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diff --git a/8172-0.txt b/8172-0.txt new file mode 100644 index 0000000..f5b7558 --- /dev/null +++ b/8172-0.txt @@ -0,0 +1,5273 @@ +The Project Gutenberg EBook of History of Astronomy, by George Forbes + +This eBook is for the use of anyone anywhere in the United States and most +other parts of the world 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. If you are not located in the United States, you'll have +to check the laws of the country where you are located before using this ebook. + +Title: History of Astronomy + +Author: George Forbes + +Release Date: June 25, 2003 [EBook #8172] +[Most recently updated: March 21, 2020] + +Language: English + +Character set encoding: UTF-8 + +*** START OF THIS PROJECT GUTENBERG EBOOK HISTORY OF ASTRONOMY *** + + + + +Produced by Jonathan Ingram, Dave Maddock, Charles Franks +and the Online Distributed Proofreading Team. + + + + +[Illustration: SIR ISAAC NEWTON +(From the bust by Roubiliac In Trinity College, Cambridge.)] + + + + +HISTORY OF ASTRONOMY +BY +GEORGE FORBES, +M.A., F.R.S., M. INST. C. E., + +(FORMERLY PROFESSOR OF NATURAL PHILOSOPHY, ANDERSON’S +COLLEGE, GLASGOW) + +AUTHOR OF “THE TRANSIT OF VENUS,” RENDU’S +“THEORY OF THE GLACIERS OF SAVOY,” ETC., ETC. + + + + +CONTENTS + + PREFACE + + BOOK I. THE GEOMETRICAL PERIOD + 1. PRIMITIVE ASTRONOMY AND ASTROLOGY + 2. ANCIENT ASTRONOMY—CHINESE AND CHALDÆANS + 3. ANCIENT GREEK ASTRONOMY + 4. THE REIGN OF EPICYCLES—FROM PTOLEMY TO COPERNICUS + + BOOK II. THE DYNAMICAL PERIOD + 5. DISCOVERY OF THE TRUE SOLAR SYSTEM—TYCHO BRAHE—KEPLER + 6. GALILEO AND THE TELESCOPE—NOTIONS OF GRAVITY BY HORROCKS, ETC. + 7. SIR ISAAC NEWTON—LAW OF UNIVERSAL GRAVITATION + 8. NEWTON’S SUCCESSORS—HALLEY, EULER, LAGRANGE, +LAPLACE, ETC. + 9. DISCOVERY OF NEW PLANETS—HERSCHEL, PIAZZI, ADAMS, +AND LE VERRIER + + BOOK III. OBSERVATION + 10. INSTRUMENTS OF PRECISION—SIZE OF THE SOLAR SYSTEM + 11. HISTORY OF THE TELESCOPE—SPECTROSCOPE + + BOOK IV. THE PHYSICAL PERIOD + 12. THE SUN + 13. THE MOON AND PLANETS + 14. COMETS AND METEORS + 15. THE STARS AND NEBULÆ + + ILLUSTRATIONS + INDEX + + + + +PREFACE + + +An attempt has been made in these pages to trace the evolution of +intellectual thought in the progress of astronomical discovery, and, by +recognising the different points of view of the different ages, to give +due credit even to the ancients. No one can expect, in a history of +astronomy of limited size, to find a treatise on “practical” or on +“theoretical astronomy,” nor a complete “descriptive astronomy,” and +still less a book on “speculative astronomy.” Something of each of +these is essential, however, for tracing the progress of thought and +knowledge which it is the object of this History to describe. + +The progress of human knowledge is measured by the increased habit of +looking at facts from new points of view, as much as by the +accumulation of facts. The mental capacity of one age does not seem to +differ from that of other ages; but it is the imagination of new points +of view that gives a wider scope to that capacity. And this is +cumulative, and therefore progressive. Aristotle viewed the solar +system as a geometrical problem; Kepler and Newton converted the point +of view into a dynamical one. Aristotle’s mental capacity to understand +the meaning of facts or to criticise a train of reasoning may have been +equal to that of Kepler or Newton, but the point of view was different. + +Then, again, new points of view are provided by the invention of new +methods in that system of logic which we call mathematics. All that +mathematics can do is to assure us that a statement A is equivalent to +statements B, C, D, or is one of the facts expressed by the statements +B, C, D; so that we may know, if B, C, and D are true, then A is true. +To many people our inability to understand all that is contained in +statements B, C, and D, without the cumbrous process of a mathematical +demonstration, proves the feebleness of the human mind as a logical +machine. For it required the new point of view imagined by Newton’s +analysis to enable people to see that, so far as planetary orbits are +concerned, Kepler’s three laws (B, C, D) were identical with Newton’s +law of gravitation (A). No one recognises more than the mathematical +astronomer this feebleness of the human intellect, and no one is more +conscious of the limitations of the logical process called mathematics, +which even now has not solved directly the problem of only three +bodies. + +These reflections, arising from the writing of this History, go to +explain the invariable humility of the great mathematical astronomers. +Newton’s comparison of himself to the child on the seashore applies to +them all. As each new discovery opens up, it may be, boundless oceans +for investigation, for wonder, and for admiration, the great +astronomers, refusing to accept mere hypotheses as true, have founded +upon these discoveries a science as exact in its observation of facts +as in theories. So it is that these men, who have built up the most +sure and most solid of all the sciences, refuse to invite others to +join them in vain speculation. The writer has, therefore, in this short +History, tried to follow that great master, Airy, whose pupil he was, +and the key to whose character was exactness and accuracy; and he +recognises that Science is impotent except in her own limited sphere. + +It has been necessary to curtail many parts of the History in the +attempt—perhaps a hopeless one—to lay before the reader in a limited +space enough about each age to illustrate its tone and spirit, the +ideals of the workers, the gradual addition of new points of view and +of new means of investigation. + +It would, indeed, be a pleasure to entertain the hope that these pages +might, among new recruits, arouse an interest in the greatest of all +the sciences, or that those who have handled the theoretical or +practical side might be led by them to read in the original some of the +classics of astronomy. Many students have much compassion for the +schoolboy of to-day, who is not allowed the luxury of learning the art +of reasoning from him who still remains pre-eminently its greatest +exponent, Euclid. These students pity also the man of to-morrow, who is +not to be allowed to read, in the original Latin of the brilliant +Kepler, how he was able—by observations taken from a moving platform, +the earth, of the directions of a moving object, Mars—to deduce the +exact shape of the path of each of these planets, and their actual +positions on these paths at any time. Kepler’s masterpiece is one of +the most interesting books that was ever written, combining wit, +imagination, ingenuity, and certainty. + +Lastly, it must be noted that, as a History of England cannot deal with +the present Parliament, so also the unfinished researches and untested +hypotheses of many well-known astronomers of to-day cannot be included +among the records of the History of Astronomy. The writer regrets the +necessity that thus arises of leaving without mention the names of many +who are now making history in astronomical work. + +G. F. + +_August_ 1_st_, 1909. + + + + +BOOK I. THE GEOMETRICAL PERIOD + +1. PRIMITIVE ASTRONOMY AND ASTROLOGY. + + +The growth of intelligence in the human race has its counterpart in +that of the individual, especially in the earliest stages. Intellectual +activity and the development of reasoning powers are in both cases +based upon the accumulation of experiences, and on the comparison, +classification, arrangement, and nomenclature of these experiences. +During the infancy of each the succession of events can be watched, but +there can be no _à priori_ anticipations. Experience alone, in both +cases, leads to the idea of cause and effect as a principle that seems +to dominate our present universe, as a rule for predicting the course +of events, and as a guide to the choice of a course of action. This +idea of cause and effect is the most potent factor in developing the +history of the human race, as of the individual. + +In no realm of nature is the principle of cause and effect more +conspicuous than in astronomy; and we fall into the habit of thinking +of its laws as not only being unchangeable in our universe, but +necessary to the conception of any universe that might have been +substituted in its place. The first inhabitants of the world were +compelled to accommodate their acts to the daily and annual +alternations of light and darkness and of heat and cold, as much as to +the irregular changes of weather, attacks of disease, and the fortune +of war. They soon came to regard the influence of the sun, in +connection with light and heat, as a cause. This led to a search for +other signs in the heavens. If the appearance of a comet was sometimes +noted simultaneously with the death of a great ruler, or an eclipse +with a scourge of plague, these might well be looked upon as causes in +the same sense that the veering or backing of the wind is regarded as a +cause of fine or foul weather. + +For these reasons we find that the earnest men of all ages have +recorded the occurrence of comets, eclipses, new stars, meteor showers, +and remarkable conjunctions of the planets, as well as plagues and +famines, floods and droughts, wars and the deaths of great rulers. +Sometimes they thought they could trace connections which might lead +them to say that a comet presaged famine, or an eclipse war. + +Even if these men were sometimes led to evolve laws of cause and effect +which now seem to us absurd, let us be tolerant, and gratefully +acknowledge that these astrologers, when they suggested such “working +hypotheses,” were laying the foundations of observation and deduction. + +If the ancient Chaldæans gave to the planetary conjunctions an +influence over terrestrial events, let us remember that in our own time +people have searched for connection between terrestrial conditions and +periods of unusual prevalence of sun spots; while De la Rue, Loewy, and +Balfour Stewart[1] thought they found a connection between sun-spot +displays and the planetary positions. Thus we find scientific men, even +in our own time, responsible for the belief that storms in the Indian +Ocean, the fertility of German vines, famines in India, and high or low +Nile-floods in Egypt follow the planetary positions. + +And, again, the desire to foretell the weather is so laudable that we +cannot blame the ancient Greeks for announcing the influence of the +moon with as much confidence as it is affirmed in Lord Wolseley’s +_Soldier’s Pocket Book_. + +Even if the scientific spirit of observation and deduction (astronomy) +has sometimes led to erroneous systems for predicting terrestrial +events (astrology), we owe to the old astronomer and astrologer alike +the deepest gratitude for their diligence in recording astronomical +events. For, out of the scanty records which have survived the +destructive acts of fire and flood, of monarchs and mobs, we have found +much that has helped to a fuller knowledge of the heavenly motions than +was possible without these records. + +So Hipparchus, about 150 B.C., and Ptolemy a little later, were able to +use the observations of Chaldæan astrologers, as well as those of +Alexandrian astronomers, and to make some discoveries which have helped +the progress of astronomy in all ages. So, also, Mr. Cowell[2] has +examined the marks made on the baked bricks used by the Chaldæans for +recording the eclipses of 1062 B.C. and 762 B.C.; and has thereby been +enabled, in the last few years, to correct the lunar tables of Hansen, +and to find a more accurate value for the secular acceleration of the +moon’s longitude and the node of her orbit than any that could be +obtained from modern observations made with instruments of the highest +precision. + +So again, Mr. Hind[3] was enabled to trace back the period during which +Halley’s comet has been a member of the solar system, and to identify +it in the Chinese observations of comets as far back as 12 B.C. Cowell +and Cromellin extended the date to 240 B.C. In the same way the comet +1861.i. has been traced back in the Chinese records to 617 A.D.[4] + +The theoretical views founded on Newton’s great law of universal +gravitation led to the conclusion that the inclination of the earth’s +equator to the plane of her orbit (the obliquity of the ecliptic) has +been diminishing slowly since prehistoric times; and this fact has been +confirmed by Egyptian and Chinese observations on the length of the +shadow of a vertical pillar, made thousands of years before the +Christian era, in summer and winter. + +There are other reasons why we must be tolerant of the crude notions of +the ancients. The historian, wishing to give credit wherever it may be +due, is met by two difficulties. Firstly, only a few records of very +ancient astronomy are extant, and the authenticity of many of these is +open to doubt. Secondly, it is very difficult to divest ourselves of +present knowledge, and to appreciate the originality of thought +required to make the first beginnings. + +With regard to the first point, we are generally dependent upon +histories written long after the events. The astronomy of Egyptians, +Babylonians, and Assyrians is known to us mainly through the Greek +historians, and for information about the Chinese we rely upon the +researches of travellers and missionaries in comparatively recent +times. The testimony of the Greek writers has fortunately been +confirmed, and we now have in addition a mass of facts translated from +the original sculptures, papyri, and inscribed bricks, dating back +thousands of years. + +In attempting to appraise the efforts of the beginners we must remember +that it was natural to look upon the earth (as all the first +astronomers did) as a circular plane, surrounded and bounded by the +heaven, which was a solid vault, or hemisphere, with its concavity +turned downwards. The stars seemed to be fixed on this vault; the moon, +and later the planets, were seen to crawl over it. It was a great step +to look on the vault as a hollow sphere carrying the sun too. It must +have been difficult to believe that at midday the stars are shining as +brightly in the blue sky as they do at night. It must have been +difficult to explain how the sun, having set in the west, could get +back to rise in the east without being seen _if_ it was always the same +sun. It was a great step to suppose the earth to be spherical, and to +ascribe the diurnal motions to its rotation. Probably the greatest step +ever made in astronomical theory was the placing of the sun, moon, and +planets at different distances from the earth instead of having them +stuck on the vault of heaven. It was a transition from “flatland” to a +space of three dimensions. + +Great progress was made when systematic observations began, such as +following the motion of the moon and planets among the stars, and the +inferred motion of the sun among the stars, by observing their +_heliacal risings_—i.e., the times of year when a star would first be +seen to rise at sunrise, and when it could last be seen to rise at +sunset. The grouping of the stars into constellations and recording +their places was a useful observation. The theoretical prediction of +eclipses of the sun and moon, and of the motions of the planets among +the stars, became later the highest goal in astronomy. + +To not one of the above important steps in the progress of astronomy +can we assign the author with certainty. Probably many of them were +independently taken by Chinese, Indian, Persian, Tartar, Egyptian, +Babylonian, Assyrian, Phoenician, and Greek astronomers. And we have +not a particle of information about the discoveries, which may have +been great, by other peoples—by the Druids, the Mexicans, and the +Peruvians, for example. + +We do know this, that all nations required to have a calendar. The +solar year, the lunar month, and the day were the units, and it is +owing to their incommensurability that we find so many calendars +proposed and in use at different times. The only object to be attained +by comparing the chronologies of ancient races is to fix the actual +dates of observations recorded, and this is not a part of a history of +astronomy. + +In conclusion, let us bear in mind the limited point of view of the +ancients when we try to estimate their merit. Let us remember that the +first astronomy was of two dimensions; the second astronomy was of +three dimensions, but still purely geometrical. Since Kepler’s day we +have had a dynamical astronomy. + +FOOTNOTES: + + [1] Trans. R. S. E., xxiii. 1864, p. 499, _On Sun Spots_, _etc_., by + B. Stewart. Also Trans. R. S. 1860-70. Also Prof. Ernest Brown, in _R. + A. S. Monthly Notices_, 1900. + + [2] _R. A. S. Monthly Notices_, Sup.; 1905. + +[Illustration: CHALDÆAN BAKED BRICK OR TABLET, +_Obverse and reverse sides_, Containing record of solar eclipse, 1062 +B.C., used lately by Cowell for rendering the lunar theory more +accurate than was possible by finest modern observations. (British +Museum collection, No. 35908.)] + + [3] _R. A. S. Monthly Notices_, vol. x., p. 65. + + [4] R. S. E. Proc., vol. x., 1880. + + + + +2. ANCIENT ASTRONOMY—THE CHINESE AND CHALDÆANS. + + +The last section must have made clear the difficulties the way of +assigning to the ancient nations their proper place in the development +of primitive notions about astronomy. The fact that some alleged +observations date back to a period before the Chinese had invented the +art of writing leads immediately to the question how far tradition can +be trusted. + +Our first detailed knowledge was gathered in the far East by +travellers, and by the Jesuit priests, and was published in the +eighteenth century. The Asiatic Society of Bengal contributed +translations of Brahmin literature. The two principal sources of +knowledge about Chinese astronomy were supplied, first by Father +Souciet, who in 1729 published _Observations Astronomical, +Geographical, Chronological, and Physical_, drawn from ancient Chinese +books; and later by Father Moyriac-de-Mailla, who in 1777-1785 +published _Annals of the Chinese Empire, translated from +Tong-Kien-Kang-Mou_. + +Bailly, in his _Astronomie Ancienne_ (1781), drew, from these and other +sources, the conclusion that all we know of the astronomical learning +of the Chinese, Indians, Chaldæans, Assyrians, and Egyptians is but the +remnant of a far more complete astronomy of which no trace can be +found. + +Delambre, in his _Histoire de l’Astronomie Ancienne_ (1817), ridicules +the opinion of Bailly, and considers that the progress made by all of +these nations is insignificant. + +It will be well now to give an idea of some of the astronomy of the +ancients not yet entirely discredited. China and Babylon may be taken +as typical examples. + +_China_.—It would appear that Fohi, the first emperor, reigned about +2952 B.C., and shortly afterwards Yu-Chi made a sphere to represent the +motions of the celestial bodies. It is also mentioned, in the book +called Chu-King, supposed to have been written in 2205 B.C., that a +similar sphere was made in the time of Yao (2357 B.C.).[1] It is said +that the Emperor Chueni (2513 B.C.) saw five planets in conjunction the +same day that the sun and moon were in conjunction. This is discussed +by Father Martin (MSS. of De Lisle); also by M. Desvignolles (Mem. +Acad. Berlin, vol. iii., p. 193), and by M. Kirsch (ditto, vol. v., p. +19), who both found that Mars, Jupiter, Saturn, and Mercury were all +between the eleventh and eighteenth degrees of Pisces, all visible +together in the evening on February 28th 2446 B.C., while on the same +day the sun and moon were in conjunction at 9 a.m., and that on March +1st the moon was in conjunction with the other four planets. But this +needs confirmation. + +Yao, referred to above, gave instructions to his astronomers to +determine the positions of the solstices and equinoxes, and they +reported the names of the stars in the places occupied by the sun at +these seasons, and in 2285 B.C. he gave them further orders. If this +account be true, it shows a knowledge that the vault of heaven is a +complete sphere, and that stars are shining at mid-day, although +eclipsed by the sun’s brightness. + +It is also asserted, in the book called _Chu-King_, that in the time of +Yao the year was known to have 365¼ days, and that he adopted 365 days +and added an intercalary day every four years (as in the Julian +Calendar). This may be true or not, but the ancient Chinese certainly +seem to have divided the circle into 365 degrees. To learn the length +of the year needed only patient observation—a characteristic of the +Chinese; but many younger nations got into a terrible mess with their +calendar from ignorance of the year’s length. + +It is stated that in 2159 B.C. the royal astronomers Hi and Ho failed +to predict an eclipse. It probably created great terror, for they were +executed in punishment for their neglect. If this account be true, it +means that in the twenty-second century B.C. some rule for calculating +eclipses was in use. Here, again, patient observation would easily lead +to the detection of the eighteen-year cycle known to the Chaldeans as +the _Saros_. It consists of 235 lunations, and in that time the pole of +the moon’s orbit revolves just once round the pole of the ecliptic, and +for this reason the eclipses in one cycle are repeated with very slight +modification in the next cycle, and so on for many centuries. + +It may be that the neglect of their duties by Hi and Ho, and their +punishment, influenced Chinese astronomy; or that the succeeding +records have not been available to later scholars; but the fact remains +that—although at long intervals observations were made of eclipses, +comets, and falling stars, and of the position of the solstices, and of +the obliquity of the ecliptic—records become rare, until 776 B.C., when +eclipses began to be recorded once more with some approach to +continuity. Shortly afterwards notices of comets were added. Biot gave +a list of these, and Mr. John Williams, in 1871, published +_Observations of Comets from 611 B.C. to 1640 A.D., Extracted from the +Chinese Annals_. + +With regard to those centuries concerning which we have no astronomical +Chinese records, it is fair to state that it is recorded that some +centuries before the Christian era, in the reign of Tsin-Chi-Hoang, all +the classical and scientific books that could be found were ordered to +be destroyed. If true, our loss therefrom is as great as from the +burning of the Alexandrian library by the Caliph Omar. He burnt all the +books because he held that they must be either consistent or +inconsistent with the Koran, and in the one case they were superfluous, +in the other case objectionable. + +_Chaldæans_.—Until the last half century historians were accustomed to +look back upon the Greeks, who led the world from the fifth to the +third century B.C., as the pioneers of art, literature, and science. +But the excavations and researches of later years make us more ready to +grant that in science as in art the Greeks only developed what they +derived from the Egyptians, Babylonians, and Assyrians. The Greek +historians said as much, in fact; and modern commentators used to +attribute the assertion to undue modesty. Since, however, the records +of the libraries have been unearthed it has been recognised that the +Babylonians were in no way inferior in the matter of original +scientific investigation to other races of the same era. + +The Chaldæans, being the most ancient Babylonians, held the same +station and dignity in the State as did the priests in Egypt, and spent +all their time in the study of philosophy and astronomy, and the arts +of divination and astrology. They held that the world of which we have +a conception is an eternal world without any beginning or ending, in +which all things are ordered by rules supported by a divine providence, +and that the heavenly bodies do not move by chance, nor by their own +will, but by the determinate will and appointment of the gods. They +recorded these movements, but mainly in the hope of tracing the will of +the gods in mundane affairs. Ptolemy (about 130 A.D.) made use of +Babylonian eclipses in the eighth century B.C. for improving his solar +and lunar tables. + +Fragments of a library at Agade have been preserved at Nineveh, from +which we learn that the star-charts were even then divided into +constellations, which were known by the names which they bear to this +day, and that the signs of the zodiac were used for determining the +courses of the sun, moon, and of the five planets Mercury, Venus, Mars, +Jupiter, and Saturn. + +We have records of observations carried on under Asshurbanapal, who +sent astronomers to different parts to study celestial phenomena. Here +is one:— + +To the Director of Observations,—My Lord, his humble servant +Nabushum-iddin, Great Astronomer of Nineveh, writes thus: “May Nabu and +Marduk be propitious to the Director of these Observations, my Lord. +The fifteenth day we observed the Node of the moon, and the moon was +eclipsed.” + +The Phoenicians are supposed to have used the stars for navigation, but +there are no records. The Egyptian priests tried to keep such +astronomical knowledge as they possessed to themselves. It is probable +that they had arbitrary rules for predicting eclipses. All that was +known to the Greeks about Egyptian science is to be found in the +writings of Diodorus Siculus. But confirmatory and more authentic facts +have been derived from late explorations. Thus we learn from E. B. +Knobel[2] about the Jewish calendar dates, on records of land sales in +Aramaic papyri at Assuan, translated by Professor A. H. Sayce and A. E. +Cowley, (1) that the lunar cycle of nineteen years was used by the Jews +in the fifth century B.C. [the present reformed Jewish calendar dating +from the fourth century A.D.], a date a “little more than a century +after the grandfathers and great-grandfathers of those whose business +is recorded had fled into Egypt with Jeremiah” (Sayce); and (2) that +the order of intercalation at that time was not dissimilar to that in +use at the present day. + +Then again, Knobel reminds us of “the most interesting discovery a few +years ago by Father Strassmeier of a Babylonian tablet recording a +partial lunar eclipse at Babylon in the seventh year of Cambyses, on +the fourteenth day of the Jewish month Tammuz.” Ptolemy, in the +Almagest (Suntaxis), says it occurred in the seventh year of Cambyses, +on the night of the seventeenth and eighteenth of the Egyptian month +Phamenoth. Pingré and Oppolzer fix the date July 16th, 533 B.C. Thus +are the relations of the chronologies of Jews and Egyptians established +by these explorations. + +FOOTNOTES: + + [1] These ancient dates are uncertain. + + [2] _R. A. S. Monthly Notices_, vol. lxviii., No. 5, March, 1908. + + + + +3. ANCIENT GREEK ASTRONOMY. + + +We have our information about the earliest Greek astronomy from +Herodotus (born 480 B.C.). He put the traditions into writing. Thales +(639-546 B.C.) is said to have predicted an eclipse, which caused much +alarm, and ended the battle between the Medes and Lydians. Airy fixed +the date May 28th, 585 B.C. But other modern astronomers give different +dates. Thales went to Egypt to study science, and learnt from its +priests the length of the year (which was kept a profound secret!), and +the signs of the zodiac, and the positions of the solstices. He held +that the sun, moon, and stars are not mere spots on the heavenly vault, +but solids; that the moon derives her light from the sun, and that this +fact explains her phases; that an eclipse of the moon happens when the +earth cuts off the sun’s light from her. He supposed the earth to be +flat, and to float upon water. He determined the ratio of the sun’s +diameter to its orbit, and apparently made out the diameter correctly +as half a degree. He left nothing in writing. + +His successors, Anaximander (610-547 B.C.) and Anaximenes (550-475 +B.C.), held absurd notions about the sun, moon, and stars, while +Heraclitus (540-500 B.C.) supposed that the stars were lighted each +night like lamps, and the sun each morning. Parmenides supposed the +earth to be a sphere. + +Pythagoras (569-470 B.C.) visited Egypt to study science. He deduced +his system, in which the earth revolves in an orbit, from fantastic +first principles, of which the following are examples: “The circular +motion is the most perfect motion,” “Fire is more worthy than earth,” +“Ten is the perfect number.” He wrote nothing, but is supposed to have +said that the earth, moon, five planets, and fixed stars all revolve +round the sun, which itself revolves round an imaginary central fire +called the Antichthon. Copernicus in the sixteenth century claimed +Pythagoras as the founder of the system which he, Copernicus, revived. + +Anaxagoras (born 499 B.C.) studied astronomy in Egypt. He explained the +return of the sun to the east each morning by its going under the flat +earth in the night. He held that in a solar eclipse the moon hides the +sun, and in a lunar eclipse the moon enters the earth’s shadow—both +excellent opinions. But he entertained absurd ideas of the vortical +motion of the heavens whisking stones into the sky, there to be ignited +by the fiery firmament to form stars. He was prosecuted for this +unsettling opinion, and for maintaining that the moon is an inhabited +earth. He was defended by Pericles (432 B.C.). + +Solon dabbled, like many others, in reforms of the calendar. The common +year of the Greeks originally had 360 days—twelve months of thirty +days. Solon’s year was 354 days. It is obvious that these erroneous +years would, before long, remove the summer to January and the winter +to July. To prevent this it was customary at regular intervals to +intercalate days or months. Meton (432 B.C.) introduced a reform based +on the nineteen-year cycle. This is not the same as the Egyptian and +Chaldean eclipse cycle called _Saros_ of 223 lunations, or a little +over eighteen years. The Metonic cycle is 235 lunations or nineteen +years, after which period the sun and moon occupy the same position +relative to the stars. It is still used for fixing the date of Easter, +the number of the year in Melon’s cycle being the golden number of our +prayer-books. Melon’s system divided the 235 lunations into months of +thirty days and omitted every sixty-third day. Of the nineteen years, +twelve had twelve months and seven had thirteen months. + +Callippus (330 B.C.) used a cycle four times as long, 940 lunations, +but one day short of Melon’s seventy-six years. This was more correct. + +Eudoxus (406-350 B.C.) is said to have travelled with Plato in Egypt. +He made astronomical observations in Asia Minor, Sicily, and Italy, and +described the starry heavens divided into constellations. His name is +connected with a planetary theory which as generally stated sounds most +fanciful. He imagined the fixed stars to be on a vault of heaven; and +the sun, moon, and planets to be upon similar vaults or spheres, +twenty-six revolving spheres in all, the motion of each planet being +resolved into its components, and a separate sphere being assigned for +each component motion. Callippus (330 B.C.) increased the number to +thirty-three. It is now generally accepted that the real existence of +these spheres was not suggested, but the idea was only a mathematical +conception to facilitate the construction of tables for predicting the +places of the heavenly bodies. + +Aristotle (384-322 B.C.) summed up the state of astronomical knowledge +in his time, and held the earth to be fixed in the centre of the world. + +Nicetas, Heraclides, and Ecphantes supposed the earth to revolve on its +axis, but to have no orbital motion. + +The short epitome so far given illustrates the extraordinary deductive +methods adopted by the ancient Greeks. But they went much farther in +the same direction. They seem to have been in great difficulty to +explain how the earth is supported, just as were those who invented the +myth of Atlas, or the Indians with the tortoise. Thales thought that +the flat earth floated on water. Anaxagoras thought that, being flat, +it would be buoyed up and supported on the air like a kite. Democritus +thought it remained fixed, like the donkey between two bundles of hay, +because it was equidistant from all parts of the containing sphere, and +there was no reason why it should incline one way rather than another. +Empedocles attributed its state of rest to centrifugal force by the +rapid circular movement of the heavens, as water is stationary in a +pail when whirled round by a string. Democritus further supposed that +the inclination of the flat earth to the ecliptic was due to the +greater weight of the southern parts owing to the exuberant vegetation. + +For further references to similar efforts of imagination the reader is +referred to Sir George Cornwall Lewis’s _Historical Survey of the +Astronomy of the Ancients_; London, 1862. His list of authorities is +very complete, but some of his conclusions are doubtful. At p. 113 of +that work he records the real opinions of Socrates as set forth by +Xenophon; and the reader will, perhaps, sympathise with Socrates in his +views on contemporary astronomy:— + +With regard to astronomy he [Socrates] considered a knowledge of it +desirable to the extent of determining the day of the year or month, +and the hour of the night, ... but as to learning the courses of the +stars, to be occupied with the planets, and to inquire about their +distances from the earth, and their orbits, and the causes of their +motions, he strongly objected to such a waste of valuable time. He +dwelt on the contradictions and conflicting opinions of the physical +philosophers, ... and, in fine, he held that the speculators on the +universe and on the laws of the heavenly bodies were no better than +madmen (_Xen. Mem_, i. 1, 11-15). + +Plato (born 429 B.C.), the pupil of Socrates, the fellow-student of +Euclid, and a follower of Pythagoras, studied science in his travels in +Egypt and elsewhere. He was held in so great reverence by all learned +men that a problem which he set to the astronomers was the keynote to +all astronomical investigation from this date till the time of Kepler +in the sixteenth century. He proposed to astronomers _the problem of +representing the courses of the planets by circular and uniform +motions_. + +Systematic observation among the Greeks began with the rise of the +Alexandrian school. Aristillus and Timocharis set up instruments and +fixed the positions of the zodiacal stars, near to which all the +planets in their orbits pass, thus facilitating the determination of +planetary motions. Aristarchus (320-250 B.C.) showed that the sun must +be at least nineteen times as far off as the moon, which is far short +of the mark. He also found the sun’s diameter, correctly, to be half a +degree. Eratosthenes (276-196 B.C.) measured the inclination to the +equator of the sun’s apparent path in the heavens—i.e., he measured the +obliquity of the ecliptic, making it 23° 51’, confirming our knowledge +of its continuous diminution during historical times. He measured an +arc of meridian, from Alexandria to Syene (Assuan), and found the +difference of latitude by the length of a shadow at noon, summer +solstice. He deduced the diameter of the earth, 250,000 stadia. +Unfortunately, we do not know the length of the stadium he used. + +Hipparchus (190-120 B.C.) may be regarded as the founder of +observational astronomy. He measured the obliquity of the ecliptic, and +agreed with Eratosthenes. He altered the length of the tropical year +from 365 days, 6 hours to 365 days, 5 hours, 53 minutes—still four +minutes too much. He measured the equation of time and the irregular +motion of the sun; and allowed for this in his calculations by +supposing that the centre, about which the sun moves uniformly, is +situated a little distance from the fixed earth. He called this point +the _excentric_. The line from the earth to the “excentric” was called +the _line of apses_. A circle having this centre was called the +_equant_, and he supposed that a radius drawn to the sun from the +excentric passes over equal arcs on the equant in equal times. He then +computed tables for predicting the place of the sun. + +He proceeded in the same way to compute Lunar tables. Making use of +Chaldæan eclipses, he was able to get an accurate value of the moon’s +mean motion. [Halley, in 1693, compared this value with his own +measurements, and so discovered the acceleration of the moon’s mean +motion. This was conclusively established, but could not be explained +by the Newtonian theory for quite a long time.] He determined the plane +of the moon’s orbit and its inclination to the ecliptic. The motion of +this plane round the pole of the ecliptic once in eighteen years +complicated the problem. He located the moon’s excentric as he had done +the sun’s. He also discovered some of the minor irregularities of the +moon’s motion, due, as Newton’s theory proves, to the disturbing action +of the sun’s attraction. + +In the year 134 B.C. Hipparchus observed a new star. This upset every +notion about the permanence of the fixed stars. He then set to work to +catalogue all the principal stars so as to know if any others appeared +or disappeared. Here his experiences resembled those of several later +astronomers, who, when in search of some special object, have been +rewarded by a discovery in a totally different direction. On comparing +his star positions with those of Timocharis and Aristillus he found no +stars that had appeared or disappeared in the interval of 150 years; +but he found that all the stars seemed to have changed their places +with reference to that point in the heavens where the ecliptic is 90° +from the poles of the earth—i.e., the equinox. He found that this could +be explained by a motion of the equinox in the direction of the +apparent diurnal motion of the stars. This discovery of _precession of +the equinoxes_, which takes place at the rate of 52".1 every year, was +necessary for the progress of accurate astronomical observations. It is +due to a steady revolution of the earth’s pole round the pole of the +ecliptic once in 26,000 years in the opposite direction to the +planetary revolutions. + +Hipparchus was also the inventor of trigonometry, both plane and +spherical. He explained the method of using eclipses for determining +the longitude. + +In connection with Hipparchus’ great discovery it may be mentioned that +modern astronomers have often attempted to fix dates in history by the +effects of precession of the equinoxes. (1) At about the date when the +Great Pyramid may have been built γ Draconis was near to the pole, and +must have been used as the pole-star. In the north face of the Great +Pyramid is the entrance to an inclined passage, and six of the nine +pyramids at Gizeh possess the same feature; all the passages being +inclined at an angle between 26° and 27° to the horizon and in the +plane of the meridian. It also appears that 4,000 years ago—i.e., about +2100 B.C.—an observer at the lower end of the passage would be able to +see γ Draconis, the then pole-star, at its lower culmination.[1] It has +been suggested that the passage was made for this purpose. On other +grounds the date assigned to the Great Pyramid is 2123 B.C. + +(2) The Chaldæans gave names to constellations now invisible from +Babylon which would have been visible in 2000 B.C., at which date it is +claimed that these people were studying astronomy. + +(3) In the Odyssey, Calypso directs Odysseus, in accordance with +Phoenician rules for navigating the Mediterranean, to keep the Great +Bear “ever on the left as he traversed the deep” when sailing from the +pillars of Hercules (Gibraltar) to Corfu. Yet such a course taken now +would land the traveller in Africa. Odysseus is said in his voyage in +springtime to have seen the Pleiades and Arcturus setting late, which +seemed to early commentators a proof of Homer’s inaccuracy. Likewise +Homer, both in the _Odyssey_[2] (v. 272-5) and in the _Iliad_ (xviii. +489), asserts that the Great Bear never set in those latitudes. Now it +has been found that the precession of the equinoxes explains all these +puzzles; shows that in springtime on the Mediterranean the Bear was +just above the horizon, near the sea but not touching it, between 750 +B.C. and 1000 B.C.; and fixes the date of the poems, thus confirming +other evidence, and establishing Homer’s character for accuracy.[3] + +(4) The orientation of Egyptian temples and Druidical stones is such +that possibly they were so placed as to assist in the observation of +the heliacal risings[4] of certain stars. If the star were known, this +would give an approximate date. Up to the present the results of these +investigations are far from being conclusive. + +Ptolemy (130 A.D.) wrote the Suntaxis, or Almagest, which includes a +cyclopedia of astronomy, containing a summary of knowledge at that +date. We have no evidence beyond his own statement that he was a +practical observer. He theorised on the planetary motions, and held +that the earth is fixed in the centre of the universe. He adopted the +excentric and equant of Hipparchus to explain the unequal motions of +the sun and moon. He adopted the epicycles and deferents which had been +used by Apollonius and others to explain the retrograde motions of the +planets. We, who know that the earth revolves round the sun once in a +year, can understand that the apparent motion of a planet is only its +motion relative to the earth. If, then, we suppose the earth fixed and +the sun to revolve round it once a year, and the planets each in its +own period, it is only necessary to impose upon each of these an +additional _annual_ motion to enable us to represent truly the apparent +motions. This way of looking at the apparent motions shows why each +planet, when nearest to the earth, seems to move for a time in a +retrograde direction. The attempts of Ptolemy and others of his time to +explain the retrograde motion in this way were only approximate. Let us +suppose each planet to have a bar with one end centred at the earth. If +at the other end of the bar one end of a shorter bar is pivotted, +having the planet at its other end, then the planet is given an annual +motion in the secondary circle (the epicycle), whose centre revolves +round the earth on the primary circle (the _deferent_), at a uniform +rate round the excentric. Ptolemy supposed the centres of the epicycles +of Mercury and Venus to be on a bar passing through the sun, and to be +between the earth and the sun. The centres of the epicycles of Mars, +Jupiter, and Saturn were supposed to be further away than the sun. +Mercury and Venus were supposed to revolve in their epicycles in their +own periodic times and in the deferent round the earth in a year. The +major planets were supposed to revolve in the deferent round the earth +in their own periodic times, and in their epicycles once in a year. + +It did not occur to Ptolemy to place the centres of the epicycles of +Mercury and Venus at the sun, and to extend the same system to the +major planets. Something of this sort had been proposed by the +Egyptians (we are told by Cicero and others), and was accepted by Tycho +Brahe; and was as true a representation of the relative motions in the +solar system as when we suppose the sun to be fixed and the earth to +revolve. + +The cumbrous system advocated by Ptolemy answered its purpose, enabling +him to predict astronomical events approximately. He improved the lunar +theory considerably, and discovered minor inequalities which could be +allowed for by the addition of new epicycles. We may look upon these +epicycles of Apollonius, and the excentric of Hipparchus, as the +responses of these astronomers to the demand of Plato for uniform +circular motions. Their use became more and more confirmed, until the +seventeenth century, when the accurate observations of Tycho Brahe +enabled Kepler to abolish these purely geometrical makeshifts, and to +substitute a system in which the sun became physically its controller. + +FOOTNOTES: + + [1] _Phil. Mag_., vol. xxiv., pp. 481-4. + + [2] + +Plaeiadas t’ esoronte kai opse duonta bootaen +‘Arkton th’ aen kai amaxan epiklaesin kaleousin, +‘Ae t’ autou strephetai kai t’ Oriona dokeuei, +Oin d’ammoros esti loetron Okeanoio. + +“The Pleiades and Boötes that setteth late, and the Bear, which they +likewise call the Wain, which turneth ever in one place, and keepeth +watch upon Orion, and alone hath no part in the baths of the ocean.” + + [3] See Pearson in the Camb. Phil. Soc. Proc., vol. iv., pt. ii., p. + 93, on whose authority the above statements are made. + + [4] See p. 6 for definition. + + + + +4. THE REIGN OF EPICYCLES—FROM PTOLEMY TO COPERNICUS. + + +After Ptolemy had published his book there seemed to be nothing more to +do for the solar system except to go on observing and finding more and +more accurate values for the constants involved--viz., the periods of +revolution, the diameter of the deferent,[1] and its ratio to that of +the epicycle,[2] the distance of the excentric[3] from the centre of +the deferent, and the position of the line of apses,[4] besides the +inclination and position of the plane of the planet’s orbit. The only +object ever aimed at in those days was to prepare tables for predicting +the places of the planets. It was not a mechanical problem; there was +no notion of a governing law of forces. + +From this time onwards all interest in astronomy seemed, in Europe at +least, to sink to a low ebb. When the Caliph Omar, in the middle of the +seventh century, burnt the library of Alexandria, which had been the +centre of intellectual progress, that centre migrated to Baghdad, and +the Arabs became the leaders of science and philosophy. In astronomy +they made careful observations. In the middle of the ninth century +Albategnius, a Syrian prince, improved the value of excentricity of the +sun’s orbit, observed the motion of the moon’s apse, and thought he +detected a smaller progression of the sun’s apse. His tables were much +more accurate than Ptolemy’s. Abul Wefa, in the tenth century, seems to +have discovered the moon’s “variation.” Meanwhile the Moors were +leaders of science in the west, and Arzachel of Toledo improved the +solar tables very much. Ulugh Begh, grandson of the great Tamerlane the +Tartar, built a fine observatory at Samarcand in the fifteenth century, +and made a great catalogue of stars, the first since the time of +Hipparchus. + +At the close of the fifteenth century King Alphonso of Spain employed +computers to produce the Alphonsine Tables (1488 A.D.), Purbach +translated Ptolemy’s book, and observations were carried out in Germany +by Müller, known as Regiomontanus, and Waltherus. + +Nicolai Copernicus, a Sclav, was born in 1473 at Thorn, in Polish +Prussia. He studied at Cracow and in Italy. He was a priest, and +settled at Frauenberg. He did not undertake continuous observations, +but devoted himself to simplifying the planetary systems and devising +means for more accurately predicting the positions of the sun, moon, +and planets. He had no idea of framing a solar system on a dynamical +basis. His great object was to increase the accuracy of the +calculations and the tables. The results of his cogitations were +printed just before his death in an interesting book, _De +Revolutionibus Orbium Celestium_. It is only by careful reading of this +book that the true position of Copernicus can be realised. He noticed +that Nicetas and others had ascribed the apparent diurnal rotation of +the heavens to a real daily rotation of the earth about its axis, in +the opposite direction to the apparent motion of the stars. Also in the +writings of Martianus Capella he learnt that the Egyptians had supposed +Mercury and Venus to revolve round the sun, and to be carried with him +in his annual motion round the earth. He noticed that the same +supposition, if extended to Mars, Jupiter, and Saturn, would explain +easily why they, and especially Mars, seem so much brighter in +opposition. For Mars would then be a great deal nearer to the earth +than at other times. It would also explain the retrograde motion of +planets when in opposition. + +We must here notice that at this stage Copernicus was actually +confronted with the system accepted later by Tycho Brahe, with the +earth fixed. But he now recalled and accepted the views of Pythagoras +and others, according to which the sun is fixed and the earth revolves; +and it must be noted that, geometrically, there is no difference of any +sort between the Egyptian or Tychonic system and that of Pythagoras as +revived by Copernicus, except that on the latter theory the stars ought +to seem to move when the earth changes its position—a test which failed +completely with the rough means of observation then available. The +radical defect of all solar systems previous to the time of Kepler +(1609 A.D.) was the slavish yielding to Plato’s dictum demanding +uniform circular motion for the planets, and the consequent evolution +of the epicycle, which was fatal to any conception of a dynamical +theory. + +Copernicus could not sever himself from this obnoxious tradition.[5] It +is true that neither the Pythagorean nor the Egypto-Tychonic system +required epicycles for explaining retrograde motion, as the Ptolemaic +theory did. Furthermore, either system could use the excentric of +Hipparchus to explain the irregular motion known as the equation of the +centre. But Copernicus remarked that he could also use an epicycle for +this purpose, or that he could use both an excentric and an epicycle +for each planet, and so bring theory still closer into accord with +observation. And this he proceeded to do.[6] Moreover, observers had +found irregularities in the moon’s motion, due, as we now know, to the +disturbing attraction of the sun. To correct for these irregularities +Copernicus introduced epicycle on epicycle in the lunar orbit. + +This is in its main features the system propounded by Copernicus. But +attention must, to state the case fully, be drawn to two points to be +found in his first and sixth books respectively. The first point +relates to the seasons, and it shows a strange ignorance of the laws of +rotating bodies. To use the words of Delambre,[7] in drawing attention +to the strange conception, + + he imagined that the earth, revolving round the sun, ought always to + show to it the same face; the contrary phenomena surprised him: to + explain them he invented a third motion, and added it to the two real + motions (rotation and orbital revolution). By this third motion the + earth, he held, made a revolution on itself and on the poles of the + ecliptic once a year ... Copernicus did not know that motion in a + straight line is the natural motion, and that motion in a curve is the + resultant of several movements. He believed, with Aristotle, that + circular motion was the natural one. + +Copernicus made this rotation of the earth’s axis about the pole of the +ecliptic retrograde (i.e., opposite to the orbital revolution), and by +making it perform more than one complete revolution in a year, the +added part being 1/26000 of the whole, he was able to include the +precession of the equinoxes in his explanation of the seasons. His +explanation of the seasons is given on leaf 10 of his book (the pages +of this book are not all numbered, only alternate pages, or leaves). + +In his sixth book he discusses the inclination of the planetary orbits +to the ecliptic. In regard to this the theory of Copernicus is unique; +and it will be best to explain this in the words of Grant in his great +work.[8] He says:— + + Copernicus, as we have already remarked, did not attack the principle + of the epicyclical theory: he merely sought to make it more simple by + placing the centre of the earth’s orbit in the centre of the universe. + This was the point to which the motions of the planets were referred, + for the planes of their orbits were made to pass through it, and their + points of least and greatest velocities were also determined with + reference to it. By this arrangement the sun was situate + mathematically near the centre of the planetary system, but he did not + appear to have any physical connexion with the planets as the centre + of their motions. + +According to Copernicus’ sixth book, the planes of the planetary orbits +do not pass through the sun, and the lines of apses do not pass through +to the sun. + +Such was the theory advanced by Copernicus: The earth moves in an +epicycle, on a deferent whose centre is a little distance from the sun. +The planets move in a similar way on epicycles, but their deferents +have no geometrical or physical relation to the sun. The moon moves on +an epicycle centred on a second epicycle, itself centred on a deferent, +excentric to the earth. The earth’s axis rotates about the pole of the +ecliptic, making one revolution and a twenty-six thousandth part of a +revolution in the sidereal year, in the opposite direction to its +orbital motion. + +In view of this fanciful structure it must be noted, in fairness to +Copernicus, that he repeatedly states that the reader is not obliged to +accept his system as showing the real motions; that it does not matter +whether they be true, even approximately, or not, so long as they +enable us to compute tables from which the places of the planets among +the stars can be predicted.[9] He says that whoever is not satisfied +with this explanation must be contented by being told that “mathematics +are for mathematicians” (Mathematicis mathematica scribuntur). + +At the same time he expresses his conviction over and over again that +the earth is in motion. It is with him a pious belief, just as it was +with Pythagoras and his school and with Aristarchus. “But” (as Dreyer +says in his most interesting book, _Tycho Brahe_) “proofs of the +physical truth of his system Copernicus had given none, and could give +none,” any more than Pythagoras or Aristarchus. + +There was nothing so startlingly simple in his system as to lead the +cautious astronomer to accept it, as there was in the later Keplerian +system; and the absence of parallax in the stars seemed to condemn his +system, which had no physical basis to recommend it, and no +simplification at all over the Egypto-Tychonic system, to which +Copernicus himself drew attention. It has been necessary to devote +perhaps undue space to the interesting work of Copernicus, because by a +curious chance his name has become so widely known. He has been spoken +of very generally as the founder of the solar system that is now +accepted. This seems unfair, and on reading over what has been written +about him at different times it will be noticed that the +astronomers—those who have evidently read his great book—are very +cautious in the words with which they eulogise him, and refrain from +attributing to him the foundation of our solar system, which is +entirely due to Kepler. It is only the more popular writers who give +the idea that a revolution had been effected when Pythagoras’ system +was revived, and when Copernicus supported his view that the earth +moves and is not fixed. + +It may be easy to explain the association of the name of Copernicus +with the Keplerian system. But the time has long passed when the +historian can support in any way this popular error, which was started +not by astronomers acquainted with Kepler’s work, but by those who +desired to put the Church in the wrong by extolling Copernicus. + +Copernicus dreaded much the abuse he expected to receive from +philosophers for opposing the authority of Aristotle, who had declared +that the earth was fixed. So he sought and obtained the support of the +Church, dedicating his great work to Pope Paul III. in a lengthy +explanatory epistle. The Bishop of Cracow set up a memorial tablet in +his honour. + +Copernicus was the most refined exponent, and almost the last +representative, of the Epicyclical School. As has been already stated, +his successor, Tycho Brahe, supported the same use of epicycles and +excentrics as Copernicus, though he held the earth to be fixed. But +Tycho Brahe was eminently a practical observer, and took little part in +theory; and his observations formed so essential a portion of the +system of Kepler that it is only fair to include his name among these +who laid the foundations of the solar system which we accept to-day. + +In now taking leave of the system of epicycles let it be remarked that +it has been held up to ridicule more than it deserves. On reading +Airy’s account of epicycles, in the beautifully clear language of his +_Six Lectures on Astronomy_, the impression is made that the jointed +bars there spoken of for describing the circles were supposed to be +real. This is no more the case than that the spheres of Eudoxus and +Callippus were supposed to be real. Both were introduced only to +illustrate the mathematical conception upon which the solar, planetary, +and lunar tables were constructed. The epicycles represented nothing +more nor less than the first terms in the Fourier series, which in the +last century has become a basis of such calculations, both in astronomy +and physics generally. + +[Illustration: “QUADRANS MURALIS SIVE TICHONICUS.” +With portrait of Tycho Brahe, instruments, etc., painted on the wall; +showing assistants using the sight, watching the clock, and recording. +(From the author’s copy of the _Astronomiæ Instauratæ Mechanica_.)] + +FOOTNOTES: + + [1] For definition see p. 22. + + [2] _Ibid_. + + [3] For definition see p. 18. + + [4] For definition see p. 18. + + [5] In his great book Copernicus says: “The movement of the heavenly + bodies is uniform, circular, perpetual, or else composed of circular + movements.” In this he proclaimed himself a follower of Pythagoras + (see p. 14), as also when he says: “The world is spherical because the + sphere is, of all figures, the most perfect” (Delambre, _Ast. Mod. + Hist_., pp. 86, 87). + + [6] Kepler tells us that Tycho Brahe was pleased with this device, and + adapted it to his own system. + + [7] _Hist. Ast._, vol. i., p. 354. + + [8] _Hist. of Phys. Ast._, p. vii. + + [9] “Est enim Astronomi proprium, historiam motuum coelestium + diligenti et artificiosa observatione colligere. Deinde causas + earundem, seu hypotheses, cum veras assequi nulla ratione possit ... + Neque enim necesse est, eas hypotheses esse veras, imo ne verisimiles + quidem, sed sufficit hoc usum, si calculum observationibus congruentem + exhibeant.” + + + + +BOOK II. THE DYNAMICAL PERIOD + +5. DISCOVERY OF THE TRUE SOLAR SYSTEM—TYCHO BRAHE—KEPLER. + + +During the period of the intellectual and aesthetic revival, at the +beginning of the sixteenth century, the “spirit of the age” was +fostered by the invention of printing, by the downfall of the Byzantine +Empire, and the scattering of Greek fugitives, carrying the treasures +of literature through Western Europe, by the works of Raphael and +Michael Angelo, by the Reformation, and by the extension of the known +world through the voyages of Spaniards and Portuguese. During that +period there came to the front the founder of accurate observational +astronomy. Tycho Brahe, a Dane, born in 1546 of noble parents, was the +most distinguished, diligent, and accurate observer of the heavens +since the days of Hipparchus, 1,700 years before. + +Tycho was devoted entirely to his science from childhood, and the +opposition of his parents only stimulated him in his efforts to +overcome difficulties. He soon grasped the hopelessness of the old +deductive methods of reasoning, and decided that no theories ought to +be indulged in until preparations had been made by the accumulation of +accurate observations. We may claim for him the title of founder of the +inductive method. + +For a complete life of this great man the reader is referred to +Dreyer’s _Tycho Brahe_, Edinburgh, 1890, containing a complete +bibliography. The present notice must be limited to noting the work +done, and the qualities of character which enabled him to attain his +scientific aims, and which have been conspicuous in many of his +successors. + +He studied in Germany, but King Frederick of Denmark, appreciating his +great talents, invited him to carry out his life’s work in that +country. He granted to him the island of Hveen, gave him a pension, and +made him a canon of the Cathedral of Roskilde. On that island Tycho +Brahe built the splendid observatory which he called Uraniborg, and, +later, a second one for his assistants and students, called +Stjerneborg. These he fitted up with the most perfect instruments, and +never lost a chance of adding to his stock of careful observations.[1] + +The account of all these instruments and observations, printed at his +own press on the island, was published by Tycho Brahe himself, and the +admirable and numerous engravings bear witness to the excellence of +design and the stability of his instruments. + +His mechanical skill was very great, and in his workmanship he was +satisfied with nothing but the best. He recognised the importance of +rigidity in the instruments, and, whereas these had generally been made +of wood, he designed them in metal. His instruments included armillae +like those which had been used in Alexandria, and other armillae +designed by himself—sextants, mural quadrants, large celestial globes +and various instruments for special purposes. He lived before the days +of telescopes and accurate clocks. He invented the method of +sub-dividing the degrees on the arc of an instrument by transversals +somewhat in the way that Pedro Nunez had proposed. + +He originated the true system of observation and reduction of +observations, recognising the fact that the best instrument in the +world is not perfect; and with each of his instruments he set to work +to find out the errors of graduation and the errors of mounting, the +necessary correction being applied to each observation. + +When he wanted to point his instrument exactly to a star he was +confronted with precisely the same difficulty as is met in gunnery and +rifle-shooting. The sights and the object aimed at cannot be in focus +together, and a great deal depends on the form of sight. Tycho Brahe +invented, and applied to the pointers of his instruments, an +aperture-sight of variable area, like the iris diaphragm used now in +photography. This enabled him to get the best result with stars of +different brightness. The telescope not having been invented, he could +not use a telescopic-sight as we now do in gunnery. This not only +removes the difficulty of focussing, but makes the minimum visible +angle smaller. Helmholtz has defined the minimum angle measurable with +the naked eye as being one minute of arc. In view of this it is simply +marvellous that, when the positions of Tycho’s standard stars are +compared with the best modern catalogues, his probable error in right +ascension is only ± 24”, 1, and in declination only ± 25”, 9. + +Clocks of a sort had been made, but Tycho Brahe found them so +unreliable that he seldom used them, and many of his +position-measurements were made by measuring the angular distances from +known stars. + +Taking into consideration the absence of either a telescope or a clock, +and reading his account of the labour he bestowed upon each +observation, we must all agree that Kepler, who inherited these +observations in MS., was justified, under the conditions then existing, +in declaring that there was no hope of anyone ever improving upon them. + +In the year 1572, on November 11th, Tycho discovered in Cassiopeia a +new star of great brilliance, and continued to observe it until the end +of January, 1573. So incredible to him was such an event that he +refused to believe his own eyes until he got others to confirm what he +saw. He made accurate observations of its distance from the nine +principal stars in Casseiopeia, and proved that it had no measurable +parallax. Later he employed the same method with the comets of 1577, +1580, 1582, 1585, 1590, 1593, and 1596, and proved that they too had no +measurable parallax and must be very distant. + +The startling discovery that stars are not necessarily permanent, that +new stars may appear, and possibly that old ones may disappear, had +upon him exactly the same effect that a similar occurrence had upon +Hipparchus 1,700 years before. He felt it his duty to catalogue all the +principal stars, so that there should be no mistake in the future. +During the construction of his catalogue of 1,000 stars he prepared and +used accurate tables of refraction deduced from his own observations. +Thus he eliminated (so far as naked eye observations required) the +effect of atmospheric refraction which makes the altitude of a star +seem greater than it really is. + +Tycho Brahe was able to correct the lunar theory by his observations. +Copernicus had introduced two epicycles on the lunar orbit in the hope +of obtaining a better accordance between theory and observation; and he +was not too ambitious, as his desire was to get the tables accurate to +ten minutes. Tycho Brahe found that the tables of Copernicus were in +error as much as two degrees. He re-discovered the inequality called +“variation” by observing the moon in all phases—a thing which had not +been attended to. [It is remarkable that in the nineteenth century Sir +George Airy established an altazimuth at Greenwich Observatory with +this special object, to get observations of the moon in all phases.] He +also discovered other lunar equalities, and wanted to add another +epicycle to the moon’s orbit, but he feared that these would soon +become unmanageable if further observations showed more new +inequalities. + +But, as it turned out, the most fruitful work of Tycho Brahe was on the +motions of the planets, and especially of the planet Mars, for it was +by an examination of these results that Kepler was led to the discovery +of his immortal laws. + +After the death of King Frederick the observatories of Tycho Brahe were +not supported. The gigantic power and industry displayed by this +determined man were accompanied, as often happens, by an overbearing +manner, intolerant of obstacles. This led to friction, and eventually +the observatories were dismantled, and Tycho Brahe was received by the +Emperor Rudolph II., who placed a house in Prague at his disposal. Here +he worked for a few years, with Kepler as one of his assistants, and he +died in the year 1601. + +It is an interesting fact that Tycho Brahe had a firm conviction that +mundane events could be predicted by astrology, and that this belief +was supported by his own predictions. + +It has already been stated that Tycho Brahe maintained that observation +must precede theory. He did not accept the Copernican theory that the +earth moves, but for a working hypothesis he used a modification of an +old Egyptian theory, mathematically identical with that of Copernicus, +but not involving a stellar parallax. He says (_De Mundi_, _etc_.) that + +the Ptolemean system was too complicated, and the new one which that +great man Copernicus had proposed, following in the footsteps of +Aristarchus of Samos, though there was nothing in it contrary to +mathematical principles, was in opposition to those of physics, as the +heavy and sluggish earth is unfit to move, and the system is even +opposed to the authority of Scripture. The absence of annual parallax +further involves an incredible distance between the outermost planet +and the fixed stars. + +We are bound to admit that in the circumstances of the case, so long as +there was no question of dynamical forces connecting the members of the +solar system, his reasoning, as we should expect from such a man, is +practical and sound. It is not surprising, then, that astronomers +generally did not readily accept the views of Copernicus, that Luther +(Luther’s _Tischreden_, pp. 22, 60) derided him in his usual pithy +manner, that Melancthon (_Initia doctrinae physicae_) said that +Scripture, and also science, are against the earth’s motion; and that +the men of science whose opinion was asked for by the cardinals (who +wished to know whether Galileo was right or wrong) looked upon +Copernicus as a weaver of fanciful theories. + +Johann Kepler is the name of the man whose place, as is generally +agreed, would have been the most difficult to fill among all those who +have contributed to the advance of astronomical knowledge. He was born +at Wiel, in the Duchy of Wurtemberg, in 1571. He held an appointment at +Gratz, in Styria, and went to join Tycho Brahe in Prague, and to assist +in reducing his observations. These came into his possession when Tycho +Brahe died, the Emperor Rudolph entrusting to him the preparation of +new tables (called the Rudolphine tables) founded on the new and +accurate observations. He had the most profound respect for the +knowledge, skill, determination, and perseverance of the man who had +reaped such a harvest of most accurate data; and though Tycho hardly +recognised the transcendent genius of the man who was working as his +assistant, and although there were disagreements between them, Kepler +held to his post, sustained by the conviction that, with these +observations to test any theory, he would be in a position to settle +for ever the problem of the solar system. + +[Illustration: PORTRAIT OF JOHANNES KEPLER. By F. +Wanderer, from Reitlinger’s “Johannes Kepler” (original in +Strassburg).] + +It has seemed to many that Plato’s demand for uniform circular motion +(linear or angular) was responsible for a loss to astronomy of good +work during fifteen hundred years, for a hundred ill-considered +speculative cosmogonies, for dissatisfaction, amounting to disgust, +with these _à priori_ guesses, and for the relegation of the science to +less intellectual races than Greeks and other Europeans. Nobody seemed +to dare to depart from this fetish of uniform angular motion and +circular orbits until the insight, boldness, and independence of Johann +Kepler opened up a new world of thought and of intellectual delight. + +While at work on the Rudolphine tables he used the old epicycles and +deferents and excentrics, but he could not make theory agree with +observation. His instincts told him that these apologists for uniform +motion were a fraud; and he proved it to himself by trying every +possible variation of the elements and finding them fail. The number of +hypotheses which he examined and rejected was almost incredible (for +example, that the planets turn round centres at a little distance from +the sun, that the epicycles have centres at a little distance from the +deferent, and so on). He says that, after using all these devices to +make theory agree with Tycho’s observations, he still found errors +amounting to eight minutes of a degree. Then he said boldly that it was +impossible that so good an observer as Tycho could have made a mistake +of eight minutes, and added: “Out of these eight minutes we will +construct a new theory that will explain the motions of all the +planets.” And he did it, with elliptic orbits having the sun in a focus +of each.[2] + +It is often difficult to define the boundaries between fancies, +imagination, hypothesis, and sound theory. This extraordinary genius +was a master in all these modes of attacking a problem. His analogy +between the spaces occupied by the five regular solids and the +distances of the planets from the sun, which filled him with so much +delight, was a display of pure fancy. His demonstration of the three +fundamental laws of planetary motion was the most strict and complete +theory that had ever been attempted. + +It has been often suggested that the revival by Copernicus of the +notion of a moving earth was a help to Kepler. No one who reads +Kepler’s great book could hold such an opinion for a moment. In fact, +the excellence of Copernicus’s book helped to prolong the life of the +epicyclical theories in opposition to Kepler’s teaching. + +All of the best theories were compared by him with observation. These +were the Ptolemaic, the Copernican, and the Tychonic. The two latter +placed all of the planetary orbits concentric with one another, the sun +being placed a little away from their common centre, and having no +apparent relation to them, and being actually outside the planes in +which they move. Kepler’s first great discovery was that the planes of +all the orbits pass through the sun; his second was that the line of +apses of each planet passes through the sun; both were contradictory to +the Copernican theory. + +He proceeds cautiously with his propositions until he arrives at his +great laws, and he concludes his book by comparing observations of +Mars, of all dates, with his theory. + +His first law states that the planets describe ellipses with the sun at +a focus of each ellipse. + +His second law (a far more difficult one to prove) states that a line +drawn from a planet to the sun sweeps over equal areas in equal times. +These two laws were published in his great work, _Astronomia Nova, sen. +Physica Coelestis tradita commentariis de Motibus Stelloe; Martis_, +Prague, 1609. + +It took him nine years more[3] to discover his third law, that the +squares of the periodic times are proportional to the cubes of the mean +distances from the sun. + +These three laws contain implicitly the law of universal gravitation. +They are simply an alternative way of expressing that law in dealing +with planets, not particles. Only, the power of the greatest human +intellect is so utterly feeble that the meaning of the words in +Kepler’s three laws could not be understood until expounded by the +logic of Newton’s dynamics. + +The joy with which Kepler contemplated the final demonstration of these +laws, the evolution of which had occupied twenty years, can hardly be +imagined by us. He has given some idea of it in a passage in his work +on _Harmonics_, which is not now quoted, only lest someone might say it +was egotistical—a term which is simply grotesque when applied to such a +man with such a life’s work accomplished. + +The whole book, _Astronomia Nova_, is a pleasure to read; the mass of +observations that are used, and the ingenuity of the propositions, +contrast strongly with the loose and imperfectly supported explanations +of all his predecessors; and the indulgent reader will excuse the +devotion of a few lines to an example of the ingenuity and beauty of +his methods. + +It may seem a hopeless task to find out the true paths of Mars and the +earth (at that time when their shape even was not known) from the +observations giving only the relative direction from night to night. +Now, Kepler had twenty years of observations of Mars to deal with. This +enabled him to use a new method, to find the earth’s orbit. Observe the +date at any time when Mars is in opposition. The earth’s position E at +that date gives the longitude of Mars M. His period is 687 days. Now +choose dates before and after the principal date at intervals of 687 +days and its multiples. Mars is in each case in the same position. Now +for any date when Mars is at M and the earth at E3 the date of the year +gives the angle E3SM. And the observation of Tycho gives the direction +of Mars compared with the sun, SE3M. So all the angles of the triangle +SEM in any of these positions of E are known, and also the ratios of +SE1, SE2, SE3, SE4 to SM and to each other. + +For the orbit of Mars observations were chosen at intervals of a year, +when the earth was always in the same place. + +But Kepler saw much farther than the geometrical facts. He realised +that the orbits are followed owing to a force directed to the sun; and +he guessed that this is the same force as the gravity that makes a +stone fall. He saw the difficulty of gravitation acting through the +void space. He compared universal gravitation to magnetism, and speaks +of the work of Gilbert of Colchester. (Gilbert’s book, _De Mundo Nostro +Sublunari, Philosophia Nova_, Amstelodami, 1651, containing similar +views, was published forty-eight years after Gilbert’s death, and +forty-two years after Kepler’s book and reference. His book _De +Magnete_ was published in 1600.) + +A few of Kepler’s views on gravitation, extracted from the Introduction +to his _Astronomia Nova_, may now be mentioned:— + +1. Every body at rest remains at rest if outside the attractive power +of other bodies. + +2. Gravity is a property of masses mutually attracting in such manner +that the earth attracts a stone much more than a stone attracts the +earth. + +3. Bodies are attracted to the earth’s centre, not because it is the +centre of the universe, but because it is the centre of the attracting +particles of the earth. + +4. If the earth be not round (but spheroidal?), then bodies at +different latitudes will not be attracted to its centre, but to +different points in the neighbourhood of that centre. + +5. If the earth and moon were not retained in their orbits by vital +force (_aut alia aligua aequipollenti_), the earth and moon would come +together. + +6. If the earth were to cease to attract its waters, the oceans would +all rise and flow to the moon. + +7. He attributes the tides to lunar attraction. Kepler had been +appointed Imperial Astronomer with a handsome salary (on paper), a +fraction of which was doled out to him very irregularly. He was led to +miserable makeshifts to earn enough to keep his family from starvation; +and proceeded to Ratisbon in 1630 to represent his claims to the Diet. +He arrived worn out and debilitated; he failed in his appeal, and died +from fever, contracted under, and fed upon, disappointment and +exhaustion. Those were not the days when men could adopt as a +profession the “research of endowment.” + +Before taking leave of Kepler, who was by no means a man of one idea, +it ought to be here recorded that he was the first to suggest that a +telescope made with both lenses convex (not a Galilean telescope) can +have cross wires in the focus, for use as a pointer to fix accurately +the positions of stars. An Englishman, Gascoigne, was the first to use +this in practice. + +From the all too brief epitome here given of Kepler’s greatest book, it +must be obvious that he had at that time some inkling of the meaning of +his laws—universal gravitation. From that moment the idea of universal +gravitation was in the air, and hints and guesses were thrown out by +many; and in time the law of gravitation would doubtless have been +discovered, though probably not by the work of one man, even if Newton +had not lived. But, if Kepler had not lived, who else could have +discovered his laws? + +FOOTNOTES: + + [1] When the writer visited M. D’Arrest, the astronomer, at + Copenhagen, in 1872, he was presented by D’Arrest with one of several + bricks collected from the ruins of Uraniborg. This was one of his most + cherished possessions until, on returning home after a prolonged + absence on astronomical work, he found that his treasure had been + tidied away from his study. + + [2] An ellipse is one of the plane, sections of a cone. It is an oval + curve, which may be drawn by fixing two pins in a sheet of paper at S + and H, fastening a string, SPH, to the two pins, and stretching it + with a pencil point at P, and moving the pencil point, while the + string is kept taut, to trace the oval ellipse, APB. S and H are the + _foci_. Kepler found the sun to be in one focus, say S. AB is the + _major axis_. DE is the _minor axis_. C is the _centre_. The direction + of AB is the _line of apses_. The ratio of CS to CA is the + _excentricity_. The position of the planet at A is the _perihelion_ + (nearest to the sun). The position of the planet at B is the + _aphelion_ (farthest from the sun). The angle ASP is the _anomaly_ + when the planet is at P. CA or a line drawn from S to D is the _mean + distance_ of the planet from the sun. + + + [3] The ruled logarithmic paper we now use was not then to be had by + going into a stationer’s shop. Else he would have accomplished this in + five minutes. + + + + +6. GALILEO AND THE TELESCOPE—NOTIONS OF GRAVITY BY HORROCKS, ETC. + + +It is now necessary to leave the subject of dynamical astronomy for a +short time in order to give some account of work in a different +direction originated by a contemporary of Kepler’s, his senior in fact +by seven years. Galileo Galilei was born at Pisa in 1564. The most +scientific part of his work dealt with terrestrial dynamics; but one of +those fortunate chances which happen only to really great men put him +in the way of originating a new branch of astronomy. + +The laws of motion had not been correctly defined. The only man of +Galileo’s time who seems to have worked successfully in the same +direction as himself was that Admirable Crichton of the Italians, +Leonardo da Vinci. Galileo cleared the ground. It had always been +noticed that things tend to come to rest; a ball rolled on the ground, +a boat moved on the water, a shot fired in the air. Galileo realised +that in all of these cases a resisting force acts to stop the motion, +and he was the first to arrive at the not very obvious law that the +motion of a body will never stop, nor vary its speed, nor change its +direction, except by the action of some force. + +It is not very obvious that a light body and a heavy one fall at the +same speed (except for the resistance of the air). Galileo proved this +on paper, but to convince the world he had to experiment from the +leaning tower of Pisa. + +At an early age he discovered the principle of isochronism of the +pendulum, which, in the hands of Huyghens in the middle of the +seventeenth century, led to the invention of the pendulum clock, +perhaps the most valuable astronomical instrument ever produced. + +These and other discoveries in dynamics may seem very obvious now; but +it is often the most every-day matters which have been found to elude +the inquiries of ordinary minds, and it required a high order of +intellect to unravel the truth and discard the stupid maxims scattered +through the works of Aristotle and accepted on his authority. A blind +worship of scientific authorities has often delayed the progress of +human knowledge, just as too much “instruction” of a youth often ruins +his “education.” Grant, in his history of Physical Astronomy, has well +said that “the sagacity and skill which Galileo displays in resolving +the phenomena of motion into their constituent elements, and hence +deriving the original principles involved in them, will ever assure to +him a distinguished place among those who have extended the domains of +science.” + +But it was work of a different kind that established Galileo’s popular +reputation. In 1609 Galileo heard that a Dutch spectacle-maker had +combined a pair of lenses so as to magnify distant objects. Working on +this hint, he solved the same problem, first on paper and then in +practice. So he came to make one of the first telescopes ever used in +astronomy. No sooner had he turned it on the heavenly bodies than he +was rewarded by such a shower of startling discoveries as forthwith +made his name the best known in Europe. He found curious irregular +black spots on the sun, revolving round it in twenty-seven days; hills +and valleys on the moon; the planets showing discs of sensible size, +not points like the fixed stars; Venus showing phases according to her +position in relation to the sun; Jupiter accompanied by four moons; +Saturn with appendages that he could not explain, but unlike the other +planets; the Milky Way composed of a multitude of separate stars. + +His fame flew over Europe like magic, and his discoveries were much +discussed—and there were many who refused to believe. Cosmo de Medici +induced him to migrate to Florence to carry on his observations. He was +received by Paul V., the Pope, at Rome, to whom he explained his +discoveries. + +He thought that these discoveries proved the truth of the Copernican +theory of the Earth’s motion; and he urged this view on friends and +foes alike. Although in frequent correspondence with Kepler, he never +alluded to the New Astronomy, and wrote to him extolling the virtue of +epicycles. He loved to argue, never shirked an encounter with any +number of disputants, and laughed as he broke down their arguments. + +Through some strange course of events, not easy to follow, the +Copernican theory, whose birth was welcomed by the Church, had now been +taken up by certain anti-clerical agitators, and was opposed by the +cardinals as well as by the dignitaries of the Reformed Church. +Galileo—a good Catholic—got mixed up in these discussions, although on +excellent terms with the Pope and his entourage. At last it came about +that Galileo was summoned to appear at Rome, where he was charged with +holding and teaching heretical opinions about the movement of the +earth; and he then solemnly abjured these opinions. There has been much +exaggeration and misstatement about his trial and punishment, and for a +long time there was a great deal of bitterness shown on both sides. But +the general verdict of the present day seems to be that, although +Galileo himself was treated with consideration, the hostility of the +Church to the views of Copernicus placed it in opposition also to the +true Keplerian system, and this led to unprofitable controversies. From +the time of Galileo onwards, for some time, opponents of religion +included the theory of the Earth’s motion in their disputations, not so +much for the love, or knowledge, of astronomy, as for the pleasure of +putting the Church in the wrong. This created a great deal of +bitterness and intolerance on both sides. Among the sufferers was +Giordano Bruno, a learned speculative philosopher, who was condemned to +be burnt at the stake. + +Galileo died on Christmas Day, 1642—the day of Newton’s birth. The +further consideration of the grand field of discovery opened out by +Galileo with his telescopes must be now postponed, to avoid +discontinuity in the history of the intellectual development of this +period, which lay in the direction of dynamical, or physical, +astronomy. + +Until the time of Kepler no one seems to have conceived the idea of +universal physical forces controlling terrestrial phenomena, and +equally applicable to the heavenly bodies. The grand discovery by +Kepler of the true relationship of the Sun to the Planets, and the +telescopic discoveries of Galileo and of those who followed him, spread +a spirit of inquiry and philosophic thought throughout Europe, and once +more did astronomy rise in estimation; and the irresistible logic of +its mathematical process of reasoning soon placed it in the position it +has ever since occupied as the foremost of the exact sciences. + +The practical application of this process of reasoning was enormously +facilitated by the invention of logarithms by Napier. He was born at +Merchistoun, near Edinburgh, in 1550, and died in 1617. By this system +the tedious arithmetical operations necessary in astronomical +calculations, especially those dealing with the trigonometrical +functions of angles, were so much simplified that Laplace declared that +by this invention the life-work of an astronomer was doubled. + +Jeremiah Horrocks (born 1619, died 1641) was an ardent admirer of Tycho +Brahe and Kepler, and was able to improve the Rudolphine tables so much +that he foretold a transit of Venus, in 1639, which these tables failed +to indicate, and was the only observer of it. His life was short, but +he accomplished a great deal, and rightly ascribed the lunar inequality +called _evection_ to variations in the value of the eccentricity and in +the direction of the line of apses, at the same time correctly +assigning _the disturbing force of the Sun_ as the cause. He discovered +the errors in Jupiter’s calculated place, due to what we now know as +the long inequality of Jupiter and Saturn, and measured with +considerable accuracy the acceleration at that date of Jupiter’s mean +motion, and indicated the retardation of Saturn’s mean motion. + +Horrocks’ investigations, so far as they could be collected, were +published posthumously in 1672, and seldom, if ever, has a man who +lived only twenty-two years originated so much scientific knowledge. + +At this period British science received a lasting impetus by the wise +initiation of a much-abused man, Charles II., who founded the Royal +Society of London, and also the Royal Observatory of Greeenwich, where +he established Flamsteed as first Astronomer Royal, especially for +lunar and stellar observations likely to be useful for navigation. At +the same time the French Academy and the Paris Observatory were +founded. All this within fourteen years, 1662-1675. + +Meanwhile gravitation in general terms was being discussed by Hooke, +Wren, Halley, and many others. All of these men felt a repugnance to +accept the idea of a force acting across the empty void of space. +Descartes (1596-1650) proposed an ethereal medium whirling round the +sun with the planets, and having local whirls revolving with the +satellites. As Delambre and Grant have said, this fiction only retarded +the progress of pure science. It had no sort of relation to the more +modern, but equally misleading, “nebular hypothesis.” While many were +talking and guessing, a giant mind was needed at this stage to make +things clear. + + + + +7. SIR ISAAC NEWTON—LAW OF UNIVERSAL GRAVITATION. + + +We now reach the period which is the culminating point of interest in +the history of dynamical astronomy. Isaac Newton was born in 1642. +Pemberton states that Newton, having quitted Cambridge to avoid the +plague, was residing at Wolsthorpe, in Lincolnshire, where he had been +born; that he was sitting one day in the garden, reflecting upon the +force which prevents a planet from flying off at a tangent and which +draws it to the sun, and upon the force which draws the moon to the +earth; and that he saw in the case of the planets that the sun’s force +must clearly be unequal at different distances, for the pull out of the +tangential line in a minute is less for Jupiter than for Mars. He then +saw that the pull of the earth on the moon would be less than for a +nearer object. It is said that while thus meditating he saw an apple +fall from a tree to the ground, and that this fact suggested the +questions: Is the force that pulled that apple from the tree the same +as the force which draws the moon to the earth? Does the attraction for +both of them follow the same law as to distance as is given by the +planetary motions round the sun? It has been stated that in this way +the first conception of universal gravitation arose.[1] + +Quite the most important event in the whole history of physical +astronomy was the publication, in 1687, of Newton’s _Principia +(Philosophiae Naturalis Principia Mathematica)_. In this great work +Newton started from the beginning of things, the laws of motion, and +carried his argument, step by step, into every branch of physical +astronomy; giving the physical meaning of Kepler’s three laws, and +explaining, or indicating the explanation of, all the known heavenly +motions and their irregularities; showing that all of these were +included in his simple statement about the law of universal +gravitation; and proceeding to deduce from that law new irregularities +in the motions of the moon which had never been noticed, and to +discover the oblate figure of the earth and the cause of the tides. +These investigations occupied the best part of his life; but he wrote +the whole of his great book in fifteen months. + +Having developed and enunciated the true laws of motion, he was able to +show that Kepler’s second law (that equal areas are described by the +line from the planet to the sun in equal times) was only another way of +saying that the centripetal force on a planet is always directed to the +sun. Also that Kepler’s first law (elliptic orbits with the sun in one +focus) was only another way of saying that the force urging a planet to +the sun varies inversely as the square of the distance. Also (if these +two be granted) it follows that Kepler’s third law is only another way +of saying that the sun’s force on different planets (besides depending +as above on distance) is proportional to their masses. + +Having further proved the, for that day, wonderful proposition that, +with the law of inverse squares, the attraction by the separate +particles of a sphere of uniform density (or one composed of concentric +spherical shells, each of uniform density) acts as if the whole mass +were collected at the centre, he was able to express the meaning of +Kepler’s laws in propositions which have been summarised as follows:— + +The law of universal gravitation.—_Every particle of matter in the +universe attracts every other particle with a force varying inversely +as the square of the distance between them, and directly as the product +of the masses of the two particles_.[2] + +But Newton did not commit himself to the law until he had answered that +question about the apple; and the above proposition now enabled him to +deal with the Moon and the apple. Gravity makes a stone fall 16.1 feet +in a second. The moon is 60 times farther from the earth’s centre than +the stone, so it ought to be drawn out of a straight course through +16.1 feet in a minute. Newton found the distance through which she is +actually drawn as a fraction of the earth’s diameter. But when he first +examined this matter he proceeded to use a wrong diameter for the +earth, and he found a serious discrepancy. This, for a time, seemed to +condemn his theory, and regretfully he laid that part of his work +aside. Fortunately, before Newton wrote the _Principia_ the French +astronomer Picard made a new and correct measure of an arc of the +meridian, from which he obtained an accurate value of the earth’s +diameter. Newton applied this value, and found, to his great joy, that +when the distance of the moon is 60 times the radius of the earth she +is attracted out of the straight course 16.1 feet per minute, and that +the force acting on a stone or an apple follows the same law as the +force acting upon the heavenly bodies.[3] + +The universality claimed for the law—if not by Newton, at least by his +commentators—was bold, and warranted only by the large number of cases +in which Newton had found it to apply. Its universality has been under +test ever since, and so far it has stood the test. There has often been +a suspicion of a doubt, when some inequality of motion in the heavenly +bodies has, for a time, foiled the astronomers in their attempts to +explain it. But improved mathematical methods have always succeeded in +the end, and so the seeming doubt has been converted into a surer +conviction of the universality of the law. + +Having once established the law, Newton proceeded to trace some of its +consequences. He saw that the figure of the earth depends partly on the +mutual gravitation of its parts, and partly on the centrifugal tendency +due to the earth’s rotation, and that these should cause a flattening +of the poles. He invented a mathematical method which he used for +computing the ratio of the polar to the equatorial diameter. + +He then noticed that the consequent bulging of matter at the equator +would be attracted by the moon unequally, the nearest parts being most +attracted; and so the moon would tend to tilt the earth when in some +parts of her orbit; and the sun would do this to a less extent, because +of its great distance. Then he proved that the effect ought to be a +rotation of the earth’s axis over a conical surface in space, exactly +as the axis of a top describes a cone, if the top has a sharp point, +and is set spinning and displaced from the vertical. He actually +calculated the amount; and so he explained the cause of the precession +of the equinoxes discovered by Hipparchus about 150 B.C. + +One of his grandest discoveries was a method of weighing the heavenly +bodies by their action on each other. By means of this principle he was +able to compare the mass of the sun with the masses of those planets +that have moons, and also to compare the mass of our moon with the mass +of the earth. + +Thus Newton, after having established his great principle, devoted his +splendid intellect to the calculation of its consequences. He proved +that if a body be projected with any velocity in free space, subject +only to a central force, varying inversely as the square of the +distance, the body must revolve in a curve which may be any one of the +sections of a cone—a circle, ellipse, parabola, or hyperbola; and he +found that those comets of which he had observations move in parabolae +round the Sun, and are thus subject to the universal law. + +Newton realised that, while planets and satellites are chiefly +controlled by the central body about which they revolve, the new law +must involve irregularities, due to their mutual action—such, in fact, +as Horrocks had indicated. He determined to put this to a test in the +case of the moon, and to calculate the sun’s effect, from its mass +compared with that of the earth, and from its distance. He proved that +the average effect upon the plane of the orbit would be to cause the +line in which it cuts the plane of the ecliptic (i.e., the line of +nodes) to revolve in the ecliptic once in about nineteen years. This +had been a known fact from the earliest ages. He also concluded that +the line of apses would revolve in the plane of the lunar orbit also in +about nineteen years; but the observed period is only ten years. For a +long time this was the one weak point in the Newtonian theory. It was +not till 1747 that Clairaut reconciled this with the theory, and showed +why Newton’s calculation was not exact. + +Newton proceeded to explain the other inequalities recognised by Tycho +Brahe and older observers, and to calculate their maximum amounts as +indicated by his theory. He further discovered from his calculations +two new inequalities, one of the apogee, the other of the nodes, and +assigned the maximum value. Grant has shown the values of some of these +as given by observation in the tables of Meyer and more modern tables, +and has compared them with the values assigned by Newton from his +theory; and the comparison is very remarkable. + + Newton. Modern Tables. + ° ’ " ° ’ " +Mean monthly motion of Apses 1.31.28 3.4.0 +Mean annual motion of nodes 19.18.1,23 19.21.22,50 +Mean value of “variation” 36.10 35.47 +Annual equation 11.51 11.14 +Inequality of mean motion of apogee 19.43 22.17 +Inequality of mean motion of nodes 9.24 9.0 + +The only serious discrepancy is the first, which has been already +mentioned. Considering that some of these perturbations had never been +discovered, that the cause of none of them had ever been known, and +that he exhibited his results, if he did not also make the discoveries, +by the synthetic methods of geometry, it is simply marvellous that he +reached to such a degree of accuracy. He invented the infinitesimal +calculus which is more suited for such calculations, but had he +expressed his results in that language he would have been +unintelligible to many. + +Newton’s method of calculating the precession of the equinoxes, already +referred to, is as beautiful as anything in the _Principia_. He had +already proved the regression of the nodes of a satellite moving in an +orbit inclined to the ecliptic. He now said that the nodes of a ring of +satellites revolving round the earth’s equator would consequently all +regress. And if joined into a solid ring its node would regress; and it +would do so, only more slowly, if encumbered by the spherical part of +the earth’s mass. Therefore the axis of the equatorial belt of the +earth must revolve round the pole of the ecliptic. Then he set to work +and found the amount due to the moon and that due to the sun, and so he +solved the mystery of 2,000 years. + +When Newton applied his law of gravitation to an explanation of the +tides he started a new field for the application of mathematics to +physical problems; and there can be little doubt that, if he could have +been furnished with complete tidal observations from different parts of +the world, his extraordinary powers of analysis would have enabled him +to reach a satisfactory theory. He certainly opened up many mines full +of intellectual gems; and his successors have never ceased in their +explorations. This has led to improved mathematical methods, which, +combined with the greater accuracy of observation, have rendered +physical astronomy of to-day the most exact of the sciences. + +Laplace only expressed the universal opinion of posterity when he said +that to the _Principia_ is assured “a pre-eminence above all the other +productions of the human intellect.” + +The name of Flamsteed, First Astronomer Royal, must here be mentioned +as having supplied Newton with the accurate data required for +completing the theory. + +The name of Edmund Halley, Second Astronomer Royal, must ever be held +in repute, not only for his own discoveries, but for the part he played +in urging Newton to commit to writing, and present to the Royal +Society, the results of his investigations. But for his friendly +insistence it is possible that the _Principia_ would never have been +written; and but for his generosity in supplying the means the Royal +Society could not have published the book. + +[Illustration: DEATH MASK OF SIR ISAAC NEWTON. +Photographed specially for this work from the original, by kind +permission of the Royal Society, London.] + +Sir Isaac Newton died in 1727, at the age of eighty-five. His body lay +in state in the Jerusalem Chamber, and was buried in Westminster Abbey. + +FOOTNOTES: + + [1] The writer inherited from his father (Professor J. D. Forbes) a + small box containing a bit of wood and a slip of paper, which had been + presented to him by Sir David Brewster. On the paper Sir David had + written these words: “If there be any truth in the story that Newton + was led to the theory of gravitation by the fall of an apple, this bit + of wood is probably a piece of the apple tree from which Newton saw + the apple fall. When I was on a pilgrimage to the house in which + Newton was born, I cut it off an ancient apple tree growing in his + garden.” When lecturing in Glasgow, about 1875, the writer showed it + to his audience. The next morning, when removing his property from the + lecture table, he found that his precious relic had been stolen. It + would be interesting to know who has got it now! + + [2] It must be noted that these words, in which the laws of + gravitation are always summarised in histories and text-books, do not + appear in the _Principia_; but, though they must have been composed by + some early commentator, it does not appear that their origin has been + traced. Nor does it appear that Newton ever extended the law beyond + the Solar System, and probably his caution would have led him to avoid + any statement of the kind until it should be proved. + With this exception the above statement of the law of universal + gravitation contains nothing that is not to be found in the + _Principia_; and the nearest approach to that statement occurs in + the Seventh Proposition of Book III.:— + Prop.: That gravitation occurs in all bodies, and that it is + proportional to the quantity of matter in each. + Cor. I.: The total attraction of gravitation on a planet arises, + and is composed, out of the attraction on the separate parts. + Cor. II.: The attraction on separate equal particles of a body is + reciprocally as the square of the distance from the particles. + + [3] It is said that, when working out this final result, the + probability of its confirming that part of his theory which he had + reluctantly abandoned years before excited him so keenly that he was + forced to hand over his calculations to a friend, to be completed by + him. + + + + +8. NEWTON’S SUCCESSORS—HALLEY, EULER, LAGRANGE, LAPLACE, ETC. + + +Edmund Halley succeeded Flamsteed as Second Astronomer Royal in 1721. +Although he did not contribute directly to the mathematical proofs of +Newton’s theory, yet his name is closely associated with some of its +greatest successes. + +He was the first to detect the acceleration of the moon’s mean motion. +Hipparchus, having compared his own observations with those of more +ancient astronomers, supplied an accurate value of the moon’s mean +motion in his time. Halley similarly deduced a value for modern times, +and found it sensibly greater. He announced this in 1693, but it was +not until 1749 that Dunthorne used modern lunar tables to compute a +lunar eclipse observed in Babylon 721 B.C., another at Alexandria 201 +B.C., a solar eclipse observed by Theon 360 A.D., and two later ones up +to the tenth century. He found that to explain these eclipses Halley’s +suggestion must be adopted, the acceleration being 10” in one century. +In 1757 Lalande again fixed it at 10.” + +The Paris Academy, in 1770, offered their prize for an investigation to +see if this could be explained by the theory of gravitation. Euler won +the prize, but failed to explain the effect, and said: “It appears to +be established by indisputable evidence that the secular inequality of +the moon’s mean motion cannot be produced by the forces of +gravitation.” + +The same subject was again proposed for a prize which was shared by +Lagrange[1] and Euler, neither finding a solution, while the latter +asserted the existence of a resisting medium in space. + +Again, in 1774, the Academy submitted the same subject, a third time, +for the prize; and again Lagrange failed to detect a cause in +gravitation. + +Laplace[2] now took the matter in hand. He tried the effect of a +non-instantaneous action of gravity, to no purpose. But in 1787 he gave +the true explanation. The principal effect of the sun on the moon’s +orbit is to diminish the earth’s influence, thus lengthening the period +to a new value generally taken as constant. But Laplace’s calculations +showed the new value to depend upon the excentricity of the earth’s +orbit, which, according; to theory, has a periodical variation of +enormous period, and has been continually diminishing for thousands of +years. Thus the solar influence has been diminishing, and the moon’s +mean motion increased. Laplace computed the amount at 10” in one +century, agreeing with observation. (Later on Adams showed that +Laplace’s calculation was wrong, and that the value he found was too +large; so, part of the acceleration is now attributed by some +astronomers to a lengthening of the day by tidal friction.) + +Another contribution by Halley to the verification of Newton’s law was +made when he went to St. Helena to catalogue the southern stars. He +measured the change in length of the second’s pendulum in different +latitudes due to the changes in gravity foretold by Newton. + +Furthermore, he discovered the long inequality of Jupiter and Saturn, +whose period is 929 years. For an investigation of this also the +Academy of Sciences offered their prize. This led Euler to write a +valuable essay disclosing a new method of computing perturbations, +called the instantaneous ellipse with variable elements. The method was +much developed by Lagrange. + +But again it was Laplace who solved the problem of the inequalities of +Jupiter and Saturn by the theory of gravitation, reducing the errors of +the tables from 20’ down to 12”, thus abolishing the use of empirical +corrections to the planetary tables, and providing another glorious +triumph for the law of gravitation. As Laplace justly said: “These +inequalities appeared formerly to be inexplicable by the law of +gravitation—they now form one of its most striking proofs.” + +Let us take one more discovery of Halley, furnishing directly a new +triumph for the theory. He noticed that Newton ascribed parabolic +orbits to the comets which he studied, so that they come from infinity, +sweep round the sun, and go off to infinity for ever, after having been +visible a few weeks or months. He collected all the reliable +observations of comets he could find, to the number of twenty-four, and +computed their parabolic orbits by the rules laid down by Newton. His +object was to find out if any of them really travelled in elongated +ellipses, practically undistinguishable, in the visible part of their +paths, from parabolæ, in which case they would be seen more than once. +He found two old comets whose orbits, in shape and position, resembled +the orbit of a comet observed by himself in 1682. Apian observed one in +1531; Kepler the other in 1607. The intervals between these appearances +is seventy-five or seventy-six years. He then examined and found old +records of similar appearance in 1456, 1380, and 1305. It is true, he +noticed, that the intervals varied by a year and a-half, and the +inclination of the orbit to the ecliptic diminished with successive +apparitions. But he knew from previous calculations that this might +easily be due to planetary perturbations. Finally, he arrived at the +conclusion that all of these comets were identical, travelling in an +ellipse so elongated that the part where the comet was seen seemed to +be part of a parabolic orbit. He then predicted its return at the end +of 1758 or beginning of 1759, when he should be dead; but, as he said, +“if it should return, according to our prediction, about the year 1758, +impartial posterity will not refuse to acknowledge that this was first +discovered by an Englishman.”[3] [_Synopsis Astronomiae Cometicae_, +1749.] + +Once again Halley’s suggestion became an inspiration for the +mathematical astronomer. Clairaut, assisted by Lalande, found that +Saturn would retard the comet 100 days, Jupiter 518 days, and predicted +its return to perihelion on April 13th, 1759. In his communication to +the French Academy, he said that a comet travelling into such distant +regions might be exposed to the influence of forces totally unknown, +and “even of some planet too far removed from the sun to be ever +perceived.” + +The excitement of astronomers towards the end of 1758 became intense; +and the honour of first catching sight of the traveller fell to an +amateur in Saxony, George Palitsch, on Christmas Day, 1758. It reached +perihelion on March 13th, 1759. + +This fact was a startling confirmation of the Newtonian theory, because +it was a new kind of calculation of perturbations, and also it added a +new member to the solar system, and gave a prospect of adding many +more. + +When Halley’s comet reappeared in 1835, Pontecoulant’s computations for +the date of perihelion passage were very exact, and afterwards he +showed that, with more exact values of the masses of Jupiter and +Saturn, his prediction was correct within two days, after an invisible +voyage of seventy-five years! + +Hind afterwards searched out many old appearances of this comet, going +back to 11 B.C., and most of these have been identified as being really +Halley’s comet by the calculations of Cowell and Cromellin[4] (of +Greenwich Observatory), who have also predicted its next perihelion +passage for April 8th to 16th, 1910, and have traced back its history +still farther, to 240 B.C. + +Already, in November, 1907, the Astronomer Royal was trying to catch it +by the aid of photography. + +FOOTNOTES: + + [1] Born 1736; died 1813. + + [2] Born 1749; died 1827. + + [3] This sentence does not appear in the original memoir communicated + to the Royal Society, but was first published in a posthumous reprint. + + [4] _R. A. S. Monthly Notices_, 1907-8. + + + + +9. DISCOVERY OF NEW PLANETS—HERSCHEL, PIAZZI, ADAMS, AND LE VERRIER. + + +It would be very interesting, but quite impossible in these pages, to +discuss all the exquisite researches of the mathematical astronomers, +and to inspire a reverence for the names connected with these +researches, which for two hundred years have been establishing the +universality of Newton’s law. The lunar and planetary theories, the +beautiful theory of Jupiter’s satellites, the figure of the earth, and +the tides, were mathematically treated by Maclaurin, D’Alembert, +Legendre, Clairaut, Euler, Lagrange, Laplace, Walmsley, Bailly, +Lalande, Delambre, Mayer, Hansen, Burchardt, Binet, Damoiseau, Plana, +Poisson, Gauss, Bessel, Bouvard, Airy, Ivory, Delaunay, Le Verrier, +Adams, and others of later date. + +By passing over these important developments it is possible to trace +some of the steps in the crowning triumph of the Newtonian theory, by +which the planet Neptune was added to the known members of the solar +system by the independent researches of Professor J.C. Adams and of M. +Le Verrier, in 1846. + +It will be best to introduce this subject by relating how the +eighteenth century increased the number of known planets, which was +then only six, including the earth. + +On March 13th, 1781, Sir William Herschel was, as usual, engaged on +examining some small stars, and, noticing that one of them appeared to +be larger than the fixed stars, suspected that it might be a comet. To +test this he increased his magnifying power from 227 to 460 and 932, +finding that, unlike the fixed stars near it, its definition was +impaired and its size increased. This convinced him that the object was +a comet, and he was not surprised to find on succeeding nights that the +position was changed, the motion being in the ecliptic. He gave the +observations of five weeks to the Royal Society without a suspicion +that the object was a new planet. + +For a long time people could not compute a satisfactory orbit for the +supposed comet, because it seemed to be near the perihelion, and no +comet had ever been observed with a perihelion distance from the sun +greater than four times the earth’s distance. Lexell was the first to +suspect that this was a new planet eighteen times as far from the sun +as the earth is. In January, 1783, Laplace published the elliptic +elements. The discoverer of a planet has a right to name it, so +Herschel called it Georgium Sidus, after the king. But Lalande urged +the adoption of the name Herschel. Bode suggested Uranus, and this was +adopted. The new planet was found to rank in size next to Jupiter and +Saturn, being 4.3 times the diameter of the earth. + +In 1787 Herschel discovered two satellites, both revolving in nearly +the same plane, inclined 80° to the ecliptic, and the motion of both +was retrograde. + +In 1772, before Herschel’s discovery, Bode[1] had discovered a curious +arbitrary law of planetary distances. Opposite each planet’s name write +the figure 4; and, in succession, add the numbers 0, 3, 6, 12, 24, 48, +96, _etc_., to the 4, always doubling the last numbers. You then get +the planetary distances. + + Mercury, dist.-- 4 4 + 0 = 4 + Venus " 7 4 + 3 = 7 + Earth " 10 4 + 6 = 10 + Mars " 15 4 + 12 = 16 + -- 4 + 24 = 28 + Jupiter dist. 52 4 + 48 = 52 + Saturn " 95 4 + 96 = 100 + (Uranus) " 192 4 + 192 = 196 + -- 4 + 384 = 388 + +All the five planets, and the earth, fitted this rule, except that +there was a blank between Mars and Jupiter. When Uranus was discovered, +also fitting the rule, the conclusion was irresistible that there is +probably a planet between Mars and Jupiter. An association of +twenty-four astronomers was now formed in Germany to search for the +planet. Almost immediately afterwards the planet was discovered, not by +any member of the association, but by Piazzi, when engaged upon his +great catalogue of stars. On January 1st, 1801, he observed a star +which had changed its place the next night. Its motion was retrograde +till January 11th, direct after the 13th. Piazzi fell ill before he had +enough observations for computing the orbit with certainty, and the +planet disappeared in the sun’s rays. Gauss published an approximate +ephemeris of probable positions when the planet should emerge from the +sun’s light. There was an exciting hunt, and on December 31st (the day +before its birthday) De Zach captured the truant, and Piazzi christened +it Ceres. + +The mean distance from the sun was found to be 2.767, agreeing with the +2.8 given by Bode’s law. Its orbit was found to be inclined over 10° to +the ecliptic, and its diameter was only 161 miles. + +On March 28th, 1802, Olbers discovered a new seventh magnitude star, +which turned out to be a planet resembling Ceres. It was called Pallas. +Gauss found its orbit to be inclined 35° to the ecliptic, and to cut +the orbit of Ceres; whence Olbers considered that these might be +fragments of a broken-up planet. He then commenced a search for other +fragments. In 1804 Harding discovered Juno, and in 1807 Olbers found +Vesta. The next one was not discovered until 1845, from which date +asteroids, or minor planets (as these small planets are called), have +been found almost every year. They now number about 700. + +It is impossible to give any idea of the interest with which the first +additions since prehistoric times to the planetary system were +received. All of those who showered congratulations upon the +discoverers regarded these discoveries in the light of rewards for +patient and continuous labours, the very highest rewards that could be +desired. And yet there remained still the most brilliant triumph of +all, the addition of another planet like Uranus, before it had ever +been seen, when the analysis of Adams and Le Verrier gave a final proof +of the powers of Newton’s great law to explain any planetary +irregularity. + +After Sir William Herschel discovered Uranus, in 1781, it was found +that astronomers had observed it on many previous occasions, mistaking +it for a fixed star of the sixth or seventh magnitude. Altogether, +nineteen observations of Uranus’s position, from the time of Flamsteed, +in 1690, had been recorded. + +In 1790 Delambre, using all these observations, prepared tables for +computing its position. These worked well enough for a time, but at +last the differences between the calculated and observed longitudes of +the planet became serious. In 1821 Bouvard undertook a revision of the +tables, but found it impossible to reconcile all the observations of +130 years (the period of revolution of Uranus is eighty-four years). So +he deliberately rejected the old ones, expressing the opinion that the +discrepancies might depend upon “some foreign and unperceived cause +which may have been acting upon the planet.” In a few years the errors +even of these tables became intolerable. In 1835 the error of longitude +was 30”; in 1838, 50”; in 1841, 70”; and, by comparing the errors +derived from observations made before and after opposition, a serious +error of the distance (radius vector) became apparent. + +In 1843 John Couch Adams came out Senior Wrangler at Cambridge, and was +free to undertake the research which as an undergraduate he had set +himself—to see whether the disturbances of Uranus could be explained by +assuming a certain orbit, and position in that orbit, of a hypothetical +planet even more distant than Uranus. Such an explanation had been +suggested, but until 1843 no one had the boldness to attack the +problem. Bessel had intended to try, but a fatal illness overtook him. + +Adams first recalculated all known causes of disturbance, using the +latest determinations of the planetary masses. Still the errors were +nearly as great as ever. He could now, however, use these errors as +being actually due to the perturbations produced by the unknown planet. + +In 1844, assuming a circular orbit, and a mean distance agreeing with +Bode’s law, he obtained a first approximation to the position of the +supposed planet. He then asked Professor Challis, of Cambridge, to +procure the latest observations of Uranus from Greenwich, which Airy +immediately supplied. Then the whole work was recalculated from the +beginning, with more exactness, and assuming a smaller mean distance. + +In September, 1845, he handed to Challis the elements of the +hypothetical planet, its mass, and its apparent position for September +30th, 1845. On September 22nd Challis wrote to Airy explaining the +matter, and declaring his belief in Adams’s capabilities. When Adams +called on him Airy was away from home, but at the end of October, 1845, +he called again, and left a paper with full particulars of his results, +which had, for the most part, reduced the discrepancies to about 1”. As +a matter of fact, it has since been found that the heliocentric place +of the new planet then given was correct within about 2°. + +Airy wrote expressing his interest, and asked for particulars about the +radius vector. Adams did not then reply, as the answer to this question +could be seen to be satisfactory by looking at the data already +supplied. He was a most unassuming man, and would not push himself +forward. He may have felt, after all the work he had done, that Airy’s +very natural inquiry showed no proportionate desire to search for the +planet. Anyway, the matter lay in embryo for nine months. + +Meanwhile, one of the ablest French astronomers, Le Verrier, +experienced in computing perturbations, was independently at work, +knowing nothing about Adams. He applied to his calculations every +possible refinement, and, considering the novelty of the problem, his +calculation was one of the most brilliant in the records of astronomy. +In criticism it has been said that these were exhibitions of skill +rather than helps to a solution of the particular problem, and that, in +claiming to find the elements of the orbit within certain limits, he +was claiming what was, under the circumstances, impossible, as the +result proved. + +In June, 1846, Le Verrier announced, in the _Comptes Rendus de +l’Academie des Sciences_, that the longitude of the disturbing planet, +for January 1st, 1847, was 325, and that the probable error did not +exceed 10°. + +This result agreed so well with Adams’s (within 1°) that Airy urged +Challis to apply the splendid Northumberland equatoreal, at Cambridge, +to the search. Challis, however, had already prepared an exhaustive +plan of attack which must in time settle the point. His first work was +to observe, and make a catalogue, or chart, of all stars near Adams’s +position. + +On August 31st, 1846, Le Verrier published the concluding part of his +labours. + +On September 18th, 1846, Le Verrier communicated his results to the +Astronomers at Berlin, and asked them to assist in searching for the +planet. By good luck Dr. Bremiker had just completed a star-chart of +the very part of the heavens including Le Verrier’s position; thus +eliminating all of Challis’s preliminary work. The letter was received +in Berlin on September 23rd; and the same evening Galle found the new +planet, of the eighth magnitude, the size of its disc agreeing with Le +Verrier’s prediction, and the heliocentric longitude agreeing within +57’. By this time Challis had recorded, without reduction, the +observations of 3,150 stars, as a commencement for his search. On +reducing these, he found a star, observed on August 12th, which was not +in the same place on July 30th. This was the planet, and he had also +observed it on August 4th. + +The feeling of wonder, admiration, and enthusiasm aroused by this +intellectual triumph was overwhelming. In the world of astronomy +reminders are met every day of the terrible limitations of human +reasoning powers; and every success that enables the mind’s eye to see +a little more clearly the meaning of things has always been heartily +welcomed by those who have themselves been engaged in like researches. +But, since the publication of the _Principia_, in 1687, there is +probably no analytical success which has raised among astronomers such +a feeling of admiration and gratitude as when Adams and Le Verrier +showed the inequalities in Uranus’s motion to mean that an unknown +planet was in a certain place in the heavens, where it was found. + +At the time there was an unpleasant display of international jealousy. +The British people thought that the earlier date of Adams’s work, and +of the observation by Challis, entitled him to at least an equal share +of credit with Le Verrier. The French, on the other hand, who, on the +announcement of the discovery by Galle, glowed with pride in the new +proof of the great powers of their astronomer, Le Verrier, whose life +had a long record of successes in calculation, were incredulous on +being told that it had all been already done by a young man whom they +had never heard of. + +These displays of jealousy have long since passed away, and there is +now universally an _entente cordiale_ that to each of these great men +belongs equally the merit of having so thoroughly calculated this +inverse problem of perturbations as to lead to the immediate discovery +of the unknown planet, since called Neptune. + +It was soon found that the planet had been observed, and its position +recorded as a fixed star by Lalande, on May 8th and 10th, 1795. + +Mr. Lassel, in the same year, 1846, with his two-feet reflector, +discovered a satellite, with retrograde motion, which gave the mass of +the planet about a twentieth of that of Jupiter. + +FOOTNOTES: + + [1] Bode’s law, or something like it, had already been fore-shadowed + by Kepler and others, especially Titius (see _Monatliche + Correspondenz_, vol. vii., p. 72). + + + + +BOOK III. OBSERVATION + +10. INSTRUMENTS OF PRECISION—STATE OF THE SOLAR SYSTEM. + + +Having now traced the progress of physical astronomy up to the time +when very striking proofs of the universality of the law of gravitation +convinced the most sceptical, it must still be borne in mind that, +while gravitation is certainly the principal force governing the +motions of the heavenly bodies, there may yet be a resisting medium in +space, and there may be electric and magnetic forces to deal with. +There may, further, be cases where the effects of luminous radiative +repulsion become apparent, and also Crookes’ vacuum-effects described +as “radiant matter.” Nor is it quite certain that Laplace’s proofs of +the instantaneous propagation of gravity are final. + +And in the future, as in the past, Tycho Brahe’s dictum must be +maintained, that all theory shall be preceded by accurate observations. +It is the pride of astronomers that their science stands above all +others in the accuracy of the facts observed, as well as in the rigid +logic of the mathematics used for interpreting these facts. + +It is interesting to trace historically the invention of those +instruments of precision which have led to this result, and, without +entering on the details required in a practical handbook, to note the +guiding principles of construction in different ages. + +It is very probable that the Chaldeans may have made spheres, like the +armillary sphere, for representing the poles of the heavens; and with +rings to show the ecliptic and zodiac, as well as the equinoctial and +solstitial colures; but we have no record. We only know that the tower +of Belus, on an eminence, was their observatory. We have, however, +distinct records of two such spheres used by the Chinese about 2500 +B.C. Gnomons, or some kind of sundial, were used by the Egyptians and +others; and many of the ancient nations measured the obliquity of the +ecliptic by the shadows of a vertical column in summer and winter. The +natural horizon was the only instrument of precision used by those who +determined star positions by the directions of their risings and +settings; while in those days the clepsydra, or waterclock, was the +best instrument for comparing their times of rising and setting. + +About 300 B.C. an observatory fitted with circular instruments for star +positions was set up at Alexandria, the then centre of civilisation. We +know almost nothing about the instruments used by Hipparchus in +preparing his star catalogues and his lunar and solar tables; but the +invention of the astrolabe is attributed to him.[1] + +In more modern times Nuremberg became a centre of astronomical culture. +Waltherus, of that town, made really accurate observations of star +altitudes, and of the distances between stars; and in 1484 A.D. he used +a kind of clock. Tycho Brahe tried these, but discarded them as being +inaccurate. + +Tycho Brahe (1546-1601 A.D.) made great improvements in armillary +spheres, quadrants, sextants, and large celestial globes. With these he +measured the positions of stars, or the distance of a comet from +several known stars. He has left us full descriptions of them, +illustrated by excellent engravings. Previous to his time such +instruments were made of wood. Tycho always used metal. He paid the +greatest attention to the stability of mounting, to the orientation of +his instruments, to the graduation of the arcs by the then new method +of transversals, and to the aperture sight used upon his pointer. There +were no telescopes in his day, and no pendulum clocks. He recognised +the fact that there must be instrumental errors. He made these as small +as was possible, measured their amount, and corrected his observations. +His table of refractions enabled him to abolish the error due to our +atmosphere so far as it could affect naked-eye observations. The +azimuth circle of Tycho’s largest quadrant had a diameter of nine feet, +and the quadrant a radius of six feet. He introduced the mural quadrant +for meridian observations.[2] + +[Illustration: ANCIENT CHINESE INSTRUMENTS, +Including quadrant, celestial globe, and two armillae, in the +Observatory at Peking. Photographed in Peking by the author in 1875, +and stolen by the Germans when the Embassies were relieved by the +allies in 1900.] + +The French Jesuits at Peking, in the seventeenth century, helped the +Chinese in their astronomy. In 1875 the writer saw and photographed, on +that part of the wall of Peking used by the Mandarins as an +observatory, the six instruments handsomely designed by Father +Verbiest, copied from the instruments of Tycho Brahe, and embellished +with Chinese dragons and emblems cast on the supports. He also saw +there two old instruments (which he was told were Arabic) of date 1279, +by Ko Show-King, astronomer to Koblai Khan, the grandson of Chenghis +Khan. One of these last is nearly identical with the armillae of Tycho; +and the other with his “armillae æquatoriæ maximæ,” with which he +observed the comet of 1585, besides fixed stars and planets.[3] + +The discovery by Galileo of the isochronism of the pendulum, followed +by Huyghens’s adaptation of that principle to clocks, has been one of +the greatest aids to accurate observation. About the same time an +equally beneficial step was the employment of the telescope as a +pointer; not the Galilean with concave eye-piece, but with a magnifying +glass to examine the focal image, at which also a fixed mark could be +placed. Kepler was the first to suggest this. Gascoigne was the first +to use it. Huyghens used a metal strip of variable width in the focus, +as a micrometer to cover a planetary disc, and so to measure the width +covered by the planet. The Marquis Malvasia, in 1662, described the +network of fine silver threads at right angles, which he used in the +focus, much as we do now. + +In the hands of such a skilful man as Tycho Brahe, the old open sights, +even without clocks, served their purpose sufficiently well to enable +Kepler to discover the true theory of the solar system. But telescopic +sights and clocks were required for proving some of Newton’s theories +of planetary perturbations. Picard’s observations at Paris from 1667 +onwards seem to embody the first use of the telescope as a pointer. He +was also the first to introduce the use of Huyghens’s clocks for +observing the right ascension of stars. Olaus Romer was born at +Copenhagen in 1644. In 1675, by careful study of the times of eclipses +of Jupiter’s satellites, he discovered that light took time to traverse +space. Its velocity is 186,000 miles per second. In 1681 he took up his +duties as astronomer at Copenhagen, and built the first transit circle +on a window-sill of his house. The iron axis was five feet long and one +and a-half inches thick, and the telescope was fixed near one end with +a counterpoise. The telescope-tube was a double cone, to prevent +flexure. Three horizontal and three vertical wires were used in the +focus. These were illuminated by a speculum, near the object-glass, +reflecting the light from a lantern placed over the axis, the upper +part of the telescope-tube being partly cut away to admit the light. A +divided circle, with pointer and reading microscope, was provided for +reading the declination. He realised the superiority of a circle with +graduations over a much larger quadrant. The collimation error was +found by reversing the instrument and using a terrestrial mark, the +azimuth error by star observations. The time was expressed in fractions +of a second. He also constructed a telescope with equatoreal mounting, +to follow a star by one axial motion. In 1728 his instruments and +observation records were destroyed by fire. + +Hevelius had introduced the vernier and tangent screw in his +measurement of arc graduations. His observatory and records were burnt +to the ground in 1679. Though an old man, he started afresh, and left +behind him a catalogue of 1,500 stars. + +Flamsteed began his duties at Greenwich Observatory, as first +Astronomer Royal, in 1676, with very poor instruments. In 1683 he put +up a mural arc of 140°, and in 1689 a better one, seventy-nine inches +radius. He conducted his measurements with great skill, and introduced +new methods to attain accuracy, using certain stars for determining the +errors of his instruments; and he always reduced his observations to a +form in which they could be readily used. He introduced new methods for +determining the position of the equinox and the right ascension of a +fundamental star. He produced a catalogue of 2,935 stars. He supplied +Sir Isaac Newton with results of observation required in his +theoretical calculations. He died in 1719. + +Halley succeeded Flamsteed to find that the whole place had been gutted +by the latter’s executors. In 1721 he got a transit instrument, and in +1726 a mural quadrant by Graham. His successor in 1742, Bradley, +replaced this by a fine brass quadrant, eight feet radius, by Bird; and +Bradley’s zenith sector was purchased for the observatory. An +instrument like this, specially designed for zenith stars, is capable +of greater rigidity than a more universal instrument; and there is no +trouble with refraction in the zenith. For these reasons Bradley had +set up this instrument at Kew, to attempt the proof of the earth’s +motion by observing the annual parallax of stars. He certainly found an +annual variation of zenith distance, but not at the times of year +required by the parallax. This led him to the discovery of the +“aberration” of light and of nutation. Bradley has been described as +the founder of the modern system of accurate observation. He died in +1762, leaving behind him thirteen folio volumes of valuable but +unreduced observations. Those relating to the stars were reduced by +Bessel and published in 1818, at Königsberg, in his well-known standard +work, _Fundamenta Astronomiae_. In it are results showing the laws of +refraction, with tables of its amount, the maximum value of aberration, +and other constants. + +Bradley was succeeded by Bliss, and he by Maskelyne (1765), who carried +on excellent work, and laid the foundations of the Nautical Almanac +(1767). Just before his death he induced the Government to replace +Bird’s quadrant by a fine new mural _circle_, six feet in diameter, by +Troughton, the divisions being read off by microscopes fixed on piers +opposite to the divided circle. In this instrument the micrometer +screw, with a divided circle for turning it, was applied for bringing +the micrometer wire actually in line with a division on the circle—a +plan which is still always adopted. + +Pond succeeded Maskelyne in 1811, and was the first to use this +instrument. From now onwards the places of stars were referred to the +pole, not to the zenith; the zero being obtained from measures on +circumpolar stars. Standard stars were used for giving the clock error. +In 1816 a new transit instrument, by Troughton, was added, and from +this date the Greenwich star places have maintained the very highest +accuracy. + +George Biddell Airy, Seventh Astronomer Royal,[4] commenced his +Greenwich labours in 1835. His first and greatest reformation in the +work of the observatory was one he had already established at +Cambridge, and is now universally adopted. He held that an observation +is not completed until it has been reduced to a useful form; and in the +case of the sun, moon, and planets these results were, in every case, +compared with the tables, and the tabular error printed. + +Airy was firmly impressed with the object for which Charles II. had +wisely founded the observatory in connection with navigation, and for +observations of the moon. Whenever a meridian transit of the moon could +be observed this was done. But, even so, there are periods in the month +when the moon is too near the sun for a transit to be well observed. +Also weather interferes with many meridian observations. To render the +lunar observations more continuous, Airy employed Troughton’s +successor, James Simms, in conjunction with the engineers, Ransome and +May, to construct an altazimuth with three-foot circles, and a +five-foot telescope, in 1847. The result was that the number of lunar +observations was immediately increased threefold, many of them being in +a part of the moon’s orbit which had previously been bare of +observations. From that date the Greenwich lunar observations have been +a model and a standard for the whole world. + +Airy also undertook to superintend the reduction of all Greenwich lunar +observations from 1750 to 1830. The value of this laborious work, which +was completed in 1848, cannot be over-estimated. + +The demands of astronomy, especially in regard to small minor planets, +required a transit instrument and mural circle with a more powerful +telescope. Airy combined the functions of both, and employed the same +constructors as before to make a _transit-circle_ with a telescope of +eleven and a-half feet focus and a circle of six-feet diameter, the +object-glass being eight inches in diameter. + +Airy, like Bradley, was impressed with the advantage of employing stars +in the zenith for determining the fundamental constants of astronomy. +He devised a _reflex zenith tube_, in which the zenith point was +determined by reflection from a surface of mercury. The design was so +simple, and seemed so perfect, that great expectations were +entertained. But unaccountable variations comparable with those of the +transit circle appeared, and the instrument was put out of use until +1903, when the present Astronomer Royal noticed that the irregularities +could be allowed for, being due to that remarkable variation in the +position of the earth’s axis included in circles of about six yards +diameter at the north and south poles, discovered at the end of the +nineteenth century. The instrument is now being used for investigating +these variations; and in the year 1907 as many as 1,545 observations of +stars were made with the reflex zenith tube. + +In connection with zenith telescopes it must be stated that Respighi, +at the Capitol Observatory at Rome, made use of a deep well with a +level mercury surface at the bottom and a telescope at the top pointing +downwards, which the writer saw in 1871. The reflection of the +micrometer wires and of a star very near the zenith (but not quite in +the zenith) can be observed together. His mercury trough was a circular +plane surface with a shallow edge to retain the mercury. The surface +quickly came to rest after disturbance by street traffic. + +Sir W. M. H. Christie, Eighth Astronomer Royal, took up his duties in +that capacity in 1881. Besides a larger altazimuth that he erected in +1898, he has widened the field of operations at Greenwich by the +extensive use of photography and the establishment of large +equatoreals. From the point of view of instruments of precision, one of +the most important new features is the astrographic equatoreal, set up +in 1892 and used for the Greenwich section of the great astrographic +chart just completed. Photography has come to be of use, not only for +depicting the sun and moon, comets and nebulae, but also to obtain +accurate relative positions of neighbouring stars; to pick up objects +that are invisible in any telescope; and, most of all perhaps, in +fixing the positions of faint satellites. Thus Saturn’s distant +satellite, Phoebe, and the sixth and seventh satellites of Jupiter, +have been followed regularly in their courses at Greenwich ever since +their discovery with the thirty-inch reflector (erected in 1897); and +while doing so Mr. Melotte made, in 1908, the splendid discovery on +some of the photographic plates of an eighth satellite of Jupiter, at +an enormous distance from the planet. From observations in the early +part of 1908, over a limited arc of its orbit, before Jupiter +approached the sun, Mr. Cowell computed a retrograde orbit and +calculated the future positions of this satellite, which enabled Mr. +Melotte to find it again in the autumn—a great triumph both of +calculation and of photographic observation. This satellite has never +been seen, and has been photographed only at Greenwich, Heidelberg, and +the Lick Observatory. + +Greenwich Observatory has been here selected for tracing the progress +of accurate measurement. But there is one instrument of great value, +the heliometer, which is not used at Greenwich. This serves the purpose +of a double image micrometer, and is made by dividing the object-glass +of a telescope along a diameter. Each half is mounted so as to slide a +distance of several inches each way on an arc whose centre is the +focus. The amount of the movement can be accurately read. Thus two +fields of view overlap, and the adjustment is made to bring an image of +one star over that of another star, and then to do the same by a +displacement in the opposite direction. The total movement of the +half-object glass is double the distance between the star images in the +focal plane. Such an instrument has long been established at Oxford, +and German astronomers have made great use of it. But in the hands of +Sir David Gill (late His Majesty’s Astronomer at the Cape of Good +Hope), and especially in his great researches on Solar and on Stellar +parallax, it has been recognised as an instrument of the very highest +accuracy, measuring the distance between stars correctly to less than a +tenth of a second of arc. + +The superiority of the heliometer over all other devices (except +photography) for measuring small angles has been specially brought into +prominence by Sir David Gill’s researches on the distance of the +sun—_i.e.,_ the scale of the solar system. A measurement of the +distance of any planet fixes the scale, and, as Venus approaches the +earth most nearly of all the planets, it used to be supposed that a +Transit of Venus offered the best opportunity for such measurement, +especially as it was thought that, as Venus entered on the solar disc, +the sweep of light round the dark disc of Venus would enable a very +precise observation to be made. The Transit of Venus in 1874, in which +the present writer assisted, overthrew this delusion. + +In 1877 Sir David Gill used Lord Crawford’s heliometer at the Island of +Ascension to measure the parallax of Mars in opposition, and found the +sun’s distance 93,080,000 miles. He considered that, while the +superiority of the heliometer had been proved, the results would be +still better with the points of light shown by minor planets rather +than with the disc of Mars. + +In 1888-9, at the Cape, he observed the minor planets Iris, Victoria, +and Sappho, and secured the co-operation of four other heliometers. His +final result was 92,870,000 miles, the parallax being 8",802 (_Cape +Obs_., Vol. VI.). + +So delicate were these measures that Gill detected a minute periodic +error of theory of twenty-seven days, owing to a periodically erroneous +position of the centre of gravity of the earth and moon to which the +position of the observer was referred. This led him to correct the mass +of the moon, and to fix its ratio to the earth’s mass = 0.012240. + +Another method of getting the distance from the sun is to measure the +velocity of the earth’s orbital motion, giving the circumference +traversed in a year, and so the radius of the orbit. This has been done +by comparing observation and experiment. The aberration of light is an +angle 20” 48, giving the ratio of the earth’s velocity to the velocity +of light. The velocity of light is 186,000 miles a second; whence the +distance to the sun is 92,780,000 miles. There seems, however, to be +some uncertainty about the true value of the aberration, any +determination of which is subject to irregularities due to the +“seasonal errors.” The velocity of light was experimentally found, in +1862, by Fizeau and Foucault, each using an independent method. These +methods have been developed, and new values found, by Cornu, +Michaelson, Newcomb, and the present writer. + +Quite lately Halm, at the Cape of Good Hope, measured spectroscopically +the velocity of the earth to and from a star by observations taken six +months apart. Thence he obtained an accurate value of the sun’s +distance.[5] + +But the remarkably erratic minor planet, Eros, discovered by Witte in +1898, approaches the earth within 15,000,000 miles at rare intervals, +and, with the aid of photography, will certainly give us the best +result. A large number of observatories combined to observe the +opposition of 1900. Their results are not yet completely reduced, but +the best value deduced so far for the parallax[6] is 8".807 ± +0".0028.[7] + +FOOTNOTES: + + [1] In 1480 Martin Behaim, of Nuremberg, produced his _astrolabe_ for + measuring the latitude, by observation of the sun, at sea. It + consisted of a graduated metal circle, suspended by a ring which was + passed over the thumb, and hung vertically. A pointer was fixed to a + pin at the centre. This arm, called the _alhidada_, worked round the + graduated circle, and was pointed to the sun. The altitude of the sun + was thus determined, and, by help of solar tables, the latitude could + be found from observations made at apparent noon. + + [2] See illustration on p. 76. + + [3] See Dreyer’s article on these instruments in _Copernicus_, Vol. I. + They were stolen by the Germans after the relief of the Embassies, in + 1900. The best description of these instruments is probably that + contained in an interesting volume, which may be seen in the library + of the R. A. S., entitled _Chinese Researches_, by Alexander Wyllie + (Shanghai, 1897). + + [4] Sir George Airy was very jealous of this honourable title. He + rightly held that there is only one Astronomer Royal at a time, as + there is only one Mikado, one Dalai Lama. He said that His Majesty’s + Astronomer at the Cape of Good Hope, His Majesty’s Astronomer for + Scotland, and His Majesty’s Astronomer for Ireland are not called + Astronomers Royal. + + [5] _Annals of the Cape Observatory_, vol. x., part 3. + + [6] The parallax of the sun is the angle subtended by the earth’s + radius at the sun’s distance. + + [7] A. R. Hinks, R.A.S.; Monthly Notices, June, 1909. + + + + +11. HISTORY OF THE TELESCOPE + + +Accounts of wonderful optical experiments by Roger Bacon (who died in +1292), and in the sixteenth century by Digges, Baptista Porta, and +Antonio de Dominis (Grant, _Hist. Ph. Ast_.), have led some to suppose +that they invented the telescope. The writer considers that it is more +likely that these notes refer to a kind of _camera obscura_, in which a +lens throws an inverted image of a landscape on the wall. + +The first telescopes were made in Holland, the originator being either +Henry Lipperhey,[1] Zacharias Jansen, or James Metius, and the date +1608 or earlier. + +In 1609 Galileo, being in Venice, heard of the invention, went home and +worked out the theory, and made a similar telescope. These telescopes +were all made with a convex object-glass and a concave eye-lens, and +this type is spoken of as the Galilean telescope. Its defects are that +it has no real focus where cross-wires can be placed, and that the +field of view is very small. Kepler suggested the convex eye-lens in +1611, and Scheiner claimed to have used one in 1617. But it was +Huyghens who really introduced them. In the seventeenth century +telescopes were made of great length, going up to 300 feet. Huyghens +also invented the compound eye-piece that bears his name, made of two +convex lenses to diminish spherical aberration. + +But the defects of colour remained, although their cause was unknown +until Newton carried out his experiments on dispersion and the solar +spectrum. To overcome the spherical aberration James Gregory,[2] of +Aberdeen and Edinburgh, in 1663, in his _Optica Promota_, proposed a +reflecting speculum of parabolic form. But it was Newton, about 1666, +who first made a reflecting telescope; and he did it with the object of +avoiding colour dispersion. + +Some time elapsed before reflectors were much used. Pound and Bradley +used one presented to the Royal Society by Hadley in 1723. Hawksbee, +Bradley, and Molyneaux made some. But James Short, of Edinburgh, made +many excellent Gregorian reflectors from 1732 till his death in 1768. + +Newton’s trouble with refractors, chromatic aberration, remained +insurmountable until John Dollond (born 1706, died 1761), after many +experiments, found out how to make an achromatic lens out of two +lenses—one of crown glass, the other of flint glass—to destroy the +colour, in a way originally suggested by Euler. He soon acquired a +great reputation for his telescopes of moderate size; but there was a +difficulty in making flint-glass lenses of large size. The first actual +inventor and constructor of an achromatic telescope was Chester Moor +Hall, who was not in trade, and did not patent it. Towards the close of +the eighteenth century a Swiss named Guinand at last succeeded in +producing larger flint-glass discs free from striae. Frauenhofer, of +Munich, took him up in 1805, and soon produced, among others, Struve’s +Dorpat refractor of 9.9 inches diameter and 13.5 feet focal length, and +another, of 12 inches diameter and 18 feet focal length, for Lamont, of +Munich. + +In the nineteenth century gigantic _reflectors_ have been made. +Lassel’s 2-foot reflector, made by himself, did much good work, and +discovered four new satellites. But Lord Rosse’s 6-foot reflector, 54 +feet focal length, constructed in 1845, is still the largest ever made. +The imperfections of our atmosphere are against the use of such large +apertures, unless it be on high mountains. During the last half century +excellent specula have been made of silvered glass, and Dr. Common’s +5-foot speculum (removed, since his death, to Harvard) has done +excellent work. Then there are the 5-foot Yerkes reflector at Chicago, +and the 4-foot by Grubb at Melbourne. + +Passing now from these large reflectors to refractors, further +improvements have been made in the manufacture of glass by Chance, of +Birmingham, Feil and Mantois, of Paris, and Schott, of Jena; while +specialists in grinding lenses, like Alvan Clark, of the U.S.A., and +others, have produced many large refractors. + +Cooke, of York, made an object-glass, 25-inch diameter, for Newall, of +Gateshead, which has done splendid work at Cambridge. We have the +Washington 26-inch by Clark, the Vienna 27-inch by Grubb, the Nice +29½-inch by Gautier, the Pulkowa 30-inch by Clark. Then there was the +sensation of Clark’s 36-inch for the Lick Observatory in California, +and finally his _tour de force_, the Yerkes 40-inch refractor, for +Chicago. + +At Greenwich there is the 28-inch photographic refractor, and the +Thompson equatoreal by Grubb, carrying both the 26-inch photographic +refractor and the 30-inch reflector. At the Cape of Good Hope we find +Mr. Frank McClean’s 24-inch refractor, with an object-glass prism for +spectroscopic work. + +It would be out of place to describe here the practical adjuncts of a +modern equatoreal—the adjustments for pointing it, the clock for +driving it, the position-micrometer and various eye-pieces, the +photographic and spectroscopic attachments, the revolving domes, +observing seats, and rising floors and different forms of mounting, the +siderostats and coelostats, and other convenient adjuncts, besides the +registering chronograph and numerous facilities for aiding observation. +On each of these a chapter might be written; but the most important +part of the whole outfit is the man behind the telescope, and it is +with him that a history is more especially concerned. + + +SPECTROSCOPE. + +Since the invention of the telescope no discovery has given so great an +impetus to astronomical physics as the spectroscope; and in giving us +information about the systems of stars and their proper motions it +rivals the telescope. + +Frauenhofer, at the beginning of the nineteenth century, while applying +Dollond’s discovery to make large achromatic telescopes, studied the +dispersion of light by a prism. Admitting the light of the sun through +a narrow slit in a window-shutter, an inverted image of the slit can be +thrown, by a lens of suitable focal length, on the wall opposite. If a +wedge or prism of glass be interposed, the image is deflected to one +side; but, as Newton had shown, the images formed by the different +colours of which white light is composed are deflected to different +extents—the violet most, the red least. The number of colours forming +images is so numerous as to form a continuous spectrum on the wall with +all the colours—red, orange, yellow, green, blue, indigo, and violet. +But Frauenhofer found with a narrow slit, well focussed by the lens, +that some colours were missing in the white light of the sun, and these +were shown by dark lines across the spectrum. These are the Frauenhofer +lines, some of which he named by the letters of the alphabet. The D +line is a very marked one in the yellow. These dark lines in the solar +spectrum had already been observed by Wollaston.[3] + +On examining artificial lights it was found that incandescent solids +and liquids (including the carbon glowing in a white gas flame) give +continuous spectra; gases, except under enormous pressure, give bright +lines. If sodium or common salt be thrown on the colourless flame of a +spirit lamp, it gives it a yellow colour, and its spectrum is a bright +yellow line agreeing in position with line D of the solar spectrum. + +In 1832 Sir David Brewster found some of the solar black lines +increased in strength towards sunset, and attributed them to absorption +in the earth’s atmosphere. He suggested that the others were due to +absorption in the sun’s atmosphere. Thereupon Professor J. D. Forbes +pointed out that during a nearly total eclipse the lines ought to be +strengthened in the same way; as that part of the sun’s light, coming +from its edge, passes through a great distance in the sun’s atmosphere. +He tried this with the annular eclipse of 1836, with a negative result +which has never been accounted for, and which seemed to condemn +Brewster’s view. + +In 1859 Kirchoff, on repeating Frauenhofer’s experiment, found that, if +a spirit lamp with salt in the flame were placed in the path of the +light, the black D line is intensified. He also found that, if he used +a limelight instead of the sunlight and passed it through the flame +with salt, the spectrum showed the D line black; or the vapour of +sodium absorbs the same light that it radiates. This proved to him the +existence of sodium in the sun’s atmosphere.[4] Iron, calcium, and +other elements were soon detected in the same way. + +Extensive laboratory researches (still incomplete) have been carried +out to catalogue (according to their wave-length on the undulatory +theory of light) all the lines of each chemical element, under all +conditions of temperature and pressure. At the same time, all the lines +have been catalogued in the light of the sun and the brighter of the +stars. + +Another method of obtaining spectra had long been known, by +transmission through, or reflection from, a grating of equidistant +lines ruled upon glass or metal. H. A. Rowland developed the art of +constructing these gratings, which requires great technical skill, and +for this astronomers owe him a debt of gratitude. + +In 1842 Doppler[5] proved that the colour of a luminous body, like the +pitch or note of a sounding body, must be changed by velocity of +approach or recession. Everyone has noticed on a railway that, on +meeting a locomotive whistling, the note is lowered after the engine +has passed. The pitch of a sound or the colour of a light depends on +the number of waves striking the ear or eye in a second. This number is +increased by approach and lowered by recession. + +Thus, by comparing the spectrum of a star alongside a spectrum of +hydrogen, we may see all the lines, and be sure that there is hydrogen +in the star; yet the lines in the star-spectrum may be all slightly +displaced to one side of the lines of the comparison spectrum. If +towards the violet end, it means mutual approach of the star and earth; +if to the red end, it means recession. The displacement of lines does +not tell us whether the motion is in the star, the earth, or both. The +displacement of the lines being measured, we can calculate the rate of +approach or recession in miles per second. + +In 1868 Huggins[6] succeeded in thus measuring the velocities of stars +in the direction of the line of sight. + +In 1873 Vogel[7] compared the spectra of the sun’s East (approaching) +limb and West (receding) limb, and the displacement of lines endorsed +the theory. This last observation was suggested by Zöllner. + +FOOTNOTES: + + [1] In the _Encyclopaedia Britannica_, article “Telescope,” and in + Grant’s _Physical Astronomy_, good reasons are given for awarding the + honour to Lipperhey. + + [2] Will the indulgent reader excuse an anecdote which may encourage + some workers who may have found their mathematics defective through + want of use? James Gregory’s nephew David had a heap of MS. notes by + Newton. These descended to a Miss Gregory, of Edinburgh, who handed + them to the present writer, when an undergraduate at Cambridge, to + examine. After perusal, he lent them to his kindest of friends, J. C. + Adams (the discoverer of Neptune), for his opinion. Adams’s final + verdict was: “I fear they are of no value. It is pretty evident that, + when he wrote these notes, _Newton’s mathematics were a little + rusty_.” + + [3] _R. S. Phil. Trans_. + + [4] The experiment had been made before by one who did not understand + its meaning;. But Sir George G. Stokes had already given verbally the + true explanation of Frauenhofer lines. + + [5] _Abh. d. Kön. Böhm. d. Wiss_., Bd. ii., 1841-42, p. 467. See also + Fizeau in the _Ann. de Chem. et de Phys_., 1870, p. 211. + + [6] _R. S. Phil. Trans_., 1868. + + [7] _Ast. Nach_., No. 1, 864. + +BOOK IV. THE PHYSICAL PERIOD + +We have seen how the theory of the solar system was slowly developed by +the constant efforts of the human mind to find out what are the rules +of cause and effect by which our conception of the present universe and +its development seems to be bound. In the primitive ages a mere record +of events in the heavens and on the earth gave the only hope of +detecting those uniform sequences from which to derive rules or laws of +cause and effect upon which to rely. Then came the geometrical age, in +which rules were sought by which to predict the movements of heavenly +bodies. Later, when the relation of the sun to the courses of the +planets was established, the sun came to be looked upon as a cause; and +finally, early in the seventeenth century, for the first time in +history, it began to be recognised that the laws of dynamics, exactly +as they had been established for our own terrestrial world, hold good, +with the same rigid invariability, at least as far as the limits of the +solar system. + +Throughout this evolution of thought and conjecture there were two +types of astronomers—those who supplied the facts, and those who +supplied the interpretation through the logic of mathematics. So +Ptolemy was dependent upon Hipparchus, Kepler on Tycho Brahe, and +Newton in much of his work upon Flamsteed. + +When Galileo directed his telescope to the heavens, when Secchi and +Huggins studied the chemistry of the stars by means of the +spectroscope, and when Warren De la Rue set up a photoheliograph at +Kew, we see that a progress in the same direction as before, in the +evolution of our conception of the universe, was being made. Without +definite expression at any particular date, it came to be an accepted +fact that not only do earthly dynamics apply to the heavenly bodies, +but that the laws we find established here, in geology, in chemistry, +and in the laws of heat, may be extended with confidence to the +heavenly bodies. Hence arose the branch of astronomy called +astronomical physics, a science which claims a large portion of the +work of the telescope, spectroscope, and photography. In this new +development it is more than ever essential to follow the dictum of +Tycho Brahe—not to make theories until all the necessary facts are +obtained. The great astronomers of to-day still hold to Sir Isaac +Newton’s declaration, “Hypotheses non fingo.” Each one may have his +suspicions of a theory to guide him in a course of observation, and may +call it a working hypothesis. But the cautious astronomer does not +proclaim these to the world; and the historian is certainly not +justified in including in his record those vague speculations founded +on incomplete data which may be demolished to-morrow, and which, +however attractive they may be, often do more harm than good to the +progress of true science. Meanwhile the accumulation of facts has been +prodigious, and the revelations of the telescope and spectroscope +entrancing. + + + + +12. THE SUN. + + +One of Galileo’s most striking discoveries, when he pointed his +telescope to the heavenly bodies, was that of the irregularly shaped +spots on the sun, with the dark central _umbra_ and the less dark, but +more extensive, _penumbra_ surrounding it, sometimes with several +umbrae in one penumbra. He has left us many drawings of these spots, +and he fixed their period of rotation as a lunar month. + +It is not certain whether Galileo, Fabricius, or Schemer was the first +to see the spots. They all did good work. The spots were found to be +ever varying in size and shape. Sometimes, when a spot disappears at +the western limb of the sun, it is never seen again. In other cases, +after a fortnight, it reappears at the eastern limb. The faculae, or +bright areas, which are seen all over the sun’s surface, but specially +in the neighbourhood of spots, and most distinctly near the sun’s edge, +were discovered by Galileo. A high telescopic power resolves their +structure into an appearance like willow-leaves, or rice-grains, fairly +uniform in size, and more marked than on other parts of the sun’s +surface. + +[Illustration: SOLAR SURFACE. +As Photographed at the Royal Observatory, Greenwich, showing sun-spots +with umbræ, penumbræ, and faculæ.] + +Speculations as to the cause of sun-spots have never ceased from +Galileo’s time to ours. He supposed them to be clouds. Scheiner[1] said +they were the indications of tumultuous movements occasionally +agitating the ocean of liquid fire of which he supposed the sun to be +composed. + +A. Wilson, of Glasgow, in 1769,[2] noticed a movement of the umbra +relative to the penumbra in the transit of the spot over the sun’s +surface; exactly as if the spot were a hollow, with a black base and +grey shelving sides. This was generally accepted, but later +investigations have contradicted its universality. Regarding the cause +of these hollows, Wilson said:— + +Whether their first production and subsequent numberless changes depend +upon the eructation of elastic vapours from below, or upon eddies or +whirlpools commencing at the surface, or upon the dissolving of the +luminous matter in the solar atmosphere, as clouds are melted and again +given out by our air; or, if the reader pleases, upon the annihilation +and reproduction of parts of this resplendent covering, is left for +theory to guess at.[3] + +Ever since that date theory has been guessing at it. The solar +astronomer is still applying all the instruments of modern research to +find out which of these suppositions, or what modification of any of +them, is nearest the truth. The obstacle—one that is perhaps fatal to a +real theory—lies in the impossibility of reproducing comparative +experiments in our laboratories or in our atmosphere. + +Sir William Herschel propounded an explanation of Wilson’s observation +which received much notice, but which, out of respect for his memory, +is not now described, as it violated the elementary laws of heat. + +Sir John Herschel noticed that the spots are mostly confined to two +zones extending to about 35° on each side of the equator, and that a +zone of equatoreal calms is free from spots. But it was R. C. +Carrington[4] who, by his continuous observations at Redhill, in +Surrey, established the remarkable fact that, while the rotation period +in the highest latitudes, 50°, where spots are seen, is +twenty-seven-and-a-half days, near the equator the period is only +twenty-five days. His splendid volume of observations of the sun led to +much new information about the average distribution of spots at +different epochs. + +Schwabe, of Dessau, began in 1826 to study the solar surface, and, +after many years of work, arrived at a law of frequency which has been +more fruitful of results than any discovery in solar physics.[5] In +1843 he announced a decennial period of maxima and minima of sun-spot +displays. In 1851 it was generally accepted, and, although a period of +eleven years has been found to be more exact, all later observations, +besides the earlier ones which have been hunted up for the purpose, go +to establish a true periodicity in the number of sun-spots. But quite +lately Schuster[6] has given reasons for admitting a number of +co-existent periods, of which the eleven-year period was predominant in +the nineteenth century. + +In 1851 Lament, a Scotchman at Munich, found a decennial period in the +daily range of magnetic declination. In 1852 Sir Edward Sabine +announced a similar period in the number of “magnetic storms” affecting +all of the three magnetic elements—declination, dip, and intensity. +Australian and Canadian observations both showed the decennial period +in all three elements. Wolf, of Zurich, and Gauthier, of Geneva, each +independently arrived at the same conclusion. + +It took many years before this coincidence was accepted as certainly +more than an accident by the old-fashioned astronomers, who want rigid +proof for every new theory. But the last doubts have long vanished, and +a connection has been further traced between violent outbursts of solar +activity and simultaneous magnetic storms. + +The frequency of the Aurora Borealis was found by Wolf to follow the +same period. In fact, it is closely allied in its cause to terrestrial +magnetism. Wolf also collected old observations tracing the periodicity +of sun-spots back to about 1700 A.D. + +Spoerer deduced a law of dependence of the average latitude of +sun-spots on the phase of the sun-spot period. + +All modern total solar eclipse observations seem to show that the shape +of the luminous corona surrounding the moon at the moment of totality +has a special distinct character during the time of a sun-spot maximum, +and another, totally different, during a sun-spot minimum. + +A suspicion is entertained that the total quantity of heat received by +the earth from the sun is subject to the same period. This would have +far-reaching effects on storms, harvests, vintages, floods, and +droughts; but it is not safe to draw conclusions of this kind except +from a very long period of observations. + +Solar photography has deprived astronomers of the type of Carrington of +the delight in devoting a life’s work to collecting data. It has now +become part of the routine work of an observatory. + +In 1845 Foucault and Fizeau took a daguerreotype photograph of the sun. +In 1850 Bond produced one of the moon of great beauty, Draper having +made some attempts at an even earlier date. But astronomical +photography really owes its beginning to De la Rue, who used the +collodion process for the moon in 1853, and constructed the Kew +photoheliograph in 1857, from which date these instruments have been +multiplied, and have given us an accurate record of the sun’s surface. +Gelatine dry plates were first used by Huggins in 1876. + +It is noteworthy that from the outset De la Rue recognised the value of +stereoscopic vision, which is now known to be of supreme accuracy. In +1853 he combined pairs of photographs of the moon in the same phase, +but under different conditions regarding libration, showing the moon +from slightly different points of view. These in the stereoscope +exhibited all the relief resulting from binocular vision, and looked +like a solid globe. In 1860 he used successive photographs of the total +solar eclipse stereoscopically, to prove that the red prominences +belong to the sun, and not to the moon. In 1861 he similarly combined +two photographs of a sun-spot, the perspective effect showing the umbra +like a floor at the bottom of a hollow penumbra; and in one case the +faculæ were discovered to be sailing over a spot apparently at some +considerable height. These appearances may be partly due to a proper +motion; but, so far as it went, this was a beautiful confirmation of +Wilson’s discovery. Hewlett, however, in 1894, after thirty years of +work, showed that the spots are not always depressions, being very +subject to disturbance. + +The Kew photographs[7] contributed a vast amount of information about +sun-spots, and they showed that the faculæ generally follow the spots +in their rotation round the sun. + +The constitution of the sun’s photosphere, the layer which is the +principal light-source on the sun, has always been a subject of great +interest; and much was done by men with exceptionally keen eyesight, +like Mr. Dawes. But it was a difficult subject, owing to the rapidity +of the changes in appearance of the so-called rice-grains, about 1” in +diameter. The rapid transformations and circulations of these +rice-grains, if thoroughly studied, might lead to a much better +knowledge of solar physics. This seemed almost hopeless, as it was +found impossible to identify any “rice-grain” in the turmoil after a +few minutes. But M. Hansky, of Pulkowa (whose recent death is +deplored), introduced successfully a scheme of photography, which might +almost be called a solar cinematograph. He took photographs of the sun +at intervals of fifteen or thirty seconds, and then enlarged selected +portions of these two hundred times, giving a picture corresponding to +a solar disc of six metres diameter. In these enlarged pictures he was +able to trace the movements, and changes of shape and brightness, of +individual rice-grains. Some granules become larger or smaller. Some +seem to rise out of a mist, as it were, and to become clearer. Others +grow feebler. Some are split in two. Some are rotated through a right +angle in a minute or less, although each of the grains may be the size +of Great Britain. Generally they move together in groups of very +various velocities, up to forty kilometres a second. These movements +seem to have definite relation to any sun-spots in the neighbourhood. +From the results already obtained it seems certain that, if this method +of observation be continued, it cannot fail to supply facts of the +greatest importance. + +It is quite impossible to do justice here to the work of all those who +are engaged on astronomical physics. The utmost that can be attempted +is to give a fair idea of the directions of human thought and +endeavour. During the last half-century America has made splendid +progress, and an entirely new process of studying the photosphere has +been independently perfected by Professor Hale at Chicago, and +Deslandres at Paris.[8] They have succeeded in photographing the sun’s +surface in monochromatic light, such as the light given off as one of +the bright lines of hydrogen or of calcium, by means of the +“Spectroheliograph.” The spectroscope is placed with its slit in the +focus of an equatoreal telescope, pointed to the sun, so that the +circular image of the sun falls on the slit. At the other end of the +spectroscope is the photographic plate. Just in front of this plate +there is another slit parallel to the first, in the position where the +image of the first slit formed by the K line of calcium falls. Thus is +obtained a photograph of the section of the sun, made by the first +slit, only in K light. As the image of the sun passes over the first +slit the photographic plate is moved at the same rate and in the same +direction behind the second slit; and as successive sections of the +sun’s image in the equatoreal enter the apparatus, so are these +sections successively thrown in their proper place on the photographic +plate, always in K light. By using a high dispersion the faculæ which +give off K light can be correctly photographed, not only at the sun’s +edge, but all over his surface. The actual mechanical method of +carrying out the observation is not quite so simple as what is here +described. + +By choosing another line of the spectrum instead of calcium K—for +example, the hydrogen line H(3)—we obtain two photographs, one showing +the appearance of the calcium floculi, and the other of the hydrogen +floculi, on the same part of the solar surface; and nothing is more +astonishing than to note the total want of resemblance in the forms +shown on the two. This mode of research promises to afford many new and +useful data. + +The spectroscope has revealed the fact that, broadly speaking, the sun +is composed of the same materials as the earth. Ångstrom was the first +to map out all of the lines to be found in the solar spectrum. But +Rowland, of Baltimore, after having perfected the art of making true +gratings with equidistant lines ruled on metal for producing spectra, +then proceeded to make a map of the solar spectrum on a large scale. + +In 1866 Lockyer[9] threw an image of the sun upon the slit of a +spectroscope, and was thus enabled to compare the spectrum of a spot +with that of the general solar surface. The observation proved the +darkness of a spot to be caused by increased absorption of light, not +only in the dark lines, which are widened, but over the entire +spectrum. In 1883 Young resolved this continuous obscurity into an +infinite number of fine lines, which have all been traced in a shadowy +way on to the general solar surface. Lockyer also detected +displacements of the spectrum lines in the spots, such as would be +produced by a rapid motion in the line of sight. It has been found that +both uprushes and downrushes occur, but there is no marked predominance +of either in a sun-spot. The velocity of motion thus indicated in the +line of sight sometimes appears to amount to 320 miles a second. But it +must be remembered that pressure of a gas has some effect in displacing +the spectral lines. So we must go on, collecting data, until a time +comes when the meaning of all the facts can be made clear. + +_Total Solar Eclipses_.—During total solar eclipses the time is so +short, and the circumstances so impressive, that drawings of the +appearance could not always be trusted. The red prominences of jagged +form that are seen round the moon’s edge, and the corona with its +streamers radiating or interlacing, have much detail that can hardly be +recorded in a sketch. By the aid of photography a number of records can +be taken during the progress of totality. From a study of these the +extent of the corona is demonstrated in one case to extend to at least +six diameters of the moon, though the eye has traced it farther. This +corona is still one of the wonders of astronomy, and leads to many +questions. What is its consistency, if it extends many million miles +from the sun’s surface? How is it that it opposed no resistance to the +motion of comets which have almost grazed the sun’s surface? Is this +the origin of the zodiacal light? The character of the corona in +photographic records has been shown to depend upon the phase of the +sun-spot period. During the sun-spot maximum the corona seems most +developed over the spot-zones—i.e., neither at the equator nor the +poles. The four great sheaves of light give it a square appearance, and +are made up of rays or plumes, delicate like the petals of a flower. +During a minimum the nebulous ring seems to be made of tufts of fine +hairs with aigrettes or radiations from both poles, and streamers from +the equator. + +[Illustration: SOLAR ECLIPSE, 1882. From drawing by W. H. Wesley, +Secretary R.A.S.; showing the prominences, the corona, and an unknown +comet.] + +On September 19th, 1868, eclipse spectroscopy began with the Indian +eclipse, in which all observers found that the red prominences showed a +bright line spectrum, indicating the presence of hydrogen and other +gases. So bright was it that Jansen exclaimed: “_Je verrai ces +lignes-là en dehors des éclipses_.” And the next day he observed the +lines at the edge of the uneclipsed sun. Huggins had suggested this +observation in February, 1868, his idea being to use prisms of such +great dispersive power that the continuous spectrum reflected by our +atmosphere should be greatly weakened, while a bright line would suffer +no diminution by the high dispersion. On October 20th Lockyer,[10] +having news of the eclipse, but not of Jansen’s observations the day +after, was able to see these lines. This was a splendid performance, +for it enabled the prominences to be observed, not only during +eclipses, but every day. Moreover, the next year Huggins was able, by +using a wide slit, to see the whole of a prominence and note its shape. +Prominences are classified, according to their form, into “flame” and +“cloud” prominences, the spectrum of the latter showing calcium, +hydrogen, and helium; that of the former including a number of metals. + +The D line of sodium is a double line, and in the same eclipse (1868) +an orange line was noticed which was afterwards found to lie close to +the two components of the D line. It did not correspond with any known +terrestrial element, and the unknown element was called “helium.” It +was not until 1895 that Sir William Ramsay found this element as a gas +in the mineral cleavite. + +The spectrum of the corona is partly continuous, indicating light +reflected from the sun’s body. But it also shows a green line +corresponding with no known terrestrial element, and the name +“coronium” has been given to the substance causing it. + +A vast number of facts have been added to our knowledge about the sun +by photography and the spectroscope. Speculations and hypotheses in +plenty have been offered, but it may be long before we have a complete +theory evolved to explain all the phenomena of the storm-swept metallic +atmosphere of the sun. + +The proceedings of scientific societies teem with such facts and +“working hypotheses,” and the best of them have been collected by Miss +Clerke in her _History of Astronomy during the Nineteenth Century_. As +to established facts, we learn from the spectroscopic researches (1) +that the continuous spectrum is derived from the _photosphere_ or solar +gaseous material compressed almost to liquid consistency; (2) that the +_reversing layer_ surrounds it and gives rise to black lines in the +spectrum; that the _chromosphere_ surrounds this, is composed mainly of +hydrogen, and is the cause of the red prominences in eclipses; and that +the gaseous _corona_ surrounds all of these, and extends to vast +distances outside the sun’s visible surface. + +FOOTNOTES: + + [1] _Rosa Ursina_, by C. Scheiner, _fol_.; Bracciani, 1630. + + [2] _R. S. Phil. Trans_., 1774. + + [3] _Ibid_, 1783. + + [4] _Observations on the Spots on the Sun, etc.,_ 4°; London and + Edinburgh, 1863. + + [5] _Periodicität der Sonnenflecken. Astron. Nach. XXI._, 1844, P. + 234. + + [6] _R.S. Phil. Trans._ (ser. A), 1906, p. 69-100. + + [7] “Researches on Solar Physics,” by De la Rue, Stewart and Loewy; + _R. S. Phil. Trans_., 1869, 1870. + + [8] “The Sun as Photographed on the K line”; _Knowledge_, London, + 1903, p. 229. + + [9] _R. S. Proc._, xv., 1867, p. 256. + + [10] _Acad. des Sc._, Paris; _C. R._, lxvii., 1868, p. 121. + + + + +13. THE MOON AND PLANETS. + + +_The Moon_.—Telescopic discoveries about the moon commence with +Galileo’s discovery that her surface has mountains and valleys, like +the earth. He also found that, while she always turns the same face to +us, there is periodically a slight twist to let us see a little round +the eastern or western edge. This was called _libration_, and the +explanation was clear when it was understood that in showing always the +same face to us she makes one revolution a month on her axis +_uniformly_, and that her revolution round the earth is not uniform. + +Galileo said that the mountains on the moon showed greater differences +of level than those on the earth. Shröter supported this opinion. W. +Herschel opposed it. But Beer and Mädler measured the heights of lunar +mountains by their shadows, and found four of them over 20,000 feet +above the surrounding plains. + +Langrenus[1] was the first to do serious work on selenography, and +named the lunar features after eminent men. Riccioli also made lunar +charts. In 1692 Cassini made a chart of the full moon. Since then we +have the charts of Schröter, Beer and Mädler (1837), and of Schmidt, of +Athens (1878); and, above all, the photographic atlas by Loewy and +Puiseux. + +The details of the moon’s surface require for their discussion a whole +book, like that of Neison or the one by Nasmyth and Carpenter. Here a +few words must suffice. Mountain ranges like our Andes or Himalayas are +rare. Instead of that, we see an immense number of circular cavities, +with rugged edges and flat interior, often with a cone in the centre, +reminding one of instantaneous photographs of the splash of a drop of +water falling into a pool. Many of these are fifty or sixty miles +across, some more. They are generally spoken of as resembling craters +of volcanoes, active or extinct, on the earth. But some of those who +have most fully studied the shapes of craters deny altogether their +resemblance to the circular objects on the moon. These so-called +craters, in many parts, are seen to be closely grouped, especially in +the snow-white parts of the moon. But there are great smooth dark +spaces, like the clear black ice on a pond, more free from craters, to +which the equally inappropriate name of seas has been given. The most +conspicuous crater, _Tycho_, is near the south pole. At full moon there +are seen to radiate from Tycho numerous streaks of light, or “rays,” +cutting through all the mountain formations, and extending over fully +half the lunar disc, like the star-shaped cracks made on a sheet of ice +by a blow. Similar cracks radiate from other large craters. It must be +mentioned that these white rays are well seen only in full light of the +sun at full moon, just as the white snow in the crevasses of a glacier +is seen bright from a distance only when the sun is high, and +disappears at sunset. Then there are deep, narrow, crooked “rills” +which may have been water-courses; also “clefts” about half a mile +wide, and often hundreds of miles long, like deep cracks in the surface +going straight through mountain and valley. + +The moon shares with the sun the advantage of being a good subject for +photography, though the planets are not. This is owing to her larger +apparent size, and the abundance of illumination. The consequence is +that the finest details of the moon, as seen in the largest telescope +in the world, may be reproduced at a cost within the reach of all. + +No certain changes have ever been observed; but several suspicions have +been expressed, especially as to the small crater _Linné_, in the _Mare +Serenitatis_. It is now generally agreed that no certainty can be +expected from drawings, and that for real evidence we must await the +verdict of photography. + +No trace of water or of an atmosphere has been found on the moon. It is +possible that the temperature is too low. In any case, no displacement +of a star by atmospheric refraction at occultation has been surely +recorded. The moon seems to be dead. + +The distance of the moon from the earth is just now the subject of +re-measurement. The base line is from Greenwich to Cape of Good Hope, +and the new feature introduced is the selection of a definite point on +a crater (Mösting A), instead of the moon’s edge, as the point whose +distance is to be measured. + +_The Inferior Planets_.—When the telescope was invented, the phases of +Venus attracted much attention; but the brightness of this planet, and +her proximity to the sun, as with Mercury also, seemed to be a bar to +the discovery of markings by which the axis and period of rotation +could be fixed. Cassini gave the rotation as twenty-three hours, by +observing a bright spot on her surface. Shröter made it 23h. 21m. 19s. +This value was supported by others. In 1890 Schiaparelli[2] announced +that Venus rotates, like our moon, once in one of her revolutions, and +always directs the same face to the sun. This property has also been +ascribed to Mercury; but in neither case has the evidence been +generally accepted. Twenty-four hours is probably about the period of +rotation for each of these planets. + +Several observers have claimed to have seen a planet within the orbit +of Mercury, either in transit over the sun’s surface or during an +eclipse. It has even been named _Vulcan_. These announcements would +have received little attention but for the fact that the motion of +Mercury has irregularities which have not been accounted for by known +planets; and Le Verrier[3] has stated that an intra-Mercurial planet or +ring of asteroids would account for the unexplained part of the motion +of the line of apses of Mercury’s orbit amounting to 38” per century. + +_Mars_.—The first study of the appearance of Mars by Miraldi led him to +believe that there were changes proceeding in the two white caps which +are seen at the planet’s poles. W. Herschel attributed these caps to +ice and snow, and the dates of his observations indicated a melting of +these ice-caps in the Martian summer. + +Schroter attributed the other markings on Mars to drifting clouds. But +Beer and Mädler, in 1830-39, identified the same dark spots as being +always in the same place, though sometimes blurred by mist in the local +winter. A spot sketched by Huyghens in 1672, one frequently seen by W. +Herschel in 1783, another by Arago in 1813, and nearly all the markings +recorded by Beer and Mädler in 1830, were seen and drawn by F. Kaiser +in Leyden during seventeen nights of the opposition of 1862 (_Ast. +Nacht._, No. 1,468), whence he deduced the period of rotation to be +24h. 37m. 22s.,62—or one-tenth of a second less than the period deduced +by R. A. Proctor from a drawing by Hooke in 1666. + +It must be noted that, if the periods of rotation both of Mercury and +Venus be about twenty-four hours, as seems probable, all the four +planets nearest to the sun rotate in the same period, while the great +planets rotate in about ten hours (Uranus and Neptune being still +indeterminate). + +The general surface of Mars is a deep yellow; but there are dark grey +or greenish patches. Sir John Herschel was the first to attribute the +ruddy colour of Mars to its soil rather than to its atmosphere. + +The observations of that keen-sighted observer Dawes led to the first +good map of Mars, in 1869. In the 1877 opposition Schiaparelli revived +interest in the planet by the discovery of canals, uniformly about +sixty miles wide, running generally on great circles, some of them +being three or four thousand miles long. During the opposition of +1881-2 the same observer re-observed the canals, and in twenty of them +he found the canals duplicated,[4] the second canal being always 200 to +400 miles distant from its fellow. + +The existence of these canals has been doubted. Mr. Lowell has now +devoted years to the subject, has drawn them over and over again, and +has photographed them; and accepts the explanation that they are +artificial, and that vegetation grows on their banks. Thus is revived +the old controversy between Whewell and Brewster as to the habitability +of the planets. The new arguments are not yet generally accepted. +Lowell believes he has, with the spectroscope, proved the existence of +water on Mars. + +One of the most unexpected and interesting of all telescopic +discoveries took place in the opposition of 1877, when Mars was +unusually near to the earth. The Washington Observatory had acquired +the fine 26-inch refractor, and Asaph Hall searched for satellites, +concealing the planet’s disc to avoid the glare. On August 11th he had +a suspicion of a satellite. This was confirmed on the 16th, and on the +following night a second one was added. They are exceedingly faint, and +can be seen only by the most powerful telescopes, and only at the times +of opposition. Their diameters are estimated at six or seven miles. It +was soon found that the first, Deimos, completes its orbit in 30h. 18m. +But the other, Phobos, at first was a puzzle, owing to its incredible +velocity being unsuspected. Later it was found that the period of +revolution was only 7h. 39m. 22s. Since the Martian day is twenty-four +and a half hours, this leads to remarkable results. Obviously the +easterly motion of the satellite overwhelms the diurnal rotation of the +planet, and Phobos must appear to the inhabitants, if they exist, to +rise in the west and set in the east, showing two or even three full +moons in a day, so that, sufficiently well for the ordinary purposes of +life, the hour of the day can be told by its phases. + +The discovery of these two satellites is, perhaps, the most interesting +telescopic visual discovery made with the large telescopes of the last +half century; photography having been the means of discovering all the +other new satellites except Jupiter’s fifth (in order of discovery). + +[Illustration: JUPITER. From a drawing by E. M. Antoniadi, showing +transit of a satellite’s shadow, the belts, and the “great red spot” +(_Monthly Notices_, R. A. S., vol. lix., pl. x.).] + +_Jupiter._—Galileo’s discovery of Jupiter’s satellites was followed by +the discovery of his belts. Zucchi and Torricelli seem to have seen +them. Fontana, in 1633, reported three belts. In 1648 Grimaldi saw but +two, and noticed that they lay parallel to the ecliptic. Dusky spots +were also noticed as transient. Hooke[5] measured the motion of one in +1664. In 1665 Cassini, with a fine telescope, 35-feet focal length, +observed many spots moving from east to west, whence he concluded that +Jupiter rotates on an axis like the earth. He watched an unusually +permanent spot during twenty-nine rotations, and fixed the period at +9h. 56m. Later he inferred that spots near the equator rotate quicker +than those in higher latitudes (the same as Carrington found for the +sun); and W. Herschel confirmed this in 1778-9. + +Jupiter’s rapid rotation ought, according to Newton’s theory, to be +accompanied by a great flattening at the poles. Cassini had noted an +oval form in 1691. This was confirmed by La Hire, Römer, and Picard. +Pound measured the ellipticity = 1/(13.25). + +W. Herschel supposed the spots to be masses of cloud in the +atmosphere—an opinion still accepted. Many of them were very permanent. +Cassini’s great spot vanished and reappeared nine times between 1665 +and 1713. It was close to the northern margin of the southern belt. +Herschel supposed the belts to be the body of the planet, and the +lighter parts to be clouds confined to certain latitudes. + +In 1665 Cassini observed transits of the four satellites, and also saw +their shadows on the planet, and worked out a lunar theory for Jupiter. +Mathematical astronomers have taken great interest in the perturbations +of the satellites, because their relative periods introduce peculiar +effects. Airy, in his delightful book, _Gravitation_, has reduced these +investigations to simple geometrical explanations. + +In 1707 and 1713 Miraldi noticed that the fourth satellite varies much +in brightness. W. Herschel found this variation to depend upon its +position in its orbit, and concluded that in the positions of +feebleness it is always presenting to us a portion of its surface, +which does not well reflect the sun’s light; proving that it always +turns the same face to Jupiter, as is the case with our moon. This fact +had also been established for Saturn’s fifth satellite, and may be true +for all satellites. + +In 1826 Struve measured the diameters of the four satellites, and found +them to be 2,429, 2,180, 3,561, and 3,046 miles. + +In modern times much interest has been taken in watching a rival to +Cassini’s famous spot. The “great red spot” was first observed by +Niesten, Pritchett, and Tempel, in 1878, as a rosy cloud attached to a +whitish zone beneath the dark southern equatorial band, shaped like the +new war balloons, 30,000 miles long and 7,000 miles across. The next +year it was brick-red. A white spot beside it completed a rotation in +less time by 5½ minutes than the red spot—a difference of 260 miles an +hour. Thus they came together again every six weeks, but the motions +did not continue uniform. The spot was feeble in 1882-4, brightened in +1886, and, after many changes, is still visible. + +Galileo’s great discovery of Jupiter’s four moons was the last word in +this connection until September 9th, 1892, when Barnard, using the +36-inch refractor of the Lick Observatory, detected a tiny spot of +light closely following the planet. This proved to be a new satellite +(fifth), nearer to the planet than any other, and revolving round it in +11h. 57m. 23s. Between its rising and setting there must be an interval +of 2½ Jovian days, and two or three full moons. The sixth and seventh +satellites were found by the examination of photographic plates at the +Lick Observatory in 1905, since which time they have been continuously +photographed, and their orbits traced, at Greenwich. On examining these +plates in 1908 Mr. Melotte detected the eighth satellite, which seems +to be revolving in a retrograde orbit three times as far from its +planet as the next one (seventh), in these two points agreeing with the +outermost of Saturn’s satellites (Phoebe). + +_Saturn._—This planet, with its marvellous ring, was perhaps the most +wonderful object of those first examined by Galileo’s telescope. He was +followed by Dominique Cassini, who detected bands like Jupiter’s belts. +Herschel established the rotation of the planet in 1775-94. From +observations during one hundred rotations he found the period to be +10h. 16m. 0s., 44. Herschel also measured the ratio of the polar to the +equatoreal diameter as 10:11. + +The ring was a complete puzzle to Galileo, most of all when the planet +reached a position where the plane of the ring was in line with the +earth, and the ring disappeared (December 4th, 1612). It was not until +1656 that Huyghens, in his small pamphlet _De Saturni Luna Observatio +Nova_, was able to suggest in a cypher the ring form; and in 1659, in +his Systema Saturnium, he gave his reasons and translated the cypher: +“The planet is surrounded by a slender flat ring, everywhere distinct +from its surface, and inclined to the ecliptic.” This theory explained +all the phases of the ring which had puzzled others. This ring was +then, and has remained ever since, a unique structure. We in this age +have got accustomed to it. But Huyghens’s discovery was received with +amazement. + +In 1675 Cassini found the ring to be double, the concentric rings being +separated by a black band—a fact which was placed beyond dispute by +Herschel, who also found that the thickness of the ring subtends an +angle less than 0".3. Shröter estimated its thickness at 500 miles. + +Many speculations have been advanced to explain the origin and +constitution of the ring. De Sejour said[6] that it was thrown off from +Saturn’s equator as a liquid ring, and afterwards solidified. He +noticed that the outside would have a greater velocity, and be less +attracted to the planet, than the inner parts, and that equilibrium +would be impossible; so he supposed it to have solidified into a number +of concentric rings, the exterior ones having the least velocity. + +Clerk Maxwell, in the Adams prize essay, gave a physico-mathematical +demonstration that the rings must be composed of meteoritic matter like +gravel. Even so, there must be collisions absorbing the energy of +rotation, and tending to make the rings eventually fall into the +planet. The slower motion of the external parts has been proved by the +spectroscope in Keeler’s hands, 1895. + +Saturn has perhaps received more than its share of attention owing to +these rings. This led to other discoveries. Huyghens in 1655, and J. D. +Cassini in 1671, discovered the sixth and eighth satellites (Titan and +Japetus). Cassini lost his satellite, and in searching for it found +Rhea (the fifth) in 1672, besides his old friend, whom he lost again. +He added the third and fourth in 1684 (Tethys and Dione). The first and +second (Mimas and Encelades) were added by Herschel in 1789, and the +seventh (Hyperion) simultaneously by Lassel and Bond in 1848. The ninth +(Phoebe) was found on photographs, by Pickering in 1898, with +retrograde motion; and he has lately added a tenth. + +The occasional disappearance of Cassini’s Japetus was found on +investigation to be due to the same causes as that of Jupiter’s fourth +satellite, and proves that it always turns the same face to the planet. + +_Uranus and Neptune_.—The splendid discoveries of Uranus and two +satellites by Sir William Herschel in 1787, and of Neptune by Adams and +Le Verrier in 1846, have been already described. Lassel added two more +satellites to Uranus in 1851, and found Neptune’s satellite in 1846. +All of the satellites of Uranus have retrograde motion, and their +orbits are inclined about 80° to the ecliptic. + +The spectroscope has shown the existence of an absorbing atmosphere on +Jupiter and Saturn, and there are suspicions that they partake +something of the character of the sun, and emit some light besides +reflecting solar light. On both planets some absorption lines seem to +agree with the aqueous vapour lines of our own atmosphere; while one, +which is a strong band in the red common to both planets, seems to +agree with a line in the spectrum of some reddish stars. + +Uranus and Neptune are difficult to observe spectroscopically, but +appear to have peculiar spectra agreeing together. Sometimes Uranus +shows Frauenhofer lines, indicating reflected solar light. But +generally these are not seen, and six broad bands of absorption appear. +One is the F. of hydrogen; another is the red-star line of Jupiter and +Saturn. Neptune is a very difficult object for the spectroscope. + +Quite lately[7] P. Lowell has announced that V. M. Slipher, at +Flagstaff Observatory, succeeded in 1907 in rendering some plates +sensitive far into the red. A reproduction is given of photographed +spectra of the four outermost planets, showing (1) a great number of +new lines and bands; (2) intensification of hydrogen F. and C. lines; +(3) a steady increase of effects (1) and (2) as we pass from Jupiter +and Saturn to Uranus, and a still greater increase in Neptune. + +_Asteroids_.—The discovery of these new planets has been described. At +the beginning of the last century it was an immense triumph to catch a +new one. Since photography was called into the service by Wolf, they +have been caught every year in shoals. It is like the difference +between sea fishing with the line and using a steam trawler. In the +1908 almanacs nearly seven hundred asteroids are included. The +computation of their perturbations and ephemerides by Euler’s and +Lagrange’s method of variable elements became so laborious that Encke +devised a special process for these, which can be applied to many other +disturbed orbits.[8] + +When a photograph is taken of a region of the heavens including an +asteroid, the stars are photographed as points because the telescope is +made to follow their motion; but the asteroids, by their proper motion, +appear as short lines. + +The discovery of Eros and the photographic attack upon its path have +been described in their relation to finding the sun’s distance. + +A group of four asteroids has lately been found, with a mean distance +and period equal to that of Jupiter. To three of these masculine names +have been given—Hector, Patroclus, Achilles; the other has not yet been +named. + +FOOTNOTES: + + [1] Langrenus (van Langren), F. Selenographia sive lumina austriae + philippica; Bruxelles, 1645. + + [2] _Astr. Nach._, 2,944. + + [3] _Acad. des Sc._, Paris; _C.R._, lxxxiii., 1876. + + [4] _Mem. Spettr. Ital._, xi., p. 28. + + [5] _R. S. Phil. Trans_., No. 1. + + [6] Grant’s _Hist. Ph. Ast_., p. 267. + + [7] _Nature_, November 12th, 1908. + + [8] _Ast. Nach_., Nos. 791, 792, 814, translated by G. B. Airy. _Naut. + Alm_., Appendix, 1856. + + + + +14. COMETS AND METEORS. + + +Ever since Halley discovered that the comet of 1682 was a member of the +solar system, these wonderful objects have had a new interest for +astronomers; and a comparison of orbits has often identified the return +of a comet, and led to the detection of an elliptic orbit where the +difference from a parabola was imperceptible in the small portion of +the orbit visible to us. A remarkable case in point was the comet of +1556, of whose identity with the comet of 1264 there could be little +doubt. Hind wanted to compute the orbit more exactly than Halley had +done. He knew that observations had been made, but they were lost. +Having expressed his desire for a search, all the observations of +Fabricius and of Heller, and also a map of the comet’s path among the +stars, were eventually unearthed in the most unlikely manner, after +being lost nearly three hundred years. Hind and others were certain +that this comet would return between 1844 and 1848, but it never +appeared. + +When the spectroscope was first applied to finding the composition of +the heavenly bodies, there was a great desire to find out what comets +are made of. The first opportunity came in 1864, when Donati observed +the spectrum of a comet, and saw three bright bands, thus proving that +it was a gas and at least partly self-luminous. In 1868 Huggins +compared the spectrum of Winnecke’s comet with that of a Geissler tube +containing olefiant gas, and found exact agreement. Nearly all comets +have shown the same spectrum.[1] A very few comets have given bright +band spectra differing from the normal type. Also a certain kind of +continuous spectrum, as well as reflected solar light showing +Frauenhofer lines, have been seen. + +[Illustration: COPY OF THE DRAWING MADE BY PAUL FABRICIUS. +To define the path of comet 1556. After being lost for 300 years, this +drawing was recovered by the prolonged efforts of Mr. Hind and +Professor Littrow in 1856.] + +When Wells’s comet, in 1882, approached very close indeed to the sun, +the spectrum changed to a mono-chromatic yellow colour, due to sodium. + +For a full account of the wonders of the cometary world the reader is +referred to books on descriptive astronomy, or to monographs on +comets.[2] Nor can the very uncertain speculations about the structure +of comets’ tails be given here. A new explanation has been proposed +almost every time that a great discovery has been made in the theory of +light, heat, chemistry, or electricity. + +Halley’s comet remained the only one of which a prediction of the +return had been confirmed, until the orbit of the small, ill-defined +comet found by Pons in 1819 was computed by Encke, and found to have a +period of 3 1/3 years. It was predicted to return in 1822, and was +recognised by him as identical with many previous comets. This comet, +called after Encke, has showed in each of its returns an inexplicable +reduction of mean distance, which led to the assertion of a resisting +medium in space until a better explanation could be found.[3] + +Since that date fourteen comets have been found with elliptic orbits, +whose aphelion distances are all about the same as Jupiter’s mean +distance; and six have an aphelion distance about ten per cent, greater +than Neptune’s mean distance. Other comets are similarly associated +with the planets Saturn and Uranus. + +The physical transformations of comets are among the most wonderful of +unexplained phenomena in the heavens. But, for physical astronomers, +the greatest interest attaches to the reduction of radius vector of +Encke’s comet, the splitting of Biela’s comet into two comets in 1846, +and the somewhat similar behaviour of other comets. It must be noted, +however, that comets have a sensible size, that all their parts cannot +travel in exactly the same orbit under the sun’s gravitation, and that +their mass is not sufficient to retain the parts together very +forcibly; also that the inevitable collision of particles, or else +fluid friction, is absorbing energy, and so reducing the comet’s +velocity. + +In 1770 Lexell discovered a comet which, as was afterwards proved by +investigations of Lexell, Burchardt, and Laplace, had in 1767 been +deflected by Jupiter out of an orbit in which it was invisible from the +earth into an orbit with a period of 5½ years, enabling it to be seen. +In 1779 it again approached Jupiter closer than some of his satellites, +and was sent off in another orbit, never to be again recognised. + +But our interest in cometary orbits has been added to by the discovery +that, owing to the causes just cited, a comet, if it does not separate +into discrete parts like Biela’s, must in time have its parts spread +out so as to cover a sensible part of the orbit, and that, when the +earth passes through such part of a comet’s orbit, a meteor shower is +the result. + +A magnificent meteor shower was seen in America on November 12th-13th, +1833, when the paths of the meteors all seemed to radiate from a point +in the constellation Leo. A similar display had been witnessed in +Mexico by Humboldt and Bonpland on November 12th, 1799. H. A. Newton +traced such records back to October 13th, A.D. 902. The orbital motion +of a cloud or stream of small particles was indicated. The period +favoured by H. A. Newton was 354½ days; another suggestion was 375½ +days, and another 33¼ years. He noticed that the advance of the date of +the shower between 902 and 1833, at the rate of one day in seventy +years, meant a progression of the node of the orbit. Adams undertook to +calculate what the amount would be on all the five suppositions that +had been made about the period. After a laborious work, he found that +none gave one day in seventy years except the 33¼-year period, which +did so exactly. H. A. Newton predicted a return of the shower on the +night of November 13th-14th, 1866. He is now dead; but many of us are +alive to recall the wonder and enthusiasm with which we saw this +prediction being fulfilled by the grandest display of meteors ever seen +by anyone now alive. + +The _progression_ of the nodes proved the path of the meteor stream to +be retrograde. The _radiant_ had almost the exact longitude of the +point towards which the earth was moving. This proved that the meteor +cluster was at perihelion. The period being known, the eccentricity of +the orbit was obtainable, also the orbital velocity of the meteors in +perihelion; and, by comparing this with the earth’s velocity, the +latitude of the radiant enabled the inclination to be determined, while +the longitude of the earth that night was the longitude of the node. In +such a way Schiaparelli was able to find first the elements of the +orbit of the August meteor shower (Perseids), and to show its identity +with the orbit of Tuttle’s comet 1862.iii. Then, in January 1867, Le +Verrier gave the elements of the November meteor shower (Leonids); and +Peters, of Altona, identified these with Oppolzer’s elements for +Tempel’s comet 1866—Schiaparelli having independently attained both of +these results. Subsequently Weiss, of Vienna, identified the meteor +shower of April 20th (Lyrids) with comet 1861. Finally, that +indefatigable worker on meteors, A. S. Herschel, added to the number, +and in 1878 gave a list of seventy-six coincidences between cometary +and meteoric orbits. + +Cometary astronomy is now largely indebted to photography, not merely +for accurate delineations of shape, but actually for the discovery of +most of them. The art has also been applied to the observation of +comets at distances from their perihelia so great as to prevent their +visual observation. Thus has Wolf, of Heidelburg, found upon old plates +the position of comet 1905.v., as a star of the 15.5 magnitude, 783 +days before the date of its discovery. From the point of view of the +importance of finding out the divergence of a cometary orbit from a +parabola, its period, and its aphelion distance, this increase of range +attains the very highest value. + +The present Astronomer Royal, appreciating this possibility, has been +searching by photography for Halley’s comet since November, 1907, +although its perihelion passage will not take place until April, 1910. + +FOOTNOTES: + + [1] In 1874, when the writer was crossing the Pacific Ocean in H.M.S. + “Scout,” Coggia’s comet unexpectedly appeared, and (while Colonel + Tupman got its positions with the sextant) he tried to use the prism + out of a portable direct-vision spectroscope, without success until it + was put in front of the object-glass of a binocular, when, to his + great joy, the three band images were clearly seen. + + [2] Such as _The World of Comets_, by A. Guillemin; _History of + Comets_, by G. R. Hind, London, 1859; _Theatrum Cometicum_, by S. de + Lubienietz, 1667; _Cometographie_, by Pingré, Paris, 1783; _Donati’s + Comet_, by Bond. + + [3] The investigations by Von Asten (of St. Petersburg) seem to + support, and later ones, especially those by Backlund (also of St. + Petersburg), seem to discredit, the idea of a resisting medium. + + + + +15. THE FIXED STARS AND NEBULÆ. + + +Passing now from our solar system, which appears to be subject to the +action of the same forces as those we experience on our globe, there +remains an innumerable host of fixed stars, nebulas, and nebulous +clusters of stars. To these the attention of astronomers has been more +earnestly directed since telescopes have been so much enlarged. +Photography also has enabled a vast amount of work to be covered in a +comparatively short period, and the spectroscope has given them the +means, not only of studying the chemistry of the heavens, but also of +detecting any motion in the line of sight from less than a mile a +second and upwards in any star, however distant, provided it be bright +enough. + +[Illustration: SIR WILLIAM HERSCHEL, F.R.S.—1738-1822. +Painted by Lemuel F. Abbott; National Portrait Gallery, Room XX.] + +In the field of telescopic discovery beyond our solar system there is +no one who has enlarged our knowledge so much as Sir William Herschel, +to whom we owe the greatest discovery in dynamical astronomy among the +stars—viz., that the law of gravitation extends to the most distant +stars, and that many of them describe elliptic orbits about each other. +W. Herschel was born at Hanover in 1738, came to England in 1758 as a +trained musician, and died in 1822. He studied science when he could, +and hired a telescope, until he learnt to make his own specula and +telescopes. He made 430 parabolic specula in twenty-one years. He +discovered 2,500 nebulæ and 806 double stars, counted the stars in +3,400 guage-fields, and compared the principal stars photometrically. + +Some of the things for which he is best known were results of those +accidents that happen only to the indefatigable enthusiast. Such was +the discovery of Uranus, which led to funds being provided for +constructing his 40-feet telescope, after which, in 1786, he settled at +Slough. In the same way, while trying to detect the annual parallax of +the stars, he failed in that quest, but discovered binary systems of +stars revolving in ellipses round each other; just as Bradley’s attack +on stellar parallax failed, but led to the discovery of aberration, +nutation, and the true velocity of light. + +_Parallax_.—The absence of stellar parallax was the great objection to +any theory of the earth’s motion prior to Kepler’s time. It is true +that Kepler’s theory itself could have been geometrically expressed +equally well with the earth or any other point fixed. But in Kepler’s +case the obviously implied physical theory of the planetary motions, +even before Newton explained the simplicity of conception involved, +made astronomers quite ready to waive the claim for a rigid proof of +the earth’s motion by measurement of an annual parallax of stars, which +they had insisted on in respect of Copernicus’s revival of the idea of +the earth’s orbital motion. + +Still, the desire to measure this parallax was only intensified by the +practical certainty of its existence, and by repeated failures. The +attempts of Bradley failed. The attempts of Piazzi and Brinkley,[1] +early in the nineteenth century, also failed. The first successes, +afterwards confirmed, were by Bessel and Henderson. Both used stars +whose proper motion had been found to be large, as this argued +proximity. Henderson, at the Cape of Good Hope, observed α Centauri, +whose annual proper motion he found to amount to 3".6, in 1832-3; and a +few years later deduced its parallax 1".16. His successor at the Cape, +Maclear, reduced this to 0".92. + +In 1835 Struve assigned a doubtful parallax of 0".261 to Vega (α Lyræ). +But Bessel’s observations, between 1837 and 1840, of 61 Cygni, a star +with the large proper motion of over 5”, established its annual +parallax to be 0".3483; and this was confirmed by Peters, who found the +value 0".349. + +Later determinations for α2 Centauri, by Gill,[2] make its parallax +0".75—This is the nearest known fixed star; and its light takes 4 1/3 +years to reach us. The lightyear is taken as the unit of measurement in +the starry heavens, as the earth’s mean distance is “the astronomical +unit” for the solar system.[3] The proper motions and parallaxes +combined tell us the velocity of the motion of these stars across the +line of sight: α Centauri 14.4 miles a second=4.2 astronomical units a +year; 61 Cygni 37.9 miles a second=11.2 astronomical units a year. +These successes led to renewed zeal, and now the distances of many +stars are known more or less accurately. + +Several of the brightest stars, which might be expected to be the +nearest, have not shown a parallax amounting to a twentieth of a second +of arc. Among these are Canopus, α Orionis, α Cygni, β Centauri, and γ +Cassiopeia. Oudemans has published a list of parallaxes observed.[4] + +_Proper Motion._—In 1718 Halley[5] detected the proper motions of +Arcturus and Sirius. In 1738 J. Cassinis[6] showed that the former had +moved five minutes of arc since Tycho Brahe fixed its position. In 1792 +Piazzi noted the motion of 61 Cygni as given above. For a long time the +greatest observed proper motion was that of a small star 1830 +Groombridge, nearly 7” a year; but others have since been found +reaching as much as 10”. + +Now the spectroscope enables the motion of stars to be detected at a +single observation, but only that part of the motion that is in the +line of sight. For a complete knowledge of a star’s motion the proper +motion and parallax must also be known. + +When Huggins first applied the Doppler principle to measure velocities +in the line of sight,[7] the faintness of star spectra diminished the +accuracy; but Vögel, in 1888, overcame this to a great extent by long +exposures of photographic plates. + +It has often been noticed that stars which seem to belong to a group of +nearly uniform magnitude have the same proper motion. The spectroscope +has shown that these have also often the same velocity in the line of +sight. Thus in the Great Bear, β, γ, δ, ε, ζ, all agree as to angular +proper motion. δ was too faint for a spectroscopic measurement, but all +the others have been shown to be approaching us at a rate of twelve to +twenty miles a second. The same has been proved for proper motion, and +line of sight motion, in the case of Pleiades and other groups. + +Maskelyne measured many proper motions of stars, from which W. +Herschel[8] came to the conclusion that these apparent motions are for +the most part due to a motion of the solar system in space towards a +point in the constellation Hercules, R.A. 257°; N. Decl. 25°. This +grand discovery has been amply confirmed, and, though opinions differ +as to the exact direction, it happens that the point first indicated by +Herschel, from totally insufficient data, agrees well with modern +estimates. + +Comparing the proper motions and parallaxes to get the actual velocity +of each star relative to our system, C.L. Struve found the probable +velocity of the solar system in space to be fifteen miles a second, or +five astronomical units a year. + +The work of Herschel in this matter has been checked by comparing +spectroscopic velocities in the line of sight which, so far as the +sun’s motion is concerned, would give a maximum rate of approach for +stars near Hercules, a maximum rate of recession for stars in the +opposite part of the heavens, and no effect for stars half-way between. +In this way the spectroscope has confirmed generally Herschel’s view of +the direction, and makes the velocity eleven miles a second, or nearly +four astronomical units a year. + +The average proper motion of a first magnitude star has been found to +be 0".25 annually, and of a sixth magnitude star 0".04. But that all +bright stars are nearer than all small stars, or that they show greater +proper motion for that reason, is found to be far from the truth. Many +statistical studies have been made in this connection, and interesting +results may be expected from this treatment in the hands of Kapteyn of +Groningen, and others.[9] + +On analysis of the directions of proper motions of stars in all parts +of the heavens, Kapteyn has shown[10] that these indicate, besides the +solar motion towards Hercules, two general drifts of stars in nearly +opposite directions, which can be detected in any part of the heavens. +This result has been confirmed from independent data by Eddington +(_R.A.S., M.N._) and Dyson (_R.S.E. Proc._). + +Photography promises to assist in the measurement of parallax and +proper motions. Herr Pulfrich, of the firm of Carl Zeiss, has vastly +extended the applications of stereoscopic vision to astronomy—a subject +which De la Rue took up in the early days of photography. He has made a +stereo-comparator of great beauty and convenience for comparing +stereoscopically two star photographs taken at different dates. Wolf of +Heidelberg has used this for many purposes. His investigations +depending on the solar motion in space are remarkable. He photographs +stars in a direction at right angles to the line of the sun’s motion. +He has taken photographs of the same region fourteen years apart, the +two positions of his camera being at the two ends of a base-line over +5,000,000,000 miles apart, or fifty-six astronomical units. On +examining these stereoscopically, some of the stars rise out of the +general plane of the stars, and seem to be much nearer. Many of the +stars are thus seen to be suspended in space at different distances +corresponding exactly to their real distances from our solar system, +except when their proper motion interferes. The effect is most +striking; the accuracy of measurement exceeds that of any other method +of measuring such displacements, and it seems that with a long interval +of time the advantage of the method increases. + +_Double Stars._—The large class of double stars has always been much +studied by amateurs, partly for their beauty and colour, and partly as +a test for telescopic definition. Among the many unexplained stellar +problems there is one noticed in double stars that is thought by some +to be likely to throw light on stellar evolution. It is this: There are +many instances where one star of the pair is comparatively faint, and +the two stars are contrasted in colour; and in every single case the +general colour of the faint companion is invariably to be classed with +colours more near to the blue end of the spectrum than that of the +principal star. + +_Binary Stars._—Sir William Herschel began his observations of double +stars in the hope of discovering an annual parallax of the stars. In +this he was following a suggestion of Galileo’s. The presumption is +that, if there be no physical connection between the stars of a pair, +the largest is the nearest, and has the greatest parallax. So, by +noting the distance between the pair at different times of the year, a +delicate test of parallax is provided, unaffected by major instrumental +errors. + +Herschel did, indeed, discover changes of distance, but not of the +character to indicate parallax. Following this by further observation, +he found that the motions were not uniform nor rectilinear, and by a +clear analysis of the movements he established the remarkable and +wholly unexpected fact that in all these cases the motion is due to a +revolution about their common centre of gravity.[11] He gave the +approximate period of revolution of some of these: Castor, 342 years; δ +Serpentis, 375 years; γ Leonis, 1,200 years; ε Bootis, 1,681 years. + +Twenty years later Sir John Herschel and Sir James South, after +re-examination of these stars, confirmed[12] and extended the results, +one pair of Coronæ having in the interval completed more than a whole +revolution. + +It is, then, to Sir William Herschel that we owe the extension of the +law of gravitation, beyond the limits of the solar system, to the whole +universe. His observations were confirmed by F.G.W. Struve (born 1793, +died 1864), who carried on the work at Dorpat. But it was first to +Savary,[13] and later to Encke and Sir John Herschel, that we owe the +computation of the elliptic elements of these stars; also the resulting +identification of their law of force with Newton’s force of gravitation +applied to the solar system, and the force that makes an apple fall to +the ground. As Grant well says in his _History_: “This may be justly +asserted to be one of the most sublime truths which astronomical +science has hitherto disclosed to the researches of the human mind.” + +Latterly the best work on double stars has been done by S. W. +Burnham,[14] at the Lick Observatory. The shortest period he found was +eleven years (κ Pegasi). In the case of some of these binaries the +parallax has been measured, from which it appears that in four of the +surest cases the orbits are about the size of the orbit of Uranus, +these being probably among the smallest stellar orbits. + +The law of gravitation having been proved to extend to the stars, a +discovery (like that of Neptune in its origin, though unlike it in the +labour and originality involved in the calculation) that entrances the +imagination became possible, and was realised by Bessel—the discovery +of an unknown body by its gravitational disturbance on one that was +visible. In 1834 and 1840 he began to suspect a want of uniformity in +the proper motion of Sirius and Procyon respectively. In 1844, in a +letter to Sir John Herschel,[15] he attributed these irregularities in +each case to the attraction of an invisible companion, the period of +revolution of Sirius being about half a century. Later he said: “I +adhere to the conviction that Procyon and Sirius form real binary +systems, consisting of a visible and an invisible star. There is no +reason to suppose luminosity an essential quality of cosmical bodies. +The visibility of countless stars is no argument against the +invisibility of countless others.” This grand conception led Peters to +compute more accurately the orbit, and to assign the place of the +invisible companion of Sirius. In 1862 Alvan G. Clark was testing a new +18-inch object-glass (now at Chicago) upon Sirius, and, knowing nothing +of these predictions, actually found the companion in the very place +assigned to it. In 1896 the companion of Procyon was discovered by +Professor Schaeberle at the Lick Observatory. + +Now, by the refined parallax determinations of Gill at the Cape, we +know that of Sirius to be 0".38. From this it has been calculated that +the mass of Sirius equals two of our suns, and its intrinsic brightness +equals twenty suns; but the companion, having a mass equal to our sun, +has only a five-hundredth part of the sun’s brightness. + +_Spectroscopic Binaries_.—On measuring the velocity of a star in the +line of sight at frequent intervals, periodic variations have been +found, leading to a belief in motion round an invisible companion. +Vogel, in 1889, discovered this in the case of Spica (α Virginis), +whose period is 4d. 0h. 19m., and the diameter of whose orbit is six +million miles. Great numbers of binaries of this type have since then +been discovered, all of short period. + +Also, in 1889, Pickering found that at regular intervals of fifty-two +days the lines in the spectrum of ζ of the Great Bear are duplicated, +indicating a relative velocity, equal to one hundred miles a second, of +two components revolving round each other, of which that apparently +single star must be composed. + +It would be interesting, no doubt, to follow in detail the accumulating +knowledge about the distances, proper motions, and orbits of the stars; +but this must be done elsewhere. Enough has been said to show how +results are accumulating which must in time unfold to us the various +stellar systems and their mutual relationships. + +_Variable Stars._—It has often happened in the history of different +branches of physical science that observation and experiment were so +far ahead of theory that hopeless confusion appeared to reign; and then +one chance result has given a clue, and from that time all differences +and difficulties in the previous researches have stood forth as natural +consequences, explaining one another in a rational sequence. So we find +parallax, proper motion, double stars, binary systems, variable stars, +and new stars all bound together. + +The logical and necessary explanation given of the cause of ordinary +spectroscopic binaries, and of irregular proper motions of Sirius and +Procyon, leads to the inference that if ever the plane of such a binary +orbit were edge-on to us there ought to be an eclipse of the luminous +partner whenever the non-luminous one is interposed between us. This +should give rise either to intermittence in the star’s light or else to +variability. It was by supposing the existence of a dark companion to +Algol that its discoverer, Goodricke of York,[16] in 1783, explained +variable stars of this type. Algol (β Persei) completes the period of +variable brightness in 68.8 hours. It loses three-fifths of its light, +and regains it in twelve hours. In 1889 Vogel,[17] with the Potsdam +spectrograph, actually found that the luminous star is receding before +each eclipse, and approaching us after each eclipse; thus entirely +supporting Goodricke’s opinion. There are many variables of the Algol +type, and information is steadily accumulating. But all variable stars +do not suffer the sudden variations of Algol. There are many types, and +the explanations of others have not proved so easy. + +The Harvard College photographs have disclosed the very great +prevalence of variability, and this is certainly one of the lines in +which modern discovery must progress. + +Roberts, in South Africa, has done splendid work on the periods of +variables of the Algol type. + +_New Stars_.—Extreme instances of variable stars are the new stars such +as those detected by Hipparchus, Tycho Brahe, and Kepler, of which many +have been found in the last half-century. One of the latest great +“Novæ” was discovered in Auriga by a Scotsman, Dr. Anderson, on +February 1st, 1892, and, with the modesty of his race, he communicated +the fact to His Majesty’s Astronomer for Scotland on an unsigned +post-card.[18] Its spectrum was observed and photographed by Huggins +and many others. It was full of bright lines of hydrogen, calcium, +helium, and others not identified. The astounding fact was that lines +were shown in pairs, bright and dark, on a faint continuous spectrum, +indicating apparently that a dark body approaching us at the rate of +550 miles a second[19] was traversing a cold nebulous atmosphere, and +was heated to incandescence by friction, like a meteor in our +atmosphere, leaving a luminous train behind it. It almost disappeared, +and on April 26th it was of the sixteenth magnitude; but on August 17th +it brightened to the tenth, showing the principal nebular band in its +spectrum, and no sign of approach or recession. It was as if it emerged +from one part of the nebula, cooled down, and rushed through another +part of the nebula, rendering the nebular gas more luminous than +itself.[20] + +Since 1892 one Nova after another has shown a spectrum as described +above, like a meteor rushing towards us and leaving a train behind, for +this seems to be the obvious meaning of the spectra. + +The same may be said of the brilliant Nova Persei, brighter at its best +than Capella, and discovered also by Dr. Anderson on February 22nd, +1901. It increased in brightness as it reached the densest part of the +nebula, then it varied for some weeks by a couple of magnitudes, up and +down, as if passing through separate nebular condensations. In +February, 1902, it could still be seen with an opera-glass. As with the +other Novæ, when it first dashed into the nebula it was vaporised and +gave a continuous spectrum with dark lines of hydrogen and helium. It +showed no bright lines paired with the dark ones to indicate a train +left behind; but in the end its own luminosity died out, and the +nebular spectrum predominated. + +The nebular illumination as seen in photographs, taken from August to +November, seemed to spread out slowly in a gradually increasing circle +at the rate of 90” in forty-eight days. Kapteyn put this down to the +velocity of light, the original outburst sending its illumination to +the nebulous gas and illuminating a spherical shell whose radius +increased at the velocity of light. This supposition seems correct, in +which case it can easily be shown from the above figures that the +distance of this Nova was 300 light years. + +_Star Catalogues._—Since the days of very accurate observations +numerous star-catalogues have been produced by individuals or by +observatories. Bradley’s monumental work may be said to head the list. +Lacaille’s, in the Southern hemisphere, was complementary. Then Piazzi, +Lalande, Groombridge, and Bessel were followed by Argelander with his +324,000 stars, Rumker’s Paramatta catalogue of the southern hemisphere, +and the frequent catalogues of national observatories. Later the +Astronomische Gesellschaft started their great catalogue, the combined +work of many observatories. Other southern ones were Gould’s at Cordova +and Stone’s at the Cape. + +After this we have a new departure. Gill at the Cape, having the comet +1882.ii. all to himself in those latitudes, wished his friends in +Europe to see it, and employed a local photographer to strap his camera +to the observatory equatoreal, driven by clockwork, and adjusted on the +comet by the eye. The result with half-an-hour’s exposure was good, so +he tried three hours. The result was such a display of sharp star +images that he resolved on the Cape Photographic Durchmusterung, which +after fourteen years, with Kapteyn’s aid in reducing, was completed. +Meanwhile the brothers Henry, of Paris, were engaged in going over +Chacornac’s zodiacal stars, and were about to catalogue the Milky Way +portion, a serious labour, when they saw Gill’s Comet photograph and +conceived the idea of doing the rest of their work by photography. Gill +had previously written to Admiral Mouchez, of the Paris Observatory, +and explained to him his project for charting the heavens +photographically, by combining the work of many observatories. This led +Admiral Mouchez to support the brothers Henry in their scheme.[21] +Gill, having got his own photographic work underway, suggested an +international astrographic chart, the materials for different zones to +be supplied by observatories of all nations, each equipped with similar +photographic telescopes. At a conference in Paris, 1887, this was +decided on, the stars on the charts going down to the fourteenth +magnitude, and the catalogues to the eleventh. + +[Illustration: GREAT COMET, NOV. 14TH, 1882. +(Exposure 2hrs. 20m.) By kind permission of Sir David Gill. From this +photograph originated all stellar chart-photography.] + +This monumental work is nearing completion. The labour involved was +immense, and the highest skill was required for devising instruments +and methods to read off the star positions from the plates. + +Then we have the Harvard College collection of photographic plates, +always being automatically added to; and their annex at Arequipa in +Peru. + +Such catalogues vary in their degree of accuracy; and fundamental +catalogues of standard stars have been compiled. These require +extension, because the differential methods of the heliometer and the +camera cannot otherwise be made absolute. + +The number of stars down to the fourteenth magnitude may be taken at +about 30,000,000; and that of all the stars visible in the greatest +modern telescopes is probably about 100,000,000. + +_Nebulæ and Star-clusters._—Our knowledge of nebulæ really dates from +the time of W. Herschel. In his great sweeps of the heavens with his +giant telescopes he opened in this direction a new branch of astronomy. +At one time he held that all nebulæ might be clusters of innumerable +minute stars at a great distance. Then he recognised the different +classes of nebulæ, and became convinced that there is a widely-diffused +“shining fluid” in space, though many so-called nebulæ could be +resolved by large telescopes into stars. He considered that the Milky +Way is a great star cluster, whose form may be conjectured from +numerous star-gaugings. He supposed that the compact “planetary nebulæ” +might show a stage of evolution from the diffuse nebulæ, and that his +classifications actually indicate various stages of development. Such +speculations, like those of the ancients about the solar system, are +apt to be harmful to true progress of knowledge unless in the hands of +the ablest mathematical physicists; and Herschel violated their +principles in other directions. But here his speculations have +attracted a great deal of attention, and, with modifications, are +accepted, at least as a working hypothesis, by a fair number of people. + +When Sir John Herschel had extended his father’s researches into the +Southern Hemisphere he was also led to the belief that some nebulae +were a phosphorescent material spread through space like fog or mist. + +Then his views were changed by the revelations due to the great +discoveries of Lord Rosse with his gigantic refractor,[22] when one +nebula after another was resolved into a cluster of minute stars. At +that time the opinion gained ground that with increase of telescopic +power this would prove to be the case with all nebulæ. + +In 1864 all doubt was dispelled by Huggins[23] in his first examination +of the spectrum of a nebula, and the subsequent extension of this +observation to other nebulæ; thus providing a certain test which +increase in the size of telescopes could never have given. In 1864 +Huggins found that all true nebulae give a spectrum of bright lines. +Three are due to hydrogen; two (discovered by Copeland) are helium +lines; others are unknown. Fifty-five lines have been photographed in +the spectrum of the Orion nebula. It seems to be pretty certain that +all true nebulae are gaseous, and show almost exactly the same +spectrum. + +Other nebulæ, and especially the white ones like that in Andromeda, +which have not yet been resolved into stars, show a continuous +spectrum; others are greenish and give no lines. + +A great deal has to be done by the chemist before the astronomer can be +on sure ground in drawing conclusions from certain portions of his +spectroscopic evidence. + +The light of the nebulas is remarkably actinic, so that photography has +a specially fine field in revealing details imperceptible in the +telescope. In 1885 the brothers Henry photographed, round the star Maia +in the Pleiades, a spiral nebula 3’ long, as bright on the plate as +that star itself, but quite invisible in the telescope; and an exposure +of four hours revealed other new nebula in the same district. That +painstaking and most careful observer, Barnard, with 10¼ hours’ +exposure, extended this nebulosity for several degrees, and discovered +to the north of the Pleiades a huge diffuse nebulosity, in a region +almost destitute of stars. By establishing a 10-inch instrument at an +altitude of 6,000 feet, Barnard has revealed the wide distribution of +nebular matter in the constellation Scorpio over a space of 4° or 5° +square. Barnard asserts that the “nebular hypothesis” would have been +killed at its birth by a knowledge of these photographs. Later he has +used still more powerful instruments, and extended his discoveries. + +The association of stars with planetary nebulæ, and the distribution of +nebulæ in the heavens, especially in relation to the Milky Way, are +striking facts, which will certainly bear fruit when the time arrives +for discarding vague speculations, and learning to read the true +physical structure and history of the starry universe. + +_Stellar Spectra._—When the spectroscope was first available for +stellar research, the leaders in this branch of astronomy were Huggins +and Father Secchi,[24] of Rome. The former began by devoting years of +work principally to the most accurate study of a few stars. The latter +devoted the years from 1863 to 1867 to a general survey of the whole +heavens, including 4,000 stars. He divided these into four principal +classes, which have been of the greatest service. Half of his stars +belonged to the first class, including Sirius, Vega, Regulus, Altair. +The characteristic feature of their spectra is the strength and breadth +of the hydrogen lines and the extreme faintness of the metallic lines. +This class of star is white to the eye, and rich in ultra violet light. + +The second class includes about three-eighths of his stars, including +Capella, Pollux, and Arcturus. These stars give a spectrum like that of +our sun, and appear yellowish to the eye. + +The third class includes α Herculis, α Orionis (Betelgeux), Mira Ceti, +and about 500 red and variable stars. The spectrum has fluted bands +shaded from blue to red, and sharply defined at the more refrangible +edge. + +The fourth class is a small one, containing no stars over fifth +magnitude, of which 152 Schjellerup, in Canes Venatici, is a good +example. This spectrum also has bands, but these are shaded on the +violet side and sharp on the red side. They are due to carbon in some +form. These stars are ruby red in the telescope. + +It would appear, then, that all stars are suns with continuous spectra, +and the classes are differentiated by the character of the absorbent +vapours of their atmospheres. + +It is very likely that, after the chemists have taught us how to +interpret all the varieties of spectrum, it will be possible to ascribe +the different spectrum-classes to different stages in the life-history +of every star. Already there are plenty of people ready to lay down +arbitrary assumptions about the lessons to be drawn from stellar +spectra. Some say that they know with certainty that each star begins +by being a nebula, and is condensed and heated by condensation until it +begins to shine as a star; that it attains a climax of temperature, +then cools down, and eventually becomes extinct. They go so far as to +declare that they know what class of spectrum belongs to each stage of +a star’s life, and how to distinguish between one that is increasing +and another that is decreasing in temperature. + +The more cautious astronomers believe that chemistry is not +sufficiently advanced to justify all of these deductions; that, until +chemists have settled the lately raised question of the transmutation +of elements, no theory can be sure. It is also held that until they +have explained, without room for doubt, the reasons for the presence of +some lines, and the absence of others, of any element in a stellar +spectrum; why the arc-spectrum of each element differs from its spark +spectrum; what are all the various changes produced in the spectrum of +a gas by all possible concomitant variations of pressure and +temperature; also the meanings of all the flutings in the spectra of +metalloids and compounds; and other equally pertinent matters—until +that time arrives the part to be played by the astronomer is one of +observation. By all means, they say, make use of “working hypotheses” +to add an interest to years of laborious research, and to serve as a +guide to the direction of further labours; but be sure not to fall into +the error of calling any mere hypothesis a theory. + +_Nebular Hypothesis._—The Nebular Hypothesis, which was first, as it +were, tentatively put forward by Laplace as a note in his _Système du +Monde_, supposes the solar system to have been a flat, disk-shaped +nebula at a high temperature in rapid rotation. In cooling it +condensed, leaving revolving rings at different distances from the +centre. These themselves were supposed to condense into the nucleus for +a rotating planet, which might, in contracting, again throw off rings +to form satellites. The speculation can be put in a really attractive +form, but is in direct opposition to many of the actual facts; and so +long as it is not favoured by those who wish to maintain the position +of astronomy as the most exact of the sciences—exact in its facts, +exact in its logic—this speculation must be recorded by the historian, +only as he records the guesses of the ancient Greeks--as an interesting +phase in the history of human thought. + +Other hypotheses, having the same end in view, are the meteoritic +hypothesis of Lockyer and the planetesimal hypothesis that has been +largely developed in the United States. These can best be read in the +original papers to various journals, references to which may be found +in the footnotes of Miss Clerke’s _History of Astronomy during the +Nineteenth Century_. The same can be said of Bredichin’s hypothesis of +comets’ tails, Arrhenius’s book on the applications of the theory of +light repulsion, the speculations on radium, the origin of the sun’s +heat and the age of the earth, the electron hypothesis of terrestrial +magnetism, and a host of similar speculations, all combining to throw +an interesting light on the evolution of a modern train of thought that +seems to delight in conjecture, while rebelling against that strict +mathematical logic which has crowned astronomy as the queen of the +sciences. + +FOOTNOTES: + + [1] _R. S. Phil Trans_., 1810 and 1817-24. + + [2] One of the most valuable contributions to our knowledge of stellar + parallaxes is the result of Gill’s work (_Cape Results_, vol. iii., + part ii., 1900). + + [3] Taking the velocity of light at 186,000 miles a second, and the + earth’s mean distance at 93,000,000 miles, 1 + light-year=5,865,696,000,000 miles or 63,072 astronomical units; 1 + astronomical unit a year=2.94 miles a second; and the earth’s orbital + velocity=18.5 miles a second. + + [4] Ast. Nacht., 1889. + + [5] R. S. Phil. Trans., 1718. + + [6] Mem. Acad. des Sciences, 1738, p. 337. + + [7] R. S Phil. Trans., 1868. + + [8] _R.S. Phil Trans._, 1783. + + [9] See Kapteyn’s address to the Royal Institution, 1908. Also Gill’s + presidential address to the British Association, 1907. + + [10] _Brit. Assoc. Rep._, 1905. + + [11] R. S. Phil. Trans., 1803, 1804. + + [12] Ibid, 1824. + + [13] Connaisance des Temps, 1830. + + [14] _R. A. S. Mem._, vol. xlvii., p. 178; _Ast. Nach._, No. 3,142; + Catalogue published by Lick Observatory, 1901. + + [15] _R. A. S., M. N._, vol. vi. + + [16] _R. S. Phil. Trans._, vol. lxxiii., p. 484. + + [17] _Astr. Nach._, No. 2,947. + + [18] _R. S. E. Trans_., vol. xxvii. In 1901 Dr. Anderson discovered + Nova Persei. + + [19] _Astr. Nach_., No. 3,079. + + [20] For a different explanation see Sir W. Huggins’s lecture, Royal + Institution, May 13th, 1892. + + [21] For the early history of the proposals for photographic + cataloguing of stars, see the _Cape Photographic Durchmusterung_, 3 + vols. (_Ann. of the Cape Observatory_, vols. in., iv., and v., + Introduction.) + + [22] _R. S. Phil. Trans._, 1850, p. 499 _et seq._ + + [23] _Ibid_, vol. cliv., p. 437. + + [24] _Brit. Assoc. Rep._, 1868, p. 165. + + + + +ILLUSTRATIONS + + + SIR ISAAC NEWTON +(From the bust by Roubiliac In Trinity College, Cambridge.) + + CHALDÆAN BAKED BRICK OR TABLET +Obverse and reverse sides, containing record of solar eclipse, 1062 +B.C., used lately by Cowell for rendering the lunar theory more +accurate than was possible by finest modern observations. (British +Museum collection, No. 35908.) + + “QUADRANS MURALIS SIVE TICHONICUS.” + With portrait of Tycho Brahe, instruments, etc., painted on the wall; + showing assistants using the sight, watching the clock, and recording. + (From the author’s copy of the _Astronomiæ Instauratæ Mechanica_.) + + PORTRAIT OF JOHANNES KEPLER. + By F. Wanderer, from Reitlinger’s “Johannes Kepler” (Original in + Strassburg). + + DEATH-MASK OF SIR ISAAC NEWTON. +Photographed specially for this work from the original, by kind +permission of the Royal Society, London. + + ANCIENT CHINESE INSTRUMENTS, +Including quadrant, celestial globe, and two armillae, in the +Observatory at Peking. Photographed in Peking by the author in 1875, +and stolen by the Germans when the Embassies were relieved by the +allies in 1900. + + SOLAR SURFACE. +As Photographed at the Royal Observatory, Greenwich, showing sun spots +with umbræ, penumbræ, and faculæ. + + SOLAR ECLIPSE, 1882. +From drawing by W. H. Wesley, Secretary R.A.S.; showing the +prominences, the corona, and an unknown comet. + + JUPITER. +From a drawing by E. M. Antoniadi, showing transit of a satellite’s +shadow, the belts, and the “great red spot” (_Monthly Notices_, R. A. +S., vol. lix., pl. x.). + + COPY OF THE DRAWING MADE BY PAUL FABRICIUS. +To define the path of comet 1556. After being lost for 300 years, this +drawing was recovered by the prolonged efforts of Mr. Hind and +Professor Littrow in 1856. + + SIR WILLIAM HERSCHEL, F.R.S.—1738-1822. +Painted by Lemuel F. Abbott; National Portrait Gallery, Room XX. + + GREAT COMET, NOV. 14TH, 1882. (Exposure 2hrs. 20m.) +By kind permission of Sir David Gill. From this photograph originated +all stellar chart-photography. + + + + +INDEX + +Abul Wefa, 24 +Acceleration of moon’s mean motion, 60 +Achromatic lens invented, 88 +Adams, J. C., 61, 65, 68, 69, 70, 87, 118, 124 +Airy, G. B., 13, 30, 37, 65, 69, 70, 80, 81, 114, 119 +Albetegnius, 24 +Alphonso, 24 +Altazimuth, 81 +Anaxagoras, 14, 16 +Anaximander, 14 +Anaximenes, 14 +Anderson, T. D., 137, 138 +Ångstrom, A. J., 102 +Antoniadi, 113 +Apian, P., 63 +Apollonius, 22, 23 +Arago, 111 +Argelander, F. W. A., 139 +Aristarchus, 18, 29 +Aristillus, 17, 19 +Aristotle, 16, 30, 47 +Arrhenius, 146 +Arzachel, 24 +Asshurbanapal, 12 +Asteroids, discovery of, 67, 119 +Astrology, ancient and modern, 1-7, 38 + +Backlund, 122 +Bacon, R., 86 +Bailly, 8, 65 +Barnard, E. E., 115, 143 +Beer and Mädler, 107, 110, 111 +Behaim, 74 +Bessel, F.W., 65, 79, 128, 134, 139 +Biela, 123 +Binet, 65 +Biot, 10 +Bird, 79, 80 +Bliss, 80 +Bode, 66, 69 +Bond, G. P., 99, 117, 122 +Bouvard, A., 65, 68 +Bradley, J., 79, 80, 81, 87, 127, 128, 139 +Bredechin, 146 +Bremiker, 71 +Brewster, D., 52, 91, 112 +Brinkley, 128 +Bruno, G., 49 +Burchardt, 65, 123 +Burnham, S. W., 134 + +Callippus, 15, 16, 31 +Carrington, R. C., 97, 99, 114 +Cassini, G. D., 107, 114, 115, 116, 117, 118 +Cassini, J., 109, 129 +Chacornac, 139 +Chaldæan astronomy, 11-13 +Challis, J., 69, 70, 71, 72 +Chance, 88 +Charles, II., 50, 81 +Chinese astronomy, 8-11 +Christie, W. M. H. (Ast. Roy.), 64, 82, 125 +Chueni, 9 +Clairaut, A. C., 56, 63, 65 +Clark, A. G., 89, 135 +Clerke, Miss, 106, 146 +Comets, 120 +Common, A. A., 88 +Cooke, 89 +Copeland, R., 142 +Copernicus, N., 14, 24-31, 37, 38, 41, 42, 49, 128 +Cornu, 85 +Cowell, P. H., 3, 5, 64, 83 +Crawford, Earl of, 84 +Cromellin, A. C., 5, 64 + +D’Alembert, 65 +Damoiseau, 65 +D’Arrest, H. L., 34 +Dawes, W. R., 100, 111 +Delambre, J. B. J., 8, 27, 51, 65, 68 +De la Rue, W., 2, 94, 99, 100, 131 +Delaunay, 65 +Democritus, 16 +Descartes, 51 +De Sejour, 117 +Deslandres, II., 101 +Desvignolles, 9 +De Zach, 67 +Digges, L., 86 +Dollond, J., 87, 90 +Dominis, A. di., 86 +Donati, 120 +Doppler, 92, 129 +Draper, 99 +Dreyer, J. L. E., 29,77 +Dunthorne, 60 +Dyson, 131 + +Eclipses, total solar, 103 +Ecphantes, 16 +Eddington, 131 +Ellipse, 41 +Empedocles, 16 +Encke, J. F., 119, 122, 123, 133 +Epicycles, 22 +Eratosthenes, 18 +Euclid, 17 +Eudoxus, 15, 31 +Euler, L., 60, 61, 62, 65, 88, 119 + +Fabricius, D.,95, 120, 121 +Feil and Mantois, 88 +Fizeau, H. L., 85, 92, 99 +Flamsteed, J., 50, 58, 68, 78, 79, 93 +Fohi, 8 +Forbes, J. D., 52, 91 +Foucault, L., 85, 99 +Frauenhofer, J., 88, 90, 91 + +Galilei, G., 38, 46-49, 77, 93, 94, 95, 96, 107, 113, 115, 116, 133 +Galle, 71, 72 +Gascoigne, W., 45, 77 +Gauss, C. F., 65, 67 +Gauthier, 98 +Gautier, 89 +Gilbert, 44 +Gill, D., 84, 85, 128, 135, 139, 140 +Goodricke, J., 136 +Gould, B. A., 139 +Grant, R., 27, 47, 51, 86, 134 +Graham, 79 +Greek astronomy, 8-11 +Gregory, J. and D., 87 +Grimaldi, 113 +Groombridge, S., 139 +Grubb, 88, 89 +Guillemin, 122 +Guinand, 88 + +Hale, G. E., 101 +Hall, A., 112 +Hall, C. M., 88 +Halley, E., 19, 51, 58, 60, 61, 62, 63, 64, 79, 120, 122, 125, 129 +Halley’s comet, 62-64 +Halm, 85 +Hansen, P. A., 3, 65 +Hansky, A. P., 100 +Harding, C. L., 67 +Heliometer, 83 +Heller, 120 +Helmholtz, H. L. F., 35 +Henderson, T., 128 +Henry, P. and P., 139, 140, 143 +Heraclides, 16 +Heraclitus, 14 +Herodotus, 13 +Herschel, W., 65, 68, 97, 107, 110, 114, 115, 116, 117, 118, 126, 127, +130, 131, 132, 141, 142 +Herschel, J., 97, 111, 133, 134, 142 +Herschel, A. S., 125 +Hevelius, J., 178 +Hind, J. R., 5, 64, 120, 121, 122 +Hipparchus, 3, 18, 19, 20, 22, 23, 24, 26, 36, 55, 60, 74, 93, 137 +Hooke, R., 51, 111, 114 +Horrocks, J., 50, 56 +Howlett, 100 +Huggins, W., 92, 93, 99, 106, 120, 129, 137, 138, 142, 144 +Humboldt and Bonpland, 124 +Huyghens, C., 47, 77, 87, 110, 116, 117 + +Ivory, 65 + +Jansen, P. J. C., 105, 106 +Jansen, Z., 86 + +Kaiser, F., 111 +Kapteyn, J. C., 131, 138, 139 +Keeler, 117 +Kepler, J., 17, 23, 26, 29, 30, 36, 37, 38-46, 48, 49, 50, 52, 53, 63, +66, 77, 87, 93, 127, 137 +Kepler’s laws, 42 +Kirchoff, G.R., 91 +Kirsch, 9 +Knobel, E.B., 12, 13 +Ko-Show-King, 76 + +Lacaile, N.L., 139 +Lagrange, J.L., 61, 62, 65, 119 +La Hire, 114 +Lalande, J.J.L., 60, 63, 65, 66, 72, 139 +Lamont, J., 98 +Langrenus, 107 +Laplace, P.S. de, 50, 58, 61, 62, 65,66, 123, 146 +Lassel, 72, 88, 117, 118 +Law of universal gravitation, 53 +Legendre, 65 +Leonardo da Vinci, 46 +Lewis, G.C., 17 +Le Verrier, U.J.J., 65, 68, 70, 71,72, 110, 118, 125 +Lexell, 66, 123 +Light year, 128 +Lipperhey, H., 86 +Littrow, 121 +Lockyer, J.N., 103, 105, 146 +Logarithms invented, 50 +Loewy, 2, 100 +Long inequality of Jupiter and Saturn, 50, 62 +Lowell, P., 111, 112, 118 +Lubienietz, S. de, 122 +Luther, M., 38 +Lunar theory, 37, 50, 56, 64 + +Maclaurin, 65 +Maclear, T., 128 +Malvasia, 77 +Martin, 9 +Maxwell, J. Clerk, 117 +Maskelyne, N., 80, 130 +McLean, F., 89 +Medici, Cosmo di, 48 +Melancthon, 38 +Melotte, 83, 116 +Meteors, 123 +Meton, 15 +Meyer, 57, 65 +Michaelson, 85 +Miraldi, 110, 114 +Molyneux, 87 +Moon, physical observations, 107 +Mouchez, 139 +Moyriac de Mailla, 8 + +Napier, Lord, 50 +Nasmyth and Carpenter, 108 +Nebulae, 141, 146 +Neison, E., 108 +Neptune, discovery of, 68-72 +Newall, 89 +Newcomb, 85 +Newton, H.A., 124 +Newton, I., 5, 19, 43, 49, 51-60, 62, 64, 68, 77, 79, 87, 90, 93, 94, +114, 127, 133 +Nicetas, 16, 25 +Niesten, 115 +Nunez, P., 35 + +Olbers, H.W.M., 67 +Omar, 11, 24 +Oppolzer, 13, 125 +Oudemans, 129 + +Palitsch, G., 64 +Parallax, solar, 85, 86 +Parmenides, 14 +Paul III., 30 +Paul V., 48 +Pemberton, 51 +Peters, C.A.F., 125, 128, 135 +Photography, 99 +Piazzi, G., 67, 128, 129, 139 +Picard, 54, 77, 114 +Pickering, E.C., 118, 135 +Pingré, 13, 122 +Plana, 65 +Planets and satellites, physical observations, 109-119 +Plato, 17, 23, 26, 40 +Poisson, 65 +Pond, J., 80 +Pons, 122 +Porta, B., 86 +Pound, 87, 114 +Pontecoulant, 64 +Precession of the equinoxes, 19-21, 55, 57 +Proctor, R.A., 111 +Pritchett, 115 +Ptolemy, 11, 13, 21, 22, 23, 24, 93 +Puiseux and Loewy, 108 +Pulfrich, 131 +Purbach, G., 24 +Pythagoras, 14, 17, 25, 29 + +Ramsay, W., 106 +Ransome and May, 81 +Reflecting telescopes invented, 87 +Regiomontanus (Müller), 24 +Respighi, 82 +Retrograde motion of planets, 22 +Riccioli, 107 +Roberts, 137 +Römer, O.,78, 114 +Rosse, Earl of, 88, 142 +Rowland, H. A., 92, 102 +Rudolph H.,37, 39 +Rumker, C., 139 + +Sabine, E., 98 +Savary, 133 +Schaeberle, J. M., 135 +Schiaparelli, G. V., 110, 111, 124, 125 +Scheiner, C., 87, 95, 96 +Schmidt, 108 +Schott, 88 +Schröter, J. H., 107, 110, 111, 124, 125 +Schuster, 98 +Schwabe, G. H., 97 +Secchi, A., 93, 144 +Short, 87 +Simms, J., 81 +Slipher, V. M., 119 +Socrates, 17 +Solon, 15 +Souciet, 8 +South, J., 133 +Spectroscope, 89-92 +Spectroheliograph, 101 +Spoerer, G. F. W., 98 +Spots on the sun, 84; +periodicity of, 97 +Stars, Parallax, 127; +proper motion, 129; +double, 132; +binaries, 132, 135; +new, 19, 36, 137; +catalogues of, 19, 36, 139; +spectra of, 143 +Stewart, B., 2, 100 +Stokes, G. G., 91 +Stone, E. J., 139 +Struve, C. L., 130 +Struve, F. G. W,, 88, 115, 128, 133 + +Telescopes invented, 47, 86; +large, 88 +Temple, 115, 125 +Thales, 13, 16 +Theon, 60 +Transit circle of Römer, 78 +Timocharis, 17, 19 +Titius, 66 +Torricelli, 113 +Troughton, E., 80 +Tupman, G. L., 120 +Tuttle, 125 +Tycho Brahe, 23, 25, 30, 33-38, 39, 40, 44, 50, 75, 77, 93, 94, 129, +137 + +Ulugh Begh, 24 +Uranus, discovery of, 65 + +Velocity of light, 86, 128; +of earth in orbit, 128 +Verbiest, 75 +Vogel, H. C., 92, 129, 135, 136 +Von Asten, 122 + +Walmsley, 65 +Walterus, B., 24, 74 +Weiss, E., 125 +Wells, 122 +Wesley, 104 +Whewell, 112 +Williams, 10 +Wilson, A., 96, 100 +Winnecke, 120 +Witte, 86 +Wollaston, 90 +Wolf, M., 119, 125, 132 +Wolf, R., 98 +Wren, C., 51 +Wyllie, A., 77 + +Yao, 9 +Young, C. A., 103 +Yu-Chi, 8 + +Zenith telescopes, 79, 82 +Zöllner, 92 +Zucchi, 113 + + +End of the Project Gutenberg EBook of History of Astronomy, by George Forbes + +*** END OF THIS PROJECT GUTENBERG EBOOK HISTORY OF ASTRONOMY *** + +***** This file should be named 8172-0.txt or 8172-0.zip ***** +This and all associated files of various formats will be found in: + http://www.gutenberg.org/8/1/7/8172/ + +Produced by Jonathan Ingram, Dave Maddock, Charles Franks +and the Online Distributed Proofreading Team. + +Updated editions will replace the previous one--the old editions will +be renamed. + +Creating the works from print editions not protected by U.S. copyright +law means that no one owns a United States copyright in these works, +so the Foundation (and you!) can copy and distribute it in the United +States without permission and without paying copyright +royalties. 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