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diff --git a/8172.txt b/8172.txt new file mode 100644 index 0000000..4a30a86 --- /dev/null +++ b/8172.txt @@ -0,0 +1,5323 @@ +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 + +Posting Date: September 8, 2014 [EBook #8172] +Release Date: May, 2005 +First Posted: June 25, 2003 + +Language: English + +Character set encoding: ASCII + +*** 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 CHALDAEANS + + 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 NEBULAE + + 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 1st, 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 _a 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 Chaldaeans 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 Chaldaean 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 Chaldaeans +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: CHALDAEAN 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 CHALDAEANS. + + +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, Chaldaeans, 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 3651/4 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. + +_Chaldaeans_.--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 Chaldaeans, 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. Pingre 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 deg. 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 +Chaldaean 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 deg. +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 gamma 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 deg. and 27 deg. 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 gamma 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 Chaldaeans 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 Booetes 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 Mueller, 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 _Astronomiae Instauratae 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 _a 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. + +[Illustration] + +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. + +[Illustration] + +[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. + deg. ' " deg. ' " +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 parabolae, 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 deg. 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 deg. 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 deg. 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 deg. + +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 deg. + +This result agreed so well with Adams's (within 1 deg.) 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 aequatoriae maximae," 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 deg., 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 Koenigsberg, 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 +291/2-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 Zoellner. + + +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. Koen. Boehm. 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. + +[Illustration: SOLAR SURFACE, As Photographed at the Royal +Observatory, Greenwich, showing sun-spots with umbrae, penumbrae, and +faculae.] + +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. + +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 deg. 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 deg., 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 faculae 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 faculae 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 faculae 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. Angstrom 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-la en dehors des eclipses_." 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 deg.; London and +Edinburgh, 1863. + +[5] _Periodicitaet 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. Shroeter supported this +opinion. W. Herschel opposed it. But Beer and Maedler 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 Schroeter, Beer and Maedler (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 _Linne_, 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 (Moesting 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. Shroeter 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 Maedler, 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 Maedler 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, Roemer, 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 51/2 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 21/2 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. Shroeter 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 deg. 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 51/2 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 3541/2 days; another suggestion was 3751/2 +days, and another 331/4 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 331/4-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 Pingre, 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 NEBULAE. + + +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 nebulae 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 alpha +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 (alpha +Lyrae). 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 alpha2 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 light year 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: alpha 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, alpha Orionis, alpha Cygni, beta +Centauri, and gamma 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 Voegel, 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, beta, gamma, delta, +epsilon, zeta, all agree as to angular proper motion. delta 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 deg.; N. Decl. 25 deg. 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; +delta Serpentis, 375 years; gamma Leonis, 1,200 years; epsilon 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 Coronae 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 (kappa 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 (alpha +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 zeta 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 (beta 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 "Novae" 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 Novae, 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. + +_Nebulae and Star-clusters._--Our knowledge of nebulae 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 nebulae might be clusters of +innumerable minute stars at a great distance. Then he recognised the +different classes of nebulae, and became convinced that there is a +widely-diffused "shining fluid" in space, though many so-called nebulae +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 +nebulae" might show a stage of evolution from the diffuse nebulae, 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 nebulae. + +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 nebulae; 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 nebulae, 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 +101/4 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 deg. or 5 deg. 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 nebulae, and the distribution +of nebulae 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 alpha Herculis, alpha 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 _Systeme 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. + + + +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 +Angstrom, 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 Maedler, 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 +Chaldaean 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 +Pingre, 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 (Mueller), 24 +Respighi, 82 +Retrograde motion of planets, 22 +Riccioli, 107 +Roberts, 137 +Roemer, 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 +Schroeter, 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 Roemer, 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 +Zoellner, 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.txt or 8172.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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