so to speak, in the air.
+  However, as many of my illustrations were well received, although
+  known only in an imperfect form from the lecture itself and the
+  newspapers, I have, contrary to my original intention, decided to
+  publish it. It is not my intention to trespass here upon the domain
+  of biology. My statements are to be taken merely as the expression
+  of the fact that no one can escape the influence of a great and
+  far-reaching idea.]
+
+  [Footnote 70: At first sight an apparent contradiction arises from
+  the admission of both heredity and adaptation; and it is undoubtedly
+  true that a strong disposition to heredity precludes great
+  capability of adaptation. But imagine the organism to be a plastic
+  mass which retains the form transmitted to it by former influences
+  until new influences modify it; the _one_ property of _plasticity_
+  will then represent capability of adaptation as well as power of
+  heredity. Analogous to this is the case of a bar of magnetised steel
+  of high coercive force: the steel retains its magnetic properties
+  until a new force displaces them. Take also a body in motion: the
+  body retains the velocity acquired in (_inherited_ from) the
+  interval of time just preceding, except it be changed in the next
+  moment by an accelerating force. In the case of the body in motion
+  the _change_ of velocity (_Abänderung_) was looked upon as a matter
+  of course, while the discovery of the principle of _inertia_ (or
+  persistence) created surprise; in Darwin's case, on the contrary,
+  _heredity_ (or persistence) was taken for granted, while the
+  principle of _variation_ (_Abänderung_) appeared novel.
+
+  Fully adequate views are, of course, to be reached only by a study
+  of the original facts emphasised by Darwin, and not by these
+  analogies. The example referring to motion, if I am not mistaken, I
+  first heard, in conversation, from my friend J. Popper, Esq., of
+  Vienna.
+
+  Many inquirers look upon the stability of the species as something
+  settled, and oppose to it the Darwinian theory. But the stability of
+  the species is itself a "theory." The essential modifications which
+  Darwin's views also are undergoing will be seen from the works of
+  Wallace [and Weismann], but more especially from a book of W. H.
+  Rolph, _Biologische Probleme_, Leipsic, 1882. Unfortunately, this
+  last talented investigator is no longer numbered among the living.]
+
+  [Footnote 71: Written in 1883.]
+
+  [Footnote 72: See Pfaundler, _Pogg. Ann., Jubelband_, p. 182.]
+
+  [Footnote 73: See the beautiful discussions of this point in
+  Hering's _Memory as a General Function of Organised Matter_ (1870),
+  Chicago, The Open Court Publishing Co., 1887. Compare also Dubois,
+  _Ueber die Uebung_, Berlin, 1881.]
+
+  [Footnote 74: Spencer, _The Principles of Psychology_. London,
+  1872.]
+
+  [Footnote 75: See the article _The Velocity of Light_, page 63.]
+
+  [Footnote 76: I am well aware that the endeavor to confine oneself
+  in natural research to _facts_ is often censured as an exaggerated
+  fear of metaphysical spooks. But I would observe, that, judged by
+  the mischief which they have wrought, the metaphysical, of all
+  spooks, are the least fabulous. It is not to be denied that many
+  forms of thought were not originally acquired by the individual, but
+  were antecedently formed, or rather prepared for, in the development
+  of the species, in some such way as Spencer, Haeckel, Hering, and
+  others have supposed, and as I myself have hinted on various
+  occasions.]
+
+  [Footnote 77: Compare, for example, _Schiller, Zerstreute
+  Betrachtungen über verschiedene ästhetische Gegenstände_.]
+
+  [Footnote 78: We must not be deceived in imagining that the
+  happiness of other people is not a very considerable and essential
+  portion of our own. It is common capital, which cannot be created by
+  the individual, and which does not perish with him. The formal and
+  material limitation of the _ego_ is necessary and sufficient only
+  for the crudest practical objects, and cannot subsist in a broad
+  conception. Humanity in its entirety may be likened to a
+  polyp-plant. The material and organic bonds of individual union
+  have, indeed, been severed; they would only have impeded freedom of
+  movement and evolution. But the ultimate aim, the psychical
+  connexion of the whole, has been attained in a much higher degree
+  through the richer development thus made possible.]
+
+  [Footnote 79: C. E. von Baer, the subsequent opponent of Darwin and
+  Haeckel, has discussed in two beautiful addresses (_Das allgemeinste
+  Gesetz der Natur in aller Entwickelung_, and _Welche Auffassung der
+  lebenden Natur ist die richtige, und wie ist diese Auffassung auf
+  die Entomologie anzuwenden_?) the narrowness of the view which
+  regards an animal in its existing state as finished and complete,
+  instead of conceiving it as a phase in the series of evolutionary
+  forms and regarding the species itself as a phase of the development
+  of the animal world in general.]
+
+
+
+
+ON THE PRINCIPLE OF COMPARISON IN PHYSICS.[80]
+
+
+Twenty years ago when Kirchhoff defined the object of mechanics as the
+"description, in complete and very simple terms, of the motions
+occurring in nature," he produced by the statement a peculiar
+impression. Fourteen years subsequently, Boltzmann, in the life-like
+picture which he drew of the great inquirer, could still speak of the
+universal astonishment at this novel method of treating mechanics, and
+we meet with epistemological treatises to-day, which plainly show how
+difficult is the acceptance of this point of view. A modest and small
+band of inquirers there were, however, to whom Kirchhoff's few words
+were tidings of a welcome and powerful ally in the epistemological
+field.
+
+Now, how does it happen that we yield our assent so reluctantly to the
+philosophical opinion of an inquirer for whose scientific achievements
+we have only words of praise? One reason probably is that few inquirers
+can find time and leisure, amid the exacting employments demanded for
+the acquisition of new knowledge, to inquire closely into that
+tremendous psychical process by which science is formed. Further, it is
+inevitable that much should be put into Kirchhoff's rigid words that
+they were not originally intended to convey, and that much should be
+found wanting in them that had always been regarded as an essential
+element of scientific knowledge. What can mere description accomplish?
+What has become of explanation, of our insight into the causal connexion
+of things?
+
+       *       *       *       *       *
+
+Permit me, for a moment, to contemplate not the results of science, but
+the mode of its _growth_, in a frank and unbiassed manner. We know of
+only _one_ source of _immediate revelation_ of scientific facts--_our
+senses_. Restricted to this source alone, thrown wholly upon his own
+resources, obliged to start always anew, what could the isolated
+individual accomplish? Of a stock of knowledge so acquired the science
+of a distant negro hamlet in darkest Africa could hardly give us a
+sufficiently humiliating conception. For there that veritable miracle of
+thought-transference has already begun its work, compared with which the
+miracles of the spiritualists are rank monstrosities--_communication by
+language_. Reflect, too, that by means of the magical characters which
+our libraries contain we can raise the spirits of the "the sovereign
+dead of old" from Faraday to Galileo and Archimedes, through ages of
+time--spirits who do not dismiss us with ambiguous and derisive
+oracles, but tell us the best they know; then shall we feel what a
+stupendous and indispensable factor in the formation of science
+_communication_ is. Not the dim, half-conscious _surmises_ of the acute
+observer of nature or critic of humanity belong to science, but only
+that which they possess clearly enough to _communicate_ to others.
+
+But how, now, do we go about this communication of a newly acquired
+experience, of a newly observed fact? As the different calls and
+battle-cries of gregarious animals are unconsciously formed signs for a
+common observation or action, irrespective of the causes which produce
+such action--a fact that already involves the germ of the concept; so
+also the words of human language, which is only more highly specialised,
+are names or signs for universally known facts, which all can observe or
+have observed. If the mental representation, accordingly, follows the
+new fact at once and _passively_, then that new fact must, of itself,
+immediately be constituted and represented in thought by facts already
+universally known and commonly observed. Memory is always ready to put
+forward for _comparison_ known facts which resemble the new event, or
+agree with it in certain features, and so renders possible that
+elementary internal judgment which the mature and definitively
+formulated judgment soon follows.
+
+Comparison, as the fundamental condition of communication, is the most
+powerful inner vital element of science. The zoölogist sees in the
+bones of the wing-membranes of bats, fingers; he compares the bones of
+the cranium with the vertebræ, the embryos of different organisms with
+one another, and the different stages of development of the same
+organism with one another. The geographer sees in Lake Garda a fjord, in
+the Sea of Aral a lake in process of drying up. The philologist compares
+different languages with one another, and the formations of the same
+language as well. If it is not customary to speak of comparative physics
+in the same sense that we speak of comparative anatomy, the reason is
+that in a science of such great experimental activity the attention is
+turned away too much from the _contemplative_ element. But like all
+other sciences, physics lives and grows by comparison.
+
+       *       *       *       *       *
+
+The manner in which the result of the comparison finds expression in the
+communication, varies of course very much. When we say that the colors
+of the spectrum are red, yellow, green, blue, and violet, the
+designations employed may possibly have been derived from the technology
+of tattooing, or they may subsequently have acquired the significance of
+standing for the colors of the rose, the lemon, the leaf, the
+corn-flower, and the violet. From the frequent repetition of such
+comparisons, however, made under the most manifold circumstances, the
+inconstant features, as compared with the permanent congruent features,
+get so obliterated that the latter acquire a fixed significance
+independent of every object and connexion, or take on as we say an
+_abstract_ or _conceptual_ import. No one thinks at the word "red" of
+any other agreement with the rose than that of color, or at the word
+"straight" of any other property of a stretched cord than the sameness
+of direction. Just so, too, numbers, originally the names of the fingers
+of the hands and feet, from being used as arrangement-signs for all
+kinds of objects, were lifted to the plane of abstract concepts. A
+verbal report (communication) of a fact that uses only these purely
+abstract implements, we call a _direct description_.
+
+The direct description of a fact of any great extent is an irksome task,
+even where the requisite notions are already completely developed. What
+a simplification it involves if we can say, the fact _A_ now considered
+comports itself, not in _one_, but in _many_ or in _all_ its features,
+like an old and well-known fact _B_. The moon comports itself as a heavy
+body does with respect to the earth; light like a wave-motion or an
+electric vibration; a magnet, as if it were laden with gravitating
+fluids, and so on. We call such a description, in which we appeal, as it
+were, to a description already and elsewhere formulated, or perhaps
+still to be precisely formulated, an _indirect description_. We are at
+liberty to supplement this description, gradually, by direct
+description, to correct it, or to replace it altogether. We see, thus,
+without difficulty, that what is called a _theory_ or a _theoretical
+idea_, falls under the category of what is here termed indirect
+description.
+
+       *       *       *       *       *
+
+What, now, is a theoretical idea? Whence do we get it? What does it
+accomplish for us? Why does it occupy a higher place in our judgment
+than the mere holding fast to a fact or an observation? Here, too,
+memory and comparison alone are in play. But instead of _a single_
+feature of resemblance culled from memory, in this case _a great system_
+of resemblances confronts us, a well-known physiognomy, by means of
+which the new fact is immediately transformed into an old acquaintance.
+Besides, it is in the power of the idea to offer us more than we
+actually see in the new fact, at the first moment; it can extend the
+fact, and enrich it with features which we are first induced to _seek_
+from such suggestions, and which are often actually found. It is this
+_rapidity_ in extending knowledge that gives to theory a preference over
+simple observation. But that preference is wholly _quantitative_.
+Qualitatively, and in real essential points, theory differs from
+observation neither in the mode of its origin nor in its last results.
+
+The adoption of a theory, however, always involves a danger. For a
+theory puts in the place of a fact _A_ in thought, always a _different_,
+but simpler and more familiar fact _B_, which in _some_ relations can
+mentally represent _A_, but for the very reason that it is different, in
+other relations cannot represent it. If now, as may readily happen,
+sufficient care is not exercised, the most fruitful theory may, in
+special circumstances, become a downright obstacle to inquiry. Thus, the
+emission-theory of light, in accustoming the physicist to think of the
+projectile path of the "light-particles" as an undifferentiated
+straight-line, demonstrably impeded the discovery of the periodicity of
+light. By putting in the place of light the more familiar phenomena of
+sound, Huygens renders light in many of its features a familiar event,
+but with respect to polarisation, which lacks the longitudinal waves
+with which alone he was acquainted, it had for him a doubly strange
+aspect. He is unable thus to grasp in abstract thought the fact of
+polarisation, which is before his eyes, whilst Newton, merely by
+adapting to the observation his thoughts, and putting this question,
+"_Annon radiorum luminis diversa sunt latera?_" abstractly grasped
+polarisation, that is, directly described it, a century before Malus. On
+the other hand, if the agreement of the fact with the idea theoretically
+representing it, extends further than its inventor originally
+anticipated, then we may be led by it to unexpected discoveries, of
+which conical refraction, circular polarisation by total reflexion,
+Hertz's waves offer ready examples, in contrast to the illustrations
+given above.
+
+Our insight into the conditions indicated will be improved, perhaps, by
+contemplating the development of some theory or other more in detail.
+Let us consider a magnetised bar of steel by the side of a second
+unmagnetised bar, in all other respects the same. The second bar gives
+no indication of the presence of iron-filings; the first attracts them.
+Also, when the iron-filings are absent, we must think of the magnetised
+bar as in a different condition from that of the unmagnetised. For, that
+the mere presence of the iron-filings does not induce the phenomenon of
+attraction is proved by the second unmagnetised bar. The ingenuous man,
+who finds in his will, as his most familiar source of power, the best
+facilities for comparison, conceives a species of _spirit_ in the
+magnet. The behavior of a warm body or of an _electrified_ body suggests
+similar ideas. This is the point of view of the oldest theory,
+_fetishism_, which the inquirers of the early Middle Ages had not yet
+overcome, and which in its last vestiges, in the conception of forces,
+still flourishes in modern physics. We see, thus, the _dramatic_ element
+need no more be absent in a scientific description, than in a thrilling
+novel.
+
+If, on subsequent examination, it be observed that a cold body, in
+contact with a hot body, warms itself, so to speak, _at the expense_ of
+the hot body; further, that when the substances are the same, the cold
+body, which, let us say, has twice the mass of the other, gains only
+half the number of degrees of temperature that the other loses, a wholly
+new impression arises. The demoniac character of the event vanishes, for
+the supposed spirit acts not by caprice, but according to fixed laws. In
+its place, however, _instinctively_ the notion of a _substance_ is
+substituted, part of which flows over from the one body to the other,
+but the total amount of which, representable by the sum of the products
+of the masses into the respective changes of temperature, remains
+constant. Black was the first to be _powerfully_ struck with this
+resemblance of thermal processes to the motion of a substance, and under
+its guidance discovered the specific heat, the heat of fusion, and the
+heat of vaporisation of bodies. Gaining strength and fixity, however,
+from these successes, this notion of substance subsequently stood in the
+way of scientific advancement. It blinded the eyes of the successors of
+Black, and prevented them from seeing the manifest fact, which every
+savage knows, that heat is _produced_ by friction. Fruitful as that
+notion was for Black, helpful as it still is to the learner to-day in
+Black's special field, permanent and universal validity as a _theory_ it
+could never maintain. But what is essential, conceptually, in it, viz.,
+the constancy of the product-sum above mentioned, retains its value and
+may be regarded as a _direct description_ of Black's facts.
+
+It stands to reason that those theories which push themselves forward
+unsought, instinctively, and wholly of their own accord, should have the
+greatest power, should carry our thoughts most with them, and exhibit
+the staunchest powers of self-preservation. On the other hand, it may
+also be observed that when critically scrutinised such theories are
+extremely apt to lose their cogency. We are constantly busied with
+"substance," its modes of action have stamped themselves indelibly upon
+our thoughts, our vividest and clearest reminiscences are associated
+with it. It should cause us no surprise, therefore, that Robert Mayer
+and Joule, who gave the final blow to Black's substantial conception of
+heat, should have re-introduced the same notion of substance in a more
+abstract and modified form, only applying to a much more extensive
+field.
+
+Here, too, the psychological circumstances which impart to the new
+conception its power, lie clearly before us. By the unusual redness of
+the venous blood in tropical climates Mayer's attention is directed to
+the lessened expenditure of internal heat and to the proportionately
+lessened _consumption of material_ by the human body in those climates.
+But as every effort of the human organism, including its mechanical
+work, is connected with the consumption of material, and as work by
+friction can engender heat, therefore heat and work appear in kind
+equivalent, and between them a proportional relation must subsist. Not
+_every_ quantity, but the appropriately calculated _sum_ of the two, as
+connected with a proportionate consumption of material, appears
+_substantial_.
+
+By exactly similar considerations, relative to the economy of the
+galvanic element, Joule arrived at his view; he found experimentally
+that the sum of the heat evolved in the circuit, of the heat consumed in
+the combustion of the gas developed, of the electro-magnetic work of
+the current, properly calculated,--in short, the sum of all the effects
+of the battery,--is connected with a proportionate consumption of zinc.
+Accordingly, this sum itself has a substantial character.
+
+Mayer was so absorbed with the view attained, that the indestructibility
+of _force_, in our phraseology _work_, appeared to him _a priori_
+evident. "The creation or annihilation of a force," he says, "lies
+without the province of human thought and power." Joule expressed
+himself to a similar effect: "It is manifestly absurd to suppose that
+the powers with which God has endowed matter can be destroyed." Strange
+to say, on the basis of such utterances, not Joule, but Mayer, was
+stamped as a metaphysician. We may be sure, however, that both men were
+merely giving expression, and that half-unconsciously, to a powerful
+_formal_ need of the new simple view, and that both would have been
+extremely surprised if it had been proposed to them that their principle
+should be submitted to a philosophical congress or ecclesiastical synod
+for a decision upon its validity. But with all agreements, the attitude
+of these two men, in other respects, was totally different. Whilst Mayer
+represented this _formal_ need with all the stupendous instinctive force
+of genius, we might say almost with the ardor of fanaticism, yet was
+withal not wanting in the conceptive ability to compute, prior to all
+other inquirers, the mechanical equivalent of heat from old physical
+constants long known and at the disposal of all, and so to set up for
+the new doctrine a programme embracing all physics and physiology;
+Joule, on the other hand, applied himself to the exact verification of
+the doctrine by beautifully conceived and masterfully executed
+experiments, extending over all departments of physics. Soon Helmholtz
+too attacked the problem, in a totally independent and characteristic
+manner. After the professional virtuosity with which this physicist
+grasped and disposed of all the points unsettled by Mayer's programme
+and more besides, what especially strikes us is the consummate critical
+lucidity of this young man of twenty-six years. In his exposition is
+wanting that vehemence and impetuosity which marked Mayer's. The
+principle of the conservation of energy is no self-evident or _a priori_
+proposition for him. What follows, on the assumption that that
+proposition obtains? In this hypothetical form, he subjugates his
+matter.
+
+I must confess, I have always marvelled at the æsthetic and ethical
+taste of many of our contemporaries who have managed to fabricate out of
+this relation of things, odious national and personal questions, instead
+of praising the good fortune that made _several_ such men work together
+and of rejoicing at the instructive diversity and idiosyncrasies of
+great minds fraught with such rich consequences for us.
+
+We know that still another theoretical conception played a part in the
+development of the principle of energy, which Mayer held aloof from,
+namely, the conception that heat, as also the other physical processes,
+are due to motion. But once the principle of energy has been reached,
+these auxiliary and transitional theories discharge no essential
+function, and we may regard the principle, like that which Black gave,
+as a contribution to the _direct description_ of a widely extended
+domain of facts.
+
+It would appear from such considerations not only advisable, but even
+necessary, with all due recognition of the helpfulness of theoretic
+ideas in research, yet gradually, as the new facts grow familiar, to
+substitute for indirect description _direct_ description, which contains
+nothing that is unessential and restricts itself absolutely to the
+abstract apprehension of facts. We might almost say, that the
+descriptive sciences, so called with a tincture of condescension, have,
+in respect of scientific character, outstripped the physical expositions
+lately in vogue. Of course, a virtue has been made of necessity here.
+
+We must admit, that it is not in our power to describe directly every
+fact, on the moment. Indeed, we should succumb in utter despair if the
+whole wealth of facts which we come step by step to know, were presented
+to us all at once. Happily, only detached and unusual features first
+strike us, and such we bring nearer to ourselves by _comparison_ with
+every-day events. Here the notions of the common speech are first
+developed. The comparisons then grow more manifold and numerous, the
+fields of facts compared more extensive, the concepts that make direct
+description possible, proportionately more general and more abstract.
+
+First we become familiar with the motion of freely falling bodies. The
+concepts of force, mass, and work are then carried over, with
+appropriate modifications, to the phenomena of electricity and
+magnetism. A stream of water is said to have suggested to Fourier the
+first distinct picture of currents of heat. A special case of vibrations
+of strings investigated by Taylor, cleared up for him a special case of
+the conduction of heat. Much in the same way that Daniel Bernoulli and
+Euler constructed the most diverse forms of vibrations of strings from
+Taylor's cases, so Fourier constructs out of simple cases of conduction
+the most multifarious motions of heat; and that method has extended
+itself over the whole of physics. Ohm forms his conception of the
+electric current in imitation of Fourier's. The latter, also, adopts
+Fick's theory of diffusion. In an analogous manner a conception of the
+magnetic current is developed. All sorts of stationary currents are thus
+made to exhibit common features, and even the condition of complete
+equilibrium in an extended medium shares these features with the
+dynamical condition of equilibrium of a stationary current. Things as
+remote as the magnetic lines of force of an electric current and the
+stream-lines of a frictionless liquid vortex enter in this way into a
+peculiar relationship of similarity. The concept of potential,
+originally enunciated for a restricted province, acquires a
+wide-reaching applicability. Things as dissimilar as pressure,
+temperature, and electromotive force, now show points of agreement in
+relation to ideas derived by definite methods from that concept: viz.,
+fall of pressure, fall of temperature, fall of potential, as also with
+the further notions of liquid, thermal, and electric strength of
+current. That relationship between systems of ideas in which the
+dissimilarity of every two homologous concepts as well as the agreement
+in logical relations of every two homologous pairs of concepts, is
+clearly brought to light, is called an _analogy_. It is an effective
+means of mastering heterogeneous fields of facts in unitary
+comprehension. The path is plainly shown in which _a universal physical
+phenomenology_ embracing all domains, will be developed.
+
+In the process described we attain for the first time to what is
+indispensable in the direct description of broad fields of fact--the
+wide-reaching _abstract concept_. And now I must put a question smacking
+of the school-master, but unavoidable: What is a concept? Is it a hazy
+representation, admitting withal of mental visualisation? No. Mental
+visualisation accompanies it only in the simplest cases, and then merely
+as an adjunct. Think, for example, of the "coefficient of
+self-induction," and seek for its visualised mental image. Or is,
+perhaps, the concept a mere word? The adoption of this forlorn idea,
+which has been actually proposed of late by a reputed mathematician
+would only throw us back a thousand years into the deepest
+scholasticism. We must, therefore, reject it.
+
+The solution is not far to seek. We must not think that sensation, or
+representation, is a purely passive process. The lowest organisms
+respond to it with a simple reflex motion, by engulfing the prey which
+approaches them. In higher organisms the centripetal stimulus encounters
+in the nervous system obstacles and aids which modify the centrifugal
+process. In still higher organisms, where prey is pursued and examined,
+the process in question may go through extensive paths of circular
+motions before it comes to relative rest. Our own life, too, is enacted
+in such processes; all that we call science may be regarded as parts, or
+middle terms, of such activities.
+
+It will not surprise us now if I say: the definition of a concept, and,
+when it is very familiar, even its name, is an _impulse_ to some
+accurately determined, often complicated, critical, comparative, or
+constructive _activity_, the usually sense-perceptive result of which is
+a term or member of the concept's scope. It matters not whether the
+concept draws the attention only to one certain sense (as sight) or to a
+phase of a sense (as color, form), or is the starting-point of a
+complicated action; nor whether the activity in question (chemical,
+anatomical, and mathematical operations) is muscular or technical, or
+performed wholly in the imagination, or only intimated. The concept is
+to the physicist what a musical note is to a piano-player. A trained
+physicist or mathematician reads a memoir like a musician reads a score.
+But just as the piano-player must first learn to move his fingers singly
+and collectively, before he can follow his notes without effort, so the
+physicist or mathematician must go through a long apprenticeship before
+he gains control, so to speak, of the manifold delicate innervations of
+his muscles and imagination. Think of how frequently the beginner in
+physics or mathematics performs more, or less, than is required, or of
+how frequently he conceives things differently from what they are! But
+if, after having had sufficient discipline, he lights upon the phrase
+"coefficient of self-induction," he knows immediately what that term
+requires of him. Long and thoroughly practised _actions_, which have
+their origin in the necessity of comparing and representing facts by
+other facts, are thus the very kernel of concepts. In fact, positive and
+philosophical philology both claim to have established that all roots
+represent concepts and stood originally for muscular activities alone.
+The slow assent of physicists to Kirchhoff's dictum now becomes
+intelligible. They best could feel the vast amount of individual labor,
+theory, and skill required before the ideal of direct description could
+be realised.
+
+       *       *       *       *       *
+
+Suppose, now, the ideal of a given province of facts is reached. Does
+description accomplish all that the inquirer can ask? In my opinion, it
+does. Description is a building up of facts in thought, and this
+building up is, in the experimental sciences, often the condition of
+actual execution. For the physicist, to take a special case, the
+metrical units are the building-stones, the concepts the directions for
+building, and the facts the result of the building. Our mental imagery
+is almost a complete substitute for the fact, and by means of it we can
+ascertain all the fact's properties. We do not know that worst which we
+ourselves have made.
+
+People require of science that it should _prophesy_, and Hertz uses that
+expression in his posthumous _Mechanics_. But, natural as it is, the
+expression is too narrow. The geologist and the palæontologist, at times
+the astronomer, and always the historian and the philologist, prophesy,
+so to speak, _backwards_. The descriptive sciences, like geometry and
+mathematics, prophesy neither forward or backwards, but seek from given
+conditions the conditioned. Let us say rather: _Science completes in
+thought facts that are only partly given_. This is rendered possible by
+description, for description presupposes the interdependence of the
+descriptive elements: otherwise nothing would be described.
+
+It is said, description leaves the sense of causality unsatisfied. In
+fact, many imagine they understand motions better when they picture to
+themselves the pulling forces; and yet the _accelerations_, the facts,
+accomplish more, without superfluous additions. I hope that the science
+of the future will discard the idea of cause and effect, as being
+formally obscure; and in my feeling that these ideas contain a strong
+tincture of fetishism, I am certainly not alone. The more proper course
+is, _to regard the abstract determinative elements of a fact as
+interdependent_, in a purely logical way, as the mathematician or
+geometer does. True, by comparison with the will, forces are brought
+nearer to our feeling; but it may be that ultimately the will itself
+will be made clearer by comparison with the accelerations of masses.
+
+If we are asked, candidly, when is a fact _clear_ to us, we must say
+"when we can reproduce it by very _simple_ and very familiar
+intellectual operations, such as the construction of accelerations, or
+the geometrical summation of accelerations, and so forth." The
+requirement of _simplicity_ is of course to the expert a different
+matter from what it is to the novice. For the first, description by a
+system of differential equations is sufficient; for the second, a
+gradual construction out of elementary laws is required. The first
+discerns at once the connexion of the two expositions. Of course, it is
+not disputed that the _artistic_ value of materially equivalent
+descriptions may not be different.
+
+Most difficult is it to persuade strangers that the grand universal laws
+of physics, such as apply indiscriminately to material, electrical,
+magnetic, and other systems, are not essentially different from
+descriptions. As compared with many sciences, physics occupies in this
+respect a position of vantage that is easily explained. Take, for
+example, anatomy. As the anatomist in his quest for agreements and
+differences in animals ascends to ever higher and higher
+_classifications_, the individual facts that represent the ultimate
+terms of the system, are still so different that they must be _singly_
+noted. Think, for example, of the common marks of the Vertebrates, of
+the class-characters of Mammals and Birds on the one hand and of Fishes
+on the other, of the double circulation of the blood on the one hand and
+of the single on the other. In the end, always _isolated_ facts remain,
+which show only a _slight_ likeness to one another.
+
+A science still more closely allied to physics, chemistry, is often in
+the same strait. The abrupt change of the qualitative properties, in all
+likelihood conditioned by the slight stability of the intermediate
+states, the remote resemblance of the co-ordinated facts of chemistry
+render the treatment of its data difficult. Pairs of bodies of different
+qualitative properties unite in different mass-ratios; but no connexion
+between the first and the last is to be noted, at first.
+
+Physics, on the other hand, reveals to us wide domains of _qualitatively
+homogeneous_ facts, differing from one another only in the number of
+equal parts into which their characteristic marks are divisible, that
+is, differing only _quantitatively_. Even where we have to deal with
+qualities (colors and sounds), quantitative characters of those
+qualities are at our disposal. Here the classification is so simple a
+task that it rarely impresses us as such, whilst in infinitely fine
+gradations, in a _continuum of facts_, our number-system is ready
+beforehand to follow as far as we wish. The co-ordinated facts are here
+extremely similar and very closely affined, as are also their
+descriptions which consist in the determination of the numerical
+measures of one given set of characters from those of a different set by
+means of familiar mathematical operations--methods of derivation. Thus,
+the common characteristics of all descriptions can be found here; and
+with them a succinct, comprehensive description, or a rule for the
+construction of all single descriptions, is assigned,--and this we call
+_law_. Well-known examples are the formulæ for freely falling bodies,
+for projectiles, for central motion, and so forth. If physics apparently
+accomplishes more by its methods than other sciences, we must remember
+that in a sense it has presented to it much simpler problems.
+
+The remaining sciences, whose facts also present a physical side, need
+not be envious of physics for this superiority; for all its acquisitions
+ultimately redound to their benefit as well. But also in other ways this
+mutual help shall and must change. Chemistry has advanced very far in
+making the methods of physics her own. Apart from older attempts, the
+periodical series of Lothar Meyer and Mendelejeff are a brilliant and
+adequate means of producing an easily surveyed system of facts, which by
+gradually becoming complete, will take the place almost of a continuum
+of facts. Further, by the study of solutions, of dissociation, in fact
+generally of phenomena which present a continuum of cases, the methods
+of thermodynamics have found entrance into chemistry. Similarly we may
+hope that, at some future day, a mathematician, letting the
+fact-continuum of embryology play before his mind, which the
+palæontologists of the future will supposedly have enriched with more
+intermediate and derivative forms between Saurian and Bird than the
+isolated Pterodactyl, Archæopteryx, Ichthyornis, and so forth, which we
+now have--that such a mathematician shall transform, by the variation of
+a few parameters, as in a dissolving view, one form into another, just
+as we transform one conic section into another.
+
+Reverting now to Kirchhoff's words, we can come to some agreement
+regarding their import. Nothing can be built without building-stones,
+mortar, scaffolding, and a builder's skill. Yet assuredly the wish is
+well founded, that will show to posterity the complete structure in its
+finished form, bereft of unsightly scaffolding. It is the pure logical
+and æsthetic sense of the mathematician that speaks out of Kirchhoff's
+words. Modern expositions of physics aspire after his ideal; that, too,
+is intelligible. But it would be a poor didactic shift, for one whose
+business it was to train architects, to say: "Here is a splendid
+edifice; if thou wouldst really build, go thou and do likewise".
+
+The barriers between the special sciences, which make division of work
+and concentration possible, but which appear to us after all as cold and
+conventional restrictions, will gradually disappear. Bridge upon bridge
+is thrown over the gaps. Contents and methods, even of the remotest
+branches, are compared. When the Congress of Natural Scientists shall
+meet a hundred years hence, we may expect that they will represent a
+unity in a higher sense than is possible to-day, not in sentiment and
+aim alone, but in method also. In the meantime, this great change will
+be helped by our keeping constantly before our minds the fact of the
+intrinsic relationship of all research, which Kirchhoff characterised
+with such classical simplicity.
+
+  FOOTNOTES:
+
+  [Footnote 80: An address delivered before the General Session of the
+  German Association of Naturalists and Physicians, at Vienna, Sept.
+  24, 1894.]
+
+
+
+
+THE PART PLAYED BY ACCIDENT IN INVENTION AND DISCOVERY.[81]
+
+
+It is characteristic of the naïve and sanguine beginnings of thought in
+youthful men and nations, that all problems are held to be soluble and
+fundamentally intelligible on the first appearance of success. The sage
+of Miletus, on seeing plants take their rise from moisture, believed he
+had comprehended the whole of nature, and he of Samos, on discovering
+that definite numbers corresponded to the lengths of harmonic strings,
+imagined he could exhaust the nature of the world by means of numbers.
+Philosophy and science in such periods are blended. Wider experience,
+however, speedily discloses the error of such a course, gives rise to
+criticism, and leads to the division and ramification of the sciences.
+
+At the same time, the necessity of a broad and general view of the world
+remains; and to meet this need philosophy parts company with special
+inquiry. It is true, the two are often found united in gigantic
+personalities. But as a rule their ways diverge more and more widely
+from each other. And if the estrangement of philosophy from science can
+reach a point where data unworthy of the nursery are not deemed too
+scanty as foundations of the world, on the other hand the thorough-paced
+specialist may go to the extreme of rejecting point-blank the
+possibility of a broader view, or at least of deeming it superfluous,
+forgetful of Voltaire's apophthegm, nowhere more applicable than here,
+_Le superflu--chose très nécessaire_.
+
+It is true, the history of philosophy, owing to the insufficiency of its
+constructive data, is and must be largely a history of error. But it
+would be the height of ingratitude on our part to forget that the seeds
+of thoughts which still fructify the soil of special research, such as
+the theory of irrationals, the conceptions of conservation, the doctrine
+of evolution, the idea of specific energies, and so forth, may be traced
+back in distant ages to philosophical sources. Furthermore, to have
+deferred or abandoned the attempt at a broad philosophical view of the
+world from a full knowledge of the insufficiency of our materials, is
+quite a different thing from never having undertaken it at all. The
+revenge of its neglect, moreover, is constantly visited upon the
+specialist by his committal of the very errors which philosophy long ago
+exposed. As a fact, in physics and physiology, particularly during the
+first half of this century, are to be met intellectual productions
+which for naïve simplicity are not a jot inferior to those of the Ionian
+school, or to the Platonic ideas, or to that much reviled ontological
+proof.
+
+Latterly, there has been evidence of a gradual change in the situation.
+Recent philosophy has set itself more modest and more attainable ends;
+it is no longer inimical to special inquiry; in fact, it is zealously
+taking part in that inquiry. On the other hand, the special sciences,
+mathematics and physics, no less than philology, have become eminently
+philosophical. The material presented is no longer accepted
+uncritically. The glance of the inquirer is bent upon neighboring
+fields, whence that material has been derived. The different special
+departments are striving for closer union, and gradually the conviction
+is gaining ground that philosophy can consist only of mutual,
+complemental criticism, interpenetration, and union of the special
+sciences into a consolidated whole. As the blood in nourishing the body
+separates into countless capillaries, only to be collected again and to
+meet in the heart, so in the science of the future all the rills of
+knowledge will gather more and more into a common and undivided stream.
+
+It is this view--not an unfamiliar one to the present generation--that I
+purpose to advocate. Entertain no hope, or rather fear, that I shall
+construct systems for you. I shall remain a natural inquirer. Nor expect
+that it is my intention to skirt all the fields of natural inquiry. I
+can attempt to be your guide only in that branch which is familiar to
+me, and even there I can assist in the furtherment of only a small
+portion of the allotted task. If I shall succeed in rendering plain to
+you the relations of physics, psychology, and the theory of knowledge,
+so that you may draw from each profit and light, redounding to the
+advantage of each, I shall regard my work as not having been in vain.
+Therefore, to illustrate by an example how, consonantly with my powers
+and views, I conceive such inquiries should be conducted, I shall treat
+to-day, in the form of a brief sketch, of the following special and
+limited subject--of _the part which accidental circumstances play in the
+development of inventions and discoveries_.
+
+       *       *       *       *       *
+
+When we Germans say of a man that he was not the inventor of
+gunpowder,[82] we impliedly cast a grave suspicion on his abilities. But
+the expression is not a felicitous one, as there is probably no
+invention in which deliberate thought had a smaller, and pure luck a
+larger, share than in this. It is well to ask, Are we justified in
+placing a low estimate on the achievement of an inventor because
+accident has assisted him in his work? Huygens, whose discoveries and
+inventions are justly sufficient to entitle him to an opinion in such
+matters, lays great emphasis on this factor. He asserts that a man
+capable of inventing the telescope without the concurrence of accident
+must have been gifted with superhuman genius.[83]
+
+A man living in the midst of civilisation finds himself surrounded by a
+host of marvellous inventions, considering none other than the means of
+satisfying the needs of daily life. Picture such a man transported to
+the epoch preceding the invention of these ingenious appliances, and
+imagine him undertaking in a serious manner to comprehend their origin.
+At first the intellectual power of the men capable of producing such
+marvels will strike him as incredible, or, if we adopt the ancient view,
+as divine. But his astonishment is considerably allayed by the
+disenchanting yet elucidative revelations of the history of primitive
+culture, which to a large extent prove that these inventions took their
+rise very slowly and by imperceptible degrees.
+
+A small hole in the ground with fire kindled in it constituted the
+primitive stove. The flesh of the quarry, wrapped with water in its
+skin, was boiled by contact with heated stones. Cooking by stones was
+also done in wooden vessels. Hollow gourds were protected from the fire
+by coats of clay. Thus, from the burned clay accidentally originated the
+enveloping pot, which rendered the gourd superfluous, although for a
+long time thereafter the clay was still spread over the gourd, or
+pressed into woven wicker-work before the potter's art assumed its final
+independence. Even then the wicker-work ornament was retained, as a sort
+of attest of its origin.
+
+We see, thus, it is by accidental circumstances, or by such as lie
+without our purpose, foresight, and power, that man is gradually led to
+the acquaintance of improved means of satisfying his wants. Let the
+reader picture to himself the genius of a man who could have foreseen
+without the help of accident that clay handled in the ordinary manner
+would produce a useful cooking utensil! The majority of the inventions
+made in the early stages of civilisation, including language, writing,
+money, and the rest, could not have been the product of deliberate
+methodical reflexion for the simple reason that no idea of their value
+and significance could have been had except from practical use. The
+invention of the bridge may have been suggested by the trunk of a tree
+which had fallen athwart a mountain-torrent; that of the tool by the use
+of a stone accidentally taken into the hand to crack nuts. The use of
+fire probably started in and was disseminated from regions where
+volcanic eruptions, hot springs, and burning jets of natural gas
+afforded opportunity for quietly observing and turning to practical
+account the properties of fire. Only after that had been done could the
+significance of the fire-drill be appreciated, an instrument which was
+probably discovered from boring a hole through a piece of wood. The
+suggestion of a distinguished inquirer that the invention of the
+fire-drill originated on the occasion of a religious ceremony is both
+fantastic and incredible. And as to the use of fire, we should no more
+attempt to derive that from the invention of the fire-drill than we
+should from the invention of sulphur matches. Unquestionably the
+opposite course was the real one.[84]
+
+Similar phenomena, though still largely veiled in obscurity, mark the
+initial transition of nations from a hunting to a nomadic life and to
+agriculture.[85] We shall not multiply examples, but content ourselves
+with the remark that the same phenomena recur in historical times, in
+the ages of great technical inventions, and, further, that regarding
+them the most whimsical notions have been circulated--notions which
+ascribe to accident an unduly exaggerated part, and one which in a
+psychological respect is absolutely impossible. The observation of steam
+escaping from a tea-kettle and of the clattering of the lid is supposed
+to have led to the invention of the steam-engine. Just think of the gap
+between this spectacle and the conception of the performance of great
+mechanical work by steam, for a man totally ignorant of the
+steam-engine! Let us suppose, however, that an engineer, versed in the
+practical construction of pumps, should accidentally dip into water an
+inverted bottle that had been filled with steam for drying and still
+retained its steam. He would see the water rush violently into the
+bottle, and the idea would very naturally suggest itself of founding on
+this experience a convenient and useful atmospheric steam-pump, which by
+imperceptible degrees, both psychologically possible and immediate,
+would then undergo a natural and gradual transformation into Watt's
+steam-engine.
+
+But granting that the most important inventions are brought to man's
+notice accidentally and in ways that are beyond his foresight, yet it
+does not follow that accident alone is sufficient to produce an
+invention. The part which man plays is by no means a passive one. Even
+the first potter in the primeval forest must have felt some stirrings of
+genius within him. In all such cases, the inventor is obliged _to take
+note_ of the new fact, he must discover and grasp its advantageous
+feature, and must have the power to turn that feature to account in the
+realisation of his purpose. He must _isolate_ the new feature, impress
+it upon his memory, unite and interweave it with the rest of his
+thought; in short, he must possess the capacity _to profit by
+experience_.
+
+The capacity to profit by experience might well be set up as a test of
+intelligence. This power varies considerably in men of the same race,
+and increases enormously as we advance from the lower animals to man.
+The former are limited in this regard almost entirely to the reflex
+actions which they have inherited with their organism, they are almost
+totally incapable of individual experience, and considering their simple
+wants are scarcely in need of it. The ivory-snail (_Eburna spirata_)
+never learns to avoid the carnivorous Actinia, no matter how often it
+may wince under the latter's shower of needles, apparently having no
+memory for pain whatever.[86] A spider can be lured forth repeatedly
+from its hole by touching its web with a tuning-fork. The moth plunges
+again and again into the flame which has burnt it. The humming-bird
+hawk-moth[87] dashes repeatedly against the painted roses of the
+wall-paper, like the unhappy and desperate thinker who never wearies of
+attacking the same insoluble chimerical problem. As aimlessly almost as
+Maxwell's gaseous molecules and in the same unreasoning manner common
+flies in their search for light and air stream against the glass pane of
+a half-opened window and remain there from sheer inability to find their
+way around the narrow frame. But a pike separated from the minnows of
+his aquarium by a glass partition, learns after the lapse of a few
+months, though only after having butted himself half to death, that he
+cannot attack these fishes with impunity. What is more, he leaves them
+in peace even after the removal of the partition, though he will bolt a
+strange fish at once. Considerable memory must be attributed to birds of
+passage, a memory which, probably owing to the absence of disturbing
+thoughts, acts with the precision of that of some idiots. Finally, the
+susceptibility to training evinced by the higher vertebrates is
+indisputable proof of the ability of these animals to profit by
+experience.
+
+A powerfully developed _mechanical_ memory, which recalls vividly and
+faithfully old situations, is sufficient for avoiding definite
+particular dangers, or for taking advantage of definite particular
+opportunities. But more is required for the development of _inventions_.
+More extensive chains of images are necessary here, the excitation by
+mutual contact of widely different trains of ideas, a more powerful,
+more manifold, and richer connexion of the contents of memory, a more
+powerful and impressionable psychical life, heightened by use. A man
+stands on the bank of a mountain-torrent, which is a serious obstacle to
+him. He remembers that he has crossed just such a torrent before on the
+trunk of a fallen tree. Hard by trees are growing. He has often moved
+the trunks of fallen trees. He has also felled trees before, and then
+moved them. To fell trees he has used sharp stones. He goes in search of
+such a stone, and as the old situations that crowd into his memory and
+are held there in living reality by the definite powerful interest which
+he has in crossing just this torrent,--as these impressions are made to
+pass before his mind in the _inverse order_ in which they were here
+evoked, he invents the bridge.
+
+There can be no doubt but the higher vertebrates adapt their actions in
+some moderate degree to circumstances. The fact that they give no
+appreciable evidence of advance by the accumulation of inventions, is
+satisfactorily explained by a difference of degree or intensity of
+intelligence as compared with man; the assumption of a difference of
+kind is not necessary. A person who saves a little every day, be it ever
+so little, has an incalculable advantage over him who daily squanders
+that amount, or is unable to keep what he has accumulated. A slight
+quantitative difference in such things explains enormous differences of
+advancement.
+
+The rules which hold good in prehistoric times also hold good in
+historical times, and the remarks made on invention may be applied
+almost without modification to discovery; for the two are distinguished
+solely by the use to which the new knowledge is put. In both cases the
+investigator is concerned with some _newly observed_ relation of new or
+old properties, abstract or concrete. It is observed, for example, that
+a substance which gives a chemical reaction _A_ is also the cause of a
+chemical reaction _B_. If this observation fulfils no purpose but that
+of furthering the scientist's insight, or of removing a source of
+intellectual discomfort, we have a discovery; but an invention, if in
+using the substance giving the reaction _A_ to produce the desired
+reaction _B_, we have a practical end in view, and seek to remove a
+source of material discomfort. The phrase, _disclosure of the connexion
+of reactions_, is broad enough to cover discoveries and inventions in
+all departments. It embraces the Pythagorean proposition, which is a
+combination of a geometrical and an arithmetical reaction, Newton's
+discovery of the connexion of Kepler's motions with the law of the
+inverse squares, as perfectly as it does the detection of some minute
+but appropriate alteration in the construction of a tool, or of some
+appropriate change in the methods of a dyeing establishment.
+
+The disclosure of new provinces of facts before unknown can only be
+brought about by accidental circumstances, under which are _remarked_
+facts that commonly go unnoticed. The achievement of the discoverer here
+consists in his _sharpened attention_, which detects the uncommon
+features of an occurrence and their determining conditions from their
+most evanescent marks,[88] and discovers means of submitting them to
+exact and full observation. Under this head belong the first disclosures
+of electrical and magnetic phenomena, Grimaldi's observation of
+interference, Arago's discovery of the increased check suffered by a
+magnetic needle vibrating in a copper envelope as compared with that
+observed in a bandbox, Foucault's observation of the stability of the
+plane of vibration of a rod accidentally struck while rotating in a
+turning-lathe, Mayer's observation of the increased redness of venous
+blood in the tropics, Kirchhoff's observation of the augmentation of the
+_D_-line in the solar spectrum by the interposition of a sodium lamp,
+Schönbein's discovery of ozone from the phosphoric smell emitted on the
+disruption of air by electric sparks, and a host of others. All these
+facts, of which unquestionably many were _seen_ numbers of times before
+they were _noticed_, are examples of the inauguration of momentous
+discoveries by accidental circumstances, and place the importance of
+strained attention in a brilliant light.
+
+But not only is a significant part played in the beginning of an inquiry
+by co-operative circumstances beyond the foresight of the investigator;
+their influence is also active in its prosecution. Dufay, thus, whilst
+following up the behavior of _one_ electrical state which he had
+assumed, discovers the existence of _two_. Fresnel learns by accident
+that the interference-bands received on ground glass are seen to better
+advantage in the open air. The diffraction-phenomenon of two slits
+proved to be considerably different from what Fraunhofer had
+anticipated, and in following up this circumstance he was led to the
+important discovery of grating-spectra. Faraday's induction-phenomenon
+departed widely from the initial conception which occasioned his
+experiments, and it is precisely this deviation that constitutes his
+real discovery.
+
+Every man has pondered on some subject. Every one of us can multiply the
+examples cited, by less illustrious ones from his own experience. I
+shall cite but one. On rounding a railway curve once, I accidentally
+remarked a striking apparent inclination of the houses and trees. I
+inferred that the direction of the total resultant _physical_
+acceleration of the body reacts _physiologically_ as the vertical.
+Afterwards, in attempting to inquire more carefully into this
+phenomenon, and this only, in a large whirling machine, the collateral
+phenomena conducted me to the sensation of angular acceleration,
+vertigo, Flouren's experiments on the section of the semi-circular
+canals etc., from which gradually resulted views relating to sensations
+of direction which are also held by Breuer and Brown, which were at
+first contested on all hands, but are now regarded on many sides as
+correct, and which have been recently enriched by the interesting
+inquiries of Breuer concerning the _macula acustica_, and Kreidel's
+experiments with magnetically orientable crustacea.[89] Not disregard of
+accident but a direct and purposeful employment of it advances research.
+
+The more powerful the psychical connexion of the memory pictures
+is,--and it varies with the individual and the mood,--the more apt is
+the same accidental observation to be productive of results. Galileo
+knows that the air has weight; he also knows of the "resistance to a
+vacuum," expressed both in weight and in the height of a column of
+water. But the two ideas dwelt asunder in his mind. It remained for
+Torricelli to vary the specific gravity of the liquid measuring the
+pressure, and not till then was the air included in the list of
+pressure-exerting fluids. The reversal of the lines of the spectrum was
+seen repeatedly before Kirchhoff, and had been mechanically explained.
+But it was left for his penetrating vision to discern the evidence of
+the connexion of this phenomenon with questions of heat, and to him
+alone through persistent labor was revealed the sweeping significance of
+the fact for the mobile equilibrium of heat. Supposing, then, that such
+a rich organic connexion of the elements of memory exists, and is the
+prime distinguishing mark of the inquirer, next in importance certainly
+is that _intense interest_ in a definite object, in a definite idea,
+which fashions advantageous combinations of thought from elements before
+disconnected, and obtrudes that idea into every observation made, and
+into every thought formed, making it enter into relationship with all
+things. Thus Bradley, deeply engrossed with the subject of aberration,
+is led to its solution by an exceedingly unobtrusive experience in
+crossing the Thames. It is permissible, therefore, to ask whether
+accident leads the discoverer, or the discoverer accident, to a
+successful outcome in scientific quests.
+
+No man should dream of solving a great problem unless he is so
+thoroughly saturated with his subject that everything else sinks into
+comparative insignificance. During a hurried meeting with Mayer in
+Heidelberg once, Jolly remarked, with a rather dubious implication, that
+if Mayer's theory were correct water could be warmed by shaking. Mayer
+went away without a word of reply. Several weeks later, and now
+unrecognised by Jolly, he rushed into the latter's presence exclaiming:
+"Es ischt aso!" (It is so, it is so!) It was only after considerable
+explanation that Jolly found out what Mayer wanted to say. The incident
+needs no comment.[90]
+
+A person deadened to sensory impressions and given up solely to the
+pursuit of his own thoughts, may also light on an idea that will divert
+his mental activity into totally new channels. In such cases it is a
+psychical accident, an intellectual experience, as distinguished from a
+physical accident, to which the person owes his discovery--a discovery
+which is here made "deductively" by means of mental copies of the world,
+instead of experimentally. _Purely_ experimental inquiry, moreover, does
+not exist, for, as Gauss says, virtually we always experiment with our
+thoughts. And it is precisely that constant, corrective interchange or
+intimate union of experiment and deduction, as it was cultivated by
+Galileo in his _Dialogues_ and by Newton in his _Optics_, that is the
+foundation of the benign fruitfulness of modern scientific inquiry as
+contrasted with that of antiquity, where observation and reflexion
+ofttimes pursued their respective courses like two strangers.
+
+We have to wait for the appearance of a favorable physical accident. The
+movement of our thoughts obeys the law of association. In the case of
+meagre experience the result of this law is simply the mechanical
+reproduction of definite sensory experiences. On the other hand, if the
+psychical life is subjected to the incessant influences of a powerful
+and rich experience, then every representative element in the mind is
+connected with so many others that the actual and natural course of the
+thoughts is easily influenced and determined by insignificant
+circumstances, which accidentally are decisive. Hereupon, the process
+termed imagination produces its protean and infinitely diversified
+forms. Now what can we do to guide this process, seeing that the
+combinatory law of the images is without our reach? Rather let us ask,
+what influence can a powerful and constantly recurring idea exert on the
+movement of our thoughts? According to what has preceded, the answer is
+involved in the question itself. The _idea_ dominates the thought of the
+inquirer, not the latter the former.
+
+Let us see, now, if we can acquire a profounder insight into the process
+of discovery. The condition of the discoverer is, as James has aptly
+remarked, not unlike the situation of a person who is trying to remember
+something that he has forgotten. Both are sensible of a gap, and have
+only a remote presentiment of what is missing. Suppose I meet in a
+company a well-known and affable gentleman whose name I have forgotten,
+and who to my horror asks to be introduced to some one. I set to work
+according to Lichtenberg's rule, and run down the alphabet in search of
+the initial letter of his name. A vague sympathy holds me at the letter
+_G_. Tentatively I add the second letter and am arrested at _e_, and
+long before I have tried the third letter _r_, the name "Gerson" sounds
+sonorously upon my ear, and my anguish is gone. While taking a walk I
+meet a gentleman from whom I receive a communication. On returning home,
+and in attending to weightier affairs, the matter slips my mind.
+Moodily, but in vain, I ransack my memory. Finally I observe that I am
+going over my walk again in thought. On the street corner in question
+the self-same gentleman stands before me and repeats his communication.
+In this process are successively recalled to consciousness all the
+percepts which were connected with the percept that was lost, and with
+them, finally, that, too, is brought to light. In the first case--where
+the experience had already been made and is permanently impressed on our
+thought--a _systematic_ procedure is both possible and easy, for we know
+that a name must be composed of a limited number of sounds. But at the
+same time it should be observed that the labor involved in such a
+combinatorial task would be enormous if the name were long and the
+responsiveness of the mind weaker.
+
+It is often said, and not wholly without justification, that the
+scientist has solved a _riddle_. Every problem in geometry may be
+clothed in the garb of a _riddle_. Thus: "What thing is that _M_ which
+has the properties _A_, _B_, _C_?" "What circle is that which touches
+the straight lines _A_, _B_, but touches _B_ in the point _C_?" The
+first two conditions marshal before the imagination the group of circles
+whose centres lie in the line of symmetry of _A_, _B_. The third
+condition reminds us of all the circles having centres in the straight
+line that stands at right angles to _B_ in _C_. The _common_ term, or
+common terms, of the two groups of images solves the riddle--satisfies
+the problem. Puzzles dealing with things or words induce similar
+processes, but the memory in such cases is exerted in many directions
+and more varied and less clearly ordered provinces of ideas are
+surveyed. The difference between the situation of a geometer who has a
+construction to make, and that of an engineer, or a scientist,
+confronted with a problem, is simply this, that the first moves in a
+field with which he is thoroughly acquainted, whereas the two latter are
+obliged to familiarise themselves with this field subsequently, and in a
+measure far transcending what is commonly required. In this process the
+mechanical engineer has at least always a definite goal before him and
+definite means to accomplish his aim, whilst in the case of the
+scientist that aim is in many instances presented only in vague and
+general outlines. Often the very formulation of the riddle devolves on
+him. Frequently it is not until the aim has been reached that the
+broader outlook requisite for systematic procedure is obtained. By far
+the larger portion of his success, therefore, is contingent on luck and
+instinct. It is immaterial, so far as its character is concerned,
+whether the process in question is brought rapidly to a conclusion in
+the brain of one man, or whether it is spun out for centuries in the
+minds of a long succession of thinkers. The same relation that a word
+solving a riddle bears to that riddle is borne by the modern conception
+of light to the facts discovered by Grimaldi, Römer, Huygens, Newton,
+Young, Malus, and Fresnel, and only by the help of this slowly developed
+conception is our mental vision enabled to embrace the broad domain of
+facts in question.
+
+A welcome complement to the discoveries which the history of
+civilisation and comparative psychology have furnished, is to be found
+in the confessions of great scientists and artists. Scientists _and_
+artists, we might say, for Liebig boldly declared there was no essential
+difference between the two. Are we to regard Leonardo da Vinci as a
+scientist or as an artist? If the artist builds up his work from a few
+motives, the scientist discovers the motives which permeate reality. If
+scientists like Lagrange or Fourier are in a certain measure artists in
+the presentation of their results, on the other hand, artists like
+Shakespeare or Ruysdael are scientists in the insight which must have
+preceded their creations.
+
+Newton, when questioned about his methods of work, could give no other
+answer but that he was wont to ponder again and again on a subject; and
+similar utterances are accredited to D'Alembert and Helmholtz.
+Scientists and artists both recommend persistent labor. After the
+repeated survey of a field has afforded opportunity for the
+interposition of advantageous accidents, has rendered all the traits
+that suit with the mood or the dominant thought more vivid, and has
+gradually relegated to the background all things that are inappropriate,
+making their future appearance impossible; then from the teeming,
+swelling host of fancies which a free and high-flown imagination calls
+forth, suddenly that particular form arises to the light which
+harmonises perfectly with the ruling idea, mood, or design. Then it is
+that that which has resulted slowly as the result of a gradual
+selection, appears as if it were the outcome of a deliberate act of
+creation. Thus are to be explained the statements of Newton, Mozart,
+Richard Wagner, and others, when they say that thoughts, melodies, and
+harmonies had poured in upon them, and that they had simply retained the
+right ones. Undoubtedly, the man of genius, too, consciously or
+instinctively, pursues systematic methods wherever it is possible; but
+in his delicate presentiment he will omit many a task or abandon it
+after a hasty trial on which a less endowed man would squander his
+energies in vain. Thus, the genius accomplishes[91] in a brief space of
+time undertakings for which the life of an ordinary man would far from
+suffice. We shall hardly go astray if we regard genius as only a slight
+deviation from the average mental endowment--as possessing simply a
+greater sensitiveness of cerebral reaction and a greater swiftness of
+reaction. The men who, obeying their inner impulses, make sacrifices for
+an idea instead of advancing their material welfare, may appear to the
+full-blooded Philistine as fools; yet we shall scarcely adopt Lombroso's
+view, that genius is to be regarded as a disease, although it is
+unfortunately true that the sensitive brains and fragile constitutions
+succumb most readily to sickness.
+
+The remark of C. G. J. Jacobi that mathematics is slow of growth and
+only reaches the truth by long and devious paths, that the way to its
+discovery must be prepared for long beforehand, and that then the truth
+will make its long-deferred appearance as if impelled by some divine
+necessity[92]--all this holds true of every science. We are astounded
+often to note that it required the combined labors of many eminent
+thinkers for a full century to reach a truth which it takes us only a
+few hours to master and which once acquired seems extremely easy to
+reach under the right sort of circumstances. To our humiliation we learn
+that even the greatest men are born more for life than for science. The
+extent to which even they are indebted to accident--to that singular
+conflux of the physical and the psychical life in which the continuous
+but yet imperfect and never-ending adaptation of the latter to the
+former finds its distinct expression--that has been the subject of our
+remarks to-day. Jacobi's poetical thought of a divine necessity acting
+in science will lose none of its loftiness for us if we discover in this
+necessity the same power that destroys the unfit and fosters the fit.
+For loftier, nobler, and more romantic than poetry is the truth and the
+reality.
+
+  FOOTNOTES:
+
+  [Footnote 81: Inaugural lecture delivered on assuming the
+  Professorship of the History and Theory of Inductive Science in the
+  University of Vienna, October 21, 1895.]
+
+  [Footnote 82: The phrase is, _Er hat das Pulver nicht erfunden_.]
+
+  [Footnote 83: "Quod si quis tanta industria exstitisset, ut ex
+  naturae principiis at geometria hanc rem eruere potuisset, eum ego
+  supra mortalium sortem ingenio valuisse dicendum crederem. Sed hoc
+  tantum abest, ut fortuito reperti artificii rationem non adhuc satis
+  explicari potuerint viri doctissimi."--Hugenii Dioptrica (de
+  telescopiis).]
+
+  [Footnote 84: I must not be understood as saying that the fire-drill
+  has played no part in the worship of fire or of the sun.]
+
+  [Footnote 85: Compare on this point the extremely interesting
+  remarks of Dr. Paul Carus in his _Philosophy of the Tool_, Chicago,
+  1893.]
+
+  [Footnote 86: Möbius, _Naturwissenschaftlicher Verein für
+  Schleswig-Holstein_, Kiel, 1893, p. 113 et seq.]
+
+  [Footnote 87: I am indebted for this observation to Professor
+  Hatscheck.]
+
+  [Footnote 88: Cf. Hoppe, _Entdecken und Finden_, 1870.]
+
+  [Footnote 89: See the lecture "Sensations of Orientation," p. 282 et
+  seq.]
+
+  [Footnote 90: This story was related to me by Jolly, and
+  subsequently repeated in a letter from him.]
+
+  [Footnote 91: I do not know whether Swift's academy of schemers in
+  Lagado, in which great discoveries and inventions were made by a
+  sort of verbal game of dice, was intended as a satire on Francis
+  Bacon's method of making discoveries by means of huge synoptic
+  tables constructed by scribes. It certainly would not have been
+  ill-placed.]
+
+  [Footnote 92: "Crescunt disciplinae lente tardeque; per varios
+  errores sero pervenitur ad veritatem. Omnia praeparata esse debent
+  diuturno et assiduo labore ad introitum veritatis novae. Jam illa
+  certo temporis momento divina quadam necessitate coacta emerget."
+
+  Quoted by Simony, _In ein ringförmiges Band einen Knoten zu machen_,
+  Vienna, 1881, p. 41.]
+
+
+
+
+ON SENSATIONS OF ORIENTATION.[93]
+
+
+Through the co-operation of a succession of inquirers, among whom are
+particularly to be mentioned Goltz of Strassburg and Breuer of Vienna,
+considerable advances have been made during the last twenty-five years
+in our knowledge of the means by which we ascertain our position in
+space and the direction of our motion, or orient ourselves, as the
+phrase goes. I presume that you are already acquainted with the
+physiological part of the processes with which our sensations of
+movement, or, more generally speaking, our sensations of orientation,
+are connected. Here I shall consider more particularly the physical side
+of the matter. In fact, I was originally led to the consideration of
+these questions by the observation of extremely simple and perfectly
+well-known physical facts, before I had any great acquaintance with
+physiology and while pursuing unbiasedly my natural thoughts; and I am
+of the conviction that the way which I have pursued, and which is
+entirely free from hypotheses, will, if you will follow my exposition,
+be that of easiest acquisition for the most of you.
+
+No man of sound common sense could ever have doubted that a pressure or
+force is requisite to set a body in motion in a given direction and that
+a contrary pressure is required to stop suddenly a body in motion.
+Though the law of inertia was first formulated with anything like
+exactness by Galileo, the facts at the basis of it were known long
+previously to men of the stamp of Leonardo da Vinci, Rabelais, and
+others, and were illustrated by them with appropriate experiments.
+Leonardo knew that by a swift stroke with a ruler one can knock out from
+a vertical column of checkers a single checker without over-throwing the
+column. The experiment with a coin resting on a piece of pasteboard
+covering a goblet, which falls into the goblet when the pasteboard is
+jerked away, like all experiments of the kind, is certainly very old.
+
+With Galileo the experience in question assumes greater clearness and
+force. In the famous dialogue on the Copernican system which cost him
+his freedom, he explains the tides in an unfelicitous, though in
+principle correct manner, by the analogue of a platter of water swung to
+and fro. In opposition to the Aristotelians of his time, who believed
+the descent of a heavy body could be accelerated by the superposition
+of another heavy body, he asserted that a body could never be
+accelerated by one lying upon it unless the first in some way impeded
+the superposed body in its descent. To seek to press a falling body by
+means of another placed upon it, is as senseless as trying to prod a man
+with a lance when the man is speeding away from one with the same
+velocity as the lance. Even this little excursion into physics can
+explain much to us. You know the peculiar sensation which one has in
+falling, as when one jumps from a high springboard into the water, and
+which is also experienced in some measure at the beginning of the
+descent of elevators and swings. The reciprocal gravitational pressure
+of the different parts of our body, which is certainly felt in some
+manner, vanishes in free descent, or, in the case of the elevator, is
+diminished on the beginning of the descent. A similar sensation would be
+experienced if we were suddenly transported to the moon where the
+acceleration of gravity is much less than upon the earth. I was led to
+these considerations in 1866 by a suggestion in physics, and having also
+taken into account the alterations of the blood-pressure in the cases in
+question, I found I coincided without knowing it with Wollaston and
+Purkinje. The first as early as 1810 in his Croonian lecture had touched
+on the subject of sea-sickness and explained it by alterations of the
+blood-pressure, and later had laid similar considerations at the basis
+of his explanation of vertigo (1820-1826).[94]
+
+Newton was the first to enunciate with perfect generality that a body
+can change the velocity and direction of its motion only by the action
+of a force, or the action of a second body. A corollary of this law
+which was first expressly deduced by Euler is that a body can never be
+set _rotating_ or made to cease rotating of itself but only by forces
+and other bodies. For example, turn an open watch which has run down
+freely backwards and forwards in your hand. The balance-wheel will not
+fully catch the rapid rotations, it does not even respond fully to the
+elastic force of the spring which proves too weak to carry the wheel
+entirely with it.
+
+Let us consider now that whether we move ourselves by means of our legs,
+or whether we are moved by a vehicle or a boat, at first only a part of
+our body is directly moved and the rest of it is afterwards set in
+motion by the first part. We see that pressures, pulls, and tensions are
+always produced between the parts of the body in this action, which
+pressures, pulls, and tensions give rise to sensations by which the
+forward or rotary movements in which we are engaged are made
+perceptible.[95] But it is quite natural that sensations so familiar
+should be little noticed and that attention should be drawn to them only
+under special circumstances when they occur unexpectedly or with unusual
+strength.
+
+[Illustration: Fig. 45.]
+
+Thus my attention was drawn to this point by the sensation of falling
+and subsequently by another singular occurrence. I was rounding a sharp
+railway curve once when I suddenly saw all the trees, houses, and
+factory chimneys along the track swerve from the vertical and assume a
+strikingly inclined position. What had hitherto appeared to me perfectly
+natural, namely, the fact that we distinguish the vertical so perfectly
+and sharply from every other direction, now struck me as enigmatical.
+Why is it that the same direction can now appear vertical to me and now
+cannot? By what is the vertical distinguished for us? (Compare Figure
+45.)
+
+The rails are raised on the convex or outward side of the track in order
+to insure the stability of the carriage as against the action of the
+centrifugal force, the whole being so arranged that the combination of
+the force of gravity with the centrifugal force of the train shall give
+rise to a force perpendicular to the plane of the rails.
+
+Let us assume, now, that under all circumstances we somehow sense the
+direction of the total resultant mass-acceleration whencesoever it may
+arise as the vertical. Then both the ordinary and the extraordinary
+phenomena will be alike rendered intelligible.[96]
+
+I was now desirous of putting the view I had reached to a more
+convenient and exact test than was possible on a railway journey where
+one has no control over the determining circumstances and cannot alter
+them at will. I accordingly had the simple apparatus constructed which
+is represented in Figure 46.
+
+In a large frame _BB_, which is fastened to the walls, rotates about a
+vertical axis _AA_ a second frame _RR_, and within the latter a third
+one _rr_, which can be set at any distance and position from the axis,
+made stationary or movable, and is provided with a chair for the
+observer.
+
+[Illustration: Fig. 46.
+
+From Mach's _Bewegungsempfindungen_, Leipsic, Engelmann, 1875.]
+
+The observer takes his seat in the chair and to prevent disturbances of
+judgment is enclosed in a paper box. If the observer together with the
+frame _rr_ be then set in uniform rotation, he will feel and see the
+beginning of the rotation both as to direction and amount very
+distinctly although every outward visible or tangible point of reference
+is wanting. If the motion be uniformly continued the sensation of
+rotation will gradually cease entirely and the observer will imagine
+himself at rest. But if _rr_ be placed outside the axis of rotation, at
+once on the rotation beginning, a strikingly apparent, palpable,
+actually visible inclination of the entire paper box is produced, slight
+when the rotation is slow, strong when the rotation is rapid, and
+continuing as long as the rotation lasts. It is absolutely impossible
+for the observer to escape perceiving the inclination, although here
+also all outward points of reference are wanting. If the observer, for
+example, is seated so as to look towards the axis, he will feel the box
+strongly tipped backwards, as it necessarily must be if the direction of
+the total resultant force is perceived as the vertical. For other
+positions of the observer the situation is similar.[97]
+
+Once, while performing one of these experiments, and after rotating so
+long that I was no longer conscious of the movement, I suddenly caused
+the apparatus to be stopped, whereupon I immediately felt and saw myself
+with the whole box rapidly flung round in rotation in the opposite
+direction, although I knew that the whole apparatus was at rest and
+every outward point of reference for the perception of motion was
+wanting. Every one who disbelieves in sensations of movement should be
+made acquainted with these phenomena. Had Newton known them and had he
+ever observed how we may actually imagine ourselves turned and displaced
+in space without the assistance of stationary bodies as points of
+reference, he would certainly have been confirmed more than ever in his
+unfortunate speculations regarding absolute space.
+
+The sensation of rotation in the opposite direction after the apparatus
+has been stopped, slowly and gradually ceases. But on accidentally
+inclining my head once during this occurrence, the axis of apparent
+rotation was also observed to incline in exactly the same manner both as
+to direction and as to amount. It is accordingly clear that the
+acceleration or retardation of rotation is felt. The acceleration
+operates as a stimulus. The sensation, however, like almost all
+sensations, though it gradually decreases, lasts perceptibly longer than
+the stimulus. Hence the long continued apparent rotation after the
+stopping of the apparatus. The organ, however, which causes the
+persistence of this sensation must have its seat in the _head_, since
+otherwise the axis of apparent rotation could not assume the same motion
+as the head.
+
+If I were to say, now, that a light had flashed upon me in making these
+last observations, the expression would be a feeble one. I ought to say
+I experienced a perfect illumination. My juvenile experiences of vertigo
+occurred to me. I remembered Flourens's experiments relative to the
+section of the semi-circular canals of the labyrinths of doves and
+rabbits, where this inquirer had observed phenomena similar to vertigo,
+but which he preferred to interpret, from his bias to the acoustic
+theory of the labyrinth, as the expression of painful auditive
+disturbances. I saw that Goltz had nearly but not quite hit the bull's
+eye with his theory of the semi-circular canals. This inquirer, who,
+from his happy habit of following his own natural thoughts without
+regard for tradition, has cleared up so much in science, spoke, as early
+as 1870, on the ground of experiments, as follows: "It is uncertain
+whether the semi-circular canals are auditive organs or not. In any
+event they form an apparatus which serves for the preservation of
+equilibrium. They are, so to speak, the sense-organs of equilibrium of
+the head and indirectly of the whole body." I remembered the galvanic
+dizziness which had been observed by Ritter and Purkinje on the passage
+of a current through the head, when the persons experimented upon
+imagined they were falling towards the cathode. The experiment was
+immediately repeated, and sometime later (1874) I was enabled to
+demonstrate the same objectively with fishes, all of which placed
+themselves sidewise and in the same direction in the field of the
+current as if at command.[98] Müller's doctrine of specific energies now
+appeared to me to bring all these new and old observations into a
+simple, connected unity.
+
+[Illustration: Fig. 47.
+
+The labyrinth of a dove (stereoscopically reproduced), from R. Ewald,
+_Nervus Octavus_, Wiesbaden, Bergmann, 1892.]
+
+Let us picture to ourselves the labyrinth of the ear with its three
+semi-circular canals lying in three mutually perpendicular planes (Comp.
+Fig. 47), the mysterious position of which inquirers have endeavored to
+explain in every possible and impossible way. Let us conceive the nerves
+of the ampullæ, or the dilated extensions of the semi-circular canals,
+equipped with a capacity for responding to every imaginable stimulus
+with a sensation of rotation just as the nerves of the retina of the eye
+when excited by pressures, by electrical or chemical stimuli always
+respond with the sensation of light; let us picture to ourselves,
+further, that the usual excitation of the ampullæ nerves is produced by
+the inertia of the contents of the semi-circular canals, which contents
+on suitable rotations in the plane of the semi-circular canal are left
+behind in the motion, or at least have a tendency to remain behind and
+consequently exert a pressure. It will be seen that on this supposition
+all the single facts which without the theory appear as so many
+different individual phenomena, become from this single point of view
+clear and intelligible.
+
+I had the satisfaction, immediately after the communication in which I
+set forth this idea,[99] of seeing a paper by Breuer appear[100] in
+which this author had arrived by entirely different methods at results
+that agreed in all essential points with my own. A few weeks later
+appeared the researches of Crum Brown of Edinburgh, whose methods were
+even still nearer mine. Breuer's paper was far richer in physiological
+respects than mine, and he had particularly gone into greater detail in
+his investigation of the collateral effects of the reflex motions and
+orientation of the eyes in the phenomena under consideration.[101] In
+addition certain experiments which I had suggested in my paper as a test
+of the correctness of the view in question had already been performed by
+Breuer. Breuer has also rendered services of the highest order in the
+further elaboration of this field. But in a physical regard, my paper
+was, of course, more complete.
+
+In order to portray to the eye the behavior of the semi-circular canals,
+I have constructed here a little apparatus. (See Fig. 48.) The large
+rotatable disc represents the osseous semi-circular canal, which is
+continuous with the bones of the head; the small disc, which is free to
+rotate on the axis of the first, represents the mobile and partly liquid
+contents of the semi-circular canal. On rotating the large disc, the
+small disc as you see remains behind. I have to turn some time before
+the small disc is carried along with the large one by friction. But if I
+now stop the large disc the small disc as you see continues to rotate.
+
+[Illustration: Fig. 48.
+
+Model representing the action of the semi-circular canals.]
+
+Simply assume now that the rotation of the small disc, say in the
+direction of the hands of a watch, would give rise to a sensation of
+rotation in the opposite direction, and conversely, and you already
+understand a good portion of the facts above set forth. The explanation
+still holds, even if the small disc does not perform appreciable
+rotations but is checked by a contrivance similar to an elastic spring,
+the tension of which disengages a sensation. Conceive, now, three such
+contrivances with their mutually perpendicular planes of rotation joined
+together so as to form a single apparatus; then to this apparatus as a
+whole, no rotation can be imparted without its being indicated by the
+small mobile discs or by the springs which are attached to them.
+Conceive both the right and the left ear equipped with such an
+apparatus, and you will find that it answers all the purposes of the
+semi-circular canals, which you see represented stereoscopically in Fig.
+47 for the ear of a dove.
+
+Of the many experiments which I have made on my own person, and the
+results of which could be predicted by the new view according to the
+behavior of the model and consequently according to the rules of
+mechanics, I shall cite but one. I fasten a horizontal board in the
+frame _RR_ of my rotatory apparatus, lie down upon the same with my
+right ear upon the board, and cause the apparatus to be uniformly
+rotated. As soon as I no longer perceive the rotation, I turn around
+upon my left ear and immediately the sensation of rotation again starts
+up with marked vividness. The experiment can be repeated as often as one
+wishes. A slight turn of the head even is sufficient for reviving the
+sensation of rotation which in the perfectly quiescent state at once
+disappears altogether.
+
+We will imitate the experiment on the model. I turn the large disc until
+finally the small disc is carried along with it. If, now, while the
+rotation continues uniform, I burn off a little thread which you see
+here, the small disc will be flipped round by a spring into its own
+plane 180°, so as now to present its opposite side to you, when the
+rotation at once begins in the opposite direction.
+
+We have consequently a very simple means for determining whether one is
+actually the subject or not of uniform and imperceptible rotations. If
+the earth rotated much more rapidly than it really does, or if our
+semi-circular canals were much more sensitive, a Nansen sleeping at the
+North Pole would be waked by a sensation of rotation every time he
+turned over. Foucault's pendulum experiment as a demonstration of the
+earth's rotation would be superfluous under such circumstances. The only
+reason we cannot prove the rotation of the earth with the help of our
+model, lies in the small angular velocity of the earth and in the
+consequent liability to great experimental errors.[102]
+
+Aristotle has said that "The sweetest of all things is knowledge." And
+he is right. But if you were to suppose that the _publication_ of a new
+view were productive of unbounded sweetness, you would be mightily
+mistaken. No one disturbs his fellow-men with a new view unpunished. Nor
+should the fact be made a subject of reproach to these fellow-men. To
+presume to revolutionise the current way of thinking with regard to any
+question, is no pleasant task, and above all not an easy one. They who
+have advanced new views know best what serious difficulties stand in
+their way. With honest and praiseworthy zeal, men set to work in search
+of everything that does not suit with them. They seek to discover
+whether they cannot explain the facts better or as well, or
+approximately as well, by the traditional views. And that, too, is
+justified. But at times some extremely artless animadversions are heard
+that almost nonplus us. "If a sixth sense existed it could not fail to
+have been discovered thousands of years ago." Indeed; there was a time,
+then, when only seven planets could have existed! But I do not believe
+that any one will lay any weight on the philological question whether
+the set of phenomena which we have been considering should be called a
+sense. The phenomena will not disappear when the name disappears. It was
+further said to me that animals exist which have no labyrinth, but which
+can yet orientate themselves, and that consequently the labyrinth has
+nothing to do with orientation. We do not walk forsooth with our legs,
+because snakes propel themselves without them!
+
+But if the promulgator of a new idea cannot hope for any great pleasure
+from its publication, yet the critical process which his views undergo
+is extremely helpful to the subject-matter of them. All the defects
+which necessarily adhere to the new view are gradually discovered and
+eliminated. Over-rating and exaggeration give way to more sober
+estimates. And so it came about that it was found unpermissible to
+attribute all functions of orientation exclusively to the labyrinth. In
+these critical labors Delage, Aubert, Breuer, Ewald, and others have
+rendered distinguished services. It can also not fail to happen that
+fresh facts become known in this process which could have been predicted
+by the new view, which actually were predicted in part, and which
+consequently furnish a support for the new view. Breuer and Ewald
+succeeded in electrically and mechanically exciting the labyrinth, and
+even single parts of the labyrinth, and thus in producing the movements
+that belong to such stimuli. It was shown that when the semi-circular
+canals were absent vertigo could not be produced, when the entire
+labyrinth was removed the orientation of the head was no longer
+possible, that without the labyrinth galvanic vertigo could not be
+induced. I myself constructed as early as 1875 an apparatus for
+observing animals in rotation, which was subsequently reinvented in
+various forms and has since received the name of "cyclostat."[103] In
+experiments with the most varied kinds of animals it was shown that, for
+example, the larvæ of frogs are not subject to vertigo until their
+semi-circular canals which at the start are wanting are developed (K.
+Schäfer). A large percentage of the deaf and dumb are afflicted with
+grave affections of the labyrinth. The American psychologist, William
+James, has made whirling experiments with many deaf and dumb subjects,
+and in a large number of them found that susceptibility to giddiness is
+wanting. He also found that many deaf and dumb people on being ducked
+under water, whereby they lose their weight and consequently have no
+longer the full assistance of their muscular sense, utterly lose their
+sense of position in space, do not know which is up and which is down,
+and are thrown into the greatest consternation,--results which do not
+occur in normal men. Such facts are convincing proof that we do not
+orientate ourselves entirely by means of the labyrinth, important as it
+is for us. Dr. Kreidl has made experiments similar to those of James and
+found that not only is vertigo absent in deaf and dumb people when
+whirled about, but that also the reflex movements of the eyes which are
+normally induced by the labyrinth are wanting. Finally, Dr. Pollak has
+found that galvanic vertigo does not exist in a large percentage of the
+deaf and dumb. Neither the jerking movements nor the uniform movements
+of the eyes were observed which normal human beings exhibit in the
+Ritter and Purkinje experiment.
+
+After the physicist has arrived at the idea that the semi-circular
+canals are the organ of sensation of rotation or of angular
+acceleration, he is next constrained to ask for the organs that mediate
+the sensation of acceleration noticed in forward movements. In
+searching for an organ for this function, he of course is not apt to
+select one that stands in no anatomical and spatial relation with the
+semi-circular canals. And in addition there are physiological
+considerations to be weighed. The preconceived opinion once having been
+abandoned that the _entire_ labyrinth is auditory in its function, there
+remains after the cochlea is reserved for sensations of tone and the
+semi-circular canals for the sensation of angular acceleration, the
+vestibule for the discharge of additional functions. The vestibule,
+particularly the part of it known as the sacculus, appeared to me, by
+reason of the so-called otoliths which it contains, eminently adapted
+for being the organ of sensation of forward acceleration or of the
+position of the head. In this conjecture I again closely coincided with
+Breuer.
+
+That a sensation of position, of direction and amount of
+mass-acceleration exists, our experience in elevators as well as of
+movement in curved paths is sufficient proof. I have also attempted to
+produce and destroy suddenly great velocities of forward movement by
+means of various contrivances of which I shall mention only one here.
+If, while enclosed in the paper box of my large whirling apparatus at
+some distance from the axis, my body is in uniform rotation which I no
+longer feel, and I then loosen the connexions of the frame _rr_ with _R_
+thus making the former moveable and I then suddenly stop the larger
+frame, my forward motion is abruptly impeded while the frame _rr_
+continues to rotate. I imagine now that I am speeding on in a straight
+line in a direction opposite to that of the checked motion.
+Unfortunately, for many reasons it cannot be proved convincingly that
+the organ in question has its seat in the head. According to the opinion
+of Delage, the labyrinth has nothing to do with this particular
+sensation of movement. Breuer, on the other hand, is of the opinion that
+the organ of forward movement in man is stunted and the persistence of
+the sensation in question is too brief to permit our instituting
+experiments as obvious as in the case of rotation. In fact, Crum Brown
+once observed while in an irritated condition peculiar vertical
+phenomena in his own person, which were all satisfactorily explained by
+an abnormally long persistence of the sensation of rotation, and I
+myself in an analogous case on the stopping of a railway train felt the
+apparent backward motion in striking intensity and for an unusual length
+of time.
+
+There is no doubt whatever that we feel changes of vertical
+acceleration, and it will appear from the following extremely probable
+that the otoliths of the vestibule are the sense-organ for the
+_direction_ of the mass-acceleration. It will then be incompatible with
+a really logical view to regard the latter as incapable of sensing
+horizontal accelerations.
+
+In the lower animals the analogue of the labyrinth is shrunk to a little
+vesicle filled with a liquid and containing tiny crystals, auditive
+stones, or otoliths, of greater specific gravity, suspended on minute
+hairs. These crystals appear physically well adapted for indicating both
+the direction of gravity and the direction of incipient movements. That
+they discharge the former function, Delage was the first to convince
+himself by experiments with lower animals which on the removal of the
+otoliths utterly lost their bearings and could no longer regain their
+normal position. Loeb also found that fishes without labyrinths swim now
+on their bellies and now on their backs. But the most remarkable, most
+beautiful, and most convincing experiment is that which Dr. Kreidl
+instituted with crustaceans. According to Hensen, certain Crustacea on
+sloughing spontaneously introduce fine grains of sand as auditive stones
+into their otolith vesicle. At the ingenious suggestion of S. Exner, Dr.
+Kreidl constrained some of these animals to put up with iron filings
+(_ferrum limatum_). If the pole of an electro-magnet be brought near the
+animal, it will at once turn its back away from the pole accompanying
+the movement with appropriate reflex motions of the eye the moment the
+current is closed, exactly as if gravity had been brought to bear upon
+the animal in the same direction as the magnetic force.[104] This, in
+fact, is what should be expected from the function ascribed to the
+otoliths. If the eyes be covered with asphalt varnish, and the auditive
+sacs removed, the crustaceans lose their sense of direction utterly,
+tumble head over heels, lie on their side or their back indifferently.
+This does not happen when the eyes only are covered. For vertebrates,
+Breuer has demonstrated by searching investigations that the otoliths,
+or better, statoliths, slide in three planes parallel to the planes of
+the semi-circular canals, and are consequently perfectly adapted for
+indicating changes both in the amount and the direction of the
+mass-acceleration.[105]
+
+I have already remarked that not every function of orientation can be
+ascribed exclusively to the labyrinth. The deaf and dumb who have to be
+immersed in water, and the crustaceans who must have their eyes closed
+if they are to be perfectly disorientated, are proof of this fact. I saw
+a blind cat at Hering's laboratory which to one who was not a very
+attentive observer behaved exactly like a seeing cat. It played nimbly
+with objects rolling on the floor, stuck its head inquisitively into
+open drawers, sprang dexterously upon chairs, ran with perfect accuracy
+through open doors, and never bumped against closed ones. The visual
+sense had here been rapidly replaced by the tactual and auditive senses.
+And it appears from Ewald's investigations that even after the
+labyrinths have been removed, animals gradually learn to move about
+again quite in the normal fashion, presumably because the eliminated
+function of the labyrinth is now performed by some part of the brain. A
+certain peculiar weakness of the muscles alone is perceptible which
+Ewald ascribes to the absence of the stimulus which is otherwise
+constantly emitted by the labyrinth (the labyrinth-tonus). But if the
+part of the brain which discharges the deputed function be removed, the
+animals are again completely disorientated and absolutely helpless.
+
+It may be said that the views enunciated by Breuer, Crum Brown and
+myself in 1873 and 1874, and which are substantially a fuller and richer
+development of Goltz's idea, have upon the whole been substantiated. At
+least they have exercised a helpful and stimulative influence. New
+problems have of course arisen in the course of the investigation which
+still await solution, and much work remains to be done. At the same time
+we see how fruitful the renewed co-operation of the various special
+departments of science may become after a period of isolation and
+invigorating labor apart.
+
+I may be permitted, therefore, to consider the relation between hearing
+and orientation from another and more general point of view. What we
+call the auditive organ is in the lower animals simply a sac containing
+auditive stones. As we ascend the scale, 1, 2, 3 semi-circular canals
+gradually develop from them, whilst the structure of the otolith organ
+itself becomes more complicated. Finally, in the higher vertebrates, and
+particularly in the mammals, a part of the latter organ (the lagena)
+becomes the cochlea, which Helmholtz explained as the organ for
+sensations of tone. In the belief that the entire labyrinth was an
+auditive organ, Helmholtz, contrary to the results of his own masterly
+analysis, originally sought to interpret another part of the labyrinth
+as the organ of noises. I showed a long time ago (1873) that every tonal
+stimulus by shortening the duration of the excitation to a few
+vibrations, gradually loses its character of pitch and takes on that of
+a sharp, dry report or noise.[106] All the intervening stages between
+tones and noises can be exhibited. Such being the case, it will hardly
+be assumed that one organ is suddenly and at some given point replaced
+in function by another. On the basis of different experiments and
+reasonings S. Exner also regards the assumption of a special organ for
+the sensing of noises as unnecessary.
+
+If we will but reflect how small a portion of the labyrinth of higher
+animals is apparently in the service of the sense of hearing, and how
+large, on the other hand, the portion is which very likely serves the
+purposes of orientation, how much the first anatomical beginnings of the
+auditive sac of lower animals resemble that part of the fully developed
+labyrinth which does not hear, the view is irresistibly suggested which
+Breuer and I (1874, 1875) expressed, that the auditive organ took its
+development from an organ for sensing movements by adaptation to weak
+periodic motional stimuli, and that many apparatuses in the lower
+animals which are held to be organs of hearing are not auditive organs
+at all.[107]
+
+This view appears to be perceptibly gaining ground. Dr. Kreidl by
+skilfully-planned experiments has arrived at the conclusion that even
+fishes do not hear, whereas E. H. Weber, in his day, regarded the
+ossicles which unite the air-bladder of fishes with the labyrinth as
+organs expressly designed for conducting sound from the former to the
+latter.[108] Störensen has investigated the excitation of sounds by the
+air-bladder of fishes, as also the conduction of shocks through Weber's
+ossicles. He regards the air-bladder as particularly adapted for
+receiving the noises made by other fishes and conducting them to the
+labyrinth. He has heard the loud grunting tones of the fishes in South
+American rivers, and is of the opinion that they allure and find each
+other in this manner. According to these views certain fishes are
+neither deaf nor dumb.[109] The question here involved might be solved
+perhaps by sharply distinguishing between the sensation of hearing
+proper, and the perception of shocks. The first-mentioned sensation may,
+even in the case of many vertebrates, be extremely restricted, or
+perhaps even absolutely wanting. But besides the auditive function,
+Weber's ossicles may perfectly well discharge some other function.
+Although, as Moreau has shown, the air-bladder itself is not an organ of
+equilibrium in the simple physical sense of Borelli, yet doubtless some
+function of this character is still reserved for it. The union with the
+labyrinth favors this conception, and so a host of new problems rises
+here before us.
+
+I should like to close with a reminiscence from the year 1863.
+Helmholtz's _Sensations of Tone_ had just been published and the
+function of the cochlea now appeared clear to the whole world. In a
+private conversation which I had with a physician, the latter declared
+it to be an almost hopeless undertaking to seek to fathom the function
+of the other parts of the labyrinth, whereas I in youthful boldness
+maintained that the question could hardly fail to be solved, and that
+very soon, although of course I had then no glimmering of how it was to
+be done. Ten years later the question was substantially solved.
+
+To-day, after having tried my powers frequently and in vain on many
+questions, I no longer believe that we can make short work of the
+problems of science. Nevertheless, I should not consider an
+"ignorabimus" as an expression of modesty, but rather as the opposite.
+That expression is a suitable one only with regard to problems which are
+wrongly formulated and which are therefore not problems at all. Every
+real problem can and will be solved in due course of time without
+supernatural divination, entirely by accurate observation and close,
+searching thought.
+
+  FOOTNOTES:
+
+  [Footnote 93: A lecture delivered on February 24, 1897, before the
+  _Verein zur Verbreitung naturwissenschaftlicher Kenntnisse in
+  Wien_.]
+
+  [Footnote 94: Wollaston, _Philosophical Transactions, Royal
+  Society_, 1810. In the same place Wollaston also describes and
+  explains the creaking of the muscles. My attention was recently
+  called to this work by Dr. W. Pascheles.--Cf. also Purkinje, _Prager
+  medicin_. _Jahrbücher_, Bd. 6, Wien, 1820.]
+
+  [Footnote 95: Similarly many external forces do not act at once on
+  all parts of the earth, and the internal forces which produce
+  deformations act at first immediately only upon limited parts. If
+  the earth were a feeling being, the tides and other terrestrial
+  events would provoke in it similar sensations to those of our
+  movements. Perhaps the slight alterations of the altitude of the
+  pole which are at present being studied are connected with the
+  continual slight deformations of the central ellipsoid occasioned by
+  seismical happenings.]
+
+  [Footnote 96: For the popular explanation by unconscious inference
+  the matter is extremely simple. We regard the railway carriage as
+  vertical and unconsciously infer the inclination of the trees. Of
+  course the opposite conclusion that we regard the trees as vertical
+  and infer the inclination of the carriage, unfortunately, is equally
+  clear on this theory.]
+
+  [Footnote 97: It will be observed that my way of thinking and
+  experimenting here is related to that which led Knight to the
+  discovery and investigation of the geotropism of plants.
+  _Philosophical Transactions_, January 9, 1806. The relations between
+  vegetable and animal geotropism have been more recently investigated
+  by J. Loeb.]
+
+  [Footnote 98: This experiment is doubtless related to the
+  galvanotropic experiment with the larvæ of frogs described ten years
+  later by L. Hermann. Compare on this point my remarks in the
+  _Anzeiger der Wiener Akademie_, 1886, No. 21. Recent experiments in
+  galvanotropism are due to J. Loeb.]
+
+  [Footnote 99: _Wiener Akad._, 6 November, 1873.]
+
+  [Footnote 100: _Wiener Gesellschaft der Aerzte_, 14 November, 1874.]
+
+  [Footnote 101: I have made a contribution to this last question in
+  my _Analysis of the Sensations_, (1886), English translation, 1897.]
+
+  [Footnote 102: In my _Grundlinien der Lehre von den
+  Bewegungsempfindungen_, 1875, the matter occupying lines 4 to 13 of
+  page 20 from below, which rests on an error, is, as I have also
+  elsewhere remarked, to be stricken out. For another experiment
+  related to that of Foucault, compare my _Mechanics_, p. 303.]
+
+  [Footnote 103: _Anzeiger der Wiener Akad._, 30 December, 1875.]
+
+  [Footnote 104: The experiment was specially interesting for me as I
+  had already attempted in 1874, although with very little confidence
+  and without success, to excite electromagnetically my own labyrinth
+  through which I had caused a current to pass.]
+
+  [Footnote 105: Perhaps the discussion concerning the peculiarity of
+  cats always falling on their feet, which occupied the Parisian
+  Academy, and, incidentally, Parisian society a few years ago, will
+  be remembered here. I believe that the questions which arose are
+  disposed of by the considerations advanced in my
+  _Bewegungsempfindungen_ (1875). I also partly gave, as early as
+  1866, the apparatus conceived by the Parisian scientists to
+  illustrate the phenomena in question. One difficulty was left
+  untouched in the Parisian debate. The otolith apparatus of the cat
+  can render it no service in _free_ descent. The cat, however, while
+  at rest, doubtless knows its position in space and is instinctively
+  conscious of the amount of movement which will put it on its feet.]
+
+  [Footnote 106: See the Appendix to the English edition of my
+  _Analysis of the Sensations_, Chicago, 1897.]
+
+  [Footnote 107: Compare my _Analysis of Sensations_, p. 123 ff.]
+
+  [Footnote 108: E. H. Weber, _De aure et auditu hominis et
+  animalium_, Lipsiae, 1820.]
+
+  [Footnote 109: Störensen, _Journ. Anat. Phys._, London, Vol. 29
+  (1895).]
+
+
+
+
+ON SOME PHENOMENA ATTENDING THE FLIGHT OF PROJECTILES.[110]
+
+
+     "I have led my ragamuffins where they were peppered."--_Falstaff._
+
+     "He goes but to see a noise that he heard."--_Midsummer Night's
+     Dream._
+
+To shoot, in the shortest time possible, as many holes as possible in
+one another's bodies, and not always for exactly pardonable objects and
+ideals, seems to have risen to the dignity of a duty with modern men,
+who, by a singular inconsistency, and in subservience to a diametrically
+contrary ideal, are bound by the equally holy obligation of making these
+holes as small as possible, and, when made, of stopping them up and of
+healing them as speedily as possible. Since, then, shooting and all that
+appertains thereto, is a very important, if not the most important,
+affair of modern life, you will doubtless not be averse to giving your
+attention for an hour to some experiments which have been undertaken,
+not for advancing the ends of war, but for promoting the ends of
+science, and which throw some light on the phenomena attending the
+flight of projectiles.
+
+Modern science strives to construct its picture of the world not from
+speculations but so far as possible from facts. It verifies its
+constructs by recourse to observation. Every newly observed fact
+completes its world-picture, and every divergence of a construct from
+observation points to some imperfection, to some lacuna in it. What is
+seen is put to the test of, and supplemented by, what is thought, which
+is again naught but the result of things previously seen. It is always
+peculiarly fascinating, therefore, to subject to direct verification by
+observation, that is, to render palpable to the senses, something which
+we have only theoretically excogitated or theoretically surmised.
+
+In 1881, on hearing in Paris the lecture of the Belgian artillerist
+Melsens, who hazarded the conjecture that projectiles travelling at a
+high rate of speed carry masses of compressed air before them which are
+instrumental in producing in bodies struck by the projectiles certain
+well-known facts of the nature of explosions, the desire arose in me of
+experimentally testing his conjecture and of rendering the phenomenon,
+if it really existed, perceptible. The desire was the stronger as I
+could say that all the means for realising it existed, and that I had in
+part already used and tested them for other purposes.
+
+And first let us get clear regarding the difficulties which have to be
+surmounted. Our task is that of observing a bullet or other projectile
+which is rushing through space at a velocity of many hundred yards a
+second, together with the disturbances which the bullet causes in the
+surrounding atmosphere. Even the opaque solid body itself, the
+projectile, is only exceptionally visible under such circumstances--only
+when it is of considerable size and when we see its line of flight in
+strong perspective abridgement so that the velocity is apparently
+diminished. We see a large projectile quite clearly when we stand behind
+the cannon and look steadily along its line of flight or in the less
+pleasant case when the projectile is speeding towards us. There is,
+however, a very simple and effective method of observing swiftly moving
+bodies with as little trouble as if they were held at rest at some point
+in their path. The method is that of illumination by a brilliant
+electric spark of extremely short duration in a dark room. But since,
+for the full intellectual comprehension of a picture presented to the
+eye, a certain, not inconsiderable interval of time is necessary, the
+method of instantaneous photography will naturally also be employed. The
+pictures, which are of extremely minute duration, are thus permanently
+recorded and can be examined and analysed at one's convenience and
+leisure.
+
+With the difficulty just mentioned is associated still another and
+greater difficulty which is due to the air. The atmosphere in its usual
+condition is generally not visible even when at rest. But the task
+presented to us is to render visible masses of air which in addition
+are moving with a high velocity.
+
+To be visible, a body must either emit light itself, must shine, or must
+affect in some way the light which falls upon it, must take up that
+light entirely or partly, absorb it, or must have a deflective effect
+upon it, that is, reflect or refract it. We cannot see the air as we can
+a flame, for it shines only exceptionally, as in a Geissler's tube. The
+atmosphere is extremely transparent and colorless; it cannot be seen,
+therefore, as a dark or colored body can, or as chlorine gas can, or
+vapor of bromine or iodine. Air, finally, has so small an index of
+refraction and so small a deflective influence upon light, that the
+refractive effect is commonly imperceptible altogether.
+
+A glass rod is visible in air or in water, but it is almost invisible in
+a mixture of benzol and bisulphuret of carbon, which has the same mean
+index of refraction as the glass. Powdered glass in the same mixture has
+a vivid coloring, because owing to the decomposition of the colors the
+indices are the same for only one color which traverses the mixture
+unimpeded, whilst the other colors undergo repeated reflexions.[111]
+
+Water is invisible in water, alcohol in alcohol. But if alcohol be mixed
+with water the flocculent streaks of the alcohol in the water will be
+seen at once and _vice versa_. And in like manner the air, too, under
+favorable circumstances, may be seen. Over a roof heated by the burning
+sun, a tremulous wavering of objects is noticeable, as there is also
+over red-hot stoves, radiators, and registers. In all these cases tiny
+flocculent masses of hot and cold air, of slightly differing
+refrangibility, are mingled together.
+
+In like manner the more highly refracting parts of non-homogeneous
+masses of glass, the so-called striæ or imperfections of the glass, are
+readily detectible among the less refracting parts which constitute the
+bulk of the same. Such glasses are unserviceable for optical purposes,
+and special attention has been devoted to the investigation of the
+methods for eliminating or avoiding these defects. The result has been
+the development of an extremely delicate method for detecting optical
+faults--the so-called method of Foucault and Toepler--which is suitable
+also for our present purpose.
+
+[Illustration: Fig. 49.]
+
+Even Huygens when trying to detect the presence of striæ in polished
+glasses viewed them under oblique illumination, usually at a
+considerable distance, so as to give full scope to the aberrations, and
+had recourse for greater exactitude to a telescope. But the method was
+carried to its highest pitch of perfection in 1867 by Toepler who
+employed the following procedure: A small luminous source _a_ (Fig. 49)
+illuminates a lens _L_ which throws an image _b_ of the luminous source.
+If the eye be so placed that the image falls on the pupil, the entire
+lens, if perfect, will appear equally illuminated, for the reason that
+all points of it send out rays to the eye. Coarse imperfections of form
+or of homogeneity are rendered visible only in case the aberrations are
+so large that the light from many spots passes by the pupil of the eye.
+But if the image _b_ be partly intercepted by the edge of a small slide,
+then those spots in the lens as thus partly darkened will appear
+brighter whose light by its greater aberrations still reaches the eye in
+spite of the intercepting slide, while those spots will appear darker
+which in consequence of aberration in the other direction throw their
+light entirely upon the slide. This artifice of the intercepting slide
+which had previously been employed by Foucault for the investigation of
+the optical imperfections of mirrors enhances enormously the delicacy of
+the method, which is still further augmented by Toepler's employment of
+a telescope behind the slide. Toepler's method, accordingly, enjoys all
+the advantages of the Huygens and the Foucault procedure combined. It is
+so delicate that the minutest irregularities in the air surrounding the
+lens can be rendered distinctly visible, as I shall show by an example.
+I place a candle before the lens _L_ (Fig. 50) and so arrange a second
+lens _M_ that the flame of the candle is imaged upon the screen _S_. As
+soon as the intercepting slide is pushed into the focus, _b_, of the
+light issuing from _a_, you see the images of the changes of density and
+the images of the movements induced in the air by the flame quite
+distinctly upon the screen. The distinctness of the phenomenon as a
+whole depends upon the position of the intercepting slide _b_. The
+removal of _b_ increases the illumination but decreases the
+distinctness. If the luminous source _a_ be removed, we see the image of
+the candle flame only upon the screen _S_. If we remove the flame and
+allow _a_ to continue shining, the screen _S_ will appear uniformly
+illuminated.
+
+[Illustration: Fig. 50.]
+
+After Toepler had sought long and in vain to render the irregularities
+produced in air by sound-waves visible by this principle, he was at last
+conducted to his goal by the favorable circumstances attending the
+production of electric sparks. The waves generated in the air by
+electric sparks and accompanying the explosive snapping of the same, are
+of sufficiently short period and sufficiently powerful to be rendered
+visible by these methods. Thus we see how by a careful regard for the
+merest and most shadowy indications of a phenomenon and by slight
+progressive and appropriate alterations of the circumstances and the
+methods, ultimately the most astounding results can be attained.
+Consider, for example, two such phenomena as the rubbing of amber and
+the electric lighting of modern streets. A person ignorant of the myriad
+minute links that join these two things together, will be absolutely
+nonplussed at their connexion, and will comprehend it no more than the
+ordinary observer who is unacquainted with embryology, anatomy, and
+paleontology will understand the connexion between a saurian and a bird.
+The high value and significance of the co-operation of inquirers through
+centuries, where each has but to take up the thread of work of his
+predecessors and spin it onwards, is rendered forcibly evident by such
+examples. And such knowledge destroys, too, in the clearest manner
+imaginable that impression of the marvellous which the spectator may
+receive from science, and at the same time is a most salutary
+admonishment to the worker in science against superciliousness. I have
+also to add the sobering remark that all our art would be in vain did
+not nature herself afford at least some slight guiding threads leading
+from a hidden phenomenon into the domain of the observable. And so it
+need not surprise us that once under particularly favorable
+circumstances an extremely powerful sound-wave which had been caused by
+the explosion of several hundred pounds of dynamite threw a directly
+visible shadow in the sunlight, as Boys has recently told us. If the
+sound-waves were absolutely without influence upon the light, this could
+not have occurred, and all our artifices would then, too, be in vain.
+And so, similarly, the phenomenon accompanying projectiles which I am
+about to show you was once in a very imperfect manner incidentally seen
+by a French artillerist, Journée, while that observer was simply
+following the line of flight of a projectile with a telescope, just as
+also the undulations produced by candle flames are in a weak degree
+directly visible and in the bright sunlight are imaged in shadowy waves
+upon a uniform white background.
+
+_Instantaneous illumination_ by the electric spark, the method of
+rendering visible small optical differences or striæ, which may hence be
+called the _striate_, or _differential_, method,[112] invented by
+Foucault and Toepler, and finally the _recording_ of the image by a
+_photographic_ plate,--these therefore are the chief means which are to
+lead us to our goal.
+
+I instituted my first experiments in the summer of 1884 with a
+target-pistol, shooting the bullet through a striate field as described
+above, and taking care that the projectile whilst in the field should
+disengage an illuminating electric spark from a Leyden jar or Franklin's
+pane, which spark produced a photographic impression of the projectile
+upon a plate, especially arranged for the purpose. I obtained the image
+of the projectile at once and without difficulty. I also readily
+obtained, with the still rather defective dry plate which I was using,
+exceedingly delicate images of the sound-waves (spark-waves). But no
+atmospheric condensation produced by the projectile was visible. I now
+determined the velocity of my projectile and found it to be only 240
+metres per second, or considerably less than the velocity of sound
+(which is 340 metres per second). I saw immediately that under such
+circumstances no noticeable compression of the air could be produced,
+for any atmospheric compression must of necessity travel forward at the
+same speed with sound (340 metres per second) and consequently would be
+always ahead of and speeding away from the projectile.
+
+I was so thoroughly convinced, however, of the existence of the supposed
+phenomenon at a velocity exceeding 340 metres per second, that I
+requested Professor Salcher, of Fiume, an Austrian port on the Gulf of
+Quarnero, to undertake the experiment with projectiles travelling at a
+high rate of speed. In the summer of 1886 Salcher in conjunction with
+Professor Riegler conducted in a spacious and suitable apartment placed
+at their disposal by the Directors of the Royal Imperial Naval Academy,
+experiments of the kind indicated and conforming in method exactly to
+those which I had instituted, with the precise results expected. The
+phenomenon, in fact, accorded perfectly with the _a priori_ sketch of it
+which I had drafted previously to the experiment. As the experimenting
+was continued, new and unforeseen features made their appearance.
+
+It would be unfair, of course, to expect from the very first experiments
+faultless and highly distinct photographs. It was sufficient that
+success was secured and that I had convinced myself that further labor
+and expenditure would not be vain. And on this score I am greatly
+indebted to the two gentlemen above mentioned.
+
+The Austrian Naval Department subsequently placed a cannon at Salcher's
+disposal in Pola, an Adriatic seaport, and I myself, together with my
+son, then a student of medicine, having received and accepted a
+courteous invitation from Krupp, repaired to Meppen, a town in Hanover,
+where we conducted with only the necessary apparatus several experiments
+on the open artillery range. All these experiments furnished tolerably
+good and complete pictures. Some little progress, too, was made. The
+outcome of our experience on both artillery ranges, however, was the
+settled conviction that really good results could be obtained only by
+the most careful conduct of the experiments in a laboratory especially
+adapted to the purpose. The expensiveness of the experiments on a large
+scale was not the determining consideration here, for the size of the
+projectile is indifferent. Given the same velocity and the results are
+quite similar, whether the projectiles are large or small. On the other
+hand, in a laboratory the experimenter has perfect control over the
+initial velocity, which, provided the proper equipment is at hand, can
+be altered at will simply by altering the charge and the weight of the
+projectile. The requisite experiments were accordingly conducted by me
+in my laboratory at Prague, partly in conjunction with my son and partly
+afterwards by him alone. The latter are the most perfect and I shall
+accordingly speak in detail here of these only.
+
+[Illustration: Fig. 51.]
+
+Picture to yourself an apparatus for detecting optical striæ set up in a
+dark room. In order not to make the description too complicated, I shall
+give the essential features only of the apparatus, leaving out of
+account altogether the minuter details which are rather of consequence
+for the technical performance of the experiment than for its
+understanding. We suppose the projectile speeding on its path,
+accordingly, through the field of our differential optical apparatus.
+On reaching the centre of the field (Fig. 51) the projectile disengages
+an illuminating electric spark _a_, and the image of the projectile, so
+produced, is photographically impressed upon the plate of the camera
+behind the intercepting slide _b_. In the last and best experiments the
+lens _L_ was replaced by a spherical silvered-glass mirror made by K.
+Fritsch (formerly Prokesch) of Vienna, whereby the apparatus was
+naturally more complicated than it appears in our diagram. The
+projectile having been carefully aimed passes in crossing the
+differential field between two vertical isolated wires which are
+connected with the two coatings of a Leyden jar, and completely filling
+the space between the wires discharges the jar. In the axis of the
+differential apparatus the circuit has a second gap _a_ which furnishes
+the illuminating spark, the image of which falls on the intercepting
+slide _b_. The wires in the differential field having occasioned
+manifold disturbances were subsequently done away with. In the new
+arrangement the projectile passes through a ring (see dotted line, Fig.
+51), to the air in which it imparts a sharp impulse which travels
+forward in the tube _r_ as a sound-wave having the approximate velocity
+of 340 metres per second, topples over through the aperture of an
+electric screen the flame of a candle situated at the other opening of
+the tube, and so discharges the jar. The length of the tube _r_ is so
+adjusted that the discharge occurs the moment the projectile enters the
+centre of the now fully clear and free field of vision. We will also
+leave out of account the fact that to secure fully the success of the
+experiment, a large jar is first discharged by the flame, and that by
+the agency of this first discharge the discharge of a second small jar
+having a spark of very short period which furnishes the spark really
+illuminating the projectile is effected. Sparks from large jars have an
+appreciable duration, and owing to the great velocity of the projectiles
+furnish blurred photographs only. By carefully husbanding the light of
+the differential apparatus, and owing to the fact that much more light
+reaches the photographic plate in this way than would otherwise reach
+it, we can obtain beautiful, strong, and sharp photographs with
+incredibly small sparks. The contours of the pictures appear as very
+delicate and very sharp, closely adjacent double lines. From their
+distance from one another, and from the velocity of the projectile, the
+duration of the illumination, or of the spark, is found to be 1/800000
+of a second. It is evident, therefore, that experiments with mechanical
+snap slides can furnish no results worthy of the name.
+
+[Illustration: Fig. 52.]
+
+Let us consider now first the picture of a projectile in the rough, as
+represented in Figure 52, and then let us examine it in its photographic
+form as seen in Figure 53. The latter picture is of a shot from an
+Austrian Mannlicher rifle. If I were not to tell you what the picture
+represented you would very likely imagine it to be a bird's eye view of
+a boat _b_ moving swiftly through the water. In front you see the
+bow-wave and behind the body a phenomenon _k_ which closely resembles
+the eddies formed in the wake of a ship. And as a matter of fact the
+dark hyperboloid arc which streams from the tip of the projectile really
+is a compressed wave of air exactly analogous to the bow-wave produced
+by a ship moving through the water, with the exception that the wave of
+air is not a surface-wave. The air-wave is produced in atmospheric space
+and encompasses the projectile in the form of a shell on all sides. The
+wave is visible for the same reason that the heated shell of air
+surrounding the candle flame of our former experiments is visible. And
+the cylinder of friction-heated air which the projectile throws off in
+the form of vortex rings really does answer to the water in the wake of
+a vessel.
+
+[Illustration: Fig. 53. Photograph of a blunted projectile.]
+
+Now just as a slowly moving boat produces no bow-wave, but the bow-wave
+is seen only when the boat moves with a speed which is greater than the
+velocity of propagation of surface-waves in water, so, in like manner,
+no wave of compression is visible in front of a projectile so long as
+the speed of the projectile is less than the velocity of sound. But if
+the speed of the projectile reaches and exceeds the velocity of sound,
+then the head-wave, as we shall call it, augments noticeably in power,
+and is more and more extended, that is, the angle made by the contours
+of the wave with the direction of flight is more and more diminished,
+just as when the speed of a boat is increased a similar phenomenon is
+noticed in connexion with the bow-wave. In fact, we can from an
+instantaneous photograph so taken approximately estimate the speed with
+which the projectile is travelling.
+
+The explanation of the bow-wave of a ship and that of the head-wave of a
+body travelling in atmospheric space both repose upon the same
+principle, long ago employed by Huygens. Conceive a number of pebbles to
+be cast into a pond of water at regular intervals in such wise that all
+the spots struck are situate in the same straight line, and that every
+spot subsequently struck lies a short space farther to the right. The
+spots first struck will furnish then the wave-circles which are widest,
+and all of them together will, at the points where they are thickest,
+form a sort of cornucopia closely resembling the bow-wave. (Fig. 54.)
+The resemblance is greater the smaller the pebbles are, and the more
+quickly they succeed each other. If a rod be dipped into the water and
+quickly carried along its surface, the falling of the pebbles will then
+take place, so to speak, uninterruptedly, and we shall have a real
+bow-wave. If we put the compressed air-wave in the place of the
+surface-waves of the water, we shall have the head-wave of the
+projectile.
+
+[Illustration: Fig. 54.]
+
+You may be disposed to say now, it is all very pretty and interesting to
+observe a projectile in its flight, but of what practical use is it?
+
+It is true, I reply, one cannot _wage war_ with photographed
+projectiles. And I have likewise often had to say to medical students
+attending my lectures on physics, when they inquired for the practical
+value of some physical observation, "You cannot, gentlemen, cure
+diseases with it." I had also once to give my opinion regarding how much
+physics should be taught at a school for millers, supposing the
+instruction there to be confined _exactly_ to what was necessary for a
+miller. I was obliged to reply: "A miller always _needs_ exactly as much
+physics as he _knows_." Knowledge which one does not possess one cannot
+use.
+
+Let us forego entirely the consideration that as a general thing every
+scientific advance, every new problem elucidated, every extension or
+enrichment of our knowledge of facts, affords a better foundation for
+practical pursuits. Let us rather put the special question, Is it not
+possible to derive some really practical knowledge from our theoretical
+acquaintance with the phenomena which take place in the space
+surrounding a projectile?
+
+No physicist who has ever studied waves of sound or photographed them
+will have the least doubt regarding the sound-wave character of the
+atmospheric condensation encompassing the head of a flying projectile.
+We have therefore, without ado, called this condensation the head-wave.
+
+Knowing this, it follows that the view of Melsens according to which the
+projectile carries along with it masses of air which it forces into the
+bodies struck, is untenable. A forward-moving sound-wave is not a
+forward-moving mass of matter but a forward-moving form of motion, just
+as a water-wave or the waves of a field of wheat are only forward-moving
+forms of motion and not movements of masses of water or masses of wheat.
+
+By interference-experiments, on which I cannot touch here but which will
+be found roughly represented in Figure 55, it was found that the
+bell-shaped head-wave in question is an extremely thin shell and that
+the condensations of the same are quite moderate, scarcely exceeding
+two-tenths of an atmosphere. There can be no question, therefore, of
+explosive effects in the body struck by the projectile through so slight
+a degree of atmospheric compression. The phenomena attending wounds from
+rifle balls, for example, are not to be explained as Melsens and Busch
+explain them, but are due, as Kocher and Reger maintain, to the effects
+of the impact of the projectile itself.
+
+[Illustration: Fig. 55.]
+
+A simple experiment will show how insignificant is the part played by
+the friction of the air, or the supposed conveyance of the air along
+with the moving projectile. If the photograph of the projectile be
+taken while passing through a flame, i. e., a visible gas, the flame
+will be seen to be, not torn and deformed, but smoothly and cleanly
+perforated, like any solid body. Within and around the flame the
+contours of the head-wave will be seen. The flickering, the extinction
+of the flame, etc., take place only after the projectile has travelled
+on a considerable distance in its path, and is then affected by the
+powder gases which hurry after the bullet or by the air preceding the
+powder-gases.
+
+The physicist who examines the head-wave and recognises its sound-wave
+character also sees that the wave in question is of the same kind with
+the short sharp waves produced by electric sparks, that it is a
+_noise_-wave. Hence, whenever any portion of the head-wave strikes the
+ear it will be heard as a report. Appearances point to the conclusion
+that the projectile carries this report along with it. In addition to
+this report, which advances with the velocity of the projectile and so
+usually travels at a speed greater than the velocity of sound, there is
+also to be heard the report of the exploding powder which travels
+forward with the ordinary velocity of sound. Hence two explosions will
+be heard, each distinct in time. The circumstance that this fact was
+long misconstrued by practical observers but when actually noticed
+frequently received grotesque explanations and that ultimately my view
+was accepted as the correct one, appears to me in itself a sufficient
+justification that researches such as we are here speaking of are not
+utterly superfluous even in practical directions. That the flashes and
+sounds of discharging artillery are used for estimating the distances of
+batteries is well known, and it stands to reason that any unclear
+theoretical conception of the facts here involved will seriously affect
+the correctness of practical calculations.
+
+It may appear astonishing to a person hearing it for the first time,
+that a single shot has a double report due to two different velocities
+of propagation. But the reflexion that projectiles whose velocity is
+less than the velocity of sound produce no head-waves (because every
+impulse imparted to the air travels forward, that is, ahead, with
+exactly the velocity of sound), throws full light when logically
+developed upon the peculiar circumstance above mentioned. If the
+projectile moves faster than sound, the air ahead of it cannot recede
+from it quickly enough. The air is condensed and warmed, and thereupon,
+as all know, the velocity of sound is augmented until the head-wave
+travels forward as rapidly as the projectile itself, so that there is no
+need whatever of any additional augmentation of the velocity of
+propagation. If such a wave were left entirely to itself, it would
+increase in length and soon pass into an ordinary sound-wave, travelling
+with less velocity. But the projectile is always behind it and so
+maintains it at its proper density and velocity. Even if the projectile
+penetrates a piece of cardboard or a board of wood, which catches and
+obstructs the head-wave, there will, as Figure 56 shows, immediately
+appear at the emerging apex a newly formed, not to say newly born,
+head-wave. We may observe on the cardboard the reflexion and diffraction
+of the head-wave, and by means of a flame its refraction, so that no
+doubt as to its nature can remain.
+
+[Illustration: Fig. 56.]
+
+Permit me, now, to illustrate the most essential of the points that I
+have just adduced, by means of a few rough drawings taken from older and
+less perfect photographs.
+
+In the sketch of Figure 57 you see the projectile, which has just left
+the barrel of the rifle, touch a wire and disengage the illuminating
+spark. At the apex of the projectile you already see the beginnings of
+a powerful head-wave, and in front of the wave a transparent fungiform
+cluster. This latter is the air which has been forced out of the barrel
+by the projectile. Circular sound-waves, noise-waves, which are soon
+overtaken by the projectile, also issue from the barrel. But behind the
+projectile opaque puffs of powder-gas rush forth. It is scarcely
+necessary to add that many other questions in ballistics may be studied
+by this method, as, for example, the movement of the gun-carriage.
+
+[Illustration: Fig. 57.]
+
+A distinguished French artillerist, M. Gossot, has applied the views of
+the head-wave here given in quite a different manner. The practice in
+measuring the velocity of projectiles is to cause the projectile to pass
+through wire screens placed at different points in its path, and by the
+tearing of these screens to give rise to electro-magnetic time-signals
+on falling slabs or rotating drums. Gossot caused these signals to be
+made directly by the impact of the head-wave, did away thus with the
+wire screens, and carried the method so far as to be able to measure the
+velocities of projectiles travelling in high altitudes, where the use of
+wire screens was quite out of the question.
+
+The laws of the resistance of fluids and of air to bodies travelling in
+them form an extremely complicated problem, which can be reasoned out
+very simply and prettily as a matter of pure philosophy but practice
+offers not a few difficulties. The same body having the velocity 2, 3, 4
+... displaces in the same interval 2, 3, 4 ... times the same mass of
+air, or the same mass of fluid, and imparts to it _in addition_ 2, 3, 4
+... times the same velocity. But for this, plainly, 4, 9, 16 ... times
+the original force is required. Hence, the resistance, it is said,
+increases with the square of the velocity. This is all very pretty and
+simple and obvious. But practice and theory are at daggers' points here.
+Practice tells us that when we increase the velocity, the law of the
+resistance changes. For every portion of the velocity the law is
+different.
+
+The studies of the talented English naval architect, Froude, have thrown
+light upon this question. Froude has shown that the resistance is
+conditioned by a combination of the most multifarious phenomena. A ship
+in motion is subjected to the friction of the water. It causes eddies
+and it generates in addition waves which radiate outward from it. Every
+one of these phenomena are dependent upon the velocity in some different
+manner, and it is consequently not astonishing that the law of the
+resistance should be a complicated one.
+
+The preceding observations suggest quite analogous reflexions for
+projectiles. Here also we have friction, the formation of eddies, and
+the generation of waves. Here, also, therefore, we should not be
+surprised at finding the law of the resistance of the air a complicated
+one, nor puzzled at learning that in actuality the law of resistance
+changes as soon as the speed of the projectile exceeds the velocity of
+sound, for this is the precise point at which one important element of
+the resistance, namely, the formation of waves, first comes into play.
+
+No one doubts that a pointed bullet pierces the air with less resistance
+than a blunt bullet. The photographs themselves show that the head-wave
+is weaker for a pointed projectile. It is not impossible, similarly,
+that forms of bullets will be invented which generate fewer eddies,
+etc., and that we shall study these phenomena also by photography. I am
+of opinion from the few experiments which I have made in this direction
+that not much more can be done by changing the form of the projectile
+when the velocity is very great, but I have not gone into the question
+thoroughly. Researches of the kind we are considering can certainly not
+be detrimental to practical artillery, and it is no less certain that
+experiments by artillerists on a large scale will be of undoubted
+benefit to physics.
+
+No one who has had the opportunity of studying modern guns and
+projectiles in their marvellous perfection, their power and precision,
+can help confessing that a high technical and scientific achievement has
+found its incarnation in these objects. We may surrender ourselves so
+completely to this impression as to forget for a moment the terrible
+purposes they serve.
+
+Permit me, therefore, before we separate, to say a few words on this
+glaring contrast. The greatest man of war and of silence which the
+present age has produced once asserted that perpetual peace is a dream,
+and not a beautiful dream at that. We may accord to this profound
+student of mankind a judgment in these matters and can also appreciate
+the soldier's horror of stagnation from all too lengthy peace. But it
+requires a strong belief in the insuperableness of mediæval barbarism to
+hope for and to expect no great improvement in international relations.
+Think of our forefathers and of the times when club law ruled supreme,
+when within the same country and the same state brutal assaults and
+equally brutal self-defence were universal and self-evident. This state
+of affairs grew so oppressive that finally a thousand and one
+circumstances compelled people to put an end to it, and the cannon had
+most to say in accomplishing the work. Yet the rule of club law was not
+abolished so quickly after all. It had simply passed to other clubs. We
+must not abandon ourselves to dreams of the Rousseau type. Questions of
+law will in a sense forever remain questions of might. Even in the
+United States where every one is as a matter of principle entitled to
+the same privileges, the ballot according to Stallo's pertinent remark
+is but a milder substitute for the club. Nor need I tell you that many
+of our own fellow-citizens are still enamored of the old original
+methods. Very, very gradually, however, as civilisation progresses, the
+intercourse of men takes on gentler forms, and no one who really knows
+the good old times will ever honestly wish them back again, however
+beautifully they may be painted and rhymed about.
+
+In the intercourse of the nations, however, the old club law still
+reigns supreme. But since its rule is taxing the intellectual, the
+moral, and the material resources of the nations to the utmost and
+constitutes scarcely less a burden in peace than in war, scarcely less a
+yoke for the victor than for the vanquished, it must necessarily grow
+more and more unendurable. Reason, fortunately, is no longer the
+exclusive possession of those who modestly call themselves the upper ten
+thousand. Here, as everywhere, the evil itself will awaken the
+intellectual and ethical forces which are destined to mitigate it. Let
+the hate of races and of nationalities run riot as it may, the
+intercourse of nations will still increase and grow more intimate. By
+the side of the problems which separate nations, the great and common
+ideals which claim the exclusive powers of the men of the future appear
+one after another in greater distinctness and in greater might.
+
+  FOOTNOTES:
+
+  [Footnote 110: A lecture delivered on Nov. 10, 1897.]
+
+  [Footnote 111: Christiansen, _Wiedemann's Annalen_, XXIII. S. 298,
+  XXIV., p. 439 (1884-1885).]
+
+  [Footnote 112: The German phrase is _Schlierenmethode_, by which
+  term the method is known even by American physicists. It is also
+  called in English the "shadow-method." But a term is necessary which
+  will cover all the derivatives, and so we have employed
+  alternatively the words _striate_ and _differential_. The etymology
+  of _schlieren_, it would seem, is uncertain. Its present use is
+  derived from its technological signification in glass-manufacturing,
+  where by _die Schlieren_ are meant the wavy streaks and
+  imperfections in glass. Hence its application to the method for
+  detecting small optical _differences_ and faults generally.
+  Professor Crew of Evanston suggests to the translator that
+  _schlieren_ may be related to our _slur_ (L. G., _slüren_, to trail,
+  to draggle), a conjecture which is doubtless correct and agrees both
+  with the meaning of _schlieren_ as given in the large German
+  dictionaries and with the intransitive use of our own verb _slur_,
+  the faults in question being conceived as "trailings," "streakings,"
+  etc.--_Trans._]
+
+
+
+
+ON INSTRUCTION IN THE CLASSICS AND THE SCIENCES.[113]
+
+
+Perhaps the most fantastic proposition that Maupertuis,[114] the
+renowned president of the Berlin Academy, ever put forward for the
+approval of his contemporaries was that of founding a city in which, to
+instruct and discipline young students, only Latin should be spoken.
+Maupertuis's Latin city remained an idle wish. But for centuries Latin
+and Greek _institutions_ exist in which our children spend a goodly
+portion of their days, and whose atmosphere constantly surrounds them,
+even when without their walls.
+
+For centuries instruction in the ancient languages has been zealously
+cultivated. For centuries its necessity has been alternately championed
+and contested. More strongly than ever are authoritative voices now
+raised against the preponderance of instruction in the classics and in
+favor of an education more suited to the needs of the time, especially
+for a more generous treatment of mathematics and the natural sciences.
+
+In accepting your invitation to speak here on the relative educational
+value of the classical and the mathematico-physical sciences in colleges
+and high schools, I find my justification in the duty and the necessity
+laid upon every teacher of forming from his own experiences an opinion
+upon this important question, as partly also in the special circumstance
+that in my youth I was personally under the influence of school-life for
+only a short time, just previous to my entering the university, and had,
+therefore, ample opportunity to observe the effects of widely different
+methods upon my own person.
+
+Passing now, to a review of the arguments which the advocates of
+instruction in the classics advance, and of what the adherents of
+instruction in the physical sciences in their turn adduce, we find
+ourselves in rather a perplexing position with respect to the arguments
+of the first named. For these have been different at different times,
+and they are even now of a very multifarious character, as must be where
+men advance, in favor of an institution that exists and which they are
+determined to retain at any cost, everything they can possibly think of.
+We shall find here much that has evidently been brought forward only to
+impress the minds of the ignorant; much, too, that was advanced in good
+faith and which is not wholly without foundation. We shall get a fair
+idea of the reasoning employed by considering, first, the arguments that
+have grown out of the historical circumstances connected with the
+original introduction of the classics, and, lastly, those which were
+subsequently adduced as accidental afterthoughts.
+
+       *       *       *       *       *
+
+Instruction in Latin, as Paulsen[115] has minutely shown, was introduced
+by the Roman Church along with Christianity. With the Latin language
+were also transmitted the scant and meagre remnants of ancient science.
+Whoever wished to acquire this ancient education, then the only one
+worthy of the name, for him the Latin language was the only and
+indispensable means; such a person had to learn Latin to rank among
+educated people.
+
+The wide-spread influence of the Roman Church wrought many and various
+results. Among those for which all are glad, we may safely count the
+establishment of a sort of _uniformity_ among the nations and of a
+regular international intercourse by means of the Latin language, which
+did much to unite the nations in the common work of civilisation,
+carried on from the fifteenth to the eighteenth century. The Latin
+language was thus long the language of scholars, and instruction in
+Latin the road to a liberal education--a shibboleth still employed,
+though long inappropriate.
+
+For scholars as a class, it is to be regretted, perhaps, that Latin has
+ceased to be the medium of international communication. But the
+attributing of the loss of this function by the Latin language to its
+incapacity to accommodate itself to the numerous new ideas and
+conceptions which have arisen in the course of the development of
+science is, in my opinion, wholly erroneous. It would be difficult to
+find a modern scientist who had enriched science with as many new ideas
+as Newton has, yet Newton knew how to express those ideas very correctly
+and precisely in the Latin language. If this view were correct, it would
+also hold true of every living language. Originally every language has
+to adapt itself to new ideas.
+
+It is far more likely that Latin was displaced as the literary vehicle
+of science by the influence of the nobility. By their desire to enjoy
+the fruits of literature and science, through a less irksome medium
+than Latin, the nobility performed for the people at large an
+undeniable service. For the days were now past when acquaintance with
+the language and literature of science was restricted to a caste, and in
+this step, perhaps, was made the most important advance of modern times.
+To-day, when international intercourse is firmly established in spite of
+the many languages employed, no one would think of reintroducing
+Latin.[116]
+
+The facility with which the ancient languages lend themselves to the
+expression of new ideas is evidenced by the fact that the great majority
+of our scientific ideas, as survivals of this period of Latin
+intercourse, bear Latin and Greek designations, while in great measure
+scientific ideas are even now invested with names from these sources.
+But to deduce from the existence and use of such terms the necessity of
+still learning Latin and Greek on the part of all who employ them is
+carrying the conclusion too far. All terms, appropriate and
+inappropriate,--and there are a large number of inappropriate and
+monstrous combinations in science,--rest on convention. The essential
+thing is, that people should associate with the sign the precise idea
+that is designated by it. It matters little whether a person can
+correctly derive the words _telegraph_, _tangent_, _ellipse_, _evolute_,
+etc., if the correct idea is present in his mind when he uses them. On
+the other hand, no matter how well he may know their etymology, his
+knowledge will be of little use to him if the correct idea is absent.
+Ask the average and fairly educated classical scholar to translate a few
+lines for you from Newton's _Principia_, or from Huygens's _Horologium_,
+and you will discover at once what an extremely subordinate rôle the
+mere knowledge of language plays in such things. Without its associated
+thought a word remains a mere sound. The fashion of employing Greek and
+Latin designations--for it can be termed nothing else--has a natural
+root in history; it is impossible for the practice to disappear
+suddenly, but it has fallen of late considerably into disuse. The terms
+_gas_, _ohm_, _Ampère_, _volt_, etc., are in international use, but they
+are not Latin nor Greek. Only the person who rates the unessential and
+accidental husk higher than its contents, can speak of the necessity of
+learning Latin or Greek for such reasons, to say nothing of spending
+eight or ten years on the task. Will not a dictionary supply in a few
+seconds all the information we wish on such subjects?[117]
+
+It is indisputable that our modern civilisation took up the threads of
+the ancient civilisation, that at many points it begins where the latter
+left off, and that centuries ago the remains of the ancient culture were
+the only culture existing in Europe. Then, of course, a classical
+education really was the liberal education, the higher education, the
+ideal education, for it was the _sole_ education. But when the same
+claim is now raised in behalf of a classical education, it must be
+uncompromisingly contested as bereft of all foundation. For our
+civilisation has gradually attained its independence; it has lifted
+itself far above the ancient civilisation, and has entered generally new
+directions of progress. Its note, its characteristic feature, is the
+enlightenment that has come from the great mathematical and physical
+researches of the last centuries, and which has permeated not only the
+practical arts and industries but is also gradually finding its way into
+all fields of thought, including philosophy and history, sociology and
+linguistics. Those traces of ancient views that are still discoverable
+in philosophy, law, art, and science, operate more as hindrances than
+helps, and will not long stand before the development of independent and
+more natural views.
+
+It ill becomes classical scholars, therefore, to regard themselves, at
+this day, as the educated class _par excellence_, to condemn as
+uneducated all persons who do not understand Latin and Greek, to
+complain that with such people profitable conversations are not to be
+carried on, etc. The most delectable stories have got into circulation,
+illustrative of the defective education of scientists and engineers. A
+renowned inquirer, for example, is said to have once announced his
+intention of holding a free course of university lectures, with the word
+"frustra"; an engineer who spent his leisure hours in collecting insects
+is said to have declared that he was studying "etymology." It is true,
+incidents of this character make us shudder or smile, according to our
+mood or temperament. But we must admit, the next moment, that in giving
+way to such feelings we have merely succumbed to a childish prejudice. A
+lack of tact but certainly no lack of education is displayed in the use
+of such half-understood expressions. Every candid person will confess
+that there are many branches of knowledge about which he had better be
+silent. We shall not be so uncharitable as to turn the tables and
+discuss the impression that classical scholars might make on a scientist
+or engineer, in speaking of science. Possibly many ludicrous stories
+might be told of them, and of far more serious import, which should
+fully compensate for the blunders of the other party.
+
+The mutual severity of judgment which we have here come upon, may also
+forcibly bring home to us how really scarce a true liberal culture is.
+We may detect in this mutual attitude, too, something of that narrow,
+mediæval arrogance of caste, where a man began, according to the special
+point of view of the speaker, with the scholar, the soldier, or the
+nobleman. Little sense or appreciation is to be found in it for the
+_common_ task of humanity, little feeling for the need of mutual
+assistance in the great work of civilisation, little breadth of mind,
+little truly liberal culture.
+
+A knowledge of Latin, and partly, also, a knowledge of Greek, is still a
+necessity for the members of a few professions by nature more or less
+directly concerned with the civilisations of antiquity, as for lawyers,
+theologians, philologists, historians, and generally for a small number
+of persons, among whom from time to time I count myself, who are
+compelled to seek for information in the Latin literature of the
+centuries just past.[118] But that all young persons in search of a
+higher education should pursue for this reason Latin and Greek to such
+excess; that persons intending to become physicians and scientists
+should come to the universities defectively educated, or even
+miseducated; and that they should be compelled to come only from schools
+that do _not_ supply them with the proper preparatory knowledge is going
+a little bit too far.
+
+       *       *       *       *       *
+
+After the conditions which had given to the study of Latin and Greek
+their high import had ceased to exist, the traditional curriculum,
+naturally, was retained. Then, the different effects of this method of
+education, good and bad, which no one had thought of at its
+introduction, were realised and noted. As natural, too, was it that
+those who had strong interests in the preservation of these studies,
+from knowing no others or from living by them, or for still other
+reasons, should emphasise the _good_ results of such instruction. They
+pointed to the good effects as if they had been consciously aimed at by
+the method and could be attained only through its agency.
+
+One real benefit that students might derive from a rightly conducted
+course in the classics would be the opening up of the rich literary
+treasures of antiquity, and intimacy with the conceptions and views of
+the world held by two advanced nations. A person who has read and
+understood the Greek and Roman authors has felt and experienced more
+than one who is restricted to the impressions of the present. He sees
+how men placed in different circumstances judge quite differently of the
+same things from what we do to-day. His own judgments will be rendered
+thus more independent. Again, the Greek and Latin authors are
+indisputably a rich fountain of recreation, of enlightenment, and of
+intellectual pleasure after the day's toil, and the individual, not less
+than civilised humanity generally, will remain grateful to them for all
+time. Who does not recall with pleasure the wanderings of Ulysses, who
+does not listen joyfully to the simple narratives of Herodotus, who
+would ever repent of having made the acquaintance of Plato's Dialogues,
+or of having tasted Lucian's divine humor? Who would give up the glances
+he has obtained into the private life of antiquity from Cicero's
+letters, from Plautus or Terence? To whom are not the portraits of
+Suetonius undying reminiscences? Who, in fact, would throw away _any_
+knowledge he had once gained?
+
+Yet people who draw from these sources only, who know only this culture,
+have surely no right to dogmatise about the value of some other culture.
+As objects of research for individuals, this literature is extremely
+valuable, but it is a different question whether it is equally valuable
+as the almost exclusive means of education of our youth.
+
+Do not other nations and other literatures exist from which we ought to
+learn? Is not nature herself our first school-mistress? Are our highest
+models always to be the Greeks, with their narrow provinciality of mind,
+that divided the world into "Greeks and barbarians," with their
+superstitions, with their eternal questioning of oracles? Aristotle with
+his incapacity to learn from facts, with his word-science; Plato with
+his heavy, interminable dialogues, with his barren, at times childish,
+dialectics--are they unsurpassable?[119] The Romans with their apathy,
+their pompous externality, set off by fulsome and bombastic phrases,
+with their narrow-minded, philistine philosophy, with their frenzied
+sensuality, with their cruel and bestial indulgence in animal and man
+baiting, with their outrageous maltreatment and plundering of their
+subjects--are they patterns worthy of imitation? Or shall, perhaps, our
+science edify itself with the works of Pliny who cites midwives as
+authorities and himself stands on their point of view?
+
+Besides, if an acquaintance with the ancient world really were attained,
+we might come to some settlement with the advocates of classical
+education. But it is words and forms, and forms and words only, that are
+supplied to our youth; and even collateral subjects are forced into the
+strait-jacket of the same rigid method and made a science of words,
+sheer feats of mechanical memory. Really, we feel ourselves set back a
+thousand years into the dull cloister-cells of the Middle Ages.
+
+This must be changed. It is possible to get acquainted with the views of
+the Greeks and Romans by a shorter road than the intellect deadening
+process of eight or ten years of declining, conjugating, analysing, and
+extemporisation. There are to-day plenty of educated persons who have
+acquired through good translations vivider, clearer, and more just views
+of classical antiquity than the graduates of our gymnasiums and
+colleges.[120]
+
+For us moderns, the Greeks and the Romans are simply two objects of
+archæological and historical research like all others. If we put them
+before our youth in fresh and living pictures, and not merely in words
+and syllables, the effect will be assured. We derive a totally different
+enjoyment from the Greeks when we approach them after a study of the
+results of modern research in the history of civilisation. We read many
+a chapter of Herodotus differently when we attack his works equipped
+with a knowledge of natural science, and with information about the
+stone age and the lake-dwellers. What our classical institutions
+_pretend_ to give can and actually will be given to our youth with much
+more fruitful results by competent _historical_ instruction, which must
+supply, not names and numbers alone, nor the mere history of dynasties
+and wars, but be in every sense of the word a true history of
+civilisation.
+
+The view still widely prevails that although all "higher, ideal
+culture," all extension of our view of the world, is acquired by
+philological and in a lesser degree by historical studies, still the
+mathematics and natural sciences should not be neglected on account of
+their usefulness. This is an opinion to which I must refuse my assent.
+It were strange if man could learn more, could draw more intellectual
+nourishment, from the shards of a few old broken jugs, from inscribed
+stones, or yellow parchments, than from all the rest of nature. True,
+man is man's first concern, but he is not his sole concern.
+
+In ceasing to regard man as the centre of the world; in discovering that
+the earth is a top whirled about the sun, which speeds off with it into
+infinite space; in finding that in the fixed stars the same elements
+exist as on earth; in meeting everywhere the same processes of which the
+life of man is merely a vanishingly small part--in such things, too, is
+a widening of our view of the world, and edification, and poetry. There
+are here perhaps grander and more significant facts than the bellowing
+of the wounded Ares, or the charming island of Calypso, or the
+ocean-stream engirdling the earth. He only should speak of the relative
+value of these two domains of thought, of their poetry, who knows both.
+
+The "utility" of physical science is, in a measure, only a _collateral_
+product of that flight of the intellect which produced science. No one,
+however, should underrate the utility of science who has shared in the
+realisation by modern industrial art of the Oriental world of fables,
+much less one upon whom those treasures have been poured, as it were,
+from the fourth dimension, without his aid or understanding.
+
+Nor may we believe that science is useful only to the practical man. Its
+influence permeates all our affairs, our whole life; everywhere its
+ideas are decisive. How differently does the jurist, the legislator, or
+the political economist think, who knows, for example, that a square
+mile of the most fertile soil can support with the solar heat annually
+consumed only a definite number of human beings, which no art or science
+can increase. Many economical theories, which open new air-paths of
+progress, air-paths in the literal sense of the word, would be made
+impossible by such knowledge.
+
+       *       *       *       *       *
+
+The eulogists of classical education love to emphasise the cultivation
+of taste which comes from employment with the ancient models. I candidly
+confess that there is something absolutely revolting in this to me. To
+form the taste, then, our youths must sacrifice ten years of their life!
+Luxury takes precedence over necessity. Have the future generations, in
+the face of the difficult problems, the great social questions, which
+they must meet, and that with strengthened mind and heart, no more
+important duties to fulfil than these?
+
+But let us assume that this end were desirable. Can taste be formed by
+rules and precepts? Do not ideals of beauty change? Is it not a
+stupendous absurdity to force one's self artificially to admire things
+which, with all their historical interest, with all their beauty in
+individual points, are for the most part foreign to the rest of our
+thoughts and feelings, provided we have such of _our own_. A nation that
+is truly such, has its own taste and will not go to others for it. And
+every individual perfect man has his own taste.[121]
+
+And what, after all, does this cultivation of taste consist in? In the
+acquisition of the personal literary style of a few select authors! What
+should we think of a people that would force its youth a thousand years
+from now, by years of practice, to master the tortuous or bombastic
+style of some successful lawyer or politician of to-day? Should we not
+justly accuse them of a woful lack of taste?
+
+The evil effects of this imagined cultivation of the taste find
+expression often enough. The young _savant_ who regards the composition
+of a scientific essay as a rhetorical exercise instead of a simple and
+unadorned presentation of the facts and the truth, still sits
+unconsciously on the school-bench, and still unwittingly represents the
+point of view of the Romans, by whom the elaboration of speeches was
+regarded as a serious scientific (!) employment.
+
+       *       *       *       *       *
+
+Far be it from me to underrate the value of the development of the
+instinct of speech and of the increased comprehension of our own
+language which comes from philological studies. By the study of a
+foreign language, especially of one which differs widely from ours, the
+signs and forms of words are first clearly distinguished from the
+thoughts which they express. Words of the closest possible
+correspondence in different languages never coincide absolutely with the
+ideas they stand for, but place in relief slightly different aspects of
+the same thing, and by the study of language the attention is directed
+to these shades of difference. But it would be far from admissible to
+contend that the study of Latin and Greek is the most fruitful and
+natural, let alone the _only_, means of attaining this end. Any one who
+will give himself the pleasure of a few hours' companionship with a
+Chinese grammar; who will seek to make clear to himself the mode of
+speech and thought of a people who never advanced as far as the analysis
+of articulate sounds, but stopped at the analysis of syllables, to whom
+our alphabetical characters, therefore, are an inexplicable puzzle, and
+who express all their rich and profound thoughts by means of a few
+syllables with variable emphasis and position,--such a person, perhaps,
+will acquire new, and extremely elucidative ideas upon the relation of
+language and thought. But should our children, therefore, study Chinese?
+Certainly not. No more, then, should they be burdened with Latin, at
+least in the measure they are.
+
+It is a beautiful achievement to reproduce a Latin thought in a modern
+language with the maximum fidelity of meaning and expression--for the
+_translator_. Moreover, we shall be very grateful to the translator for
+his performance. But to demand this feat of every educated man, without
+consideration of the sacrifice of time and labor which it entails, is
+unreasonable. And for this very reason, as classical teachers admit,
+that ideal is never perfectly attained, except in rare cases with
+scholars possessed of special talents and great industry. Without
+slurring, therefore, the high importance of the study of the ancient
+languages as a profession, we may yet feel sure that the instinct for
+speech which is part of every liberal education can, and must, be
+acquired in a different way. Should we, indeed, be forever lost if the
+Greeks had not lived before us?
+
+The fact is, we must carry our demands further than the representatives
+of classical philology. We must ask of every educated man a fair
+scientific conception of the nature and value of language, of the
+formation of language, of the alteration of the meaning of roots, of the
+degeneration of fixed forms of speech to grammatical forms, in brief, of
+all the main results of modern comparative philology. We should judge
+that this were attainable by a careful study of our mother tongue and of
+the languages next allied to it, and subsequently of the more ancient
+tongues from which the former are derived. If any one object that this
+is too difficult and entails too much labor, I should advise such a
+person to place side by side an English, a Dutch, a Danish, a Swedish,
+and a German Bible, and to compare a few lines of them; he will be
+amazed at the multitude of suggestions that offer themselves.[122] In
+fact, I believe that a really progressive, fruitful, rational, and
+instructive study of languages can be conducted only on this plan. Many
+of my audience will remember, perhaps, the bright and encouraging
+effect, like that of a ray of sunlight on a gloomy day, which the meagre
+and furtive remarks on comparative philology in Curtius's Greek grammar
+wrought in that barren and lifeless desert of verbal quibbles.
+
+       *       *       *       *       *
+
+The principal result obtained by the present method of studying the
+ancient languages is that which comes from the student's employment with
+their complicated grammars. It consists in the sharpening of the
+attention and in the exercise of the judgment by the practice of
+subsuming special cases under general rules, and of distinguishing
+between different cases. Obviously, the same result can be reached by
+many other methods; for example, by difficult games of cards. Every
+science, the mathematics and the physical sciences included, accomplish
+as much, if not more, in this disciplining of the judgment. In addition,
+the matter treated by those sciences has a much higher intrinsic
+interest for young people, and so engages spontaneously their attention;
+while on the other hand they are elucidative and useful in other
+directions in which grammar can accomplish nothing.
+
+Who cares, so far as the matter of it is concerned, whether we say
+_hominum_ or _hominorum_ in the genitive plural, interesting as the fact
+may be for the philologist? And who would dispute that the intellectual
+need of causal insight is awakened not by grammar but by the natural
+sciences?
+
+It is not our intention, therefore, to gainsay in the least the good
+influence which the study of Latin and Greek grammar _also_ exercises on
+the sharpening of the judgment. In so far as the study of words as such
+must greatly promote lucidity and accuracy of expression, in so far as
+Latin and Greek are not yet wholly indispensable to many branches of
+knowledge, we willingly concede to them a place in our schools, but
+would demand that the disproportionate amount of time allotted to them,
+wrongly withdrawn from other useful studies, should be considerably
+curtailed. That in the end Latin and Greek will not be employed as the
+universal means of education, we are fully convinced. They will be
+relegated to the closet of the scholar or professional philologist, and
+gradually make way for the modern languages and the modern science of
+language.
+
+Long ago Locke reduced to their proper limits the exaggerated notions
+which obtained of the close connexion of thought and speech, of logic
+and grammar, and recent investigators have established on still surer
+foundations his views. How little a complicated grammar is necessary for
+expressing delicate shades of thought is demonstrated by the Italians
+and French, who, although they have almost totally discarded the
+grammatical redundancies of the Romans, are yet not surpassed by the
+latter in accuracy of thought, and whose poetical, but especially whose
+scientific literature, as no one will dispute, can bear favorable
+comparison with the Roman.
+
+Reviewing again the arguments advanced in favor of the study of the
+ancient languages, we are obliged to say that in the main and as
+applied to the present, they are wholly devoid of force. In so far as
+the aims which this study theoretically pursues are still worthy of
+attainment, they appear to us as altogether too narrow, and are
+surpassed in this only by the means employed. As almost the sole,
+indisputable result of this study we must count the increase of the
+student's skill and precision in expression. One inclined to be
+uncharitable might say that our gymnasiums and classical academies turn
+out men who can speak and write, but, unfortunately, have little to
+write or speak about. Of that broad, liberal view, of that famed
+universal culture, which the classical curriculum is supposed to yield,
+serious words need not be lost. This culture might, perhaps, more
+properly be termed the contracted or lopsided culture.
+
+       *       *       *       *       *
+
+While considering the study of languages we threw a few side glances at
+mathematics and the natural sciences. Let us now inquire whether these,
+as branches of study, cannot accomplish much that is to be attained in
+no other way. I shall meet with no contradiction when I say that without
+at least an elementary mathematical and scientific education a man
+remains a total stranger in the world in which he lives, a stranger in
+the civilisation of the time that bears him. Whatever he meets in
+nature, or in the industrial world, either does not appeal to him at
+all, from his having neither eye nor ear for it, or it speaks to him in
+a totally unintelligible language.
+
+A real understanding of the world and its civilisation, however, is not
+the only result of the study of mathematics and the physical sciences.
+Much more essential for the preparatory school is the _formal_
+cultivation which comes from these studies, the strengthening of the
+reason and the judgment, the exercise of the imagination. Mathematics,
+physics, chemistry, and the so-called descriptive sciences are so much
+alike in this respect, that, apart from a few points, we need not
+separate them in our discussion.
+
+Logical sequence and continuity of ideas, so necessary for fruitful
+thought, are _par excellence_ the results of mathematics; the ability to
+follow facts with thoughts, that is, to observe or collect experiences,
+is chiefly developed by the natural sciences. Whether we notice that the
+sides and the angles of a triangle are connected in a definite way, that
+an equilateral triangle possesses certain definite properties of
+symmetry, or whether we notice the deflexion of a magnetic needle by an
+electric current, the dissolution of zinc in diluted sulphuric acid,
+whether we remark that the wings of a butterfly are slightly colored on
+the under, and the fore-wings of the moth on the upper, surface:
+indiscriminately here we proceed from _observations_, from individual
+acts of immediate intuitive knowledge. The field of observation is more
+restricted and lies closer at hand in mathematics; it is more varied and
+broader but more difficult to compass in the natural sciences. The
+essential thing, however, is for the student to learn to make
+observations in all these fields. The philosophical question whether our
+acts of knowledge in mathematics are of a special kind is here of no
+importance for us. It is true, of course, that the observation can be
+practised by languages also. But no one, surely, will deny, that the
+concrete, living pictures presented in the fields just mentioned possess
+different and more powerful attractions for the mind of the youth than
+the abstract and hazy figures which language offers, and on which the
+attention is certainly not so spontaneously bestowed, nor with such good
+results.[123]
+
+Observation having revealed the different properties of a given
+geometrical or physical object, it is discovered that in many cases
+these properties _depend_ in some way upon one another. This
+interdependence of properties (say that of equal sides and equal angles
+at the base of a triangle, the relation of pressure to motion,) is
+nowhere so distinctly marked, nowhere is the necessity and permanency of
+the interdependence so plainly noticeable, as in the fields mentioned.
+Hence the continuity and logical consequence of the ideas which we
+acquire in those fields. The relative simplicity and perspicuity of
+geometrical and physical relations supply here the conditions of natural
+and easy progress. Relations of equal simplicity are not met with in
+the fields which the study of language opens up. Many of you, doubtless,
+have often wondered at the little respect for the notions of cause and
+effect and their connexion that is sometimes found among professed
+representatives of the classical studies. The explanation is probably to
+be sought in the fact that the analogous relation of motive and action
+familiar to them from their studies, presents nothing like the clear
+simplicity and determinateness that the relation of cause and effect
+does.
+
+That perfect mental grasp of all possible cases, that economical order
+and organic union of the thoughts which comes from it, which has grown
+for every one who has ever tasted it a permanent need which he seeks to
+satisfy in every new province, can be developed only by employment with
+the relative simplicity of mathematical and scientific investigations.
+
+When a set of facts comes into apparent conflict with another set of
+facts, and a problem is presented, its solution consists ordinarily in a
+more refined distinction or in a more extended view of the facts, as may
+be aptly illustrated by Newton's solution of the problem of dispersion.
+When a new mathematical or scientific fact is _demonstrated_, or
+_explained_, such demonstration also rests simply upon showing the
+connexion of the new fact with the facts already known; for example,
+that the radius of a circle can be laid off as chord exactly six times
+in the circle is explained or proved by dividing the regular hexagon
+inscribed in the circle into equilateral triangles. That the quantity of
+heat developed in a second in a wire conveying an electric current is
+quadrupled on the doubling of the strength of the current, we explain
+from the doubling of the fall of the potential due to the doubling of
+the current's intensity, as also from the doubling of the quantity
+flowing through, in a word, from the quadrupling of the work done. In
+point of principle, explanation and direct proof do not differ much.
+
+He who solves scientifically a geometrical, physical, or technical
+problem, easily remarks that his procedure is a _methodical_ mental
+quest, rendered possible by the economical order of the province--a
+simplified purposeful quest as contrasted with unmethodical,
+unscientific guess-work. The geometer, for example, who has to construct
+a circle touching two given straight lines, casts his eye over the
+relations of symmetry of the desired construction, and seeks the centre
+of his circle solely in the line of symmetry of the two straight lines.
+The person who wants a triangle of which two angles and the sum of the
+sides are given, grasps in his mind the determinateness of the form of
+this triangle and restricts his search for it to a certain group of
+triangles of the _same form_. Under very different circumstances,
+therefore, the simplicity, the intellectual perviousness, of the
+subject-matter of mathematics and natural science is felt, and promotes
+both the discipline and the self-confidence of the reason.
+
+Unquestionably, much more will be attained by instruction in the
+mathematics and the natural sciences than now is, when more natural
+methods are adopted. One point of importance here is that young students
+should not be spoiled by premature abstraction, but should be made
+acquainted with their material from living pictures of it before they
+are made to work with it by purely ratiocinative methods. A good stock
+of geometrical experience could be obtained, for example, from
+geometrical drawing and from the practical construction of models. In
+the place of the unfruitful method of Euclid, which is only fit for
+special, restricted uses, a broader and more conscious method must be
+adopted, as Hankel has pointed out.[124] Then, if, on reviewing
+geometry, and after it presents no substantial difficulties, the more
+general points of view, the principles of scientific method are placed
+in relief and brought to consciousness, as Von Nagel,[125] J. K.
+Becker,[126] Mann,[127] and others have well done, fruitful results will
+be surely attained. In the same way, the subject-matter of the natural
+sciences should be made familiar by pictures and experiment before a
+profounder and reasoned grasp of these subjects is attempted. Here the
+emphasis of the more general points of view is to be postponed.
+
+Before my present audience it would be superfluous for me to contend
+further that mathematics and natural science are justified constituents
+of a sound education,--a claim that even philologists, after some
+resistance, have conceded. Here I may count upon assent when I say that
+mathematics and the natural sciences pursued alone as means of
+instruction yield a richer education in matter and form, a more general
+education, an education better adapted to the needs and spirit of the
+time,--than the philological branches pursued alone would yield.
+
+But how shall this idea be realised in the curricula of our intermediate
+educational institutions? It is unquestionable in my mind that the
+German _Realschulen_ and _Realgymnasien_, where the exclusive classical
+course is for the most part replaced by mathematics, science, and modern
+languages, give the _average_ man a more timely education than the
+gymnasium proper, although they are not yet regarded as fit preparatory
+schools for future theologians and professional philologists. The German
+gymnasiums are too one-sided. With these the first changes are to be
+made; of these alone we shall speak here. Possibly a _single_
+preparatory school, suitably planned, might serve all purposes.
+
+Shall we, then, in our gymnasiums fill out the hours of study which
+stand at our disposal, or are still to be wrested from the classicists,
+with as great and as varied a quantity of mathematical and scientific
+matter as possible? Expect no such proposition from me. No one will
+suggest such a course who has himself been actively engaged in
+scientific thought. Thoughts can be awakened and fructified as a field
+is fructified by sunshine and rain. But thoughts cannot be juggled out
+and worried out by heaping up materials and the hours of instruction,
+nor by any sort of precepts: they must grow naturally of their own free
+accord. Furthermore, thoughts cannot be accumulated beyond a certain
+limit in a single head, any more than the produce of a field can be
+increased beyond certain limits.
+
+I believe that the amount of matter necessary for a useful education,
+such as should be offered to _all_ the pupils of a preparatory school,
+is very small. If I had the requisite influence, I should, in all
+composure, and fully convinced that I was doing what was best, first
+greatly curtail in the lower classes the amount of matter in both the
+classical and the scientific courses; I should cut down considerably the
+number of the school hours and the work done outside the school. I am
+not with many teachers of opinion that ten hours work a day for a child
+is not too much. I am convinced that the mature men who offer this
+advice so lightly are themselves unable to give their attention
+successfully for as long a time to any subject that is new to them, (for
+example, to elementary mathematics or physics,) and I would ask every
+one who thinks the contrary to make the experiment upon himself.
+Learning and teaching are not routine office-work that can be kept up
+mechanically for long periods. But even such work tires in the end. If
+our young men are not to enter the universities with blunted and
+impoverished minds, if they are not to leave in the preparatory schools
+their vital energy, which they should there gather, great changes must
+be made. Waiving the injurious effects of overwork upon the body, the
+consequences of it for the mind seem to me positively dreadful.
+
+I know of nothing more terrible than the poor creatures who have learned
+too much. Instead of that sound powerful judgment which would probably
+have grown up if they had learned nothing, their thoughts creep timidly
+and hypnotically after words, principles, and formulæ, constantly by the
+same paths. What they have acquired is a spider's web of thoughts too
+weak to furnish sure supports, but complicated enough to produce
+confusion.
+
+But how shall better methods of mathematical and scientific education be
+combined with the decrease of the subject-matter of instruction? I
+think, by abandoning systematic instruction altogether, at least in so
+far as that is required of _all_ young pupils. I see no necessity
+whatever that the graduates of our high schools and preparatory schools
+should be little philologists, and at the same time little
+mathematicians, physicists, and botanists; in fact, I do not see the
+possibility of such a result. I see in the endeavor to attain this
+result, in which every instructor seeks for his own branch a place apart
+from the others, the main mistake of our whole system. I should be
+satisfied if every young student could come into living contact with
+and pursue to their ultimate logical consequences merely a _few_
+mathematical or scientific discoveries. Such instruction would be mainly
+and naturally associated with selections from the great scientific
+classics. A few powerful and lucid ideas could thus be made to take root
+in the mind and receive thorough elaboration. This accomplished, our
+youth would make a different showing from what they do to-day.[128]
+
+What need is there, for example, of burdening the head of a young
+student with all the details of botany? The student who has botanised
+under the guidance of a teacher finds on all hands, not indifferent
+things, but known or unknown things, by which he is stimulated, and his
+gain made permanent. I express here, not my own, but the opinion of a
+friend, a practical teacher. Again, it is not at all necessary that all
+the matter that is offered in the schools should be learned. The best
+that we have learned, that which has remained with us for life, outlived
+the test of examination. How can the mind thrive when matter is heaped
+on matter, and new materials piled constantly on old, undigested
+materials? The question here is not so much that of the accumulation of
+positive knowledge as of intellectual discipline. It seems also
+unnecessary that _all_ branches should be treated at school, and that
+exactly the same studies should be pursued in all schools. A single
+philological, a single historical, a single mathematical, a single
+scientific branch, pursued as common subjects of instruction for all
+pupils, are sufficient to accomplish all that is necessary for the
+intellectual development. On the other hand, a wholesome mutual stimulus
+would be produced by this greater variety in the positive culture of
+men. Uniforms are excellent for soldiers, but they will not fit heads.
+Charles V. learned this, and it should never be forgotten. On the
+contrary, teachers and pupils both need considerable latitude, if they
+are to yield good results.
+
+With John Karl Becker I am of the opinion that the utility and amount
+for individuals of every study should be precisely determined. All that
+exceeds this amount should be unconditionally banished from the lower
+classes. With respect to mathematics, Becker,[129] in my judgment, has
+admirably solved this question.
+
+With respect to the upper classes the demand assumes a different form.
+Here also the amount of matter obligatory on all pupils ought not to
+exceed a certain limit. But in the great mass of knowledge that a young
+man must acquire to-day for his profession it is no longer just that ten
+years of his youth should be wasted with mere preludes. The upper
+classes should supply a truly useful preparation for the professions,
+and should not be modelled upon the wants merely of future lawyers,
+ministers, and philologists. Again, it would be both foolish and
+impossible to attempt to prepare the same person properly for all the
+different professions. In such case the function of the schools would
+be, as Lichtenberg feared, simply to select the persons best fitted for
+being drilled, whilst precisely the finest special talents, which do not
+submit to indiscriminate discipline, would be excluded from the contest.
+Hence, a certain amount of liberty in the choice of studies must be
+introduced in the upper classes, by means of which it will be free for
+every one who is clear about the choice of his profession to devote his
+chief attention either to the study of the philologico-historical or to
+that of the mathematico-scientific branches. Then the matter now treated
+could be retained, and in some branches, perhaps, judiciously
+extended,[130] without burdening the scholar with many branches or
+increasing the number of the hours of study. With more homogeneous work
+the student's capacity for work increases, one part of his labor
+supporting the other instead of obstructing it. If, however, a young man
+should subsequently choose a different profession, then it is _his_
+business to make up what he has lost. No harm certainly will come to
+society from this change, nor could it be regarded as a misfortune if
+philologists and lawyers with mathematical educations or physical
+scientists with classical educations should now and then appear.
+
+       *       *       *       *       *
+
+The view is now wide-spread that a Latin and Greek education no longer
+meets the general wants of the times, that a more opportune, a more
+"liberal" education exists. The phrase, "a liberal education," has been
+greatly misused. A truly liberal education is unquestionably very rare.
+The _schools_ can hardly offer such; at best they can only bring home to
+the student the necessity of it. It is, then, his business to acquire,
+as best he can, a more or less liberal education. It would be very
+difficult, too, at any one time to give a definition of a "liberal"
+education which would satisfy every one, still more difficult to give
+one which would hold good for a hundred years. The educational ideal, in
+fact, varies much. To one, a knowledge of classical antiquity appears
+not too dearly bought "with early death." We have no objection to this
+person, or to those who think like him, pursuing their ideal after their
+own fashion. But we may certainly protest strongly against the
+realisation of such ideals on our own children. Another,--Plato, for
+example,--puts men ignorant of geometry on a level with animals.[131]
+If such narrow views had the magical powers of the sorceress Circe, many
+a man who perhaps justly thought himself well educated would become
+conscious of a not very flattering transformation of himself. Let us
+seek, therefore, in our educational system to meet the wants of the
+present, and not establish prejudices for the future.
+
+But how does it come, we must ask, that institutions so antiquated as
+the German gymnasiums could subsist so long in opposition to public
+opinion? The answer is simple. The schools were first organised by the
+Church; since the Reformation they have been in the hands of the State.
+On so large a scale, the plan presents many advantages. Means can be
+placed at the disposal of education such as no private source, at least
+in Europe, could furnish. Work can be conducted upon the same plan in
+many schools, and so experiments made of extensive scope which would be
+otherwise impossible. A single man with influence and ideas can under
+such circumstances do great things for the promotion of education.
+
+But the matter has also its reverse aspect. The party in power works for
+its own interests, uses the schools for its special purposes.
+Educational competition is excluded, for all successful attempts at
+improvement are impossible unless undertaken or permitted by the State.
+By the uniformity of the people's education, a prejudice once in vogue
+is permanently established. The highest intelligences, the strongest
+wills cannot overthrow it suddenly. In fact, as everything is adapted to
+the view in question, a sudden change would be physically impossible.
+The two classes which virtually hold the reins of power in the State,
+the jurists and theologians, know only the one-sided, predominantly
+classical culture which they have acquired in the State schools, and
+would have this culture alone valued. Others accept this opinion from
+credulity; others, underestimating their true worth for society, bow
+before the power of the prevalent opinion; others, again, affect the
+opinion of the ruling classes even against their better judgment, so as
+to abide on the same plane of respect with the latter. I will make no
+charges, but I must confess that the deportment of medical men with
+respect to the question of the qualification of graduates of your
+_Realschulen_ has frequently made that impression upon me. Let us
+remember, finally, that an influential statesman, even within the
+boundaries which the law and public opinion set him, can do serious harm
+to the cause of education by considering his own one-sided views
+infallible, and in enforcing them recklessly and inconsiderately--which
+not only _can_ happen, but has, repeatedly, happened.[132] The monopoly
+of education by the State[133] thus assumes in our eyes a somewhat
+different aspect. And to revert to the question above asked, there is
+not the slightest doubt that the German gymnasiums in their present
+form would have ceased to exist long ago if the State had not supported
+them.
+
+All this must be changed. But the change will not be made of itself, nor
+without our energetic interference, and it will be made slowly. But the
+path is marked out for us, the will of the people must acquire and exert
+upon our school legislation a greater and more powerful influence.
+Furthermore, the questions at issue must be publicly and candidly
+discussed that the views of the people may be clarified. All who feel
+the insufficiency of the existing _régime_ must combine into a powerful
+organisation that their views may acquire impressiveness and the
+opinions of the individual not die away unheard.
+
+I recently read, gentlemen, in an excellent book of travels, that the
+Chinese speak with unwillingness of politics. Conversations of this sort
+are usually cut short with the remark that they may bother about such
+things whose business it is and who are paid for it. Now it seems to me
+that it is not only the business of the State, but a very serious
+concern of all of us, how our children shall be educated in the public
+schools at _our_ cost.
+
+  FOOTNOTES:
+
+  [Footnote 113: An address delivered before the Congress of Delegates
+  of the German Realschulmännerverein, at Dortmund, April 16, 1886.
+  The full title of the address reads: "On the Relative Educational
+  Value of the Classics and the Mathematico-Physical Sciences in
+  Colleges and High Schools."
+
+  Although substantially contained in an address which I was to have
+  made at the meeting of Natural Scientists at Salzburg in 1881
+  (deferred on account of the Paris Exposition), and in the
+  Introduction to a course of lectures on "Physical Instruction in
+  Preparatory Schools," which I delivered in 1883, the invitation of
+  the German Realschulmännerverein afforded me the first opportunity
+  of putting my views upon this subject before a large circle of
+  readers. Owing to the place and circumstances of delivery, my
+  remarks apply of course, primarily, only to German schools, but,
+  with slight modifications, made in this translation, are not without
+  force for the institutions of other countries. In giving here
+  expression to a strong personal conviction formed long ago, it is a
+  matter of deep satisfaction to me to find that they agree in many
+  points with the views recently advanced in independent form by
+  Paulsen (_Geschichte des gelehrten Unterrichts_, Leipsic, 1885) and
+  Frary (_La question du latin_, Paris, Cerf, 1885). It is not my
+  desire nor effort here to say much that is new, but merely to
+  contribute my mite towards bringing about the inevitable revolution
+  now preparing in the world of elementary instruction. In the opinion
+  of experienced educationists the first result of that revolution
+  will be to make Greek and mathematics alternately optional subjects
+  in the higher classes of the German Gymnasium and in the
+  corresponding institutions of other countries, as has been done in
+  the splendid system of instruction in Denmark. The gap between the
+  German classical Gymnasium and the German Realgymnasium, or between
+  classical and scientific schools generally, can thus be bridged
+  over, and the remaining inevitable transformations will then be
+  accomplished in relative peace and quiet. (Prague, May, 1886.)]
+
+  [Footnote 114: Maupertuis, _Oeuvres_, Dresden, 1752, p. 339.]
+
+  [Footnote 115: F. Paulsen, _Geschichte des gelehrten Unterrichts_,
+  Leipsic, 1885.]
+
+  [Footnote 116: There is a peculiar irony of fate in the fact that
+  while Leibnitz was casting about for a new vehicle of universal
+  linguistic intercourse, the Latin language which still subserved
+  this purpose the best of all, was dropping more and more out of use,
+  and that Leibnitz himself contributed not the least to this result.]
+
+  [Footnote 117: As a rule, the human brain is too much, and wrongly,
+  burdened with things which might be more conveniently and accurately
+  preserved in books where they could be found at a moment's notice.
+  In a recent letter to me from Düsseldorf, Judge Hartwich writes:
+
+  "A host of words exist which are out and out Latin or Greek, yet are
+  employed with perfect correctness by people of good education who
+  never had the good luck to be taught the ancient languages. For
+  example, words like 'dynasty.' ... The child learns such words as
+  parts of the common stock of speech, or even as parts of his
+  mother-tongue, just as he does the words 'father,' 'mother,'
+  'bread,' 'milk.' Does the ordinary mortal know the etymology of
+  these Saxon words? Did it not require the almost incredible industry
+  of the Grimms and other Teutonic philologists to throw the merest
+  glimmerings of light upon the origin and growth of our own
+  mother-tongue? Besides, do not thousands of people of so-called
+  classical education use every moment hosts of words of foreign
+  origin whose derivation they do not know? Very few of them think it
+  worth while to look up such words in the dictionaries, although they
+  love to maintain that people should study the ancient languages for
+  the sake of etymology alone."]
+
+  [Footnote 118: Standing remote from the legal profession I should
+  not have ventured to declare that the study of Greek was not
+  necessary for the jurists; yet this view was taken in the debate
+  that followed this lecture by professional jurists of high standing.
+  According to this opinion, the preparatory education obtained in the
+  German Realgymnasium would also be sufficient for the future jurists
+  and insufficient only for theologians and philologists. [In England
+  and America not only is Greek not necessary, but the law-Latin is so
+  peculiar that even persons of _good_ classical education cannot
+  understand it.--_Tr._]]
+
+  [Footnote 119: In emphasising here the weak sides of the writings of
+  Plato and Aristotle, forced on my attention while reading them in
+  German translations, I, of course, have no intention of underrating
+  the great merits and the high historical importance of these two
+  men. Their importance must not be measured by the fact that our
+  speculative philosophy still moves to a great extent in their paths
+  of thought. The more probable conclusion is that this branch has
+  made very little progress in the last two thousand years. Natural
+  science also was implicated for centuries in the meshes of the
+  Aristotelian thought, and owes its rise mainly to having thrown off
+  those fetters.]
+
+  [Footnote 120: I would not for a moment contend that we derive
+  exactly the same profit from reading a Greek author in a translation
+  as from reading him in the original; but the difference, the excess
+  of gain in the second case, appears to me, and probably will to most
+  men who are not professional philologists, to be too dearly bought
+  with the expenditure of eight years of valuable time.]
+
+  [Footnote 121: "The temptation," Judge Hartwich writes, "to regard
+  the 'taste' of the ancients as so lofty and unsurpassable appears to
+  me to have its chief origin in the fact that the ancients were
+  unexcelled in the representation of the nude. First, by their
+  unremitting care of the human body they produced splendid models;
+  and secondly, in their gymnasiums and in their athletic games they
+  had these models constantly before their eyes. No wonder, then, that
+  their statues still excite our admiration! For the form, the ideal
+  of the human body has not changed in the course of the centuries.
+  But with intellectual matters it is totally different; they change
+  from century to century, nay, from decennium to decennium. It is
+  very natural now, that people should unconsciously apply what is
+  thus so easily seen, namely, the works of sculpture, as a universal
+  criterion of the highly developed taste of the ancients--a fallacy
+  against which people cannot, in my judgment, be too strongly
+  warned."]
+
+  [Footnote 122: English: "In the beginning God created the heaven and
+  the earth. And the earth was without form and void; and darkness was
+  upon the face of the deep. And the spirit of God moved upon the face
+  of the waters."--Dutch: "In het begin schiep God den hemel en de
+  aarde. De aarde nu was woest en ledig, en duisternis was op den
+  afgrond; en de Geest Gods zwefde op de wateren."--Danish: "I
+  Begyndelsen skabte Gud Himmelen og Jorden. Og Jorden var ode og tom,
+  og der var morkt ovenover Afgrunden, og Guds Aand svoevede ovenover
+  Vandene."--Swedish: "I begynnelsen skapade Gud Himmel och Jord. Och
+  Jorden war öde och tom, och mörker war pä djupet, och Gods Ande
+  swäfde öfwer wattnet."--German: "Am Anfang schuf Gott Himmel und
+  Erde. Und die Erde war wüst und leer, und es war finster auf der
+  Tiefe; und der Geist Gottes schwebte auf dem Wasser."]
+
+  [Footnote 123: Compare Herzen's excellent remarks, _De
+  l'enseignement secondaire dans la Suisse romande_, Lausanne, 1886.]
+
+  [Footnote 124: _Geschichte der Mathematik_, Leipsic, 1874.]
+
+  [Footnote 125: _Geometrische Analyse_, Ulm, 1886.]
+
+  [Footnote 126: In his text-books of elementary mathematics]
+
+  [Footnote 127: _Abhandlungen aus dem Gebiete der Mathematik_,
+  Würzburg, 1883.]
+
+  [Footnote 128: My idea here is an appropriate selection of readings
+  from Galileo, Huygens, Newton, etc. The choice is so easily made
+  that there can be no question of difficulties. The contents would be
+  discussed with the students, and the original experiments performed
+  with them. Those scholars alone should receive this instruction in
+  the upper classes who did not look forward to systematical
+  instruction in the physical sciences. I do not make this proposition
+  of reform here for the first time. I have no doubt, moreover, that
+  such radical changes will only be slowly introduced.]
+
+  [Footnote 129: _Die Mathematik als Lehrgegenstand des Gymnasiums_,
+  Berlin, 1883.]
+
+  [Footnote 130: Wrong as it is to burden future physicians and
+  scientists with Greek for the sake of the theologians and
+  philologists, it would be just as wrong to compel theologians and
+  philologists, on account of the physicians, to study such subjects
+  as analytical geometry. Moreover, I cannot believe that ignorance of
+  analytical geometry would be a serious hindrance to a physician that
+  was otherwise well versed in quantitative thought. No special
+  advantage generally is observable in the graduates of the Austrian
+  gymnasiums, all of whom have studied analytical geometry. [Refers to
+  an assertion of Dubois-Reymond.]]
+
+  [Footnote 131: Compare M. Cantor, _Geschichte der Mathematik_,
+  Leipsic, 1880, Vol. I. p. 193.]
+
+  [Footnote 132: Compare Paulsen, _l. c._, pp. 607, 688.]
+
+  [Footnote 133: It is to be hoped that the Americans will jealously
+  guard their schools and universities against the influence of the
+  State.]
+
+
+
+
+APPENDIX.
+
+I.
+
+A CONTRIBUTION TO THE HISTORY OF ACOUSTICS.[134]
+
+
+While searching for papers by Amontons, several volumes of the Memoirs
+of the Paris Academy for the first years of the eighteenth century, fell
+into my hands. It is difficult to portray the delight which one
+experiences in running over the leaves of these volumes. One sees as an
+actual spectator almost the rise of the most important discoveries and
+witnesses the progress of many fields of knowledge from almost total
+ignorance to relatively perfect clearness.
+
+I propose to discuss here the fundamental researches of Sauveur in
+Acoustics. It is astonishing how extraordinarily near Sauveur was to the
+view which Helmholtz was the first to adopt in its full extent a hundred
+and fifty years later.
+
+The _Histoire de l'Académie_ for 1700, p. 131, tells us that Sauveur had
+succeeded in making music an object of scientific research, and that he
+had invested the new science with the name of "acoustics." On five
+successive pages a number of discoveries are recorded which are more
+fully discussed in the volume for the year following.
+
+Sauveur regards the _simplicity_ of the ratios obtaining between the
+rates of vibration of consonances as something universally known.[135]
+He is in hope, by further research, of determining the chief rules of
+musical composition and of fathoming the "metaphysics of the agreeable,"
+the main law of which he asserts to be the union of "simplicity with
+multiplicity." Precisely as Euler[136] did a number of years later, he
+regards a consonance as more perfect according as the ratio of its
+vibrational rates is expressed in smaller whole numbers, because the
+smaller these whole numbers are the oftener the vibrations of the two
+tones coincide, and hence the more readily they are apprehended. As the
+limit of consonance, he takes the ratio 5:6, although he does not
+conceal the fact that practice, sharpened attention, habit, taste, and
+even prejudice play collateral rôles in the matter, and that
+consequently the question is not a purely scientific one.
+
+Sauveur's ideas took their development from his having instituted at
+all points more exact quantitative investigations than his predecessors.
+He is first desirous of determining as the foundation of musical tuning
+a fixed note of one hundred vibrations which can be reproduced at any
+time; the fixing of the notes of musical instruments by the common
+tuning pipes then in use with rates of vibration unknown, appearing to
+him inadequate. According to Mersenne (_Harmonie Universelle_, 1636), a
+given cord seventeen feet long and weighted with eight pounds executes
+eight visible vibrations in a second. By diminishing its length then in
+a given proportion we obtain a proportionately augmented rate of
+vibration. But this procedure appears too uncertain to Sauveur, and he
+employs for his purpose the beats (_battemens_), which were known to the
+organ-makers of his day, and which he correctly explains as due to the
+alternate coincidence and non-coincidence of the same vibrational phases
+of differently pitched notes.[137] At every coincidence there is a
+swelling of the sound, and hence the number of beats per second will be
+equal to the difference of the rates of vibration. If we tune two of
+three organ-pipes to the remaining one in the ratio of the minor and
+major third, the mutual ratio of the rates of vibration of the first two
+will be as 24: 25, that is to say, for every 24 vibrations to the lower
+note there will be 25 to the higher, and one beat. If the two pipes give
+together four beats in a second, then the higher has the fixed tone of
+100 vibrations. The open pipe in question will consequently be five feet
+in length. We also determine by this procedure the absolute rates of
+vibration of all the other notes.
+
+It follows at once that a pipe eight times as long or 40 feet in length
+will yield a vibrational rate of 12½, which Sauveur ascribes to the
+lowest audible tone, and further also that a pipe 64 times as small will
+execute 6,400 vibrations, which Sauveur took for the highest audible
+limit. The author's delight at his successful enumeration of the
+"imperceptible vibrations" is unmistakably asserted here, and it is
+justified when we reflect that to-day even Sauveur's principle, slightly
+modified, constitutes the simplest and most delicate means we have for
+exactly determining rates of vibration. Far more important still,
+however, is a second observation which Sauveur made while studying
+beats, and to which we shall revert later.
+
+Strings whose lengths can be altered by movable bridges are much easier
+to handle than pipes in such investigations, and it was natural that
+Sauveur should soon resort to their use.
+
+One of his bridges accidentally not having been brought into full and
+hard contact with the string, and consequently only imperfectly impeding
+the vibrations, Sauveur discovered the harmonic overtones of the string,
+at first by the unaided ear, and concluded from this fact that the
+string was divided into aliquot parts. The string when plucked, and
+when the bridge stood at the third division for example, yielded the
+twelfth of its fundamental note. At the suggestion of some
+academician[138] probably, variously colored paper riders were placed at
+the nodes (_noeuds_) and ventral segments (_ventres_), and the division
+of the string due to the excitation of the overtones (_sons
+harmoniques_) belonging to its fundamental note (_son fondamental_) thus
+rendered visible. For the clumsy bridge the more convenient feather or
+brush was soon substituted. . While engaged in these investigations
+Sauveur also observed the sympathetic vibration of a string induced by
+the excitation of a second one in unison with it. He also discovered
+that the overtone of a string can respond to another string tuned to its
+note. He even went further and discovered that on exciting one string
+the overtone which it has in common with another, differently pitched
+string can be produced on that other; for example, on strings having for
+their vibrational ratio 3:4, the fourth of the lower and the third of
+the higher may be made to respond. It follows indisputably from this
+that the excited string yields overtones simultaneously with its
+fundamental tone. Previously to this Sauveur's attention had been drawn
+by other observers to the fact that the overtones of musical instruments
+can be picked out by attentive listening, particularly in the
+night.[139] He himself mentions the simultaneous sounding of the
+overtones and the fundamental tone.[140] That he did not give the proper
+consideration to this circumstance was, as will afterwards be seen,
+fatal to his theory.
+
+While studying beats Sauveur makes the remark that they are
+_displeasing_ to the ear. He held the beats were distinctly audible only
+when less than six occurred in a second. Larger numbers were not
+distinctly perceptible and gave rise accordingly to no disturbance. He
+then attempts to reduce the difference between consonance and dissonance
+to a question of beats. Let us hear his own words.[141]
+
+     "Beats are unpleasing to the ear because of the unevenness of the
+     sound, and it may be held with much plausibility that the reason
+     why octaves are so pleasing is that we never hear their beats.[142]
+
+     "In following out this idea, we find that the chords whose beats we
+     cannot hear are precisely those which the musicians call
+     consonances and that those whose beats are heard are the
+     dissonances, and that when a chord is a dissonance in one octave
+     and a consonance in another, it beats in the one and does not beat
+     in the other. Consequently it is called an imperfect consonance. It
+     is very easy by the principles of M. Sauveur, here established, to
+     ascertain what chords beat and in what octaves, above or below the
+     fixed note. If this hypothesis be correct, it will disclose the
+     true source of the rules of composition, hitherto unknown to
+     science, and given over almost entirely to judgment by the ear.
+     These sorts of natural judgment, marvellous though they may
+     sometimes appear, are not so but have very real causes, the
+     knowledge of which belongs to science, provided it can gain
+     possession thereof."[143]
+
+Sauveur thus correctly discerns in beats the cause of the disturbance
+of consonance, to which all disharmony is "probably" to be referred. It
+will be seen, however, that according to his view all distant intervals
+must necessarily be consonances and all near intervals dissonances. He
+also overlooks the absolute difference in point of principle between his
+old view, mentioned at the outset, and his new view, rather attempting
+to obliterate it.
+
+R. Smith[144] takes note of the theory of Sauveur and calls attention to
+the first of the above-mentioned defects. Being himself essentially
+involved in the old view of Sauveur, which is usually attributed to
+Euler, he yet approaches in his criticism a brief step nearer to the
+modern theory, as appears from the following passage.[145]
+
+     "The truth is, this gentleman confounds the distinction between
+     perfect and imperfect consonances, by comparing imperfect
+     consonances which beat because the succession of their short
+     cycles[146] is periodically confused and interrupted, with perfect
+     ones which cannot beat, because the succession of their short
+     cycles is never confused nor interrupted.
+
+     "The _fluttering roughness_ above mentioned is perceivable in all
+     other perfect consonances, in a smaller degree in proportion as
+     their cycles are shorter and simpler, and their pitch is higher;
+     and is of a _different kind_ from the _smoother beats_ and
+     undulations of _tempered consonances_; because we can alter the
+     rate of the latter by altering the temperament, but not of the
+     former, the consonance being perfect at a given pitch: And because
+     a judicious ear can often hear, at the same time, both the
+     flutterings and the beats of a tempered consonance; sufficiently
+     distinct from each other.
+
+     "For nothing gives greater offence to the hearer, though ignorant
+     of the cause of it, than those rapid, piercing beats of high and
+     loud sounds, which make imperfect consonances with one another. And
+     yet a few slow beats, like the slow undulations of a close shake
+     now and then introduced, are far from being disagreeable."
+
+Smith is accordingly clear that other "roughnesses" exist besides the
+beats which Sauveur considered, and if the investigations had been
+continued on the basis of Sauveur's idea, these additional roughnesses
+would have turned out to be the beats of the overtones, and the theory
+thus have attained the point of view of Helmholtz.
+
+Reviewing the differences between Sauveur's and Helmholtz's theories, we
+find the following:
+
+1. The theory according to which consonance depends on the frequent and
+regular coincidence of vibrations and their ease of enumeration, appears
+from the new point of view inadmissible. The simplicity of the ratios
+obtaining between the rates of vibration is indeed a _mathematical_
+characteristic of consonance as well as a _physical_ condition thereof,
+for the reason that the coincidence of the overtones as also their
+further physical and physiological consequences is connected with this
+fact. But no _physiological_ or _psychological_ explanation of
+consonance is given by this fact, for the simple reason that in the
+acoustic nerve-process nothing corresponding to the periodicity of the
+sonant stimulus is discoverable.
+
+2. In the recognition of beats as a disturbance of consonance, both
+theories agree. Sauveur's theory, however, does not take into account
+the fact that clangs, or musical sounds generally, are composite and
+that the disturbance in the consonances of distant intervals principally
+arise from the beats of the overtones. Furthermore, Sauveur was wrong in
+asserting that the number of beats must be less than six in a second in
+order to produce disturbances. Even Smith knows that very slow beats are
+not a cause of disturbance, and Helmholtz found a much higher number
+(33) for the maximum of disturbance. Finally, Sauveur did not consider
+that although the number of beats increases with the recession from
+unison, yet their _strength_ is diminished. On the basis of the
+principle of specific energies and of the laws of sympathetic vibration
+the new theory finds that two atmospheric motions of like amplitude but
+different periods, _a_ sin(_rt_) and _a_ sin[(_r_ + [rho])(_t_ +
+[tau])], cannot be communicated with the same amplitude to the same
+nervous end-organ. On the contrary, an end-organ that reacts best to the
+period _r_ responds more weakly to the period _r_ + [rho], the two
+amplitudes bearing to each other the proportion _a_: [phi]_a_. Here
+[phi] decreases when [rho] increases, and when [rho] = 0 it becomes
+equal to 1, so that only the portion of the stimulus [phi]_a_ is subject
+to beats, and the portion (1-[phi])_a_ continues smoothly onward without
+disturbance.
+
+If there is any moral to be drawn from the history of this theory, it is
+that considering how near Sauveur's errors were to the truth, it
+behooves us to exercise some caution also with regard to the new theory.
+And in reality there seems to be reason for doing so.
+
+The fact that a musician will never confound a more perfectly consonant
+chord on a poorly tuned piano with a less perfectly consonant chord on a
+well tuned piano, although the roughness in the two cases may be the
+same, is sufficient indication that the degree of roughness is not the
+only characteristic of a harmony. As the musician knows, even the
+harmonic beauties of a Beethoven sonata are not easily effaced on a
+poorly tuned piano; they scarcely suffer more than a Raphael
+drawing executed in rough unfinished strokes. The _positive
+physiologico-psychological_ characteristic which distinguishes one
+harmony from another is not given by the beats. Nor is this
+characteristic to be found in the fact that, for example, in sounding a
+major third the fifth partial tone of the lower note coincides with the
+fourth of the higher note. This characteristic comes into consideration
+only for the investigating and abstracting reason. If we should regard
+it also as characteristic of the sensation, we should lapse into a
+fundamental error which would be quite analogous to that cited in (1).
+
+The _positive physiological_ characteristics of the intervals would
+doubtless be speedily revealed if it were possible to conduct aperiodic,
+for example galvanic, stimuli to the single sound-sensing organs, in
+which case the beats would be totally eliminated. Unfortunately such an
+experiment can hardly be regarded as practicable. The employment of
+acoustic stimuli of short duration and consequently also free from
+beats, involves the additional difficulty of a pitch not precisely
+determinable.
+
+  FOOTNOTES:
+
+  [Footnote 134: This article, which appeared in the Proceedings of
+  the German Mathematical Society of Prague for the year 1892, is
+  printed as a supplement to the article on "The Causes of Harmony,"
+  at page 32.]
+
+  [Footnote 135: The present exposition is taken from the volumes for
+  1700 (published in 1703) and for 1701 (published in 1704), and
+  partly also from the _Histoire de l'Académie_ and partly from the
+  _Mémoires_. Sauveur's later works enter less into consideration
+  here.]
+
+  [Footnote 136: Euler, _Tentamen novae theoriae musicae_, Petropoli,
+  1739.]
+
+  [Footnote 137: In attempting to perform his experiment of beats
+  before the Academy, Sauveur was not quite successful. _Histoire de
+  l'Académie_, Année 1700, p. 136.]
+
+  [Footnote 138: _Histoire de l'Académie_, Année 1701, p. 134.]
+
+  [Footnote 139: _Ibid._, p. 298.]
+
+  [Footnote 140: _Histoire de l'Académie_, Année 1702, p. 91.]
+
+  [Footnote 141: From the _Histoire de l'Académie_, Année 1700, p.
+  139.]
+
+  [Footnote 142: Because all octaves in use in music offer too great
+  differences of rates of vibration.]
+
+  [Footnote 143: "Les battemens ne plaisent pas à l'Oreille, à cause
+  de l'inégalité du son, et l'on peut croire avec beaucoup d'apparence
+  que ce qui rend les Octaves si agréables, c'est qu'on n'y entend
+  jamais de battemens.
+
+  "En suivant cette idée, on trouve que les accords dont on ne peut
+  entendre les battemens, sont justement ceux que les Musiciens
+  traitent de Consonances, et que ceux dont les battemens se font
+  sentir, sont les Dissonances, et que quand un accord est Dissonance
+  dans une certaine octave et Consonance dans une autre, c'est qu'il
+  bat dans l'une, et qu'il ne bat pas dans l'autre. Aussi est il
+  traité de Consonance imparfaite. Il est fort aisé par les principes
+  de Mr. Sauveur qu'on a établis ici, de voir quels accords battent,
+  et dans quelles Octaves au-dessus on au-dessous du son fixe. Si
+  cette hypothèse est vraye, elle découvrira la véritable source des
+  Règles de la composition, inconnue jusqu'à présent à la Philosophie,
+  qui s'en remettait presque entièrement au jugement de l'Oreille. Ces
+  sortes de jugemens naturels, quelque bisarres qu'ils paroissent
+  quelquefois, ne le sont point, ils ont des causes très réelles, dont
+  la connaissance appartient à la Philosophie, pourvue qu'elle s'en
+  puisse mettre en possession."]
+
+  [Footnote 144: _Harmonics or the Philosophy of Musical Sounds_,
+  Cambridge, 1749. I saw this book only hastily in 1864 and drew
+  attention to it in a work published in 1866. I did not come into its
+  actual possession until three years ago and then only did I learn
+  its exact contents.]
+
+  [Footnote 145: _Harmonics_, pp. 118 and 243.]
+
+  [Footnote 146: "Short cycle" is the period in which the same phases
+  of the two co-operant tones are repeated.]
+
+
+
+
+II.
+
+REMARKS ON THE THEORY OF SPATIAL VISION.[147]
+
+
+According to Herbart, spatial vision rests on reproduction-series. In
+such an event, of course, and if the supposition is correct, the
+magnitudes of the residua with which the percepts or representations are
+coalesced (the helps to coalescence) are of cardinal influence.
+Furthermore, since the coalescences must first be fully perfected before
+they make their appearance, and since upon their appearance the
+inhibitory ratios are brought into play, ultimately, then, if we leave
+out of account the accidental order of time in which the percepts are
+given, everything in spatial vision depends on the oppositions and
+affinities, or, in brief, on the qualities of the percepts, which enter
+into series.
+
+Let us see how the theory stands with respect to the special facts
+involved.
+
+1. If intersecting series only, running anteriorly and posteriorly, are
+requisite for the production of spatial sensation, why are not analogues
+of them found in all the senses?
+
+2. Why do we measure differently colored objects and variegated objects
+with one and the same spatial measure? How do we recognise differently
+colored objects as the same in size? Where do we get our measure of
+space from and what is it?
+
+3. Why is it that differently colored figures of the same form reproduce
+one another and are recognised as the same?
+
+Here are difficulties enough. Herbart is unable to solve them by his
+theory. The unprejudiced student sees at once that his "inhibition by
+reason of form" and "preference by reason of form" are absolutely
+impossible. Think of Herbart's example of the red and black letters.
+
+The "help to coalescence" is a passport, so to speak, made out to the
+name and person of the percept. A percept which is coalesced with
+another cannot reproduce all others qualitatively different from it for
+the simple reason that the latter are in like manner coalesced with one
+another. Two qualitatively different series certainly do not reproduce
+themselves because they present the same order of degree of coalescence.
+
+If it is certain that only things simultaneous and things which are
+alike are reproduced, a basic principle of Herbart's psychology which
+even the most absolute empiricists will not deny, nothing remains but to
+modify the theory of spatial perception or to invent in its place a new
+principle in the manner indicated, a step which hardly any one would
+seriously undertake. The new principle could not fail to throw all
+psychology into the most dreadful confusion.
+
+As to the modification which is needed there can be hardly any doubt as
+to how in the face of the facts and conformably to Herbart's own
+principles it is to be carried out. If two differently colored figures
+of equal size reproduce each other and are recognised as equal, the
+result can be due to nothing but to the existence in both series of
+presentations of a presentation or percept which is qualitatively _the
+same_. The colors are different. Consequently, like or equal percepts
+must be connected with the colors which are yet independent of the
+colors. We have not to look long for them, for they are the like effects
+of the muscular feelings of the eye when confronted by the two figures.
+We might say we reach the vision of space by the registering of
+light-sensations in a schedule of graduated muscle-sensations.[148]
+
+A few considerations will show the likelihood of the rôle of the
+muscle-sensations. The muscular apparatus of _one_ eye is unsymmetrical.
+The two eyes together form a system which is vertical in symmetry. This
+already explains much.
+
+1. The _position_ of a figure influences its view. According to the
+position in which objects are viewed different muscle-sensations come
+into play and the impression is altered. To recognise inverted letters
+as such long experience is required. The best proof of this are the
+letters d, b, p, q, which are represented by the same figure in
+different positions and yet are always distinguished as different.[149]
+
+2. It will not escape the attentive observer that for the same reasons
+and even with the same figure and in the same position the fixation
+point is also decisive. The figure seems to change _during_ the act of
+vision. For example, an eight-pointed star constructed by successively
+joining in a regular octagon the first corner with the fourth, the
+fourth with the seventh, etc., skipping in every case two corners,
+assumes alternately, according to where we suffer the centre of vision
+to rest, a predominantly architectonic or a freer and more open
+character. Vertical and horizontal lines are always differently
+apprehended from what oblique lines are.
+
+[Illustration: Fig. 58.]
+
+3. The reason why we prefer vertical symmetry and regard it as something
+special in its kind, whereas we do not recognise horizontal symmetry at
+all immediately, is due to the vertical symmetry of the muscular
+apparatus of the eye. The left-hand side _a_ of the accompanying
+vertically-symmetrical figure induces in the left eye the same muscular
+feelings as the right-hand side _b_ does in the right eye. The pleasing
+effect of symmetry has its cause primarily in the repetition of muscular
+feelings. That a repetition actually occurs here, sometimes sufficiently
+marked in character as to lead to the confounding of objects, is proved
+apart from the theory by the fact which is familiar to every one _quem
+dii oderunt_ that children frequently reverse figures from the right to
+the left, but never from above downwards; for example, write [epsilon]
+instead of 3 until they finally come to notice the slight difference.
+Figure 50 shows how pleasing the repetition of muscular feelings may be.
+As will be readily understood, vertical and horizontal lines exhibit
+relations similar to symmetrical figures which are immediately disturbed
+when oblique positions are chosen for the lines. Compare what Helmholtz
+says regarding the repetition and coincidence of partial tones.
+
+[Illustration: Fig. 59.]
+
+I may be permitted to add a general remark. It is a quite universal
+phenomenon in psychology that certain qualitatively quite different
+series of percepts mutually awaken and reproduce one another and in a
+certain aspect produce the appearance of sameness or similarity. We say
+of such series that they are of like or of similar form, naming their
+abstracted likeness _form_.
+
+     1. Of spatial figures we have already spoken.
+
+     2. We call two melodies like melodies when they present the same
+     succession of pitch-ratios; the absolute pitch (or key) may be as
+     different as can be. We can so select the melodies that not even
+     two partial tones of the notes in each are common. Yet we recognise
+     the melodies as alike. And, what is more, we notice the form of the
+     melody more readily and recognise it again more easily than the key
+     (the absolute pitch) in which it was played.
+
+     3. We recognise in two different melodies the same rhythm no matter
+     how different the melodies may be otherwise. We know and recognise
+     the rhythm more easily even than the absolute duration (the tempo).
+
+These examples will suffice. In all these and in all similar cases the
+recognition and likeness cannot depend upon the qualities of the
+percepts, for these are different. On the other hand recognition,
+conformably to the principles of psychology, is possible only with
+percepts which are the same in quality. Consequently there is no other
+escape than to imagine the qualitatively unlike percepts of the two
+series as necessarily connected with other percepts which are
+qualitatively alike.
+
+Since in differently colored figures of like form, like muscular
+feelings are necessarily induced if the figures are recognised as alike,
+so there must necessarily lie at the basis of all forms also, and we
+might even say at the basis of all abstractions, percepts of a peculiar
+quality. And this holds true for space and form as well as for time,
+rhythm, pitch, the form of melodies, intensity, etc. But whence is
+psychology to derive all these qualities? Have no fear, they will all be
+found, as were the sensations of muscles for the theory of space. The
+organism is at present still rich enough to meet all the requirements of
+psychology in this direction, and it is even time to give serious ear to
+the question of "corporeal resonance" which psychology so loves to dwell
+on.
+
+Different psychical qualities appear to bear a very intimate mutual
+relation to one another. Special research on the subject, as well also
+as the demonstration that this remark may be generally employed in
+physics, will follow later.[150]
+
+  FOOTNOTES:
+
+  [Footnote 147: This article, designed to illustrate historically
+  that on Symmetry, at page 89, first appeared in Fichte's
+  _Zeitschrift für Philosophie_, for 1865.]
+
+  [Footnote 148: Comp. Cornelius, _Ueber das Sehen_; Wundt, _Theorie
+  der Sinneswahrnehmung_.]
+
+  [Footnote 149: Comp. Mach, _Ueber das Sehen von Lagen and Winkeln_.
+  _Sitzungsb. der Wiener Akademie_, 1861.]
+
+  [Footnote 150: Comp. Mach, _Zur Theorie des Gehörorgans_.
+  _Sitsungsber, der Wiener Akad._, 1863.--_Ueber einige Erscheinungen
+  der physiolog. Akustik._ _Ibid._, 1864.]
+
+
+
+
+INDEX.
+
+
+  Absolute, temperature, 162;
+    time, 204;
+    forecasts, have no signification in science, 206.
+
+  Abstract, meaning of the term, 240.
+
+  Abstraction, 180, 200, 208, 231.
+
+  Acceleration, organ for forward, 299 et seq.
+
+  Accelerations, 204, 216, footnote, 225-226, 253.
+
+  Accident, logical and historical, in science, 160, 168, 170, 213;
+    in inventions and discoveries, 262 et seq.
+
+  Accord, the pure triple, 46.
+
+  Accumulators, electrical, 125 et seq.;
+    132, footnote.
+
+  Acoustic color, 36.
+
+  Acoustics, Sauveur on, 375 et seq.
+
+  Action and reaction, importance of the principle of, 191.
+
+  Adaptation, in organic and inorganic matter, 216, 229;
+    in scientific thought, 214-235.
+
+  Æsthetics, computation as a principle of, 34;
+    researches in, 89, footnote;
+    repetition, a principle of, 91.
+
+  Africa, 186, 234, 237.
+
+  Agreeable effects, due to repetition of sensations, 92, 97 et seq.
+
+  Agriculture, transition to, 265.
+
+  Air-gun, 135.
+
+  Alcohol and water, mixture of oil and, in Plateau's experiments, 4.
+
+  Algebra, economy of, 196.
+
+  Alien thoughts in science, 196.
+
+  All, the, 88.
+
+  Amontons, 174, 346.
+
+  Ampère, the word, 314.
+
+  Ampère's swimmer, 207.
+
+  Analogies, mechanical, 157, 160;
+    generally, 236-258.
+
+  Analogy, defined, 250.
+
+  Analysis, 188.
+
+  Analytical geometry, not necessary to physicians, 370, footnote.
+
+  Anatomic structures, transparent stereoscopic views of, 74.
+
+  Anatomy, character of research in, 255.
+
+  Andrieu, Jules, 49, footnote.
+
+  Animals, the psychical activity of, 190, 231;
+    the language of, 238;
+    their capacity for experience, 266 et seq.
+
+  Animism, 186, 187, 243, 254.
+
+  Anisotropic optical fields, 227.
+
+  Apparatus for producing movements of rotation, 287 et seq.
+
+  Arabesque, an inverted, 95.
+
+  Arabian Nights, 219.
+
+  Arago, 270.
+
+  Aral, the Sea of, 239.
+
+  Archæopteryx, 257.
+
+  Archimedes, 4, 237.
+
+  Arcimboldo, Giuseppe, 36.
+
+  Area, principle of least superficial, 10 et seq.
+
+  Ares, the bellowing of the wounded, 272.
+
+  Aristotelians, 283.
+
+  Aristotle, 348, 296.
+
+  Art, development of, 28 et seq.
+
+  Artillery, practical, 334-335.
+
+  Artistic value of scientific descriptions, 254.
+
+  Arts, practical, 108.
+
+  Ascent, heights of, 143-151.
+
+  Asia, 234.
+
+  Assyrians, the art of, 79.
+
+  Astronomer, measures celestial by terrestrial distances, 136.
+
+  Astronomy, antecedent to psychology, 90;
+    rigidity of its truths, 221.
+
+  Atomic theories, 104.
+
+  Atoms, 207.
+
+  Attention, the rôle of, in sensuous perception, 35 et seq.
+
+  Attraction, generally, 226;
+    of liquid particles, 13-14;
+    in electricity, 109 et seq.
+
+  Aubert, 298.
+
+  Audition. See _Ear_.
+
+  Austrian gymnasiums, 370, footnote.
+
+  Axioms, instinctive knowledge, 190.
+
+
+  Babbage, on the economy of machinery, 196.
+
+  Bach, 20.
+
+  Backwards, prophesying, 253.
+
+  Bacon, Lord, 48, 280.
+
+  Baer, C. E. von, 235.
+
+  Balance, electrical, 127, footnote;
+    torsion, 109, 168.
+
+  Balloon, a hydrogen, 199.
+
+  Barbarism and civilisation, 335 et seq.
+
+  Bass-clef, 101.
+
+  Bass, fundamental, 44.
+
+  Beats, 40-45, 377 et seq.
+
+  Beautiful, our notions of, variable, 99.
+
+  Beauty, objects of, in nature, 91.
+
+  Becker, J. K., 364, 369.
+
+  Beethoven, 39, 44.
+
+  Beginnings of science, 189, 191.
+
+  Belvedere Gallery at Vienna, 36.
+
+  Bernoulli, Daniel, on the conservation of living force, 149;
+    on the vibrations of strings, 249.
+
+  Bernoulli, James, on the centre of oscillation, 149.
+
+  Bernoulli, John, on the conservation of living force, 149;
+    on the principle of virtual velocities, 151.
+
+  Bible, parallel passages from, for language study, 356.
+
+  Binocular vision, 66 et seq.
+
+  Black, his theory of caloric, 138, 162;
+    on quantity of heat, 166, 174;
+    on latent heat, 167, 178;
+    researches in heat generally, 244.
+
+  Blind cat, 303.
+
+  Bodies, heavy, seek their places, 224 et seq.;
+    rotating, 285.
+
+  Body, a mental symbol for groups of sensations, 200-203;
+    the human, our knowledge of, 90.
+
+  Boltzmann, 236.
+
+  Booth, Mr., 77.
+
+  Borelli, 217.
+
+  Boulder, a granite, 233.
+
+  Bow-wave of ships and moving projectiles, 323 et seq.
+
+  Boys, 317.
+
+  Bradley, 273.
+
+  Brahman, the, 63.
+
+  Brain, localisation of functions in, 210.
+
+  Breuer, 272, 282 et seq., 293, 298, 300, 301, 303, 306.
+
+  Brewster, his stereoscope, 73.
+
+  Bridge, invention of the, 264, 268.
+
+  British Association, 108.
+
+  Brooklyn Bridge, 75, footnote.
+
+  Brown, Crum, 293, 301.
+
+  Building, our concepts directions for, 253;
+    facts the result of, 253;
+    science compared to, 257.
+
+  Building-stones, metrical units are, 253.
+
+  Busch, 328.
+
+  Business of a merchant, science compared to the, 16.
+
+  Butterfly, a, 22.
+
+
+  Calculating machines, their economical character, 196.
+
+  Caloric, theory of, stood in the way of scientific advancement, 138, 167.
+
+  Calypso, the island of, 351.
+
+  Canterbury, Archbishop of, 39.
+
+  Cantor, M., 361, footnote.
+
+  Capacity, electrical, 116 et seq., 123;
+    thermal, 123;
+    specific inductive, 117.
+
+  Capulets and Montagues, 87.
+
+  Cards, difficult games of, 357.
+
+  Carnot, S., excludes perpetual motion in heat, 156, 162;
+    his mechanical view of physics, 156;
+    on thermodynamics, 160 et seq.;
+    his principle, 162;
+    also, 191.
+
+  Carus, Dr. Paul, 265, footnote.
+
+  Casselli's telegraph, 26.
+
+  Cassini, 51.
+
+  Cauchy, character of the intellectual activity of a, 195.
+
+  Causal insight, awakened by science, 357.
+
+  Causality, 157-159, 190, 198 et seq., 221 et seq., 237, 253, 254.
+
+  Cause and effect, 198 et seq. See also _Causality_.
+
+  Centimetre-gramme-second system, 111.
+
+  Centre of gravity, must lie as low as possible for equilibrium to
+  subsist, 15;
+    Torricelli's principle of, 150 et seq.
+
+  Centre of oscillation, 149.
+
+  Change, method of, in science, 230.
+
+  Changeable character of bodies, 202.
+
+  Changes, physical, how they occur, 205.
+
+  Character, a Universal Real, 192.
+
+  Character, like the forms of liquids, 3;
+    persons of, 24.
+
+  Charles the Fifth, 369.
+
+  Chemical, elements, 202;
+    symbols, 192;
+    current, 118.
+
+  Chemistry, character of research in, 255;
+    the method of thermodynamics in, 257.
+
+  Child, a, modes of thought of, 223;
+    looking into a moat, 208.
+
+  Child of the forest, his interpretation of new events, 218-219.
+
+  Childish questions, 199-200.
+
+  Children, the drawings of, 201-202.
+
+  Chinese language, economy of, 192;
+    study of, 354.
+
+  Chinese philosopher, an old, 186.
+
+  Chinese, speak with unwillingness of politics, 374;
+    the art of, 79-80.
+
+  Chosen, many are called but few are, 65.
+
+  Christ, saying of, 65.
+
+  Christianity, Latin introduced with, 311.
+
+  Christians and Jews, monotheism of the, 187.
+
+  Church and State, 88.
+
+  Cicero, 318.
+
+  Circe, 372.
+
+  Circle, the figure of least area with given periphery, 12.
+
+  Circular polarisation, 242.
+
+  Civilisation and barbarism, 335 et seq.
+
+  Civilisation, some phenomena of, explained by binocular vision, 74.
+
+  Civilised man, his modes of conception and interpretation, 219.
+
+  Clapeyron, 162.
+
+  Class-characters of animals, 255.
+
+  Classical, culture, the good and bad effects of, 347;
+    scholars, not the only educated people, 345.
+
+  Classics, on instruction in, 338-374;
+    the scientific, 368.
+
+  Classification in science, 255.
+
+  Clausius, on thermodynamics, 165;
+    on reversible cycles, 176.
+
+  Claviatur, Mach's, 42-43.
+
+  Club-law, 335.
+
+  Cochlea, the, a species of piano-forte, 19.
+
+  Cockchafer, 86.
+
+  Coefficient of self-induction, 250, 252.
+
+  Colophonium, solution of, 7.
+
+  Color, acoustic, 36.
+
+  Color-sensation, 210.
+
+  Color-signs, their economy, 192.
+
+  Colors, origin of the names of, 239.
+
+  Column, body moving behind a, 202.
+
+  Communication, its functions, import and fruits, 197, 238 et seq.;
+    by language, 237;
+    high importance of, 191 et seq.
+
+  Comparative physics, 239.
+
+  Comparison in science, 231, 238 et seq.
+
+  Computation, a principle of æsthetics, 34.
+
+  Concepts, abstract, defined, 250-252;
+    metrical, in electricity, 107 et seq.
+
+  Conceptual, meaning of the term, 240.
+
+  Conceptual thought, 192.
+
+  Concha, 18.
+
+  Condensers, electrical, 125 et seq. 132, footnote.
+
+  Conductors and non-conductors. See _Electrical_, etc.
+
+  Conformity in the deportment of the energies, 171-175.
+
+  Confusion of objects, cause of, 95.
+
+  Conic sections, 257.
+
+  Conical refraction, 29, 242.
+
+  Conservation of energy, 137 et seq. See _Energy_.
+
+  Conservation of weight or mass, 203.
+
+  Consonance, connexion of the simple natural numbers with, 33;
+    Euclid's definition of, 33;
+    explanation of, 42;
+    scientific definition of, 44;
+    and dissonance reduced to beats, 376, 370, 383.
+
+  Consonant intervals, 43.
+
+  Constancy of matter, 203.
+
+  Constant, the dielectric, 117.
+
+  Constants, the natural, 193.
+
+  Continuum of facts, 256 et seq.
+
+  Cornelius, 388, footnote.
+
+  Corti, the Marchese, his discovery of minute rods in the labyrinth of
+  the ear, 19.
+
+  Coulomb, his electrical researches, 108, 109, 113;
+    his notion of quantity of electricity, 173;
+    his torsion-balance, 168.
+
+  Crew, Prof. Henry, 317, footnote.
+
+  Criticism, Socrates the father of scientific, 1, 16.
+
+  _Critique of Pure Reason_, Kant's, 188.
+
+  Crucible, derivation of the word, 49, footnote.
+
+  Crustacea, auditory filaments of, 29, 272, 302.
+
+  Cube of oil, 5.
+
+  Culture, ancient and modern, 344.
+
+  Currents, chemical, 118;
+    electrical, 118;
+    galvanic, 132;
+    measurement of electrical, 135-136;
+    of heat, 244, 249-250;
+    strength of, 250.
+
+  Curtius, 356.
+
+  Curved lines, their asymmetry, 98.
+
+  Curves, how their laws are investigated, 206.
+
+  Cycles, reversible, Clausius on, 176.
+
+  Cyclical processes, closed, 175.
+
+  Cyclops, 67.
+
+  Cyclostat, 298.
+
+  Cylinder, of oil, 6;
+    mass of gas enclosed in a, 179.
+
+
+  D'Alembert, on the causes of harmony, 34;
+    his principle, 142, 149, 154;
+    also 234, 279.
+
+  Danish schools, 338, footnote.
+
+  Darwin, his study of organic nature, 215 et seq.;
+    his methods of research, 216.
+
+  Deaf and dumb, not subject to giddiness, 299.
+
+  Deaf person, with a piano, analyses sounds, 27.
+
+  Death and life, 186.
+
+  Definition, compendious, 197.
+
+  Deiters, 19.
+
+  Delage, 298, 301, 302.
+
+  Democritus, his mechanical conception of the world, 155, 187.
+
+  Demonstration, character of, 362.
+
+  Deportment of the energies, conformity in the, 171-175.
+
+  Derivation, laws only methods of, 256.
+
+  Descent, Galileo's laws of, 193;
+    generally, 143 et seq., 204, 215.
+
+  Description, 108, 191, 236, 237;
+    a condition of scientific knowledge, 193;
+    direct and indirect, 240;
+    in physics, 197, 199.
+
+  Descriptive sciences, their resemblance to the abstract, 248.
+
+  Determinants, 195.
+
+  Diderot, 234.
+
+  Dielectric constant, the, 117.
+
+  Difference-engine, the, 196.
+
+  Differential coefficients, their relation to symmetry, 98.
+
+  Differential laws, 204.
+
+  Differential method, for detecting optical imperfections, 317.
+
+  Diffraction, 91, 194.
+
+  Diffusion, Fick's theory of, 249.
+
+  Discharge of Leyden jars, 114 et seq.
+
+  Discoveries, the gist of, 270, 375.
+
+  Discovery and invention, distinction between, 269.
+
+  Dissonance, explanation of, 42;
+    definition of, 33, 44. See _Consonance_.
+
+  Distances, estimation of, by the eye, 68 et seq.
+
+  Dogs, like tuning-forks, 23;
+    their mentality, 190.
+
+  Domenech, Abbé, 92.
+
+  Dramatic element in science, 243.
+
+  Drop of water, on a greased plate, 8;
+    on the end of a stick, 8;
+    in free descent, 8.
+
+  Dubois, 218.
+
+  Dubois-Reymond, 370, footnote.
+
+  Dufay, 271.
+
+  Dynamics, foundations of, 153 et seq.
+
+
+  Ear, researches in the theory of, 17 et seq.;
+    diagram of, 18;
+    its analysis of sounds, 20 et seq.;
+    a puzzle-lock, 28;
+    reflected in a mirror, 93;
+    no symmetry in its sensation, 103.
+
+  Earth, its oblateness not due to its original fluid condition, 2;
+    rotation of, 204;
+    internal disturbances of, 285.
+
+  Economical, nature of physical inquiry, 186;
+    procedure of the human mind, 186;
+    order of physics, 197;
+    schematism of science, 206;
+    tools of science, 207;
+    coefficient of dynamos, 133.
+
+  Economy, of the actions of nature, 15;
+    the purpose of science, 16;
+    of language, 191 et seq.;
+    of the industrial arts, 192;
+    of mathematics, 195-196;
+    of machinery, 196;
+    of self-preservation, our first knowledge derived from, 197;
+    generally, 186 et seq., 269.
+
+  Education, higher, 86;
+    liberal, 341 et seq., 371.
+
+  Efflux, liquid, 150.
+
+  Ego, its nature, 234-235.
+
+  Egypt, 234.
+
+  Egyptians, art of, 78 et seq., 201.
+
+  Eighteenth century, the scientific achievements of, 187, 188.
+
+  Eleatics, on motion, 158.
+
+  Electrical, attraction and repulsion, 109 et seq., 168;
+    capacity, 116 et seq.;
+    force, 110, 119, 168;
+    spark, 117, 127, 132, 133, 190;
+    energy, measurement of, 128 et seq., 169;
+    currents, conceptions of, 118, 132, 135-136, 226-227, 249, 250;
+    fluids, 112 et seq., 228;
+    pendulums, 110;
+    levels, 173;
+    potential, 121 et seq.;
+    quantity, 111, 118, 119.
+
+  Electricity, as a substance and as a motion, 170;
+    difference between the conceptions of heat and, 168 et seq.,
+    rôle of work in, 120 et seq.;
+    galvanic, 134.
+    See _Electrical_.
+
+  Electrometer, W. Thomson's absolute, 127, footnote.
+
+  Electrometers, 122, 127.
+
+  Electrostatic unit, 111.
+
+  Electrostatics, concepts of, 107 et seq.
+
+  Elements, interdependence of the sensuous, 179;
+    of bodies, 202;
+    of phenomena, equations between, 205;
+    of sensations, 200;
+    used instead of sensations, 208-209.
+
+  Ellipse, equation of, 205;
+    the word, 342.
+
+  Embryology, possible future state of, 257.
+
+  Energies, conformity in the deportment of, 171-175;
+    differences of, 175.
+
+  Energy, a metrical notion, 178;
+    conservation of, 137 et seq.;
+    defined, 139;
+    metaphysical establishment of the doctrine of, 183;
+    kinetic, 177;
+    potential, 128 et seq.;
+    substantial conception of, 164, 185, 244 et seq.;
+    conservation of, in electrical phenomena, 131 et seq.;
+    limits of principle of, 175;
+    principle of, in physics, 160-166;
+    sources of principle of, 179, 181;
+    thermal, 177;
+    Thomas Young on, 173.
+
+  Energy-value of heat, 178, footnote.
+
+  Enlightenment, the, 188.
+
+  Entropy, a metrical notion, 178.
+
+  Environment, stability of our, 206.
+
+  Equations for obtaining facts, 180;
+    between the elements of phenomena, 205.
+
+  Equilibrium, conditions of, in simple machines, 151;
+    figures of liquid, 4 et seq.;
+    general condition of, 15;
+    in the State, 15.
+
+  Etymology, the word, misused for entomology, 316.
+
+  Euclid, on consonance and dissonance, 33;
+    his geometry, 364.
+
+  Euler, on the causes of harmony, 34;
+    impression of the mathematical processes on, 196;
+    on the vibrations of strings, 249, 285, 376.
+
+  Euler and Hermann's principle, 149.
+
+  Euthyphron, questioned by Socrates, 1.
+
+  Evolute, the word, 342.
+
+  Evolution, theory of, as applied to ideas, 216 et seq.
+
+  Ewald, 298, 304.
+
+  Excluded perpetual motion, logical root of the principle of, 182.
+
+  Exner, S., 302, 305.
+
+  Experience, communication of, 191;
+    our ready, 199;
+    the principle of energy derived from, 179;
+    the wellspring of all knowledge of nature, 181;
+    incongruence between thought and, 206.
+
+  Experimental research, function of, 181.
+
+  Explanation, nature of, 194, 237, 362.
+
+  Eye, cannot analyse colors, 20;
+    researches in the theory of the, 18 et seq.;
+    loss of, as affecting vision, 98.
+
+  Eyes, purpose of, 66 et seq.;
+    their structure symmetrical not identical, 96.
+
+
+  Face, human, inverted, 95.
+
+  Facts and ideas, necessary to science, 231.
+
+  Facts, description of, 108;
+    agreement of, 180;
+    relations of, 180;
+    how represented, 206;
+    reflected in imagination, 220 et seq.;
+    the result of constructions, 253;
+    a continuum of, 256 et seq.;
+    equations for obtaining, 180.
+
+  Falling bodies, 204, 215;
+    Galileo on the law of, 143 et seq., 284.
+
+  Falling, cats, 303, footnote.
+
+  Falstaff, 309.
+
+  Familiar intermediate links of thought, 198.
+
+  Faraday, 191, 217, 237;
+    his conception of electricity, 114, 271.
+
+  Fechner, theory of Corti's fibres, 19 et seq.
+
+  Feeling, cannot be explained by motions of atoms, 208 et seq.
+
+  Fetishism, 186, 243, 254;
+    in our physical concepts, 187.
+
+  Fibres of Corti, 17 et seq.
+
+  Fick, his theory of diffusion, 249.
+
+  Figures, symmetry of, 92 et seq.
+
+  Figures of liquid equilibrium, 4 et seq.
+
+  Fire, use of, 264.
+
+  Fishes, 306.
+
+  Fixed note, determining of a, 377.
+
+  Fizeau, his determination of the velocity of light, 55 et seq.
+
+  Flats, reversed into sharps, 101.
+
+  Flouren's experiments, 272, 290.
+
+  Flower-girl, the baskets of a, 95.
+
+  Fluids, electrical, 112 et seq.
+
+  Force, electric, 110, 119, 168;
+    unit of 111;
+    living, 137, 149, 184;
+    generally 253.
+    See the related headings.
+
+  Forces, will compared to, 254.
+
+  Foreseeing events, 220 et seq.
+
+  Formal conceptions, rôle of, 183.
+
+  Formal need of a clear view of facts, 183, 246;
+    how far it corresponds to nature, 184.
+
+  Formative forces of liquids, 4.
+
+  Forms of liquids, 3 et seq.
+
+  Forward movement, sensation of, 300.
+
+  Forwards, prophesying, 253.
+
+  Foucault, 57, 70, 296.
+
+  Foucault and Toepler, method of, for detecting optical faults, 313
+  et seq., 320.
+
+  Foundation of scientific thought, primitive acts of knowledge, the, 190.
+
+  Fourier, on processes of heat, 249, 278.
+
+  Fox, a, 234.
+
+  Franklin's pane, 116.
+
+  Frary, 338, footnote.
+
+  Fraunhofer, 271.
+
+  Freezing-point, lowered by pressure, 162.
+
+  Fresnel, 271.
+
+  Fritsch, 321.
+
+  Frogs, larvæ of, not subject to vertigo, 298.
+
+  Froude, 333.
+
+  Frustra, misuse of the word, 345.
+
+  Future, science of the, 213.
+
+
+  Galileo, on the motion of pendulums, 21;
+    his attempted measurement of the velocity of light, 50 et seq.;
+    his exclusion of a perpetual motion, 143;
+    on velocities acquired in free descent, 143-147;
+    on the law of inertia, 146-147;
+    on virtual velocities, 150;
+    on work, 172;
+    his laws of descent, 193;
+    on falling bodies, 225;
+    great results of his study of nature, 214 et seq.;
+    his rude scientific implements, 215;
+    selections from his works for use in instruction, 368;
+    also 105, 182, 187, 237, 272, 274, 283.
+
+  Galle, observes the planet Neptune, 29.
+
+  Galvanic, electricity, 134;
+    current, 132;
+    dizziness, 291;
+    vertigo, 298.
+
+  Galvanoscope, 135.
+
+  Galvanotropism, 291.
+
+  Garda, Lake, 239.
+
+  Gas, the word, 264;
+    mass of, enclosed in a cylinder, 179.
+
+  Gases, tensions of, for scales of temperature, 174.
+
+  Gauss, on the foundations of dynamics, 154;
+    his principle, 154;
+    also, 108, 274.
+
+  Genius, 279, 280.
+
+  Geography, comparison in, 239.
+
+  Geometers, in our eyes, 72.
+
+  Geotropism, 289.
+
+  German schools and gymnasiums, 372, 373, 338, footnote.
+
+  Ghosts, photographic, 73.
+
+  Glass, invisible in a mixture of the same refrangibility, 312;
+    powdered, visible in a mixture of the same refrangibility, 312.
+
+  Glove, in a mirror, 93.
+
+  Goethe, quotations from, 9, 31, 49, 88;
+    on the cause of harmony, 35.
+
+  Goltz, 282, 291.
+
+  Gossot, 332.
+
+  Gothic cathedral, 94.
+
+  Gravitation, discovery of, 225 et seq.
+
+  Gravity, how to get rid of the effects of, in liquids, 4;
+    also 228.
+
+  Gray, Elisha, his telautograph, 26.
+
+  Greased plate, drop of water on a, 8.
+
+  Great minds, idiosyncrasies of, 247.
+
+  Greek language, scientific terms derivedfrom, 342-343;
+    common words derived from, 343, footnote;
+    still necessary for some professions, 346;
+    its literary wealth, 347-348;
+    narrowness and one-sidedness of its literature, 348-349;
+    its excessive study useless, 349-350;
+    its study sharpens the judgment, 357-358;
+    a knowledge of it not necessary to a liberal education, 371.
+
+  Greeks, their provinciality and narrow-mindedness, 349;
+    now only objects of historical research, 350.
+
+  Griesinger, 184.
+
+  Grimaldi, 270.
+
+  Grimm, 344, footnote.
+
+  Grunting fishes, 306.
+
+
+  Habitudes of thought, 199, 224, 227, 232.
+
+  Haeckel, 222, 235.
+
+  Hamilton, deduction of the conical refraction of light, 29.
+
+  Hankel, 364.
+
+  Harmonics, 38, 40.
+
+  Harmony, on the causes of, 32 et seq.;
+    laws of the theory of, explained, 30;
+    the investigation of the ancients concerning, 32;
+    generally, 103.
+    See _Consonance_.
+
+  Harris, electrical balance of, 127, footnote.
+
+  Hartwich, Judge, 343, 353, footnote.
+
+  Hat, a high silk, 24.
+
+  Hats, ladies', development of, 64.
+
+  Head-wave of a projectile, 323 et seq.
+
+  Hearing and orientation, relation between, 304 et seq.
+
+  Heat, a material substance, 177;
+    difference between the conceptions of electricity and, 168 et seq.;
+    substantial conception of, 243 et seq.;
+    Carnot on, 156, 160 et seq.;
+    Fourier on the conduction of, 249;
+    not necessarily a motion, 167, 170, 171;
+    mechanical equivalent of, 164, 167;
+    of liquefaction, 178;
+    quantity of, 166;
+    latent, 167, 178, 244;
+    specific, 166, 244;
+    the conceptions of, 160-171;
+    machine, 160;
+    a measure of electrical energy, 133 et seq.;
+    mechanical theory of, 133;
+    where does it come from? 200.
+
+  Heavy bodies, sinking of, 222.
+
+  Heights of ascent, 143-151.
+
+  Helm, 172.
+
+  Helmholtz, applies the principle of energy to electricity, 184;
+    his telestereoscope, 84;
+    his theory of Corti's fibres, 19 et seq.;
+    on harmony, 35, 99;
+    on the conservation of energy, 165, 247;
+    his method of thought, 247;
+    also 138, 305, 307, 375, 383.
+
+  Hensen, V., on the auditory function of the filaments of Crustacea, 29,
+  302.
+
+  Herbart, 386 et seq.
+
+  Herbartians, on motion, 158.
+
+  Herculaneum, art in, 80.
+
+  Heredity, in organic and inorganic matter, 216, footnote.
+
+  Hering, on development, 222;
+    on vision, 210.
+
+  Hermann, E., on the economy of the industrial arts, 192.
+
+  Hermann, L., 291.
+
+  Herodotus, 26, 234, 347, 350.
+
+  Hertz, his waves, 242;
+    his use of the phrase "prophesy," 253.
+
+  Herzen, 361, footnote.
+
+  Hindu mathematicians, their beautiful problems, 30.
+
+  Holtz's electric machine, 132.
+
+  Horse, 63.
+
+  Household, physics compared to a well-kept, 197.
+
+  Housekeeping in science and civil life, 198.
+
+  Hudson, the, 94.
+
+  Human beings, puzzle-locks, 27.
+
+  Human body, our knowledge of, 90.
+
+  Human mind, must proceed economically, 186.
+
+  Humanity, likened to a polyp-plant, 235.
+
+  Huygens, his mechanical view of physics, 155;
+    on the nature of light and heat, 155-156;
+    his principle of the heights of ascent, 149;
+    on the law of inertia and the motion of a compound pendulum, 147-149;
+    on the impossible perpetual motion, 147-148;
+    on work, 173;
+    selections from his works for use in instruction, 368;
+    his view of light, 227-228, 262.
+
+  Huygens, optical method for detecting imperfections in optical glasses
+  313.
+
+  Hydrogen balloon, 199.
+
+  Hydrostatics, Stevinus's principle of, 141.
+
+  Hypotheses, their rôle in explanation, 228 et seq.
+
+
+  Ichthyornis, 257.
+
+  Ichthyosaurus, 63.
+
+  Idea? what is a theoretical, 241.
+
+  Idealism, 209.
+
+  Ideas, a product of organic nature, 217 et seq.;
+    and facts, necessary to science, 231;
+    not all of life, 233;
+    their growth and importance, 233;
+    a product of universal evolution, 235;
+    the history of, 227 et seq.;
+    in great minds, 228;
+    the rich contents of, 197;
+    their unsettled character in common life, their clarification in
+    science, 1-2.
+
+  Ideography, the Chinese, 192.
+
+  Imagery, mental, 253.
+
+  Imagination, facts reflected in, 220 et seq.
+
+  Inclined plane, law of, 140-141.
+
+  Incomprehensible, the, 186.
+
+  Indian, his modes of conception and interpretation, 218 et seq.
+
+  Individual, a thread on which pearls are strung, 234-235.
+
+  Industrial arts, economy of the, E. Hermann on, 192.
+
+  Inertia, law of, 143 et seq., 146 et seq., 216, footnote, 283 et seq.
+
+  Innate concepts of the understanding, Kant on, 199.
+
+  Innervation, visual, 99.
+
+  Inquirer, his division of labor, 105;
+    compared to a shoemaker, 105-106;
+    what constitutes the great, 191;
+    the true, seeks the truth everywhere, 63 et seq.;
+    the, compared to a wooer, 45.
+
+  Instinctive knowledge, 189, 190.
+
+  Instruction, aim of, the saving of experience, 191;
+    in the classics, mathematics, and sciences, 338-374;
+    limitation of matter of, 365 et seq.
+
+  Insulators, 130.
+
+  Integrals, 195.
+
+  Intellectual development, conditions of, 286 et seq.
+
+  Intentions, acts of nature compared to, 14-15.
+
+  Interconnexion of nature, 182.
+
+  Interdependence, of properties, 361;
+    of the sensuous elements of the world, 179.
+
+  Interference experiments with the head-wave of moving projectiles,
+  327-328.
+
+  International intercourse, established by Latin, 341.
+
+  International measures, 108.
+
+  Invention, discovery and, distinction between, 269.
+
+  Inventions, requisites for the development of, 266, 268 et seq.
+
+  Iron-filings, 220, 243.
+
+  Italian art, 234.
+
+
+  Jacobi, C. G. J., on mathematics, 280.
+
+  James, W., 275, 299.
+
+  Java, 163.
+
+  Jews and Christians, monotheism of the, 187.
+
+  Jolly, Professor von, 112, 274.
+
+  Joule, J. P., on the conservation of energy, 163-165, 167, 183;
+    his conception of energy, 245;
+    his metaphysics, 183, 246;
+    his method of thought, 247;
+    also 137, 138.
+
+  Journée, 317.
+
+  Judge, criminal, the natural philosopher compared to a, 48.
+
+  Judgment, essentially economy of thought, 201-202;
+    sharpened by languages and sciences, 357-358;
+    also 232-233, 238.
+
+  Juliet, Romeo and, 87.
+
+  Jupiter, its satellites employed in the determination of the velocity of
+  light, 51 et seq.
+
+  Jurisprudence, Latin and Greek unnecessary for the study of, 346,
+  footnote.
+
+
+  Kant, his hypothesis of the origin of the planetary system, 5;
+    his _Critique of Pure Reason_, 188;
+    on innate concepts of the understanding, 199;
+    on time, 204;
+    also footnote, 93.
+
+  Kepler, 187, 270.
+
+  Kinetic energy, 177.
+
+  Kirchhoff, his epistemological ideas, 257-258;
+    his definition of mechanics, 236, 258, 271, 273.
+
+  Knight, 289.
+
+  Knowledge, a product of organic nature, 217 et seq., 235;
+    instinctive, 190;
+    made possible by economy of thought, 198;
+    our first, derived from the economy of self-preservation, 197;
+    the theory of, 203;
+    our primitive acts of the foundation of science, 190.
+
+  Kocher, 328.
+
+  Koenig, measurement of the velocity of sound, 57 et seq.
+
+  Kölliker, 19.
+
+  Kopisch, 61.
+
+  Kreidl, 299, 302, 306;
+    his experiments, 272.
+
+  Krupp, 319.
+
+
+  Labels, the value of, 201.
+
+  Labor, the accumulation of, the foundation of wealth and power, 198;
+    inquirer's division of, 105, 258.
+
+  Labyrinth, of the ear, 18, 291, 305.
+
+  Lactantius, on the study of moral and physical science, 89.
+
+  Ladder of our abstraction, the, 208.
+
+  Ladies, their eyes, 71;
+    like tuning-forks, 23-24.
+
+  Lagrange, on Huygens's principle, 149;
+    on the principle of virtual velocities, 150-155;
+    character of the intellectual activity of a, 195, 278.
+
+  Lake-dwellers, 46, 271.
+
+  Lamp-shade, 70.
+
+  Lane's unit jar, 115.
+
+  Language, knowledge of the nature of, demanded by a liberal education,
+  356;
+    relationship between, and thought, 358;
+    communication by 237;
+    economy of, 191 et seq.;
+    human its character, 238;
+    of animals, 238;
+    instruction in, 338 et seq.;
+    its methods, 192.
+
+  Laplace, on the atoms of the brain, 188;
+    on the scientific achievements of the eighteenth century, 188;
+    his hypothesis of the origin of the planetary system, 5.
+
+  Latent heat, 167, 178, 244.
+
+  Latin city of Maupertuis, 339.
+
+  Latin, instruction in, 311 et seq.;
+    introduced with the Christian Church, 340;
+    the language of scholars, the medium of international intercourse,
+    its power, utility, and final abandonment, 341-347;
+    the wealth of its literature, 348;
+    the excessive study of, 346, 349, 354, 355;
+    its power to sharpen the judgment, 357-358.
+
+  Lavish extravagance of science, 189.
+
+  Law, a, defined, 256;
+    a natural, not contained in the conformity of the energies, 175.
+
+  Law-maker, motives of not always discernible, 9.
+
+  Layard, 79.
+
+  Learning, its nature, 366 et seq.
+
+  Least superficial area, principle of, accounted for by the mutual
+  attractions of liquid particles, 13-14;
+    illustrated by a pulley arrangement, 12-13;
+    also 9 et seq.
+
+  Leibnitz, on harmony, 33;
+    on international intercourse, 342, footnote.
+
+  Lessing, quotation from, 47.
+
+  Letters of the alphabet, their symmetry, 94, 97.
+
+  Level heights of work, 172-174.
+
+  Lever, a, in action, 222.
+
+  Leverrier, prediction of the planet Neptune, 29.
+
+  Leyden jar, 114.
+
+  Liberal education, a, 341 et seq., 359, 371.
+
+  Libraries, thoughts stored up in, 237.
+
+  Lichtenberg, on instruction, 276, 370.
+
+  Licius, a Chinese philosopher, 213.
+
+  Liebig, 163, 278.
+
+  Life and death, 186.
+
+  Light, history of as elucidating how theories obstruct research, 242;
+    Huygens's and Newton's views of, 227-228;
+    its different conceptions, 226;
+    rectilinear propagation of, 194;
+    rôle of, in vision, 81;
+    spatial and temporal periodicity of, explains optical phenomena, 194;
+    numerical velocity of, 58;
+    where does it go to? 199;
+    generally, 48 et seq.
+
+  Like effects in like circumstances, 199.
+
+  Likeness, 388, 391.
+
+  Lilliput, 84.
+
+  Lines, straight, their symmetry, 98;
+    curved, their asymmetry, 98;
+    of force, 249.
+
+  Links of thought, intermediate, 198.
+
+  Liquefaction, latent heat of, 178.
+
+  Liquid, efflux, law of, 150;
+    equilibrium, figures of, 4 et seq.;
+    the latter produced in open air, 7-8;
+    their beauty and multiplicity of form, 7, 8;
+    made permanent by melted colophonium, 7.
+
+  Liquids, forms of, 1-16;
+    difference between, and solids, 2;
+    their mobility and adaptiveness of form, 3;
+    the courtiers _par excellence_ of the natural bodies, 3;
+    possess under certain circumstances forms of their own, 3.
+
+  Living force, 137, 184;
+    law of the conservation of, 149.
+
+  Lloyd, observation of the conical refraction of light, 29.
+
+  Lobster, of Lake Mohrin, the, 61.
+
+  Localisation, cerebral, 210.
+
+  Locke, on language and thought, 358.
+
+  Locomotive, steam in the boiler of, 219.
+
+  Loeb, J., 289, 291, 302.
+
+  Logarithms, 195, 219;
+    in music, 103-104.
+
+  Logical root, of the principle of energy, 181;
+    of the principle of excluded perpetual motion, 182.
+
+  Lombroso, 280.
+
+  Lucian, 347.
+
+
+  _Macula acustica_, 272.
+
+  Magic lantern, 96.
+
+  Magic powers of nature, 189.
+
+  Magical power of science, belief in the, 189.
+
+  Magnet, a, 220;
+    will compared to the pressure of a, 14;
+    coercive force of a, 216.
+
+  Magnetic needle, near a current, 207.
+
+  Magnetised bar of steel, 242-243.
+
+  Major and minor keys in music, 100 et seq.
+
+  Malus, 242.
+
+  Man, a fragment of nature's life, 49;
+    his life embraces others, 234.
+
+  Mann, 364.
+
+  Manuscript in a mirror, 93.
+
+  Maple syrup, statues of, on Moon, 4.
+
+  Marx, 35.
+
+  Material, the relations of work with heat and the consumption of, 245
+  et seq.
+
+  Mathematical methods, their character, 197-198.
+
+  Mathematics, economy of, 195;
+    on instruction in, 338-374;
+    C. G. J. Jacobi on, 280.
+
+  Matter, constancy of, 203;
+    its nature, 203;
+    the notion of, 213.
+
+  Maupertuis, his Latin city, 338.
+
+  Maximal and minimal problems, their rôle in physics, 14, footnote.
+
+  Mayer, J. R., his conception of energy, 245, 246;
+    his methods of thought, 247;
+    on the conservation of energy, 163, 164, 165, 167, 183, 184;
+    his metaphysical utterances, 183, 246;
+    also 138, 184, 191, 217, 271, 274.
+
+  Measurement, definition of, 206.
+
+  Measures, international, 108.
+
+  Mécanique céleste, 90, 188;
+    sociale, and morale, the, 90.
+
+  Mechanical, conception of the world, 105, 155 et seq., 188, 207;
+    energy, W. Thomson on waste of, 175;
+    analogies between ---- and thermal energy, 17 et seq.;
+    equivalent of heat, electricity, etc., 164, 167 et seq.;
+    mythology, 207;
+    phenomena, physical events as, 182;
+    philosophy, 188;
+    physics, 155-160, 212;
+    substitution-value of heat, 178, footnote.
+
+  Mechanics, Kirchhoff's definition of, 236.
+
+  Medicine, students of, 326.
+
+  Melody, 101.
+
+  Melsens, 310, 327.
+
+  Memory, a treasure-house for comparison, 230;
+    common elements impressed upon the, 180;
+    its importance, 238;
+    science disburdens the, 193.
+
+  Mendelejeff, his periodical series, 256.
+
+  Mental, adaptation, 214-235;
+    completion of phenomena, 220;
+    imagery, 253;
+    imitation, our schematic, 199;
+    processes, economical, 195;
+    reproduction, 198;
+    visualisation, 250.
+
+  Mephistopheles, 88.
+
+  Mercantile principle, a miserly, at the basis of science, 15.
+
+  Mersenne, 377.
+
+  Mesmerism, the mental state of ordinary minds, 228.
+
+  Metaphysical establishment of doctrine of energy, 183.
+
+  Metaphysical spooks, 222.
+
+  Metrical, concepts of electricity, 107 et seq.;
+    notions, energy and entropy are, 178;
+    units, the building-stones of the physicist, 253.
+
+  Metronomes, 41.
+
+  Meyer, Lothar, his periodical series, 256.
+
+  Middle Ages, 243, 349.
+
+  Midsummer Night's Dream, 309.
+
+  Mill, John Stuart, 230.
+
+  Millers, school for, 326.
+
+  Mill-wheel, doing work, 161.
+
+  Mimicking facts in thought, 189, 193.
+
+  Minor and major keys in music, 100 et seq.
+
+  Mirror, symmetrical reversion of objects in, 92 et seq.
+
+  Miserly mercantile principle at the basis of science, 15.
+
+  Moat, child looking into, 208.
+
+  Modern scientists, adherents of the mechanical philosophy, 188.
+
+  Molecular theories, 104.
+
+  Molecules, 203, 207.
+
+  Molière, 234.
+
+  Momentum, 184.
+
+  Monocular vision, 98.
+
+  Monotheism of the Christians and Jews, 187.
+
+  Montagues and Capulets, 87.
+
+  Moon, eclipse of, 219;
+    lightness of bodies on, 4;
+    the study of the, 90, 284.
+
+  Moreau, 307.
+
+  Mosaic of thought, 192.
+
+  Motion, a perpetual, 181;
+    quantity of, 184;
+    the Eleatics on, 158;
+    Wundt on, 158;
+    the Herbartians on, 158.
+
+  Motions, natural and violent, 226;
+    their familiar character, 157.
+
+  Mountains of the earth, would crumble if very large, 3;
+    weight of bodies on, 112.
+
+  Mozart, 44, 279.
+
+  Müller, Johann, 291.
+
+  Multiplication-table, 195.
+
+  Multiplier, 132.
+
+  Music, band of, its _tempo_ accelerated and retarded, 53;
+    the principle of repetition in, 99 et seq.;
+    its notation, mathematically illustrated, 103-104.
+
+  Musical notes, reversion of, 101 et seq.;
+    their economy, 192.
+
+  Musical scale, a species of one-dimensional space, 105.
+
+  Mystery, in physics, 222;
+    science can dispense with, 189.
+
+  Mysticism, numerical, 33;
+    in the principle of energy, 184.
+
+  Mythology, the mechanical, of philosophy, 207.
+
+
+  Nagel, von, 364.
+
+  Nansen, 296.
+
+  Napoleon, picture representing the tomb of, 36.
+
+  Nations, intercourse and ideas of, 336-337.
+
+  Natural constants, 193.
+
+  Natural law, a, not contained in the conformity of the energies, 175.
+
+  Natural laws, abridged descriptions, 193;
+    likened to type, 193.
+
+  Natural motions, 225.
+
+  Natural selection in scientific theories, 63, 218.
+
+  Nature, experience the well-spring of all knowledge of, 181;
+    fashions of, 64;
+    first knowledge of, instinctive, 189;
+    general interconnexion of, 182;
+    has many sides, 217;
+    her forces compared to purposes, 14-15;
+    likened to a good man of business, 15;
+    the economy of her actions, 15;
+    how she appears to other animals, 83 et seq.;
+    inquiry of, viewed as a torture, 48-49;
+    view of, as something designedly concealed from man, 49;
+    like a covetous tailor, 9-10;
+    magic powers of, 189;
+    our view of, modified by binocular vision, 82;
+    the experimental method a questioning of, 48.
+
+  Negro hamlet, the science of a, 237.
+
+  Neptune, prediction and discovery of the planet, 29.
+
+  New views, 296 et seq.
+
+  Newton, describes polarisation, 242;
+    expresses his wealth of thought in Latin, 341;
+    his discovery of gravitation, 225 et seq.;
+    his solution of dispersion, 362;
+    his principle of the equality of pressure and counterpressure, 191;
+    his view of light, 227-228;
+    on absolute time, 204;
+    selections from his works for use in instruction, 368;
+    also 270, 274, 279, 285, 289.
+
+  Nobility, they displace Latin, 342.
+
+  Notation, musical, mathematically illustrated, 103-104.
+
+  Numbers, economy of, 195;
+    their connexion with consonance, 32.
+
+  Numerical mysticism, 33.
+
+  Nursery, the questions of the, 199.
+
+
+  Observation, 310.
+
+  Observation, in science, 261.
+
+  Ocean-stream, 272.
+
+  Oettingen, Von, 103.
+
+  Ohm, on electric currents, 249.
+
+  Ohm, the word, 343.
+
+  Oil, alcohol, water, and, employed in Plateau's experiments, 4;
+    free mass of, assumes the shape of a sphere, 12;
+    geometrical figures of, 5 et seq.
+
+  One-eyed people, vision of, 98.
+
+  Ophthalmoscope, 18.
+
+  Optic nerves, 96.
+
+  Optimism and pessimism, 234.
+
+  Order of physics, 197.
+
+  Organ, bellows of an, 135.
+
+  Organic nature, results of Darwin's studies of, 215 et seq.
+    See _Adaptation_ and _Heredity_.
+
+  Oriental world of fables, 273.
+
+  Orientation, sensations of, 282 et seq.
+
+  Oscillation, centre of, 147 et seq.
+
+  Ostwald, 172.
+
+  Otoliths, 301 et seq.
+
+  Overtones, 28, 40, 349.
+
+  Ozone, Schöbein's discovery of, 271.
+
+
+  Painted things, the difference between real and, 68.
+
+  Palestrina, 44.
+
+  Parameter, 257.
+
+  Partial tones, 390.
+
+  Particles, smallest, 104.
+
+  Pascheles, Dr. W., 285.
+
+  Paulsen, 338, 340, 373.
+
+  Pearls of life, strung on the individual as on a thread, 234-235.
+
+  Pencil surpasses the mathematician in intelligence, 196.
+
+  Pendulum, motion of a, 144 et seq.,
+    increased motion of, due to slight impulses, 21;
+    electrical, 110.
+
+  Percepts, of like form, 390.
+
+  Periodical, changes, 181;
+    series, 256.
+
+  Permanent, changes, 181, 199;
+    elements of the world, 194.
+
+  Perpetual motion, a, 181;
+    defined, 139;
+    impossibility of, 139 et seq.;
+    the principle of the, excluded, 140 et seq.;
+    excluded from general physics, 162.
+
+  Personality, its nature, 234-235.
+
+  Perspective, 76 et seq.;
+    contraction of, 74 et seq.;
+    distortion of, 77.
+
+  Pessimism and optimism, 234.
+
+  Pharaohs, 85.
+
+  Phenomenology, a universal physical, 250.
+
+  Philistine, modes of thought of, 223.
+
+  Philology, comparison in, 239.
+
+  Philosopher, an ancient, on the moral and physical sciences, 89.
+
+  Philosophy, its character at all times, 186;
+    mechanical, 155 et seq., 188, 207, 259 et seq.
+
+  Phonetic alphabets, their economy, 192.
+
+  Photography, by the electric spark, 318 et seq.
+
+  Photography of projectiles, 309-337.
+
+  Photography, stupendous advances of, 74.
+
+  Physical, concepts, fetishism in our, 187;
+    ideas and principles, their nature, 204;
+    inquiry, the economical nature of, 186;
+    research, object of 207, 209.
+
+  Physical phenomena, as mechanical phenomena, 182;
+    relations between, 205.
+
+  Physico-mechanical view of the world, 155, 187, 188, 207 et seq.
+
+  Physics, compared to a well-kept household, 197;
+    economical experience, 197;
+    the principles of, descriptive, 199;
+    the methods of, 209;
+    its method characterised, 211;
+    comparison in, 239;
+    the facts of, qualitatively homogeneous, 255;
+    how it began, 37;
+    helped by psychology, 104;
+    study of its own character, 189;
+    the goal of, 207, 209.
+
+  Physiological psychology, its methods, 211 et seq.
+
+  Physiology, its scope, 212.
+
+  Piano, its mirrored counterpart, 100 et seq.;
+    used to illustrate the facts of sympathetic vibration, 25 et seq.
+
+  Piano-player, a speaker compared to, 192.
+
+  Picture, physical, a, 110.
+
+  Pike, learns by experience, 267.
+
+  Pillars of Corti, 19.
+
+  Places, heavy bodies seek their, 224 et seq.
+
+  Planetary system, origin of, illustrated, 5.
+
+  Plasticity of organic nature, 216.
+
+  Plateau, his law of free liquid equilibrium, 9;
+    his method of getting rid of the effects of gravity, 4.
+
+  Plates of oil, thin, 6.
+
+  Plato, 347, 371.
+
+  Plautus, 347.
+
+  Playfair, 138.
+
+  Pleasant effects, cause of, 94 et seq.
+
+  Pliny, 349.
+
+  Poetry and science, 30, 31, 351.
+
+  Poinsot, on the foundations of mechanics, 152 et seq.
+
+  Polarisation, 91;
+    abstractly described by Newton, 242.
+
+  Politics, Chinese speak with unwillingness of, 374.
+
+  Pollak, 299.
+
+  Polyp plant, humanity likened to a, 235.
+
+  Pompeii, 234;
+    art in, 80.
+
+  Popper J., 172, 216.
+
+  Potential, social, 15;
+    electrical, 121 et seq.;
+    measurement of, 126;
+    fall of, 177;
+    swarm of notions in the idea of, 197;
+    its wide scope, 250.
+
+  Pottery, invention of, 263.
+
+  Prediction, 221 et seq.
+
+  Prejudice, the function, power, and dangers of, 232-233.
+
+  Preparatory schools, the defects of the German, 346-347;
+    what they should teach, 364 et seq.
+
+  Pressure of a stone or of a magnet, will compared to, 14;
+    also 157.
+
+  Primitive acts of knowledge the foundation of scientific thought, 190.
+
+  Problem, nature of a, 223.
+
+  Problems which are wrongly formulated, 308.
+
+  Process, Carnot's, 161 et seq.
+
+  Projectiles, the effects of the impact of, 310, 327-328;
+    seen with the naked eye, 311, 317;
+    measuring the velocity of, 332;
+    photography of, 309-337.
+
+  Prony's brake, 132.
+
+  Proof, nature of, 284.
+
+  Prophesying events, 220 et seq.
+
+  Psalms, quotation from the, 89.
+
+  Pseudoscope, Wheatstone's, 96.
+
+  Psychology, preceded by astronomy, 90;
+    how reached, 91 et seq.;
+    helps physical science, 104;
+    its method the same as that of physics, 207 et seq.
+
+  Pully arrangement, illustrating principle of least superficial area,
+  12-13.
+
+  Purkinje, 284, 285, 291, 299.
+
+  Purposes, the acts of nature compared to, 14-15;
+    nature pursues no, 66.
+
+  Puzzle-lock, a, 26.
+
+  Puzzles, 277.
+
+  Pyramid of oil, 6.
+
+  Pythagoras, his discovery of the laws of harmony, 32, 259.
+
+
+  Quality of tones, 36.
+
+  Quantitative investigation, the goal of, 180.
+
+  Quantity of electricity, 111, 118, 119, 167-170, 173;
+    of heat, 166, 167-171, 174, 177, 244;
+    of motion, 184.
+
+  Quests made of the inquirer, not by him, 30.
+
+  Quételet, 15, footnote.
+
+
+  Rabelais, 283.
+
+  Raindrop, form of, 3.
+
+  Rameau, 34.
+
+  Reaction and action, principle of, 191.
+
+  Reactions, disclosure of the connexion of, 270 et seq.
+
+  Realgymnasien, 365.
+
+  Realschulen, 365, 373.
+
+  Reason, stands above the senses, 105.
+
+  Reflex action, 210.
+
+  Reflexion, produces symmetrical reversion of objects, 93 et seq.
+
+  Refraction, 29, 193, 194, 208, 230, 231.
+
+  Reger, 328.
+
+  Reliefs, photographs of, 68.
+
+  Repetition, its rôle in æsthetics, 89, footnote, 91 et seq., 97, 98
+  et seq., 390.
+
+  Reproduction of facts in thought, 189, 193, 198, 253.
+
+  Repulsion, electric, 109 et seq., 168.
+
+  Research, function of experimental 181;
+    the aim of, 205.
+
+  Resemblances between facts, 255.
+
+  Resin, solution of, 7.
+
+  Resistance, laws of, for bodies travelling in air and fluids, 333 et seq.
+
+  Resonance, corporeal, 392.
+
+  Response of sonorous bodies, 25.
+
+  Retina, the corresponding spots of 98;
+    nerves of compared to fingers of a hand, 96 et seq.
+
+  Reversible processes, 161 et seq., 175, 176, 181, 182.
+
+  Rhine, the, 94.
+
+  Richard the Third, 77.
+
+  Riddles, 277.
+
+  Riders, 379.
+
+  Riegler, 319.
+
+  Riess, experiment with the thermo-electrometer, 133 et seq., 169.
+
+  Rigid connexions, 142.
+
+  Rind of a fruit, 190.
+
+  Rings of oil, illustrating formation of rings of Saturn, 5.
+
+  Ritter, 291, 299.
+
+  Rods of Corti, 19.
+
+  Rolph, W. H., 216.
+
+  Roman Church, Latin introduced with the, 340 et seq.
+
+  Romans, their provinciality and narrow-mindedness, 270.
+
+  Romeo and Juliet, 87.
+
+  Römer, Olaf, 51 et seq.
+
+  Roots, the nature of, in language, 252.
+
+  Rosetti, his experiment on the work required to develop electricity, 131.
+
+  Rotating bodies, 285.
+
+  Rotation, apparatus of, in physics, 59 et seq.;
+    sensations of, 288 et seq.
+
+  Rousseau, 336.
+
+  Rubber pyramid, illustrating the principle of least superficial area,
+  10-11.
+
+  Ruysdael, 279.
+
+
+  Sachs, Hans, 106.
+
+  Salcher, Prof. 319.
+
+  Salviati, 144.
+
+  Saturn, rings of, their formation illustrated, 5.
+
+  Saurians, 257.
+
+  Sauveur, on acoustics, 34, 375 et seq.
+
+  Savage, modes of conception and interpretation of a, 218 et seq.
+
+  Schäfer, K., 298.
+
+  _Schlierenmethode_, 317.
+
+  Schönbein's discovery of ozone, 271.
+
+  School-boy, copy-book of, 92.
+
+  Schoolmen, 214.
+
+  Schools, State-control of, 372 et seq.
+
+  Schopenhauer, 190.
+
+  Schultze, Max, 19.
+
+  Science, a miserly mercantile principle at its basis, 15;
+    compared to a business, 16;
+    viewed as a maximum or minimum problem, 16, footnote;
+    its process not greatly different from the intellectual activity of
+    ordinary life, 16, footnote;
+    economy of its task, 16;
+    relation of, to poetry, 30, 31, 351;
+    the church of, 67;
+    beginnings of, 189, 191;
+    belief in the magical power of, 189;
+    can dispense with mystery, 189;
+    lavish extravagance of, 189;
+    economy of the terminology of, 192;
+    partly made up of the intelligence of others, 196;
+    stripped of mystery, 197;
+    its true power, 197;
+    the economical schematism of, 206;
+    the object of, 206;
+    the tools of, 207;
+    does not create facts, 211;
+    of the future, 213;
+    revolution in, dating from Galileo, 214 et seq.;
+    the natural foe of the marvellous, 224;
+    characterised, 227;
+    growth of, 237;
+    dramatic element in, 243;
+    described, 251;
+    its function, 253;
+    classification in, 255, 259 et seq.;
+    the way of discovery in, 316.
+    See also _Physics_.
+
+  Sciences, partition of the, 86;
+    the barriers and relations between the 257-258;
+    on instruction in the, 338-374.
+
+  Scientific, criticism, Socrates the father of, 1, 16;
+    discoveries, their fate, 138;
+    knowledge, involves description, 193;
+    thought, transformation and adaptation in, 214-235;
+    thought, advanced by new experiences, 223 et seq.;
+    thought, the difficulty of, 366;
+    terms, 342-343;
+    founded on primitive acts of knowledge, 190.
+
+  Scientists, stories about their ignorance, 342.
+
+  Screw, the, 62.
+
+  Sea-sickness, 284.
+
+  Secret computation, Leibnitz's, 33.
+
+  Seek their places, bodies, 226.
+
+  Self-induction, coefficient of, 250, 252.
+
+  Self-observation, 211.
+
+  Self-preservation, our first knowledge derived from the economy of, 197;
+    struggle for, among ideas, 228.
+
+  Semi-circular canals, 290 et seq.
+
+  Sensation of rounding a railway curve, 286.
+
+  Sensations, analysed, 251;
+    when similar, produce agreeable effects, 96;
+    their character, 200;
+    defined, 209;
+    of orientation, 282 et seq.
+
+  Sense-elements, 179.
+
+  Senses, theory of, 104;
+    the source of our knowledge of facts, 237.
+
+  Seventh, the troublesome, 46.
+
+  Shadow method, 313 et seq., 317 footnote.
+
+  Shadows, rôle of, in vision, 81.
+
+  Shakespeare, 278.
+
+  Sharps, reversed into flats, 101.
+
+  Shell, spherical, law of attraction for a, 124, footnote.
+
+  Shoemaker, inquirer compared to, 105-106.
+
+  Shooting, 309.
+
+  Shots, double report of, 229 et seq.
+
+  Similarity, 249.
+
+  Simony, 280.
+
+  Simplicity, a varying element in description, 254.
+
+  Sines, law of the, 193.
+
+  Sinking of heavy bodies, 222.
+
+  Sixth sense, 297.
+
+  Smith, R., on acoustics, 34, 381, 383.
+
+  Soap-films, Van der Mensbrugghe's experiment with, 11-12.
+
+  Soapsuds, films and figures of, 7.
+
+  Social potential, 15.
+
+  Socrates, the father of scientific criticism, 1, 16.
+
+  Sodium, 202.
+
+  Sodium-light, vibrations of, as a measure of time, 205.
+
+  Solidity, conception of, by the eye, 71 et seq.;
+    spatial, photographs of, 73.
+
+  Solids, and liquids, their difference merely one of degree, 2.
+
+  Sonorous bodies, 24 et seq.
+
+  Soret, J. P., 89.
+
+  Sounds, symmetry of, 99 et seq.;
+    generally, 22-47, 212.
+
+  Sound-waves rendered visible, 315 et seq.
+
+  Sources of the principle of energy, 179 et seq.
+
+  Space, 205;
+    sensation of, 210.
+
+  Spark, electric, 117, 127, 132, 133, 190.
+
+  Spatial vision, 386.
+
+  Species, stability of, a theory, 216.
+
+  Specific energies, 291.
+
+  Specific heat, 166, 244.
+
+  Specific inductive capacity, 117.
+
+  Spectral analysis of sound, 27.
+
+  Spectrum, mental associations of the, 190.
+
+  Speech, the instinct of, cultivated by languages, 354.
+
+  Spencer, 218, 222.
+
+  Sphere, a soft rotating, 2;
+    the figure of least surface, 12;
+    electrical capacity of, 123 et seq.
+
+  Spherical shell, law of attraction for 124, footnote.
+
+  Spiders, the eyes of, 67.
+
+  Spirits, as explanation of the world 186, 243.
+
+  Spiritualism, modern, 187.
+
+  Spooks, metaphysical, 222.
+
+  Squinting, 72.
+
+  Stability of our environment, 206.
+
+  Stallo, 336.
+
+  Stars, the fixed, 90.
+
+  State, benefits and evils of its control of the schools, 372 et seq.;
+    the Church and, 88.
+
+  Statical electricity, 134.
+
+  Stationary currents, 249.
+
+  Statoliths, 303.
+
+  Steam-engine, 160, 265.
+
+  Steeple-jacks, 75.
+
+  Stereoscope, Wheatstone and Brewster's, 73.
+
+  Stevinus, on the inclined plane, 140;
+    on hydrostatics, 141;
+    on the equilibrium of systems, 142;
+    discovers the principle of virtual velocities, 150;
+    characterisation of his thought, 142;
+    also 182, 187, 191.
+
+  Stone Age, 46, 321.
+
+  Störensen, 306.
+
+  Stove, primitive, 263.
+
+  Straight line, a, its symmetry, 98.
+
+  Straight, meaning of the word, 240.
+
+  Street, vista into a, 75.
+
+  Striae, in glass, 313.
+
+  Striate method, for detecting optical imperfections, 317.
+
+  Striking distance, 115, 127.
+
+  Strings, vibrations of, 249.
+
+  Struggle for existence among ideas, 217.
+
+  Substance, heat conceived as a, 177, 243 et seq.;
+    electricity as a, 170;
+    the source of our notion of, 199;
+    rôle of the notion of, 203, 244 et seq.;
+    energy conceived as a, 164, 185, 244 et seq.
+
+  Substitution-value of heat, 178, footnote.
+
+  Suetonius, 348.
+
+  Sulphur, specific inductive capacity of, 117.
+
+  Sun, human beings could not exist on, 3.
+
+  Swift, 84, 280.
+
+  Swimmer, Ampère's, 207.
+
+  Symmetry, definition of, 92;
+    figures of, 92 et seq.;
+    plane of, 94;
+    vertical and horizontal, 94;
+    in music, 99 et seq.
+
+  Sympathetic vibration, 22 et seq., 379.
+
+
+  Tailor, nature like a covetous, 9-10.
+
+  Tangent, the word, 263.
+
+  Taste, doubtful cultivation of, by the classics, 352-353;
+    of the ancients, 353.
+
+  Taylor, on the vibration of strings, 249.
+
+  Teaching, its nature, 366 et seq.
+
+  Telegraph, the word, 263.
+
+  Telescope, 262.
+
+  Telestereoscope, the, 84.
+
+  Temperament, even, in tuning, 47.
+
+  Temperature, absolute, 162;
+    differences of, 205;
+    differences of, viewed as level surfaces, 161;
+    heights of, 174;
+    scale of, derived from tensions of gases, 174.
+
+  Terence, 347.
+
+  Terms, scientific, 342-343.
+
+  Thales, 259.
+
+  Theories, their scope, function, and power, 241-242;
+    must be replaced by direct description, 248.
+
+  Thermal, energy, 174, 177;
+    capacity, 123, footnote.
+
+  Thermodynamics, 160 et seq.
+
+  Thermoelectrometer, Riess's, 133, 169.
+
+  Thing-in-itself, the, 200.
+
+  Things, mental symbols for groups of sensations, 200-201.
+
+  Thomson, James, on the lowering of the freezing-point of water by
+  pressure, 162.
+
+  Thomson, W., his absolute electrometer, 127, footnote;
+    on thermodynamics, 162;
+    on the conservation of energy, 165;
+    on the mechanical measures of temperature, 174, footnote;
+    on waste of mechanical energy, 175;
+    also 108, 173, footnote.
+
+  Thought, habitudes of, 199, 224, 227, 232;
+    relationship between language and, 329;
+    incongruence between experience and, 206;
+    luxuriance of a fully developed, 58;
+    transformation in scientific, 214-235.
+
+  Thoughts, their development and the struggle for existence among them,
+  63;
+    importance of erroneous, 65;
+    as reproductions of facts, 107.
+
+  Thread, the individual a, on which pearls are strung, 234-235.
+
+  Tides, 283.
+
+  Timbre, 37, 38, 39.
+
+  Time, 178, 204, 205, footnote.
+
+  Toepler and Foucault, method of, for detecting optical faults, 313
+  et seq., 320.
+
+  Tone-figures, 91.
+
+  Tones, 22-47, 99 et seq., 212.
+
+  Torsion, moment of, 132.
+
+  Torsion-balance, Coulomb's, 109, 168.
+
+  Torricelli, on virtual velocities, 150;
+    his law of liquid efflux, 150;
+    on the atmosphere, 273.
+
+  Tourist, journey of, work of the inquirer compared to, 17, 29, 30.
+
+  Transatlantic cable, 108.
+
+  Transformation and adaptation in scientific thought, 214-235.
+
+  Transformation of ideas, 63.
+
+  Transformative law of the energies, 172.
+
+  Translation, difficulties of, 354.
+
+  Tree, conceptual life compared to a, 231.
+
+  Triangle, mutual dependence of the sides and angles of a, 179.
+
+  Triple accord, 46.
+
+  Truth, wooed by the inquirer, 45;
+    difficulty of its acquisition, 46.
+
+  Tumblers, resounding, 23.
+
+  Tuning-forks, explanation of their motion, 22 et seq.
+
+  Tylor, 186.
+
+  Tympanum, 18.
+
+  Type, natural laws likened to, 193;
+    words compared to, 191.
+
+
+  Ulysses, 347.
+
+  Understanding, what it means, 211.
+
+  Uniforms, do not fit heads, 369.
+
+  Unique determination, 181-182.
+
+  Unison, 43.
+
+  Unit, electrostatic, 111.
+    See _Force_ and _Work_.
+
+  United States, 336.
+
+  Universal Real Character, a, 192.
+
+  Utility of physical science, 351.
+
+
+  Variation, the method of, in science, 230;
+    in biology, 216.
+
+  Velocity, of light, 48 et seq.;
+    of the descent of bodies, 143 et seq.;
+    meaning of, 204;
+    virtual, 149-155.
+
+  _Verstandesbegriffe_, 199.
+
+  Vertical, perception of the, 272, 286 et seq.;
+    symmetry, 389.
+
+  Vertigo, 285, 290.
+
+  Vestibule of the ear, 300.
+
+  Vibration, 22 et seq.
+
+  Vibration-figures, 91.
+
+  Vinci, Leonardo da, 278, 283.
+
+  Violent motions, 225.
+
+  Virtual velocities, 149-155.
+
+  Visibility, general conditions of, 312.
+
+  Vision, symmetry of our apparatus of, 96.
+    See _Eye_.
+
+  Visual nerves, 96.
+
+  Visualisation, mental, 250.
+
+  Volt, the word, 343.
+
+  Volta, 127, footnote, 134.
+
+  Voltaire, 260.
+
+  Voltaire's ingènu, 219.
+
+  Vowels, composed of simple musical notes, 26.
+
+
+  Wagner, Richard, 279.
+
+  Wald, F., 178, footnote.
+
+  Wallace, 216.
+
+  War, and peace, reflexions upon, 309, 335 et seq.
+
+  Waste of mechanical energy, W. Thomson on, 175.
+
+  Watches, experiment with, 41;
+    in a mirror, 93.
+
+  Water, jet of, resolved into drops, 60;
+    free, solid figures of, 8;
+    objects reflected in, 94, 191;
+    possible modes of measurement of, 170.
+
+  Watt, 266.
+
+  Wealth, the foundation of, 198.
+
+  Weapons, modern, 335.
+
+  Weber, 108, 306.
+
+  Weight of bodies, varies with their distance from the centre of the
+  earth, 112.
+
+  Weismann, 216.
+
+  Wheatstone, his stereoscope, 73;
+    his pseudoscope, 96;
+    also 59.
+
+  Wheel, history and importance of, 61 et seq.
+
+  Whewell, on the formation of science, 231.
+
+  Whole, the, 204, footnote.
+
+  Why, the question, 199, 223.
+
+  Will, Schopenhauer on the, 190;
+    man's most familiar source of power, 243;
+    used to explain the world, 186;
+    forces compared to, 254;
+    compared to pressure, 14.
+
+  Windmill, a rotating, 53.
+
+  Wire frames and nets, for constructing liquid figures of equilibrium,
+  4 et seq.
+
+  Witchcraft, 187.
+
+  Wollaston, 284, 285.
+
+  Wonderful, science the natural foe of the, 224.
+
+  Woods, the relative distance of trees in, 68.
+
+  Wooer, inquirer compared to a, 45.
+
+  Words and sounds, 343.
+
+  Words, compared to type, 191.
+
+  Work, of liquid forces of attraction, 14;
+    in electricity, 173;
+    measure of, 119 et seq., 130, 223;
+    relation of, with heat, 162, 245 et seq.;
+    amount required to develop electricity, 131 et seq.;
+    produces various physical changes, 139;
+    substantial conception of, 183-184.
+    See _Energy_.
+
+  World, the, what it consists of, 208.
+
+  World-particles, 203.
+
+  Wronsky, 172.
+
+  Wundt, on causality and the axioms of physics, 157-159; 359 footnote.
+
+
+  Xenophon, 49, footnote.
+
+
+  Young, Thomas, on energy, 173.
+
+
+  Zelter, 35.
+
+  Zeuner, 171.
+
+  Zoölogy, comparison in, 239.
+
+
+
+
+THE WORKS OF ERNST MACH.
+
+THE SCIENCE OF MECHANICS.
+
+A CRITICAL AND HISTORICAL EXPOSITION OF ITS PRINCIPLES.
+
+By DR. ERNST MACH.
+
+PROFESSOR OF THE HISTORY AND THEORY OF INDUCTIVE SCIENCE IN THE
+UNIVERSITY OF VIENNA.
+
+Translated from the Second German Edition By THOMAS J. McCORMACK.
+
+
+250 Cuts. 534 Pages. Half Morocco, Gilt Top, Marginal Analyses.
+
+Exhaustive Index. Price $2.50.
+
+
+
+
+TABLE OF CONTENTS.
+
+
+STATICS.
+
+     The Lever.
+
+     The Inclined Plane.
+
+     The Composition of Forces.
+
+     Virtual Velocities.
+
+     Statics in Their Application to Fluids.
+
+     Statics in Their Application to Gases.
+
+
+DYNAMICS.
+
+     Galileo's Achievements.
+
+     Achievements of Huygens.
+
+     Achievements of Newton.
+
+     Principle of Reaction.
+
+     Criticism of the Principle of Reaction and of the Concept of Mass.
+
+     Newton's Views of Time, Space, and Motion.
+
+     Critique of the Newtonian Enunciations.
+
+     Retrospect of the Development of Dynamics.
+
+
+THE EXTENSION OF THE PRINCIPLES OF MECHANICS.
+
+     Scope of the Newtonian Principles.
+
+     Formulæ and Units of Mechanics.
+
+     Conservation of Momentum, Conservation of the Centre of Gravity,
+     and Conservation of Areas.
+
+     Laws of Impact.
+
+     D'Alembert's Principle.
+
+     Principle of _Vis Viva_.
+
+     Principle of Least Constraint.
+
+     Principle of Least Action.
+
+     Hamilton's Principle.
+
+     Hydrostatic and Hydrodynamic Questions.
+
+
+FORMAL DEVELOPMENT OF MECHANICS.
+
+     The Isoperimetrical Problems.
+
+     Theological, Animistic, and Mystical Points of View in Mechanics.
+
+     Analytical Mechanics.
+
+     The Economy of Science.
+
+
+THE RELATION OF MECHANICS TO OTHER DEPARTMENTS OF KNOWLEDGE.
+
+     Relations of Mechanics to Physics.
+
+     Relations of Mechanics to Physiology.
+
+
+
+
+PRESS NOTICES.
+
+
+"The appearance of a translation into English of this remarkable book
+should serve to revivify in this country [England] the somewhat
+stagnating treatment of its subject, and should call up the thoughts
+which puzzle us when we think of them, and that is not sufficiently
+often.... Professor Mach is a striking instance of the combination of
+great mathematical knowledge with experimental skill, as exemplified not
+only by the elegant illustrations of mechanical principles which abound
+in this treatise, but also from his brilliant experiments on the
+photography of bullets.... A careful study of Professor Mach's work, and
+a treatment with more experimental illustration, on the lines laid down
+in the interesting diagrams of his _Science of Mechanics_, will do much
+to revivify theoretical mechanical science, as developed from the
+elements by rigorous logical treatment."--Prof. A. G. Greenhill, in
+_Nature_, London.
+
+"Those who are curious to learn how the principles of mechanics have
+been evolved, from what source they take their origin, and how far they
+can be deemed of positive and permanent value, will find Dr. Mach's able
+treatise entrancingly interesting.... The book is a remarkable one in
+many respects, while the mixture of history with the latest scientific
+principles and absolute mathematical deductions makes it exceedingly
+attractive."--_Mechanical World_, Manchester and London, England.
+
+"Mach's Mechanics is unique. It is not a text-book, but forms a useful
+supplement to the ordinary text-book. The latter is usually a skeleton
+outline, full of mathematical symbols and other abstractions. Mach's
+book has 'muscle and clothing,' and being written from the historical
+standpoint, introduces the leading contributors in succession, tells
+what they did and how they did it, and often what manner of men they
+were. Thus it is that the pages glow, as it were, with a certain
+humanism, quite delightful in a scientific book.... The book is
+handsomely printed, and deserves a warm reception from all interested in
+the progress of science."--_The Physical Review_, New York and London.
+
+"Mr. T. J. McCormack, by his effective translation, where translation
+was no light task, of this masterly treatise upon the earliest and most
+fundamental of the sciences, has rendered no slight service to the
+English speaking student. The German and English languages are generally
+accounted second to none in their value as instruments for the
+expression of scientific thought; but the conversion bodily of an
+abstruse work from one into the other, so as to preserve all the meaning
+and spirit of the original and to set it easily and naturally into its
+new form, is a task of the greatest difficulty, and when performed so
+well as in the present instance, merits great commendation. Dr. Mach has
+created for his own works the severest possible standard of judgment. To
+expect no more from the books of such a master than from the elementary
+productions of an ordinary teacher in the science would be undue
+moderation. Our author has lifted what, to many of us, was at one time a
+course of seemingly unprofitable mental gymnastics, encompassed only at
+vast expenditure of intellectual effort, into a study possessing a deep
+philosophical value and instinct with life and interest. 'No profit
+grows where is no pleasure ta'en,' and the emancipated collegian will
+turn with pleasure from the narrow methods of the text-book to where the
+science is made to illustrate, by a treatment at once broad and deep,
+the fundamental connexion between all the physical sciences, taken
+together."--_The Mining Journal_, London, England.
+
+"As a history of mechanics, the work is admirable."--_The Nation_, New
+York.
+
+"An excellent book, admirably illustrated."--_The Literary World_,
+London, England.
+
+"Sets forth the elements of its subject with a lucidity, clearness, and
+force unknown in the mathematical text-books ... is admirably fitted to
+serve students as an introduction on historical lines to the principles
+of mechanical science."--_Canadian Mining and Mechanical Review_,
+Ottawa, Can.
+
+"A masterly book.... To any one who feels that he does not know as much
+as he ought to about physics, we can commend it most heartily as a
+scholarly and able treatise ... both interesting and profitable."--A. M.
+Wellington, in _Engineering News_, New York.
+
+"The book as a whole is unique, and is a valuable addition to any
+library of science or philosophy.... Reproductions of quaint old
+portraits and vignettes give piquancy to the pages. The numerous
+marginal titles form a complete epitome of the work; and there is that
+invaluable adjunct, a good index. Altogether the publishers are to be
+congratulated upon producing a technical work that is thoroughly
+attractive in its make-up."--Prof. D. W. Hering, in _Science_.
+
+"There is one other point upon which this volume should be commended,
+and that is the perfection of the translation. It is a common fault that
+books of the greatest interest and value in the original are oftenest
+butchered or made ridiculous by a clumsy translator. The present is a
+noteworthy exception."--_Railway Age_.
+
+"The book is admirably printed and bound.... The presswork is
+unexcelled by any technical books that have come to our hands for some
+time, and the engravings and figures are all clearly and well
+executed."--_Railroad Gazette_.
+
+
+
+
+TESTIMONIALS OF PROMINENT EDUCATORS.
+
+
+"I am delighted with Professor Mach's _Science of Mechanics_."--_M. E.
+Cooley_, Professor of Mechanical Engineering, Ann Arbor, Mich.
+
+"You have done a good service to science in publishing Mach's _Science
+of Mechanics_ in English. I shall take every opportunity to recommend it
+to young students as a source of much interesting information and
+inspiration."--_M. I. Pupin_, Professor of Mechanics, Columbia College,
+New York.
+
+"Mach's _Science of Mechanics_ is an admirable ... book."--_Prof. E. A.
+Fuertes_, Director of the College of Civil Engineering of Cornell
+University, Ithaca, N. Y.
+
+"I congratulate you upon producing the work in such good style and in so
+good a translation. I bought a copy of it a year ago, very shortly after
+you issued it. The book itself is deserving of the highest admiration;
+and you are entitled to the thanks of all English-speaking physicists
+for the publication of this translation."--_D. W. Hering_, Professor of
+Physics, University of the City of New York, New York.
+
+"I have read Mach's _Science of Mechanics_ with great pleasure. The book
+is exceedingly interesting."--_W. F. Magie_, Professor of Physics,
+Princeton University, Princeton, N. J.
+
+"The _Science of Mechanics_ by Mach, translated by T. J. McCormack, I
+regard as a most valuable work, not only for acquainting the student
+with the history of the development of Mechanics, but as serving to
+present to him most favorably the fundamental ideas of Mechanics and
+their rational connexion with the highest mathematical developments. It
+is a most profitable book to read along with the study of a text-book of
+Mechanics, and I shall take pleasure in recommending its perusal by my
+students."--_S. W. Robinson_, Professor of Mechanical Engineering, Ohio
+State University, Columbus, Ohio.
+
+"I am delighted with Mach's 'Mechanics.' I will call the attention to it
+of students and instructors who have the Mechanics or Physics to study
+or teach."--_J. E. Davies_, University of Wisconsin, Madison, Wis.
+
+"There can be but one opinion as to the value of Mach's work in this
+translation. No instructor in physics should be without a copy of
+it."--_Henry Crew_, Professor of Physics in the Northwestern University,
+Evanston, Ill.
+
+
+
+
+POPULAR SCIENTIFIC LECTURES.
+
+A PORTRAYAL OF THE SPIRIT AND METHODS OF SCIENCE.
+
+By DR. ERNST MACH.
+
+PROFESSOR OF THE HISTORY AND THEORY OF INDUCTIVE SCIENCE IN THE
+UNIVERSITY OF VIENNA.
+
+Translated by THOMAS J. McCORMACK.
+
+_Third Edition, Revised Throughout and Greatly Enlarged._
+
+
+Cloth, Gilt Top. Exhaustively Indexed. Pages, 415. Cuts, 59. Price,
+$1.50.
+
+
+
+
+TITLES OF THE LECTURES.
+
+
+     The Forms of Liquids.
+
+     The Fibres of Corti.
+
+     On the Causes of Harmony.
+
+     On the Velocity of Light.
+
+     Why Has Man Two Eyes?
+
+     On Symmetry.
+
+     On the Fundamental Concepts of Static Electricity.
+
+     On the Principle of the Conservation of Energy.
+
+     On the Economical Nature of Physical Inquiry.
+
+     On the Principle of Comparison in Physics.
+
+     On the Part Played by Accident in Invention and Discovery.
+
+     On Sensations of Orientation.
+
+     On the Relative Educational Value of the Classics and the
+     Mathematico-Physical Sciences.
+
+     A Contribution to the History of Acoustics.
+
+     Remarks on the Theory of Spatial Vision.
+
+     On Transformation and Adaptation in Scientific Thought.
+
+
+PRESS NOTICES.
+
+"A most fascinating volume, treating of phenomena in which all are
+interested, in a delightful style and with wonderful clearness. For
+lightness of touch and yet solid value of information the chapter 'Why
+Has Man Two Eyes?' has scarcely a rival in the whole realm of popular
+scientific writing."--_The Boston Traveller_.
+
+"Truly remarkable in the insight they give into the relationship of the
+various fields cultivated under the name of Physics.... A vein of humor
+is met here and there reminding the reader of Heaviside, never offending
+one's taste. These features, together with the lightness of touch with
+which Mr. McCormack has rendered them, make the volume one that may be
+fairly called rare. The spirit of the author is preserved in such
+attractive, really delightful, English that one is assured nothing has
+been lost by translation."--Prof. Henry Crew, in _The Astrophysical
+Journal_.
+
+"A very delightful and useful book.... The author treats some of the
+most recondite problems of natural science, in so charmingly untechnical
+a way, with such a wealth of bright illustration, as makes his meaning
+clear to the person of ordinary intelligence and education.... This is a
+work that should find a place in every library, and that people should
+be encouraged to read."--_Daily Picayune_, New Orleans.
+
+"In his translation Mr. McCormack has well preserved the frank, simple,
+and pleasing style of this famous lecturer on scientific topics.
+Professor Mach deals with the live facts, the salient points of science,
+and not with its mysticism or dead traditions. He uses the simplest of
+illustrations and expresses himself clearly, tersely, and with a
+delightful freshness that makes entertaining reading of what in other
+hands would be dull and prosy."--_Engineering News_, N. Y.
+
+"The general reader is led by plain and easy steps along a delightful
+way through what would be to him without such a help a complicated maze
+of difficulties. Marvels are invented and science is revealed as the
+natural foe to mysteries."--_The Chautauquan_.
+
+"The beautiful quality of the work is not marred by abstruse discussions
+which would require a scientist to fathom, but is so simple and so clear
+that it brings us into direct contact with the matter treated."--_The
+Boston Post_.
+
+"A masterly exposition of important scientific truths."--_Scotsman_,
+Edinburgh.
+
+"These lectures by Dr. Mach are delightfully simple and frank; there is
+no dryness or darkness of technicalities, and science and common life do
+not seem separated by a gulf.... The style is admirable, and the whole
+volume seems gloriously alive and human."--_Providence Journal_, R. I.
+
+"The non-scientific reader who desires to learn something of modern
+scientific theories, and the reasons for their existence, cannot do
+better than carefully study these lectures. The English is excellent
+throughout, and reflects great credit on the translator."--_Manufacturer
+and Builder_.
+
+"We like the quiet, considerate intelligence of these
+lectures."--_Independent_, New York.
+
+"Professor Mach's lectures are so pleasantly written and illumined with
+such charm of illustration that they have all the interest of lively
+fiction."--_New York Com. Advertiser_.
+
+"The literary and philosophical suggestiveness of the book is very
+rich." _Hartford Seminary Record_.
+
+"All are presented so skilfully that one can imagine that Professor
+Mach's hearers departed from his lecture-room with the conviction that
+science was a matter for abecedarians. Will please those who find the
+fairy tales of science more absorbing than fiction."--_The Pilot_,
+Boston.
+
+"Professor Mach ... is a master in physics.... His book is a good one
+and will serve a good purpose, both for instruction and
+suggestion."--Prof. A. E. Dolbear, in _The Dial_.
+
+"The most beautiful ideas are unfolded in the exposition."--_Catholic
+World_, New York.
+
+
+
+
+THE ANALYSIS OF THE SENSATIONS
+
+By DR. ERNST MACH.
+
+PROFESSOR OF THE HISTORY AND THEORY OF INDUCTIVE SCIENCE IN THE
+UNIVERSITY OF VIENNA.
+
+
+Pages, 208. Illustrations, 37. Indexed.
+
+(Price, Cloth, $1.25.)
+
+
+
+
+CONTENTS.
+
+
+     Introductory: Antimetaphysical.
+
+     The Chief Points of View for the Investigation of the Senses.
+
+     The Space-Sensations of the Eye.
+
+     Space-Sensation, Continued.
+
+     The Relations of the Sight-Sensations to One Another and to the
+     Other Psychical Elements.
+
+     The Sensation of Time.
+
+     The Sensation of Sound.
+
+     Influence of the Preceding Investigations on the Mode of Conceiving
+     Physics.
+
+
+"A wonderfully original little book. Like everything he writes a work of
+genius."--_Prof. W. James_ of Harvard.
+
+"I consider each work of Professor Mach a distinct acquisition to a
+library of science."--_Prof. D. W. Hering_, New York University.
+
+"There is no work known to the writer which, in its general scientific
+bearings, is more likely to repay richly thorough study. We are all
+interested in nature in one way or another, and our interests can only
+be heightened and clarified by Mach's wonderfully original and wholesome
+book. It is not saying too much to maintain that every intelligent
+person should have a copy of it,--and should study that copy."--_Prof.
+J. E. Trevor_, Cornell.
+
+"Students may here make the acquaintance of some of the open questions
+of sensation and at the same time take a lesson in the charm of
+scientific modesty that can hardly be excelled."--_Prof. E. C. Sanford_,
+Clark University.
+
+"It exhibits keen observation and acute thought, with many new and
+interesting experiments by way of illustration. Moreover, the style is
+light and even lively--a rare merit in a German prose work, and still
+rarer in a translation of one."--_The Literary World_, London.
+
+
+CHICAGO: The Open Court Publishing Company 324 DEARBORN STREET.
+
+LONDON: Kegan Paul, Trench, Trübner, & Company.
+
+
+
+
+CATALOGUE OF PUBLICATIONS
+
+OF THE
+
+OPEN COURT PUBLISHING CO.
+
+
+COPE, E. D.
+
+     THE PRIMARY FACTORS OF ORGANIC EVOLUTION.
+
+     121 cuts. Pp., xvi, 547. Cloth, $2.00, net.
+
+MÜLLER, F. MAX.
+
+     THREE INTRODUCTORY LECTURES ON THE SCIENCE OF THOUGHT.
+
+     With a correspondence on "Thought Without Words," between F. Max
+     Müller and Francis Galton, the Duke of Argyll, George J. Romanes
+     and others. 128 pages. Cloth, 75 cents. Paper, 25 cents.
+
+     THREE LECTURES ON THE SCIENCE OF LANGUAGE.
+
+     The Oxford University Extension Lectures, with a Supplement, "My
+     Predecessors." 112 pages. 2nd Edition. Cloth, 75 cents. Paper, 25c.
+
+ROMANES, GEORGE JOHN.
+
+     DARWIN AND AFTER DARWIN.
+
+     An Exposition of the Darwinian Theory and a Discussion of
+     Post-Darwinian Questions. Three Vols., $4.00. Singly, as follows:
+
+     1. THE DARWINIAN THEORY. 460 pages. 125 illustrations. Cloth,
+     $2.00.
+
+     2. POST-DARWINIAN QUESTIONS. Heredity and Utility. Pp. 338. $1.50.
+
+     3. POST-DARWINIAN QUESTIONS. Isolation and Physiological Selection.
+     Pp. 181. $1.00.
+
+     AN EXAMINATION OF WEISMANNISM.
+
+     236 pages. Cloth, $1.00. Paper, 35c.
+
+     THOUGHTS ON RELIGION.
+
+     Edited by Charles Gore, M. A., Canon of Westminster. Third Edition,
+     Pages, 184. Cloth, gilt top, $1.25.
+
+RIBOT, TH.
+
+     THE PSYCHOLOGY OF ATTENTION.
+
+     THE DISEASES OF PERSONALITY.
+
+     THE DISEASES OF THE WILL.
+
+     Authorised translations. Cloth, 75 cents each. Paper, 25 cents.
+     _Full set, cloth, $1.75, net._
+
+MACH, ERNST.
+
+     THE SCIENCE OF MECHANICS.
+
+     A CRITICAL AND HISTORICAL EXPOSITION OF ITS PRINCIPLES. Translated
+     by T. J. MCCORMACK. 250 cuts. 534 pages. 1/2 m., gilt top. $2.50.
+
+     POPULAR SCIENTIFIC LECTURES.
+
+     Third Edition. 415 pages. 59 cuts. Cloth, gilt top. Net, $1.50.
+
+     THE ANALYSIS OF THE SENSATIONS.
+
+     Pp. 208. 37 cuts. Cloth, $1.25, net.
+
+GOODWIN, REV. T. A.
+
+     LOVERS THREE THOUSAND YEARS AGO.
+
+     As Indicated by the Song of Solomon. Pp. 41. Boards, 50c.
+
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+
+     ENGLISH SECULARISM. A CONFESSION OF BELIEF.
+
+     Pp. 146. Cloth, 50c., net.
+
+CORNILL, CARL HEINRICH.
+
+     THE PROPHETS OF ISRAEL.
+
+     Popular Sketches from Old Testament History. Pp., 200. Cloth,
+     $1.00.
+
+     THE RISE OF THE PEOPLE OF ISRAEL.
+
+     See _Epitomes of Three Sciences_, below.
+
+BINET, ALFRED.
+
+     THE PSYCHIC LIFE OF MICRO-ORGANISMS.
+
+     Authorised translation. 135 pages. Cloth, 75 cents; Paper, 25
+     cents.
+
+     ON DOUBLE CONSCIOUSNESS.
+
+     Studies in Experimental Psychology. 93 pages. Paper, 15 cents.
+
+WAGNER, RICHARD
+
+     A PILGRIMAGE TO BEETHOVEN.
+
+     A Novelette. Frontispiece, portrait of Beethoven. Pp. 40. Boards,
+     50c.
+
+WEISMANN, AUGUST.
+
+     GERMINAL SELECTION. AS A SOURCE OF DEFINITE VARIATION.
+
+     Pp. 73. Paper, 25c.
+
+NOIRÉ, LUDWIG.
+
+     ON THE ORIGIN OF LANGUAGE. Pp. 57. Paper, 15c.
+
+FREYTAG, GUSTAV.
+
+     THE LOST MANUSCRIPT. A Novel.
+
+     2 vols. 953 pages. Extra cloth, $4.00. One vol., cl., $1.00; paper,
+     75c.
+
+     MARTIN LUTHER.
+
+     Illustrated. Pp. 130. Cloth, $1.00. Paper, 25c.
+
+HERING, EWALD.
+
+     ON MEMORY, and THE SPECIFIC ENERGIES OF THE NERVOUS SYSTEM. Pp. 50.
+     Paper, 15c.
+
+TRUMBULL, M. M.
+
+     THE FREE TRADE STRUGGLE IN ENGLAND.
+
+     Second Edition. 296 pages. Cloth, 75 cents; paper, 25 cents.
+
+     WHEELBARROW: ARTICLES AND DISCUSSIONS ON THE LABOR QUESTION.
+
+     With portrait of the author. 303 pages. Cloth, $1.00; paper, 35
+     cents.
+
+     EARL GREY ON RECIPROCITY AND CIVIL SERVICE REFORM.
+
+     With Comments by Gen. M. M. Trumbull. Price, 10 cents.
+
+GOETHE AND SCHILLER'S XENIONS.
+
+     Selected and translated by Paul Carus. Album form. Pp., 162. Cl.,
+     $1.00
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+OLDENBERG, H.
+
+     ANCIENT INDIA: ITS LANGUAGE AND RELIGIONS.
+
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+CARUS, PAUL.
+
+     THE ETHICAL PROBLEM.
+
+     90 pages. Cloth, 50 cents; Paper, 30 cents.
+
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+
+     Second edition, enlarged and revised. 372 pp. Cl., $1.50. Paper,
+     50c.
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+<pre>
+
+The Project Gutenberg EBook of Popular scientific lectures, by Ernst Mach
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Popular scientific lectures
+
+Author: Ernst Mach
+
+Translator: Thomas Joseph McCormack
+
+Release Date: April 22, 2012 [EBook #39508]
+
+Language: English
+
+Character set encoding: UTF-8
+
+*** START OF THIS PROJECT GUTENBERG EBOOK POPULAR SCIENTIFIC LECTURES ***
+
+
+
+
+Produced by Anna Hall, Albert László and the Online
+Distributed Proofreading Team at http://www.pgdp.net (This
+file was produced from images generously made available
+by The Internet Archive)
+
+
+
+
+
+
+</pre>
+
+<p><span class="pagenum"><a name="Page_i" id="Page_i">[Pg i]</a></span></p>
+
+<p><span class="pagenum"><a name="Page_ii" id="Page_ii">[Pg ii]</a></span></p>
+<h1>POPULAR SCIENTIFIC LECTURES.</h1>
+
+
+<hr/>
+
+<h2><a name="BY_THE_SAME_AUTHOR" id="BY_THE_SAME_AUTHOR">BY THE SAME AUTHOR.</a></h2>
+
+
+<blockquote><p><span class="smcap">The Science of Mechanics.</span> Translated from the
+Second German Edition by T. J. McCormack.
+250 Cuts and Illustrations. 534 Pages. Half
+Morocco, Gilt Top. Price, $2.50.</p>
+
+<p><span class="smcap">Contributions to the Analysis of the Sensations.</span>
+Translated by C. M. Williams. With Notes and
+New Additions by the Author. 200 Pages. 36
+Cuts. Price, $1.00.</p>
+
+<p><span class="smcap">Popular Scientific Lectures.</span> Translated by T.
+J. McCormack. Third Revised and Enlarged
+Edition. 411 Pages. 59 Cuts. Cloth, $1.50;
+Paper, 50 cents.</p></blockquote>
+
+<p class="center">THE OPEN COURT PUBLISHING CO.,<br />
+<span class="small">324 DEARBORN ST., CHICAGO.</span>
+</p><p><span class="pagenum"><a name="Page_iii" id="Page_iii">[Pg iii]</a></span></p>
+
+<hr/>
+
+
+<p class="center big bold">POPULAR<br />
+SCIENTIFIC LECTURES</p>
+
+<p class="center"><span class="small">BY</span><br/>
+ERNST MACH</p>
+
+<p class="center small">FORMERLY PROFESSOR OF PHYSICS IN THE UNIVERSITY OF PRAGUE, NOW
+PROFESSOR OF THE HISTORY AND THEORY OF INDUCTIVE
+SCIENCE IN THE UNIVERSITY OF VIENNA</p>
+
+<p class="center"><span class="small">TRANSLATED<br/>
+BY<br/></span>
+THOMAS J. McCORMACK</p>
+
+<p class="center">THIRD EDITION, REVISED AND ENLARGED</p>
+<hr/>
+<p class="center small">WITH FIFTY-NINE CUTS AND DIAGRAMS</p>
+<hr/>
+<p class="center big">CHICAGO<br/>
+THE OPEN COURT PUBLISHING COMPANY</p>
+
+<p class="center small">FOR SALE BY<br/>
+<span class="smcap">Kegan Paul, Trench, Truebner &amp; Co.</span>, LONDON<br/>
+1898
+</p><p><span class="pagenum"><a name="Page_iv" id="Page_iv">[Pg iv]</a></span></p>
+
+
+<hr/>
+
+<p class="center">COPYRIGHT</p>
+
+<p class="center"><span class="smcap">By The Open Court Publishing Co.</span></p>
+
+<div class="center">
+<table border="0" cellpadding="0" cellspacing="0" summary="copyright dates">
+<tr><td align="left">Pages 1-258&nbsp;</td><td align="left">&nbsp;in 1894.</td></tr>
+<tr><td align="left">Pages 338-374&nbsp;</td><td align="left">&nbsp;in 1894.</td></tr>
+<tr><td align="left">Pages 259-281&nbsp;</td><td align="left">&nbsp;in 1896.</td></tr>
+<tr><td align="left">Pages 282-308&nbsp;</td><td align="left">&nbsp;in 1897.</td></tr>
+<tr><td align="left">Pages 309-337&nbsp;</td><td align="left">&nbsp;in 1898.</td></tr>
+</table></div>
+
+<hr class="chap" />
+<p><span class="pagenum"><a name="Page_v" id="Page_v">[Pg v]</a></span></p>
+
+
+
+
+<h2><a name="AUTHORS_PREFACE_TO_THE_FIRST" id="AUTHORS_PREFACE_TO_THE_FIRST">AUTHOR'S PREFACE TO THE FIRST
+EDITION.</a></h2>
+
+
+<p>Popular lectures, owing to the knowledge they presuppose,
+and the time they occupy, can afford only a <i>modicum</i>
+of instruction. They must select for this purpose easy subjects,
+and restrict themselves to the exposition of the simplest and the
+most essential points. Nevertheless, by an appropriate choice of
+the matter, the <i>charm</i> and the <i>poetry</i> of research can be conveyed
+by them. It is only necessary to set forth the attractive and the
+alluring features of a problem, and to show what broad domains
+of fact can be illuminated by the light radiating from the solution
+of a single and ofttimes unobtrusive point.</p>
+
+<p>Furthermore, such lectures can exercise a favorable influence
+by showing the substantial sameness of scientific and every-day
+thought. The public, in this way, loses its shyness towards scientific
+questions, and acquires an interest in scientific work which is
+a great help to the inquirer. The latter, in his turn, is brought to
+understand that his work is a small part only of the universal process
+of life, and that the results of his labors must redound to the
+benefit not only of himself and a few of his associates, but to that
+of the collective whole.</p>
+
+<p>I sincerely hope that these lectures, in the present excellent
+translation, will be productive of good in the direction indicated.</p>
+
+<p class="right">
+<span class="smcap">E. Mach.</span><br />
+</p>
+
+<p><span class="smcap">Prague</span>, December, 1894.</p><hr class="chap" /><p><span class="pagenum"><a name="Page_vii" id="Page_vii">[Pg vii]</a><br /><a name="Page_vi" id="Page_vi">[Pg vi]</a></span></p>
+
+
+
+
+<h2><a name="TRANSLATORS_NOTE_TO_THE" id="TRANSLATORS_NOTE_TO_THE">TRANSLATOR'S NOTE TO THE
+THIRD EDITION.</a></h2>
+
+
+<p>The present third edition of this work has been enlarged by
+the addition of a new lecture, "On Some Phenomena Attending
+the Flight of Projectiles." The additions to the second
+consisted of the following four lectures and articles: Professor
+Mach's Vienna Inaugural Lecture, "The Part Played by Accident
+in Invention and Discovery," the lecture on "Sensations of Orientation,"
+recently delivered and summing up the results of an important
+psychological investigation, and two historical articles (see
+Appendix) on Acoustics and Sight.</p>
+
+<p>The lectures extend over a long period, from 1864 to 1898,
+and differ greatly in style, contents, and purpose. They were first
+published in collected form in English; afterwards two German
+editions were called for.</p>
+
+<p>As the dates of the first five lectures are not given in the footnotes
+they are here appended. The first lecture, "On the Forms
+of Liquids," was delivered in 1868 and published with that "On
+Symmetry" in 1872 (Prague). The second and third lectures, on
+acoustics, were first published in 1865 (Graz); the fourth and fifth,
+on optics, in 1867 (Graz). They belong to the earliest period of
+Professor Mach's scientific activity, and with the lectures on electrostatics
+and education will more than realise the hope expressed in
+the author's Preface.</p>
+
+<p>The eighth, ninth, tenth, eleventh, and twelfth lectures are of<span class="pagenum"><a name="Page_viii" id="Page_viii">[Pg viii]</a></span>
+a more philosophical character and deal principally with the methods
+and nature of scientific inquiry. In the ideas summarised in
+them will be found one of the most important contributions to the
+theory of knowledge made in the last quarter of a century. Significant
+hints in psychological method, and exemplary specimen-researches
+in psychology and physics, are also presented; while in
+physics many ideas find their first discussion that afterwards, under
+other names and other authorship, became rallying-cries in this
+department of inquiry.</p>
+
+<p>All the proofs of this translation have been read by Professor
+Mach himself.</p>
+
+<p class="right">
+<span class="smcap">T. J. McCormack.</span><br />
+</p>
+
+<p><span class="smcap">La Salle, Ill.</span>, May, 1898.</p>
+<hr class="chap" />
+<p><span class="pagenum"><a name="Page_ix" id="Page_ix">[Pg ix]</a></span></p>
+
+
+
+
+<h2><a name="TABLE_OF_CONTENTS" id="TABLE_OF_CONTENTS">TABLE OF CONTENTS.</a></h2>
+
+
+<ul class="toc">
+<li>&nbsp; &nbsp;<span class="label smcap">page</span></li>
+<li><a href="#THE_FORMS_OF_LIQUIDS">The Forms of Liquids</a>&nbsp; &nbsp;<span class="label">1</span></li>
+<li><a href="#THE_FIBRES_OF_CORTI">The Fibres of Corti</a>&nbsp; &nbsp;<span class="label">17</span></li>
+<li><a href="#ON_THE_CAUSES_OF_HARMONY">On the Causes of Harmony</a>&nbsp; &nbsp;<span class="label">32</span></li>
+<li><a href="#THE_VELOCITY_OF_LIGHT">The Velocity of Light</a>&nbsp; &nbsp;<span class="label">48</span></li>
+<li><a href="#WHY_HAS_MAN_TWO_EYES">Why Has Man Two Eyes?</a>&nbsp; &nbsp;<span class="label">66</span></li>
+<li><a href="#ON_SYMMETRY">On Symmetry</a>&nbsp; &nbsp;<span class="label">89</span></li>
+<li><a href="#ON_THE_FUNDAMENTAL_CONCEPTS">On the Fundamental Concepts of Electrostatics</a>&nbsp; &nbsp;<span class="label">107</span></li>
+<li><a href="#ON_THE_PRINCIPLE_OF_THE_CONSERVATION">On the Principle of the Conservation of Energy</a>&nbsp; &nbsp;<span class="label">137</span></li>
+<li><a href="#THE_ECONOMICAL_NATURE_OF">On the Economical Nature of Physical Inquiry</a>&nbsp; &nbsp;<span class="label">186</span></li>
+<li><a href="#ON_TRANSFORMATION_AND_ADAPTATION">On Transformation and Adaptation in Scientific Thought</a>&nbsp; &nbsp;<span class="label">214</span></li>
+<li><a href="#ON_THE_PRINCIPLE_OF_COMPARISON">On the Principle of Comparison in Physics</a>&nbsp; &nbsp;<span class="label">236</span></li>
+<li><a href="#THE_PART_PLAYED_BY_ACCIDENT_IN">On the Part Played by Accident in Invention and Discovery</a>&nbsp; &nbsp;<span class="label">259</span></li>
+<li><a href="#ON_SENSATIONS_OF_ORIENTATION93">On Sensations of Orientation</a>&nbsp; &nbsp;<span class="label">282</span></li>
+<li><a href="#ON_SOME_PHENOMENA_ATTENDING">On Some Phenomena Attending the Flight of Projectiles</a>&nbsp; &nbsp;<span class="label">309</span></li>
+<li><a href="#ON_INSTRUCTION_IN_THE_CLASSICS">On Instruction in the Classics and the Mathematico-Physical Sciences</a>&nbsp; &nbsp;<span class="label">338</span></li>
+<li><a href="#APPENDIX">Appendixes.</a>
+<ul class="tocsub"><li><a href="#A_CONTRIBUTION_TO_THE_HISTORY_OF_ACOUSTICS">A Contribution to the History of Acoustics</a>&nbsp; &nbsp;<span class="label">375</span></li>
+<li><a href="#REMARKS_ON_THE_THEORY_OF_SPATIAL_VISION">Remarks on the Theory of Spatial Vision</a>&nbsp; &nbsp;<span class="label">386</span></li></ul></li>
+<li><a href="#INDEX">Index</a>&nbsp; &nbsp;<span class="label">393</span></li>
+</ul>
+<p><span class="pagenum"><a name="Page_x" id="Page_x">[Pg x]</a><br /><a name="Page_1" id="Page_1">[Pg 1]</a></span></p>
+
+
+<hr class="chap" />
+
+<h2><a name="THE_FORMS_OF_LIQUIDS" id="THE_FORMS_OF_LIQUIDS">THE FORMS OF LIQUIDS.</a></h2>
+
+
+<p>What thinkest thou, dear Euthyphron, that the
+holy is, and the just, and the good? Is the holy
+holy because the gods love it, or are the gods holy because
+they love the holy? By such easy questions did
+the wise Socrates make the market-place of Athens unsafe
+and relieve presumptuous young statesmen of the
+burden of imaginary knowledge, by showing them how
+confused, unclear, and self-contradictory their ideas
+were.</p>
+
+<p>You know the fate of the importunate questioner.
+So called good society avoided him on the promenade.
+Only the ignorant accompanied him. And finally he
+drank the cup of hemlock&mdash;a lot which we ofttimes
+wish would fall to modern critics of his stamp.</p>
+
+<p>What we have learned from Socrates, however,&mdash;our
+inheritance from him,&mdash;is scientific criticism.
+Every one who busies himself with science recognises
+how unsettled and indefinite the notions are which he
+has brought with him from common life, and how, on
+a minute examination of things, old differences are<span class="pagenum"><a name="Page_2" id="Page_2">[Pg 2]</a></span>
+effaced and new ones introduced. The history of science
+is full of examples of this constant change, development,
+and clarification of ideas.</p>
+
+<p>But we will not linger by this general consideration
+of the fluctuating character of ideas, which becomes a
+source of real uncomfortableness, when we reflect that
+it applies to almost every notion of life. Rather shall
+we observe by the study of a physical example how
+much a thing changes when it is closely examined, and
+how it assumes, when thus considered, increasing definiteness
+of form.</p>
+
+<p>The majority of you think, perhaps, you know
+quite well the distinction between a liquid and a solid.
+And precisely persons who have never busied themselves
+with physics will consider this question one of
+the easiest that can be put. But the physicist knows
+that it is one of the most difficult. I shall mention
+here only the experiments of Tresca, which show that
+solids subjected to high pressures behave exactly as
+liquids do; for example, may be made to flow out in
+the form of jets from orifices in the bottoms of vessels.
+The supposed difference of kind between liquids and
+solids is thus shown to be a mere difference of degree.</p>
+
+<p>The common inference that because the earth is
+oblate in form, it was originally fluid, is an error, in
+the light of these facts. True, a rotating sphere, a few
+inches in diameter will assume an oblate form only
+if it is very soft, for example, is composed of freshly
+kneaded clay or some viscous stuff. But the earth,<span class="pagenum"><a name="Page_3" id="Page_3">[Pg 3]</a></span>
+even if it consisted of the rigidest stone, could not
+help being crushed by its tremendous weight, and must
+perforce behave as a fluid. Even our mountains could
+not extend beyond a certain height without crumbling.
+The earth <i>may</i> once have been fluid, but this by no
+means follows from its oblateness.</p>
+
+<p>The particles of a liquid are displaced on the application
+of the slightest pressure; a liquid conforms
+exactly to the shapes of the vessels in which it is contained;
+it possesses no form of its own, as you have
+all learned in the schools. Accommodating itself in
+the most trifling respects to the conditions of the vessel
+in which it is placed, and showing, even on its surface,
+where one would suppose it had the freest play, nothing
+but a polished, smiling, expressionless countenance,
+it is the courtier <i>par excellence</i> of the natural bodies.</p>
+
+<p>Liquids have no form of their own! No, not for the
+superficial observer. But persons who have observed
+that a raindrop is round and never angular, will not be
+disposed to accept this dogma so unconditionally.</p>
+
+<p>It is fair to suppose that every man, even the weakest,
+would possess a character, if it were not too difficult
+in this world to keep it. So, too, we must suppose
+that liquids would possess forms of their own, if
+the pressure of the circumstances permitted it,&mdash;if
+they were not crushed by their own weights.</p>
+
+<p>An astronomer once calculated that human beings
+could not exist on the sun, apart from its great heat,
+because they would be crushed to pieces there by their<span class="pagenum"><a name="Page_4" id="Page_4">[Pg 4]</a></span>
+own weight. The greater mass of this body would
+also make the weight of the human body there much
+greater. But on the moon, because here we should
+be much lighter, we could jump as high as the church-steeples
+without any difficulty, with the same muscular
+power which we now possess. Statues and "plaster"
+casts of syrup are undoubtedly things of fancy, even
+on the moon, but maple-syrup would flow so slowly
+there that we could easily build a maple-syrup man on
+the moon, for the fun of the thing, just as our children
+here build snow-men.</p>
+
+<p>Accordingly, if liquids have no form of their own
+with us on earth, they have, perhaps, a form of their
+own on the moon, or on some smaller and lighter heavenly
+body. The problem, then, simply is to get rid of
+the effects of gravity; and, this done, we shall be able
+to find out what the peculiar forms of liquids are.</p>
+
+<p>The problem was solved by Plateau of Ghent, whose
+method was to immerse the liquid in another of the
+same specific gravity.<a name="FNanchor_1_1" id="FNanchor_1_1"></a><a href="#Footnote_1_1" class="fnanchor">[1]</a> He employed for his experiments
+oil and a mixture of alcohol and water. By
+Archimedes's well-known principle, the oil in this mixture
+loses its entire weight. It no longer sinks beneath
+its weight; its formative forces, be they ever so
+weak, are now in full play.</p>
+
+<p>As a fact, we now see, to our surprise, that the oil,
+instead of spreading out into a layer, or lying in a<span class="pagenum"><a name="Page_5" id="Page_5">[Pg 5]</a></span>
+formless mass, assumes the shape of a beautiful and
+perfect sphere, freely suspended in the mixture, as
+the moon is in space. We can construct in this way a
+sphere of oil several inches in diameter.</p>
+
+<p>If, now, we affix a thin plate to a
+wire and insert the plate in the oil
+sphere, we can, by twisting the wire
+between our fingers, set the whole ball
+in rotation. Doing this, the ball assumes
+an oblate shape, and we can, if
+we are skilful enough, separate by such
+rotation a ring from the ball, like that
+which surrounds Saturn. This ring is
+finally rent asunder, and, breaking up
+into a number of smaller balls, exhibits
+to us a kind of model of the origin of
+the planetary system according to the
+hypothesis of Kant and Laplace.</p>
+
+<div class="figright" style="width: 150px;">
+<img src="images/i_015.jpg" width="150" height="491" alt="" />
+<span class="caption">Fig. 1.</span>
+</div>
+
+<p>Still more curious are the phenomena
+exhibited when the formative
+forces of the liquid are partly disturbed
+by putting in contact with the liquid's
+surface some rigid body. If we immerse,
+for example, the wire framework of a cube in our
+mass of oil, the oil will everywhere stick to the wire
+framework. If the quantity of oil is exactly sufficient
+we shall obtain an oil cube with perfectly smooth walls.
+If there is too much or too little oil, the walls of the
+cube will bulge out or cave in. In this manner we<span class="pagenum"><a name="Page_6" id="Page_6">[Pg 6]</a></span>
+can produce all kinds of geometrical figures of oil, for
+example, a three-sided pyramid, a cylinder (by bringing
+the oil between two wire rings), and so on. Interesting
+is the change of form that occurs when we
+gradually suck out the oil by means of a glass tube
+from the cube or pyramid. The wire holds the oil
+fast. The figure grows smaller and smaller, until it is
+at last quite thin. Ultimately it consists simply of a
+number of thin, smooth plates of oil, which extend
+from the edges of the cube to the centre, where they
+meet in a small drop. The same is true of the pyramid.</p>
+
+<div class="figcenter" style="width: 300px;">
+<img src="images/i_016.jpg" width="300" height="204" alt="" />
+<span class="caption">Fig. 2.</span>
+</div>
+
+<p>The idea now suggests itself that liquid figures as
+thin as this, and possessing, therefore, so slight a
+weight, cannot be crushed or deformed by their weight;
+just as a small, soft ball of clay is not affected in this
+respect by its weight. This being the case, we no
+longer need our mixture of alcohol and water for the
+production of figures, but can construct them in the<span class="pagenum"><a name="Page_7" id="Page_7">[Pg 7]</a></span>
+open air. And Plateau, in fact, found that these thin
+figures, or at least very similar ones, could be produced
+in the air, by dipping the wire nets described
+in a solution of soap and water and quickly drawing
+them out again. The experiment is not difficult. The
+figure is formed of itself. The preceding drawing
+represents to the eye the forms obtained with cubical
+and pyramidal nets. In the cube, thin, smooth films
+of soap-suds proceed from the edges to a small, quadratic
+film in the centre. In the pyramid, a film proceeds
+from each edge to the centre.</p>
+
+<p>These figures are so beautiful that they hardly admit
+of appropriate description. Their great regularity
+and geometrical exactness evokes surprise from all who
+see them for the first time. Unfortunately, they are of
+only short duration. They burst, on the drying of the
+solution in the air, but only after exhibiting to us the
+most brilliant play of colors, such as is often seen in
+soap-bubbles. Partly their beauty of form and partly
+our desire to examine them more minutely induces us
+to conceive of methods of endowing them with permanent
+form. This is very simply done.<a name="FNanchor_2_2" id="FNanchor_2_2"></a><a href="#Footnote_2_2" class="fnanchor">[2]</a> Instead of
+dipping the wire nets in solutions of soap, we dip them
+in pure melted colophonium (resin). When drawn
+out the figure at once forms and solidifies by contact
+with the air.</p>
+
+<p>It is to be remarked that also solid fluid-figures can<span class="pagenum"><a name="Page_8" id="Page_8">[Pg 8]</a></span>
+be constructed in the open air, if their weight be light
+enough, or the wire nets of very small dimensions. If
+we make, for example, of very fine wire a cubical net
+whose sides measure about one-eighth of an inch in
+length, we need simply to dip this net in water to obtain
+a small solid cube of water. With a piece of blotting
+paper the superfluous water may be easily removed
+and the sides of the cube made smooth.</p>
+
+<p>Yet another simple method may be devised for observing
+these figures. A drop of water on a greased
+glass plate will not run if it is small enough, but will
+be flattened by its weight, which presses it against
+its support. The smaller the drop the less the flattening.
+The smaller the drop the nearer it approaches
+the form of a sphere. On the other hand, a drop suspended
+from a stick is elongated by its weight. The
+undermost parts of a drop of water on a support are
+pressed against the support, and the upper parts are
+pressed against the lower parts because the latter cannot
+yield. But when a drop falls freely downward
+all its parts move equally fast; no part is impeded by
+another; no part presses against another. A freely
+falling drop, accordingly, is not affected by its weight;
+it acts as if it were weightless; it assumes a spherical
+form.</p>
+
+<p>A moment's glance at the soap-film figures produced
+by our various wire models, reveals to us a great
+multiplicity of form. But great as this multiplicity is,<span class="pagenum"><a name="Page_9" id="Page_9">[Pg 9]</a></span>
+the common features of the figures also are easily discernible.</p>
+
+<div class="poem"><div class="stanza">
+<span class="i0">"All forms of Nature are allied, though none is the same as the other;<br /></span>
+<span class="i0">Thus, their common chorus points to a hidden law."<br /></span>
+</div></div>
+
+<p>This hidden law Plateau discovered. It may be
+expressed, somewhat prosily, as follows:</p>
+
+<p>1) If several plane liquid films meet in a figure
+they are always three in number, and, taken in pairs,
+form, each with another, nearly equal angles.</p>
+
+<p>2) If several liquid edges meet in a figure they are
+always four in number, and, taken in pairs, form, each
+with another, nearly equal angles.</p>
+
+<p>This is a strange law, and its reason is not evident.
+But we might apply this criticism to almost all laws.
+It is not always that the motives of a law-maker are
+discernible in the form of the law he constructs. But
+our law admits of analysis into very simple elements
+or reasons. If we closely examine the paragraphs
+which state it, we shall find that their meaning is simply
+this, that the surface of the liquid assumes the shape
+of smallest area that is possible under the circumstances.</p>
+
+<p>If, therefore, some extraordinarily intelligent tailor,
+possessing a knowledge of all the artifices of the higher
+mathematics, should set himself the task of so covering
+the wire frame of a cube with cloth that every piece
+of cloth should be connected with the wire and joined
+with the remaining cloth, and should seek to accomplish
+this feat with the greatest saving of material, he<span class="pagenum"><a name="Page_10" id="Page_10">[Pg 10]</a></span>
+would construct no other figure than that which is here
+formed on the wire frame in our solution of soap and
+water. Nature acts in the construction of liquid figures
+on the principle of a covetous tailor, and gives no
+thought in her work to the fashions. But, strange to
+say, in this work, the most beautiful fashions are
+of themselves produced.</p>
+
+<p>The two paragraphs which state our law apply primarily
+only to soap-film figures, and are not applicable,
+of course, to solid oil-figures. But the principle that
+the superficial area of the liquid shall be the least
+possible under the circumstances, is applicable to all
+fluid figures. He who understands not only the letter
+but also the reason of the law will not be at a loss
+when confronted with cases to which the letter does
+not accurately apply. And this is the case with the
+principle of least superficial area. It is a sure guide
+for us even in cases in which the above-stated paragraphs
+are not applicable.</p>
+
+<p>Our first task will now be, to show by a palpable
+illustration the mode of formation of liquid figures by
+the principle of least superficial area. The oil on the
+wire pyramid in our mixture of alcohol and water, being
+unable to leave the wire edges, clings to them, and
+the given mass of oil strives so to shape itself that its
+surface shall have the least possible area. Suppose
+we attempt to imitate this phenomenon. We take a
+wire pyramid, draw over it a stout film of rubber, and
+in place of the wire handle insert a small tube leading<span class="pagenum"><a name="Page_11" id="Page_11">[Pg 11]</a></span>
+into the interior of the space enclosed by the rubber
+(Fig. 3). Through this tube we can blow in or suck
+out air. The quantity of air in the enclosure represents
+the quantity of oil. The stretched rubber film,
+which, clinging to the wire edges,
+does its utmost to contract, represents
+the surface of the oil endeavoring
+to decrease its area. By
+blowing in, and drawing out the air,
+now, we actually obtain all the oil
+pyramidal figures, from those bulged
+out to those hollowed in. Finally, when
+all the air is pumped or sucked out, the
+soap-film figure is exhibited. The rubber
+films strike together, assume the form of planes,
+and meet at four sharp edges in the centre of the
+pyramid.</p>
+
+<div class="figleft" style="width: 150px;">
+<img src="images/i_021.jpg" width="150" height="256" alt="" />
+<span class="caption">Fig. 3.</span>
+</div>
+
+<div class="figright" style="width: 300px;">
+<img src="images/i_021-1.jpg" width="300" height="173" alt="" />
+<span class="caption">Fig. 4.</span>
+</div>
+
+<p>The tendency of soap-films to assume smaller forms
+may be directly demonstrated by a method of Van der
+Mensbrugghe. If we dip a square wire frame to which<span class="pagenum"><a name="Page_12" id="Page_12">[Pg 12]</a></span>
+a handle is attached into a solution of soap and water,
+we shall obtain on the frame a beautiful, plane film of
+soap-suds. (Fig. 4.) On this we lay a thread having its
+two ends tied together. If, now, we puncture the part
+enclosed by the thread, we shall obtain a soap-film
+having a circular hole in it, whose circumference is
+the thread. The remainder of the film decreasing in
+area as much as it can, the hole assumes the largest
+area that it can. But the figure of largest area, with
+a given periphery, is the circle.</p>
+
+<div class="figcenter" style="width: 400px;">
+<img src="images/i_022.jpg" width="400" height="182" alt="" />
+<span class="caption">Fig. 5.</span>
+</div>
+
+<p>Similarly, by the principle of least superficial area,
+a freely suspended mass of oil assumes the shape of a
+sphere. The sphere is the form of least surface for a
+given content. This is evident. The more we put
+into a travelling-bag, the nearer its shape approaches
+the spherical form.</p>
+
+<p>The connexion of the two above-mentioned paragraphs
+with the principle of least superficial area may
+be shown by a yet simpler example. Picture to yourselves
+four fixed pulleys, <i>a</i>, <i>b</i>, <i>c</i>, <i>d</i>, and two movable<span class="pagenum"><a name="Page_13" id="Page_13">[Pg 13]</a></span>
+rings <i>f</i>, <i>g</i> (Fig. 5); about the pulleys and through the
+rings imagine a smooth cord passed, fastened at one
+extremity to a nail <i>e</i>, and loaded at the other with a
+weight <i>h</i>. Now this weight always tends to sink, or,
+what is the same thing, always tends to make the portion
+of the string <i>e h</i> as long as possible, and consequently
+the remainder of the string, wound round the
+pulleys, as short as possible. The strings must remain
+connected with the pulleys, and on account of the rings
+also with each other. The conditions of the case, accordingly,
+are similar to those of the liquid figures discussed.
+The result also is a similar one. When, as
+in the right hand figure of the cut, four pairs of strings
+meet, a different configuration must be established.
+The consequence of the endeavor of the string to
+shorten itself is that the rings separate from each other,
+and that now at all points only three pairs of strings
+meet, every two at equal angles of one hundred and
+twenty degrees. As a fact, by this arrangement the
+greatest possible shortening of the string is attained;
+as can be easily proved by geometry.</p>
+
+<p>This will help us to some extent to understand the
+creation of beautiful and complicated figures by the
+simple tendency of liquids to assume surfaces of least
+superficial area. But the question arises, <i>Why</i> do
+liquids seek surfaces of least superficial area?</p>
+
+<p>The particles of a liquid cling together. Drops
+brought into contact coalesce. We can say, liquid
+particles attract each other. If so, they seek to come<span class="pagenum"><a name="Page_14" id="Page_14">[Pg 14]</a></span>
+as close as they can to each other. The particles at
+the surface will endeavor to penetrate as far as they
+can into the interior. This process will not stop, cannot
+stop, until the surface has become as small as under
+the circumstances it possibly can become, until as
+few particles as possible remain at the surface, until
+as many particles as possible have penetrated into the
+interior, until the forces of attraction have no more
+work to perform.<a name="FNanchor_3_3" id="FNanchor_3_3"></a><a href="#Footnote_3_3" class="fnanchor">[3]</a></p>
+
+<p>The root of the principle of least surface is to be
+sought, accordingly, in another and much simpler
+principle, which may be illustrated by some such analogy
+as this. We can <i>conceive</i> of the natural forces of
+attraction and repulsion as purposes or intentions of
+nature. As a matter of fact, that interior pressure
+which we feel before an act and which we call an intention
+or purpose, is not, in a final analysis, so essentially
+different from the pressure of a stone on its support,
+or the pressure of a magnet on another, that it is
+necessarily unallowable to use for both the same term&mdash;at
+least for well-defined purposes.<a name="FNanchor_4_4" id="FNanchor_4_4"></a><a href="#Footnote_4_4" class="fnanchor">[4]</a> It is the purpose
+of nature, accordingly, to bring the iron nearer
+the magnet, the stone nearer the centre of the earth,
+and so forth. If such a purpose can be realised, it is
+carried out. But where she cannot realise her purposes,
+nature does nothing. In this respect she acts
+exactly as a good man of business does.</p>
+<p><span class="pagenum"><a name="Page_15" id="Page_15">[Pg 15]</a></span></p>
+<p>It is a constant purpose of nature to bring weights
+lower. We can raise a weight by causing another,
+larger weight to sink; that is, by satisfying another,
+more powerful, purpose of nature. If we fancy we
+are making nature serve our purposes in this, it will
+be found, upon closer examination, that the contrary
+is true, and that nature has employed us to attain her
+purposes.</p>
+
+<p>Equilibrium, rest, exists only, but then always, when
+nature is brought to a halt in her purposes, when the
+forces of nature are as fully satisfied as, under the
+circumstances, they can be. Thus, for example, heavy
+bodies are in equilibrium, when their so-called centre
+of gravity lies as low as it possibly can, or when as
+much weight as the circumstances admit of has sunk
+as low as it can.</p>
+
+<p>The idea forcibly suggests itself that perhaps this
+principle also holds good in other realms. Equilibrium
+exists also in the state when the purposes of the parties
+are as fully satisfied as for the time being they can
+be, or, as we may say, jestingly, in the language of
+physics, when the social potential is a maximum.<a name="FNanchor_5_5" id="FNanchor_5_5"></a><a href="#Footnote_5_5" class="fnanchor">[5]</a></p>
+
+<p>You see, our miserly mercantile principle is replete
+with consequences.<a name="FNanchor_6_6" id="FNanchor_6_6"></a><a href="#Footnote_6_6" class="fnanchor">[6]</a> The result of sober research, it
+has become as fruitful for physics as the dry questions
+of Socrates for science generally. If the principle
+seems to lack in ideality, the more ideal are the fruits
+which it bears.</p>
+<p><span class="pagenum"><a name="Page_16" id="Page_16">[Pg 16]</a></span></p>
+<p>But why, tell me, should science be ashamed of
+such a principle? Is science<a name="FNanchor_7_7" id="FNanchor_7_7"></a><a href="#Footnote_7_7" class="fnanchor">[7]</a> itself anything more
+than&mdash;a business? Is not its task to acquire with the
+least possible work, in the least possible time, with the
+least possible thought, the greatest possible part of
+eternal truth?</p>
+<p><span class="pagenum"><a name="Page_17" id="Page_17">[Pg 17]</a></span></p>
+
+
+
+<h2><a name="THE_FIBRES_OF_CORTI" id="THE_FIBRES_OF_CORTI">THE FIBRES OF CORTI.</a></h2>
+
+
+<p>Whoever has roamed through a beautiful country
+knows that the tourist's delights increase
+with his progress. How pretty that wooded dell must
+look from yonder hill! Whither does that clear brook
+flow, that hides itself in yonder sedge? If I only
+knew how the landscape looked behind that mountain!
+Thus even the child thinks in his first rambles. It is
+also true of the natural philosopher.</p>
+
+<p>The first questions are forced upon the attention of
+the inquirer by practical considerations; the subsequent
+ones are not. An irresistible attraction draws
+him to these; a nobler interest which far transcends the
+mere needs of life. Let us look at a special case.</p>
+
+<p>For a long time the structure of the organ of hearing
+has actively engaged the attention of anatomists.
+A considerable number of brilliant discoveries has been
+brought to light by their labors, and a splendid array
+of facts and truths established. But with these facts
+a host of new enigmas has been presented.</p>
+
+<p>Whilst in the theory of the organisation and functions<span class="pagenum"><a name="Page_18" id="Page_18">[Pg 18]</a></span>
+of the eye comparative clearness has been attained;
+whilst, hand in hand with this, ophthalmology
+has reached a degree of perfection which the preceding
+century could hardly have dreamed of, and by the
+help of the ophthalmoscope the observing physician
+penetrates into the profoundest recesses of the eye,
+the theory of the ear is still much shrouded in mysterious
+darkness, full of attraction for the investigator.</p>
+
+<p>Look at this model of the ear. Even at that familiar
+part by whose extent we measure the quantity of
+people's intelligence, even at the external ear, the
+problems begin. You see here a succession of helixes
+or spiral windings, at times very pretty, whose significance
+we cannot accurately state, yet for which there
+must certainly be some reason.</p>
+
+<div class="figright" style="width: 300px;">
+<img src="images/i_028.jpg" width="300" height="205" alt="" />
+<span class="caption">Fig. 6.</span>
+</div>
+
+<p>The shell or concha of the ear, <i>a</i> in the annexed
+diagram, conducts the sound into the curved auditory
+passage <i>b</i>, which is terminated by a thin membrane,
+the so-called tympanic membrane, <i>e</i>. This membrane
+is set in motion by the sound, and in its turn sets in
+motion a series of little bones of very peculiar formation,
+<i>c</i>. At the end of all is the labyrinth
+<i>d</i>. The labyrinth consists of a group of
+cavities filled with a liquid, in which the
+innumerable fibres of the nerve of hearing
+are imbedded. By the vibration of the chain of
+bones <i>c</i>, the liquid of the labyrinth is shaken, and the
+auditory nerve excited. Here the process of hearing<span class="pagenum"><a name="Page_19" id="Page_19">[Pg 19]</a></span>
+begins. So much is certain. But the details of the
+process are one and all unanswered questions.</p>
+
+<p>To these old puzzles, the Marchese Corti, as late
+as 1851, added a new enigma. And, strange to say,
+it is this last enigma, which, perhaps, has first received
+its correct solution. This will be the subject of our
+remarks to-day.</p>
+
+<p>Corti found in the cochlea, or snail-shell of the
+labyrinth, a large number of microscopic fibres placed
+side by side in geometrically graduated order. According
+to Kölliker their number is three thousand. They
+were also the subject of investigation at the hands of
+Max Schultze and Deiters.</p>
+
+<p>A description of the details of this organ would
+only weary you, besides not rendering the matter much
+clearer. I prefer, therefore, to state briefly what in
+the opinion of prominent investigators like Helmholtz
+and Fechner is the peculiar function of Corti's fibres.
+The cochlea, it seems, contains a large number of
+elastic fibres of graduated lengths (Fig. 7), to which
+the branches of the auditory nerve are
+attached. These fibres, called the fibres,
+pillars, or rods of Corti, being of unequal
+length, must also be of unequal elasticity,
+and, consequently, pitched to different
+notes. The cochlea, therefore, is a species of pianoforte.</p>
+
+<div class="figleft" style="width: 300px;">
+<img src="images/i_029.jpg" width="300" height="290" alt="" />
+<span class="caption">Fig. 7.</span>
+</div>
+
+<p>What, now, may be the office of this structure,
+which is found in no other organ of sense? May it<span class="pagenum"><a name="Page_20" id="Page_20">[Pg 20]</a></span>
+not be connected with some special property of the
+ear? It is quite probable; for the ear possesses a very
+similar power. You know that it is possible to follow
+the individual voices of a symphony. Indeed, the
+feat is possible even in a fugue of Bach, where it is certainly
+no inconsiderable achievement. The ear can
+pick out the single constituent tonal parts, not only of a
+harmony, but of the wildest clash of music imaginable.
+The musical ear analyses every agglomeration of tones.</p>
+
+<p>The eye does not possess this ability. Who, for
+example, could tell from the mere sight of white, without
+a previous experimental knowledge of the fact,
+that white is composed of a mixture of other colors?
+Could it be, now, that these two facts, the property of
+the ear just mentioned, and the structure discovered
+by Corti, are really connected? It is very probable.
+The enigma is solved if we assume that every note of
+definite pitch has its special string in this pianoforte
+of Corti, and, therefore, its special branch of the auditory
+nerve attached to that string. But before I can
+make this point perfectly plain to you, I must ask
+you to follow me a few steps into the dry domain of
+physics.</p>
+
+<p>Look at this pendulum. Forced from its position
+of equilibrium by an impulse, it begins to swing with a
+definite time of oscillation, dependent upon its length.
+Longer pendulums swing more slowly, shorter ones
+more quickly. We will suppose our pendulum to execute
+one to-and-fro movement in a second.</p><p><span class="pagenum"><a name="Page_21" id="Page_21">[Pg 21]</a></span></p>
+
+<p>This pendulum, now, can be thrown into violent
+vibration in two ways; either by a <i>single</i> heavy impulse,
+or by a <i>number</i> of properly communicated slight
+impulses. For example, we impart to the pendulum,
+while at rest in its position of equilibrium, a very slight
+impulse. It will execute a very small vibration. As
+it passes a third time its position of equilibrium, a
+second having elapsed, we impart to it again a slight
+shock, in the same direction with the first. Again after
+the lapse of a second, on its fifth passage through the
+position of equilibrium, we strike it again in the same
+manner; and so continue. You see, by this process
+the shocks imparted augment continually the motion
+of the pendulum. After each slight impulse, the pendulum
+reaches out a little further in its swing, and
+finally acquires a considerable motion.<a name="FNanchor_8_8" id="FNanchor_8_8"></a><a href="#Footnote_8_8" class="fnanchor">[8]</a></p>
+
+<p>But this is not the case under all circumstances.
+It is possible only when the impulses imparted synchronise
+with the swings of the pendulum. If we
+should communicate the second impulse at the end of
+half a second and in the same direction with the first
+impulse, its effects would counteract the motion of the
+pendulum. It is easily seen that our little impulses
+help the motion of the pendulum more and more, according
+as their time accords with the time of the
+pendulum. If we strike the pendulum in any other
+time than in that of its vibration, in some instances, it
+is true, we shall augment its vibration, but in others<span class="pagenum"><a name="Page_22" id="Page_22">[Pg 22]</a></span>
+again, we shall obstruct it. Our impulses will be less
+effective the more the motion of our own hand departs
+from the motion of the pendulum.</p>
+
+<p>What is true of the pendulum holds true of every
+vibrating body. A tuning-fork when it sounds, also
+vibrates. It vibrates more rapidly when its sound is
+higher; more slowly when it is deeper. The standard
+<i>A</i> of our musical scale is produced by about four hundred
+and fifty vibrations in a second.</p>
+
+<p>I place by the side of each other on this table two
+tuning-forks, exactly alike, resting on resonant cases.
+I strike the first one a sharp blow, so that it emits a
+loud note, and immediately grasp it again with my
+hand to quench its note. Nevertheless, you still hear
+the note distinctly sounded, and by feeling it you may
+convince yourselves that the other fork which was not
+struck now vibrates.</p>
+
+<p>I now attach a small bit of wax to one of the forks.
+It is thrown thus out of tune; its note is made a little
+deeper. I now repeat the same experiment with the
+two forks, now of unequal pitch, by striking one of
+them and again grasping it with my hand; but in the
+present case the note ceases the very instant I touch
+the fork.</p>
+
+<p>What has happened here in these two experiments?
+Simply this. The vibrating fork imparts to the air and
+to the table four hundred and fifty shocks a second,
+which are carried over to the other fork. If the other
+fork is pitched to the same note, that is to say, if it<span class="pagenum"><a name="Page_23" id="Page_23">[Pg 23]</a></span>
+vibrates when struck in the same time with the first,
+then the shocks first emitted, no matter how slight they
+may be, are sufficient to throw the second fork into rapid
+sympathetic vibration. But when the time of vibration
+of the two forks is slightly different, this does not
+take place. We may strike as many forks as we will, the
+fork tuned to <i>A</i> is perfectly indifferent to their notes;
+is deaf, in fact, to all except its own; and if you strike
+three, or four, or five, or any number whatsoever, of
+forks all at the same time, so as to make the shocks
+which come from them ever so great, the <i>A</i> fork will
+not join in with their vibrations unless another fork <i>A</i>
+is found in the collection struck. It picks out, in other
+words, from all the notes sounded, that which accords
+with it.</p>
+
+<p>The same is true of all bodies which can yield
+notes. Tumblers resound when a piano is played, on
+the striking of certain notes, and so do window panes.
+Nor is the phenomenon without analogy in other provinces.
+Take a dog that answers to the name "Nero."
+He lies under your table. You speak of Domitian,
+Vespasian, and Marcus Aurelius Antoninus, you call
+upon all the names of the Roman Emperors that occur
+to you, but the dog does not stir, although a slight
+tremor of his ear tells you of a faint response of his
+consciousness. But the moment you call "Nero" he
+jumps joyfully towards you. The tuning-fork is like
+your dog. It answers to the name <i>A</i>.</p>
+
+<p>You smile, ladies. You shake your heads. The<span class="pagenum"><a name="Page_24" id="Page_24">[Pg 24]</a></span>
+simile does not catch your fancy. But I have another,
+which is very near to you: and for punishment you shall
+hear it. You, too, are like tuning-forks. Many are the
+hearts that throb with ardor for you, of which you take
+no notice, but are cold. Yet what does it profit you!
+Soon the heart will come that beats in just the proper
+rhythm, and then your knell, too, has struck. Then
+your heart, too, will beat in unison, whether you will
+or no.</p>
+
+<p>The law of sympathetic vibration, here propounded
+for sounding bodies, suffers some modification for
+bodies incompetent to yield notes. Bodies of this
+kind vibrate to almost every note. A high silk hat,
+we know, will not sound; but if you will hold your
+hat in your hand when attending your next concert you
+will not only hear the pieces played, but also feel them
+with your fingers. It is exactly so with men. People
+who are themselves able to give tone to their surroundings,
+bother little about the prattle of others. But the
+person without character tarries everywhere: in the
+temperance hall, and at the bar of the public-house&mdash;everywhere
+where a committee is formed. The high
+silk hat is among bells what the weakling is among
+men of conviction.</p>
+
+<p>A sonorous body, therefore, always sounds when
+its special note, either alone or in company with others,
+is struck. We may now go a step further. What will
+be the behaviour of a group of sonorous bodies which
+in the pitch of their notes form a scale? Let us picture<span class="pagenum"><a name="Page_25" id="Page_25">[Pg 25]</a></span>
+to ourselves, for example (Fig. 8), a series of rods
+or strings pitched to the notes <i>c d e f g</i>.... On a
+musical instrument the accord <i>c e g</i> is struck. Every
+one of the rods of Fig. 8 will see if its special note is
+contained in the accord, and if it finds
+it, it will respond. The rod <i>c</i> will give
+at once the note <i>c</i>, the rod <i>e</i> the note <i>e</i>,
+the rod <i>g</i> the note <i>g</i>. All the other
+rods will remain at rest, will not sound.</p>
+
+<div class="figright" style="width: 300px;">
+<img src="images/i_035.jpg" width="300" height="337" alt="" />
+<span class="caption">Fig. 8.</span>
+</div>
+
+<p>We need not look about us long
+for such an instrument. Every piano
+is an instrument of this kind, with which the experiment
+mentioned may be executed with splendid success.
+Two pianos stand here by the side of each other,
+both tuned alike. We will employ the first for exciting
+the notes, while we will allow the second to respond;
+after having first pressed upon the loud pedal,
+so as to render all the strings capable of motion.</p>
+
+<p>Every harmony struck with vigor on the first piano
+is distinctly repeated on the second. To prove that
+it is the same strings that are sounded in both pianos,
+we repeat the experiment in a slightly changed form.
+We let go the loud pedal of the second piano and
+pressing on the keys <i>c e g</i> of that instrument vigorously
+strike the harmony <i>c e g</i> on the first piano. The harmony
+<i>c e g</i> is now also sounded on the second piano.
+But if we press only on one key <i>g</i> of one piano, while
+we strike <i>c e g</i> on the other, only <i>g</i> will be sounded on<span class="pagenum"><a name="Page_26" id="Page_26">[Pg 26]</a></span>
+the second. It is thus always the like strings of the
+two pianos that excite each other.</p>
+
+<p>The piano can reproduce any sound that is composed
+of its musical notes. It will reproduce, for example,
+very distinctly, a vowel sound that is sung into
+it. And in truth physics has proved that the vowels
+may be regarded as composed of simple musical
+notes.</p>
+
+<p>You see that by the exciting of definite tones in the
+air quite definite motions are set up with mechanical
+necessity in the piano. The idea might be made use
+of for the performance of some pretty pieces of wizardry.
+Imagine a box in which is a stretched string
+of definite pitch. This is thrown into motion as often
+as its note is sung or whistled. Now it would not be
+a very difficult task for a skilful mechanic to so construct
+the box that the vibrating cord would close a
+galvanic circuit and open the lock. And it would not
+be a much more difficult task to construct a box which
+would open at the whistling of a certain melody. Sesame!
+and the bolts fall. Truly, we should have here
+a veritable puzzle-lock. Still another fragment rescued
+from that old kingdom of fables, of which our day
+has realised so much, that world of fairy-stories to
+which the latest contributions are Casselli's telegraph,
+by which one can write at a distance in one's own hand,
+and Prof. Elisha Gray's telautograph. What would
+the good old Herodotus have said to these things who
+even in Egypt shook his head at much that he saw?<span class="pagenum"><a name="Page_27" id="Page_27">[Pg 27]</a></span>
+&#7952;&#956;&#959;&#7985; &#956;&#7953;&#957;e &#959;&#973; &#960;&#953;&#963;&#964;&#945;, just as simple-heartedly as then,
+when he heard of the circumnavigation of Africa.</p>
+
+<p>A new puzzle-lock! But why invent one? Are
+not we human beings ourselves puzzle-locks? Think
+of the stupendous groups of thoughts, feelings, and
+emotions that can be aroused in us by a word! Are
+there not moments in all our lives when a mere name
+drives the blood to our hearts? Who that has attended
+a large mass-meeting has not experienced what
+tremendous quantities of energy and motion can be
+evolved by the innocent words, "Liberty, Equality,
+Fraternity."</p>
+
+<p>But let us return to the subject proper of our discourse.
+Let us look again at our piano, or what will
+do just as well, at some other contrivance of the same
+character. What does this instrument do? Plainly,
+it decomposes, it analyses every agglomeration of
+sounds set up in the air into its individual component
+parts, each tone being taken up by a different string;
+it performs a real spectral analysis of sound. A person
+completely deaf, with the help of a piano, simply by
+touching the strings or examining their vibrations with
+a microscope, might investigate the sonorous motion of
+the air, and pick out the separate tones excited in it.</p>
+
+<p>The ear has the same capacity as this piano. The
+ear performs for the mind what the piano performs for
+a person who is deaf. The mind without the ear is
+deaf. But a deaf person, with the piano, does hear
+after a fashion, though much less vividly, and more<span class="pagenum"><a name="Page_28" id="Page_28">[Pg 28]</a></span>
+clumsily, than with the ear. The ear, thus, also decomposes
+sound into its component tonal parts. I shall
+now not be deceived, I think, if I assume that you
+already have a presentiment of what the function of
+Corti's fibres is. We can make the matter very plain to
+ourselves. We will use the one piano for exciting the
+sounds, and we shall imagine the second one in the
+ear of the observer in the place of Corti's fibres, which
+is a model of such an instrument. To every string of
+the piano in the ear we will suppose a special fibre of
+the auditory nerve attached, so that this fibre and this
+alone, is irritated when the string is thrown into vibration.
+If we strike now an accord on the external
+piano, for every tone of that accord a definite string of
+the internal piano will sound and as many different
+nervous fibres will be irritated as there are notes in
+the accord. The simultaneous sense-impressions due
+to different notes can thus be preserved unmingled and
+be separated by the attention. It is the same as with
+the five fingers of the hand. With each finger I can
+touch something different. Now the ear has three thousand
+such fingers, and each one is designed for the
+touching of a different tone.<a name="FNanchor_9_9" id="FNanchor_9_9"></a><a href="#Footnote_9_9" class="fnanchor">[9]</a> Our ear is a puzzle-lock
+of the kind mentioned. It opens at the magic melody
+of a sound. But it is a stupendously ingenious lock.
+Not only one tone, but every tone makes it open; but
+each one differently. To each tone it replies with a
+different sensation.</p>
+<p><span class="pagenum"><a name="Page_29" id="Page_29">[Pg 29]</a></span></p>
+<p>More than once it has happened in the history of
+science that a phenomenon predicted by theory, has
+not been brought within the range of actual observation
+until long afterwards. Leverrier predicted the
+existence and the place of the planet Neptune, but it
+was not until sometime later that Galle actually found
+the planet at the predicted spot. Hamilton unfolded
+theoretically the phenomenon of the so-called conical
+refraction of light, but it was reserved for Lloyd some
+time subsequently to observe the fact. The fortunes
+of Helmholtz's theory of Corti's fibres have been somewhat
+similar. This theory, too, received its substantial
+confirmation from the subsequent observations of
+V. Hensen. On the free surface of the bodies of Crustacea,
+connected with the auditory nerves, rows of little
+hairy filaments of varying lengths and thicknesses
+are found, which to some extent are the analogues of
+Corti's fibres. Hensen saw these hairs vibrate when
+sounds were excited, and when different notes were
+struck different hairs were set in vibration.</p>
+
+<p>I have compared the work of the physical inquirer
+to the journey of the tourist. When the tourist ascends
+a new hill he obtains of the whole district a
+different view. When the inquirer has found the solution
+of one enigma, the solution of a host of others
+falls into his hands.</p>
+
+<p>Surely you have often felt the strange impression experienced<span class="pagenum"><a name="Page_30" id="Page_30">[Pg 30]</a></span>
+when in singing through the scale the octave
+is reached, and nearly the same sensation is produced
+as by the fundamental tone. The phenomenon finds its
+explanation in the view here laid down of the ear. And
+not only this phenomenon but all the laws of the theory
+of harmony may be grasped and verified from this
+point of view with a clearness before undreamt of.
+Unfortunately, I must content myself to-day with the
+simple indication of these beautiful prospects. Their
+consideration would lead us too far aside into the fields
+of other sciences.</p>
+
+<p>The searcher of nature, too, must restrain himself
+in his path. He also is drawn along from one beauty
+to another as the tourist from dale to dale, and as circumstances
+generally draw men from one condition of
+life into others. It is not he so much that makes the
+quests, as that the quests are made of him. Yet let
+him profit by his time, and let not his glance rove aimlessly
+hither and thither. For soon the evening sun
+will shine, and ere he has caught a full glimpse of the
+wonders close by, a mighty hand will seize him and
+lead him away into a different world of puzzles.</p>
+
+<p>Respected hearers, science once stood in an entirely
+different relation to poetry. The old Hindu
+mathematicians wrote their theorems in verses, and
+lotus-flowers, roses, and lilies, beautiful sceneries,
+lakes, and mountains figured in their problems.</p>
+
+<p>"Thou goest forth on this lake in a boat. A lily
+juts forth, one palm above the water. A breeze bends<span class="pagenum"><a name="Page_31" id="Page_31">[Pg 31]</a></span>
+it downwards, and it vanishes two palms from its previous
+spot beneath the surface. Quick, mathematician,
+tell me how deep is the lake!"</p>
+
+<p>Thus spoke an ancient Hindu scholar. This poetry,
+and rightly, has disappeared from science, but from
+its dry leaves another poetry is wafted aloft which cannot
+be described to him who has never felt it. Whoever
+will fully enjoy this poetry must put his hand to
+the plough, must himself investigate. Therefore,
+enough of this! I shall reckon myself fortunate if you
+do not repent of this brief excursion into the flowered
+dale of physiology, and if you take with yourselves the
+belief that we can say of science what we say of poetry,</p>
+
+<div class="poem"><div class="stanza">
+<span class="i0">"Who the song would understand,<br /></span>
+<span class="i0">Needs must seek the song's own land;<br /></span>
+<span class="i0">Who the minstrel understand<br /></span>
+<span class="i0">Needs must seek the minstrel's land."<br /></span>
+<span class="pagenum"><a name="Page_32" id="Page_32">[Pg 32]</a></span></div></div>
+
+
+
+
+<h2><a name="ON_THE_CAUSES_OF_HARMONY" id="ON_THE_CAUSES_OF_HARMONY">ON THE CAUSES OF HARMONY.</a></h2>
+
+
+<p>We are to speak to-day of a theme which is perhaps
+of somewhat more general interest&mdash;<i>the causes of
+the harmony of musical sounds</i>. The first and simplest
+experiences relative to harmony are very ancient. Not
+so the explanation of its laws. These were first supplied
+by the investigators of a recent epoch. Allow me
+an historical retrospect.</p>
+
+<p>Pythagoras (586 B. C.) knew that the note yielded
+by a string of steady tension was converted into its
+octave when the length of the string was reduced one-half,
+and into its fifth when reduced two-thirds; and
+that then the first fundamental tone was consonant
+with the two others. He knew generally that the same
+string under fixed tension gives consonant tones when
+successively divided into lengths that are in the proportions
+of the simplest natural numbers; that is, in
+the proportions of 1:2, 2:3, 3:4, 4:5.</p>
+
+<p>Pythagoras failed to reveal the causes of these laws.
+What have consonant tones to do with the simple natural
+numbers? That is the question we should ask<span class="pagenum"><a name="Page_33" id="Page_33">[Pg 33]</a></span>
+to-day. But this circumstance must have appeared
+less strange than inexplicable to Pythagoras. This
+philosopher sought for the causes of harmony in the
+occult, miraculous powers of numbers. His procedure
+was largely the cause of the upgrowth of a numerical
+mysticism, of which the traces may still be detected in
+our oneirocritical books and among some scientists, to
+whom marvels are more attractive than lucidity.</p>
+
+<p>Euclid (300 B. C.) gives a definition of consonance
+and dissonance that could hardly be improved upon,
+in point of verbal accuracy. The consonance (&#963;&#965;&#956;&#966;&#969;&#957;&#8055;&#945;)
+of two tones, he says, is the mixture, the
+blending (&#954;&#961;&#8118;&#963;&#953;&#962;) of those two tones; dissonance
+(&#948;&#953;&#945;&#966;&#969;&#957;&#8055;&#945;), on the other hand, is the incapacity of
+the tones to blend (&#7936;&#956;&#953;&#958;&#8055;&#945;), whereby they are made
+harsh for the ear. The person who knows the correct
+explanation of the phenomenon hears it, so to speak,
+reverberated in these words of Euclid. Still, Euclid
+did not know the true cause of harmony. He had unwittingly
+come very near to the truth, but without
+really grasping it.</p>
+
+<p>Leibnitz (1646-1716 A. D.) resumed the question
+which his predecessors had left unsolved. He, of
+course, knew that musical notes were produced by vibrations,
+that twice as many vibrations corresponded
+to the octave as to the fundamental tone, etc. A passionate
+lover of mathematics, he sought for the cause
+of harmony in the secret computation and comparison
+of the simple numbers of vibrations and in the secret<span class="pagenum"><a name="Page_34" id="Page_34">[Pg 34]</a></span>
+satisfaction of the soul at this occupation. But how,
+we ask, if one does not know that musical notes are
+vibrations? The computation and the satisfaction at
+the computation must indeed be pretty secret if it is
+unknown. What queer ideas philosophers have! Could
+anything more wearisome be imagined than computation
+as a principle of æsthetics? Yes, you are not
+utterly wrong in your conjecture, yet you may be sure
+that Leibnitz's theory is not wholly nonsense, although
+it is difficult to make out precisely what he meant by
+his secret computation.</p>
+
+<p>The great Euler (1707-1783) sought the cause of
+harmony, almost as Leibnitz did, in the pleasure which
+the soul derives from the contemplation of order in the
+numbers of the vibrations.<a name="FNanchor_10_10" id="FNanchor_10_10"></a><a href="#Footnote_10_10" class="fnanchor">[10]</a></p>
+
+<p>Rameau and D'Alembert (1717-1783) approached
+nearer to the truth. They knew that in every sound
+available in music besides the fundamental note also
+the twelfth and the next higher third could be heard;
+and further that the resemblance between a fundamental
+tone and its octave was always strongly marked.
+Accordingly, the combination of the octave, fifth, third,
+etc., with the fundamental tone appeared to them "natural."
+They possessed, we must admit, the correct
+point of view; but with the simple naturalness of a
+phenomenon no inquirer can rest content; for it is precisely
+this naturalness for which he seeks his explanations.</p>
+<p><span class="pagenum"><a name="Page_35" id="Page_35">[Pg 35]</a></span></p>
+<p>Rameau's remark dragged along through the whole
+modern period, but without leading to the full discovery
+of the truth. Marx places it at the head of his
+theory of composition, but makes no further application
+of it. Also Goethe and Zelter in their correspondence
+were, so to speak, on the brink of the truth.
+Zelter knew of Rameau's view. Finally, you will be
+appalled at the difficulty of the problem, when I tell
+you that till very recent times even professors of physics
+were dumb when asked what were the causes of
+harmony.</p>
+
+<p>Not till quite recently did Helmholtz find the solution
+of the question. But to make this solution clear
+to you I must first speak of some experimental principles
+of physics and psychology.</p>
+
+<p>1) In every process of perception, in every observation,
+the attention plays a highly important part.
+We need not look about us long for proofs of this.
+You receive, for example, a letter written in a very
+poor hand. Do your best, you cannot make it out.
+You put together now these, now those lines, yet you
+cannot construct from them a single intelligible character.
+Not until you direct your attention to groups
+of lines which really belong together, is the reading of
+the letter possible. Manuscripts, the letters of which
+are formed of minute figures and scrolls, can only be
+read at a considerable distance, where the attention is<span class="pagenum"><a name="Page_36" id="Page_36">[Pg 36]</a></span>
+no longer diverted from the significant outlines to the
+details. A beautiful example of this class is furnished
+by the famous iconographs of Giuseppe Arcimboldo in
+the basement of the Belvedere gallery at Vienna. These
+are symbolic representations of water, fire, etc.: human
+heads composed of aquatic animals and of combustibles.
+At a short distance one sees only the details,
+at a greater distance only the whole figure. Yet
+a point can be easily found at which, by a simple voluntary
+movement of the attention, there is no difficulty
+in seeing now the whole figure and now the smaller
+forms of which it is composed. A picture is often seen
+representing the tomb of Napoleon. The tomb is surrounded
+by dark trees between which the bright heavens
+are visible as background. One can look a long time
+at this picture without noticing anything except the
+trees, but suddenly, on the attention being accidentally
+directed to the bright background, one sees
+the figure of Napoleon between the trees. This case
+shows us very distinctly the important part which attention
+plays. The same sensuous object can, solely
+by the interposition of attention, give rise to wholly
+different perceptions.</p>
+
+<p>If I strike a harmony, or chord, on this piano, by
+a mere effort of attention you can fix every tone of
+that harmony. You then hear most distinctly the
+fixed tone, and all the rest appear as a mere addition,
+altering only the quality, or acoustic color, of the primary
+tone. The effect of the same harmony is essentially<span class="pagenum"><a name="Page_37" id="Page_37">[Pg 37]</a></span>
+modified if we direct our attention to different
+tones.</p>
+
+<p>Strike in succession two harmonies, for example,
+the two represented in the annexed diagram, and first
+fix by the attention the upper note <i>e</i>, afterwards the
+base <i>e</i>-<i>a</i>; in the two cases you will hear the same
+sequence of harmonies differently.
+In the first case, you have the impression
+as if the fixed tone remained
+unchanged and simply altered
+its <i>timbre</i>; in the second case,
+the whole acoustic agglomeration
+seems to fall sensibly in depth.
+There is an art of composition to guide the attention
+of the hearer. But there is also an art of hearing,
+which is not the gift of every person.</p>
+
+<div class="figright" style="width: 200px;">
+<img src="images/i_047.jpg" width="200" height="178" alt="" />
+<span class="caption">Fig. 9.</span>
+</div>
+
+<p>The piano-player knows the remarkable effects obtained
+when one of the keys of a chord that is struck
+is let loose. Bar 1 played on the piano sounds almost
+like bar 2. The note which lies next to the key let
+loose resounds after its release as if it were freshly
+struck. The attention no longer occupied with the
+upper note is by that very fact insensibly led to the
+upper note.</p>
+
+<div class="figcenter" style="width: 500px;">
+<img src="images/i_047-1.jpg" width="500" height="175" alt="" />
+<span class="caption">Fig. 10.</span>
+</div>
+<p><span class="pagenum"><a name="Page_38" id="Page_38">[Pg 38]</a></span></p>
+
+<p>Any tolerably cultivated musical ear can perform
+the resolution of a harmony into its component parts.
+By much practice we can go even further. Then,
+every musical sound heretofore regarded as simple
+can be resolved into a subordinate succession
+of musical tones. For example,
+if I strike on the piano the note 1, (annexed
+diagram,) we shall hear, if we
+make the requisite effort of attention,
+besides the loud fundamental note the
+feebler, higher overtones, or harmonics,
+2 ... 7, that is, the octave, the twelfth, the double
+octave, and the third, the fifth, and the seventh of
+the double octave.</p>
+
+<div class="figright" style="width: 200px;">
+<img src="images/i_048.jpg" width="200" height="237" alt="" />
+<span class="caption">Fig. 11.</span>
+</div>
+
+<p>The same is true of every musically available
+sound. Each yields, with varying degrees of intensity,
+besides its fundamental note, also the octave, the
+twelfth, the double octave, etc. The phenomenon is
+observable with special facility on the open and closed
+flue-pipes of organs. According, now, as certain overtones
+are more or less distinctly emphasised in a
+sound, the <i>timbre</i> of the sound changes&mdash;that peculiar
+quality of the sound by which we distinguish the music
+of the piano from that of the violin, the clarinet, etc.</p>
+
+<p>On the piano these overtones can be very easily
+rendered audible. If I strike, for example, sharply
+note 1 of the foregoing series, whilst I simply press
+down upon, one after another, the keys 2, 3, ... 7,
+the notes 2, 3, ... 7 will continue to sound after the<span class="pagenum"><a name="Page_39" id="Page_39">[Pg 39]</a></span>
+striking of 1, because the strings corresponding to
+these notes, now freed from their dampers, are thrown
+into sympathetic vibration.</p>
+
+<p>As you know, this sympathetic vibration of the like-pitched
+strings with the overtones is really not to be
+conceived as sympathy, but rather as lifeless mechanical
+necessity. We must not think of this sympathetic
+vibration as an ingenious journalist pictured it, who
+tells a gruesome story of Beethoven's F minor sonata,
+Op. 2, that I cannot withhold from you. "At the
+last London Industrial Exhibition nineteen virtuosos
+played the F minor sonata on the same piano. When
+the twentieth stepped up to the instrument to play by
+way of variation the same production, to the terror of
+all present the piano began to render the sonata of its
+own accord. The Archbishop of Canterbury, who
+happened to be present, was set to work and forthwith
+expelled the F minor devil."</p>
+
+<p>Although, now, the overtones or harmonics which
+we have discussed are heard only upon a special effort
+of the attention, nevertheless they play a highly important
+part in the formation of musical <i>timbre</i>, as also
+in the production of the consonance and dissonance of
+sounds. This may strike you as singular. How can
+a thing which is heard only under exceptional circumstances
+be of importance generally for audition?</p>
+
+<p>But consider some familiar incidents of your every-day
+life. Think of how many things you see which
+you do not notice, which never strike your attention<span class="pagenum"><a name="Page_40" id="Page_40">[Pg 40]</a></span>
+until they are missing. A friend calls upon you; you
+cannot understand why he looks so changed. Not
+until you make a close examination do you discover
+that his hair has been cut. It is not difficult to tell
+the publisher of a work from its letter-press, and yet
+no one can state precisely the points by which this
+style of type is so strikingly different from that style.
+I have often recognised a book which I was in search
+of from a simple piece of unprinted white paper that
+peeped out from underneath the heap of books covering
+it, and yet I had never carefully examined the
+paper, nor could I have stated its difference from other
+papers.</p>
+
+<p>What we must remember, therefore, is that every
+sound that is musically available yields, besides its
+fundamental note, its octave, its twelfth, its double
+octave, etc., as overtones or harmonics, and that these
+are important for the agreeable combination of several
+musical sounds.</p>
+
+<p>2) One other fact still remains to be dealt with.
+Look at this tuning-fork. It yields, when struck, a perfectly
+smooth tone. But if you strike in company with
+it a second fork which is of slightly different pitch, and
+which alone also gives a perfectly smooth tone, you
+will hear, if you set both forks on the table, or hold
+both before your ear, a uniform tone no longer, but a
+number of shocks of tones. The rapidity of the shocks
+increases with the difference of the pitch of the forks.
+These shocks, which become very disagreeable for the<span class="pagenum"><a name="Page_41" id="Page_41">[Pg 41]</a></span>
+ear when they amount to thirty-three in a second, are
+called "beats."</p>
+
+<p>Always, when one of two like musical sounds is
+thrown out of unison with the other, beats arise. Their
+number increases with the divergence from unison, and
+simultaneously they grow more unpleasant. Their
+roughness reaches its maximum at about thirty-three
+beats in a second. On a still further departure from
+unison, and a consequent increase of the number of
+beats, the unpleasant effect is diminished, so that tones
+which are widely apart in pitch no longer produce
+offensive beats.</p>
+
+<p>To give yourselves a clear idea of the production
+of beats, take two metronomes and set them almost
+alike. You can, for that matter, set the two exactly
+alike. You need not fear that they will strike alike.
+The metronomes usually for sale in the shops are poor
+enough to yield, when set alike, appreciably unequal
+strokes. Set, now, these two metronomes, which strike
+at unequal intervals, in motion; you will readily see
+that their strokes alternately coincide and conflict with
+each other. The alternation is quicker the greater the
+difference of time of the two metronomes.</p>
+
+<p>If metronomes are not to be had, the experiment
+may be performed with two watches.</p>
+
+<p>Beats arise in the same way. The rhythmical
+shocks of two sounding bodies, of unequal pitch, sometimes
+coincide, sometimes interfere, whereby they alternately<span class="pagenum"><a name="Page_42" id="Page_42">[Pg 42]</a></span>
+augment and enfeeble each other's effects.
+Hence the shock-like, unpleasant swelling of the tone.</p>
+
+<p>Now that we have made ourselves acquainted with
+overtones and beats, we may proceed to the answer of
+our main question, Why do certain relations of pitch
+produce pleasant sounds, consonances, others unpleasant
+sounds, dissonances? It will be readily seen that
+all the unpleasant effects of simultaneous sound-combinations
+are the result of beats produced by those
+combinations. Beats are the only sin, the sole evil of
+music. Consonance is the coalescence of sounds without
+appreciable beats.</p>
+
+<div class="figright" style="width: 182px;">
+<img src="images/i_052.jpg" width="182" height="800" alt="" />
+<span class="caption">Fig. 12.</span>
+</div>
+
+<p>To make this perfectly clear to you I have constructed
+the model which you see in Fig. 12. It represents
+a claviatur. At its top a movable strip of wood
+<i>aa</i> with the marks 1, 2 ... 6 is placed. By setting
+this strip in any position, for example, in that where the
+mark 1 is over the note <i>c</i> of the claviatur, the marks
+2, 3 ... 6, as you see, stand over the overtones of <i>c</i>.
+The same happens when the strip is placed in any
+other position. A second, exactly similar strip, <i>bb</i>,
+possesses the same properties. Thus, together, the
+two strips, in any two positions, point out by their<span class="pagenum"><a name="Page_43" id="Page_43">[Pg 43]</a></span>
+marks all the tones brought into play upon the simultaneous
+sounding of the notes indicated by the marks 1.</p>
+
+<p>The two strips, placed over the same fundamental
+note, show that also all the overtones of those notes
+coincide. The first note is simply intensified by the
+other. The single overtones of a sound lie too far apart
+to permit appreciable beats. The second sound supplies
+nothing new, consequently, also, no new beats.
+Unison is the most perfect consonance.</p>
+
+<p>Moving one of the two strips along the other is
+equivalent to a departure from unison. All the overtones
+of the one sound now fall alongside those of the
+other; beats are at once produced; the combination
+of the tones becomes unpleasant: we obtain a dissonance.
+If we move the strip further and further along,
+we shall find that as a general rule the overtones always
+fall alongside each other, that is, always produce
+beats and dissonances. Only in a few quite definite
+positions do the overtones partially coincide. Such
+positions, therefore, signify higher degrees of euphony&mdash;they
+point out <i>the consonant intervals</i>.</p>
+
+<p>These consonant intervals can be readily found experimentally
+by cutting Fig. 12 out of paper and moving
+<i>bb</i> lengthwise along <i>aa</i>. The most perfect consonances
+are the octave and the twelfth, since in these two cases
+the overtones of the one sound coincide absolutely
+with those of the other. In the octave, for example,
+1<i>b</i> falls on 2<i>a</i>, 2<i>b</i> on 4<i>a</i>, 3<i>b</i> on 6<i>a</i>. Consonances,
+therefore, are simultaneous sound-combinations not<span class="pagenum"><a name="Page_44" id="Page_44">[Pg 44]</a></span>
+accompanied by disagreeable beats. This, by the way,
+is, expressed in English, what Euclid said in Greek.</p>
+
+<p>Only such sounds are consonant as possess in common
+some portion of their partial tones. Plainly we
+must recognise between such sounds, also when struck
+one after another, a certain affinity. For the second
+sound, by virtue of the common overtones, will produce
+partly the same sensation as the first. The octave is
+the most striking exemplification of this. When we
+reach the octave in the ascent of the scale we actually
+fancy we hear the fundamental tone repeated. The
+foundations of harmony, therefore, are the foundations
+of melody.</p>
+
+<p>Consonance is the coalescence of sounds without
+appreciable beats! This principle is competent to introduce
+wonderful order and logic into the doctrines
+of the fundamental bass. The compendiums of the
+theory of harmony which (Heaven be witness!) have
+stood hitherto little behind the cook-books in subtlety
+of logic, are rendered extraordinarily clear and simple.
+And what is more, all that the great masters, such as
+Palestrina, Mozart, Beethoven, unconsciously got
+right, and of which heretofore no text-book could render
+just account, receives from the preceding principle
+its perfect verification.</p>
+
+<p>But the beauty of the theory is, that it bears upon
+its face the stamp of truth. It is no phantom of the
+brain. Every musician can hear for himself the beats
+which the overtones of his musical sounds produce.<span class="pagenum"><a name="Page_45" id="Page_45">[Pg 45]</a></span>
+Every musician can satisfy himself that for any given
+case the number and the harshness of the beats can
+be calculated beforehand, and that they occur in exactly
+the measure that theory determines.</p>
+
+<p>This is the answer which Helmholtz gave to the
+question of Pythagoras, so far as it can be explained
+with the means now at my command. A long period
+of time lies between the raising and the solving of this
+question. More than once were eminent inquirers
+nearer to the answer than they dreamed of.</p>
+
+<p>The inquirer seeks the truth. I do not know if the
+truth seeks the inquirer. But were that so, then the
+history of science would vividly remind us of that
+classical rendezvous, so often immortalised by painters
+and poets. A high garden wall. At the right a
+youth, at the left a maiden. The youth sighs, the
+maiden sighs! Both wait. Neither dreams how near
+the other is.</p>
+
+<p>I like this simile. Truth suffers herself to be
+courted, but she has evidently no desire to be won.
+She flirts at times disgracefully. Above all, she is determined
+to be merited, and has naught but contempt
+for the man who will win her too quickly. And if,
+forsooth, one breaks his head in his efforts of conquest,
+what matter is it, another will come, and truth is always
+young. At times, indeed, it really seems as if
+she were well disposed towards her admirer, but that
+admitted&mdash;never! Only when Truth is in exceptionally
+good spirits does she bestow upon her wooer a glance<span class="pagenum"><a name="Page_46" id="Page_46">[Pg 46]</a></span>
+of encouragement. For, thinks Truth, if I do not do
+something, in the end the fellow will not seek me at all.</p>
+
+<p>This one fragment of truth, then, we have, and it
+shall never escape us. But when I reflect what it has
+cost in labor and in the lives of thinking men, how it
+painfully groped its way through centuries, a half-matured
+thought, before it became complete; when I
+reflect that it is the toil of more than two thousand
+years that speaks out of this unobtrusive model of
+mine, then, without dissimulation, I almost repent me
+of the jest I have made.</p>
+
+<p>And think of how much we still lack! When, several
+thousand years hence, boots, top-hats, hoops, pianos,
+and bass-viols are dug out of the earth, out of the
+newest alluvium as fossils of the nineteenth century;
+when the scientists of that time shall pursue their
+studies both upon these wonderful structures and upon
+our modern Broadways, as we to-day make studies of
+the implements of the stone age and of the prehistoric
+lake-dwellings&mdash;then, too, perhaps, people will be unable
+to comprehend how we could come so near to
+many great truths without grasping them. And thus
+it is for all time the unsolved dissonance, for all time
+the troublesome seventh, that everywhere resounds in
+our ears; we feel, perhaps, that it will find its solution,
+but we shall never live to see the day of the pure
+triple accord, nor shall our remotest descendants.</p>
+
+<p>Ladies, if it is the sweet purpose of your life to
+sow confusion, it is the purpose of mine to be clear;<span class="pagenum"><a name="Page_47" id="Page_47">[Pg 47]</a></span>
+and so I must confess to you a slight transgression
+that I have been guilty of. On one point I have told
+you an untruth. But you will pardon me this falsehood,
+if in full repentance I make it good. The model
+represented in Fig. 12 does not tell the whole truth, for
+it is based upon the so-called "even temperament"
+system of tuning. The overtones, however, of musical
+sounds are not tempered, but purely tuned. By means
+of this slight inexactness the model is made considerably
+simpler. In this form it is fully adequate for
+ordinary purposes, and no one who makes use of it in
+his studies need be in fear of appreciable error.</p>
+
+<p>If you should demand of me, however, the full
+truth, I could give you that only by the help of a mathematical
+formula. I should have to take the chalk into
+my hands and&mdash;think of it!&mdash;reckon in your presence.
+This you might take amiss. Nor shall it happen.
+I have resolved to do no more reckoning for to-day.
+I shall reckon now only upon your forbearance, and
+this you will surely not gainsay me when you reflect
+that I have made only a limited use of my privilege to
+weary you. I could have taken up much more of
+your time, and may, therefore, justly close with Lessing's
+epigram:</p>
+
+<div class="poem"><div class="stanza">
+<span class="i0">"If thou hast found in all these pages naught that's worth the thanks,<br /></span>
+<span class="i0">At least have gratitude for what I've spared thee."<br /></span>
+<span class="pagenum"><a name="Page_48" id="Page_48">[Pg 48]</a></span></div></div>
+
+
+
+
+<h2><a name="THE_VELOCITY_OF_LIGHT" id="THE_VELOCITY_OF_LIGHT">THE VELOCITY OF LIGHT.</a></h2>
+
+
+<p>When a criminal judge has a right crafty knave
+before him, one well versed in the arts of prevarication,
+his main object is to wring a confession from
+the culprit by a few skilful questions. In almost a similar
+position the natural philosopher seems to be placed
+with respect to nature. True, his functions here are
+more those of the spy than the judge; but his object
+remains pretty much the same. Her hidden motives
+and laws of action is what nature must be made to
+confess. Whether a confession will be extracted depends
+upon the shrewdness of the inquirer. Not without
+reason, therefore, did Lord Bacon call the experimental
+method a questioning of nature. The
+art consists in so putting our questions that they
+may not remain unanswered without a breach of etiquette.</p>
+
+<p>Look, too, at the countless tools, engines, and instruments
+of torture with which man conducts his
+inquisitions of nature, and which mock the poet's
+words:</p><p><span class="pagenum"><a name="Page_49" id="Page_49">[Pg 49]</a></span></p>
+
+<div class="poem"><div class="stanza">
+<span class="i0">"Mysterious even in open day,<br /></span>
+<span class="i0">Nature retains her veil, despite our clamors;<br /></span>
+<span class="i0">That which she doth not willingly display<br /></span>
+<span class="i0">Cannot be wrenched from her with levers, screws, and hammers."<br /></span>
+</div></div>
+
+<p>Look at these instruments and you will see that the
+comparison with torture also is admissible.<a name="FNanchor_11_11" id="FNanchor_11_11"></a><a href="#Footnote_11_11" class="fnanchor">[11]</a></p>
+
+<p>This view of nature, as of something designedly
+concealed from man, that can be unveiled only by
+force or dishonesty, chimed in better with the conceptions
+of the ancients than with modern notions. A
+Grecian philosopher once said, in offering his opinion
+of the natural science of his time, that it could only be
+displeasing to the gods to see men endeavoring to spy
+out what the gods were not minded to reveal to them.<a name="FNanchor_12_12" id="FNanchor_12_12"></a><a href="#Footnote_12_12" class="fnanchor">[12]</a>
+Of course all the contemporaries of the speaker were
+not of his opinion.</p>
+
+<p>Traces of this view may still be found to-day, but
+upon the whole we are now not so narrow-minded.
+We believe no longer that nature designedly hides
+herself. We know now from the history of science
+that our questions are sometimes meaningless, and
+that, therefore, no answer can be forthcoming. Soon
+we shall see how man, with all his thoughts and quests,
+is only a fragment of nature's life.</p>
+
+<p><span class="pagenum"><a name="Page_50" id="Page_50">[Pg 50]</a></span></p><p>Picture, then, as your fancy dictates, the tools of
+the physicist as instruments of torture or as engines of
+endearment, at all events a chapter from the history of
+those implements will be of interest to you, and it will
+not be unpleasant to learn what were the peculiar difficulties
+that led to the invention of such strange apparatus.</p>
+
+<p>Galileo (born at Pisa in 1564, died at Arcetri in
+1642) was the first who asked what was the velocity
+of light, that is, what time it would take for a light
+struck at one place to become visible at another, a
+certain distance away.<a name="FNanchor_13_13" id="FNanchor_13_13"></a><a href="#Footnote_13_13" class="fnanchor">[13]</a></p>
+
+<p>The method which Galileo devised was as simple
+as it was natural. Two practised observers, with
+muffled lanterns, were to take up positions in a dark
+night at a considerable distance
+from each other, one at
+<i>A</i> and one at <i>B</i>. At a moment
+previously fixed upon, <i>A</i> was
+instructed to unmask his lantern; while as soon as <i>B</i>
+saw the light of <i>A</i>'s lantern he was to unmask his.
+Now it is clear that the time which <i>A</i> counted from
+the uncovering of his lantern until he caught sight of
+the light of <i>B</i>'s would be the time which it would take
+light to travel from <i>A</i> to <i>B</i> and from <i>B</i> back to <i>A</i>.</p>
+
+<div class="figleft" style="width: 300px;">
+<img src="images/i_060.jpg" width="300" height="93" alt="" />
+<span class="caption">Fig. 13.</span>
+</div>
+
+<p>The experiment was not executed, nor could it, in
+the nature of the case, have been a success. As we<span class="pagenum"><a name="Page_51" id="Page_51">[Pg 51]</a></span>
+now know, light travels too rapidly to be thus noted.
+The time elapsing between the arrival of the light at
+<i>B</i> and its perception by the observer, with that between
+the decision to uncover and the uncovering of
+the lantern, is, as we now know, incomparably greater
+than the time which it takes light to travel the greatest
+earthly distances. The great velocity of light will be
+made apparent, if we reflect that a flash of lightning
+in the night illuminates instantaneously a very extensive
+region, whilst the single reflected claps of thunder
+arrive at the observer's ear very gradually and in appreciable
+succession.</p>
+
+<p>During his life, then, the efforts of Galileo to determine
+the velocity of light remained uncrowned with
+success. But the subsequent history of the measurement
+of the velocity of light is intimately associated
+with his name, for with the telescope which he constructed
+he discovered the four satellites of Jupiter,
+and these furnished the next occasion for the determination
+of the velocity of light.</p>
+
+<p>The terrestrial spaces were too small for Galileo's
+experiment. The measurement was first executed
+when the spaces of the planetary system were employed.
+Olaf Römer, (born at Aarhuus in 1644, died
+at Copenhagen in 1710) accomplished the feat (1675-1676),
+while watching with Cassini at the observatory
+of Paris the revolutions of Jupiter's moons.</p>
+
+<div class="figcenter" style="width: 600px;">
+<img src="images/i_062.jpg" width="600" height="373" alt="" />
+<span class="caption">Fig. 14.</span>
+</div>
+
+<p>Let <i>AB</i> (Fig. 14) be Jupiter's orbit. Let <i>S</i> stand
+for the sun, <i>E</i> for the earth, <i>J</i> for Jupiter, and <i>T</i> for<span class="pagenum"><a name="Page_52" id="Page_52">[Pg 52]</a></span>
+Jupiter's first satellite. When the earth is at <i>E</i><sub>1</sub> we
+see the satellite enter regularly into Jupiter's shadow,
+and by watching the time between two successive
+eclipses, can calculate its time of revolution. The
+time which Römer noted was forty-two hours, twenty-eight
+minutes, and thirty-five seconds. Now, as the
+earth passes along in its orbit towards E<sub>2</sub>, the revolutions
+of the satellite grow apparently longer and longer:
+the eclipses take place later and later. The greatest
+retardation of the eclipse, which occurs when the earth
+is at <i>E</i><sub>2</sub>, amounts to sixteen minutes and twenty-six
+seconds. As the earth passes back again to <i>E</i><sub>1</sub>, the
+revolutions grow apparently shorter, and they occur
+in exactly the time that they first did when the earth
+arrives at <i>E</i><sub>1</sub>. It is to be remarked that Jupiter changes
+only very slightly its position during one revolution of
+the earth. Römer guessed at once that these periodical
+changes of the time of revolution of Jupiter's satellite<span class="pagenum"><a name="Page_53" id="Page_53">[Pg 53]</a></span>
+were not actual, but apparent changes, which were
+in some way connected with the velocity of light.</p>
+
+<p>Let us make this matter clear to ourselves by a simile.
+We receive regularly by the post, news of the
+political status at our capital. However far away we
+may be from the capital, we hear the news of every
+event, later it is true, but of all equally late. The
+events reach us in the same succession of time as that
+in which they took place. But if we are travelling
+away from the capital, every successive post will have
+a greater distance to pass over, and the events will
+reach us more slowly than they took place. The reverse
+will be the case if we are approaching the capital.</p>
+
+<p>At rest, we hear a piece of music played in the
+same <i>tempo</i> at all distances. But the <i>tempo</i> will be
+seemingly accelerated if we are carried
+rapidly towards the band, or retarded if
+we are carried rapidly away from it.<a name="FNanchor_14_14" id="FNanchor_14_14"></a><a href="#Footnote_14_14" class="fnanchor">[14]</a></p>
+
+<div class="figleft" style="width: 150px;">
+<img src="images/i_063.jpg" width="150" height="143" alt="" />
+<span class="caption">Fig. 15.</span>
+</div>
+
+<p>Picture to yourself a cross, say the
+sails of a wind-mill (Fig. 15), in uniform
+rotation about its centre. Clearly, the rotation of the
+cross will appear to you more slowly executed if you
+are carried very rapidly away from it. For the post
+which in this case conveys to you the light and brings
+to you the news of the successive positions of the cross
+will have to travel in each successive instant over a
+longer path.</p>
+<p><span class="pagenum"><a name="Page_54" id="Page_54">[Pg 54]</a></span></p>
+<p>Now this must also be the case with the rotation
+(the revolution) of the satellite of Jupiter. The greatest
+retardation of the eclipse (16-1/2 minutes), due to
+the passage of the earth from <i>E</i><sub>1</sub> to <i>E</i><sub>2</sub>, or to its removal
+from Jupiter by a distance equal to the diameter
+of the orbit of the earth, plainly corresponds to the
+time which it takes light to traverse a distance equal to
+the diameter of the earth's orbit. The velocity of light,
+that is, the distance described by light in a second, as
+determined by this calculation, is 311,000 kilometres,<a name="FNanchor_15_15" id="FNanchor_15_15"></a><a href="#Footnote_15_15" class="fnanchor">[15]</a>
+or 193,000 miles. A subsequent correction of the diameter
+of the earth's orbit, gives, by the same method,
+the velocity of light as approximately 186,000 miles a
+second.</p>
+
+<p>The method is exactly that of Galileo; only better
+conditions are selected. Instead of a short terrestrial
+distance we have the diameter of the earth's orbit,
+three hundred and seven million kilometres; in place
+of the uncovered and covered lanterns we have the
+satellite of Jupiter, which alternately appears and disappears.
+Galileo, therefore, although he could not
+carry out himself the proposed measurement, found
+the lantern by which it was ultimately executed.</p>
+
+<p>Physicists did not long remain satisfied with this
+beautiful discovery. They sought after easier methods
+of measuring the velocity of light, such as might
+be performed on the earth. This was possible after the
+difficulties of the problem were clearly exposed. A
+measurement of the kind referred to was executed in
+1849 by Fizeau (born at Paris in 1819).</p>
+<p><span class="pagenum"><a name="Page_55" id="Page_55">[Pg 55]</a></span></p>
+<p>I shall endeavor to make the principle of Fizeau's
+apparatus clear to you. Let <i>s</i> (Fig. 16) be a disk free
+to rotate about its centre, and perforated at its rim
+with a series of holes. Let <i>l</i> be a luminous point
+casting its light on an unsilvered glass, <i>a</i>, inclined at
+an angle of forty-five degrees to the axis of the disk.
+The ray of light, reflected at this point, passes through
+one of the holes of the disk and falls at right angles
+upon a mirror <i>b</i>, erected at a point about five miles
+distant. From the mirror <i>b</i> the light is again reflected,
+passes once more through the hole in <i>s</i>, and, penetrating
+the glass plate, finally strikes the eye, <i>o</i>, of the observer.
+The eye, <i>o</i>, thus, sees the image of the luminous
+point <i>l</i> through the glass plate and the hole of
+the disk in the mirror <i>b</i>.</p>
+
+<div class="figcenter" style="width: 600px;">
+<img src="images/i_065.jpg" width="600" height="226" alt="" />
+<span class="caption">Fig. 16.</span>
+</div>
+
+<p>If, now, the disk be set in rotation, the unpierced
+spaces between the apertures will alternately take the
+place of the apertures, and the eye o will now see the
+image of the luminous point in <i>b</i> only at interrupted
+intervals. On increasing the rapidity of the rotation,<span class="pagenum"><a name="Page_56" id="Page_56">[Pg 56]</a></span>
+however, the interruptions for the eye become again
+unnoticeable, and the eye sees the mirror <i>b</i> uniformly
+illuminated.</p>
+
+<p>But all this holds true only for relatively small velocities
+of the disk, when the light sent through an
+aperture in <i>s</i> to <i>b</i> on its return strikes the aperture at
+almost the same place and passes through it a second
+time. Conceive, now, the speed of the disk to be so increased
+that the light on its return finds before it an
+unpierced space instead of an aperture, it will then no
+longer be able to reach the eye. We then see the
+mirror <i>b</i> only when no light is emitted from it, but
+only when light is sent to it; it is covered when light
+comes from it. In this case, accordingly, the mirror
+will always appear dark.</p>
+
+<p>If the velocity of rotation at this point were still
+further increased, the light sent through one aperture
+could not, of course, on its return pass through the
+same aperture but might strike the next and reach
+the eye by that. Hence, by constantly increasing the
+velocity of the rotation, the mirror <i>b</i> may be made to
+appear alternately bright and dark. Plainly, now, if
+we know the number of apertures of the disk, the number
+of rotations per second, and the distance <i>sb</i>, we
+can calculate the velocity of light. The result agrees
+with that obtained by Römer.</p>
+
+<p>The experiment is not quite as simple as my exposition
+might lead you to believe. Care must be
+taken that the light shall travel back and forth over<span class="pagenum"><a name="Page_57" id="Page_57">[Pg 57]</a></span>
+the miles of distance <i>sb</i> and <i>bs</i> undispersed. This
+difficulty is obviated by means of telescopes.</p>
+
+<p>If we examine Fizeau's apparatus closely, we shall
+recognise in it an old acquaintance: the arrangement
+of Galileo's experiment. The luminous point <i>l</i> is the
+lantern <i>A</i>, while the rotation of the perforated disk performs
+mechanically the uncovering and covering of the
+lantern. Instead of the unskilful observer <i>B</i> we have
+the mirror <i>b</i>, which is unfailingly illuminated the instant
+the light arrives from <i>s</i>. The disk <i>s</i>, by alternately
+transmitting and intercepting the reflected light, assists
+the observer <i>o</i>. Galileo's experiment is here executed,
+so to speak, countless times in a second, yet the total
+result admits of actual observation. If I might be
+pardoned the use of a phrase of Darwin's in this field,
+I should say that Fizeau's apparatus was the descendant
+of Galileo's lantern.</p>
+
+<p>A still more refined and delicate method for the
+measurement of the velocity of light was employed by
+Foucault, but a description of it here would lead us
+too far from our subject.</p>
+
+<p>The measurement of the velocity of sound is easily
+executed by the method of Galileo. It was unnecessary,
+therefore, for physicists to rack their brains further
+about the matter; but the idea which with light
+grew out of necessity was applied also in this field.
+Koenig of Paris constructs an apparatus for the measurement
+of the velocity of sound which is closely allied
+to the method of Fizeau.</p><p><span class="pagenum"><a name="Page_58" id="Page_58">[Pg 58]</a></span></p>
+
+<p>The apparatus is very simple. It consists of two
+electrical clock-works which strike simultaneously,
+with perfect precision, tenths of seconds. If we place
+the two clock-works directly side by side, we hear
+their strokes simultaneously, wherever we stand. But
+if we take our stand by the side of one of the works
+and place the other at some distance from us, in general
+a coincidence of the strokes will now not be heard.
+The companion strokes of the remote clock-work arrive,
+as sound, later. The first stroke of the remote
+work is heard, for example, immediately after the first
+of the adjacent work, and so on. But by increasing
+the distance we may produce again a coincidence of the
+strokes. For example, the first stroke of the remote
+work coincides with the second of the near work, the
+second of the remote work with the third of the near
+work, and so on. If, now, the works strike tenths of
+seconds and the distance between them is increased
+until the first coincidence is noted, plainly that distance
+is travelled over by the sound in a tenth of a
+second.</p>
+
+<p>We meet frequently the phenomenon here presented,
+that a thought which centuries of slow and
+painful endeavor are necessary to produce, when once
+developed, fairly thrives. It spreads and runs everywhere,
+even entering minds in which it could never
+have arisen. It simply cannot be eradicated.</p>
+
+<p>The determination of the velocity of light is not the
+only case in which the direct perception of the senses<span class="pagenum"><a name="Page_59" id="Page_59">[Pg 59]</a></span>
+is too slow and clumsy for use. The usual method
+of studying events too fleet for direct observation consists
+in putting into reciprocal action with them other
+events already known, the velocities of all of which
+are capable of comparison. The result is
+usually unmistakable, and susceptible of
+direct inference respecting the character of
+the event which is unknown. The velocity
+of electricity cannot be determined by direct
+observation. But it was ascertained
+by Wheatstone, simply by the expedient of
+watching an electric spark in a mirror rotating with
+tremendous known velocity.</p>
+
+<div class="figleft" style="width: 150px;">
+<img src="images/i_069.jpg" width="150" height="238" alt="" />
+<span class="caption">Fig. 17.</span>
+</div>
+
+<div class="figright" style="width: 200px;">
+<img src="images/i_069-1.jpg" width="200" height="189" alt="" />
+<span class="caption">Fig. 18.</span>
+</div>
+
+<p>If we wave a staff irregularly hither and thither,
+simple observation cannot determine how quickly it
+moves at each point of its course. But let us look at
+the staff through holes in the rim of a
+rapidly rotating disk (Fig. 17). We
+shall then see the moving staff only
+in certain positions, namely, when a
+hole passes in front of the eye. The
+single pictures of the staff remain for a
+time impressed upon the eye; we think we see several
+staffs, having some such disposition as that represented
+in Fig. 18. If, now, the holes of the disk are equally
+far apart, and the disk is rotated with uniform velocity,
+we see clearly that the staff has moved slowly
+from <i>a</i> to <i>b</i>, more quickly from <i>b</i> to <i>c</i>, still more quickly
+from <i>c</i> to <i>d</i>, and with its greatest velocity from <i>d</i> to <i>e</i>.</p><p><span class="pagenum"><a name="Page_60" id="Page_60">[Pg 60]</a></span></p>
+
+<p>A jet of water flowing from an orifice in the bottom
+of a vessel has the appearance of perfect quiet and
+uniformity, but if we illuminate it for a second, in a
+dark room, by means of an electric flash we shall see
+that the jet is composed of separate drops. By their
+quick descent the images of the drops are
+obliterated and the jet appears uniform.
+Let us look at the jet through the rotating
+disk. The disk is supposed to be rotated so
+rapidly that while the second aperture
+passes into the place of the first, drop 1
+falls into the place of 2, 2 into the place of 3, and so on.
+We see drops then always in the same places. The
+jet appears to be at rest. If we turn the disk a trifle
+more slowly, then while the second aperture passes
+into the place of the first, drop 1 will have fallen somewhat
+lower than 2, 2 somewhat lower than 3, etc.
+Through every successive aperture we shall see drops
+in successively lower positions. The jet will appear to
+be flowing slowly downwards.</p>
+
+<div class="figright" style="width: 150px;">
+<img src="images/i_070.jpg" width="150" height="184" alt="" />
+<span class="caption">Fig. 19.</span>
+</div>
+
+<p>Now let us turn the disk more rapidly. Then while
+the second aperture is passing into the place of the
+first, drop 1 will not quite have reached the place of 2,
+but will be found slightly above 2, 2 slightly above 3,
+etc. Through the successive apertures we shall see
+the drops at successively higher places. It will now
+look as if the jet were flowing upwards, as if the drops
+were rising from the lower vessel into the higher.</p>
+
+<p>You see, physics grows gradually more and more<span class="pagenum"><a name="Page_61" id="Page_61">[Pg 61]</a></span>
+terrible. The physicist will soon have it in his power
+to play the part of the famous lobster chained to the
+bottom of the Lake of Mohrin, whose direful mission,
+if ever liberated, the poet Kopisch humorously describes
+as that of a reversal of all the events of the
+world; the rafters of houses become trees again, cows
+calves, honey flowers, chickens eggs, and the poet's
+own poem flows back into his inkstand.</p>
+<p><span class="pagenum"><a name="Page_62" id="Page_62">[Pg 62]</a></span></p><p><span class="pagenum"><a name="Page_63" id="Page_63">[Pg 63]</a></span></p><p><span class="pagenum"><a name="Page_64" id="Page_64">[Pg 64]</a></span></p>
+<hr class="tb" />
+
+<p>You will now allow me the privilege of a few general
+remarks. You have seen that the same principle
+often lies at the basis of large classes of apparatus
+designed for different purposes. Frequently it is some
+very unobtrusive idea which is productive of so much
+fruit and of such extensive transformations in physical
+technics. It is not otherwise here than in practical
+life.</p>
+
+<p>The wheel of a waggon appears to us a very simple
+and insignificant creation. But its inventor was certainly
+a man of genius. The round trunk of a tree
+perhaps first accidentally led to the observation of the
+ease with which a load can be moved on a roller.
+Now, the step from a simple supporting roller to a
+fixed roller, or wheel, appears a very easy one. At
+least it appears very easy to us who are accustomed
+from childhood up to the action of the wheel. But if
+we put ourselves vividly into the position of a man
+who never saw a wheel, but had to invent one, we shall
+begin to have some idea of its difficulties. Indeed, it
+is even doubtful whether a single man could have accomplished
+this feat, whether perhaps centuries were
+not necessary to form the first wheel from the primitive
+roller.<a name="FNanchor_16_16" id="FNanchor_16_16"></a><a href="#Footnote_16_16" class="fnanchor">[16]</a></p>
+
+<p>History does not name the progressive minds who
+constructed the first wheel; their time lies far back of
+the historic period. No scientific academy crowned
+their efforts, no society of engineers elected them
+honorary members. They still live only in the stupendous
+results which they called forth. Take from
+us the wheel, and little will remain of the arts and industries
+of modern life. All disappears. From the
+spinning-wheel to the spinning-mill, from the turning-lathe
+to the rolling-mill, from the wheelbarrow to the
+railway train, all vanishes.</p>
+
+<p>In science the wheel is equally important. Whirling
+machines, as the simplest means of obtaining quick
+motions with inconsiderable changes of place, play a
+part in all branches of physics. You know Wheatstone's
+rotating mirror, Fizeau's wheel, Plateau's perforated
+rotating disks, etc. Almost the same principle
+lies at the basis of all these apparatus. They differ
+from one another no more than the pen-knife differs,
+in the purposes it serves, from the knife of the anatomist
+or the knife of the vine-dresser. Almost the same
+might be said of the screw.</p>
+
+<p>It will now perhaps be clear to you that new
+thoughts do not spring up suddenly. Thoughts need
+their time to ripen, grow, and develop in, like every
+natural product; for man, with his thoughts, is also a
+part of nature.</p>
+
+<p>Slowly, gradually, and laboriously one thought is
+transformed into a different thought, as in all likelihood
+one animal species is gradually transformed into new
+species. Many ideas arise simultaneously. They fight
+the battle for existence not otherwise than do the
+Ichthyosaurus, the Brahman, and the horse.</p>
+
+<p>A few remain to spread rapidly over all fields of
+knowledge, to be redeveloped, to be again split up, to
+begin again the struggle from the start. As many
+animal species long since conquered, the relicts of
+ages past, still live in remote regions where their enemies
+cannot reach them, so also we find conquered
+ideas still living on in the minds of many men. Whoever
+will look carefully into his own soul will acknowledge
+that thoughts battle as obstinately for existence
+as animals. Who will gainsay that many vanquished
+modes of thought still haunt obscure crannies of his
+brain, too faint-hearted to step out into the clear light
+of reason? What inquirer does not know that the
+hardest battle, in the transformation of his ideas, is
+fought with himself.</p>
+
+<p>Similar phenomena meet the natural inquirer in all
+paths and in the most trifling matters. The true inquirer
+seeks the truth everywhere, in his country-walks
+and on the streets of the great city. If he is
+not too learned, he will observe that certain things,
+like ladies' hats, are constantly subject to change. I
+have not pursued special studies on this subject, but
+as long as I can remember, one form has always
+gradually changed into another. First, they wore hats
+with long projecting rims, within which, scarcely accessible
+with a telescope, lay concealed the face of the
+beautiful wearer. The rim grew smaller and smaller;
+the bonnet shrank to the irony of a hat. Now a tremendous
+superstructure is beginning to grow up in its
+place, and the gods only know what its limits will be.
+It is not otherwise with ladies' hats than with butterflies,
+whose multiplicity of form often simply comes
+from a slight excrescence on the wing of one species
+developing in a cognate species to a tremendous fold.
+Nature, too, has its fashions, but they last thousands
+of years. I could elucidate this idea by many additional
+examples; for instance, by the history of the
+evolution of the coat, if I were not fearful that my
+gossip might prove irksome to you.</p>
+<p><span class="pagenum"><a name="Page_65" id="Page_65">[Pg 65]</a></span></p><p><span class="pagenum"><a name="Page_66" id="Page_66">[Pg 66]</a></span></p>
+<hr class="tb" />
+
+<p>We have now wandered through an odd corner of
+the history of science. What have we learned? The
+solution of a small, I might almost say insignificant,
+problem&mdash;the measurement of the velocity of light.
+And more than two centuries have worked at its solution!
+Three of the most eminent natural philosophers,
+Galileo, an Italian, Römer, a Dane, and Fizeau, a
+Frenchman, have fairly shared its labors. And so it
+is with countless other questions. When we contemplate
+thus the many blossoms of thought that must
+wither and fall before one shall bloom, then shall we
+first truly appreciate Christ's weighty but little consolatory
+words: "Many be called but few are chosen."</p>
+
+<p>Such is the testimony of every page of history.
+But is history right? Are really only those chosen
+whom she names? Have those lived and battled in
+vain, who have won no prize?</p>
+
+<p>I doubt it. And so will every one who has felt the
+pangs of sleepless nights spent in thought, at first fruitless,
+but in the end successful. No thought in such
+struggles was thought in vain; each one, even the most
+insignificant, nay, even the erroneous thought, that
+which apparently was the least productive, served to
+prepare the way for those that afterwards bore fruit.
+And as in the thought of the individual naught is in
+vain, so, also, it is in that of humanity.</p>
+
+<p>Galileo wished to measure the velocity of light.
+He had to close his eyes before his wish was realised.
+But he at least found the lantern by which his successor
+could accomplish the task.</p>
+
+<p>And so I may maintain that we all, so far as inclination
+goes, are working at the civilisation of the future.
+If only we all strive for the right, then are we <i>all</i>
+called and <i>all</i> chosen!</p>
+
+
+
+
+<h2><a name="WHY_HAS_MAN_TWO_EYES" id="WHY_HAS_MAN_TWO_EYES">WHY HAS MAN TWO EYES?</a></h2>
+
+
+<p>Why has man two eyes? That the pretty symmetry
+of his face may not be disturbed, the
+artist answers. That his second eye may furnish a
+substitute for his first if that be lost, says the far-sighted
+economist. That we may weep with two eyes
+at the sins of the world, replies the religious enthusiast.</p>
+
+<p>Odd opinions! Yet if you should approach a modern
+scientist with this question you might consider
+yourself fortunate if you escaped with less than a rebuff.
+"Pardon me, madam, or my dear sir," he would
+say, with stern expression, "man fulfils no purpose in
+the possession of his eyes; nature is not a person, and
+consequently not so vulgar as to pursue purposes of
+any kind."</p>
+
+<p>Still an unsatisfactory answer! I once knew a professor
+who would shut with horror the mouths of his
+pupils if they put to him such an unscientific question.</p>
+
+<p>But ask a more tolerant person, ask me. I, I candidly
+confess, do not know exactly why man has two<span class="pagenum"><a name="Page_67" id="Page_67">[Pg 67]</a></span>
+eyes, but the reason partly is, I think, that I may see
+you here before me to-night and talk with you upon
+this delightful subject.</p>
+
+<p>Again you smile incredulously. Now this is one of
+those questions that a hundred wise men together
+could not answer. You have heard, so far, only five of
+these wise men. You will certainly want to be spared
+the opinions of the other ninety-five. To the first you
+will reply that we should look just as pretty if we were
+born with only one eye, like the Cyclops; to the second
+we should be much better off, according to his
+principle, if we had four or eight eyes, and that in this
+respect we are vastly inferior to spiders; to the third,
+that you are not just in the mood to weep; to the
+fourth, that the unqualified interdiction of the question
+excites rather than satisfies your curiosity; while of
+me you will dispose by saying that my pleasure is not
+as intense as I think, and certainly not great enough
+to justify the existence of a double eye in man since
+the fall of Adam.</p>
+
+<p>But since you are not satisfied with my brief and
+obvious answer, you have only yourselves to blame
+for the consequences. You must now listen to a longer
+and more learned explanation, such as it is in my
+power to give.</p>
+
+<p>As the church of science, however, debars the question
+"Why?" let us put the matter in a purely orthodox
+way: Man has two eyes, what <i>more</i> can he see with
+two than with one?</p><p><span class="pagenum"><a name="Page_68" id="Page_68">[Pg 68]</a></span></p>
+
+<p>I will invite you to take a walk with me? We see
+before us a wood. What is it that makes this real
+wood contrast so favorably with a painted wood, no
+matter how perfect the painting may be? What makes
+the one so much more lovely than the other? Is it the
+vividness of the coloring, the distribution of the lights
+and the shadows? I think
+not. On the contrary, it
+seems to me that in this
+respect painting can accomplish
+very much.</p>
+
+<p>The cunning hand of
+the painter can conjure up
+with a few strokes of his
+brush forms of wonderful
+plasticity. By the help of
+other means even more
+can be attained. Photographs
+of reliefs are so
+plastic that we often imagine
+we can actually lay
+hold of the elevations and
+depressions.</p>
+
+<div class="figleft" style="width: 300px;">
+<img src="images/i_078.jpg" width="300" height="496" alt="" />
+<span class="caption">Fig. 20.</span>
+</div>
+
+<p>But one thing the painter never can give with the
+vividness that nature does&mdash;the difference of near and
+far. In the real woods you see plainly that you can
+lay hold of some trees, but that others are inaccessibly
+far. The picture of the painter is rigid. The picture
+of the real woods changes on the slightest movement.<span class="pagenum"><a name="Page_69" id="Page_69">[Pg 69]</a></span>
+Now this branch is hidden behind that; now that behind
+this. The trees are alternately visible and invisible.</p>
+
+<p>Let us look at this matter a little more closely.
+For convenience sake we shall remain upon the highway,
+I, II. (Fig. 20.) To the right and the left lies the
+forest. Standing at I, we see, let us say, three trees
+(1, 2, 3) in a line, so that the two remote ones are
+covered by the nearest. Moving further along, this
+changes. At II we shall not have to look round so far
+to see the remotest tree 3 as to see the nearer tree 2,
+nor so far to see this as to see 1. <i>Hence, as we move
+onward, objects that are near to us seem to lag behind as
+compared with objects that are remote from us, the lagging
+increasing with the proximity of the objects.</i> Very remote
+objects, towards which we must always look in the
+same direction as we proceed, appear to travel along
+with us.</p>
+
+<p>If we should see, therefore, jutting above the brow
+of yonder hill the tops of two trees whose distance
+from us we were in doubt about, we should have in
+our hands a very easy means of deciding the question.
+We should take a few steps forward, say to the right,
+and the tree-top which receded most to the left would
+be the one nearer to us. In truth, from the amount
+of the recession a geometer could actually determine
+the distance of the trees from us without ever going
+near them. It is simply the scientific development of<span class="pagenum"><a name="Page_70" id="Page_70">[Pg 70]</a></span>
+this perception that enables us to measure the distances
+of the stars.</p>
+
+<p><i>Hence, from change of view in forward motion the
+distances of objects in our field of vision can be measured.</i></p>
+
+<p>Rigorously, however, even forward motion is not
+necessary. For every observer is composed really of
+<i>two</i> observers. Man has <i>two</i> eyes. The right eye is
+a short step ahead of the left eye in the right-hand direction.
+Hence, the two eyes receive <i>different</i> pictures
+of the same woods. The right eye will see the
+near trees displaced to the left, and the left eye will
+see them displaced to the right, the displacement being
+greater, the greater the proximity. This difference is
+sufficient for forming ideas of distance.</p>
+
+<p>We may now readily convince ourselves of the following
+facts:</p>
+
+<p>1. With one eye, the other being shut, you have a
+very uncertain judgment of distances. You will find
+it, for example, no easy task, with one eye shut, to
+thrust a stick through a ring hung up before you; you
+will miss the ring in almost every instance.</p>
+
+<p>2. You see the same object differently with the
+right eye from what you do with the left.</p>
+
+<p>Place a lamp-shade on the table in front of you
+with its broad opening turned downwards, and look
+at it from above. (Fig. 21.) You will see with your
+right eye the image 2, with your left eye the image 1.
+Again, place the shade with its wide opening turned
+upwards; you will receive with your right eye the image<span class="pagenum"><a name="Page_71" id="Page_71">[Pg 71]</a></span>
+4, with your left eye the image 3. Euclid mentions
+phenomena of this character.</p>
+
+<p>3. Finally, you know that it is easy to judge of
+distances with both eyes. Accordingly your judgment
+must spring in some way from a co-operation of the
+two eyes. In the preceding example the openings in
+the different images received by the two eyes seem
+displaced with respect to one another, and this displacement
+is sufficient for the inference that the one
+opening is nearer than the other.</p>
+
+<div class="figcenter" style="width: 450px;">
+<img src="images/i_081.jpg" width="450" height="446" alt="" />
+<span class="caption">Fig. 21.</span>
+</div>
+
+<p>I have no doubt that you, ladies, have frequently
+received delicate compliments upon your eyes, but I<span class="pagenum"><a name="Page_72" id="Page_72">[Pg 72]</a></span>
+feel sure that no one has ever told you, and I know not
+whether it will flatter you, that you have in your eyes,
+be they blue or black, little geometricians. You say
+you know nothing of them? Well, for that matter,
+neither do I. But the facts are as I tell you.</p>
+
+<p>You understand little of geometry? I shall accept
+that confession. Yet with the help of your two eyes
+you judge of distances? Surely that is a geometrical
+problem. And what is more, you know the solution
+of this problem: for you estimate distances correctly.
+If, then, <i>you</i> do not solve the problem, the little geometricians
+in your eyes must do it clandestinely and whisper
+the solution to you. I doubt not they are fleet little
+fellows.</p>
+
+<p>What amazes me most here is, that you know nothing
+about these little geometricians. But perhaps they
+also know nothing about you. Perhaps they are models
+of punctuality, routine clerks who bother about
+nothing but their fixed work. In that case we may
+be able to deceive the gentlemen.</p>
+
+<p>If we present to our right eye an image which looks
+exactly like the lamp-shade for the right eye, and to
+our left eye an image which looks exactly like a lamp-shade
+for the left eye, we shall imagine that we see
+the whole lamp-shade bodily before us.</p>
+
+<p>You know the experiment. If you are practised in
+squinting, you can perform it directly with the figure,
+looking with your right eye at the right image, and
+with your left eye at the left image. In this way the<span class="pagenum"><a name="Page_73" id="Page_73">[Pg 73]</a></span>
+experiment was first performed by Elliott. Improved
+and perfected, its form is Wheatstone's stereoscope,
+made so popular and useful by Brewster.</p>
+
+<p>By taking two photographs of the same object from
+two different points, corresponding to the two eyes, a
+very clear three-dimensional picture of distant places
+or buildings can be produced by the stereoscope.</p>
+
+<p>But the stereoscope accomplishes still more than
+this. It can visualise things for us which we never see
+with equal clearness in real objects. You know that
+if you move much while your photograph is being
+taken, your picture will come out like that of a Hindu
+deity, with several heads or several arms, which, at
+the spaces where they overlap, show forth with equal
+distinctness, so that we seem to see the one picture
+<i>through</i> the other. If a person moves quickly away
+from the camera before the impression is completed,
+the objects behind him will also be imprinted upon
+the photograph; the person will look transparent.
+Photographic ghosts are made in this way.</p>
+
+<p>Some very useful applications may be made of this
+discovery. For example, if we photograph a machine
+stereoscopically, successively removing during the
+operation the single parts (where of course the impression
+suffers interruptions), we obtain a transparent
+view, endowed with all the marks of spatial solidity,
+in which is distinctly visualised the interaction of parts
+normally concealed. I have employed this method for<span class="pagenum"><a name="Page_74" id="Page_74">[Pg 74]</a></span>
+obtaining transparent stereoscopic views of anatomical
+structures.</p>
+
+<p>You see, photography is making stupendous advances,
+and there is great danger that in time some
+malicious artist will photograph his innocent patrons
+with solid views of their most secret thoughts and
+emotions. How tranquil politics will then be! What
+rich harvests our detective force will reap!</p>
+<p><span class="pagenum"><a name="Page_75" id="Page_75">[Pg 75]</a></span><span class="pagenum"><a name="Page_76" id="Page_76">[Pg 76]</a></span><span class="pagenum"><a name="Page_77" id="Page_77">[Pg 77]</a></span><span class="pagenum"><a name="Page_78" id="Page_78">[Pg 78]</a></span><span class="pagenum"><a name="Page_79" id="Page_79">[Pg 79]</a></span><span class="pagenum"><a name="Page_80" id="Page_80">[Pg 80]</a></span><span class="pagenum"><a name="Page_81" id="Page_81">[Pg 81]</a></span><span class="pagenum"><a name="Page_82" id="Page_82">[Pg 82]</a></span><span class="pagenum"><a name="Page_83" id="Page_83">[Pg 83]</a></span><span class="pagenum"><a name="Page_84" id="Page_84">[Pg 84]</a></span><span class="pagenum"><a name="Page_85" id="Page_85">[Pg 85]</a></span><span class="pagenum"><a name="Page_86" id="Page_86">[Pg 86]</a></span></p>
+<hr class="tb" />
+
+<p>By the joint action of the two eyes, therefore, we
+arrive at our judgments of distances, as also of the
+forms of bodies.</p>
+
+<p>Permit me to mention here a few additional facts
+connected with this subject, which will assist us in the
+comprehension of certain phenomena in the history of
+civilisation.</p>
+
+<p>You have often heard, and know from personal experience,
+that remote objects appear perspectively
+dwarfed. In fact, it is easy to satisfy yourself that
+you can cover the image of a man a few feet away
+from you simply by holding up your finger a short distance
+in front of your eye. Still, as a general rule,
+you do not notice this shrinkage of objects. On the
+contrary, you imagine you see a man at the end of a
+large hall, as large as you see him near by you. For
+your eye, in its measurement of the distances, makes
+remote objects correspondingly larger. The eye, so to
+speak, is aware of this perspective contraction and is
+not deceived by it, although its possessor is unconscious
+of the fact. All persons who have attempted to draw
+from nature have vividly felt the difficulty which this
+superior dexterity of the eye causes the perspective
+conception. Not until one's judgment of distances is
+made uncertain, by their size, or from lack of points
+of reference, or from being too quickly changed, is the
+perspective rendered very prominent.</p>
+
+<p>On sweeping round a curve on a rapidly moving
+railway train, where a wide prospect is suddenly
+opened up, the men upon distant hills appear like
+dolls.<a name="FNanchor_17_17" id="FNanchor_17_17"></a><a href="#Footnote_17_17" class="fnanchor">[17]</a> You have at the moment, here, no known
+references for the measurement of distances. The
+stones at the entrance of a tunnel grow visibly larger
+as we ride towards it; they shrink visibly in size as we
+ride from it.</p>
+
+<p>Usually both eyes work together. As certain views
+are frequently repeated, and lead always to substantially
+the same judgments of distances, the eyes in
+time must acquire a special skill in geometrical constructions.
+In the end, undoubtedly, this skill is so
+increased that a single eye alone is often tempted to
+exercise that office.</p>
+
+<p>Permit me to elucidate this point by an example.
+Is any sight more familiar to you than that of a vista
+down a long street? Who has not looked with hopeful
+eyes time and again into a street and measured its
+depth. I will take you now into an art-gallery where
+I will suppose you to see a picture representing a vista
+into a street. The artist has not spared his rulers to
+get his perspective perfect. The geometrician in your
+left eye thinks, "Ah ha! I have computed that case a
+hundred times or more. I know it by heart. It is a
+vista into a street," he continues; "where the houses
+are lower is the remote end." The geometrician in
+the right eye, too much at his ease to question his
+possibly peevish comrade in the matter, answers the
+same. But the sense of duty of these punctual little
+fellows is at once rearoused. They set to work at their
+calculations and immediately find that all the points
+of the picture are equally distant from them, that is,
+lie all upon a plane surface.</p>
+
+<p>What opinion will you now accept, the first or the
+second? If you accept the first you will see distinctly
+the vista. If you accept the second you will see nothing
+but a painted sheet of distorted images.</p>
+
+<p>It seems to you a trifling matter to look at a picture
+and understand its perspective. Yet centuries
+elapsed before humanity came fully to appreciate this
+trifle, and even the majority of you first learned it from
+education.</p>
+
+<p>I can remember very distinctly that at three years
+of age all perspective drawings appeared to me as
+gross caricatures of objects. I could not understand
+why artists made tables so broad at one end and so
+narrow at the other. Real tables seemed to me just
+as broad at one end as at the other, because my eye
+made and interpreted its calculations without my intervention.
+But that the picture of the table on the
+plane surface was not to be conceived as a plane painted
+surface but stood for a table and so was to be imaged
+with all the attributes of extension was a joke that I
+did not understand. But I have the consolation that
+whole nations have not understood it.</p>
+
+<p>Ingenuous people there are who take the mock
+murders of the stage for real murders, the dissembled
+actions of the players for real actions, and who can
+scarcely restrain themselves, when the characters of the
+play are sorely pressed, from running in deep indignation
+to their assistance. Others, again, can never forget
+that the beautiful landscapes of the stage are
+painted, that Richard III. is only the actor, Mr. Booth,
+whom they have met time and again at the clubs.</p>
+
+<p>Both points of view are equally mistaken. To look
+at a drama or a picture properly one must understand
+that both are <i>shows</i>, simply <i>denoting</i> something real.
+A certain preponderance of the intellectual life over
+the sensuous life is requisite for such an achievement,
+where the intellectual elements are safe from destruction
+by the direct sensuous impressions. A certain
+liberty in choosing one's point of view is necessary, a
+sort of humor, I might say, which is strongly wanting
+in children and in childlike peoples.</p>
+
+<p>Let us look at a few historical facts. I shall not
+take you as far back as the stone age, although we
+possess sketches from this epoch which show very original
+ideas of perspective. But let us begin our sight-seeing
+in the tombs and ruined temples of ancient
+Egypt, where the numberless reliefs and gorgeous colorings
+have defied the ravages of thousands of years.</p>
+
+<p>A rich and motley life is here opened to us. We
+find the Egyptians represented in all conditions of life.
+What at once strikes our attention in these pictures
+is the delicacy of their technical execution. The contours
+are extremely exact and distinct. But on the
+other hand only a few bright colors are found, unblended
+and without trace of transition. Shadows are
+totally wanting. The paint is laid on the surfaces in
+equal thicknesses.</p>
+
+<p>Shocking for the modern eye is the perspective.
+All the figures are equally large, with the exception of
+the king, whose form is unduly exaggerated. Near and
+far appear equally large. Perspective contraction is
+nowhere employed. A pond with water-fowl is represented
+flat, as if its surface were vertical.</p>
+
+<p>Human figures are portrayed as they are never
+seen, the legs from the side, the face in profile. The
+breast lies in its full breadth across the plane of representation.
+The heads of cattle appear in profile,
+while the horns lie in the plane of the drawing. The
+principle which the Egyptians followed might be best
+expressed by saying that their figures are pressed in
+the plane of the drawing as plants are pressed in a
+herbarium.</p>
+
+<p>The matter is simply explained. If the Egyptians
+were accustomed to looking at things ingenuously
+with both eyes at once, the construction of perspective
+pictures in space could not be familiar to them.
+They saw all arms, all legs on real men in their natural
+lengths. The figures pressed into the planes resembled
+more closely, of course, in their eyes the
+originals than perspective pictures could.</p>
+
+<p>This will be better understood if we reflect that
+painting was developed from relief. The minor dissimilarities
+between the pressed figures and the originals
+must gradually have compelled men to the adoption
+of perspective drawing. But physiologically the
+painting of the Egyptians is just as much justified as
+the drawings of our children are.</p>
+
+<p>A slight advance beyond the Egyptians is shown
+by the Assyrians. The reliefs rescued from the ruined
+mounds of Nimrod at Mossul are, upon the whole,
+similar to the Egyptian reliefs. They were made known
+to us principally by Layard.</p>
+
+<p>Painting enters on a new phase among the Chinese.
+This people have a marked feeling for perspective
+and correct shading, yet without being very logical
+in the application of their principles. Here, too,
+it seems, they took the first step but did not go far.
+In harmony with this immobility is their constitution,
+in which the muzzle and the bamboo-rod play significant
+functions. In accord with it, too, is their
+language, which like the language of children has not
+yet developed into a grammar, or, rather, according
+to the modern conception, has not yet degenerated
+into a grammar. It is the same also with their music
+which is satisfied with the five-toned scale.</p>
+
+<p>The mural paintings at Herculaneum and Pompeii
+are distinguished by grace of representation, as also
+by a pronounced sense for perspective and correct illumination,
+yet they are not at all scrupulous in construction.
+Here still we find abbreviations avoided.
+But to offset this defect, the members of the body are
+brought into unnatural positions, in which they appear
+in their full lengths. Abridgements are more frequently
+observed in clothed than in unclothed figures.</p>
+
+<p>A satisfactory explanation of these phenomena first
+occurred to me on the making of a few simple experiments
+which show how differently one may see the
+same object, after some mastery of one's senses has
+been attained, simply by the arbitrary
+movement of the attention.</p>
+
+<div class="figcenter" style="width: 150px;">
+<img src="images/i_090.jpg" width="150" height="191" alt="" />
+<span class="caption">Fig. 22.</span>
+</div>
+
+<p>Look at the annexed drawing (Fig. 22).
+It represents a folded sheet of paper with
+either its depressed or its elevated side
+turned towards you, as you wish. You can
+conceive the drawing in either sense, and
+in either case it will appear to you differently.</p>
+
+<p>If, now, you have a real folded sheet of paper on
+the table before you, with its sharp edges turned towards
+you, you can, on looking at it with one eye, see
+the sheet alternately elevated, as it really is, or depressed.
+Here, however, a remarkable phenomenon
+is presented. When you see the sheet properly, neither
+illumination nor form presents anything conspicuous.
+When you see it bent back you see it perspectively
+distorted. Light and shadow appear much brighter
+or darker, or as if overlaid thickly with bright colors.
+Light and shadow now appear devoid of all cause.
+They no longer harmonise with the body's form, and
+are thus rendered much more prominent.</p>
+
+<p>In common life we employ the perspective and
+illumination of objects to determine their forms and
+position. Hence we do not notice the lights, the
+shadows, and the distortions. They first powerfully
+enter consciousness when we employ a different construction
+from the usual spatial one. In looking at
+the planar image of a camera obscura we are amazed
+at the plenitude of the light and the profundity of the
+shadows, both of which we do not notice in real objects.</p>
+
+<p>In my earliest youth the shadows and lights on pictures
+appeared to me as spots void of meaning. When
+I began to draw I regarded shading as a mere custom
+of artists. I once drew the portrait of our pastor, a
+friend of the family, and shaded, from no necessity,
+but simply from having seen something similar in
+other pictures, the whole half of his face black. I was
+subjected for this to a severe criticism on the part of
+my mother, and my deeply offended artist's pride is
+probably the reason that these facts remained so
+strongly impressed upon my memory.</p>
+
+<p>You see, then, that many strange things, not only
+in the life of individuals, but also in that of humanity,
+and in the history of general civilisation, may be explained
+from the simple fact that man has two eyes.</p>
+
+<p>Change man's eye and you change his conception
+of the world. We have observed the truth of this fact
+among our nearest kin, the Egyptians, the Chinese,
+and the lake-dwellers; how must it be among some of
+our remoter relatives,&mdash;with monkeys and other animals?
+Nature must appear totally different to animals
+equipped with substantially different eyes from those
+of men, as, for example, to insects. But for the present
+science must forego the pleasure of portraying this
+appearance, as we know very little as yet of the mode
+of operation of these organs.</p>
+
+<p>It is an enigma even how nature appears to animals
+closely related to man; as to birds, who see
+scarcely anything with two eyes at once, but since
+their eyes are placed on opposite sides of their heads,
+have a separate field of vision for each.<a name="FNanchor_18_18" id="FNanchor_18_18"></a><a href="#Footnote_18_18" class="fnanchor">[18]</a></p>
+
+<p>The soul of man is pent up in the prison-house of
+his head; it looks at nature through its two windows,
+the eyes. It would also fain know how nature looks
+through other windows. A desire apparently never to
+be fulfilled. But our love for nature is inventive, and
+here, too, much has been accomplished.</p>
+
+<p>Placing before me an angular mirror, consisting of
+two plane mirrors slightly inclined to each other, I see
+my face twice reflected. In the right-hand mirror I
+obtain a view of the right side, and in the left-hand
+mirror a view of the left
+side, of my face. Also
+I shall see the face of a
+person standing in front
+of me, more to the right with my right eye, more to
+the left with my left. But in order to obtain such
+widely different views of a face as those shown in the
+angular mirror, my two eyes would have to be set much
+further apart from each other than they actually are.</p>
+
+<div class="figright" style="width: 220px;">
+<img src="images/i_093.jpg" width="220" height="54" alt="" />
+<span class="caption">Fig. 23.</span>
+</div>
+
+<p>Squinting with my right eye at the image in the
+right-hand mirror, with my left eye at the image in
+the left-hand mirror, my vision will be the vision of a
+giant having an enormous head with his two eyes set
+far apart. This, also, is the impression which my own
+face makes upon me. I see it now, single and solid.
+Fixing my gaze, the relief from second to second is
+magnified, the eyebrows start forth prominently from
+above the eyes, the nose seems to grow a foot in
+length, my mustache shoots forth like a fountain from
+my lip, the teeth seem to retreat immeasurably. But
+by far the most horrible aspect of the phenomenon is
+the nose.</p>
+
+<p>Interesting in this connexion is the telestereoscope
+of Helmholtz. In the telestereoscope we view a landscape
+by looking with our right eye (Fig. 24) through
+the mirror <i>a</i> into the mirror <i>A</i>, and with our left eye
+through the mirror <i>b</i> into the mirror <i>B</i>. The mirrors
+<i>A</i> and <i>B</i> stand far apart.
+Again we see with the
+widely separated eyes
+of a giant. Everything
+appears dwarfed and
+near us. The distant
+mountains look like
+moss-covered stones at our feet. Between, you see the
+reduced model of a city, a veritable Liliput. You
+are tempted almost to stroke with your hand the soft
+forest and city, did you not fear that you might prick
+your fingers on the sharp, needle-shaped steeples, or
+that they might crackle and break off.</p>
+
+<div class="figleft" style="width: 350px;">
+<img src="images/i_094.jpg" width="350" height="201" alt="" />
+<span class="caption">Fig. 24.</span>
+</div>
+
+<p>Liliput is no fable. We need only Swift's eyes,
+the telestereoscope, to see it.</p>
+
+<p>Picture to yourself the reverse case. Let us suppose
+ourselves so small that we could take long walks
+in a forest of moss, and that our eyes were correspondingly
+near each other. The moss-fibres would appear
+like trees. On them we should see strange, unshapely
+monsters creeping about. Branches of the oak-tree,
+at whose base our moss-forest lay, would seem to us
+dark, immovable, myriad-branched clouds, painted
+high on the vault of heaven; just as the inhabitants
+of Saturn, forsooth, might see their enormous ring.
+On the tree-trunks of our mossy woodland we should
+find colossal globes several feet in diameter, brilliantly
+transparent, swayed by the winds with slow, peculiar
+motions. We should approach inquisitively and should
+find that these globes, in which here and there animals
+were gaily sporting, were liquid globes, in fact
+that they were water. A short, incautious step, the
+slightest contact, and woe betide us, our arm is irresistibly
+drawn by an invisible power into the interior of
+the sphere and held there unrelentingly fast! A drop
+of dew has engulfed in its capillary maw a manikin,
+in revenge for the thousands of drops that its big human
+counterparts have quaffed at breakfast. Thou
+shouldst have known, thou pygmy natural scientist,
+that with thy present puny bulk thou shouldst not joke
+with capillarity!</p>
+
+<p>My terror at the accident brings me back to my
+senses. I see I have turned idyllic. You must pardon
+me. A patch of greensward, a moss or heather forest
+with its tiny inhabitants have incomparably more
+charms for me than many a bit of literature with its
+apotheosis of human character. If I had the gift of
+writing novels I should certainly not make John and
+Mary my characters. Nor should I transfer my loving
+pair to the Nile, nor to the age of the old Egyptian
+Pharaohs, although perhaps I should choose that time
+in preference to the present. For I must candidly
+confess that I hate the rubbish of history, interesting
+though it may be as a mere phenomenon, because we
+cannot simply observe it but must also <i>feel</i> it, because
+it comes to us mostly with supercilious arrogance,
+mostly unvanquished. The hero of my novel would be
+a cockchafer, venturing forth in his fifth year for the
+first time with his newly grown wings into the light,
+free air. Truly it could do no harm if man would thus
+throw off his inherited and acquired narrowness of
+mind by making himself acquainted with the world-view
+of allied creatures. He could not help gaining
+incomparably more in this way than the inhabitant of
+a small town would in circumnavigating the globe and
+getting acquainted with the views of strange peoples.</p>
+<p><span class="pagenum"><a name="Page_87" id="Page_87">[Pg 87]</a></span></p><p><span class="pagenum"><a name="Page_88" id="Page_88">[Pg 88]</a></span></p><p><span class="pagenum"><a name="Page_89" id="Page_89">[Pg 89]</a></span></p>
+<hr class="tb" />
+
+<p>I have now conducted you, by many paths and by-ways,
+rapidly over hedge and ditch, to show you what
+wide vistas we may reach in every field by the rigorous
+pursuit of a single scientific fact. A close examination
+of the two eyes of man has conducted us not
+only into the dim recesses of humanity's childhood,
+but has also carried us far beyond the bourne of human
+life.</p>
+
+<p>It has surely often struck you as strange that the
+sciences are divided into two great groups; that the
+so-called humanistic sciences, belonging to the so-called
+"higher education," are placed in almost a hostile
+attitude to the natural sciences.</p>
+
+<p>I must confess I do not overmuch believe in this
+partition of the sciences. I believe that this view will
+appear as childlike and ingenuous to a matured age
+as the want of perspective in the old paintings of Egypt
+does to us. Can it really be that "higher culture" is to
+be gotten only from a few old pots and palimpsests,
+which are at best mere scraps of nature, or that more
+is to be learned from them alone than from all the rest
+of nature? I believe that both these sciences are simply
+parts of the same science, which have begun at
+different ends. If these two ends still act towards
+each other as the Montagues and Capulets, if their retainers
+still indulge in lively tilts, I believe that after
+all they are not in earnest. On the one side there is
+surely a Romeo, and on the other a Juliet, who, some
+day, it is hoped, will unite the two houses with a less
+tragic sequel than that of the play.</p>
+
+<p>Philology began with the unqualified reverence and
+apotheosis of the Greeks. Now it has begun to draw
+other languages, other peoples and their histories, into
+its sphere; it has, through the mediation of comparative
+linguistics, already struck up, though as yet somewhat
+cautiously, a friendship with physiology.</p>
+
+<p>Physical science began in the witch's kitchen. It
+now embraces the organic and inorganic worlds, and
+with the physiology of articulation and the theory of
+the senses, has even pushed its researches, at times
+impertinently, into the province of mental phenomena.</p>
+
+<p>In short, we come to the understanding of much
+within us solely by directing our glance without, and
+<i>vice versa</i>. Every object belongs to both sciences.
+You, ladies, are very interesting and difficult problems
+for the psychologist, but you are also extremely pretty
+phenomena of nature. Church and State are objects
+of the historian's research, but not less phenomena of
+nature, and in part, indeed, very curious phenomena.
+If the historical sciences have inaugurated wide extensions
+of view by presenting to us the thoughts of
+new and strange peoples, the physical sciences in a
+certain sense do this in a still greater degree. In
+making man disappear in the All, in annihilating him,
+so to speak, they force him to take an unprejudiced
+position without himself, and to form his judgments by
+a different standard from that of the petty human.</p>
+
+<p>But if you should ask me now why man has two
+eyes, I should answer:</p>
+
+<p>That he may look at nature justly and accurately;
+that he may come to understand that he himself, with
+all his views, correct and incorrect, with all his <i>haute
+politique</i>, is simply an evanescent shred of nature;
+that, to speak with Mephistopheles, he is a part of the
+part, and that it is absolutely unjustified,</p>
+
+<div class="poem"><div class="stanza">
+<span class="i0">"For man, the microcosmic fool, to see<br /></span>
+<span class="i0">Himself a whole so frequently."<br /></span>
+</div></div>
+
+
+
+
+<h2><a name="ON_SYMMETRY" id="ON_SYMMETRY">ON SYMMETRY.</a></h2><p><a name="FNanchor_19_19" id="FNanchor_19_19"></a><a href="#Footnote_19_19" class="fnanchor">[19]</a></p>
+
+
+<p>An ancient philosopher once remarked that people
+who cudgelled their brains about the nature of
+the moon reminded him of men who discussed the
+laws and institutions of a distant city of which they
+had heard no more than the name. The true philosopher,
+he said, should turn his glance within, should
+study himself and his notions of right and wrong; only
+thence could he derive real profit.</p>
+
+<p>This ancient formula for happiness might be restated
+in the familiar words of the Psalm:</p>
+
+<div class="poem"><div class="stanza">
+<span class="i0">"Dwell in the land, and verily thou shalt be fed."<br /></span>
+</div></div>
+
+<p>To-day, if he could rise from the dead and walk
+about among us, this philosopher would marvel much
+at the different turn which matters have taken.</p>
+<p><span class="pagenum"><a name="Page_90" id="Page_90">[Pg 90]</a></span></p>
+<p>The motions of the moon and the other heavenly
+bodies are accurately known. Our knowledge of the
+motions of our own body is by far not so complete.
+The mountains and natural divisions of the moon have
+been accurately outlined on maps, but physiologists
+are just beginning to find their way in the geography
+of the brain. The chemical constitution of many fixed
+stars has already been investigated. The chemical
+processes of the animal body are questions of much
+greater difficulty and complexity. We have our <i>Mécanique
+céleste</i>. But a <i>Mécanique sociale</i> or a <i>Mécanique
+morale</i> of equal trustworthiness remains to be written.</p>
+
+<p>Our philosopher would indeed admit that we have
+made great progress. But we have not followed his
+advice. The patient has recovered, but he took for his
+recovery exactly the opposite of what the doctor prescribed.</p>
+
+<p>Humanity is now returned, much wiser, from its
+journey in celestial space, against which it was so
+solemnly warned. Men, after having become acquainted
+with the great and simple facts of the world without,
+are now beginning to examine critically the world
+within. It sounds absurd, but it is true, that only after
+we have thought about the moon are we able to take
+up ourselves. It was necessary that we should acquire
+simple and clear ideas in a less complicated domain,
+before we entered the more intricate one of psychology,
+and with these ideas astronomy principally furnished
+us.</p><p><span class="pagenum"><a name="Page_91" id="Page_91">[Pg 91]</a></span></p>
+
+<p>To attempt any description of that stupendous
+movement, which, originally springing out of the physical
+sciences, went beyond the domain of physics and is
+now occupied with the problems of psychology, would
+be presumptuous in this place. I shall only attempt
+here, to illustrate to you by a few simple examples the
+methods by which the province of psychology can be
+reached from the facts of the physical world&mdash;especially
+the adjacent province of sense-perception. And I wish
+it to be remembered that my brief attempt is not to be
+taken as a measure of the present state of such scientific
+questions.</p>
+<p><span class="pagenum"><a name="Page_92" id="Page_92">[Pg 92]</a></span></p><p><span class="pagenum"><a name="Page_93" id="Page_93">[Pg 93]</a></span></p><p><span class="pagenum"><a name="Page_94" id="Page_94">[Pg 94]</a></span></p><p><span class="pagenum"><a name="Page_95" id="Page_95">[Pg 95]</a></span></p><p><span class="pagenum"><a name="Page_96" id="Page_96">[Pg 96]</a></span></p><p><span class="pagenum"><a name="Page_97" id="Page_97">[Pg 97]</a></span></p><p><span class="pagenum"><a name="Page_98" id="Page_98">[Pg 98]</a></span></p><p><span class="pagenum"><a name="Page_99" id="Page_99">[Pg 99]</a></span></p><p><span class="pagenum"><a name="Page_100" id="Page_100">[Pg 100]</a></span></p><p><span class="pagenum"><a name="Page_101" id="Page_101">[Pg 101]</a></span></p><p><span class="pagenum"><a name="Page_102" id="Page_102">[Pg 102]</a></span></p><p><span class="pagenum"><a name="Page_103" id="Page_103">[Pg 103]</a></span></p><p><span class="pagenum"><a name="Page_104" id="Page_104">[Pg 104]</a></span></p>
+<hr class="tb" />
+
+<p>It is a well-known fact that some objects please us,
+while others do not. Generally speaking, anything
+that is constructed according to fixed and logically
+followed rules, is a product of tolerable beauty. We see
+thus nature herself, who always acts according to fixed
+rules, constantly producing such pretty things. Every
+day the physicist is confronted in his workshop with
+the most beautiful vibration-figures, tone-figures, phenomena
+of polarisation, and forms of diffraction.</p>
+
+<p>A rule always presupposes a repetition. Repetitions,
+therefore, will probably be found to play some
+important part in the production of agreeable effects.
+Of course, the nature of agreeable effects is not exhausted
+by this. Furthermore, the repetition of a
+physical event becomes the source of agreeable effects
+only when it is connected with a repetition of sensations.</p>
+
+<p>An excellent example that repetition of sensations
+is a source of agreeable effects is furnished by the
+copy-book of every schoolboy, which is usually a treasure-house
+of such things, and only in need of an Abbé
+Domenech to become celebrated. Any figure, no matter
+how crude or poor, if several times repeated, with
+the repetitions placed in line, will produce a tolerable
+frieze.</p>
+
+<div class="figright" style="width: 300px;">
+<img src="images/i_102.jpg" width="300" height="185" alt="" />
+<span class="caption">Fig. 25.</span>
+</div>
+
+<p>Also the pleasant effect of symmetry is due to the
+repetition of sensations. Let us abandon ourselves a
+moment to this thought, yet not imagine when we have
+developed it, that we have fully exhausted the nature
+of the agreeable, much less of the beautiful.</p>
+
+<p>First, let us get a clear conception of what symmetry
+is. And in preference to a definition let us take
+a living picture. You know that the reflexion of an
+object in a mirror has a great likeness to the object itself.
+All its proportions and outlines are the same.
+Yet there is a difference between the object and its reflexion
+in the mirror, which you will readily observe.</p>
+
+<p>Hold your right hand before a mirror, and you will
+see in the mirror a left hand. Your right glove will
+produce its mate in the glass. For you could never
+use the reflexion of your right glove, if it were present
+to you as a real thing, for covering your right hand,
+but only for covering your left. Similarly, your right
+ear will give as its reflexion a left ear; and you will at
+once perceive that the left half of your body could very
+easily be substituted for the reflexion of your right half.
+Now just as in the place of a missing right ear a left ear
+cannot be put, unless the lobule of the ear be turned upwards,
+or the opening into the concha backwards, so,
+despite all similarity of form, the reflexion of an object
+can never take the place of the object itself.<a name="FNanchor_20_20" id="FNanchor_20_20"></a><a href="#Footnote_20_20" class="fnanchor">[20]</a></p>
+
+<p>The reason of this difference between the object
+and its reflexion is simple. The reflexion appears as
+far behind the mirror as the object is in front of it. The
+parts of the object, accordingly, which are nearest the
+mirror will also be nearest the mirror in the reflexion.
+Consequently, the succession of the parts in the reflexion
+will be reversed, as may best be seen in the reflexion
+of the face of a watch or of a manuscript.</p>
+
+<p>It will also be readily seen, that if a point of the object
+be joined with its reflexion in the image, the line
+of junction will cut the mirror at right angles and be
+bisected by it. This holds true of all corresponding
+points of object and image.</p>
+
+<p>If, now, we can divide an object by a plane into
+two halves so that each half, as seen in the reflecting
+plane of division, is a reproduction of the other half,
+such an object is termed symmetrical, and the plane
+of division is called the plane of symmetry.</p>
+
+<p>If the plane of symmetry is vertical, we can say
+that the body is vertically symmetrical. An example
+of vertical symmetry is a Gothic cathedral.</p>
+
+<p>If the plane of symmetry is horizontal, we can say
+that the object is horizontally symmetrical. A landscape
+on the shores of a lake with its reflexion in the
+water, is a system of horizontal symmetry.</p>
+
+<p>Exactly here is a noticeable difference. The vertical
+symmetry of a Gothic cathedral strikes us at once,
+whereas we can travel up and down the whole length
+of the Rhine or the Hudson without becoming aware
+of the symmetry between objects and their reflexions
+in the water. Vertical symmetry pleases us, whilst
+horizontal symmetry is indifferent, and is noticed only
+by the experienced eye.</p>
+
+<p>Whence arises this difference? I say from the fact
+that vertical symmetry produces a repetition of the
+same sensation, while horizontal symmetry does not.
+I shall now show that this is so.</p>
+
+<p>Let us look at the following letters:</p>
+
+<p class="center">d b
+q p
+</p>
+
+<p>It is a fact known to all mothers and teachers, that
+children in their first attempts to read and write, constantly
+confound d and b, and q and p, but never d
+and q, or b and p. Now d and b and q and p are the
+two halves of a <i>vertically</i> symmetrical figure, while d
+and q, and b and p are two halves of a <i>horizontally</i> symmetrical
+figure. The first two are confounded; but
+confusion is only possible of things that excite in us
+the same or similar sensations.</p>
+
+<p>Figures of two flower-girls are frequently seen on
+the decorations of gardens and of drawing-rooms, one
+of whom carries a flower-basket in her right hand and
+the other a flower-basket in her left. All know how
+apt we are, unless we are very careful, to confound these
+figures with one another.</p>
+
+<p>While turning a thing round from right to left is
+scarcely noticed, the eye is not at all indifferent to the
+turning of a thing upside down. A human face which
+has been turned upside down is scarcely recognisable
+as a face, and makes an impression which is altogether
+strange. The reason of this is not to be sought in the
+unwontedness of the sight, for it is just as difficult to
+recognise an arabesque that has been inverted, where
+there can be no question of a habit. This curious fact
+is the foundation of the familiar jokes played with the
+portraits of unpopular personages, which are so drawn
+that in the upright position of the page an exact picture
+of the person is presented, but on being inverted
+some popular animal is shown.</p>
+
+<p>It is a fact, then, that the two halves of a vertically
+symmetrical figure are easily confounded and that they
+therefore probably produce very nearly the same sensations.
+The question, accordingly, arises, <i>why</i> do the
+two halves of a vertically symmetrical figure produce
+the same or similar sensations? The answer is: Because
+our apparatus of vision, which consists of our
+eyes and of the accompanying muscular apparatus is
+itself vertically symmetrical.<a name="FNanchor_21_21" id="FNanchor_21_21"></a><a href="#Footnote_21_21" class="fnanchor">[21]</a></p>
+
+<p>Whatever external resemblances one eye may have
+with another they are still not alike. The right eye of
+a man cannot take the place of a left eye any more
+than a left ear or left hand can take the place of a
+right one. By artificial means, we can change the part
+which each of our eyes plays. (Wheatstone's pseudoscope.)
+But we then find ourselves in an entirely new
+and strange world. What is convex appears concave;
+what is concave, convex. What is distant appears
+near, and what is near appears far.</p>
+
+<p>The left eye is the reflexion of the right. And the
+light-feeling retina of the left eye is a reflexion of the
+light-feeling retina of the right, in all its functions.</p>
+
+<p>The lense of the eye, like a magic lantern, casts
+images of objects on the retina. And you may picture
+to yourself the light-feeling retina of the eye, with its
+countless nerves, as a hand with innumerable fingers,
+adapted to feeling light. The ends of the visual nerves,
+like our fingers, are endowed with varying degrees of
+sensitiveness. The two retinæ act like a right and a
+left hand; the sensation of touch and the sensation of
+light in the two instances are similar.</p>
+
+<p>Examine the right-hand portion of this letter T:
+namely, T. Instead of the two retinæ on which this
+image falls, imagine feeling the object, my two hands.
+The &#9484;, grasped with the right hand, gives a different
+sensation from that which it gives when grasped with
+the left. But if we turn our character about from right
+to left, thus: &#9488;, it will give the same sensation in the
+left hand that it gave before in the right. The sensation
+is repeated.</p>
+
+<p>If we take a whole T, the right half will produce in
+the right hand the same sensation that the left half
+produces in the left, and <i>vice versa</i>.</p>
+
+<p>The symmetrical figure gives the same sensation
+twice.</p>
+
+<p>If we turn the T over thus: &#9500;, or invert the half
+T thus: L, so long as we do not change the position
+of our hands we can make no use of the foregoing reasoning.</p>
+
+<p>The retinæ, in fact, are exactly like our two hands.
+They, too, have their thumbs and index fingers, though
+they are thousands in number; and we may say the
+thumbs are on the side of the eye near the nose,
+and the remaining fingers on the side away from the
+nose.</p>
+
+<p>With this I hope to have made perfectly clear that
+the pleasing effect of symmetry is chiefly due to the
+repetition of sensations, and that the effect in question
+takes place in symmetrical figures, only where
+there is a repetition of sensation. The pleasing effect
+of regular figures, the preference which straight lines,
+especially vertical and horizontal straight lines, enjoy,
+is founded on a similar reason. A straight line,
+both in a horizontal and in a vertical position, can cast
+on the two retinæ the same image, which falls moreover
+on symmetrically corresponding spots. This also,
+it would appear, is the reason of our psychological
+preference of straight to curved lines, and not their
+property of being the shortest distance between two
+points. The straight line is felt, to put the matter
+briefly, as symmetrical to itself, which is the case also
+with the plane. Curved lines are felt as deviations
+from straight lines, that is, as deviations from symmetry.<a name="FNanchor_22_22" id="FNanchor_22_22"></a><a href="#Footnote_22_22" class="fnanchor">[22]</a>
+The presence of a sense for symmetry in people
+possessing only one eye from birth, is indeed a riddle.
+Of course, the sense of symmetry, although primarily
+acquired by means of the eyes, cannot be wholly limited
+to the visual organs. It must also be deeply
+rooted in other parts of the organism by ages of practice
+and can thus not be eliminated forthwith by the
+loss of one eye. Also, when an eye is lost, the symmetrical
+muscular apparatus is left, as is also the
+symmetrical apparatus of innervation.</p>
+
+<p>It appears, however, unquestionable that the phenomena
+mentioned have, in the main, their origin in
+the peculiar structure of our eyes. It will therefore
+be seen at once that our notions of what is beautiful
+and ugly would undergo a change if our eyes were different.
+Also, if this view is correct, the theory of the
+so-called eternally beautiful is somewhat mistaken. It
+can scarcely be doubted that our culture, or form of
+civilisation, which stamps upon the human body its
+unmistakable traces, should not also modify our conceptions
+of the beautiful. Was not formerly the development
+of all musical beauty restricted to the narrow
+limits of a five-toned scale?</p>
+
+<p>The fact that a repetition of sensations is productive
+of pleasant effects is not restricted to the realm of
+the visible. To-day, both the musician and the physicist
+know that the harmonic or the melodic addition
+of one tone to another affects us agreeably only when
+the added tone reproduces a part of the sensation
+which the first one excited. When I add an octave
+to a fundamental tone, I hear in the octave a part of
+what was heard in the fundamental tone. (Helmholtz.)
+But it is not my purpose to develop this idea
+fully here.<a name="FNanchor_23_23" id="FNanchor_23_23"></a><a href="#Footnote_23_23" class="fnanchor">[23]</a> We shall only ask to-day, whether there
+is anything similar to the symmetry of figures in the
+province of sounds.</p>
+
+<p>Look at the reflexion of your piano in the mirror.</p>
+
+<p>You will at once remark that you have never seen
+such a piano in the actual world, for it has its high
+keys to the left and its low ones to the right. Such
+pianos are not manufactured.</p>
+
+<p>If you could sit down at such a piano and play in
+your usual manner, plainly every step which you
+imagined you were performing in the upward scale
+would be executed as a corresponding step in the
+downward scale. The effect would be not a little surprising.</p>
+
+<p>For the practised musician who is always accustomed
+to hearing certain sounds produced when certain
+keys are struck, it is quite an anomalous spectacle
+to watch a player in the glass and to observe that he
+always does the opposite of what we hear.</p>
+
+<p>But still more remarkable would be the effect of
+attempting to strike a harmony on such a piano. For
+a melody it is not indifferent whether we execute a
+step in an upward or a downward scale. But for a
+harmony, so great a difference is not produced by reversal.
+I always retain the same consonance whether
+I add to a fundamental note an upper or a lower third.
+Only the order of the intervals of the harmony is reversed.
+In point of fact, when we execute a movement
+in a major key on our reflected piano, we hear a
+sound in a minor key, and <i>vice versa</i>.</p>
+
+<p>It now remains to execute the experiments indicated.
+Instead of playing upon the piano in the mirror,
+which is impossible, or of having a piano of this
+kind built, which would be somewhat expensive, we
+may perform our experiments in a simpler manner, as
+follows:</p>
+
+<p>1) We play on our own piano in our usual manner,
+look into the mirror, and then repeat on our real piano
+what we see in the mirror. In this way we transform
+all steps upwards into corresponding steps downwards.
+We play a movement, and then another movement,
+which, with respect to the key-board, is symmetrical
+to the first.</p>
+
+<p>2) We place a mirror beneath the music in which
+the notes are reflected as in a body of water, and play
+according to the notes in the mirror. In this way also,
+all steps upwards are changed into corresponding,
+equal steps downwards.</p>
+
+<p>3) We turn the music upside down and read the
+notes from right to left and from below upwards. In
+doing this, we must regard all sharps as flats and all
+flats as sharps, because they correspond to half lines
+and spaces. Besides, in this use of the music we can
+only employ the bass clef, as only in this clef are the
+notes not changed by symmetrical reversal.</p>
+
+<p>You can judge of the effect of these experiments
+from the examples which appear in the annexed musical
+cut. (Page 102.) The movement which appears in
+the upper lines is symmetrically reversed in the lower.</p>
+
+<p>The effect of the experiments may be briefly formulated.
+The melody is rendered unrecognisable. The
+harmony suffers a transposition from a major into a
+minor key and <i>vice versa</i>. The study of these pretty
+effects, which have long been familiar to physicists
+and musicians, was revived some years ago by Von
+Oettingen.<a name="FNanchor_24_24" id="FNanchor_24_24"></a><a href="#Footnote_24_24" class="fnanchor">[24]</a></p>
+
+<div class="figcenter" style="width: 525px;">
+<img src="images/i_112.jpg" width="525" height="800" alt="" />
+<span class="caption">Fig. 26.</span><br />
+<a href="music/112a.mid">Listen to 1.</a><br />
+<a href="music/112b.mid">Listen to 2.</a><br />
+<a href="music/112c.mid">Listen to 3.</a><br />
+<a href="music/112d.mid">Listen to 4.</a><br />
+<a href="music/112e.mid">Listen to 5.</a><br />
+<a href="music/112f.mid">Listen to 6.</a><br />
+<a href="music/112g.mid">Listen to 7.</a><br />
+<a href="music/112h.mid">Listen to 8.</a><br />
+</div>
+
+<p>(See pages 101 and 103.)]</p>
+
+<p>Now, although in all the preceding examples I have
+transposed steps upward into equal and similar steps
+downward, that is, as we may justly say, have played
+for every movement the movement which is symmetrical
+to it, yet the ear notices either little or nothing of
+symmetry. The transposition from a major to a minor
+key is the sole indication of symmetry remaining. The
+symmetry is there for the mind, but is wanting for
+sensation. No symmetry exists for the ear, because a
+reversal of musical sounds conditions no repetition of
+sensations. If we had an ear for height and an ear
+for depth, just as we have an eye for the right and an
+eye for the left, we should also find that symmetrical
+sound-structures existed for our auditory organs. The
+contrast of major and minor for the ear corresponds to
+inversion for the eye, which is also only symmetry for
+the mind, but not for sensation.</p>
+
+<p>By way of supplement to what I have said, I will
+add a brief remark for my mathematical readers.</p>
+
+<p>Our musical notation is essentially a graphical representation
+of a piece of music in the form of curves,
+where the time is the abscissæ, and the logarithms of
+the number of vibrations the ordinates. The deviations
+of musical notation from this principle are only
+such as facilitate interpretation, or are due to historical
+accidents.</p>
+
+<p>If, now, it be further observed that the sensation
+of pitch also is proportional to the logarithm of the
+number of vibrations, and that the intervals between
+the notes correspond to the differences of the logarithms
+of the numbers of vibrations, the justification
+will be found in these facts of calling the harmonies
+and melodies which appear in the mirror, symmetrical
+to the original ones.</p>
+<p><span class="pagenum"><a name="Page_105" id="Page_105">[Pg 105]</a></span></p><p><span class="pagenum"><a name="Page_106" id="Page_106">[Pg 106]</a></span></p><p><span class="pagenum"><a name="Page_107" id="Page_107">[Pg 107]</a></span></p>
+<hr class="tb" />
+
+<p>I simply wish to bring home to your minds by these
+fragmentary remarks that the progress of the physical
+sciences has been of great help to those branches of
+psychology that have not scorned to consider the results
+of physical research. On the other hand, psychology
+is beginning to return, as it were, in a spirit
+of thankfulness, the powerful stimulus which it received
+from physics.</p>
+
+<p>The theories of physics which reduce all phenomena
+to the motion and equilibrium of smallest particles,
+the so-called molecular theories, have been
+gravely threatened by the progress of the theory of the
+senses and of space, and we may say that their days
+are numbered.</p>
+
+<p>I have shown elsewhere<a name="FNanchor_25_25" id="FNanchor_25_25"></a><a href="#Footnote_25_25" class="fnanchor">[25]</a> that the musical scale is
+simply a species of space&mdash;a space, however, of only
+one dimension, and that, a one-sided one. If, now, a
+person who could only hear, should attempt to develop
+a conception of the world in this, his linear space, he
+would become involved in many difficulties, as his space
+would be incompetent to comprehend the many sides
+of the relations of reality. But is it any more justifiable
+for us, to attempt to force the whole world into the
+space of our eye, in aspects in which it is not accessible
+to the eye? Yet this is the dilemma of all molecular
+theories.</p>
+
+<p>We possess, however, a sense, which, with respect
+to the scope of the relations which it can comprehend,
+is richer than any other. It is our reason. This stands
+above the senses. It alone is competent to found a
+permanent and sufficient view of the world. The
+mechanical conception of the world has performed
+wonders since Galileo's time. But it must now yield
+to a broader view of things. A further development of
+this idea is beyond the limits of my present purpose.</p>
+
+<p>One more point and I have done. The advice of
+our philosopher to restrict ourselves to what is near
+at hand and useful in our researches, which finds a
+kind of exemplification in the present cry of inquirers
+for limitation and division of labor, must not be too
+slavishly followed. In the seclusion of our closets, we
+often rack our brains in vain to fulfil a work, the
+means of accomplishing which lies before our very
+doors. If the inquirer must be perforce a shoemaker,
+tapping constantly at his last, it may perhaps be permitted
+him to be a shoemaker of the type of Hans
+Sachs, who did not deem it beneath him to take a
+look now and then at his neighbor's work and to
+comment on the latter's doings.</p>
+
+<p>Let this be my apology, therefore, if I have forsaken
+for a moment to-day the last of my specialty.</p>
+
+
+
+
+<h2><a name="ON_THE_FUNDAMENTAL_CONCEPTS" id="ON_THE_FUNDAMENTAL_CONCEPTS">ON THE FUNDAMENTAL CONCEPTS
+OF ELECTROSTATICS.</a><a name="FNanchor_26_26" id="FNanchor_26_26"></a><a href="#Footnote_26_26" class="fnanchor">[26]</a></h2>
+
+
+<p>The task has been assigned me to develop before
+you in a popular manner the fundamental quantitative
+concepts of electrostatics&mdash;"quantity of electricity,"
+"potential," "capacity," and so forth. It
+would not be difficult, even within the brief limits of
+an hour, to delight the eye with hosts of beautiful experiments
+and to fill the imagination with numerous
+and varied conceptions. But we should, in such a
+case, be still far from a lucid and easy grasp of the
+phenomena. The means would still fail us for reproducing
+the facts accurately in thought&mdash;a procedure
+which for the theoretical and practical man is of equal
+importance. These means are the <i>metrical concepts</i> of
+electricity.</p>
+
+<p>As long as the pursuit of the facts of a given province
+of phenomena is in the hands of a few isolated
+investigators, as long as every experiment can be easily
+repeated, the fixing of the collected facts by provisional<span class="pagenum"><a name="Page_108" id="Page_108">[Pg 108]</a></span>
+description is ordinarily sufficient. But the case is
+different when the whole world must make use of the
+results reached by many, as happens when the science
+acquires broader foundations and scope, and
+particularly so when it begins to supply intellectual
+nourishment to an important branch of the practical
+arts, and to draw from that province in return stupendous
+empirical results. Then the facts must be so
+described that individuals in all places and at all times
+can, from a few easily obtained elements, put the facts
+accurately together in thought, and reproduce them
+from the description. This is done with the help of
+the metrical concepts and the international measures.</p>
+
+<p>The work which was begun in this direction in the
+period of the purely scientific development of the science,
+especially by Coulomb (1784), Gauss (1833), and
+Weber (1846), was powerfully stimulated by the requirements
+of the great technical undertakings manifested
+since the laying of the first transatlantic cable,
+and brought to a brilliant conclusion by the labors of
+the British Association, 1861, and of the Paris Congress,
+1881, chiefly through the exertions of Sir William
+Thomson.</p>
+
+<p>It is plain, that in the time allotted to me I cannot
+conduct you over all the long and tortuous paths which
+the science has actually pursued, that it will not be
+possible at every step to remind you of all the little
+precautions for the avoidance of error which the early
+steps have taught us. On the contrary, I must make<span class="pagenum"><a name="Page_109" id="Page_109">[Pg 109]</a></span>
+shift with the simplest and rudest tools. I shall conduct
+you by the shortest paths from the facts to the
+ideas, in doing which, of course, it will not be possible
+to anticipate all the stray and chance ideas which may
+and must arise from prospects into the by-paths which
+we leave untrodden.</p>
+<p><span class="pagenum"><a name="Page_110" id="Page_110">[Pg 110]</a></span></p><p><span class="pagenum"><a name="Page_111" id="Page_111">[Pg 111]</a></span></p><p><span class="pagenum"><a name="Page_112" id="Page_112">[Pg 112]</a></span></p><p><span class="pagenum"><a name="Page_113" id="Page_113">[Pg 113]</a></span></p><p><span class="pagenum"><a name="Page_114" id="Page_114">[Pg 114]</a></span></p><p><span class="pagenum"><a name="Page_115" id="Page_115">[Pg 115]</a></span></p><p><span class="pagenum"><a name="Page_116" id="Page_116">[Pg 116]</a></span></p><p><span class="pagenum"><a name="Page_117" id="Page_117">[Pg 117]</a></span></p><p><span class="pagenum"><a name="Page_118" id="Page_118">[Pg 118]</a></span></p><p><span class="pagenum"><a name="Page_119" id="Page_119">[Pg 119]</a></span></p><p><span class="pagenum"><a name="Page_120" id="Page_120">[Pg 120]</a></span></p><p><span class="pagenum"><a name="Page_121" id="Page_121">[Pg 121]</a></span></p><p><span class="pagenum"><a name="Page_122" id="Page_122">[Pg 122]</a></span></p><p><span class="pagenum"><a name="Page_123" id="Page_123">[Pg 123]</a></span></p><p><span class="pagenum"><a name="Page_124" id="Page_124">[Pg 124]</a></span></p><p><span class="pagenum"><a name="Page_125" id="Page_125">[Pg 125]</a></span></p><p><span class="pagenum"><a name="Page_126" id="Page_126">[Pg 126]</a></span></p><p><span class="pagenum"><a name="Page_127" id="Page_127">[Pg 127]</a></span></p>
+<hr class="tb" />
+
+<p>Here are two small, light bodies (Fig. 27) of equal
+size, freely suspended, which we "electrify" either
+by friction with a third body or by contact with a body
+already electrified. At once a repulsive force is set
+up which drives the two bodies away from each other
+in opposition to the action of gravity. This force could
+accomplish anew the same mechanical work which
+was expended to produce it.<a name="FNanchor_27_27" id="FNanchor_27_27"></a><a href="#Footnote_27_27" class="fnanchor">[27]</a></p>
+
+<div class="figleft" style="width: 150px;">
+<img src="images/i_119-1.jpg" width="150" height="253" alt="" />
+<span class="caption">Fig. 27.</span>
+</div>
+
+<div class="figright" style="width: 250px;">
+<img src="images/i_119-2.jpg" width="250" height="170" alt="" />
+<span class="caption">Fig. 28.</span>
+</div>
+
+<p>Coulomb, now, by means of delicate experiments
+with the torsion-balance, satisfied himself that if the
+bodies in question, say at a distance of two centimetres,
+repelled each other with the same force with
+which a milligramme-weight strives to fall to the
+ground, at half that distance, or at one centimetre,
+they would repel each other with the force of four
+milligrammes, and at double that distance, or at four
+centimetres, they would repel each other with the force
+of only one-fourth of a milligramme. He found that
+the electrical force acts inversely as the square of the
+distance.</p>
+
+<p>Let us imagine, now, that we possessed some
+means of measuring electrical repulsion by weights,
+a means which would be supplied, for example, by our
+electrical pendulums; then we could make the following
+observation.</p>
+
+<p>The body <i>A</i> (Fig. 28) is repelled by the body <i>K</i> at
+a distance of two centimetres with a force of one milligramme.
+If we touch <i>A</i>, now, with an equal body <i>B</i>,
+the half of this force of repulsion will pass to the body
+<i>B</i>; both <i>A</i> and <i>B</i>, now, at a distance of two centimetres
+from <i>K</i>, are repelled only with the force of one-half
+a milligramme. But both together are repelled
+still with the force of one milligramme. Hence, <i>the
+divisibility of electrical force</i> among bodies in contact <i>is
+a fact</i>. It is a useful, but by no means a necessary
+supplement to this fact, to imagine an electrical fluid
+present in the body <i>A</i>, with the quantity of which the
+electrical force varies, and half of which flows over to
+<i>B</i>. For, in the place of the new physical picture,
+thus, an old, familiar one is substituted, which moves
+spontaneously in its wonted courses.</p>
+
+<p>Adhering to this idea, we define the <i>unit</i> of electrical
+quantity, according to the now almost universally
+adopted centimetre-gramme-second (C. G. S.) system,
+as that quantity which at a distance of one centimetre
+repels an equal quantity with unit of force, that
+is, with a force which in one second would impart to
+a mass of one gramme a velocity-increment of a centimetre.
+As a gramme mass acquires through the action
+of gravity a velocity-increment of about 981 centimetres
+in a second, accordingly, a gramme is attracted
+to the earth with 981, or, in round numbers, 1000 units
+of force of the centimetre-gramme-second system,
+while a milligramme-weight would strive to fall to the
+earth with approximately the unit force of this system.</p>
+
+<p>We may easily obtain by this means a clear idea of
+what the unit quantity of electricity is. Two small
+bodies, <i>K</i>, weighing each a gramme, are hung up by
+vertical threads, five metres in length and almost
+weightless, so as to touch each other. If the two bodies
+be equally electrified and move apart upon electrification
+to a distance of one centimetre, their charge is approximately
+equivalent to the electrostatic unit of electric
+quantity, for the repulsion then holds in equilibrium
+a gravitational force-component of approximately
+one milligramme, which strives to bring the bodies together.</p>
+
+<p>Vertically beneath a small sphere suspended from
+the equilibrated beam of a balance a second sphere is
+placed at a distance of a centimetre. If both be equally
+electrified the sphere suspended from the balance will
+be rendered apparently lighter by the repulsion. If by
+adding a weight of one milligramme equilibrium is
+restored, each of the spheres contains in round numbers
+the electrostatic unit of electrical quantity.</p>
+
+<p>In view of the fact that the same electrical bodies
+exert at different distances different forces upon one
+another, exception might be taken to the measure of
+quantity here developed. What kind of a quantity is
+that which now weighs more, and now weighs less, so
+to speak? But this apparent deviation from the
+method of determination commonly used in practical
+life, that by weight, is, closely considered, an agreement.
+On a high mountain a heavy mass also is less
+powerfully attracted to the earth than at the level of
+the sea, and if it is permitted us in our determinations
+to neglect the consideration of level, it is only because
+the comparison of a body with fixed conventional
+weights is invariably effected at the same level. In
+fact, if we were to make one of the two weights equilibrated
+on our balance approach sensibly to the centre
+of the earth, by suspending it from a very long thread,
+as Prof. von Jolly of Munich suggested, we should
+make the gravity of that weight, its heaviness, proportionately
+greater.</p>
+
+<p>Let us picture to ourselves, now, two different
+electrical fluids, a positive and a negative fluid, of such
+nature that the particles of the one attract the particles
+of the other according to the law of the inverse squares,
+but the particles of the same fluid repel each other by
+the same law; in non-electrical bodies let us imagine
+the two fluids uniformly distributed in equal quantities,
+in electric bodies one of the two in excess; in
+conductors, further, let us imagine the fluids mobile,
+in non-conductors immobile; having formed such pictures,
+we possess the conception which Coulomb developed
+and to which he gave mathematical precision.
+We have only to give this conception free play in our
+minds and we shall see as in a clear picture the fluid
+particles, say of a positively charged conductor, receding
+from one another as far as they can, all making
+for the surface of the conductor and there seeking out
+the prominent parts and points until the greatest possible
+amount of work has been performed. On increasing
+the size of the surface, we see a dispersion,
+on decreasing its size we see a condensation of the particles.
+In a second, non-electrified conductor brought
+into the vicinity of the first, we see the two fluids immediately
+separate, the positive collecting itself on the
+remote and the negative on the adjacent side of its
+surface. In the fact that this conception reproduces,
+lucidly and spontaneously, all the data which arduous
+research only slowly and gradually discovered, is contained
+its advantage and scientific value. With this,
+too, its value is exhausted. We must not seek in nature
+for the two hypothetical fluids which we have
+added as simple mental adjuncts, if we would not go
+astray. Coulomb's view may be replaced by a totally
+different one, for example, by that of Faraday, and the
+most proper course is always, after the general survey
+is obtained, to go back to the actual facts, to the electrical
+forces.</p>
+
+<div class="figleft" style="width: 300px;">
+<img src="images/i_124-1.jpg" width="300" height="310" alt="" />
+<span class="caption">Fig. 29.</span>
+</div>
+
+<div class="figright" style="width: 300px;">
+<img src="images/i_124-2.jpg" width="300" height="276" alt="" />
+<span class="caption">Fig. 30.</span>
+</div>
+
+<p>We will now make ourselves familiar with the concept
+of electrical quantity, and with the method of
+measuring or estimating it. Imagine a common Leyden
+jar (Fig. 29), the inner and outer coatings of which
+are connected together by means of two common metallic
+knobs placed about a centimetre apart. If the
+inside coating be charged with the quantity of electricity
++<i>q</i>, on the outer coating a distribution of the
+electricities will take place. A positive quantity almost
+equal<a name="FNanchor_28_28" id="FNanchor_28_28"></a><a href="#Footnote_28_28" class="fnanchor">[28]</a> to the quantity +<i>q</i> flows off to the earth, while
+a corresponding quantity-<i>q</i> is still left on the outer
+coating. The knobs of the jar receive their portion of
+these quantities and when the quantity <i>q</i> is sufficiently
+great a rupture of the insulating air between the knobs,
+accompanied by the self-discharge of the jar, takes
+place. For any given distance and size of the knobs,
+a charge of a definite electric quantity <i>q</i> is always necessary
+for the spontaneous discharge of the jar.</p>
+
+<p>Let us insulate, now, the outer coating of a Lane's
+unit jar <i>L</i>, the jar just described, and put in connexion
+with it the inner coating of a jar <i>F</i> exteriorly connected
+with the earth (Fig. 30). Every time that <i>L</i> is
+charged with +<i>q</i>, a like quantity +<i>q</i> is collected on
+the inner coating of <i>F</i>, and the spontaneous discharge
+of the jar <i>L</i>, which is now
+again empty, takes place. The
+number of the discharges of
+the jar <i>L</i> furnishes us, thus,
+with a measure of the quantity
+collected in the jar <i>F</i>, and
+if after 1, 2, 3, ... spontaneous
+discharges of <i>L</i> the jar <i>F</i> is
+discharged, it is evident that the charge of <i>F</i> has been
+proportionately augmented.</p>
+
+<div class="figleft" style="width: 300px;">
+<img src="images/i_125.jpg" width="300" height="255" alt="" />
+<span class="caption">Fig. 31.</span>
+</div>
+
+<p>Let us supply now, to effect the spontaneous discharge,
+the jar <i>F</i> with knobs of the same size and
+at the same distance apart as those of the jar <i>L</i> (Fig.
+31). If we find, then, that five discharges of the unit
+jar take place before one spontaneous discharge of the
+jar <i>F</i> occurs, plainly the jar <i>F</i>, for equal distances between
+the knobs of the two jars, equal striking distances,
+is able to hold five times the quantity of electricity
+that <i>L</i> can, that is, has five times the <i>capacity</i>
+of <i>L</i>.<a name="FNanchor_29_29" id="FNanchor_29_29"></a><a href="#Footnote_29_29" class="fnanchor">[29]</a></p>
+
+<div class="figright" style="width: 400px;">
+<img src="images/i_126.jpg" width="400" height="345" alt="" />
+<span class="caption">Fig. 32.</span>
+</div>
+
+<p>We will now replace the unit jar <i>L</i>, with which we
+measure electricity, so to speak, <i>into</i> the jar <i>F</i>, by a
+Franklin's pane, consisting of two parallel flat metal
+plates (Fig. 32), separated only by air. If here, for
+example, thirty spontaneous discharges of the pane are
+sufficient to fill the jar, ten discharges will be found
+sufficient if the air-space between the two plates be
+filled with a cake of sulphur. Hence, the capacity
+of a Franklin's pane of sulphur is about three times
+greater than that of one of the same shape and size
+made of air, or, as it is the custom to say, the specific
+inductive capacity of sulphur (that of air being taken
+as the unit) is about 3.<a name="FNanchor_30_30" id="FNanchor_30_30"></a><a href="#Footnote_30_30" class="fnanchor">[30]</a> We are here arrived at a
+very simple fact, which clearly shows us the significance
+of the number called <i>dielectric constant</i>, or <i>specific
+inductive capacity</i>, the knowledge of which is so important
+for the theory of submarine cables.</p>
+
+<p>Let us consider a jar <i>A</i>, which is charged with a
+certain quantity of electricity. We can discharge the
+jar directly. But we can also discharge the jar <i>A</i>
+(Fig. 33) partly into a jar <i>B</i>, by connecting the two
+outer coatings with each other. In this operation a
+portion of the quantity of electricity passes, accompanied
+by sparks, into the jar <i>B</i>, and we now find both
+jars charged.</p>
+
+<div class="figleft" style="width: 300px;">
+<img src="images/i_127-1.jpg" width="300" height="283" alt="" />
+<span class="caption">Fig. 33.</span>
+</div>
+
+<div class="figright" style="width: 300px;">
+<img src="images/i_127-s.jpg" width="300" height="214" alt="" />
+<span class="caption">Fig. 34.</span>
+</div>
+
+<p>It may be shown as follows that the conception of
+a constant quantity of electricity can be regarded as
+the expression of a pure fact. Picture to yourself any
+sort of electrical conductor (Fig. 34); cut it up into a
+large number of small pieces, and place these pieces by
+means of an insulated rod at a distance of one centimetre
+from an electrical body which acts with unit of
+force on an equal and like-constituted body at the
+same distance. Take the sum of the forces which
+this last body exerts on the single pieces of the conductor.
+The sum of these forces will be the quantity
+of electricity on the whole conductor. It remains the
+same, whether we change the form and the size of the
+conductor, or whether we bring it near or move it
+away from a second electrical conductor, so long as we
+keep it insulated, that is, do not discharge it.</p>
+
+<p>A basis of reality for the notion of electric quantity
+seems also to present itself from another quarter.
+If a current, that is, in the usual view, a definite
+quantity of electricity per second, is sent through a
+column of acidulated water; in the direction of the
+positive stream, hydrogen, but in the opposite direction,
+oxygen is liberated at the extremities of the column.
+For a given quantity of electricity a given quantity
+of oxygen appears. You may picture the column
+of water as a column of hydrogen and a column of
+oxygen, fitted into each other, and may say the electric
+current is a chemical current and <i>vice versa</i>. Although
+this notion is more difficult to adhere to in the field of
+statical electricity and with non-decomposable conductors,
+its further development is by no means hopeless.</p>
+
+<p>The concept quantity of electricity, thus, is not so
+aerial as might appear, but is able to conduct us with
+certainty through a multitude of varied phenomena,
+and is suggested to us by the facts in almost palpable
+form. We can collect electrical force in a body, measure
+it out with one body
+into another, carry it
+over from one body into
+another, just as we can
+collect a liquid in a vessel,
+measure it out with
+one vessel into another,
+or pour it from one into
+another.</p>
+
+<p>For the analysis of
+mechanical phenomena,
+a metrical notion, derived
+from experience,
+and bearing the designation <i>work</i>, has proved itself
+useful. A machine can be set in motion only when
+the forces acting on it can perform work.</p>
+
+<div class="figleft" style="width: 350px;">
+<img src="images/i_129.jpg" width="350" height="431" alt="" />
+<span class="caption">Fig. 35.</span>
+</div>
+
+<p>Let us consider, for example, a wheel and axle
+(Fig. 35) having the radii 1 and 2 metres, loaded respectively
+with the weights 2 and 1 kilogrammes. On
+turning the wheel and axle, the 1 kilogramme-weight,
+let us say, sinks two metres, while the 2 kilogramme-weight
+rises one metre. On both sides the product</p>
+
+<p class="center">KGR. M. KGR. M.</p>
+
+<p class="center"> 1 × 2 = 2 × 1.
+</p>
+
+<p>is equal. So long as this is so, the wheel and axle will
+not move of itself. But if we take such loads, or so
+change the radii of the wheels, that this product (kgr.
+× metre) on displacement is in excess on one side,
+that side will sink. As we see, this product is characteristic
+for mechanical events, and for this reason has
+been invested with a special name, <i>work</i>.</p>
+
+<p>In all mechanical processes, and as all physical
+processes present a mechanical side, in all physical
+processes, work plays a determinative part. Electrical
+forces, also, produce only changes in which work is performed.
+To the extent that forces come into play in
+electrical phenomena, electrical phenomena, be they
+what they may, extend into the domain of mechanics
+and are subject to the laws which hold in this domain.
+The universally adopted measure of work,
+now, is the product of the force into the distance
+through which it acts, and in the C. G. S. system, the
+unit of work is the action through one centimetre of
+a force which would impart in one second to a
+gramme-mass a velocity-increment of one centimetre,
+that is, in round numbers, the action through a centimetre
+of a pressure equal to the weight of a milligramme.
+From a positively charged body, electricity,
+yielding to the force of repulsion and performing work,
+flows off to the earth, providing conducting connexions
+exist. To a negatively charged body, on the other
+hand, the earth under the same circumstances gives
+off positive electricity. The electrical work possible
+in the interaction of a body with the earth, characterises
+the electrical condition of that body. We will call
+the work which must be expended on the unit quantity
+of positive electricity to raise it from the earth to the
+body <i>K</i> the <i>potential</i> of the body <i>K</i>.<a name="FNanchor_31_31" id="FNanchor_31_31"></a><a href="#Footnote_31_31" class="fnanchor">[31]</a></p>
+
+<p>We ascribe to the body <i>K</i> in the C. G. S. system
+the potential +1, if we must expend the unit of work
+to raise the positive electrostatic unit of electric quantity
+from the earth to that body; the potential -1, if
+we gain in this procedure the unit of work; the potential
+0, if no work at all is performed in the operation.</p>
+
+<p>The different parts of one and the same electrical
+conductor in electrical equilibrium have the same potential,
+for otherwise the electricity would perform
+work and move about upon the conductor, and equilibrium
+would not have existed. Different conductors of
+equal potential, put in connexion with one another, do
+not exchange electricity any more than bodies of equal
+temperature in contact exchange heat, or in connected
+vessels, in which the same pressures exist, liquids
+flow from one vessel to the other. Exchange of electricity
+takes place only between conductors of different
+potentials, but in conductors of given form and position
+a definite difference of potential is necessary for
+a spark, which pierces the insulating air, to pass
+between them.</p>
+
+<p>On being connected, every two conductors assume
+at once the same potential. With this the means
+is given of determining the potential of a conductor
+through the agency of a second conductor expressly
+adapted to the purpose called an electrometer, just as
+we determine the temperature of a body with a thermometer.
+The values of the potentials of bodies obtained
+in this way simplify vastly our analysis of their
+electrical behavior, as will be evident from what has
+been said.</p>
+
+<p>Think of a positively charged conductor. Double
+all the electrical forces exerted by this conductor on a
+point charged with unit quantity, that is, double the
+quantity at each point, or what is the same thing,
+double the total charge. Plainly, equilibrium still subsists.
+But carry, now, the positive electrostatic unit
+towards the conductor. Everywhere we shall have to
+overcome double the force of repulsion we did before,
+everywhere we shall have to expend double the work.
+By doubling the charge of the conductor a double potential
+has been produced. Charge and potential go
+hand in hand, are proportional. Consequently, calling
+the total quantity of electricity of a conductor <i>Q</i>
+and its potential <i>V</i>, we can write: <i>Q</i> = <i>CV</i>, where <i>C</i>
+stands for a constant, the import of which will be understood
+simply from noting that <i>C</i> = <i>Q</i>/<i>V</i>.<a name="FNanchor_32_32" id="FNanchor_32_32"></a><a href="#Footnote_32_32" class="fnanchor">[32]</a> But the
+division of a number representing the units of quantity
+of a conductor by the number representing its
+units of potential tells us the quantity which falls to
+the share of the unit of potential. Now the number
+<i>C</i> here we call the capacity of a conductor, and have
+substituted, thus, in the place of the old relative determination
+of capacity, an absolute determination.<a name="FNanchor_33_33" id="FNanchor_33_33"></a><a href="#Footnote_33_33" class="fnanchor">[33]</a></p>
+
+<p>In simple cases the connexion between charge, potential,
+and capacity is easily ascertained. Our conductor,
+let us say, is a sphere of radius <i>r</i>, suspended
+free in a large body of air. There being no other conductors
+in the vicinity, the charge <i>q</i> will then distribute
+itself uniformly upon the surface of the sphere, and
+simple geometrical considerations yield for its potential
+the expression <i>V</i> = <i>q</i>/<i>r</i>. Hence, <i>q</i>/<i>V</i> = <i>r</i>; that is,
+the capacity of a sphere is measured by its radius, and
+in the C. G. S. system in centimetres.<a name="FNanchor_34_34" id="FNanchor_34_34"></a><a href="#Footnote_34_34" class="fnanchor">[34]</a> It is clear
+also, since a potential is a quantity divided by a length,
+that a quantity divided by a potential must be a length.</p>
+
+<p>Imagine (Fig. 36) a jar composed of two concentric
+conductive spherical shells of the radii <i>r</i> and <i>r</i><sub>1</sub>,
+having only air between them. Connecting the outside
+sphere with the earth, and charging the inside
+sphere by means of a thin, insulated wire passing
+through the first, with the quantity <i>Q</i>, we shall have
+<i>V</i> = (<i>r</i><sub>1</sub>-<i>r</i>)/(<i>r</i><sub>1</sub><i>r</i>)<i>Q</i>, and for the capacity in this case
+(<i>r</i><sub>1</sub><i>r</i>)/(<i>r</i><sub>1</sub>-<i>r</i>), or, to take
+a specific example, if <i>r</i> = 16
+and <i>r</i><sub>1</sub> = 19, a capacity of
+about 100 centimetres.</p>
+
+<div class="figright" style="width: 350px;">
+<img src="images/i_134.jpg" width="350" height="352" alt="" />
+<span class="caption">Fig. 36.</span>
+</div>
+
+<p>We shall now use these
+simple cases for illustrating
+the principle by which
+capacity and potential are
+determined. First, it is
+clear that we can use the
+jar composed of concentric spheres with its known capacity
+as our unit jar and by means of this ascertain,
+in the manner above laid down, the capacity of any
+given jar <i>F</i>. We find, for example, that 37 discharges
+of this unit jar of the capacity 100, just charges the
+jar investigated at the same striking distance, that is,
+at the same potential. Hence, the capacity of the jar
+investigated is 3700 centimetres. The large battery
+of the Prague physical laboratory, which consists of
+sixteen such jars, all of nearly equal size, has a capacity,
+therefore, of something like 50,000 centimetres,
+or the capacity of a sphere, a kilometre in diameter,
+freely suspended in atmospheric space. This remark
+distinctly shows us the great superiority which Leyden
+jars possess for the storage of electricity as compared
+with common conductors. In fact, as Faraday pointed
+out, jars differ from simple conductors mainly by their
+great capacity.</p>
+
+<div class="figcenter" style="width: 450px;">
+<img src="images/i_135.jpg" width="450" height="356" alt="" />
+<span class="caption">Fig. 37.</span>
+</div>
+
+<p>For determining potential, imagine the inner coating
+of a jar <i>F</i>, the outer coating of which communicates
+with the ground, connected by a long, thin wire
+with a conductive sphere <i>K</i> placed free in a large atmospheric
+space, compared with whose dimensions
+the radius of the sphere vanishes. (Fig. 37.) The
+jar and the sphere assume at once the same potential.
+But on the surface of the sphere, if that be sufficiently
+far removed from all other conductors, a uniform layer
+of electricity will be found. If the sphere, having the
+radius <i>r</i>, contains the charge <i>q</i>, its potential is <i>V</i> = <i>q</i>/<i>r</i>.
+If the upper half of the sphere be severed from the
+lower half and equilibrated on a balance with one of
+whose beams it is connected by silk threads, the upper
+half will be repelled from the lower half with the force
+<i>P</i> = <i>q</i><sup>2</sup>/8<i>r</i><sup>2</sup> = 1/8<i>V</i><sup>2</sup>. This repulsion <i>P</i> may be counter-balanced
+by additional weights placed on the beam-end,
+and so ascertained. The potential is then <i>V</i> =
+&#8730;(8<i>P</i>).<a name="FNanchor_35_35" id="FNanchor_35_35"></a><a href="#Footnote_35_35" class="fnanchor">[35]</a></p>
+
+<p>That the potential is proportional to the square
+root of the force is not difficult to see. A doubling or
+trebling of the potential means that the charge of all
+the parts is doubled or trebled; hence their combined
+power of repulsion quadrupled or nonupled.</p>
+
+<p>Let us consider a special case. I wish to produce
+the potential 40 on the sphere. What additional weight
+must I give to the half sphere in grammes that the
+force of repulsion shall maintain the balance in exact
+equilibrium? As a gramme weight is approximately
+equivalent to 1000 units of force, we have only the
+following simple example to work out: 40×40 = 8×
+1000.<i>x</i>, where <i>x</i> stands for the number of grammes.
+In round numbers we get <i>x</i> = 0.2 gramme. I charge
+the jar. The balance is deflected; I have reached,
+or rather passed, the potential 40, and you see when I
+discharge the jar the associated spark.<a name="FNanchor_36_36" id="FNanchor_36_36"></a><a href="#Footnote_36_36" class="fnanchor">[36]</a></p>
+
+<p>The striking distance between the knobs of a machine
+increases with the difference of the potential,
+although not proportionately to that difference. The
+striking distance increases faster than the potential
+difference. For a distance between the knobs of one
+centimetre on this machine the difference of potential
+is 110. It can easily be increased tenfold. Of the
+tremendous differences of potential which occur in
+nature some idea may be obtained from the fact that
+the striking distances of lightning in thunder-storms
+is counted by miles. The differences of potential in
+galvanic batteries are considerably smaller than those
+of our machine, for it takes fully one hundred elements
+to give a spark of microscopic striking distance.</p>
+<p><span class="pagenum"><a name="Page_128" id="Page_128">[Pg 128]</a></span></p><p><span class="pagenum"><a name="Page_129" id="Page_129">[Pg 129]</a></span></p><p><span class="pagenum"><a name="Page_130" id="Page_130">[Pg 130]</a></span></p><p><span class="pagenum"><a name="Page_131" id="Page_131">[Pg 131]</a></span></p><p><span class="pagenum"><a name="Page_132" id="Page_132">[Pg 132]</a></span></p><p><span class="pagenum"><a name="Page_133" id="Page_133">[Pg 133]</a></span></p><p><span class="pagenum"><a name="Page_134" id="Page_134">[Pg 134]</a></span></p>
+<hr class="tb" />
+
+<p>We shall now employ the ideas reached to shed
+some light upon another important relation between
+electrical and mechanical phenomena. We shall investigate
+what is the potential <i>energy</i>, or the <i>store of
+work</i>, contained in a charged conductor, for example,
+in a jar.</p>
+
+<p>If we bring a quantity of electricity up to a conductor,
+or, to speak less pictorially, if we generate by
+work electrical force in a conductor, this force is able
+to produce anew the work by which it was generated.
+How great, now, is the energy or capacity for work of
+a conductor of known charge <i>Q</i> and known potential
+<i>V</i>?</p>
+
+<p>Imagine the given charge <i>Q</i> divided into very small
+parts <i>q</i>, <i>q</i><sub>1</sub>, <i>q</i><sub>2</sub> ..., and these little parts successively
+carried up to the conductor. The first very small
+quantity <i>q</i> is brought up without any appreciable work
+and produces by its presence a small potential <i>V</i><sub>'</sub>. To
+bring up the second quantity, accordingly, we must do
+the work <i>q</i><sub>'</sub><i>V</i><sub>'</sub>, and similarly for the quantities which
+follow the work <i>q</i><sub>''</sub><i>V</i><sub>''</sub>, <i>q</i><sub>'''</sub><i>V</i><sub>'''</sub>, and so forth. Now,
+as the potential rises proportionately to the quantities
+added until the value <i>V</i> is reached, we have, agreeably
+to the graphical representation of Fig. 38, for the
+total work performed,</p>
+
+<p class="center"><i>W</i> = 1/2<i>QV</i>,
+</p>
+
+<p>which corresponds to the total energy of the charged
+conductor. Using the equation <i>Q</i> = <i>CV</i>, where <i>C</i>
+stands for capacity, we also have,</p>
+
+<p class="center"><i>W</i> = 1/2<i>CV</i><sup>2</sup>, or <i>W</i> = <i>Q</i><sup>2</sup>/2<i>C</i>.
+</p>
+
+<p>It will be helpful, perhaps, to elucidate this idea
+by an analogy from the province of mechanics. If we
+pump a quantity of liquid, <i>Q</i>, gradually into a cylindrical
+vessel (Fig. 39), the level of the liquid in the
+vessel will gradually rise. The more we have pumped
+in, the greater the pressure we must overcome, or the
+higher the level to which we must lift the liquid. The
+stored-up work is rendered again available when the
+heavy liquid <i>Q</i>, which reaches up to the level <i>h</i>, flows
+out. This work <i>W</i> corresponds to the fall of the whole
+liquid weight <i>Q</i>, through the distance <i>h</i>/2 or through
+the altitude of its centre of gravity. We have</p>
+
+<p class="center"><i>W</i> = 1/2<i>Qh</i>.
+</p>
+
+<p>Further, since <i>Q</i> = <i>Kh</i>, or since the weight of the
+liquid and the height <i>h</i> are proportional, we get also</p>
+
+<p class="center"><i>W</i> = 1/2<i>Kh</i><sup>2</sup> and <i>W</i> = <i>Q</i><sup>2</sup>/2<i>K</i>.
+</p>
+
+<div class="figleft" style="width: 300px;">
+<img src="images/i_139-1.jpg" width="300" height="208" alt="" />
+<span class="caption">Fig. 38.</span>
+</div>
+
+<div class="figright" style="width: 300px;">
+<img src="images/i_139-2.jpg" width="300" height="283" alt="" />
+<span class="caption">Fig. 39.</span>
+</div>
+
+<p>As a special case let us consider our jar. Its capacity
+is <i>C</i> = 3700, its potential <i>V</i> = 110; accordingly,
+its quantity <i>Q</i> = <i>CV</i> = 407,000 electrostatic units and
+its energy <i>W</i> = 1/2<i>QV</i> = 22,385,000 C. G. S. units of
+work.</p>
+
+<p>The unit of work of the C. G. S. system is not readily
+appreciable by the senses, nor does it well admit of
+representation, as we are accustomed to work with
+weights. Let us adopt, therefore, as our unit of work
+the gramme-centimetre, or the gravitational pressure
+of a gramme-weight through the distance of a centimetre,
+which in round numbers is 1000 times greater
+than the unit assumed above; in this case, our numerical
+result will be approximately 1000 times smaller.
+Again, if we pass, as more familiar in practice, to the
+kilogramme-metre as our unit of work, our unit, the
+distance being increased a hundred fold, and the weight
+a thousand fold, will be 100,000 times larger. The
+numerical result expressing the work done is in this
+case 100,000 times less, being in round numbers 0.22
+kilogramme-metre. We can obtain a clear idea of the
+work done here by letting a kilogramme-weight fall 22
+centimetres.</p>
+
+<p>This amount of work, accordingly, is performed on
+the charging of the jar, and on its discharge appears
+again, according to the circumstances, partly as sound,
+partly as a mechanical disruption of insulators, partly
+as light and heat, and so forth.</p>
+
+<p>The large battery of the Prague physical laboratory,
+with its sixteen jars charged to equal potentials,
+furnishes, although the effect of the discharge is imposing,
+a total amount of work of only three kilogramme-metres.</p>
+
+<p>In the development of the ideas above laid down
+we are not restricted to the method there pursued; in
+fact, that method was selected only as one especially
+fitted to familiarise us with the phenomena. On the
+contrary, the connexion of the physical processes is so
+multifarious that we can come at the same event from
+very different directions. Particularly are electrical
+phenomena connected with all other physical events;
+and so intimate is this connexion that we might justly
+call the study of electricity the theory of the general
+connexion of physical processes.</p>
+
+<p>With respect to the principle of the conservation
+of energy which unites electrical with mechanical phenomena,
+I should like to point out briefly two ways of
+following up the study of this connexion.</p>
+
+<p>A few years ago Professor Rosetti, taking an influence-machine,
+which he set in motion by means of
+weights alternately in the electrical and non-electrical
+condition with the same velocities, determined the
+mechanical work expended in the two cases and was
+thus enabled, after deducting the work of friction, to
+ascertain the mechanical work consumed in the development
+of the electricity.</p>
+
+<p>I myself have made this experiment in a modified,
+and, as I think, more advantageous form. Instead
+of determining the work of friction by special trial, I
+arranged my apparatus so that it was eliminated of itself
+in the measurement and could consequently be
+neglected. The so-called fixed disk of the machine, the
+axis of which is placed vertically, is suspended somewhat
+like a chandelier by three vertical threads of
+equal lengths <i>l</i> at a distance <i>r</i> from the axis. Only
+when the machine is excited does this fixed disk, which
+represents a Prony's brake, receive, through its reciprocal
+action with the rotating disk, a deflexion <i>&#945;</i> and a
+moment of torsion which is expressed by <i>D</i> = <i>(Pr<sup>2</sup>/l)&#945;</i>,
+where <i>P</i> is the weight of the disk.<a name="FNanchor_37_37" id="FNanchor_37_37"></a><a href="#Footnote_37_37" class="fnanchor">[37]</a> The angle <i>&#945;</i> is
+determined by a mirror set in the disk. The work expended
+in <i>n</i> rotations is given by <i>2n&#960;D</i>.</p>
+
+<p>If we close the machine, as Rosetti did, we obtain
+a continuous current which has all the properties of a
+very weak galvanic current; for example, it produces a
+deflexion in a multiplier which we interpose, and so
+forth. We can directly ascertain, now, the mechanical
+work expended in the maintenance of this current.</p>
+
+<p>If we charge a jar by means of a machine, the energy
+of the jar employed in the production of sparks,
+in the disruption of the insulators, etc., corresponds
+to a part only of the mechanical work expended, a
+second part of it being consumed in the arc which
+forms the circuit.<a name="FNanchor_38_38" id="FNanchor_38_38"></a><a href="#Footnote_38_38" class="fnanchor">[38]</a> This machine, with the interposed
+jar, affords in miniature a picture of the transference
+of force, or more properly of work. And in fact nearly
+the same laws hold here for the economical coefficient
+as obtain for large dynamo-machines.</p>
+
+<p>Another means of investigating electrical energy is
+by its transformation into heat. A long time ago
+(1838), before the mechanical theory of heat had attained
+its present popularity, Riess performed experiments
+in this field with the help of his electrical
+air-thermometer or thermo-electrometer.</p>
+
+<div class="figleft" style="width: 200px;">
+<img src="images/i_143.jpg" width="200" height="320" alt="" />
+<span class="caption">Fig. 40.</span>
+</div>
+
+<p>If the discharge be conducted
+through a fine wire
+passing through the globe of
+the air-thermometer, a development
+of heat is observed
+proportional to the expression
+above-discussed <i>W</i> = 1/2<i>QV</i>.
+Although the total energy has
+not yet been transformed
+into measurable heat by this
+means, in as much as a portion
+is left behind in the spark in the air outside the thermometer,
+still everything tends to show that the total
+heat developed in all parts of the conductor and along
+all the paths of discharge is the equivalent of the work
+1/2<i>QV</i>.</p>
+
+<p>It is not important here whether the electrical energy
+is transformed all at once or partly, by degrees.
+For example, if of two equal jars one is charged with
+the quantity <i>Q</i> at the potential <i>V</i> the energy present
+is 1/2<i>QV</i>. If the first jar be discharged into the second,
+<i>V</i>, since the capacity is now doubled, falls to <i>V</i>/2.
+Accordingly, the energy 1/4<i>QV</i> remains, while 1/4<i>QV</i> is
+transformed in the spark of discharge into heat. The
+remainder, however, is equally distributed between
+the two jars so that each on discharge is still able to
+transform 1/8<i>QV</i> into heat.</p>
+<p><span class="pagenum"><a name="Page_135" id="Page_135">[Pg 135]</a></span></p><p><span class="pagenum"><a name="Page_136" id="Page_136">[Pg 136]</a></span></p><p><span class="pagenum"><a name="Page_137" id="Page_137">[Pg 137]</a></span></p>
+<hr class="tb" />
+
+<p>We have here discussed electricity in the limited
+phenomenal form in which it was known to the inquirers
+before Volta, and which has been called, perhaps
+not very felicitously, "statical electricity." It is
+evident, however, that the nature of electricity is everywhere
+one and the same; that a substantial difference
+between statical and galvanic electricity does not exist.
+Only the quantitative circumstances in the two provinces
+are so widely different that totally new aspects
+of phenomena may appear in the second, for example,
+magnetic effects, which in the first remained unnoticed,
+whilst, <i>vice versa</i>, in the second field statical attractions
+and repulsions are scarcely appreciable. As a fact,
+we can easily show the magnetic effect of the current
+of discharge of an influence-machine on the galvanoscope
+although we could hardly have made the original
+discovery of the magnetic effects with this current.
+The statical distant action of the wire poles of
+a galvanic element also would hardly have been noticed
+had not the phenomenon been known from a
+different quarter in a striking form.</p>
+
+<p>If we wished to characterise the two fields in their
+chief and most general features, we should say that in
+the first, high potentials and small quantities come
+into play, in the second small potentials and large
+quantities. A jar which is discharging and a galvanic
+element deport themselves somewhat like an air-gun
+and the bellows of an organ. The first gives forth
+suddenly under a very high pressure a small quantity
+of air; the latter liberates gradually under a very slight
+pressure a large quantity of air.</p>
+
+<p>In point of principle, too, nothing prevents our retaining
+the electrostatical units in the domain of galvanic
+electricity and in measuring, for example, the
+strength of a current by the number of electrostatic
+units which flow per second through its cross-section.
+But this would be in a double aspect impractical. In
+the first place, we should totally neglect the magnetic
+facilities for measurement so conveniently offered by
+the current, and substitute for this easy means a method
+which can be applied only with difficulty and is not
+capable of great exactness. In the second place our
+units would be much too small, and we should find
+ourselves in the predicament of the astronomer who
+attempted to measure celestial distances in metres instead
+of in radii of the earth and the earth's orbit; for
+the current which by the magnetic C. G. S. standard
+represents the unit, would require a flow of some
+30,000,000,000 electrostatic units per second through
+its cross-section. Accordingly, different units must
+be adopted here. The development of this point, however,
+lies beyond my present task.</p>
+
+
+
+
+<h2><a name="ON_THE_PRINCIPLE_OF_THE_CONSERVATION" id="ON_THE_PRINCIPLE_OF_THE_CONSERVATION">ON THE PRINCIPLE OF THE CONSERVATION
+OF ENERGY.</a><a name="FNanchor_39_39" id="FNanchor_39_39"></a><a href="#Footnote_39_39" class="fnanchor">[39]</a></h2>
+
+
+<p>In a popular lecture, distinguished for its charming
+simplicity and clearness, which Joule delivered in
+the year 1847,<a name="FNanchor_40_40" id="FNanchor_40_40"></a><a href="#Footnote_40_40" class="fnanchor">[40]</a> that famous physicist declares that the
+living force which a heavy body has acquired by its
+descent through a certain height and which it carries
+with it in the form of the velocity with which it is impressed,
+is the <i>equivalent</i> of the attraction of gravity
+through the space fallen through, and that it would be
+"absurd" to assume that this living force could be destroyed
+without some restitution of that equivalent.
+He then adds: "You will therefore be surprised to
+hear that until very <i>recently</i> the universal opinion has
+been that living force could be absolutely and irrevocably
+destroyed at any one's option." Let us add
+that to-day, after forty-seven years, the <i>law of the conservation
+of energy</i>, wherever civilisation exists, is accepted
+as a fully established truth and receives the
+widest applications in all domains of natural science.</p>
+
+<p><span class="pagenum"><a name="Page_138" id="Page_138">[Pg 138]</a></span></p><p>The fate of all momentous discoveries is similar.
+On their first appearance they are regarded by the
+majority of men as errors. J. R. Mayer's work on the
+principle of energy (1842) was rejected by the first
+physical journal of Germany; Helmholtz's treatise
+(1847) met with no better success; and even Joule, to
+judge from an intimation of Playfair, seems to have
+encountered difficulties with his first publication (1843).
+Gradually, however, people are led to see that the new
+view was long prepared for and ready for enunciation,
+only that a few favored minds had perceived it much
+earlier than the rest, and in this way the opposition of
+the majority is overcome. With proofs of the fruitfulness
+of the new view, with its success, confidence
+in it increases. The majority of the men who employ
+it cannot enter into a deep-going analysis of it; for
+them, its success is its proof. It can thus happen that
+a view which has led to the greatest discoveries, like
+Black's theory of caloric, in a subsequent period in a
+province where it does not apply may actually become
+an obstacle to progress by its blinding our eyes to facts
+which do not fit in with our favorite conceptions. If
+a theory is to be protected from this dubious rôle, the
+grounds and motives of its evolution and existence
+must be examined from time to time with the utmost
+care.</p>
+
+<p>The most multifarious physical changes, thermal,<span class="pagenum"><a name="Page_139" id="Page_139">[Pg 139]</a></span>
+electrical, chemical, and so forth, can be brought
+about by mechanical work. When such alterations
+are reversed they yield anew the mechanical work in
+exactly the quantity which was required for the production
+of the part reversed. This is the <i>principle of
+the conservation of energy</i>; "energy" being the term
+which has gradually come into use for that "indestructible
+something" of which the measure is mechanical
+<i>work</i>.</p>
+
+<p>How did we acquire this idea? What are the
+sources from which we have drawn it? This question
+is not only of interest in itself, but also for the important
+reason above touched upon. The opinions which
+are held concerning the foundations of the law of energy
+still diverge very widely from one another. Many
+trace the principle to the impossibility of a perpetual
+motion, which they regard either as sufficiently proved
+by experience, or as self-evident. In the province of
+pure mechanics the impossibility of a perpetual motion,
+or the continuous production of <i>work</i> without
+some <i>permanent</i> alteration, is easily demonstrated. Accordingly,
+if we start from the theory that all physical
+processes are purely <i>mechanical</i> processes, motions of
+molecules and atoms, we embrace also, by this <i>mechanical</i>
+conception of physics, the impossibility of a
+perpetual motion in the <i>whole</i> physical domain. At
+present this view probably counts the most adherents.
+Other inquirers, however, are for accepting only a
+purely <i>experimental</i> establishment of the law of energy.</p><p><span class="pagenum"><a name="Page_140" id="Page_140">[Pg 140]</a></span></p>
+
+<p>It will appear, from the discussion to follow, that
+<i>all</i> the factors mentioned have co-operated in the development
+of the view in question; but that in addition
+to them a logical and purely formal factor, hitherto
+little considered, has also played a very important part.</p>
+
+
+<h3>I. THE PRINCIPLE OF THE EXCLUDED PERPETUAL
+MOTION.</h3>
+
+<p>The law of energy in its modern form is not identical
+with the principle of the excluded perpetual motion,
+but it is very closely
+related to it. The latter
+principle, however, is by
+no means new, for in the
+province of mechanics it
+has controlled for centuries
+the thoughts and investigations
+of the greatest thinkers. Let us convince
+ourselves of this by the study of a few historical
+examples.</p>
+
+<div class="figright" style="width: 300px;">
+<img src="images/i_150.jpg" width="300" height="272" alt="" />
+<span class="caption">Fig. 41.</span>
+</div>
+
+<p>S. Stevinus, in his famous work <i>Hypomnemata mathematica</i>,
+Tom. IV, <i>De statica</i>, (Leyden, 1605, p. 34),
+treats of the equilibrium of bodies on inclined planes.</p>
+
+<p>Over a triangular prism <i>ABC</i>, one side of which,
+<i>AC</i>, is horizontal, an endless cord or chain is slung,
+to which at equal distances apart fourteen balls of
+equal weight are attached, as represented in cross-section
+in Figure 41. Since we can imagine the lower<span class="pagenum"><a name="Page_141" id="Page_141">[Pg 141]</a></span>
+symmetrical part of the cord <i>ABC</i> taken away, Stevinus
+concludes that the four balls on <i>AB</i> hold in equilibrium
+the two balls on <i>BC</i>. For if the equilibrium were
+for a moment disturbed, it could never subsist: the
+cord would keep moving round forever in the same direction,&mdash;we
+should have a perpetual motion. He says:</p>
+
+<blockquote><p>"But if this took place, our row or ring of balls would come
+once more into their original position, and from the same cause the
+eight globes to the left would again be heavier than the six to the
+right, and therefore those eight would sink a second time and these
+six rise, and all the globes would keep up, of themselves, <i>a continuous
+and unending motion, which is false</i>."<a name="FNanchor_41_41" id="FNanchor_41_41"></a><a href="#Footnote_41_41" class="fnanchor">[41]</a></p></blockquote>
+
+<p>Stevinus, now, easily derives from this principle
+the laws of equilibrium on the inclined plane and numerous
+other fruitful consequences.</p>
+
+<p>In the chapter "Hydrostatics" of
+the same work, page 114, Stevinus sets
+up the following principle: "Aquam
+datam, datum sibi intra aquam locum
+servare,"&mdash;a given mass of water preserves
+within water its given place.</p>
+
+<div class="figright" style="width: 150px;">
+<img src="images/i_151.jpg" width="150" height="172" alt="" />
+<span class="caption">Fig. 42.</span>
+</div>
+
+<p>This principle is demonstrated as follows (see Fig.
+42):</p>
+
+<blockquote><p>"For, assuming it to be possible by natural means, let us suppose
+that A does not preserve the place assigned to it, but sinks
+down to D. This being posited, the water which succeeds A will,
+for the same reason, also flow down to <i>D</i>; <i>A</i> will be forced out of
+its place in <i>D</i>; and thus this body of water, for the conditions in it
+are everywhere the same, <i>will set up a perpetual motion, which is
+absurd</i>."<a name="FNanchor_42_42" id="FNanchor_42_42"></a><a href="#Footnote_42_42" class="fnanchor">[42]</a></p></blockquote><p><span class="pagenum"><a name="Page_142" id="Page_142">[Pg 142]</a></span></p>
+
+<p>From this all the principles of hydrostatics are deduced.
+On this occasion Stevinus also first develops
+the thought so fruitful for modern analytical mechanics
+that the equilibrium of a system is not destroyed by
+the addition of rigid connexions. As we know, the
+principle of the conservation of the centre of gravity
+is now sometimes deduced from D'Alembert's principle
+with the help of that remark. If we were to reproduce
+Stevinus's demonstration to-day, we should have
+to change it slightly. We find no difficulty in imagining
+the cord on the prism possessed of unending uniform
+motion if all hindrances are thought away, but
+we should protest against the assumption of an accelerated
+motion or even against that of a uniform motion,
+if the resistances were not removed. Moreover,
+for greater precision of proof, the string of balls might
+be replaced by a heavy homogeneous cord of infinite
+flexibility. But all this does not affect in the least the
+historical value of Stevinus's thoughts. It is a fact,
+Stevinus deduces apparently much simpler truths from
+the principle of an impossible perpetual motion.</p>
+<p><span class="pagenum"><a name="Page_143" id="Page_143">[Pg 143]</a></span></p>
+<p>In the process of thought which conducted Galileo
+to his discoveries at the end of the sixteenth century,
+the following principle plays an important part, that
+a body in virtue of the velocity acquired in its descent
+can rise exactly as high as it fell. This principle,
+which appears frequently and with much clearness in
+Galileo's thought, is simply another form of the principle
+of excluded perpetual motion, as we shall see it
+is also in Huygens.</p>
+
+<p>Galileo, as we know, arrived at the law of uniformly
+accelerated motion by <i>a priori</i> considerations, as that
+law which was the "simplest and most natural," after
+having first assumed a different law which he was compelled
+to reject. To verify his law he executed experiments
+with falling bodies on inclined planes, measuring
+the times of descent by the weights of the water
+which flowed out of a small orifice in a large vessel.
+In this experiment he assumes as a fundamental principle,
+that the velocity acquired in descent down an
+inclined plane always corresponds to the vertical height
+descended through, a conclusion which for him is the
+immediate outcome of the fact that a body which has
+fallen down one inclined plane can, with the velocity it
+has acquired, rise on another plane of any inclination
+only to the same vertical height. This principle of
+the height of ascent also led him, as it seems, to the
+law of inertia. Let us hear his own masterful words
+in the <i>Dialogo terzo</i> (<i>Opere</i>, Padova, 1744, Tom. III).
+On page 96 we read:</p><p><span class="pagenum"><a name="Page_144" id="Page_144">[Pg 144]</a></span></p>
+
+<blockquote><p>"I take it for granted that the velocities acquired by a body
+in descent down planes of different inclinations are equal if the
+heights of those planes are equal."<a name="FNanchor_43_43" id="FNanchor_43_43"></a><a href="#Footnote_43_43" class="fnanchor">[43]</a></p></blockquote>
+
+<p>Then he makes Salviati say in the dialogue:<a name="FNanchor_44_44" id="FNanchor_44_44"></a><a href="#Footnote_44_44" class="fnanchor">[44]</a></p>
+
+<blockquote><p>"What you say seems very probable, but I wish to go further
+and by an experiment so to increase the probability of it that it shall
+amount almost to absolute demonstration. Suppose this sheet of
+paper to be a vertical wall, and from a nail driven in it a ball of lead
+weighing two or three ounces to hang by a very fine thread <i>AB</i> four
+or five feet long. (Fig. 43.) On the wall mark a horizontal line <i>DC</i>
+perpendicular to the vertical <i>AB</i>, which latter ought to hang about
+two inches from the wall. If now the thread <i>AB</i> with the ball
+attached take the position <i>AC</i> and the ball be let go, you will see
+the ball first descend through the arc <i>CB</i> and passing beyond
+<i>B</i> rise through the arc
+<i>BD</i> almost to the level
+of the line <i>CD</i>, being
+prevented from reaching
+it exactly by the resistance
+of the air and
+of the thread. From
+this we may truly conclude
+that its impetus at
+the point <i>B</i>, acquired by
+its descent through the
+arc <i>CB</i>, is sufficient to
+urge it through a similar arc <i>BD</i> to the same height. Having
+performed this experiment and repeated it several times, let us
+drive in the wall, in the projection of the vertical <i>AB</i>, as at <i>E</i> or
+at <i>F</i>, a nail five or six inches long, so that the thread <i>AC</i>, carrying
+as before the ball through the arc <i>CB</i>, at the moment it reaches
+the position <i>AB</i>, shall strike the nail <i>E</i>, and the ball be thus compelled
+to move up the arc <i>BG</i> described about <i>E</i> as centre.
+Then we shall see what the same impetus will here accomplish,
+acquired now as before at the same point <i>B</i>, which then drove the
+same moving body through the arc <i>BD</i> to the height of the horizontal
+<i>CD</i>. Now gentlemen, you will be pleased to see the ball
+rise to the horizontal line at the point <i>G</i>, and the same thing also
+happen if the nail be placed lower as at <i>F</i>, in which case the ball
+would describe the arc <i>BJ</i>, always terminating its ascent precisely
+at the line <i>CD</i>. If the nail be placed so low that the length of
+thread below it does not reach to the height of <i>CD</i> (which would
+happen if <i>F</i> were nearer <i>B</i> than to the intersection of <i>AB</i> with the
+horizontal <i>CD</i>), then the thread will wind itself about the nail.
+This experiment leaves no room for doubt as to the truth of the
+supposition. For as the two arcs <i>CB</i>, <i>DB</i> are equal and similarly
+situated, the momentum acquired in the descent of the arc <i>CB</i> is
+the same as that acquired in the descent of the arc <i>DB</i>; but the
+momentum acquired at <i>B</i> by the descent through the arc <i>CB</i> is capable
+of driving up the same moving body through the arc <i>BD</i>;
+hence also the momentum acquired in the descent <i>DB</i> is equal to
+that which drives the same moving body through the same arc
+from <i>B</i> to <i>D</i>, so that in general every momentum acquired in the
+descent of an arc is equal to that which causes the same moving
+body to ascend through the same arc; but all the momenta which
+cause the ascent of all the arcs <i>BD</i>, <i>BG</i>, <i>BJ</i>, are equal since they
+are made by the same momentum acquired in the descent <i>CB</i>, as
+the experiment shows: therefore all the momenta acquired in the
+descent of the arcs <i>DB</i>, <i>GB</i>, <i>JB</i> are equal."</p></blockquote>
+
+<p><span class="pagenum"><a name="Page_145" id="Page_145">[Pg 145]</a></span></p>
+<div class="figcenter" style="width: 300px;">
+<img src="images/i_155.jpg" width="300" height="246" alt="" />
+<span class="caption">Fig. 43.</span>
+</div>
+<p><span class="pagenum"><a name="Page_146" id="Page_146">[Pg 146]</a></span></p>
+
+<p>The remark relative to the pendulum may be applied
+to the inclined plane and leads to the law of inertia.
+We read on page 124:<a name="FNanchor_45_45" id="FNanchor_45_45"></a><a href="#Footnote_45_45" class="fnanchor">[45]</a></p>
+<p><span class="pagenum"><a name="Page_147" id="Page_147">[Pg 147]</a></span></p>
+<blockquote><p>"It is plain now that a movable body, starting from rest at <i>A</i>
+and descending down the inclined plane <i>AB</i>, acquires a velocity
+proportional to the increment of its time: the velocity possessed
+at <i>B</i> is the greatest of the velocities acquired, and by its nature
+immutably impressed, provided all causes of new acceleration or
+retardation are taken away: I say acceleration, having in view its
+possible further progress along the plane extended; retardation, in
+view of the possibility of its being reversed and made to mount the
+ascending plane <i>BC</i>. But in the horizontal plane <i>GH</i> its equable
+motion, according to its velocity as acquired in the descent from <i>A</i>
+to <i>B</i>, will be continued <i>ad infinitum</i>." (Fig. 44.)</p></blockquote>
+
+<div class="figcenter" style="width: 400px;">
+<img src="images/i_157.jpg" width="400" height="156" alt="" />
+<span class="caption">Fig. 44.</span>
+</div>
+
+<p>Huygens, upon whose shoulders the mantel of Galileo
+fell, forms a sharper conception of the law of inertia
+and generalises the principle respecting the heights of
+ascent which was so fruitful in Galileo's hands. He
+employs the latter principle in the solution of the problem
+of the centre of oscillation and is perfectly clear in
+the statement that the principle respecting the heights
+of ascent is identical with the principle of the excluded
+perpetual motion.</p>
+
+<p>The following important passages then occur (Hugenii,
+<i>Horologium oscillatorium, pars secunda</i>). <i>Hypotheses</i>:</p>
+
+<p><span class="pagenum"><a name="Page_148" id="Page_148">[Pg 148]</a></span></p><blockquote><p>"If gravity did not exist, nor the atmosphere obstruct the motions
+of bodies, a body would keep up forever the motion once impressed
+upon it, with equable velocity, in a straight line."<a name="FNanchor_46_46" id="FNanchor_46_46"></a><a href="#Footnote_46_46" class="fnanchor">[46]</a></p></blockquote>
+
+<p>In part four of the <i>Horologium de centro oscillationis</i>
+we read:</p>
+
+<blockquote><p>"If any number of weights be set in motion by the force of
+gravity, the common centre of gravity of the weights as a whole
+cannot possibly rise higher than the place which it occupied when
+the motion began.</p>
+
+<p>"That this hypothesis of ours may arouse no scruples, we
+will state that it simply imports, what no one has ever denied, that
+heavy bodies do not move <i>upwards</i>.&mdash;And truly if the devisers of
+the new machines who make such futile attempts to construct a
+perpetual motion would acquaint themselves with this principle,
+they could easily be brought to see their errors and to understand
+that the thing is utterly impossible by mechanical means."<a name="FNanchor_47_47" id="FNanchor_47_47"></a><a href="#Footnote_47_47" class="fnanchor">[47]</a></p></blockquote>
+
+<p>There is possibly a Jesuitical mental reservation
+contained in the words "mechanical means." One
+might be led to believe from them that Huygens held
+a non-mechanical perpetual motion for possible.</p>
+
+<p>The generalisation of Galileo's principle is still
+more clearly put in Prop. IV of the same chapter:</p>
+
+<blockquote><p>"If a pendulum, composed of several weights, set in motion
+from rest, complete any part of its full oscillation, and from that
+point onwards, the individual weights, with their common connexions
+dissolved, change their acquired velocities upwards and ascend
+as far as they can, the common centre of gravity of all will be carried
+up to the same altitude with that which it occupied before the
+beginning of the oscillation."<a name="FNanchor_48_48" id="FNanchor_48_48"></a><a href="#Footnote_48_48" class="fnanchor">[48]</a></p></blockquote>
+
+<p><span class="pagenum"><a name="Page_149" id="Page_149">[Pg 149]</a></span></p><p>On this last principle now, which is a generalisation,
+applied to a system of masses, of one of Galileo's
+ideas respecting a single mass and which from Huygens's
+explanation we recognise as the principle of excluded
+perpetual motion, Huygens grounds his theory
+of the centre of oscillation. Lagrange characterises
+this principle as precarious and is rejoiced at James
+Bernoulli's successful attempt, in 1681, to reduce the
+theory of the centre of oscillation to the laws of the
+lever, which appeared to him clearer. All the great
+inquirers of the seventeenth and eighteenth centuries
+broke a lance on this problem, and it led ultimately,
+in conjunction with the principle of virtual velocities,
+to the principle enunciated by D'Alembert in 1743 in
+his <i>Traité de dynamique</i>, though previously employed
+in a somewhat different form by Euler and Hermann.</p>
+
+<p>Furthermore, the Huygenian principle respecting
+the heights of ascent became the foundation of the
+"law of the conservation of living force," as that was
+enunciated by John and Daniel Bernoulli and employed<span class="pagenum"><a name="Page_150" id="Page_150">[Pg 150]</a></span>
+with such signal success by the latter in his
+<i>Hydrodynamics</i>. The theorems of the Bernoullis differ
+in form only from Lagrange's expression in the <i>Analytical
+Mechanics</i>.</p>
+
+<p>The manner in which Torricelli reached his famous
+law of efflux for liquids leads again to our principle.
+Torricelli assumed that the liquid which flows out of
+the basal orifice of a vessel cannot by its velocity of
+efflux ascend to a greater height than its level in the
+vessel.</p>
+
+<p>Let us next consider a point which belongs to pure
+mechanics, the history of the principle of <i>virtual motions</i>
+or <i>virtual velocities</i>. This principle was not first
+enunciated, as is usually stated, and as Lagrange also
+asserts, by Galileo, but earlier, by Stevinus. In his
+<i>Trochleostatica</i> of the above-cited work, page 72, he
+says:</p>
+
+<blockquote><p>"Observe that this axiom of statics holds good here:</p>
+
+<p>"As the space of the body acting is to the space of the body
+acted upon, so is the power of the body acted upon to the power of
+the body acting."<a name="FNanchor_49_49" id="FNanchor_49_49"></a><a href="#Footnote_49_49" class="fnanchor">[49]</a></p></blockquote>
+
+<p>Galileo, as we know, recognised the truth of the
+principle in the consideration of the simple machines,
+and also deduced the laws of the equilibrium of liquids
+from it.</p>
+
+<p>Torricelli carries the principle back to the properties
+of the centre of gravity. The condition controlling<span class="pagenum"><a name="Page_151" id="Page_151">[Pg 151]</a></span>
+equilibrium in a simple machine, in which power
+and load are represented by weights, is that the common
+centre of gravity of the weights shall not sink.
+Conversely, if the centre of gravity cannot sink equilibrium
+obtains, because heavy bodies of themselves
+do not move upwards. In this form the principle of
+virtual velocities is identical with Huygens's principle
+of the impossibility of a perpetual motion.</p>
+
+<p>John Bernoulli, in 1717, first perceived the universal
+import of the principle of virtual movements for all
+systems; a discovery stated in a letter to Varignon.
+Finally, Lagrange gives a general demonstration of
+the principle and founds upon it his whole <i>Analytical
+Mechanics</i>. But this general demonstration is based
+after all upon Huygens and Torricelli's remarks. Lagrange,
+as is known, conceives simple pulleys arranged
+in the directions of the forces of the system, passes a
+cord through these pulleys, and appends to its free
+extremity a weight which is a common measure of all
+the forces of the system. With no difficulty, now, the
+number of elements of each pulley may be so chosen
+that the forces in question shall be replaced by them.
+It is then clear that if the weight at the extremity cannot
+sink, equilibrium subsists, because heavy bodies
+cannot of themselves move upwards. If we do not go
+so far, but wish to abide by Torricelli's idea, we may
+conceive every individual force of the system replaced
+by a special weight suspended from a cord passing
+over a pulley in the direction of the force and attached<span class="pagenum"><a name="Page_152" id="Page_152">[Pg 152]</a></span>
+at its point of application. Equilibrium subsists then
+when the common centre of gravity of all the weights
+together cannot sink. The fundamental supposition
+of this demonstration is plainly the impossibility of a
+perpetual motion.</p>
+
+<p>Lagrange tried in every way to supply a proof free
+from extraneous elements and fully satisfactory, but
+without complete success. Nor were his successors
+more fortunate.</p>
+
+<p>The whole of mechanics, thus, is based upon an
+idea, which, though unequivocal, is yet unwonted and
+not coequal with the other principles and axioms of
+mechanics. Every student of mechanics, at some stage
+of his progress, feels the uncomfortableness of this
+state of affairs; every one wishes it removed; but seldom
+is the difficulty stated in words. Accordingly, the
+zealous pupil of the science is highly rejoiced when he
+reads in a master like Poinsot (<i>Théorie générale de
+l'équilibre et du mouvement des systèmes</i>) the following
+passage, in which that author is giving his opinion of
+the <i>Analytical Mechanics</i>:</p>
+
+<blockquote><p>"In the meantime, because our attention in that work was first
+wholly engrossed with the consideration of its beautiful development
+of mechanics, which seemed to spring complete from a single
+formula, we naturally believed that the science was completed or
+that it only remained to seek the demonstration of the principle of
+virtual velocities. But that quest brought back all the difficulties
+that we had overcome by the principle itself. That law so general,
+wherein are mingled the vague and unfamiliar ideas of infinitely
+small movements and of perturbations of equilibrium, only grew<span class="pagenum"><a name="Page_153" id="Page_153">[Pg 153]</a></span>
+obscure upon examination; and the work of Lagrange supplying
+nothing clearer than the march of analysis, we saw plainly that the
+clouds had only appeared lifted from the course of mechanics because
+they had, so to speak, been gathered at the very origin of that
+science.</p>
+
+<p>"At bottom, a general demonstration of the principle of virtual
+velocities would be equivalent to the establishment of the whole
+of mechanics upon a different basis: for the demonstration of a
+law which embraces a whole science is neither more nor less than
+the reduction of that science to another law just as general, but
+evident, or at least more simple than the first, and which, consequently,
+would render that useless."<a name="FNanchor_50_50" id="FNanchor_50_50"></a><a href="#Footnote_50_50" class="fnanchor">[50]</a></p></blockquote>
+
+<p>According to Poinsot, therefore, a proof of the
+principle of virtual movements is tantamount to a total
+rehabilitation of mechanics.</p>
+
+<p>Another circumstance of discomfort to the mathematician
+is, that in the historical form in which mechanics
+at present exists, dynamics is founded on
+statics, whereas it is desirable that in a science which
+pretends to deductive completeness the more special
+statical theorems should be deducible from the more
+general dynamical principles.</p>
+<p><span class="pagenum"><a name="Page_154" id="Page_154">[Pg 154]</a></span></p>
+<p>In fact, a great master, Gauss, gave expression to
+this desire in his presentment of the principle of least
+constraint (Crelle's <i>Journal für reine und angewandte
+Mathematik</i>, Vol. IV, p. 233) in the following words:
+"Proper as it is that in the gradual development of a
+science, and in the instruction of individuals, the easy
+should precede the difficult, the simple the complex,
+the special the general, yet the mind, when once it has
+reached a higher point of view, demands the contrary
+course, in which all statics shall appear simply as a
+special case of mechanics." Gauss's own principle,
+now, possesses all the requisites of universality, but
+its difficulty is that it is not immediately intelligible
+and that Gauss deduced it with the help of D'Alembert's
+principle, a procedure which left matters where
+they were before.</p>
+
+<p>Whence, now, is derived this strange part which
+the principle of virtual motion plays in mechanics?
+For the present I shall only make this reply. It would
+be difficult for me to tell the difference of impression
+which Lagrange's proof of the principle made on me
+when I first took it up as a student and when I subsequently
+resumed it after having made historical researches.
+It first appeared to me insipid, chiefly on
+account of the pulleys and the cords which did not fit
+in with the mathematical view, and whose action I
+would much rather have discovered from the principle<span class="pagenum"><a name="Page_155" id="Page_155">[Pg 155]</a></span>
+itself than have taken for granted. But now that I
+have studied the history of the science I cannot imagine
+a more beautiful demonstration.</p>
+
+<p>In fact, through all mechanics it is this self-same
+principle of excluded perpetual motion which accomplishes
+almost all, which displeased Lagrange, but
+which he still had to employ, at least tacitly, in his own
+demonstration. If we give this principle its proper
+place and setting, the paradox is explained.</p>
+
+<p>The principle of excluded perpetual motion is thus
+no new discovery; it has been the guiding idea, for
+three hundred years, of all the great inquirers. But
+the principle cannot properly be <i>based</i> upon mechanical
+perceptions. For long before the development of
+mechanics the conviction of its truth existed and even
+contributed to that development. Its power of conviction,
+therefore, must have more universal and
+deeper roots. We shall revert to this point.</p>
+
+
+<h3>II. MECHANICAL PHYSICS.</h3>
+
+<p>It cannot be denied that an unmistakable tendency
+has prevailed, from Democritus to the present day, to
+explain <i>all</i> physical events <i>mechanically</i>. Not to mention
+earlier obscure expressions of that tendency we
+read in Huygens the following:<a name="FNanchor_51_51" id="FNanchor_51_51"></a><a href="#Footnote_51_51" class="fnanchor">[51]</a></p>
+
+<blockquote><p>"There can be no doubt that light consists of the <i>motion</i> of a
+certain substance. For if we examine its production, we find that
+here on earth it is principally fire and flame which engender it, both
+of which contain beyond doubt bodies which are in rapid movement,
+since they dissolve and destroy many other bodies more solid
+than they: while if we regard its effects, we see that when light is
+accumulated, say by concave mirrors, it has the property of combustion
+just as fire has, that is to say, it disunites the parts of
+bodies, which is assuredly a proof of <i>motion</i>, at least in the <i>true
+philosophy</i>, in which the causes of all natural effects are conceived
+as <i>mechanical</i> causes. Which in my judgment must be accomplished
+or all hope of ever understanding physics renounced."<a name="FNanchor_52_52" id="FNanchor_52_52"></a><a href="#Footnote_52_52" class="fnanchor">[52]</a></p></blockquote><p><span class="pagenum"><a name="Page_156" id="Page_156">[Pg 156]</a></span></p>
+
+<p>S. Carnot,<a name="FNanchor_53_53" id="FNanchor_53_53"></a><a href="#Footnote_53_53" class="fnanchor">[53]</a> in introducing the principle of excluded
+perpetual motion into the theory of heat, makes the
+following apology:</p>
+
+<blockquote><p>"It will be objected here, perhaps, that a perpetual motion
+proved impossible for <i>purely mechanical actions</i>, is perhaps not so
+when the influence of <i>heat</i> or of electricity is employed. But can
+phenomena of heat or electricity be thought of as due to anything
+else than to <i>certain motions of bodies</i>, and as such must they not be
+subject to the general laws of mechanics?"<a name="FNanchor_54_54" id="FNanchor_54_54"></a><a href="#Footnote_54_54" class="fnanchor">[54]</a></p></blockquote>
+
+<p><span class="pagenum"><a name="Page_157" id="Page_157">[Pg 157]</a></span></p><p>These examples, which might be multiplied by
+quotations from recent literature indefinitely, show
+that a tendency to explain all things mechanically
+actually exists. This tendency is also intelligible.
+Mechanical events as simple motions in space and
+time best admit of observation and pursuit by the help
+of our highly organised senses. We reproduce mechanical
+processes almost without effort in our imagination.
+Pressure as a circumstance that produces motion
+is very familiar to us from daily experience. All
+changes which the individual personally produces in
+his environment, or humanity brings about by means
+of the arts in the world, are effected through the instrumentality
+of <i>motions</i>. Almost of necessity, therefore,
+motion appears to us as the most important
+physical factor. Moreover, mechanical properties may
+be discovered in all physical events. The sounding
+bell trembles, the heated body expands, the electrified
+body attracts other bodies. Why, therefore, should
+we not attempt to grasp all events under their mechanical
+aspect, since that is so easily apprehended and
+most accessible to observation and measurement? In
+fact, no objection <i>is</i> to be made to the attempt to elucidate
+the properties of physical events by mechanical
+<i>analogies</i>.</p>
+
+<p>But modern physics has proceeded <i>very far</i> in this
+direction. The point of view which Wundt represents
+in his excellent treatise <i>On the Physical Axioms</i> is probably<span class="pagenum"><a name="Page_158" id="Page_158">[Pg 158]</a></span>
+shared by the majority of physicists. The axioms
+of physics which Wundt sets up are as follows:</p>
+
+<p>1. All natural causes are motional causes.</p>
+
+<p>2. Every motional cause lies outside the object
+moved.</p>
+
+<p>3. All motional causes act in the direction of the
+straight line of junction, and so forth.</p>
+
+<p>4. The effect of every cause persists.</p>
+
+<p>5. Every effect involves an equal countereffect.</p>
+
+<p>6. Every effect is equivalent to its cause.</p>
+
+<p>These principles might be studied properly enough
+as fundamental principles of mechanics. But when
+they are set up as axioms of physics, their enunciation
+is simply tantamount to a negation of all events except
+motion.</p>
+
+<p>According to Wundt, all changes of nature are
+mere changes of place. All causes are motional causes
+(page 26). Any discussion of the philosophical grounds
+on which Wundt supports his theory would lead us
+deep into the speculations of the Eleatics and the
+Herbartians. Change of place, Wundt holds, is the
+<i>only</i> change of a thing in which a thing remains identical
+with itself. If a thing changed <i>qualitatively</i>, we
+should be obliged to imagine that something was annihilated
+and something else created in its place, which
+is not to be reconciled with our idea of the identity of
+the object observed and of the indestructibility of
+matter. But we have only to remember that the Eleatics
+encountered difficulties of exactly the same sort<span class="pagenum"><a name="Page_159" id="Page_159">[Pg 159]</a></span>
+in motion. Can we not also imagine that a thing is
+destroyed in <i>one</i> place and in <i>another</i> an exactly similar
+thing created? After all, do we really know <i>more</i>
+why a body leaves one place and appears in another,
+than why a <i>cold</i> body grows <i>warm</i>? Granted that we
+had a perfect knowledge of the mechanical processes
+of nature, could we and should we, for that reason,
+<i>put out of the world</i> all other processes that we do not
+understand? On this principle it would really be the
+simplest course to deny the existence of the whole
+world. This is the point at which the Eleatics ultimately
+arrived, and the school of Herbart stopped
+little short of the same goal.</p>
+
+<p>Physics treated in this sense supplies us simply
+with a diagram of the world, in which we do not know
+reality again. It happens, in fact, to men who give
+themselves up to this view for many years, that the
+world of sense from which they start as a province of
+the greatest familiarity, suddenly becomes, in their
+eyes, the supreme "world-riddle."</p>
+
+<p>Intelligible as it is, therefore, that the efforts of
+thinkers have always been bent upon the "reduction
+of all physical processes to the motions of atoms," it
+must yet be affirmed that this is a chimerical ideal.
+This ideal has often played an effective part in popular
+lectures, but in the workshop of the serious inquirer
+it has discharged scarcely the least function.
+What has really been achieved in mechanical physics
+is either the <i>elucidation</i> of physical processes by more<span class="pagenum"><a name="Page_160" id="Page_160">[Pg 160]</a></span>
+familiar <i>mechanical analogies</i>, (for example, the theories
+of light and of electricity,) or the exact <i>quantitative</i>
+ascertainment of the connexion of mechanical processes
+with other physical processes, for example, the
+results of thermodynamics.</p>
+
+
+<h3>III. THE PRINCIPLE OF ENERGY IN PHYSICS.</h3>
+
+<p>We can know only from <i>experience</i> that mechanical
+processes produce other physical transformations, or
+<i>vice versa</i>. The attention was first directed to the connexion
+of mechanical processes, especially the performance
+of work, with changes of thermal conditions
+by the invention of the steam-engine, and by its great
+technical importance. Technical interests and the
+need of scientific lucidity meeting in the mind of S.
+Carnot led to the remarkable development from which
+thermodynamics flowed. It is simply <i>an accident of
+history</i> that the development in question was not connected
+with the practical applications of <i>electricity</i>.</p>
+
+<p>In the determination of the maximum quantity of
+<i>work</i> that, generally, a heat-machine, or, to take a
+special case, a steam-engine, can perform with the
+expenditure of a <i>given</i> amount of heat of combustion,
+Carnot is guided by mechanical analogies. A body can
+do work on being heated, by expanding under pressure.
+But to do this the body must receive heat from a <i>hotter</i>
+body. Heat, therefore, to do work, must pass from a
+hotter body to a colder body, just as water must fall
+from a higher level to a lower level to put a mill-wheel<span class="pagenum"><a name="Page_161" id="Page_161">[Pg 161]</a></span>
+in motion. Differences of temperature, accordingly,
+represent forces able to do work exactly as do differences
+of height in heavy bodies. Carnot pictures to
+himself an ideal process in which no heat flows away
+unused, that is, without doing work. With a given expenditure
+of heat, accordingly, this process furnishes
+the maximum of work. An analogue of the process
+would be a mill-wheel which scooping its water out of
+a higher level would slowly carry it to a lower level
+without the loss of a drop. A peculiar property of the
+process is, that with the expenditure of the same work
+the water can be raised again exactly to its original
+level. This property of <i>reversibility</i> is also shared by
+the process of Carnot. His process also can be reversed
+by the expenditure of the same amount of work,
+and the heat again brought back to its original temperature
+level.</p>
+
+<p>Suppose, now, we had <i>two</i> different reversible processes
+<i>A</i>, <i>B</i>, such that in <i>A</i> a quantity of heat, <i>Q</i>,
+flowing off from the temperature <i>t</i><sub>1</sub> to the lower temperature
+<i>t</i><sub>2</sub> should perform the work <i>W</i>, but in <i>B</i> under
+the same circumstances it should perform a greater
+quantity of work <i>W</i> + <i>W'</i>; then, we could join <i>B</i> in
+the sense assigned and <i>A</i> in the reverse sense into a
+<i>single</i> process. Here <i>A</i> would reverse the transformation
+of heat produced by <i>B</i> and would leave a surplus
+of work <i>W'</i>, produced, so to speak, from nothing.
+The combination would present a perpetual motion.</p>
+
+<p>With the feeling, now, that it makes little difference<span class="pagenum"><a name="Page_162" id="Page_162">[Pg 162]</a></span>
+whether the mechanical laws are broken directly
+or indirectly (by processes of heat), and convinced of
+the existence of a <i>universal</i> law-ruled connexion of nature,
+Carnot here excludes for the first time from the
+province of <i>general</i> physics the possibility of a perpetual
+motion. <i>But it follows, then, that the quantity
+of work W, produced by the passage of a quantity of heat
+Q from a temperature t<sub>1</sub> to a temperature t<sub>2</sub>, is independent
+of the nature of the substances as also of the character
+of the process, so far as that is unaccompanied by
+loss, but is wholly dependent upon the temperature t<sub>1</sub>, t<sub>2</sub>.</i></p>
+
+<p>This important principle has been fully confirmed
+by the special researches of Carnot himself (1824), of
+Clapeyron (1834), and of Sir William Thomson (1849),
+now Lord Kelvin. The principle was reached <i>without
+any assumption whatever</i> concerning the nature of heat,
+simply by the exclusion of a perpetual motion. Carnot,
+it is true, was an adherent of the theory of Black, according
+to which the sum-total of the quantity of heat
+in the world is constant, but so far as his investigations
+have been hitherto considered the decision on
+this point is of no consequence. Carnot's principle
+led to the most remarkable results. W. Thomson
+(1848) founded upon it the ingenious idea of an "absolute"
+scale of temperature. James Thomson (1849)
+conceived a Carnot process to take place with water
+freezing under pressure and, therefore, performing
+work. He discovered, thus, that the freezing point is
+lowered 0·0075° Celsius by every additional atmosphere<span class="pagenum"><a name="Page_163" id="Page_163">[Pg 163]</a></span>
+of pressure. This is mentioned merely as an
+example.</p>
+
+<p>About twenty years after the publication of Carnot's
+book a further advance was made by J. R. Mayer
+and J. P. Joule. Mayer, while engaged as a physician
+in the service of the Dutch, observed, during a
+process of bleeding in Java, an unusual redness of the
+venous blood. In agreement with Liebig's theory of
+animal heat he connected this fact with the diminished
+loss of heat in warmer climates, and with the diminished
+expenditure of organic combustibles. The total
+expenditure of heat of a man at rest must be equal to
+the total heat of combustion. But since <i>all</i> organic actions,
+even the mechanical actions, must be set down
+to the credit of the heat of combustion, some connexion
+must exist between mechanical work and expenditure
+of heat.</p>
+
+<p>Joule started from quite similar convictions concerning
+the galvanic battery. A heat of association
+equivalent to the consumption of the zinc can be made
+to appear in the galvanic cell. If a current is set up,
+a part of this heat appears in the conductor of the
+current. The interposition of an apparatus for the
+decomposition of water causes a part of this heat to
+disappear, which on the burning of the explosive gas
+formed, is reproduced. If the current runs an electromotor,
+a portion of the heat again disappears, which,
+on the consumption of the work by friction, again
+makes its appearance. Accordingly, both the heat<span class="pagenum"><a name="Page_164" id="Page_164">[Pg 164]</a></span>
+produced and the work produced, appeared to Joule
+also as connected with the consumption of material.
+The thought was therefore present, both to Mayer and
+to Joule, of regarding heat and work as equivalent
+quantities, so connected with each other that what is
+lost in one form universally appears in another. The
+result of this was a <i>substantial</i> conception of heat and
+of work, and <i>ultimately a substantial conception of energy</i>.
+Here every physical change of condition is regarded
+as energy, the destruction of which generates
+work or equivalent heat. An electric charge, for example,
+is energy.</p>
+
+<p>In 1842 Mayer had calculated from the physical
+constants then universally accepted that by the disappearance
+of one kilogramme-calorie 365 kilogramme-metres
+of work could be performed, and <i>vice versa</i>.
+Joule, on the other hand, by a long series of delicate
+and varied experiments beginning in 1843 ultimately
+determined the mechanical equivalent of the kilogramme-calorie,
+more exactly, as 425 kilogramme-metres.</p>
+
+<p>If we estimate every change of physical condition
+by the <i>mechanical work</i> which can be performed upon
+the <i>disappearance</i> of that condition, and call this measure
+<i>energy</i>, then we can measure all physical changes
+of condition, no matter how different they may be,
+with the same common measure, and say: <i>the sum-total
+of all energy remains constant</i>. This is the form that
+the principle of excluded perpetual motion received at<span class="pagenum"><a name="Page_165" id="Page_165">[Pg 165]</a></span>
+the hands of Mayer, Joule, Helmholtz, and W. Thomson
+in its extension to the whole domain of physics.</p>
+
+<p>After it had been proved that heat must <i>disappear</i>
+if mechanical work was to be done at its expense,
+Carnot's principle could no longer be regarded as a
+complete expression of the facts. Its improved form
+was first given, in 1850, by Clausius, whom Thomson
+followed in 1851. It runs thus: "If a quantity of heat
+<i>Q'</i> is transformed into work in a reversible process,
+<i>another</i> quantity of heat <i>Q</i> of the absolute<a name="FNanchor_55_55" id="FNanchor_55_55"></a><a href="#Footnote_55_55" class="fnanchor">[55]</a> temperature
+<i>T<sub>1</sub></i> is lowered to the absolute temperature <i>T<sub>2</sub></i>."
+Here <i>Q'</i> is dependent only on <i>Q</i>, <i>T<sub>1</sub></i>, <i>T<sub>2</sub></i>, but is independent
+of the substances used and of the character of
+the process, so far as that is unaccompanied by loss.
+Owing to this last fact, it is sufficient to find the relation
+which obtains for some one well-known physical
+substance, say a gas, and some definite simple process.
+The relation found will be the one that holds
+generally. We get, thus,</p>
+
+<p class="center"><i>Q'/(Q' + Q)</i> = <i>(T<sub>1</sub>-T<sub>2</sub>)/T<sub>1</sub></i> (1)
+</p>
+
+<p>that is, the quotient of the available heat <i>Q'</i> transformed
+into work divided by the sum of the transformed
+and transferred heats (the total sum used), the
+so-called <i>economical coefficient</i> of the process, is,</p>
+
+<p><i>(T<sub>1</sub>-T<sub>2</sub>)/T<sub>1</sub></i>.</p>
+<p><span class="pagenum"><a name="Page_166" id="Page_166">[Pg 166]</a></span></p>
+
+<h3>IV. THE CONCEPTIONS OF HEAT.</h3>
+
+<p>When a cold body is put in contact with a warm
+body it is observed that the first body is warmed and
+that the second body is cooled. We may say that the
+first body is warmed <i>at the expense of</i> the second body.
+This suggests the notion of a thing, or heat-substance,
+which passes from the one body to the other. If two
+masses of water <i>m</i>, <i>m'</i>, of unequal temperatures, be
+put together, it will be found, upon the rapid equalisation
+of the temperatures, that the respective changes
+of temperatures <i>u</i> and <i>u'</i> are inversely proportional to
+the masses and of opposite signs, so that the algebraical
+sum of the products is,</p>
+
+<p class="center"><i>mu</i> + <i>m'u'</i> = 0.
+</p>
+
+<p>Black called the products <i>mu</i>, <i>m'u'</i>, which are decisive
+for our knowledge of the process, <i>quantities of heat</i>.
+We may form a very clear <i>picture</i> of these products
+by conceiving them with Black as measures of the
+quantities of some substance. But the essential thing
+is not this picture but the <i>constancy</i> of the sum of these
+products in simple processes of conduction. If a quantity
+of heat disappears at one point, an equally large
+quantity will make its appearance at some other point.
+The retention of this idea leads to the discovery of
+specific heat. Black, finally, perceives that also something
+else may appear for a vanished quantity of heat,
+namely: the fusion or vaporisation of a definite quantity<span class="pagenum"><a name="Page_167" id="Page_167">[Pg 167]</a></span>
+of matter. He adheres here still to this favorite
+view, though with some freedom, and considers the
+vanished quantity of heat as still present, but as <i>latent</i>.</p>
+
+<p>The generally accepted notion of a caloric, or heat-stuff,
+was strongly shaken by the work of Mayer and
+Joule. If the quantity of heat can be increased and
+diminished, people said, heat cannot be a substance,
+but must be a <i>motion</i>. The subordinate part of this
+statement has become much more popular than all the
+rest of the doctrine of energy. But we may convince
+ourselves that the motional conception of heat is now
+as unessential as was formerly its conception as a substance.
+Both ideas were favored or impeded solely
+by accidental historical circumstances. It does not
+follow that heat is not a substance from the fact that
+a mechanical equivalent exists for quantity of heat.
+We will make this clear by the following question
+which bright students have sometimes put to me. Is
+there a mechanical equivalent of electricity as there is
+a mechanical equivalent of heat? Yes, and no. There
+is no mechanical equivalent of <i>quantity</i> of electricity
+as there is an equivalent of <i>quantity</i> of heat, because
+the same quantity of electricity has a very different
+capacity for work, according to the circumstances in
+which it is placed; but there <i>is</i> a mechanical equivalent
+of electrical energy.</p>
+
+<p>Let us ask another question. Is there a mechanical
+equivalent of water? No, there is no mechanical
+equivalent of quantity of water, but there is a mechanical<span class="pagenum"><a name="Page_168" id="Page_168">[Pg 168]</a></span>
+equivalent of weight of water multiplied by
+its distance of descent.</p>
+
+<p>When a Leyden jar is discharged and work thereby
+performed, we do not picture to ourselves that the
+quantity of electricity disappears as work is done, but
+we simply assume that the electricities come into different
+positions, equal quantities of positive and negative
+electricity being united with one another.</p>
+
+<p>What, now, is the reason of this difference of view
+in our treatment of heat and of electricity? The reason
+is purely historical, wholly conventional, and, what
+is still more important, is wholly indifferent. I may
+be allowed to establish this assertion.</p>
+
+<p>In 1785 Coulomb constructed his torsion balance,
+by which he was enabled to measure the repulsion of
+electrified bodies. Suppose we have two small balls,
+<i>A</i>, <i>B</i>, which over their whole extent are similarly
+electrified. These two balls will exert on one another,
+at a certain distance <i>r</i> of their centres, a certain repulsion
+<i>p</i>. We bring into contact with <i>B</i> now a ball
+<i>C</i>, suffer both to be equally electrified, and then measure
+the repulsion of <i>B</i> from <i>A</i> and of <i>C</i> from <i>A</i> at the
+same distance <i>r</i>. The sum of these repulsions is again
+<i>p</i>. Accordingly something has remained constant.
+If we ascribe this effect to a substance, then we infer
+naturally its constancy. But the essential point of the
+exposition is the divisibility of the electric force <i>p</i> and
+not the simile of substance.</p>
+
+<p>In 1838 Riess constructed his electrical air-thermometer<span class="pagenum"><a name="Page_169" id="Page_169">[Pg 169]</a></span>
+(the thermoelectrometer). This gives a measure
+of the quantity of heat produced by the discharge of
+jars. This quantity of heat is not proportional to the
+quantity of electricity contained in the jar by Coulomb's
+measure, but if <i>Q</i> be this quantity and <i>C</i> be the
+capacity, is proportional to <i>Q</i><sup>2</sup>/2<i>C</i>, or, more simply
+still, to the energy of the charged jar. If, now, we
+discharge the jar completely through the thermometer,
+we obtain a certain quantity of heat, <i>W</i>. But if
+we make the discharge through the thermometer into
+a second jar, we obtain a quantity less than <i>W</i>. But we
+may obtain the remainder by completely discharging
+both jars through the air-thermometer, when it will
+again be proportional to the energy of the two jars. On
+the first, incomplete discharge, accordingly, a part of
+the electricity's capacity for work was lost.</p>
+
+<p>When the charge of a jar produces heat its energy
+is changed and its value by Riess's thermometer is decreased.
+But by Coulomb's measure the quantity remains
+unaltered.</p>
+
+<p>Now let us imagine that Riess's thermometer had
+been invented before Coulomb's torsion balance, which
+is not a difficult feat, since both inventions are independent
+of each other; what would be more natural than
+that the "quantity" of electricity contained in a jar
+should be measured by the heat produced in the thermometer?
+But then, this so-called quantity of electricity
+would decrease on the production of heat or on
+the performance of work, whereas it now remains unchanged;<span class="pagenum"><a name="Page_170" id="Page_170">[Pg 170]</a></span>
+in that case, therefore, electricity would not
+be a <i>substance</i> but a <i>motion</i>, whereas now it is still a
+substance. The reason, therefore, why we have other
+notions of electricity than we have of heat, is purely
+historical, accidental, and conventional.</p>
+
+<p>This is also the case with other physical things.
+Water does not disappear when work is done. Why?
+Because we measure quantity of water with scales, just
+as we do electricity. But suppose the capacity of
+water for work were called quantity, and had to be
+measured, therefore, by a mill instead of by scales;
+then this quantity also would disappear as it performed
+the work. It may, now, be easily conceived
+that many substances are not so easily got at as water.
+In that case we should be unable to carry out the one
+kind of measurement with the scales whilst many other
+modes of measurement would still be left us.</p>
+
+<p>In the case of heat, now, the historically established
+measure of "quantity" is accidentally the work-value
+of the heat. Accordingly, its quantity disappears when
+work is done. But that heat is not a substance follows
+from this as little as does the opposite conclusion that
+it is a substance. In Black's case the quantity of heat
+remains constant because the heat passes into no <i>other</i>
+form of energy.</p>
+
+<p>If any one to-day should still wish to think of heat
+as a substance, we might allow that person this liberty
+with little ado. He would only have to assume that
+that which we call quantity of heat was the energy of<span class="pagenum"><a name="Page_171" id="Page_171">[Pg 171]</a></span>
+a substance whose quantity remained unaltered, but
+whose energy changed. In point of fact we might
+much better say, in analogy with the other terms of
+physics, energy of heat, instead of quantity of heat.</p>
+
+<p>When we wonder, therefore, at the discovery that
+heat is motion, we wonder at something that was never
+discovered. It is perfectly indifferent and possesses
+not the slightest scientific value, whether we think of
+heat as a substance or not. The fact is, heat behaves
+in some connexions like a substance, in others not.
+Heat is latent in steam as oxygen is latent in water.</p>
+
+
+<h3>V. THE CONFORMITY IN THE DEPORTMENT OF THE
+ENERGIES.</h3>
+
+<p>The foregoing reflexions will gain in lucidity from
+a consideration of the conformity which obtains in the
+behavior of all energies, a point to which I called attention
+long ago.<a name="FNanchor_56_56" id="FNanchor_56_56"></a><a href="#Footnote_56_56" class="fnanchor">[56]</a></p>
+
+<p>A weight <i>P</i> at a height <i>H</i><sub>1</sub> represents an energy
+<i>W</i><sub>1</sub> = <i>PH</i><sub>1</sub>. If we suffer the weight to sink to a lower
+height <i>H</i><sub>2</sub>, during which work is done, and the work
+done is employed in the production of living force,
+heat, or an electric charge, in short, is transformed,
+then the energy <i>W</i><sub>2</sub> = <i>PH</i><sub>2</sub> is still <i>left</i>. The equation
+subsists</p>
+
+<p><span class="pagenum"><a name="Page_172" id="Page_172">[Pg 172]</a></span></p><p><i>W</i><sub>1</sub>/<i>H</i><sub>1</sub> = <i>W</i><sub>2</sub>/<i>H</i><sub>2</sub>, (2)
+or, denoting the <i>transformed</i> energy by <i>W</i>' = <i>W</i><sub>1</sub>-<i>W</i><sub>2</sub>
+and the <i>transferred</i> energy, that transported to the
+lower level, by <i>W</i> = <i>W</i><sub>2</sub>,</p>
+
+<p class="center"><i>W</i>'/(<i>W</i>' + <i>W</i>) = (<i>H</i><sub>1</sub>-<i>H</i><sub>2</sub>)/<i>H</i><sub>1</sub>, (3)
+</p>
+
+<p>an equation in all respects analogous to equation (1)
+at page 165. The property in question, therefore, is
+by no means peculiar to heat. Equation (2) gives the
+relation between the energy taken from the higher
+level and that deposited on the lower level (the energy
+left behind); it says that these <i>energies</i> are proportional
+to the <i>heights of the levels</i>. An equation analogous
+to equation (2) may be set up for <i>every</i> form of
+energy; hence the equation which corresponds to
+equation (3), and so to equation (1), may be regarded
+as valid for every form. For electricity, for example,
+<i>H</i><sub>1</sub>, <i>H</i><sub>2</sub> signify the potentials.</p>
+
+<p>When we observe for the first time the agreement
+here indicated in the transformative law of the energies,
+it appears surprising and unexpected, for we do
+not perceive at once its reason. But to him who pursues
+the comparative historical method that reason
+will not long remain a secret.</p>
+
+<p>Since Galileo, mechanical work, though long under
+a different name, has been a <i>fundamental concept</i> of
+mechanics, as also a very important notion in the applied
+sciences. The transformation of work into living<span class="pagenum"><a name="Page_173" id="Page_173">[Pg 173]</a></span>
+force, and of living force into work, suggests directly
+the notion of energy&mdash;the idea having been first
+fruitfully employed by Huygens, although Thomas
+Young first called it by the <i>name</i> of "energy." Let
+us add to this the constancy of weight (really the constancy
+of mass) and we shall see that with respect to
+mechanical energy it is involved in the very definition
+of the term that the capacity for work or the potential
+energy of a weight is proportional to the height of the
+level at which it is, in the geometrical sense, and that
+it decreases on the lowering of the weight, on transformation,
+proportionally to the height of the level.
+The zero level here is wholly arbitrary. With this,
+equation (2) is given, from which all the other forms
+follow.</p>
+
+<p>When we reflect on the tremendous start which
+mechanics had over the other branches of physics, it
+is not to be wondered at that the attempt was always
+made to apply the notions of that science wherever
+this was possible. Thus the notion of mass, for example,
+was imitated by Coulomb in the notion of
+quantity of electricity. In the further development
+of the theory of electricity, the notion of work was
+likewise immediately introduced in the theory of potential,
+and heights of electrical level were measured
+by the work of unit of quantity raised to that level.
+But with this the preceding equation with all its consequences
+is given for electrical energy. The case with
+the other energies was similar.</p><p><span class="pagenum"><a name="Page_174" id="Page_174">[Pg 174]</a></span></p>
+
+<p><i>Thermal</i> energy, however, appears as a special
+case. Only by the peculiar experiments mentioned
+could it be discovered that heat is an energy. But the
+measure of this energy by Black's quantity of heat is
+the outcome of fortuitous circumstances. In the first
+place, the accidental slight variability of the capacity
+for heat <i>c</i> with the temperature, and the accidental
+slight deviation of the usual thermometrical scales
+from the scale derived from <i>the tensions of gases</i>, brings
+it about that the notion "quantity of heat" can be set
+up and that the quantity of heat <i>ct</i> corresponding to a
+difference of temperature <i>t</i> is nearly proportional to
+the energy of the heat. It is a quite accidental historical
+circumstance that Amontons hit upon the idea
+of measuring temperature by the tension of a gas. It
+is certain in this that he did not think of the work of
+the heat.<a name="FNanchor_57_57" id="FNanchor_57_57"></a><a href="#Footnote_57_57" class="fnanchor">[57]</a> But the numbers standing for temperature,
+thus, are made proportional to the tensions of
+gases, that is, to the work done by gases, with otherwise
+equal changes of volume. It thus happens that
+<i>temperature heights</i> and <i>level heights of work</i> are proportional
+to one another.</p>
+
+<p>If properties of the thermal condition varying
+greatly from the tensions of gases had been chosen,
+this relation would have assumed very complicated
+forms, and the agreement between heat and the other
+energies above considered would not subsist. It is<span class="pagenum"><a name="Page_175" id="Page_175">[Pg 175]</a></span>
+very instructive to reflect upon this point. A <i>natural
+law</i>, therefore, is not implied in the conformity of the
+behavior of the energies, but this conformity is rather
+conditioned by the uniformity of our modes of conception
+and is also partly a matter of good fortune.</p>
+
+
+<h3>VI. THE DIFFERENCES OF THE ENERGIES AND THE
+LIMITS OF THE PRINCIPLE OF ENERGY.</h3>
+
+<p>Of every quantity of heat <i>Q</i> which does work in a
+reversible process (one unaccompanied by loss) between
+the absolute temperatures <i>T</i><sub>1</sub>, <i>T</i><sub>2</sub>, only the portion</p>
+
+<p>(<i>T</i><sub>1</sub>-<i>T</i><sub>2</sub>)/<i>T</i><sub>1</sub></p>
+
+<p>is transformed into work, while the remainder is transferred
+to the lower temperature-level <i>T</i><sub>2</sub>. This transferred
+portion can, upon the reversal of the process,
+with the same expenditure of work, again be brought
+back to the level <i>T</i><sub>1</sub>. But if the process is not reversible,
+then more heat than in the foregoing case flows
+to the lower level, and the surplus can no longer be
+brought back to the higher level <i>T</i><sub>2</sub> without some <i>special</i>
+expenditure. W. Thomson (1852), accordingly,
+drew attention to the fact, that in all non-reversible,
+that is, in all real thermal processes, quantities of heat
+are lost for mechanical work, and that accordingly a
+dissipation or waste of mechanical energy is taking
+place. In all cases, heat is only partially transformed
+into work, but frequently work is wholly transformed<span class="pagenum"><a name="Page_176" id="Page_176">[Pg 176]</a></span>
+into heat. Hence, a tendency exists towards a diminution
+of the <i>mechanical</i> energy and towards an increase
+of the <i>thermal</i> energy of the world.</p>
+
+<p>For a simple, closed cyclical process, accompanied
+by no loss, in which the quantity of heat <i>Q_</i>{1} is taken
+from the level <i>T_</i>{1}, and the quantity <i>Q_</i>{2} is deposited
+upon the level <i>T_</i>{2}, the following relation, agreeably to
+equation (2), exists,</p>
+
+<p class="center">-(<i>Q</i><sub>1</sub>/<i>T</i><sub>1</sub>) + (<i>Q</i><sub>2</sub>/<i>T</i><sub>2</sub>) = 0.
+</p>
+
+<p>Similarly, for any number of compound reversible
+cycles Clausius finds the algebraical sum</p>
+
+<p class="center">&#931;<i>Q</i>/<i>T</i> = 0,
+</p>
+
+<p>and supposing the temperature to change continuously,</p>
+
+<p class="center">&#8747;<i>dQ</i>/<i>T</i> = 0 (4)
+</p>
+
+<p>Here the elements of the quantities of heat deducted
+from a given level are reckoned negative, and the elements
+imparted to it, positive. If the process is not
+reversible, then expression (4), which Clausius calls
+<i>entropy</i>, increases. In actual practice this is always
+the case, and Clausius finds himself led to the statement:</p>
+
+<p>1. That the energy of the world remains constant.</p>
+
+<p>2. That the entropy of the world tends toward a
+maximum.</p>
+
+<p>Once we have noted the above-indicated conformity
+in the behavior of different energies, the <i>peculiarity</i><span class="pagenum"><a name="Page_177" id="Page_177">[Pg 177]</a></span>
+of thermal energy here mentioned must strike us.
+Whence is this peculiarity derived, for, generally every
+energy passes only partly into another form, which is
+also true of thermal energy? The explanation will be
+found in the following.</p>
+
+<p>Every transformation of a special kind of energy <i>A</i>
+is accompanied with a fall of potential of that particular
+kind of energy, including heat. But whilst for the
+other kinds of energy a transformation and therefore a
+loss of energy on the part of the kind sinking in potential
+is connected with the fall of the potential, with
+heat the case is different. Heat can suffer a fall of
+potential without sustaining a loss of energy, at least
+according to the customary mode of estimation. If a
+weight sinks, it must create perforce kinetic energy,
+or heat, or some other form of energy. Also, an electrical
+charge cannot suffer a fall of potential without
+loss of energy, i. e., without transformation. But heat
+can pass with a fall of temperature to a body of greater
+capacity and the same thermal energy still be preserved,
+so long as we regard <i>every quantity</i> of heat as
+energy. This it is that gives to heat, besides its
+property of energy, in many cases the character of a
+material <i>substance</i>, or quantity.</p>
+
+<p>If we look at the matter in an unprejudiced light,
+we must ask if there is any scientific sense or purpose
+in still considering as energy a quantity of heat that
+can no longer be transformed into mechanical work,
+(for example, the heat of a closed equably warmed<span class="pagenum"><a name="Page_178" id="Page_178">[Pg 178]</a></span>
+material system). The principle of energy certainly
+plays in this case a wholly superfluous rôle, which is
+assigned to it only from habit.<a name="FNanchor_58_58" id="FNanchor_58_58"></a><a href="#Footnote_58_58" class="fnanchor">[58]</a> To maintain the principle
+of energy in the face of a knowledge of the dissipation
+or waste of mechanical energy, in the face of
+the increase of entropy is equivalent almost to the
+liberty which Black took when he regarded the heat
+of liquefaction as still present but latent.<a name="FNanchor_59_59" id="FNanchor_59_59"></a><a href="#Footnote_59_59" class="fnanchor">[59]</a> It is to be
+remarked further, that the expressions "energy of the
+world" and "entropy of the world" are slightly permeated
+with scholasticism. Energy and entropy are
+<i>metrical</i> notions. What meaning can there be in applying
+these notions to a case in which they are not
+applicable, in which their values are not determinable?</p>
+
+<p>If we could really determine the entropy of the
+world it would represent a true, absolute measure of
+time. In this way is best seen the utter tautology of
+a statement that the entropy of the world increases
+with the time. Time, and the fact that certain changes
+take place only in a definite sense, are one and the
+same thing.</p>
+
+<p><span class="pagenum"><a name="Page_179" id="Page_179">[Pg 179]</a></span></p>
+<h3>VII. THE SOURCES OF THE PRINCIPLE OF ENERGY.</h3>
+
+<p>We are now prepared to answer the question, What
+are the sources of the principle of energy? All knowledge
+of nature is derived in the last instance from experience.
+In this sense they are right who look upon
+the principle of energy as a result of experience.</p>
+
+<p>Experience teaches that the sense-elements &#945;&#946;&#947;&#948;...
+into which the world may be decomposed, are subject
+to change. It tells us further, that certain of these
+elements are <i>connected</i> with other elements, so that they
+appear and disappear together; or, that the appearance
+of the elements of one class is connected with the
+disappearance of the elements of the other class. We
+will avoid here the notions of cause and effect because
+of their obscurity and equivocalness. The result
+of experience may be expressed as follows: <i>The
+sensuous elements of the world (&#945;&#946;&#947;&#948;...) show themselves
+to be interdependent.</i> This interdependence is
+best represented by some such conception as is in
+geometry that of the mutual dependence of the sides
+and angles of a triangle, only much more varied and
+complex.</p>
+
+<p>As an example, we may take a mass of gas enclosed
+in a cylinder and possessed of a definite volume (&#945;),
+which we change by a pressure (&#946;) on the piston, at
+the same time feeling the cylinder with our hand and<span class="pagenum"><a name="Page_180" id="Page_180">[Pg 180]</a></span>
+receiving a sensation of heat (&#947;). Increase of pressure
+diminishes the volume and increases the sensation
+of heat.</p>
+
+<p>The various facts of experience are not in all respects
+alike. Their common sensuous elements are
+placed in relief by a process of abstraction and thus
+impressed upon the memory. In this way the expression
+is obtained of the features of <i>agreement</i> of extensive
+groups of facts. The simplest sentence which we can
+utter is, by the very nature of language, an abstraction
+of this kind. But account must also be taken of the
+<i>differences</i> of related facts. Facts may be so nearly related
+as to contain the same kind of a &#945;&#946;&#947;..., but the
+relation be such that the &#945;&#946;&#947;... of the one differ
+from the &#945;&#946;&#947;... of the other only by the number of
+equal parts into which they can be divided. Such
+being the case, if rules can be given for deducing <i>from
+one another</i> the numbers which are the measures of
+these &#945;&#946;&#947;..., then we possess in such rules the <i>most
+general</i> expression of a group of facts, as also that expression
+which corresponds to all its differences. This
+is the goal of quantitative investigation.</p>
+
+<p>If this goal be reached what we have found is that
+between the &#945;&#946;&#947;... of a group of facts, or better, between
+the numbers which are their measures, a number
+of equations exists. The simple fact of change
+brings it about that the number of these equations
+must be smaller than the number of the &#945;&#946;&#947;.... If
+the former be smaller by one than the latter, then one<span class="pagenum"><a name="Page_181" id="Page_181">[Pg 181]</a></span>
+portion of the &#945;&#946;&#947;... is <i>uniquely</i> determined by the
+other portion.</p>
+
+<p>The quest of relations of this last kind is the most
+important function of special experimental research,
+because we are enabled by it to complete in thought
+facts that are only partly given. It is self-evident that
+only experience can ascertain that between the &#945;&#946;&#947;...
+relations exist and of what kind they are. Further,
+only experience can tell that the relations that exist
+between the &#945;&#946;&#947;... are such that changes of them
+can be reversed. If this were not the fact all occasion
+for the enunciation of the principle of energy, as is
+easily seen, would be wanting. In experience, therefore,
+is buried the ultimate well-spring of all knowledge
+of nature, and consequently, in this sense, also
+the ultimate source of the principle of energy.</p>
+
+<p>But this does not exclude the fact that the principle
+of energy has also a logical root, as will now be
+shown. Let us assume on the basis of experience that
+one group of sensuous elements &#945;&#946;&#947;... determines
+<i>uniquely</i> another group &#955;&#956;&#957;.... Experience further
+teaches that changes of &#945;&#946;&#947;... can be <i>reversed</i>. It
+is then a logical consequence of this observation, that
+every time that &#945;&#946;&#947;... assume the same values this
+is also the case with &#955;&#956;&#957;.... Or, that purely <i>periodical</i>
+changes of &#945;&#946;&#947;... can produce no <i>permanent</i>
+changes of &#955;&#956;&#957;.... If the group &#955;&#956;&#957;... is a mechanical
+group, then a perpetual motion is excluded.</p><p><span class="pagenum"><a name="Page_182" id="Page_182">[Pg 182]</a></span></p>
+
+<p>It will be said that this is a vicious circle, which
+we will grant. But psychologically, the situation is
+essentially different, whether I think simply of the
+unique determination and reversibility of events, or
+whether I exclude a perpetual motion. The attention
+takes in the two cases different directions and diffuses
+light over different sides of the question, which logically
+of course are necessarily connected.</p>
+
+<p>Surely that firm, logical setting of the thoughts noticeable
+in the great inquirers, Stevinus, Galileo, and
+the rest, which, consciously or instinctively, was supported
+by a fine feeling for the slightest contradictions,
+has no other purpose than to limit the bounds of
+thought and so exempt it from the possibility of error.
+In this, therefore, the logical root of the principle of
+excluded perpetual motion is given, namely, in that
+universal conviction which existed even before the development
+of mechanics and co-operated in that development.</p>
+
+<p>It is perfectly natural that the principle of excluded
+perpetual motion should have been first developed in
+the simple domain of pure mechanics. Towards the
+transference of that principle into the domain of general
+physics the idea contributed much that all physical
+phenomena are mechanical phenomena. But the
+foregoing discussion shows how little essential this
+notion is. The issue really involved is the recognition
+of a general interconnexion of nature. This once established,
+we see with Carnot that it is indifferent<span class="pagenum"><a name="Page_183" id="Page_183">[Pg 183]</a></span>
+whether the mechanical laws are broken directly or
+circuitously.</p>
+
+<p>The principle of the excluded perpetual motion is
+very closely related to the modern principle of energy,
+but it is not identical with it, for the latter is to be
+deduced from the former only by means of a definite
+<i>formal conception</i>. As may be seen from the preceding
+exposition, the perpetual motion can be excluded without
+our employing or possessing the notion of <i>work</i>.
+The modern principle of energy results primarily from
+a <i>substantial</i> conception of work and of every change
+of physical condition which by being reversed produces
+work. The strong need of such a conception,
+which is by no means necessary, but in a formal sense
+is very convenient and lucid, is exhibited in the case
+of J. R. Mayer and Joule. It was before remarked
+that this conception was suggested to both inquirers
+by the observation that both the production of heat
+and the production of mechanical work were connected
+with an expenditure of substance. Mayer says: "Ex
+nihilo nil fit," and in another place, "The creation or
+destruction of a force (work) lies without the province
+of human activity." In Joule we find this passage:
+"It is manifestly <i>absurd</i> to suppose that the powers
+with which God has endowed matter can be destroyed."</p>
+
+<p>Some writers have observed in such statements the
+attempt at a <i>metaphysical</i> establishment of the doctrine
+of energy. But we see in them simply the formal need
+of a simple, clear, and living grasp of the facts, which<span class="pagenum"><a name="Page_184" id="Page_184">[Pg 184]</a></span>
+receives its development in practical and technical life,
+and which we carry over, as best we can, into the
+province of science. As a fact, Mayer writes to Griesinger:
+"If, finally, you ask me how I became involved
+in the whole affair, my answer is simply this: Engaged
+during a sea voyage almost exclusively with the study
+of physiology, I discovered the new theory for the
+sufficient reason that I <i>vividly felt the need of it</i>."</p>
+
+<p>The substantial conception of work (energy) is by
+no means a necessary one. And it is far from true that
+the problem is solved with the recognition of the need
+of such a conception. Rather let us see how Mayer
+gradually endeavored to satisfy that need. He first
+regards quantity of motion, or momentum, <i>mv</i>, as the
+equivalent of work, and did not light, until later, on
+the notion of living force (<i>mv<sup>2</sup>/2</i>). In the province
+of electricity he was unable to assign the expression
+which is the equivalent of work. This was done later
+by Helmholtz. The formal need, therefore, is <i>first</i>
+present, and our conception of nature is subsequently
+gradually <i>adapted</i> to it.</p>
+
+<p>The laying bare of the experimental, logical, and
+formal root of the present principle of energy will perhaps
+contribute much to the removal of the mysticism
+which still clings to this principle. With respect to
+our formal need of a very simple, palpable, substantial
+conception of the processes in our environment, it
+remains an open question how far nature corresponds
+to that need, or how far we can satisfy it. In one<span class="pagenum"><a name="Page_185" id="Page_185">[Pg 185]</a></span>
+phase of the preceding discussions it would seem as
+if the substantial notion of the principle of energy, like
+Black's material conception of heat, has its natural
+limits in facts, beyond which it can only be artificially
+adhered to.</p><hr class="chap" /><p><span class="pagenum"><a name="Page_186" id="Page_186">[Pg 186]</a></span></p>
+
+
+
+
+<h2><a name="THE_ECONOMICAL_NATURE_OF" id="THE_ECONOMICAL_NATURE_OF">THE ECONOMICAL NATURE OF
+PHYSICAL INQUIRY.</a><a name="FNanchor_60_60" id="FNanchor_60_60"></a><a href="#Footnote_60_60" class="fnanchor">[60]</a></h2>
+
+
+<p>When the human mind, with its limited powers,
+attempts to mirror in itself the rich life of the
+world, of which it is itself only a small part, and which
+it can never hope to exhaust, it has every reason for
+proceeding economically. Hence that tendency, expressed
+in the philosophy of all times, to compass by
+a few organic thoughts the fundamental features of
+reality. "Life understands not death, nor death life."
+So spake an old Chinese philosopher. Yet in his unceasing
+desire to diminish the boundaries of the incomprehensible,
+man has always been engaged in attempts
+to understand death by life and life by death.</p>
+
+<p>Among the ancient civilised peoples, nature was
+filled with demons and spirits having the feelings and
+desires of men. In all essential features, this animistic
+view of nature, as Tylor<a name="FNanchor_61_61" id="FNanchor_61_61"></a><a href="#Footnote_61_61" class="fnanchor">[61]</a> has aptly termed it, is shared
+in common by the fetish-worshipper of modern Africa
+and the most advanced nations of antiquity. As a
+theory of the world it has never completely disappeared.
+The monotheism of the Christians never fully
+overcame it, no more than did that of the Jews. In
+the belief in witchcraft and in the superstitions of the
+sixteenth and seventeenth centuries, the centuries of
+the rise of natural science, it assumed frightful pathological
+dimensions. Whilst Stevinus, Kepler, and
+Galileo were slowly rearing the fabric of modern physical
+science, a cruel and relentless war was waged
+with firebrand and rack against the devils that glowered
+from every corner. To-day even, apart from all survivals
+of that period, apart from the traces of fetishism
+which still inhere in our physical concepts,<a name="FNanchor_62_62" id="FNanchor_62_62"></a><a href="#Footnote_62_62" class="fnanchor">[62]</a> those
+very ideas still covertly lurk in the practices of modern
+spiritualism.</p>
+<p><span class="pagenum"><a name="Page_187" id="Page_187">[Pg 187]</a></span></p>
+
+<p>By the side of this animistic conception of the
+world, we meet from time to time, in different forms,
+from Democritus to the present day, another view,
+which likewise claims exclusive competency to comprehend
+the universe. This view may be characterised
+as the <i>physico-mechanical</i> view of the world. To-day,
+that view holds, indisputably, the first place in the
+thoughts of men, and determines the ideals and the
+character of our times. The coming of the mind of
+man into the full consciousness of its powers, in the
+eighteenth century, was a period of genuine disillusionment.
+It produced the splendid precedent of a life<span class="pagenum"><a name="Page_188" id="Page_188">[Pg 188]</a></span>
+really worthy of man, competent to overcome the old
+barbarism in the practical fields of life; it created the
+<i>Critique of Pure Reason</i>, which banished into the realm
+of shadows the sham-ideas of the old metaphysics; it
+pressed into the hands of the mechanical philosophy
+the reins which it now holds.</p>
+
+<p>The oft-quoted words of the great Laplace,<a name="FNanchor_63_63" id="FNanchor_63_63"></a><a href="#Footnote_63_63" class="fnanchor">[63]</a> which
+I will now give, have the ring of a jubilant toast to
+the scientific achievements of the eighteenth century:
+"A mind to which were given for a single instant all
+the forces of nature and the mutual positions of all its
+masses, if it were otherwise powerful enough to subject
+these problems to analysis, could grasp, with a
+single formula, the motions of the largest masses as
+well as of the smallest atoms; nothing would be uncertain
+for it; the future and the past would lie revealed
+before its eyes." In writing these words, Laplace,
+as we know, had also in mind the atoms of the
+brain. That idea has been expressed more forcibly
+still by some of his followers, and it is not too much
+to say that Laplace's ideal is substantially that of the
+great majority of modern scientists.</p>
+
+<p>Gladly do we accord to the creator of the <i>Mécanique
+céleste</i> the sense of lofty pleasure awakened in
+him by the great success of the Enlightenment, to
+which we too owe our intellectual freedom. But to-day,
+with minds undisturbed and before <i>new</i> tasks, it<span class="pagenum"><a name="Page_189" id="Page_189">[Pg 189]</a></span>
+becomes physical science to secure itself against self-deception
+by a careful study of its character, so that
+it can pursue with greater sureness its true objects.
+If I step, therefore, beyond the narrow precincts of my
+specialty in this discussion, to trespass on friendly
+neighboring domains, I may plead in my excuse that
+the subject-matter of knowledge is common to all domains
+of research, and that fixed, sharp lines of demarcation
+cannot be drawn.</p>
+
+<p>The belief in occult magic powers of nature has
+gradually died away, but in its place a new belief has
+arisen, the belief in the magical power of science.
+Science throws her treasures, not like a capricious
+fairy into the laps of a favored few, but into the laps
+of all humanity, with a lavish extravagance that no
+legend ever dreamt of! Not without apparent justice,
+therefore, do her distant admirers impute to her the
+power of opening up unfathomable abysses of nature,
+to which the senses cannot penetrate. Yet she who
+came to bring light into the world, can well dispense
+with the darkness of mystery, and with pompous show,
+which she needs neither for the justification of her
+aims nor for the adornment of her plain achievements.</p>
+
+<p>The homely beginnings of science will best reveal
+to us its simple, unchangeable character. Man acquires
+his first knowledge of nature half-consciously
+and automatically, from an instinctive habit of mimicking
+and forecasting facts in thought, of supplementing
+sluggish experience with the swift wings of thought,<span class="pagenum"><a name="Page_190" id="Page_190">[Pg 190]</a></span>
+at first only for his material welfare. When he hears
+a noise in the underbrush he constructs there, just as
+the animal does, the enemy which he fears; when he
+sees a certain rind he forms mentally the image of the
+fruit which he is in search of; just as we mentally associate
+a certain kind of matter with a certain line in
+the spectrum or an electric spark with the friction of a
+piece of glass. A knowledge of causality in this form
+certainly reaches far below the level of Schopenhauer's
+pet dog, to whom it was ascribed. It probably exists
+in the whole animal world, and confirms that great
+thinker's statement regarding the will which created
+the intellect for its purposes. These primitive psychical
+functions are rooted in the economy of our organism
+not less firmly than are motion and digestion.
+Who would deny that we feel in them, too, the elemental
+power of a long practised logical and physiological
+activity, bequeathed to us as an heirloom from
+our forefathers?</p>
+
+<p>Such primitive acts of knowledge constitute to-day
+the solidest foundation of scientific thought. Our instinctive
+knowledge, as we shall briefly call it, by virtue
+of the conviction that we have consciously and
+intentionally contributed nothing to its formation, confronts
+us with an authority and logical power which
+consciously acquired knowledge even from familiar
+sources and of easily tested fallibility can never possess.
+All so-called axioms are such instinctive knowledge.
+Not consciously gained knowledge alone, but powerful<span class="pagenum"><a name="Page_191" id="Page_191">[Pg 191]</a></span>
+intellectual instinct, joined with vast conceptive powers,
+constitute the great inquirer. The greatest advances
+of science have always consisted in some successful
+formulation, in clear, abstract, and communicable terms,
+of what was instinctively known long before, and of
+thus making it the permanent property of humanity.
+By Newton's principle of the equality of pressure and
+counterpressure, whose truth all before him had felt, but
+which no predecessor had abstractly formulated, mechanics
+was placed by a single stroke on a higher level.
+Our statement might also be historically justified by
+examples from the scientific labors of Stevinus, S.
+Carnot, Faraday, J. R. Mayer, and others.</p>
+
+<p>All this, however, is merely the soil from which
+science starts. The first real beginnings of science
+appear in society, particularly in the manual arts,
+where the necessity for the communication of experience
+arises. Here, where some new discovery is to
+be described and related, the compulsion is first felt of
+clearly defining in consciousness the important and
+essential features of that discovery, as many writers
+can testify. The aim of instruction is simply the saving
+of experience; the labor of one man is made to
+take the place of that of another.</p>
+
+<p>The most wonderful economy of communication is
+found in language. Words are comparable to type,
+which spare the repetition of written signs and thus
+serve a multitude of purposes; or to the few sounds
+of which our numberless different words are composed.<span class="pagenum"><a name="Page_192" id="Page_192">[Pg 192]</a></span>
+Language, with its helpmate, conceptual thought, by
+fixing the essential and rejecting the unessential, constructs
+its rigid pictures of the fluid world on the plan
+of a mosaic, at a sacrifice of exactness and fidelity but
+with a saving of tools and labor. Like a piano-player
+with previously prepared sounds, a speaker excites in
+his listener thoughts previously prepared, but fitting
+many cases, which respond to the speaker's summons
+with alacrity and little effort.</p>
+
+<p>The principles which a prominent political economist,
+E. Hermann,<a name="FNanchor_64_64" id="FNanchor_64_64"></a><a href="#Footnote_64_64" class="fnanchor">[64]</a> has formulated for the economy of
+the industrial arts, are also applicable to the ideas of
+common life and of science. The economy of language
+is augmented, of course, in the terminology of science.
+With respect to the economy of written intercourse
+there is scarcely a doubt that science itself will realise
+that grand old dream of the philosophers of a Universal
+Real Character. That time is not far distant.
+Our numeral characters, the symbols of mathematical
+analysis, chemical symbols, and musical notes, which
+might easily be supplemented by a system of color-signs,
+together with some phonetic alphabets now in
+use, are all beginnings in this direction. The logical
+extension of what we have, joined with a use of the
+ideas which the Chinese ideography furnishes us, will
+render the special invention and promulgation of a
+Universal Character wholly superfluous.</p>
+
+<p>The communication of scientific knowledge always<span class="pagenum"><a name="Page_193" id="Page_193">[Pg 193]</a></span>
+involves description, that is, a mimetic reproduction
+of facts in thought, the object of which is to replace
+and save the trouble of new experience. Again, to
+save the labor of instruction and of acquisition, concise,
+abridged description is sought. This is really all
+that natural laws are. Knowing the value of the acceleration
+of gravity, and Galileo's laws of descent, we
+possess simple and compendious directions for reproducing
+in thought all possible motions of falling bodies.
+A formula of this kind is a complete substitute
+for a full table of motions of descent, because by means
+of the formula the data of such a table can be easily
+constructed at a moment's notice without the least
+burdening of the memory.</p>
+
+<p>No human mind could comprehend all the individual
+cases of refraction. But knowing the index of refraction
+for the two media presented, and the familiar
+law of the sines, we can easily reproduce or fill out in
+thought every conceivable case of refraction. The advantage
+here consists in the disburdening of the memory;
+an end immensely furthered by the written preservation
+of the natural constants. More than this comprehensive
+and condensed report about facts is not
+contained in a natural law of this sort. In reality, the
+law always contains less than the fact itself, because it
+does not reproduce the fact as a whole but only in
+that aspect of it which is important for us, the rest being
+either intentionally or from necessity omitted.
+Natural laws may be likened to intellectual type of a<span class="pagenum"><a name="Page_194" id="Page_194">[Pg 194]</a></span>
+higher order, partly movable, partly stereotyped, which
+last on new editions of experience may become downright
+impediments.</p>
+
+<p>When we look over a province of facts for the first
+time, it appears to us diversified, irregular, confused,
+full of contradictions. We first succeed in grasping
+only single facts, unrelated with the others. The
+province, as we are wont to say, is not <i>clear</i>. By and
+by we discover the simple, permanent elements of the
+mosaic, out of which we can mentally construct the
+whole province. When we have reached a point where
+we can discover everywhere the same facts, we no
+longer feel lost in this province; we comprehend it
+without effort; it is <i>explained</i> for us.</p>
+
+<p>Let me illustrate this by an example. As soon as
+we have grasped the fact of the rectilinear propagation
+of light, the regular course of our thoughts stumbles
+at the phenomena of refraction and diffraction. As soon
+as we have cleared matters up by our index of refraction
+we discover that a special index is necessary for
+each color. Soon after we have accustomed ourselves
+to the fact that light added to light increases its intensity,
+we suddenly come across a case of total darkness
+produced by this cause. Ultimately, however,
+we see everywhere in the overwhelming multifariousness
+of optical phenomena the fact of the spatial and
+temporal periodicity of light, with its velocity of propagation
+dependent on the medium and the period. This
+tendency of obtaining a survey of a given province<span class="pagenum"><a name="Page_195" id="Page_195">[Pg 195]</a></span>
+with the least expenditure of thought, and of representing
+all its facts by some one single mental process,
+may be justly termed an economical one.</p>
+
+<p>The greatest perfection of mental economy is attained
+in that science which has reached the highest
+formal development, and which is widely employed in
+physical inquiry, namely, in mathematics. Strange as
+it may sound, the power of mathematics rests upon
+its evasion of all unnecessary thought and on its wonderful
+saving of mental operations. Even those arrangement-signs
+which we call numbers are a system
+of marvellous simplicity and economy. When we employ
+the multiplication-table in multiplying numbers
+of several places, and so use the results of old operations
+of counting instead of performing the whole of
+each operation anew; when we consult our table of
+logarithms, replacing and saving thus new calculations
+by old ones already performed; when we employ
+determinants instead of always beginning afresh the
+solution of a system of equations; when we resolve
+new integral expressions into familiar old integrals;
+we see in this simply a feeble reflexion of the intellectual
+activity of a Lagrange or a Cauchy, who, with
+the keen discernment of a great military commander,
+substituted for new operations whole hosts of old ones.
+No one will dispute me when I say that the most elementary
+as well as the highest mathematics are economically-ordered
+experiences of counting, put in forms
+ready for use.</p><p><span class="pagenum"><a name="Page_196" id="Page_196">[Pg 196]</a></span></p>
+
+<p>In algebra we perform, as far as possible, all numerical
+operations which are identical in form once
+for all, so that only a remnant of work is left for the
+individual case. The use of the signs of algebra and
+analysis, which are merely symbols of operations to
+be performed, is due to the observation that we can
+materially disburden the mind in this way and spare
+its powers for more important and more difficult duties,
+by imposing all mechanical operations upon the
+hand. One result of this method, which attests its
+economical character, is the construction of calculating
+machines. The mathematician Babbage, the inventor
+of the difference-engine, was probably the first who
+clearly perceived this fact, and he touched upon it,
+although only cursorily, in his work, <i>The Economy of
+Manufactures and Machinery</i>.</p>
+
+<p>The student of mathematics often finds it hard to
+throw off the uncomfortable feeling that his science, in
+the person of his pencil, surpasses him in intelligence,&mdash;an
+impression which the great Euler confessed he
+often could not get rid of. This feeling finds a sort of
+justification when we reflect that the majority of the
+ideas we deal with were conceived by others, often
+centuries ago. In great measure it is really the intelligence
+of other people that confronts us in science.
+The moment we look at matters in this light, the uncanniness
+and magical character of our impressions
+cease, especially when we remember that we can think
+over again at will any one of those alien thoughts.</p><p><span class="pagenum"><a name="Page_197" id="Page_197">[Pg 197]</a></span></p>
+
+<p>Physics is experience, arranged in economical order.
+By this order not only is a broad and comprehensive
+view of what we have rendered possible, but also
+the defects and the needful alterations are made manifest,
+exactly as in a well-kept household. Physics
+shares with mathematics the advantages of succinct
+description and of brief, compendious definition, which
+precludes confusion, even in ideas where, with no apparent
+burdening of the brain, hosts of others are contained.
+Of these ideas the rich contents can be produced
+at any moment and displayed in their full perceptual
+light. Think of the swarm of well-ordered notions
+pent up in the idea of the potential. Is it wonderful
+that ideas containing so much finished labor should
+be easy to work with?</p>
+
+<p>Our first knowledge, thus, is a product of the
+economy of self-preservation. By communication, the
+experience of <i>many</i> persons, individually acquired at
+first, is collected in <i>one</i>. The communication of
+knowledge and the necessity which every one feels of
+managing his stock of experience with the least expenditure
+of thought, compel us to put our knowledge in
+economical forms. But here we have a clue which
+strips science of all its mystery, and shows us what its
+power really is. With respect to specific results it
+yields us nothing that we could not reach in a sufficiently
+long time without methods. There is no problem
+in all mathematics that cannot be solved by direct
+counting. But with the present implements of mathematics<span class="pagenum"><a name="Page_198" id="Page_198">[Pg 198]</a></span>
+many operations of counting can be performed
+in a few minutes which without mathematical methods
+would take a lifetime. Just as a single human being,
+restricted wholly to the fruits of his own labor, could
+never amass a fortune, but on the contrary the accumulation
+of the labor of many men in the hands of one is
+the foundation of wealth and power, so, also, no knowledge
+worthy of the name can be gathered up in a
+single human mind limited to the span of a human life
+and gifted only with finite powers, except by the most
+exquisite economy of thought and by the careful
+amassment of the economically ordered experience of
+thousands of co-workers. What strikes us here as the
+fruits of sorcery are simply the rewards of excellent
+housekeeping, as are the like results in civil life. But
+the business of science has this advantage over every
+other enterprise, that from <i>its</i> amassment of wealth no
+one suffers the least loss. This, too, is its blessing,
+its freeing and saving power.</p>
+
+<p>The recognition of the economical character of
+science will now help us, perhaps, to understand better
+certain physical notions.</p>
+
+<p>Those elements of an event which we call "cause
+and effect" are certain salient features of it, which are
+important for its mental reproduction. Their importance
+wanes and the attention is transferred to fresh
+characters the moment the event or experience in
+question becomes familiar. If the connexion of such
+features strikes us as a necessary one, it is simply because<span class="pagenum"><a name="Page_199" id="Page_199">[Pg 199]</a></span>
+the interpolation of certain intermediate links
+with which we are very familiar, and which possess,
+therefore, higher authority for us, is often attended
+with success in our explanations. That <i>ready</i> experience
+fixed in the mosaic of the mind with which we meet
+new events, Kant calls an innate concept of the understanding
+(<i>Verstandesbegriff</i>).</p>
+
+<p>The grandest principles of physics, resolved into
+their elements, differ in no wise from the descriptive
+principles of the natural historian. The question,
+"Why?" which is always appropriate where the explanation
+of a contradiction is concerned, like all proper
+habitudes of thought, can overreach itself and be asked
+where nothing remains to be understood. Suppose we
+were to attribute to nature the property of producing
+like effects in like circumstances; just these like circumstances
+we should not know how to find. Nature
+exists once only. Our schematic mental imitation alone
+produces like events. Only in the mind, therefore, does
+the mutual dependence of certain features exist.</p>
+
+<p>All our efforts to mirror the world in thought would
+be futile if we found nothing permanent in the varied
+changes of things. It is this that impels us to form the
+notion of substance, the source of which is not different
+from that of the modern ideas relative to the conservation
+of energy. The history of physics furnishes
+numerous examples of this impulse in almost all fields,
+and pretty examples of it may be traced back to the
+nursery. "Where does the light go to when it is put<span class="pagenum"><a name="Page_200" id="Page_200">[Pg 200]</a></span>
+out?" asks the child. The sudden shrivelling up of a
+hydrogen balloon is inexplicable to a child; it looks
+everywhere for the large body which was just there
+but is now gone.</p>
+
+<p>Where does heat come from? Where does heat
+go to? Such childish questions in the mouths of mature
+men shape the character of a century.</p>
+
+<p>In mentally separating a body from the changeable
+environment in which it moves, what we really do
+is to extricate a group of sensations on which our
+thoughts are fastened and which is of relatively greater
+stability than the others, from the stream of all our
+sensations. Absolutely unalterable this group is not.
+Now this, now that member of it appears and disappears,
+or is altered. In its full identity it never recurs.
+Yet the sum of its constant elements as compared
+with the sum of its changeable ones, especially if we
+consider the continuous character of the transition, is
+always so great that for the purpose in hand the former
+usually appear sufficient to determine the body's identity.
+But because we can separate from the group
+every single member without the body's ceasing to be
+for us the same, we are easily led to believe that after
+abstracting all the members something additional
+would remain. It thus comes to pass that we form
+the notion of a substance distinct from its attributes,
+of a thing-in-itself, whilst our sensations are regarded
+merely as symbols or indications of the properties of
+this thing-in-itself. But it would be much better to<span class="pagenum"><a name="Page_201" id="Page_201">[Pg 201]</a></span>
+say that bodies or things are compendious mental symbols
+for groups of sensations&mdash;symbols that do not exist
+outside of thought. Thus, the merchant regards
+the labels of his boxes merely as indexes of their contents,
+and not the contrary. He invests their contents,
+not their labels, with real value. The same
+economy which induces us to analyse a group and to
+establish special signs for its component parts, parts
+which also go to make up other groups, may likewise
+induce us to mark out by some single symbol a whole
+group.</p>
+
+<p>On the old Egyptian monuments we see objects
+represented which do not reproduce a single visual
+impression, but are composed of various impressions.
+The heads and the legs of the figures appear in profile,
+the head-dress and the breast are seen from the
+front, and so on. We have here, so to speak, a mean
+view of the objects, in forming which the sculptor has
+retained what he deemed essential, and neglected what
+he thought indifferent. We have living exemplifications
+of the processes put into stone on the walls of
+these old temples, in the drawings of our children, and
+we also observe a faithful analogue of them in the formation
+of ideas in our own minds. Only in virtue of
+some such facility of view as that indicated, are we
+allowed to speak of a body. When we speak of a cube
+with trimmed corners&mdash;a figure which is not a cube&mdash;we
+do so from a natural instinct of economy, which
+prefers to add to an old familiar conception a correction<span class="pagenum"><a name="Page_202" id="Page_202">[Pg 202]</a></span>
+instead of forming an entirely new one. This is
+the process of all judgment.</p>
+
+<p>The crude notion of "body" can no more stand
+the test of analysis than can the art of the Egyptians
+or that of our little children. The physicist who sees
+a body flexed, stretched, melted, and vaporised, cuts
+up this body into smaller permanent parts; the chemist
+splits it up into elements. Yet even an element is
+not unalterable. Take sodium. When warmed, the
+white, silvery mass becomes a liquid, which, when the
+heat is increased and the air shut out, is transformed
+into a violet vapor, and on the heat being still more
+increased glows with a yellow light. If the name sodium
+is still retained, it is because of the continuous
+character of the transitions and from a necessary instinct
+of economy. By condensing the vapor, the
+white metal may be made to reappear. Indeed, even
+after the metal is thrown into water and has passed
+into sodium hydroxide, the vanished properties may
+by skilful treatment still be made to appear; just as a
+moving body which has passed behind a column and
+is lost to view for a moment may make its appearance
+after a time. It is unquestionably very convenient
+always to have ready the name and thought for a
+group of properties wherever that group by any possibility
+can appear. But more than a compendious economical
+symbol for these phenomena, that name and
+thought is not. It would be a mere empty word for
+one in whom it did not awaken a large group of well-ordered<span class="pagenum"><a name="Page_203" id="Page_203">[Pg 203]</a></span>
+sense-impressions. And the same is true of
+the molecules and atoms into which the chemical element
+is still further analysed.</p>
+
+<p>True, it is customary to regard the conservation of
+weight, or, more precisely, the conservation of mass,
+as a direct proof of the constancy of matter. But this
+proof is dissolved, when we go to the bottom of it,
+into such a multitude of instrumental and intellectual
+operations, that in a sense it will be found to constitute
+simply an equation which our ideas in imitating
+facts have to satisfy. That obscure, mysterious lump
+which we involuntarily add in thought, we seek for in
+vain outside the mind.</p>
+
+<p>It is always, thus, the crude notion of substance
+that is slipping unnoticed into science, proving itself
+constantly insufficient, and ever under the necessity of
+being reduced to smaller and smaller world-particles.
+Here, as elsewhere, the lower stage is not rendered
+indispensable by the higher which is built upon it, no
+more than the simplest mode of locomotion, walking,
+is rendered superfluous by the most elaborate means of
+transportation. Body, as a compound of light and
+touch sensations, knit together by sensations of space,
+must be as familiar to the physicist who seeks it, as to
+the animal who hunts its prey. But the student of the
+theory of knowledge, like the geologist and the astronomer,
+must be permitted to reason back from the forms
+which are created before his eyes to others which he
+finds ready made for him.</p><p><span class="pagenum"><a name="Page_204" id="Page_204">[Pg 204]</a></span></p>
+
+<p>All physical ideas and principles are succinct directions,
+frequently involving subordinate directions,
+for the employment of economically classified experiences,
+ready for use. Their conciseness, as also the
+fact that their contents are rarely exhibited in full,
+often invests them with the semblance of independent
+existence. Poetical myths regarding such ideas,&mdash;for
+example, that of Time, the producer and devourer of
+all things,&mdash;do not concern us here. We need only
+remind the reader that even Newton speaks of an <i>absolute</i>
+time independent of all phenomena, and of an
+absolute space&mdash;views which even Kant did not shake
+off, and which are often seriously entertained to-day.
+For the natural inquirer, determinations of time are
+merely abbreviated statements of the dependence of
+one event upon another, and nothing more. When
+we say the acceleration of a freely falling body is 9·810
+metres per second, we mean the velocity of the body
+with respect to the centre of the earth is 9·810 metres
+greater when the earth has performed an additional
+86400th part of its rotation&mdash;a fact which itself can be
+determined only by the earth's relation to other heavenly
+bodies. Again, in velocity is contained simply a
+relation of the position of a body to the position of
+the earth.<a name="FNanchor_65_65" id="FNanchor_65_65"></a><a href="#Footnote_65_65" class="fnanchor">[65]</a> Instead of referring events to the earth
+we may refer them to a clock, or even to our internal
+sensation of time. Now, because all are connected,
+and each may be made the measure of the rest, the illusion
+easily arises that time has significance independently
+of all.<a name="FNanchor_66_66" id="FNanchor_66_66"></a><a href="#Footnote_66_66" class="fnanchor">[66]</a></p>
+
+<p><span class="pagenum"><a name="Page_205" id="Page_205">[Pg 205]</a></span></p><p>The aim of research is the discovery of the equations
+which subsist between the elements of phenomena.
+The equation of an ellipse expresses the universal
+<i>conceivable</i> relation between its co-ordinates, of which
+only the real values have <i>geometrical</i> significance.
+Similarly, the equations between the elements of <i>phenomena</i>
+express a universal, mathematically conceivable
+relation. Here, however, for many values only
+certain directions of change are <i>physically</i> admissible.
+As in the ellipse only certain <i>values</i> satisfying the
+equation are realised, so in the physical world only
+certain <i>changes</i> of value occur. Bodies are always accelerated
+towards the earth. Differences of temperature,
+left to themselves, always grow less; and so on.
+Similarly, with respect to space, mathematical and
+physiological researches have shown that the space of
+experience is simply an <i>actual</i> case of many conceivable
+cases, about whose peculiar properties experience
+alone can instruct us. The elucidation which this idea
+diffuses cannot be questioned, despite the absurd uses
+to which it has been put.</p>
+
+<p>Let us endeavor now to summarise the results of<span class="pagenum"><a name="Page_206" id="Page_206">[Pg 206]</a></span>
+our survey. In the economical schematism of science
+lie both its strength and its weakness. Facts are always
+represented at a sacrifice of completeness and
+never with greater precision than fits the needs of the
+moment. The incongruence between thought and experience,
+therefore, will continue to subsist as long as
+the two pursue their course side by side; but it will
+be continually diminished.</p>
+
+<p>In reality, the point involved is always the completion
+of some partial experience; the derivation of
+one portion of a phenomenon from some other. In
+this act our ideas must be based directly upon sensations.
+We call this measuring.<a name="FNanchor_67_67" id="FNanchor_67_67"></a><a href="#Footnote_67_67" class="fnanchor">[67]</a> The condition of
+science, both in its origin and in its application, is a
+<i>great relative stability</i> of our environment. What it
+teaches us is interdependence. Absolute forecasts,
+consequently, have no significance in science. With
+great changes in celestial space we should lose our
+co-ordinate systems of space and time.</p>
+
+<p>When a geometer wishes to understand the form of
+a curve, he first resolves it into small rectilinear elements.
+In doing this, however, he is fully aware that
+these elements are only provisional and arbitrary devices
+for comprehending in parts what he cannot comprehend
+as a whole. When the law of the curve is
+found he no longer thinks of the elements. Similarly,
+it would not become physical science to see in its self-created,<span class="pagenum"><a name="Page_207" id="Page_207">[Pg 207]</a></span>
+changeable, economical tools, molecules and
+atoms, realities behind phenomena, forgetful of the
+lately acquired sapience of her older sister, philosophy,
+in substituting a mechanical mythology for the old
+animistic or metaphysical scheme, and thus creating
+no end of suppositious problems. The atom must remain
+a tool for representing phenomena, like the
+functions of mathematics. Gradually, however, as
+the intellect, by contact with its subject-matter, grows
+in discipline, physical science will give up its mosaic
+play with stones and will seek out the boundaries and
+forms of the bed in which the living stream of phenomena
+flows. The goal which it has set itself is the
+<i>simplest</i> and <i>most economical</i> abstract expression of facts.</p>
+<p><span class="pagenum"><a name="Page_208" id="Page_208">[Pg 208]</a></span></p><p><span class="pagenum"><a name="Page_209" id="Page_209">[Pg 209]</a></span></p><p><span class="pagenum"><a name="Page_210" id="Page_210">[Pg 210]</a></span></p><p><span class="pagenum"><a name="Page_211" id="Page_211">[Pg 211]</a></span></p><p><span class="pagenum"><a name="Page_212" id="Page_212">[Pg 212]</a></span></p><p><span class="pagenum"><a name="Page_213" id="Page_213">[Pg 213]</a></span></p><p><span class="pagenum"><a name="Page_214" id="Page_214">[Pg 214]</a></span></p>
+<hr class="tb" />
+
+<p>The question now remains, whether the same
+method of research which till now we have tacitly restricted
+to physics, is also applicable in the psychical
+domain. This question will appear superfluous to the
+physical inquirer. Our physical and psychical views
+spring in exactly the same manner from instinctive
+knowledge. We read the thoughts of men in their
+acts and facial expressions without knowing how.
+Just as we predict the behavior of a magnetic needle
+placed near a current by imagining Ampère's swimmer
+in the current, similarly we predict in thought the
+acts and behavior of men by assuming sensations, feelings,
+and wills similar to our own connected with their
+bodies. What we here instinctively perform would
+appear to us as one of the subtlest achievements of
+science, far outstripping in significance and ingenuity
+Ampère's rule of the swimmer, were it not that every
+child unconsciously accomplished it. The question
+simply is, therefore, to grasp scientifically, that is, by
+conceptional thought, what we are already familiar
+with from other sources. And here much is to be
+accomplished. A long sequence of facts is to be disclosed
+between the physics of expression and movement
+and feeling and thought.</p>
+
+<p>We hear the question, "But how is it possible to
+explain feeling by the motions of the atoms of the
+brain?" Certainly this will never be done, no more
+than light or heat will ever be deduced from the law
+of refraction. We need not deplore, therefore, the
+lack of ingenious solutions of this question. The problem
+is not a problem. A child looking over the walls
+of a city or of a fort into the moat below sees with
+astonishment living people in it, and not knowing of
+the portal which connects the wall with the moat, cannot
+understand how they could have got down from
+the high ramparts. So it is with the notions of physics.
+We cannot climb up into the province of psychology
+by the ladder of our abstractions, but we can climb
+down into it.</p>
+
+<p>Let us look at the matter without bias. The world
+consists of colors, sounds, temperatures, pressures,
+spaces, times, and so forth, which now we shall not
+call sensations, nor phenomena, because in either term
+an arbitrary, one-sided theory is embodied, but simply
+<i>elements</i>. The fixing of the flux of these elements,
+whether mediately or immediately, is the real object of
+physical research. As long as, neglecting our own
+body, we employ ourselves with the interdependence
+of those groups of elements which, including men and
+animals, make up <i>foreign</i> bodies, we are physicists.
+For example, we investigate the change of the red
+color of a body as produced by a change of illumination.
+But the moment we consider the special influence
+on the red of the elements constituting our
+body, outlined by the well-known perspective with
+head invisible, we are at work in the domain of physiological
+psychology. We close our eyes, and the red
+together with the whole visible world disappears.
+There exists, thus, in the perspective field of every sense
+a portion which exercises on all the rest a different
+and more powerful influence than the rest upon one
+another. With this, however, all is said. In the light
+of this remark, we call <i>all</i> elements, in so far as we regard
+them as dependent on this special part (our body),
+<i>sensations</i>. That the world is our sensation, in this
+sense, cannot be questioned. But to make a system
+of conduct out of this provisional conception, and to
+abide its slaves, is as unnecessary for us as would be
+a similar course for a mathematician who, in varying a
+series of variables of a function which were previously
+assumed to be constant, or in interchanging the independent
+variables, finds his method to be the source
+of some very surprising ideas for him.<a name="FNanchor_68_68" id="FNanchor_68_68"></a><a href="#Footnote_68_68" class="fnanchor">[68]</a></p>
+
+<p>If we look at the matter in this unbiassed light it
+will appear indubitable that the method of physiological
+psychology is none other than that of physics;
+what is more, that this science is a part of physics.
+Its subject-matter is not different from that of physics.
+It will unquestionably determine the relations
+the sensations bear to the physics of our body. We
+have already learned from a member of this academy
+(Hering) that in all probability a sixfold manifoldness
+of the chemical processes of the visual substance corresponds
+to the sixfold manifoldness of color-sensation,
+and a threefold manifoldness of the physiological processes
+to the threefold manifoldness of space-sensations.
+The paths of reflex actions and of the will are
+followed up and disclosed; it is ascertained what region
+of the brain subserves the function of speech,
+what region the function of locomotion, etc. That
+which still clings to our body, namely, our thoughts,
+will, when those investigations are finished, present no
+difficulties new in principle. When experience has
+once clearly exhibited these facts and science has
+marshalled them in economic and perspicuous order,
+there is no doubt that we shall <i>understand</i> them. For
+other "understanding" than a mental mastery of facts
+never existed. Science does not create facts from facts,
+but simply <i>orders</i> known facts.</p>
+
+<p>Let us look, now, a little more closely into the modes
+of research of physiological psychology. We have a
+very clear idea of how a body moves in the space encompassing
+it. With our optical field of sight we are
+very familiar. But we are unable to state, as a rule,
+how we have come by an idea, from what corner of
+our intellectual field of sight it has entered, or by what
+region the impulse to a motion is sent forth. Moreover,
+we shall never get acquainted with this mental
+field of view from self-observation alone. Self-observation,
+in conjunction with physiological research,
+which seeks out physical connexions, can put this field
+of vision in a clear light before us, and will thus first
+really reveal to us our inner man.</p>
+
+<p>Primarily, natural science, or physics, in its widest
+sense, makes us acquainted with only the firmest connexions
+of groups of elements. Provisorily, we may
+not bestow too much attention on the single constituents
+of those groups, if we are desirous of retaining a
+comprehensible whole. Instead of equations between
+the primitive variables, physics gives us, as much the
+easiest course, equations between <i>functions</i> of those
+variables. Physiological psychology teaches us how
+to separate the visible, the tangible, and the audible
+from bodies&mdash;a labor which is subsequently richly requited,
+as the division of the subjects of physics well
+shows. Physiology further analyses the visible into
+light and space sensations; the first into colors, the
+last also into their component parts; it resolves noises
+into sounds, these into tones, and so on. Unquestionably
+this analysis can be carried much further than it
+has been. It will be possible in the end to exhibit the
+common elements at the basis of very abstract but
+definite logical acts of like form,&mdash;elements which the
+acute jurist and mathematician, as it were, <i>feels</i> out,
+with absolute certainty, where the uninitiated hears
+only empty words. Physiology, in a word, will reveal
+to us the true real elements of the world. Physiological
+psychology bears to physics in its widest sense a relation
+similar to that which chemistry bears to physics
+in its narrowest sense. But far greater than the mutual
+support of physics and chemistry will be that
+which natural science and psychology will render each
+other. And the results that shall spring from this
+union will, in all likelihood, far outstrip those of the
+modern mechanical physics.</p>
+
+<p>What those ideas are with which we shall comprehend
+the world when the closed circuit of physical and
+psychological facts shall lie complete before us, (that
+circuit of which we now see only two disjoined parts,)
+cannot be foreseen at the outset of the work. The
+men will be found who will see what is right and
+will have the courage, instead of wandering in the
+intricate paths of logical and historical accident, to
+enter on the straight ways to the heights from which
+the mighty stream of facts can be surveyed. Whether
+the notion which we now call matter will continue to
+have a scientific significance beyond the crude purposes
+of common life, we do not know. But we certainly
+shall wonder how colors and tones which were
+such innermost parts of us could suddenly get lost in
+our physical world of atoms; how we could be suddenly
+surprised that something which outside us simply
+clicked and beat, in our heads should make light
+and music; and how we could ask whether matter can
+feel, that is to say, whether a mental symbol for a
+group of sensations can feel?</p>
+
+<p>We cannot mark out in hard and fast lines the
+science of the future, but we can foresee that the rigid
+walls which now divide man from the world will gradually
+disappear; that human beings will not only confront
+each other, but also the entire organic and so-called
+lifeless world, with less selfishness and with livelier
+sympathy. Just such a presentiment as this perhaps
+possessed the great Chinese philosopher Licius
+some two thousand years ago when, pointing to a heap
+of mouldering human bones, he said to his scholars in
+the rigid, lapidary style of his tongue: "These and I
+alone have the knowledge that we neither live nor are
+dead."</p>
+
+
+
+
+<h2><a name="ON_TRANSFORMATION_AND_ADAPTATION" id="ON_TRANSFORMATION_AND_ADAPTATION">ON TRANSFORMATION AND ADAPTATION
+IN SCIENTIFIC THOUGHT.</a><a name="FNanchor_69_69" id="FNanchor_69_69"></a><a href="#Footnote_69_69" class="fnanchor">[69]</a></h2>
+
+
+<p>It was towards the close of the sixteenth century
+that Galileo with a superb indifference to the dialectic
+arts and sophistic subtleties of the Schoolmen of
+his time, turned the attention of his brilliant mind
+to nature. By nature his ideas were transformed and
+released from the fetters of inherited prejudice. At
+once the mighty revolution was felt, that was therewith
+effected in the realm of human thought&mdash;felt indeed in
+circles far remote and wholly unrelated to the sphere
+of science, felt in strata of society that hitherto had
+only indirectly recognised the influence of scientific
+thought.</p>
+<p><span class="pagenum"><a name="Page_215" id="Page_215">[Pg 215]</a></span></p>
+<p>And how great and how far-reaching that revolution
+was! From the beginning of the seventeenth century
+till its close we see arising, at least in embryo,
+almost all that plays a part in the natural and technical
+science of to-day, almost all that in the two centuries
+following so wonderfully transformed the facial
+appearance of the earth, and all that is moving onward
+in process of such mighty evolution to-day. And all
+this, the direct result of Galilean ideas, the direct outcome
+of that freshly awakened sense for the investigation
+of natural phenomena which taught the Tuscan
+philosopher to form the concept and the law of falling
+bodies from the <i>observation</i> of a falling stone! Galileo
+began his investigations without an implement worthy
+of the name; he measured time in the most primitive
+way, by the efflux of water. Yet soon afterwards the
+telescope, the microscope, the barometer, the thermometer,
+the air-pump, the steam engine, the pendulum,
+and the electrical machine were invented in rapid
+succession. The fundamental theorems of dynamical
+science, of optics, of heat, and of electricity were all
+disclosed in the century that followed Galileo.</p>
+
+<p>Of scarcely less importance, it seems, was that
+movement which was prepared for by the illustrious
+biologists of the hundred years just past, and formally
+begun by the late Mr. Darwin. Galileo quickened the
+sense for the simpler phenomena of <i>inorganic</i> nature.
+And with the same simplicity and frankness that
+marked the efforts of Galileo, and without the aid of<span class="pagenum"><a name="Page_216" id="Page_216">[Pg 216]</a></span>
+technical or scientific instruments, without physical or
+chemical experiment, but solely by the power of
+thought and observation, Darwin grasps a new property
+of <i>organic</i> nature&mdash;which we may briefly call its
+<i>plasticity</i>.<a name="FNanchor_70_70" id="FNanchor_70_70"></a><a href="#Footnote_70_70" class="fnanchor">[70]</a> With the same directness of purpose, Darwin,
+too, pursues his way. With the same candor
+and love of truth, he points out the strength and the
+weakness of his demonstrations. With masterly equanimity
+he holds aloof from the discussion of irrelevant
+subjects and wins alike the admiration of his adherents
+and of his adversaries.</p>
+
+<p>Scarcely thirty years have elapsed<a name="FNanchor_71_71" id="FNanchor_71_71"></a><a href="#Footnote_71_71" class="fnanchor">[71]</a> since Darwin first
+propounded the principles of his theory of evolution.<span class="pagenum"><a name="Page_217" id="Page_217">[Pg 217]</a></span>
+Yet, already we see his ideas firmly rooted in every
+branch of human thought, however remote. Everywhere,
+in history, in philosophy, even in the physical
+sciences, we hear the watchwords: heredity, adaptation,
+selection. We speak of the struggle for existence
+among the heavenly bodies and of the struggle for existence
+in the world of molecules.<a name="FNanchor_72_72" id="FNanchor_72_72"></a><a href="#Footnote_72_72" class="fnanchor">[72]</a></p>
+
+<p>The impetus given by Galileo to scientific thought
+was marked in every direction; thus, his pupil, Borelli,
+founded the school of exact medicine, from
+whence proceeded even distinguished mathematicians.
+And now Darwinian ideas, in the same way, are animating
+all provinces of research. It is true, nature is
+not made up of two distinct parts, the inorganic and
+the organic; nor must these two divisions be treated
+perforce by totally distinct methods. Many <i>sides</i>, however,
+nature has. Nature is like a thread in an intricate
+tangle, which must be followed and traced, now from
+this point, now from that. But we must never imagine,&mdash;and
+this physicists have learned from Faraday and
+J. R. Mayer,&mdash;that progress along paths once entered
+upon is the <i>only</i> means of reaching the truth.</p>
+
+<p>It will devolve upon the specialists of the future to
+determine the relative tenability and fruitfulness of the
+Darwinian ideas in the different provinces. Here I
+wish simply to consider the growth of natural <i>knowledge</i>
+in the light of the theory of evolution. For knowledge,
+too, is a product of organic nature. And although<span class="pagenum"><a name="Page_218" id="Page_218">[Pg 218]</a></span>
+ideas, as such, do not comport themselves in all respects
+like independent organic individuals, and although
+violent comparisons should be avoided, still, if Darwin
+reasoned rightly, the general imprint of evolution and
+transformation must be noticeable in ideas also.</p>
+
+<p>I shall waive here the consideration of the fruitful
+topic of the transmission of ideas or rather of the
+transmission of the aptitude for certain ideas.<a name="FNanchor_73_73" id="FNanchor_73_73"></a><a href="#Footnote_73_73" class="fnanchor">[73]</a> Nor
+would it come within my province to discuss psychical
+evolution in any form, as Spencer<a name="FNanchor_74_74" id="FNanchor_74_74"></a><a href="#Footnote_74_74" class="fnanchor">[74]</a> and many other
+modern psychologists have done, with varying success.
+Neither shall I enter upon a discussion of the
+struggle for existence and of natural selection among
+scientific theories.<a name="FNanchor_75_75" id="FNanchor_75_75"></a><a href="#Footnote_75_75" class="fnanchor">[75]</a> We shall consider here only such
+processes of transformation as every student can easily
+observe in his own mind.</p>
+<p><span class="pagenum"><a name="Page_219" id="Page_219">[Pg 219]</a></span></p><p><span class="pagenum"><a name="Page_220" id="Page_220">[Pg 220]</a></span></p><p><span class="pagenum"><a name="Page_221" id="Page_221">[Pg 221]</a></span></p><p><span class="pagenum"><a name="Page_222" id="Page_222">[Pg 222]</a></span></p><p><span class="pagenum"><a name="Page_223" id="Page_223">[Pg 223]</a></span></p><p><span class="pagenum"><a name="Page_224" id="Page_224">[Pg 224]</a></span></p><p><span class="pagenum"><a name="Page_225" id="Page_225">[Pg 225]</a></span></p><p><span class="pagenum"><a name="Page_226" id="Page_226">[Pg 226]</a></span></p><p><span class="pagenum"><a name="Page_227" id="Page_227">[Pg 227]</a></span></p><p><span class="pagenum"><a name="Page_228" id="Page_228">[Pg 228]</a></span></p><p><span class="pagenum"><a name="Page_229" id="Page_229">[Pg 229]</a></span></p><p><span class="pagenum"><a name="Page_230" id="Page_230">[Pg 230]</a></span></p><p><span class="pagenum"><a name="Page_231" id="Page_231">[Pg 231]</a></span></p><p><span class="pagenum"><a name="Page_232" id="Page_232">[Pg 232]</a></span></p><p><span class="pagenum"><a name="Page_233" id="Page_233">[Pg 233]</a></span></p>
+<hr class="tb" />
+
+<p>The child of the forest picks out and pursues with
+marvellous acuteness the trails of animals. He outwits
+and overreaches his foes with surpassing cunning.
+He is perfectly at home in the sphere of his peculiar
+experience. But confront him with an unwonted phenomenon;
+place him face to face with a technical product
+of modern civilisation, and he will lapse into impotency
+and helplessness. Here are facts which he
+does not comprehend. If he endeavors to grasp their
+meaning, he misinterprets them. He fancies the moon,
+when eclipsed, to be tormented by an evil spirit. To
+his mind a puffing locomotive is a living monster. The
+letter accompanying a commission with which he is
+entrusted, having once revealed his thievishness, is in
+his imagination a conscious being, which he must hide
+beneath a stone, before venturing to commit a fresh
+trespass. Arithmetic to him is like the art of the
+geomancers in the Arabian Nights,&mdash;an art which is
+able to accomplish every imaginable impossibility.
+And, like Voltaire's <i>ingénu</i>, when placed in our social
+world, he plays, as we think, the maddest pranks.</p>
+
+<p>With the man who has made the achievements of
+modern science and civilisation his own, the case is
+quite different. He sees the moon pass temporarily
+into the shadow of the earth. He feels in his thoughts
+the water growing hot in the boiler of the locomotive;
+he feels also the increase of the tension which pushes
+the piston forward. Where he is not able to trace the
+direct relation of things he has recourse to his yard-stick
+and table of logarithms, which aid and facilitate
+his thought without predominating over it. Such opinions
+as he cannot concur in, are at least known to him,
+and he knows how to meet them in argument.</p>
+
+<p>Now, wherein does the difference between these
+two men consist? The train of thought habitually
+employed by the first one does not correspond to the
+facts that he sees. He is surprised and nonplussed
+at every step. But the thoughts of the second man
+follow and anticipate events, his thoughts have become
+adapted or accommodated to the larger field of
+observation and activity in which he is located; he conceives
+things as they are. The Indian's sphere of experience,
+however, is quite different; his bodily organs
+of sense are in constant activity; he is ever intensely
+alert and on the watch for his foes; or, his entire attention
+and energy are engaged in procuring sustenance.
+Now, how can such a creature project his mind
+into futurity, foresee or prophesy? This is not possible
+until our fellow-beings have, in a measure, relieved
+us of our concern for existence. It is then that we
+acquire freedom for observation, and not infrequently
+too that narrowness of thought which society helps and
+teaches us to disregard.</p>
+
+<p>If we move for a time within a fixed circle of phenomena
+which recur with unvarying uniformity, our
+thoughts gradually adapt themselves to our environment;
+our ideas reflect unconsciously our surroundings.
+The stone we hold in our hand, when dropped,
+not only falls to the ground in reality; it also falls in
+our thoughts. Iron-filings dart towards a magnet in
+imagination as well as in fact, and, when thrown into
+a fire, they grew hot in conception as well.</p>
+
+<p>The impulse to complete mentally a phenomenon
+that has been only partially observed, has not its origin
+in the phenomenon itself; of this fact, we are fully
+sensible. And we well know that it does not lie within
+the sphere of our volition. It seems to confront us
+rather as a power and a law imposed from without
+and controlling both thought and facts.</p>
+
+<p>The fact that we are able by the help of this law to
+prophesy and forecast, merely proves a sameness or
+uniformity of environment sufficient to effect a mental
+adaptation of this kind. A necessity of fulfilment,
+however, is not contained in this compulsory principle
+which controls our thoughts; nor is it in any way determined
+by the possibility of prediction. We are always
+obliged, in fact, to await the completion of what
+has been predicted. Errors and departures are constantly
+discernible, and are slight only in provinces of
+great rigid constancy, as in astronomy.</p>
+
+<p>In cases where our thoughts follow the connexion
+of events with ease, and in instances where we positively
+forefeel the course of a phenomenon, it is natural
+to fancy that the latter is determined by and must
+conform to our thoughts. But the belief in that mysterious
+agency called <i>causality</i>, which holds thought and
+event in unison, is violently shaken when a person first
+enters a province of inquiry in which he has previously
+had no experience. Take for instance the strange
+interaction of electric currents and magnets, or the
+reciprocal action of currents, which seem to defy all
+the resources of mechanical science. Let him be confronted
+with such phenomena and he will immediately
+feel himself forsaken by his power of prediction; he
+will bring nothing with him into this strange field of
+events but the hope of soon being able to adapt his
+ideas to the new conditions there presented.</p>
+
+<p>A person constructs from a bone the remaining
+anatomy of an animal; or from the visible part of a
+half-concealed wing of a butterfly he infers and reconstructs
+the part concealed. He does so with a feeling
+of highest confidence in the accuracy of his results;
+and in these processes we find nothing preternatural
+or transcendent. But when physicists adapt their
+thoughts to conform to the dynamical course of events
+in time, we invariably surround their investigations
+with a metaphysical halo; yet these latter adaptations
+bear quite the same character as the former, and our
+only reason for investing them with a metaphysical
+garb, perhaps, is their high practical value.<a name="FNanchor_76_76" id="FNanchor_76_76"></a><a href="#Footnote_76_76" class="fnanchor">[76]</a></p>
+
+<p>Let us consider for a moment what takes place
+when the field of observation to which our ideas have
+been adapted and now conform, becomes enlarged.
+We had, let us say, always seen heavy bodies sink
+when their support was taken away; we had also seen,
+perhaps, that the sinking of heavier bodies forced
+lighter bodies upwards. But now we see a lever in
+action, and we are suddenly struck with the fact that
+a lighter body is lifting another of much greater weight.
+Our customary train of thought demands its rights;
+the new and unwonted event likewise demands its
+rights. From this conflict between thought and fact
+the <i>problem</i> arises; out of this partial contrariety springs
+the question, "Why?" With the new adaptation to the
+enlarged field of observation, the problem disappears,
+or, in other words, is solved. In the instance cited,
+we must adopt the habit of always considering the
+mechanical work performed.</p>
+
+<p>The child just awakening into consciousness of the
+world, knows no problem. The bright flower, the
+ringing bell, are all new to it; yet it is surprised at
+nothing. The out and out Philistine, whose only
+thoughts lie in the beaten path of his every-day pursuits,
+likewise has no problems. Everything goes its
+wonted course, and if perchance a thing go wrong at
+times, it is at most a mere object of curiosity and
+not worth serious consideration. In fact, the question
+"Why?" loses all warrant in relations where we are
+familiar with every aspect of events. But the capable
+and talented young man has his head full of problems;
+he has acquired, to a greater or less degree, certain
+habitudes of thought, and at the same time he is constantly
+observing what is new and unwonted, and in
+his case there is no end to the questions, "Why?"</p>
+
+<p>Thus, the factor which most promotes scientific
+thought is the gradual widening of the field of experience.
+We scarcely notice events we are accustomed
+to; the latter do not really develop their intellectual
+significance until placed in contrast with something to
+which we are unaccustomed. Things that at home
+are passed by unnoticed, delight us when abroad,
+though they may appear in only slightly different forms.
+The sun shines with heightened radiance, the flowers
+bloom in brighter colors, our fellow-men accost us
+with lighter and happier looks. And, returning home,
+we find even the old familiar scenes more inspiring
+and suggestive than before.</p>
+
+<p>Every motive that prompts and stimulates us to
+modify and transform our thoughts, proceeds from
+what is new, uncommon, and not understood. Novelty
+excites wonder in persons whose fixed habits of thought
+are shaken and disarranged by what they see. But the
+element of wonder never lies in the phenomenon or
+event observed; its place is in the person observing.
+People of more vigorous mental type aim at once at an
+<i>adaptation of thought</i> that will conform to what they
+have observed. Thus does science eventually become
+the natural foe of the wonderful. The sources of the
+marvellous are unveiled, and surprise gives way to
+calm interpretation.</p>
+
+<p>Let us consider such a mental transformative process
+in detail. The circumstance that heavy bodies
+fall to the earth appears perfectly natural and regular.
+But when a person observes that wood floats upon
+water, and that flames and smoke rise in the air, then
+the contrary of the first phenomenon is presented.
+An olden theory endeavors to explain these facts by imputing
+to substances the power of volition, as that attribute
+which is most familiar to man. It asserted
+that every substance seeks its proper place, heavy
+bodies tending downwards and light ones upwards.
+It soon turned out, however, that even smoke had
+weight, that it, too, sought its place below, and that
+it was forced upwards only because of the downward
+tendency of the air, as wood is forced to the surface of
+water because the water exerts the greater downward
+pressure.</p>
+
+<p>Again, we see a body thrown into the air. It ascends.
+How is it that it does not seek its proper place? Why
+does the velocity of its "violent" motion decrease as
+it rises, while that of its "natural" fall increases as it
+descends. If we mark closely the relation between
+these two facts, the problem will solve itself. We shall
+see, as Galileo did, that the decrease of velocity in
+rising and the increase of velocity in falling are one
+and the same phenomenon, viz., an increase of velocity
+towards the earth. Accordingly, it is not a place
+that is assigned to the body, but an increase of velocity
+towards the earth.</p>
+
+<p>By this idea the movements of heavy bodies are
+rendered perfectly familiar. Newton, now, firmly
+grasping this new way of thinking, sees the moon and
+the planets moving in their paths upon principles similar
+to those which determine the motion of a projectile
+thrown into the air. Yet the movements of the
+planets were marked by peculiarities which compelled
+him once more to modify slightly his customary mode
+of thought. The heavenly bodies, or rather the parts
+composing them, do not move with constant accelerations
+towards each other, but "attract each other,"
+directly as the mass and inversely as the square of the
+distance.</p>
+
+<p>This latter notion, which includes the one applying
+to terrestrial bodies as a special case, is, as we see,
+quite different from the conception from which we
+started. How limited in scope was the original idea
+and to what a multitude of phenomena is not the present
+one applicable! Yet there is a trace, after all,
+of the "search for place" in the expression "attraction."
+And it would be folly, indeed, for us to avoid,
+with punctilious dread, this conception of "attraction"
+as bearing marks of its pedigree. It is the historical
+base of the Newtonian conception and it still continues
+to direct our thoughts in the paths so long familiar to
+us. Thus, the happiest ideas do not fall from heaven,
+but spring from notions already existing.</p>
+
+<p>Similarly, a ray of light was first regarded as a continuous
+and homogeneous straight line. It then became
+the path of projection for minute missiles; then
+an aggregate of the paths of countless different kinds
+of missiles. It became periodic; it acquired various
+sides; and ultimately it even lost its motion in a
+straight line.</p>
+
+<p>The electric current was conceived originally as
+the flow of a hypothetical fluid. To this conception
+was soon added the notion of a chemical current, the
+notion of an electric, magnetic, and anisotropic optical
+field, intimately connected with the path of the current.
+And the richer a conception becomes in following
+and keeping pace with facts, the better adapted it
+is to anticipate them.</p>
+
+<p>Adaptive processes of this kind have no assignable
+beginning, inasmuch as every problem that incites
+to new adaptation, presupposes a fixed habitude of
+thought. Moreover, they have no visible end; in so
+far as experience never ceases. Science, accordingly,
+stands midway in the evolutionary process; and science
+may advantageously direct and promote this process,
+but it can never take its place. That science is inconceivable
+the principles of which would enable a person
+with no experience to construct the world of experience,
+without a knowledge of it. One might just as
+well expect to become a great musician, solely by the
+aid of theory, and without musical experience; or to
+become a painter by following the directions of a text-book.</p>
+
+<p>In glancing over the history of an idea with which
+we have become perfectly familiar, we are no longer
+able to appreciate the full significance of its growth.
+The deep and vital changes that have been effected in
+the course of its evolution, are recognisable only from
+the astounding narrowness of view with which great
+contemporary scientists have occasionally opposed
+each other. Huygens's wave-theory of light was incomprehensible
+to Newton, and Newton's idea of universal
+gravity was unintelligible to Huygens. But a
+century afterwards both notions were reconcilable,
+even in ordinary minds.</p>
+
+<p>On the other hand, the original creations of pioneer
+intellects, unconsciously formed, do not assume
+a foreign garb; their form is their own. In them,
+childlike simplicity is joined to the maturity of manhood,
+and they are not to be compared with processes
+of thought in the average mind. The latter are carried
+on as are the acts of persons in the state of mesmerism,
+where actions involuntarily follow the images which
+the words of other persons suggest to their minds.</p>
+
+<p>The ideas that have become most familiar through
+long experience, are the very ones that intrude themselves
+into the conception of every new fact observed.
+In every instance, thus, they become involved in a
+struggle for self-preservation, and it is just they that
+are seized by the inevitable process of transformation.</p>
+
+<p>Upon this process rests substantially the method
+of explaining by hypothesis new and uncomprehended
+phenomena. Thus, instead of forming entirely new
+notions to explain the movements of the heavenly
+bodies and the phenomena of the tides, we imagine the
+material particles composing the bodies of the universe
+to possess weight or gravity with respect to one another.
+Similarly, we imagine electrified bodies to be
+freighted with fluids that attract and repel, or we conceive
+the space between them to be in a state of elastic
+tension. In so doing, we substitute for new ideas
+distinct and more familiar notions of old experience&mdash;notions
+which to a great extent run unimpeded in their
+courses, although they too must suffer partial transformation.</p>
+
+<p>The animal cannot construct new members to perform
+every new function that circumstances and fate
+demand of it. On the contrary it is obliged to make
+use of those it already possesses. When a vertebrate
+animal chances into an environment where it must
+learn to fly or swim, an additional pair of extremities is
+not grown for the purpose. On the contrary, the animal
+must adapt and transform a pair that it already
+has.</p>
+
+<p>The construction of hypotheses, therefore, is not
+the product of artificial scientific methods. This process
+is unconsciously carried on in the very infancy of
+science. Even later, hypotheses do not become detrimental
+and dangerous to progress except when more
+reliance is placed on them than on the facts themselves;
+when the contents of the former are more
+highly valued than the latter, and when, rigidly adhering
+to hypothetical notions, we overestimate the
+ideas we possess as compared with those we have to
+acquire.</p>
+
+<p>The extension of our sphere of experience always
+involves a transformation of our ideas. It matters not
+whether the face of nature becomes actually altered,
+presenting new and strange phenomena, or whether
+these phenomena are brought to light by an intentional
+or accidental turn of observation. In fact, all the varied
+methods of scientific inquiry and of purposive
+mental adaptation enumerated by John Stuart Mill,
+those of observation as well as those of experiment,
+are ultimately recognisable as forms of one fundamental
+method, the method of change, or variation. It is
+through change of circumstances that the natural philosopher
+learns. This process, however, is by no means
+confined to the investigator of nature. The historian,
+the philosopher, the jurist, the mathematician, the
+artist, the æsthetician,<a name="FNanchor_77_77" id="FNanchor_77_77"></a><a href="#Footnote_77_77" class="fnanchor">[77]</a> all illuminate and unfold their
+ideas by producing from the rich treasures of memory
+similar, but different, cases; thus, they observe and
+experiment in their thoughts. Even if all sense-experience
+should suddenly cease, the events of the days
+past would meet in different attitudes in the mind
+and the process of adaptation would still continue&mdash;a
+process which, in contradistinction to the adaptation
+of thoughts to facts in practical spheres, would be
+strictly theoretical, being an adaptation of thoughts to
+thoughts.</p>
+
+<p>The method of change or variation brings before us
+like cases of phenomena, having partly the same and
+partly different elements. It is only by comparing
+different cases of refracted light at changing angles of
+incidence that the common factor, the constancy of
+the refractive index, is disclosed. And only by comparing
+the refractions of light of different colors, does
+the difference, the inequality of the indices of refraction,
+arrest the attention. Comparison based upon
+change leads the mind simultaneously to the highest
+abstractions and to the finest distinctions.</p>
+
+<p>Undoubtedly, the animal also is able to distinguish
+between the similar and dissimilar of two cases. Its
+consciousness is aroused by a noise or a rustling, and
+its motor centre is put in readiness. The sight of the
+creature causing the disturbance, will, according to its
+size, provoke flight or prompt pursuit; and in the latter
+case, the more exact distinctions will determine the
+mode of attack. But man alone attains to the faculty
+of voluntary and conscious comparison. Man alone
+can, by his power of abstraction, rise, in one moment,
+to the comprehension of principles like the conservation
+of mass or the conservation of energy, and in the
+next observe and mark the arrangement of the iron
+lines in the spectrum. In thus dealing with the objects
+of his conceptual life, his ideas unfold and expand,
+like his nervous system, into a widely ramified
+and organically articulated tree, on which he may follow
+every limb to its farthermost branches, and, when
+occasion demands, return to the trunk from which he
+started.</p>
+
+<p>The English philosopher Whewell has remarked
+that two things are requisite to the formation of science:
+facts and ideas. Ideas alone lead to empty
+speculation; mere facts can yield no organic knowledge.
+We see that all depends upon the capacity of
+adapting existing notions to fresh facts.</p>
+
+<p>Over-readiness to yield to every new fact prevents
+fixed habits of thought from arising. Excessively rigid
+habits of thought impede freedom of observation. In
+the struggle, in the compromise between judgment
+and prejudgment (prejudice), if we may use the term,
+our understanding of things broadens.</p>
+
+<p>Habitual judgment, applied to a new case without
+antecedent tests, we call prejudgment or prejudice.
+Who does not know its terrible power! But we think
+less often of the importance and utility of prejudice.
+Physically, no one could exist, if he had to guide and
+regulate the circulation, respiration, and digestion of
+his body by conscious and purposive acts. So, too,
+no one could exist intellectually if he had to form judgments
+on every passing experience, instead of allowing
+himself to be controlled by the judgments he has
+already formed. Prejudice is a sort of reflex motion
+in the province of intelligence.</p>
+
+<p>On prejudices, that is, on habitual judgments not
+tested in every case to which they are applied, reposes
+a goodly portion of the thought and work of the natural
+scientist. On prejudices reposes most of the conduct
+of society. With the sudden disappearance of
+prejudice society would hopelessly dissolve. That
+prince displayed a deep insight into the power of intellectual
+habit, who quelled the loud menaces and
+demands of his body-guard for arrears of pay and compelled
+them to turn about and march, by simply pronouncing
+the regular word of command; he well knew
+that they would be unable to resist that.</p>
+
+<p>Not until the discrepancy between habitual judgments
+and facts becomes great is the investigator implicated
+in appreciable illusion. Then tragic complications
+and catastrophes occur in the practical life of
+individuals and nations&mdash;crises where man, placing
+custom above life, instead of pressing it into the service
+of life, becomes the victim of his error. The very
+power which in intellectual life advances, fosters, and
+sustains us, may in other circumstances delude and
+destroy us.</p>
+<p><span class="pagenum"><a name="Page_234" id="Page_234">[Pg 234]</a></span></p><p><span class="pagenum"><a name="Page_235" id="Page_235">[Pg 235]</a></span></p><p><span class="pagenum"><a name="Page_236" id="Page_236">[Pg 236]</a></span></p>
+<hr class="tb" />
+
+<p>Ideas are not all of life. They are only momentary
+efflorescences of light, designed to illuminate the paths
+of the will. But as delicate reagents on our organic
+evolution our ideas are of paramount importance. No
+theory can gainsay the vital transformation which we
+feel taking place within us through their agency. Nor
+is it necessary that we should have a proof of this process.
+We are immediately assured of it.</p>
+
+<p>The transformation of ideas thus appears as a part
+of the general evolution of life, as a part of its adaptation
+to a constantly widening sphere of action. A
+granite boulder on a mountain-side tends towards the
+earth below. It must abide in its resting-place for
+thousands of years before its support gives way. The
+shrub that grows at its base is farther advanced; it
+accommodates itself to summer and winter. The fox
+which, overcoming the force of gravity, creeps to the
+summit where he has scented his prey, is freer in his
+movements than either. The arm of man reaches
+further still; and scarcely anything of note happens
+in Africa or Asia that does not leave an imprint upon
+his life. What an immense portion of the life of
+other men is reflected in ourselves; their joys, their
+affections, their happiness and misery! And this too,
+when we survey only our immediate surroundings,
+and confine our attention to modern literature. How
+much more do we experience when we travel through
+ancient Egypt with Herodotus, when we stroll through
+the streets of Pompeii, when we carry ourselves back
+to the gloomy period of the crusades or to the golden
+age of Italian art, now making the acquaintance of a
+physician of Molière, and now that of a Diderot or of
+a D'Alembert. What a great part of the life of others,
+of their character and their purpose, do we not absorb
+through poetry and music! And although they only
+gently touch the chords of our emotions, like the memory
+of youth softly breathing upon the spirit of an
+aged man, we have nevertheless lived them over again
+in part. How great and comprehensive does self become
+in this conception; and how insignificant the
+person! Egoistical systems both of optimism and pessimism
+perish with their narrow standard of the import
+of intellectual life. We feel that the real pearls
+of life lie in the ever changing contents of consciousness,
+and that the person is merely an indifferent symbolical
+thread on which they are strung.<a name="FNanchor_78_78" id="FNanchor_78_78"></a><a href="#Footnote_78_78" class="fnanchor">[78]</a></p>
+
+<p>We are prepared, thus, to regard ourselves and
+every one of our ideas as a product and a subject of
+universal evolution; and in this way we shall advance
+sturdily and unimpeded along the paths which the
+future will throw open to us.<a name="FNanchor_79_79" id="FNanchor_79_79"></a><a href="#Footnote_79_79" class="fnanchor">[79]</a></p>
+
+
+
+
+<h2><a name="ON_THE_PRINCIPLE_OF_COMPARISON" id="ON_THE_PRINCIPLE_OF_COMPARISON">ON THE PRINCIPLE OF COMPARISON
+IN PHYSICS.</a><a name="FNanchor_80_80" id="FNanchor_80_80"></a><a href="#Footnote_80_80" class="fnanchor">[80]</a></h2>
+
+
+<p>Twenty years ago when Kirchhoff defined the object
+of mechanics as the "description, in complete
+and very simple terms, of the motions occurring in nature,"
+he produced by the statement a peculiar impression.
+Fourteen years subsequently, Boltzmann, in the
+life-like picture which he drew of the great inquirer,
+could still speak of the universal astonishment at this
+novel method of treating mechanics, and we meet with
+epistemological treatises to-day, which plainly show
+how difficult is the acceptance of this point of view. A
+modest and small band of inquirers there were, however,
+to whom Kirchhoff's few words were tidings of a
+welcome and powerful ally in the epistemological field.</p>
+
+<p>Now, how does it happen that we yield our assent
+so reluctantly to the philosophical opinion of an inquirer
+for whose scientific achievements we have only
+words of praise? One reason probably is that few inquirers
+can find time and leisure, amid the exacting<span class="pagenum"><a name="Page_237" id="Page_237">[Pg 237]</a></span>
+employments demanded for the acquisition of new
+knowledge, to inquire closely into that tremendous
+psychical process by which science is formed. Further,
+it is inevitable that much should be put into Kirchhoff's
+rigid words that they were not originally intended to
+convey, and that much should be found wanting in
+them that had always been regarded as an essential
+element of scientific knowledge. What can mere description
+accomplish? What has become of explanation,
+of our insight into the causal connexion of things?</p>
+<p><span class="pagenum"><a name="Page_238" id="Page_238">[Pg 238]</a></span></p><p><span class="pagenum"><a name="Page_239" id="Page_239">[Pg 239]</a></span></p>
+<hr class="tb" />
+
+<p>Permit me, for a moment, to contemplate not the
+results of science, but the mode of its <i>growth</i>, in a
+frank and unbiassed manner. We know of only <i>one</i>
+source of <i>immediate revelation</i> of scientific facts&mdash;<i>our
+senses</i>. Restricted to this source alone, thrown wholly
+upon his own resources, obliged to start always anew,
+what could the isolated individual accomplish? Of a
+stock of knowledge so acquired the science of a distant
+negro hamlet in darkest Africa could hardly give
+us a sufficiently humiliating conception. For there
+that veritable miracle of thought-transference has already
+begun its work, compared with which the miracles
+of the spiritualists are rank monstrosities&mdash;<i>communication
+by language</i>. Reflect, too, that by means
+of the magical characters which our libraries contain
+we can raise the spirits of the "the sovereign dead of
+old" from Faraday to Galileo and Archimedes, through
+ages of time&mdash;spirits who do not dismiss us with ambiguous
+and derisive oracles, but tell us the best they
+know; then shall we feel what a stupendous and indispensable
+factor in the formation of science <i>communication</i>
+is. Not the dim, half-conscious <i>surmises</i>
+of the acute observer of nature or critic of humanity
+belong to science, but only that which they possess
+clearly enough to <i>communicate</i> to others.</p>
+
+<p>But how, now, do we go about this communication
+of a newly acquired experience, of a newly observed
+fact? As the different calls and battle-cries of gregarious
+animals are unconsciously formed signs for
+a common observation or action, irrespective of the
+causes which produce such action&mdash;a fact that already
+involves the germ of the concept; so also the words
+of human language, which is only more highly specialised,
+are names or signs for universally known
+facts, which all can observe or have observed. If the
+mental representation, accordingly, follows the new
+fact at once and <i>passively</i>, then that new fact must, of
+itself, immediately be constituted and represented in
+thought by facts already universally known and commonly
+observed. Memory is always ready to put forward
+for <i>comparison</i> known facts which resemble the
+new event, or agree with it in certain features, and
+so renders possible that elementary internal judgment
+which the mature and definitively formulated judgment
+soon follows.</p>
+
+<p>Comparison, as the fundamental condition of communication,
+is the most powerful inner vital element
+of science. The zoölogist sees in the bones of the
+wing-membranes of bats, fingers; he compares the
+bones of the cranium with the vertebræ, the embryos
+of different organisms with one another, and the different
+stages of development of the same organism
+with one another. The geographer sees in Lake Garda
+a fjord, in the Sea of Aral a lake in process of drying
+up. The philologist compares different languages with
+one another, and the formations of the same language
+as well. If it is not customary to speak of comparative
+physics in the same sense that we speak of comparative
+anatomy, the reason is that in a science of
+such great experimental activity the attention is turned
+away too much from the <i>contemplative</i> element. But
+like all other sciences, physics lives and grows by
+comparison.</p>
+<p><span class="pagenum"><a name="Page_240" id="Page_240">[Pg 240]</a></span></p><p><span class="pagenum"><a name="Page_241" id="Page_241">[Pg 241]</a></span></p>
+<hr class="tb" />
+
+<p>The manner in which the result of the comparison
+finds expression in the communication, varies of course
+very much. When we say that the colors of the spectrum
+are red, yellow, green, blue, and violet, the designations
+employed may possibly have been derived
+from the technology of tattooing, or they may subsequently
+have acquired the significance of standing for
+the colors of the rose, the lemon, the leaf, the corn-flower,
+and the violet. From the frequent repetition
+of such comparisons, however, made under the most
+manifold circumstances, the inconstant features, as
+compared with the permanent congruent features, get
+so obliterated that the latter acquire a fixed significance
+independent of every object and connexion, or take on
+as we say an <i>abstract</i> or <i>conceptual</i> import. No one
+thinks at the word "red" of any other agreement with
+the rose than that of color, or at the word "straight"
+of any other property of a stretched cord than the
+sameness of direction. Just so, too, numbers, originally
+the names of the fingers of the hands and feet,
+from being used as arrangement-signs for all kinds of
+objects, were lifted to the plane of abstract concepts.
+A verbal report (communication) of a fact that uses
+only these purely abstract implements, we call a <i>direct
+description</i>.</p>
+
+<p>The direct description of a fact of any great extent
+is an irksome task, even where the requisite notions
+are already completely developed. What a simplification
+it involves if we can say, the fact <i>A</i> now
+considered comports itself, not in <i>one</i>, but in <i>many</i> or
+in <i>all</i> its features, like an old and well-known fact <i>B</i>.
+The moon comports itself as a heavy body does with
+respect to the earth; light like a wave-motion or an
+electric vibration; a magnet, as if it were laden with
+gravitating fluids, and so on. We call such a description,
+in which we appeal, as it were, to a description
+already and elsewhere formulated, or perhaps still to
+be precisely formulated, an <i>indirect description</i>. We
+are at liberty to supplement this description, gradually,
+by direct description, to correct it, or to replace it altogether.
+We see, thus, without difficulty, that what is
+called a <i>theory</i> or a <i>theoretical idea</i>, falls under the
+category of what is here termed indirect description.</p>
+<p><span class="pagenum"><a name="Page_242" id="Page_242">[Pg 242]</a></span></p><p><span class="pagenum"><a name="Page_243" id="Page_243">[Pg 243]</a></span></p><p><span class="pagenum"><a name="Page_244" id="Page_244">[Pg 244]</a></span></p><p><span class="pagenum"><a name="Page_245" id="Page_245">[Pg 245]</a></span></p><p><span class="pagenum"><a name="Page_246" id="Page_246">[Pg 246]</a></span></p><p><span class="pagenum"><a name="Page_247" id="Page_247">[Pg 247]</a></span></p><p><span class="pagenum"><a name="Page_248" id="Page_248">[Pg 248]</a></span></p><p><span class="pagenum"><a name="Page_249" id="Page_249">[Pg 249]</a></span></p><p><span class="pagenum"><a name="Page_250" id="Page_250">[Pg 250]</a></span></p><p><span class="pagenum"><a name="Page_251" id="Page_251">[Pg 251]</a></span></p><p><span class="pagenum"><a name="Page_252" id="Page_252">[Pg 252]</a></span></p>
+<hr class="tb" />
+
+<p>What, now, is a theoretical idea? Whence do we
+get it? What does it accomplish for us? Why does it
+occupy a higher place in our judgment than the mere
+holding fast to a fact or an observation? Here, too,
+memory and comparison alone are in play. But instead
+of <i>a single</i> feature of resemblance culled from
+memory, in this case <i>a great system</i> of resemblances
+confronts us, a well-known physiognomy, by means of
+which the new fact is immediately transformed into an
+old acquaintance. Besides, it is in the power of the
+idea to offer us more than we actually see in the new
+fact, at the first moment; it can extend the fact, and
+enrich it with features which we are first induced to
+<i>seek</i> from such suggestions, and which are often actually
+found. It is this <i>rapidity</i> in extending knowledge
+that gives to theory a preference over simple observation.
+But that preference is wholly <i>quantitative</i>.
+Qualitatively, and in real essential points, theory differs
+from observation neither in the mode of its origin
+nor in its last results.</p>
+
+<p>The adoption of a theory, however, always involves
+a danger. For a theory puts in the place of a fact <i>A</i>
+in thought, always a <i>different</i>, but simpler and more
+familiar fact <i>B</i>, which in <i>some</i> relations can mentally
+represent <i>A</i>, but for the very reason that it is different,
+in other relations cannot represent it. If now, as
+may readily happen, sufficient care is not exercised,
+the most fruitful theory may, in special circumstances,
+become a downright obstacle to inquiry. Thus, the
+emission-theory of light, in accustoming the physicist
+to think of the projectile path of the "light-particles"
+as an undifferentiated straight-line, demonstrably impeded
+the discovery of the periodicity of light. By
+putting in the place of light the more familiar phenomena
+of sound, Huygens renders light in many of
+its features a familiar event, but with respect to polarisation,
+which lacks the longitudinal waves with which
+alone he was acquainted, it had for him a doubly
+strange aspect. He is unable thus to grasp in abstract
+thought the fact of polarisation, which is before his
+eyes, whilst Newton, merely by adapting to the observation
+his thoughts, and putting this question, "<i>Annon
+radiorum luminis diversa sunt latera?</i>" abstractly
+grasped polarisation, that is, directly described it, a
+century before Malus. On the other hand, if the
+agreement of the fact with the idea theoretically representing
+it, extends further than its inventor originally
+anticipated, then we may be led by it to unexpected
+discoveries, of which conical refraction, circular polarisation
+by total reflexion, Hertz's waves offer ready
+examples, in contrast to the illustrations given above.</p>
+
+<p>Our insight into the conditions indicated will be
+improved, perhaps, by contemplating the development
+of some theory or other more in detail. Let us consider
+a magnetised bar of steel by the side of a second
+unmagnetised bar, in all other respects the same. The
+second bar gives no indication of the presence of iron-filings;
+the first attracts them. Also, when the iron-filings
+are absent, we must think of the magnetised
+bar as in a different condition from that of the unmagnetised.
+For, that the mere presence of the iron-filings
+does not induce the phenomenon of attraction is proved
+by the second unmagnetised bar. The ingenuous man,
+who finds in his will, as his most familiar source of
+power, the best facilities for comparison, conceives a
+species of <i>spirit</i> in the magnet. The behavior of a
+warm body or of an <i>electrified</i> body suggests similar
+ideas. This is the point of view of the oldest theory,
+<i>fetishism</i>, which the inquirers of the early Middle
+Ages had not yet overcome, and which in its last vestiges,
+in the conception of forces, still flourishes in
+modern physics. We see, thus, the <i>dramatic</i> element
+need no more be absent in a scientific description, than
+in a thrilling novel.</p>
+
+<p>If, on subsequent examination, it be observed that
+a cold body, in contact with a hot body, warms itself,
+so to speak, <i>at the expense</i> of the hot body; further,
+that when the substances are the same, the cold body,
+which, let us say, has twice the mass of the other,
+gains only half the number of degrees of temperature
+that the other loses, a wholly new impression arises.
+The demoniac character of the event vanishes, for the
+supposed spirit acts not by caprice, but according to
+fixed laws. In its place, however, <i>instinctively</i> the
+notion of a <i>substance</i> is substituted, part of which flows
+over from the one body to the other, but the total
+amount of which, representable by the sum of the products
+of the masses into the respective changes of
+temperature, remains constant. Black was the first to
+be <i>powerfully</i> struck with this resemblance of thermal
+processes to the motion of a substance, and under its
+guidance discovered the specific heat, the heat of fusion,
+and the heat of vaporisation of bodies. Gaining
+strength and fixity, however, from these successes,
+this notion of substance subsequently stood in the way
+of scientific advancement. It blinded the eyes of the
+successors of Black, and prevented them from seeing
+the manifest fact, which every savage knows, that heat
+is <i>produced</i> by friction. Fruitful as that notion was
+for Black, helpful as it still is to the learner to-day in
+Black's special field, permanent and universal validity
+as a <i>theory</i> it could never maintain. But what is essential,
+conceptually, in it, viz., the constancy of the product-sum
+above mentioned, retains its value and may
+be regarded as a <i>direct description</i> of Black's facts.</p>
+
+<p>It stands to reason that those theories which push
+themselves forward unsought, instinctively, and wholly
+of their own accord, should have the greatest power,
+should carry our thoughts most with them, and exhibit
+the staunchest powers of self-preservation. On the
+other hand, it may also be observed that when critically
+scrutinised such theories are extremely apt to
+lose their cogency. We are constantly busied with
+"substance," its modes of action have stamped themselves
+indelibly upon our thoughts, our vividest and
+clearest reminiscences are associated with it. It should
+cause us no surprise, therefore, that Robert Mayer and
+Joule, who gave the final blow to Black's substantial
+conception of heat, should have re-introduced the
+same notion of substance in a more abstract and modified
+form, only applying to a much more extensive
+field.</p>
+
+<p>Here, too, the psychological circumstances which
+impart to the new conception its power, lie clearly before
+us. By the unusual redness of the venous blood
+in tropical climates Mayer's attention is directed to
+the lessened expenditure of internal heat and to the
+proportionately lessened <i>consumption of material</i> by the
+human body in those climates. But as every effort of
+the human organism, including its mechanical work,
+is connected with the consumption of material, and as
+work by friction can engender heat, therefore heat and
+work appear in kind equivalent, and between them a
+proportional relation must subsist. Not <i>every</i> quantity,
+but the appropriately calculated <i>sum</i> of the two, as
+connected with a proportionate consumption of material,
+appears <i>substantial</i>.</p>
+
+<p>By exactly similar considerations, relative to the
+economy of the galvanic element, Joule arrived at his
+view; he found experimentally that the sum of the
+heat evolved in the circuit, of the heat consumed in the
+combustion of the gas developed, of the electro-magnetic
+work of the current, properly calculated,&mdash;in
+short, the sum of all the effects of the battery,&mdash;is connected
+with a proportionate consumption of zinc. Accordingly,
+this sum itself has a substantial character.</p>
+
+<p>Mayer was so absorbed with the view attained,
+that the indestructibility of <i>force</i>, in our phraseology
+<i>work</i>, appeared to him <i>a priori</i> evident. "The creation
+or annihilation of a force," he says, "lies without
+the province of human thought and power." Joule
+expressed himself to a similar effect: "It is manifestly
+absurd to suppose that the powers with which God
+has endowed matter can be destroyed." Strange to
+say, on the basis of such utterances, not Joule, but
+Mayer, was stamped as a metaphysician. We may
+be sure, however, that both men were merely giving
+expression, and that half-unconsciously, to a powerful
+<i>formal</i> need of the new simple view, and that both
+would have been extremely surprised if it had been
+proposed to them that their principle should be submitted
+to a philosophical congress or ecclesiastical
+synod for a decision upon its validity. But with all
+agreements, the attitude of these two men, in other
+respects, was totally different. Whilst Mayer represented
+this <i>formal</i> need with all the stupendous instinctive
+force of genius, we might say almost with the
+ardor of fanaticism, yet was withal not wanting in the
+conceptive ability to compute, prior to all other inquirers,
+the mechanical equivalent of heat from old
+physical constants long known and at the disposal of
+all, and so to set up for the new doctrine a programme
+embracing all physics and physiology; Joule, on the
+other hand, applied himself to the exact verification of
+the doctrine by beautifully conceived and masterfully
+executed experiments, extending over all departments
+of physics. Soon Helmholtz too attacked the problem,
+in a totally independent and characteristic manner.
+After the professional virtuosity with which this physicist
+grasped and disposed of all the points unsettled
+by Mayer's programme and more besides, what especially
+strikes us is the consummate critical lucidity of
+this young man of twenty-six years. In his exposition
+is wanting that vehemence and impetuosity which
+marked Mayer's. The principle of the conservation
+of energy is no self-evident or <i>a priori</i> proposition for
+him. What follows, on the assumption that that proposition
+obtains? In this hypothetical form, he subjugates
+his matter.</p>
+
+<p>I must confess, I have always marvelled at the
+æsthetic and ethical taste of many of our contemporaries
+who have managed to fabricate out of this relation
+of things, odious national and personal questions,
+instead of praising the good fortune that made <i>several</i>
+such men work together and of rejoicing at the instructive
+diversity and idiosyncrasies of great minds
+fraught with such rich consequences for us.</p>
+
+<p>We know that still another theoretical conception
+played a part in the development of the principle of
+energy, which Mayer held aloof from, namely, the conception
+that heat, as also the other physical processes,
+are due to motion. But once the principle of energy
+has been reached, these auxiliary and transitional theories
+discharge no essential function, and we may regard
+the principle, like that which Black gave, as a
+contribution to the <i>direct description</i> of a widely extended
+domain of facts.</p>
+
+<p>It would appear from such considerations not only
+advisable, but even necessary, with all due recognition
+of the helpfulness of theoretic ideas in research,
+yet gradually, as the new facts grow familiar, to substitute
+for indirect description <i>direct</i> description, which
+contains nothing that is unessential and restricts itself
+absolutely to the abstract apprehension of facts. We
+might almost say, that the descriptive sciences, so
+called with a tincture of condescension, have, in respect
+of scientific character, outstripped the physical
+expositions lately in vogue. Of course, a virtue has
+been made of necessity here.</p>
+
+<p>We must admit, that it is not in our power to describe
+directly every fact, on the moment. Indeed,
+we should succumb in utter despair if the whole wealth
+of facts which we come step by step to know, were
+presented to us all at once. Happily, only detached
+and unusual features first strike us, and such we bring
+nearer to ourselves by <i>comparison</i> with every-day
+events. Here the notions of the common speech are
+first developed. The comparisons then grow more
+manifold and numerous, the fields of facts compared
+more extensive, the concepts that make direct description
+possible, proportionately more general and more
+abstract.</p>
+
+<p>First we become familiar with the motion of freely
+falling bodies. The concepts of force, mass, and work
+are then carried over, with appropriate modifications,
+to the phenomena of electricity and magnetism. A
+stream of water is said to have suggested to Fourier
+the first distinct picture of currents of heat. A special
+case of vibrations of strings investigated by Taylor,
+cleared up for him a special case of the conduction of
+heat. Much in the same way that Daniel Bernoulli
+and Euler constructed the most diverse forms of vibrations
+of strings from Taylor's cases, so Fourier constructs
+out of simple cases of conduction the most
+multifarious motions of heat; and that method has
+extended itself over the whole of physics. Ohm forms
+his conception of the electric current in imitation of
+Fourier's. The latter, also, adopts Fick's theory of
+diffusion. In an analogous manner a conception of
+the magnetic current is developed. All sorts of stationary
+currents are thus made to exhibit common
+features, and even the condition of complete equilibrium
+in an extended medium shares these features
+with the dynamical condition of equilibrium of a stationary
+current. Things as remote as the magnetic
+lines of force of an electric current and the stream-lines
+of a frictionless liquid vortex enter in this way
+into a peculiar relationship of similarity. The concept
+of potential, originally enunciated for a restricted
+province, acquires a wide-reaching applicability.
+Things as dissimilar as pressure, temperature,
+and electromotive force, now show points of agreement
+in relation to ideas derived by definite methods
+from that concept: viz., fall of pressure, fall of temperature,
+fall of potential, as also with the further notions
+of liquid, thermal, and electric strength of current.
+That relationship between systems of ideas in
+which the dissimilarity of every two homologous concepts
+as well as the agreement in logical relations
+of every two homologous pairs of concepts, is clearly
+brought to light, is called an <i>analogy</i>. It is an effective
+means of mastering heterogeneous fields of facts in
+unitary comprehension. The path is plainly shown in
+which <i>a universal physical phenomenology</i> embracing all
+domains, will be developed.</p>
+
+<p>In the process described we attain for the first time
+to what is indispensable in the direct description of
+broad fields of fact&mdash;the wide-reaching <i>abstract concept</i>.
+And now I must put a question smacking of the school-master,
+but unavoidable: What is a concept? Is it a
+hazy representation, admitting withal of mental visualisation?
+No. Mental visualisation accompanies it
+only in the simplest cases, and then merely as an adjunct.
+Think, for example, of the "coefficient of self-induction,"
+and seek for its visualised mental image.
+Or is, perhaps, the concept a mere word? The adoption
+of this forlorn idea, which has been actually proposed
+of late by a reputed mathematician would only
+throw us back a thousand years into the deepest scholasticism.
+We must, therefore, reject it.</p>
+
+<p>The solution is not far to seek. We must not think
+that sensation, or representation, is a purely passive
+process. The lowest organisms respond to it with a
+simple reflex motion, by engulfing the prey which approaches
+them. In higher organisms the centripetal
+stimulus encounters in the nervous system obstacles
+and aids which modify the centrifugal process. In still
+higher organisms, where prey is pursued and examined,
+the process in question may go through extensive
+paths of circular motions before it comes to relative
+rest. Our own life, too, is enacted in such
+processes; all that we call science may be regarded
+as parts, or middle terms, of such activities.</p>
+
+<p>It will not surprise us now if I say: the definition
+of a concept, and, when it is very familiar, even its
+name, is an <i>impulse</i> to some accurately determined,
+often complicated, critical, comparative, or constructive
+<i>activity</i>, the usually sense-perceptive result of
+which is a term or member of the concept's scope. It
+matters not whether the concept draws the attention
+only to one certain sense (as sight) or to a phase of a
+sense (as color, form), or is the starting-point of a
+complicated action; nor whether the activity in question
+(chemical, anatomical, and mathematical operations)
+is muscular or technical, or performed wholly
+in the imagination, or only intimated. The concept is
+to the physicist what a musical note is to a piano-player.
+A trained physicist or mathematician reads a
+memoir like a musician reads a score. But just as the
+piano-player must first learn to move his fingers singly
+and collectively, before he can follow his notes without
+effort, so the physicist or mathematician must go
+through a long apprenticeship before he gains control,
+so to speak, of the manifold delicate innervations
+of his muscles and imagination. Think of how frequently
+the beginner in physics or mathematics performs
+more, or less, than is required, or of how frequently
+he conceives things differently from what they
+are! But if, after having had sufficient discipline, he
+lights upon the phrase "coefficient of self-induction,"
+he knows immediately what that term requires of him.
+Long and thoroughly practised <i>actions</i>, which have
+their origin in the necessity of comparing and representing
+facts by other facts, are thus the very kernel
+of concepts. In fact, positive and philosophical philology
+both claim to have established that all roots
+represent concepts and stood originally for muscular
+activities alone. The slow assent of physicists to
+Kirchhoff's dictum now becomes intelligible. They
+best could feel the vast amount of individual labor,
+theory, and skill required before the ideal of direct
+description could be realised.</p>
+<p><span class="pagenum"><a name="Page_253" id="Page_253">[Pg 253]</a></span></p><p><span class="pagenum"><a name="Page_254" id="Page_254">[Pg 254]</a></span></p><p><span class="pagenum"><a name="Page_255" id="Page_255">[Pg 255]</a></span></p><p><span class="pagenum"><a name="Page_256" id="Page_256">[Pg 256]</a></span></p><p><span class="pagenum"><a name="Page_257" id="Page_257">[Pg 257]</a></span></p><p><span class="pagenum"><a name="Page_258" id="Page_258">[Pg 258]</a></span></p><p><span class="pagenum"><a name="Page_259" id="Page_259">[Pg 259]</a></span></p>
+<hr class="tb" />
+
+<p>Suppose, now, the ideal of a given province of
+facts is reached. Does description accomplish all that
+the inquirer can ask? In my opinion, it does. Description
+is a building up of facts in thought, and this
+building up is, in the experimental sciences, often the
+condition of actual execution. For the physicist, to
+take a special case, the metrical units are the building-stones,
+the concepts the directions for building, and
+the facts the result of the building. Our mental
+imagery is almost a complete substitute for the fact,
+and by means of it we can ascertain all the fact's properties.
+We do not know that worst which we ourselves
+have made.</p>
+
+<p>People require of science that it should <i>prophesy</i>,
+and Hertz uses that expression in his posthumous
+<i>Mechanics</i>. But, natural as it is, the expression is too
+narrow. The geologist and the palæontologist, at times
+the astronomer, and always the historian and the philologist,
+prophesy, so to speak, <i>backwards</i>. The descriptive
+sciences, like geometry and mathematics, prophesy
+neither forward or backwards, but seek from given
+conditions the conditioned. Let us say rather: <i>Science
+completes in thought facts that are only partly given</i>.
+This is rendered possible by description, for description
+presupposes the interdependence of the descriptive
+elements: otherwise nothing would be described.</p>
+
+<p>It is said, description leaves the sense of causality
+unsatisfied. In fact, many imagine they understand
+motions better when they picture to themselves the
+pulling forces; and yet the <i>accelerations</i>, the facts,
+accomplish more, without superfluous additions. I
+hope that the science of the future will discard the
+idea of cause and effect, as being formally obscure;
+and in my feeling that these ideas contain a strong
+tincture of fetishism, I am certainly not alone. The
+more proper course is, <i>to regard the abstract determinative
+elements of a fact as interdependent</i>, in a purely logical
+way, as the mathematician or geometer does.
+True, by comparison with the will, forces are brought
+nearer to our feeling; but it may be that ultimately the
+will itself will be made clearer by comparison with the
+accelerations of masses.</p>
+
+<p>If we are asked, candidly, when is a fact <i>clear</i> to
+us, we must say "when we can reproduce it by very
+<i>simple</i> and very familiar intellectual operations, such
+as the construction of accelerations, or the geometrical
+summation of accelerations, and so forth." The
+requirement of <i>simplicity</i> is of course to the expert
+a different matter from what it is to the novice. For
+the first, description by a system of differential equations
+is sufficient; for the second, a gradual construction
+out of elementary laws is required. The first
+discerns at once the connexion of the two expositions.
+Of course, it is not disputed that the <i>artistic</i> value of
+materially equivalent descriptions may not be different.</p>
+
+<p>Most difficult is it to persuade strangers that the
+grand universal laws of physics, such as apply indiscriminately
+to material, electrical, magnetic, and other
+systems, are not essentially different from descriptions.
+As compared with many sciences, physics occupies in
+this respect a position of vantage that is easily explained.
+Take, for example, anatomy. As the anatomist
+in his quest for agreements and differences in
+animals ascends to ever higher and higher <i>classifications</i>,
+the individual facts that represent the ultimate
+terms of the system, are still so different that they
+must be <i>singly</i> noted. Think, for example, of the common
+marks of the Vertebrates, of the class-characters
+of Mammals and Birds on the one hand and of Fishes
+on the other, of the double circulation of the blood on
+the one hand and of the single on the other. In the
+end, always <i>isolated</i> facts remain, which show only a
+<i>slight</i> likeness to one another.</p>
+
+<p>A science still more closely allied to physics, chemistry,
+is often in the same strait. The abrupt change
+of the qualitative properties, in all likelihood conditioned
+by the slight stability of the intermediate states,
+the remote resemblance of the co-ordinated facts of
+chemistry render the treatment of its data difficult.
+Pairs of bodies of different qualitative properties unite
+in different mass-ratios; but no connexion between
+the first and the last is to be noted, at first.</p>
+
+<p>Physics, on the other hand, reveals to us wide domains
+of <i>qualitatively homogeneous</i> facts, differing from
+one another only in the number of equal parts into
+which their characteristic marks are divisible, that is,
+differing only <i>quantitatively</i>. Even where we have to
+deal with qualities (colors and sounds), quantitative
+characters of those qualities are at our disposal. Here
+the classification is so simple a task that it rarely impresses
+us as such, whilst in infinitely fine gradations,
+in a <i>continuum of facts</i>, our number-system is ready beforehand
+to follow as far as we wish. The co-ordinated
+facts are here extremely similar and very closely affined,
+as are also their descriptions which consist in
+the determination of the numerical measures of one
+given set of characters from those of a different set by
+means of familiar mathematical operations&mdash;methods
+of derivation. Thus, the common characteristics of
+all descriptions can be found here; and with them a
+succinct, comprehensive description, or a rule for the
+construction of all single descriptions, is assigned,&mdash;and
+this we call <i>law</i>. Well-known examples are the
+formulæ for freely falling bodies, for projectiles, for
+central motion, and so forth. If physics apparently
+accomplishes more by its methods than other sciences,
+we must remember that in a sense it has presented to
+it much simpler problems.</p>
+
+<p>The remaining sciences, whose facts also present a
+physical side, need not be envious of physics for this
+superiority; for all its acquisitions ultimately redound
+to their benefit as well. But also in other ways this
+mutual help shall and must change. Chemistry has advanced
+very far in making the methods of physics her
+own. Apart from older attempts, the periodical series
+of Lothar Meyer and Mendelejeff are a brilliant and
+adequate means of producing an easily surveyed system
+of facts, which by gradually becoming complete,
+will take the place almost of a continuum of facts.
+Further, by the study of solutions, of dissociation, in
+fact generally of phenomena which present a continuum
+of cases, the methods of thermodynamics have
+found entrance into chemistry. Similarly we may hope
+that, at some future day, a mathematician, letting the
+fact-continuum of embryology play before his mind,
+which the palæontologists of the future will supposedly
+have enriched with more intermediate and derivative
+forms between Saurian and Bird than the isolated
+Pterodactyl, Archæopteryx, Ichthyornis, and so forth,
+which we now have&mdash;that such a mathematician shall
+transform, by the variation of a few parameters, as in
+a dissolving view, one form into another, just as we
+transform one conic section into another.</p>
+
+<p>Reverting now to Kirchhoff's words, we can come
+to some agreement regarding their import. Nothing
+can be built without building-stones, mortar, scaffolding,
+and a builder's skill. Yet assuredly the wish is
+well founded, that will show to posterity the complete
+structure in its finished form, bereft of unsightly scaffolding.
+It is the pure logical and æsthetic sense of the
+mathematician that speaks out of Kirchhoff's words.
+Modern expositions of physics aspire after his ideal;
+that, too, is intelligible. But it would be a poor didactic
+shift, for one whose business it was to train
+architects, to say: "Here is a splendid edifice; if thou
+wouldst really build, go thou and do likewise".</p>
+
+<p>The barriers between the special sciences, which
+make division of work and concentration possible, but
+which appear to us after all as cold and conventional
+restrictions, will gradually disappear. Bridge upon
+bridge is thrown over the gaps. Contents and methods,
+even of the remotest branches, are compared.
+When the Congress of Natural Scientists shall meet a
+hundred years hence, we may expect that they will
+represent a unity in a higher sense than is possible to-day,
+not in sentiment and aim alone, but in method
+also. In the meantime, this great change will be
+helped by our keeping constantly before our minds the
+fact of the intrinsic relationship of all research, which
+Kirchhoff characterised with such classical simplicity.</p>
+
+
+
+
+<h2><a name="THE_PART_PLAYED_BY_ACCIDENT_IN" id="THE_PART_PLAYED_BY_ACCIDENT_IN">THE PART PLAYED BY ACCIDENT IN
+INVENTION AND DISCOVERY.</a><a name="FNanchor_81_81" id="FNanchor_81_81"></a><a href="#Footnote_81_81" class="fnanchor">[81]</a></h2>
+
+
+<p>It is characteristic of the naïve and sanguine
+beginnings of thought in youthful men and
+nations, that all problems are held to be soluble and
+fundamentally intelligible on the first appearance of
+success. The sage of Miletus, on seeing plants take
+their rise from moisture, believed he had comprehended
+the whole of nature, and he of Samos, on discovering
+that definite numbers corresponded to the
+lengths of harmonic strings, imagined he could exhaust
+the nature of the world by means of numbers.
+Philosophy and science in such periods are blended.
+Wider experience, however, speedily discloses the
+error of such a course, gives rise to criticism, and
+leads to the division and ramification of the sciences.</p>
+
+<p>At the same time, the necessity of a broad and
+general view of the world remains; and to meet this
+need philosophy parts company with special inquiry.<span class="pagenum"><a name="Page_260" id="Page_260">[Pg 260]</a></span>
+It is true, the two are often found united in gigantic
+personalities. But as a rule their ways diverge more
+and more widely from each other. And if the estrangement
+of philosophy from science can reach a point
+where data unworthy of the nursery are not deemed too
+scanty as foundations of the world, on the other hand
+the thorough-paced specialist may go to the extreme
+of rejecting point-blank the possibility of a broader
+view, or at least of deeming it superfluous, forgetful
+of Voltaire's apophthegm, nowhere more applicable
+than here, <i>Le superflu&mdash;chose très nécessaire</i>.</p>
+
+<p>It is true, the history of philosophy, owing to the
+insufficiency of its constructive data, is and must be
+largely a history of error. But it would be the height
+of ingratitude on our part to forget that the seeds of
+thoughts which still fructify the soil of special research,
+such as the theory of irrationals, the conceptions
+of conservation, the doctrine of evolution, the
+idea of specific energies, and so forth, may be traced
+back in distant ages to philosophical sources. Furthermore,
+to have deferred or abandoned the attempt
+at a broad philosophical view of the world from a full
+knowledge of the insufficiency of our materials, is
+quite a different thing from never having undertaken
+it at all. The revenge of its neglect, moreover, is
+constantly visited upon the specialist by his committal
+of the very errors which philosophy long ago exposed.
+As a fact, in physics and physiology, particularly
+during the first half of this century, are to be<span class="pagenum"><a name="Page_261" id="Page_261">[Pg 261]</a></span>
+met intellectual productions which for naïve simplicity
+are not a jot inferior to those of the Ionian school, or
+to the Platonic ideas, or to that much reviled ontological
+proof.</p>
+
+<p>Latterly, there has been evidence of a gradual
+change in the situation. Recent philosophy has set
+itself more modest and more attainable ends; it is
+no longer inimical to special inquiry; in fact, it is
+zealously taking part in that inquiry. On the other
+hand, the special sciences, mathematics and physics,
+no less than philology, have become eminently philosophical.
+The material presented is no longer accepted
+uncritically. The glance of the inquirer is
+bent upon neighboring fields, whence that material
+has been derived. The different special departments
+are striving for closer union, and gradually the conviction
+is gaining ground that philosophy can consist
+only of mutual, complemental criticism, interpenetration,
+and union of the special sciences into a consolidated
+whole. As the blood in nourishing the body
+separates into countless capillaries, only to be collected
+again and to meet in the heart, so in the science
+of the future all the rills of knowledge will gather
+more and more into a common and undivided stream.</p>
+
+<p>It is this view&mdash;not an unfamiliar one to the present
+generation&mdash;that I purpose to advocate. Entertain
+no hope, or rather fear, that I shall construct
+systems for you. I shall remain a natural inquirer.
+Nor expect that it is my intention to skirt all the<span class="pagenum"><a name="Page_262" id="Page_262">[Pg 262]</a></span>
+fields of natural inquiry. I can attempt to be your
+guide only in that branch which is familiar to me, and
+even there I can assist in the furtherment of only a
+small portion of the allotted task. If I shall succeed
+in rendering plain to you the relations of physics,
+psychology, and the theory of knowledge, so that you
+may draw from each profit and light, redounding to
+the advantage of each, I shall regard my work as not
+having been in vain. Therefore, to illustrate by an
+example how, consonantly with my powers and views,
+I conceive such inquiries should be conducted, I shall
+treat to-day, in the form of a brief sketch, of the following
+special and limited subject&mdash;of <i>the part which
+accidental circumstances play in the development of inventions
+and discoveries</i>.</p>
+<p><span class="pagenum"><a name="Page_263" id="Page_263">[Pg 263]</a></span></p><p><span class="pagenum"><a name="Page_264" id="Page_264">[Pg 264]</a></span></p><p><span class="pagenum"><a name="Page_265" id="Page_265">[Pg 265]</a></span></p><p><span class="pagenum"><a name="Page_266" id="Page_266">[Pg 266]</a></span></p><p><span class="pagenum"><a name="Page_267" id="Page_267">[Pg 267]</a></span></p><p><span class="pagenum"><a name="Page_268" id="Page_268">[Pg 268]</a></span></p><p><span class="pagenum"><a name="Page_269" id="Page_269">[Pg 269]</a></span></p><p><span class="pagenum"><a name="Page_270" id="Page_270">[Pg 270]</a></span></p><p><span class="pagenum"><a name="Page_271" id="Page_271">[Pg 271]</a></span></p><p><span class="pagenum"><a name="Page_272" id="Page_272">[Pg 272]</a></span></p><p><span class="pagenum"><a name="Page_273" id="Page_273">[Pg 273]</a></span></p><p><span class="pagenum"><a name="Page_274" id="Page_274">[Pg 274]</a></span></p><p><span class="pagenum"><a name="Page_275" id="Page_275">[Pg 275]</a></span></p><p><span class="pagenum"><a name="Page_276" id="Page_276">[Pg 276]</a></span></p><p><span class="pagenum"><a name="Page_277" id="Page_277">[Pg 277]</a></span></p><p><span class="pagenum"><a name="Page_278" id="Page_278">[Pg 278]</a></span></p><p><span class="pagenum"><a name="Page_279" id="Page_279">[Pg 279]</a></span></p><p><span class="pagenum"><a name="Page_280" id="Page_280">[Pg 280]</a></span></p><p><span class="pagenum"><a name="Page_281" id="Page_281">[Pg 281]</a></span></p><p><span class="pagenum"><a name="Page_282" id="Page_282">[Pg 282]</a></span></p>
+<hr class="tb" />
+
+<p>When we Germans say of a man that he was not
+the inventor of gunpowder,<a name="FNanchor_82_82" id="FNanchor_82_82"></a><a href="#Footnote_82_82" class="fnanchor">[82]</a> we impliedly cast a grave
+suspicion on his abilities. But the expression is not
+a felicitous one, as there is probably no invention in
+which deliberate thought had a smaller, and pure luck
+a larger, share than in this. It is well to ask, Are we
+justified in placing a low estimate on the achievement
+of an inventor because accident has assisted him in
+his work? Huygens, whose discoveries and inventions
+are justly sufficient to entitle him to an opinion
+in such matters, lays great emphasis on this factor.
+He asserts that a man capable of inventing the telescope
+without the concurrence of accident must have
+been gifted with superhuman genius.<a name="FNanchor_83_83" id="FNanchor_83_83"></a><a href="#Footnote_83_83" class="fnanchor">[83]</a></p>
+
+<p>A man living in the midst of civilisation finds himself
+surrounded by a host of marvellous inventions,
+considering none other than the means of satisfying
+the needs of daily life. Picture such a man transported
+to the epoch preceding the invention of these
+ingenious appliances, and imagine him undertaking
+in a serious manner to comprehend their origin. At
+first the intellectual power of the men capable of producing
+such marvels will strike him as incredible, or,
+if we adopt the ancient view, as divine. But his astonishment
+is considerably allayed by the disenchanting
+yet elucidative revelations of the history of primitive
+culture, which to a large extent prove that these
+inventions took their rise very slowly and by imperceptible
+degrees.</p>
+
+<p>A small hole in the ground with fire kindled in it
+constituted the primitive stove. The flesh of the
+quarry, wrapped with water in its skin, was boiled by
+contact with heated stones. Cooking by stones was
+also done in wooden vessels. Hollow gourds were
+protected from the fire by coats of clay. Thus, from
+the burned clay accidentally originated the enveloping
+pot, which rendered the gourd superfluous, although
+for a long time thereafter the clay was still spread
+over the gourd, or pressed into woven wicker-work
+before the potter's art assumed its final independence.
+Even then the wicker-work ornament was retained, as
+a sort of attest of its origin.</p>
+
+<p>We see, thus, it is by accidental circumstances, or
+by such as lie without our purpose, foresight, and
+power, that man is gradually led to the acquaintance
+of improved means of satisfying his wants. Let the
+reader picture to himself the genius of a man who
+could have foreseen without the help of accident that
+clay handled in the ordinary manner would produce a
+useful cooking utensil! The majority of the inventions
+made in the early stages of civilisation, including
+language, writing, money, and the rest, could not
+have been the product of deliberate methodical reflexion
+for the simple reason that no idea of their
+value and significance could have been had except
+from practical use. The invention of the bridge may
+have been suggested by the trunk of a tree which had
+fallen athwart a mountain-torrent; that of the tool by
+the use of a stone accidentally taken into the hand to
+crack nuts. The use of fire probably started in and
+was disseminated from regions where volcanic eruptions,
+hot springs, and burning jets of natural gas
+afforded opportunity for quietly observing and turning
+to practical account the properties of fire. Only
+after that had been done could the significance of the
+fire-drill be appreciated, an instrument which was
+probably discovered from boring a hole through a
+piece of wood. The suggestion of a distinguished inquirer
+that the invention of the fire-drill originated on
+the occasion of a religious ceremony is both fantastic
+and incredible. And as to the use of fire, we should
+no more attempt to derive that from the invention of
+the fire-drill than we should from the invention of sulphur
+matches. Unquestionably the opposite course
+was the real one.<a name="FNanchor_84_84" id="FNanchor_84_84"></a><a href="#Footnote_84_84" class="fnanchor">[84]</a></p>
+
+<p>Similar phenomena, though still largely veiled in
+obscurity, mark the initial transition of nations from
+a hunting to a nomadic life and to agriculture.<a name="FNanchor_85_85" id="FNanchor_85_85"></a><a href="#Footnote_85_85" class="fnanchor">[85]</a> We
+shall not multiply examples, but content ourselves
+with the remark that the same phenomena recur in
+historical times, in the ages of great technical inventions,
+and, further, that regarding them the most
+whimsical notions have been circulated&mdash;notions which
+ascribe to accident an unduly exaggerated part, and
+one which in a psychological respect is absolutely impossible.
+The observation of steam escaping from a
+tea-kettle and of the clattering of the lid is supposed
+to have led to the invention of the steam-engine. Just
+think of the gap between this spectacle and the conception
+of the performance of great mechanical work
+by steam, for a man totally ignorant of the steam-engine!
+Let us suppose, however, that an engineer,
+versed in the practical construction of pumps, should
+accidentally dip into water an inverted bottle that had
+been filled with steam for drying and still retained its
+steam. He would see the water rush violently into
+the bottle, and the idea would very naturally suggest
+itself of founding on this experience a convenient and
+useful atmospheric steam-pump, which by imperceptible
+degrees, both psychologically possible and immediate,
+would then undergo a natural and gradual transformation
+into Watt's steam-engine.</p>
+
+<p>But granting that the most important inventions
+are brought to man's notice accidentally and in ways
+that are beyond his foresight, yet it does not follow
+that accident alone is sufficient to produce an invention.
+The part which man plays is by no means a
+passive one. Even the first potter in the primeval
+forest must have felt some stirrings of genius within
+him. In all such cases, the inventor is obliged <i>to take
+note</i> of the new fact, he must discover and grasp its
+advantageous feature, and must have the power to
+turn that feature to account in the realisation of his
+purpose. He must <i>isolate</i> the new feature, impress it
+upon his memory, unite and interweave it with the
+rest of his thought; in short, he must possess the capacity
+<i>to profit by experience</i>.</p>
+
+<p>The capacity to profit by experience might well be
+set up as a test of intelligence. This power varies
+considerably in men of the same race, and increases
+enormously as we advance from the lower animals to
+man. The former are limited in this regard almost
+entirely to the reflex actions which they have inherited
+with their organism, they are almost totally incapable
+of individual experience, and considering their simple
+wants are scarcely in need of it. The ivory-snail
+(<i>Eburna spirata</i>) never learns to avoid the carnivorous
+Actinia, no matter how often it may wince under the
+latter's shower of needles, apparently having no memory
+for pain whatever.<a name="FNanchor_86_86" id="FNanchor_86_86"></a><a href="#Footnote_86_86" class="fnanchor">[86]</a> A spider can be lured forth
+repeatedly from its hole by touching its web with a
+tuning-fork. The moth plunges again and again into
+the flame which has burnt it. The humming-bird
+hawk-moth<a name="FNanchor_87_87" id="FNanchor_87_87"></a><a href="#Footnote_87_87" class="fnanchor">[87]</a> dashes repeatedly against the painted
+roses of the wall-paper, like the unhappy and desperate
+thinker who never wearies of attacking the same
+insoluble chimerical problem. As aimlessly almost as
+Maxwell's gaseous molecules and in the same unreasoning
+manner common flies in their search for light
+and air stream against the glass pane of a half-opened
+window and remain there from sheer inability to find
+their way around the narrow frame. But a pike separated
+from the minnows of his aquarium by a glass
+partition, learns after the lapse of a few months,
+though only after having butted himself half to death,
+that he cannot attack these fishes with impunity.
+What is more, he leaves them in peace even after the
+removal of the partition, though he will bolt a strange
+fish at once. Considerable memory must be attributed
+to birds of passage, a memory which, probably
+owing to the absence of disturbing thoughts, acts with
+the precision of that of some idiots. Finally, the
+susceptibility to training evinced by the higher vertebrates
+is indisputable proof of the ability of these animals
+to profit by experience.</p>
+
+<p>A powerfully developed <i>mechanical</i> memory, which
+recalls vividly and faithfully old situations, is sufficient
+for avoiding definite particular dangers, or for taking
+advantage of definite particular opportunities. But
+more is required for the development of <i>inventions</i>.
+More extensive chains of images are necessary here,
+the excitation by mutual contact of widely different
+trains of ideas, a more powerful, more manifold, and
+richer connexion of the contents of memory, a more
+powerful and impressionable psychical life, heightened
+by use. A man stands on the bank of a mountain-torrent,
+which is a serious obstacle to him. He remembers
+that he has crossed just such a torrent before
+on the trunk of a fallen tree. Hard by trees are
+growing. He has often moved the trunks of fallen
+trees. He has also felled trees before, and then moved
+them. To fell trees he has used sharp stones. He
+goes in search of such a stone, and as the old situations
+that crowd into his memory and are held there in living
+reality by the definite powerful interest which he
+has in crossing just this torrent,&mdash;as these impressions
+are made to pass before his mind in the <i>inverse order</i> in
+which they were here evoked, he invents the bridge.</p>
+
+<p>There can be no doubt but the higher vertebrates
+adapt their actions in some moderate degree to circumstances.
+The fact that they give no appreciable
+evidence of advance by the accumulation of inventions,
+is satisfactorily explained by a difference of degree
+or intensity of intelligence as compared with
+man; the assumption of a difference of kind is not
+necessary. A person who saves a little every day, be
+it ever so little, has an incalculable advantage over
+him who daily squanders that amount, or is unable to
+keep what he has accumulated. A slight quantitative
+difference in such things explains enormous differences
+of advancement.</p>
+
+<p>The rules which hold good in prehistoric times
+also hold good in historical times, and the remarks
+made on invention may be applied almost without
+modification to discovery; for the two are distinguished
+solely by the use to which the new knowledge
+is put. In both cases the investigator is concerned
+with some <i>newly observed</i> relation of new or old properties,
+abstract or concrete. It is observed, for example,
+that a substance which gives a chemical reaction
+<i>A</i> is also the cause of a chemical reaction <i>B</i>. If this
+observation fulfils no purpose but that of furthering
+the scientist's insight, or of removing a source of intellectual
+discomfort, we have a discovery; but an invention,
+if in using the substance giving the reaction
+<i>A</i> to produce the desired reaction <i>B</i>, we have a practical
+end in view, and seek to remove a source of material
+discomfort. The phrase, <i>disclosure of the connexion
+of reactions</i>, is broad enough to cover discoveries
+and inventions in all departments. It embraces the
+Pythagorean proposition, which is a combination of a
+geometrical and an arithmetical reaction, Newton's
+discovery of the connexion of Kepler's motions with
+the law of the inverse squares, as perfectly as it does
+the detection of some minute but appropriate alteration
+in the construction of a tool, or of some appropriate
+change in the methods of a dyeing establishment.</p>
+
+<p>The disclosure of new provinces of facts before
+unknown can only be brought about by accidental circumstances,
+under which are <i>remarked</i> facts that commonly
+go unnoticed. The achievement of the discoverer
+here consists in his <i>sharpened attention</i>, which
+detects the uncommon features of an occurrence and
+their determining conditions from their most evanescent
+marks,<a name="FNanchor_88_88" id="FNanchor_88_88"></a><a href="#Footnote_88_88" class="fnanchor">[88]</a> and discovers means of submitting them
+to exact and full observation. Under this head belong
+the first disclosures of electrical and magnetic
+phenomena, Grimaldi's observation of interference,
+Arago's discovery of the increased check suffered by a
+magnetic needle vibrating in a copper envelope as
+compared with that observed in a bandbox, Foucault's
+observation of the stability of the plane of vibration
+of a rod accidentally struck while rotating in a turning-lathe,
+Mayer's observation of the increased redness
+of venous blood in the tropics, Kirchhoff's observation
+of the augmentation of the <i>D</i>-line in the solar
+spectrum by the interposition of a sodium lamp,
+Schönbein's discovery of ozone from the phosphoric
+smell emitted on the disruption of air by electric
+sparks, and a host of others. All these facts, of which
+unquestionably many were <i>seen</i> numbers of times before
+they were <i>noticed</i>, are examples of the inauguration
+of momentous discoveries by accidental circumstances,
+and place the importance of strained attention
+in a brilliant light.</p>
+
+<p>But not only is a significant part played in the beginning
+of an inquiry by co-operative circumstances
+beyond the foresight of the investigator; their influence
+is also active in its prosecution. Dufay, thus, whilst
+following up the behavior of <i>one</i> electrical state which
+he had assumed, discovers the existence of <i>two</i>. Fresnel
+learns by accident that the interference-bands received
+on ground glass are seen to better advantage
+in the open air. The diffraction-phenomenon of two
+slits proved to be considerably different from what
+Fraunhofer had anticipated, and in following up this
+circumstance he was led to the important discovery of
+grating-spectra. Faraday's induction-phenomenon departed
+widely from the initial conception which occasioned
+his experiments, and it is precisely this deviation
+that constitutes his real discovery.</p>
+
+<p>Every man has pondered on some subject. Every
+one of us can multiply the examples cited, by less illustrious
+ones from his own experience. I shall cite
+but one. On rounding a railway curve once, I accidentally
+remarked a striking apparent inclination of
+the houses and trees. I inferred that the direction of
+the total resultant <i>physical</i> acceleration of the body
+reacts <i>physiologically</i> as the vertical. Afterwards, in
+attempting to inquire more carefully into this phenomenon,
+and this only, in a large whirling machine,
+the collateral phenomena conducted me to the sensation
+of angular acceleration, vertigo, Flouren's experiments
+on the section of the semi-circular canals
+etc., from which gradually resulted views relating to
+sensations of direction which are also held by Breuer
+and Brown, which were at first contested on all hands,
+but are now regarded on many sides as correct, and
+which have been recently enriched by the interesting
+inquiries of Breuer concerning the <i>macula acustica</i>, and
+Kreidel's experiments with magnetically orientable
+crustacea.<a name="FNanchor_89_89" id="FNanchor_89_89"></a><a href="#Footnote_89_89" class="fnanchor">[89]</a> Not disregard of accident but a direct and
+purposeful employment of it advances research.</p>
+
+<p>The more powerful the psychical connexion of the
+memory pictures is,&mdash;and it varies with the individual
+and the mood,&mdash;the more apt is the same accidental
+observation to be productive of results. Galileo knows
+that the air has weight; he also knows of the "resistance
+to a vacuum," expressed both in weight and
+in the height of a column of water. But the two ideas
+dwelt asunder in his mind. It remained for Torricelli
+to vary the specific gravity of the liquid measuring the
+pressure, and not till then was the air included in the
+list of pressure-exerting fluids. The reversal of the
+lines of the spectrum was seen repeatedly before
+Kirchhoff, and had been mechanically explained. But
+it was left for his penetrating vision to discern the
+evidence of the connexion of this phenomenon with
+questions of heat, and to him alone through persistent
+labor was revealed the sweeping significance of the
+fact for the mobile equilibrium of heat. Supposing,
+then, that such a rich organic connexion of the elements
+of memory exists, and is the prime distinguishing
+mark of the inquirer, next in importance certainly
+is that <i>intense interest</i> in a definite object, in a definite
+idea, which fashions advantageous combinations of
+thought from elements before disconnected, and obtrudes
+that idea into every observation made, and into
+every thought formed, making it enter into relationship
+with all things. Thus Bradley, deeply engrossed
+with the subject of aberration, is led to its solution
+by an exceedingly unobtrusive experience in crossing
+the Thames. It is permissible, therefore, to ask
+whether accident leads the discoverer, or the discoverer
+accident, to a successful outcome in scientific
+quests.</p>
+
+<p>No man should dream of solving a great problem
+unless he is so thoroughly saturated with his subject
+that everything else sinks into comparative insignificance.
+During a hurried meeting with Mayer in Heidelberg
+once, Jolly remarked, with a rather dubious
+implication, that if Mayer's theory were correct water
+could be warmed by shaking. Mayer went away without
+a word of reply. Several weeks later, and now
+unrecognised by Jolly, he rushed into the latter's presence
+exclaiming: "Es ischt aso!" (It is so, it is
+so!) It was only after considerable explanation that
+Jolly found out what Mayer wanted to say. The incident
+needs no comment.<a name="FNanchor_90_90" id="FNanchor_90_90"></a><a href="#Footnote_90_90" class="fnanchor">[90]</a></p>
+
+<p>A person deadened to sensory impressions and
+given up solely to the pursuit of his own thoughts,
+may also light on an idea that will divert his mental
+activity into totally new channels. In such cases it is
+a psychical accident, an intellectual experience, as
+distinguished from a physical accident, to which the
+person owes his discovery&mdash;a discovery which is here
+made "deductively" by means of mental copies of the
+world, instead of experimentally. <i>Purely</i> experimental
+inquiry, moreover, does not exist, for, as Gauss says,
+virtually we always experiment with our thoughts.
+And it is precisely that constant, corrective interchange
+or intimate union of experiment and deduction,
+as it was cultivated by Galileo in his <i>Dialogues</i>
+and by Newton in his <i>Optics</i>, that is the foundation of
+the benign fruitfulness of modern scientific inquiry as
+contrasted with that of antiquity, where observation
+and reflexion ofttimes pursued their respective courses
+like two strangers.</p>
+
+<p>We have to wait for the appearance of a favorable
+physical accident. The movement of our thoughts
+obeys the law of association. In the case of meagre
+experience the result of this law is simply the mechanical
+reproduction of definite sensory experiences. On
+the other hand, if the psychical life is subjected to the
+incessant influences of a powerful and rich experience,
+then every representative element in the mind is connected
+with so many others that the actual and natural
+course of the thoughts is easily influenced and determined
+by insignificant circumstances, which accidentally
+are decisive. Hereupon, the process termed imagination
+produces its protean and infinitely diversified
+forms. Now what can we do to guide this process,
+seeing that the combinatory law of the images is without
+our reach? Rather let us ask, what influence can
+a powerful and constantly recurring idea exert on the
+movement of our thoughts? According to what has
+preceded, the answer is involved in the question itself.
+The <i>idea</i> dominates the thought of the inquirer, not
+the latter the former.</p>
+
+<p>Let us see, now, if we can acquire a profounder
+insight into the process of discovery. The condition
+of the discoverer is, as James has aptly remarked, not
+unlike the situation of a person who is trying to remember
+something that he has forgotten. Both are
+sensible of a gap, and have only a remote presentiment
+of what is missing. Suppose I meet in a company
+a well-known and affable gentleman whose name
+I have forgotten, and who to my horror asks to be introduced
+to some one. I set to work according to
+Lichtenberg's rule, and run down the alphabet in
+search of the initial letter of his name. A vague sympathy
+holds me at the letter <i>G</i>. Tentatively I add the
+second letter and am arrested at <i>e</i>, and long before I
+have tried the third letter <i>r</i>, the name "Gerson" sounds
+sonorously upon my ear, and my anguish is gone.
+While taking a walk I meet a gentleman from whom
+I receive a communication. On returning home, and
+in attending to weightier affairs, the matter slips my
+mind. Moodily, but in vain, I ransack my memory.
+Finally I observe that I am going over my walk again
+in thought. On the street corner in question the self-same
+gentleman stands before me and repeats his
+communication. In this process are successively recalled
+to consciousness all the percepts which were
+connected with the percept that was lost, and with
+them, finally, that, too, is brought to light. In the
+first case&mdash;where the experience had already been
+made and is permanently impressed on our thought&mdash;a
+<i>systematic</i> procedure is both possible and easy, for
+we know that a name must be composed of a limited
+number of sounds. But at the same time it should be
+observed that the labor involved in such a combinatorial
+task would be enormous if the name were long
+and the responsiveness of the mind weaker.</p>
+
+<p>It is often said, and not wholly without justification,
+that the scientist has solved a <i>riddle</i>. Every problem
+in geometry may be clothed in the garb of a <i>riddle</i>.
+Thus: "What thing is that <i>M</i> which has the properties
+<i>A</i>, <i>B</i>, <i>C</i>?" "What circle is that which touches
+the straight lines <i>A</i>, <i>B</i>, but touches <i>B</i> in the point <i>C</i>?"
+The first two conditions marshal before the imagination
+the group of circles whose centres lie in the line
+of symmetry of <i>A</i>, <i>B</i>. The third condition reminds
+us of all the circles having centres in the straight line
+that stands at right angles to <i>B</i> in <i>C</i>. The <i>common</i>
+term, or common terms, of the two groups of images
+solves the riddle&mdash;satisfies the problem. Puzzles dealing
+with things or words induce similar processes, but
+the memory in such cases is exerted in many directions
+and more varied and less clearly ordered provinces
+of ideas are surveyed. The difference between
+the situation of a geometer who has a construction to
+make, and that of an engineer, or a scientist, confronted
+with a problem, is simply this, that the first
+moves in a field with which he is thoroughly acquainted,
+whereas the two latter are obliged to familiarise
+themselves with this field subsequently, and in
+a measure far transcending what is commonly required.
+In this process the mechanical engineer has
+at least always a definite goal before him and definite
+means to accomplish his aim, whilst in the case of the
+scientist that aim is in many instances presented only
+in vague and general outlines. Often the very formulation
+of the riddle devolves on him. Frequently it
+is not until the aim has been reached that the broader
+outlook requisite for systematic procedure is obtained.
+By far the larger portion of his success, therefore, is
+contingent on luck and instinct. It is immaterial, so
+far as its character is concerned, whether the process
+in question is brought rapidly to a conclusion in the
+brain of one man, or whether it is spun out for centuries
+in the minds of a long succession of thinkers.
+The same relation that a word solving a riddle bears
+to that riddle is borne by the modern conception of
+light to the facts discovered by Grimaldi, Römer,
+Huygens, Newton, Young, Malus, and Fresnel, and
+only by the help of this slowly developed conception
+is our mental vision enabled to embrace the broad
+domain of facts in question.</p>
+
+<p>A welcome complement to the discoveries which
+the history of civilisation and comparative psychology
+have furnished, is to be found in the confessions of
+great scientists and artists. Scientists <i>and</i> artists, we
+might say, for Liebig boldly declared there was no
+essential difference between the two. Are we to regard
+Leonardo da Vinci as a scientist or as an artist?
+If the artist builds up his work from a few motives,
+the scientist discovers the motives which permeate
+reality. If scientists like Lagrange or Fourier are in
+a certain measure artists in the presentation of their
+results, on the other hand, artists like Shakespeare or
+Ruysdael are scientists in the insight which must
+have preceded their creations.</p>
+
+<p>Newton, when questioned about his methods of
+work, could give no other answer but that he was
+wont to ponder again and again on a subject; and
+similar utterances are accredited to D'Alembert and
+Helmholtz. Scientists and artists both recommend
+persistent labor. After the repeated survey of a field
+has afforded opportunity for the interposition of advantageous
+accidents, has rendered all the traits that
+suit with the mood or the dominant thought more
+vivid, and has gradually relegated to the background
+all things that are inappropriate, making their future
+appearance impossible; then from the teeming, swelling
+host of fancies which a free and high-flown imagination
+calls forth, suddenly that particular form
+arises to the light which harmonises perfectly with
+the ruling idea, mood, or design. Then it is that that
+which has resulted slowly as the result of a gradual
+selection, appears as if it were the outcome of a deliberate
+act of creation. Thus are to be explained the
+statements of Newton, Mozart, Richard Wagner, and
+others, when they say that thoughts, melodies, and
+harmonies had poured in upon them, and that they
+had simply retained the right ones. Undoubtedly,
+the man of genius, too, consciously or instinctively,
+pursues systematic methods wherever it is possible;
+but in his delicate presentiment he will omit many a
+task or abandon it after a hasty trial on which a less
+endowed man would squander his energies in vain.
+Thus, the genius accomplishes<a name="FNanchor_91_91" id="FNanchor_91_91"></a><a href="#Footnote_91_91" class="fnanchor">[91]</a> in a brief space of
+time undertakings for which the life of an ordinary
+man would far from suffice. We shall hardly go astray
+if we regard genius as only a slight deviation from
+the average mental endowment&mdash;as possessing simply
+a greater sensitiveness of cerebral reaction and a
+greater swiftness of reaction. The men who, obeying
+their inner impulses, make sacrifices for an idea instead
+of advancing their material welfare, may appear
+to the full-blooded Philistine as fools; yet we shall
+scarcely adopt Lombroso's view, that genius is to be
+regarded as a disease, although it is unfortunately
+true that the sensitive brains and fragile constitutions
+succumb most readily to sickness.</p>
+
+<p>The remark of C. G. J. Jacobi that mathematics
+is slow of growth and only reaches the truth by long
+and devious paths, that the way to its discovery must
+be prepared for long beforehand, and that then the
+truth will make its long-deferred appearance as if impelled
+by some divine necessity<a name="FNanchor_92_92" id="FNanchor_92_92"></a><a href="#Footnote_92_92" class="fnanchor">[92]</a>&mdash;all this holds true
+of every science. We are astounded often to note
+that it required the combined labors of many eminent
+thinkers for a full century to reach a truth which it
+takes us only a few hours to master and which once
+acquired seems extremely easy to reach under the
+right sort of circumstances. To our humiliation we
+learn that even the greatest men are born more for
+life than for science. The extent to which even they
+are indebted to accident&mdash;to that singular conflux of
+the physical and the psychical life in which the continuous
+but yet imperfect and never-ending adaptation
+of the latter to the former finds its distinct expression&mdash;that
+has been the subject of our remarks to-day.
+Jacobi's poetical thought of a divine necessity acting
+in science will lose none of its loftiness for us if we
+discover in this necessity the same power that destroys
+the unfit and fosters the fit. For loftier, nobler,
+and more romantic than poetry is the truth and the
+reality.</p>
+
+
+
+
+<h2><a name="ON_SENSATIONS_OF_ORIENTATION93" id="ON_SENSATIONS_OF_ORIENTATION93">ON SENSATIONS OF ORIENTATION.</a><a name="FNanchor_93_93" id="FNanchor_93_93"></a><a href="#Footnote_93_93" class="fnanchor">[93]</a></h2>
+
+
+<p>Through the co-operation of a succession of inquirers,
+among whom are particularly to be mentioned
+Goltz of Strassburg and Breuer of Vienna,
+considerable advances have been made during the
+last twenty-five years in our knowledge of the means
+by which we ascertain our position in space and the
+direction of our motion, or orient ourselves, as the
+phrase goes. I presume that you are already acquainted
+with the physiological part of the processes
+with which our sensations of movement, or, more generally
+speaking, our sensations of orientation, are connected.
+Here I shall consider more particularly the
+physical side of the matter. In fact, I was originally
+led to the consideration of these questions by the
+observation of extremely simple and perfectly well-known
+physical facts, before I had any great acquaintance
+with physiology and while pursuing unbiasedly
+my natural thoughts; and I am of the conviction that<span class="pagenum"><a name="Page_283" id="Page_283">[Pg 283]</a></span>
+the way which I have pursued, and which is entirely
+free from hypotheses, will, if you will follow my exposition,
+be that of easiest acquisition for the most of
+you.</p>
+
+<p>No man of sound common sense could ever have
+doubted that a pressure or force is requisite to set a
+body in motion in a given direction and that a contrary
+pressure is required to stop suddenly a body in
+motion. Though the law of inertia was first formulated
+with anything like exactness by Galileo, the
+facts at the basis of it were known long previously to
+men of the stamp of Leonardo da Vinci, Rabelais,
+and others, and were illustrated by them with appropriate
+experiments. Leonardo knew that by a swift
+stroke with a ruler one can knock out from a vertical
+column of checkers a single checker without over-throwing
+the column. The experiment with a coin
+resting on a piece of pasteboard covering a goblet,
+which falls into the goblet when the pasteboard is
+jerked away, like all experiments of the kind, is certainly
+very old.</p>
+
+<p>With Galileo the experience in question assumes
+greater clearness and force. In the famous dialogue
+on the Copernican system which cost him his freedom,
+he explains the tides in an unfelicitous, though
+in principle correct manner, by the analogue of a
+platter of water swung to and fro. In opposition to
+the Aristotelians of his time, who believed the descent<span class="pagenum"><a name="Page_284" id="Page_284">[Pg 284]</a></span>
+of a heavy body could be accelerated by the
+superposition of another heavy body, he asserted that
+a body could never be accelerated by one lying upon
+it unless the first in some way impeded the superposed
+body in its descent. To seek to press a falling
+body by means of another placed upon it, is as senseless
+as trying to prod a man with a lance when the man
+is speeding away from one with the same velocity as
+the lance. Even this little excursion into physics can
+explain much to us. You know the peculiar sensation
+which one has in falling, as when one jumps from a
+high springboard into the water, and which is also
+experienced in some measure at the beginning of the
+descent of elevators and swings. The reciprocal gravitational
+pressure of the different parts of our body,
+which is certainly felt in some manner, vanishes in
+free descent, or, in the case of the elevator, is diminished
+on the beginning of the descent. A similar sensation
+would be experienced if we were suddenly
+transported to the moon where the acceleration of
+gravity is much less than upon the earth. I was led
+to these considerations in 1866 by a suggestion in
+physics, and having also taken into account the alterations
+of the blood-pressure in the cases in question,
+I found I coincided without knowing it with Wollaston
+and Purkinje. The first as early as 1810 in his Croonian
+lecture had touched on the subject of sea-sickness
+and explained it by alterations of the blood-pressure,<span class="pagenum"><a name="Page_285" id="Page_285">[Pg 285]</a></span>
+and later had laid similar considerations at the
+basis of his explanation of vertigo (1820-1826).<a name="FNanchor_94_94" id="FNanchor_94_94"></a><a href="#Footnote_94_94" class="fnanchor">[94]</a></p>
+
+<p>Newton was the first to enunciate with perfect
+generality that a body can change the velocity and
+direction of its motion only by the action of a force,
+or the action of a second body. A corollary of this
+law which was first expressly deduced by Euler is
+that a body can never be set <i>rotating</i> or made to cease
+rotating of itself but only by forces and other bodies.
+For example, turn an open watch which has run down
+freely backwards and forwards in your hand. The
+balance-wheel will not fully catch the rapid rotations,
+it does not even respond fully to the elastic force of
+the spring which proves too weak to carry the wheel
+entirely with it.</p>
+
+<p>Let us consider now that whether we move ourselves
+by means of our legs, or whether we are
+moved by a vehicle or a boat, at first only a part
+of our body is directly moved and the rest of it is
+afterwards set in motion by the first part. We see
+that pressures, pulls, and tensions are always produced
+between the parts of the body in this action,
+which pressures, pulls, and tensions give rise to sensations
+by which the forward or rotary movements in
+which we are engaged are made perceptible.<a name="FNanchor_95_95" id="FNanchor_95_95"></a><a href="#Footnote_95_95" class="fnanchor">[95]</a> But it
+is quite natural that sensations so familiar should be
+little noticed and that attention should be drawn to
+them only under special circumstances when they occur
+unexpectedly or with unusual strength.</p>
+
+<p><span class="pagenum"><a name="Page_286" id="Page_286">[Pg 286]</a></span></p>
+<div class="figcenter" style="width: 450px;">
+<img src="images/i_296.jpg" width="450" height="330" alt="" />
+<span class="caption">Fig. 45.</span>
+</div>
+
+<p>Thus my attention was drawn to this point by the
+sensation of falling and subsequently by another singular
+occurrence. I was rounding a sharp railway
+curve once when I suddenly saw all the trees, houses,
+and factory chimneys along the track swerve from the
+vertical and assume a strikingly inclined position.
+What had hitherto appeared to me perfectly natural,
+namely, the fact that we distinguish the vertical so
+perfectly and sharply from every other direction, now<span class="pagenum"><a name="Page_287" id="Page_287">[Pg 287]</a></span>
+struck me as enigmatical. Why is it that the same
+direction can now appear vertical to me and now cannot?
+By what is the vertical distinguished for us?
+(Compare Figure 45.)</p>
+
+<p>The rails are raised on the convex or outward side
+of the track in order to insure the stability of the carriage
+as against the action of the centrifugal force, the
+whole being so arranged that the combination of the
+force of gravity with the centrifugal force of the train
+shall give rise to a force perpendicular to the plane
+of the rails.</p>
+
+<p>Let us assume, now, that under all circumstances
+we somehow sense the direction of the total resultant
+mass-acceleration whencesoever it may arise as the
+vertical. Then both the ordinary and the extraordinary
+phenomena will be alike rendered intelligible.<a name="FNanchor_96_96" id="FNanchor_96_96"></a><a href="#Footnote_96_96" class="fnanchor">[96]</a></p>
+
+<p>I was now desirous of putting the view I had
+reached to a more convenient and exact test than was
+possible on a railway journey where one has no control
+over the determining circumstances and cannot
+alter them at will. I accordingly had the simple apparatus
+constructed which is represented in Figure 46.</p>
+
+<p>In a large frame <i>BB</i>, which is fastened to the walls,
+rotates about a vertical axis <i>AA</i> a second frame <i>RR</i>,
+and within the latter a third one <i>rr</i>, which can be set<span class="pagenum"><a name="Page_288" id="Page_288">[Pg 288]</a></span>
+at any distance and position from the axis, made stationary
+or movable, and is provided with a chair for
+the observer.</p>
+
+<div class="figcenter" style="width: 600px;">
+<img src="images/i_298.jpg" width="600" height="385" alt="" />
+<span class="caption">Fig. 46.</span>
+</div>
+
+<p>From Mach's <i>Bewegungsempfindungen</i>, Leipsic, Engelmann, 1875.]</p>
+
+<p>The observer takes his seat in the chair and to
+prevent disturbances of judgment is enclosed in a paper
+box. If the observer together with the frame <i>rr</i>
+be then set in uniform rotation, he will feel and see
+the beginning of the rotation both as to direction and
+amount very distinctly although every outward visible
+or tangible point of reference is wanting. If the motion
+be uniformly continued the sensation of rotation
+will gradually cease entirely and the observer will imagine
+himself at rest. But if <i>rr</i> be placed outside the
+axis of rotation, at once on the rotation beginning, a
+strikingly apparent, palpable, actually visible inclination
+of the entire paper box is produced, slight when<span class="pagenum"><a name="Page_289" id="Page_289">[Pg 289]</a></span>
+the rotation is slow, strong when the rotation is rapid,
+and continuing as long as the rotation lasts. It is absolutely
+impossible for the observer to escape perceiving
+the inclination, although here also all outward
+points of reference are wanting. If the observer, for
+example, is seated so as to look towards the axis, he
+will feel the box strongly tipped backwards, as it necessarily
+must be if the direction of the total resultant
+force is perceived as the vertical. For other positions
+of the observer the situation is similar.<a name="FNanchor_97_97" id="FNanchor_97_97"></a><a href="#Footnote_97_97" class="fnanchor">[97]</a></p>
+
+<p>Once, while performing one of these experiments,
+and after rotating so long that I was no longer conscious
+of the movement, I suddenly caused the apparatus
+to be stopped, whereupon I immediately felt
+and saw myself with the whole box rapidly flung round
+in rotation in the opposite direction, although I knew
+that the whole apparatus was at rest and every outward
+point of reference for the perception of motion
+was wanting. Every one who disbelieves in sensations
+of movement should be made acquainted with
+these phenomena. Had Newton known them and had
+he ever observed how we may actually imagine ourselves
+turned and displaced in space without the assistance
+of stationary bodies as points of reference, he
+would certainly have been confirmed more than ever<span class="pagenum"><a name="Page_290" id="Page_290">[Pg 290]</a></span>
+in his unfortunate speculations regarding absolute
+space.</p>
+
+<p>The sensation of rotation in the opposite direction
+after the apparatus has been stopped, slowly and gradually
+ceases. But on accidentally inclining my head
+once during this occurrence, the axis of apparent rotation
+was also observed to incline in exactly the same
+manner both as to direction and as to amount. It is
+accordingly clear that the acceleration or retardation
+of rotation is felt. The acceleration operates as a
+stimulus. The sensation, however, like almost all
+sensations, though it gradually decreases, lasts perceptibly
+longer than the stimulus. Hence the long
+continued apparent rotation after the stopping of the
+apparatus. The organ, however, which causes the
+persistence of this sensation must have its seat in the
+<i>head</i>, since otherwise the axis of apparent rotation
+could not assume the same motion as the head.</p>
+
+<p>If I were to say, now, that a light had flashed
+upon me in making these last observations, the expression
+would be a feeble one. I ought to say I experienced
+a perfect illumination. My juvenile experiences
+of vertigo occurred to me. I remembered
+Flourens's experiments relative to the section of the
+semi-circular canals of the labyrinths of doves and
+rabbits, where this inquirer had observed phenomena
+similar to vertigo, but which he preferred to interpret,
+from his bias to the acoustic theory of the labyrinth,
+as the expression of painful auditive disturbances. I<span class="pagenum"><a name="Page_291" id="Page_291">[Pg 291]</a></span>
+saw that Goltz had nearly but not quite hit the bull's
+eye with his theory of the semi-circular canals. This
+inquirer, who, from his happy habit of following his
+own natural thoughts without regard for tradition,
+has cleared up so much in science, spoke, as early as
+1870, on the ground of experiments, as follows: "It
+is uncertain whether the semi-circular canals are auditive
+organs or not. In any event they form an apparatus
+which serves for the preservation of equilibrium.
+They are, so to speak, the sense-organs of equilibrium
+of the head and indirectly of the whole body." I
+remembered the galvanic dizziness which had been
+observed by Ritter and Purkinje on the passage of a
+current through the head, when the persons experimented
+upon imagined they were falling towards the
+cathode. The experiment was immediately repeated,
+and sometime later (1874) I was enabled to demonstrate
+the same objectively with fishes, all of which
+placed themselves sidewise and in the same direction
+in the field of the current as if at command.<a name="FNanchor_98_98" id="FNanchor_98_98"></a><a href="#Footnote_98_98" class="fnanchor">[98]</a> Müller's
+doctrine of specific energies now appeared to me
+to bring all these new and old observations into a simple,
+connected unity.</p>
+
+<div class="figcenter" style="width: 600px;">
+<img src="images/i_302.jpg" width="600" height="406" alt="" />
+<span class="caption">Fig. 47.</span>
+</div>
+
+<p>The labyrinth of a dove (stereoscopically reproduced), from R. Ewald,
+<i>Nervus Octavus</i>, Wiesbaden, Bergmann, 1892.]</p>
+
+<p>Let us picture to ourselves the labyrinth of the
+ear with its three semi-circular canals lying in three
+mutually perpendicular planes (Comp. Fig. 47), the<span class="pagenum"><a name="Page_292" id="Page_292">[Pg 292]</a></span>
+mysterious position of which inquirers have endeavored
+to explain in every possible and impossible way.
+Let us conceive the nerves of the ampullæ, or the dilated
+extensions of the semi-circular canals, equipped
+with a capacity for responding to every imaginable
+stimulus with a sensation of rotation just as the nerves
+of the retina of the eye when excited by pressures,
+by electrical or chemical stimuli always respond with
+the sensation of light; let us picture to ourselves,
+further, that the usual excitation of the ampullæ
+nerves is produced by the inertia of the contents of
+the semi-circular canals, which contents on suitable
+rotations in the plane of the semi-circular canal are
+left behind in the motion, or at least have a tendency<span class="pagenum"><a name="Page_293" id="Page_293">[Pg 293]</a></span>
+to remain behind and consequently exert a pressure.
+It will be seen that on this supposition all the single
+facts which without the theory appear as so many
+different individual phenomena, become from this single
+point of view clear and intelligible.</p>
+
+<p>I had the satisfaction, immediately after the communication
+in which I set forth this idea,<a name="FNanchor_99_99" id="FNanchor_99_99"></a><a href="#Footnote_99_99" class="fnanchor">[99]</a> of seeing a
+paper by Breuer appear<a name="FNanchor_100_100" id="FNanchor_100_100"></a><a href="#Footnote_100_100" class="fnanchor">[100]</a> in which this author had
+arrived by entirely different methods at results that
+agreed in all essential points with my own. A few
+weeks later appeared the researches of Crum Brown
+of Edinburgh, whose methods were even still nearer
+mine. Breuer's paper was far richer in physiological
+respects than mine, and he had particularly gone
+into greater detail in his investigation of the collateral
+effects of the reflex motions and orientation of
+the eyes in the phenomena under consideration.<a name="FNanchor_101_101" id="FNanchor_101_101"></a><a href="#Footnote_101_101" class="fnanchor">[101]</a> In
+addition certain experiments which I had suggested in
+my paper as a test of the correctness of the view
+in question had already been performed by Breuer.
+Breuer has also rendered services of the highest order
+in the further elaboration of this field. But in a
+physical regard, my paper was, of course, more complete.</p>
+
+<p>In order to portray to the eye the behavior of the
+semi-circular canals, I have constructed here a little<span class="pagenum"><a name="Page_294" id="Page_294">[Pg 294]</a></span>
+apparatus. (See Fig. 48.) The large rotatable disc
+represents the osseous semi-circular canal, which is
+continuous with the bones of the head; the small disc,
+which is free to rotate on the axis of the first, represents
+the mobile and partly liquid contents of the semi-circular
+canal. On rotating the large disc, the small
+disc as you see remains
+behind. I
+have to turn some
+time before the
+small disc is carried
+along with the large
+one by friction. But
+if I now stop the
+large disc the small
+disc as you see continues
+to rotate.</p>
+
+<div class="figcenter" style="width: 350px;">
+<img src="images/i_304.jpg" width="350" height="497" alt="" />
+<span class="caption">Fig. 48.</span>
+</div>
+
+<p>Model representing the action of the semi-circular
+canals.]</p>
+
+<p>Simply assume
+now that the rotation
+of the small
+disc, say in the direction
+of the hands
+of a watch, would
+give rise to a sensation of rotation in the opposite
+direction, and conversely, and you already understand
+a good portion of the facts above set forth.
+The explanation still holds, even if the small disc
+does not perform appreciable rotations but is checked
+by a contrivance similar to an elastic spring, the tension<span class="pagenum"><a name="Page_295" id="Page_295">[Pg 295]</a></span>
+of which disengages a sensation. Conceive, now,
+three such contrivances with their mutually perpendicular
+planes of rotation joined together so as to
+form a single apparatus; then to this apparatus as a
+whole, no rotation can be imparted without its being
+indicated by the small mobile discs or by the springs
+which are attached to them. Conceive both the right
+and the left ear equipped with such an apparatus, and
+you will find that it answers all the purposes of the
+semi-circular canals, which you see represented stereoscopically
+in Fig. 47 for the ear of a dove.</p>
+
+<p>Of the many experiments which I have made on
+my own person, and the results of which could be
+predicted by the new view according to the behavior
+of the model and consequently according to the rules
+of mechanics, I shall cite but one. I fasten a horizontal
+board in the frame <i>RR</i> of my rotatory apparatus,
+lie down upon the same with my right ear upon the
+board, and cause the apparatus to be uniformly rotated.
+As soon as I no longer perceive the rotation,
+I turn around upon my left ear and immediately the
+sensation of rotation again starts up with marked vividness.
+The experiment can be repeated as often as
+one wishes. A slight turn of the head even is sufficient
+for reviving the sensation of rotation which in
+the perfectly quiescent state at once disappears altogether.</p>
+
+<p>We will imitate the experiment on the model. I
+turn the large disc until finally the small disc is carried<span class="pagenum"><a name="Page_296" id="Page_296">[Pg 296]</a></span>
+along with it. If, now, while the rotation continues
+uniform, I burn off a little thread which you
+see here, the small disc will be flipped round by a
+spring into its own plane 180°, so as now to present
+its opposite side to you, when the rotation at once begins
+in the opposite direction.</p>
+
+<p>We have consequently a very simple means for determining
+whether one is actually the subject or not
+of uniform and imperceptible rotations. If the earth
+rotated much more rapidly than it really does, or if
+our semi-circular canals were much more sensitive, a
+Nansen sleeping at the North Pole would be waked
+by a sensation of rotation every time he turned over.
+Foucault's pendulum experiment as a demonstration
+of the earth's rotation would be superfluous under
+such circumstances. The only reason we cannot prove
+the rotation of the earth with the help of our model,
+lies in the small angular velocity of the earth and in
+the consequent liability to great experimental errors.<a name="FNanchor_102_102" id="FNanchor_102_102"></a><a href="#Footnote_102_102" class="fnanchor">[102]</a></p>
+
+<p>Aristotle has said that "The sweetest of all
+things is knowledge." And he is right. But if you
+were to suppose that the <i>publication</i> of a new view
+were productive of unbounded sweetness, you would
+be mightily mistaken. No one disturbs his fellow-men
+with a new view unpunished. Nor should the fact be
+made a subject of reproach to these fellow-men. To<span class="pagenum"><a name="Page_297" id="Page_297">[Pg 297]</a></span>
+presume to revolutionise the current way of thinking
+with regard to any question, is no pleasant task, and
+above all not an easy one. They who have advanced
+new views know best what serious difficulties stand in
+their way. With honest and praiseworthy zeal, men
+set to work in search of everything that does not
+suit with them. They seek to discover whether they
+cannot explain the facts better or as well, or approximately
+as well, by the traditional views. And that,
+too, is justified. But at times some extremely artless
+animadversions are heard that almost nonplus us.
+"If a sixth sense existed it could not fail to have
+been discovered thousands of years ago." Indeed;
+there was a time, then, when only seven planets could
+have existed! But I do not believe that any one will
+lay any weight on the philological question whether
+the set of phenomena which we have been considering
+should be called a sense. The phenomena will not
+disappear when the name disappears. It was further
+said to me that animals exist which have no labyrinth,
+but which can yet orientate themselves, and that consequently
+the labyrinth has nothing to do with orientation.
+We do not walk forsooth with our legs, because
+snakes propel themselves without them!</p>
+
+<p>But if the promulgator of a new idea cannot hope
+for any great pleasure from its publication, yet the
+critical process which his views undergo is extremely
+helpful to the subject-matter of them. All the defects
+which necessarily adhere to the new view are gradually<span class="pagenum"><a name="Page_298" id="Page_298">[Pg 298]</a></span>
+discovered and eliminated. Over-rating and exaggeration
+give way to more sober estimates. And
+so it came about that it was found unpermissible to
+attribute all functions of orientation exclusively to the
+labyrinth. In these critical labors Delage, Aubert,
+Breuer, Ewald, and others have rendered distinguished
+services. It can also not fail to happen that
+fresh facts become known in this process which could
+have been predicted by the new view, which actually
+were predicted in part, and which consequently furnish
+a support for the new view. Breuer and Ewald
+succeeded in electrically and mechanically exciting
+the labyrinth, and even single parts of the labyrinth,
+and thus in producing the movements that belong to
+such stimuli. It was shown that when the semi-circular
+canals were absent vertigo could not be produced,
+when the entire labyrinth was removed the orientation
+of the head was no longer possible, that without
+the labyrinth galvanic vertigo could not be induced. I
+myself constructed as early as 1875 an apparatus for
+observing animals in rotation, which was subsequently
+reinvented in various forms and has since received the
+name of "cyclostat."<a name="FNanchor_103_103" id="FNanchor_103_103"></a><a href="#Footnote_103_103" class="fnanchor">[103]</a> In experiments with the most
+varied kinds of animals it was shown that, for example,
+the larvæ of frogs are not subject to vertigo until
+their semi-circular canals which at the start are wanting
+are developed (K. Schäfer). A large percentage
+of the deaf and dumb are afflicted with grave affections<span class="pagenum"><a name="Page_299" id="Page_299">[Pg 299]</a></span>
+of the labyrinth. The American psychologist,
+William James, has made whirling experiments with
+many deaf and dumb subjects, and in a large number
+of them found that susceptibility to giddiness is wanting.
+He also found that many deaf and dumb people
+on being ducked under water, whereby they lose their
+weight and consequently have no longer the full assistance
+of their muscular sense, utterly lose their
+sense of position in space, do not know which is up
+and which is down, and are thrown into the greatest
+consternation,&mdash;results which do not occur in normal
+men. Such facts are convincing proof that we do not
+orientate ourselves entirely by means of the labyrinth,
+important as it is for us. Dr. Kreidl has made experiments
+similar to those of James and found that
+not only is vertigo absent in deaf and dumb people
+when whirled about, but that also the reflex movements
+of the eyes which are normally induced by the
+labyrinth are wanting. Finally, Dr. Pollak has found
+that galvanic vertigo does not exist in a large percentage
+of the deaf and dumb. Neither the jerking
+movements nor the uniform movements of the eyes
+were observed which normal human beings exhibit in
+the Ritter and Purkinje experiment.</p>
+
+<p>After the physicist has arrived at the idea that the
+semi-circular canals are the organ of sensation of rotation
+or of angular acceleration, he is next constrained
+to ask for the organs that mediate the sensation
+of acceleration noticed in forward movements.<span class="pagenum"><a name="Page_300" id="Page_300">[Pg 300]</a></span>
+In searching for an organ for this function, he of
+course is not apt to select one that stands in no anatomical
+and spatial relation with the semi-circular
+canals. And in addition there are physiological considerations
+to be weighed. The preconceived opinion
+once having been abandoned that the <i>entire</i> labyrinth
+is auditory in its function, there remains after the
+cochlea is reserved for sensations of tone and the
+semi-circular canals for the sensation of angular acceleration,
+the vestibule for the discharge of additional
+functions. The vestibule, particularly the part of it
+known as the sacculus, appeared to me, by reason of
+the so-called otoliths which it contains, eminently
+adapted for being the organ of sensation of forward
+acceleration or of the position of the head. In this
+conjecture I again closely coincided with Breuer.</p>
+
+<p>That a sensation of position, of direction and
+amount of mass-acceleration exists, our experience in
+elevators as well as of movement in curved paths is
+sufficient proof. I have also attempted to produce and
+destroy suddenly great velocities of forward movement
+by means of various contrivances of which I
+shall mention only one here. If, while enclosed in
+the paper box of my large whirling apparatus at some
+distance from the axis, my body is in uniform rotation
+which I no longer feel, and I then loosen the connexions
+of the frame <i>rr</i> with <i>R</i> thus making the former
+moveable and I then suddenly stop the larger frame,
+my forward motion is abruptly impeded while the<span class="pagenum"><a name="Page_301" id="Page_301">[Pg 301]</a></span>
+frame <i>rr</i> continues to rotate. I imagine now that I
+am speeding on in a straight line in a direction opposite
+to that of the checked motion. Unfortunately, for
+many reasons it cannot be proved convincingly that
+the organ in question has its seat in the head. According
+to the opinion of Delage, the labyrinth has
+nothing to do with this particular sensation of movement.
+Breuer, on the other hand, is of the opinion
+that the organ of forward movement in man is stunted
+and the persistence of the sensation in question is too
+brief to permit our instituting experiments as obvious
+as in the case of rotation. In fact, Crum Brown once
+observed while in an irritated condition peculiar vertical
+phenomena in his own person, which were all
+satisfactorily explained by an abnormally long persistence
+of the sensation of rotation, and I myself in an
+analogous case on the stopping of a railway train felt
+the apparent backward motion in striking intensity
+and for an unusual length of time.</p>
+
+<p>There is no doubt whatever that we feel changes
+of vertical acceleration, and it will appear from the
+following extremely probable that the otoliths of the
+vestibule are the sense-organ for the <i>direction</i> of the
+mass-acceleration. It will then be incompatible with
+a really logical view to regard the latter as incapable
+of sensing horizontal accelerations.</p>
+
+<p>In the lower animals the analogue of the labyrinth
+is shrunk to a little vesicle filled with a liquid and
+containing tiny crystals, auditive stones, or otoliths, of<span class="pagenum"><a name="Page_302" id="Page_302">[Pg 302]</a></span>
+greater specific gravity, suspended on minute hairs.
+These crystals appear physically well adapted for indicating
+both the direction of gravity and the direction
+of incipient movements. That they discharge the former
+function, Delage was the first to convince himself
+by experiments with lower animals which on the removal
+of the otoliths utterly lost their bearings and
+could no longer regain their normal position. Loeb
+also found that fishes without labyrinths swim now on
+their bellies and now on their backs. But the most
+remarkable, most beautiful, and most convincing experiment
+is that which Dr. Kreidl instituted with
+crustaceans. According to Hensen, certain Crustacea
+on sloughing spontaneously introduce fine grains of
+sand as auditive stones into their otolith vesicle. At
+the ingenious suggestion of S. Exner, Dr. Kreidl constrained
+some of these animals to put up with iron
+filings (<i>ferrum limatum</i>). If the pole of an electro-magnet
+be brought near the animal, it will at once
+turn its back away from the pole accompanying the
+movement with appropriate reflex motions of the eye
+the moment the current is closed, exactly as if gravity
+had been brought to bear upon the animal in the
+same direction as the magnetic force.<a name="FNanchor_104_104" id="FNanchor_104_104"></a><a href="#Footnote_104_104" class="fnanchor">[104]</a> This, in fact,
+is what should be expected from the function ascribed
+to the otoliths. If the eyes be covered with asphalt<span class="pagenum"><a name="Page_303" id="Page_303">[Pg 303]</a></span>
+varnish, and the auditive sacs removed, the crustaceans
+lose their sense of direction utterly, tumble
+head over heels, lie on their side or their back indifferently.
+This does not happen when the eyes only
+are covered. For vertebrates, Breuer has demonstrated
+by searching investigations that the otoliths,
+or better, statoliths, slide in three planes parallel to
+the planes of the semi-circular canals, and are consequently
+perfectly adapted for indicating changes
+both in the amount and the direction of the mass-acceleration.<a name="FNanchor_105_105" id="FNanchor_105_105"></a><a href="#Footnote_105_105" class="fnanchor">[105]</a></p>
+
+<p>I have already remarked that not every function
+of orientation can be ascribed exclusively to the labyrinth.
+The deaf and dumb who have to be immersed
+in water, and the crustaceans who must have their
+eyes closed if they are to be perfectly disorientated, are
+proof of this fact. I saw a blind cat at Hering's laboratory
+which to one who was not a very attentive observer
+behaved exactly like a seeing cat. It played
+nimbly with objects rolling on the floor, stuck its head
+inquisitively into open drawers, sprang dexterously
+upon chairs, ran with perfect accuracy through open<span class="pagenum"><a name="Page_304" id="Page_304">[Pg 304]</a></span>
+doors, and never bumped against closed ones. The
+visual sense had here been rapidly replaced by the
+tactual and auditive senses. And it appears from
+Ewald's investigations that even after the labyrinths
+have been removed, animals gradually learn to move
+about again quite in the normal fashion, presumably
+because the eliminated function of the labyrinth is
+now performed by some part of the brain. A certain
+peculiar weakness of the muscles alone is perceptible
+which Ewald ascribes to the absence of the stimulus
+which is otherwise constantly emitted by the labyrinth
+(the labyrinth-tonus). But if the part of the
+brain which discharges the deputed function be removed,
+the animals are again completely disorientated
+and absolutely helpless.</p>
+
+<p>It may be said that the views enunciated by Breuer,
+Crum Brown and myself in 1873 and 1874, and which
+are substantially a fuller and richer development of
+Goltz's idea, have upon the whole been substantiated.
+At least they have exercised a helpful and stimulative
+influence. New problems have of course arisen in the
+course of the investigation which still await solution,
+and much work remains to be done. At the same
+time we see how fruitful the renewed co-operation of
+the various special departments of science may become
+after a period of isolation and invigorating labor
+apart.</p>
+
+<p>I may be permitted, therefore, to consider the relation
+between hearing and orientation from another<span class="pagenum"><a name="Page_305" id="Page_305">[Pg 305]</a></span>
+and more general point of view. What we call the
+auditive organ is in the lower animals simply a sac
+containing auditive stones. As we ascend the scale,
+1, 2, 3 semi-circular canals gradually develop from
+them, whilst the structure of the otolith organ itself
+becomes more complicated. Finally, in the higher
+vertebrates, and particularly in the mammals, a part
+of the latter organ (the lagena) becomes the cochlea,
+which Helmholtz explained as the organ for sensations
+of tone. In the belief that the entire labyrinth
+was an auditive organ, Helmholtz, contrary to the results
+of his own masterly analysis, originally sought
+to interpret another part of the labyrinth as the organ
+of noises. I showed a long time ago (1873) that every
+tonal stimulus by shortening the duration of the excitation
+to a few vibrations, gradually loses its character
+of pitch and takes on that of a sharp, dry report or
+noise.<a name="FNanchor_106_106" id="FNanchor_106_106"></a><a href="#Footnote_106_106" class="fnanchor">[106]</a> All the intervening stages between tones and
+noises can be exhibited. Such being the case, it will
+hardly be assumed that one organ is suddenly and at
+some given point replaced in function by another. On
+the basis of different experiments and reasonings S.
+Exner also regards the assumption of a special organ
+for the sensing of noises as unnecessary.</p>
+
+<p>If we will but reflect how small a portion of the
+labyrinth of higher animals is apparently in the service
+of the sense of hearing, and how large, on the other<span class="pagenum"><a name="Page_306" id="Page_306">[Pg 306]</a></span>
+hand, the portion is which very likely serves the purposes
+of orientation, how much the first anatomical
+beginnings of the auditive sac of lower animals resemble
+that part of the fully developed labyrinth which
+does not hear, the view is irresistibly suggested which
+Breuer and I (1874, 1875) expressed, that the auditive
+organ took its development from an organ for sensing
+movements by adaptation to weak periodic motional
+stimuli, and that many apparatuses in the lower animals
+which are held to be organs of hearing are not
+auditive organs at all.<a name="FNanchor_107_107" id="FNanchor_107_107"></a><a href="#Footnote_107_107" class="fnanchor">[107]</a></p>
+
+<p>This view appears to be perceptibly gaining
+ground. Dr. Kreidl by skilfully-planned experiments
+has arrived at the conclusion that even fishes do not
+hear, whereas E. H. Weber, in his day, regarded the
+ossicles which unite the air-bladder of fishes with the
+labyrinth as organs expressly designed for conducting
+sound from the former to the latter.<a name="FNanchor_108_108" id="FNanchor_108_108"></a><a href="#Footnote_108_108" class="fnanchor">[108]</a> Störensen has
+investigated the excitation of sounds by the air-bladder
+of fishes, as also the conduction of shocks through
+Weber's ossicles. He regards the air-bladder as particularly
+adapted for receiving the noises made by
+other fishes and conducting them to the labyrinth.
+He has heard the loud grunting tones of the fishes
+in South American rivers, and is of the opinion that
+they allure and find each other in this manner. According
+to these views certain fishes are neither deaf
+nor dumb.<a name="FNanchor_109_109" id="FNanchor_109_109"></a><a href="#Footnote_109_109" class="fnanchor">[109]</a> The question here involved might be
+solved perhaps by sharply distinguishing between the
+sensation of hearing proper, and the perception of
+shocks. The first-mentioned sensation may, even in
+the case of many vertebrates, be extremely restricted,
+or perhaps even absolutely wanting. But besides the
+auditive function, Weber's ossicles may perfectly well
+discharge some other function. Although, as Moreau
+has shown, the air-bladder itself is not an organ of
+equilibrium in the simple physical sense of Borelli,
+yet doubtless some function of this character is still
+reserved for it. The union with the labyrinth favors
+this conception, and so a host of new problems rises
+here before us.</p>
+<p><span class="pagenum"><a name="Page_307" id="Page_307">[Pg 307]</a></span></p>
+<p>I should like to close with a reminiscence from the
+year 1863. Helmholtz's <i>Sensations of Tone</i> had just
+been published and the function of the cochlea now
+appeared clear to the whole world. In a private conversation
+which I had with a physician, the latter declared
+it to be an almost hopeless undertaking to seek
+to fathom the function of the other parts of the labyrinth,
+whereas I in youthful boldness maintained that
+the question could hardly fail to be solved, and that
+very soon, although of course I had then no glimmering
+of how it was to be done. Ten years later the
+question was substantially solved.</p>
+
+<p>To-day, after having tried my powers frequently
+and in vain on many questions, I no longer believe<span class="pagenum"><a name="Page_308" id="Page_308">[Pg 308]</a></span>
+that we can make short work of the problems of science.
+Nevertheless, I should not consider an "ignorabimus"
+as an expression of modesty, but rather as
+the opposite. That expression is a suitable one only
+with regard to problems which are wrongly formulated
+and which are therefore not problems at all.
+Every real problem can and will be solved in due
+course of time without supernatural divination, entirely
+by accurate observation and close, searching
+thought.</p><hr class="chap" /><p><span class="pagenum"><a name="Page_309" id="Page_309">[Pg 309]</a></span></p>
+
+
+
+
+<h2><a name="ON_SOME_PHENOMENA_ATTENDING" id="ON_SOME_PHENOMENA_ATTENDING">ON SOME PHENOMENA ATTENDING
+THE FLIGHT OF PROJECTILES.</a><a name="FNanchor_110_110" id="FNanchor_110_110"></a><a href="#Footnote_110_110" class="fnanchor">[110]</a></h2>
+
+
+<blockquote><p>"I have led my ragamuffins where they were
+peppered."&mdash;<i>Falstaff.</i></p>
+
+<p>"He goes but to see a noise that he heard."&mdash;<i>Midsummer
+Night's Dream.</i></p></blockquote>
+
+<p>To shoot, in the shortest time possible, as many
+holes as possible in one another's bodies, and
+not always for exactly pardonable objects and ideals,
+seems to have risen to the dignity of a duty with modern
+men, who, by a singular inconsistency, and in
+subservience to a diametrically contrary ideal, are
+bound by the equally holy obligation of making these
+holes as small as possible, and, when made, of stopping
+them up and of healing them as speedily as
+possible. Since, then, shooting and all that appertains
+thereto, is a very important, if not the most important,
+affair of modern life, you will doubtless not be averse
+to giving your attention for an hour to some experiments
+which have been undertaken, not for advancing
+the ends of war, but for promoting the ends of science,<span class="pagenum"><a name="Page_310" id="Page_310">[Pg 310]</a></span>
+and which throw some light on the phenomena
+attending the flight of projectiles.</p>
+
+<p>Modern science strives to construct its picture of
+the world not from speculations but so far as possible
+from facts. It verifies its constructs by recourse to
+observation. Every newly observed fact completes
+its world-picture, and every divergence of a construct
+from observation points to some imperfection, to some
+lacuna in it. What is seen is put to the test of, and
+supplemented by, what is thought, which is again
+naught but the result of things previously seen. It
+is always peculiarly fascinating, therefore, to subject
+to direct verification by observation, that is, to render
+palpable to the senses, something which we have only
+theoretically excogitated or theoretically surmised.</p>
+
+<p>In 1881, on hearing in Paris the lecture of the Belgian
+artillerist Melsens, who hazarded the conjecture
+that projectiles travelling at a high rate of speed carry
+masses of compressed air before them which are instrumental
+in producing in bodies struck by the projectiles
+certain well-known facts of the nature of explosions,
+the desire arose in me of experimentally testing
+his conjecture and of rendering the phenomenon,
+if it really existed, perceptible. The desire was the
+stronger as I could say that all the means for realising
+it existed, and that I had in part already used and
+tested them for other purposes.</p>
+
+<p>And first let us get clear regarding the difficulties
+which have to be surmounted. Our task is that of<span class="pagenum"><a name="Page_311" id="Page_311">[Pg 311]</a></span>
+observing a bullet or other projectile which is rushing
+through space at a velocity of many hundred yards a
+second, together with the disturbances which the bullet
+causes in the surrounding atmosphere. Even the
+opaque solid body itself, the projectile, is only exceptionally
+visible under such circumstances&mdash;only when
+it is of considerable size and when we see its line of
+flight in strong perspective abridgement so that the
+velocity is apparently diminished. We see a large
+projectile quite clearly when we stand behind the cannon
+and look steadily along its line of flight or in the
+less pleasant case when the projectile is speeding towards
+us. There is, however, a very simple and effective
+method of observing swiftly moving bodies with as
+little trouble as if they were held at rest at some point
+in their path. The method is that of illumination by
+a brilliant electric spark of extremely short duration
+in a dark room. But since, for the full intellectual
+comprehension of a picture presented to the eye, a
+certain, not inconsiderable interval of time is necessary,
+the method of instantaneous photography will
+naturally also be employed. The pictures, which are
+of extremely minute duration, are thus permanently
+recorded and can be examined and analysed at one's
+convenience and leisure.</p>
+
+<p>With the difficulty just mentioned is associated
+still another and greater difficulty which is due to the
+air. The atmosphere in its usual condition is generally
+not visible even when at rest. But the task presented<span class="pagenum"><a name="Page_312" id="Page_312">[Pg 312]</a></span>
+to us is to render visible masses of air which
+in addition are moving with a high velocity.</p>
+
+<p>To be visible, a body must either emit light itself,
+must shine, or must affect in some way the light which
+falls upon it, must take up that light entirely or partly,
+absorb it, or must have a deflective effect upon it, that
+is, reflect or refract it. We cannot see the air as we
+can a flame, for it shines only exceptionally, as in a
+Geissler's tube. The atmosphere is extremely transparent
+and colorless; it cannot be seen, therefore, as
+a dark or colored body can, or as chlorine gas can,
+or vapor of bromine or iodine. Air, finally, has so
+small an index of refraction and so small a deflective
+influence upon light, that the refractive effect is commonly
+imperceptible altogether.</p>
+
+<p>A glass rod is visible in air or in water, but it is
+almost invisible in a mixture of benzol and bisulphuret
+of carbon, which has the same mean index of refraction
+as the glass. Powdered glass in the same mixture
+has a vivid coloring, because owing to the decomposition
+of the colors the indices are the same
+for only one color which traverses the mixture unimpeded,
+whilst the other colors undergo repeated reflexions.<a name="FNanchor_111_111" id="FNanchor_111_111"></a><a href="#Footnote_111_111" class="fnanchor">[111]</a></p>
+
+<p>Water is invisible in water, alcohol in alcohol. But
+if alcohol be mixed with water the flocculent streaks
+of the alcohol in the water will be seen at once and<span class="pagenum"><a name="Page_313" id="Page_313">[Pg 313]</a></span>
+<i>vice versa</i>. And in like manner the air, too, under
+favorable circumstances, may be seen. Over a roof
+heated by the burning sun, a tremulous wavering of
+objects is noticeable, as there is also over red-hot
+stoves, radiators, and registers. In all these cases
+tiny flocculent masses of hot and cold air, of slightly
+differing refrangibility, are mingled together.</p>
+
+<p>In like manner the more highly refracting parts of
+non-homogeneous masses of glass, the so-called striæ
+or imperfections of the glass, are readily detectible
+among the less refracting parts which constitute the
+bulk of the same. Such glasses are unserviceable for
+optical purposes, and special attention has been devoted
+to the investigation of the methods for eliminating
+or avoiding these defects. The result has been
+the development of an extremely delicate method for
+detecting optical faults&mdash;the so-called method of Foucault
+and Toepler&mdash;which is suitable also for our
+present purpose.</p>
+
+<div class="figcenter" style="width: 600px;">
+<img src="images/i_324.jpg" width="600" height="169" alt="" />
+<span class="caption">Fig. 49.</span>
+</div>
+
+<p>Even Huygens when trying to detect the presence
+of striæ in polished glasses viewed them under oblique
+illumination, usually at a considerable distance, so as
+to give full scope to the aberrations, and had recourse
+for greater exactitude to a telescope. But the method
+was carried to its highest pitch of perfection in 1867
+by Toepler who employed the following procedure:
+A small luminous source <i>a</i> (Fig. 49) illuminates a lens
+<i>L</i> which throws an image <i>b</i> of the luminous source.
+If the eye be so placed that the image falls on the<span class="pagenum"><a name="Page_314" id="Page_314">[Pg 314]</a></span>
+pupil, the entire lens, if perfect, will appear equally
+illuminated, for the reason that all points of it send
+out rays to the eye. Coarse imperfections of form or
+of homogeneity are rendered visible only in case the
+aberrations are so large that the light from many spots
+passes by the pupil of the eye. But if the image <i>b</i> be
+partly intercepted by the edge of a small slide, then
+those spots in the lens as thus partly darkened will
+appear brighter whose light by its greater aberrations
+still reaches the eye in spite of the intercepting slide,
+while those spots will appear darker which in consequence
+of aberration in the other direction throw their
+light entirely upon the slide. This artifice of the intercepting
+slide which had previously been employed
+by Foucault for the investigation of the optical imperfections
+of mirrors enhances enormously the delicacy
+of the method, which is still further augmented by
+Toepler's employment of a telescope behind the slide.
+Toepler's method, accordingly, enjoys all the advantages
+of the Huygens and the Foucault procedure
+combined. It is so delicate that the minutest irregularities
+in the air surrounding the lens can be rendered
+distinctly visible, as I shall show by an example. I<span class="pagenum"><a name="Page_315" id="Page_315">[Pg 315]</a></span>
+place a candle before the lens <i>L</i> (Fig. 50) and so arrange
+a second lens <i>M</i> that the flame of the candle is
+imaged upon the screen <i>S</i>. As soon as the intercepting
+slide is pushed into the focus, <i>b</i>, of the light issuing
+from <i>a</i>, you see the images of the changes of
+density and the images of the movements induced in
+the air by the flame quite distinctly upon the screen.
+The distinctness of the phenomenon as a whole depends
+upon the position of the intercepting slide <i>b</i>.
+The removal of <i>b</i> increases the illumination but decreases
+the distinctness. If the luminous source <i>a</i> be
+removed, we see the image of the candle flame only
+upon the screen <i>S</i>. If we remove the flame and allow
+<i>a</i> to continue shining, the screen <i>S</i> will appear uniformly
+illuminated.</p>
+
+<div class="figcenter" style="width: 700px;">
+<img src="images/i_325.jpg" width="700" height="265" alt="" />
+<span class="caption">Fig. 50.</span>
+</div>
+
+<p>After Toepler had sought long and in vain to render
+the irregularities produced in air by sound-waves
+visible by this principle, he was at last conducted to
+his goal by the favorable circumstances attending the
+production of electric sparks. The waves generated
+in the air by electric sparks and accompanying the
+explosive snapping of the same, are of sufficiently<span class="pagenum"><a name="Page_316" id="Page_316">[Pg 316]</a></span>
+short period and sufficiently powerful to be rendered
+visible by these methods. Thus we see how by a
+careful regard for the merest and most shadowy indications
+of a phenomenon and by slight progressive
+and appropriate alterations of the circumstances and
+the methods, ultimately the most astounding results
+can be attained. Consider, for example, two such
+phenomena as the rubbing of amber and the electric
+lighting of modern streets. A person ignorant of the
+myriad minute links that join these two things together,
+will be absolutely nonplussed at their connexion,
+and will comprehend it no more than the ordinary
+observer who is unacquainted with embryology, anatomy,
+and paleontology will understand the connexion
+between a saurian and a bird. The high value and
+significance of the co-operation of inquirers through
+centuries, where each has but to take up the thread of
+work of his predecessors and spin it onwards, is rendered
+forcibly evident by such examples. And such
+knowledge destroys, too, in the clearest manner imaginable
+that impression of the marvellous which the
+spectator may receive from science, and at the same
+time is a most salutary admonishment to the worker
+in science against superciliousness. I have also to
+add the sobering remark that all our art would be in
+vain did not nature herself afford at least some slight
+guiding threads leading from a hidden phenomenon
+into the domain of the observable. And so it need
+not surprise us that once under particularly favorable<span class="pagenum"><a name="Page_317" id="Page_317">[Pg 317]</a></span>
+circumstances an extremely powerful sound-wave
+which had been caused by the explosion of several
+hundred pounds of dynamite threw a directly visible
+shadow in the sunlight, as Boys has recently told us.
+If the sound-waves were absolutely without influence
+upon the light, this could not have occurred, and all
+our artifices would then, too, be in vain. And so,
+similarly, the phenomenon accompanying projectiles
+which I am about to show you was once in a very imperfect
+manner incidentally seen by a French artillerist,
+Journée, while that observer was simply following
+the line of flight of a projectile with a telescope, just
+as also the undulations produced by candle flames are
+in a weak degree directly visible and in the bright sunlight
+are imaged in shadowy waves upon a uniform
+white background.</p>
+
+<p><i>Instantaneous illumination</i> by the electric spark,
+the method of rendering visible small optical differences
+or striæ, which may hence be called the <i>striate</i>,
+or <i>differential</i>, method,<a name="FNanchor_112_112" id="FNanchor_112_112"></a><a href="#Footnote_112_112" class="fnanchor">[112]</a> invented by Foucault and
+Toepler, and finally the <i>recording</i> of the image by a <i>photographic</i>
+plate,&mdash;these therefore are the chief means
+which are to lead us to our goal.</p>
+<p><span class="pagenum"><a name="Page_318" id="Page_318">[Pg 318]</a></span></p>
+<p>I instituted my first experiments in the summer of
+1884 with a target-pistol, shooting the bullet through
+a striate field as described above, and taking care that
+the projectile whilst in the field should disengage an
+illuminating electric spark from a Leyden jar or Franklin's
+pane, which spark produced a photographic impression
+of the projectile upon a plate, especially arranged
+for the purpose. I obtained the image of the
+projectile at once and without difficulty. I also readily
+obtained, with the still rather defective dry plate which
+I was using, exceedingly delicate images of the sound-waves
+(spark-waves). But no atmospheric condensation
+produced by the projectile was visible. I now
+determined the velocity of my projectile and found it
+to be only 240 metres per second, or considerably less
+than the velocity of sound (which is 340 metres per
+second). I saw immediately that under such circumstances
+no noticeable compression of the air could be
+produced, for any atmospheric compression must of
+necessity travel forward at the same speed with sound
+(340 metres per second) and consequently would be
+always ahead of and speeding away from the projectile.</p>
+
+<p>I was so thoroughly convinced, however, of the
+existence of the supposed phenomenon at a velocity
+exceeding 340 metres per second, that I requested<span class="pagenum"><a name="Page_319" id="Page_319">[Pg 319]</a></span>
+Professor Salcher, of Fiume, an Austrian port on the
+Gulf of Quarnero, to undertake the experiment with
+projectiles travelling at a high rate of speed. In the
+summer of 1886 Salcher in conjunction with Professor
+Riegler conducted in a spacious and suitable apartment
+placed at their disposal by the Directors of the
+Royal Imperial Naval Academy, experiments of the
+kind indicated and conforming in method exactly to
+those which I had instituted, with the precise results
+expected. The phenomenon, in fact, accorded perfectly
+with the <i>a priori</i> sketch of it which I had drafted
+previously to the experiment. As the experimenting
+was continued, new and unforeseen features made their
+appearance.</p>
+
+<p>It would be unfair, of course, to expect from the
+very first experiments faultless and highly distinct photographs.
+It was sufficient that success was secured
+and that I had convinced myself that further labor
+and expenditure would not be vain. And on this
+score I am greatly indebted to the two gentlemen
+above mentioned.</p>
+
+<p>The Austrian Naval Department subsequently
+placed a cannon at Salcher's disposal in Pola, an
+Adriatic seaport, and I myself, together with my son,
+then a student of medicine, having received and accepted
+a courteous invitation from Krupp, repaired to
+Meppen, a town in Hanover, where we conducted
+with only the necessary apparatus several experiments
+on the open artillery range. All these experiments<span class="pagenum"><a name="Page_320" id="Page_320">[Pg 320]</a></span>
+furnished tolerably good and complete pictures. Some
+little progress, too, was made. The outcome of our
+experience on both artillery ranges, however, was the
+settled conviction that really good results could be
+obtained only by the most careful conduct of the experiments
+in a laboratory especially adapted to the
+purpose. The expensiveness of the experiments on
+a large scale was not the determining consideration
+here, for the size of the projectile is indifferent. Given
+the same velocity and the results are quite similar,
+whether the projectiles are large or small. On the
+other hand, in a laboratory the experimenter has perfect
+control over the initial velocity, which, provided
+the proper equipment is at hand, can be altered at
+will simply by altering the charge and the weight of
+the projectile. The requisite experiments were accordingly
+conducted by me in my laboratory at Prague,
+partly in conjunction with my son and partly afterwards
+by him alone. The latter are the most perfect
+and I shall accordingly speak in detail here of
+these only.</p>
+
+<div class="figcenter" style="width: 600px;">
+<img src="images/i_331.jpg" width="600" height="341" alt="" />
+<span class="caption">Fig. 51.</span>
+</div>
+
+<p>Picture to yourself an apparatus for detecting optical
+striæ set up in a dark room. In order not to
+make the description too complicated, I shall give the
+essential features only of the apparatus, leaving out
+of account altogether the minuter details which are
+rather of consequence for the technical performance
+of the experiment than for its understanding. We
+suppose the projectile speeding on its path, accordingly,<span class="pagenum"><a name="Page_321" id="Page_321">[Pg 321]</a></span>
+through the field of our differential optical apparatus.
+On reaching the centre of the field (Fig. 51)
+the projectile disengages an illuminating electric spark
+<i>a</i>, and the image of the projectile, so produced, is photographically
+impressed upon the plate of the camera
+behind the intercepting slide <i>b</i>. In the last and
+best experiments the lens <i>L</i> was replaced by a spherical
+silvered-glass mirror made by K. Fritsch (formerly
+Prokesch) of Vienna, whereby the apparatus was
+naturally more complicated than it appears in our diagram.
+The projectile having been carefully aimed
+passes in crossing the differential field between two
+vertical isolated wires which are connected with the
+two coatings of a Leyden jar, and completely filling
+the space between the wires discharges the jar. In
+the axis of the differential apparatus the circuit has a
+second gap <i>a</i> which furnishes the illuminating spark,
+the image of which falls on the intercepting slide <i>b</i>.
+The wires in the differential field having occasioned<span class="pagenum"><a name="Page_322" id="Page_322">[Pg 322]</a></span>
+manifold disturbances were subsequently done away
+with. In the new arrangement the projectile passes
+through a ring (see dotted line, Fig. 51), to the air in
+which it imparts a sharp impulse which travels forward
+in the tube <i>r</i> as a sound-wave having the approximate
+velocity of 340 metres per second, topples
+over through the aperture of an electric screen the
+flame of a candle situated at the other opening of the
+tube, and so discharges the jar. The length of the
+tube <i>r</i> is so adjusted that the discharge occurs the
+moment the projectile enters the centre of the now
+fully clear and free field of vision. We will also leave
+out of account the fact that to secure fully the success
+of the experiment, a large jar is first discharged
+by the flame, and that by the agency of this first discharge
+the discharge of a second small jar having a
+spark of very short period which furnishes the spark
+really illuminating the projectile is effected. Sparks
+from large jars have an appreciable duration, and
+owing to the great velocity of the projectiles furnish
+blurred photographs only. By carefully husbanding
+the light of the differential apparatus, and owing to
+the fact that much more light reaches the photographic
+plate in this way than would otherwise reach
+it, we can obtain beautiful, strong, and sharp photographs
+with incredibly small sparks. The contours of
+the pictures appear as very delicate and very sharp,
+closely adjacent double lines. From their distance
+from one another, and from the velocity of the projectile,<span class="pagenum"><a name="Page_323" id="Page_323">[Pg 323]</a></span>
+the duration of the illumination, or of the spark,
+is found to be 1/800000 of a second. It is evident,
+therefore, that experiments with mechanical snap
+slides can furnish no results worthy of the name.</p>
+
+<div class="figcenter" style="width: 400px;">
+<img src="images/i_333.jpg" width="400" height="517" alt="" />
+<span class="caption">Fig. 52.</span>
+</div>
+
+<p>Let us consider now first the picture of a projectile
+in the rough, as represented in Figure 52, and
+then let us examine it in its photographic form as seen
+in Figure 53. The latter picture is of a shot from an
+Austrian Mannlicher rifle. If I were not to tell you
+what the picture represented you would very likely
+imagine it to be a bird's eye view of a boat <i>b</i> moving
+swiftly through the water. In front you see the bow-wave
+and behind the body a phenomenon <i>k</i> which
+closely resembles the eddies formed in the wake of a<span class="pagenum"><a name="Page_324" id="Page_324">[Pg 324]</a></span>
+ship. And as a matter of fact the dark hyperboloid
+arc which streams from the tip of the projectile really
+is a compressed wave of air exactly analogous to the
+bow-wave produced by a ship moving through the
+water, with the exception that the wave of air is not
+a surface-wave. The air-wave is produced in atmospheric
+space and encompasses the projectile in the
+form of a shell on all sides. The wave is visible for
+the same reason that the heated shell of air surrounding
+the candle flame of our former experiments is visible.
+And the cylinder of friction-heated air which the
+projectile throws off in the form of vortex rings really
+does answer to the water in the wake of a vessel.</p>
+
+<div class="figleft" style="width: 300px;">
+<img src="images/i_334.jpg" width="300" height="363" alt="" />
+<span class="caption">Fig. 53. Photograph of a blunted projectile.]</span>
+</div>
+
+<p><span class="pagenum"><a name="Page_325" id="Page_325">[Pg 325]</a></span></p>
+
+<p>Now just as a slowly moving boat produces no
+bow-wave, but the bow-wave is seen only when the
+boat moves with a speed which is greater than the
+velocity of propagation of surface-waves in water, so,
+in like manner, no wave of compression is visible in
+front of a projectile so long as the speed of the projectile
+is less than the velocity of sound. But if the
+speed of the projectile reaches and exceeds the velocity
+of sound, then the head-wave, as we shall call it,
+augments noticeably in power, and is more and more
+extended, that is, the angle made by the contours of
+the wave with the direction of flight is more and more
+diminished, just as when the speed of a boat is increased
+a similar phenomenon is noticed in connexion
+with the bow-wave. In fact, we can from an instantaneous
+photograph so taken approximately estimate
+the speed with which the projectile is travelling.</p>
+
+<p>The explanation of the bow-wave of a ship and
+that of the head-wave of a body travelling in atmospheric
+space both repose upon the same principle,
+long ago employed by Huygens. Conceive a number
+of pebbles to be cast into a pond of water at regular
+intervals in such wise that all the spots struck are situate
+in the same straight line, and that every spot
+subsequently struck lies a short space farther to the
+right. The spots first struck will furnish then the
+wave-circles which are widest, and all of them together
+will, at the points where they are thickest,
+form a sort of cornucopia closely resembling the bow-wave.<span class="pagenum"><a name="Page_326" id="Page_326">[Pg 326]</a></span>
+(Fig. 54.) The resemblance is greater the
+smaller the pebbles are, and the more quickly they
+succeed each other. If a rod be dipped into the water
+and quickly carried along its surface, the falling of
+the pebbles will then take place, so to speak, uninterruptedly,
+and we shall have a real bow-wave. If we
+put the compressed air-wave in the place of the surface-waves
+of the water, we shall have the head-wave
+of the projectile.</p>
+
+<div class="figcenter" style="width: 600px;">
+<img src="images/i_336.jpg" width="600" height="265" alt="" />
+<span class="caption">Fig. 54.</span>
+</div>
+
+<p>You may be disposed to say now, it is all very
+pretty and interesting to observe a projectile in its
+flight, but of what practical use is it?</p>
+
+<p>It is true, I reply, one cannot <i>wage war</i> with photographed
+projectiles. And I have likewise often had
+to say to medical students attending my lectures on
+physics, when they inquired for the practical value of
+some physical observation, "You cannot, gentlemen,
+cure diseases with it." I had also once to give my
+opinion regarding how much physics should be taught
+at a school for millers, supposing the instruction
+there to be confined <i>exactly</i> to what was necessary for<span class="pagenum"><a name="Page_327" id="Page_327">[Pg 327]</a></span>
+a miller. I was obliged to reply: "A miller always
+<i>needs</i> exactly as much physics as he <i>knows</i>." Knowledge
+which one does not possess one cannot use.</p>
+
+<p>Let us forego entirely the consideration that as a
+general thing every scientific advance, every new
+problem elucidated, every extension or enrichment of
+our knowledge of facts, affords a better foundation for
+practical pursuits. Let us rather put the special
+question, Is it not possible to derive some really practical
+knowledge from our theoretical acquaintance
+with the phenomena which take place in the space
+surrounding a projectile?</p>
+
+<p>No physicist who has ever studied waves of sound
+or photographed them will have the least doubt regarding
+the sound-wave character of the atmospheric
+condensation encompassing the head of a flying projectile.
+We have therefore, without ado, called this
+condensation the head-wave.</p>
+
+<p>Knowing this, it follows that the view of Melsens
+according to which the projectile carries along with
+it masses of air which it forces into the bodies struck,
+is untenable. A forward-moving sound-wave is not a
+forward-moving mass of matter but a forward-moving
+form of motion, just as a water-wave or the waves of
+a field of wheat are only forward-moving forms of motion
+and not movements of masses of water or masses
+of wheat.</p>
+
+<p>By interference-experiments, on which I cannot
+touch here but which will be found roughly represented<span class="pagenum"><a name="Page_328" id="Page_328">[Pg 328]</a></span>
+in Figure 55, it was found that the bell-shaped
+head-wave in question is an extremely thin shell and
+that the condensations of the same are quite moderate,
+scarcely exceeding two-tenths of an atmosphere.
+There can be no question, therefore, of explosive effects
+in the body struck by the projectile through so
+slight a degree of atmospheric compression. The
+phenomena attending wounds from rifle balls, for example,
+are not to be explained as Melsens and Busch
+explain them, but are due, as Kocher and Reger maintain,
+to the effects of the impact of the projectile itself.</p>
+
+<div class="figright" style="width: 400px;">
+<img src="images/i_338.jpg" width="400" height="394" alt="" />
+<span class="caption">Fig. 55.</span>
+</div>
+
+<p>A simple experiment will show how insignificant is
+the part played by the friction of the air, or the supposed
+conveyance of the air along with the moving
+projectile. If the photograph of the projectile be<span class="pagenum"><a name="Page_329" id="Page_329">[Pg 329]</a></span>
+taken while passing through a flame, i. e., a visible
+gas, the flame will be seen to be, not torn and deformed,
+but smoothly and cleanly perforated, like any
+solid body. Within and around the flame the contours
+of the head-wave will be seen. The flickering,
+the extinction of the flame, etc., take place only after
+the projectile has travelled on a considerable distance
+in its path, and is then affected by the powder gases
+which hurry after the bullet or by the air preceding
+the powder-gases.</p>
+
+<p>The physicist who examines the head-wave and
+recognises its sound-wave character also sees that the
+wave in question is of the same kind with the short
+sharp waves produced by electric sparks, that it is a
+<i>noise</i>-wave. Hence, whenever any portion of the head-wave
+strikes the ear it will be heard as a report. Appearances
+point to the conclusion that the projectile
+carries this report along with it. In addition to this
+report, which advances with the velocity of the projectile
+and so usually travels at a speed greater than the
+velocity of sound, there is also to be heard the report
+of the exploding powder which travels forward with
+the ordinary velocity of sound. Hence two explosions
+will be heard, each distinct in time. The circumstance
+that this fact was long misconstrued by
+practical observers but when actually noticed frequently
+received grotesque explanations and that ultimately
+my view was accepted as the correct one, appears
+to me in itself a sufficient justification that<span class="pagenum"><a name="Page_330" id="Page_330">[Pg 330]</a></span>
+researches such as we are here speaking of are not utterly
+superfluous even in practical directions. That
+the flashes and sounds of discharging artillery are
+used for estimating the distances of batteries is well
+known, and it stands to reason that any unclear theoretical
+conception of the facts here involved will seriously
+affect the correctness of practical calculations.</p>
+
+<p>It may appear astonishing to a person hearing it
+for the first time, that a single shot has a double report
+due to two different velocities of propagation.
+But the reflexion that projectiles whose velocity is less
+than the velocity of sound produce no head-waves (because
+every impulse imparted to the air travels forward,
+that is, ahead, with exactly the velocity of
+sound), throws full light when logically developed
+upon the peculiar circumstance above mentioned. If
+the projectile moves faster than sound, the air ahead
+of it cannot recede from it quickly enough. The air
+is condensed and warmed, and thereupon, as all know,
+the velocity of sound is augmented until the head-wave
+travels forward as rapidly as the projectile itself, so
+that there is no need whatever of any additional augmentation
+of the velocity of propagation. If such a
+wave were left entirely to itself, it would increase in
+length and soon pass into an ordinary sound-wave,
+travelling with less velocity. But the projectile is always
+behind it and so maintains it at its proper density
+and velocity. Even if the projectile penetrates a
+piece of cardboard or a board of wood, which catches<span class="pagenum"><a name="Page_331" id="Page_331">[Pg 331]</a></span>
+and obstructs the head-wave, there will, as Figure 56
+shows, immediately appear at the emerging apex a
+newly formed, not to say newly born, head-wave. We
+may observe on the cardboard the reflexion and diffraction
+of the head-wave, and by means of a flame
+its refraction, so that no doubt as to its nature can remain.</p>
+
+<div class="figright" style="width: 350px;">
+<img src="images/i_341.jpg" width="350" height="411" alt="" />
+<span class="caption">Fig. 56.</span>
+</div>
+
+<p>Permit me, now, to illustrate the most essential of
+the points that I have just adduced, by means of a few
+rough drawings taken from older and less perfect photographs.</p>
+
+<p>In the sketch of Figure 57 you see the projectile,
+which has just left the barrel of the rifle, touch a wire
+and disengage the illuminating spark. At the apex of<span class="pagenum"><a name="Page_332" id="Page_332">[Pg 332]</a></span>
+the projectile you already see the beginnings of a
+powerful head-wave, and in front of the wave a transparent
+fungiform cluster. This latter is the air which
+has been forced out of the barrel by the projectile.
+Circular sound-waves, noise-waves, which are soon
+overtaken by the projectile, also issue from the barrel.
+But behind the projectile opaque puffs of powder-gas
+rush forth. It is scarcely necessary to add that many
+other questions in ballistics may be studied by this
+method, as, for example, the movement of the gun-carriage.</p>
+
+<div class="figleft" style="width: 450px;">
+<img src="images/i_342.jpg" width="450" height="354" alt="" />
+<span class="caption">Fig. 57.</span>
+</div>
+
+<p>A distinguished French artillerist, M. Gossot, has
+applied the views of the head-wave here given in quite
+a different manner. The practice in measuring the
+velocity of projectiles is to cause the projectile to pass
+through wire screens placed at different points in its
+path, and by the tearing of these screens to give rise<span class="pagenum"><a name="Page_333" id="Page_333">[Pg 333]</a></span>
+to electro-magnetic time-signals on falling slabs or
+rotating drums. Gossot caused these signals to be
+made directly by the impact of the head-wave, did
+away thus with the wire screens, and carried the
+method so far as to be able to measure the velocities
+of projectiles travelling in high altitudes, where the
+use of wire screens was quite out of the question.</p>
+
+<p>The laws of the resistance of fluids and of air to
+bodies travelling in them form an extremely complicated
+problem, which can be reasoned out very simply
+and prettily as a matter of pure philosophy but
+practice offers not a few difficulties. The same
+body having the velocity 2, 3, 4 ... displaces in the
+same interval 2, 3, 4 ... times the same mass of air,
+or the same mass of fluid, and imparts to it <i>in addition</i>
+2, 3, 4 ... times the same velocity. But for this,
+plainly, 4, 9, 16 ... times the original force is required.
+Hence, the resistance, it is said, increases
+with the square of the velocity. This is all very pretty
+and simple and obvious. But practice and theory are
+at daggers' points here. Practice tells us that when
+we increase the velocity, the law of the resistance
+changes. For every portion of the velocity the law is
+different.</p>
+
+<p>The studies of the talented English naval architect,
+Froude, have thrown light upon this question.
+Froude has shown that the resistance is conditioned
+by a combination of the most multifarious phenomena.
+A ship in motion is subjected to the friction of<span class="pagenum"><a name="Page_334" id="Page_334">[Pg 334]</a></span>
+the water. It causes eddies and it generates in addition
+waves which radiate outward from it. Every one
+of these phenomena are dependent upon the velocity
+in some different manner, and it is consequently not
+astonishing that the law of the resistance should be a
+complicated one.</p>
+
+<p>The preceding observations suggest quite analogous
+reflexions for projectiles. Here also we have friction,
+the formation of eddies, and the generation of
+waves. Here, also, therefore, we should not be surprised
+at finding the law of the resistance of the air a
+complicated one, nor puzzled at learning that in actuality
+the law of resistance changes as soon as the
+speed of the projectile exceeds the velocity of sound,
+for this is the precise point at which one important
+element of the resistance, namely, the formation of
+waves, first comes into play.</p>
+
+<p>No one doubts that a pointed bullet pierces the
+air with less resistance than a blunt bullet. The
+photographs themselves show that the head-wave is
+weaker for a pointed projectile. It is not impossible,
+similarly, that forms of bullets will be invented which
+generate fewer eddies, etc., and that we shall study
+these phenomena also by photography. I am of opinion
+from the few experiments which I have made in
+this direction that not much more can be done by
+changing the form of the projectile when the velocity
+is very great, but I have not gone into the question
+thoroughly. Researches of the kind we are considering<span class="pagenum"><a name="Page_335" id="Page_335">[Pg 335]</a></span>
+can certainly not be detrimental to practical artillery,
+and it is no less certain that experiments by artillerists
+on a large scale will be of undoubted benefit
+to physics.</p>
+
+<p>No one who has had the opportunity of studying
+modern guns and projectiles in their marvellous perfection,
+their power and precision, can help confessing
+that a high technical and scientific achievement has
+found its incarnation in these objects. We may surrender
+ourselves so completely to this impression as
+to forget for a moment the terrible purposes they
+serve.</p>
+
+<p>Permit me, therefore, before we separate, to say a
+few words on this glaring contrast. The greatest man
+of war and of silence which the present age has produced
+once asserted that perpetual peace is a dream,
+and not a beautiful dream at that. We may accord
+to this profound student of mankind a judgment in
+these matters and can also appreciate the soldier's
+horror of stagnation from all too lengthy peace. But
+it requires a strong belief in the insuperableness of
+mediæval barbarism to hope for and to expect no
+great improvement in international relations. Think
+of our forefathers and of the times when club law
+ruled supreme, when within the same country and the
+same state brutal assaults and equally brutal self-defence
+were universal and self-evident. This state
+of affairs grew so oppressive that finally a thousand
+and one circumstances compelled people to put an<span class="pagenum"><a name="Page_336" id="Page_336">[Pg 336]</a></span>
+end to it, and the cannon had most to say in accomplishing
+the work. Yet the rule of club law was not
+abolished so quickly after all. It had simply passed
+to other clubs. We must not abandon ourselves to
+dreams of the Rousseau type. Questions of law will
+in a sense forever remain questions of might. Even
+in the United States where every one is as a matter
+of principle entitled to the same privileges, the ballot
+according to Stallo's pertinent remark is but a milder
+substitute for the club. Nor need I tell you that
+many of our own fellow-citizens are still enamored of
+the old original methods. Very, very gradually, however,
+as civilisation progresses, the intercourse of men
+takes on gentler forms, and no one who really knows
+the good old times will ever honestly wish them back
+again, however beautifully they may be painted and
+rhymed about.</p>
+
+<p>In the intercourse of the nations, however, the old
+club law still reigns supreme. But since its rule is
+taxing the intellectual, the moral, and the material resources
+of the nations to the utmost and constitutes
+scarcely less a burden in peace than in war, scarcely
+less a yoke for the victor than for the vanquished, it
+must necessarily grow more and more unendurable.
+Reason, fortunately, is no longer the exclusive possession
+of those who modestly call themselves the
+upper ten thousand. Here, as everywhere, the evil
+itself will awaken the intellectual and ethical forces
+which are destined to mitigate it. Let the hate of<span class="pagenum"><a name="Page_337" id="Page_337">[Pg 337]</a></span>
+races and of nationalities run riot as it may, the intercourse
+of nations will still increase and grow more intimate.
+By the side of the problems which separate
+nations, the great and common ideals which claim the
+exclusive powers of the men of the future appear one
+after another in greater distinctness and in greater
+might.</p><hr class="chap" /><p><span class="pagenum"><a name="Page_338" id="Page_338">[Pg 338]</a></span></p>
+
+
+
+
+<h2><a name="ON_INSTRUCTION_IN_THE_CLASSICS" id="ON_INSTRUCTION_IN_THE_CLASSICS">ON INSTRUCTION IN THE CLASSICS
+AND THE SCIENCES.</a><a name="FNanchor_113_113" id="FNanchor_113_113"></a><a href="#Footnote_113_113" class="fnanchor">[113]</a></h2>
+
+
+<p>Perhaps the most fantastic proposition that Maupertuis,<a name="FNanchor_114_114" id="FNanchor_114_114"></a><a href="#Footnote_114_114" class="fnanchor">[114]</a>
+the renowned president of the Berlin
+Academy, ever put forward for the approval of his
+contemporaries was that of founding a city in which,
+to instruct and discipline young students, only Latin
+should be spoken. Maupertuis's Latin city remained
+an idle wish. But for centuries Latin and Greek <i>institutions</i>
+exist in which our children spend a goodly
+portion of their days, and whose atmosphere constantly
+surrounds them, even when without their walls.</p>
+<p><span class="pagenum"><a name="Page_339" id="Page_339">[Pg 339]</a></span></p>
+<p>For centuries instruction in the ancient languages
+has been zealously cultivated. For centuries its necessity
+has been alternately championed and contested.
+More strongly than ever are authoritative voices now
+raised against the preponderance of instruction in the
+classics and in favor of an education more suited to
+the needs of the time, especially for a more generous
+treatment of mathematics and the natural sciences.</p>
+
+<p>In accepting your invitation to speak here on the
+relative educational value of the classical and the
+mathematico-physical sciences in colleges and high
+schools, I find my justification in the duty and the
+necessity laid upon every teacher of forming from his
+own experiences an opinion upon this important question,
+as partly also in the special circumstance that in
+my youth I was personally under the influence of
+school-life for only a short time, just previous to my
+entering the university, and had, therefore, ample opportunity
+to observe the effects of widely different
+methods upon my own person.</p>
+
+<p>Passing now, to a review of the arguments which
+the advocates of instruction in the classics advance,<span class="pagenum"><a name="Page_340" id="Page_340">[Pg 340]</a></span>
+and of what the adherents of instruction in the physical
+sciences in their turn adduce, we find ourselves in
+rather a perplexing position with respect to the arguments
+of the first named. For these have been different
+at different times, and they are even now of a very
+multifarious character, as must be where men advance,
+in favor of an institution that exists and which they are
+determined to retain at any cost, everything they can
+possibly think of. We shall find here much that has
+evidently been brought forward only to impress the
+minds of the ignorant; much, too, that was advanced
+in good faith and which is not wholly without foundation.
+We shall get a fair idea of the reasoning employed
+by considering, first, the arguments that have grown
+out of the historical circumstances connected with the
+original introduction of the classics, and, lastly, those
+which were subsequently adduced as accidental afterthoughts.</p>
+<p><span class="pagenum"><a name="Page_341" id="Page_341">[Pg 341]</a></span></p><p><span class="pagenum"><a name="Page_342" id="Page_342">[Pg 342]</a></span></p><p><span class="pagenum"><a name="Page_343" id="Page_343">[Pg 343]</a></span></p><p><span class="pagenum"><a name="Page_344" id="Page_344">[Pg 344]</a></span></p><p><span class="pagenum"><a name="Page_345" id="Page_345">[Pg 345]</a></span></p><p><span class="pagenum"><a name="Page_346" id="Page_346">[Pg 346]</a></span></p><p><span class="pagenum"><a name="Page_347" id="Page_347">[Pg 347]</a></span></p>
+<hr class="tb" />
+
+<p>Instruction in Latin, as Paulsen<a name="FNanchor_115_115" id="FNanchor_115_115"></a><a href="#Footnote_115_115" class="fnanchor">[115]</a> has minutely
+shown, was introduced by the Roman Church along
+with Christianity. With the Latin language were also
+transmitted the scant and meagre remnants of ancient
+science. Whoever wished to acquire this ancient education,
+then the only one worthy of the name, for him
+the Latin language was the only and indispensable
+means; such a person had to learn Latin to rank
+among educated people.</p>
+
+<p>The wide-spread influence of the Roman Church
+wrought many and various results. Among those for
+which all are glad, we may safely count the establishment
+of a sort of <i>uniformity</i> among the nations and of a
+regular international intercourse by means of the Latin
+language, which did much to unite the nations in the
+common work of civilisation, carried on from the fifteenth
+to the eighteenth century. The Latin language
+was thus long the language of scholars, and instruction
+in Latin the road to a liberal education&mdash;a shibboleth
+still employed, though long inappropriate.</p>
+
+<p>For scholars as a class, it is to be regretted, perhaps,
+that Latin has ceased to be the medium of international
+communication. But the attributing of the
+loss of this function by the Latin language to its incapacity
+to accommodate itself to the numerous new
+ideas and conceptions which have arisen in the course
+of the development of science is, in my opinion, wholly
+erroneous. It would be difficult to find a modern
+scientist who had enriched science with as many new
+ideas as Newton has, yet Newton knew how to express
+those ideas very correctly and precisely in the
+Latin language. If this view were correct, it would
+also hold true of every living language. Originally
+every language has to adapt itself to new ideas.</p>
+
+<p>It is far more likely that Latin was displaced as
+the literary vehicle of science by the influence of the
+nobility. By their desire to enjoy the fruits of literature
+and science, through a less irksome medium than
+Latin, the nobility performed for the people at large
+an undeniable service. For the days were now past
+when acquaintance with the language and literature of
+science was restricted to a caste, and in this step, perhaps,
+was made the most important advance of modern
+times. To-day, when international intercourse is firmly
+established in spite of the many languages employed,
+no one would think of reintroducing Latin.<a name="FNanchor_116_116" id="FNanchor_116_116"></a><a href="#Footnote_116_116" class="fnanchor">[116]</a></p>
+
+<p>The facility with which the ancient languages lend
+themselves to the expression of new ideas is evidenced
+by the fact that the great majority of our scientific
+ideas, as survivals of this period of Latin intercourse,
+bear Latin and Greek designations, while in great
+measure scientific ideas are even now invested with
+names from these sources. But to deduce from the
+existence and use of such terms the necessity of still
+learning Latin and Greek on the part of all who employ
+them is carrying the conclusion too far. All terms,
+appropriate and inappropriate,&mdash;and there are a large
+number of inappropriate and monstrous combinations
+in science,&mdash;rest on convention. The essential thing
+is, that people should associate with the sign the precise
+idea that is designated by it. It matters little
+whether a person can correctly derive the words <i>telegraph</i>,
+<i>tangent</i>, <i>ellipse</i>, <i>evolute</i>, etc., if the correct idea
+is present in his mind when he uses them. On the
+other hand, no matter how well he may know their etymology,
+his knowledge will be of little use to him if
+the correct idea is absent. Ask the average and fairly
+educated classical scholar to translate a few lines for
+you from Newton's <i>Principia</i>, or from Huygens's <i>Horologium</i>,
+and you will discover at once what an extremely
+subordinate rôle the mere knowledge of language
+plays in such things. Without its associated
+thought a word remains a mere sound. The fashion of
+employing Greek and Latin designations&mdash;for it can
+be termed nothing else&mdash;has a natural root in history;
+it is impossible for the practice to disappear suddenly,
+but it has fallen of late considerably into disuse. The
+terms <i>gas</i>, <i>ohm</i>, <i>Ampère</i>, <i>volt</i>, etc., are in international
+use, but they are not Latin nor Greek. Only the person
+who rates the unessential and accidental husk
+higher than its contents, can speak of the necessity of
+learning Latin or Greek for such reasons, to say nothing
+of spending eight or ten years on the task. Will
+not a dictionary supply in a few seconds all the information
+we wish on such subjects?<a name="FNanchor_117_117" id="FNanchor_117_117"></a><a href="#Footnote_117_117" class="fnanchor">[117]</a></p>
+
+<p>It is indisputable that our modern civilisation took
+up the threads of the ancient civilisation, that at
+many points it begins where the latter left off, and
+that centuries ago the remains of the ancient culture
+were the only culture existing in Europe. Then, of
+course, a classical education really was the liberal education,
+the higher education, the ideal education, for
+it was the <i>sole</i> education. But when the same claim
+is now raised in behalf of a classical education, it must
+be uncompromisingly contested as bereft of all foundation.
+For our civilisation has gradually attained
+its independence; it has lifted itself far above the ancient
+civilisation, and has entered generally new directions
+of progress. Its note, its characteristic feature,
+is the enlightenment that has come from the great
+mathematical and physical researches of the last centuries,
+and which has permeated not only the practical
+arts and industries but is also gradually finding
+its way into all fields of thought, including philosophy
+and history, sociology and linguistics. Those traces
+of ancient views that are still discoverable in philosophy,
+law, art, and science, operate more as hindrances
+than helps, and will not long stand before the development
+of independent and more natural views.</p>
+
+<p>It ill becomes classical scholars, therefore, to regard
+themselves, at this day, as the educated class
+<i>par excellence</i>, to condemn as uneducated all persons
+who do not understand Latin and Greek, to complain
+that with such people profitable conversations are not
+to be carried on, etc. The most delectable stories
+have got into circulation, illustrative of the defective
+education of scientists and engineers. A renowned
+inquirer, for example, is said to have once announced
+his intention of holding a free course of university lectures,
+with the word "frustra"; an engineer who spent
+his leisure hours in collecting insects is said to have
+declared that he was studying "etymology." It is
+true, incidents of this character make us shudder or
+smile, according to our mood or temperament. But
+we must admit, the next moment, that in giving way
+to such feelings we have merely succumbed to a childish
+prejudice. A lack of tact but certainly no lack of
+education is displayed in the use of such half-understood
+expressions. Every candid person will confess
+that there are many branches of knowledge about which
+he had better be silent. We shall not be so uncharitable
+as to turn the tables and discuss the impression
+that classical scholars might make on a scientist or
+engineer, in speaking of science. Possibly many ludicrous
+stories might be told of them, and of far more
+serious import, which should fully compensate for the
+blunders of the other party.</p>
+
+<p>The mutual severity of judgment which we have
+here come upon, may also forcibly bring home to us
+how really scarce a true liberal culture is. We may
+detect in this mutual attitude, too, something of that
+narrow, mediæval arrogance of caste, where a man
+began, according to the special point of view of the
+speaker, with the scholar, the soldier, or the nobleman.
+Little sense or appreciation is to be found in it for the
+<i>common</i> task of humanity, little feeling for the need of
+mutual assistance in the great work of civilisation,
+little breadth of mind, little truly liberal culture.</p>
+
+<p>A knowledge of Latin, and partly, also, a knowledge
+of Greek, is still a necessity for the members of
+a few professions by nature more or less directly concerned
+with the civilisations of antiquity, as for lawyers,
+theologians, philologists, historians, and generally
+for a small number of persons, among whom
+from time to time I count myself, who are compelled
+to seek for information in the Latin literature of the
+centuries just past.<a name="FNanchor_118_118" id="FNanchor_118_118"></a><a href="#Footnote_118_118" class="fnanchor">[118]</a> But that all young persons in
+search of a higher education should pursue for this
+reason Latin and Greek to such excess; that persons
+intending to become physicians and scientists should
+come to the universities defectively educated, or even
+miseducated; and that they should be compelled to
+come only from schools that do <i>not</i> supply them with
+the proper preparatory knowledge is going a little bit
+too far.</p>
+<p><span class="pagenum"><a name="Page_348" id="Page_348">[Pg 348]</a></span></p><p><span class="pagenum"><a name="Page_349" id="Page_349">[Pg 349]</a></span></p><p><span class="pagenum"><a name="Page_350" id="Page_350">[Pg 350]</a></span></p><p><span class="pagenum"><a name="Page_351" id="Page_351">[Pg 351]</a></span></p><p><span class="pagenum"><a name="Page_352" id="Page_352">[Pg 352]</a></span></p>
+<hr class="tb" />
+
+<p>After the conditions which had given to the study
+of Latin and Greek their high import had ceased to
+exist, the traditional curriculum, naturally, was retained.
+Then, the different effects of this method of
+education, good and bad, which no one had thought of
+at its introduction, were realised and noted. As natural,
+too, was it that those who had strong interests
+in the preservation of these studies, from knowing no
+others or from living by them, or for still other reasons,
+should emphasise the <i>good</i> results of such instruction.
+They pointed to the good effects as if they
+had been consciously aimed at by the method and could
+be attained only through its agency.</p>
+
+<p>One real benefit that students might derive from
+a rightly conducted course in the classics would be
+the opening up of the rich literary treasures of antiquity,
+and intimacy with the conceptions and views
+of the world held by two advanced nations. A person
+who has read and understood the Greek and Roman
+authors has felt and experienced more than one who is
+restricted to the impressions of the present. He sees
+how men placed in different circumstances judge quite
+differently of the same things from what we do to-day.
+His own judgments will be rendered thus more independent.
+Again, the Greek and Latin authors are indisputably
+a rich fountain of recreation, of enlightenment,
+and of intellectual pleasure after the day's toil, and
+the individual, not less than civilised humanity generally,
+will remain grateful to them for all time. Who
+does not recall with pleasure the wanderings of Ulysses,
+who does not listen joyfully to the simple narratives
+of Herodotus, who would ever repent of having
+made the acquaintance of Plato's Dialogues, or of
+having tasted Lucian's divine humor? Who would
+give up the glances he has obtained into the private
+life of antiquity from Cicero's letters, from Plautus or
+Terence? To whom are not the portraits of Suetonius
+undying reminiscences? Who, in fact, would throw
+away <i>any</i> knowledge he had once gained?</p>
+
+<p>Yet people who draw from these sources only, who
+know only this culture, have surely no right to dogmatise
+about the value of some other culture. As objects
+of research for individuals, this literature is extremely
+valuable, but it is a different question whether
+it is equally valuable as the almost exclusive means of
+education of our youth.</p>
+
+<p>Do not other nations and other literatures exist
+from which we ought to learn? Is not nature herself
+our first school-mistress? Are our highest models always
+to be the Greeks, with their narrow provinciality
+of mind, that divided the world into "Greeks and barbarians,"
+with their superstitions, with their eternal
+questioning of oracles? Aristotle with his incapacity
+to learn from facts, with his word-science; Plato with
+his heavy, interminable dialogues, with his barren, at
+times childish, dialectics&mdash;are they unsurpassable?<a name="FNanchor_119_119" id="FNanchor_119_119"></a><a href="#Footnote_119_119" class="fnanchor">[119]</a>
+The Romans with their apathy, their pompous externality,
+set off by fulsome and bombastic phrases, with
+their narrow-minded, philistine philosophy, with their
+frenzied sensuality, with their cruel and bestial indulgence
+in animal and man baiting, with their outrageous
+maltreatment and plundering of their subjects&mdash;are
+they patterns worthy of imitation? Or shall, perhaps,
+our science edify itself with the works of Pliny who
+cites midwives as authorities and himself stands on
+their point of view?</p>
+
+<p>Besides, if an acquaintance with the ancient world
+really were attained, we might come to some settlement
+with the advocates of classical education. But it
+is words and forms, and forms and words only, that
+are supplied to our youth; and even collateral subjects
+are forced into the strait-jacket of the same
+rigid method and made a science of words, sheer feats
+of mechanical memory. Really, we feel ourselves set
+back a thousand years into the dull cloister-cells of the
+Middle Ages.</p>
+
+<p>This must be changed. It is possible to get acquainted
+with the views of the Greeks and Romans by
+a shorter road than the intellect deadening process
+of eight or ten years of declining, conjugating, analysing,
+and extemporisation. There are to-day plenty of
+educated persons who have acquired through good
+translations vivider, clearer, and more just views of
+classical antiquity than the graduates of our gymnasiums
+and colleges.<a name="FNanchor_120_120" id="FNanchor_120_120"></a><a href="#Footnote_120_120" class="fnanchor">[120]</a></p>
+
+<p>For us moderns, the Greeks and the Romans are
+simply two objects of archæological and historical research
+like all others. If we put them before our
+youth in fresh and living pictures, and not merely in
+words and syllables, the effect will be assured. We
+derive a totally different enjoyment from the Greeks
+when we approach them after a study of the results
+of modern research in the history of civilisation. We
+read many a chapter of Herodotus differently when we
+attack his works equipped with a knowledge of natural
+science, and with information about the stone age and
+the lake-dwellers. What our classical institutions <i>pretend</i>
+to give can and actually will be given to our youth
+with much more fruitful results by competent <i>historical</i>
+instruction, which must supply, not names and numbers
+alone, nor the mere history of dynasties and wars,
+but be in every sense of the word a true history of
+civilisation.</p>
+
+<p>The view still widely prevails that although all
+"higher, ideal culture," all extension of our view of
+the world, is acquired by philological and in a lesser
+degree by historical studies, still the mathematics and
+natural sciences should not be neglected on account
+of their usefulness. This is an opinion to which I must
+refuse my assent. It were strange if man could learn
+more, could draw more intellectual nourishment, from
+the shards of a few old broken jugs, from inscribed
+stones, or yellow parchments, than from all the rest
+of nature. True, man is man's first concern, but he
+is not his sole concern.</p>
+
+<p>In ceasing to regard man as the centre of the world;
+in discovering that the earth is a top whirled about
+the sun, which speeds off with it into infinite space;
+in finding that in the fixed stars the same elements
+exist as on earth; in meeting everywhere the same
+processes of which the life of man is merely a vanishingly
+small part&mdash;in such things, too, is a widening of
+our view of the world, and edification, and poetry.
+There are here perhaps grander and more significant
+facts than the bellowing of the wounded Ares, or the
+charming island of Calypso, or the ocean-stream engirdling
+the earth. He only should speak of the relative
+value of these two domains of thought, of their
+poetry, who knows both.</p>
+
+<p>The "utility" of physical science is, in a measure,
+only a <i>collateral</i> product of that flight of the intellect
+which produced science. No one, however, should
+underrate the utility of science who has shared in the
+realisation by modern industrial art of the Oriental
+world of fables, much less one upon whom those treasures
+have been poured, as it were, from the fourth dimension,
+without his aid or understanding.</p>
+
+<p>Nor may we believe that science is useful only to
+the practical man. Its influence permeates all our affairs,
+our whole life; everywhere its ideas are decisive.
+How differently does the jurist, the legislator, or the
+political economist think, who knows, for example,
+that a square mile of the most fertile soil can support
+with the solar heat annually consumed only a definite
+number of human beings, which no art or science can
+increase. Many economical theories, which open new
+air-paths of progress, air-paths in the literal sense of
+the word, would be made impossible by such knowledge.</p>
+<p><span class="pagenum"><a name="Page_353" id="Page_353">[Pg 353]</a></span></p><p><span class="pagenum"><a name="Page_354" id="Page_354">[Pg 354]</a></span></p>
+<hr class="tb" />
+
+<p>The eulogists of classical education love to emphasise
+the cultivation of taste which comes from employment
+with the ancient models. I candidly confess
+that there is something absolutely revolting in this to
+me. To form the taste, then, our youths must sacrifice
+ten years of their life! Luxury takes precedence over
+necessity. Have the future generations, in the face
+of the difficult problems, the great social questions,
+which they must meet, and that with strengthened
+mind and heart, no more important duties to fulfil than
+these?</p>
+
+<p>But let us assume that this end were desirable.
+Can taste be formed by rules and precepts? Do not
+ideals of beauty change? Is it not a stupendous absurdity
+to force one's self artificially to admire things
+which, with all their historical interest, with all their
+beauty in individual points, are for the most part
+foreign to the rest of our thoughts and feelings, provided
+we have such of <i>our own</i>. A nation that is
+truly such, has its own taste and will not go to others
+for it. And every individual perfect man has his own
+taste.<a name="FNanchor_121_121" id="FNanchor_121_121"></a><a href="#Footnote_121_121" class="fnanchor">[121]</a></p>
+
+<p>And what, after all, does this cultivation of taste
+consist in? In the acquisition of the personal literary
+style of a few select authors! What should we think
+of a people that would force its youth a thousand
+years from now, by years of practice, to master the
+tortuous or bombastic style of some successful lawyer
+or politician of to-day? Should we not justly accuse
+them of a woful lack of taste?</p>
+
+<p>The evil effects of this imagined cultivation of the
+taste find expression often enough. The young <i>savant</i>
+who regards the composition of a scientific essay as a
+rhetorical exercise instead of a simple and unadorned
+presentation of the facts and the truth, still sits unconsciously
+on the school-bench, and still unwittingly represents
+the point of view of the Romans, by whom the
+elaboration of speeches was regarded as a serious scientific (!)
+employment.</p>
+<p><span class="pagenum"><a name="Page_355" id="Page_355">[Pg 355]</a></span></p><p><span class="pagenum"><a name="Page_356" id="Page_356">[Pg 356]</a></span></p><p><span class="pagenum"><a name="Page_357" id="Page_357">[Pg 357]</a></span></p>
+<hr class="tb" />
+
+<p>Far be it from me to underrate the value of the development
+of the instinct of speech and of the increased
+comprehension of our own language which comes from
+philological studies. By the study of a foreign language,
+especially of one which differs widely from ours,
+the signs and forms of words are first clearly distinguished
+from the thoughts which they express. Words
+of the closest possible correspondence in different languages
+never coincide absolutely with the ideas they
+stand for, but place in relief slightly different aspects
+of the same thing, and by the study of language the
+attention is directed to these shades of difference. But
+it would be far from admissible to contend that the
+study of Latin and Greek is the most fruitful and natural,
+let alone the <i>only</i>, means of attaining this end.
+Any one who will give himself the pleasure of a few
+hours' companionship with a Chinese grammar; who
+will seek to make clear to himself the mode of speech
+and thought of a people who never advanced as far as
+the analysis of articulate sounds, but stopped at the
+analysis of syllables, to whom our alphabetical characters,
+therefore, are an inexplicable puzzle, and who
+express all their rich and profound thoughts by means
+of a few syllables with variable emphasis and position,&mdash;such
+a person, perhaps, will acquire new, and extremely
+elucidative ideas upon the relation of language
+and thought. But should our children, therefore,
+study Chinese? Certainly not. No more, then,
+should they be burdened with Latin, at least in the
+measure they are.</p>
+
+<p>It is a beautiful achievement to reproduce a Latin
+thought in a modern language with the maximum fidelity
+of meaning and expression&mdash;for the <i>translator</i>.
+Moreover, we shall be very grateful to the translator
+for his performance. But to demand this feat of every
+educated man, without consideration of the sacrifice of
+time and labor which it entails, is unreasonable. And
+for this very reason, as classical teachers admit, that
+ideal is never perfectly attained, except in rare cases
+with scholars possessed of special talents and great
+industry. Without slurring, therefore, the high importance
+of the study of the ancient languages as a
+profession, we may yet feel sure that the instinct for
+speech which is part of every liberal education can,
+and must, be acquired in a different way. Should we,
+indeed, be forever lost if the Greeks had not lived before
+us?</p>
+
+<p>The fact is, we must carry our demands further
+than the representatives of classical philology. We
+must ask of every educated man a fair scientific conception
+of the nature and value of language, of the
+formation of language, of the alteration of the meaning
+of roots, of the degeneration of fixed forms of
+speech to grammatical forms, in brief, of all the main
+results of modern comparative philology. We should
+judge that this were attainable by a careful study of
+our mother tongue and of the languages next allied to
+it, and subsequently of the more ancient tongues from
+which the former are derived. If any one object that
+this is too difficult and entails too much labor, I should
+advise such a person to place side by side an English,
+a Dutch, a Danish, a Swedish, and a German Bible, and
+to compare a few lines of them; he will be amazed at
+the multitude of suggestions that offer themselves.<a name="FNanchor_122_122" id="FNanchor_122_122"></a><a href="#Footnote_122_122" class="fnanchor">[122]</a>
+In fact, I believe that a really progressive, fruitful, rational,
+and instructive study of languages can be conducted
+only on this plan. Many of my audience will
+remember, perhaps, the bright and encouraging effect,
+like that of a ray of sunlight on a gloomy day, which
+the meagre and furtive remarks on comparative philology
+in Curtius's Greek grammar wrought in that
+barren and lifeless desert of verbal quibbles.</p>
+<p><span class="pagenum"><a name="Page_358" id="Page_358">[Pg 358]</a></span></p><p><span class="pagenum"><a name="Page_359" id="Page_359">[Pg 359]</a></span></p>
+<hr class="tb" />
+
+<p>The principal result obtained by the present method
+of studying the ancient languages is that which comes
+from the student's employment with their complicated
+grammars. It consists in the sharpening of the attention
+and in the exercise of the judgment by the practice
+of subsuming special cases under general rules,
+and of distinguishing between different cases. Obviously,
+the same result can be reached by many other
+methods; for example, by difficult games of cards.
+Every science, the mathematics and the physical sciences
+included, accomplish as much, if not more, in
+this disciplining of the judgment. In addition, the
+matter treated by those sciences has a much higher intrinsic
+interest for young people, and so engages spontaneously
+their attention; while on the other hand they
+are elucidative and useful in other directions in which
+grammar can accomplish nothing.</p>
+
+<p>Who cares, so far as the matter of it is concerned,
+whether we say <i>hominum</i> or <i>hominorum</i> in the genitive
+plural, interesting as the fact may be for the philologist?
+And who would dispute that the intellectual
+need of causal insight is awakened not by grammar
+but by the natural sciences?</p>
+
+<p>It is not our intention, therefore, to gainsay in the
+least the good influence which the study of Latin and
+Greek grammar <i>also</i> exercises on the sharpening of the
+judgment. In so far as the study of words as such
+must greatly promote lucidity and accuracy of expression,
+in so far as Latin and Greek are not yet
+wholly indispensable to many branches of knowledge,
+we willingly concede to them a place in our schools,
+but would demand that the disproportionate amount of
+time allotted to them, wrongly withdrawn from other
+useful studies, should be considerably curtailed. That
+in the end Latin and Greek will not be employed as
+the universal means of education, we are fully convinced.
+They will be relegated to the closet of the
+scholar or professional philologist, and gradually make
+way for the modern languages and the modern science
+of language.</p>
+
+<p>Long ago Locke reduced to their proper limits the
+exaggerated notions which obtained of the close connexion
+of thought and speech, of logic and grammar,
+and recent investigators have established on still surer
+foundations his views. How little a complicated grammar
+is necessary for expressing delicate shades of
+thought is demonstrated by the Italians and French,
+who, although they have almost totally discarded the
+grammatical redundancies of the Romans, are yet not
+surpassed by the latter in accuracy of thought, and
+whose poetical, but especially whose scientific literature,
+as no one will dispute, can bear favorable comparison
+with the Roman.</p>
+
+<p>Reviewing again the arguments advanced in favor
+of the study of the ancient languages, we are obliged
+to say that in the main and as applied to the present,
+they are wholly devoid of force. In so far as the
+aims which this study theoretically pursues are still
+worthy of attainment, they appear to us as altogether
+too narrow, and are surpassed in this only by the
+means employed. As almost the sole, indisputable result
+of this study we must count the increase of the
+student's skill and precision in expression. One inclined
+to be uncharitable might say that our gymnasiums
+and classical academies turn out men who can
+speak and write, but, unfortunately, have little to write
+or speak about. Of that broad, liberal view, of that
+famed universal culture, which the classical curriculum
+is supposed to yield, serious words need not be lost.
+This culture might, perhaps, more properly be termed
+the contracted or lopsided culture.</p>
+<p><span class="pagenum"><a name="Page_360" id="Page_360">[Pg 360]</a></span></p><p><span class="pagenum"><a name="Page_361" id="Page_361">[Pg 361]</a></span></p><p><span class="pagenum"><a name="Page_362" id="Page_362">[Pg 362]</a></span><span class="pagenum"><a name="Page_363" id="Page_363">[Pg 363]</a></span></p><p><span class="pagenum"><a name="Page_364" id="Page_364">[Pg 364]</a></span></p><p><span class="pagenum"><a name="Page_365" id="Page_365">[Pg 365]</a></span></p><p><span class="pagenum"><a name="Page_366" id="Page_366">[Pg 366]</a></span></p><p><span class="pagenum"><a name="Page_367" id="Page_367">[Pg 367]</a></span></p><p><span class="pagenum"><a name="Page_368" id="Page_368">[Pg 368]</a></span></p><p><span class="pagenum"><a name="Page_369" id="Page_369">[Pg 369]</a></span></p><p><span class="pagenum"><a name="Page_370" id="Page_370">[Pg 370]</a></span><span class="pagenum"><a name="Page_371" id="Page_371">[Pg 371]</a></span></p>
+<hr class="tb" />
+
+<p>While considering the study of languages we threw
+a few side glances at mathematics and the natural sciences.
+Let us now inquire whether these, as branches
+of study, cannot accomplish much that is to be attained
+in no other way. I shall meet with no contradiction
+when I say that without at least an elementary mathematical
+and scientific education a man remains a total
+stranger in the world in which he lives, a stranger in
+the civilisation of the time that bears him. Whatever
+he meets in nature, or in the industrial world, either
+does not appeal to him at all, from his having neither
+eye nor ear for it, or it speaks to him in a totally unintelligible
+language.</p>
+
+<p>A real understanding of the world and its civilisation,
+however, is not the only result of the study of
+mathematics and the physical sciences. Much more
+essential for the preparatory school is the <i>formal</i> cultivation
+which comes from these studies, the strengthening
+of the reason and the judgment, the exercise
+of the imagination. Mathematics, physics, chemistry,
+and the so-called descriptive sciences are so much
+alike in this respect, that, apart from a few points, we
+need not separate them in our discussion.</p>
+
+<p>Logical sequence and continuity of ideas, so necessary
+for fruitful thought, are <i>par excellence</i> the results of
+mathematics; the ability to follow facts with thoughts,
+that is, to observe or collect experiences, is chiefly developed
+by the natural sciences. Whether we notice
+that the sides and the angles of a triangle are connected
+in a definite way, that an equilateral triangle possesses
+certain definite properties of symmetry, or whether we
+notice the deflexion of a magnetic needle by an electric
+current, the dissolution of zinc in diluted sulphuric
+acid, whether we remark that the wings of a butterfly
+are slightly colored on the under, and the fore-wings
+of the moth on the upper, surface: indiscriminately
+here we proceed from <i>observations</i>, from individual
+acts of immediate intuitive knowledge. The field of
+observation is more restricted and lies closer at hand
+in mathematics; it is more varied and broader but
+more difficult to compass in the natural sciences. The
+essential thing, however, is for the student to learn to
+make observations in all these fields. The philosophical
+question whether our acts of knowledge in mathematics
+are of a special kind is here of no importance
+for us. It is true, of course, that the observation can
+be practised by languages also. But no one, surely,
+will deny, that the concrete, living pictures presented
+in the fields just mentioned possess different
+and more powerful attractions for the mind of the
+youth than the abstract and hazy figures which language
+offers, and on which the attention is certainly not
+so spontaneously bestowed, nor with such good results.<a name="FNanchor_123_123" id="FNanchor_123_123"></a><a href="#Footnote_123_123" class="fnanchor">[123]</a></p>
+
+<p>Observation having revealed the different properties
+of a given geometrical or physical object, it is discovered
+that in many cases these properties <i>depend</i> in
+some way upon one another. This interdependence
+of properties (say that of equal sides and equal angles
+at the base of a triangle, the relation of pressure to
+motion,) is nowhere so distinctly marked, nowhere is
+the necessity and permanency of the interdependence
+so plainly noticeable, as in the fields mentioned.
+Hence the continuity and logical consequence of the
+ideas which we acquire in those fields. The relative
+simplicity and perspicuity of geometrical and physical
+relations supply here the conditions of natural and
+easy progress. Relations of equal simplicity are not
+met with in the fields which the study of language
+opens up. Many of you, doubtless, have often wondered
+at the little respect for the notions of cause and
+effect and their connexion that is sometimes found
+among professed representatives of the classical studies.
+The explanation is probably to be sought in the
+fact that the analogous relation of motive and action
+familiar to them from their studies, presents nothing
+like the clear simplicity and determinateness that the
+relation of cause and effect does.</p>
+
+<p>That perfect mental grasp of all possible cases,
+that economical order and organic union of the thoughts
+which comes from it, which has grown for every one
+who has ever tasted it a permanent need which he
+seeks to satisfy in every new province, can be developed
+only by employment with the relative simplicity of
+mathematical and scientific investigations.</p>
+
+<p>When a set of facts comes into apparent conflict
+with another set of facts, and a problem is presented,
+its solution consists ordinarily in a more refined distinction
+or in a more extended view of the facts, as
+may be aptly illustrated by Newton's solution of the
+problem of dispersion. When a new mathematical or
+scientific fact is <i>demonstrated</i>, or <i>explained</i>, such demonstration
+also rests simply upon showing the connexion
+of the new fact with the facts already known; for
+example, that the radius of a circle can be laid off as
+chord exactly six times in the circle is explained or
+proved by dividing the regular hexagon inscribed in
+the circle into equilateral triangles. That the quantity
+of heat developed in a second in a wire conveying an
+electric current is quadrupled on the doubling of the
+strength of the current, we explain from the doubling of
+the fall of the potential due to the doubling of the
+current's intensity, as also from the doubling of the
+quantity flowing through, in a word, from the quadrupling
+of the work done. In point of principle, explanation
+and direct proof do not differ much.</p>
+
+<p>He who solves scientifically a geometrical, physical,
+or technical problem, easily remarks that his
+procedure is a <i>methodical</i> mental quest, rendered possible
+by the economical order of the province&mdash;a simplified
+purposeful quest as contrasted with unmethodical,
+unscientific guess-work. The geometer, for example,
+who has to construct a circle touching two given
+straight lines, casts his eye over the relations of symmetry
+of the desired construction, and seeks the centre
+of his circle solely in the line of symmetry of the two
+straight lines. The person who wants a triangle of
+which two angles and the sum of the sides are given,
+grasps in his mind the determinateness of the form of
+this triangle and restricts his search for it to a certain
+group of triangles of the <i>same form</i>. Under very different
+circumstances, therefore, the simplicity, the intellectual
+perviousness, of the subject-matter of mathematics
+and natural science is felt, and promotes both
+the discipline and the self-confidence of the reason.</p>
+
+<p>Unquestionably, much more will be attained by instruction
+in the mathematics and the natural sciences
+than now is, when more natural methods are adopted.
+One point of importance here is that young students
+should not be spoiled by premature abstraction, but
+should be made acquainted with their material from
+living pictures of it before they are made to work with
+it by purely ratiocinative methods. A good stock of
+geometrical experience could be obtained, for example,
+from geometrical drawing and from the practical
+construction of models. In the place of the unfruitful
+method of Euclid, which is only fit for special, restricted
+uses, a broader and more conscious method
+must be adopted, as Hankel has pointed out.<a name="FNanchor_124_124" id="FNanchor_124_124"></a><a href="#Footnote_124_124" class="fnanchor">[124]</a> Then,
+if, on reviewing geometry, and after it presents no
+substantial difficulties, the more general points of view,
+the principles of scientific method are placed in relief
+and brought to consciousness, as Von Nagel,<a name="FNanchor_125_125" id="FNanchor_125_125"></a><a href="#Footnote_125_125" class="fnanchor">[125]</a> J. K.
+Becker,<a name="FNanchor_126_126" id="FNanchor_126_126"></a><a href="#Footnote_126_126" class="fnanchor">[126]</a> Mann,<a name="FNanchor_127_127" id="FNanchor_127_127"></a><a href="#Footnote_127_127" class="fnanchor">[127]</a> and others have well done, fruitful
+results will be surely attained. In the same way,
+the subject-matter of the natural sciences should be
+made familiar by pictures and experiment before a
+profounder and reasoned grasp of these subjects is
+attempted. Here the emphasis of the more general
+points of view is to be postponed.</p>
+
+<p>Before my present audience it would be superfluous
+for me to contend further that mathematics and natural
+science are justified constituents of a sound education,&mdash;a
+claim that even philologists, after some
+resistance, have conceded. Here I may count upon
+assent when I say that mathematics and the natural
+sciences pursued alone as means of instruction yield a
+richer education in matter and form, a more general
+education, an education better adapted to the needs
+and spirit of the time,&mdash;than the philological branches
+pursued alone would yield.</p>
+
+<p>But how shall this idea be realised in the curricula
+of our intermediate educational institutions? It is unquestionable
+in my mind that the German <i>Realschulen</i>
+and <i>Realgymnasien</i>, where the exclusive classical course
+is for the most part replaced by mathematics, science,
+and modern languages, give the <i>average</i> man a more
+timely education than the gymnasium proper, although
+they are not yet regarded as fit preparatory schools for
+future theologians and professional philologists. The
+German gymnasiums are too one-sided. With these
+the first changes are to be made; of these alone we
+shall speak here. Possibly a <i>single</i> preparatory school,
+suitably planned, might serve all purposes.</p>
+
+<p>Shall we, then, in our gymnasiums fill out the hours
+of study which stand at our disposal, or are still to be
+wrested from the classicists, with as great and as varied
+a quantity of mathematical and scientific matter
+as possible? Expect no such proposition from me.
+No one will suggest such a course who has himself
+been actively engaged in scientific thought. Thoughts
+can be awakened and fructified as a field is fructified
+by sunshine and rain. But thoughts cannot be juggled
+out and worried out by heaping up materials and
+the hours of instruction, nor by any sort of precepts:
+they must grow naturally of their own free accord.
+Furthermore, thoughts cannot be accumulated beyond
+a certain limit in a single head, any more than the produce
+of a field can be increased beyond certain limits.</p>
+
+<p>I believe that the amount of matter necessary for a
+useful education, such as should be offered to <i>all</i> the
+pupils of a preparatory school, is very small. If I had
+the requisite influence, I should, in all composure, and
+fully convinced that I was doing what was best, first
+greatly curtail in the lower classes the amount of matter
+in both the classical and the scientific courses; I
+should cut down considerably the number of the school
+hours and the work done outside the school. I am
+not with many teachers of opinion that ten hours work
+a day for a child is not too much. I am convinced
+that the mature men who offer this advice so lightly
+are themselves unable to give their attention successfully
+for as long a time to any subject that is new to
+them, (for example, to elementary mathematics or
+physics,) and I would ask every one who thinks the
+contrary to make the experiment upon himself. Learning
+and teaching are not routine office-work that can
+be kept up mechanically for long periods. But even
+such work tires in the end. If our young men are
+not to enter the universities with blunted and impoverished
+minds, if they are not to leave in the preparatory
+schools their vital energy, which they should
+there gather, great changes must be made. Waiving
+the injurious effects of overwork upon the body, the
+consequences of it for the mind seem to me positively
+dreadful.</p>
+
+<p>I know of nothing more terrible than the poor creatures
+who have learned too much. Instead of that
+sound powerful judgment which would probably have
+grown up if they had learned nothing, their thoughts
+creep timidly and hypnotically after words, principles,
+and formulæ, constantly by the same paths. What
+they have acquired is a spider's web of thoughts too
+weak to furnish sure supports, but complicated enough
+to produce confusion.</p>
+
+<p>But how shall better methods of mathematical and
+scientific education be combined with the decrease of
+the subject-matter of instruction? I think, by abandoning
+systematic instruction altogether, at least in so
+far as that is required of <i>all</i> young pupils. I see no
+necessity whatever that the graduates of our high
+schools and preparatory schools should be little philologists,
+and at the same time little mathematicians,
+physicists, and botanists; in fact, I do not see the possibility
+of such a result. I see in the endeavor to attain
+this result, in which every instructor seeks for his
+own branch a place apart from the others, the main
+mistake of our whole system. I should be satisfied if
+every young student could come into living contact
+with and pursue to their ultimate logical consequences
+merely a <i>few</i> mathematical or scientific discoveries.
+Such instruction would be mainly and naturally associated
+with selections from the great scientific classics.
+A few powerful and lucid ideas could thus be made
+to take root in the mind and receive thorough elaboration.
+This accomplished, our youth would make a
+different showing from what they do to-day.<a name="FNanchor_128_128" id="FNanchor_128_128"></a><a href="#Footnote_128_128" class="fnanchor">[128]</a></p>
+
+<p>What need is there, for example, of burdening the
+head of a young student with all the details of botany?
+The student who has botanised under the guidance of
+a teacher finds on all hands, not indifferent things, but
+known or unknown things, by which he is stimulated,
+and his gain made permanent. I express here, not my
+own, but the opinion of a friend, a practical teacher.
+Again, it is not at all necessary that all the matter that
+is offered in the schools should be learned. The best
+that we have learned, that which has remained with
+us for life, outlived the test of examination. How can
+the mind thrive when matter is heaped on matter, and
+new materials piled constantly on old, undigested materials?
+The question here is not so much that of the
+accumulation of positive knowledge as of intellectual
+discipline. It seems also unnecessary that <i>all</i> branches
+should be treated at school, and that exactly the same
+studies should be pursued in all schools. A single
+philological, a single historical, a single mathematical,
+a single scientific branch, pursued as common subjects
+of instruction for all pupils, are sufficient to accomplish
+all that is necessary for the intellectual development.
+On the other hand, a wholesome mutual stimulus
+would be produced by this greater variety in the
+positive culture of men. Uniforms are excellent for
+soldiers, but they will not fit heads. Charles V. learned
+this, and it should never be forgotten. On the contrary,
+teachers and pupils both need considerable latitude, if
+they are to yield good results.</p>
+
+<p>With John Karl Becker I am of the opinion that
+the utility and amount for individuals of every study
+should be precisely determined. All that exceeds this
+amount should be unconditionally banished from the
+lower classes. With respect to mathematics, Becker,<a name="FNanchor_129_129" id="FNanchor_129_129"></a><a href="#Footnote_129_129" class="fnanchor">[129]</a>
+in my judgment, has admirably solved this question.</p>
+
+<p>With respect to the upper classes the demand assumes
+a different form. Here also the amount of matter
+obligatory on all pupils ought not to exceed a certain
+limit. But in the great mass of knowledge that a
+young man must acquire to-day for his profession it is
+no longer just that ten years of his youth should be
+wasted with mere preludes. The upper classes should
+supply a truly useful preparation for the professions,
+and should not be modelled upon the wants merely of
+future lawyers, ministers, and philologists. Again, it
+would be both foolish and impossible to attempt to
+prepare the same person properly for all the different
+professions. In such case the function of the schools
+would be, as Lichtenberg feared, simply to select the
+persons best fitted for being drilled, whilst precisely the
+finest special talents, which do not submit to indiscriminate
+discipline, would be excluded from the contest.
+Hence, a certain amount of liberty in the choice
+of studies must be introduced in the upper classes, by
+means of which it will be free for every one who is clear
+about the choice of his profession to devote his chief
+attention either to the study of the philologico-historical
+or to that of the mathematico-scientific branches.
+Then the matter now treated could be retained, and in
+some branches, perhaps, judiciously extended,<a name="FNanchor_130_130" id="FNanchor_130_130"></a><a href="#Footnote_130_130" class="fnanchor">[130]</a> without
+burdening the scholar with many branches or increasing
+the number of the hours of study. With more
+homogeneous work the student's capacity for work increases,
+one part of his labor supporting the other
+instead of obstructing it. If, however, a young man
+should subsequently choose a different profession, then
+it is <i>his</i> business to make up what he has lost. No
+harm certainly will come to society from this change,
+nor could it be regarded as a misfortune if philologists
+and lawyers with mathematical educations or physical
+scientists with classical educations should now and
+then appear.</p>
+<p><span class="pagenum"><a name="Page_372" id="Page_372">[Pg 372]</a></span></p><p><span class="pagenum"><a name="Page_373" id="Page_373">[Pg 373]</a></span><span class="pagenum"><a name="Page_374" id="Page_374">[Pg 374]</a></span></p><p><span class="pagenum"><a name="Page_375" id="Page_375">[Pg 375]</a></span></p>
+<hr class="tb" />
+
+<p>The view is now wide-spread that a Latin and
+Greek education no longer meets the general wants of
+the times, that a more opportune, a more "liberal"
+education exists. The phrase, "a liberal education,"
+has been greatly misused. A truly liberal education is
+unquestionably very rare. The <i>schools</i> can hardly offer
+such; at best they can only bring home to the student
+the necessity of it. It is, then, his business to acquire,
+as best he can, a more or less liberal education. It
+would be very difficult, too, at any one time to give a
+definition of a "liberal" education which would satisfy
+every one, still more difficult to give one which would
+hold good for a hundred years. The educational
+ideal, in fact, varies much. To one, a knowledge of
+classical antiquity appears not too dearly bought "with
+early death." We have no objection to this person,
+or to those who think like him, pursuing their ideal
+after their own fashion. But we may certainly protest
+strongly against the realisation of such ideals on our
+own children. Another,&mdash;Plato, for example,&mdash;puts
+men ignorant of geometry on a level with animals.<a name="FNanchor_131_131" id="FNanchor_131_131"></a><a href="#Footnote_131_131" class="fnanchor">[131]</a>
+If such narrow views had the magical powers of the
+sorceress Circe, many a man who perhaps justly
+thought himself well educated would become conscious
+of a not very flattering transformation of himself.
+Let us seek, therefore, in our educational system
+to meet the wants of the present, and not establish
+prejudices for the future.</p>
+
+<p>But how does it come, we must ask, that institutions
+so antiquated as the German gymnasiums could
+subsist so long in opposition to public opinion? The
+answer is simple. The schools were first organised by
+the Church; since the Reformation they have been in
+the hands of the State. On so large a scale, the plan
+presents many advantages. Means can be placed at
+the disposal of education such as no private source, at
+least in Europe, could furnish. Work can be conducted
+upon the same plan in many schools, and so
+experiments made of extensive scope which would be
+otherwise impossible. A single man with influence
+and ideas can under such circumstances do great
+things for the promotion of education.</p>
+
+<p>But the matter has also its reverse aspect. The
+party in power works for its own interests, uses the
+schools for its special purposes. Educational competition
+is excluded, for all successful attempts at improvement
+are impossible unless undertaken or permitted
+by the State. By the uniformity of the people's
+education, a prejudice once in vogue is permanently
+established. The highest intelligences, the strongest
+wills cannot overthrow it suddenly. In fact, as everything
+is adapted to the view in question, a sudden
+change would be physically impossible. The two
+classes which virtually hold the reins of power in the
+State, the jurists and theologians, know only the one-sided,
+predominantly classical culture which they have
+acquired in the State schools, and would have this culture
+alone valued. Others accept this opinion from
+credulity; others, underestimating their true worth for
+society, bow before the power of the prevalent opinion;
+others, again, affect the opinion of the ruling
+classes even against their better judgment, so as to
+abide on the same plane of respect with the latter. I
+will make no charges, but I must confess that the deportment
+of medical men with respect to the question
+of the qualification of graduates of your <i>Realschulen</i>
+has frequently made that impression upon me. Let
+us remember, finally, that an influential statesman,
+even within the boundaries which the law and public
+opinion set him, can do serious harm to the cause
+of education by considering his own one-sided views
+infallible, and in enforcing them recklessly and inconsiderately&mdash;which
+not only <i>can</i> happen, but has, repeatedly,
+happened.<a name="FNanchor_132_132" id="FNanchor_132_132"></a><a href="#Footnote_132_132" class="fnanchor">[132]</a> The monopoly of education by
+the State<a name="FNanchor_133_133" id="FNanchor_133_133"></a><a href="#Footnote_133_133" class="fnanchor">[133]</a> thus assumes in our eyes a somewhat different
+aspect. And to revert to the question above asked,
+there is not the slightest doubt that the German gymnasiums
+in their present form would have ceased to
+exist long ago if the State had not supported them.</p>
+
+<p>All this must be changed. But the change will
+not be made of itself, nor without our energetic interference,
+and it will be made slowly. But the path is
+marked out for us, the will of the people must acquire
+and exert upon our school legislation a greater and
+more powerful influence. Furthermore, the questions
+at issue must be publicly and candidly discussed that
+the views of the people may be clarified. All who feel
+the insufficiency of the existing <i>régime</i> must combine
+into a powerful organisation that their views may
+acquire impressiveness and the opinions of the individual
+not die away unheard.</p>
+
+<p>I recently read, gentlemen, in an excellent book of
+travels, that the Chinese speak with unwillingness of
+politics. Conversations of this sort are usually cut
+short with the remark that they may bother about such
+things whose business it is and who are paid for it.
+Now it seems to me that it is not only the business of
+the State, but a very serious concern of all of us, how
+our children shall be educated in the public schools
+at <i>our</i> cost.</p>
+
+
+
+
+<h2><a name="APPENDIX" id="APPENDIX">APPENDIX.</a></h2>
+
+<p class="center">I.</p>
+
+<h3><a id="A_CONTRIBUTION_TO_THE_HISTORY_OF_ACOUSTICS"></a>A CONTRIBUTION TO THE HISTORY OF ACOUSTICS.<a name="FNanchor_134_134" id="FNanchor_134_134"></a><a href="#Footnote_134_134" class="fnanchor">[134]</a></h3>
+
+
+<p>While searching for papers by Amontons, several
+volumes of the Memoirs of the Paris Academy
+for the first years of the eighteenth century, fell
+into my hands. It is difficult to portray the delight
+which one experiences in running over the leaves of
+these volumes. One sees as an actual spectator almost
+the rise of the most important discoveries and witnesses
+the progress of many fields of knowledge from
+almost total ignorance to relatively perfect clearness.</p>
+
+<p>I propose to discuss here the fundamental researches
+of Sauveur in Acoustics. It is astonishing
+how extraordinarily near Sauveur was to the view
+which Helmholtz was the first to adopt in its full extent
+a hundred and fifty years later.</p>
+
+<p>The <i>Histoire de l'Académie</i> for 1700, p. 131, tells
+us that Sauveur had succeeded in making music an<span class="pagenum"><a name="Page_376" id="Page_376">[Pg 376]</a></span>
+object of scientific research, and that he had invested
+the new science with the name of "acoustics." On
+five successive pages a number of discoveries are recorded
+which are more fully discussed in the volume
+for the year following.</p>
+
+<p>Sauveur regards the <i>simplicity</i> of the ratios obtaining
+between the rates of vibration of consonances as
+something universally known.<a name="FNanchor_135_135" id="FNanchor_135_135"></a><a href="#Footnote_135_135" class="fnanchor">[135]</a> He is in hope, by
+further research, of determining the chief rules of musical
+composition and of fathoming the "metaphysics
+of the agreeable," the main law of which he asserts
+to be the union of "simplicity with multiplicity."
+Precisely as Euler<a name="FNanchor_136_136" id="FNanchor_136_136"></a><a href="#Footnote_136_136" class="fnanchor">[136]</a> did a number of years later, he
+regards a consonance as more perfect according as
+the ratio of its vibrational rates is expressed in smaller
+whole numbers, because the smaller these whole numbers
+are the oftener the vibrations of the two tones
+coincide, and hence the more readily they are apprehended.
+As the limit of consonance, he takes the
+ratio 5:6, although he does not conceal the fact that
+practice, sharpened attention, habit, taste, and even
+prejudice play collateral rôles in the matter, and that
+consequently the question is not a purely scientific
+one.</p>
+
+<p>Sauveur's ideas took their development from his<span class="pagenum"><a name="Page_377" id="Page_377">[Pg 377]</a></span>
+having instituted at all points more exact quantitative
+investigations than his predecessors. He is first desirous
+of determining as the foundation of musical
+tuning a fixed note of one hundred vibrations which
+can be reproduced at any time; the fixing of the notes
+of musical instruments by the common tuning pipes
+then in use with rates of vibration unknown, appearing
+to him inadequate. According to Mersenne (<i>Harmonie
+Universelle</i>, 1636), a given cord seventeen feet
+long and weighted with eight pounds executes eight
+visible vibrations in a second. By diminishing its
+length then in a given proportion we obtain a proportionately
+augmented rate of vibration. But this procedure
+appears too uncertain to Sauveur, and he employs
+for his purpose the beats (<i>battemens</i>), which were
+known to the organ-makers of his day, and which he
+correctly explains as due to the alternate coincidence
+and non-coincidence of the same vibrational phases of
+differently pitched notes.<a name="FNanchor_137_137" id="FNanchor_137_137"></a><a href="#Footnote_137_137" class="fnanchor">[137]</a> At every coincidence there
+is a swelling of the sound, and hence the number of
+beats per second will be equal to the difference of the
+rates of vibration. If we tune two of three organ-pipes
+to the remaining one in the ratio of the minor and major
+third, the mutual ratio of the rates of vibration of
+the first two will be as 24: 25, that is to say, for every
+24 vibrations to the lower note there will be 25 to the
+higher, and one beat. If the two pipes give together<span class="pagenum"><a name="Page_378" id="Page_378">[Pg 378]</a></span>
+four beats in a second, then the higher has the fixed
+tone of 100 vibrations. The open pipe in question
+will consequently be five feet in length. We also determine
+by this procedure the absolute rates of vibration
+of all the other notes.</p>
+
+<p>It follows at once that a pipe eight times as long
+or 40 feet in length will yield a vibrational rate of
+12-1/2, which Sauveur ascribes to the lowest audible
+tone, and further also that a pipe 64 times as small
+will execute 6,400 vibrations, which Sauveur took for
+the highest audible limit. The author's delight at his
+successful enumeration of the "imperceptible vibrations"
+is unmistakably asserted here, and it is justified
+when we reflect that to-day even Sauveur's principle,
+slightly modified, constitutes the simplest and most
+delicate means we have for exactly determining rates
+of vibration. Far more important still, however, is a
+second observation which Sauveur made while studying
+beats, and to which we shall revert later.</p>
+
+<p>Strings whose lengths can be altered by movable
+bridges are much easier to handle than pipes in such
+investigations, and it was natural that Sauveur should
+soon resort to their use.</p>
+
+<p>One of his bridges accidentally not having been
+brought into full and hard contact with the string,
+and consequently only imperfectly impeding the vibrations,
+Sauveur discovered the harmonic overtones of
+the string, at first by the unaided ear, and concluded
+from this fact that the string was divided into aliquot<span class="pagenum"><a name="Page_379" id="Page_379">[Pg 379]</a></span>
+parts. The string when plucked, and when the bridge
+stood at the third division for example, yielded the
+twelfth of its fundamental note. At the suggestion
+of some academician<a name="FNanchor_138_138" id="FNanchor_138_138"></a><a href="#Footnote_138_138" class="fnanchor">[138]</a> probably, variously colored
+paper riders were placed at the nodes (<i>noeuds</i>) and
+ventral segments (<i>ventres</i>), and the division of the
+string due to the excitation of the overtones (<i>sons
+harmoniques</i>) belonging to its fundamental note (<i>son
+fondamental</i>) thus rendered visible. For the clumsy
+bridge the more convenient feather or brush was soon
+substituted.
+.
+While engaged in these investigations Sauveur also
+observed the sympathetic vibration of a string induced
+by the excitation of a second one in unison with it.
+He also discovered that the overtone of a string can
+respond to another string tuned to its note. He even
+went further and discovered that on exciting one string
+the overtone which it has in common with another,
+differently pitched string can be produced on that
+other; for example, on strings having for their vibrational
+ratio 3:4, the fourth of the lower and the third
+of the higher may be made to respond. It follows indisputably
+from this that the excited string yields
+overtones simultaneously with its fundamental tone.
+Previously to this Sauveur's attention had been drawn
+by other observers to the fact that the overtones of
+musical instruments can be picked out by attentive
+listening, particularly in the night.<a name="FNanchor_139_139" id="FNanchor_139_139"></a><a href="#Footnote_139_139" class="fnanchor">[139]</a> He himself mentions<span class="pagenum"><a name="Page_380" id="Page_380">[Pg 380]</a></span>
+the simultaneous sounding of the overtones and
+the fundamental tone.<a name="FNanchor_140_140" id="FNanchor_140_140"></a><a href="#Footnote_140_140" class="fnanchor">[140]</a> That he did not give the
+proper consideration to this circumstance was, as will
+afterwards be seen, fatal to his theory.</p>
+
+<p>While studying beats Sauveur makes the remark
+that they are <i>displeasing</i> to the ear. He held the beats
+were distinctly audible only when less than six occurred
+in a second. Larger numbers were not distinctly
+perceptible and gave rise accordingly to no
+disturbance. He then attempts to reduce the difference
+between consonance and dissonance to a question
+of beats. Let us hear his own words.<a name="FNanchor_141_141" id="FNanchor_141_141"></a><a href="#Footnote_141_141" class="fnanchor">[141]</a></p>
+
+<blockquote><p>"Beats are unpleasing to the ear because of the unevenness
+of the sound, and it may be held with much plausibility that the
+reason why octaves are so pleasing is that we never hear their
+beats.<a name="FNanchor_142_142" id="FNanchor_142_142"></a><a href="#Footnote_142_142" class="fnanchor">[142]</a></p>
+
+<p>"In following out this idea, we find that the chords whose
+beats we cannot hear are precisely those which the musicians call
+consonances and that those whose beats are heard are the dissonances,
+and that when a chord is a dissonance in one octave and a
+consonance in another, it beats in the one and does not beat in the
+other. Consequently it is called an imperfect consonance. It is
+very easy by the principles of M. Sauveur, here established, to ascertain
+what chords beat and in what octaves, above or below the
+fixed note. If this hypothesis be correct, it will disclose the true
+source of the rules of composition, hitherto unknown to science,
+and given over almost entirely to judgment by the ear. These
+sorts of natural judgment, marvellous though they may sometimes
+appear, are not so but have very real causes, the knowledge of
+which belongs to science, provided it can gain possession thereof."<a name="FNanchor_143_143" id="FNanchor_143_143"></a><a href="#Footnote_143_143" class="fnanchor">[143]</a></p></blockquote>
+
+<p><span class="pagenum"><a name="Page_381" id="Page_381">[Pg 381]</a></span></p><p>Sauveur thus correctly discerns in beats the cause
+of the disturbance of consonance, to which all disharmony
+is "probably" to be referred. It will be seen,
+however, that according to his view all distant intervals
+must necessarily be consonances and all near intervals
+dissonances. He also overlooks the absolute
+difference in point of principle between his old view,
+mentioned at the outset, and his new view, rather attempting
+to obliterate it.</p>
+
+<p>R. Smith<a name="FNanchor_144_144" id="FNanchor_144_144"></a><a href="#Footnote_144_144" class="fnanchor">[144]</a> takes note of the theory of Sauveur and
+calls attention to the first of the above-mentioned defects.
+Being himself essentially involved in the old
+view of Sauveur, which is usually attributed to Euler,
+he yet approaches in his criticism a brief step nearer<span class="pagenum"><a name="Page_382" id="Page_382">[Pg 382]</a></span>
+to the modern theory, as appears from the following
+passage.<a name="FNanchor_145_145" id="FNanchor_145_145"></a><a href="#Footnote_145_145" class="fnanchor">[145]</a></p>
+
+<blockquote><p>"The truth is, this gentleman confounds the distinction between
+perfect and imperfect consonances, by comparing imperfect
+consonances which beat because the succession of their short cycles<a name="FNanchor_146_146" id="FNanchor_146_146"></a><a href="#Footnote_146_146" class="fnanchor">[146]</a>
+is periodically confused and interrupted, with perfect ones
+which cannot beat, because the succession of their short cycles is
+never confused nor interrupted.</p>
+
+<p>"The <i>fluttering roughness</i> above mentioned is perceivable
+in all other perfect consonances, in a smaller degree in proportion
+as their cycles are shorter and simpler, and their pitch is higher;
+and is of a <i>different kind</i> from the <i>smoother beats</i> and undulations
+of <i>tempered consonances</i>; because we can alter the rate of
+the latter by altering the temperament, but not of the former, the
+consonance being perfect at a given pitch: And because a judicious
+ear can often hear, at the same time, both the flutterings and the
+beats of a tempered consonance; sufficiently distinct from each
+other.</p>
+
+<p>"For nothing gives greater offence to the hearer, though ignorant
+of the cause of it, than those rapid, piercing beats of high
+and loud sounds, which make imperfect consonances with one another.
+And yet a few slow beats, like the slow undulations of a
+close shake now and then introduced, are far from being disagreeable."</p></blockquote>
+
+<p>Smith is accordingly clear that other "roughnesses"
+exist besides the beats which Sauveur considered,
+and if the investigations had been continued
+on the basis of Sauveur's idea, these additional roughnesses
+would have turned out to be the beats of the<span class="pagenum"><a name="Page_383" id="Page_383">[Pg 383]</a></span>
+overtones, and the theory thus have attained the
+point of view of Helmholtz.</p>
+
+<p>Reviewing the differences between Sauveur's and
+Helmholtz's theories, we find the following:</p>
+
+<p>1. The theory according to which consonance depends
+on the frequent and regular coincidence of vibrations
+and their ease of enumeration, appears from
+the new point of view inadmissible. The simplicity
+of the ratios obtaining between the rates of vibration
+is indeed a <i>mathematical</i> characteristic of consonance
+as well as a <i>physical</i> condition thereof, for the reason
+that the coincidence of the overtones as also their
+further physical and physiological consequences is
+connected with this fact. But no <i>physiological</i> or <i>psychological</i>
+explanation of consonance is given by this
+fact, for the simple reason that in the acoustic nerve-process
+nothing corresponding to the periodicity of
+the sonant stimulus is discoverable.</p>
+
+<p>2. In the recognition of beats as a disturbance of
+consonance, both theories agree. Sauveur's theory,
+however, does not take into account the fact that
+clangs, or musical sounds generally, are composite
+and that the disturbance in the consonances of distant
+intervals principally arise from the beats of the overtones.
+Furthermore, Sauveur was wrong in asserting
+that the number of beats must be less than six in a
+second in order to produce disturbances. Even Smith
+knows that very slow beats are not a cause of disturbance,
+and Helmholtz found a much higher number<span class="pagenum"><a name="Page_384" id="Page_384">[Pg 384]</a></span>
+(33) for the maximum of disturbance. Finally, Sauveur
+did not consider that although the number of
+beats increases with the recession from unison, yet
+their <i>strength</i> is diminished. On the basis of the
+principle of specific energies and of the laws of sympathetic
+vibration the new theory finds that two atmospheric
+motions of like amplitude but different periods,
+<i>a</i> sin(<i>rt</i>) and <i>a</i> sin[(<i>r</i> + &#961;)(<i>t</i> + &#964;)], cannot be
+communicated with the same amplitude to the same
+nervous end-organ. On the contrary, an end-organ
+that reacts best to the period <i>r</i> responds more weakly
+to the period <i>r</i> + &#961;, the two amplitudes bearing to each
+other the proportion <i>a</i>: &#966;<i>a</i>. Here &#966; decreases when
+&#961; increases, and when &#961; = 0 it becomes equal to 1, so
+that only the portion of the stimulus &#966;<i>a</i> is subject to
+beats, and the portion (1-&#966;)<i>a</i> continues smoothly
+onward without disturbance.</p>
+
+<p>If there is any moral to be drawn from the history
+of this theory, it is that considering how near Sauveur's
+errors were to the truth, it behooves us to exercise
+some caution also with regard to the new theory.
+And in reality there seems to be reason for
+doing so.</p>
+
+<p>The fact that a musician will never confound a
+more perfectly consonant chord on a poorly tuned
+piano with a less perfectly consonant chord on a well
+tuned piano, although the roughness in the two cases
+may be the same, is sufficient indication that the degree
+of roughness is not the only characteristic of a<span class="pagenum"><a name="Page_385" id="Page_385">[Pg 385]</a></span>
+harmony. As the musician knows, even the harmonic
+beauties of a Beethoven sonata are not easily effaced
+on a poorly tuned piano; they scarcely suffer more
+than a Raphael drawing executed in rough unfinished
+strokes. The <i>positive physiologico-psychological</i> characteristic
+which distinguishes one harmony from another
+is not given by the beats. Nor is this characteristic
+to be found in the fact that, for example, in sounding
+a major third the fifth partial tone of the lower note
+coincides with the fourth of the higher note. This
+characteristic comes into consideration only for the
+investigating and abstracting reason. If we should
+regard it also as characteristic of the sensation, we
+should lapse into a fundamental error which would
+be quite analogous to that cited in (1).</p>
+
+<p>The <i>positive physiological</i> characteristics of the intervals
+would doubtless be speedily revealed if it were
+possible to conduct aperiodic, for example galvanic,
+stimuli to the single sound-sensing organs, in which
+case the beats would be totally eliminated. Unfortunately
+such an experiment can hardly be regarded as
+practicable. The employment of acoustic stimuli of
+short duration and consequently also free from beats,
+involves the additional difficulty of a pitch not precisely
+determinable.</p><hr class="chap" /><p><span class="pagenum"><a name="Page_386" id="Page_386">[Pg 386]</a></span></p>
+
+
+
+
+<p class="center">II.</p>
+
+<h3><a id="REMARKS_ON_THE_THEORY_OF_SPATIAL_VISION"></a>REMARKS ON THE THEORY OF SPATIAL VISION.<a name="FNanchor_147_147" id="FNanchor_147_147"></a><a href="#Footnote_147_147" class="fnanchor">[147]</a></h3>
+
+
+<p>According to Herbart, spatial vision rests on reproduction-series.
+In such an event, of course, and
+if the supposition is correct, the magnitudes of the
+residua with which the percepts or representations
+are coalesced (the helps to coalescence) are of cardinal
+influence. Furthermore, since the coalescences
+must first be fully perfected before they make their
+appearance, and since upon their appearance the inhibitory
+ratios are brought into play, ultimately, then,
+if we leave out of account the accidental order of time
+in which the percepts are given, everything in spatial
+vision depends on the oppositions and affinities, or,
+in brief, on the qualities of the percepts, which enter
+into series.</p>
+
+<p>Let us see how the theory stands with respect to
+the special facts involved.</p>
+
+<p>1. If intersecting series only, running anteriorly
+and posteriorly, are requisite for the production of
+spatial sensation, why are not analogues of them found
+in all the senses?</p>
+
+<p>2. Why do we measure differently colored objects<span class="pagenum"><a name="Page_387" id="Page_387">[Pg 387]</a></span>
+and variegated objects with one and the same spatial
+measure? How do we recognise differently colored
+objects as the same in size? Where do we get our
+measure of space from and what is it?</p>
+
+<p>3. Why is it that differently colored figures of the
+same form reproduce one another and are recognised
+as the same?</p>
+
+<p>Here are difficulties enough. Herbart is unable to
+solve them by his theory. The unprejudiced student
+sees at once that his "inhibition by reason of form"
+and "preference by reason of form" are absolutely
+impossible. Think of Herbart's example of the red
+and black letters.</p>
+
+<p>The "help to coalescence" is a passport, so to
+speak, made out to the name and person of the percept.
+A percept which is coalesced with another cannot
+reproduce all others qualitatively different from it
+for the simple reason that the latter are in like manner
+coalesced with one another. Two qualitatively different
+series certainly do not reproduce themselves because
+they present the same order of degree of coalescence.</p>
+
+<p>If it is certain that only things simultaneous and
+things which are alike are reproduced, a basic principle
+of Herbart's psychology which even the most
+absolute empiricists will not deny, nothing remains
+but to modify the theory of spatial perception or to
+invent in its place a new principle in the manner indicated,
+a step which hardly any one would seriously<span class="pagenum"><a name="Page_388" id="Page_388">[Pg 388]</a></span>
+undertake. The new principle could not fail to throw
+all psychology into the most dreadful confusion.</p>
+
+<p>As to the modification which is needed there can
+be hardly any doubt as to how in the face of the facts
+and conformably to Herbart's own principles it is to
+be carried out. If two differently colored figures of
+equal size reproduce each other and are recognised as
+equal, the result can be due to nothing but to the existence
+in both series of presentations of a presentation
+or percept which is qualitatively <i>the same</i>. The
+colors are different. Consequently, like or equal percepts
+must be connected with the colors which are
+yet independent of the colors. We have not to look
+long for them, for they are the like effects of the muscular
+feelings of the eye when confronted by the two
+figures. We might say we reach the vision of space
+by the registering of light-sensations in a schedule of
+graduated muscle-sensations.<a name="FNanchor_148_148" id="FNanchor_148_148"></a><a href="#Footnote_148_148" class="fnanchor">[148]</a></p>
+
+<p>A few considerations will show the likelihood of
+the rôle of the muscle-sensations. The muscular apparatus
+of <i>one</i> eye is unsymmetrical. The two eyes
+together form a system which is vertical in symmetry.
+This already explains much.</p>
+
+<p>1. The <i>position</i> of a figure influences its view. According
+to the position in which objects are viewed
+different muscle-sensations come into play and the
+impression is altered. To recognise inverted letters<span class="pagenum"><a name="Page_389" id="Page_389">[Pg 389]</a></span>
+as such long experience is required. The best proof
+of this are the letters d, b, p, q, which are represented
+by the same figure in different positions and yet are
+always distinguished as different.<a name="FNanchor_149_149" id="FNanchor_149_149"></a><a href="#Footnote_149_149" class="fnanchor">[149]</a></p>
+
+<p>2. It will not escape the attentive observer that for
+the same reasons and even with the same figure and
+in the same position the fixation point is also decisive.
+The figure seems to change <i>during</i> the act of vision.
+For example, an eight-pointed star constructed by
+successively joining in a regular octagon the first corner
+with the fourth, the fourth with the seventh, etc.,
+skipping in every case two corners, assumes alternately,
+according to where we suffer the centre of vision
+to rest, a predominantly architectonic or a freer
+and more open character. Vertical and horizontal
+lines are always differently apprehended from what
+oblique lines are.</p>
+
+<div class="figleft" style="width: 300px;">
+<img src="images/i_399.jpg" width="300" height="130" alt="" />
+<span class="caption">Fig. 58.</span>
+</div>
+
+<p>3. The reason why we prefer vertical symmetry
+and regard it as something special in its kind, whereas
+we do not recognise
+horizontal symmetry
+at all immediately, is
+due to the vertical
+symmetry of the muscular
+apparatus of the eye. The left-hand side <i>a</i> of
+the accompanying vertically-symmetrical figure induces
+in the left eye the same muscular feelings as the<span class="pagenum"><a name="Page_390" id="Page_390">[Pg 390]</a></span>
+right-hand side <i>b</i> does in the right eye. The pleasing
+effect of symmetry has its cause primarily in the repetition
+of muscular feelings. That a repetition actually
+occurs here, sometimes sufficiently marked in character
+as to lead to the confounding of objects, is
+proved apart from the theory by the fact which is
+familiar to every one <i>quem dii oderunt</i> that children
+frequently reverse figures from the right to the left,
+but never from above downwards; for example, write
+ε instead of 3 until they finally come to notice the
+slight difference. Figure 50 shows how pleasing the
+repetition of muscular
+feelings may be. As
+will be readily understood,
+vertical and horizontal lines exhibit relations
+similar to symmetrical figures which are immediately
+disturbed when oblique positions are chosen for the
+lines. Compare what Helmholtz says regarding the
+repetition and coincidence of partial tones.</p>
+
+<div class="figright" style="width: 400px;">
+<img src="images/i_400.jpg" width="400" height="88" alt="" />
+<span class="caption">Fig. 59.</span>
+</div>
+
+<p>I may be permitted to add a general remark. It
+is a quite universal phenomenon in psychology that
+certain qualitatively quite different series of percepts
+mutually awaken and reproduce one another and in a
+certain aspect produce the appearance of sameness or
+similarity. We say of such series that they are of
+like or of similar form, naming their abstracted likeness
+<i>form</i>.</p>
+
+<blockquote><p>1. Of spatial figures we have already spoken.</p>
+
+<p>2. We call two melodies like melodies when they<span class="pagenum"><a name="Page_391" id="Page_391">[Pg 391]</a></span>
+present the same succession of pitch-ratios;
+the absolute pitch (or key) may be as different
+as can be. We can so select the melodies that
+not even two partial tones of the notes in each
+are common. Yet we recognise the melodies
+as alike. And, what is more, we notice the
+form of the melody more readily and recognise
+it again more easily than the key (the absolute
+pitch) in which it was played.</p>
+
+<p>3. We recognise in two different melodies the
+same rhythm no matter how different the melodies
+may be otherwise. We know and recognise
+the rhythm more easily even than the absolute
+duration (the tempo).</p></blockquote>
+
+<p>These examples will suffice. In all these and in
+all similar cases the recognition and likeness cannot
+depend upon the qualities of the percepts, for these
+are different. On the other hand recognition, conformably
+to the principles of psychology, is possible
+only with percepts which are the same in quality.
+Consequently there is no other escape than to imagine
+the qualitatively unlike percepts of the two series as
+necessarily connected with other percepts which are
+qualitatively alike.</p>
+
+<p>Since in differently colored figures of like form, like
+muscular feelings are necessarily induced if the figures
+are recognised as alike, so there must necessarily lie
+at the basis of all forms also, and we might even say
+at the basis of all abstractions, percepts of a peculiar<span class="pagenum"><a name="Page_392" id="Page_392">[Pg 392]</a></span>
+quality. And this holds true for space and form as
+well as for time, rhythm, pitch, the form of melodies,
+intensity, etc. But whence is psychology to derive all
+these qualities? Have no fear, they will all be found,
+as were the sensations of muscles for the theory of
+space. The organism is at present still rich enough
+to meet all the requirements of psychology in this direction,
+and it is even time to give serious ear to the
+question of "corporeal resonance" which psychology
+so loves to dwell on.</p>
+
+<p>Different psychical qualities appear to bear a very
+intimate mutual relation to one another. Special research
+on the subject, as well also as the demonstration
+that this remark may be generally employed in
+physics, will follow later.<a name="FNanchor_150_150" id="FNanchor_150_150"></a><a href="#Footnote_150_150" class="fnanchor">[150]</a></p>
+<p><span class="pagenum"><a name="Page_393" id="Page_393">[Pg 393]</a></span></p>
+
+
+
+<h2><a name="INDEX" id="INDEX">INDEX.</a></h2>
+
+
+<ul class="IX"><li>Absolute, temperature, <a href="#Page_162">162</a>;</li>
+<li><span style="margin-left: 1em;">time, <a href="#Page_204">204</a>;</span></li>
+<li><span style="margin-left: 1em;">forecasts, have no signification in science, <a href="#Page_206">206</a>.</span></li>
+
+<li>Abstract, meaning of the term, <a href="#Page_240">240</a>.</li>
+
+<li>Abstraction, <a href="#Page_180">180</a>, <a href="#Page_200">200</a>, <a href="#Page_208">208</a>, <a href="#Page_231">231</a>.</li>
+
+<li>Acceleration, organ for forward, <a href="#Page_299">299</a> et seq.</li>
+
+<li>Accelerations, <a href="#Page_204">204</a>, <a href="#Page_216">216</a>, footnote, <a href="#Page_225">225</a>-<a href="#Page_226">226</a>, <a href="#Page_253">253</a>.</li>
+
+<li>Accident, logical and historical, in science, <a href="#Page_160">160</a>, <a href="#Page_168">168</a>, <a href="#Page_170">170</a>, <a href="#Page_213">213</a>;</li>
+<li><span style="margin-left: 1em;">in inventions and discoveries, <a href="#Page_262">262</a> et seq.</span></li>
+
+<li>Accord, the pure triple, <a href="#Page_46">46</a>.</li>
+
+<li>Accumulators, electrical, <a href="#Page_125">125</a> et seq.;</li>
+<li><span style="margin-left: 1em;"><a href="#Page_132">132</a>, footnote.</span></li>
+
+<li>Acoustic color, <a href="#Page_36">36</a>.</li>
+
+<li>Acoustics, Sauveur on, <a href="#Page_375">375</a> et seq.</li>
+
+<li>Action and reaction, importance of the principle of, <a href="#Page_191">191</a>.</li>
+
+<li>Adaptation, in organic and inorganic matter, <a href="#Page_216">216</a>, <a href="#Page_229">229</a>;</li>
+<li><span style="margin-left: 1em;">in scientific thought, <a href="#Page_214">214</a>-<a href="#Page_235">235</a>.</span></li>
+
+<li>Æsthetics, computation as a principle of, <a href="#Page_34">34</a>;</li>
+<li><span style="margin-left: 1em;">researches in, <a href="#Page_89">89</a>, footnote;</span></li>
+<li><span style="margin-left: 1em;">repetition, a principle of, <a href="#Page_91">91</a>.</span></li>
+
+<li>Africa, <a href="#Page_186">186</a>, <a href="#Page_234">234</a>, <a href="#Page_237">237</a>.</li>
+
+<li>Agreeable effects, due to repetition of sensations, <a href="#Page_92">92</a>, <a href="#Page_97">97</a> et seq.</li>
+
+<li>Agriculture, transition to, <a href="#Page_265">265</a>.</li>
+
+<li>Air-gun, <a href="#Page_135">135</a>.</li>
+
+<li>Alcohol and water, mixture of oil and, in Plateau's experiments, <a href="#Page_4">4</a>.</li>
+
+<li>Algebra, economy of, <a href="#Page_196">196</a>.</li>
+
+<li>Alien thoughts in science, <a href="#Page_196">196</a>.</li>
+
+<li>All, the, <a href="#Page_88">88</a>.</li>
+
+<li>Amontons, <a href="#Page_174">174</a>, <a href="#Page_346">346</a>.</li>
+
+<li>Ampère, the word, <a href="#Page_314">314</a>.</li>
+
+<li>Ampère's swimmer, <a href="#Page_207">207</a>.</li>
+
+<li>Analogies, mechanical, <a href="#Page_157">157</a>, <a href="#Page_160">160</a>;</li>
+<li><span style="margin-left: 1em;">generally, <a href="#Page_236">236</a>-<a href="#Page_258">258</a>.</span></li>
+
+<li>Analogy, defined, <a href="#Page_250">250</a>.</li>
+
+<li>Analysis, <a href="#Page_188">188</a>.</li>
+
+<li>Analytical geometry, not necessary to physicians, <a href="#Page_370">370</a>, footnote.</li>
+
+<li>Anatomic structures, transparent stereoscopic views of, <a href="#Page_74">74</a>.</li>
+
+<li>Anatomy, character of research in, <a href="#Page_255">255</a>.</li>
+
+<li>Andrieu, Jules, <a href="#Page_49">49</a>, footnote.</li>
+
+<li>Animals, the psychical activity of, <a href="#Page_190">190</a>, <a href="#Page_231">231</a>;</li>
+<li><span style="margin-left: 1em;">the language of, <a href="#Page_238">238</a>;</span></li>
+<li><span style="margin-left: 1em;">their capacity for experience, <a href="#Page_266">266</a> et seq.</span></li>
+
+<li>Animism, <a href="#Page_186">186</a>, <a href="#Page_187">187</a>, <a href="#Page_243">243</a>, <a href="#Page_254">254</a>.</li>
+
+<li>Anisotropic optical fields, <a href="#Page_227">227</a>.</li>
+
+<li>Apparatus for producing movements of rotation, <a href="#Page_287">287</a> et seq.</li>
+
+<li>Arabesque, an inverted, <a href="#Page_95">95</a>.</li>
+
+<li>Arabian Nights, <a href="#Page_219">219</a>.</li>
+
+<li>Arago, <a href="#Page_270">270</a>.</li>
+
+<li>Aral, the Sea of, <a href="#Page_239">239</a>.</li>
+
+<li>Archæopteryx, <a href="#Page_257">257</a>.</li>
+
+<li>Archimedes, <a href="#Page_4">4</a>, <a href="#Page_237">237</a>.</li>
+
+<li>Arcimboldo, Giuseppe, <a href="#Page_36">36</a>.</li>
+
+<li>Area, principle of least superficial, <a href="#Page_10">10</a> et seq.</li>
+
+<li>Ares, the bellowing of the wounded, <a href="#Page_272">272</a>.</li>
+
+<li>Aristotelians, <a href="#Page_283">283</a>.</li>
+
+<li>Aristotle, <a href="#Page_348">348</a>, <a href="#Page_296">296</a>.</li>
+
+<li>Art, development of, <a href="#Page_28">28</a> et seq.</li>
+
+<li>Artillery, practical, <a href="#Page_334">334</a>-<a href="#Page_335">335</a>.</li>
+
+<li>Artistic value of scientific descriptions, <a href="#Page_254">254</a>.</li>
+
+<li>Arts, practical, <a href="#Page_108">108</a>.</li>
+
+<li>Ascent, heights of, <a href="#Page_143">143</a>-<a href="#Page_151">151</a>.</li>
+
+<li><span class="pagenum"><a name="Page_394" id="Page_394">[Pg 394]</a></span>Asia, 234.</li>
+
+<li>Assyrians, the art of, <a href="#Page_79">79</a>.</li>
+
+<li>Astronomer, measures celestial by terrestrial distances, <a href="#Page_136">136</a>.</li>
+
+<li>Astronomy, antecedent to psychology, <a href="#Page_90">90</a>;</li>
+<li><span style="margin-left: 1em;">rigidity of its truths, <a href="#Page_221">221</a>.</span></li>
+
+<li>Atomic theories, <a href="#Page_104">104</a>.</li>
+
+<li>Atoms, <a href="#Page_207">207</a>.</li>
+
+<li>Attention, the rôle of, in sensuous perception, <a href="#Page_35">35</a> et seq.</li>
+
+<li>Attraction, generally, <a href="#Page_226">226</a>;</li>
+<li><span style="margin-left: 1em;">of liquid particles, <a href="#Page_13">13</a>-<a href="#Page_14">14</a>;</span></li>
+<li><span style="margin-left: 1em;">in electricity, <a href="#Page_109">109</a> et seq.</span></li>
+
+<li>Aubert, <a href="#Page_298">298</a>.</li>
+
+<li>Audition. See <i>Ear</i>.</li>
+
+<li>Austrian gymnasiums, <a href="#Page_370">370</a>, footnote.</li>
+
+<li>Axioms, instinctive knowledge, <a href="#Page_190">190</a>.</li>
+
+</ul>
+
+<ul class="IX"><li>Babbage, on the economy of machinery, <a href="#Page_196">196</a>.</li>
+
+<li>Bach, <a href="#Page_20">20</a>.</li>
+
+<li>Backwards, prophesying, <a href="#Page_253">253</a>.</li>
+
+<li>Bacon, Lord, <a href="#Page_48">48</a>, <a href="#Page_280">280</a>.</li>
+
+<li>Baer, C. E. von, <a href="#Page_235">235</a>.</li>
+
+<li>Balance, electrical, <a href="#Page_127">127</a>, footnote;</li>
+<li><span style="margin-left: 1em;">torsion, <a href="#Page_109">109</a>, <a href="#Page_168">168</a>.</span></li>
+
+<li>Balloon, a hydrogen, <a href="#Page_199">199</a>.</li>
+
+<li>Barbarism and civilisation, <a href="#Page_335">335</a> et seq.</li>
+
+<li>Bass-clef, <a href="#Page_101">101</a>.</li>
+
+<li>Bass, fundamental, <a href="#Page_44">44</a>.</li>
+
+<li>Beats, <a href="#Page_40">40</a>-<a href="#Page_45">45</a>, <a href="#Page_377">377</a> et seq.</li>
+
+<li>Beautiful, our notions of, variable, <a href="#Page_99">99</a>.</li>
+
+<li>Beauty, objects of, in nature, <a href="#Page_91">91</a>.</li>
+
+<li>Becker, J. K., <a href="#Page_364">364</a>, <a href="#Page_369">369</a>.</li>
+
+<li>Beethoven, <a href="#Page_39">39</a>, <a href="#Page_44">44</a>.</li>
+
+<li>Beginnings of science, <a href="#Page_189">189</a>, <a href="#Page_191">191</a>.</li>
+
+<li>Belvedere Gallery at Vienna, <a href="#Page_36">36</a>.</li>
+
+<li>Bernoulli, Daniel, on the conservation of living force, <a href="#Page_149">149</a>;</li>
+<li><span style="margin-left: 1em;">on the vibrations of strings, <a href="#Page_249">249</a>.</span></li>
+
+<li>Bernoulli, James, on the centre of oscillation, <a href="#Page_149">149</a>.</li>
+
+<li>Bernoulli, John, on the conservation of living force, <a href="#Page_149">149</a>;</li>
+<li><span style="margin-left: 1em;">on the principle of virtual velocities, <a href="#Page_151">151</a>.</span></li>
+
+<li>Bible, parallel passages from, for language study, <a href="#Page_356">356</a>.</li>
+
+<li>Binocular vision, <a href="#Page_66">66</a> et seq.</li>
+
+<li>Black, his theory of caloric, <a href="#Page_138">138</a>, <a href="#Page_162">162</a>;</li>
+<li><span style="margin-left: 1em;">on quantity of heat, <a href="#Page_166">166</a>, <a href="#Page_174">174</a>;</span></li>
+<li><span style="margin-left: 1em;">on latent heat, <a href="#Page_167">167</a>, <a href="#Page_178">178</a>;</span></li>
+<li><span style="margin-left: 1em;">researches in heat generally, <a href="#Page_244">244</a>.</span></li>
+
+<li>Blind cat, <a href="#Page_303">303</a>.</li>
+
+<li>Bodies, heavy, seek their places, <a href="#Page_224">224</a> et seq.;</li>
+<li><span style="margin-left: 1em;">rotating, <a href="#Page_285">285</a>.</span></li>
+
+<li>Body, a mental symbol for groups of sensations, <a href="#Page_200">200</a>-<a href="#Page_203">203</a>;</li>
+<li><span style="margin-left: 1em;">the human, our knowledge of, <a href="#Page_90">90</a>.</span></li>
+
+<li>Boltzmann, <a href="#Page_236">236</a>.</li>
+
+<li>Booth, Mr., <a href="#Page_77">77</a>.</li>
+
+<li>Borelli, <a href="#Page_217">217</a>.</li>
+
+<li>Boulder, a granite, <a href="#Page_233">233</a>.</li>
+
+<li>Bow-wave of ships and moving projectiles, <a href="#Page_323">323</a> et seq.</li>
+
+<li>Boys, <a href="#Page_317">317</a>.</li>
+
+<li>Bradley, <a href="#Page_273">273</a>.</li>
+
+<li>Brahman, the, <a href="#Page_63">63</a>.</li>
+
+<li>Brain, localisation of functions in, <a href="#Page_210">210</a>.</li>
+
+<li>Breuer, <a href="#Page_272">272</a>, <a href="#Page_282">282</a> et seq., <a href="#Page_293">293</a>, <a href="#Page_298">298</a>, <a href="#Page_300">300</a>, <a href="#Page_301">301</a>, <a href="#Page_303">303</a>, <a href="#Page_306">306</a>.</li>
+
+<li>Brewster, his stereoscope, <a href="#Page_73">73</a>.</li>
+
+<li>Bridge, invention of the, <a href="#Page_264">264</a>, <a href="#Page_268">268</a>.</li>
+
+<li>British Association, <a href="#Page_108">108</a>.</li>
+
+<li>Brooklyn Bridge, <a href="#Page_75">75</a>, footnote.</li>
+
+<li>Brown, Crum, <a href="#Page_293">293</a>, <a href="#Page_301">301</a>.</li>
+
+<li>Building, our concepts directions for, <a href="#Page_253">253</a>;</li>
+<li><span style="margin-left: 1em;">facts the result of, <a href="#Page_253">253</a>;</span></li>
+<li><span style="margin-left: 1em;">science compared to, <a href="#Page_257">257</a>.</span></li>
+
+<li>Building-stones, metrical units are, <a href="#Page_253">253</a>.</li>
+
+<li>Busch, <a href="#Page_328">328</a>.</li>
+
+<li>Business of a merchant, science compared to the, <a href="#Page_16">16</a>.</li>
+
+<li>Butterfly, a, <a href="#Page_22">22</a>.</li>
+</ul>
+
+<ul class="IX"><li>Calculating machines, their economical character, <a href="#Page_196">196</a>.</li>
+
+<li>Caloric, theory of, stood in the way of scientific advancement, <a href="#Page_138">138</a>, <a href="#Page_167">167</a>.</li>
+
+<li>Calypso, the island of, <a href="#Page_351">351</a>.</li>
+
+<li>Canterbury, Archbishop of, <a href="#Page_39">39</a>.</li>
+
+<li>Cantor, M., <a href="#Page_361">361</a>, footnote.</li>
+
+<li>Capacity, electrical, <a href="#Page_116">116</a> et seq., <a href="#Page_123">123</a>;</li>
+<li><span style="margin-left: 1em;">thermal, <a href="#Page_123">123</a>;</span></li>
+<li><span style="margin-left: 1em;">specific inductive, <a href="#Page_117">117</a>.</span></li>
+
+<li>Capulets and Montagues, <a href="#Page_87">87</a>.</li>
+
+<li>Cards, difficult games of, <a href="#Page_357">357</a>.</li>
+
+<li>Carnot, S., excludes perpetual motion in heat, <a href="#Page_156">156</a>, <a href="#Page_162">162</a>;</li>
+<li><span style="margin-left: 1em;">his mechanical view of physics, <a href="#Page_156">156</a>;</span></li>
+<li><span class="pagenum"><a name="Page_395" id="Page_395">[Pg 395]</a></span><span style="margin-left: 1em;">on thermodynamics, <a href="#Page_160">160</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">his principle, <a href="#Page_162">162</a>;</span></li>
+<li><span style="margin-left: 1em;">also, <a href="#Page_191">191</a>.</span></li>
+
+<li>Carus, Dr. Paul, <a href="#Page_265">265</a>, footnote.</li>
+
+<li>Casselli's telegraph, <a href="#Page_26">26</a>.</li>
+
+<li>Cassini, <a href="#Page_51">51</a>.</li>
+
+<li>Cauchy, character of the intellectual activity of a, <a href="#Page_195">195</a>.</li>
+
+<li>Causal insight, awakened by science, <a href="#Page_357">357</a>.</li>
+
+<li>Causality, <a href="#Page_157">157</a>-<a href="#Page_159">159</a>, <a href="#Page_190">190</a>, <a href="#Page_198">198</a> et seq., <a href="#Page_221">221</a> et seq., <a href="#Page_237">237</a>, <a href="#Page_253">253</a>, <a href="#Page_254">254</a>.</li>
+
+<li>Cause and effect, <a href="#Page_198">198</a> et seq. See also <i>Causality</i>.</li>
+
+<li>Centimetre-gramme-second system, <a href="#Page_111">111</a>.</li>
+
+<li>Centre of gravity, must lie as low as possible for equilibrium to subsist, <a href="#Page_15">15</a>;</li>
+<li><span style="margin-left: 1em;">Torricelli's principle of, <a href="#Page_150">150</a> et seq.</span></li>
+
+<li>Centre of oscillation, <a href="#Page_149">149</a>.</li>
+
+<li>Change, method of, in science, <a href="#Page_230">230</a>.</li>
+
+<li>Changeable character of bodies, <a href="#Page_202">202</a>.</li>
+
+<li>Changes, physical, how they occur, <a href="#Page_205">205</a>.</li>
+
+<li>Character, a Universal Real, <a href="#Page_192">192</a>.</li>
+
+<li>Character, like the forms of liquids, <a href="#Page_3">3</a>;</li>
+<li><span style="margin-left: 1em;">persons of, <a href="#Page_24">24</a>.</span></li>
+
+<li>Charles the Fifth, <a href="#Page_369">369</a>.</li>
+
+<li>Chemical, elements, <a href="#Page_202">202</a>;</li>
+<li><span style="margin-left: 1em;">symbols, <a href="#Page_192">192</a>;</span></li>
+<li><span style="margin-left: 1em;">current, <a href="#Page_118">118</a>.</span></li>
+
+<li>Chemistry, character of research in, <a href="#Page_255">255</a>;</li>
+<li><span style="margin-left: 1em;">the method of thermodynamics in, <a href="#Page_257">257</a>.</span></li>
+
+<li>Child, a, modes of thought of, <a href="#Page_223">223</a>;</li>
+<li><span style="margin-left: 1em;">looking into a moat, <a href="#Page_208">208</a>.</span></li>
+
+<li>Child of the forest, his interpretation of new events, <a href="#Page_218">218</a>-<a href="#Page_219">219</a>.</li>
+
+<li>Childish questions, <a href="#Page_199">199</a>-<a href="#Page_200">200</a>.</li>
+
+<li>Children, the drawings of, <a href="#Page_201">201</a>-<a href="#Page_202">202</a>.</li>
+
+<li>Chinese language, economy of, <a href="#Page_192">192</a>;</li>
+<li><span style="margin-left: 1em;">study of, <a href="#Page_354">354</a>.</span></li>
+
+<li>Chinese philosopher, an old, <a href="#Page_186">186</a>.</li>
+
+<li>Chinese, speak with unwillingness of politics, <a href="#Page_374">374</a>;</li>
+<li><span style="margin-left: 1em;">the art of, <a href="#Page_79">79</a>-<a href="#Page_80">80</a>.</span></li>
+
+<li>Chosen, many are called but few are, <a href="#Page_65">65</a>.</li>
+
+<li>Christ, saying of, <a href="#Page_65">65</a>.</li>
+
+<li>Christianity, Latin introduced with, <a href="#Page_311">311</a>.</li>
+
+<li>Christians and Jews, monotheism of the, <a href="#Page_187">187</a>.</li>
+
+<li>Church and State, <a href="#Page_88">88</a>.</li>
+
+<li>Cicero, <a href="#Page_318">318</a>.</li>
+
+<li>Circe, <a href="#Page_372">372</a>.</li>
+
+<li>Circle, the figure of least area with given periphery, <a href="#Page_12">12</a>.</li>
+
+<li>Circular polarisation, <a href="#Page_242">242</a>.</li>
+
+<li>Civilisation and barbarism, <a href="#Page_335">335</a> et seq.</li>
+
+<li>Civilisation, some phenomena of, explained by binocular vision, <a href="#Page_74">74</a>.</li>
+
+<li>Civilised man, his modes of conception and interpretation, <a href="#Page_219">219</a>.</li>
+
+<li>Clapeyron, <a href="#Page_162">162</a>.</li>
+
+<li>Class-characters of animals, <a href="#Page_255">255</a>.</li>
+
+<li>Classical, culture, the good and bad effects of, <a href="#Page_347">347</a>;</li>
+<li><span style="margin-left: 1em;">scholars, not the only educated people, <a href="#Page_345">345</a>.</span></li>
+
+<li>Classics, on instruction in, <a href="#Page_338">338</a>-<a href="#Page_374">374</a>;</li>
+<li><span style="margin-left: 1em;">the scientific, <a href="#Page_368">368</a>.</span></li>
+
+<li>Classification in science, <a href="#Page_255">255</a>.</li>
+
+<li>Clausius, on thermodynamics, <a href="#Page_165">165</a>;</li>
+<li><span style="margin-left: 1em;">on reversible cycles, <a href="#Page_176">176</a>.</span></li>
+
+<li>Claviatur, Mach's, <a href="#Page_42">42</a>-<a href="#Page_43">43</a>.</li>
+
+<li>Club-law, <a href="#Page_335">335</a>.</li>
+
+<li>Cochlea, the, a species of piano-forte, <a href="#Page_19">19</a>.</li>
+
+<li>Cockchafer, <a href="#Page_86">86</a>.</li>
+
+<li>Coefficient of self-induction, <a href="#Page_250">250</a>, <a href="#Page_252">252</a>.</li>
+
+<li>Colophonium, solution of, <a href="#Page_7">7</a>.</li>
+
+<li>Color, acoustic, <a href="#Page_36">36</a>.</li>
+
+<li>Color-sensation, <a href="#Page_210">210</a>.</li>
+
+<li>Color-signs, their economy, <a href="#Page_192">192</a>.</li>
+
+<li>Colors, origin of the names of, <a href="#Page_239">239</a>.</li>
+
+<li>Column, body moving behind a, <a href="#Page_202">202</a>.</li>
+
+<li>Communication, its functions, import and fruits, <a href="#Page_197">197</a>, <a href="#Page_238">238</a> et seq.;</li>
+<li><span style="margin-left: 1em;">by language, <a href="#Page_237">237</a>;</span></li>
+<li><span style="margin-left: 1em;">high importance of, <a href="#Page_191">191</a> et seq.</span></li>
+
+<li>Comparative physics, <a href="#Page_239">239</a>.</li>
+
+<li>Comparison in science, <a href="#Page_231">231</a>, <a href="#Page_238">238</a> et seq.</li>
+
+<li>Computation, a principle of æsthetics, <a href="#Page_34">34</a>.</li>
+
+<li>Concepts, abstract, defined, <a href="#Page_250">250</a>-<a href="#Page_252">252</a>;</li>
+<li><span style="margin-left: 1em;">metrical, in electricity, <a href="#Page_107">107</a> et seq.</span></li>
+
+<li>Conceptual, meaning of the term, <a href="#Page_240">240</a>.</li>
+
+<li>Conceptual thought, <a href="#Page_192">192</a>.</li>
+
+<li>Concha, <a href="#Page_18">18</a>.</li>
+
+<li>Condensers, electrical, <a href="#Page_125">125</a> et seq. <a href="#Page_132">132</a>, footnote.</li>
+
+<li><span class="pagenum"><a name="Page_396" id="Page_396">[Pg 396]</a></span>Conductors and non-conductors. See <i>Electrical</i>, etc.</li>
+
+<li>Conformity in the deportment of the energies, <a href="#Page_171">171</a>-<a href="#Page_175">175</a>.</li>
+
+<li>Confusion of objects, cause of, <a href="#Page_95">95</a>.</li>
+
+<li>Conic sections, <a href="#Page_257">257</a>.</li>
+
+<li>Conical refraction, <a href="#Page_29">29</a>, <a href="#Page_242">242</a>.</li>
+
+<li>Conservation of energy, <a href="#Page_137">137</a> et seq. See <i>Energy</i>.</li>
+
+<li>Conservation of weight or mass, <a href="#Page_203">203</a>.</li>
+
+<li>Consonance, connexion of the simple natural numbers with, <a href="#Page_33">33</a>;</li>
+<li><span style="margin-left: 1em;">Euclid's definition of, <a href="#Page_33">33</a>;</span></li>
+<li><span style="margin-left: 1em;">explanation of, <a href="#Page_42">42</a>;</span></li>
+<li><span style="margin-left: 1em;">scientific definition of, <a href="#Page_44">44</a>;</span></li>
+<li><span style="margin-left: 1em;">and dissonance reduced to beats, <a href="#Page_376">376</a>, <a href="#Page_370">370</a>, <a href="#Page_383">383</a>.</span></li>
+
+<li>Consonant intervals, <a href="#Page_43">43</a>.</li>
+
+<li>Constancy of matter, <a href="#Page_203">203</a>.</li>
+
+<li>Constant, the dielectric, <a href="#Page_117">117</a>.</li>
+
+<li>Constants, the natural, <a href="#Page_193">193</a>.</li>
+
+<li>Continuum of facts, <a href="#Page_256">256</a> et seq.</li>
+
+<li>Cornelius, <a href="#Page_388">388</a>, footnote.</li>
+
+<li>Corti, the Marchese, his discovery of minute rods in the labyrinth of the ear, <a href="#Page_19">19</a>.</li>
+
+<li>Coulomb, his electrical researches, <a href="#Page_108">108</a>, <a href="#Page_109">109</a>, <a href="#Page_113">113</a>;</li>
+<li><span style="margin-left: 1em;">his notion of quantity of electricity, <a href="#Page_173">173</a>;</span></li>
+<li><span style="margin-left: 1em;">his torsion-balance, <a href="#Page_168">168</a>.</span></li>
+
+<li>Crew, Prof. Henry, <a href="#Page_317">317</a>, footnote.</li>
+
+<li>Criticism, Socrates the father of scientific, <a href="#Page_1">1</a>, <a href="#Page_16">16</a>.</li>
+
+<li><i>Critique of Pure Reason</i>, Kant's, <a href="#Page_188">188</a>.</li>
+
+<li>Crucible, derivation of the word, <a href="#Page_49">49</a>, footnote.</li>
+
+<li>Crustacea, auditory filaments of, <a href="#Page_29">29</a>, <a href="#Page_272">272</a>, <a href="#Page_302">302</a>.</li>
+
+<li>Cube of oil, <a href="#Page_5">5</a>.</li>
+
+<li>Culture, ancient and modern, <a href="#Page_344">344</a>.</li>
+
+<li>Currents, chemical, <a href="#Page_118">118</a>;</li>
+<li><span style="margin-left: 1em;">electrical, <a href="#Page_118">118</a>;</span></li>
+<li><span style="margin-left: 1em;">galvanic, <a href="#Page_132">132</a>;</span></li>
+<li><span style="margin-left: 1em;">measurement of electrical, <a href="#Page_135">135</a>-<a href="#Page_136">136</a>;</span></li>
+<li><span style="margin-left: 1em;">of heat, <a href="#Page_244">244</a>, <a href="#Page_249">249</a>-<a href="#Page_250">250</a>;</span></li>
+<li><span style="margin-left: 1em;">strength of, <a href="#Page_250">250</a>.</span></li>
+
+<li>Curtius, <a href="#Page_356">356</a>.</li>
+
+<li>Curved lines, their asymmetry, <a href="#Page_98">98</a>.</li>
+
+<li>Curves, how their laws are investigated, <a href="#Page_206">206</a>.</li>
+
+<li>Cycles, reversible, Clausius on, <a href="#Page_176">176</a>.</li>
+
+<li>Cyclical processes, closed, <a href="#Page_175">175</a>.</li>
+
+<li>Cyclops, <a href="#Page_67">67</a>.</li>
+
+<li>Cyclostat, <a href="#Page_298">298</a>.</li>
+
+<li>Cylinder, of oil, <a href="#Page_6">6</a>;</li>
+<li><span style="margin-left: 1em;">mass of gas enclosed in a, <a href="#Page_179">179</a>.</span></li>
+
+</ul>
+
+<ul class="IX"><li>D'Alembert, on the causes of harmony, <a href="#Page_34">34</a>;</li>
+<li><span style="margin-left: 1em;">his principle, <a href="#Page_142">142</a>, <a href="#Page_149">149</a>, <a href="#Page_154">154</a>;</span></li>
+<li><span style="margin-left: 1em;">also <a href="#Page_234">234</a>, <a href="#Page_279">279</a>.</span></li>
+
+<li>Danish schools, <a href="#Page_338">338</a>, footnote.</li>
+
+<li>Darwin, his study of organic nature, <a href="#Page_215">215</a> et seq.;</li>
+<li><span style="margin-left: 1em;">his methods of research, <a href="#Page_216">216</a>.</span></li>
+
+<li>Deaf and dumb, not subject to giddiness, <a href="#Page_299">299</a>.</li>
+
+<li>Deaf person, with a piano, analyses sounds, <a href="#Page_27">27</a>.</li>
+
+<li>Death and life, <a href="#Page_186">186</a>.</li>
+
+<li>Definition, compendious, <a href="#Page_197">197</a>.</li>
+
+<li>Deiters, <a href="#Page_19">19</a>.</li>
+
+<li>Delage, <a href="#Page_298">298</a>, <a href="#Page_301">301</a>, <a href="#Page_302">302</a>.</li>
+
+<li>Democritus, his mechanical conception of the world, <a href="#Page_155">155</a>, <a href="#Page_187">187</a>.</li>
+
+<li>Demonstration, character of, <a href="#Page_362">362</a>.</li>
+
+<li>Deportment of the energies, conformity in the, <a href="#Page_171">171</a>-<a href="#Page_175">175</a>.</li>
+
+<li>Derivation, laws only methods of, <a href="#Page_256">256</a>.</li>
+
+<li>Descent, Galileo's laws of, <a href="#Page_193">193</a>;</li>
+<li><span style="margin-left: 1em;">generally, <a href="#Page_143">143</a> et seq., <a href="#Page_204">204</a>, <a href="#Page_215">215</a>.</span></li>
+
+<li>Description, <a href="#Page_108">108</a>, <a href="#Page_191">191</a>, <a href="#Page_236">236</a>, <a href="#Page_237">237</a>;</li>
+<li><span style="margin-left: 1em;">a condition of scientific knowledge, <a href="#Page_193">193</a>;</span></li>
+<li><span style="margin-left: 1em;">direct and indirect, <a href="#Page_240">240</a>;</span></li>
+<li><span style="margin-left: 1em;">in physics, <a href="#Page_197">197</a>, <a href="#Page_199">199</a>.</span></li>
+
+<li>Descriptive sciences, their resemblance to the abstract, <a href="#Page_248">248</a>.</li>
+
+<li>Determinants, <a href="#Page_195">195</a>.</li>
+
+<li>Diderot, <a href="#Page_234">234</a>.</li>
+
+<li>Dielectric constant, the, <a href="#Page_117">117</a>.</li>
+
+<li>Difference-engine, the, <a href="#Page_196">196</a>.</li>
+
+<li>Differential coefficients, their relation to symmetry, <a href="#Page_98">98</a>.</li>
+
+<li>Differential laws, <a href="#Page_204">204</a>.</li>
+
+<li>Differential method, for detecting optical imperfections, <a href="#Page_317">317</a>.</li>
+
+<li>Diffraction, <a href="#Page_91">91</a>, <a href="#Page_194">194</a>.</li>
+
+<li>Diffusion, Fick's theory of, <a href="#Page_249">249</a>.</li>
+
+<li>Discharge of Leyden jars, <a href="#Page_114">114</a> et seq.</li>
+
+<li>Discoveries, the gist of, <a href="#Page_270">270</a>, <a href="#Page_375">375</a>.</li>
+
+<li>Discovery and invention, distinction between, <a href="#Page_269">269</a>.</li>
+
+<li>Dissonance, explanation of, <a href="#Page_42">42</a>;</li>
+<li><span style="margin-left: 1em;">definition of, <a href="#Page_33">33</a>, <a href="#Page_44">44</a>. See <i>Consonance</i>.</span></li>
+
+<li>Distances, estimation of, by the eye, <a href="#Page_68">68</a> et seq.</li>
+
+<li>Dogs, like tuning-forks, <a href="#Page_23">23</a>;</li>
+<li><span class="pagenum"><a name="Page_397" id="Page_397">[Pg 397]</a></span><span style="margin-left: 1em;">their mentality, <a href="#Page_190">190</a>.</span></li>
+
+<li>Domenech, Abbé, <a href="#Page_92">92</a>.</li>
+
+<li>Dramatic element in science, <a href="#Page_243">243</a>.</li>
+
+<li>Drop of water, on a greased plate, <a href="#Page_8">8</a>;</li>
+<li><span style="margin-left: 1em;">on the end of a stick, <a href="#Page_8">8</a>;</span></li>
+<li><span style="margin-left: 1em;">in free descent, <a href="#Page_8">8</a>.</span></li>
+
+<li>Dubois, <a href="#Page_218">218</a>.</li>
+
+<li>Dubois-Reymond, <a href="#Page_370">370</a>, footnote.</li>
+
+<li>Dufay, <a href="#Page_271">271</a>.</li>
+
+<li>Dynamics, foundations of, <a href="#Page_153">153</a> et seq.</li>
+
+</ul>
+
+<ul class="IX"><li>Ear, researches in the theory of, <a href="#Page_17">17</a> et seq.;</li>
+<li><span style="margin-left: 1em;">diagram of, <a href="#Page_18">18</a>;</span></li>
+<li><span style="margin-left: 1em;">its analysis of sounds, <a href="#Page_20">20</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">a puzzle-lock, <a href="#Page_28">28</a>;</span></li>
+<li><span style="margin-left: 1em;">reflected in a mirror, <a href="#Page_93">93</a>;</span></li>
+<li><span style="margin-left: 1em;">no symmetry in its sensation, <a href="#Page_103">103</a>.</span></li>
+
+<li>Earth, its oblateness not due to its original fluid condition, <a href="#Page_2">2</a>;</li>
+<li><span style="margin-left: 1em;">rotation of, <a href="#Page_204">204</a>;</span></li>
+<li><span style="margin-left: 1em;">internal disturbances of, <a href="#Page_285">285</a>.</span></li>
+
+<li>Economical, nature of physical inquiry, <a href="#Page_186">186</a>;</li>
+<li><span style="margin-left: 1em;">procedure of the human mind, <a href="#Page_186">186</a>;</span></li>
+<li><span style="margin-left: 1em;">order of physics, <a href="#Page_197">197</a>;</span></li>
+<li><span style="margin-left: 1em;">schematism of science, <a href="#Page_206">206</a>;</span></li>
+<li><span style="margin-left: 1em;">tools of science, <a href="#Page_207">207</a>;</span></li>
+<li><span style="margin-left: 1em;">coefficient of dynamos, <a href="#Page_133">133</a>.</span></li>
+
+<li>Economy, of the actions of nature, <a href="#Page_15">15</a>;</li>
+<li><span style="margin-left: 1em;">the purpose of science, <a href="#Page_16">16</a>;</span></li>
+<li><span style="margin-left: 1em;">of language, <a href="#Page_191">191</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">of the industrial arts, <a href="#Page_192">192</a>;</span></li>
+<li><span style="margin-left: 1em;">of mathematics, <a href="#Page_195">195</a>-<a href="#Page_196">196</a>;</span></li>
+<li><span style="margin-left: 1em;">of machinery, <a href="#Page_196">196</a>;</span></li>
+<li><span style="margin-left: 1em;">of self-preservation, our first knowledge derived from, <a href="#Page_197">197</a>;</span></li>
+<li><span style="margin-left: 1em;">generally, <a href="#Page_186">186</a> et seq., <a href="#Page_269">269</a>.</span></li>
+
+<li>Education, higher, <a href="#Page_86">86</a>;</li>
+<li><span style="margin-left: 1em;">liberal, <a href="#Page_341">341</a> et seq., <a href="#Page_371">371</a>.</span></li>
+
+<li>Efflux, liquid, <a href="#Page_150">150</a>.</li>
+
+<li>Ego, its nature, <a href="#Page_234">234</a>-<a href="#Page_235">235</a>.</li>
+
+<li>Egypt, <a href="#Page_234">234</a>.</li>
+
+<li>Egyptians, art of, <a href="#Page_78">78</a> et seq., <a href="#Page_201">201</a>.</li>
+
+<li>Eighteenth century, the scientific achievements of, <a href="#Page_187">187</a>, <a href="#Page_188">188</a>.</li>
+
+<li>Eleatics, on motion, <a href="#Page_158">158</a>.</li>
+
+<li>Electrical, attraction and repulsion, <a href="#Page_109">109</a> et seq., <a href="#Page_168">168</a>;</li>
+<li><span style="margin-left: 1em;">capacity, <a href="#Page_116">116</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">force, <a href="#Page_110">110</a>, <a href="#Page_119">119</a>, <a href="#Page_168">168</a>;</span></li>
+<li><span style="margin-left: 1em;">spark, <a href="#Page_117">117</a>, <a href="#Page_127">127</a>, <a href="#Page_132">132</a>, <a href="#Page_133">133</a>, <a href="#Page_190">190</a>;</span></li>
+<li><span style="margin-left: 1em;">energy, measurement of, <a href="#Page_128">128</a> et seq., <a href="#Page_169">169</a>;</span></li>
+<li><span style="margin-left: 1em;">currents, conceptions of, <a href="#Page_118">118</a>, <a href="#Page_132">132</a>, <a href="#Page_135">135</a>-<a href="#Page_136">136</a>, <a href="#Page_226">226</a>-<a href="#Page_227">227</a>, <a href="#Page_249">249</a>, <a href="#Page_250">250</a>;</span></li>
+<li><span style="margin-left: 1em;">fluids, <a href="#Page_112">112</a> et seq., <a href="#Page_228">228</a>;</span></li>
+<li><span style="margin-left: 1em;">pendulums, <a href="#Page_110">110</a>;</span></li>
+<li><span style="margin-left: 1em;">levels, <a href="#Page_173">173</a>;</span></li>
+<li><span style="margin-left: 1em;">potential, <a href="#Page_121">121</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">quantity, <a href="#Page_111">111</a>, <a href="#Page_118">118</a>, <a href="#Page_119">119</a>.</span></li>
+
+<li>Electricity, as a substance and as a motion, <a href="#Page_170">170</a>;</li>
+<li><span style="margin-left: 1em;">difference between the conceptions of heat and, <a href="#Page_168">168</a> et seq.,</span></li>
+<li><span style="margin-left: 1em;">rôle of work in, <a href="#Page_120">120</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">galvanic, <a href="#Page_134">134</a>.</span></li>
+<li><span style="margin-left: 1em;">See <i>Electrical</i>.</span></li>
+
+<li>Electrometer, W. Thomson's absolute, <a href="#Page_127">127</a>, footnote.</li>
+
+<li>Electrometers, <a href="#Page_122">122</a>, <a href="#Page_127">127</a>.</li>
+
+<li>Electrostatic unit, <a href="#Page_111">111</a>.</li>
+
+<li>Electrostatics, concepts of, <a href="#Page_107">107</a> et seq.</li>
+
+<li>Elements, interdependence of the sensuous, <a href="#Page_179">179</a>;</li>
+<li><span style="margin-left: 1em;">of bodies, <a href="#Page_202">202</a>;</span></li>
+<li><span style="margin-left: 1em;">of phenomena, equations between, <a href="#Page_205">205</a>;</span></li>
+<li><span style="margin-left: 1em;">of sensations, <a href="#Page_200">200</a>;</span></li>
+<li><span style="margin-left: 1em;">used instead of sensations, <a href="#Page_208">208</a>-<a href="#Page_209">209</a>.</span></li>
+
+<li>Ellipse, equation of, <a href="#Page_205">205</a>;</li>
+<li><span style="margin-left: 1em;">the word, <a href="#Page_342">342</a>.</span></li>
+
+<li>Embryology, possible future state of, <a href="#Page_257">257</a>.</li>
+
+<li>Energies, conformity in the deportment of, <a href="#Page_171">171</a>-<a href="#Page_175">175</a>;</li>
+<li><span style="margin-left: 1em;">differences of, <a href="#Page_175">175</a>.</span></li>
+
+<li>Energy, a metrical notion, <a href="#Page_178">178</a>;</li>
+<li><span style="margin-left: 1em;">conservation of, <a href="#Page_137">137</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">defined, <a href="#Page_139">139</a>;</span></li>
+<li><span style="margin-left: 1em;">metaphysical establishment of the doctrine of, <a href="#Page_183">183</a>;</span></li>
+<li><span style="margin-left: 1em;">kinetic, <a href="#Page_177">177</a>;</span></li>
+<li><span style="margin-left: 1em;">potential, <a href="#Page_128">128</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">substantial conception of, <a href="#Page_164">164</a>, <a href="#Page_185">185</a>, <a href="#Page_244">244</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">conservation of, in electrical phenomena, <a href="#Page_131">131</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">limits of principle of, <a href="#Page_175">175</a>;</span></li>
+<li><span style="margin-left: 1em;">principle of, in physics, <a href="#Page_160">160</a>-<a href="#Page_166">166</a>;</span></li>
+<li><span style="margin-left: 1em;">sources of principle of, <a href="#Page_179">179</a>, <a href="#Page_181">181</a>;</span></li>
+<li><span style="margin-left: 1em;">thermal, <a href="#Page_177">177</a>;</span></li>
+<li><span style="margin-left: 1em;">Thomas Young on, <a href="#Page_173">173</a>.</span></li>
+
+<li>Energy-value of heat, <a href="#Page_178">178</a>, footnote.</li>
+
+<li>Enlightenment, the, <a href="#Page_188">188</a>.</li>
+
+<li>Entropy, a metrical notion, <a href="#Page_178">178</a>.</li>
+
+<li>Environment, stability of our, <a href="#Page_206">206</a>.</li>
+
+<li>Equations for obtaining facts, <a href="#Page_180">180</a>;</li>
+<li><span style="margin-left: 1em;">between the elements of phenomena, <a href="#Page_205">205</a>.</span></li>
+
+<li>Equilibrium, conditions of, in simple machines, <a href="#Page_151">151</a>;</li>
+<li><span style="margin-left: 1em;">figures of liquid, <a href="#Page_4">4</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">general condition of, <a href="#Page_15">15</a>;</span></li>
+<li><span style="margin-left: 1em;">in the State, <a href="#Page_15">15</a>.</span></li>
+
+<li>Etymology, the word, misused for entomology, <a href="#Page_316">316</a>.</li>
+
+<li>Euclid, on consonance and dissonance, <a href="#Page_33">33</a>;</li>
+<li><span style="margin-left: 1em;">his geometry, <a href="#Page_364">364</a>.</span></li>
+
+<li><span class="pagenum"><a name="Page_398" id="Page_398">[Pg 398]</a></span>Euler, on the causes of harmony, <a href="#Page_34">34</a>;</li>
+<li><span style="margin-left: 1em;">impression of the mathematical processes on, <a href="#Page_196">196</a>;</span></li>
+<li><span style="margin-left: 1em;">on the vibrations of strings, <a href="#Page_249">249</a>, <a href="#Page_285">285</a>, <a href="#Page_376">376</a>.</span></li>
+
+<li>Euler and Hermann's principle, <a href="#Page_149">149</a>.</li>
+
+<li>Euthyphron, questioned by Socrates, <a href="#Page_1">1</a>.</li>
+
+<li>Evolute, the word, <a href="#Page_342">342</a>.</li>
+
+<li>Evolution, theory of, as applied to ideas, <a href="#Page_216">216</a> et seq.</li>
+
+<li>Ewald, <a href="#Page_298">298</a>, <a href="#Page_304">304</a>.</li>
+
+<li>Excluded perpetual motion, logical root of the principle of, <a href="#Page_182">182</a>.</li>
+
+<li>Exner, S., <a href="#Page_302">302</a>, <a href="#Page_305">305</a>.</li>
+
+<li>Experience, communication of, <a href="#Page_191">191</a>;</li>
+<li><span style="margin-left: 1em;">our ready, <a href="#Page_199">199</a>;</span></li>
+<li><span style="margin-left: 1em;">the principle of energy derived from, <a href="#Page_179">179</a>;</span></li>
+<li><span style="margin-left: 1em;">the wellspring of all knowledge of nature, <a href="#Page_181">181</a>;</span></li>
+<li><span style="margin-left: 1em;">incongruence between thought and, <a href="#Page_206">206</a>.</span></li>
+
+<li>Experimental research, function of, <a href="#Page_181">181</a>.</li>
+
+<li>Explanation, nature of, <a href="#Page_194">194</a>, <a href="#Page_237">237</a>, <a href="#Page_362">362</a>.</li>
+
+<li>Eye, cannot analyse colors, <a href="#Page_20">20</a>;</li>
+<li><span style="margin-left: 1em;">researches in the theory of the, <a href="#Page_18">18</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">loss of, as affecting vision, <a href="#Page_98">98</a>.</span></li>
+
+<li>Eyes, purpose of, <a href="#Page_66">66</a> et seq.;</li>
+<li><span style="margin-left: 1em;">their structure symmetrical not identical, <a href="#Page_96">96</a>.</span></li>
+
+</ul>
+
+<ul class="IX"><li>Face, human, inverted, <a href="#Page_95">95</a>.</li>
+
+<li>Facts and ideas, necessary to science, <a href="#Page_231">231</a>.</li>
+
+<li>Facts, description of, <a href="#Page_108">108</a>;</li>
+<li><span style="margin-left: 1em;">agreement of, <a href="#Page_180">180</a>;</span></li>
+<li><span style="margin-left: 1em;">relations of, <a href="#Page_180">180</a>;</span></li>
+<li><span style="margin-left: 1em;">how represented, <a href="#Page_206">206</a>;</span></li>
+<li><span style="margin-left: 1em;">reflected in imagination, <a href="#Page_220">220</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">the result of constructions, <a href="#Page_253">253</a>;</span></li>
+<li><span style="margin-left: 1em;">a continuum of, <a href="#Page_256">256</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">equations for obtaining, <a href="#Page_180">180</a>.</span></li>
+
+<li>Falling bodies, <a href="#Page_204">204</a>, <a href="#Page_215">215</a>;</li>
+<li><span style="margin-left: 1em;">Galileo on the law of, <a href="#Page_143">143</a> et seq., <a href="#Page_284">284</a>.</span></li>
+
+<li>Falling, cats, <a href="#Page_303">303</a>, footnote.</li>
+
+<li>Falstaff, <a href="#Page_309">309</a>.</li>
+
+<li>Familiar intermediate links of thought, <a href="#Page_198">198</a>.</li>
+
+<li>Faraday, <a href="#Page_191">191</a>, <a href="#Page_217">217</a>, <a href="#Page_237">237</a>;</li>
+<li><span style="margin-left: 1em;">his conception of electricity, <a href="#Page_114">114</a>, <a href="#Page_271">271</a>.</span></li>
+
+<li>Fechner, theory of Corti's fibres, <a href="#Page_19">19</a> et seq.</li>
+
+<li>Feeling, cannot be explained by motions of atoms, <a href="#Page_208">208</a> et seq.</li>
+
+<li>Fetishism, <a href="#Page_186">186</a>, <a href="#Page_243">243</a>, <a href="#Page_254">254</a>;</li>
+<li><span style="margin-left: 1em;">in our physical concepts, <a href="#Page_187">187</a>.</span></li>
+
+<li>Fibres of Corti, <a href="#Page_17">17</a> et seq.</li>
+
+<li>Fick, his theory of diffusion, <a href="#Page_249">249</a>.</li>
+
+<li>Figures, symmetry of, <a href="#Page_92">92</a> et seq.</li>
+
+<li>Figures of liquid equilibrium, <a href="#Page_4">4</a> et seq.</li>
+
+<li>Fire, use of, <a href="#Page_264">264</a>.</li>
+
+<li>Fishes, <a href="#Page_306">306</a>.</li>
+
+<li>Fixed note, determining of a, <a href="#Page_377">377</a>.</li>
+
+<li>Fizeau, his determination of the velocity of light, <a href="#Page_55">55</a> et seq.</li>
+
+<li>Flats, reversed into sharps, <a href="#Page_101">101</a>.</li>
+
+<li>Flouren's experiments, <a href="#Page_272">272</a>, <a href="#Page_290">290</a>.</li>
+
+<li>Flower-girl, the baskets of a, <a href="#Page_95">95</a>.</li>
+
+<li>Fluids, electrical, <a href="#Page_112">112</a> et seq.</li>
+
+<li>Force, electric, <a href="#Page_110">110</a>, <a href="#Page_119">119</a>, <a href="#Page_168">168</a>;</li>
+<li><span style="margin-left: 1em;">unit of <a href="#Page_111">111</a>;</span></li>
+<li><span style="margin-left: 1em;">living, <a href="#Page_137">137</a>, <a href="#Page_149">149</a>, <a href="#Page_184">184</a>;</span></li>
+<li><span style="margin-left: 1em;">generally <a href="#Page_253">253</a>.</span></li>
+<li><span style="margin-left: 1em;">See the related headings.</span></li>
+
+<li>Forces, will compared to, <a href="#Page_254">254</a>.</li>
+
+<li>Foreseeing events, <a href="#Page_220">220</a> et seq.</li>
+
+<li>Formal conceptions, rôle of, <a href="#Page_183">183</a>.</li>
+
+<li>Formal need of a clear view of facts, <a href="#Page_183">183</a>, <a href="#Page_246">246</a>;</li>
+<li><span style="margin-left: 1em;">how far it corresponds to nature, <a href="#Page_184">184</a>.</span></li>
+
+<li>Formative forces of liquids, <a href="#Page_4">4</a>.</li>
+
+<li>Forms of liquids, <a href="#Page_3">3</a> et seq.</li>
+
+<li>Forward movement, sensation of, <a href="#Page_300">300</a>.</li>
+
+<li>Forwards, prophesying, <a href="#Page_253">253</a>.</li>
+
+<li>Foucault, <a href="#Page_57">57</a>, <a href="#Page_70">70</a>, <a href="#Page_296">296</a>.</li>
+
+<li>Foucault and Toepler, method of, for detecting optical faults, <a href="#Page_313">313</a> et seq., <a href="#Page_320">320</a>.</li>
+
+<li>Foundation of scientific thought, primitive acts of knowledge, the, <a href="#Page_190">190</a>.</li>
+
+<li>Fourier, on processes of heat, <a href="#Page_249">249</a>, <a href="#Page_278">278</a>.</li>
+
+<li>Fox, a, <a href="#Page_234">234</a>.</li>
+
+<li>Franklin's pane, <a href="#Page_116">116</a>.</li>
+
+<li>Frary, <a href="#Page_338">338</a>, footnote.</li>
+
+<li>Fraunhofer, <a href="#Page_271">271</a>.</li>
+
+<li>Freezing-point, lowered by pressure, <a href="#Page_162">162</a>.</li>
+
+<li>Fresnel, <a href="#Page_271">271</a>.</li>
+
+<li>Fritsch, <a href="#Page_321">321</a>.</li>
+
+<li>Frogs, larvæ of, not subject to vertigo, <a href="#Page_298">298</a>.</li>
+
+<li>Froude, <a href="#Page_333">333</a>.</li>
+
+<li>Frustra, misuse of the word, <a href="#Page_345">345</a>.</li>
+
+<li>Future, science of the, <a href="#Page_213">213</a>.</li>
+
+</ul>
+
+<ul class="IX"><li>Galileo, on the motion of pendulums, <a href="#Page_21">21</a>;</li>
+<li><span style="margin-left: 1em;">his attempted measurement of the velocity of light, <a href="#Page_50">50</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">his exclusion of a perpetual motion, <a href="#Page_143">143</a>;</span></li>
+<li><span style="margin-left: 1em;">on velocities acquired in free descent, <a href="#Page_143">143</a>-<a href="#Page_147">147</a>;</span></li>
+<li><span style="margin-left: 1em;">on the law of inertia, <a href="#Page_146">146</a>-<a href="#Page_147">147</a>;</span></li>
+<li><span style="margin-left: 1em;">on virtual velocities, <a href="#Page_150">150</a>;</span></li>
+<li><span style="margin-left: 1em;">on work, <a href="#Page_172">172</a>;</span></li>
+<li><span style="margin-left: 1em;">his laws of descent, <a href="#Page_193">193</a>;</span></li>
+<li><span style="margin-left: 1em;">on falling bodies, <a href="#Page_225">225</a>;</span></li>
+<li><span style="margin-left: 1em;">great results of his study of nature, <a href="#Page_214">214</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">his rude scientific implements, <a href="#Page_215">215</a>;</span></li>
+<li><span style="margin-left: 1em;">selections from his works for use in instruction, <a href="#Page_368">368</a>;</span></li>
+<li><span class="pagenum"><a name="Page_399" id="Page_399">[Pg 399]</a></span><span style="margin-left: 1em;">also <a href="#Page_105">105</a>, <a href="#Page_182">182</a>, <a href="#Page_187">187</a>, <a href="#Page_237">237</a>, <a href="#Page_272">272</a>, <a href="#Page_274">274</a>, <a href="#Page_283">283</a>.</span></li>
+
+<li>Galle, observes the planet Neptune, <a href="#Page_29">29</a>.</li>
+
+<li>Galvanic, electricity, <a href="#Page_134">134</a>;</li>
+<li><span style="margin-left: 1em;">current, <a href="#Page_132">132</a>;</span></li>
+<li><span style="margin-left: 1em;">dizziness, <a href="#Page_291">291</a>;</span></li>
+<li><span style="margin-left: 1em;">vertigo, <a href="#Page_298">298</a>.</span></li>
+
+<li>Galvanoscope, <a href="#Page_135">135</a>.</li>
+
+<li>Galvanotropism, <a href="#Page_291">291</a>.</li>
+
+<li>Garda, Lake, <a href="#Page_239">239</a>.</li>
+
+<li>Gas, the word, <a href="#Page_264">264</a>;</li>
+<li><span style="margin-left: 1em;">mass of, enclosed in a cylinder, <a href="#Page_179">179</a>.</span></li>
+
+<li>Gases, tensions of, for scales of temperature, <a href="#Page_174">174</a>.</li>
+
+<li>Gauss, on the foundations of dynamics, <a href="#Page_154">154</a>;</li>
+<li><span style="margin-left: 1em;">his principle, <a href="#Page_154">154</a>;</span></li>
+<li><span style="margin-left: 1em;">also, <a href="#Page_108">108</a>, <a href="#Page_274">274</a>.</span></li>
+
+<li>Genius, <a href="#Page_279">279</a>, <a href="#Page_280">280</a>.</li>
+
+<li>Geography, comparison in, <a href="#Page_239">239</a>.</li>
+
+<li>Geometers, in our eyes, <a href="#Page_72">72</a>.</li>
+
+<li>Geotropism, <a href="#Page_289">289</a>.</li>
+
+<li>German schools and gymnasiums, <a href="#Page_372">372</a>, <a href="#Page_373">373</a>, <a href="#Page_338">338</a>, footnote.</li>
+
+<li>Ghosts, photographic, <a href="#Page_73">73</a>.</li>
+
+<li>Glass, invisible in a mixture of the same refrangibility, <a href="#Page_312">312</a>;</li>
+<li><span style="margin-left: 1em;">powdered, visible in a mixture of the same refrangibility, <a href="#Page_312">312</a>.</span></li>
+
+<li>Glove, in a mirror, <a href="#Page_93">93</a>.</li>
+
+<li>Goethe, quotations from, <a href="#Page_9">9</a>, <a href="#Page_31">31</a>, <a href="#Page_49">49</a>, <a href="#Page_88">88</a>;</li>
+<li><span style="margin-left: 1em;">on the cause of harmony, <a href="#Page_35">35</a>.</span></li>
+
+<li>Goltz, <a href="#Page_282">282</a>, <a href="#Page_291">291</a>.</li>
+
+<li>Gossot, <a href="#Page_332">332</a>.</li>
+
+<li>Gothic cathedral, <a href="#Page_94">94</a>.</li>
+
+<li>Gravitation, discovery of, <a href="#Page_225">225</a> et seq.</li>
+
+<li>Gravity, how to get rid of the effects of, in liquids, <a href="#Page_4">4</a>;</li>
+<li><span style="margin-left: 1em;">also <a href="#Page_228">228</a>.</span></li>
+
+<li>Gray, Elisha, his telautograph, <a href="#Page_26">26</a>.</li>
+
+<li>Greased plate, drop of water on a, <a href="#Page_8">8</a>.</li>
+
+<li>Great minds, idiosyncrasies of, <a href="#Page_247">247</a>.</li>
+
+<li>Greek language, scientific terms derivedfrom, <a href="#Page_342">342</a>-<a href="#Page_343">343</a>;</li>
+<li><span style="margin-left: 1em;">common words derived from, <a href="#Page_343">343</a>, footnote;</span></li>
+<li><span style="margin-left: 1em;">still necessary for some professions, <a href="#Page_346">346</a>;</span></li>
+<li><span style="margin-left: 1em;">its literary wealth, <a href="#Page_347">347</a>-<a href="#Page_348">348</a>;</span></li>
+<li><span style="margin-left: 1em;">narrowness and one-sidedness of its literature, <a href="#Page_348">348</a>-<a href="#Page_349">349</a>;</span></li>
+<li><span style="margin-left: 1em;">its excessive study useless, <a href="#Page_349">349</a>-<a href="#Page_350">350</a>;</span></li>
+<li><span style="margin-left: 1em;">its study sharpens the judgment, <a href="#Page_357">357</a>-<a href="#Page_358">358</a>;</span></li>
+<li><span style="margin-left: 1em;">a knowledge of it not necessary to a liberal education, <a href="#Page_371">371</a>.</span></li>
+
+<li>Greeks, their provinciality and narrow-mindedness, <a href="#Page_349">349</a>;</li>
+<li><span style="margin-left: 1em;">now only objects of historical research, <a href="#Page_350">350</a>.</span></li>
+
+<li>Griesinger, <a href="#Page_184">184</a>.</li>
+
+<li>Grimaldi, <a href="#Page_270">270</a>.</li>
+
+<li>Grimm, <a href="#Page_344">344</a>, footnote.</li>
+
+<li>Grunting fishes, <a href="#Page_306">306</a>.</li>
+
+</ul>
+
+<ul class="IX"><li>Habitudes of thought, <a href="#Page_199">199</a>, <a href="#Page_224">224</a>, <a href="#Page_227">227</a>, <a href="#Page_232">232</a>.</li>
+
+<li>Haeckel, <a href="#Page_222">222</a>, <a href="#Page_235">235</a>.</li>
+
+<li>Hamilton, deduction of the conical refraction of light, <a href="#Page_29">29</a>.</li>
+
+<li>Hankel, <a href="#Page_364">364</a>.</li>
+
+<li>Harmonics, <a href="#Page_38">38</a>, <a href="#Page_40">40</a>.</li>
+
+<li>Harmony, on the causes of, <a href="#Page_32">32</a> et seq.;</li>
+<li><span style="margin-left: 1em;">laws of the theory of, explained, <a href="#Page_30">30</a>;</span></li>
+<li><span style="margin-left: 1em;">the investigation of the ancients concerning, <a href="#Page_32">32</a>;</span></li>
+<li><span style="margin-left: 1em;">generally, <a href="#Page_103">103</a>.</span></li>
+<li><span style="margin-left: 1em;">See <i>Consonance</i>.</span></li>
+
+<li>Harris, electrical balance of, <a href="#Page_127">127</a>, footnote.</li>
+
+<li>Hartwich, Judge, <a href="#Page_343">343</a>, <a href="#Page_353">353</a>, footnote.</li>
+
+<li>Hat, a high silk, <a href="#Page_24">24</a>.</li>
+
+<li>Hats, ladies', development of, <a href="#Page_64">64</a>.</li>
+
+<li>Head-wave of a projectile, <a href="#Page_323">323</a> et seq.</li>
+
+<li>Hearing and orientation, relation between, <a href="#Page_304">304</a> et seq.</li>
+
+<li>Heat, a material substance, <a href="#Page_177">177</a>;</li>
+<li><span style="margin-left: 1em;">difference between the conceptions of electricity and, <a href="#Page_168">168</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">substantial conception of, <a href="#Page_243">243</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">Carnot on, <a href="#Page_156">156</a>, <a href="#Page_160">160</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">Fourier on the conduction of, <a href="#Page_249">249</a>;</span></li>
+<li><span style="margin-left: 1em;">not necessarily a motion, <a href="#Page_167">167</a>, <a href="#Page_170">170</a>, <a href="#Page_171">171</a>;</span></li>
+<li><span style="margin-left: 1em;">mechanical equivalent of, <a href="#Page_164">164</a>, <a href="#Page_167">167</a>;</span></li>
+<li><span style="margin-left: 1em;">of liquefaction, <a href="#Page_178">178</a>;</span></li>
+<li><span style="margin-left: 1em;">quantity of, <a href="#Page_166">166</a>;</span></li>
+<li><span style="margin-left: 1em;">latent, <a href="#Page_167">167</a>, <a href="#Page_178">178</a>, <a href="#Page_244">244</a>;</span></li>
+<li><span style="margin-left: 1em;">specific, <a href="#Page_166">166</a>, <a href="#Page_244">244</a>;</span></li>
+<li><span style="margin-left: 1em;">the conceptions of, <a href="#Page_160">160</a>-<a href="#Page_171">171</a>;</span></li>
+<li><span style="margin-left: 1em;">machine, <a href="#Page_160">160</a>;</span></li>
+<li><span style="margin-left: 1em;">a measure of electrical energy, <a href="#Page_133">133</a> et seq.;</span></li>
+<li><span class="pagenum"><a name="Page_400" id="Page_400">[Pg 400]</a></span><span style="margin-left: 1em;">mechanical theory of, <a href="#Page_133">133</a>;</span></li>
+<li><span style="margin-left: 1em;">where does it come from? <a href="#Page_200">200</a>.</span></li>
+
+<li>Heavy bodies, sinking of, <a href="#Page_222">222</a>.</li>
+
+<li>Heights of ascent, <a href="#Page_143">143</a>-<a href="#Page_151">151</a>.</li>
+
+<li>Helm, <a href="#Page_172">172</a>.</li>
+
+<li>Helmholtz, applies the principle of energy to electricity, <a href="#Page_184">184</a>;</li>
+<li><span style="margin-left: 1em;">his telestereoscope, <a href="#Page_84">84</a>;</span></li>
+<li><span style="margin-left: 1em;">his theory of Corti's fibres, <a href="#Page_19">19</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">on harmony, <a href="#Page_35">35</a>, <a href="#Page_99">99</a>;</span></li>
+<li><span style="margin-left: 1em;">on the conservation of energy, <a href="#Page_165">165</a>, <a href="#Page_247">247</a>;</span></li>
+<li><span style="margin-left: 1em;">his method of thought, <a href="#Page_247">247</a>;</span></li>
+<li><span style="margin-left: 1em;">also <a href="#Page_138">138</a>, <a href="#Page_305">305</a>, <a href="#Page_307">307</a>, <a href="#Page_375">375</a>, <a href="#Page_383">383</a>.</span></li>
+
+<li>Hensen, V., on the auditory function of the filaments of Crustacea, <a href="#Page_29">29</a>, <a href="#Page_302">302</a>.</li>
+
+<li>Herbart, <a href="#Page_386">386</a> et seq.</li>
+
+<li>Herbartians, on motion, <a href="#Page_158">158</a>.</li>
+
+<li>Herculaneum, art in, <a href="#Page_80">80</a>.</li>
+
+<li>Heredity, in organic and inorganic matter, <a href="#Page_216">216</a>, footnote.</li>
+
+<li>Hering, on development, <a href="#Page_222">222</a>;</li>
+<li><span style="margin-left: 1em;">on vision, <a href="#Page_210">210</a>.</span></li>
+
+<li>Hermann, E., on the economy of the industrial arts, <a href="#Page_192">192</a>.</li>
+
+<li>Hermann, L., <a href="#Page_291">291</a>.</li>
+
+<li>Herodotus, <a href="#Page_26">26</a>, <a href="#Page_234">234</a>, <a href="#Page_347">347</a>, <a href="#Page_350">350</a>.</li>
+
+<li>Hertz, his waves, <a href="#Page_242">242</a>;</li>
+<li><span style="margin-left: 1em;">his use of the phrase "prophesy," <a href="#Page_253">253</a>.</span></li>
+
+<li>Herzen, <a href="#Page_361">361</a>, footnote.</li>
+
+<li>Hindu mathematicians, their beautiful problems, <a href="#Page_30">30</a>.</li>
+
+<li>Holtz's electric machine, <a href="#Page_132">132</a>.</li>
+
+<li>Horse, <a href="#Page_63">63</a>.</li>
+
+<li>Household, physics compared to a well-kept, <a href="#Page_197">197</a>.</li>
+
+<li>Housekeeping in science and civil life, <a href="#Page_198">198</a>.</li>
+
+<li>Hudson, the, <a href="#Page_94">94</a>.</li>
+
+<li>Human beings, puzzle-locks, <a href="#Page_27">27</a>.</li>
+
+<li>Human body, our knowledge of, <a href="#Page_90">90</a>.</li>
+
+<li>Human mind, must proceed economically, <a href="#Page_186">186</a>.</li>
+
+<li>Humanity, likened to a polyp-plant, <a href="#Page_235">235</a>.</li>
+
+<li>Huygens, his mechanical view of physics, <a href="#Page_155">155</a>;</li>
+<li><span style="margin-left: 1em;">on the nature of light and heat, <a href="#Page_155">155</a>-<a href="#Page_156">156</a>;</span></li>
+<li><span style="margin-left: 1em;">his principle of the heights of ascent, <a href="#Page_149">149</a>;</span></li>
+<li><span style="margin-left: 1em;">on the law of inertia and the motion of a compound pendulum, <a href="#Page_147">147</a>-<a href="#Page_149">149</a>;</span></li>
+<li><span style="margin-left: 1em;">on the impossible perpetual motion, <a href="#Page_147">147</a>-<a href="#Page_148">148</a>;</span></li>
+<li><span style="margin-left: 1em;">on work, <a href="#Page_173">173</a>;</span></li>
+<li><span style="margin-left: 1em;">selections from his works for use in instruction, <a href="#Page_368">368</a>;</span></li>
+<li><span style="margin-left: 1em;">his view of light, <a href="#Page_227">227</a>-<a href="#Page_228">228</a>, <a href="#Page_262">262</a>.</span></li>
+
+<li>Huygens, optical method for detecting imperfections in optical glasses <a href="#Page_313">313</a>.</li>
+
+<li>Hydrogen balloon, <a href="#Page_199">199</a>.</li>
+
+<li>Hydrostatics, Stevinus's principle of, <a href="#Page_141">141</a>.</li>
+
+<li>Hypotheses, their rôle in explanation, <a href="#Page_228">228</a> et seq.</li>
+
+</ul>
+
+<ul class="IX"><li>Ichthyornis, <a href="#Page_257">257</a>.</li>
+
+<li>Ichthyosaurus, <a href="#Page_63">63</a>.</li>
+
+<li>Idea? what is a theoretical, <a href="#Page_241">241</a>.</li>
+
+<li>Idealism, <a href="#Page_209">209</a>.</li>
+
+<li>Ideas, a product of organic nature, <a href="#Page_217">217</a> et seq.;</li>
+<li><span style="margin-left: 1em;">and facts, necessary to science, <a href="#Page_231">231</a>;</span></li>
+<li><span style="margin-left: 1em;">not all of life, <a href="#Page_233">233</a>;</span></li>
+<li><span style="margin-left: 1em;">their growth and importance, <a href="#Page_233">233</a>;</span></li>
+<li><span style="margin-left: 1em;">a product of universal evolution, <a href="#Page_235">235</a>;</span></li>
+<li><span style="margin-left: 1em;">the history of, <a href="#Page_227">227</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">in great minds, <a href="#Page_228">228</a>;</span></li>
+<li><span style="margin-left: 1em;">the rich contents of, <a href="#Page_197">197</a>;</span></li>
+<li><span style="margin-left: 1em;">their unsettled character in common life, their clarification in science, <a href="#Page_1">1</a>-<a href="#Page_2">2</a>.</span></li>
+
+<li>Ideography, the Chinese, <a href="#Page_192">192</a>.</li>
+
+<li>Imagery, mental, <a href="#Page_253">253</a>.</li>
+
+<li>Imagination, facts reflected in, <a href="#Page_220">220</a> et seq.</li>
+
+<li>Inclined plane, law of, <a href="#Page_140">140</a>-<a href="#Page_141">141</a>.</li>
+
+<li>Incomprehensible, the, <a href="#Page_186">186</a>.</li>
+
+<li>Indian, his modes of conception and interpretation, <a href="#Page_218">218</a> et seq.</li>
+
+<li>Individual, a thread on which pearls are strung, <a href="#Page_234">234</a>-<a href="#Page_235">235</a>.</li>
+
+<li>Industrial arts, economy of the, E. Hermann on, <a href="#Page_192">192</a>.</li>
+
+<li>Inertia, law of, <a href="#Page_143">143</a> et seq., <a href="#Page_146">146</a> et seq., <a href="#Page_216">216</a>, footnote, <a href="#Page_283">283</a> et seq.</li>
+
+<li>Innate concepts of the understanding, Kant on, <a href="#Page_199">199</a>.</li>
+
+<li>Innervation, visual, <a href="#Page_99">99</a>.</li>
+
+<li>Inquirer, his division of labor, <a href="#Page_105">105</a>;</li>
+<li><span style="margin-left: 1em;">compared to a shoemaker, <a href="#Page_105">105</a>-<a href="#Page_106">106</a>;</span></li>
+<li><span style="margin-left: 1em;">what constitutes the great, <a href="#Page_191">191</a>;</span></li>
+<li><span style="margin-left: 1em;">the true, seeks the truth everywhere, <a href="#Page_63">63</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">the, compared to a wooer, <a href="#Page_45">45</a>.</span></li>
+
+<li>Instinctive knowledge, <a href="#Page_189">189</a>, <a href="#Page_190">190</a>.</li>
+
+<li><span class="pagenum"><a name="Page_401" id="Page_401">[Pg 401]</a></span>Instruction, aim of, the saving of experience, <a href="#Page_191">191</a>;</li>
+<li><span style="margin-left: 1em;">in the classics, mathematics, and sciences, <a href="#Page_338">338</a>-<a href="#Page_374">374</a>;</span></li>
+<li><span style="margin-left: 1em;">limitation of matter of, <a href="#Page_365">365</a> et seq.</span></li>
+
+<li>Insulators, <a href="#Page_130">130</a>.</li>
+
+<li>Integrals, <a href="#Page_195">195</a>.</li>
+
+<li>Intellectual development, conditions of, <a href="#Page_286">286</a> et seq.</li>
+
+<li>Intentions, acts of nature compared to, <a href="#Page_14">14</a>-<a href="#Page_15">15</a>.</li>
+
+<li>Interconnexion of nature, <a href="#Page_182">182</a>.</li>
+
+<li>Interdependence, of properties, <a href="#Page_361">361</a>;</li>
+<li><span style="margin-left: 1em;">of the sensuous elements of the world, <a href="#Page_179">179</a>.</span></li>
+
+<li>Interference experiments with the head-wave of moving projectiles, <a href="#Page_327">327</a>-<a href="#Page_328">328</a>.</li>
+
+<li>International intercourse, established by Latin, <a href="#Page_341">341</a>.</li>
+
+<li>International measures, <a href="#Page_108">108</a>.</li>
+
+<li>Invention, discovery and, distinction between, <a href="#Page_269">269</a>.</li>
+
+<li>Inventions, requisites for the development of, <a href="#Page_266">266</a>, <a href="#Page_268">268</a> et seq.</li>
+
+<li>Iron-filings, <a href="#Page_220">220</a>, <a href="#Page_243">243</a>.</li>
+
+<li>Italian art, <a href="#Page_234">234</a>.</li>
+
+</ul>
+
+<ul class="IX"><li>Jacobi, C. G. J., on mathematics, <a href="#Page_280">280</a>.</li>
+
+<li>James, W., <a href="#Page_275">275</a>, <a href="#Page_299">299</a>.</li>
+
+<li>Java, <a href="#Page_163">163</a>.</li>
+
+<li>Jews and Christians, monotheism of the, <a href="#Page_187">187</a>.</li>
+
+<li>Jolly, Professor von, <a href="#Page_112">112</a>, <a href="#Page_274">274</a>.</li>
+
+<li>Joule, J. P., on the conservation of energy, <a href="#Page_163">163</a>-<a href="#Page_165">165</a>, <a href="#Page_167">167</a>, <a href="#Page_183">183</a>;</li>
+<li><span style="margin-left: 1em;">his conception of energy, <a href="#Page_245">245</a>;</span></li>
+<li><span style="margin-left: 1em;">his metaphysics, <a href="#Page_183">183</a>, <a href="#Page_246">246</a>;</span></li>
+<li><span style="margin-left: 1em;">his method of thought, <a href="#Page_247">247</a>;</span></li>
+<li><span style="margin-left: 1em;">also <a href="#Page_137">137</a>, <a href="#Page_138">138</a>.</span></li>
+
+<li>Journée, <a href="#Page_317">317</a>.</li>
+
+<li>Judge, criminal, the natural philosopher compared to a, <a href="#Page_48">48</a>.</li>
+
+<li>Judgment, essentially economy of thought, <a href="#Page_201">201</a>-<a href="#Page_202">202</a>;</li>
+<li><span style="margin-left: 1em;">sharpened by languages and sciences, <a href="#Page_357">357</a>-<a href="#Page_358">358</a>;</span></li>
+<li><span style="margin-left: 1em;">also <a href="#Page_232">232</a>-<a href="#Page_233">233</a>, <a href="#Page_238">238</a>.</span></li>
+
+<li>Juliet, Romeo and, <a href="#Page_87">87</a>.</li>
+
+<li>Jupiter, its satellites employed in the determination of the velocity of light, <a href="#Page_51">51</a> et seq.</li>
+
+<li>Jurisprudence, Latin and Greek unnecessary for the study of, <a href="#Page_346">346</a>, footnote.</li>
+
+</ul>
+
+<ul class="IX"><li>Kant, his hypothesis of the origin of the planetary system, <a href="#Page_5">5</a>;</li>
+<li><span style="margin-left: 1em;">his <i>Critique of Pure Reason</i>, <a href="#Page_188">188</a>;</span></li>
+<li><span style="margin-left: 1em;">on innate concepts of the understanding, <a href="#Page_199">199</a>;</span></li>
+<li><span style="margin-left: 1em;">on time, <a href="#Page_204">204</a>;</span></li>
+<li><span style="margin-left: 1em;">also footnote, <a href="#Page_93">93</a>.</span></li>
+
+<li>Kepler, <a href="#Page_187">187</a>, <a href="#Page_270">270</a>.</li>
+
+<li>Kinetic energy, <a href="#Page_177">177</a>.</li>
+
+<li>Kirchhoff, his epistemological ideas, <a href="#Page_257">257</a>-<a href="#Page_258">258</a>;</li>
+<li><span style="margin-left: 1em;">his definition of mechanics, <a href="#Page_236">236</a>, <a href="#Page_258">258</a>, <a href="#Page_271">271</a>, <a href="#Page_273">273</a>.</span></li>
+
+<li>Knight, <a href="#Page_289">289</a>.</li>
+
+<li>Knowledge, a product of organic nature, <a href="#Page_217">217</a> et seq., <a href="#Page_235">235</a>;</li>
+<li><span style="margin-left: 1em;">instinctive, <a href="#Page_190">190</a>;</span></li>
+<li><span style="margin-left: 1em;">made possible by economy of thought, <a href="#Page_198">198</a>;</span></li>
+<li><span style="margin-left: 1em;">our first, derived from the economy of self-preservation, <a href="#Page_197">197</a>;</span></li>
+<li><span style="margin-left: 1em;">the theory of, <a href="#Page_203">203</a>;</span></li>
+<li><span style="margin-left: 1em;">our primitive acts of the foundation of science, <a href="#Page_190">190</a>.</span></li>
+
+<li>Kocher, <a href="#Page_328">328</a>.</li>
+
+<li>Koenig, measurement of the velocity of sound, <a href="#Page_57">57</a> et seq.</li>
+
+<li>Kölliker, <a href="#Page_19">19</a>.</li>
+
+<li>Kopisch, <a href="#Page_61">61</a>.</li>
+
+<li>Kreidl, <a href="#Page_299">299</a>, <a href="#Page_302">302</a>, <a href="#Page_306">306</a>;</li>
+<li><span style="margin-left: 1em;">his experiments, <a href="#Page_272">272</a>.</span></li>
+
+<li>Krupp, <a href="#Page_319">319</a>.</li>
+
+</ul>
+
+<ul class="IX"><li>Labels, the value of, <a href="#Page_201">201</a>.</li>
+
+<li>Labor, the accumulation of, the foundation of wealth and power, <a href="#Page_198">198</a>;</li>
+<li><span style="margin-left: 1em;">inquirer's division of, <a href="#Page_105">105</a>, <a href="#Page_258">258</a>.</span></li>
+
+<li>Labyrinth, of the ear, <a href="#Page_18">18</a>, <a href="#Page_291">291</a>, <a href="#Page_305">305</a>.</li>
+
+<li>Lactantius, on the study of moral and physical science, <a href="#Page_89">89</a>.</li>
+
+<li>Ladder of our abstraction, the, <a href="#Page_208">208</a>.</li>
+
+<li>Ladies, their eyes, <a href="#Page_71">71</a>;</li>
+<li><span style="margin-left: 1em;">like tuning-forks, <a href="#Page_23">23</a>-<a href="#Page_24">24</a>.</span></li>
+
+<li>Lagrange, on Huygens's principle, <a href="#Page_149">149</a>;</li>
+<li><span style="margin-left: 1em;">on the principle of virtual velocities, <a href="#Page_150">150</a>-<a href="#Page_155">155</a>;</span></li>
+<li><span style="margin-left: 1em;">character of the intellectual activity of a, <a href="#Page_195">195</a>, <a href="#Page_278">278</a>.</span></li>
+
+<li>Lake-dwellers, <a href="#Page_46">46</a>, <a href="#Page_271">271</a>.</li>
+
+<li>Lamp-shade, <a href="#Page_70">70</a>.</li>
+
+<li>Lane's unit jar, <a href="#Page_115">115</a>.</li>
+
+<li>Language, knowledge of the nature of, demanded by a liberal education, <a href="#Page_356">356</a>;</li>
+<li><span style="margin-left: 1em;">relationship between, and thought, <a href="#Page_358">358</a>;</span></li>
+<li><span style="margin-left: 1em;">communication by <a href="#Page_237">237</a>;</span></li>
+<li><span style="margin-left: 1em;">economy of, <a href="#Page_191">191</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">human its character, <a href="#Page_238">238</a>;</span></li>
+<li><span class="pagenum"><a name="Page_402" id="Page_402">[Pg 402]</a></span><span style="margin-left: 1em;">of animals, <a href="#Page_238">238</a>;</span></li>
+<li><span style="margin-left: 1em;">instruction in, <a href="#Page_338">338</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">its methods, <a href="#Page_192">192</a>.</span></li>
+
+<li>Laplace, on the atoms of the brain, <a href="#Page_188">188</a>;</li>
+<li><span style="margin-left: 1em;">on the scientific achievements of the eighteenth century, <a href="#Page_188">188</a>;</span></li>
+<li><span style="margin-left: 1em;">his hypothesis of the origin of the planetary system, <a href="#Page_5">5</a>.</span></li>
+
+<li>Latent heat, <a href="#Page_167">167</a>, <a href="#Page_178">178</a>, <a href="#Page_244">244</a>.</li>
+
+<li>Latin city of Maupertuis, <a href="#Page_339">339</a>.</li>
+
+<li>Latin, instruction in, <a href="#Page_311">311</a> et seq.;</li>
+<li><span style="margin-left: 1em;">introduced with the Christian Church, <a href="#Page_340">340</a>;</span></li>
+<li><span style="margin-left: 1em;">the language of scholars, the medium of international intercourse, its power, utility, and final abandonment, <a href="#Page_341">341</a>-<a href="#Page_347">347</a>;</span></li>
+<li><span style="margin-left: 1em;">the wealth of its literature, <a href="#Page_348">348</a>;</span></li>
+<li><span style="margin-left: 1em;">the excessive study of, <a href="#Page_346">346</a>, <a href="#Page_349">349</a>, <a href="#Page_354">354</a>, <a href="#Page_355">355</a>;</span></li>
+<li><span style="margin-left: 1em;">its power to sharpen the judgment, <a href="#Page_357">357</a>-<a href="#Page_358">358</a>.</span></li>
+
+<li>Lavish extravagance of science, <a href="#Page_189">189</a>.</li>
+
+<li>Law, a, defined, <a href="#Page_256">256</a>;</li>
+<li><span style="margin-left: 1em;">a natural, not contained in the conformity of the energies, <a href="#Page_175">175</a>.</span></li>
+
+<li>Law-maker, motives of not always discernible, <a href="#Page_9">9</a>.</li>
+
+<li>Layard, <a href="#Page_79">79</a>.</li>
+
+<li>Learning, its nature, <a href="#Page_366">366</a> et seq.</li>
+
+<li>Least superficial area, principle of, accounted for by the mutual attractions of liquid particles, <a href="#Page_13">13</a>-<a href="#Page_14">14</a>;</li>
+<li><span style="margin-left: 1em;">illustrated by a pulley arrangement, <a href="#Page_12">12</a>-<a href="#Page_13">13</a>;</span></li>
+<li><span style="margin-left: 1em;">also <a href="#Page_9">9</a> et seq.</span></li>
+
+<li>Leibnitz, on harmony, <a href="#Page_33">33</a>;</li>
+<li><span style="margin-left: 1em;">on international intercourse, <a href="#Page_342">342</a>, footnote.</span></li>
+
+<li>Lessing, quotation from, <a href="#Page_47">47</a>.</li>
+
+<li>Letters of the alphabet, their symmetry, <a href="#Page_94">94</a>, <a href="#Page_97">97</a>.</li>
+
+<li>Level heights of work, <a href="#Page_172">172</a>-<a href="#Page_174">174</a>.</li>
+
+<li>Lever, a, in action, <a href="#Page_222">222</a>.</li>
+
+<li>Leverrier, prediction of the planet Neptune, <a href="#Page_29">29</a>.</li>
+
+<li>Leyden jar, <a href="#Page_114">114</a>.</li>
+
+<li>Liberal education, a, <a href="#Page_341">341</a> et seq., <a href="#Page_359">359</a>, <a href="#Page_371">371</a>.</li>
+
+<li>Libraries, thoughts stored up in, <a href="#Page_237">237</a>.</li>
+
+<li>Lichtenberg, on instruction, <a href="#Page_276">276</a>, <a href="#Page_370">370</a>.</li>
+
+<li>Licius, a Chinese philosopher, <a href="#Page_213">213</a>.</li>
+
+<li>Liebig, <a href="#Page_163">163</a>, <a href="#Page_278">278</a>.</li>
+
+<li>Life and death, <a href="#Page_186">186</a>.</li>
+
+<li>Light, history of as elucidating how theories obstruct research, <a href="#Page_242">242</a>;</li>
+<li><span style="margin-left: 1em;">Huygens's and Newton's views of, <a href="#Page_227">227</a>-<a href="#Page_228">228</a>;</span></li>
+<li><span style="margin-left: 1em;">its different conceptions, <a href="#Page_226">226</a>;</span></li>
+<li><span style="margin-left: 1em;">rectilinear propagation of, <a href="#Page_194">194</a>;</span></li>
+<li><span style="margin-left: 1em;">rôle of, in vision, <a href="#Page_81">81</a>;</span></li>
+<li><span style="margin-left: 1em;">spatial and temporal periodicity of, explains optical phenomena, <a href="#Page_194">194</a>;</span></li>
+<li><span style="margin-left: 1em;">numerical velocity of, <a href="#Page_58">58</a>;</span></li>
+<li><span style="margin-left: 1em;">where does it go to? <a href="#Page_199">199</a>;</span></li>
+<li><span style="margin-left: 1em;">generally, <a href="#Page_48">48</a> et seq.</span></li>
+
+<li>Like effects in like circumstances, <a href="#Page_199">199</a>.</li>
+
+<li>Likeness, <a href="#Page_388">388</a>, <a href="#Page_391">391</a>.</li>
+
+<li>Lilliput, <a href="#Page_84">84</a>.</li>
+
+<li>Lines, straight, their symmetry, <a href="#Page_98">98</a>;</li>
+<li><span style="margin-left: 1em;">curved, their asymmetry, <a href="#Page_98">98</a>;</span></li>
+<li><span style="margin-left: 1em;">of force, <a href="#Page_249">249</a>.</span></li>
+
+<li>Links of thought, intermediate, <a href="#Page_198">198</a>.</li>
+
+<li>Liquefaction, latent heat of, <a href="#Page_178">178</a>.</li>
+
+<li>Liquid, efflux, law of, <a href="#Page_150">150</a>;</li>
+<li><span style="margin-left: 1em;">equilibrium, figures of, <a href="#Page_4">4</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">the latter produced in open air, <a href="#Page_7">7</a>-<a href="#Page_8">8</a>;</span></li>
+<li><span style="margin-left: 1em;">their beauty and multiplicity of form, <a href="#Page_7">7</a>, <a href="#Page_8">8</a>;</span></li>
+<li><span style="margin-left: 1em;">made permanent by melted colophonium, <a href="#Page_7">7</a>.</span></li>
+
+<li>Liquids, forms of, <a href="#Page_1">1</a>-<a href="#Page_16">16</a>;</li>
+<li><span style="margin-left: 1em;">difference between, and solids, <a href="#Page_2">2</a>;</span></li>
+<li><span style="margin-left: 1em;">their mobility and adaptiveness of form, <a href="#Page_3">3</a>;</span></li>
+<li><span style="margin-left: 1em;">the courtiers <i>par excellence</i> of the natural bodies, <a href="#Page_3">3</a>;</span></li>
+<li><span style="margin-left: 1em;">possess under certain circumstances forms of their own, <a href="#Page_3">3</a>.</span></li>
+
+<li>Living force, <a href="#Page_137">137</a>, <a href="#Page_184">184</a>;</li>
+<li><span style="margin-left: 1em;">law of the conservation of, <a href="#Page_149">149</a>.</span></li>
+
+<li>Lloyd, observation of the conical refraction of light, <a href="#Page_29">29</a>.</li>
+
+<li>Lobster, of Lake Mohrin, the, <a href="#Page_61">61</a>.</li>
+
+<li>Localisation, cerebral, <a href="#Page_210">210</a>.</li>
+
+<li>Locke, on language and thought, <a href="#Page_358">358</a>.</li>
+
+<li>Locomotive, steam in the boiler of, <a href="#Page_219">219</a>.</li>
+
+<li>Loeb, J., <a href="#Page_289">289</a>, <a href="#Page_291">291</a>, <a href="#Page_302">302</a>.</li>
+
+<li>Logarithms, <a href="#Page_195">195</a>, <a href="#Page_219">219</a>;</li>
+<li><span style="margin-left: 1em;">in music, <a href="#Page_103">103</a>-<a href="#Page_104">104</a>.</span></li>
+
+<li>Logical root, of the principle of energy, <a href="#Page_181">181</a>;</li>
+<li><span style="margin-left: 1em;">of the principle of excluded perpetual motion, <a href="#Page_182">182</a>.</span></li>
+
+<li>Lombroso, <a href="#Page_280">280</a>.</li>
+
+<li>Lucian, <a href="#Page_347">347</a>.</li>
+
+</ul>
+
+<ul class="IX"><li><i>Macula acustica</i>, <a href="#Page_272">272</a>.</li>
+
+<li>Magic lantern, <a href="#Page_96">96</a>.</li>
+
+<li>Magic powers of nature, <a href="#Page_189">189</a>.</li>
+
+<li><span class="pagenum"><a name="Page_403" id="Page_403">[Pg 403]</a></span>Magical power of science, belief in the, <a href="#Page_189">189</a>.</li>
+
+<li>Magnet, a, <a href="#Page_220">220</a>;</li>
+<li><span style="margin-left: 1em;">will compared to the pressure of a, <a href="#Page_14">14</a>;</span></li>
+<li><span style="margin-left: 1em;">coercive force of a, <a href="#Page_216">216</a>.</span></li>
+
+<li>Magnetic needle, near a current, <a href="#Page_207">207</a>.</li>
+
+<li>Magnetised bar of steel, <a href="#Page_242">242</a>-<a href="#Page_243">243</a>.</li>
+
+<li>Major and minor keys in music, <a href="#Page_100">100</a> et seq.</li>
+
+<li>Malus, <a href="#Page_242">242</a>.</li>
+
+<li>Man, a fragment of nature's life, <a href="#Page_49">49</a>;</li>
+<li><span style="margin-left: 1em;">his life embraces others, <a href="#Page_234">234</a>.</span></li>
+
+<li>Mann, <a href="#Page_364">364</a>.</li>
+
+<li>Manuscript in a mirror, <a href="#Page_93">93</a>.</li>
+
+<li>Maple syrup, statues of, on Moon, <a href="#Page_4">4</a>.</li>
+
+<li>Marx, <a href="#Page_35">35</a>.</li>
+
+<li>Material, the relations of work with heat and the consumption of, <a href="#Page_245">245</a> et seq.</li>
+
+<li>Mathematical methods, their character, <a href="#Page_197">197</a>-<a href="#Page_198">198</a>.</li>
+
+<li>Mathematics, economy of, <a href="#Page_195">195</a>;</li>
+<li><span style="margin-left: 1em;">on instruction in, <a href="#Page_338">338</a>-<a href="#Page_374">374</a>;</span></li>
+<li><span style="margin-left: 1em;">C. G. J. Jacobi on, <a href="#Page_280">280</a>.</span></li>
+
+<li>Matter, constancy of, <a href="#Page_203">203</a>;</li>
+<li><span style="margin-left: 1em;">its nature, <a href="#Page_203">203</a>;</span></li>
+<li><span style="margin-left: 1em;">the notion of, <a href="#Page_213">213</a>.</span></li>
+
+<li>Maupertuis, his Latin city, <a href="#Page_338">338</a>.</li>
+
+<li>Maximal and minimal problems, their rôle in physics, <a href="#Page_14">14</a>, footnote.</li>
+
+<li>Mayer, J. R., his conception of energy, <a href="#Page_245">245</a>, <a href="#Page_246">246</a>;</li>
+<li><span style="margin-left: 1em;">his methods of thought, <a href="#Page_247">247</a>;</span></li>
+<li><span style="margin-left: 1em;">on the conservation of energy, <a href="#Page_163">163</a>, <a href="#Page_164">164</a>, <a href="#Page_165">165</a>, <a href="#Page_167">167</a>, <a href="#Page_183">183</a>, <a href="#Page_184">184</a>;</span></li>
+<li><span style="margin-left: 1em;">his metaphysical utterances, <a href="#Page_183">183</a>, <a href="#Page_246">246</a>;</span></li>
+<li><span style="margin-left: 1em;">also <a href="#Page_138">138</a>, <a href="#Page_184">184</a>, <a href="#Page_191">191</a>, <a href="#Page_217">217</a>, <a href="#Page_271">271</a>, <a href="#Page_274">274</a>.</span></li>
+
+<li>Measurement, definition of, <a href="#Page_206">206</a>.</li>
+
+<li>Measures, international, <a href="#Page_108">108</a>.</li>
+
+<li>Mécanique céleste, <a href="#Page_90">90</a>, <a href="#Page_188">188</a>;</li>
+<li><span style="margin-left: 1em;">sociale, and morale, the, <a href="#Page_90">90</a>.</span></li>
+
+<li>Mechanical, conception of the world, <a href="#Page_105">105</a>, <a href="#Page_155">155</a> et seq., <a href="#Page_188">188</a>, <a href="#Page_207">207</a>;</li>
+<li><span style="margin-left: 1em;">energy, W. Thomson on waste of, <a href="#Page_175">175</a>;</span></li>
+<li><span style="margin-left: 1em;">analogies between &mdash;&mdash; and thermal energy, <a href="#Page_17">17</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">equivalent of heat, electricity, etc., <a href="#Page_164">164</a>, <a href="#Page_167">167</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">mythology, <a href="#Page_207">207</a>;</span></li>
+<li><span style="margin-left: 1em;">phenomena, physical events as, <a href="#Page_182">182</a>;</span></li>
+<li><span style="margin-left: 1em;">philosophy, <a href="#Page_188">188</a>;</span></li>
+<li><span style="margin-left: 1em;">physics, <a href="#Page_155">155</a>-<a href="#Page_160">160</a>, <a href="#Page_212">212</a>;</span></li>
+<li><span style="margin-left: 1em;">substitution-value of heat, <a href="#Page_178">178</a>, footnote.</span></li>
+
+<li>Mechanics, Kirchhoff's definition of, <a href="#Page_236">236</a>.</li>
+
+<li>Medicine, students of, <a href="#Page_326">326</a>.</li>
+
+<li>Melody, <a href="#Page_101">101</a>.</li>
+
+<li>Melsens, <a href="#Page_310">310</a>, <a href="#Page_327">327</a>.</li>
+
+<li>Memory, a treasure-house for comparison, <a href="#Page_230">230</a>;</li>
+<li><span style="margin-left: 1em;">common elements impressed upon the, <a href="#Page_180">180</a>;</span></li>
+<li><span style="margin-left: 1em;">its importance, <a href="#Page_238">238</a>;</span></li>
+<li><span style="margin-left: 1em;">science disburdens the, <a href="#Page_193">193</a>.</span></li>
+
+<li>Mendelejeff, his periodical series, <a href="#Page_256">256</a>.</li>
+
+<li>Mental, adaptation, <a href="#Page_214">214</a>-<a href="#Page_235">235</a>;</li>
+<li><span style="margin-left: 1em;">completion of phenomena, <a href="#Page_220">220</a>;</span></li>
+<li><span style="margin-left: 1em;">imagery, <a href="#Page_253">253</a>;</span></li>
+<li><span style="margin-left: 1em;">imitation, our schematic, <a href="#Page_199">199</a>;</span></li>
+<li><span style="margin-left: 1em;">processes, economical, <a href="#Page_195">195</a>;</span></li>
+<li><span style="margin-left: 1em;">reproduction, <a href="#Page_198">198</a>;</span></li>
+<li><span style="margin-left: 1em;">visualisation, <a href="#Page_250">250</a>.</span></li>
+
+<li>Mephistopheles, <a href="#Page_88">88</a>.</li>
+
+<li>Mercantile principle, a miserly, at the basis of science, <a href="#Page_15">15</a>.</li>
+
+<li>Mersenne, <a href="#Page_377">377</a>.</li>
+
+<li>Mesmerism, the mental state of ordinary minds, <a href="#Page_228">228</a>.</li>
+
+<li>Metaphysical establishment of doctrine of energy, <a href="#Page_183">183</a>.</li>
+
+<li>Metaphysical spooks, <a href="#Page_222">222</a>.</li>
+
+<li>Metrical, concepts of electricity, <a href="#Page_107">107</a> et seq.;</li>
+<li><span style="margin-left: 1em;">notions, energy and entropy are, <a href="#Page_178">178</a>;</span></li>
+<li><span style="margin-left: 1em;">units, the building-stones of the physicist, <a href="#Page_253">253</a>.</span></li>
+
+<li>Metronomes, <a href="#Page_41">41</a>.</li>
+
+<li>Meyer, Lothar, his periodical series, <a href="#Page_256">256</a>.</li>
+
+<li>Middle Ages, <a href="#Page_243">243</a>, <a href="#Page_349">349</a>.</li>
+
+<li>Midsummer Night's Dream, <a href="#Page_309">309</a>.</li>
+
+<li>Mill, John Stuart, <a href="#Page_230">230</a>.</li>
+
+<li>Millers, school for, <a href="#Page_326">326</a>.</li>
+
+<li>Mill-wheel, doing work, <a href="#Page_161">161</a>.</li>
+
+<li>Mimicking facts in thought, <a href="#Page_189">189</a>, <a href="#Page_193">193</a>.</li>
+
+<li>Minor and major keys in music, <a href="#Page_100">100</a> et seq.</li>
+
+<li>Mirror, symmetrical reversion of objects in, <a href="#Page_92">92</a> et seq.</li>
+
+<li>Miserly mercantile principle at the basis of science, <a href="#Page_15">15</a>.</li>
+
+<li>Moat, child looking into, <a href="#Page_208">208</a>.</li>
+
+<li>Modern scientists, adherents of the mechanical philosophy, <a href="#Page_188">188</a>.</li>
+
+<li>Molecular theories, <a href="#Page_104">104</a>.</li>
+
+<li>Molecules, <a href="#Page_203">203</a>, <a href="#Page_207">207</a>.</li>
+
+<li>Molière, <a href="#Page_234">234</a>.</li>
+
+<li>Momentum, <a href="#Page_184">184</a>.</li>
+
+<li>Monocular vision, <a href="#Page_98">98</a>.</li>
+
+<li><span class="pagenum"><a name="Page_404" id="Page_404">[Pg 404]</a></span>Monotheism of the Christians and Jews, <a href="#Page_187">187</a>.</li>
+
+<li>Montagues and Capulets, <a href="#Page_87">87</a>.</li>
+
+<li>Moon, eclipse of, <a href="#Page_219">219</a>;</li>
+<li><span style="margin-left: 1em;">lightness of bodies on, <a href="#Page_4">4</a>;</span></li>
+<li><span style="margin-left: 1em;">the study of the, <a href="#Page_90">90</a>, <a href="#Page_284">284</a>.</span></li>
+
+<li>Moreau, <a href="#Page_307">307</a>.</li>
+
+<li>Mosaic of thought, <a href="#Page_192">192</a>.</li>
+
+<li>Motion, a perpetual, <a href="#Page_181">181</a>;</li>
+<li><span style="margin-left: 1em;">quantity of, <a href="#Page_184">184</a>;</span></li>
+<li><span style="margin-left: 1em;">the Eleatics on, <a href="#Page_158">158</a>;</span></li>
+<li><span style="margin-left: 1em;">Wundt on, <a href="#Page_158">158</a>;</span></li>
+<li><span style="margin-left: 1em;">the Herbartians on, <a href="#Page_158">158</a>.</span></li>
+
+<li>Motions, natural and violent, <a href="#Page_226">226</a>;</li>
+<li><span style="margin-left: 1em;">their familiar character, <a href="#Page_157">157</a>.</span></li>
+
+<li>Mountains of the earth, would crumble if very large, <a href="#Page_3">3</a>;</li>
+<li><span style="margin-left: 1em;">weight of bodies on, <a href="#Page_112">112</a>.</span></li>
+
+<li>Mozart, <a href="#Page_44">44</a>, <a href="#Page_279">279</a>.</li>
+
+<li>Müller, Johann, <a href="#Page_291">291</a>.</li>
+
+<li>Multiplication-table, <a href="#Page_195">195</a>.</li>
+
+<li>Multiplier, <a href="#Page_132">132</a>.</li>
+
+<li>Music, band of, its <i>tempo</i> accelerated and retarded, <a href="#Page_53">53</a>;</li>
+<li><span style="margin-left: 1em;">the principle of repetition in, <a href="#Page_99">99</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">its notation, mathematically illustrated, <a href="#Page_103">103</a>-<a href="#Page_104">104</a>.</span></li>
+
+<li>Musical notes, reversion of, <a href="#Page_101">101</a> et seq.;</li>
+<li><span style="margin-left: 1em;">their economy, <a href="#Page_192">192</a>.</span></li>
+
+<li>Musical scale, a species of one-dimensional space, <a href="#Page_105">105</a>.</li>
+
+<li>Mystery, in physics, <a href="#Page_222">222</a>;</li>
+<li><span style="margin-left: 1em;">science can dispense with, <a href="#Page_189">189</a>.</span></li>
+
+<li>Mysticism, numerical, <a href="#Page_33">33</a>;</li>
+<li><span style="margin-left: 1em;">in the principle of energy, <a href="#Page_184">184</a>.</span></li>
+
+<li>Mythology, the mechanical, of philosophy, <a href="#Page_207">207</a>.</li>
+
+</ul>
+
+<ul class="IX"><li>Nagel, von, <a href="#Page_364">364</a>.</li>
+
+<li>Nansen, <a href="#Page_296">296</a>.</li>
+
+<li>Napoleon, picture representing the tomb of, <a href="#Page_36">36</a>.</li>
+
+<li>Nations, intercourse and ideas of, <a href="#Page_336">336</a>-<a href="#Page_337">337</a>.</li>
+
+<li>Natural constants, <a href="#Page_193">193</a>.</li>
+
+<li>Natural law, a, not contained in the conformity of the energies, <a href="#Page_175">175</a>.</li>
+
+<li>Natural laws, abridged descriptions, <a href="#Page_193">193</a>;</li>
+<li><span style="margin-left: 1em;">likened to type, <a href="#Page_193">193</a>.</span></li>
+
+<li>Natural motions, <a href="#Page_225">225</a>.</li>
+
+<li>Natural selection in scientific theories, <a href="#Page_63">63</a>, <a href="#Page_218">218</a>.</li>
+
+<li>Nature, experience the well-spring of all knowledge of, <a href="#Page_181">181</a>;</li>
+<li><span style="margin-left: 1em;">fashions of, <a href="#Page_64">64</a>;</span></li>
+<li><span style="margin-left: 1em;">first knowledge of, instinctive, <a href="#Page_189">189</a>;</span></li>
+<li><span style="margin-left: 1em;">general interconnexion of, <a href="#Page_182">182</a>;</span></li>
+<li><span style="margin-left: 1em;">has many sides, <a href="#Page_217">217</a>;</span></li>
+<li><span style="margin-left: 1em;">her forces compared to purposes, <a href="#Page_14">14</a>-<a href="#Page_15">15</a>;</span></li>
+<li><span style="margin-left: 1em;">likened to a good man of business, <a href="#Page_15">15</a>;</span></li>
+<li><span style="margin-left: 1em;">the economy of her actions, <a href="#Page_15">15</a>;</span></li>
+<li><span style="margin-left: 1em;">how she appears to other animals, <a href="#Page_83">83</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">inquiry of, viewed as a torture, <a href="#Page_48">48</a>-<a href="#Page_49">49</a>;</span></li>
+<li><span style="margin-left: 1em;">view of, as something designedly concealed from man, <a href="#Page_49">49</a>;</span></li>
+<li><span style="margin-left: 1em;">like a covetous tailor, <a href="#Page_9">9</a>-<a href="#Page_10">10</a>;</span></li>
+<li><span style="margin-left: 1em;">magic powers of, <a href="#Page_189">189</a>;</span></li>
+<li><span style="margin-left: 1em;">our view of, modified by binocular vision, <a href="#Page_82">82</a>;</span></li>
+<li><span style="margin-left: 1em;">the experimental method a questioning of, <a href="#Page_48">48</a>.</span></li>
+
+<li>Negro hamlet, the science of a, <a href="#Page_237">237</a>.</li>
+
+<li>Neptune, prediction and discovery of the planet, <a href="#Page_29">29</a>.</li>
+
+<li>New views, <a href="#Page_296">296</a> et seq.</li>
+
+<li>Newton, describes polarisation, <a href="#Page_242">242</a>;</li>
+<li><span style="margin-left: 1em;">expresses his wealth of thought in Latin, <a href="#Page_341">341</a>;</span></li>
+<li><span style="margin-left: 1em;">his discovery of gravitation, <a href="#Page_225">225</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">his solution of dispersion, <a href="#Page_362">362</a>;</span></li>
+<li><span style="margin-left: 1em;">his principle of the equality of pressure and counterpressure, <a href="#Page_191">191</a>;</span></li>
+<li><span style="margin-left: 1em;">his view of light, <a href="#Page_227">227</a>-<a href="#Page_228">228</a>;</span></li>
+<li><span style="margin-left: 1em;">on absolute time, <a href="#Page_204">204</a>;</span></li>
+<li><span style="margin-left: 1em;">selections from his works for use in instruction, <a href="#Page_368">368</a>;</span></li>
+<li><span style="margin-left: 1em;">also <a href="#Page_270">270</a>, <a href="#Page_274">274</a>, <a href="#Page_279">279</a>, <a href="#Page_285">285</a>, <a href="#Page_289">289</a>.</span></li>
+
+<li>Nobility, they displace Latin, <a href="#Page_342">342</a>.</li>
+
+<li>Notation, musical, mathematically illustrated, <a href="#Page_103">103</a>-<a href="#Page_104">104</a>.</li>
+
+<li>Numbers, economy of, <a href="#Page_195">195</a>;</li>
+<li><span style="margin-left: 1em;">their connexion with consonance, <a href="#Page_32">32</a>.</span></li>
+
+<li>Numerical mysticism, <a href="#Page_33">33</a>.</li>
+
+<li>Nursery, the questions of the, <a href="#Page_199">199</a>.</li>
+
+</ul>
+
+<ul class="IX"><li>Observation, <a href="#Page_310">310</a>.</li>
+
+<li>Observation, in science, <a href="#Page_261">261</a>.</li>
+
+<li>Ocean-stream, <a href="#Page_272">272</a>.</li>
+
+<li>Oettingen, Von, <a href="#Page_103">103</a>.</li>
+
+<li>Ohm, on electric currents, <a href="#Page_249">249</a>.</li>
+
+<li>Ohm, the word, <a href="#Page_343">343</a>.</li>
+
+<li>Oil, alcohol, water, and, employed in Plateau's experiments, <a href="#Page_4">4</a>;</li>
+<li><span style="margin-left: 1em;">free mass of, assumes the shape of a sphere, <a href="#Page_12">12</a>;</span></li>
+<li><span style="margin-left: 1em;">geometrical figures of, <a href="#Page_5">5</a> et seq.</span></li>
+
+<li>One-eyed people, vision of, <a href="#Page_98">98</a>.</li>
+
+<li>Ophthalmoscope, <a href="#Page_18">18</a>.</li>
+
+<li>Optic nerves, <a href="#Page_96">96</a>.</li>
+
+<li><span class="pagenum"><a name="Page_405" id="Page_405">[Pg 405]</a></span>Optimism and pessimism, <a href="#Page_234">234</a>.</li>
+
+<li>Order of physics, <a href="#Page_197">197</a>.</li>
+
+<li>Organ, bellows of an, <a href="#Page_135">135</a>.</li>
+
+<li>Organic nature, results of Darwin's studies of, <a href="#Page_215">215</a> et seq.</li>
+<li><span style="margin-left: 1em;">See <i>Adaptation</i> and <i>Heredity</i>.</span></li>
+
+<li>Oriental world of fables, <a href="#Page_273">273</a>.</li>
+
+<li>Orientation, sensations of, <a href="#Page_282">282</a> et seq.</li>
+
+<li>Oscillation, centre of, <a href="#Page_147">147</a> et seq.</li>
+
+<li>Ostwald, <a href="#Page_172">172</a>.</li>
+
+<li>Otoliths, <a href="#Page_301">301</a> et seq.</li>
+
+<li>Overtones, <a href="#Page_28">28</a>, <a href="#Page_40">40</a>, <a href="#Page_349">349</a>.</li>
+
+<li>Ozone, Schöbein's discovery of, <a href="#Page_271">271</a>.</li>
+
+</ul>
+
+<ul class="IX"><li>Painted things, the difference between real and, <a href="#Page_68">68</a>.</li>
+
+<li>Palestrina, <a href="#Page_44">44</a>.</li>
+
+<li>Parameter, <a href="#Page_257">257</a>.</li>
+
+<li>Partial tones, <a href="#Page_390">390</a>.</li>
+
+<li>Particles, smallest, <a href="#Page_104">104</a>.</li>
+
+<li>Pascheles, Dr. W., <a href="#Page_285">285</a>.</li>
+
+<li>Paulsen, <a href="#Page_338">338</a>, <a href="#Page_340">340</a>, <a href="#Page_373">373</a>.</li>
+
+<li>Pearls of life, strung on the individual as on a thread, <a href="#Page_234">234</a>-<a href="#Page_235">235</a>.</li>
+
+<li>Pencil surpasses the mathematician in intelligence, <a href="#Page_196">196</a>.</li>
+
+<li>Pendulum, motion of a, <a href="#Page_144">144</a> et seq.,</li>
+<li><span style="margin-left: 1em;">increased motion of, due to slight impulses, <a href="#Page_21">21</a>;</span></li>
+<li><span style="margin-left: 1em;">electrical, <a href="#Page_110">110</a>.</span></li>
+
+<li>Percepts, of like form, <a href="#Page_390">390</a>.</li>
+
+<li>Periodical, changes, <a href="#Page_181">181</a>;</li>
+<li><span style="margin-left: 1em;">series, <a href="#Page_256">256</a>.</span></li>
+
+<li>Permanent, changes, <a href="#Page_181">181</a>, <a href="#Page_199">199</a>;</li>
+<li><span style="margin-left: 1em;">elements of the world, <a href="#Page_194">194</a>.</span></li>
+
+<li>Perpetual motion, a, <a href="#Page_181">181</a>;</li>
+<li><span style="margin-left: 1em;">defined, <a href="#Page_139">139</a>;</span></li>
+<li><span style="margin-left: 1em;">impossibility of, <a href="#Page_139">139</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">the principle of the, excluded, <a href="#Page_140">140</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">excluded from general physics, <a href="#Page_162">162</a>.</span></li>
+
+<li>Personality, its nature, <a href="#Page_234">234</a>-<a href="#Page_235">235</a>.</li>
+
+<li>Perspective, <a href="#Page_76">76</a> et seq.;</li>
+<li><span style="margin-left: 1em;">contraction of, <a href="#Page_74">74</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">distortion of, <a href="#Page_77">77</a>.</span></li>
+
+<li>Pessimism and optimism, <a href="#Page_234">234</a>.</li>
+
+<li>Pharaohs, <a href="#Page_85">85</a>.</li>
+
+<li>Phenomenology, a universal physical, <a href="#Page_250">250</a>.</li>
+
+<li>Philistine, modes of thought of, <a href="#Page_223">223</a>.</li>
+
+<li>Philology, comparison in, <a href="#Page_239">239</a>.</li>
+
+<li>Philosopher, an ancient, on the moral and physical sciences, <a href="#Page_89">89</a>.</li>
+
+<li>Philosophy, its character at all times, <a href="#Page_186">186</a>;</li>
+<li><span style="margin-left: 1em;">mechanical, <a href="#Page_155">155</a> et seq., <a href="#Page_188">188</a>, <a href="#Page_207">207</a>, <a href="#Page_259">259</a> et seq.</span></li>
+
+<li>Phonetic alphabets, their economy, <a href="#Page_192">192</a>.</li>
+
+<li>Photography, by the electric spark, <a href="#Page_318">318</a> et seq.</li>
+
+<li>Photography of projectiles, <a href="#Page_309">309</a>-<a href="#Page_337">337</a>.</li>
+
+<li>Photography, stupendous advances of, <a href="#Page_74">74</a>.</li>
+
+<li>Physical, concepts, fetishism in our, <a href="#Page_187">187</a>;</li>
+<li><span style="margin-left: 1em;">ideas and principles, their nature, <a href="#Page_204">204</a>;</span></li>
+<li><span style="margin-left: 1em;">inquiry, the economical nature of, <a href="#Page_186">186</a>;</span></li>
+<li><span style="margin-left: 1em;">research, object of <a href="#Page_207">207</a>, <a href="#Page_209">209</a>.</span></li>
+
+<li>Physical phenomena, as mechanical phenomena, <a href="#Page_182">182</a>;</li>
+<li><span style="margin-left: 1em;">relations between, <a href="#Page_205">205</a>.</span></li>
+
+<li>Physico-mechanical view of the world, <a href="#Page_155">155</a>, <a href="#Page_187">187</a>, <a href="#Page_188">188</a>, <a href="#Page_207">207</a> et seq.</li>
+
+<li>Physics, compared to a well-kept household, <a href="#Page_197">197</a>;</li>
+<li><span style="margin-left: 1em;">economical experience, <a href="#Page_197">197</a>;</span></li>
+<li><span style="margin-left: 1em;">the principles of, descriptive, <a href="#Page_199">199</a>;</span></li>
+<li><span style="margin-left: 1em;">the methods of, <a href="#Page_209">209</a>;</span></li>
+<li><span style="margin-left: 1em;">its method characterised, <a href="#Page_211">211</a>;</span></li>
+<li><span style="margin-left: 1em;">comparison in, <a href="#Page_239">239</a>;</span></li>
+<li><span style="margin-left: 1em;">the facts of, qualitatively homogeneous, <a href="#Page_255">255</a>;</span></li>
+<li><span style="margin-left: 1em;">how it began, <a href="#Page_37">37</a>;</span></li>
+<li><span style="margin-left: 1em;">helped by psychology, <a href="#Page_104">104</a>;</span></li>
+<li><span style="margin-left: 1em;">study of its own character, <a href="#Page_189">189</a>;</span></li>
+<li><span style="margin-left: 1em;">the goal of, <a href="#Page_207">207</a>, <a href="#Page_209">209</a>.</span></li>
+
+<li>Physiological psychology, its methods, <a href="#Page_211">211</a> et seq.</li>
+
+<li>Physiology, its scope, <a href="#Page_212">212</a>.</li>
+
+<li>Piano, its mirrored counterpart, <a href="#Page_100">100</a> et seq.;</li>
+<li><span style="margin-left: 1em;">used to illustrate the facts of sympathetic vibration, <a href="#Page_25">25</a> et seq.</span></li>
+
+<li>Piano-player, a speaker compared to, <a href="#Page_192">192</a>.</li>
+
+<li>Picture, physical, a, <a href="#Page_110">110</a>.</li>
+
+<li>Pike, learns by experience, <a href="#Page_267">267</a>.</li>
+
+<li>Pillars of Corti, <a href="#Page_19">19</a>.</li>
+
+<li>Places, heavy bodies seek their, <a href="#Page_224">224</a> et seq.</li>
+
+<li>Planetary system, origin of, illustrated, <a href="#Page_5">5</a>.</li>
+
+<li>Plasticity of organic nature, <a href="#Page_216">216</a>.</li>
+
+<li>Plateau, his law of free liquid equilibrium, <a href="#Page_9">9</a>;</li>
+<li><span style="margin-left: 1em;">his method of getting rid of the effects of gravity, <a href="#Page_4">4</a>.</span></li>
+
+<li>Plates of oil, thin, <a href="#Page_6">6</a>.</li>
+
+<li>Plato, <a href="#Page_347">347</a>, <a href="#Page_371">371</a>.</li>
+
+<li>Plautus, <a href="#Page_347">347</a>.</li>
+
+<li>Playfair, <a href="#Page_138">138</a>.</li>
+
+<li><span class="pagenum"><a name="Page_406" id="Page_406">[Pg 406]</a></span>Pleasant effects, cause of, <a href="#Page_94">94</a> et seq.</li>
+
+<li>Pliny, <a href="#Page_349">349</a>.</li>
+
+<li>Poetry and science, <a href="#Page_30">30</a>, <a href="#Page_31">31</a>, <a href="#Page_351">351</a>.</li>
+
+<li>Poinsot, on the foundations of mechanics, <a href="#Page_152">152</a> et seq.</li>
+
+<li>Polarisation, <a href="#Page_91">91</a>;</li>
+<li><span style="margin-left: 1em;">abstractly described by Newton, <a href="#Page_242">242</a>.</span></li>
+
+<li>Politics, Chinese speak with unwillingness of, <a href="#Page_374">374</a>.</li>
+
+<li>Pollak, <a href="#Page_299">299</a>.</li>
+
+<li>Polyp plant, humanity likened to a, <a href="#Page_235">235</a>.</li>
+
+<li>Pompeii, <a href="#Page_234">234</a>;</li>
+<li><span style="margin-left: 1em;">art in, <a href="#Page_80">80</a>.</span></li>
+
+<li>Popper J., <a href="#Page_172">172</a>, <a href="#Page_216">216</a>.</li>
+
+<li>Potential, social, <a href="#Page_15">15</a>;</li>
+<li><span style="margin-left: 1em;">electrical, <a href="#Page_121">121</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">measurement of, <a href="#Page_126">126</a>;</span></li>
+<li><span style="margin-left: 1em;">fall of, <a href="#Page_177">177</a>;</span></li>
+<li><span style="margin-left: 1em;">swarm of notions in the idea of, <a href="#Page_197">197</a>;</span></li>
+<li><span style="margin-left: 1em;">its wide scope, <a href="#Page_250">250</a>.</span></li>
+
+<li>Pottery, invention of, <a href="#Page_263">263</a>.</li>
+
+<li>Prediction, <a href="#Page_221">221</a> et seq.</li>
+
+<li>Prejudice, the function, power, and dangers of, <a href="#Page_232">232</a>-<a href="#Page_233">233</a>.</li>
+
+<li>Preparatory schools, the defects of the German, <a href="#Page_346">346</a>-<a href="#Page_347">347</a>;</li>
+<li><span style="margin-left: 1em;">what they should teach, <a href="#Page_364">364</a> et seq.</span></li>
+
+<li>Pressure of a stone or of a magnet, will compared to, <a href="#Page_14">14</a>;</li>
+<li><span style="margin-left: 1em;">also <a href="#Page_157">157</a>.</span></li>
+
+<li>Primitive acts of knowledge the foundation of scientific thought, <a href="#Page_190">190</a>.</li>
+
+<li>Problem, nature of a, <a href="#Page_223">223</a>.</li>
+
+<li>Problems which are wrongly formulated, <a href="#Page_308">308</a>.</li>
+
+<li>Process, Carnot's, <a href="#Page_161">161</a> et seq.</li>
+
+<li>Projectiles, the effects of the impact of, <a href="#Page_310">310</a>, <a href="#Page_327">327</a>-<a href="#Page_328">328</a>;</li>
+<li><span style="margin-left: 1em;">seen with the naked eye, <a href="#Page_311">311</a>, <a href="#Page_317">317</a>;</span></li>
+<li><span style="margin-left: 1em;">measuring the velocity of, <a href="#Page_332">332</a>;</span></li>
+<li><span style="margin-left: 1em;">photography of, <a href="#Page_309">309</a>-<a href="#Page_337">337</a>.</span></li>
+
+<li>Prony's brake, <a href="#Page_132">132</a>.</li>
+
+<li>Proof, nature of, <a href="#Page_284">284</a>.</li>
+
+<li>Prophesying events, <a href="#Page_220">220</a> et seq.</li>
+
+<li>Psalms, quotation from the, <a href="#Page_89">89</a>.</li>
+
+<li>Pseudoscope, Wheatstone's, <a href="#Page_96">96</a>.</li>
+
+<li>Psychology, preceded by astronomy, <a href="#Page_90">90</a>;</li>
+<li><span style="margin-left: 1em;">how reached, <a href="#Page_91">91</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">helps physical science, <a href="#Page_104">104</a>;</span></li>
+<li><span style="margin-left: 1em;">its method the same as that of physics, <a href="#Page_207">207</a> et seq.</span></li>
+
+<li>Pully arrangement, illustrating principle of least superficial area, <a href="#Page_12">12</a>-<a href="#Page_13">13</a>.</li>
+
+<li>Purkinje, <a href="#Page_284">284</a>, <a href="#Page_285">285</a>, <a href="#Page_291">291</a>, <a href="#Page_299">299</a>.</li>
+
+<li>Purposes, the acts of nature compared to, <a href="#Page_14">14</a>-<a href="#Page_15">15</a>;</li>
+<li><span style="margin-left: 1em;">nature pursues no, <a href="#Page_66">66</a>.</span></li>
+
+<li>Puzzle-lock, a, <a href="#Page_26">26</a>.</li>
+
+<li>Puzzles, <a href="#Page_277">277</a>.</li>
+
+<li>Pyramid of oil, <a href="#Page_6">6</a>.</li>
+
+<li>Pythagoras, his discovery of the laws of harmony, <a href="#Page_32">32</a>, <a href="#Page_259">259</a>.</li>
+
+</ul>
+
+<ul class="IX"><li>Quality of tones, <a href="#Page_36">36</a>.</li>
+
+<li>Quantitative investigation, the goal of, <a href="#Page_180">180</a>.</li>
+
+<li>Quantity of electricity, <a href="#Page_111">111</a>, <a href="#Page_118">118</a>, <a href="#Page_119">119</a>, <a href="#Page_167">167</a>-<a href="#Page_170">170</a>, <a href="#Page_173">173</a>;</li>
+<li><span style="margin-left: 1em;">of heat, <a href="#Page_166">166</a>, <a href="#Page_167">167</a>-<a href="#Page_171">171</a>, <a href="#Page_174">174</a>, <a href="#Page_177">177</a>, <a href="#Page_244">244</a>;</span></li>
+<li><span style="margin-left: 1em;">of motion, <a href="#Page_184">184</a>.</span></li>
+
+<li>Quests made of the inquirer, not by him, <a href="#Page_30">30</a>.</li>
+
+<li>Quételet, <a href="#Page_15">15</a>, footnote.</li>
+
+</ul>
+
+<ul class="IX"><li>Rabelais, <a href="#Page_283">283</a>.</li>
+
+<li>Raindrop, form of, <a href="#Page_3">3</a>.</li>
+
+<li>Rameau, <a href="#Page_34">34</a>.</li>
+
+<li>Reaction and action, principle of, <a href="#Page_191">191</a>.</li>
+
+<li>Reactions, disclosure of the connexion of, <a href="#Page_270">270</a> et seq.</li>
+
+<li>Realgymnasien, <a href="#Page_365">365</a>.</li>
+
+<li>Realschulen, <a href="#Page_365">365</a>, <a href="#Page_373">373</a>.</li>
+
+<li>Reason, stands above the senses, <a href="#Page_105">105</a>.</li>
+
+<li>Reflex action, <a href="#Page_210">210</a>.</li>
+
+<li>Reflexion, produces symmetrical reversion of objects, <a href="#Page_93">93</a> et seq.</li>
+
+<li>Refraction, <a href="#Page_29">29</a>, <a href="#Page_193">193</a>, <a href="#Page_194">194</a>, <a href="#Page_208">208</a>, <a href="#Page_230">230</a>, <a href="#Page_231">231</a>.</li>
+
+<li>Reger, <a href="#Page_328">328</a>.</li>
+
+<li>Reliefs, photographs of, <a href="#Page_68">68</a>.</li>
+
+<li>Repetition, its rôle in æsthetics, <a href="#Page_89">89</a>, footnote, <a href="#Page_91">91</a> et seq., <a href="#Page_97">97</a>, <a href="#Page_98">98</a> et seq., <a href="#Page_390">390</a>.</li>
+
+<li>Reproduction of facts in thought, <a href="#Page_189">189</a>, <a href="#Page_193">193</a>, <a href="#Page_198">198</a>, <a href="#Page_253">253</a>.</li>
+
+<li>Repulsion, electric, <a href="#Page_109">109</a> et seq., <a href="#Page_168">168</a>.</li>
+
+<li>Research, function of experimental <a href="#Page_181">181</a>;</li>
+<li><span style="margin-left: 1em;">the aim of, <a href="#Page_205">205</a>.</span></li>
+
+<li>Resemblances between facts, <a href="#Page_255">255</a>.</li>
+
+<li>Resin, solution of, <a href="#Page_7">7</a>.</li>
+
+<li>Resistance, laws of, for bodies travelling in air and fluids, <a href="#Page_333">333</a> et seq.</li>
+
+<li>Resonance, corporeal, <a href="#Page_392">392</a>.</li>
+
+<li>Response of sonorous bodies, <a href="#Page_25">25</a>.</li>
+
+<li>Retina, the corresponding spots of <a href="#Page_98">98</a>;</li>
+<li><span class="pagenum"><a name="Page_407" id="Page_407">[Pg 407]</a></span><span style="margin-left: 1em;">nerves of compared to fingers of a hand, <a href="#Page_96">96</a> et seq.</span></li>
+
+<li>Reversible processes, <a href="#Page_161">161</a> et seq., <a href="#Page_175">175</a>, <a href="#Page_176">176</a>, <a href="#Page_181">181</a>, <a href="#Page_182">182</a>.</li>
+
+<li>Rhine, the, <a href="#Page_94">94</a>.</li>
+
+<li>Richard the Third, <a href="#Page_77">77</a>.</li>
+
+<li>Riddles, <a href="#Page_277">277</a>.</li>
+
+<li>Riders, <a href="#Page_379">379</a>.</li>
+
+<li>Riegler, <a href="#Page_319">319</a>.</li>
+
+<li>Riess, experiment with the thermo-electrometer, <a href="#Page_133">133</a> et seq., <a href="#Page_169">169</a>.</li>
+
+<li>Rigid connexions, <a href="#Page_142">142</a>.</li>
+
+<li>Rind of a fruit, <a href="#Page_190">190</a>.</li>
+
+<li>Rings of oil, illustrating formation of rings of Saturn, <a href="#Page_5">5</a>.</li>
+
+<li>Ritter, <a href="#Page_291">291</a>, <a href="#Page_299">299</a>.</li>
+
+<li>Rods of Corti, <a href="#Page_19">19</a>.</li>
+
+<li>Rolph, W. H., <a href="#Page_216">216</a>.</li>
+
+<li>Roman Church, Latin introduced with the, <a href="#Page_340">340</a> et seq.</li>
+
+<li>Romans, their provinciality and narrow-mindedness, <a href="#Page_270">270</a>.</li>
+
+<li>Romeo and Juliet, <a href="#Page_87">87</a>.</li>
+
+<li>Römer, Olaf, <a href="#Page_51">51</a> et seq.</li>
+
+<li>Roots, the nature of, in language, <a href="#Page_252">252</a>.</li>
+
+<li>Rosetti, his experiment on the work required to develop electricity, <a href="#Page_131">131</a>.</li>
+
+<li>Rotating bodies, <a href="#Page_285">285</a>.</li>
+
+<li>Rotation, apparatus of, in physics, <a href="#Page_59">59</a> et seq.;</li>
+<li><span style="margin-left: 1em;">sensations of, <a href="#Page_288">288</a> et seq.</span></li>
+
+<li>Rousseau, <a href="#Page_336">336</a>.</li>
+
+<li>Rubber pyramid, illustrating the principle of least superficial area, <a href="#Page_10">10</a>-<a href="#Page_11">11</a>.</li>
+
+<li>Ruysdael, <a href="#Page_279">279</a>.</li>
+</ul>
+
+<ul class="IX">
+<li>Sachs, Hans, <a href="#Page_106">106</a>.</li>
+
+<li>Salcher, Prof. <a href="#Page_319">319</a>.</li>
+
+<li>Salviati, <a href="#Page_144">144</a>.</li>
+
+<li>Saturn, rings of, their formation illustrated, <a href="#Page_5">5</a>.</li>
+
+<li>Saurians, <a href="#Page_257">257</a>.</li>
+
+<li>Sauveur, on acoustics, <a href="#Page_34">34</a>, <a href="#Page_375">375</a> et seq.</li>
+
+<li>Savage, modes of conception and interpretation of a, <a href="#Page_218">218</a> et seq.</li>
+
+<li>Schäfer, K., <a href="#Page_298">298</a>.</li>
+
+<li><i>Schlierenmethode</i>, <a href="#Page_317">317</a>.</li>
+
+<li>Schönbein's discovery of ozone, <a href="#Page_271">271</a>.</li>
+
+<li>School-boy, copy-book of, <a href="#Page_92">92</a>.</li>
+
+<li>Schoolmen, <a href="#Page_214">214</a>.</li>
+
+<li>Schools, State-control of, <a href="#Page_372">372</a> et seq.</li>
+
+<li>Schopenhauer, <a href="#Page_190">190</a>.</li>
+
+<li>Schultze, Max, <a href="#Page_19">19</a>.</li>
+
+<li>Science, a miserly mercantile principle at its basis, <a href="#Page_15">15</a>;</li>
+<li><span style="margin-left: 1em;">compared to a business, <a href="#Page_16">16</a>;</span></li>
+<li><span style="margin-left: 1em;">viewed as a maximum or minimum problem, <a href="#Page_16">16</a>, footnote;</span></li>
+<li><span style="margin-left: 1em;">its process not greatly different from the intellectual activity of ordinary life, <a href="#Page_16">16</a>, footnote;</span></li>
+<li><span style="margin-left: 1em;">economy of its task, <a href="#Page_16">16</a>;</span></li>
+<li><span style="margin-left: 1em;">relation of, to poetry, <a href="#Page_30">30</a>, <a href="#Page_31">31</a>, <a href="#Page_351">351</a>;</span></li>
+<li><span style="margin-left: 1em;">the church of, <a href="#Page_67">67</a>;</span></li>
+<li><span style="margin-left: 1em;">beginnings of, <a href="#Page_189">189</a>, <a href="#Page_191">191</a>;</span></li>
+<li><span style="margin-left: 1em;">belief in the magical power of, <a href="#Page_189">189</a>;</span></li>
+<li><span style="margin-left: 1em;">can dispense with mystery, <a href="#Page_189">189</a>;</span></li>
+<li><span style="margin-left: 1em;">lavish extravagance of, <a href="#Page_189">189</a>;</span></li>
+<li><span style="margin-left: 1em;">economy of the terminology of, <a href="#Page_192">192</a>;</span></li>
+<li><span style="margin-left: 1em;">partly made up of the intelligence of others, <a href="#Page_196">196</a>;</span></li>
+<li><span style="margin-left: 1em;">stripped of mystery, <a href="#Page_197">197</a>;</span></li>
+<li><span style="margin-left: 1em;">its true power, <a href="#Page_197">197</a>;</span></li>
+<li><span style="margin-left: 1em;">the economical schematism of, <a href="#Page_206">206</a>;</span></li>
+<li><span style="margin-left: 1em;">the object of, <a href="#Page_206">206</a>;</span></li>
+<li><span style="margin-left: 1em;">the tools of, <a href="#Page_207">207</a>;</span></li>
+<li><span style="margin-left: 1em;">does not create facts, <a href="#Page_211">211</a>;</span></li>
+<li><span style="margin-left: 1em;">of the future, <a href="#Page_213">213</a>;</span></li>
+<li><span style="margin-left: 1em;">revolution in, dating from Galileo, <a href="#Page_214">214</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">the natural foe of the marvellous, <a href="#Page_224">224</a>;</span></li>
+<li><span style="margin-left: 1em;">characterised, <a href="#Page_227">227</a>;</span></li>
+<li><span style="margin-left: 1em;">growth of, <a href="#Page_237">237</a>;</span></li>
+<li><span style="margin-left: 1em;">dramatic element in, <a href="#Page_243">243</a>;</span></li>
+<li><span style="margin-left: 1em;">described, <a href="#Page_251">251</a>;</span></li>
+<li><span style="margin-left: 1em;">its function, <a href="#Page_253">253</a>;</span></li>
+<li><span style="margin-left: 1em;">classification in, <a href="#Page_255">255</a>, <a href="#Page_259">259</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">the way of discovery in, <a href="#Page_316">316</a>.</span></li>
+<li><span style="margin-left: 1em;">See also <i>Physics</i>.</span></li>
+
+<li>Sciences, partition of the, <a href="#Page_86">86</a>;</li>
+<li><span style="margin-left: 1em;">the barriers and relations between the <a href="#Page_257">257</a>-<a href="#Page_258">258</a>;</span></li>
+<li><span style="margin-left: 1em;">on instruction in the, <a href="#Page_338">338</a>-<a href="#Page_374">374</a>.</span></li>
+
+<li>Scientific, criticism, Socrates the father of, <a href="#Page_1">1</a>, <a href="#Page_16">16</a>;</li>
+<li><span style="margin-left: 1em;">discoveries, their fate, <a href="#Page_138">138</a>;</span></li>
+<li><span style="margin-left: 1em;">knowledge, involves description, <a href="#Page_193">193</a>;</span></li>
+<li><span style="margin-left: 1em;">thought, transformation and adaptation in, <a href="#Page_214">214</a>-<a href="#Page_235">235</a>;</span></li>
+<li><span style="margin-left: 1em;">thought, advanced by new experiences, <a href="#Page_223">223</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">thought, the difficulty of, <a href="#Page_366">366</a>;</span></li>
+<li><span style="margin-left: 1em;">terms, <a href="#Page_342">342</a>-<a href="#Page_343">343</a>;</span></li>
+<li><span style="margin-left: 1em;">founded on primitive acts of knowledge, <a href="#Page_190">190</a>.</span></li>
+
+<li>Scientists, stories about their ignorance, <a href="#Page_342">342</a>.</li>
+
+<li>Screw, the, <a href="#Page_62">62</a>.</li>
+
+<li>Sea-sickness, <a href="#Page_284">284</a>.</li>
+
+<li>Secret computation, Leibnitz's, <a href="#Page_33">33</a>.</li>
+
+<li>Seek their places, bodies, <a href="#Page_226">226</a>.</li>
+
+<li>Self-induction, coefficient of, <a href="#Page_250">250</a>, <a href="#Page_252">252</a>.</li>
+
+<li>Self-observation, <a href="#Page_211">211</a>.</li>
+
+<li><span class="pagenum"><a name="Page_408" id="Page_408">[Pg 408]</a></span>Self-preservation, our first knowledge derived from the economy of, <a href="#Page_197">197</a>;</li>
+<li><span style="margin-left: 1em;">struggle for, among ideas, <a href="#Page_228">228</a>.</span></li>
+
+<li>Semi-circular canals, <a href="#Page_290">290</a> et seq.</li>
+
+<li>Sensation of rounding a railway curve, <a href="#Page_286">286</a>.</li>
+
+<li>Sensations, analysed, <a href="#Page_251">251</a>;</li>
+<li><span style="margin-left: 1em;">when similar, produce agreeable effects, <a href="#Page_96">96</a>;</span></li>
+<li><span style="margin-left: 1em;">their character, <a href="#Page_200">200</a>;</span></li>
+<li><span style="margin-left: 1em;">defined, <a href="#Page_209">209</a>;</span></li>
+<li><span style="margin-left: 1em;">of orientation, <a href="#Page_282">282</a> et seq.</span></li>
+
+<li>Sense-elements, <a href="#Page_179">179</a>.</li>
+
+<li>Senses, theory of, <a href="#Page_104">104</a>;</li>
+<li><span style="margin-left: 1em;">the source of our knowledge of facts, <a href="#Page_237">237</a>.</span></li>
+
+<li>Seventh, the troublesome, <a href="#Page_46">46</a>.</li>
+
+<li>Shadow method, <a href="#Page_313">313</a> et seq., <a href="#Page_317">317</a> footnote.</li>
+
+<li>Shadows, rôle of, in vision, <a href="#Page_81">81</a>.</li>
+
+<li>Shakespeare, <a href="#Page_278">278</a>.</li>
+
+<li>Sharps, reversed into flats, <a href="#Page_101">101</a>.</li>
+
+<li>Shell, spherical, law of attraction for a, <a href="#Page_124">124</a>, footnote.</li>
+
+<li>Shoemaker, inquirer compared to, <a href="#Page_105">105</a>-<a href="#Page_106">106</a>.</li>
+
+<li>Shooting, <a href="#Page_309">309</a>.</li>
+
+<li>Shots, double report of, <a href="#Page_229">229</a> et seq.</li>
+
+<li>Similarity, <a href="#Page_249">249</a>.</li>
+
+<li>Simony, <a href="#Page_280">280</a>.</li>
+
+<li>Simplicity, a varying element in description, <a href="#Page_254">254</a>.</li>
+
+<li>Sines, law of the, <a href="#Page_193">193</a>.</li>
+
+<li>Sinking of heavy bodies, <a href="#Page_222">222</a>.</li>
+
+<li>Sixth sense, <a href="#Page_297">297</a>.</li>
+
+<li>Smith, R., on acoustics, <a href="#Page_34">34</a>, <a href="#Page_381">381</a>, <a href="#Page_383">383</a>.</li>
+
+<li>Soap-films, Van der Mensbrugghe's experiment with, <a href="#Page_11">11</a>-<a href="#Page_12">12</a>.</li>
+
+<li>Soapsuds, films and figures of, <a href="#Page_7">7</a>.</li>
+
+<li>Social potential, <a href="#Page_15">15</a>.</li>
+
+<li>Socrates, the father of scientific criticism, <a href="#Page_1">1</a>, <a href="#Page_16">16</a>.</li>
+
+<li>Sodium, <a href="#Page_202">202</a>.</li>
+
+<li>Sodium-light, vibrations of, as a measure of time, <a href="#Page_205">205</a>.</li>
+
+<li>Solidity, conception of, by the eye, <a href="#Page_71">71</a> et seq.;</li>
+<li><span style="margin-left: 1em;">spatial, photographs of, <a href="#Page_73">73</a>.</span></li>
+
+<li>Solids, and liquids, their difference merely one of degree, <a href="#Page_2">2</a>.</li>
+
+<li>Sonorous bodies, <a href="#Page_24">24</a> et seq.</li>
+
+<li>Soret, J. P., <a href="#Page_89">89</a>.</li>
+
+<li>Sounds, symmetry of, <a href="#Page_99">99</a> et seq.;</li>
+<li><span style="margin-left: 1em;">generally, <a href="#Page_22">22</a>-<a href="#Page_47">47</a>, <a href="#Page_212">212</a>.</span></li>
+
+<li>Sound-waves rendered visible, <a href="#Page_315">315</a> et seq.</li>
+
+<li>Sources of the principle of energy, <a href="#Page_179">179</a> et seq.</li>
+
+<li>Space, <a href="#Page_205">205</a>;</li>
+<li><span style="margin-left: 1em;">sensation of, <a href="#Page_210">210</a>.</span></li>
+
+<li>Spark, electric, <a href="#Page_117">117</a>, <a href="#Page_127">127</a>, <a href="#Page_132">132</a>, <a href="#Page_133">133</a>, <a href="#Page_190">190</a>.</li>
+
+<li>Spatial vision, <a href="#Page_386">386</a>.</li>
+
+<li>Species, stability of, a theory, <a href="#Page_216">216</a>.</li>
+
+<li>Specific energies, <a href="#Page_291">291</a>.</li>
+
+<li>Specific heat, <a href="#Page_166">166</a>, <a href="#Page_244">244</a>.</li>
+
+<li>Specific inductive capacity, <a href="#Page_117">117</a>.</li>
+
+<li>Spectral analysis of sound, <a href="#Page_27">27</a>.</li>
+
+<li>Spectrum, mental associations of the, <a href="#Page_190">190</a>.</li>
+
+<li>Speech, the instinct of, cultivated by languages, <a href="#Page_354">354</a>.</li>
+
+<li>Spencer, <a href="#Page_218">218</a>, <a href="#Page_222">222</a>.</li>
+
+<li>Sphere, a soft rotating, <a href="#Page_2">2</a>;</li>
+<li><span style="margin-left: 1em;">the figure of least surface, <a href="#Page_12">12</a>;</span></li>
+<li><span style="margin-left: 1em;">electrical capacity of, <a href="#Page_123">123</a> et seq.</span></li>
+
+<li>Spherical shell, law of attraction for <a href="#Page_124">124</a>, footnote.</li>
+
+<li>Spiders, the eyes of, <a href="#Page_67">67</a>.</li>
+
+<li>Spirits, as explanation of the world <a href="#Page_186">186</a>, <a href="#Page_243">243</a>.</li>
+
+<li>Spiritualism, modern, <a href="#Page_187">187</a>.</li>
+
+<li>Spooks, metaphysical, <a href="#Page_222">222</a>.</li>
+
+<li>Squinting, <a href="#Page_72">72</a>.</li>
+
+<li>Stability of our environment, <a href="#Page_206">206</a>.</li>
+
+<li>Stallo, <a href="#Page_336">336</a>.</li>
+
+<li>Stars, the fixed, <a href="#Page_90">90</a>.</li>
+
+<li>State, benefits and evils of its control of the schools, <a href="#Page_372">372</a> et seq.;</li>
+<li><span style="margin-left: 1em;">the Church and, <a href="#Page_88">88</a>.</span></li>
+
+<li>Statical electricity, <a href="#Page_134">134</a>.</li>
+
+<li>Stationary currents, <a href="#Page_249">249</a>.</li>
+
+<li>Statoliths, <a href="#Page_303">303</a>.</li>
+
+<li>Steam-engine, <a href="#Page_160">160</a>, <a href="#Page_265">265</a>.</li>
+
+<li>Steeple-jacks, <a href="#Page_75">75</a>.</li>
+
+<li>Stereoscope, Wheatstone and Brewster's, <a href="#Page_73">73</a>.</li>
+
+<li>Stevinus, on the inclined plane, <a href="#Page_140">140</a>;</li>
+<li><span style="margin-left: 1em;">on hydrostatics, <a href="#Page_141">141</a>;</span></li>
+<li><span style="margin-left: 1em;">on the equilibrium of systems, <a href="#Page_142">142</a>;</span></li>
+<li><span style="margin-left: 1em;">discovers the principle of virtual velocities, <a href="#Page_150">150</a>;</span></li>
+<li><span style="margin-left: 1em;">characterisation of his thought, <a href="#Page_142">142</a>;</span></li>
+<li><span style="margin-left: 1em;">also <a href="#Page_182">182</a>, <a href="#Page_187">187</a>, <a href="#Page_191">191</a>.</span></li>
+
+<li>Stone Age, <a href="#Page_46">46</a>, <a href="#Page_321">321</a>.</li>
+
+<li>Störensen, <a href="#Page_306">306</a>.</li>
+
+<li>Stove, primitive, <a href="#Page_263">263</a>.</li>
+
+<li>Straight line, a, its symmetry, <a href="#Page_98">98</a>.</li>
+
+<li>Straight, meaning of the word, <a href="#Page_240">240</a>.</li>
+
+<li><span class="pagenum"><a name="Page_409" id="Page_409">[Pg 409]</a></span>Street, vista into a, <a href="#Page_75">75</a>.</li>
+
+<li>Striae, in glass, <a href="#Page_313">313</a>.</li>
+
+<li>Striate method, for detecting optical imperfections, <a href="#Page_317">317</a>.</li>
+
+<li>Striking distance, <a href="#Page_115">115</a>, <a href="#Page_127">127</a>.</li>
+
+<li>Strings, vibrations of, <a href="#Page_249">249</a>.</li>
+
+<li>Struggle for existence among ideas, <a href="#Page_217">217</a>.</li>
+
+<li>Substance, heat conceived as a, <a href="#Page_177">177</a>, <a href="#Page_243">243</a> et seq.;</li>
+<li><span style="margin-left: 1em;">electricity as a, <a href="#Page_170">170</a>;</span></li>
+<li><span style="margin-left: 1em;">the source of our notion of, <a href="#Page_199">199</a>;</span></li>
+<li><span style="margin-left: 1em;">rôle of the notion of, <a href="#Page_203">203</a>, <a href="#Page_244">244</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">energy conceived as a, <a href="#Page_164">164</a>, <a href="#Page_185">185</a>, <a href="#Page_244">244</a> et seq.</span></li>
+
+<li>Substitution-value of heat, <a href="#Page_178">178</a>, footnote.</li>
+
+<li>Suetonius, <a href="#Page_348">348</a>.</li>
+
+<li>Sulphur, specific inductive capacity of, <a href="#Page_117">117</a>.</li>
+
+<li>Sun, human beings could not exist on, <a href="#Page_3">3</a>.</li>
+
+<li>Swift, <a href="#Page_84">84</a>, <a href="#Page_280">280</a>.</li>
+
+<li>Swimmer, Ampère's, <a href="#Page_207">207</a>.</li>
+
+<li>Symmetry, definition of, <a href="#Page_92">92</a>;</li>
+<li><span style="margin-left: 1em;">figures of, <a href="#Page_92">92</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">plane of, <a href="#Page_94">94</a>;</span></li>
+<li><span style="margin-left: 1em;">vertical and horizontal, <a href="#Page_94">94</a>;</span></li>
+<li><span style="margin-left: 1em;">in music, <a href="#Page_99">99</a> et seq.</span></li>
+
+<li>Sympathetic vibration, <a href="#Page_22">22</a> et seq., <a href="#Page_379">379</a>.</li>
+
+</ul>
+
+<ul class="IX"><li>Tailor, nature like a covetous, <a href="#Page_9">9</a>-<a href="#Page_10">10</a>.</li>
+
+<li>Tangent, the word, <a href="#Page_263">263</a>.</li>
+
+<li>Taste, doubtful cultivation of, by the classics, <a href="#Page_352">352</a>-<a href="#Page_353">353</a>;</li>
+<li><span style="margin-left: 1em;">of the ancients, <a href="#Page_353">353</a>.</span></li>
+
+<li>Taylor, on the vibration of strings, <a href="#Page_249">249</a>.</li>
+
+<li>Teaching, its nature, <a href="#Page_366">366</a> et seq.</li>
+
+<li>Telegraph, the word, <a href="#Page_263">263</a>.</li>
+
+<li>Telescope, <a href="#Page_262">262</a>.</li>
+
+<li>Telestereoscope, the, <a href="#Page_84">84</a>.</li>
+
+<li>Temperament, even, in tuning, <a href="#Page_47">47</a>.</li>
+
+<li>Temperature, absolute, <a href="#Page_162">162</a>;</li>
+<li><span style="margin-left: 1em;">differences of, <a href="#Page_205">205</a>;</span></li>
+<li><span style="margin-left: 1em;">differences of, viewed as level surfaces, <a href="#Page_161">161</a>;</span></li>
+<li><span style="margin-left: 1em;">heights of, <a href="#Page_174">174</a>;</span></li>
+<li><span style="margin-left: 1em;">scale of, derived from tensions of gases, <a href="#Page_174">174</a>.</span></li>
+
+<li>Terence, <a href="#Page_347">347</a>.</li>
+
+<li>Terms, scientific, <a href="#Page_342">342</a>-<a href="#Page_343">343</a>.</li>
+
+<li>Thales, <a href="#Page_259">259</a>.</li>
+
+<li>Theories, their scope, function, and power, <a href="#Page_241">241</a>-<a href="#Page_242">242</a>;</li>
+<li><span style="margin-left: 1em;">must be replaced by direct description, <a href="#Page_248">248</a>.</span></li>
+
+<li>Thermal, energy, <a href="#Page_174">174</a>, <a href="#Page_177">177</a>;</li>
+<li><span style="margin-left: 1em;">capacity, <a href="#Page_123">123</a>, footnote.</span></li>
+
+<li>Thermodynamics, <a href="#Page_160">160</a> et seq.</li>
+
+<li>Thermoelectrometer, Riess's, <a href="#Page_133">133</a>, <a href="#Page_169">169</a>.</li>
+
+<li>Thing-in-itself, the, <a href="#Page_200">200</a>.</li>
+
+<li>Things, mental symbols for groups of sensations, <a href="#Page_200">200</a>-<a href="#Page_201">201</a>.</li>
+
+<li>Thomson, James, on the lowering of the freezing-point of water by pressure, <a href="#Page_162">162</a>.</li>
+
+<li>Thomson, W., his absolute electrometer, <a href="#Page_127">127</a>, footnote;</li>
+<li><span style="margin-left: 1em;">on thermodynamics, <a href="#Page_162">162</a>;</span></li>
+<li><span style="margin-left: 1em;">on the conservation of energy, <a href="#Page_165">165</a>;</span></li>
+<li><span style="margin-left: 1em;">on the mechanical measures of temperature, <a href="#Page_174">174</a>, footnote;</span></li>
+<li><span style="margin-left: 1em;">on waste of mechanical energy, <a href="#Page_175">175</a>;</span></li>
+<li><span style="margin-left: 1em;">also <a href="#Page_108">108</a>, <a href="#Page_173">173</a>, footnote.</span></li>
+
+<li>Thought, habitudes of, <a href="#Page_199">199</a>, <a href="#Page_224">224</a>, <a href="#Page_227">227</a>, <a href="#Page_232">232</a>;</li>
+<li><span style="margin-left: 1em;">relationship between language and, <a href="#Page_329">329</a>;</span></li>
+<li><span style="margin-left: 1em;">incongruence between experience and, <a href="#Page_206">206</a>;</span></li>
+<li><span style="margin-left: 1em;">luxuriance of a fully developed, <a href="#Page_58">58</a>;</span></li>
+<li><span style="margin-left: 1em;">transformation in scientific, <a href="#Page_214">214</a>-<a href="#Page_235">235</a>.</span></li>
+
+<li>Thoughts, their development and the struggle for existence among them, <a href="#Page_63">63</a>;</li>
+<li><span style="margin-left: 1em;">importance of erroneous, <a href="#Page_65">65</a>;</span></li>
+<li><span style="margin-left: 1em;">as reproductions of facts, <a href="#Page_107">107</a>.</span></li>
+
+<li>Thread, the individual a, on which pearls are strung, <a href="#Page_234">234</a>-<a href="#Page_235">235</a>.</li>
+
+<li>Tides, <a href="#Page_283">283</a>.</li>
+
+<li>Timbre, <a href="#Page_37">37</a>, <a href="#Page_38">38</a>, <a href="#Page_39">39</a>.</li>
+
+<li>Time, <a href="#Page_178">178</a>, <a href="#Page_204">204</a>, <a href="#Page_205">205</a>, footnote.</li>
+
+<li>Toepler and Foucault, method of, for detecting optical faults, <a href="#Page_313">313</a> et seq., <a href="#Page_320">320</a>.</li>
+
+<li>Tone-figures, <a href="#Page_91">91</a>.</li>
+
+<li>Tones, <a href="#Page_22">22</a>-<a href="#Page_47">47</a>, <a href="#Page_99">99</a> et seq., <a href="#Page_212">212</a>.</li>
+
+<li>Torsion, moment of, <a href="#Page_132">132</a>.</li>
+
+<li>Torsion-balance, Coulomb's, <a href="#Page_109">109</a>, <a href="#Page_168">168</a>.</li>
+
+<li>Torricelli, on virtual velocities, <a href="#Page_150">150</a>;</li>
+<li><span style="margin-left: 1em;">his law of liquid efflux, <a href="#Page_150">150</a>;</span></li>
+<li><span style="margin-left: 1em;">on the atmosphere, <a href="#Page_273">273</a>.</span></li>
+
+<li>Tourist, journey of, work of the inquirer compared to, <a href="#Page_17">17</a>, <a href="#Page_29">29</a>, <a href="#Page_30">30</a>.</li>
+
+<li>Transatlantic cable, <a href="#Page_108">108</a>.</li>
+
+<li>Transformation and adaptation in scientific thought, <a href="#Page_214">214</a>-<a href="#Page_235">235</a>.</li>
+
+<li>Transformation of ideas, <a href="#Page_63">63</a>.</li>
+
+<li>Transformative law of the energies, <a href="#Page_172">172</a>.</li>
+
+<li><span class="pagenum"><a name="Page_410" id="Page_410">[Pg 410]</a></span>Translation, difficulties of, <a href="#Page_354">354</a>.</li>
+
+<li>Tree, conceptual life compared to a, <a href="#Page_231">231</a>.</li>
+
+<li>Triangle, mutual dependence of the sides and angles of a, <a href="#Page_179">179</a>.</li>
+
+<li>Triple accord, <a href="#Page_46">46</a>.</li>
+
+<li>Truth, wooed by the inquirer, <a href="#Page_45">45</a>;</li>
+<li><span style="margin-left: 1em;">difficulty of its acquisition, <a href="#Page_46">46</a>.</span></li>
+
+<li>Tumblers, resounding, <a href="#Page_23">23</a>.</li>
+
+<li>Tuning-forks, explanation of their motion, <a href="#Page_22">22</a> et seq.</li>
+
+<li>Tylor, <a href="#Page_186">186</a>.</li>
+
+<li>Tympanum, <a href="#Page_18">18</a>.</li>
+
+<li>Type, natural laws likened to, <a href="#Page_193">193</a>;</li>
+<li><span style="margin-left: 1em;">words compared to, <a href="#Page_191">191</a>.</span></li>
+
+</ul>
+
+<ul class="IX"><li>Ulysses, <a href="#Page_347">347</a>.</li>
+
+<li>Understanding, what it means, <a href="#Page_211">211</a>.</li>
+
+<li>Uniforms, do not fit heads, <a href="#Page_369">369</a>.</li>
+
+<li>Unique determination, <a href="#Page_181">181</a>-<a href="#Page_182">182</a>.</li>
+
+<li>Unison, <a href="#Page_43">43</a>.</li>
+
+<li>Unit, electrostatic, <a href="#Page_111">111</a>.</li>
+<li><span style="margin-left: 1em;">See <i>Force</i> and <i>Work</i>.</span></li>
+
+<li>United States, <a href="#Page_336">336</a>.</li>
+
+<li>Universal Real Character, a, <a href="#Page_192">192</a>.</li>
+
+<li>Utility of physical science, <a href="#Page_351">351</a>.</li>
+
+</ul>
+
+<ul class="IX"><li>Variation, the method of, in science, <a href="#Page_230">230</a>;</li>
+<li><span style="margin-left: 1em;">in biology, <a href="#Page_216">216</a>.</span></li>
+
+<li>Velocity, of light, <a href="#Page_48">48</a> et seq.;</li>
+<li><span style="margin-left: 1em;">of the descent of bodies, <a href="#Page_143">143</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">meaning of, <a href="#Page_204">204</a>;</span></li>
+<li><span style="margin-left: 1em;">virtual, <a href="#Page_149">149</a>-<a href="#Page_155">155</a>.</span></li>
+
+<li><i>Verstandesbegriffe</i>, <a href="#Page_199">199</a>.</li>
+
+<li>Vertical, perception of the, <a href="#Page_272">272</a>, <a href="#Page_286">286</a> et seq.;</li>
+<li><span style="margin-left: 1em;">symmetry, <a href="#Page_389">389</a>.</span></li>
+
+<li>Vertigo, <a href="#Page_285">285</a>, <a href="#Page_290">290</a>.</li>
+
+<li>Vestibule of the ear, <a href="#Page_300">300</a>.</li>
+
+<li>Vibration, <a href="#Page_22">22</a> et seq.</li>
+
+<li>Vibration-figures, <a href="#Page_91">91</a>.</li>
+
+<li>Vinci, Leonardo da, <a href="#Page_278">278</a>, <a href="#Page_283">283</a>.</li>
+
+<li>Violent motions, <a href="#Page_225">225</a>.</li>
+
+<li>Virtual velocities, <a href="#Page_149">149</a>-<a href="#Page_155">155</a>.</li>
+
+<li>Visibility, general conditions of, <a href="#Page_312">312</a>.</li>
+
+<li>Vision, symmetry of our apparatus of, <a href="#Page_96">96</a>.</li>
+<li><span style="margin-left: 1em;">See <i>Eye</i>.</span></li>
+
+<li>Visual nerves, <a href="#Page_96">96</a>.</li>
+
+<li>Visualisation, mental, <a href="#Page_250">250</a>.</li>
+
+<li>Volt, the word, <a href="#Page_343">343</a>.</li>
+
+<li>Volta, <a href="#Page_127">127</a>, footnote, <a href="#Page_134">134</a>.</li>
+
+<li>Voltaire, <a href="#Page_260">260</a>.</li>
+
+<li>Voltaire's ingènu, <a href="#Page_219">219</a>.</li>
+
+<li>Vowels, composed of simple musical notes, <a href="#Page_26">26</a>.</li>
+
+</ul>
+
+<ul class="IX"><li>Wagner, Richard, <a href="#Page_279">279</a>.</li>
+
+<li>Wald, F., <a href="#Page_178">178</a>, footnote.</li>
+
+<li>Wallace, <a href="#Page_216">216</a>.</li>
+
+<li>War, and peace, reflexions upon, <a href="#Page_309">309</a>, <a href="#Page_335">335</a> et seq.</li>
+
+<li>Waste of mechanical energy, W. Thomson on, <a href="#Page_175">175</a>.</li>
+
+<li>Watches, experiment with, <a href="#Page_41">41</a>;</li>
+<li><span style="margin-left: 1em;">in a mirror, <a href="#Page_93">93</a>.</span></li>
+
+<li>Water, jet of, resolved into drops, <a href="#Page_60">60</a>;</li>
+<li><span style="margin-left: 1em;">free, solid figures of, <a href="#Page_8">8</a>;</span></li>
+<li><span style="margin-left: 1em;">objects reflected in, <a href="#Page_94">94</a>, <a href="#Page_191">191</a>;</span></li>
+<li><span style="margin-left: 1em;">possible modes of measurement of, <a href="#Page_170">170</a>.</span></li>
+
+<li>Watt, <a href="#Page_266">266</a>.</li>
+
+<li>Wealth, the foundation of, <a href="#Page_198">198</a>.</li>
+
+<li>Weapons, modern, <a href="#Page_335">335</a>.</li>
+
+<li>Weber, <a href="#Page_108">108</a>, <a href="#Page_306">306</a>.</li>
+
+<li>Weight of bodies, varies with their distance from the centre of the earth, <a href="#Page_112">112</a>.</li>
+
+<li>Weismann, <a href="#Page_216">216</a>.</li>
+
+<li>Wheatstone, his stereoscope, <a href="#Page_73">73</a>;</li>
+<li><span style="margin-left: 1em;">his pseudoscope, <a href="#Page_96">96</a>;</span></li>
+<li><span style="margin-left: 1em;">also <a href="#Page_59">59</a>.</span></li>
+
+<li>Wheel, history and importance of, <a href="#Page_61">61</a> et seq.</li>
+
+<li>Whewell, on the formation of science, <a href="#Page_231">231</a>.</li>
+
+<li>Whole, the, <a href="#Page_204">204</a>, footnote.</li>
+
+<li>Why, the question, <a href="#Page_199">199</a>, <a href="#Page_223">223</a>.</li>
+
+<li>Will, Schopenhauer on the, <a href="#Page_190">190</a>;</li>
+<li><span style="margin-left: 1em;">man's most familiar source of power, <a href="#Page_243">243</a>;</span></li>
+<li><span style="margin-left: 1em;">used to explain the world, <a href="#Page_186">186</a>;</span></li>
+<li><span style="margin-left: 1em;">forces compared to, <a href="#Page_254">254</a>;</span></li>
+<li><span style="margin-left: 1em;">compared to pressure, <a href="#Page_14">14</a>.</span></li>
+
+<li>Windmill, a rotating, <a href="#Page_53">53</a>.</li>
+
+<li>Wire frames and nets, for constructing liquid figures of equilibrium, <a href="#Page_4">4</a> et seq.</li>
+
+<li>Witchcraft, <a href="#Page_187">187</a>.</li>
+
+<li>Wollaston, <a href="#Page_284">284</a>, <a href="#Page_285">285</a>.</li>
+
+<li>Wonderful, science the natural foe of the, <a href="#Page_224">224</a>.</li>
+
+<li>Woods, the relative distance of trees in, <a href="#Page_68">68</a>.</li>
+
+<li>Wooer, inquirer compared to a, <a href="#Page_45">45</a>.</li>
+
+<li>Words and sounds, <a href="#Page_343">343</a>.</li>
+
+<li>Words, compared to type, <a href="#Page_191">191</a>.</li>
+
+<li><span class="pagenum"><a name="Page_411" id="Page_411">[Pg 411]</a></span>Work, of liquid forces of attraction, <a href="#Page_14">14</a>;</li>
+<li><span style="margin-left: 1em;">in electricity, <a href="#Page_173">173</a>;</span></li>
+<li><span style="margin-left: 1em;">measure of, <a href="#Page_119">119</a> et seq., <a href="#Page_130">130</a>, <a href="#Page_223">223</a>;</span></li>
+<li><span style="margin-left: 1em;">relation of, with heat, <a href="#Page_162">162</a>, <a href="#Page_245">245</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">amount required to develop electricity, <a href="#Page_131">131</a> et seq.;</span></li>
+<li><span style="margin-left: 1em;">produces various physical changes, <a href="#Page_139">139</a>;</span></li>
+<li><span style="margin-left: 1em;">substantial conception of, <a href="#Page_183">183</a>-<a href="#Page_184">184</a>.</span></li>
+<li><span style="margin-left: 1em;">See <i>Energy</i>.</span></li>
+
+<li>World, the, what it consists of, <a href="#Page_208">208</a>.</li>
+
+<li>World-particles, <a href="#Page_203">203</a>.</li>
+
+<li>Wronsky, <a href="#Page_172">172</a>.</li>
+
+<li>Wundt, on causality and the axioms of physics, <a href="#Page_157">157</a>-<a href="#Page_159">159</a>; <a href="#Page_359">359</a> footnote.</li>
+
+</ul>
+
+<ul class="IX"><li>Xenophon, <a href="#Page_49">49</a>, footnote.</li>
+
+</ul>
+
+<ul class="IX"><li>Young, Thomas, on energy, <a href="#Page_173">173</a>.</li>
+
+</ul>
+
+<ul class="IX"><li>Zelter, <a href="#Page_35">35</a>.</li>
+
+<li>Zeuner, <a href="#Page_171">171</a>.</li>
+
+<li>Zoölogy, comparison in, <a href="#Page_239">239</a>.</li></ul>
+
+<p><span class="pagenum"><a name="Page_412" id="Page_412">[Pg 412]</a><br /><a name="Page_413" id="Page_413">[Pg 413]</a></span></p>
+
+<hr class="chap" />
+
+
+<h2>THE SCIENCE OF MECHANICS.</h2>
+
+<p class="center">A CRITICAL AND HISTORICAL EXPOSITION OF ITS
+PRINCIPLES.</p>
+
+<p class="center bold">By DR. ERNST MACH.</p>
+
+<p class="center small">PROFESSOR OF THE HISTORY AND THEORY OF INDUCTIVE SCIENCE IN THE
+UNIVERSITY OF VIENNA.</p>
+
+<p class="center">Translated from the Second German Edition<br />
+<span class="bold">By THOMAS J. McCORMACK.</span></p>
+
+<hr/>
+<p class="center">250 Cuts. 534 Pages. Half Morocco, Gilt Top, Marginal Analyses.<br/>
+Exhaustive Index. Price $2.50.</p>
+
+
+<hr/>
+
+<h3><a name="TABLE_OF_CONTENTS2" id="TABLE_OF_CONTENTS2">TABLE OF CONTENTS.</a></h3>
+
+
+<p><span class="smcap">Statics.</span></p>
+
+<ul class="IX"><li>The Lever.</li>
+
+<li>The Inclined Plane.</li>
+
+<li>The Composition of Forces.</li>
+
+<li>Virtual Velocities.</li>
+
+<li>Statics in Their Application to Fluids.</li>
+
+<li>Statics in Their Application to Gases.</li></ul>
+
+
+
+<p><span class="smcap">Dynamics.</span></p>
+
+<ul class="IX"><li>Galileo's Achievements.</li>
+
+<li>Achievements of Huygens.</li>
+
+<li>Achievements of Newton.</li>
+
+<li>Principle of Reaction.</li>
+
+<li>Criticism of the Principle of Reaction
+and of the Concept of Mass.</li>
+
+<li>Newton's Views of Time, Space, and
+Motion.</li>
+
+<li>Critique of the Newtonian Enunciations.</li>
+
+<li>Retrospect of the Development of
+Dynamics.</li></ul>
+
+
+
+<p><span class="smcap">The Extension of the Principles of Mechanics.</span></p>
+
+<ul class="IX"><li>Scope of the Newtonian Principles.</li>
+
+<li>Formulæ and Units of Mechanics.</li>
+
+<li>Conservation of Momentum, Conservation
+of the Centre of Gravity,
+and Conservation of Areas.</li>
+
+<li>Laws of Impact.</li>
+
+<li>D'Alembert's Principle.</li>
+
+<li>Principle of <i>Vis Viva</i>.</li>
+
+<li>Principle of Least Constraint.</li>
+
+<li>Principle of Least Action.</li>
+
+<li>Hamilton's Principle.</li>
+
+<li>Hydrostatic and Hydrodynamic
+Questions.</li></ul>
+
+
+
+<p><span class="smcap">Formal Development of Mechanics.</span></p>
+
+<ul class="IX"><li>The Isoperimetrical Problems.</li>
+
+<li>Theological, Animistic, and Mystical
+Points of View in Mechanics.</li>
+
+<li>Analytical Mechanics.</li>
+
+<li>The Economy of Science.</li></ul>
+
+
+<p><span class="smcap">The Relation of Mechanics to Other Departments of Knowledge.</span></p>
+
+<ul class="IX">
+<li>Relations of Mechanics to Physics.</li>
+
+<li>Relations of Mechanics to Physiology.</li></ul>
+
+
+<p><span class="pagenum"><a name="Page_414" id="Page_414">[Pg 414]</a></span></p>
+
+
+
+
+<h2><a name="PRESS_NOTICES" id="PRESS_NOTICES">PRESS NOTICES.</a></h2>
+
+
+<p>"The appearance of a translation into English of this remarkable book
+should serve to revivify in this country [England] the somewhat stagnating
+treatment of its subject, and should call up the thoughts which puzzle us when
+we think of them, and that is not sufficiently often.... Professor Mach is a
+striking instance of the combination of great mathematical knowledge with
+experimental skill, as exemplified not only by the elegant illustrations of mechanical
+principles which abound in this treatise, but also from his brilliant
+experiments on the photography of bullets.... A careful study of Professor
+Mach's work, and a treatment with more experimental illustration, on the
+lines laid down in the interesting diagrams of his <i>Science of Mechanics</i>, will
+do much to revivify theoretical mechanical science, as developed from the
+elements by rigorous logical treatment."&mdash;Prof. A. G. Greenhill, in <i>Nature</i>,
+London.</p>
+
+<p>"Those who are curious to learn how the principles of mechanics have
+been evolved, from what source they take their origin, and how far they can
+be deemed of positive and permanent value, will find Dr. Mach's able treatise
+entrancingly interesting.... The book is a remarkable one in many respects,
+while the mixture of history with the latest scientific principles and
+absolute mathematical deductions makes it exceedingly attractive."&mdash;<i>Mechanical
+World</i>, Manchester and London, England.</p>
+
+<p>"Mach's Mechanics is unique. It is not a text-book, but forms a useful
+supplement to the ordinary text-book. The latter is usually a skeleton outline,
+full of mathematical symbols and other abstractions. Mach's book has
+'muscle and clothing,' and being written from the historical standpoint, introduces
+the leading contributors in succession, tells what they did and how
+they did it, and often what manner of men they were. Thus it is that the
+pages glow, as it were, with a certain humanism, quite delightful in a scientific
+book.... The book is handsomely printed, and deserves a warm reception
+from all interested in the progress of science."&mdash;<i>The Physical Review</i>, New
+York and London.</p>
+
+<p>"Mr. T. J. McCormack, by his effective translation, where translation
+was no light task, of this masterly treatise upon the earliest and most fundamental
+of the sciences, has rendered no slight service to the English speaking
+student. The German and English languages are generally accounted
+second to none in their value as instruments for the expression of scientific
+thought; but the conversion bodily of an abstruse work from one into the
+other, so as to preserve all the meaning and spirit of the original and to set it
+easily and naturally into its new form, is a task of the greatest difficulty, and<span class="pagenum"><a name="Page_415" id="Page_415">[Pg 415]</a></span>
+when performed so well as in the present instance, merits great commendation.
+Dr. Mach has created for his own works the severest possible standard
+of judgment. To expect no more from the books of such a master than from
+the elementary productions of an ordinary teacher in the science would be
+undue moderation. Our author has lifted what, to many of us, was at one
+time a course of seemingly unprofitable mental gymnastics, encompassed
+only at vast expenditure of intellectual effort, into a study possessing a deep
+philosophical value and instinct with life and interest. 'No profit grows
+where is no pleasure ta'en,' and the emancipated collegian will turn with
+pleasure from the narrow methods of the text-book to where the science is
+made to illustrate, by a treatment at once broad and deep, the fundamental
+connexion between all the physical sciences, taken together."&mdash;<i>The Mining
+Journal</i>, London, England.</p>
+
+<p>"As a history of mechanics, the work is admirable."&mdash;<i>The Nation</i>, New
+York.</p>
+
+<p>"An excellent book, admirably illustrated."&mdash;<i>The Literary World</i>, London,
+England.</p>
+
+<p>"Sets forth the elements of its subject with a lucidity, clearness, and
+force unknown in the mathematical text-books ... is admirably fitted to
+serve students as an introduction on historical lines to the principles of mechanical
+science."&mdash;<i>Canadian Mining and Mechanical Review</i>, Ottawa, Can.</p>
+
+<p>"A masterly book.... To any one who feels that he does not know as
+much as he ought to about physics, we can commend it most heartily as a
+scholarly and able treatise ... both interesting and profitable."&mdash;A. M.
+Wellington, in <i>Engineering News</i>, New York.</p>
+
+<p>"The book as a whole is unique, and is a valuable addition to any library
+of science or philosophy.... Reproductions of quaint old portraits and
+vignettes give piquancy to the pages. The numerous marginal titles form a
+complete epitome of the work; and there is that invaluable adjunct, a good
+index. Altogether the publishers are to be congratulated upon producing a
+technical work that is thoroughly attractive in its make-up."&mdash;Prof. D. W.
+Hering, in <i>Science</i>.</p>
+
+<p>"There is one other point upon which this volume should be commended,
+and that is the perfection of the translation. It is a common fault that books
+of the greatest interest and value in the original are oftenest butchered or
+made ridiculous by a clumsy translator. The present is a noteworthy exception."&mdash;<i>Railway
+Age</i>.</p><p><span class="pagenum"><a name="Page_416" id="Page_416">[Pg 416]</a></span></p>
+
+<p>"The book is admirably printed and bound.... The presswork is unexcelled
+by any technical books that have come to our hands for some time,
+and the engravings and figures are all clearly and well executed."&mdash;<i>Railroad
+Gazette</i>.</p>
+
+
+
+
+<h2><a name="TESTIMONIALS_OF_PROMINENT_EDUCATORS" id="TESTIMONIALS_OF_PROMINENT_EDUCATORS">TESTIMONIALS OF PROMINENT EDUCATORS.</a></h2>
+
+
+<p>"I am delighted with Professor Mach's <i>Science of Mechanics</i>."&mdash;<i>M. E.
+Cooley</i>, Professor of Mechanical Engineering, Ann Arbor, Mich.</p>
+
+<p>"You have done a good service to science in publishing Mach's <i>Science
+of Mechanics</i> in English. I shall take every opportunity to recommend it to
+young students as a source of much interesting information and inspiration."&mdash;<i>M.
+I. Pupin</i>, Professor of Mechanics, Columbia College, New York.</p>
+
+<p>"Mach's <i>Science of Mechanics</i> is an admirable ... book."&mdash;<i>Prof. E. A.
+Fuertes</i>, Director of the College of Civil Engineering of Cornell University,
+Ithaca, N. Y.</p>
+
+<p>"I congratulate you upon producing the work in such good style and in
+so good a translation. I bought a copy of it a year ago, very shortly after you
+issued it. The book itself is deserving of the highest admiration; and you
+are entitled to the thanks of all English-speaking physicists for the publication
+of this translation."&mdash;<i>D. W. Hering</i>, Professor of Physics, University of
+the City of New York, New York.</p>
+
+<p>"I have read Mach's <i>Science of Mechanics</i> with great pleasure. The book
+is exceedingly interesting."&mdash;<i>W. F. Magie</i>, Professor of Physics, Princeton
+University, Princeton, N. J.</p>
+
+<p>"The <i>Science of Mechanics</i> by Mach, translated by T. J. McCormack, I
+regard as a most valuable work, not only for acquainting the student with the
+history of the development of Mechanics, but as serving to present to him
+most favorably the fundamental ideas of Mechanics and their rational connexion
+with the highest mathematical developments. It is a most profitable
+book to read along with the study of a text-book of Mechanics, and I shall
+take pleasure in recommending its perusal by my students."&mdash;<i>S. W. Robinson</i>,
+Professor of Mechanical Engineering, Ohio State University, Columbus, Ohio.</p>
+
+<p>"I am delighted with Mach's 'Mechanics.' I will call the attention to
+it of students and instructors who have the Mechanics or Physics to study or
+teach."&mdash;<i>J. E. Davies</i>, University of Wisconsin, Madison, Wis.</p>
+
+<p>"There can be but one opinion as to the value of Mach's work in this
+translation. No instructor in physics should be without a copy of it."&mdash;<i>Henry
+Crew</i>, Professor of Physics in the Northwestern University, Evanston, Ill.</p><hr class="chap" /><p><span class="pagenum"><a name="Page_417" id="Page_417">[Pg 417]</a></span></p>
+
+
+
+
+<h2><a name="POPULAR_SCIENTIFIC_LECTURES" id="POPULAR_SCIENTIFIC_LECTURES">POPULAR SCIENTIFIC LECTURES.</a></h2>
+
+<p class="center">A PORTRAYAL OF THE SPIRIT AND METHODS
+OF SCIENCE.</p>
+
+<p class="center bold">By DR. ERNST MACH.</p>
+
+<p class="small center">PROFESSOR OF THE HISTORY AND THEORY OF INDUCTIVE SCIENCE IN THE
+UNIVERSITY OF VIENNA.</p>
+
+<p class="center bold">Translated by THOMAS J. McCORMACK.</p>
+
+<p class="center"><i>Third Edition, Revised Throughout and Greatly Enlarged.</i></p>
+
+<hr/>
+
+<p class="center">Cloth, Gilt Top. Exhaustively Indexed. Pages, 415. Cuts, 59. Price, $1.50.</p>
+
+<hr/>
+
+
+<h3><a name="TITLES_OF_THE_LECTURES" id="TITLES_OF_THE_LECTURES">TITLES OF THE LECTURES.</a></h3>
+
+
+<ul class="IX"><li>The Forms of Liquids.</li>
+
+<li>The Fibres of Corti.</li>
+
+<li>On the Causes of Harmony.</li>
+
+<li>On the Velocity of Light.</li>
+
+<li>Why Has Man Two Eyes?</li>
+
+<li>On Symmetry.</li>
+
+<li>On the Fundamental Concepts of Static Electricity.</li>
+
+<li>On the Principle of the Conservation of Energy.</li>
+
+<li>On the Economical Nature of Physical Inquiry.</li>
+
+<li>On the Principle of Comparison in Physics.</li>
+
+<li>On the Part Played by Accident in Invention and Discovery.</li>
+
+<li>On Sensations of Orientation.</li>
+
+<li>On the Relative Educational Value of the Classics and the Mathematico-Physical Sciences.</li>
+
+<li>A Contribution to the History of Acoustics.</li>
+
+<li>Remarks on the Theory of Spatial Vision.</li>
+
+<li>On Transformation and Adaptation in Scientific Thought.</li></ul>
+
+
+
+<h2>PRESS NOTICES.</h2>
+
+<p>"A most fascinating volume, treating of phenomena in which all are interested,
+in a delightful style and with wonderful clearness. For lightness
+of touch and yet solid value of information the chapter 'Why Has Man Two
+Eyes?' has scarcely a rival in the whole realm of popular scientific writing."&mdash;<i>The
+Boston Traveller</i>.</p>
+
+<p>"Truly remarkable in the insight they give into the relationship of the
+various fields cultivated under the name of Physics.... A vein of humor is
+met here and there reminding the reader of Heaviside, never offending one's
+taste. These features, together with the lightness of touch with which Mr.
+McCormack has rendered them, make the volume one that may be fairly
+called rare. The spirit of the author is preserved in such attractive, really
+delightful, English that one is assured nothing has been lost by translation."&mdash;Prof.
+Henry Crew, in <i>The Astrophysical Journal</i>.</p><p><span class="pagenum"><a name="Page_418" id="Page_418">[Pg 418]</a></span></p>
+
+<p>"A very delightful and useful book.... The author treats some of the
+most recondite problems of natural science, in so charmingly untechnical a
+way, with such a wealth of bright illustration, as makes his meaning clear to
+the person of ordinary intelligence and education.... This is a work that
+should find a place in every library, and that people should be encouraged to
+read."&mdash;<i>Daily Picayune</i>, New Orleans.</p>
+
+<p>"In his translation Mr. McCormack has well preserved the frank, simple,
+and pleasing style of this famous lecturer on scientific topics. Professor
+Mach deals with the live facts, the salient points of science, and not with its
+mysticism or dead traditions. He uses the simplest of illustrations and expresses
+himself clearly, tersely, and with a delightful freshness that makes
+entertaining reading of what in other hands would be dull and prosy."&mdash;<i>Engineering
+News</i>, N. Y.</p>
+
+<p>"The general reader is led by plain and easy steps along a delightful way
+through what would be to him without such a help a complicated maze of
+difficulties. Marvels are invented and science is revealed as the natural foe
+to mysteries."&mdash;<i>The Chautauquan</i>.</p>
+
+<p>"The beautiful quality of the work is not marred by abstruse discussions
+which would require a scientist to fathom, but is so simple and so clear that
+it brings us into direct contact with the matter treated."&mdash;<i>The Boston Post</i>.</p>
+
+<p>"A masterly exposition of important scientific truths."&mdash;<i>Scotsman</i>, Edinburgh.</p>
+
+<p>"These lectures by Dr. Mach are delightfully simple and frank; there is
+no dryness or darkness of technicalities, and science and common life do not
+seem separated by a gulf.... The style is admirable, and the whole volume
+seems gloriously alive and human."&mdash;<i>Providence Journal</i>, R. I.</p>
+
+<p>"The non-scientific reader who desires to learn something of modern
+scientific theories, and the reasons for their existence, cannot do better than
+carefully study these lectures. The English is excellent throughout, and reflects
+great credit on the translator."&mdash;<i>Manufacturer and Builder</i>.</p>
+
+<p>"We like the quiet, considerate intelligence of these lectures."&mdash;<i>Independent</i>,
+New York.</p>
+
+<p>"Professor Mach's lectures are so pleasantly written and illumined with
+such charm of illustration that they have all the interest of lively fiction."&mdash;<i>New
+York Com. Advertiser</i>.</p>
+
+<p>"The literary and philosophical suggestiveness of the book is very rich."
+<i>Hartford Seminary Record</i>.</p><p><span class="pagenum"><a name="Page_419" id="Page_419">[Pg 419]</a></span></p>
+
+<p>"All are presented so skilfully that one can imagine that Professor Mach's
+hearers departed from his lecture-room with the conviction that science was
+a matter for abecedarians. Will please those who find the fairy tales of
+science more absorbing than fiction."&mdash;<i>The Pilot</i>, Boston.</p>
+
+<p>"Professor Mach ... is a master in physics.... His book is a good one
+and will serve a good purpose, both for instruction and suggestion."&mdash;Prof.
+A. E. Dolbear, in <i>The Dial</i>.</p>
+
+<p>"The most beautiful ideas are unfolded in the exposition."&mdash;<i>Catholic
+World</i>, New York.</p>
+
+
+
+
+<h2><a name="THE_ANALYSIS_OF_THE_SENSATIONS" id="THE_ANALYSIS_OF_THE_SENSATIONS">THE ANALYSIS OF THE SENSATIONS</a></h2>
+
+<p class="center bold">By DR. ERNST MACH.</p>
+
+<p class="center small">PROFESSOR OF THE HISTORY AND THEORY OF INDUCTIVE SCIENCE IN THE
+UNIVERSITY OF VIENNA.</p>
+
+<hr/>
+
+<p class="center">Pages, 208. Illustrations, 37. Indexed.</p>
+
+<p class="center">(Price, Cloth, $1.25.)</p>
+
+<hr/>
+
+
+<h3><a name="CONTENTS" id="CONTENTS">CONTENTS.</a></h3>
+
+
+<ul class="IX"><li>Introductory: Antimetaphysical.</li>
+
+<li>The Chief Points of View for the Investigation
+of the Senses.</li>
+
+<li>The Space-Sensations of the Eye.</li>
+
+<li>Space-Sensation, Continued.</li>
+
+<li>The Relations of the Sight-Sensations
+to One Another and to the
+Other Psychical Elements.</li>
+
+<li>The Sensation of Time.</li>
+
+<li>The Sensation of Sound.</li>
+
+<li>Influence of the Preceding Investigations
+on the Mode of Conceiving
+Physics.</li></ul>
+
+<hr/>
+
+<p>"A wonderfully original little book. Like everything he writes a work of
+genius."&mdash;<i>Prof. W. James</i> of Harvard.</p>
+
+<p>"I consider each work of Professor Mach a distinct acquisition to a
+library of science."&mdash;<i>Prof. D. W. Hering</i>, New York University.</p>
+
+<p>"There is no work known to the writer which, in its general scientific
+bearings, is more likely to repay richly thorough study. We are all interested
+in nature in one way or another, and our interests can only be heightened
+and clarified by Mach's wonderfully original and wholesome book. It is not
+saying too much to maintain that every intelligent person should have a copy
+of it,&mdash;and should study that copy."&mdash;<i>Prof. J. E. Trevor</i>, Cornell.</p>
+
+<p>"Students may here make the acquaintance of some of the open questions
+of sensation and at the same time take a lesson in the charm of scientific
+modesty that can hardly be excelled."&mdash;<i>Prof. E. C. Sanford</i>, Clark University.</p>
+
+<p>"It exhibits keen observation and acute thought, with many new and interesting
+experiments by way of illustration. Moreover, the style is light
+and even lively&mdash;a rare merit in a German prose work, and still rarer in a
+translation of one."&mdash;<i>The Literary World</i>, London.</p>
+
+<hr/>
+
+<p class="center">CHICAGO:<br />
+<span class="bold">The Open Court Publishing Company</span><br />
+324 DEARBORN STREET.</p>
+
+<p class="center">LONDON: Kegan Paul, Trench, Trübner, &amp; Company.</p><hr class="chap" />
+<p><span class="pagenum"><a name="Page_420" id="Page_420">[Pg 420]</a></span></p>
+
+
+
+
+<h2><a name="CATALOGUE_OF_PUBLICATIONS" id="CATALOGUE_OF_PUBLICATIONS">CATALOGUE OF PUBLICATIONS</a></h2>
+
+<p class="center small">OF THE<br />
+<span class="big">OPEN COURT PUBLISHING CO.</span></p>
+
+<hr/>
+
+<p>COPE, E. D.</p>
+
+<blockquote><p>THE PRIMARY FACTORS OF ORGANIC EVOLUTION.</p></blockquote>
+
+<blockquote><p>121 cuts. Pp., xvi, 547. Cloth, $2.00, net.</p></blockquote>
+
+<p>MÜLLER, F. MAX.</p>
+
+<blockquote><p>THREE INTRODUCTORY LECTURES ON THE SCIENCE OF THOUGHT.</p></blockquote>
+
+<blockquote><p>With a correspondence on "Thought Without Words," between F. Max Müller and Francis Galton, the Duke of Argyll, George J. Romanes and others. 128 pages. Cloth, 75 cents. Paper, 25 cents.</p></blockquote>
+
+<blockquote><p>THREE LECTURES ON THE SCIENCE OF LANGUAGE.</p></blockquote>
+
+<blockquote><p>The Oxford University Extension Lectures, with a Supplement, "My Predecessors." 112 pages. 2nd Edition. Cloth, 75 cents. Paper, 25c.</p></blockquote>
+
+<p>ROMANES, GEORGE JOHN.</p>
+
+<blockquote><p>DARWIN AND AFTER DARWIN.</p></blockquote>
+
+<blockquote><p>An Exposition of the Darwinian Theory and a Discussion of Post-Darwinian Questions. Three Vols., $4.00. Singly, as follows:</p>
+
+<p>1. <span class="smcap">The Darwinian Theory.</span> 460 pages. 125 illustrations. Cloth, $2.00.</p>
+
+<p>2. <span class="smcap">Post-Darwinian Questions.</span> Heredity and Utility. Pp. 338. $1.50.</p>
+
+<p>3. <span class="smcap">Post-Darwinian Questions.</span> Isolation and Physiological Selection. Pp. 181. $1.00.</p></blockquote>
+
+<blockquote><p>AN EXAMINATION OF WEISMANNISM.</p></blockquote>
+
+<blockquote><p>236 pages. Cloth, $1.00. Paper, 35c.</p></blockquote>
+
+<blockquote><p>THOUGHTS ON RELIGION.</p></blockquote>
+
+<blockquote><p>Edited by Charles Gore, M. A., Canon of Westminster. Third Edition, Pages, 184. Cloth, gilt top, $1.25.</p></blockquote>
+
+<p>RIBOT, TH.</p>
+
+<blockquote><p>THE PSYCHOLOGY OF ATTENTION.</p>
+
+<p>THE DISEASES OF PERSONALITY.</p>
+
+<p>THE DISEASES OF THE WILL.</p></blockquote>
+
+<blockquote><p>Authorised translations. Cloth, 75 cents each. Paper, 25 cents. <i>Full set, cloth, $1.75, net.</i></p></blockquote>
+
+<p>MACH, ERNST.</p>
+
+<blockquote><p>THE SCIENCE OF MECHANICS.</p></blockquote>
+
+<blockquote><p><span class="smcap">A Critical and Historical Exposition of its Principles.</span> Translated by <span class="smcap">T. J. McCormack</span>. 250 cuts. 534 pages. 1/2 m., gilt top. $2.50.</p></blockquote>
+
+<blockquote><p>POPULAR SCIENTIFIC LECTURES.</p></blockquote>
+
+<blockquote><p>Third Edition. 415 pages. 59 cuts. Cloth, gilt top. Net, $1.50.</p></blockquote>
+
+<blockquote><p>THE ANALYSIS OF THE SENSATIONS.</p></blockquote>
+
+<blockquote><p>Pp. 208. 37 cuts. Cloth, $1.25, net.</p></blockquote>
+
+<p>GOODWIN, REV. T. A.</p>
+
+<blockquote><p>LOVERS THREE THOUSAND YEARS AGO.</p></blockquote>
+
+<blockquote><p>As Indicated by the Song of Solomon. Pp. 41. Boards, 50c.</p></blockquote>
+
+<p>HOLYOAKE, G. J.</p>
+
+<blockquote><p>ENGLISH SECULARISM. <span class="smcap">A Confession of Belief.</span></p></blockquote>
+
+<blockquote><p>Pp. 146. Cloth, 50c., net.</p></blockquote>
+
+<p>CORNILL, CARL HEINRICH.</p>
+
+<blockquote><p>THE PROPHETS OF ISRAEL.</p></blockquote>
+
+<blockquote><p>Popular Sketches from Old Testament History. Pp., 200. Cloth, $1.00.</p></blockquote>
+
+<blockquote><p>THE RISE OF THE PEOPLE OF ISRAEL.</p></blockquote>
+
+<blockquote><p>See <i>Epitomes of Three Sciences</i>, below.</p></blockquote>
+
+<p>BINET, ALFRED.</p>
+
+<blockquote><p>THE PSYCHIC LIFE OF MICRO-ORGANISMS.</p></blockquote>
+
+<blockquote><p>Authorised translation. 135 pages. Cloth, 75 cents; Paper, 25 cents.</p></blockquote>
+
+<blockquote><p>ON DOUBLE CONSCIOUSNESS.</p></blockquote>
+
+<blockquote><p>Studies in Experimental Psychology. 93 pages. Paper, 15 cents.</p></blockquote><p><span class="pagenum"><a name="Page_421" id="Page_421">[Pg 421]</a></span></p>
+
+<p>WAGNER, RICHARD</p>
+
+<blockquote><p>A PILGRIMAGE TO BEETHOVEN.</p></blockquote>
+
+<blockquote><p>A Novelette. Frontispiece, portrait of Beethoven. Pp. 40. Boards, 50c.</p></blockquote>
+
+<p>WEISMANN, AUGUST.</p>
+
+<blockquote><p>GERMINAL SELECTION. <span class="smcap">As a Source of Definite Variation.</span></p></blockquote>
+
+<blockquote><p>Pp. 73. Paper, 25c.</p></blockquote>
+
+<p>NOIRÉ, LUDWIG.</p>
+
+<blockquote><p>ON THE ORIGIN OF LANGUAGE. Pp. 57. Paper, 15c.</p></blockquote>
+
+<p>FREYTAG, GUSTAV.</p>
+
+<blockquote><p>THE LOST MANUSCRIPT. A Novel.</p></blockquote>
+
+<blockquote><p>2 vols. 953 pages. Extra cloth, $4.00. One vol., cl., $1.00; paper, 75c.</p></blockquote>
+
+<blockquote><p>MARTIN LUTHER.</p></blockquote>
+
+<blockquote><p>Illustrated. Pp. 130. Cloth, $1.00. Paper, 25c.</p></blockquote>
+
+<p>HERING, EWALD.</p>
+
+<blockquote><p>ON MEMORY, and THE SPECIFIC ENERGIES OF THE NERVOUS
+SYSTEM. Pp. 50. Paper, 15c.</p></blockquote>
+
+<p>TRUMBULL, M. M.</p>
+
+<blockquote><p>THE FREE TRADE STRUGGLE IN ENGLAND.</p></blockquote>
+
+<blockquote><p>Second Edition. 296 pages. Cloth, 75 cents; paper, 25 cents.</p></blockquote>
+
+<blockquote><p>WHEELBARROW: <span class="smcap">Articles and Discussions on the Labor Question</span>.</p></blockquote>
+
+<blockquote><p>With portrait of the author. 303 pages. Cloth, $1.00; paper, 35 cents.</p></blockquote>
+
+<blockquote><p>EARL GREY ON RECIPROCITY AND CIVIL SERVICE REFORM.</p></blockquote>
+
+<blockquote><p>With Comments by Gen. M. M. Trumbull. Price, 10 cents.</p></blockquote>
+
+<p>GOETHE AND SCHILLER'S XENIONS.</p>
+
+<blockquote><p>Selected and translated by Paul Carus. Album form. Pp., 162. Cl., $1.00</p></blockquote>
+
+<p>OLDENBERG, H.</p>
+
+<blockquote><p>ANCIENT INDIA: ITS LANGUAGE AND RELIGIONS.</p></blockquote>
+
+<blockquote><p>Pp. 100. Cloth, 50c. Paper, 25c.</p></blockquote>
+
+<p>CARUS, PAUL.</p>
+
+<blockquote><p>THE ETHICAL PROBLEM.</p></blockquote>
+
+<blockquote><p>90 pages. Cloth, 50 cents; Paper, 30 cents.</p></blockquote>
+
+<blockquote><p>FUNDAMENTAL PROBLEMS.</p></blockquote>
+
+<blockquote><p>Second edition, enlarged and revised. 372 pp. Cl., $1.50. Paper, 50c.</p></blockquote>
+
+<blockquote><p>HOMILIES OF SCIENCE.</p></blockquote>
+
+<blockquote><p>317 pages. Cloth, Gilt Top, $1.50.</p></blockquote>
+
+<blockquote><p>THE IDEA OF GOD.</p></blockquote>
+
+<blockquote><p>Fourth edition. 32 pages. Paper, 15 cents.</p></blockquote>
+
+<blockquote><p>THE SOUL OF MAN.</p></blockquote>
+
+<blockquote><p>With 152 cuts and diagrams. 458 pages. Cloth, $3.00.</p></blockquote>
+
+<blockquote><p>TRUTH IN FICTION. <span class="smcap">Twelve Tales with a Moral.</span></p></blockquote>
+
+<blockquote><p>Fine laid paper, white and gold binding, gilt edges. Pp. 111. $1.00.</p></blockquote>
+
+<blockquote><p>THE RELIGION OF SCIENCE.</p></blockquote>
+
+<blockquote><p>Second, extra edition. Price, 50 cents. R. S. L. edition, 25c. Pp. 103.</p></blockquote>
+
+<blockquote><p>PRIMER OF PHILOSOPHY.</p></blockquote>
+
+<blockquote><p>240 pages. Second Edition. Cloth, $1.00. Paper, 25c.</p></blockquote>
+
+<blockquote><p>THREE LECTURES: (1) <span class="smcap">The Philosophy of the Tool.</span> Pages, 24. Paper,
+10c. (2) <span class="smcap">Our Need of Philosophy.</span> Pages, 14. Paper, 5c. (3) <span class="smcap">Science
+a Religious Revelation.</span> Pages, 21. Paper, 5c.</p></blockquote>
+
+<blockquote><p>THE GOSPEL OF BUDDHA. According to Old Records.</p></blockquote>
+
+<blockquote><p>4th Edition. Pp., 275. Cloth, $1.00. Paper, 35 cents. In German, $1.25.</p></blockquote>
+
+<blockquote><p>BUDDHISM AND ITS CHRISTIAN CRITICS.</p></blockquote>
+
+<blockquote><p>Pages, 311. Cloth, $1.25.</p></blockquote>
+
+<blockquote><p>KARMA. <span class="smcap">A Story of Early Buddhism.</span></p></blockquote>
+
+<blockquote><p>Illustrated by Japanese artists. 2nd Edition. Crêpe paper, 75 cents.</p></blockquote>
+
+<p>GARBE, RICHARD.</p>
+
+<blockquote><p>THE REDEMPTION OF THE BRAHMAN. <span class="smcap">A Tale of Hindu Life.</span></p></blockquote>
+
+<blockquote><p>Laid paper. Gilt top. 96 pages. Price, 75c. Paper, 25c.</p></blockquote>
+
+<blockquote><p>THE PHILOSOPHY OF ANCIENT INDIA.</p></blockquote>
+
+<blockquote><p>Pp. 89. Cloth, 50c. Paper, 25c.</p></blockquote>
+
+<p>EPITOMES OF THREE SCIENCES.</p>
+
+<blockquote><p>1. <span class="smcap">The Study of Sanskrit.</span> By <i>H. Oldenberg</i>. 2. <span class="smcap">Experimental Psychology.</span>
+By <i>Joseph Jastrow</i>. 3. <span class="smcap">The Rise of the People of Israel.</span> By
+<i>C. H. Cornill</i>. 140 pages. Cloth, reduced to 50 cents.</p></blockquote><p><span class="pagenum"><a name="Page_422" id="Page_422">[Pg 422]</a></span></p>
+
+
+
+
+<h2><a name="The_Religion_of_Science_Library" id="The_Religion_of_Science_Library">The Religion of Science Library.</a></h2>
+
+
+<p>A collection of bi-monthly publications, most of which are reprints of
+books published by The Open Court Publishing Company. Yearly, $1.50.
+Separate copies according to prices quoted. The books are printed upon
+good paper, from large type.</p>
+
+<p>The Religion of Science Library, by its extraordinarily reasonable price,
+will place a large number of valuable books within the reach of all readers.</p>
+
+<p>The following have already appeared in the series:</p>
+
+<blockquote><p>No. 1. <i>The Religion of Science.</i> By <span class="smcap">Paul Carus</span>. 25c.</p>
+
+<p>2. <i>Three Introductory Lectures on the Science of Thought.</i> By <span class="smcap">F. Max Müller</span>. 25c.</p>
+
+<p>3. <i>Three Lectures on the Science of Language.</i> By <span class="smcap">F. Max Müller</span>. 25c.</p>
+
+<p>4. <i>The Diseases of Personality.</i> By <span class="smcap">Th. Ribot</span>. 25c.</p>
+
+<p>5. <i>The Psychology of Attention.</i> By <span class="smcap">Th. Ribot</span>. 25c.</p>
+
+<p>6. <i>The Psychic Life of Micro-Organisms.</i> By <span class="smcap">Alfred Binet</span>. 25c.</p>
+
+<p>7. <i>The Nature of the State.</i> By <span class="smcap">Paul Carus</span>. 15c.</p>
+
+<p>8. <i>On Double Consciousness.</i> By <span class="smcap">Alfred Binet</span>. 15c.</p>
+
+<p>9. <i>Fundamental Problems.</i> By <span class="smcap">Paul Carus</span>. 50c.</p>
+
+<p>10. <i>The Diseases of the Will.</i> By <span class="smcap">Th. Ribot</span>. 25c.</p>
+
+<p>11. <i>The Origin of Language.</i> By <span class="smcap">Ludwig Noire</span>. 15c.</p>
+
+<p>12. <i>The Free Trade Struggle in England.</i> By <span class="smcap">M. M. Trumbull</span>. 25c.</p>
+
+<p>13. <i>Wheelbarrow on the Labor Question.</i> By <span class="smcap">M. M. Trumbull</span>. 35c.</p>
+
+<p>14. <i>The Gospel of Buddha.</i> By <span class="smcap">Paul Carus</span>. 35c.</p>
+
+<p>15. <i>The Primer of Philosophy.</i> By <span class="smcap">Paul Carus</span>. 25c.</p>
+
+<p>16. <i>On Memory</i>, and <i>The Specific Energies of the Nervous System</i>. By <span class="smcap">Prof. Ewald Hering</span>. 15c.</p>
+
+<p>17. <i>The Redemption of the Brahman.</i> A Tale of Hindu Life. By <span class="smcap">Richard Garbe</span>. 25c.</p>
+
+<p>18. <i>An Examination of Weismannism.</i> By <span class="smcap">G. J. Romanes</span>. 35c.</p>
+
+<p>19. <i>On Germinal Selection.</i> By <span class="smcap">August Weismann</span>. 25c.</p>
+
+<p>20. <i>Lovers Three Thousand Years Ago.</i> By <span class="smcap">T. A. Goodwin</span>. 15c.</p>
+
+<p>21. <i>Popular Scientific Lectures.</i> By <span class="smcap">Ernst Mach</span>. 50c.</p>
+
+<p>22. <i>Ancient India: Its Language and Religions.</i> By <span class="smcap">H. Oldenberg</span>. 25c.</p>
+
+<p>23. <i>The Prophets of Ancient Israel.</i> By <span class="smcap">Prof. C. H. Cornill</span>. 25c.</p>
+
+<p>24. <i>Homilies of Science.</i> By <span class="smcap">Paul Carus</span>. 35c.</p>
+
+<p>25. <i>Thoughts on Religion.</i> By <span class="smcap">G. J. Romanes</span>. 50 cents.</p>
+
+<p>26. <i>The Philosophy of Ancient India.</i> By <span class="smcap">Prof. Richard Garbe</span>. 25c.</p>
+
+<p>27. <i>Martin Luther.</i> By <span class="smcap">Gustav Freytag</span>. 25c.</p>
+
+<p>28. <i>English Secularism.</i> By <span class="smcap">George Jacob Holyoake</span>. 25c.</p>
+
+<p>29. <i>On Orthogenesis.</i> By <span class="smcap">Th. Eimer</span>. 25c.</p>
+
+<p>30. <i>Chinese Philosophy.</i> By <span class="smcap">Paul Carus</span>. 25c.</p>
+
+<p>31. <i>The Lost Manuscript.</i> By <span class="smcap">Gustav Freytag</span>. 60c.</p></blockquote>
+<p><span class="pagenum"><a name="Page_423" id="Page_423">[Pg 423]</a></span></p>
+<hr class="tb" />
+
+<p class="center">THE OPEN COURT PUBLISHING CO.</p>
+
+<p class="center"><span class="smcap">324 Dearborn Street, Chicago, Ill.</span><br />
+LONDON: Kegan Paul, Trench, Trübner &amp; Co</p>
+
+<hr class="chap" />
+
+
+<h2><a name="THE_OPEN_COURT" id="THE_OPEN_COURT">THE OPEN COURT</a></h2>
+
+<p class="center small">A MONTHLY MAGAZINE</p>
+
+<p class="center bold">Devoted to the Science of Religion, the Religion of Science, and
+the Extension of the Religious Parliament Idea.</p>
+
+
+<p><i>THE OPEN COURT</i> does not understand by religion any creed or dogmatic
+belief, but man's world-conception in so far as it regulates his conduct.</p>
+
+<p>The old dogmatic conception of religion is based upon the science of past
+ages; to base religion upon the maturest and truest thought of the present
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+the Religion of Science, that is, the religion of verified and verifiable truth.</p>
+
+<p>Although opposed to irrational orthodoxy and narrow bigotry, <i>The Open
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+It criticises their errors unflinchingly but without animosity, and endeavors
+to preserve of them all that is true and good.</p>
+
+<p>The current numbers of <i>The Open Court</i> contain valuable original articles
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+
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+<li><span class="smcap">Prof. Ernst Mach</span>,</li>
+<li><span class="smcap">Rabbi Emil Hirsch</span>,</li>
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+<li><span class="smcap">Prof. C. Lombroso</span>,</li>
+<li><span class="smcap">Prof. E. Haeckel</span>,</li>
+<li><span class="smcap">Prof. H. Höffding</span>,</li>
+<li><span class="smcap">Dr. F. Oswald</span>,</li>
+<li><span class="smcap">Prof. J. Delb&oelig;uf</span>,</li>
+<li><span class="smcap">Prof. F. Jodl</span>,</li>
+<li><span class="smcap">Prof. H. M. Stanley</span>,</li>
+<li><span class="smcap">G. Ferrero</span>,</li>
+<li><span class="smcap">J. Venn</span>,</li>
+<li><span class="smcap">Prof. H. von Holst</span>.</li>
+</ul>
+
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+<p>Per Copy, 50 cents; Yearly, $2.00. In England and all countries in U.P.U.
+per Copy, 2s 6d; Yearly, 9s 6d.</p>
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+<hr class="tb" />
+<p>FOOTNOTES:</p>
+
+<div class="footnote"><p><a name="Footnote_1_1" id="Footnote_1_1"></a><a href="#FNanchor_1_1"><span class="label">[1]</span></a> <i>Statique expérimentale et théorique des liquids</i>, 1873. See also <i>The Science
+of Mechanics</i>, p. 384 et seqq., The Open Court Publishing Co., Chicago, 1893.</p></div>
+
+<div class="footnote"><p><a name="Footnote_2_2" id="Footnote_2_2"></a><a href="#FNanchor_2_2"><span class="label">[2]</span></a> Compare Mach, <i>Ueber die Molecularwirkung der Flüssigkeiten</i>, Reports
+of the Vienna Academy, 1862.</p></div>
+
+<div class="footnote"><p><a name="Footnote_3_3" id="Footnote_3_3"></a><a href="#FNanchor_3_3"><span class="label">[3]</span></a> In almost all branches of physics that are well worked out such maximal
+and minimal problems play an important part.</p></div>
+
+<div class="footnote"><p><a name="Footnote_4_4" id="Footnote_4_4"></a><a href="#FNanchor_4_4"><span class="label">[4]</span></a> Compare Mach, <i>Vorträge über Psychophysik</i>, Vienna, 1863, page 41; <i>Compendium
+der Physik für Mediciner</i>, Vienna, 1863, page 234; and also <i>The Science
+of Mechanics</i>, Chicago, 1893, pp. 84 and 464.</p></div>
+
+<div class="footnote"><p><a name="Footnote_5_5" id="Footnote_5_5"></a><a href="#FNanchor_5_5"><span class="label">[5]</span></a> Like reflexions are found in Quételet, <i>Du système sociale</i>.</p></div>
+
+<div class="footnote"><p><a name="Footnote_6_6" id="Footnote_6_6"></a><a href="#FNanchor_6_6"><span class="label">[6]</span></a> For the full development of this idea see the essay "On the Economical
+Nature of Physical Inquiry," p. 186, and the chapter on "The Economy of
+Science," in my <i>Mechanics</i> (Chicago: The Open Court Publishing Company,
+1893), p. 481.</p></div>
+
+<div class="footnote"><p><a name="Footnote_7_7" id="Footnote_7_7"></a><a href="#FNanchor_7_7"><span class="label">[7]</span></a> Science may be regarded as a maximum or minimum problem, exactly
+as the business of the merchant. In fact, the intellectual activity of natural
+inquiry is not so greatly different from that exercised in ordinary life as is
+usually supposed.</p></div>
+
+<div class="footnote"><p><a name="Footnote_8_8" id="Footnote_8_8"></a><a href="#FNanchor_8_8"><span class="label">[8]</span></a> This experiment, with its associated reflexions, is due to Galileo.</p></div>
+
+<div class="footnote"><p><a name="Footnote_9_9" id="Footnote_9_9"></a><a href="#FNanchor_9_9"><span class="label">[9]</span></a> A development of the theory of musical audition differing in many
+points from the theory of Helmholtz here expounded, will be found in my
+<i>Contributions to the Analysis of the Sensations</i> (English translation by C. M.
+Williams), Chicago, The Open Court Publishing Company, 1897.</p></div>
+
+<div class="footnote"><p><a name="Footnote_10_10" id="Footnote_10_10"></a><a href="#FNanchor_10_10"><span class="label">[10]</span></a> Sauveur also set out from Leibnitz's idea, but arrived by independent
+researches at a different theory, which was very near to that of Helmholtz.
+Compare on this point Sauveur, <i>Mémoires de l'Académie des Sciences</i>, Paris,
+1700-1705, and R. Smith, <i>Harmonics</i>, Cambridge, 1749. (See <i>Appendix</i>, p. 346.)</p></div>
+
+<div class="footnote"><p><a name="Footnote_11_11" id="Footnote_11_11"></a><a href="#FNanchor_11_11"><span class="label">[11]</span></a> According to Mr. Jules Andrieu, the idea that nature must be tortured
+to reveal her secrets is preserved in the name <i>crucible</i>&mdash;from the Latin <i>crux</i>,
+a cross. But, more probably, <i>crucible</i> is derived from some Old French or
+Teutonic form, as <i>cruche</i>, <i>kroes</i>, <i>krus</i>, etc., a pot or jug (cf. Modern English
+<i>crock</i>, <i>cruse</i>, and German <i>Krug</i>).&mdash;<i>Trans.</i></p></div>
+
+<div class="footnote"><p><a name="Footnote_12_12" id="Footnote_12_12"></a><a href="#FNanchor_12_12"><span class="label">[12]</span></a> Xenophon, Memorabilia iv, 7, puts into the mouth of Socrates these
+words: &#959;&#8020;&#964;&#949; &#947;&#8048;&#961; &#949;&#8017;&#961;&#949;&#964;&#8048; &#7936;&#957;&#952;&#961;&#8061;&#960;&#959;&#953;&#962; &#945;&#8016;&#964;&#8048; &#7952;&#957;&#8057;&#956;&#953;&#950;&#949;&#957; &#949;&#7990;&#957;&#945;&#953;, &#959;&#8020;&#964;&#949; &#967;&#945;&#961;&#8055;&#950;&#949;&#963;&#952;&#945;&#953;
+&#952;&#949;&#959;&#8150;&#962; &#7938;&#957; &#7969;&#947;&#949;&#8150;&#964;&#959; &#964;&#8056;&#957; &#950;&#951;&#964;&#959;&#8166;&#957;&#964;&#945; &#7939; &#7952;&#954;&#949;&#8150;&#957;&#959;&#953; &#963;&#945;&#966;&#951;&#957;&#8055;&#963;&#945;&#953; &#959;&#8016;&#954; &#7952;&#946;&#959;&#965;&#955;&#8053;&#952;&#951;&#963;&#945;&#957;.</p></div>
+
+<div class="footnote"><p><a name="Footnote_13_13" id="Footnote_13_13"></a><a href="#FNanchor_13_13"><span class="label">[13]</span></a> Galilei, <i>Discorsi e dimostrazione matematiche</i>. Leyden, 1638. <i>Dialogo
+Primo.</i></p></div>
+
+<div class="footnote"><p><a name="Footnote_14_14" id="Footnote_14_14"></a><a href="#FNanchor_14_14"><span class="label">[14]</span></a> In the same way, the pitch of a locomotive-whistle is higher as the
+locomotive rapidly approaches an observer, and lower when rapidly leaving
+him than if the locomotive were at rest.&mdash;<i>Trans.</i></p></div>
+
+<div class="footnote"><p><a name="Footnote_15_15" id="Footnote_15_15"></a><a href="#FNanchor_15_15"><span class="label">[15]</span></a> A kilometre is 0.621 or nearly five-eighths of a statute mile.</p></div>
+
+<div class="footnote"><p><a name="Footnote_16_16" id="Footnote_16_16"></a><a href="#FNanchor_16_16"><span class="label">[16]</span></a> Observe, also, the respect in which the wheel is held in India, Japan
+and other Buddhistic countries, as the emblem of power, order, and law, and
+of the superiority of mind over matter. The consciousness of the importance of
+this invention seems to have lingered long in the minds of these nations.&mdash;<i>Tr.</i></p></div>
+
+<div class="footnote"><p><a name="Footnote_17_17" id="Footnote_17_17"></a><a href="#FNanchor_17_17"><span class="label">[17]</span></a> This effect is particularly noticeable in the size of workmen on high
+chimneys and church-steeples&mdash;"steeple Jacks." When the cables were slung
+from the towers of the Brooklyn bridge (277 feet high), the men sent out in
+baskets to paint them, appeared, against the broad background of heaven and
+water, like flies.&mdash;<i>Trans.</i></p></div>
+
+<div class="footnote"><p><a name="Footnote_18_18" id="Footnote_18_18"></a><a href="#FNanchor_18_18"><span class="label">[18]</span></a> See Joh. Müller, <i>Vergleichende Physiologie des Gesichtssinnes</i>, Leipsic,
+1826.</p></div>
+
+<div class="footnote"><p><a name="Footnote_19_19" id="Footnote_19_19"></a><a href="#FNanchor_19_19"><span class="label">[19]</span></a> Delivered before the German Casino of Prague, in the winter of 1871.
+</p>
+<p>
+A fuller treatment of the problems of this lecture will be found in my <i>Contributions
+to the Analysis of the Sensations</i> (Jena, 1886), English Translation,
+Chicago, 1895. J. P. Soret, <i>Sur la perception du beau</i> (Geneva, 1892), also regards
+repetition as a principle of æsthetics. His discussions of the <i>æsthetical</i>
+side of the subject are much more detailed than mine. But with respect to
+the psychological and physiological foundation of the principle, I am convinced
+that the <i>Contributions to the Analysis of the Sensations</i> go deeper.&mdash;<span class="smcap">Mach</span>
+(1894).</p></div>
+
+<div class="footnote"><p><a name="Footnote_20_20" id="Footnote_20_20"></a><a href="#FNanchor_20_20"><span class="label">[20]</span></a> Kant, in his <i>Prolegomena zu jeder künftigen Metaphysik</i>, also refers to
+this fact, but for a different purpose.</p></div>
+
+<div class="footnote"><p><a name="Footnote_21_21" id="Footnote_21_21"></a><a href="#FNanchor_21_21"><span class="label">[21]</span></a> Compare Mach, <i>Fichte's Zeitschrift für Philosophie</i>, 1864, p. 1.</p></div>
+
+<div class="footnote"><p><a name="Footnote_22_22" id="Footnote_22_22"></a><a href="#FNanchor_22_22"><span class="label">[22]</span></a> The fact that the first and second differential coefficients of a curve are
+directly seen, but the higher coefficients not, is very simply explained. The
+first gives the position of the tangent, the declination of the straight line from
+the position of symmetry, the second the declination of the curve from the
+straight line. It is, perhaps, not unprofitable to remark here that the ordinary
+method of testing rulers and plane surfaces (by reversed applications)
+ascertains the deviation of the object from symmetry to itself.</p></div>
+
+<div class="footnote"><p><a name="Footnote_23_23" id="Footnote_23_23"></a><a href="#FNanchor_23_23"><span class="label">[23]</span></a> See the lecture <i>On the Causes of Harmony</i>.</p></div>
+
+<div class="footnote"><p><a name="Footnote_24_24" id="Footnote_24_24"></a><a href="#FNanchor_24_24"><span class="label">[24]</span></a> A. von Oettingen, <i>Harmoniesystem in dualer Entwicklung</i>. Leipsic and
+Dorpat, 1866.</p></div>
+
+<div class="footnote"><p><a name="Footnote_25_25" id="Footnote_25_25"></a><a href="#FNanchor_25_25"><span class="label">[25]</span></a> Compare Mach's <i>Zur Theorie des Gehörorgans</i>, Vienna Academy, 1863.</p></div>
+
+<div class="footnote"><p><a name="Footnote_26_26" id="Footnote_26_26"></a><a href="#FNanchor_26_26"><span class="label">[26]</span></a> A lecture delivered at the International Electrical Exhibition, in Vienna,
+on September 4, 1883.</p></div>
+
+<div class="footnote"><p><a name="Footnote_27_27" id="Footnote_27_27"></a><a href="#FNanchor_27_27"><span class="label">[27]</span></a> If the two bodies were oppositely electrified they would exert attractions
+upon each other.</p></div>
+
+<div class="footnote"><p><a name="Footnote_28_28" id="Footnote_28_28"></a><a href="#FNanchor_28_28"><span class="label">[28]</span></a> The quantity which flows off is in point of fact less than <i>q</i>. It would be
+equal to the quantity <i>q</i> only if the inner coating of the jar were wholly encompassed
+by the outer coating.</p></div>
+
+<div class="footnote"><p><a name="Footnote_29_29" id="Footnote_29_29"></a><a href="#FNanchor_29_29"><span class="label">[29]</span></a> Rigorously, of course, this is not correct. First, it is to be noted that the
+jar <i>L</i> is discharged simultaneously with the electrode of the machine. The
+jar <i>F</i>, on the other hand, is always discharged simultaneously with the outer
+coating of the jar <i>L</i>. Hence, if we call the capacity of the electrode of the
+machine <i>E</i>, that of the unit jar <i>L</i>, that of the outer coating of <i>L</i>, <i>A</i>, and that of
+the principal jar <i>F</i>, then this equation would exist for the example in the text:
+(<i>F</i> + <i>A</i>)/(<i>L</i> + <i>E</i>) = 5. A cause of further departure from absolute exactness is
+the residual charge.</p></div>
+
+<div class="footnote"><p><a name="Footnote_30_30" id="Footnote_30_30"></a><a href="#FNanchor_30_30"><span class="label">[30]</span></a> Making allowance for the corrections indicated in the preceding footnote,
+I have obtained for the dielectric constant of sulphur the number 3.2,
+which agrees practically with the results obtained by more delicate methods.
+For the highest attainable precision one should by rights immerse the two
+plates of the condenser first wholly in air and then wholly in sulphur, if the
+ratio of the capacities is to correspond to the dielectric constant. In point of
+fact, however, the error which arises from inserting simply a plate of sulphur
+that exactly fills the space between the two plates, is of no consequence.</p></div>
+
+<div class="footnote"><p><a name="Footnote_31_31" id="Footnote_31_31"></a><a href="#FNanchor_31_31"><span class="label">[31]</span></a> As this definition in its simple form is apt to give rise to misunderstandings,
+elucidations are usually added to it. It is clear that we cannot lift a
+quantity of electricity to <i>K</i>, without changing the distribution on <i>K</i> and the
+potential on <i>K</i>. Hence, the charges on <i>K</i> must be conceived as fixed, and so
+small a quantity raised that no appreciable change is produced by it. Taking
+the work thus expended as many times as the small quantity in question is
+contained in the unit of quantity, we shall obtain the potential. The potential
+of a body <i>K</i> may be briefly and precisely defined as follows: If we expend
+the element of work <i>dW</i> to raise the element of positive quantity <i>dQ</i> from the
+earth to the conductor, the potential of a conductor <i>K</i> will be given by <i>V</i> =
+<i>dW</i>/<i>dQ</i>.</p></div>
+
+<div class="footnote"><p><a name="Footnote_32_32" id="Footnote_32_32"></a><a href="#FNanchor_32_32"><span class="label">[32]</span></a> In this article the solidus or slant stroke is used for the usual fractional
+sign of division. Where plus or minus signs occur in the numerator or denominator,
+brackets or a vinculum is used.&mdash;<i>Tr.</i></p></div>
+
+<div class="footnote"><p><a name="Footnote_33_33" id="Footnote_33_33"></a><a href="#FNanchor_33_33"><span class="label">[33]</span></a> A sort of agreement exists between the notions of thermal and electrical
+capacity, but the difference between the two ideas also should be carefully
+borne in mind. The thermal capacity of a body depends solely upon that body
+itself. The electrical capacity of a body <i>K</i> is influenced by all bodies in its
+vicinity, inasmuch as the charge of these bodies is able to alter the potential
+of <i>K</i>. To give, therefore, an unequivocal significance to the notion of the capacity
+(<i>C</i>) of a body <i>K</i>, <i>C</i> is defined as the relation <i>Q</i>/<i>V</i> for the body <i>K</i> in a
+certain given position of all neighboring bodies, and during connexion of all
+neighboring conductors with the earth. In practice the situation is much
+simpler. The capacity, for example, of a jar, the inner coating of which is
+almost enveloped by its outer coating, communicating with the ground, is not
+sensibly affected by charged or uncharged adjacent conductors.</p></div>
+
+<div class="footnote"><p><a name="Footnote_34_34" id="Footnote_34_34"></a><a href="#FNanchor_34_34"><span class="label">[34]</span></a> These formulæ easily follow from Newton's theorem that a homogeneous
+spherical shell, whose elements obey the law of the inverse squares, exerts no
+force whatever on points within it but acts on points without as if the whole
+mass were concentrated at its centre. The formulæ next adduced also flow
+from this proposition.</p></div>
+
+<div class="footnote"><p><a name="Footnote_35_35" id="Footnote_35_35"></a><a href="#FNanchor_35_35"><span class="label">[35]</span></a> The energy of a sphere of radius <i>r</i> charged with the quantity <i>q</i> is
+1/2(<i>q</i><sup>2</sup>/<i>r</i>). If the radius increase by the space <i>dr</i> a loss of energy occurs, and
+the work done is 1/2(<i>q</i><sup>2</sup>/<i>r</i><sup>2</sup>)<i>dr</i>. Letting <i>p</i> denote the uniform electrical pressure
+on unit of surface of the sphere, the work done is also 4<i>r</i><sup>2</sup>&#960;<i>pdr</i>. Hence
+<i>p</i> = (1/8<i>r</i><sup>2</sup>&#960;)(<i>q</i><sup>2</sup>/<i>r</i><sup>2</sup>). Subjected to the same superficial pressure on all sides,
+say in a fluid, our half sphere would be an equilibrium. Hence we must make
+the pressure <i>p</i> act on the surface of the great circle to obtain the effect on the
+balance, which is <i>r</i><sup>2</sup>&#960;<i>p</i> = 1/8(<i>q</i><sup>2</sup>/<i>r</i><sup>2</sup>) = 1/8<i>V</i><sup>2</sup>.</p></div>
+
+<div class="footnote"><p><a name="Footnote_36_36" id="Footnote_36_36"></a><a href="#FNanchor_36_36"><span class="label">[36]</span></a> The arrangement described is for several reasons not fitted for the actual
+measurement of potential. Thomson's absolute electrometer is based upon
+an ingenious modification of the electrical balance of Harris and Volta. Of
+two large plane parallel plates, one communicates with the earth, while the
+other is brought to the potential to be measured. A small movable superficial
+portion <i>f</i> of this last hangs from the balance for the determination of the
+attraction <i>P</i>. The distance of the plates from each other being <i>D</i> we get <i>V</i> =
+<i>D</i>&#8730;(8&#960;<i>P</i>/<i>f</i>).</p></div>
+
+<div class="footnote"><p><a name="Footnote_37_37" id="Footnote_37_37"></a><a href="#FNanchor_37_37"><span class="label">[37]</span></a> This moment of torsion needs a supplementary correction, on account of
+the vertical electric attraction of the excited disks. This is done by changing
+the weight of the disk by means of additional weights and by making a second
+reading of the angles of deflexion.</p></div>
+
+<div class="footnote"><p><a name="Footnote_38_38" id="Footnote_38_38"></a><a href="#FNanchor_38_38"><span class="label">[38]</span></a> The jar in our experiment acts like an accumulator, being charged by a
+dynamo machine. The relation which obtains between the expended and the
+available work may be gathered from the following simple exposition. A
+Holtz machine <i>H</i> (Fig. 40) is charging a unit jar <i>L</i>, which after <i>n</i> discharges
+of quantity <i>q</i> and potential <i>v</i>, charges the jar <i>F</i> with the quantity <i>Q</i> at the potential
+<i>V</i>. The energy of the unit-jar discharges is lost and that of the jar <i>F</i>
+alone is left. Hence the ratio of the available work to the total work expended
+is
+</p>
+<p>
+<i>½QV/[½QV + (n/2)qv]</i> and as <i>Q</i> = <i>nq</i>, also <i>V/(V + v)</i>.
+</p>
+
+<p>
+If, now, we interpose no unit jar, still the parts of the machine and the wires
+of conduction are themselves virtually such unit jars and the formula still
+subsists <i>V</i>/(<i>V</i> + &#931;<i>v</i>), in which &#931;<i>v</i> represents the sum of all the successively introduced
+differences of potential in the circuit of connexion.</p></div>
+
+<div class="footnote"><p><a name="Footnote_39_39" id="Footnote_39_39"></a><a href="#FNanchor_39_39"><span class="label">[39]</span></a> Published in Vol. 5, No. I, of <i>The Monist</i>, October, 1894, being in part
+a re-elaboration of the treatise <i>Ueber die Erhaltung der Arbeit</i>, Prague, 1872.</p></div>
+
+<div class="footnote"><p><a name="Footnote_40_40" id="Footnote_40_40"></a><a href="#FNanchor_40_40"><span class="label">[40]</span></a> <i>On Matter, Living Force, and Heat</i>, Joule: <i>Scientific Papers</i>, London,
+1884, I, p. 265.</p></div>
+
+<div class="footnote"><p><a name="Footnote_41_41" id="Footnote_41_41"></a><a href="#FNanchor_41_41"><span class="label">[41]</span></a> "Atqui hoc si sit, globorum series sive corona eundem situm cum priore
+habebit, eademque de causa octo globi sinistri ponderosiores erunt sex dextris,
+ideoque rursus octo illi descendent, sex illi ascendent, istique globi ex sese
+<i>continuum et aeternum motum efficient, quod est falsum</i>."</p></div>
+
+<div class="footnote"><p><a name="Footnote_42_42" id="Footnote_42_42"></a><a href="#FNanchor_42_42"><span class="label">[42]</span></a> "A igitur, (si ullo modo per naturam fieri possit) locum sibi tributum
+non servato, ac delabatur in <i>D</i>; quibus positis aqua quae ipsi <i>A</i> succedit eandem
+ob causam deffluet in <i>D</i>, eademque ab alia istinc expelletur, atque adeo
+aqua haec (cum ubique eadem ratio sit) <i>motum instituet perpetuum, quod absurdum
+fuerit</i>."</p></div>
+
+<div class="footnote"><p><a name="Footnote_43_43" id="Footnote_43_43"></a><a href="#FNanchor_43_43"><span class="label">[43]</span></a> "Accipio, gradus velocitatis ejusdem mobilis super diversas planorum
+inclinationes acquisitos tunc esse aequales, cum eorundum planorum elevationes
+aequales sint."</p></div>
+
+<div class="footnote"><p><a name="Footnote_44_44" id="Footnote_44_44"></a><a href="#FNanchor_44_44"><span class="label">[44]</span></a> "Voi molto probabilmente discorrete, ma oltre al veri simile voglio con
+una esperienza crescer tanto la probabilità, che poco gli manchi all'agguagliarsi
+ad una ben necessaria dimostrazione. Figuratevi questo foglio essere
+una parete eretta all'orizzonte, e da un chiodo fitto in essa pendere una palla
+di piombo d'un'oncia, o due, sospesa dal sottil filo <i>AB</i> lungo due, o tre braccia
+perpendicolare all'orizzonte, e nella parete segnate una linea orizontale <i>DC</i>
+segante a squadra il perpendicolo <i>AB</i>, il quale sia lontano dalla parete due
+dita in circa, trasferendo poi il filo <i>AB</i> colla palla in <i>AC</i>, lasciata essa palla in
+libertà, la quale primieramente vedrete scendere descrivendo l'arco <i>CBD</i>, e
+di tanto trapassare il termine <i>B</i>, che scorrendo per l'arco <i>BD</i> sormonterà fino
+quasi alla segnata parallela <i>CD</i>, restando di per vernirvi per piccolissimo intervallo,
+toltogli il precisamente arrivarvi dall'impedimento dell'aria, e del
+filo. Dal che possiamo veracemente concludere, che l'impeto acquistato nel
+punto <i>B</i> dalla palla nello scendere per l'arco <i>CB</i>, fu tanto, che bastò a risospingersi
+per un simile arco <i>BD</i> alla medesima altezza; fatta, e più volte reiterata
+cotale esperienza, voglio, che fiechiamo nella parete rasente al perpendicolo
+<i>AB</i> un chiodo come in <i>E</i>, ovvero in <i>F</i>, che sporga in fuori cinque, o
+sei dita, e questo acciocchè il filo <i>AC</i> tornando come prima a riportar la palla
+<i>C</i> per l'arco <i>CB</i>, giunta che ella sia in <i>B</i>, inoppando il filo nel chiodo <i>E</i>, sia
+costretta a camminare per la circonferenza <i>BG</i> descritta in torno al centro <i>E</i>,
+dal che vedremo quello, che potrà far quel medesimo impeto, che dianzi concepizo
+nel medesimo termine <i>B</i>, sospinse l'istesso mobile per l'arco <i>ED</i> all'altezza
+dell'orizzonale <i>CD</i>. Ora, Signori, voi vedrete con gusto condursi la
+palla all'orizzontale nel punto <i>G</i>, e l'istesso accadere, l'intoppo si metesse
+più basso, come in <i>F</i>, dove la palla descriverebbe l'arco <i>BJ</i>, terminando sempre
+la sua salita precisamente nella linea <i>CD</i>, e quando l'intoppe del chiodo
+fusse tanto basso, che l'avanzo del filo sotto di lui non arivasse all'altezza di
+<i>CD</i> (il che accaderebbe, quando fusse più vicino al punto <i>B</i>, che al segamento
+dell' <i>AB</i> coll'orizzontale <i>CD</i>), allora il filo cavalcherebbe il chiodo, e
+segli avolgerebbe intorno. Questa esperienza non lascia luogo di dubitare
+della verità del supposto: imperocchè essendo li due archi <i>CB</i>, <i>DB</i> equali e
+similmento posti, l'acquisto di momento fatto per la scesa nell'arco <i>CB</i>, è il
+medesimo, che il fatto per la scesa dell'arco <i>DB</i>; ma il momento acquistato
+in <i>B</i> per l'arco <i>CB</i> è potente a risospingere in su il medesimo mobile per l'arco
+<i>BD</i>; adunque anco il momento acquistato nella scesa <i>DB</i> è eguale a quello,
+che sospigne l'istesso mobile pel medesimo arco da <i>B</i> in <i>D</i>, sicche universal-mente
+ogni memento acquistato per la scesa d'un arco è eguale a quello, che
+può far risalire l'istesso mobile pel medesimo arco: ma i momenti tutti che
+fanno resalire per tutti gli archi <i>BD</i>, <i>BG</i>, <i>BJ</i> sono eguali, poichè son fatti
+dal istesso medesimo momento acquistato per la scesa <i>CB</i>, come mostra
+l'esperienza: adunque tutti i momenti, che si acquistano per le scese negli
+archi <i>DB</i>, <i>GB</i>, <i>JB</i> sono eguali."</p></div>
+
+<div class="footnote"><p><a name="Footnote_45_45" id="Footnote_45_45"></a><a href="#FNanchor_45_45"><span class="label">[45]</span></a> "Constat jam, quod mobile ex quiete in <i>A</i> descendens per <i>AB</i>, gradus
+acquirit velocitatis juxta temporis ipsius incrementum: gradum vero in <i>B</i>
+esse maximum acquisitorum, et suapte natura immutabiliter impressum, sublatis
+scilicet causis accelerationis novae, aut retardationis: accelerationis inquam,
+si adhuc super extenso plano ulterius progrederetur; retardationis
+vero, dum super planum acclive <i>BC</i> fit reflexio: in horizontali autem <i>GH</i>
+aequabilis motus juxta gradum velocitatis ex <i>A</i> in <i>B</i> acquisitae in infinitum
+extenderetur."</p></div>
+
+<div class="footnote"><p><a name="Footnote_46_46" id="Footnote_46_46"></a><a href="#FNanchor_46_46"><span class="label">[46]</span></a> "Si gravitas non esset, neque aër motui corporum officeret, unumquodque
+eorum, acceptum semel motum continuaturum velocitate aequabili, secundum
+lineam rectam."</p></div>
+
+<div class="footnote"><p><a name="Footnote_47_47" id="Footnote_47_47"></a><a href="#FNanchor_47_47"><span class="label">[47]</span></a> "Si pondera quotlibet, vi gravitatis suae, moveri incipiant; non posse
+centrum gravitatis ex ipsis compositae altius, quam ubi incipiente motu reperiebatur,
+ascendere.
+</p>
+<p>
+"Ipsa vero hypothesis nostra quominus scrupulum moveat, nihil aliud
+sibi velle ostendemus, quam, quod nemo unquam negavit, gravia nempe sursum
+non ferri.&mdash;Et sane, si hac eadem uti scirent novorum operum machinatores,
+qui motum perpetuum irrito conatu moliuntur, facile suos ipsi errores
+deprehenderent, intelligerentque rem eam mechanica ratione haud quaquam
+possibilem esse."</p></div>
+
+<div class="footnote"><p><a name="Footnote_48_48" id="Footnote_48_48"></a><a href="#FNanchor_48_48"><span class="label">[48]</span></a> "Si pendulum e pluribus ponderibus compositum, atque e quiete dimissum,
+partem quamcunque oscillationis integrae confecerit, atque inde porro
+intelligantur pondera ejus singula, relicto communi vinculo, celeritates acquisitas
+sursum convertere, ac quousque possunt ascendere; hoc facto centrum
+gravitatis ex omnibus compositae, ad eandem altitudinem reversum erit, quam
+ante inceptam oscillationem obtinebat."</p></div>
+
+<div class="footnote"><p><a name="Footnote_49_49" id="Footnote_49_49"></a><a href="#FNanchor_49_49"><span class="label">[49]</span></a> "Notato autem hic illud staticum axioma etiam locum habere:
+</p>
+
+<div class="poem"><div class="stanza">
+<span class="i0">"Ut spatium agentis ad spatium patientis<br /></span>
+<span class="i0">Sic potentia patientis ad potentiam agentis."<br /></span>
+</div></div>
+</div>
+
+<div class="footnote"><p><a name="Footnote_50_50" id="Footnote_50_50"></a><a href="#FNanchor_50_50"><span class="label">[50]</span></a> "Cependant, comme dans cet ouvrage on ne fut d'abord attentif qu'à
+considérer ce beau développement de la mécanique qui semblait sortir tout
+entière d'une seule et même formule, on crut naturellement que la science etait
+faite, et qu'il ne restait plus qu'à chercher la démonstration du principe des
+vitesses virtuelles. Mais cette recherche ramena toutes les difficultés qu'on
+avait franchies par le principe même. Cette loi si générale, où se mêlent des
+idées vagues et étrangères de mouvements infinement petits et de perturbation
+d'équilibre, ne fit en quelque sorte que s'obsurcir à l'examen; et le livre de
+Lagrange n'offrant plus alors rien de clair que la marche des calculs, on vit
+bien que les nuages n'avaient paru levé sur le cours de la mécanique que
+parcequ'ils étaient, pour ainsi dire, rassemblés à l'origine même do cette
+science.
+</p>
+<p>
+"Une démonstration générale du principe des vitesses virtuelles devait
+au fond revenir a établir le mécanique entière sur une autre base: car la demonstration
+d'une loi qui embrasse toute une science ne peut être autre chose
+qua la reduction de cette science à une autre loi aussi générale, mais évidente,
+ou du moins plus simple que la première, et qui partant la rende inutile."</p></div>
+
+<div class="footnote"><p><a name="Footnote_51_51" id="Footnote_51_51"></a><a href="#FNanchor_51_51"><span class="label">[51]</span></a> <i>Traité de la lumière</i>, Leyden, 1690, p. 2.</p></div>
+
+<div class="footnote"><p><a name="Footnote_52_52" id="Footnote_52_52"></a><a href="#FNanchor_52_52"><span class="label">[52]</span></a> "L'on ne sçaurait douter que la lumière ne consiste dans le <i>mouvement</i> de
+certaine matière. Car soit qu'on regarde sa production, on trouve qu'içy sur
+la terre c'est principalement le feu et la flamme qui l'engendrent, lesquels
+contient sans doute des corps qui sont dans un mouvement rapide, puis qu'ils
+dissolvent et fondent plusieurs autres corps des plus solides: soit qu'on regarde
+ses effets, on voit que quand la lumière est ramasseé, comme par des
+miroires concaves, elle a la vertu de brûler comme le feu. c-est-à-dire qu'elle
+desunit les parties des corps; ce qui marque assurément du <i>mouvement</i>, au
+moins dans la <i>vraye Philosophie</i>, dans laquelle on conçoit la cause de tous les
+effets naturels par des raisons de <i>mechanique</i>. Ce qu'il faut faire à mon avis,
+ou bien renoncer à tout espérance de jamais rien comprendre dans la Physique."</p></div>
+
+<div class="footnote"><p><a name="Footnote_53_53" id="Footnote_53_53"></a><a href="#FNanchor_53_53"><span class="label">[53]</span></a> <i>Sur la puissance motrice du feu</i>. (Paris, 1824.)</p></div>
+
+<div class="footnote"><p><a name="Footnote_54_54" id="Footnote_54_54"></a><a href="#FNanchor_54_54"><span class="label">[54]</span></a> "On objectra peut-être ici que le mouvement perpétuel, démontré impossible
+par les <i>seules actions mécaniques</i>, ne l'est peut-être pas lorsqu'on
+emploie l'influence soit de la <i>chaleur</i>, soit de l'électricité; mais pent-on concevoir
+les phénomènes de la chaleur et de l'électricité comme dus à autre
+chose qu'à des <i>mouvements quelconques des corps</i> et comme tels ne doivent-ils
+pas être soumis aux lois générales de la mécanique?"</p></div>
+
+<div class="footnote"><p><a name="Footnote_55_55" id="Footnote_55_55"></a><a href="#FNanchor_55_55"><span class="label">[55]</span></a> By this is meant the temperature of a Celsius scale, the zero of which is
+273° below the melting-point of ice.</p></div>
+
+<div class="footnote"><p><a name="Footnote_56_56" id="Footnote_56_56"></a><a href="#FNanchor_56_56"><span class="label">[56]</span></a> I first drew attention to this fact in my treatise <i>Ueber die Erhaltung der
+Arbeit</i>, Prague, 1872. Before this, Zeuner had pointed out the analogy between
+mechanical and thermal energy. I have given a more extensive development
+of this idea in a communication to the <i>Sitzungsberichte der Wiener</i>
+<i>Akademie</i>, December, 1892, entitled <i>Geschichte und Kritik des Carnot'schen
+Wärmegesetzes</i>. Compare also the works of Popper (1884), Helm (1887),
+Wronsky (1888), and Ostwald (1892).</p></div>
+
+<div class="footnote"><p><a name="Footnote_57_57" id="Footnote_57_57"></a><a href="#FNanchor_57_57"><span class="label">[57]</span></a> Sir William Thomson first consciously and intentionally introduced
+(1848, 1851) a <i>mechanical</i> measure of temperature similar to the electric measure
+of potential.</p></div>
+
+<div class="footnote"><p><a name="Footnote_58_58" id="Footnote_58_58"></a><a href="#FNanchor_58_58"><span class="label">[58]</span></a> Compare my <i>Analysis of the Sensations</i>, Jena, 1886: English translation,
+Chicago, 1897.</p></div>
+
+<div class="footnote"><p><a name="Footnote_59_59" id="Footnote_59_59"></a><a href="#FNanchor_59_59"><span class="label">[59]</span></a> A better terminology appears highly desirable in the place of the usual
+misleading one. Sir William Thomson (1852) appears to have felt this need,
+and it has been clearly expressed by F. Wald (1889). We should call the work
+which corresponds to a vanished quantity of heat its mechanical substitution-value;
+while that work which can be <i>actually</i> performed in the passage of a
+thermal condition <i>A</i> to a condition <i>B</i>, alone deserves the name of the <i>energy-value</i>
+of this change of condition. In this way the <i>arbitrary</i> substantial conception
+of the processes would be preserved and misapprehensions forestalled.</p></div>
+
+<div class="footnote"><p><a name="Footnote_60_60" id="Footnote_60_60"></a><a href="#FNanchor_60_60"><span class="label">[60]</span></a> An address delivered before the anniversary meeting of the Imperial
+Academy of Sciences, at Vienna, May 25, 1882.</p></div>
+
+<div class="footnote"><p><a name="Footnote_61_61" id="Footnote_61_61"></a><a href="#FNanchor_61_61"><span class="label">[61]</span></a> <i>Primitive Culture.</i></p></div>
+
+<div class="footnote"><p><a name="Footnote_62_62" id="Footnote_62_62"></a><a href="#FNanchor_62_62"><span class="label">[62]</span></a> Tylor, <i>loc. cit.</i></p></div>
+
+<div class="footnote"><p><a name="Footnote_63_63" id="Footnote_63_63"></a><a href="#FNanchor_63_63"><span class="label">[63]</span></a> <i>Essai philosophique sur les probabilités</i>. 6th Ed. Paris, 1840, p. 4. The
+necessary consideration of the initial velocities is lacking in this formulation.</p></div>
+
+<div class="footnote"><p><a name="Footnote_64_64" id="Footnote_64_64"></a><a href="#FNanchor_64_64"><span class="label">[64]</span></a> <i>Principien der Wirthschaftslehre</i>, Vienna, 1873.</p></div>
+
+<div class="footnote"><p><a name="Footnote_65_65" id="Footnote_65_65"></a><a href="#FNanchor_65_65"><span class="label">[65]</span></a> It is clear from this that all so-called elementary (differential) laws involve
+a relation to the whole.</p></div>
+
+<div class="footnote"><p><a name="Footnote_66_66" id="Footnote_66_66"></a><a href="#FNanchor_66_66"><span class="label">[66]</span></a> If it be objected, that in the case of perturbations of the velocity of rotation
+of the earth, we could be sensible of such perturbations, and being obliged
+to have some measure of time, we should resort to the period of vibration of
+the waves of sodium light,&mdash;all that this would show is that for practical reasons
+we should select that event which best served us as the <i>simplest</i> common
+measure of the others.</p></div>
+
+<div class="footnote"><p><a name="Footnote_67_67" id="Footnote_67_67"></a><a href="#FNanchor_67_67"><span class="label">[67]</span></a> Measurement, in fact, is the definition of one phenomenon by another
+(standard) phenomenon.</p></div>
+
+<div class="footnote"><p><a name="Footnote_68_68" id="Footnote_68_68"></a><a href="#FNanchor_68_68"><span class="label">[68]</span></a> I have represented the point of view here taken for more than thirty
+years and developed it in various writings (<i>Erhaltung der Arbeit</i>, 1872, parts
+of which are published in the article on <i>The Conservation of Energy</i> in this
+collection; <i>The Forms of Liquids</i>, 1872, also published in this collection; and
+the <i>Bewegungsempfindungen</i>, 1875). The idea, though known to philosophers,
+is unfamiliar to the majority of physicists. It is a matter of deep regret to me,
+therefore, that the title and author of a small tract which accorded with my
+views in numerous details and which I remember having caught a glance of
+in a very busy period (1879-1880), have so completely disappeared from my
+memory that all efforts to obtain a clue to them have hitherto been fruitless.</p></div>
+
+<div class="footnote"><p><a name="Footnote_69_69" id="Footnote_69_69"></a><a href="#FNanchor_69_69"><span class="label">[69]</span></a> Inaugural Address, delivered on assuming the Rectorate of the University
+of Prague, October 18, 1883.
+</p>
+<p>
+The idea presented in this essay is neither new nor remote. I have touched
+upon it myself on several occasions (first in 1867), but have never made it the
+subject of a formal disquisition. Doubtless, others, too, have treated it; it
+lies, so to speak, in the air. However, as many of my illustrations were well
+received, although known only in an imperfect form from the lecture itself
+and the newspapers, I have, contrary to my original intention, decided to
+publish it. It is not my intention to trespass here upon the domain of biology.
+My statements are to be taken merely as the expression of the fact that no one
+can escape the influence of a great and far-reaching idea.</p></div>
+
+<div class="footnote"><p><a name="Footnote_70_70" id="Footnote_70_70"></a><a href="#FNanchor_70_70"><span class="label">[70]</span></a> At first sight an apparent contradiction arises from the admission of both
+heredity and adaptation; and it is undoubtedly true that a strong disposition
+to heredity precludes great capability of adaptation. But imagine the organism
+to be a plastic mass which retains the form transmitted to it by former
+influences until new influences modify it; the <i>one</i> property of <i>plasticity</i> will
+then represent capability of adaptation as well as power of heredity. Analogous
+to this is the case of a bar of magnetised steel of high coercive force:
+the steel retains its magnetic properties until a new force displaces them.
+Take also a body in motion: the body retains the velocity acquired in (<i>inherited</i>
+from) the interval of time just preceding, except it be changed in the
+next moment by an accelerating force. In the case of the body in motion the
+<i>change</i> of velocity (<i>Abänderung</i>) was looked upon as a matter of course, while
+the discovery of the principle of <i>inertia</i> (or persistence) created surprise; in
+Darwin's case, on the contrary, <i>heredity</i> (or persistence) was taken for granted,
+while the principle of <i>variation</i> (<i>Abänderung</i>) appeared novel.
+</p>
+<p>
+Fully adequate views are, of course, to be reached only by a study of the
+original facts emphasised by Darwin, and not by these analogies. The example
+referring to motion, if I am not mistaken, I first heard, in conversation,
+from my friend J. Popper, Esq., of Vienna.
+</p>
+<p>
+Many inquirers look upon the stability of the species as something settled,
+and oppose to it the Darwinian theory. But the stability of the species is itself
+a "theory." The essential modifications which Darwin's views also are
+undergoing will be seen from the works of Wallace [and Weismann], but more
+especially from a book of W. H. Rolph, <i>Biologische Probleme</i>, Leipsic, 1882.
+Unfortunately, this last talented investigator is no longer numbered among
+the living.</p></div>
+
+<div class="footnote"><p><a name="Footnote_71_71" id="Footnote_71_71"></a><a href="#FNanchor_71_71"><span class="label">[71]</span></a> Written in 1883.</p></div>
+
+<div class="footnote"><p><a name="Footnote_72_72" id="Footnote_72_72"></a><a href="#FNanchor_72_72"><span class="label">[72]</span></a> See Pfaundler, <i>Pogg. Ann., Jubelband</i>, p. 182.</p></div>
+
+<div class="footnote"><p><a name="Footnote_73_73" id="Footnote_73_73"></a><a href="#FNanchor_73_73"><span class="label">[73]</span></a> See the beautiful discussions of this point in Hering's <i>Memory as a General
+Function of Organised Matter</i> (1870), Chicago, The Open Court Publishing
+Co., 1887. Compare also Dubois, <i>Ueber die Uebung</i>, Berlin, 1881.</p></div>
+
+<div class="footnote"><p><a name="Footnote_74_74" id="Footnote_74_74"></a><a href="#FNanchor_74_74"><span class="label">[74]</span></a> Spencer, <i>The Principles of Psychology</i>. London, 1872.</p></div>
+
+<div class="footnote"><p><a name="Footnote_75_75" id="Footnote_75_75"></a><a href="#FNanchor_75_75"><span class="label">[75]</span></a> See the article <i>The Velocity of Light</i>, page 63.</p></div>
+
+<div class="footnote"><p><a name="Footnote_76_76" id="Footnote_76_76"></a><a href="#FNanchor_76_76"><span class="label">[76]</span></a> I am well aware that the endeavor to confine oneself in natural research
+to <i>facts</i> is often censured as an exaggerated fear of metaphysical spooks.
+But I would observe, that, judged by the mischief which they have wrought,
+the metaphysical, of all spooks, are the least fabulous. It is not to be denied
+that many forms of thought were not originally acquired by the individual, but
+were antecedently formed, or rather prepared for, in the development of the
+species, in some such way as Spencer, Haeckel, Hering, and others have
+supposed, and as I myself have hinted on various occasions.</p></div>
+
+<div class="footnote"><p><a name="Footnote_77_77" id="Footnote_77_77"></a><a href="#FNanchor_77_77"><span class="label">[77]</span></a> Compare, for example, <i>Schiller, Zerstreute Betrachtungen über verschiedene
+ästhetische Gegenstände</i>.</p></div>
+
+<div class="footnote"><p><a name="Footnote_78_78" id="Footnote_78_78"></a><a href="#FNanchor_78_78"><span class="label">[78]</span></a> We must not be deceived in imagining that the happiness of other people
+is not a very considerable and essential portion of our own. It is common
+capital, which cannot be created by the individual, and which does not perish
+with him. The formal and material limitation of the <i>ego</i> is necessary and sufficient
+only for the crudest practical objects, and cannot subsist in a broad conception.
+Humanity in its entirety may be likened to a polyp-plant. The
+material and organic bonds of individual union have, indeed, been severed;
+they would only have impeded freedom of movement and evolution. But the
+ultimate aim, the psychical connexion of the whole, has been attained in a
+much higher degree through the richer development thus made possible.</p></div>
+
+<div class="footnote"><p><a name="Footnote_79_79" id="Footnote_79_79"></a><a href="#FNanchor_79_79"><span class="label">[79]</span></a> C. E. von Baer, the subsequent opponent of Darwin and Haeckel, has
+discussed in two beautiful addresses (<i>Das allgemeinste Gesetz der Natur in
+aller Entwickelung</i>, and <i>Welche Auffassung der lebenden Natur ist die richtige,
+und wie ist diese Auffassung auf die Entomologie anzuwenden</i>?) the
+narrowness of the view which regards an animal in its existing state as
+finished and complete, instead of conceiving it as a phase in the series of evolutionary
+forms and regarding the species itself as a phase of the development
+of the animal world in general.</p></div>
+
+<div class="footnote"><p><a name="Footnote_80_80" id="Footnote_80_80"></a><a href="#FNanchor_80_80"><span class="label">[80]</span></a> An address delivered before the General Session of the German Association
+of Naturalists and Physicians, at Vienna, Sept. 24, 1894.</p></div>
+
+<div class="footnote"><p><a name="Footnote_81_81" id="Footnote_81_81"></a><a href="#FNanchor_81_81"><span class="label">[81]</span></a> Inaugural lecture delivered on assuming the Professorship of the History
+and Theory of Inductive Science in the University of Vienna, October
+21, 1895.</p></div>
+
+<div class="footnote"><p><a name="Footnote_82_82" id="Footnote_82_82"></a><a href="#FNanchor_82_82"><span class="label">[82]</span></a> The phrase is, <i>Er hat das Pulver nicht erfunden</i>.</p></div>
+
+<div class="footnote"><p><a name="Footnote_83_83" id="Footnote_83_83"></a><a href="#FNanchor_83_83"><span class="label">[83]</span></a> "Quod si quis tanta industria exstitisset, ut ex naturae principiis at geometria
+hanc rem eruere potuisset, eum ego supra mortalium sortem ingenio
+valuisse dicendum crederem. Sed hoc tantum abest, ut fortuito reperti artificii
+rationem non adhuc satis explicari potuerint viri doctissimi."&mdash;Hugenii
+Dioptrica (de telescopiis).</p></div>
+
+<div class="footnote"><p><a name="Footnote_84_84" id="Footnote_84_84"></a><a href="#FNanchor_84_84"><span class="label">[84]</span></a> I must not be understood as saying that the fire-drill has played no part
+in the worship of fire or of the sun.</p></div>
+
+<div class="footnote"><p><a name="Footnote_85_85" id="Footnote_85_85"></a><a href="#FNanchor_85_85"><span class="label">[85]</span></a> Compare on this point the extremely interesting remarks of Dr. Paul
+Carus in his <i>Philosophy of the Tool</i>, Chicago, 1893.</p></div>
+
+<div class="footnote"><p><a name="Footnote_86_86" id="Footnote_86_86"></a><a href="#FNanchor_86_86"><span class="label">[86]</span></a> Möbius, <i>Naturwissenschaftlicher Verein für Schleswig-Holstein</i>, Kiel,
+1893, p. 113 et seq.</p></div>
+
+<div class="footnote"><p><a name="Footnote_87_87" id="Footnote_87_87"></a><a href="#FNanchor_87_87"><span class="label">[87]</span></a> I am indebted for this observation to Professor Hatscheck.</p></div>
+
+<div class="footnote"><p><a name="Footnote_88_88" id="Footnote_88_88"></a><a href="#FNanchor_88_88"><span class="label">[88]</span></a> Cf. Hoppe, <i>Entdecken und Finden</i>, 1870.</p></div>
+
+<div class="footnote"><p><a name="Footnote_89_89" id="Footnote_89_89"></a><a href="#FNanchor_89_89"><span class="label">[89]</span></a> See the lecture "Sensations of Orientation," p. 282 et seq.</p></div>
+
+<div class="footnote"><p><a name="Footnote_90_90" id="Footnote_90_90"></a><a href="#FNanchor_90_90"><span class="label">[90]</span></a> This story was related to me by Jolly, and subsequently repeated in a
+letter from him.</p></div>
+
+<div class="footnote"><p><a name="Footnote_91_91" id="Footnote_91_91"></a><a href="#FNanchor_91_91"><span class="label">[91]</span></a> I do not know whether Swift's academy of schemers in Lagado, in
+which great discoveries and inventions were made by a sort of verbal game
+of dice, was intended as a satire on Francis Bacon's method of making discoveries
+by means of huge synoptic tables constructed by scribes. It certainly
+would not have been ill-placed.</p></div>
+
+<div class="footnote"><p><a name="Footnote_92_92" id="Footnote_92_92"></a><a href="#FNanchor_92_92"><span class="label">[92]</span></a> "Crescunt disciplinae lente tardeque; per varios errores sero pervenitur
+ad veritatem. Omnia praeparata esse debent diuturno et assiduo labore
+ad introitum veritatis novae. Jam illa certo temporis momento divina quadam
+necessitate coacta emerget."
+</p>
+<p>
+Quoted by Simony, <i>In ein ringförmiges Band einen Knoten zu machen</i>,
+Vienna, 1881, p. 41.</p></div>
+
+<div class="footnote"><p><a name="Footnote_93_93" id="Footnote_93_93"></a><a href="#FNanchor_93_93"><span class="label">[93]</span></a> A lecture delivered on February 24, 1897, before the <i>Verein zur Verbreitung
+naturwissenschaftlicher Kenntnisse in Wien</i>.</p></div>
+
+<div class="footnote"><p><a name="Footnote_94_94" id="Footnote_94_94"></a><a href="#FNanchor_94_94"><span class="label">[94]</span></a> Wollaston, <i>Philosophical Transactions, Royal Society</i>, 1810. In the same
+place Wollaston also describes and explains the creaking of the muscles.
+My attention was recently called to this work by Dr. W. Pascheles.&mdash;Cf. also
+Purkinje, <i>Prager medicin</i>. <i>Jahrbücher</i>, Bd. 6, Wien, 1820.</p></div>
+
+<div class="footnote"><p><a name="Footnote_95_95" id="Footnote_95_95"></a><a href="#FNanchor_95_95"><span class="label">[95]</span></a> Similarly many external forces do not act at once on all parts of the
+earth, and the internal forces which produce deformations act at first immediately
+only upon limited parts. If the earth were a feeling being, the tides
+and other terrestrial events would provoke in it similar sensations to those
+of our movements. Perhaps the slight alterations of the altitude of the
+pole which are at present being studied are connected with the continual
+slight deformations of the central ellipsoid occasioned by seismical happenings.</p></div>
+
+<div class="footnote"><p><a name="Footnote_96_96" id="Footnote_96_96"></a><a href="#FNanchor_96_96"><span class="label">[96]</span></a> For the popular explanation by unconscious inference the matter is extremely
+simple. We regard the railway carriage as vertical and unconsciously
+infer the inclination of the trees. Of course the opposite conclusion that we
+regard the trees as vertical and infer the inclination of the carriage, unfortunately,
+is equally clear on this theory.</p></div>
+
+<div class="footnote"><p><a name="Footnote_97_97" id="Footnote_97_97"></a><a href="#FNanchor_97_97"><span class="label">[97]</span></a> It will be observed that my way of thinking and experimenting here is
+related to that which led Knight to the discovery and investigation of the
+geotropism of plants. <i>Philosophical Transactions</i>, January 9, 1806. The relations
+between vegetable and animal geotropism have been more recently investigated
+by J. Loeb.</p></div>
+
+<div class="footnote"><p><a name="Footnote_98_98" id="Footnote_98_98"></a><a href="#FNanchor_98_98"><span class="label">[98]</span></a> This experiment is doubtless related to the galvanotropic experiment
+with the larvæ of frogs described ten years later by L. Hermann. Compare
+on this point my remarks in the <i>Anzeiger der Wiener Akademie</i>, 1886, No. 21.
+Recent experiments in galvanotropism are due to J. Loeb.</p></div>
+
+<div class="footnote"><p><a name="Footnote_99_99" id="Footnote_99_99"></a><a href="#FNanchor_99_99"><span class="label">[99]</span></a> <i>Wiener Akad.</i>, 6 November, 1873.</p></div>
+
+<div class="footnote"><p><a name="Footnote_100_100" id="Footnote_100_100"></a><a href="#FNanchor_100_100"><span class="label">[100]</span></a> <i>Wiener Gesellschaft der Aerzte</i>, 14 November, 1874.</p></div>
+
+<div class="footnote"><p><a name="Footnote_101_101" id="Footnote_101_101"></a><a href="#FNanchor_101_101"><span class="label">[101]</span></a> I have made a contribution to this last question in my <i>Analysis of the
+Sensations</i>, (1886), English translation, 1897.</p></div>
+
+<div class="footnote"><p><a name="Footnote_102_102" id="Footnote_102_102"></a><a href="#FNanchor_102_102"><span class="label">[102]</span></a> In my <i>Grundlinien der Lehre von den Bewegungsempfindungen</i>, 1875,
+the matter occupying lines 4 to 13 of page 20 from below, which rests on an
+error, is, as I have also elsewhere remarked, to be stricken out. For another
+experiment related to that of Foucault, compare my <i>Mechanics</i>, p. 303.</p></div>
+
+<div class="footnote"><p><a name="Footnote_103_103" id="Footnote_103_103"></a><a href="#FNanchor_103_103"><span class="label">[103]</span></a> <i>Anzeiger der Wiener Akad.</i>, 30 December, 1875.</p></div>
+
+<div class="footnote"><p><a name="Footnote_104_104" id="Footnote_104_104"></a><a href="#FNanchor_104_104"><span class="label">[104]</span></a> The experiment was specially interesting for me as I had already attempted
+in 1874, although with very little confidence and without success, to
+excite electromagnetically my own labyrinth through which I had caused a
+current to pass.</p></div>
+
+<div class="footnote"><p><a name="Footnote_105_105" id="Footnote_105_105"></a><a href="#FNanchor_105_105"><span class="label">[105]</span></a> Perhaps the discussion concerning the peculiarity of cats always falling
+on their feet, which occupied the Parisian Academy, and, incidentally, Parisian
+society a few years ago, will be remembered here. I believe that the
+questions which arose are disposed of by the considerations advanced in my
+<i>Bewegungsempfindungen</i> (1875). I also partly gave, as early as 1866, the apparatus
+conceived by the Parisian scientists to illustrate the phenomena in
+question. One difficulty was left untouched in the Parisian debate. The
+otolith apparatus of the cat can render it no service in <i>free</i> descent. The
+cat, however, while at rest, doubtless knows its position in space and is instinctively
+conscious of the amount of movement which will put it on its feet.</p></div>
+
+<div class="footnote"><p><a name="Footnote_106_106" id="Footnote_106_106"></a><a href="#FNanchor_106_106"><span class="label">[106]</span></a> See the Appendix to the English edition of my <i>Analysis of the Sensations</i>,
+Chicago, 1897.</p></div>
+
+<div class="footnote"><p><a name="Footnote_107_107" id="Footnote_107_107"></a><a href="#FNanchor_107_107"><span class="label">[107]</span></a> Compare my <i>Analysis of Sensations</i>, p. 123 ff.</p></div>
+
+<div class="footnote"><p><a name="Footnote_108_108" id="Footnote_108_108"></a><a href="#FNanchor_108_108"><span class="label">[108]</span></a> E. H. Weber, <i>De aure et auditu hominis et animalium</i>, Lipsiae, 1820.</p></div>
+
+<div class="footnote"><p><a name="Footnote_109_109" id="Footnote_109_109"></a><a href="#FNanchor_109_109"><span class="label">[109]</span></a> Störensen, <i>Journ. Anat. Phys.</i>, London, Vol. 29 (1895).</p></div>
+
+<div class="footnote"><p><a name="Footnote_110_110" id="Footnote_110_110"></a><a href="#FNanchor_110_110"><span class="label">[110]</span></a> A lecture delivered on Nov. 10, 1897.</p></div>
+
+<div class="footnote"><p><a name="Footnote_111_111" id="Footnote_111_111"></a><a href="#FNanchor_111_111"><span class="label">[111]</span></a> Christiansen, <i>Wiedemann's Annalen</i>, XXIII. S. 298, XXIV., p. 439 (1884-1885).</p></div>
+
+<div class="footnote"><p><a name="Footnote_112_112" id="Footnote_112_112"></a><a href="#FNanchor_112_112"><span class="label">[112]</span></a> The German phrase is <i>Schlierenmethode</i>, by which term the method is
+known even by American physicists. It is also called in English the "shadow-method."
+But a term is necessary which will cover all the derivatives, and
+so we have employed alternatively the words <i>striate</i> and <i>differential</i>. The
+etymology of <i>schlieren</i>, it would seem, is uncertain. Its present use is derived
+from its technological signification in glass-manufacturing, where by <i>die
+Schlieren</i> are meant the wavy streaks and imperfections in glass. Hence its
+application to the method for detecting small optical <i>differences</i> and faults
+generally. Professor Crew of Evanston suggests to the translator that <i>schlieren</i>
+may be related to our <i>slur</i> (L. G., <i>slüren</i>, to trail, to draggle), a conjecture
+which is doubtless correct and agrees both with the meaning of <i>schlieren</i> as
+given in the large German dictionaries and with the intransitive use of our
+own verb <i>slur</i>, the faults in question being conceived as "trailings," "streakings,"
+etc.&mdash;<i>Trans.</i></p></div>
+
+<div class="footnote"><p><a name="Footnote_113_113" id="Footnote_113_113"></a><a href="#FNanchor_113_113"><span class="label">[113]</span></a> An address delivered before the Congress of Delegates of the German
+Realschulmännerverein, at Dortmund, April 16, 1886. The full title of the
+address reads: "On the Relative Educational Value of the Classics and the
+Mathematico-Physical Sciences in Colleges and High Schools."
+</p>
+<p>
+Although substantially contained in an address which I was to have made
+at the meeting of Natural Scientists at Salzburg in 1881 (deferred on account
+of the Paris Exposition), and in the Introduction to a course of lectures on
+"Physical Instruction in Preparatory Schools," which I delivered in 1883, the
+invitation of the German Realschulmännerverein afforded me the first opportunity
+of putting my views upon this subject before a large circle of readers.
+Owing to the place and circumstances of delivery, my remarks apply of course,
+primarily, only to German schools, but, with slight modifications, made in
+this translation, are not without force for the institutions of other countries.
+In giving here expression to a strong personal conviction formed long ago, it
+is a matter of deep satisfaction to me to find that they agree in many points
+with the views recently advanced in independent form by Paulsen (<i>Geschichte
+des gelehrten Unterrichts</i>, Leipsic, 1885) and Frary (<i>La question du latin</i>,
+Paris, Cerf, 1885). It is not my desire nor effort here to say much that is new,
+but merely to contribute my mite towards bringing about the inevitable revolution
+now preparing in the world of elementary instruction. In the opinion
+of experienced educationists the first result of that revolution will be to make
+Greek and mathematics alternately optional subjects in the higher classes of
+the German Gymnasium and in the corresponding institutions of other countries,
+as has been done in the splendid system of instruction in Denmark. The
+gap between the German classical Gymnasium and the German Realgymnasium,
+or between classical and scientific schools generally, can thus be bridged
+over, and the remaining inevitable transformations will then be accomplished
+in relative peace and quiet. (Prague, May, 1886.)</p></div>
+
+<div class="footnote"><p><a name="Footnote_114_114" id="Footnote_114_114"></a><a href="#FNanchor_114_114"><span class="label">[114]</span></a> Maupertuis, <i>&OElig;uvres</i>, Dresden, 1752, p. 339.</p></div>
+
+<div class="footnote"><p><a name="Footnote_115_115" id="Footnote_115_115"></a><a href="#FNanchor_115_115"><span class="label">[115]</span></a> F. Paulsen, <i>Geschichte des gelehrten Unterrichts</i>, Leipsic, 1885.</p></div>
+
+<div class="footnote"><p><a name="Footnote_116_116" id="Footnote_116_116"></a><a href="#FNanchor_116_116"><span class="label">[116]</span></a> There is a peculiar irony of fate in the fact that while Leibnitz was casting
+about for a new vehicle of universal linguistic intercourse, the Latin language
+which still subserved this purpose the best of all, was dropping more
+and more out of use, and that Leibnitz himself contributed not the least to
+this result.</p></div>
+
+<div class="footnote"><p><a name="Footnote_117_117" id="Footnote_117_117"></a><a href="#FNanchor_117_117"><span class="label">[117]</span></a> As a rule, the human brain is too much, and wrongly, burdened with
+things which might be more conveniently and accurately preserved in books
+where they could be found at a moment's notice. In a recent letter to me
+from Düsseldorf, Judge Hartwich writes:
+</p>
+<p>
+"A host of words exist which are out and out Latin or Greek, yet are employed
+with perfect correctness by people of good education who never had
+the good luck to be taught the ancient languages. For example, words like
+'dynasty.' ... The child learns such words as parts of the common stock of
+speech, or even as parts of his mother-tongue, just as he does the words
+'father,' 'mother,' 'bread,' 'milk.' Does the ordinary mortal know the etymology
+of these Saxon words? Did it not require the almost incredible
+industry of the Grimms and other Teutonic philologists to throw the merest
+glimmerings of light upon the origin and growth of our own mother-tongue?
+Besides, do not thousands of people of so-called classical education use
+every moment hosts of words of foreign origin whose derivation they do not
+know? Very few of them think it worth while to look up such words in the
+dictionaries, although they love to maintain that people should study the
+ancient languages for the sake of etymology alone."</p></div>
+
+<div class="footnote"><p><a name="Footnote_118_118" id="Footnote_118_118"></a><a href="#FNanchor_118_118"><span class="label">[118]</span></a> Standing remote from the legal profession I should not have ventured to
+declare that the study of Greek was not necessary for the jurists; yet this
+view was taken in the debate that followed this lecture by professional jurists
+of high standing. According to this opinion, the preparatory education obtained
+in the German Realgymnasium would also be sufficient for the future
+jurists and insufficient only for theologians and philologists. [In England and
+America not only is Greek not necessary, but the law-Latin is so peculiar that
+even persons of <i>good</i> classical education cannot understand it.&mdash;<i>Tr.</i>]</p></div>
+
+<div class="footnote"><p><a name="Footnote_119_119" id="Footnote_119_119"></a><a href="#FNanchor_119_119"><span class="label">[119]</span></a> In emphasising here the weak sides of the writings of Plato and Aristotle,
+forced on my attention while reading them in German translations, I, of
+course, have no intention of underrating the great merits and the high historical
+importance of these two men. Their importance must not be measured
+by the fact that our speculative philosophy still moves to a great extent
+in their paths of thought. The more probable conclusion is that this branch
+has made very little progress in the last two thousand years. Natural science
+also was implicated for centuries in the meshes of the Aristotelian thought,
+and owes its rise mainly to having thrown off those fetters.</p></div>
+
+<div class="footnote"><p><a name="Footnote_120_120" id="Footnote_120_120"></a><a href="#FNanchor_120_120"><span class="label">[120]</span></a> I would not for a moment contend that we derive exactly the same profit
+from reading a Greek author in a translation as from reading him in the original;
+but the difference, the excess of gain in the second case, appears to me,
+and probably will to most men who are not professional philologists, to be
+too dearly bought with the expenditure of eight years of valuable time.</p></div>
+
+<div class="footnote"><p><a name="Footnote_121_121" id="Footnote_121_121"></a><a href="#FNanchor_121_121"><span class="label">[121]</span></a> "The temptation," Judge Hartwich writes, "to regard the 'taste' of the
+ancients as so lofty and unsurpassable appears to me to have its chief origin
+in the fact that the ancients were unexcelled in the representation of the
+nude. First, by their unremitting care of the human body they produced
+splendid models; and secondly, in their gymnasiums and in their athletic
+games they had these models constantly before their eyes. No wonder, then,
+that their statues still excite our admiration! For the form, the ideal of the
+human body has not changed in the course of the centuries. But with intellectual
+matters it is totally different; they change from century to century,
+nay, from decennium to decennium. It is very natural now, that people
+should unconsciously apply what is thus so easily seen, namely, the works of
+sculpture, as a universal criterion of the highly developed taste of the ancients&mdash;a
+fallacy against which people cannot, in my judgment, be too strongly
+warned."</p></div>
+
+<div class="footnote"><p><a name="Footnote_122_122" id="Footnote_122_122"></a><a href="#FNanchor_122_122"><span class="label">[122]</span></a> English: "In the beginning God created the heaven and the earth.
+And the earth was without form and void; and darkness was upon the face
+of the deep. And the spirit of God moved upon the face of the waters."&mdash;Dutch:
+"In het begin schiep God den hemel en de aarde. De aarde nu was
+woest en ledig, en duisternis was op den afgrond; en de Geest Gods zwefde
+op de wateren."&mdash;Danish: "I Begyndelsen skabte Gud Himmelen og Jorden.
+Og Jorden var ode og tom, og der var morkt ovenover Afgrunden, og
+Guds Aand svoevede ovenover Vandene."&mdash;Swedish: "I begynnelsen skapade
+Gud Himmel och Jord. Och Jorden war öde och tom, och mörker war
+pä djupet, och Gods Ande swäfde öfwer wattnet."&mdash;German: "Am Anfang
+schuf Gott Himmel und Erde. Und die Erde war wüst und leer, und es war
+finster auf der Tiefe; und der Geist Gottes schwebte auf dem Wasser."</p></div>
+
+<div class="footnote"><p><a name="Footnote_123_123" id="Footnote_123_123"></a><a href="#FNanchor_123_123"><span class="label">[123]</span></a> Compare Herzen's excellent remarks, <i>De l'enseignement secondaire dans
+la Suisse romande</i>, Lausanne, 1886.</p></div>
+
+<div class="footnote"><p><a name="Footnote_124_124" id="Footnote_124_124"></a><a href="#FNanchor_124_124"><span class="label">[124]</span></a> <i>Geschichte der Mathematik</i>, Leipsic, 1874.</p></div>
+
+<div class="footnote"><p><a name="Footnote_125_125" id="Footnote_125_125"></a><a href="#FNanchor_125_125"><span class="label">[125]</span></a> <i>Geometrische Analyse</i>, Ulm, 1886.</p></div>
+
+<div class="footnote"><p><a name="Footnote_126_126" id="Footnote_126_126"></a><a href="#FNanchor_126_126"><span class="label">[126]</span></a> In his text-books of elementary mathematics</p></div>
+
+<div class="footnote"><p><a name="Footnote_127_127" id="Footnote_127_127"></a><a href="#FNanchor_127_127"><span class="label">[127]</span></a> <i>Abhandlungen aus dem Gebiete der Mathematik</i>, Würzburg, 1883.</p></div>
+
+<div class="footnote"><p><a name="Footnote_128_128" id="Footnote_128_128"></a><a href="#FNanchor_128_128"><span class="label">[128]</span></a> My idea here is an appropriate selection of readings from Galileo, Huygens,
+Newton, etc. The choice is so easily made that there can be no question
+of difficulties. The contents would be discussed with the students, and
+the original experiments performed with them. Those scholars alone should
+receive this instruction in the upper classes who did not look forward to systematical
+instruction in the physical sciences. I do not make this proposition
+of reform here for the first time. I have no doubt, moreover, that such radical
+changes will only be slowly introduced.</p></div>
+
+<div class="footnote"><p><a name="Footnote_129_129" id="Footnote_129_129"></a><a href="#FNanchor_129_129"><span class="label">[129]</span></a> <i>Die Mathematik als Lehrgegenstand des Gymnasiums</i>, Berlin, 1883.</p></div>
+
+<div class="footnote"><p><a name="Footnote_130_130" id="Footnote_130_130"></a><a href="#FNanchor_130_130"><span class="label">[130]</span></a> Wrong as it is to burden future physicians and scientists with Greek for
+the sake of the theologians and philologists, it would be just as wrong to compel
+theologians and philologists, on account of the physicians, to study such
+subjects as analytical geometry. Moreover, I cannot believe that ignorance
+of analytical geometry would be a serious hindrance to a physician that was
+otherwise well versed in quantitative thought. No special advantage generally
+is observable in the graduates of the Austrian gymnasiums, all of whom have
+studied analytical geometry. [Refers to an assertion of Dubois-Reymond.]</p></div>
+
+<div class="footnote"><p><a name="Footnote_131_131" id="Footnote_131_131"></a><a href="#FNanchor_131_131"><span class="label">[131]</span></a> Compare M. Cantor, <i>Geschichte der Mathematik</i>, Leipsic, 1880, Vol. I. p.
+193.</p></div>
+
+<div class="footnote"><p><a name="Footnote_132_132" id="Footnote_132_132"></a><a href="#FNanchor_132_132"><span class="label">[132]</span></a> Compare Paulsen, <i>l. c.</i>, pp. 607, 688.</p></div>
+
+<div class="footnote"><p><a name="Footnote_133_133" id="Footnote_133_133"></a><a href="#FNanchor_133_133"><span class="label">[133]</span></a> It is to be hoped that the Americans will jealously guard their schools
+and universities against the influence of the State.</p></div>
+
+<div class="footnote"><p><a name="Footnote_134_134" id="Footnote_134_134"></a><a href="#FNanchor_134_134"><span class="label">[134]</span></a> This article, which appeared in the Proceedings of the German Mathematical
+Society of Prague for the year 1892, is printed as a supplement to the
+article on "The Causes of Harmony," at page 32.</p></div>
+
+<div class="footnote"><p><a name="Footnote_135_135" id="Footnote_135_135"></a><a href="#FNanchor_135_135"><span class="label">[135]</span></a> The present exposition is taken from the volumes for 1700 (published in
+1703) and for 1701 (published in 1704), and partly also from the <i>Histoire de
+l'Académie</i> and partly from the <i>Mémoires</i>. Sauveur's later works enter less
+into consideration here.</p></div>
+
+<div class="footnote"><p><a name="Footnote_136_136" id="Footnote_136_136"></a><a href="#FNanchor_136_136"><span class="label">[136]</span></a> Euler, <i>Tentamen novae theoriae musicae</i>, Petropoli, 1739.</p></div>
+
+<div class="footnote"><p><a name="Footnote_137_137" id="Footnote_137_137"></a><a href="#FNanchor_137_137"><span class="label">[137]</span></a> In attempting to perform his experiment of beats before the Academy,
+Sauveur was not quite successful. <i>Histoire de l'Académie</i>, Année 1700, p. 136.</p></div>
+
+<div class="footnote"><p><a name="Footnote_138_138" id="Footnote_138_138"></a><a href="#FNanchor_138_138"><span class="label">[138]</span></a> <i>Histoire de l'Académie</i>, Année 1701, p. 134.</p></div>
+
+<div class="footnote"><p><a name="Footnote_139_139" id="Footnote_139_139"></a><a href="#FNanchor_139_139"><span class="label">[139]</span></a> <i>Ibid.</i>, p. 298.</p></div>
+
+<div class="footnote"><p><a name="Footnote_140_140" id="Footnote_140_140"></a><a href="#FNanchor_140_140"><span class="label">[140]</span></a> <i>Histoire de l'Académie</i>, Année 1702, p. 91.</p></div>
+
+<div class="footnote"><p><a name="Footnote_141_141" id="Footnote_141_141"></a><a href="#FNanchor_141_141"><span class="label">[141]</span></a> From the <i>Histoire de l'Académie</i>, Année 1700, p. 139.</p></div>
+
+<div class="footnote"><p><a name="Footnote_142_142" id="Footnote_142_142"></a><a href="#FNanchor_142_142"><span class="label">[142]</span></a> Because all octaves in use in music offer too great differences of rates
+of vibration.</p></div>
+
+<div class="footnote"><p><a name="Footnote_143_143" id="Footnote_143_143"></a><a href="#FNanchor_143_143"><span class="label">[143]</span></a> "Les battemens ne plaisent pas à l'Oreille, à cause de l'inégalité du son,
+et l'on peut croire avec beaucoup d'apparence que ce qui rend les Octaves si
+agréables, c'est qu'on n'y entend jamais de battemens.
+</p>
+<p>
+"En suivant cette idée, on trouve que les accords dont on ne peut entendre
+les battemens, sont justement ceux que les Musiciens traitent de Consonances,
+et que ceux dont les battemens se font sentir, sont les Dissonances, et que
+quand un accord est Dissonance dans une certaine octave et Consonance
+dans une autre, c'est qu'il bat dans l'une, et qu'il ne bat pas dans l'autre.
+Aussi est il traité de Consonance imparfaite. Il est fort aisé par les principes
+de Mr. Sauveur qu'on a établis ici, de voir quels accords battent, et dans
+quelles Octaves au-dessus on au-dessous du son fixe. Si cette hypothèse est
+vraye, elle découvrira la véritable source des Règles de la composition, inconnue
+jusqu'à présent à la Philosophie, qui s'en remettait presque entièrement
+au jugement de l'Oreille. Ces sortes de jugemens naturels, quelque
+bisarres qu'ils paroissent quelquefois, ne le sont point, ils ont des causes
+très réelles, dont la connaissance appartient à la Philosophie, pourvue qu'elle
+s'en puisse mettre en possession."</p></div>
+
+<div class="footnote"><p><a name="Footnote_144_144" id="Footnote_144_144"></a><a href="#FNanchor_144_144"><span class="label">[144]</span></a> <i>Harmonics or the Philosophy of Musical Sounds</i>, Cambridge, 1749. I saw
+this book only hastily in 1864 and drew attention to it in a work published in
+1866. I did not come into its actual possession until three years ago and then
+only did I learn its exact contents.</p></div>
+
+<div class="footnote"><p><a name="Footnote_145_145" id="Footnote_145_145"></a><a href="#FNanchor_145_145"><span class="label">[145]</span></a> <i>Harmonics</i>, pp. 118 and 243.</p></div>
+
+<div class="footnote"><p><a name="Footnote_146_146" id="Footnote_146_146"></a><a href="#FNanchor_146_146"><span class="label">[146]</span></a> "Short cycle" is the period in which the same phases of the two co-operant
+tones are repeated.</p></div>
+
+<div class="footnote"><p><a name="Footnote_147_147" id="Footnote_147_147"></a><a href="#FNanchor_147_147"><span class="label">[147]</span></a> This article, designed to illustrate historically that on Symmetry, at
+page 89, first appeared in Fichte's <i>Zeitschrift für Philosophie</i>, for 1865.</p></div>
+
+<div class="footnote"><p><a name="Footnote_148_148" id="Footnote_148_148"></a><a href="#FNanchor_148_148"><span class="label">[148]</span></a> Comp. Cornelius, <i>Ueber das Sehen</i>; Wundt, <i>Theorie der Sinneswahrnehmung</i>.</p></div>
+
+<div class="footnote"><p><a name="Footnote_149_149" id="Footnote_149_149"></a><a href="#FNanchor_149_149"><span class="label">[149]</span></a> Comp. Mach, <i>Ueber das Sehen von Lagen and Winkeln</i>. <i>Sitzungsb. der
+Wiener Akademie</i>, 1861.</p></div>
+
+<div class="footnote"><p><a name="Footnote_150_150" id="Footnote_150_150"></a><a href="#FNanchor_150_150"><span class="label">[150]</span></a> Comp. Mach, <i>Zur Theorie des Gehörorgans</i>. <i>Sitsungsber, der Wiener
+Akad.</i>, 1863.&mdash;<i>Ueber einige Erscheinungen der physiolog. Akustik.</i> <i>Ibid.</i>, 1864.</p></div>
+
+
+
+
+
+
+
+
+
+<pre>
+
+
+
+
+
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diff --git a/LICENSE.txt b/LICENSE.txt
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+This eBook, including all associated images, markup, improvements,
+metadata, and any other content or labor, has been confirmed to be
+in the PUBLIC DOMAIN IN THE UNITED STATES.
+
+Procedures for determining public domain status are described in
+the "Copyright How-To" at https://www.gutenberg.org.
+
+No investigation has been made concerning possible copyrights in
+jurisdictions other than the United States. Anyone seeking to utilize
+this eBook outside of the United States should confirm copyright
+status under the laws that apply to them.
diff --git a/README.md b/README.md
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+Project Gutenberg (https://www.gutenberg.org) public repository for
+eBook #39508 (https://www.gutenberg.org/ebooks/39508)
author	Roger Frank <rfrank@pglaf.org>	2025-10-14 20:12:57 -0700
committer	Roger Frank <rfrank@pglaf.org>	2025-10-14 20:12:57 -0700
commit	fd160cc57b7185c689d615b757c84cbf98ee9ce4 (patch)
tree	e415054a3f519bc3ec93125ab81a8ea279c4a0ef