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diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000..6833f05 --- /dev/null +++ b/.gitattributes @@ -0,0 +1,3 @@ +* text=auto +*.txt text +*.md text diff --git a/8172-0.txt b/8172-0.txt new file mode 100644 index 0000000..f5b7558 --- /dev/null +++ b/8172-0.txt @@ -0,0 +1,5273 @@ +The Project Gutenberg EBook of History of Astronomy, by George Forbes + +This eBook is for the use of anyone anywhere in the United States and most +other parts of the world at no cost and with almost no restrictions +whatsoever. You may copy it, give it away or re-use it under the terms of +the Project Gutenberg License included with this eBook or online at +www.gutenberg.org. If you are not located in the United States, you'll have +to check the laws of the country where you are located before using this ebook. + +Title: History of Astronomy + +Author: George Forbes + +Release Date: June 25, 2003 [EBook #8172] +[Most recently updated: March 21, 2020] + +Language: English + +Character set encoding: UTF-8 + +*** START OF THIS PROJECT GUTENBERG EBOOK HISTORY OF ASTRONOMY *** + + + + +Produced by Jonathan Ingram, Dave Maddock, Charles Franks +and the Online Distributed Proofreading Team. + + + + +[Illustration: SIR ISAAC NEWTON +(From the bust by Roubiliac In Trinity College, Cambridge.)] + + + + +HISTORY OF ASTRONOMY +BY +GEORGE FORBES, +M.A., F.R.S., M. INST. C. E., + +(FORMERLY PROFESSOR OF NATURAL PHILOSOPHY, ANDERSON’S +COLLEGE, GLASGOW) + +AUTHOR OF “THE TRANSIT OF VENUS,” RENDU’S +“THEORY OF THE GLACIERS OF SAVOY,” ETC., ETC. + + + + +CONTENTS + + PREFACE + + BOOK I. THE GEOMETRICAL PERIOD + 1. PRIMITIVE ASTRONOMY AND ASTROLOGY + 2. ANCIENT ASTRONOMY—CHINESE AND CHALDÆANS + 3. ANCIENT GREEK ASTRONOMY + 4. THE REIGN OF EPICYCLES—FROM PTOLEMY TO COPERNICUS + + BOOK II. THE DYNAMICAL PERIOD + 5. DISCOVERY OF THE TRUE SOLAR SYSTEM—TYCHO BRAHE—KEPLER + 6. GALILEO AND THE TELESCOPE—NOTIONS OF GRAVITY BY HORROCKS, ETC. + 7. SIR ISAAC NEWTON—LAW OF UNIVERSAL GRAVITATION + 8. NEWTON’S SUCCESSORS—HALLEY, EULER, LAGRANGE, +LAPLACE, ETC. + 9. DISCOVERY OF NEW PLANETS—HERSCHEL, PIAZZI, ADAMS, +AND LE VERRIER + + BOOK III. OBSERVATION + 10. INSTRUMENTS OF PRECISION—SIZE OF THE SOLAR SYSTEM + 11. HISTORY OF THE TELESCOPE—SPECTROSCOPE + + BOOK IV. THE PHYSICAL PERIOD + 12. THE SUN + 13. THE MOON AND PLANETS + 14. COMETS AND METEORS + 15. THE STARS AND NEBULÆ + + ILLUSTRATIONS + INDEX + + + + +PREFACE + + +An attempt has been made in these pages to trace the evolution of +intellectual thought in the progress of astronomical discovery, and, by +recognising the different points of view of the different ages, to give +due credit even to the ancients. No one can expect, in a history of +astronomy of limited size, to find a treatise on “practical” or on +“theoretical astronomy,” nor a complete “descriptive astronomy,” and +still less a book on “speculative astronomy.” Something of each of +these is essential, however, for tracing the progress of thought and +knowledge which it is the object of this History to describe. + +The progress of human knowledge is measured by the increased habit of +looking at facts from new points of view, as much as by the +accumulation of facts. The mental capacity of one age does not seem to +differ from that of other ages; but it is the imagination of new points +of view that gives a wider scope to that capacity. And this is +cumulative, and therefore progressive. Aristotle viewed the solar +system as a geometrical problem; Kepler and Newton converted the point +of view into a dynamical one. Aristotle’s mental capacity to understand +the meaning of facts or to criticise a train of reasoning may have been +equal to that of Kepler or Newton, but the point of view was different. + +Then, again, new points of view are provided by the invention of new +methods in that system of logic which we call mathematics. All that +mathematics can do is to assure us that a statement A is equivalent to +statements B, C, D, or is one of the facts expressed by the statements +B, C, D; so that we may know, if B, C, and D are true, then A is true. +To many people our inability to understand all that is contained in +statements B, C, and D, without the cumbrous process of a mathematical +demonstration, proves the feebleness of the human mind as a logical +machine. For it required the new point of view imagined by Newton’s +analysis to enable people to see that, so far as planetary orbits are +concerned, Kepler’s three laws (B, C, D) were identical with Newton’s +law of gravitation (A). No one recognises more than the mathematical +astronomer this feebleness of the human intellect, and no one is more +conscious of the limitations of the logical process called mathematics, +which even now has not solved directly the problem of only three +bodies. + +These reflections, arising from the writing of this History, go to +explain the invariable humility of the great mathematical astronomers. +Newton’s comparison of himself to the child on the seashore applies to +them all. As each new discovery opens up, it may be, boundless oceans +for investigation, for wonder, and for admiration, the great +astronomers, refusing to accept mere hypotheses as true, have founded +upon these discoveries a science as exact in its observation of facts +as in theories. So it is that these men, who have built up the most +sure and most solid of all the sciences, refuse to invite others to +join them in vain speculation. The writer has, therefore, in this short +History, tried to follow that great master, Airy, whose pupil he was, +and the key to whose character was exactness and accuracy; and he +recognises that Science is impotent except in her own limited sphere. + +It has been necessary to curtail many parts of the History in the +attempt—perhaps a hopeless one—to lay before the reader in a limited +space enough about each age to illustrate its tone and spirit, the +ideals of the workers, the gradual addition of new points of view and +of new means of investigation. + +It would, indeed, be a pleasure to entertain the hope that these pages +might, among new recruits, arouse an interest in the greatest of all +the sciences, or that those who have handled the theoretical or +practical side might be led by them to read in the original some of the +classics of astronomy. Many students have much compassion for the +schoolboy of to-day, who is not allowed the luxury of learning the art +of reasoning from him who still remains pre-eminently its greatest +exponent, Euclid. These students pity also the man of to-morrow, who is +not to be allowed to read, in the original Latin of the brilliant +Kepler, how he was able—by observations taken from a moving platform, +the earth, of the directions of a moving object, Mars—to deduce the +exact shape of the path of each of these planets, and their actual +positions on these paths at any time. Kepler’s masterpiece is one of +the most interesting books that was ever written, combining wit, +imagination, ingenuity, and certainty. + +Lastly, it must be noted that, as a History of England cannot deal with +the present Parliament, so also the unfinished researches and untested +hypotheses of many well-known astronomers of to-day cannot be included +among the records of the History of Astronomy. The writer regrets the +necessity that thus arises of leaving without mention the names of many +who are now making history in astronomical work. + +G. F. + +_August_ 1_st_, 1909. + + + + +BOOK I. THE GEOMETRICAL PERIOD + +1. PRIMITIVE ASTRONOMY AND ASTROLOGY. + + +The growth of intelligence in the human race has its counterpart in +that of the individual, especially in the earliest stages. Intellectual +activity and the development of reasoning powers are in both cases +based upon the accumulation of experiences, and on the comparison, +classification, arrangement, and nomenclature of these experiences. +During the infancy of each the succession of events can be watched, but +there can be no _à priori_ anticipations. Experience alone, in both +cases, leads to the idea of cause and effect as a principle that seems +to dominate our present universe, as a rule for predicting the course +of events, and as a guide to the choice of a course of action. This +idea of cause and effect is the most potent factor in developing the +history of the human race, as of the individual. + +In no realm of nature is the principle of cause and effect more +conspicuous than in astronomy; and we fall into the habit of thinking +of its laws as not only being unchangeable in our universe, but +necessary to the conception of any universe that might have been +substituted in its place. The first inhabitants of the world were +compelled to accommodate their acts to the daily and annual +alternations of light and darkness and of heat and cold, as much as to +the irregular changes of weather, attacks of disease, and the fortune +of war. They soon came to regard the influence of the sun, in +connection with light and heat, as a cause. This led to a search for +other signs in the heavens. If the appearance of a comet was sometimes +noted simultaneously with the death of a great ruler, or an eclipse +with a scourge of plague, these might well be looked upon as causes in +the same sense that the veering or backing of the wind is regarded as a +cause of fine or foul weather. + +For these reasons we find that the earnest men of all ages have +recorded the occurrence of comets, eclipses, new stars, meteor showers, +and remarkable conjunctions of the planets, as well as plagues and +famines, floods and droughts, wars and the deaths of great rulers. +Sometimes they thought they could trace connections which might lead +them to say that a comet presaged famine, or an eclipse war. + +Even if these men were sometimes led to evolve laws of cause and effect +which now seem to us absurd, let us be tolerant, and gratefully +acknowledge that these astrologers, when they suggested such “working +hypotheses,” were laying the foundations of observation and deduction. + +If the ancient Chaldæans gave to the planetary conjunctions an +influence over terrestrial events, let us remember that in our own time +people have searched for connection between terrestrial conditions and +periods of unusual prevalence of sun spots; while De la Rue, Loewy, and +Balfour Stewart[1] thought they found a connection between sun-spot +displays and the planetary positions. Thus we find scientific men, even +in our own time, responsible for the belief that storms in the Indian +Ocean, the fertility of German vines, famines in India, and high or low +Nile-floods in Egypt follow the planetary positions. + +And, again, the desire to foretell the weather is so laudable that we +cannot blame the ancient Greeks for announcing the influence of the +moon with as much confidence as it is affirmed in Lord Wolseley’s +_Soldier’s Pocket Book_. + +Even if the scientific spirit of observation and deduction (astronomy) +has sometimes led to erroneous systems for predicting terrestrial +events (astrology), we owe to the old astronomer and astrologer alike +the deepest gratitude for their diligence in recording astronomical +events. For, out of the scanty records which have survived the +destructive acts of fire and flood, of monarchs and mobs, we have found +much that has helped to a fuller knowledge of the heavenly motions than +was possible without these records. + +So Hipparchus, about 150 B.C., and Ptolemy a little later, were able to +use the observations of Chaldæan astrologers, as well as those of +Alexandrian astronomers, and to make some discoveries which have helped +the progress of astronomy in all ages. So, also, Mr. Cowell[2] has +examined the marks made on the baked bricks used by the Chaldæans for +recording the eclipses of 1062 B.C. and 762 B.C.; and has thereby been +enabled, in the last few years, to correct the lunar tables of Hansen, +and to find a more accurate value for the secular acceleration of the +moon’s longitude and the node of her orbit than any that could be +obtained from modern observations made with instruments of the highest +precision. + +So again, Mr. Hind[3] was enabled to trace back the period during which +Halley’s comet has been a member of the solar system, and to identify +it in the Chinese observations of comets as far back as 12 B.C. Cowell +and Cromellin extended the date to 240 B.C. In the same way the comet +1861.i. has been traced back in the Chinese records to 617 A.D.[4] + +The theoretical views founded on Newton’s great law of universal +gravitation led to the conclusion that the inclination of the earth’s +equator to the plane of her orbit (the obliquity of the ecliptic) has +been diminishing slowly since prehistoric times; and this fact has been +confirmed by Egyptian and Chinese observations on the length of the +shadow of a vertical pillar, made thousands of years before the +Christian era, in summer and winter. + +There are other reasons why we must be tolerant of the crude notions of +the ancients. The historian, wishing to give credit wherever it may be +due, is met by two difficulties. Firstly, only a few records of very +ancient astronomy are extant, and the authenticity of many of these is +open to doubt. Secondly, it is very difficult to divest ourselves of +present knowledge, and to appreciate the originality of thought +required to make the first beginnings. + +With regard to the first point, we are generally dependent upon +histories written long after the events. The astronomy of Egyptians, +Babylonians, and Assyrians is known to us mainly through the Greek +historians, and for information about the Chinese we rely upon the +researches of travellers and missionaries in comparatively recent +times. The testimony of the Greek writers has fortunately been +confirmed, and we now have in addition a mass of facts translated from +the original sculptures, papyri, and inscribed bricks, dating back +thousands of years. + +In attempting to appraise the efforts of the beginners we must remember +that it was natural to look upon the earth (as all the first +astronomers did) as a circular plane, surrounded and bounded by the +heaven, which was a solid vault, or hemisphere, with its concavity +turned downwards. The stars seemed to be fixed on this vault; the moon, +and later the planets, were seen to crawl over it. It was a great step +to look on the vault as a hollow sphere carrying the sun too. It must +have been difficult to believe that at midday the stars are shining as +brightly in the blue sky as they do at night. It must have been +difficult to explain how the sun, having set in the west, could get +back to rise in the east without being seen _if_ it was always the same +sun. It was a great step to suppose the earth to be spherical, and to +ascribe the diurnal motions to its rotation. Probably the greatest step +ever made in astronomical theory was the placing of the sun, moon, and +planets at different distances from the earth instead of having them +stuck on the vault of heaven. It was a transition from “flatland” to a +space of three dimensions. + +Great progress was made when systematic observations began, such as +following the motion of the moon and planets among the stars, and the +inferred motion of the sun among the stars, by observing their +_heliacal risings_—i.e., the times of year when a star would first be +seen to rise at sunrise, and when it could last be seen to rise at +sunset. The grouping of the stars into constellations and recording +their places was a useful observation. The theoretical prediction of +eclipses of the sun and moon, and of the motions of the planets among +the stars, became later the highest goal in astronomy. + +To not one of the above important steps in the progress of astronomy +can we assign the author with certainty. Probably many of them were +independently taken by Chinese, Indian, Persian, Tartar, Egyptian, +Babylonian, Assyrian, Phoenician, and Greek astronomers. And we have +not a particle of information about the discoveries, which may have +been great, by other peoples—by the Druids, the Mexicans, and the +Peruvians, for example. + +We do know this, that all nations required to have a calendar. The +solar year, the lunar month, and the day were the units, and it is +owing to their incommensurability that we find so many calendars +proposed and in use at different times. The only object to be attained +by comparing the chronologies of ancient races is to fix the actual +dates of observations recorded, and this is not a part of a history of +astronomy. + +In conclusion, let us bear in mind the limited point of view of the +ancients when we try to estimate their merit. Let us remember that the +first astronomy was of two dimensions; the second astronomy was of +three dimensions, but still purely geometrical. Since Kepler’s day we +have had a dynamical astronomy. + +FOOTNOTES: + + [1] Trans. R. S. E., xxiii. 1864, p. 499, _On Sun Spots_, _etc_., by + B. Stewart. Also Trans. R. S. 1860-70. Also Prof. Ernest Brown, in _R. + A. S. Monthly Notices_, 1900. + + [2] _R. A. S. Monthly Notices_, Sup.; 1905. + +[Illustration: CHALDÆAN BAKED BRICK OR TABLET, +_Obverse and reverse sides_, Containing record of solar eclipse, 1062 +B.C., used lately by Cowell for rendering the lunar theory more +accurate than was possible by finest modern observations. (British +Museum collection, No. 35908.)] + + [3] _R. A. S. Monthly Notices_, vol. x., p. 65. + + [4] R. S. E. Proc., vol. x., 1880. + + + + +2. ANCIENT ASTRONOMY—THE CHINESE AND CHALDÆANS. + + +The last section must have made clear the difficulties the way of +assigning to the ancient nations their proper place in the development +of primitive notions about astronomy. The fact that some alleged +observations date back to a period before the Chinese had invented the +art of writing leads immediately to the question how far tradition can +be trusted. + +Our first detailed knowledge was gathered in the far East by +travellers, and by the Jesuit priests, and was published in the +eighteenth century. The Asiatic Society of Bengal contributed +translations of Brahmin literature. The two principal sources of +knowledge about Chinese astronomy were supplied, first by Father +Souciet, who in 1729 published _Observations Astronomical, +Geographical, Chronological, and Physical_, drawn from ancient Chinese +books; and later by Father Moyriac-de-Mailla, who in 1777-1785 +published _Annals of the Chinese Empire, translated from +Tong-Kien-Kang-Mou_. + +Bailly, in his _Astronomie Ancienne_ (1781), drew, from these and other +sources, the conclusion that all we know of the astronomical learning +of the Chinese, Indians, Chaldæans, Assyrians, and Egyptians is but the +remnant of a far more complete astronomy of which no trace can be +found. + +Delambre, in his _Histoire de l’Astronomie Ancienne_ (1817), ridicules +the opinion of Bailly, and considers that the progress made by all of +these nations is insignificant. + +It will be well now to give an idea of some of the astronomy of the +ancients not yet entirely discredited. China and Babylon may be taken +as typical examples. + +_China_.—It would appear that Fohi, the first emperor, reigned about +2952 B.C., and shortly afterwards Yu-Chi made a sphere to represent the +motions of the celestial bodies. It is also mentioned, in the book +called Chu-King, supposed to have been written in 2205 B.C., that a +similar sphere was made in the time of Yao (2357 B.C.).[1] It is said +that the Emperor Chueni (2513 B.C.) saw five planets in conjunction the +same day that the sun and moon were in conjunction. This is discussed +by Father Martin (MSS. of De Lisle); also by M. Desvignolles (Mem. +Acad. Berlin, vol. iii., p. 193), and by M. Kirsch (ditto, vol. v., p. +19), who both found that Mars, Jupiter, Saturn, and Mercury were all +between the eleventh and eighteenth degrees of Pisces, all visible +together in the evening on February 28th 2446 B.C., while on the same +day the sun and moon were in conjunction at 9 a.m., and that on March +1st the moon was in conjunction with the other four planets. But this +needs confirmation. + +Yao, referred to above, gave instructions to his astronomers to +determine the positions of the solstices and equinoxes, and they +reported the names of the stars in the places occupied by the sun at +these seasons, and in 2285 B.C. he gave them further orders. If this +account be true, it shows a knowledge that the vault of heaven is a +complete sphere, and that stars are shining at mid-day, although +eclipsed by the sun’s brightness. + +It is also asserted, in the book called _Chu-King_, that in the time of +Yao the year was known to have 365¼ days, and that he adopted 365 days +and added an intercalary day every four years (as in the Julian +Calendar). This may be true or not, but the ancient Chinese certainly +seem to have divided the circle into 365 degrees. To learn the length +of the year needed only patient observation—a characteristic of the +Chinese; but many younger nations got into a terrible mess with their +calendar from ignorance of the year’s length. + +It is stated that in 2159 B.C. the royal astronomers Hi and Ho failed +to predict an eclipse. It probably created great terror, for they were +executed in punishment for their neglect. If this account be true, it +means that in the twenty-second century B.C. some rule for calculating +eclipses was in use. Here, again, patient observation would easily lead +to the detection of the eighteen-year cycle known to the Chaldeans as +the _Saros_. It consists of 235 lunations, and in that time the pole of +the moon’s orbit revolves just once round the pole of the ecliptic, and +for this reason the eclipses in one cycle are repeated with very slight +modification in the next cycle, and so on for many centuries. + +It may be that the neglect of their duties by Hi and Ho, and their +punishment, influenced Chinese astronomy; or that the succeeding +records have not been available to later scholars; but the fact remains +that—although at long intervals observations were made of eclipses, +comets, and falling stars, and of the position of the solstices, and of +the obliquity of the ecliptic—records become rare, until 776 B.C., when +eclipses began to be recorded once more with some approach to +continuity. Shortly afterwards notices of comets were added. Biot gave +a list of these, and Mr. John Williams, in 1871, published +_Observations of Comets from 611 B.C. to 1640 A.D., Extracted from the +Chinese Annals_. + +With regard to those centuries concerning which we have no astronomical +Chinese records, it is fair to state that it is recorded that some +centuries before the Christian era, in the reign of Tsin-Chi-Hoang, all +the classical and scientific books that could be found were ordered to +be destroyed. If true, our loss therefrom is as great as from the +burning of the Alexandrian library by the Caliph Omar. He burnt all the +books because he held that they must be either consistent or +inconsistent with the Koran, and in the one case they were superfluous, +in the other case objectionable. + +_Chaldæans_.—Until the last half century historians were accustomed to +look back upon the Greeks, who led the world from the fifth to the +third century B.C., as the pioneers of art, literature, and science. +But the excavations and researches of later years make us more ready to +grant that in science as in art the Greeks only developed what they +derived from the Egyptians, Babylonians, and Assyrians. The Greek +historians said as much, in fact; and modern commentators used to +attribute the assertion to undue modesty. Since, however, the records +of the libraries have been unearthed it has been recognised that the +Babylonians were in no way inferior in the matter of original +scientific investigation to other races of the same era. + +The Chaldæans, being the most ancient Babylonians, held the same +station and dignity in the State as did the priests in Egypt, and spent +all their time in the study of philosophy and astronomy, and the arts +of divination and astrology. They held that the world of which we have +a conception is an eternal world without any beginning or ending, in +which all things are ordered by rules supported by a divine providence, +and that the heavenly bodies do not move by chance, nor by their own +will, but by the determinate will and appointment of the gods. They +recorded these movements, but mainly in the hope of tracing the will of +the gods in mundane affairs. Ptolemy (about 130 A.D.) made use of +Babylonian eclipses in the eighth century B.C. for improving his solar +and lunar tables. + +Fragments of a library at Agade have been preserved at Nineveh, from +which we learn that the star-charts were even then divided into +constellations, which were known by the names which they bear to this +day, and that the signs of the zodiac were used for determining the +courses of the sun, moon, and of the five planets Mercury, Venus, Mars, +Jupiter, and Saturn. + +We have records of observations carried on under Asshurbanapal, who +sent astronomers to different parts to study celestial phenomena. Here +is one:— + +To the Director of Observations,—My Lord, his humble servant +Nabushum-iddin, Great Astronomer of Nineveh, writes thus: “May Nabu and +Marduk be propitious to the Director of these Observations, my Lord. +The fifteenth day we observed the Node of the moon, and the moon was +eclipsed.” + +The Phoenicians are supposed to have used the stars for navigation, but +there are no records. The Egyptian priests tried to keep such +astronomical knowledge as they possessed to themselves. It is probable +that they had arbitrary rules for predicting eclipses. All that was +known to the Greeks about Egyptian science is to be found in the +writings of Diodorus Siculus. But confirmatory and more authentic facts +have been derived from late explorations. Thus we learn from E. B. +Knobel[2] about the Jewish calendar dates, on records of land sales in +Aramaic papyri at Assuan, translated by Professor A. H. Sayce and A. E. +Cowley, (1) that the lunar cycle of nineteen years was used by the Jews +in the fifth century B.C. [the present reformed Jewish calendar dating +from the fourth century A.D.], a date a “little more than a century +after the grandfathers and great-grandfathers of those whose business +is recorded had fled into Egypt with Jeremiah” (Sayce); and (2) that +the order of intercalation at that time was not dissimilar to that in +use at the present day. + +Then again, Knobel reminds us of “the most interesting discovery a few +years ago by Father Strassmeier of a Babylonian tablet recording a +partial lunar eclipse at Babylon in the seventh year of Cambyses, on +the fourteenth day of the Jewish month Tammuz.” Ptolemy, in the +Almagest (Suntaxis), says it occurred in the seventh year of Cambyses, +on the night of the seventeenth and eighteenth of the Egyptian month +Phamenoth. Pingré and Oppolzer fix the date July 16th, 533 B.C. Thus +are the relations of the chronologies of Jews and Egyptians established +by these explorations. + +FOOTNOTES: + + [1] These ancient dates are uncertain. + + [2] _R. A. S. Monthly Notices_, vol. lxviii., No. 5, March, 1908. + + + + +3. ANCIENT GREEK ASTRONOMY. + + +We have our information about the earliest Greek astronomy from +Herodotus (born 480 B.C.). He put the traditions into writing. Thales +(639-546 B.C.) is said to have predicted an eclipse, which caused much +alarm, and ended the battle between the Medes and Lydians. Airy fixed +the date May 28th, 585 B.C. But other modern astronomers give different +dates. Thales went to Egypt to study science, and learnt from its +priests the length of the year (which was kept a profound secret!), and +the signs of the zodiac, and the positions of the solstices. He held +that the sun, moon, and stars are not mere spots on the heavenly vault, +but solids; that the moon derives her light from the sun, and that this +fact explains her phases; that an eclipse of the moon happens when the +earth cuts off the sun’s light from her. He supposed the earth to be +flat, and to float upon water. He determined the ratio of the sun’s +diameter to its orbit, and apparently made out the diameter correctly +as half a degree. He left nothing in writing. + +His successors, Anaximander (610-547 B.C.) and Anaximenes (550-475 +B.C.), held absurd notions about the sun, moon, and stars, while +Heraclitus (540-500 B.C.) supposed that the stars were lighted each +night like lamps, and the sun each morning. Parmenides supposed the +earth to be a sphere. + +Pythagoras (569-470 B.C.) visited Egypt to study science. He deduced +his system, in which the earth revolves in an orbit, from fantastic +first principles, of which the following are examples: “The circular +motion is the most perfect motion,” “Fire is more worthy than earth,” +“Ten is the perfect number.” He wrote nothing, but is supposed to have +said that the earth, moon, five planets, and fixed stars all revolve +round the sun, which itself revolves round an imaginary central fire +called the Antichthon. Copernicus in the sixteenth century claimed +Pythagoras as the founder of the system which he, Copernicus, revived. + +Anaxagoras (born 499 B.C.) studied astronomy in Egypt. He explained the +return of the sun to the east each morning by its going under the flat +earth in the night. He held that in a solar eclipse the moon hides the +sun, and in a lunar eclipse the moon enters the earth’s shadow—both +excellent opinions. But he entertained absurd ideas of the vortical +motion of the heavens whisking stones into the sky, there to be ignited +by the fiery firmament to form stars. He was prosecuted for this +unsettling opinion, and for maintaining that the moon is an inhabited +earth. He was defended by Pericles (432 B.C.). + +Solon dabbled, like many others, in reforms of the calendar. The common +year of the Greeks originally had 360 days—twelve months of thirty +days. Solon’s year was 354 days. It is obvious that these erroneous +years would, before long, remove the summer to January and the winter +to July. To prevent this it was customary at regular intervals to +intercalate days or months. Meton (432 B.C.) introduced a reform based +on the nineteen-year cycle. This is not the same as the Egyptian and +Chaldean eclipse cycle called _Saros_ of 223 lunations, or a little +over eighteen years. The Metonic cycle is 235 lunations or nineteen +years, after which period the sun and moon occupy the same position +relative to the stars. It is still used for fixing the date of Easter, +the number of the year in Melon’s cycle being the golden number of our +prayer-books. Melon’s system divided the 235 lunations into months of +thirty days and omitted every sixty-third day. Of the nineteen years, +twelve had twelve months and seven had thirteen months. + +Callippus (330 B.C.) used a cycle four times as long, 940 lunations, +but one day short of Melon’s seventy-six years. This was more correct. + +Eudoxus (406-350 B.C.) is said to have travelled with Plato in Egypt. +He made astronomical observations in Asia Minor, Sicily, and Italy, and +described the starry heavens divided into constellations. His name is +connected with a planetary theory which as generally stated sounds most +fanciful. He imagined the fixed stars to be on a vault of heaven; and +the sun, moon, and planets to be upon similar vaults or spheres, +twenty-six revolving spheres in all, the motion of each planet being +resolved into its components, and a separate sphere being assigned for +each component motion. Callippus (330 B.C.) increased the number to +thirty-three. It is now generally accepted that the real existence of +these spheres was not suggested, but the idea was only a mathematical +conception to facilitate the construction of tables for predicting the +places of the heavenly bodies. + +Aristotle (384-322 B.C.) summed up the state of astronomical knowledge +in his time, and held the earth to be fixed in the centre of the world. + +Nicetas, Heraclides, and Ecphantes supposed the earth to revolve on its +axis, but to have no orbital motion. + +The short epitome so far given illustrates the extraordinary deductive +methods adopted by the ancient Greeks. But they went much farther in +the same direction. They seem to have been in great difficulty to +explain how the earth is supported, just as were those who invented the +myth of Atlas, or the Indians with the tortoise. Thales thought that +the flat earth floated on water. Anaxagoras thought that, being flat, +it would be buoyed up and supported on the air like a kite. Democritus +thought it remained fixed, like the donkey between two bundles of hay, +because it was equidistant from all parts of the containing sphere, and +there was no reason why it should incline one way rather than another. +Empedocles attributed its state of rest to centrifugal force by the +rapid circular movement of the heavens, as water is stationary in a +pail when whirled round by a string. Democritus further supposed that +the inclination of the flat earth to the ecliptic was due to the +greater weight of the southern parts owing to the exuberant vegetation. + +For further references to similar efforts of imagination the reader is +referred to Sir George Cornwall Lewis’s _Historical Survey of the +Astronomy of the Ancients_; London, 1862. His list of authorities is +very complete, but some of his conclusions are doubtful. At p. 113 of +that work he records the real opinions of Socrates as set forth by +Xenophon; and the reader will, perhaps, sympathise with Socrates in his +views on contemporary astronomy:— + +With regard to astronomy he [Socrates] considered a knowledge of it +desirable to the extent of determining the day of the year or month, +and the hour of the night, ... but as to learning the courses of the +stars, to be occupied with the planets, and to inquire about their +distances from the earth, and their orbits, and the causes of their +motions, he strongly objected to such a waste of valuable time. He +dwelt on the contradictions and conflicting opinions of the physical +philosophers, ... and, in fine, he held that the speculators on the +universe and on the laws of the heavenly bodies were no better than +madmen (_Xen. Mem_, i. 1, 11-15). + +Plato (born 429 B.C.), the pupil of Socrates, the fellow-student of +Euclid, and a follower of Pythagoras, studied science in his travels in +Egypt and elsewhere. He was held in so great reverence by all learned +men that a problem which he set to the astronomers was the keynote to +all astronomical investigation from this date till the time of Kepler +in the sixteenth century. He proposed to astronomers _the problem of +representing the courses of the planets by circular and uniform +motions_. + +Systematic observation among the Greeks began with the rise of the +Alexandrian school. Aristillus and Timocharis set up instruments and +fixed the positions of the zodiacal stars, near to which all the +planets in their orbits pass, thus facilitating the determination of +planetary motions. Aristarchus (320-250 B.C.) showed that the sun must +be at least nineteen times as far off as the moon, which is far short +of the mark. He also found the sun’s diameter, correctly, to be half a +degree. Eratosthenes (276-196 B.C.) measured the inclination to the +equator of the sun’s apparent path in the heavens—i.e., he measured the +obliquity of the ecliptic, making it 23° 51’, confirming our knowledge +of its continuous diminution during historical times. He measured an +arc of meridian, from Alexandria to Syene (Assuan), and found the +difference of latitude by the length of a shadow at noon, summer +solstice. He deduced the diameter of the earth, 250,000 stadia. +Unfortunately, we do not know the length of the stadium he used. + +Hipparchus (190-120 B.C.) may be regarded as the founder of +observational astronomy. He measured the obliquity of the ecliptic, and +agreed with Eratosthenes. He altered the length of the tropical year +from 365 days, 6 hours to 365 days, 5 hours, 53 minutes—still four +minutes too much. He measured the equation of time and the irregular +motion of the sun; and allowed for this in his calculations by +supposing that the centre, about which the sun moves uniformly, is +situated a little distance from the fixed earth. He called this point +the _excentric_. The line from the earth to the “excentric” was called +the _line of apses_. A circle having this centre was called the +_equant_, and he supposed that a radius drawn to the sun from the +excentric passes over equal arcs on the equant in equal times. He then +computed tables for predicting the place of the sun. + +He proceeded in the same way to compute Lunar tables. Making use of +Chaldæan eclipses, he was able to get an accurate value of the moon’s +mean motion. [Halley, in 1693, compared this value with his own +measurements, and so discovered the acceleration of the moon’s mean +motion. This was conclusively established, but could not be explained +by the Newtonian theory for quite a long time.] He determined the plane +of the moon’s orbit and its inclination to the ecliptic. The motion of +this plane round the pole of the ecliptic once in eighteen years +complicated the problem. He located the moon’s excentric as he had done +the sun’s. He also discovered some of the minor irregularities of the +moon’s motion, due, as Newton’s theory proves, to the disturbing action +of the sun’s attraction. + +In the year 134 B.C. Hipparchus observed a new star. This upset every +notion about the permanence of the fixed stars. He then set to work to +catalogue all the principal stars so as to know if any others appeared +or disappeared. Here his experiences resembled those of several later +astronomers, who, when in search of some special object, have been +rewarded by a discovery in a totally different direction. On comparing +his star positions with those of Timocharis and Aristillus he found no +stars that had appeared or disappeared in the interval of 150 years; +but he found that all the stars seemed to have changed their places +with reference to that point in the heavens where the ecliptic is 90° +from the poles of the earth—i.e., the equinox. He found that this could +be explained by a motion of the equinox in the direction of the +apparent diurnal motion of the stars. This discovery of _precession of +the equinoxes_, which takes place at the rate of 52".1 every year, was +necessary for the progress of accurate astronomical observations. It is +due to a steady revolution of the earth’s pole round the pole of the +ecliptic once in 26,000 years in the opposite direction to the +planetary revolutions. + +Hipparchus was also the inventor of trigonometry, both plane and +spherical. He explained the method of using eclipses for determining +the longitude. + +In connection with Hipparchus’ great discovery it may be mentioned that +modern astronomers have often attempted to fix dates in history by the +effects of precession of the equinoxes. (1) At about the date when the +Great Pyramid may have been built γ Draconis was near to the pole, and +must have been used as the pole-star. In the north face of the Great +Pyramid is the entrance to an inclined passage, and six of the nine +pyramids at Gizeh possess the same feature; all the passages being +inclined at an angle between 26° and 27° to the horizon and in the +plane of the meridian. It also appears that 4,000 years ago—i.e., about +2100 B.C.—an observer at the lower end of the passage would be able to +see γ Draconis, the then pole-star, at its lower culmination.[1] It has +been suggested that the passage was made for this purpose. On other +grounds the date assigned to the Great Pyramid is 2123 B.C. + +(2) The Chaldæans gave names to constellations now invisible from +Babylon which would have been visible in 2000 B.C., at which date it is +claimed that these people were studying astronomy. + +(3) In the Odyssey, Calypso directs Odysseus, in accordance with +Phoenician rules for navigating the Mediterranean, to keep the Great +Bear “ever on the left as he traversed the deep” when sailing from the +pillars of Hercules (Gibraltar) to Corfu. Yet such a course taken now +would land the traveller in Africa. Odysseus is said in his voyage in +springtime to have seen the Pleiades and Arcturus setting late, which +seemed to early commentators a proof of Homer’s inaccuracy. Likewise +Homer, both in the _Odyssey_[2] (v. 272-5) and in the _Iliad_ (xviii. +489), asserts that the Great Bear never set in those latitudes. Now it +has been found that the precession of the equinoxes explains all these +puzzles; shows that in springtime on the Mediterranean the Bear was +just above the horizon, near the sea but not touching it, between 750 +B.C. and 1000 B.C.; and fixes the date of the poems, thus confirming +other evidence, and establishing Homer’s character for accuracy.[3] + +(4) The orientation of Egyptian temples and Druidical stones is such +that possibly they were so placed as to assist in the observation of +the heliacal risings[4] of certain stars. If the star were known, this +would give an approximate date. Up to the present the results of these +investigations are far from being conclusive. + +Ptolemy (130 A.D.) wrote the Suntaxis, or Almagest, which includes a +cyclopedia of astronomy, containing a summary of knowledge at that +date. We have no evidence beyond his own statement that he was a +practical observer. He theorised on the planetary motions, and held +that the earth is fixed in the centre of the universe. He adopted the +excentric and equant of Hipparchus to explain the unequal motions of +the sun and moon. He adopted the epicycles and deferents which had been +used by Apollonius and others to explain the retrograde motions of the +planets. We, who know that the earth revolves round the sun once in a +year, can understand that the apparent motion of a planet is only its +motion relative to the earth. If, then, we suppose the earth fixed and +the sun to revolve round it once a year, and the planets each in its +own period, it is only necessary to impose upon each of these an +additional _annual_ motion to enable us to represent truly the apparent +motions. This way of looking at the apparent motions shows why each +planet, when nearest to the earth, seems to move for a time in a +retrograde direction. The attempts of Ptolemy and others of his time to +explain the retrograde motion in this way were only approximate. Let us +suppose each planet to have a bar with one end centred at the earth. If +at the other end of the bar one end of a shorter bar is pivotted, +having the planet at its other end, then the planet is given an annual +motion in the secondary circle (the epicycle), whose centre revolves +round the earth on the primary circle (the _deferent_), at a uniform +rate round the excentric. Ptolemy supposed the centres of the epicycles +of Mercury and Venus to be on a bar passing through the sun, and to be +between the earth and the sun. The centres of the epicycles of Mars, +Jupiter, and Saturn were supposed to be further away than the sun. +Mercury and Venus were supposed to revolve in their epicycles in their +own periodic times and in the deferent round the earth in a year. The +major planets were supposed to revolve in the deferent round the earth +in their own periodic times, and in their epicycles once in a year. + +It did not occur to Ptolemy to place the centres of the epicycles of +Mercury and Venus at the sun, and to extend the same system to the +major planets. Something of this sort had been proposed by the +Egyptians (we are told by Cicero and others), and was accepted by Tycho +Brahe; and was as true a representation of the relative motions in the +solar system as when we suppose the sun to be fixed and the earth to +revolve. + +The cumbrous system advocated by Ptolemy answered its purpose, enabling +him to predict astronomical events approximately. He improved the lunar +theory considerably, and discovered minor inequalities which could be +allowed for by the addition of new epicycles. We may look upon these +epicycles of Apollonius, and the excentric of Hipparchus, as the +responses of these astronomers to the demand of Plato for uniform +circular motions. Their use became more and more confirmed, until the +seventeenth century, when the accurate observations of Tycho Brahe +enabled Kepler to abolish these purely geometrical makeshifts, and to +substitute a system in which the sun became physically its controller. + +FOOTNOTES: + + [1] _Phil. Mag_., vol. xxiv., pp. 481-4. + + [2] + +Plaeiadas t’ esoronte kai opse duonta bootaen +‘Arkton th’ aen kai amaxan epiklaesin kaleousin, +‘Ae t’ autou strephetai kai t’ Oriona dokeuei, +Oin d’ammoros esti loetron Okeanoio. + +“The Pleiades and Boötes that setteth late, and the Bear, which they +likewise call the Wain, which turneth ever in one place, and keepeth +watch upon Orion, and alone hath no part in the baths of the ocean.” + + [3] See Pearson in the Camb. Phil. Soc. Proc., vol. iv., pt. ii., p. + 93, on whose authority the above statements are made. + + [4] See p. 6 for definition. + + + + +4. THE REIGN OF EPICYCLES—FROM PTOLEMY TO COPERNICUS. + + +After Ptolemy had published his book there seemed to be nothing more to +do for the solar system except to go on observing and finding more and +more accurate values for the constants involved--viz., the periods of +revolution, the diameter of the deferent,[1] and its ratio to that of +the epicycle,[2] the distance of the excentric[3] from the centre of +the deferent, and the position of the line of apses,[4] besides the +inclination and position of the plane of the planet’s orbit. The only +object ever aimed at in those days was to prepare tables for predicting +the places of the planets. It was not a mechanical problem; there was +no notion of a governing law of forces. + +From this time onwards all interest in astronomy seemed, in Europe at +least, to sink to a low ebb. When the Caliph Omar, in the middle of the +seventh century, burnt the library of Alexandria, which had been the +centre of intellectual progress, that centre migrated to Baghdad, and +the Arabs became the leaders of science and philosophy. In astronomy +they made careful observations. In the middle of the ninth century +Albategnius, a Syrian prince, improved the value of excentricity of the +sun’s orbit, observed the motion of the moon’s apse, and thought he +detected a smaller progression of the sun’s apse. His tables were much +more accurate than Ptolemy’s. Abul Wefa, in the tenth century, seems to +have discovered the moon’s “variation.” Meanwhile the Moors were +leaders of science in the west, and Arzachel of Toledo improved the +solar tables very much. Ulugh Begh, grandson of the great Tamerlane the +Tartar, built a fine observatory at Samarcand in the fifteenth century, +and made a great catalogue of stars, the first since the time of +Hipparchus. + +At the close of the fifteenth century King Alphonso of Spain employed +computers to produce the Alphonsine Tables (1488 A.D.), Purbach +translated Ptolemy’s book, and observations were carried out in Germany +by Müller, known as Regiomontanus, and Waltherus. + +Nicolai Copernicus, a Sclav, was born in 1473 at Thorn, in Polish +Prussia. He studied at Cracow and in Italy. He was a priest, and +settled at Frauenberg. He did not undertake continuous observations, +but devoted himself to simplifying the planetary systems and devising +means for more accurately predicting the positions of the sun, moon, +and planets. He had no idea of framing a solar system on a dynamical +basis. His great object was to increase the accuracy of the +calculations and the tables. The results of his cogitations were +printed just before his death in an interesting book, _De +Revolutionibus Orbium Celestium_. It is only by careful reading of this +book that the true position of Copernicus can be realised. He noticed +that Nicetas and others had ascribed the apparent diurnal rotation of +the heavens to a real daily rotation of the earth about its axis, in +the opposite direction to the apparent motion of the stars. Also in the +writings of Martianus Capella he learnt that the Egyptians had supposed +Mercury and Venus to revolve round the sun, and to be carried with him +in his annual motion round the earth. He noticed that the same +supposition, if extended to Mars, Jupiter, and Saturn, would explain +easily why they, and especially Mars, seem so much brighter in +opposition. For Mars would then be a great deal nearer to the earth +than at other times. It would also explain the retrograde motion of +planets when in opposition. + +We must here notice that at this stage Copernicus was actually +confronted with the system accepted later by Tycho Brahe, with the +earth fixed. But he now recalled and accepted the views of Pythagoras +and others, according to which the sun is fixed and the earth revolves; +and it must be noted that, geometrically, there is no difference of any +sort between the Egyptian or Tychonic system and that of Pythagoras as +revived by Copernicus, except that on the latter theory the stars ought +to seem to move when the earth changes its position—a test which failed +completely with the rough means of observation then available. The +radical defect of all solar systems previous to the time of Kepler +(1609 A.D.) was the slavish yielding to Plato’s dictum demanding +uniform circular motion for the planets, and the consequent evolution +of the epicycle, which was fatal to any conception of a dynamical +theory. + +Copernicus could not sever himself from this obnoxious tradition.[5] It +is true that neither the Pythagorean nor the Egypto-Tychonic system +required epicycles for explaining retrograde motion, as the Ptolemaic +theory did. Furthermore, either system could use the excentric of +Hipparchus to explain the irregular motion known as the equation of the +centre. But Copernicus remarked that he could also use an epicycle for +this purpose, or that he could use both an excentric and an epicycle +for each planet, and so bring theory still closer into accord with +observation. And this he proceeded to do.[6] Moreover, observers had +found irregularities in the moon’s motion, due, as we now know, to the +disturbing attraction of the sun. To correct for these irregularities +Copernicus introduced epicycle on epicycle in the lunar orbit. + +This is in its main features the system propounded by Copernicus. But +attention must, to state the case fully, be drawn to two points to be +found in his first and sixth books respectively. The first point +relates to the seasons, and it shows a strange ignorance of the laws of +rotating bodies. To use the words of Delambre,[7] in drawing attention +to the strange conception, + + he imagined that the earth, revolving round the sun, ought always to + show to it the same face; the contrary phenomena surprised him: to + explain them he invented a third motion, and added it to the two real + motions (rotation and orbital revolution). By this third motion the + earth, he held, made a revolution on itself and on the poles of the + ecliptic once a year ... Copernicus did not know that motion in a + straight line is the natural motion, and that motion in a curve is the + resultant of several movements. He believed, with Aristotle, that + circular motion was the natural one. + +Copernicus made this rotation of the earth’s axis about the pole of the +ecliptic retrograde (i.e., opposite to the orbital revolution), and by +making it perform more than one complete revolution in a year, the +added part being 1/26000 of the whole, he was able to include the +precession of the equinoxes in his explanation of the seasons. His +explanation of the seasons is given on leaf 10 of his book (the pages +of this book are not all numbered, only alternate pages, or leaves). + +In his sixth book he discusses the inclination of the planetary orbits +to the ecliptic. In regard to this the theory of Copernicus is unique; +and it will be best to explain this in the words of Grant in his great +work.[8] He says:— + + Copernicus, as we have already remarked, did not attack the principle + of the epicyclical theory: he merely sought to make it more simple by + placing the centre of the earth’s orbit in the centre of the universe. + This was the point to which the motions of the planets were referred, + for the planes of their orbits were made to pass through it, and their + points of least and greatest velocities were also determined with + reference to it. By this arrangement the sun was situate + mathematically near the centre of the planetary system, but he did not + appear to have any physical connexion with the planets as the centre + of their motions. + +According to Copernicus’ sixth book, the planes of the planetary orbits +do not pass through the sun, and the lines of apses do not pass through +to the sun. + +Such was the theory advanced by Copernicus: The earth moves in an +epicycle, on a deferent whose centre is a little distance from the sun. +The planets move in a similar way on epicycles, but their deferents +have no geometrical or physical relation to the sun. The moon moves on +an epicycle centred on a second epicycle, itself centred on a deferent, +excentric to the earth. The earth’s axis rotates about the pole of the +ecliptic, making one revolution and a twenty-six thousandth part of a +revolution in the sidereal year, in the opposite direction to its +orbital motion. + +In view of this fanciful structure it must be noted, in fairness to +Copernicus, that he repeatedly states that the reader is not obliged to +accept his system as showing the real motions; that it does not matter +whether they be true, even approximately, or not, so long as they +enable us to compute tables from which the places of the planets among +the stars can be predicted.[9] He says that whoever is not satisfied +with this explanation must be contented by being told that “mathematics +are for mathematicians” (Mathematicis mathematica scribuntur). + +At the same time he expresses his conviction over and over again that +the earth is in motion. It is with him a pious belief, just as it was +with Pythagoras and his school and with Aristarchus. “But” (as Dreyer +says in his most interesting book, _Tycho Brahe_) “proofs of the +physical truth of his system Copernicus had given none, and could give +none,” any more than Pythagoras or Aristarchus. + +There was nothing so startlingly simple in his system as to lead the +cautious astronomer to accept it, as there was in the later Keplerian +system; and the absence of parallax in the stars seemed to condemn his +system, which had no physical basis to recommend it, and no +simplification at all over the Egypto-Tychonic system, to which +Copernicus himself drew attention. It has been necessary to devote +perhaps undue space to the interesting work of Copernicus, because by a +curious chance his name has become so widely known. He has been spoken +of very generally as the founder of the solar system that is now +accepted. This seems unfair, and on reading over what has been written +about him at different times it will be noticed that the +astronomers—those who have evidently read his great book—are very +cautious in the words with which they eulogise him, and refrain from +attributing to him the foundation of our solar system, which is +entirely due to Kepler. It is only the more popular writers who give +the idea that a revolution had been effected when Pythagoras’ system +was revived, and when Copernicus supported his view that the earth +moves and is not fixed. + +It may be easy to explain the association of the name of Copernicus +with the Keplerian system. But the time has long passed when the +historian can support in any way this popular error, which was started +not by astronomers acquainted with Kepler’s work, but by those who +desired to put the Church in the wrong by extolling Copernicus. + +Copernicus dreaded much the abuse he expected to receive from +philosophers for opposing the authority of Aristotle, who had declared +that the earth was fixed. So he sought and obtained the support of the +Church, dedicating his great work to Pope Paul III. in a lengthy +explanatory epistle. The Bishop of Cracow set up a memorial tablet in +his honour. + +Copernicus was the most refined exponent, and almost the last +representative, of the Epicyclical School. As has been already stated, +his successor, Tycho Brahe, supported the same use of epicycles and +excentrics as Copernicus, though he held the earth to be fixed. But +Tycho Brahe was eminently a practical observer, and took little part in +theory; and his observations formed so essential a portion of the +system of Kepler that it is only fair to include his name among these +who laid the foundations of the solar system which we accept to-day. + +In now taking leave of the system of epicycles let it be remarked that +it has been held up to ridicule more than it deserves. On reading +Airy’s account of epicycles, in the beautifully clear language of his +_Six Lectures on Astronomy_, the impression is made that the jointed +bars there spoken of for describing the circles were supposed to be +real. This is no more the case than that the spheres of Eudoxus and +Callippus were supposed to be real. Both were introduced only to +illustrate the mathematical conception upon which the solar, planetary, +and lunar tables were constructed. The epicycles represented nothing +more nor less than the first terms in the Fourier series, which in the +last century has become a basis of such calculations, both in astronomy +and physics generally. + +[Illustration: “QUADRANS MURALIS SIVE TICHONICUS.” +With portrait of Tycho Brahe, instruments, etc., painted on the wall; +showing assistants using the sight, watching the clock, and recording. +(From the author’s copy of the _Astronomiæ Instauratæ Mechanica_.)] + +FOOTNOTES: + + [1] For definition see p. 22. + + [2] _Ibid_. + + [3] For definition see p. 18. + + [4] For definition see p. 18. + + [5] In his great book Copernicus says: “The movement of the heavenly + bodies is uniform, circular, perpetual, or else composed of circular + movements.” In this he proclaimed himself a follower of Pythagoras + (see p. 14), as also when he says: “The world is spherical because the + sphere is, of all figures, the most perfect” (Delambre, _Ast. Mod. + Hist_., pp. 86, 87). + + [6] Kepler tells us that Tycho Brahe was pleased with this device, and + adapted it to his own system. + + [7] _Hist. Ast._, vol. i., p. 354. + + [8] _Hist. of Phys. Ast._, p. vii. + + [9] “Est enim Astronomi proprium, historiam motuum coelestium + diligenti et artificiosa observatione colligere. Deinde causas + earundem, seu hypotheses, cum veras assequi nulla ratione possit ... + Neque enim necesse est, eas hypotheses esse veras, imo ne verisimiles + quidem, sed sufficit hoc usum, si calculum observationibus congruentem + exhibeant.” + + + + +BOOK II. THE DYNAMICAL PERIOD + +5. DISCOVERY OF THE TRUE SOLAR SYSTEM—TYCHO BRAHE—KEPLER. + + +During the period of the intellectual and aesthetic revival, at the +beginning of the sixteenth century, the “spirit of the age” was +fostered by the invention of printing, by the downfall of the Byzantine +Empire, and the scattering of Greek fugitives, carrying the treasures +of literature through Western Europe, by the works of Raphael and +Michael Angelo, by the Reformation, and by the extension of the known +world through the voyages of Spaniards and Portuguese. During that +period there came to the front the founder of accurate observational +astronomy. Tycho Brahe, a Dane, born in 1546 of noble parents, was the +most distinguished, diligent, and accurate observer of the heavens +since the days of Hipparchus, 1,700 years before. + +Tycho was devoted entirely to his science from childhood, and the +opposition of his parents only stimulated him in his efforts to +overcome difficulties. He soon grasped the hopelessness of the old +deductive methods of reasoning, and decided that no theories ought to +be indulged in until preparations had been made by the accumulation of +accurate observations. We may claim for him the title of founder of the +inductive method. + +For a complete life of this great man the reader is referred to +Dreyer’s _Tycho Brahe_, Edinburgh, 1890, containing a complete +bibliography. The present notice must be limited to noting the work +done, and the qualities of character which enabled him to attain his +scientific aims, and which have been conspicuous in many of his +successors. + +He studied in Germany, but King Frederick of Denmark, appreciating his +great talents, invited him to carry out his life’s work in that +country. He granted to him the island of Hveen, gave him a pension, and +made him a canon of the Cathedral of Roskilde. On that island Tycho +Brahe built the splendid observatory which he called Uraniborg, and, +later, a second one for his assistants and students, called +Stjerneborg. These he fitted up with the most perfect instruments, and +never lost a chance of adding to his stock of careful observations.[1] + +The account of all these instruments and observations, printed at his +own press on the island, was published by Tycho Brahe himself, and the +admirable and numerous engravings bear witness to the excellence of +design and the stability of his instruments. + +His mechanical skill was very great, and in his workmanship he was +satisfied with nothing but the best. He recognised the importance of +rigidity in the instruments, and, whereas these had generally been made +of wood, he designed them in metal. His instruments included armillae +like those which had been used in Alexandria, and other armillae +designed by himself—sextants, mural quadrants, large celestial globes +and various instruments for special purposes. He lived before the days +of telescopes and accurate clocks. He invented the method of +sub-dividing the degrees on the arc of an instrument by transversals +somewhat in the way that Pedro Nunez had proposed. + +He originated the true system of observation and reduction of +observations, recognising the fact that the best instrument in the +world is not perfect; and with each of his instruments he set to work +to find out the errors of graduation and the errors of mounting, the +necessary correction being applied to each observation. + +When he wanted to point his instrument exactly to a star he was +confronted with precisely the same difficulty as is met in gunnery and +rifle-shooting. The sights and the object aimed at cannot be in focus +together, and a great deal depends on the form of sight. Tycho Brahe +invented, and applied to the pointers of his instruments, an +aperture-sight of variable area, like the iris diaphragm used now in +photography. This enabled him to get the best result with stars of +different brightness. The telescope not having been invented, he could +not use a telescopic-sight as we now do in gunnery. This not only +removes the difficulty of focussing, but makes the minimum visible +angle smaller. Helmholtz has defined the minimum angle measurable with +the naked eye as being one minute of arc. In view of this it is simply +marvellous that, when the positions of Tycho’s standard stars are +compared with the best modern catalogues, his probable error in right +ascension is only ± 24”, 1, and in declination only ± 25”, 9. + +Clocks of a sort had been made, but Tycho Brahe found them so +unreliable that he seldom used them, and many of his +position-measurements were made by measuring the angular distances from +known stars. + +Taking into consideration the absence of either a telescope or a clock, +and reading his account of the labour he bestowed upon each +observation, we must all agree that Kepler, who inherited these +observations in MS., was justified, under the conditions then existing, +in declaring that there was no hope of anyone ever improving upon them. + +In the year 1572, on November 11th, Tycho discovered in Cassiopeia a +new star of great brilliance, and continued to observe it until the end +of January, 1573. So incredible to him was such an event that he +refused to believe his own eyes until he got others to confirm what he +saw. He made accurate observations of its distance from the nine +principal stars in Casseiopeia, and proved that it had no measurable +parallax. Later he employed the same method with the comets of 1577, +1580, 1582, 1585, 1590, 1593, and 1596, and proved that they too had no +measurable parallax and must be very distant. + +The startling discovery that stars are not necessarily permanent, that +new stars may appear, and possibly that old ones may disappear, had +upon him exactly the same effect that a similar occurrence had upon +Hipparchus 1,700 years before. He felt it his duty to catalogue all the +principal stars, so that there should be no mistake in the future. +During the construction of his catalogue of 1,000 stars he prepared and +used accurate tables of refraction deduced from his own observations. +Thus he eliminated (so far as naked eye observations required) the +effect of atmospheric refraction which makes the altitude of a star +seem greater than it really is. + +Tycho Brahe was able to correct the lunar theory by his observations. +Copernicus had introduced two epicycles on the lunar orbit in the hope +of obtaining a better accordance between theory and observation; and he +was not too ambitious, as his desire was to get the tables accurate to +ten minutes. Tycho Brahe found that the tables of Copernicus were in +error as much as two degrees. He re-discovered the inequality called +“variation” by observing the moon in all phases—a thing which had not +been attended to. [It is remarkable that in the nineteenth century Sir +George Airy established an altazimuth at Greenwich Observatory with +this special object, to get observations of the moon in all phases.] He +also discovered other lunar equalities, and wanted to add another +epicycle to the moon’s orbit, but he feared that these would soon +become unmanageable if further observations showed more new +inequalities. + +But, as it turned out, the most fruitful work of Tycho Brahe was on the +motions of the planets, and especially of the planet Mars, for it was +by an examination of these results that Kepler was led to the discovery +of his immortal laws. + +After the death of King Frederick the observatories of Tycho Brahe were +not supported. The gigantic power and industry displayed by this +determined man were accompanied, as often happens, by an overbearing +manner, intolerant of obstacles. This led to friction, and eventually +the observatories were dismantled, and Tycho Brahe was received by the +Emperor Rudolph II., who placed a house in Prague at his disposal. Here +he worked for a few years, with Kepler as one of his assistants, and he +died in the year 1601. + +It is an interesting fact that Tycho Brahe had a firm conviction that +mundane events could be predicted by astrology, and that this belief +was supported by his own predictions. + +It has already been stated that Tycho Brahe maintained that observation +must precede theory. He did not accept the Copernican theory that the +earth moves, but for a working hypothesis he used a modification of an +old Egyptian theory, mathematically identical with that of Copernicus, +but not involving a stellar parallax. He says (_De Mundi_, _etc_.) that + +the Ptolemean system was too complicated, and the new one which that +great man Copernicus had proposed, following in the footsteps of +Aristarchus of Samos, though there was nothing in it contrary to +mathematical principles, was in opposition to those of physics, as the +heavy and sluggish earth is unfit to move, and the system is even +opposed to the authority of Scripture. The absence of annual parallax +further involves an incredible distance between the outermost planet +and the fixed stars. + +We are bound to admit that in the circumstances of the case, so long as +there was no question of dynamical forces connecting the members of the +solar system, his reasoning, as we should expect from such a man, is +practical and sound. It is not surprising, then, that astronomers +generally did not readily accept the views of Copernicus, that Luther +(Luther’s _Tischreden_, pp. 22, 60) derided him in his usual pithy +manner, that Melancthon (_Initia doctrinae physicae_) said that +Scripture, and also science, are against the earth’s motion; and that +the men of science whose opinion was asked for by the cardinals (who +wished to know whether Galileo was right or wrong) looked upon +Copernicus as a weaver of fanciful theories. + +Johann Kepler is the name of the man whose place, as is generally +agreed, would have been the most difficult to fill among all those who +have contributed to the advance of astronomical knowledge. He was born +at Wiel, in the Duchy of Wurtemberg, in 1571. He held an appointment at +Gratz, in Styria, and went to join Tycho Brahe in Prague, and to assist +in reducing his observations. These came into his possession when Tycho +Brahe died, the Emperor Rudolph entrusting to him the preparation of +new tables (called the Rudolphine tables) founded on the new and +accurate observations. He had the most profound respect for the +knowledge, skill, determination, and perseverance of the man who had +reaped such a harvest of most accurate data; and though Tycho hardly +recognised the transcendent genius of the man who was working as his +assistant, and although there were disagreements between them, Kepler +held to his post, sustained by the conviction that, with these +observations to test any theory, he would be in a position to settle +for ever the problem of the solar system. + +[Illustration: PORTRAIT OF JOHANNES KEPLER. By F. +Wanderer, from Reitlinger’s “Johannes Kepler” (original in +Strassburg).] + +It has seemed to many that Plato’s demand for uniform circular motion +(linear or angular) was responsible for a loss to astronomy of good +work during fifteen hundred years, for a hundred ill-considered +speculative cosmogonies, for dissatisfaction, amounting to disgust, +with these _à priori_ guesses, and for the relegation of the science to +less intellectual races than Greeks and other Europeans. Nobody seemed +to dare to depart from this fetish of uniform angular motion and +circular orbits until the insight, boldness, and independence of Johann +Kepler opened up a new world of thought and of intellectual delight. + +While at work on the Rudolphine tables he used the old epicycles and +deferents and excentrics, but he could not make theory agree with +observation. His instincts told him that these apologists for uniform +motion were a fraud; and he proved it to himself by trying every +possible variation of the elements and finding them fail. The number of +hypotheses which he examined and rejected was almost incredible (for +example, that the planets turn round centres at a little distance from +the sun, that the epicycles have centres at a little distance from the +deferent, and so on). He says that, after using all these devices to +make theory agree with Tycho’s observations, he still found errors +amounting to eight minutes of a degree. Then he said boldly that it was +impossible that so good an observer as Tycho could have made a mistake +of eight minutes, and added: “Out of these eight minutes we will +construct a new theory that will explain the motions of all the +planets.” And he did it, with elliptic orbits having the sun in a focus +of each.[2] + +It is often difficult to define the boundaries between fancies, +imagination, hypothesis, and sound theory. This extraordinary genius +was a master in all these modes of attacking a problem. His analogy +between the spaces occupied by the five regular solids and the +distances of the planets from the sun, which filled him with so much +delight, was a display of pure fancy. His demonstration of the three +fundamental laws of planetary motion was the most strict and complete +theory that had ever been attempted. + +It has been often suggested that the revival by Copernicus of the +notion of a moving earth was a help to Kepler. No one who reads +Kepler’s great book could hold such an opinion for a moment. In fact, +the excellence of Copernicus’s book helped to prolong the life of the +epicyclical theories in opposition to Kepler’s teaching. + +All of the best theories were compared by him with observation. These +were the Ptolemaic, the Copernican, and the Tychonic. The two latter +placed all of the planetary orbits concentric with one another, the sun +being placed a little away from their common centre, and having no +apparent relation to them, and being actually outside the planes in +which they move. Kepler’s first great discovery was that the planes of +all the orbits pass through the sun; his second was that the line of +apses of each planet passes through the sun; both were contradictory to +the Copernican theory. + +He proceeds cautiously with his propositions until he arrives at his +great laws, and he concludes his book by comparing observations of +Mars, of all dates, with his theory. + +His first law states that the planets describe ellipses with the sun at +a focus of each ellipse. + +His second law (a far more difficult one to prove) states that a line +drawn from a planet to the sun sweeps over equal areas in equal times. +These two laws were published in his great work, _Astronomia Nova, sen. +Physica Coelestis tradita commentariis de Motibus Stelloe; Martis_, +Prague, 1609. + +It took him nine years more[3] to discover his third law, that the +squares of the periodic times are proportional to the cubes of the mean +distances from the sun. + +These three laws contain implicitly the law of universal gravitation. +They are simply an alternative way of expressing that law in dealing +with planets, not particles. Only, the power of the greatest human +intellect is so utterly feeble that the meaning of the words in +Kepler’s three laws could not be understood until expounded by the +logic of Newton’s dynamics. + +The joy with which Kepler contemplated the final demonstration of these +laws, the evolution of which had occupied twenty years, can hardly be +imagined by us. He has given some idea of it in a passage in his work +on _Harmonics_, which is not now quoted, only lest someone might say it +was egotistical—a term which is simply grotesque when applied to such a +man with such a life’s work accomplished. + +The whole book, _Astronomia Nova_, is a pleasure to read; the mass of +observations that are used, and the ingenuity of the propositions, +contrast strongly with the loose and imperfectly supported explanations +of all his predecessors; and the indulgent reader will excuse the +devotion of a few lines to an example of the ingenuity and beauty of +his methods. + +It may seem a hopeless task to find out the true paths of Mars and the +earth (at that time when their shape even was not known) from the +observations giving only the relative direction from night to night. +Now, Kepler had twenty years of observations of Mars to deal with. This +enabled him to use a new method, to find the earth’s orbit. Observe the +date at any time when Mars is in opposition. The earth’s position E at +that date gives the longitude of Mars M. His period is 687 days. Now +choose dates before and after the principal date at intervals of 687 +days and its multiples. Mars is in each case in the same position. Now +for any date when Mars is at M and the earth at E3 the date of the year +gives the angle E3SM. And the observation of Tycho gives the direction +of Mars compared with the sun, SE3M. So all the angles of the triangle +SEM in any of these positions of E are known, and also the ratios of +SE1, SE2, SE3, SE4 to SM and to each other. + +For the orbit of Mars observations were chosen at intervals of a year, +when the earth was always in the same place. + +But Kepler saw much farther than the geometrical facts. He realised +that the orbits are followed owing to a force directed to the sun; and +he guessed that this is the same force as the gravity that makes a +stone fall. He saw the difficulty of gravitation acting through the +void space. He compared universal gravitation to magnetism, and speaks +of the work of Gilbert of Colchester. (Gilbert’s book, _De Mundo Nostro +Sublunari, Philosophia Nova_, Amstelodami, 1651, containing similar +views, was published forty-eight years after Gilbert’s death, and +forty-two years after Kepler’s book and reference. His book _De +Magnete_ was published in 1600.) + +A few of Kepler’s views on gravitation, extracted from the Introduction +to his _Astronomia Nova_, may now be mentioned:— + +1. Every body at rest remains at rest if outside the attractive power +of other bodies. + +2. Gravity is a property of masses mutually attracting in such manner +that the earth attracts a stone much more than a stone attracts the +earth. + +3. Bodies are attracted to the earth’s centre, not because it is the +centre of the universe, but because it is the centre of the attracting +particles of the earth. + +4. If the earth be not round (but spheroidal?), then bodies at +different latitudes will not be attracted to its centre, but to +different points in the neighbourhood of that centre. + +5. If the earth and moon were not retained in their orbits by vital +force (_aut alia aligua aequipollenti_), the earth and moon would come +together. + +6. If the earth were to cease to attract its waters, the oceans would +all rise and flow to the moon. + +7. He attributes the tides to lunar attraction. Kepler had been +appointed Imperial Astronomer with a handsome salary (on paper), a +fraction of which was doled out to him very irregularly. He was led to +miserable makeshifts to earn enough to keep his family from starvation; +and proceeded to Ratisbon in 1630 to represent his claims to the Diet. +He arrived worn out and debilitated; he failed in his appeal, and died +from fever, contracted under, and fed upon, disappointment and +exhaustion. Those were not the days when men could adopt as a +profession the “research of endowment.” + +Before taking leave of Kepler, who was by no means a man of one idea, +it ought to be here recorded that he was the first to suggest that a +telescope made with both lenses convex (not a Galilean telescope) can +have cross wires in the focus, for use as a pointer to fix accurately +the positions of stars. An Englishman, Gascoigne, was the first to use +this in practice. + +From the all too brief epitome here given of Kepler’s greatest book, it +must be obvious that he had at that time some inkling of the meaning of +his laws—universal gravitation. From that moment the idea of universal +gravitation was in the air, and hints and guesses were thrown out by +many; and in time the law of gravitation would doubtless have been +discovered, though probably not by the work of one man, even if Newton +had not lived. But, if Kepler had not lived, who else could have +discovered his laws? + +FOOTNOTES: + + [1] When the writer visited M. D’Arrest, the astronomer, at + Copenhagen, in 1872, he was presented by D’Arrest with one of several + bricks collected from the ruins of Uraniborg. This was one of his most + cherished possessions until, on returning home after a prolonged + absence on astronomical work, he found that his treasure had been + tidied away from his study. + + [2] An ellipse is one of the plane, sections of a cone. It is an oval + curve, which may be drawn by fixing two pins in a sheet of paper at S + and H, fastening a string, SPH, to the two pins, and stretching it + with a pencil point at P, and moving the pencil point, while the + string is kept taut, to trace the oval ellipse, APB. S and H are the + _foci_. Kepler found the sun to be in one focus, say S. AB is the + _major axis_. DE is the _minor axis_. C is the _centre_. The direction + of AB is the _line of apses_. The ratio of CS to CA is the + _excentricity_. The position of the planet at A is the _perihelion_ + (nearest to the sun). The position of the planet at B is the + _aphelion_ (farthest from the sun). The angle ASP is the _anomaly_ + when the planet is at P. CA or a line drawn from S to D is the _mean + distance_ of the planet from the sun. + + + [3] The ruled logarithmic paper we now use was not then to be had by + going into a stationer’s shop. Else he would have accomplished this in + five minutes. + + + + +6. GALILEO AND THE TELESCOPE—NOTIONS OF GRAVITY BY HORROCKS, ETC. + + +It is now necessary to leave the subject of dynamical astronomy for a +short time in order to give some account of work in a different +direction originated by a contemporary of Kepler’s, his senior in fact +by seven years. Galileo Galilei was born at Pisa in 1564. The most +scientific part of his work dealt with terrestrial dynamics; but one of +those fortunate chances which happen only to really great men put him +in the way of originating a new branch of astronomy. + +The laws of motion had not been correctly defined. The only man of +Galileo’s time who seems to have worked successfully in the same +direction as himself was that Admirable Crichton of the Italians, +Leonardo da Vinci. Galileo cleared the ground. It had always been +noticed that things tend to come to rest; a ball rolled on the ground, +a boat moved on the water, a shot fired in the air. Galileo realised +that in all of these cases a resisting force acts to stop the motion, +and he was the first to arrive at the not very obvious law that the +motion of a body will never stop, nor vary its speed, nor change its +direction, except by the action of some force. + +It is not very obvious that a light body and a heavy one fall at the +same speed (except for the resistance of the air). Galileo proved this +on paper, but to convince the world he had to experiment from the +leaning tower of Pisa. + +At an early age he discovered the principle of isochronism of the +pendulum, which, in the hands of Huyghens in the middle of the +seventeenth century, led to the invention of the pendulum clock, +perhaps the most valuable astronomical instrument ever produced. + +These and other discoveries in dynamics may seem very obvious now; but +it is often the most every-day matters which have been found to elude +the inquiries of ordinary minds, and it required a high order of +intellect to unravel the truth and discard the stupid maxims scattered +through the works of Aristotle and accepted on his authority. A blind +worship of scientific authorities has often delayed the progress of +human knowledge, just as too much “instruction” of a youth often ruins +his “education.” Grant, in his history of Physical Astronomy, has well +said that “the sagacity and skill which Galileo displays in resolving +the phenomena of motion into their constituent elements, and hence +deriving the original principles involved in them, will ever assure to +him a distinguished place among those who have extended the domains of +science.” + +But it was work of a different kind that established Galileo’s popular +reputation. In 1609 Galileo heard that a Dutch spectacle-maker had +combined a pair of lenses so as to magnify distant objects. Working on +this hint, he solved the same problem, first on paper and then in +practice. So he came to make one of the first telescopes ever used in +astronomy. No sooner had he turned it on the heavenly bodies than he +was rewarded by such a shower of startling discoveries as forthwith +made his name the best known in Europe. He found curious irregular +black spots on the sun, revolving round it in twenty-seven days; hills +and valleys on the moon; the planets showing discs of sensible size, +not points like the fixed stars; Venus showing phases according to her +position in relation to the sun; Jupiter accompanied by four moons; +Saturn with appendages that he could not explain, but unlike the other +planets; the Milky Way composed of a multitude of separate stars. + +His fame flew over Europe like magic, and his discoveries were much +discussed—and there were many who refused to believe. Cosmo de Medici +induced him to migrate to Florence to carry on his observations. He was +received by Paul V., the Pope, at Rome, to whom he explained his +discoveries. + +He thought that these discoveries proved the truth of the Copernican +theory of the Earth’s motion; and he urged this view on friends and +foes alike. Although in frequent correspondence with Kepler, he never +alluded to the New Astronomy, and wrote to him extolling the virtue of +epicycles. He loved to argue, never shirked an encounter with any +number of disputants, and laughed as he broke down their arguments. + +Through some strange course of events, not easy to follow, the +Copernican theory, whose birth was welcomed by the Church, had now been +taken up by certain anti-clerical agitators, and was opposed by the +cardinals as well as by the dignitaries of the Reformed Church. +Galileo—a good Catholic—got mixed up in these discussions, although on +excellent terms with the Pope and his entourage. At last it came about +that Galileo was summoned to appear at Rome, where he was charged with +holding and teaching heretical opinions about the movement of the +earth; and he then solemnly abjured these opinions. There has been much +exaggeration and misstatement about his trial and punishment, and for a +long time there was a great deal of bitterness shown on both sides. But +the general verdict of the present day seems to be that, although +Galileo himself was treated with consideration, the hostility of the +Church to the views of Copernicus placed it in opposition also to the +true Keplerian system, and this led to unprofitable controversies. From +the time of Galileo onwards, for some time, opponents of religion +included the theory of the Earth’s motion in their disputations, not so +much for the love, or knowledge, of astronomy, as for the pleasure of +putting the Church in the wrong. This created a great deal of +bitterness and intolerance on both sides. Among the sufferers was +Giordano Bruno, a learned speculative philosopher, who was condemned to +be burnt at the stake. + +Galileo died on Christmas Day, 1642—the day of Newton’s birth. The +further consideration of the grand field of discovery opened out by +Galileo with his telescopes must be now postponed, to avoid +discontinuity in the history of the intellectual development of this +period, which lay in the direction of dynamical, or physical, +astronomy. + +Until the time of Kepler no one seems to have conceived the idea of +universal physical forces controlling terrestrial phenomena, and +equally applicable to the heavenly bodies. The grand discovery by +Kepler of the true relationship of the Sun to the Planets, and the +telescopic discoveries of Galileo and of those who followed him, spread +a spirit of inquiry and philosophic thought throughout Europe, and once +more did astronomy rise in estimation; and the irresistible logic of +its mathematical process of reasoning soon placed it in the position it +has ever since occupied as the foremost of the exact sciences. + +The practical application of this process of reasoning was enormously +facilitated by the invention of logarithms by Napier. He was born at +Merchistoun, near Edinburgh, in 1550, and died in 1617. By this system +the tedious arithmetical operations necessary in astronomical +calculations, especially those dealing with the trigonometrical +functions of angles, were so much simplified that Laplace declared that +by this invention the life-work of an astronomer was doubled. + +Jeremiah Horrocks (born 1619, died 1641) was an ardent admirer of Tycho +Brahe and Kepler, and was able to improve the Rudolphine tables so much +that he foretold a transit of Venus, in 1639, which these tables failed +to indicate, and was the only observer of it. His life was short, but +he accomplished a great deal, and rightly ascribed the lunar inequality +called _evection_ to variations in the value of the eccentricity and in +the direction of the line of apses, at the same time correctly +assigning _the disturbing force of the Sun_ as the cause. He discovered +the errors in Jupiter’s calculated place, due to what we now know as +the long inequality of Jupiter and Saturn, and measured with +considerable accuracy the acceleration at that date of Jupiter’s mean +motion, and indicated the retardation of Saturn’s mean motion. + +Horrocks’ investigations, so far as they could be collected, were +published posthumously in 1672, and seldom, if ever, has a man who +lived only twenty-two years originated so much scientific knowledge. + +At this period British science received a lasting impetus by the wise +initiation of a much-abused man, Charles II., who founded the Royal +Society of London, and also the Royal Observatory of Greeenwich, where +he established Flamsteed as first Astronomer Royal, especially for +lunar and stellar observations likely to be useful for navigation. At +the same time the French Academy and the Paris Observatory were +founded. All this within fourteen years, 1662-1675. + +Meanwhile gravitation in general terms was being discussed by Hooke, +Wren, Halley, and many others. All of these men felt a repugnance to +accept the idea of a force acting across the empty void of space. +Descartes (1596-1650) proposed an ethereal medium whirling round the +sun with the planets, and having local whirls revolving with the +satellites. As Delambre and Grant have said, this fiction only retarded +the progress of pure science. It had no sort of relation to the more +modern, but equally misleading, “nebular hypothesis.” While many were +talking and guessing, a giant mind was needed at this stage to make +things clear. + + + + +7. SIR ISAAC NEWTON—LAW OF UNIVERSAL GRAVITATION. + + +We now reach the period which is the culminating point of interest in +the history of dynamical astronomy. Isaac Newton was born in 1642. +Pemberton states that Newton, having quitted Cambridge to avoid the +plague, was residing at Wolsthorpe, in Lincolnshire, where he had been +born; that he was sitting one day in the garden, reflecting upon the +force which prevents a planet from flying off at a tangent and which +draws it to the sun, and upon the force which draws the moon to the +earth; and that he saw in the case of the planets that the sun’s force +must clearly be unequal at different distances, for the pull out of the +tangential line in a minute is less for Jupiter than for Mars. He then +saw that the pull of the earth on the moon would be less than for a +nearer object. It is said that while thus meditating he saw an apple +fall from a tree to the ground, and that this fact suggested the +questions: Is the force that pulled that apple from the tree the same +as the force which draws the moon to the earth? Does the attraction for +both of them follow the same law as to distance as is given by the +planetary motions round the sun? It has been stated that in this way +the first conception of universal gravitation arose.[1] + +Quite the most important event in the whole history of physical +astronomy was the publication, in 1687, of Newton’s _Principia +(Philosophiae Naturalis Principia Mathematica)_. In this great work +Newton started from the beginning of things, the laws of motion, and +carried his argument, step by step, into every branch of physical +astronomy; giving the physical meaning of Kepler’s three laws, and +explaining, or indicating the explanation of, all the known heavenly +motions and their irregularities; showing that all of these were +included in his simple statement about the law of universal +gravitation; and proceeding to deduce from that law new irregularities +in the motions of the moon which had never been noticed, and to +discover the oblate figure of the earth and the cause of the tides. +These investigations occupied the best part of his life; but he wrote +the whole of his great book in fifteen months. + +Having developed and enunciated the true laws of motion, he was able to +show that Kepler’s second law (that equal areas are described by the +line from the planet to the sun in equal times) was only another way of +saying that the centripetal force on a planet is always directed to the +sun. Also that Kepler’s first law (elliptic orbits with the sun in one +focus) was only another way of saying that the force urging a planet to +the sun varies inversely as the square of the distance. Also (if these +two be granted) it follows that Kepler’s third law is only another way +of saying that the sun’s force on different planets (besides depending +as above on distance) is proportional to their masses. + +Having further proved the, for that day, wonderful proposition that, +with the law of inverse squares, the attraction by the separate +particles of a sphere of uniform density (or one composed of concentric +spherical shells, each of uniform density) acts as if the whole mass +were collected at the centre, he was able to express the meaning of +Kepler’s laws in propositions which have been summarised as follows:— + +The law of universal gravitation.—_Every particle of matter in the +universe attracts every other particle with a force varying inversely +as the square of the distance between them, and directly as the product +of the masses of the two particles_.[2] + +But Newton did not commit himself to the law until he had answered that +question about the apple; and the above proposition now enabled him to +deal with the Moon and the apple. Gravity makes a stone fall 16.1 feet +in a second. The moon is 60 times farther from the earth’s centre than +the stone, so it ought to be drawn out of a straight course through +16.1 feet in a minute. Newton found the distance through which she is +actually drawn as a fraction of the earth’s diameter. But when he first +examined this matter he proceeded to use a wrong diameter for the +earth, and he found a serious discrepancy. This, for a time, seemed to +condemn his theory, and regretfully he laid that part of his work +aside. Fortunately, before Newton wrote the _Principia_ the French +astronomer Picard made a new and correct measure of an arc of the +meridian, from which he obtained an accurate value of the earth’s +diameter. Newton applied this value, and found, to his great joy, that +when the distance of the moon is 60 times the radius of the earth she +is attracted out of the straight course 16.1 feet per minute, and that +the force acting on a stone or an apple follows the same law as the +force acting upon the heavenly bodies.[3] + +The universality claimed for the law—if not by Newton, at least by his +commentators—was bold, and warranted only by the large number of cases +in which Newton had found it to apply. Its universality has been under +test ever since, and so far it has stood the test. There has often been +a suspicion of a doubt, when some inequality of motion in the heavenly +bodies has, for a time, foiled the astronomers in their attempts to +explain it. But improved mathematical methods have always succeeded in +the end, and so the seeming doubt has been converted into a surer +conviction of the universality of the law. + +Having once established the law, Newton proceeded to trace some of its +consequences. He saw that the figure of the earth depends partly on the +mutual gravitation of its parts, and partly on the centrifugal tendency +due to the earth’s rotation, and that these should cause a flattening +of the poles. He invented a mathematical method which he used for +computing the ratio of the polar to the equatorial diameter. + +He then noticed that the consequent bulging of matter at the equator +would be attracted by the moon unequally, the nearest parts being most +attracted; and so the moon would tend to tilt the earth when in some +parts of her orbit; and the sun would do this to a less extent, because +of its great distance. Then he proved that the effect ought to be a +rotation of the earth’s axis over a conical surface in space, exactly +as the axis of a top describes a cone, if the top has a sharp point, +and is set spinning and displaced from the vertical. He actually +calculated the amount; and so he explained the cause of the precession +of the equinoxes discovered by Hipparchus about 150 B.C. + +One of his grandest discoveries was a method of weighing the heavenly +bodies by their action on each other. By means of this principle he was +able to compare the mass of the sun with the masses of those planets +that have moons, and also to compare the mass of our moon with the mass +of the earth. + +Thus Newton, after having established his great principle, devoted his +splendid intellect to the calculation of its consequences. He proved +that if a body be projected with any velocity in free space, subject +only to a central force, varying inversely as the square of the +distance, the body must revolve in a curve which may be any one of the +sections of a cone—a circle, ellipse, parabola, or hyperbola; and he +found that those comets of which he had observations move in parabolae +round the Sun, and are thus subject to the universal law. + +Newton realised that, while planets and satellites are chiefly +controlled by the central body about which they revolve, the new law +must involve irregularities, due to their mutual action—such, in fact, +as Horrocks had indicated. He determined to put this to a test in the +case of the moon, and to calculate the sun’s effect, from its mass +compared with that of the earth, and from its distance. He proved that +the average effect upon the plane of the orbit would be to cause the +line in which it cuts the plane of the ecliptic (i.e., the line of +nodes) to revolve in the ecliptic once in about nineteen years. This +had been a known fact from the earliest ages. He also concluded that +the line of apses would revolve in the plane of the lunar orbit also in +about nineteen years; but the observed period is only ten years. For a +long time this was the one weak point in the Newtonian theory. It was +not till 1747 that Clairaut reconciled this with the theory, and showed +why Newton’s calculation was not exact. + +Newton proceeded to explain the other inequalities recognised by Tycho +Brahe and older observers, and to calculate their maximum amounts as +indicated by his theory. He further discovered from his calculations +two new inequalities, one of the apogee, the other of the nodes, and +assigned the maximum value. Grant has shown the values of some of these +as given by observation in the tables of Meyer and more modern tables, +and has compared them with the values assigned by Newton from his +theory; and the comparison is very remarkable. + + Newton. Modern Tables. + ° ’ " ° ’ " +Mean monthly motion of Apses 1.31.28 3.4.0 +Mean annual motion of nodes 19.18.1,23 19.21.22,50 +Mean value of “variation” 36.10 35.47 +Annual equation 11.51 11.14 +Inequality of mean motion of apogee 19.43 22.17 +Inequality of mean motion of nodes 9.24 9.0 + +The only serious discrepancy is the first, which has been already +mentioned. Considering that some of these perturbations had never been +discovered, that the cause of none of them had ever been known, and +that he exhibited his results, if he did not also make the discoveries, +by the synthetic methods of geometry, it is simply marvellous that he +reached to such a degree of accuracy. He invented the infinitesimal +calculus which is more suited for such calculations, but had he +expressed his results in that language he would have been +unintelligible to many. + +Newton’s method of calculating the precession of the equinoxes, already +referred to, is as beautiful as anything in the _Principia_. He had +already proved the regression of the nodes of a satellite moving in an +orbit inclined to the ecliptic. He now said that the nodes of a ring of +satellites revolving round the earth’s equator would consequently all +regress. And if joined into a solid ring its node would regress; and it +would do so, only more slowly, if encumbered by the spherical part of +the earth’s mass. Therefore the axis of the equatorial belt of the +earth must revolve round the pole of the ecliptic. Then he set to work +and found the amount due to the moon and that due to the sun, and so he +solved the mystery of 2,000 years. + +When Newton applied his law of gravitation to an explanation of the +tides he started a new field for the application of mathematics to +physical problems; and there can be little doubt that, if he could have +been furnished with complete tidal observations from different parts of +the world, his extraordinary powers of analysis would have enabled him +to reach a satisfactory theory. He certainly opened up many mines full +of intellectual gems; and his successors have never ceased in their +explorations. This has led to improved mathematical methods, which, +combined with the greater accuracy of observation, have rendered +physical astronomy of to-day the most exact of the sciences. + +Laplace only expressed the universal opinion of posterity when he said +that to the _Principia_ is assured “a pre-eminence above all the other +productions of the human intellect.” + +The name of Flamsteed, First Astronomer Royal, must here be mentioned +as having supplied Newton with the accurate data required for +completing the theory. + +The name of Edmund Halley, Second Astronomer Royal, must ever be held +in repute, not only for his own discoveries, but for the part he played +in urging Newton to commit to writing, and present to the Royal +Society, the results of his investigations. But for his friendly +insistence it is possible that the _Principia_ would never have been +written; and but for his generosity in supplying the means the Royal +Society could not have published the book. + +[Illustration: DEATH MASK OF SIR ISAAC NEWTON. +Photographed specially for this work from the original, by kind +permission of the Royal Society, London.] + +Sir Isaac Newton died in 1727, at the age of eighty-five. His body lay +in state in the Jerusalem Chamber, and was buried in Westminster Abbey. + +FOOTNOTES: + + [1] The writer inherited from his father (Professor J. D. Forbes) a + small box containing a bit of wood and a slip of paper, which had been + presented to him by Sir David Brewster. On the paper Sir David had + written these words: “If there be any truth in the story that Newton + was led to the theory of gravitation by the fall of an apple, this bit + of wood is probably a piece of the apple tree from which Newton saw + the apple fall. When I was on a pilgrimage to the house in which + Newton was born, I cut it off an ancient apple tree growing in his + garden.” When lecturing in Glasgow, about 1875, the writer showed it + to his audience. The next morning, when removing his property from the + lecture table, he found that his precious relic had been stolen. It + would be interesting to know who has got it now! + + [2] It must be noted that these words, in which the laws of + gravitation are always summarised in histories and text-books, do not + appear in the _Principia_; but, though they must have been composed by + some early commentator, it does not appear that their origin has been + traced. Nor does it appear that Newton ever extended the law beyond + the Solar System, and probably his caution would have led him to avoid + any statement of the kind until it should be proved. + With this exception the above statement of the law of universal + gravitation contains nothing that is not to be found in the + _Principia_; and the nearest approach to that statement occurs in + the Seventh Proposition of Book III.:— + Prop.: That gravitation occurs in all bodies, and that it is + proportional to the quantity of matter in each. + Cor. I.: The total attraction of gravitation on a planet arises, + and is composed, out of the attraction on the separate parts. + Cor. II.: The attraction on separate equal particles of a body is + reciprocally as the square of the distance from the particles. + + [3] It is said that, when working out this final result, the + probability of its confirming that part of his theory which he had + reluctantly abandoned years before excited him so keenly that he was + forced to hand over his calculations to a friend, to be completed by + him. + + + + +8. NEWTON’S SUCCESSORS—HALLEY, EULER, LAGRANGE, LAPLACE, ETC. + + +Edmund Halley succeeded Flamsteed as Second Astronomer Royal in 1721. +Although he did not contribute directly to the mathematical proofs of +Newton’s theory, yet his name is closely associated with some of its +greatest successes. + +He was the first to detect the acceleration of the moon’s mean motion. +Hipparchus, having compared his own observations with those of more +ancient astronomers, supplied an accurate value of the moon’s mean +motion in his time. Halley similarly deduced a value for modern times, +and found it sensibly greater. He announced this in 1693, but it was +not until 1749 that Dunthorne used modern lunar tables to compute a +lunar eclipse observed in Babylon 721 B.C., another at Alexandria 201 +B.C., a solar eclipse observed by Theon 360 A.D., and two later ones up +to the tenth century. He found that to explain these eclipses Halley’s +suggestion must be adopted, the acceleration being 10” in one century. +In 1757 Lalande again fixed it at 10.” + +The Paris Academy, in 1770, offered their prize for an investigation to +see if this could be explained by the theory of gravitation. Euler won +the prize, but failed to explain the effect, and said: “It appears to +be established by indisputable evidence that the secular inequality of +the moon’s mean motion cannot be produced by the forces of +gravitation.” + +The same subject was again proposed for a prize which was shared by +Lagrange[1] and Euler, neither finding a solution, while the latter +asserted the existence of a resisting medium in space. + +Again, in 1774, the Academy submitted the same subject, a third time, +for the prize; and again Lagrange failed to detect a cause in +gravitation. + +Laplace[2] now took the matter in hand. He tried the effect of a +non-instantaneous action of gravity, to no purpose. But in 1787 he gave +the true explanation. The principal effect of the sun on the moon’s +orbit is to diminish the earth’s influence, thus lengthening the period +to a new value generally taken as constant. But Laplace’s calculations +showed the new value to depend upon the excentricity of the earth’s +orbit, which, according; to theory, has a periodical variation of +enormous period, and has been continually diminishing for thousands of +years. Thus the solar influence has been diminishing, and the moon’s +mean motion increased. Laplace computed the amount at 10” in one +century, agreeing with observation. (Later on Adams showed that +Laplace’s calculation was wrong, and that the value he found was too +large; so, part of the acceleration is now attributed by some +astronomers to a lengthening of the day by tidal friction.) + +Another contribution by Halley to the verification of Newton’s law was +made when he went to St. Helena to catalogue the southern stars. He +measured the change in length of the second’s pendulum in different +latitudes due to the changes in gravity foretold by Newton. + +Furthermore, he discovered the long inequality of Jupiter and Saturn, +whose period is 929 years. For an investigation of this also the +Academy of Sciences offered their prize. This led Euler to write a +valuable essay disclosing a new method of computing perturbations, +called the instantaneous ellipse with variable elements. The method was +much developed by Lagrange. + +But again it was Laplace who solved the problem of the inequalities of +Jupiter and Saturn by the theory of gravitation, reducing the errors of +the tables from 20’ down to 12”, thus abolishing the use of empirical +corrections to the planetary tables, and providing another glorious +triumph for the law of gravitation. As Laplace justly said: “These +inequalities appeared formerly to be inexplicable by the law of +gravitation—they now form one of its most striking proofs.” + +Let us take one more discovery of Halley, furnishing directly a new +triumph for the theory. He noticed that Newton ascribed parabolic +orbits to the comets which he studied, so that they come from infinity, +sweep round the sun, and go off to infinity for ever, after having been +visible a few weeks or months. He collected all the reliable +observations of comets he could find, to the number of twenty-four, and +computed their parabolic orbits by the rules laid down by Newton. His +object was to find out if any of them really travelled in elongated +ellipses, practically undistinguishable, in the visible part of their +paths, from parabolæ, in which case they would be seen more than once. +He found two old comets whose orbits, in shape and position, resembled +the orbit of a comet observed by himself in 1682. Apian observed one in +1531; Kepler the other in 1607. The intervals between these appearances +is seventy-five or seventy-six years. He then examined and found old +records of similar appearance in 1456, 1380, and 1305. It is true, he +noticed, that the intervals varied by a year and a-half, and the +inclination of the orbit to the ecliptic diminished with successive +apparitions. But he knew from previous calculations that this might +easily be due to planetary perturbations. Finally, he arrived at the +conclusion that all of these comets were identical, travelling in an +ellipse so elongated that the part where the comet was seen seemed to +be part of a parabolic orbit. He then predicted its return at the end +of 1758 or beginning of 1759, when he should be dead; but, as he said, +“if it should return, according to our prediction, about the year 1758, +impartial posterity will not refuse to acknowledge that this was first +discovered by an Englishman.”[3] [_Synopsis Astronomiae Cometicae_, +1749.] + +Once again Halley’s suggestion became an inspiration for the +mathematical astronomer. Clairaut, assisted by Lalande, found that +Saturn would retard the comet 100 days, Jupiter 518 days, and predicted +its return to perihelion on April 13th, 1759. In his communication to +the French Academy, he said that a comet travelling into such distant +regions might be exposed to the influence of forces totally unknown, +and “even of some planet too far removed from the sun to be ever +perceived.” + +The excitement of astronomers towards the end of 1758 became intense; +and the honour of first catching sight of the traveller fell to an +amateur in Saxony, George Palitsch, on Christmas Day, 1758. It reached +perihelion on March 13th, 1759. + +This fact was a startling confirmation of the Newtonian theory, because +it was a new kind of calculation of perturbations, and also it added a +new member to the solar system, and gave a prospect of adding many +more. + +When Halley’s comet reappeared in 1835, Pontecoulant’s computations for +the date of perihelion passage were very exact, and afterwards he +showed that, with more exact values of the masses of Jupiter and +Saturn, his prediction was correct within two days, after an invisible +voyage of seventy-five years! + +Hind afterwards searched out many old appearances of this comet, going +back to 11 B.C., and most of these have been identified as being really +Halley’s comet by the calculations of Cowell and Cromellin[4] (of +Greenwich Observatory), who have also predicted its next perihelion +passage for April 8th to 16th, 1910, and have traced back its history +still farther, to 240 B.C. + +Already, in November, 1907, the Astronomer Royal was trying to catch it +by the aid of photography. + +FOOTNOTES: + + [1] Born 1736; died 1813. + + [2] Born 1749; died 1827. + + [3] This sentence does not appear in the original memoir communicated + to the Royal Society, but was first published in a posthumous reprint. + + [4] _R. A. S. Monthly Notices_, 1907-8. + + + + +9. DISCOVERY OF NEW PLANETS—HERSCHEL, PIAZZI, ADAMS, AND LE VERRIER. + + +It would be very interesting, but quite impossible in these pages, to +discuss all the exquisite researches of the mathematical astronomers, +and to inspire a reverence for the names connected with these +researches, which for two hundred years have been establishing the +universality of Newton’s law. The lunar and planetary theories, the +beautiful theory of Jupiter’s satellites, the figure of the earth, and +the tides, were mathematically treated by Maclaurin, D’Alembert, +Legendre, Clairaut, Euler, Lagrange, Laplace, Walmsley, Bailly, +Lalande, Delambre, Mayer, Hansen, Burchardt, Binet, Damoiseau, Plana, +Poisson, Gauss, Bessel, Bouvard, Airy, Ivory, Delaunay, Le Verrier, +Adams, and others of later date. + +By passing over these important developments it is possible to trace +some of the steps in the crowning triumph of the Newtonian theory, by +which the planet Neptune was added to the known members of the solar +system by the independent researches of Professor J.C. Adams and of M. +Le Verrier, in 1846. + +It will be best to introduce this subject by relating how the +eighteenth century increased the number of known planets, which was +then only six, including the earth. + +On March 13th, 1781, Sir William Herschel was, as usual, engaged on +examining some small stars, and, noticing that one of them appeared to +be larger than the fixed stars, suspected that it might be a comet. To +test this he increased his magnifying power from 227 to 460 and 932, +finding that, unlike the fixed stars near it, its definition was +impaired and its size increased. This convinced him that the object was +a comet, and he was not surprised to find on succeeding nights that the +position was changed, the motion being in the ecliptic. He gave the +observations of five weeks to the Royal Society without a suspicion +that the object was a new planet. + +For a long time people could not compute a satisfactory orbit for the +supposed comet, because it seemed to be near the perihelion, and no +comet had ever been observed with a perihelion distance from the sun +greater than four times the earth’s distance. Lexell was the first to +suspect that this was a new planet eighteen times as far from the sun +as the earth is. In January, 1783, Laplace published the elliptic +elements. The discoverer of a planet has a right to name it, so +Herschel called it Georgium Sidus, after the king. But Lalande urged +the adoption of the name Herschel. Bode suggested Uranus, and this was +adopted. The new planet was found to rank in size next to Jupiter and +Saturn, being 4.3 times the diameter of the earth. + +In 1787 Herschel discovered two satellites, both revolving in nearly +the same plane, inclined 80° to the ecliptic, and the motion of both +was retrograde. + +In 1772, before Herschel’s discovery, Bode[1] had discovered a curious +arbitrary law of planetary distances. Opposite each planet’s name write +the figure 4; and, in succession, add the numbers 0, 3, 6, 12, 24, 48, +96, _etc_., to the 4, always doubling the last numbers. You then get +the planetary distances. + + Mercury, dist.-- 4 4 + 0 = 4 + Venus " 7 4 + 3 = 7 + Earth " 10 4 + 6 = 10 + Mars " 15 4 + 12 = 16 + -- 4 + 24 = 28 + Jupiter dist. 52 4 + 48 = 52 + Saturn " 95 4 + 96 = 100 + (Uranus) " 192 4 + 192 = 196 + -- 4 + 384 = 388 + +All the five planets, and the earth, fitted this rule, except that +there was a blank between Mars and Jupiter. When Uranus was discovered, +also fitting the rule, the conclusion was irresistible that there is +probably a planet between Mars and Jupiter. An association of +twenty-four astronomers was now formed in Germany to search for the +planet. Almost immediately afterwards the planet was discovered, not by +any member of the association, but by Piazzi, when engaged upon his +great catalogue of stars. On January 1st, 1801, he observed a star +which had changed its place the next night. Its motion was retrograde +till January 11th, direct after the 13th. Piazzi fell ill before he had +enough observations for computing the orbit with certainty, and the +planet disappeared in the sun’s rays. Gauss published an approximate +ephemeris of probable positions when the planet should emerge from the +sun’s light. There was an exciting hunt, and on December 31st (the day +before its birthday) De Zach captured the truant, and Piazzi christened +it Ceres. + +The mean distance from the sun was found to be 2.767, agreeing with the +2.8 given by Bode’s law. Its orbit was found to be inclined over 10° to +the ecliptic, and its diameter was only 161 miles. + +On March 28th, 1802, Olbers discovered a new seventh magnitude star, +which turned out to be a planet resembling Ceres. It was called Pallas. +Gauss found its orbit to be inclined 35° to the ecliptic, and to cut +the orbit of Ceres; whence Olbers considered that these might be +fragments of a broken-up planet. He then commenced a search for other +fragments. In 1804 Harding discovered Juno, and in 1807 Olbers found +Vesta. The next one was not discovered until 1845, from which date +asteroids, or minor planets (as these small planets are called), have +been found almost every year. They now number about 700. + +It is impossible to give any idea of the interest with which the first +additions since prehistoric times to the planetary system were +received. All of those who showered congratulations upon the +discoverers regarded these discoveries in the light of rewards for +patient and continuous labours, the very highest rewards that could be +desired. And yet there remained still the most brilliant triumph of +all, the addition of another planet like Uranus, before it had ever +been seen, when the analysis of Adams and Le Verrier gave a final proof +of the powers of Newton’s great law to explain any planetary +irregularity. + +After Sir William Herschel discovered Uranus, in 1781, it was found +that astronomers had observed it on many previous occasions, mistaking +it for a fixed star of the sixth or seventh magnitude. Altogether, +nineteen observations of Uranus’s position, from the time of Flamsteed, +in 1690, had been recorded. + +In 1790 Delambre, using all these observations, prepared tables for +computing its position. These worked well enough for a time, but at +last the differences between the calculated and observed longitudes of +the planet became serious. In 1821 Bouvard undertook a revision of the +tables, but found it impossible to reconcile all the observations of +130 years (the period of revolution of Uranus is eighty-four years). So +he deliberately rejected the old ones, expressing the opinion that the +discrepancies might depend upon “some foreign and unperceived cause +which may have been acting upon the planet.” In a few years the errors +even of these tables became intolerable. In 1835 the error of longitude +was 30”; in 1838, 50”; in 1841, 70”; and, by comparing the errors +derived from observations made before and after opposition, a serious +error of the distance (radius vector) became apparent. + +In 1843 John Couch Adams came out Senior Wrangler at Cambridge, and was +free to undertake the research which as an undergraduate he had set +himself—to see whether the disturbances of Uranus could be explained by +assuming a certain orbit, and position in that orbit, of a hypothetical +planet even more distant than Uranus. Such an explanation had been +suggested, but until 1843 no one had the boldness to attack the +problem. Bessel had intended to try, but a fatal illness overtook him. + +Adams first recalculated all known causes of disturbance, using the +latest determinations of the planetary masses. Still the errors were +nearly as great as ever. He could now, however, use these errors as +being actually due to the perturbations produced by the unknown planet. + +In 1844, assuming a circular orbit, and a mean distance agreeing with +Bode’s law, he obtained a first approximation to the position of the +supposed planet. He then asked Professor Challis, of Cambridge, to +procure the latest observations of Uranus from Greenwich, which Airy +immediately supplied. Then the whole work was recalculated from the +beginning, with more exactness, and assuming a smaller mean distance. + +In September, 1845, he handed to Challis the elements of the +hypothetical planet, its mass, and its apparent position for September +30th, 1845. On September 22nd Challis wrote to Airy explaining the +matter, and declaring his belief in Adams’s capabilities. When Adams +called on him Airy was away from home, but at the end of October, 1845, +he called again, and left a paper with full particulars of his results, +which had, for the most part, reduced the discrepancies to about 1”. As +a matter of fact, it has since been found that the heliocentric place +of the new planet then given was correct within about 2°. + +Airy wrote expressing his interest, and asked for particulars about the +radius vector. Adams did not then reply, as the answer to this question +could be seen to be satisfactory by looking at the data already +supplied. He was a most unassuming man, and would not push himself +forward. He may have felt, after all the work he had done, that Airy’s +very natural inquiry showed no proportionate desire to search for the +planet. Anyway, the matter lay in embryo for nine months. + +Meanwhile, one of the ablest French astronomers, Le Verrier, +experienced in computing perturbations, was independently at work, +knowing nothing about Adams. He applied to his calculations every +possible refinement, and, considering the novelty of the problem, his +calculation was one of the most brilliant in the records of astronomy. +In criticism it has been said that these were exhibitions of skill +rather than helps to a solution of the particular problem, and that, in +claiming to find the elements of the orbit within certain limits, he +was claiming what was, under the circumstances, impossible, as the +result proved. + +In June, 1846, Le Verrier announced, in the _Comptes Rendus de +l’Academie des Sciences_, that the longitude of the disturbing planet, +for January 1st, 1847, was 325, and that the probable error did not +exceed 10°. + +This result agreed so well with Adams’s (within 1°) that Airy urged +Challis to apply the splendid Northumberland equatoreal, at Cambridge, +to the search. Challis, however, had already prepared an exhaustive +plan of attack which must in time settle the point. His first work was +to observe, and make a catalogue, or chart, of all stars near Adams’s +position. + +On August 31st, 1846, Le Verrier published the concluding part of his +labours. + +On September 18th, 1846, Le Verrier communicated his results to the +Astronomers at Berlin, and asked them to assist in searching for the +planet. By good luck Dr. Bremiker had just completed a star-chart of +the very part of the heavens including Le Verrier’s position; thus +eliminating all of Challis’s preliminary work. The letter was received +in Berlin on September 23rd; and the same evening Galle found the new +planet, of the eighth magnitude, the size of its disc agreeing with Le +Verrier’s prediction, and the heliocentric longitude agreeing within +57’. By this time Challis had recorded, without reduction, the +observations of 3,150 stars, as a commencement for his search. On +reducing these, he found a star, observed on August 12th, which was not +in the same place on July 30th. This was the planet, and he had also +observed it on August 4th. + +The feeling of wonder, admiration, and enthusiasm aroused by this +intellectual triumph was overwhelming. In the world of astronomy +reminders are met every day of the terrible limitations of human +reasoning powers; and every success that enables the mind’s eye to see +a little more clearly the meaning of things has always been heartily +welcomed by those who have themselves been engaged in like researches. +But, since the publication of the _Principia_, in 1687, there is +probably no analytical success which has raised among astronomers such +a feeling of admiration and gratitude as when Adams and Le Verrier +showed the inequalities in Uranus’s motion to mean that an unknown +planet was in a certain place in the heavens, where it was found. + +At the time there was an unpleasant display of international jealousy. +The British people thought that the earlier date of Adams’s work, and +of the observation by Challis, entitled him to at least an equal share +of credit with Le Verrier. The French, on the other hand, who, on the +announcement of the discovery by Galle, glowed with pride in the new +proof of the great powers of their astronomer, Le Verrier, whose life +had a long record of successes in calculation, were incredulous on +being told that it had all been already done by a young man whom they +had never heard of. + +These displays of jealousy have long since passed away, and there is +now universally an _entente cordiale_ that to each of these great men +belongs equally the merit of having so thoroughly calculated this +inverse problem of perturbations as to lead to the immediate discovery +of the unknown planet, since called Neptune. + +It was soon found that the planet had been observed, and its position +recorded as a fixed star by Lalande, on May 8th and 10th, 1795. + +Mr. Lassel, in the same year, 1846, with his two-feet reflector, +discovered a satellite, with retrograde motion, which gave the mass of +the planet about a twentieth of that of Jupiter. + +FOOTNOTES: + + [1] Bode’s law, or something like it, had already been fore-shadowed + by Kepler and others, especially Titius (see _Monatliche + Correspondenz_, vol. vii., p. 72). + + + + +BOOK III. OBSERVATION + +10. INSTRUMENTS OF PRECISION—STATE OF THE SOLAR SYSTEM. + + +Having now traced the progress of physical astronomy up to the time +when very striking proofs of the universality of the law of gravitation +convinced the most sceptical, it must still be borne in mind that, +while gravitation is certainly the principal force governing the +motions of the heavenly bodies, there may yet be a resisting medium in +space, and there may be electric and magnetic forces to deal with. +There may, further, be cases where the effects of luminous radiative +repulsion become apparent, and also Crookes’ vacuum-effects described +as “radiant matter.” Nor is it quite certain that Laplace’s proofs of +the instantaneous propagation of gravity are final. + +And in the future, as in the past, Tycho Brahe’s dictum must be +maintained, that all theory shall be preceded by accurate observations. +It is the pride of astronomers that their science stands above all +others in the accuracy of the facts observed, as well as in the rigid +logic of the mathematics used for interpreting these facts. + +It is interesting to trace historically the invention of those +instruments of precision which have led to this result, and, without +entering on the details required in a practical handbook, to note the +guiding principles of construction in different ages. + +It is very probable that the Chaldeans may have made spheres, like the +armillary sphere, for representing the poles of the heavens; and with +rings to show the ecliptic and zodiac, as well as the equinoctial and +solstitial colures; but we have no record. We only know that the tower +of Belus, on an eminence, was their observatory. We have, however, +distinct records of two such spheres used by the Chinese about 2500 +B.C. Gnomons, or some kind of sundial, were used by the Egyptians and +others; and many of the ancient nations measured the obliquity of the +ecliptic by the shadows of a vertical column in summer and winter. The +natural horizon was the only instrument of precision used by those who +determined star positions by the directions of their risings and +settings; while in those days the clepsydra, or waterclock, was the +best instrument for comparing their times of rising and setting. + +About 300 B.C. an observatory fitted with circular instruments for star +positions was set up at Alexandria, the then centre of civilisation. We +know almost nothing about the instruments used by Hipparchus in +preparing his star catalogues and his lunar and solar tables; but the +invention of the astrolabe is attributed to him.[1] + +In more modern times Nuremberg became a centre of astronomical culture. +Waltherus, of that town, made really accurate observations of star +altitudes, and of the distances between stars; and in 1484 A.D. he used +a kind of clock. Tycho Brahe tried these, but discarded them as being +inaccurate. + +Tycho Brahe (1546-1601 A.D.) made great improvements in armillary +spheres, quadrants, sextants, and large celestial globes. With these he +measured the positions of stars, or the distance of a comet from +several known stars. He has left us full descriptions of them, +illustrated by excellent engravings. Previous to his time such +instruments were made of wood. Tycho always used metal. He paid the +greatest attention to the stability of mounting, to the orientation of +his instruments, to the graduation of the arcs by the then new method +of transversals, and to the aperture sight used upon his pointer. There +were no telescopes in his day, and no pendulum clocks. He recognised +the fact that there must be instrumental errors. He made these as small +as was possible, measured their amount, and corrected his observations. +His table of refractions enabled him to abolish the error due to our +atmosphere so far as it could affect naked-eye observations. The +azimuth circle of Tycho’s largest quadrant had a diameter of nine feet, +and the quadrant a radius of six feet. He introduced the mural quadrant +for meridian observations.[2] + +[Illustration: ANCIENT CHINESE INSTRUMENTS, +Including quadrant, celestial globe, and two armillae, in the +Observatory at Peking. Photographed in Peking by the author in 1875, +and stolen by the Germans when the Embassies were relieved by the +allies in 1900.] + +The French Jesuits at Peking, in the seventeenth century, helped the +Chinese in their astronomy. In 1875 the writer saw and photographed, on +that part of the wall of Peking used by the Mandarins as an +observatory, the six instruments handsomely designed by Father +Verbiest, copied from the instruments of Tycho Brahe, and embellished +with Chinese dragons and emblems cast on the supports. He also saw +there two old instruments (which he was told were Arabic) of date 1279, +by Ko Show-King, astronomer to Koblai Khan, the grandson of Chenghis +Khan. One of these last is nearly identical with the armillae of Tycho; +and the other with his “armillae æquatoriæ maximæ,” with which he +observed the comet of 1585, besides fixed stars and planets.[3] + +The discovery by Galileo of the isochronism of the pendulum, followed +by Huyghens’s adaptation of that principle to clocks, has been one of +the greatest aids to accurate observation. About the same time an +equally beneficial step was the employment of the telescope as a +pointer; not the Galilean with concave eye-piece, but with a magnifying +glass to examine the focal image, at which also a fixed mark could be +placed. Kepler was the first to suggest this. Gascoigne was the first +to use it. Huyghens used a metal strip of variable width in the focus, +as a micrometer to cover a planetary disc, and so to measure the width +covered by the planet. The Marquis Malvasia, in 1662, described the +network of fine silver threads at right angles, which he used in the +focus, much as we do now. + +In the hands of such a skilful man as Tycho Brahe, the old open sights, +even without clocks, served their purpose sufficiently well to enable +Kepler to discover the true theory of the solar system. But telescopic +sights and clocks were required for proving some of Newton’s theories +of planetary perturbations. Picard’s observations at Paris from 1667 +onwards seem to embody the first use of the telescope as a pointer. He +was also the first to introduce the use of Huyghens’s clocks for +observing the right ascension of stars. Olaus Romer was born at +Copenhagen in 1644. In 1675, by careful study of the times of eclipses +of Jupiter’s satellites, he discovered that light took time to traverse +space. Its velocity is 186,000 miles per second. In 1681 he took up his +duties as astronomer at Copenhagen, and built the first transit circle +on a window-sill of his house. The iron axis was five feet long and one +and a-half inches thick, and the telescope was fixed near one end with +a counterpoise. The telescope-tube was a double cone, to prevent +flexure. Three horizontal and three vertical wires were used in the +focus. These were illuminated by a speculum, near the object-glass, +reflecting the light from a lantern placed over the axis, the upper +part of the telescope-tube being partly cut away to admit the light. A +divided circle, with pointer and reading microscope, was provided for +reading the declination. He realised the superiority of a circle with +graduations over a much larger quadrant. The collimation error was +found by reversing the instrument and using a terrestrial mark, the +azimuth error by star observations. The time was expressed in fractions +of a second. He also constructed a telescope with equatoreal mounting, +to follow a star by one axial motion. In 1728 his instruments and +observation records were destroyed by fire. + +Hevelius had introduced the vernier and tangent screw in his +measurement of arc graduations. His observatory and records were burnt +to the ground in 1679. Though an old man, he started afresh, and left +behind him a catalogue of 1,500 stars. + +Flamsteed began his duties at Greenwich Observatory, as first +Astronomer Royal, in 1676, with very poor instruments. In 1683 he put +up a mural arc of 140°, and in 1689 a better one, seventy-nine inches +radius. He conducted his measurements with great skill, and introduced +new methods to attain accuracy, using certain stars for determining the +errors of his instruments; and he always reduced his observations to a +form in which they could be readily used. He introduced new methods for +determining the position of the equinox and the right ascension of a +fundamental star. He produced a catalogue of 2,935 stars. He supplied +Sir Isaac Newton with results of observation required in his +theoretical calculations. He died in 1719. + +Halley succeeded Flamsteed to find that the whole place had been gutted +by the latter’s executors. In 1721 he got a transit instrument, and in +1726 a mural quadrant by Graham. His successor in 1742, Bradley, +replaced this by a fine brass quadrant, eight feet radius, by Bird; and +Bradley’s zenith sector was purchased for the observatory. An +instrument like this, specially designed for zenith stars, is capable +of greater rigidity than a more universal instrument; and there is no +trouble with refraction in the zenith. For these reasons Bradley had +set up this instrument at Kew, to attempt the proof of the earth’s +motion by observing the annual parallax of stars. He certainly found an +annual variation of zenith distance, but not at the times of year +required by the parallax. This led him to the discovery of the +“aberration” of light and of nutation. Bradley has been described as +the founder of the modern system of accurate observation. He died in +1762, leaving behind him thirteen folio volumes of valuable but +unreduced observations. Those relating to the stars were reduced by +Bessel and published in 1818, at Königsberg, in his well-known standard +work, _Fundamenta Astronomiae_. In it are results showing the laws of +refraction, with tables of its amount, the maximum value of aberration, +and other constants. + +Bradley was succeeded by Bliss, and he by Maskelyne (1765), who carried +on excellent work, and laid the foundations of the Nautical Almanac +(1767). Just before his death he induced the Government to replace +Bird’s quadrant by a fine new mural _circle_, six feet in diameter, by +Troughton, the divisions being read off by microscopes fixed on piers +opposite to the divided circle. In this instrument the micrometer +screw, with a divided circle for turning it, was applied for bringing +the micrometer wire actually in line with a division on the circle—a +plan which is still always adopted. + +Pond succeeded Maskelyne in 1811, and was the first to use this +instrument. From now onwards the places of stars were referred to the +pole, not to the zenith; the zero being obtained from measures on +circumpolar stars. Standard stars were used for giving the clock error. +In 1816 a new transit instrument, by Troughton, was added, and from +this date the Greenwich star places have maintained the very highest +accuracy. + +George Biddell Airy, Seventh Astronomer Royal,[4] commenced his +Greenwich labours in 1835. His first and greatest reformation in the +work of the observatory was one he had already established at +Cambridge, and is now universally adopted. He held that an observation +is not completed until it has been reduced to a useful form; and in the +case of the sun, moon, and planets these results were, in every case, +compared with the tables, and the tabular error printed. + +Airy was firmly impressed with the object for which Charles II. had +wisely founded the observatory in connection with navigation, and for +observations of the moon. Whenever a meridian transit of the moon could +be observed this was done. But, even so, there are periods in the month +when the moon is too near the sun for a transit to be well observed. +Also weather interferes with many meridian observations. To render the +lunar observations more continuous, Airy employed Troughton’s +successor, James Simms, in conjunction with the engineers, Ransome and +May, to construct an altazimuth with three-foot circles, and a +five-foot telescope, in 1847. The result was that the number of lunar +observations was immediately increased threefold, many of them being in +a part of the moon’s orbit which had previously been bare of +observations. From that date the Greenwich lunar observations have been +a model and a standard for the whole world. + +Airy also undertook to superintend the reduction of all Greenwich lunar +observations from 1750 to 1830. The value of this laborious work, which +was completed in 1848, cannot be over-estimated. + +The demands of astronomy, especially in regard to small minor planets, +required a transit instrument and mural circle with a more powerful +telescope. Airy combined the functions of both, and employed the same +constructors as before to make a _transit-circle_ with a telescope of +eleven and a-half feet focus and a circle of six-feet diameter, the +object-glass being eight inches in diameter. + +Airy, like Bradley, was impressed with the advantage of employing stars +in the zenith for determining the fundamental constants of astronomy. +He devised a _reflex zenith tube_, in which the zenith point was +determined by reflection from a surface of mercury. The design was so +simple, and seemed so perfect, that great expectations were +entertained. But unaccountable variations comparable with those of the +transit circle appeared, and the instrument was put out of use until +1903, when the present Astronomer Royal noticed that the irregularities +could be allowed for, being due to that remarkable variation in the +position of the earth’s axis included in circles of about six yards +diameter at the north and south poles, discovered at the end of the +nineteenth century. The instrument is now being used for investigating +these variations; and in the year 1907 as many as 1,545 observations of +stars were made with the reflex zenith tube. + +In connection with zenith telescopes it must be stated that Respighi, +at the Capitol Observatory at Rome, made use of a deep well with a +level mercury surface at the bottom and a telescope at the top pointing +downwards, which the writer saw in 1871. The reflection of the +micrometer wires and of a star very near the zenith (but not quite in +the zenith) can be observed together. His mercury trough was a circular +plane surface with a shallow edge to retain the mercury. The surface +quickly came to rest after disturbance by street traffic. + +Sir W. M. H. Christie, Eighth Astronomer Royal, took up his duties in +that capacity in 1881. Besides a larger altazimuth that he erected in +1898, he has widened the field of operations at Greenwich by the +extensive use of photography and the establishment of large +equatoreals. From the point of view of instruments of precision, one of +the most important new features is the astrographic equatoreal, set up +in 1892 and used for the Greenwich section of the great astrographic +chart just completed. Photography has come to be of use, not only for +depicting the sun and moon, comets and nebulae, but also to obtain +accurate relative positions of neighbouring stars; to pick up objects +that are invisible in any telescope; and, most of all perhaps, in +fixing the positions of faint satellites. Thus Saturn’s distant +satellite, Phoebe, and the sixth and seventh satellites of Jupiter, +have been followed regularly in their courses at Greenwich ever since +their discovery with the thirty-inch reflector (erected in 1897); and +while doing so Mr. Melotte made, in 1908, the splendid discovery on +some of the photographic plates of an eighth satellite of Jupiter, at +an enormous distance from the planet. From observations in the early +part of 1908, over a limited arc of its orbit, before Jupiter +approached the sun, Mr. Cowell computed a retrograde orbit and +calculated the future positions of this satellite, which enabled Mr. +Melotte to find it again in the autumn—a great triumph both of +calculation and of photographic observation. This satellite has never +been seen, and has been photographed only at Greenwich, Heidelberg, and +the Lick Observatory. + +Greenwich Observatory has been here selected for tracing the progress +of accurate measurement. But there is one instrument of great value, +the heliometer, which is not used at Greenwich. This serves the purpose +of a double image micrometer, and is made by dividing the object-glass +of a telescope along a diameter. Each half is mounted so as to slide a +distance of several inches each way on an arc whose centre is the +focus. The amount of the movement can be accurately read. Thus two +fields of view overlap, and the adjustment is made to bring an image of +one star over that of another star, and then to do the same by a +displacement in the opposite direction. The total movement of the +half-object glass is double the distance between the star images in the +focal plane. Such an instrument has long been established at Oxford, +and German astronomers have made great use of it. But in the hands of +Sir David Gill (late His Majesty’s Astronomer at the Cape of Good +Hope), and especially in his great researches on Solar and on Stellar +parallax, it has been recognised as an instrument of the very highest +accuracy, measuring the distance between stars correctly to less than a +tenth of a second of arc. + +The superiority of the heliometer over all other devices (except +photography) for measuring small angles has been specially brought into +prominence by Sir David Gill’s researches on the distance of the +sun—_i.e.,_ the scale of the solar system. A measurement of the +distance of any planet fixes the scale, and, as Venus approaches the +earth most nearly of all the planets, it used to be supposed that a +Transit of Venus offered the best opportunity for such measurement, +especially as it was thought that, as Venus entered on the solar disc, +the sweep of light round the dark disc of Venus would enable a very +precise observation to be made. The Transit of Venus in 1874, in which +the present writer assisted, overthrew this delusion. + +In 1877 Sir David Gill used Lord Crawford’s heliometer at the Island of +Ascension to measure the parallax of Mars in opposition, and found the +sun’s distance 93,080,000 miles. He considered that, while the +superiority of the heliometer had been proved, the results would be +still better with the points of light shown by minor planets rather +than with the disc of Mars. + +In 1888-9, at the Cape, he observed the minor planets Iris, Victoria, +and Sappho, and secured the co-operation of four other heliometers. His +final result was 92,870,000 miles, the parallax being 8",802 (_Cape +Obs_., Vol. VI.). + +So delicate were these measures that Gill detected a minute periodic +error of theory of twenty-seven days, owing to a periodically erroneous +position of the centre of gravity of the earth and moon to which the +position of the observer was referred. This led him to correct the mass +of the moon, and to fix its ratio to the earth’s mass = 0.012240. + +Another method of getting the distance from the sun is to measure the +velocity of the earth’s orbital motion, giving the circumference +traversed in a year, and so the radius of the orbit. This has been done +by comparing observation and experiment. The aberration of light is an +angle 20” 48, giving the ratio of the earth’s velocity to the velocity +of light. The velocity of light is 186,000 miles a second; whence the +distance to the sun is 92,780,000 miles. There seems, however, to be +some uncertainty about the true value of the aberration, any +determination of which is subject to irregularities due to the +“seasonal errors.” The velocity of light was experimentally found, in +1862, by Fizeau and Foucault, each using an independent method. These +methods have been developed, and new values found, by Cornu, +Michaelson, Newcomb, and the present writer. + +Quite lately Halm, at the Cape of Good Hope, measured spectroscopically +the velocity of the earth to and from a star by observations taken six +months apart. Thence he obtained an accurate value of the sun’s +distance.[5] + +But the remarkably erratic minor planet, Eros, discovered by Witte in +1898, approaches the earth within 15,000,000 miles at rare intervals, +and, with the aid of photography, will certainly give us the best +result. A large number of observatories combined to observe the +opposition of 1900. Their results are not yet completely reduced, but +the best value deduced so far for the parallax[6] is 8".807 ± +0".0028.[7] + +FOOTNOTES: + + [1] In 1480 Martin Behaim, of Nuremberg, produced his _astrolabe_ for + measuring the latitude, by observation of the sun, at sea. It + consisted of a graduated metal circle, suspended by a ring which was + passed over the thumb, and hung vertically. A pointer was fixed to a + pin at the centre. This arm, called the _alhidada_, worked round the + graduated circle, and was pointed to the sun. The altitude of the sun + was thus determined, and, by help of solar tables, the latitude could + be found from observations made at apparent noon. + + [2] See illustration on p. 76. + + [3] See Dreyer’s article on these instruments in _Copernicus_, Vol. I. + They were stolen by the Germans after the relief of the Embassies, in + 1900. The best description of these instruments is probably that + contained in an interesting volume, which may be seen in the library + of the R. A. S., entitled _Chinese Researches_, by Alexander Wyllie + (Shanghai, 1897). + + [4] Sir George Airy was very jealous of this honourable title. He + rightly held that there is only one Astronomer Royal at a time, as + there is only one Mikado, one Dalai Lama. He said that His Majesty’s + Astronomer at the Cape of Good Hope, His Majesty’s Astronomer for + Scotland, and His Majesty’s Astronomer for Ireland are not called + Astronomers Royal. + + [5] _Annals of the Cape Observatory_, vol. x., part 3. + + [6] The parallax of the sun is the angle subtended by the earth’s + radius at the sun’s distance. + + [7] A. R. Hinks, R.A.S.; Monthly Notices, June, 1909. + + + + +11. HISTORY OF THE TELESCOPE + + +Accounts of wonderful optical experiments by Roger Bacon (who died in +1292), and in the sixteenth century by Digges, Baptista Porta, and +Antonio de Dominis (Grant, _Hist. Ph. Ast_.), have led some to suppose +that they invented the telescope. The writer considers that it is more +likely that these notes refer to a kind of _camera obscura_, in which a +lens throws an inverted image of a landscape on the wall. + +The first telescopes were made in Holland, the originator being either +Henry Lipperhey,[1] Zacharias Jansen, or James Metius, and the date +1608 or earlier. + +In 1609 Galileo, being in Venice, heard of the invention, went home and +worked out the theory, and made a similar telescope. These telescopes +were all made with a convex object-glass and a concave eye-lens, and +this type is spoken of as the Galilean telescope. Its defects are that +it has no real focus where cross-wires can be placed, and that the +field of view is very small. Kepler suggested the convex eye-lens in +1611, and Scheiner claimed to have used one in 1617. But it was +Huyghens who really introduced them. In the seventeenth century +telescopes were made of great length, going up to 300 feet. Huyghens +also invented the compound eye-piece that bears his name, made of two +convex lenses to diminish spherical aberration. + +But the defects of colour remained, although their cause was unknown +until Newton carried out his experiments on dispersion and the solar +spectrum. To overcome the spherical aberration James Gregory,[2] of +Aberdeen and Edinburgh, in 1663, in his _Optica Promota_, proposed a +reflecting speculum of parabolic form. But it was Newton, about 1666, +who first made a reflecting telescope; and he did it with the object of +avoiding colour dispersion. + +Some time elapsed before reflectors were much used. Pound and Bradley +used one presented to the Royal Society by Hadley in 1723. Hawksbee, +Bradley, and Molyneaux made some. But James Short, of Edinburgh, made +many excellent Gregorian reflectors from 1732 till his death in 1768. + +Newton’s trouble with refractors, chromatic aberration, remained +insurmountable until John Dollond (born 1706, died 1761), after many +experiments, found out how to make an achromatic lens out of two +lenses—one of crown glass, the other of flint glass—to destroy the +colour, in a way originally suggested by Euler. He soon acquired a +great reputation for his telescopes of moderate size; but there was a +difficulty in making flint-glass lenses of large size. The first actual +inventor and constructor of an achromatic telescope was Chester Moor +Hall, who was not in trade, and did not patent it. Towards the close of +the eighteenth century a Swiss named Guinand at last succeeded in +producing larger flint-glass discs free from striae. Frauenhofer, of +Munich, took him up in 1805, and soon produced, among others, Struve’s +Dorpat refractor of 9.9 inches diameter and 13.5 feet focal length, and +another, of 12 inches diameter and 18 feet focal length, for Lamont, of +Munich. + +In the nineteenth century gigantic _reflectors_ have been made. +Lassel’s 2-foot reflector, made by himself, did much good work, and +discovered four new satellites. But Lord Rosse’s 6-foot reflector, 54 +feet focal length, constructed in 1845, is still the largest ever made. +The imperfections of our atmosphere are against the use of such large +apertures, unless it be on high mountains. During the last half century +excellent specula have been made of silvered glass, and Dr. Common’s +5-foot speculum (removed, since his death, to Harvard) has done +excellent work. Then there are the 5-foot Yerkes reflector at Chicago, +and the 4-foot by Grubb at Melbourne. + +Passing now from these large reflectors to refractors, further +improvements have been made in the manufacture of glass by Chance, of +Birmingham, Feil and Mantois, of Paris, and Schott, of Jena; while +specialists in grinding lenses, like Alvan Clark, of the U.S.A., and +others, have produced many large refractors. + +Cooke, of York, made an object-glass, 25-inch diameter, for Newall, of +Gateshead, which has done splendid work at Cambridge. We have the +Washington 26-inch by Clark, the Vienna 27-inch by Grubb, the Nice +29½-inch by Gautier, the Pulkowa 30-inch by Clark. Then there was the +sensation of Clark’s 36-inch for the Lick Observatory in California, +and finally his _tour de force_, the Yerkes 40-inch refractor, for +Chicago. + +At Greenwich there is the 28-inch photographic refractor, and the +Thompson equatoreal by Grubb, carrying both the 26-inch photographic +refractor and the 30-inch reflector. At the Cape of Good Hope we find +Mr. Frank McClean’s 24-inch refractor, with an object-glass prism for +spectroscopic work. + +It would be out of place to describe here the practical adjuncts of a +modern equatoreal—the adjustments for pointing it, the clock for +driving it, the position-micrometer and various eye-pieces, the +photographic and spectroscopic attachments, the revolving domes, +observing seats, and rising floors and different forms of mounting, the +siderostats and coelostats, and other convenient adjuncts, besides the +registering chronograph and numerous facilities for aiding observation. +On each of these a chapter might be written; but the most important +part of the whole outfit is the man behind the telescope, and it is +with him that a history is more especially concerned. + + +SPECTROSCOPE. + +Since the invention of the telescope no discovery has given so great an +impetus to astronomical physics as the spectroscope; and in giving us +information about the systems of stars and their proper motions it +rivals the telescope. + +Frauenhofer, at the beginning of the nineteenth century, while applying +Dollond’s discovery to make large achromatic telescopes, studied the +dispersion of light by a prism. Admitting the light of the sun through +a narrow slit in a window-shutter, an inverted image of the slit can be +thrown, by a lens of suitable focal length, on the wall opposite. If a +wedge or prism of glass be interposed, the image is deflected to one +side; but, as Newton had shown, the images formed by the different +colours of which white light is composed are deflected to different +extents—the violet most, the red least. The number of colours forming +images is so numerous as to form a continuous spectrum on the wall with +all the colours—red, orange, yellow, green, blue, indigo, and violet. +But Frauenhofer found with a narrow slit, well focussed by the lens, +that some colours were missing in the white light of the sun, and these +were shown by dark lines across the spectrum. These are the Frauenhofer +lines, some of which he named by the letters of the alphabet. The D +line is a very marked one in the yellow. These dark lines in the solar +spectrum had already been observed by Wollaston.[3] + +On examining artificial lights it was found that incandescent solids +and liquids (including the carbon glowing in a white gas flame) give +continuous spectra; gases, except under enormous pressure, give bright +lines. If sodium or common salt be thrown on the colourless flame of a +spirit lamp, it gives it a yellow colour, and its spectrum is a bright +yellow line agreeing in position with line D of the solar spectrum. + +In 1832 Sir David Brewster found some of the solar black lines +increased in strength towards sunset, and attributed them to absorption +in the earth’s atmosphere. He suggested that the others were due to +absorption in the sun’s atmosphere. Thereupon Professor J. D. Forbes +pointed out that during a nearly total eclipse the lines ought to be +strengthened in the same way; as that part of the sun’s light, coming +from its edge, passes through a great distance in the sun’s atmosphere. +He tried this with the annular eclipse of 1836, with a negative result +which has never been accounted for, and which seemed to condemn +Brewster’s view. + +In 1859 Kirchoff, on repeating Frauenhofer’s experiment, found that, if +a spirit lamp with salt in the flame were placed in the path of the +light, the black D line is intensified. He also found that, if he used +a limelight instead of the sunlight and passed it through the flame +with salt, the spectrum showed the D line black; or the vapour of +sodium absorbs the same light that it radiates. This proved to him the +existence of sodium in the sun’s atmosphere.[4] Iron, calcium, and +other elements were soon detected in the same way. + +Extensive laboratory researches (still incomplete) have been carried +out to catalogue (according to their wave-length on the undulatory +theory of light) all the lines of each chemical element, under all +conditions of temperature and pressure. At the same time, all the lines +have been catalogued in the light of the sun and the brighter of the +stars. + +Another method of obtaining spectra had long been known, by +transmission through, or reflection from, a grating of equidistant +lines ruled upon glass or metal. H. A. Rowland developed the art of +constructing these gratings, which requires great technical skill, and +for this astronomers owe him a debt of gratitude. + +In 1842 Doppler[5] proved that the colour of a luminous body, like the +pitch or note of a sounding body, must be changed by velocity of +approach or recession. Everyone has noticed on a railway that, on +meeting a locomotive whistling, the note is lowered after the engine +has passed. The pitch of a sound or the colour of a light depends on +the number of waves striking the ear or eye in a second. This number is +increased by approach and lowered by recession. + +Thus, by comparing the spectrum of a star alongside a spectrum of +hydrogen, we may see all the lines, and be sure that there is hydrogen +in the star; yet the lines in the star-spectrum may be all slightly +displaced to one side of the lines of the comparison spectrum. If +towards the violet end, it means mutual approach of the star and earth; +if to the red end, it means recession. The displacement of lines does +not tell us whether the motion is in the star, the earth, or both. The +displacement of the lines being measured, we can calculate the rate of +approach or recession in miles per second. + +In 1868 Huggins[6] succeeded in thus measuring the velocities of stars +in the direction of the line of sight. + +In 1873 Vogel[7] compared the spectra of the sun’s East (approaching) +limb and West (receding) limb, and the displacement of lines endorsed +the theory. This last observation was suggested by Zöllner. + +FOOTNOTES: + + [1] In the _Encyclopaedia Britannica_, article “Telescope,” and in + Grant’s _Physical Astronomy_, good reasons are given for awarding the + honour to Lipperhey. + + [2] Will the indulgent reader excuse an anecdote which may encourage + some workers who may have found their mathematics defective through + want of use? James Gregory’s nephew David had a heap of MS. notes by + Newton. These descended to a Miss Gregory, of Edinburgh, who handed + them to the present writer, when an undergraduate at Cambridge, to + examine. After perusal, he lent them to his kindest of friends, J. C. + Adams (the discoverer of Neptune), for his opinion. Adams’s final + verdict was: “I fear they are of no value. It is pretty evident that, + when he wrote these notes, _Newton’s mathematics were a little + rusty_.” + + [3] _R. S. Phil. Trans_. + + [4] The experiment had been made before by one who did not understand + its meaning;. But Sir George G. Stokes had already given verbally the + true explanation of Frauenhofer lines. + + [5] _Abh. d. Kön. Böhm. d. Wiss_., Bd. ii., 1841-42, p. 467. See also + Fizeau in the _Ann. de Chem. et de Phys_., 1870, p. 211. + + [6] _R. S. Phil. Trans_., 1868. + + [7] _Ast. Nach_., No. 1, 864. + +BOOK IV. THE PHYSICAL PERIOD + +We have seen how the theory of the solar system was slowly developed by +the constant efforts of the human mind to find out what are the rules +of cause and effect by which our conception of the present universe and +its development seems to be bound. In the primitive ages a mere record +of events in the heavens and on the earth gave the only hope of +detecting those uniform sequences from which to derive rules or laws of +cause and effect upon which to rely. Then came the geometrical age, in +which rules were sought by which to predict the movements of heavenly +bodies. Later, when the relation of the sun to the courses of the +planets was established, the sun came to be looked upon as a cause; and +finally, early in the seventeenth century, for the first time in +history, it began to be recognised that the laws of dynamics, exactly +as they had been established for our own terrestrial world, hold good, +with the same rigid invariability, at least as far as the limits of the +solar system. + +Throughout this evolution of thought and conjecture there were two +types of astronomers—those who supplied the facts, and those who +supplied the interpretation through the logic of mathematics. So +Ptolemy was dependent upon Hipparchus, Kepler on Tycho Brahe, and +Newton in much of his work upon Flamsteed. + +When Galileo directed his telescope to the heavens, when Secchi and +Huggins studied the chemistry of the stars by means of the +spectroscope, and when Warren De la Rue set up a photoheliograph at +Kew, we see that a progress in the same direction as before, in the +evolution of our conception of the universe, was being made. Without +definite expression at any particular date, it came to be an accepted +fact that not only do earthly dynamics apply to the heavenly bodies, +but that the laws we find established here, in geology, in chemistry, +and in the laws of heat, may be extended with confidence to the +heavenly bodies. Hence arose the branch of astronomy called +astronomical physics, a science which claims a large portion of the +work of the telescope, spectroscope, and photography. In this new +development it is more than ever essential to follow the dictum of +Tycho Brahe—not to make theories until all the necessary facts are +obtained. The great astronomers of to-day still hold to Sir Isaac +Newton’s declaration, “Hypotheses non fingo.” Each one may have his +suspicions of a theory to guide him in a course of observation, and may +call it a working hypothesis. But the cautious astronomer does not +proclaim these to the world; and the historian is certainly not +justified in including in his record those vague speculations founded +on incomplete data which may be demolished to-morrow, and which, +however attractive they may be, often do more harm than good to the +progress of true science. Meanwhile the accumulation of facts has been +prodigious, and the revelations of the telescope and spectroscope +entrancing. + + + + +12. THE SUN. + + +One of Galileo’s most striking discoveries, when he pointed his +telescope to the heavenly bodies, was that of the irregularly shaped +spots on the sun, with the dark central _umbra_ and the less dark, but +more extensive, _penumbra_ surrounding it, sometimes with several +umbrae in one penumbra. He has left us many drawings of these spots, +and he fixed their period of rotation as a lunar month. + +It is not certain whether Galileo, Fabricius, or Schemer was the first +to see the spots. They all did good work. The spots were found to be +ever varying in size and shape. Sometimes, when a spot disappears at +the western limb of the sun, it is never seen again. In other cases, +after a fortnight, it reappears at the eastern limb. The faculae, or +bright areas, which are seen all over the sun’s surface, but specially +in the neighbourhood of spots, and most distinctly near the sun’s edge, +were discovered by Galileo. A high telescopic power resolves their +structure into an appearance like willow-leaves, or rice-grains, fairly +uniform in size, and more marked than on other parts of the sun’s +surface. + +[Illustration: SOLAR SURFACE. +As Photographed at the Royal Observatory, Greenwich, showing sun-spots +with umbræ, penumbræ, and faculæ.] + +Speculations as to the cause of sun-spots have never ceased from +Galileo’s time to ours. He supposed them to be clouds. Scheiner[1] said +they were the indications of tumultuous movements occasionally +agitating the ocean of liquid fire of which he supposed the sun to be +composed. + +A. Wilson, of Glasgow, in 1769,[2] noticed a movement of the umbra +relative to the penumbra in the transit of the spot over the sun’s +surface; exactly as if the spot were a hollow, with a black base and +grey shelving sides. This was generally accepted, but later +investigations have contradicted its universality. Regarding the cause +of these hollows, Wilson said:— + +Whether their first production and subsequent numberless changes depend +upon the eructation of elastic vapours from below, or upon eddies or +whirlpools commencing at the surface, or upon the dissolving of the +luminous matter in the solar atmosphere, as clouds are melted and again +given out by our air; or, if the reader pleases, upon the annihilation +and reproduction of parts of this resplendent covering, is left for +theory to guess at.[3] + +Ever since that date theory has been guessing at it. The solar +astronomer is still applying all the instruments of modern research to +find out which of these suppositions, or what modification of any of +them, is nearest the truth. The obstacle—one that is perhaps fatal to a +real theory—lies in the impossibility of reproducing comparative +experiments in our laboratories or in our atmosphere. + +Sir William Herschel propounded an explanation of Wilson’s observation +which received much notice, but which, out of respect for his memory, +is not now described, as it violated the elementary laws of heat. + +Sir John Herschel noticed that the spots are mostly confined to two +zones extending to about 35° on each side of the equator, and that a +zone of equatoreal calms is free from spots. But it was R. C. +Carrington[4] who, by his continuous observations at Redhill, in +Surrey, established the remarkable fact that, while the rotation period +in the highest latitudes, 50°, where spots are seen, is +twenty-seven-and-a-half days, near the equator the period is only +twenty-five days. His splendid volume of observations of the sun led to +much new information about the average distribution of spots at +different epochs. + +Schwabe, of Dessau, began in 1826 to study the solar surface, and, +after many years of work, arrived at a law of frequency which has been +more fruitful of results than any discovery in solar physics.[5] In +1843 he announced a decennial period of maxima and minima of sun-spot +displays. In 1851 it was generally accepted, and, although a period of +eleven years has been found to be more exact, all later observations, +besides the earlier ones which have been hunted up for the purpose, go +to establish a true periodicity in the number of sun-spots. But quite +lately Schuster[6] has given reasons for admitting a number of +co-existent periods, of which the eleven-year period was predominant in +the nineteenth century. + +In 1851 Lament, a Scotchman at Munich, found a decennial period in the +daily range of magnetic declination. In 1852 Sir Edward Sabine +announced a similar period in the number of “magnetic storms” affecting +all of the three magnetic elements—declination, dip, and intensity. +Australian and Canadian observations both showed the decennial period +in all three elements. Wolf, of Zurich, and Gauthier, of Geneva, each +independently arrived at the same conclusion. + +It took many years before this coincidence was accepted as certainly +more than an accident by the old-fashioned astronomers, who want rigid +proof for every new theory. But the last doubts have long vanished, and +a connection has been further traced between violent outbursts of solar +activity and simultaneous magnetic storms. + +The frequency of the Aurora Borealis was found by Wolf to follow the +same period. In fact, it is closely allied in its cause to terrestrial +magnetism. Wolf also collected old observations tracing the periodicity +of sun-spots back to about 1700 A.D. + +Spoerer deduced a law of dependence of the average latitude of +sun-spots on the phase of the sun-spot period. + +All modern total solar eclipse observations seem to show that the shape +of the luminous corona surrounding the moon at the moment of totality +has a special distinct character during the time of a sun-spot maximum, +and another, totally different, during a sun-spot minimum. + +A suspicion is entertained that the total quantity of heat received by +the earth from the sun is subject to the same period. This would have +far-reaching effects on storms, harvests, vintages, floods, and +droughts; but it is not safe to draw conclusions of this kind except +from a very long period of observations. + +Solar photography has deprived astronomers of the type of Carrington of +the delight in devoting a life’s work to collecting data. It has now +become part of the routine work of an observatory. + +In 1845 Foucault and Fizeau took a daguerreotype photograph of the sun. +In 1850 Bond produced one of the moon of great beauty, Draper having +made some attempts at an even earlier date. But astronomical +photography really owes its beginning to De la Rue, who used the +collodion process for the moon in 1853, and constructed the Kew +photoheliograph in 1857, from which date these instruments have been +multiplied, and have given us an accurate record of the sun’s surface. +Gelatine dry plates were first used by Huggins in 1876. + +It is noteworthy that from the outset De la Rue recognised the value of +stereoscopic vision, which is now known to be of supreme accuracy. In +1853 he combined pairs of photographs of the moon in the same phase, +but under different conditions regarding libration, showing the moon +from slightly different points of view. These in the stereoscope +exhibited all the relief resulting from binocular vision, and looked +like a solid globe. In 1860 he used successive photographs of the total +solar eclipse stereoscopically, to prove that the red prominences +belong to the sun, and not to the moon. In 1861 he similarly combined +two photographs of a sun-spot, the perspective effect showing the umbra +like a floor at the bottom of a hollow penumbra; and in one case the +faculæ were discovered to be sailing over a spot apparently at some +considerable height. These appearances may be partly due to a proper +motion; but, so far as it went, this was a beautiful confirmation of +Wilson’s discovery. Hewlett, however, in 1894, after thirty years of +work, showed that the spots are not always depressions, being very +subject to disturbance. + +The Kew photographs[7] contributed a vast amount of information about +sun-spots, and they showed that the faculæ generally follow the spots +in their rotation round the sun. + +The constitution of the sun’s photosphere, the layer which is the +principal light-source on the sun, has always been a subject of great +interest; and much was done by men with exceptionally keen eyesight, +like Mr. Dawes. But it was a difficult subject, owing to the rapidity +of the changes in appearance of the so-called rice-grains, about 1” in +diameter. The rapid transformations and circulations of these +rice-grains, if thoroughly studied, might lead to a much better +knowledge of solar physics. This seemed almost hopeless, as it was +found impossible to identify any “rice-grain” in the turmoil after a +few minutes. But M. Hansky, of Pulkowa (whose recent death is +deplored), introduced successfully a scheme of photography, which might +almost be called a solar cinematograph. He took photographs of the sun +at intervals of fifteen or thirty seconds, and then enlarged selected +portions of these two hundred times, giving a picture corresponding to +a solar disc of six metres diameter. In these enlarged pictures he was +able to trace the movements, and changes of shape and brightness, of +individual rice-grains. Some granules become larger or smaller. Some +seem to rise out of a mist, as it were, and to become clearer. Others +grow feebler. Some are split in two. Some are rotated through a right +angle in a minute or less, although each of the grains may be the size +of Great Britain. Generally they move together in groups of very +various velocities, up to forty kilometres a second. These movements +seem to have definite relation to any sun-spots in the neighbourhood. +From the results already obtained it seems certain that, if this method +of observation be continued, it cannot fail to supply facts of the +greatest importance. + +It is quite impossible to do justice here to the work of all those who +are engaged on astronomical physics. The utmost that can be attempted +is to give a fair idea of the directions of human thought and +endeavour. During the last half-century America has made splendid +progress, and an entirely new process of studying the photosphere has +been independently perfected by Professor Hale at Chicago, and +Deslandres at Paris.[8] They have succeeded in photographing the sun’s +surface in monochromatic light, such as the light given off as one of +the bright lines of hydrogen or of calcium, by means of the +“Spectroheliograph.” The spectroscope is placed with its slit in the +focus of an equatoreal telescope, pointed to the sun, so that the +circular image of the sun falls on the slit. At the other end of the +spectroscope is the photographic plate. Just in front of this plate +there is another slit parallel to the first, in the position where the +image of the first slit formed by the K line of calcium falls. Thus is +obtained a photograph of the section of the sun, made by the first +slit, only in K light. As the image of the sun passes over the first +slit the photographic plate is moved at the same rate and in the same +direction behind the second slit; and as successive sections of the +sun’s image in the equatoreal enter the apparatus, so are these +sections successively thrown in their proper place on the photographic +plate, always in K light. By using a high dispersion the faculæ which +give off K light can be correctly photographed, not only at the sun’s +edge, but all over his surface. The actual mechanical method of +carrying out the observation is not quite so simple as what is here +described. + +By choosing another line of the spectrum instead of calcium K—for +example, the hydrogen line H(3)—we obtain two photographs, one showing +the appearance of the calcium floculi, and the other of the hydrogen +floculi, on the same part of the solar surface; and nothing is more +astonishing than to note the total want of resemblance in the forms +shown on the two. This mode of research promises to afford many new and +useful data. + +The spectroscope has revealed the fact that, broadly speaking, the sun +is composed of the same materials as the earth. Ångstrom was the first +to map out all of the lines to be found in the solar spectrum. But +Rowland, of Baltimore, after having perfected the art of making true +gratings with equidistant lines ruled on metal for producing spectra, +then proceeded to make a map of the solar spectrum on a large scale. + +In 1866 Lockyer[9] threw an image of the sun upon the slit of a +spectroscope, and was thus enabled to compare the spectrum of a spot +with that of the general solar surface. The observation proved the +darkness of a spot to be caused by increased absorption of light, not +only in the dark lines, which are widened, but over the entire +spectrum. In 1883 Young resolved this continuous obscurity into an +infinite number of fine lines, which have all been traced in a shadowy +way on to the general solar surface. Lockyer also detected +displacements of the spectrum lines in the spots, such as would be +produced by a rapid motion in the line of sight. It has been found that +both uprushes and downrushes occur, but there is no marked predominance +of either in a sun-spot. The velocity of motion thus indicated in the +line of sight sometimes appears to amount to 320 miles a second. But it +must be remembered that pressure of a gas has some effect in displacing +the spectral lines. So we must go on, collecting data, until a time +comes when the meaning of all the facts can be made clear. + +_Total Solar Eclipses_.—During total solar eclipses the time is so +short, and the circumstances so impressive, that drawings of the +appearance could not always be trusted. The red prominences of jagged +form that are seen round the moon’s edge, and the corona with its +streamers radiating or interlacing, have much detail that can hardly be +recorded in a sketch. By the aid of photography a number of records can +be taken during the progress of totality. From a study of these the +extent of the corona is demonstrated in one case to extend to at least +six diameters of the moon, though the eye has traced it farther. This +corona is still one of the wonders of astronomy, and leads to many +questions. What is its consistency, if it extends many million miles +from the sun’s surface? How is it that it opposed no resistance to the +motion of comets which have almost grazed the sun’s surface? Is this +the origin of the zodiacal light? The character of the corona in +photographic records has been shown to depend upon the phase of the +sun-spot period. During the sun-spot maximum the corona seems most +developed over the spot-zones—i.e., neither at the equator nor the +poles. The four great sheaves of light give it a square appearance, and +are made up of rays or plumes, delicate like the petals of a flower. +During a minimum the nebulous ring seems to be made of tufts of fine +hairs with aigrettes or radiations from both poles, and streamers from +the equator. + +[Illustration: SOLAR ECLIPSE, 1882. From drawing by W. H. Wesley, +Secretary R.A.S.; showing the prominences, the corona, and an unknown +comet.] + +On September 19th, 1868, eclipse spectroscopy began with the Indian +eclipse, in which all observers found that the red prominences showed a +bright line spectrum, indicating the presence of hydrogen and other +gases. So bright was it that Jansen exclaimed: “_Je verrai ces +lignes-là en dehors des éclipses_.” And the next day he observed the +lines at the edge of the uneclipsed sun. Huggins had suggested this +observation in February, 1868, his idea being to use prisms of such +great dispersive power that the continuous spectrum reflected by our +atmosphere should be greatly weakened, while a bright line would suffer +no diminution by the high dispersion. On October 20th Lockyer,[10] +having news of the eclipse, but not of Jansen’s observations the day +after, was able to see these lines. This was a splendid performance, +for it enabled the prominences to be observed, not only during +eclipses, but every day. Moreover, the next year Huggins was able, by +using a wide slit, to see the whole of a prominence and note its shape. +Prominences are classified, according to their form, into “flame” and +“cloud” prominences, the spectrum of the latter showing calcium, +hydrogen, and helium; that of the former including a number of metals. + +The D line of sodium is a double line, and in the same eclipse (1868) +an orange line was noticed which was afterwards found to lie close to +the two components of the D line. It did not correspond with any known +terrestrial element, and the unknown element was called “helium.” It +was not until 1895 that Sir William Ramsay found this element as a gas +in the mineral cleavite. + +The spectrum of the corona is partly continuous, indicating light +reflected from the sun’s body. But it also shows a green line +corresponding with no known terrestrial element, and the name +“coronium” has been given to the substance causing it. + +A vast number of facts have been added to our knowledge about the sun +by photography and the spectroscope. Speculations and hypotheses in +plenty have been offered, but it may be long before we have a complete +theory evolved to explain all the phenomena of the storm-swept metallic +atmosphere of the sun. + +The proceedings of scientific societies teem with such facts and +“working hypotheses,” and the best of them have been collected by Miss +Clerke in her _History of Astronomy during the Nineteenth Century_. As +to established facts, we learn from the spectroscopic researches (1) +that the continuous spectrum is derived from the _photosphere_ or solar +gaseous material compressed almost to liquid consistency; (2) that the +_reversing layer_ surrounds it and gives rise to black lines in the +spectrum; that the _chromosphere_ surrounds this, is composed mainly of +hydrogen, and is the cause of the red prominences in eclipses; and that +the gaseous _corona_ surrounds all of these, and extends to vast +distances outside the sun’s visible surface. + +FOOTNOTES: + + [1] _Rosa Ursina_, by C. Scheiner, _fol_.; Bracciani, 1630. + + [2] _R. S. Phil. Trans_., 1774. + + [3] _Ibid_, 1783. + + [4] _Observations on the Spots on the Sun, etc.,_ 4°; London and + Edinburgh, 1863. + + [5] _Periodicität der Sonnenflecken. Astron. Nach. XXI._, 1844, P. + 234. + + [6] _R.S. Phil. Trans._ (ser. A), 1906, p. 69-100. + + [7] “Researches on Solar Physics,” by De la Rue, Stewart and Loewy; + _R. S. Phil. Trans_., 1869, 1870. + + [8] “The Sun as Photographed on the K line”; _Knowledge_, London, + 1903, p. 229. + + [9] _R. S. Proc._, xv., 1867, p. 256. + + [10] _Acad. des Sc._, Paris; _C. R._, lxvii., 1868, p. 121. + + + + +13. THE MOON AND PLANETS. + + +_The Moon_.—Telescopic discoveries about the moon commence with +Galileo’s discovery that her surface has mountains and valleys, like +the earth. He also found that, while she always turns the same face to +us, there is periodically a slight twist to let us see a little round +the eastern or western edge. This was called _libration_, and the +explanation was clear when it was understood that in showing always the +same face to us she makes one revolution a month on her axis +_uniformly_, and that her revolution round the earth is not uniform. + +Galileo said that the mountains on the moon showed greater differences +of level than those on the earth. Shröter supported this opinion. W. +Herschel opposed it. But Beer and Mädler measured the heights of lunar +mountains by their shadows, and found four of them over 20,000 feet +above the surrounding plains. + +Langrenus[1] was the first to do serious work on selenography, and +named the lunar features after eminent men. Riccioli also made lunar +charts. In 1692 Cassini made a chart of the full moon. Since then we +have the charts of Schröter, Beer and Mädler (1837), and of Schmidt, of +Athens (1878); and, above all, the photographic atlas by Loewy and +Puiseux. + +The details of the moon’s surface require for their discussion a whole +book, like that of Neison or the one by Nasmyth and Carpenter. Here a +few words must suffice. Mountain ranges like our Andes or Himalayas are +rare. Instead of that, we see an immense number of circular cavities, +with rugged edges and flat interior, often with a cone in the centre, +reminding one of instantaneous photographs of the splash of a drop of +water falling into a pool. Many of these are fifty or sixty miles +across, some more. They are generally spoken of as resembling craters +of volcanoes, active or extinct, on the earth. But some of those who +have most fully studied the shapes of craters deny altogether their +resemblance to the circular objects on the moon. These so-called +craters, in many parts, are seen to be closely grouped, especially in +the snow-white parts of the moon. But there are great smooth dark +spaces, like the clear black ice on a pond, more free from craters, to +which the equally inappropriate name of seas has been given. The most +conspicuous crater, _Tycho_, is near the south pole. At full moon there +are seen to radiate from Tycho numerous streaks of light, or “rays,” +cutting through all the mountain formations, and extending over fully +half the lunar disc, like the star-shaped cracks made on a sheet of ice +by a blow. Similar cracks radiate from other large craters. It must be +mentioned that these white rays are well seen only in full light of the +sun at full moon, just as the white snow in the crevasses of a glacier +is seen bright from a distance only when the sun is high, and +disappears at sunset. Then there are deep, narrow, crooked “rills” +which may have been water-courses; also “clefts” about half a mile +wide, and often hundreds of miles long, like deep cracks in the surface +going straight through mountain and valley. + +The moon shares with the sun the advantage of being a good subject for +photography, though the planets are not. This is owing to her larger +apparent size, and the abundance of illumination. The consequence is +that the finest details of the moon, as seen in the largest telescope +in the world, may be reproduced at a cost within the reach of all. + +No certain changes have ever been observed; but several suspicions have +been expressed, especially as to the small crater _Linné_, in the _Mare +Serenitatis_. It is now generally agreed that no certainty can be +expected from drawings, and that for real evidence we must await the +verdict of photography. + +No trace of water or of an atmosphere has been found on the moon. It is +possible that the temperature is too low. In any case, no displacement +of a star by atmospheric refraction at occultation has been surely +recorded. The moon seems to be dead. + +The distance of the moon from the earth is just now the subject of +re-measurement. The base line is from Greenwich to Cape of Good Hope, +and the new feature introduced is the selection of a definite point on +a crater (Mösting A), instead of the moon’s edge, as the point whose +distance is to be measured. + +_The Inferior Planets_.—When the telescope was invented, the phases of +Venus attracted much attention; but the brightness of this planet, and +her proximity to the sun, as with Mercury also, seemed to be a bar to +the discovery of markings by which the axis and period of rotation +could be fixed. Cassini gave the rotation as twenty-three hours, by +observing a bright spot on her surface. Shröter made it 23h. 21m. 19s. +This value was supported by others. In 1890 Schiaparelli[2] announced +that Venus rotates, like our moon, once in one of her revolutions, and +always directs the same face to the sun. This property has also been +ascribed to Mercury; but in neither case has the evidence been +generally accepted. Twenty-four hours is probably about the period of +rotation for each of these planets. + +Several observers have claimed to have seen a planet within the orbit +of Mercury, either in transit over the sun’s surface or during an +eclipse. It has even been named _Vulcan_. These announcements would +have received little attention but for the fact that the motion of +Mercury has irregularities which have not been accounted for by known +planets; and Le Verrier[3] has stated that an intra-Mercurial planet or +ring of asteroids would account for the unexplained part of the motion +of the line of apses of Mercury’s orbit amounting to 38” per century. + +_Mars_.—The first study of the appearance of Mars by Miraldi led him to +believe that there were changes proceeding in the two white caps which +are seen at the planet’s poles. W. Herschel attributed these caps to +ice and snow, and the dates of his observations indicated a melting of +these ice-caps in the Martian summer. + +Schroter attributed the other markings on Mars to drifting clouds. But +Beer and Mädler, in 1830-39, identified the same dark spots as being +always in the same place, though sometimes blurred by mist in the local +winter. A spot sketched by Huyghens in 1672, one frequently seen by W. +Herschel in 1783, another by Arago in 1813, and nearly all the markings +recorded by Beer and Mädler in 1830, were seen and drawn by F. Kaiser +in Leyden during seventeen nights of the opposition of 1862 (_Ast. +Nacht._, No. 1,468), whence he deduced the period of rotation to be +24h. 37m. 22s.,62—or one-tenth of a second less than the period deduced +by R. A. Proctor from a drawing by Hooke in 1666. + +It must be noted that, if the periods of rotation both of Mercury and +Venus be about twenty-four hours, as seems probable, all the four +planets nearest to the sun rotate in the same period, while the great +planets rotate in about ten hours (Uranus and Neptune being still +indeterminate). + +The general surface of Mars is a deep yellow; but there are dark grey +or greenish patches. Sir John Herschel was the first to attribute the +ruddy colour of Mars to its soil rather than to its atmosphere. + +The observations of that keen-sighted observer Dawes led to the first +good map of Mars, in 1869. In the 1877 opposition Schiaparelli revived +interest in the planet by the discovery of canals, uniformly about +sixty miles wide, running generally on great circles, some of them +being three or four thousand miles long. During the opposition of +1881-2 the same observer re-observed the canals, and in twenty of them +he found the canals duplicated,[4] the second canal being always 200 to +400 miles distant from its fellow. + +The existence of these canals has been doubted. Mr. Lowell has now +devoted years to the subject, has drawn them over and over again, and +has photographed them; and accepts the explanation that they are +artificial, and that vegetation grows on their banks. Thus is revived +the old controversy between Whewell and Brewster as to the habitability +of the planets. The new arguments are not yet generally accepted. +Lowell believes he has, with the spectroscope, proved the existence of +water on Mars. + +One of the most unexpected and interesting of all telescopic +discoveries took place in the opposition of 1877, when Mars was +unusually near to the earth. The Washington Observatory had acquired +the fine 26-inch refractor, and Asaph Hall searched for satellites, +concealing the planet’s disc to avoid the glare. On August 11th he had +a suspicion of a satellite. This was confirmed on the 16th, and on the +following night a second one was added. They are exceedingly faint, and +can be seen only by the most powerful telescopes, and only at the times +of opposition. Their diameters are estimated at six or seven miles. It +was soon found that the first, Deimos, completes its orbit in 30h. 18m. +But the other, Phobos, at first was a puzzle, owing to its incredible +velocity being unsuspected. Later it was found that the period of +revolution was only 7h. 39m. 22s. Since the Martian day is twenty-four +and a half hours, this leads to remarkable results. Obviously the +easterly motion of the satellite overwhelms the diurnal rotation of the +planet, and Phobos must appear to the inhabitants, if they exist, to +rise in the west and set in the east, showing two or even three full +moons in a day, so that, sufficiently well for the ordinary purposes of +life, the hour of the day can be told by its phases. + +The discovery of these two satellites is, perhaps, the most interesting +telescopic visual discovery made with the large telescopes of the last +half century; photography having been the means of discovering all the +other new satellites except Jupiter’s fifth (in order of discovery). + +[Illustration: JUPITER. From a drawing by E. M. Antoniadi, showing +transit of a satellite’s shadow, the belts, and the “great red spot” +(_Monthly Notices_, R. A. S., vol. lix., pl. x.).] + +_Jupiter._—Galileo’s discovery of Jupiter’s satellites was followed by +the discovery of his belts. Zucchi and Torricelli seem to have seen +them. Fontana, in 1633, reported three belts. In 1648 Grimaldi saw but +two, and noticed that they lay parallel to the ecliptic. Dusky spots +were also noticed as transient. Hooke[5] measured the motion of one in +1664. In 1665 Cassini, with a fine telescope, 35-feet focal length, +observed many spots moving from east to west, whence he concluded that +Jupiter rotates on an axis like the earth. He watched an unusually +permanent spot during twenty-nine rotations, and fixed the period at +9h. 56m. Later he inferred that spots near the equator rotate quicker +than those in higher latitudes (the same as Carrington found for the +sun); and W. Herschel confirmed this in 1778-9. + +Jupiter’s rapid rotation ought, according to Newton’s theory, to be +accompanied by a great flattening at the poles. Cassini had noted an +oval form in 1691. This was confirmed by La Hire, Römer, and Picard. +Pound measured the ellipticity = 1/(13.25). + +W. Herschel supposed the spots to be masses of cloud in the +atmosphere—an opinion still accepted. Many of them were very permanent. +Cassini’s great spot vanished and reappeared nine times between 1665 +and 1713. It was close to the northern margin of the southern belt. +Herschel supposed the belts to be the body of the planet, and the +lighter parts to be clouds confined to certain latitudes. + +In 1665 Cassini observed transits of the four satellites, and also saw +their shadows on the planet, and worked out a lunar theory for Jupiter. +Mathematical astronomers have taken great interest in the perturbations +of the satellites, because their relative periods introduce peculiar +effects. Airy, in his delightful book, _Gravitation_, has reduced these +investigations to simple geometrical explanations. + +In 1707 and 1713 Miraldi noticed that the fourth satellite varies much +in brightness. W. Herschel found this variation to depend upon its +position in its orbit, and concluded that in the positions of +feebleness it is always presenting to us a portion of its surface, +which does not well reflect the sun’s light; proving that it always +turns the same face to Jupiter, as is the case with our moon. This fact +had also been established for Saturn’s fifth satellite, and may be true +for all satellites. + +In 1826 Struve measured the diameters of the four satellites, and found +them to be 2,429, 2,180, 3,561, and 3,046 miles. + +In modern times much interest has been taken in watching a rival to +Cassini’s famous spot. The “great red spot” was first observed by +Niesten, Pritchett, and Tempel, in 1878, as a rosy cloud attached to a +whitish zone beneath the dark southern equatorial band, shaped like the +new war balloons, 30,000 miles long and 7,000 miles across. The next +year it was brick-red. A white spot beside it completed a rotation in +less time by 5½ minutes than the red spot—a difference of 260 miles an +hour. Thus they came together again every six weeks, but the motions +did not continue uniform. The spot was feeble in 1882-4, brightened in +1886, and, after many changes, is still visible. + +Galileo’s great discovery of Jupiter’s four moons was the last word in +this connection until September 9th, 1892, when Barnard, using the +36-inch refractor of the Lick Observatory, detected a tiny spot of +light closely following the planet. This proved to be a new satellite +(fifth), nearer to the planet than any other, and revolving round it in +11h. 57m. 23s. Between its rising and setting there must be an interval +of 2½ Jovian days, and two or three full moons. The sixth and seventh +satellites were found by the examination of photographic plates at the +Lick Observatory in 1905, since which time they have been continuously +photographed, and their orbits traced, at Greenwich. On examining these +plates in 1908 Mr. Melotte detected the eighth satellite, which seems +to be revolving in a retrograde orbit three times as far from its +planet as the next one (seventh), in these two points agreeing with the +outermost of Saturn’s satellites (Phoebe). + +_Saturn._—This planet, with its marvellous ring, was perhaps the most +wonderful object of those first examined by Galileo’s telescope. He was +followed by Dominique Cassini, who detected bands like Jupiter’s belts. +Herschel established the rotation of the planet in 1775-94. From +observations during one hundred rotations he found the period to be +10h. 16m. 0s., 44. Herschel also measured the ratio of the polar to the +equatoreal diameter as 10:11. + +The ring was a complete puzzle to Galileo, most of all when the planet +reached a position where the plane of the ring was in line with the +earth, and the ring disappeared (December 4th, 1612). It was not until +1656 that Huyghens, in his small pamphlet _De Saturni Luna Observatio +Nova_, was able to suggest in a cypher the ring form; and in 1659, in +his Systema Saturnium, he gave his reasons and translated the cypher: +“The planet is surrounded by a slender flat ring, everywhere distinct +from its surface, and inclined to the ecliptic.” This theory explained +all the phases of the ring which had puzzled others. This ring was +then, and has remained ever since, a unique structure. We in this age +have got accustomed to it. But Huyghens’s discovery was received with +amazement. + +In 1675 Cassini found the ring to be double, the concentric rings being +separated by a black band—a fact which was placed beyond dispute by +Herschel, who also found that the thickness of the ring subtends an +angle less than 0".3. Shröter estimated its thickness at 500 miles. + +Many speculations have been advanced to explain the origin and +constitution of the ring. De Sejour said[6] that it was thrown off from +Saturn’s equator as a liquid ring, and afterwards solidified. He +noticed that the outside would have a greater velocity, and be less +attracted to the planet, than the inner parts, and that equilibrium +would be impossible; so he supposed it to have solidified into a number +of concentric rings, the exterior ones having the least velocity. + +Clerk Maxwell, in the Adams prize essay, gave a physico-mathematical +demonstration that the rings must be composed of meteoritic matter like +gravel. Even so, there must be collisions absorbing the energy of +rotation, and tending to make the rings eventually fall into the +planet. The slower motion of the external parts has been proved by the +spectroscope in Keeler’s hands, 1895. + +Saturn has perhaps received more than its share of attention owing to +these rings. This led to other discoveries. Huyghens in 1655, and J. D. +Cassini in 1671, discovered the sixth and eighth satellites (Titan and +Japetus). Cassini lost his satellite, and in searching for it found +Rhea (the fifth) in 1672, besides his old friend, whom he lost again. +He added the third and fourth in 1684 (Tethys and Dione). The first and +second (Mimas and Encelades) were added by Herschel in 1789, and the +seventh (Hyperion) simultaneously by Lassel and Bond in 1848. The ninth +(Phoebe) was found on photographs, by Pickering in 1898, with +retrograde motion; and he has lately added a tenth. + +The occasional disappearance of Cassini’s Japetus was found on +investigation to be due to the same causes as that of Jupiter’s fourth +satellite, and proves that it always turns the same face to the planet. + +_Uranus and Neptune_.—The splendid discoveries of Uranus and two +satellites by Sir William Herschel in 1787, and of Neptune by Adams and +Le Verrier in 1846, have been already described. Lassel added two more +satellites to Uranus in 1851, and found Neptune’s satellite in 1846. +All of the satellites of Uranus have retrograde motion, and their +orbits are inclined about 80° to the ecliptic. + +The spectroscope has shown the existence of an absorbing atmosphere on +Jupiter and Saturn, and there are suspicions that they partake +something of the character of the sun, and emit some light besides +reflecting solar light. On both planets some absorption lines seem to +agree with the aqueous vapour lines of our own atmosphere; while one, +which is a strong band in the red common to both planets, seems to +agree with a line in the spectrum of some reddish stars. + +Uranus and Neptune are difficult to observe spectroscopically, but +appear to have peculiar spectra agreeing together. Sometimes Uranus +shows Frauenhofer lines, indicating reflected solar light. But +generally these are not seen, and six broad bands of absorption appear. +One is the F. of hydrogen; another is the red-star line of Jupiter and +Saturn. Neptune is a very difficult object for the spectroscope. + +Quite lately[7] P. Lowell has announced that V. M. Slipher, at +Flagstaff Observatory, succeeded in 1907 in rendering some plates +sensitive far into the red. A reproduction is given of photographed +spectra of the four outermost planets, showing (1) a great number of +new lines and bands; (2) intensification of hydrogen F. and C. lines; +(3) a steady increase of effects (1) and (2) as we pass from Jupiter +and Saturn to Uranus, and a still greater increase in Neptune. + +_Asteroids_.—The discovery of these new planets has been described. At +the beginning of the last century it was an immense triumph to catch a +new one. Since photography was called into the service by Wolf, they +have been caught every year in shoals. It is like the difference +between sea fishing with the line and using a steam trawler. In the +1908 almanacs nearly seven hundred asteroids are included. The +computation of their perturbations and ephemerides by Euler’s and +Lagrange’s method of variable elements became so laborious that Encke +devised a special process for these, which can be applied to many other +disturbed orbits.[8] + +When a photograph is taken of a region of the heavens including an +asteroid, the stars are photographed as points because the telescope is +made to follow their motion; but the asteroids, by their proper motion, +appear as short lines. + +The discovery of Eros and the photographic attack upon its path have +been described in their relation to finding the sun’s distance. + +A group of four asteroids has lately been found, with a mean distance +and period equal to that of Jupiter. To three of these masculine names +have been given—Hector, Patroclus, Achilles; the other has not yet been +named. + +FOOTNOTES: + + [1] Langrenus (van Langren), F. Selenographia sive lumina austriae + philippica; Bruxelles, 1645. + + [2] _Astr. Nach._, 2,944. + + [3] _Acad. des Sc._, Paris; _C.R._, lxxxiii., 1876. + + [4] _Mem. Spettr. Ital._, xi., p. 28. + + [5] _R. S. Phil. Trans_., No. 1. + + [6] Grant’s _Hist. Ph. Ast_., p. 267. + + [7] _Nature_, November 12th, 1908. + + [8] _Ast. Nach_., Nos. 791, 792, 814, translated by G. B. Airy. _Naut. + Alm_., Appendix, 1856. + + + + +14. COMETS AND METEORS. + + +Ever since Halley discovered that the comet of 1682 was a member of the +solar system, these wonderful objects have had a new interest for +astronomers; and a comparison of orbits has often identified the return +of a comet, and led to the detection of an elliptic orbit where the +difference from a parabola was imperceptible in the small portion of +the orbit visible to us. A remarkable case in point was the comet of +1556, of whose identity with the comet of 1264 there could be little +doubt. Hind wanted to compute the orbit more exactly than Halley had +done. He knew that observations had been made, but they were lost. +Having expressed his desire for a search, all the observations of +Fabricius and of Heller, and also a map of the comet’s path among the +stars, were eventually unearthed in the most unlikely manner, after +being lost nearly three hundred years. Hind and others were certain +that this comet would return between 1844 and 1848, but it never +appeared. + +When the spectroscope was first applied to finding the composition of +the heavenly bodies, there was a great desire to find out what comets +are made of. The first opportunity came in 1864, when Donati observed +the spectrum of a comet, and saw three bright bands, thus proving that +it was a gas and at least partly self-luminous. In 1868 Huggins +compared the spectrum of Winnecke’s comet with that of a Geissler tube +containing olefiant gas, and found exact agreement. Nearly all comets +have shown the same spectrum.[1] A very few comets have given bright +band spectra differing from the normal type. Also a certain kind of +continuous spectrum, as well as reflected solar light showing +Frauenhofer lines, have been seen. + +[Illustration: COPY OF THE DRAWING MADE BY PAUL FABRICIUS. +To define the path of comet 1556. After being lost for 300 years, this +drawing was recovered by the prolonged efforts of Mr. Hind and +Professor Littrow in 1856.] + +When Wells’s comet, in 1882, approached very close indeed to the sun, +the spectrum changed to a mono-chromatic yellow colour, due to sodium. + +For a full account of the wonders of the cometary world the reader is +referred to books on descriptive astronomy, or to monographs on +comets.[2] Nor can the very uncertain speculations about the structure +of comets’ tails be given here. A new explanation has been proposed +almost every time that a great discovery has been made in the theory of +light, heat, chemistry, or electricity. + +Halley’s comet remained the only one of which a prediction of the +return had been confirmed, until the orbit of the small, ill-defined +comet found by Pons in 1819 was computed by Encke, and found to have a +period of 3 1/3 years. It was predicted to return in 1822, and was +recognised by him as identical with many previous comets. This comet, +called after Encke, has showed in each of its returns an inexplicable +reduction of mean distance, which led to the assertion of a resisting +medium in space until a better explanation could be found.[3] + +Since that date fourteen comets have been found with elliptic orbits, +whose aphelion distances are all about the same as Jupiter’s mean +distance; and six have an aphelion distance about ten per cent, greater +than Neptune’s mean distance. Other comets are similarly associated +with the planets Saturn and Uranus. + +The physical transformations of comets are among the most wonderful of +unexplained phenomena in the heavens. But, for physical astronomers, +the greatest interest attaches to the reduction of radius vector of +Encke’s comet, the splitting of Biela’s comet into two comets in 1846, +and the somewhat similar behaviour of other comets. It must be noted, +however, that comets have a sensible size, that all their parts cannot +travel in exactly the same orbit under the sun’s gravitation, and that +their mass is not sufficient to retain the parts together very +forcibly; also that the inevitable collision of particles, or else +fluid friction, is absorbing energy, and so reducing the comet’s +velocity. + +In 1770 Lexell discovered a comet which, as was afterwards proved by +investigations of Lexell, Burchardt, and Laplace, had in 1767 been +deflected by Jupiter out of an orbit in which it was invisible from the +earth into an orbit with a period of 5½ years, enabling it to be seen. +In 1779 it again approached Jupiter closer than some of his satellites, +and was sent off in another orbit, never to be again recognised. + +But our interest in cometary orbits has been added to by the discovery +that, owing to the causes just cited, a comet, if it does not separate +into discrete parts like Biela’s, must in time have its parts spread +out so as to cover a sensible part of the orbit, and that, when the +earth passes through such part of a comet’s orbit, a meteor shower is +the result. + +A magnificent meteor shower was seen in America on November 12th-13th, +1833, when the paths of the meteors all seemed to radiate from a point +in the constellation Leo. A similar display had been witnessed in +Mexico by Humboldt and Bonpland on November 12th, 1799. H. A. Newton +traced such records back to October 13th, A.D. 902. The orbital motion +of a cloud or stream of small particles was indicated. The period +favoured by H. A. Newton was 354½ days; another suggestion was 375½ +days, and another 33¼ years. He noticed that the advance of the date of +the shower between 902 and 1833, at the rate of one day in seventy +years, meant a progression of the node of the orbit. Adams undertook to +calculate what the amount would be on all the five suppositions that +had been made about the period. After a laborious work, he found that +none gave one day in seventy years except the 33¼-year period, which +did so exactly. H. A. Newton predicted a return of the shower on the +night of November 13th-14th, 1866. He is now dead; but many of us are +alive to recall the wonder and enthusiasm with which we saw this +prediction being fulfilled by the grandest display of meteors ever seen +by anyone now alive. + +The _progression_ of the nodes proved the path of the meteor stream to +be retrograde. The _radiant_ had almost the exact longitude of the +point towards which the earth was moving. This proved that the meteor +cluster was at perihelion. The period being known, the eccentricity of +the orbit was obtainable, also the orbital velocity of the meteors in +perihelion; and, by comparing this with the earth’s velocity, the +latitude of the radiant enabled the inclination to be determined, while +the longitude of the earth that night was the longitude of the node. In +such a way Schiaparelli was able to find first the elements of the +orbit of the August meteor shower (Perseids), and to show its identity +with the orbit of Tuttle’s comet 1862.iii. Then, in January 1867, Le +Verrier gave the elements of the November meteor shower (Leonids); and +Peters, of Altona, identified these with Oppolzer’s elements for +Tempel’s comet 1866—Schiaparelli having independently attained both of +these results. Subsequently Weiss, of Vienna, identified the meteor +shower of April 20th (Lyrids) with comet 1861. Finally, that +indefatigable worker on meteors, A. S. Herschel, added to the number, +and in 1878 gave a list of seventy-six coincidences between cometary +and meteoric orbits. + +Cometary astronomy is now largely indebted to photography, not merely +for accurate delineations of shape, but actually for the discovery of +most of them. The art has also been applied to the observation of +comets at distances from their perihelia so great as to prevent their +visual observation. Thus has Wolf, of Heidelburg, found upon old plates +the position of comet 1905.v., as a star of the 15.5 magnitude, 783 +days before the date of its discovery. From the point of view of the +importance of finding out the divergence of a cometary orbit from a +parabola, its period, and its aphelion distance, this increase of range +attains the very highest value. + +The present Astronomer Royal, appreciating this possibility, has been +searching by photography for Halley’s comet since November, 1907, +although its perihelion passage will not take place until April, 1910. + +FOOTNOTES: + + [1] In 1874, when the writer was crossing the Pacific Ocean in H.M.S. + “Scout,” Coggia’s comet unexpectedly appeared, and (while Colonel + Tupman got its positions with the sextant) he tried to use the prism + out of a portable direct-vision spectroscope, without success until it + was put in front of the object-glass of a binocular, when, to his + great joy, the three band images were clearly seen. + + [2] Such as _The World of Comets_, by A. Guillemin; _History of + Comets_, by G. R. Hind, London, 1859; _Theatrum Cometicum_, by S. de + Lubienietz, 1667; _Cometographie_, by Pingré, Paris, 1783; _Donati’s + Comet_, by Bond. + + [3] The investigations by Von Asten (of St. Petersburg) seem to + support, and later ones, especially those by Backlund (also of St. + Petersburg), seem to discredit, the idea of a resisting medium. + + + + +15. THE FIXED STARS AND NEBULÆ. + + +Passing now from our solar system, which appears to be subject to the +action of the same forces as those we experience on our globe, there +remains an innumerable host of fixed stars, nebulas, and nebulous +clusters of stars. To these the attention of astronomers has been more +earnestly directed since telescopes have been so much enlarged. +Photography also has enabled a vast amount of work to be covered in a +comparatively short period, and the spectroscope has given them the +means, not only of studying the chemistry of the heavens, but also of +detecting any motion in the line of sight from less than a mile a +second and upwards in any star, however distant, provided it be bright +enough. + +[Illustration: SIR WILLIAM HERSCHEL, F.R.S.—1738-1822. +Painted by Lemuel F. Abbott; National Portrait Gallery, Room XX.] + +In the field of telescopic discovery beyond our solar system there is +no one who has enlarged our knowledge so much as Sir William Herschel, +to whom we owe the greatest discovery in dynamical astronomy among the +stars—viz., that the law of gravitation extends to the most distant +stars, and that many of them describe elliptic orbits about each other. +W. Herschel was born at Hanover in 1738, came to England in 1758 as a +trained musician, and died in 1822. He studied science when he could, +and hired a telescope, until he learnt to make his own specula and +telescopes. He made 430 parabolic specula in twenty-one years. He +discovered 2,500 nebulæ and 806 double stars, counted the stars in +3,400 guage-fields, and compared the principal stars photometrically. + +Some of the things for which he is best known were results of those +accidents that happen only to the indefatigable enthusiast. Such was +the discovery of Uranus, which led to funds being provided for +constructing his 40-feet telescope, after which, in 1786, he settled at +Slough. In the same way, while trying to detect the annual parallax of +the stars, he failed in that quest, but discovered binary systems of +stars revolving in ellipses round each other; just as Bradley’s attack +on stellar parallax failed, but led to the discovery of aberration, +nutation, and the true velocity of light. + +_Parallax_.—The absence of stellar parallax was the great objection to +any theory of the earth’s motion prior to Kepler’s time. It is true +that Kepler’s theory itself could have been geometrically expressed +equally well with the earth or any other point fixed. But in Kepler’s +case the obviously implied physical theory of the planetary motions, +even before Newton explained the simplicity of conception involved, +made astronomers quite ready to waive the claim for a rigid proof of +the earth’s motion by measurement of an annual parallax of stars, which +they had insisted on in respect of Copernicus’s revival of the idea of +the earth’s orbital motion. + +Still, the desire to measure this parallax was only intensified by the +practical certainty of its existence, and by repeated failures. The +attempts of Bradley failed. The attempts of Piazzi and Brinkley,[1] +early in the nineteenth century, also failed. The first successes, +afterwards confirmed, were by Bessel and Henderson. Both used stars +whose proper motion had been found to be large, as this argued +proximity. Henderson, at the Cape of Good Hope, observed α Centauri, +whose annual proper motion he found to amount to 3".6, in 1832-3; and a +few years later deduced its parallax 1".16. His successor at the Cape, +Maclear, reduced this to 0".92. + +In 1835 Struve assigned a doubtful parallax of 0".261 to Vega (α Lyræ). +But Bessel’s observations, between 1837 and 1840, of 61 Cygni, a star +with the large proper motion of over 5”, established its annual +parallax to be 0".3483; and this was confirmed by Peters, who found the +value 0".349. + +Later determinations for α2 Centauri, by Gill,[2] make its parallax +0".75—This is the nearest known fixed star; and its light takes 4 1/3 +years to reach us. The lightyear is taken as the unit of measurement in +the starry heavens, as the earth’s mean distance is “the astronomical +unit” for the solar system.[3] The proper motions and parallaxes +combined tell us the velocity of the motion of these stars across the +line of sight: α Centauri 14.4 miles a second=4.2 astronomical units a +year; 61 Cygni 37.9 miles a second=11.2 astronomical units a year. +These successes led to renewed zeal, and now the distances of many +stars are known more or less accurately. + +Several of the brightest stars, which might be expected to be the +nearest, have not shown a parallax amounting to a twentieth of a second +of arc. Among these are Canopus, α Orionis, α Cygni, β Centauri, and γ +Cassiopeia. Oudemans has published a list of parallaxes observed.[4] + +_Proper Motion._—In 1718 Halley[5] detected the proper motions of +Arcturus and Sirius. In 1738 J. Cassinis[6] showed that the former had +moved five minutes of arc since Tycho Brahe fixed its position. In 1792 +Piazzi noted the motion of 61 Cygni as given above. For a long time the +greatest observed proper motion was that of a small star 1830 +Groombridge, nearly 7” a year; but others have since been found +reaching as much as 10”. + +Now the spectroscope enables the motion of stars to be detected at a +single observation, but only that part of the motion that is in the +line of sight. For a complete knowledge of a star’s motion the proper +motion and parallax must also be known. + +When Huggins first applied the Doppler principle to measure velocities +in the line of sight,[7] the faintness of star spectra diminished the +accuracy; but Vögel, in 1888, overcame this to a great extent by long +exposures of photographic plates. + +It has often been noticed that stars which seem to belong to a group of +nearly uniform magnitude have the same proper motion. The spectroscope +has shown that these have also often the same velocity in the line of +sight. Thus in the Great Bear, β, γ, δ, ε, ζ, all agree as to angular +proper motion. δ was too faint for a spectroscopic measurement, but all +the others have been shown to be approaching us at a rate of twelve to +twenty miles a second. The same has been proved for proper motion, and +line of sight motion, in the case of Pleiades and other groups. + +Maskelyne measured many proper motions of stars, from which W. +Herschel[8] came to the conclusion that these apparent motions are for +the most part due to a motion of the solar system in space towards a +point in the constellation Hercules, R.A. 257°; N. Decl. 25°. This +grand discovery has been amply confirmed, and, though opinions differ +as to the exact direction, it happens that the point first indicated by +Herschel, from totally insufficient data, agrees well with modern +estimates. + +Comparing the proper motions and parallaxes to get the actual velocity +of each star relative to our system, C.L. Struve found the probable +velocity of the solar system in space to be fifteen miles a second, or +five astronomical units a year. + +The work of Herschel in this matter has been checked by comparing +spectroscopic velocities in the line of sight which, so far as the +sun’s motion is concerned, would give a maximum rate of approach for +stars near Hercules, a maximum rate of recession for stars in the +opposite part of the heavens, and no effect for stars half-way between. +In this way the spectroscope has confirmed generally Herschel’s view of +the direction, and makes the velocity eleven miles a second, or nearly +four astronomical units a year. + +The average proper motion of a first magnitude star has been found to +be 0".25 annually, and of a sixth magnitude star 0".04. But that all +bright stars are nearer than all small stars, or that they show greater +proper motion for that reason, is found to be far from the truth. Many +statistical studies have been made in this connection, and interesting +results may be expected from this treatment in the hands of Kapteyn of +Groningen, and others.[9] + +On analysis of the directions of proper motions of stars in all parts +of the heavens, Kapteyn has shown[10] that these indicate, besides the +solar motion towards Hercules, two general drifts of stars in nearly +opposite directions, which can be detected in any part of the heavens. +This result has been confirmed from independent data by Eddington +(_R.A.S., M.N._) and Dyson (_R.S.E. Proc._). + +Photography promises to assist in the measurement of parallax and +proper motions. Herr Pulfrich, of the firm of Carl Zeiss, has vastly +extended the applications of stereoscopic vision to astronomy—a subject +which De la Rue took up in the early days of photography. He has made a +stereo-comparator of great beauty and convenience for comparing +stereoscopically two star photographs taken at different dates. Wolf of +Heidelberg has used this for many purposes. His investigations +depending on the solar motion in space are remarkable. He photographs +stars in a direction at right angles to the line of the sun’s motion. +He has taken photographs of the same region fourteen years apart, the +two positions of his camera being at the two ends of a base-line over +5,000,000,000 miles apart, or fifty-six astronomical units. On +examining these stereoscopically, some of the stars rise out of the +general plane of the stars, and seem to be much nearer. Many of the +stars are thus seen to be suspended in space at different distances +corresponding exactly to their real distances from our solar system, +except when their proper motion interferes. The effect is most +striking; the accuracy of measurement exceeds that of any other method +of measuring such displacements, and it seems that with a long interval +of time the advantage of the method increases. + +_Double Stars._—The large class of double stars has always been much +studied by amateurs, partly for their beauty and colour, and partly as +a test for telescopic definition. Among the many unexplained stellar +problems there is one noticed in double stars that is thought by some +to be likely to throw light on stellar evolution. It is this: There are +many instances where one star of the pair is comparatively faint, and +the two stars are contrasted in colour; and in every single case the +general colour of the faint companion is invariably to be classed with +colours more near to the blue end of the spectrum than that of the +principal star. + +_Binary Stars._—Sir William Herschel began his observations of double +stars in the hope of discovering an annual parallax of the stars. In +this he was following a suggestion of Galileo’s. The presumption is +that, if there be no physical connection between the stars of a pair, +the largest is the nearest, and has the greatest parallax. So, by +noting the distance between the pair at different times of the year, a +delicate test of parallax is provided, unaffected by major instrumental +errors. + +Herschel did, indeed, discover changes of distance, but not of the +character to indicate parallax. Following this by further observation, +he found that the motions were not uniform nor rectilinear, and by a +clear analysis of the movements he established the remarkable and +wholly unexpected fact that in all these cases the motion is due to a +revolution about their common centre of gravity.[11] He gave the +approximate period of revolution of some of these: Castor, 342 years; δ +Serpentis, 375 years; γ Leonis, 1,200 years; ε Bootis, 1,681 years. + +Twenty years later Sir John Herschel and Sir James South, after +re-examination of these stars, confirmed[12] and extended the results, +one pair of Coronæ having in the interval completed more than a whole +revolution. + +It is, then, to Sir William Herschel that we owe the extension of the +law of gravitation, beyond the limits of the solar system, to the whole +universe. His observations were confirmed by F.G.W. Struve (born 1793, +died 1864), who carried on the work at Dorpat. But it was first to +Savary,[13] and later to Encke and Sir John Herschel, that we owe the +computation of the elliptic elements of these stars; also the resulting +identification of their law of force with Newton’s force of gravitation +applied to the solar system, and the force that makes an apple fall to +the ground. As Grant well says in his _History_: “This may be justly +asserted to be one of the most sublime truths which astronomical +science has hitherto disclosed to the researches of the human mind.” + +Latterly the best work on double stars has been done by S. W. +Burnham,[14] at the Lick Observatory. The shortest period he found was +eleven years (κ Pegasi). In the case of some of these binaries the +parallax has been measured, from which it appears that in four of the +surest cases the orbits are about the size of the orbit of Uranus, +these being probably among the smallest stellar orbits. + +The law of gravitation having been proved to extend to the stars, a +discovery (like that of Neptune in its origin, though unlike it in the +labour and originality involved in the calculation) that entrances the +imagination became possible, and was realised by Bessel—the discovery +of an unknown body by its gravitational disturbance on one that was +visible. In 1834 and 1840 he began to suspect a want of uniformity in +the proper motion of Sirius and Procyon respectively. In 1844, in a +letter to Sir John Herschel,[15] he attributed these irregularities in +each case to the attraction of an invisible companion, the period of +revolution of Sirius being about half a century. Later he said: “I +adhere to the conviction that Procyon and Sirius form real binary +systems, consisting of a visible and an invisible star. There is no +reason to suppose luminosity an essential quality of cosmical bodies. +The visibility of countless stars is no argument against the +invisibility of countless others.” This grand conception led Peters to +compute more accurately the orbit, and to assign the place of the +invisible companion of Sirius. In 1862 Alvan G. Clark was testing a new +18-inch object-glass (now at Chicago) upon Sirius, and, knowing nothing +of these predictions, actually found the companion in the very place +assigned to it. In 1896 the companion of Procyon was discovered by +Professor Schaeberle at the Lick Observatory. + +Now, by the refined parallax determinations of Gill at the Cape, we +know that of Sirius to be 0".38. From this it has been calculated that +the mass of Sirius equals two of our suns, and its intrinsic brightness +equals twenty suns; but the companion, having a mass equal to our sun, +has only a five-hundredth part of the sun’s brightness. + +_Spectroscopic Binaries_.—On measuring the velocity of a star in the +line of sight at frequent intervals, periodic variations have been +found, leading to a belief in motion round an invisible companion. +Vogel, in 1889, discovered this in the case of Spica (α Virginis), +whose period is 4d. 0h. 19m., and the diameter of whose orbit is six +million miles. Great numbers of binaries of this type have since then +been discovered, all of short period. + +Also, in 1889, Pickering found that at regular intervals of fifty-two +days the lines in the spectrum of ζ of the Great Bear are duplicated, +indicating a relative velocity, equal to one hundred miles a second, of +two components revolving round each other, of which that apparently +single star must be composed. + +It would be interesting, no doubt, to follow in detail the accumulating +knowledge about the distances, proper motions, and orbits of the stars; +but this must be done elsewhere. Enough has been said to show how +results are accumulating which must in time unfold to us the various +stellar systems and their mutual relationships. + +_Variable Stars._—It has often happened in the history of different +branches of physical science that observation and experiment were so +far ahead of theory that hopeless confusion appeared to reign; and then +one chance result has given a clue, and from that time all differences +and difficulties in the previous researches have stood forth as natural +consequences, explaining one another in a rational sequence. So we find +parallax, proper motion, double stars, binary systems, variable stars, +and new stars all bound together. + +The logical and necessary explanation given of the cause of ordinary +spectroscopic binaries, and of irregular proper motions of Sirius and +Procyon, leads to the inference that if ever the plane of such a binary +orbit were edge-on to us there ought to be an eclipse of the luminous +partner whenever the non-luminous one is interposed between us. This +should give rise either to intermittence in the star’s light or else to +variability. It was by supposing the existence of a dark companion to +Algol that its discoverer, Goodricke of York,[16] in 1783, explained +variable stars of this type. Algol (β Persei) completes the period of +variable brightness in 68.8 hours. It loses three-fifths of its light, +and regains it in twelve hours. In 1889 Vogel,[17] with the Potsdam +spectrograph, actually found that the luminous star is receding before +each eclipse, and approaching us after each eclipse; thus entirely +supporting Goodricke’s opinion. There are many variables of the Algol +type, and information is steadily accumulating. But all variable stars +do not suffer the sudden variations of Algol. There are many types, and +the explanations of others have not proved so easy. + +The Harvard College photographs have disclosed the very great +prevalence of variability, and this is certainly one of the lines in +which modern discovery must progress. + +Roberts, in South Africa, has done splendid work on the periods of +variables of the Algol type. + +_New Stars_.—Extreme instances of variable stars are the new stars such +as those detected by Hipparchus, Tycho Brahe, and Kepler, of which many +have been found in the last half-century. One of the latest great +“Novæ” was discovered in Auriga by a Scotsman, Dr. Anderson, on +February 1st, 1892, and, with the modesty of his race, he communicated +the fact to His Majesty’s Astronomer for Scotland on an unsigned +post-card.[18] Its spectrum was observed and photographed by Huggins +and many others. It was full of bright lines of hydrogen, calcium, +helium, and others not identified. The astounding fact was that lines +were shown in pairs, bright and dark, on a faint continuous spectrum, +indicating apparently that a dark body approaching us at the rate of +550 miles a second[19] was traversing a cold nebulous atmosphere, and +was heated to incandescence by friction, like a meteor in our +atmosphere, leaving a luminous train behind it. It almost disappeared, +and on April 26th it was of the sixteenth magnitude; but on August 17th +it brightened to the tenth, showing the principal nebular band in its +spectrum, and no sign of approach or recession. It was as if it emerged +from one part of the nebula, cooled down, and rushed through another +part of the nebula, rendering the nebular gas more luminous than +itself.[20] + +Since 1892 one Nova after another has shown a spectrum as described +above, like a meteor rushing towards us and leaving a train behind, for +this seems to be the obvious meaning of the spectra. + +The same may be said of the brilliant Nova Persei, brighter at its best +than Capella, and discovered also by Dr. Anderson on February 22nd, +1901. It increased in brightness as it reached the densest part of the +nebula, then it varied for some weeks by a couple of magnitudes, up and +down, as if passing through separate nebular condensations. In +February, 1902, it could still be seen with an opera-glass. As with the +other Novæ, when it first dashed into the nebula it was vaporised and +gave a continuous spectrum with dark lines of hydrogen and helium. It +showed no bright lines paired with the dark ones to indicate a train +left behind; but in the end its own luminosity died out, and the +nebular spectrum predominated. + +The nebular illumination as seen in photographs, taken from August to +November, seemed to spread out slowly in a gradually increasing circle +at the rate of 90” in forty-eight days. Kapteyn put this down to the +velocity of light, the original outburst sending its illumination to +the nebulous gas and illuminating a spherical shell whose radius +increased at the velocity of light. This supposition seems correct, in +which case it can easily be shown from the above figures that the +distance of this Nova was 300 light years. + +_Star Catalogues._—Since the days of very accurate observations +numerous star-catalogues have been produced by individuals or by +observatories. Bradley’s monumental work may be said to head the list. +Lacaille’s, in the Southern hemisphere, was complementary. Then Piazzi, +Lalande, Groombridge, and Bessel were followed by Argelander with his +324,000 stars, Rumker’s Paramatta catalogue of the southern hemisphere, +and the frequent catalogues of national observatories. Later the +Astronomische Gesellschaft started their great catalogue, the combined +work of many observatories. Other southern ones were Gould’s at Cordova +and Stone’s at the Cape. + +After this we have a new departure. Gill at the Cape, having the comet +1882.ii. all to himself in those latitudes, wished his friends in +Europe to see it, and employed a local photographer to strap his camera +to the observatory equatoreal, driven by clockwork, and adjusted on the +comet by the eye. The result with half-an-hour’s exposure was good, so +he tried three hours. The result was such a display of sharp star +images that he resolved on the Cape Photographic Durchmusterung, which +after fourteen years, with Kapteyn’s aid in reducing, was completed. +Meanwhile the brothers Henry, of Paris, were engaged in going over +Chacornac’s zodiacal stars, and were about to catalogue the Milky Way +portion, a serious labour, when they saw Gill’s Comet photograph and +conceived the idea of doing the rest of their work by photography. Gill +had previously written to Admiral Mouchez, of the Paris Observatory, +and explained to him his project for charting the heavens +photographically, by combining the work of many observatories. This led +Admiral Mouchez to support the brothers Henry in their scheme.[21] +Gill, having got his own photographic work underway, suggested an +international astrographic chart, the materials for different zones to +be supplied by observatories of all nations, each equipped with similar +photographic telescopes. At a conference in Paris, 1887, this was +decided on, the stars on the charts going down to the fourteenth +magnitude, and the catalogues to the eleventh. + +[Illustration: GREAT COMET, NOV. 14TH, 1882. +(Exposure 2hrs. 20m.) By kind permission of Sir David Gill. From this +photograph originated all stellar chart-photography.] + +This monumental work is nearing completion. The labour involved was +immense, and the highest skill was required for devising instruments +and methods to read off the star positions from the plates. + +Then we have the Harvard College collection of photographic plates, +always being automatically added to; and their annex at Arequipa in +Peru. + +Such catalogues vary in their degree of accuracy; and fundamental +catalogues of standard stars have been compiled. These require +extension, because the differential methods of the heliometer and the +camera cannot otherwise be made absolute. + +The number of stars down to the fourteenth magnitude may be taken at +about 30,000,000; and that of all the stars visible in the greatest +modern telescopes is probably about 100,000,000. + +_Nebulæ and Star-clusters._—Our knowledge of nebulæ really dates from +the time of W. Herschel. In his great sweeps of the heavens with his +giant telescopes he opened in this direction a new branch of astronomy. +At one time he held that all nebulæ might be clusters of innumerable +minute stars at a great distance. Then he recognised the different +classes of nebulæ, and became convinced that there is a widely-diffused +“shining fluid” in space, though many so-called nebulæ could be +resolved by large telescopes into stars. He considered that the Milky +Way is a great star cluster, whose form may be conjectured from +numerous star-gaugings. He supposed that the compact “planetary nebulæ” +might show a stage of evolution from the diffuse nebulæ, and that his +classifications actually indicate various stages of development. Such +speculations, like those of the ancients about the solar system, are +apt to be harmful to true progress of knowledge unless in the hands of +the ablest mathematical physicists; and Herschel violated their +principles in other directions. But here his speculations have +attracted a great deal of attention, and, with modifications, are +accepted, at least as a working hypothesis, by a fair number of people. + +When Sir John Herschel had extended his father’s researches into the +Southern Hemisphere he was also led to the belief that some nebulae +were a phosphorescent material spread through space like fog or mist. + +Then his views were changed by the revelations due to the great +discoveries of Lord Rosse with his gigantic refractor,[22] when one +nebula after another was resolved into a cluster of minute stars. At +that time the opinion gained ground that with increase of telescopic +power this would prove to be the case with all nebulæ. + +In 1864 all doubt was dispelled by Huggins[23] in his first examination +of the spectrum of a nebula, and the subsequent extension of this +observation to other nebulæ; thus providing a certain test which +increase in the size of telescopes could never have given. In 1864 +Huggins found that all true nebulae give a spectrum of bright lines. +Three are due to hydrogen; two (discovered by Copeland) are helium +lines; others are unknown. Fifty-five lines have been photographed in +the spectrum of the Orion nebula. It seems to be pretty certain that +all true nebulae are gaseous, and show almost exactly the same +spectrum. + +Other nebulæ, and especially the white ones like that in Andromeda, +which have not yet been resolved into stars, show a continuous +spectrum; others are greenish and give no lines. + +A great deal has to be done by the chemist before the astronomer can be +on sure ground in drawing conclusions from certain portions of his +spectroscopic evidence. + +The light of the nebulas is remarkably actinic, so that photography has +a specially fine field in revealing details imperceptible in the +telescope. In 1885 the brothers Henry photographed, round the star Maia +in the Pleiades, a spiral nebula 3’ long, as bright on the plate as +that star itself, but quite invisible in the telescope; and an exposure +of four hours revealed other new nebula in the same district. That +painstaking and most careful observer, Barnard, with 10¼ hours’ +exposure, extended this nebulosity for several degrees, and discovered +to the north of the Pleiades a huge diffuse nebulosity, in a region +almost destitute of stars. By establishing a 10-inch instrument at an +altitude of 6,000 feet, Barnard has revealed the wide distribution of +nebular matter in the constellation Scorpio over a space of 4° or 5° +square. Barnard asserts that the “nebular hypothesis” would have been +killed at its birth by a knowledge of these photographs. Later he has +used still more powerful instruments, and extended his discoveries. + +The association of stars with planetary nebulæ, and the distribution of +nebulæ in the heavens, especially in relation to the Milky Way, are +striking facts, which will certainly bear fruit when the time arrives +for discarding vague speculations, and learning to read the true +physical structure and history of the starry universe. + +_Stellar Spectra._—When the spectroscope was first available for +stellar research, the leaders in this branch of astronomy were Huggins +and Father Secchi,[24] of Rome. The former began by devoting years of +work principally to the most accurate study of a few stars. The latter +devoted the years from 1863 to 1867 to a general survey of the whole +heavens, including 4,000 stars. He divided these into four principal +classes, which have been of the greatest service. Half of his stars +belonged to the first class, including Sirius, Vega, Regulus, Altair. +The characteristic feature of their spectra is the strength and breadth +of the hydrogen lines and the extreme faintness of the metallic lines. +This class of star is white to the eye, and rich in ultra violet light. + +The second class includes about three-eighths of his stars, including +Capella, Pollux, and Arcturus. These stars give a spectrum like that of +our sun, and appear yellowish to the eye. + +The third class includes α Herculis, α Orionis (Betelgeux), Mira Ceti, +and about 500 red and variable stars. The spectrum has fluted bands +shaded from blue to red, and sharply defined at the more refrangible +edge. + +The fourth class is a small one, containing no stars over fifth +magnitude, of which 152 Schjellerup, in Canes Venatici, is a good +example. This spectrum also has bands, but these are shaded on the +violet side and sharp on the red side. They are due to carbon in some +form. These stars are ruby red in the telescope. + +It would appear, then, that all stars are suns with continuous spectra, +and the classes are differentiated by the character of the absorbent +vapours of their atmospheres. + +It is very likely that, after the chemists have taught us how to +interpret all the varieties of spectrum, it will be possible to ascribe +the different spectrum-classes to different stages in the life-history +of every star. Already there are plenty of people ready to lay down +arbitrary assumptions about the lessons to be drawn from stellar +spectra. Some say that they know with certainty that each star begins +by being a nebula, and is condensed and heated by condensation until it +begins to shine as a star; that it attains a climax of temperature, +then cools down, and eventually becomes extinct. They go so far as to +declare that they know what class of spectrum belongs to each stage of +a star’s life, and how to distinguish between one that is increasing +and another that is decreasing in temperature. + +The more cautious astronomers believe that chemistry is not +sufficiently advanced to justify all of these deductions; that, until +chemists have settled the lately raised question of the transmutation +of elements, no theory can be sure. It is also held that until they +have explained, without room for doubt, the reasons for the presence of +some lines, and the absence of others, of any element in a stellar +spectrum; why the arc-spectrum of each element differs from its spark +spectrum; what are all the various changes produced in the spectrum of +a gas by all possible concomitant variations of pressure and +temperature; also the meanings of all the flutings in the spectra of +metalloids and compounds; and other equally pertinent matters—until +that time arrives the part to be played by the astronomer is one of +observation. By all means, they say, make use of “working hypotheses” +to add an interest to years of laborious research, and to serve as a +guide to the direction of further labours; but be sure not to fall into +the error of calling any mere hypothesis a theory. + +_Nebular Hypothesis._—The Nebular Hypothesis, which was first, as it +were, tentatively put forward by Laplace as a note in his _Système du +Monde_, supposes the solar system to have been a flat, disk-shaped +nebula at a high temperature in rapid rotation. In cooling it +condensed, leaving revolving rings at different distances from the +centre. These themselves were supposed to condense into the nucleus for +a rotating planet, which might, in contracting, again throw off rings +to form satellites. The speculation can be put in a really attractive +form, but is in direct opposition to many of the actual facts; and so +long as it is not favoured by those who wish to maintain the position +of astronomy as the most exact of the sciences—exact in its facts, +exact in its logic—this speculation must be recorded by the historian, +only as he records the guesses of the ancient Greeks--as an interesting +phase in the history of human thought. + +Other hypotheses, having the same end in view, are the meteoritic +hypothesis of Lockyer and the planetesimal hypothesis that has been +largely developed in the United States. These can best be read in the +original papers to various journals, references to which may be found +in the footnotes of Miss Clerke’s _History of Astronomy during the +Nineteenth Century_. The same can be said of Bredichin’s hypothesis of +comets’ tails, Arrhenius’s book on the applications of the theory of +light repulsion, the speculations on radium, the origin of the sun’s +heat and the age of the earth, the electron hypothesis of terrestrial +magnetism, and a host of similar speculations, all combining to throw +an interesting light on the evolution of a modern train of thought that +seems to delight in conjecture, while rebelling against that strict +mathematical logic which has crowned astronomy as the queen of the +sciences. + +FOOTNOTES: + + [1] _R. S. Phil Trans_., 1810 and 1817-24. + + [2] One of the most valuable contributions to our knowledge of stellar + parallaxes is the result of Gill’s work (_Cape Results_, vol. iii., + part ii., 1900). + + [3] Taking the velocity of light at 186,000 miles a second, and the + earth’s mean distance at 93,000,000 miles, 1 + light-year=5,865,696,000,000 miles or 63,072 astronomical units; 1 + astronomical unit a year=2.94 miles a second; and the earth’s orbital + velocity=18.5 miles a second. + + [4] Ast. Nacht., 1889. + + [5] R. S. Phil. Trans., 1718. + + [6] Mem. Acad. des Sciences, 1738, p. 337. + + [7] R. S Phil. Trans., 1868. + + [8] _R.S. Phil Trans._, 1783. + + [9] See Kapteyn’s address to the Royal Institution, 1908. Also Gill’s + presidential address to the British Association, 1907. + + [10] _Brit. Assoc. Rep._, 1905. + + [11] R. S. Phil. Trans., 1803, 1804. + + [12] Ibid, 1824. + + [13] Connaisance des Temps, 1830. + + [14] _R. A. S. Mem._, vol. xlvii., p. 178; _Ast. Nach._, No. 3,142; + Catalogue published by Lick Observatory, 1901. + + [15] _R. A. S., M. N._, vol. vi. + + [16] _R. S. Phil. Trans._, vol. lxxiii., p. 484. + + [17] _Astr. Nach._, No. 2,947. + + [18] _R. S. E. Trans_., vol. xxvii. In 1901 Dr. Anderson discovered + Nova Persei. + + [19] _Astr. Nach_., No. 3,079. + + [20] For a different explanation see Sir W. Huggins’s lecture, Royal + Institution, May 13th, 1892. + + [21] For the early history of the proposals for photographic + cataloguing of stars, see the _Cape Photographic Durchmusterung_, 3 + vols. (_Ann. of the Cape Observatory_, vols. in., iv., and v., + Introduction.) + + [22] _R. S. Phil. Trans._, 1850, p. 499 _et seq._ + + [23] _Ibid_, vol. cliv., p. 437. + + [24] _Brit. Assoc. Rep._, 1868, p. 165. + + + + +ILLUSTRATIONS + + + SIR ISAAC NEWTON +(From the bust by Roubiliac In Trinity College, Cambridge.) + + CHALDÆAN BAKED BRICK OR TABLET +Obverse and reverse sides, containing record of solar eclipse, 1062 +B.C., used lately by Cowell for rendering the lunar theory more +accurate than was possible by finest modern observations. (British +Museum collection, No. 35908.) + + “QUADRANS MURALIS SIVE TICHONICUS.” + With portrait of Tycho Brahe, instruments, etc., painted on the wall; + showing assistants using the sight, watching the clock, and recording. + (From the author’s copy of the _Astronomiæ Instauratæ Mechanica_.) + + PORTRAIT OF JOHANNES KEPLER. + By F. Wanderer, from Reitlinger’s “Johannes Kepler” (Original in + Strassburg). + + DEATH-MASK OF SIR ISAAC NEWTON. +Photographed specially for this work from the original, by kind +permission of the Royal Society, London. + + ANCIENT CHINESE INSTRUMENTS, +Including quadrant, celestial globe, and two armillae, in the +Observatory at Peking. Photographed in Peking by the author in 1875, +and stolen by the Germans when the Embassies were relieved by the +allies in 1900. + + SOLAR SURFACE. +As Photographed at the Royal Observatory, Greenwich, showing sun spots +with umbræ, penumbræ, and faculæ. + + SOLAR ECLIPSE, 1882. +From drawing by W. H. Wesley, Secretary R.A.S.; showing the +prominences, the corona, and an unknown comet. + + JUPITER. +From a drawing by E. M. Antoniadi, showing transit of a satellite’s +shadow, the belts, and the “great red spot” (_Monthly Notices_, R. A. +S., vol. lix., pl. x.). + + COPY OF THE DRAWING MADE BY PAUL FABRICIUS. +To define the path of comet 1556. After being lost for 300 years, this +drawing was recovered by the prolonged efforts of Mr. Hind and +Professor Littrow in 1856. + + SIR WILLIAM HERSCHEL, F.R.S.—1738-1822. +Painted by Lemuel F. Abbott; National Portrait Gallery, Room XX. + + GREAT COMET, NOV. 14TH, 1882. (Exposure 2hrs. 20m.) +By kind permission of Sir David Gill. From this photograph originated +all stellar chart-photography. + + + + +INDEX + +Abul Wefa, 24 +Acceleration of moon’s mean motion, 60 +Achromatic lens invented, 88 +Adams, J. C., 61, 65, 68, 69, 70, 87, 118, 124 +Airy, G. B., 13, 30, 37, 65, 69, 70, 80, 81, 114, 119 +Albetegnius, 24 +Alphonso, 24 +Altazimuth, 81 +Anaxagoras, 14, 16 +Anaximander, 14 +Anaximenes, 14 +Anderson, T. D., 137, 138 +Ångstrom, A. J., 102 +Antoniadi, 113 +Apian, P., 63 +Apollonius, 22, 23 +Arago, 111 +Argelander, F. W. A., 139 +Aristarchus, 18, 29 +Aristillus, 17, 19 +Aristotle, 16, 30, 47 +Arrhenius, 146 +Arzachel, 24 +Asshurbanapal, 12 +Asteroids, discovery of, 67, 119 +Astrology, ancient and modern, 1-7, 38 + +Backlund, 122 +Bacon, R., 86 +Bailly, 8, 65 +Barnard, E. E., 115, 143 +Beer and Mädler, 107, 110, 111 +Behaim, 74 +Bessel, F.W., 65, 79, 128, 134, 139 +Biela, 123 +Binet, 65 +Biot, 10 +Bird, 79, 80 +Bliss, 80 +Bode, 66, 69 +Bond, G. P., 99, 117, 122 +Bouvard, A., 65, 68 +Bradley, J., 79, 80, 81, 87, 127, 128, 139 +Bredechin, 146 +Bremiker, 71 +Brewster, D., 52, 91, 112 +Brinkley, 128 +Bruno, G., 49 +Burchardt, 65, 123 +Burnham, S. W., 134 + +Callippus, 15, 16, 31 +Carrington, R. C., 97, 99, 114 +Cassini, G. D., 107, 114, 115, 116, 117, 118 +Cassini, J., 109, 129 +Chacornac, 139 +Chaldæan astronomy, 11-13 +Challis, J., 69, 70, 71, 72 +Chance, 88 +Charles, II., 50, 81 +Chinese astronomy, 8-11 +Christie, W. M. H. (Ast. Roy.), 64, 82, 125 +Chueni, 9 +Clairaut, A. C., 56, 63, 65 +Clark, A. G., 89, 135 +Clerke, Miss, 106, 146 +Comets, 120 +Common, A. A., 88 +Cooke, 89 +Copeland, R., 142 +Copernicus, N., 14, 24-31, 37, 38, 41, 42, 49, 128 +Cornu, 85 +Cowell, P. H., 3, 5, 64, 83 +Crawford, Earl of, 84 +Cromellin, A. C., 5, 64 + +D’Alembert, 65 +Damoiseau, 65 +D’Arrest, H. L., 34 +Dawes, W. R., 100, 111 +Delambre, J. B. J., 8, 27, 51, 65, 68 +De la Rue, W., 2, 94, 99, 100, 131 +Delaunay, 65 +Democritus, 16 +Descartes, 51 +De Sejour, 117 +Deslandres, II., 101 +Desvignolles, 9 +De Zach, 67 +Digges, L., 86 +Dollond, J., 87, 90 +Dominis, A. di., 86 +Donati, 120 +Doppler, 92, 129 +Draper, 99 +Dreyer, J. L. E., 29,77 +Dunthorne, 60 +Dyson, 131 + +Eclipses, total solar, 103 +Ecphantes, 16 +Eddington, 131 +Ellipse, 41 +Empedocles, 16 +Encke, J. F., 119, 122, 123, 133 +Epicycles, 22 +Eratosthenes, 18 +Euclid, 17 +Eudoxus, 15, 31 +Euler, L., 60, 61, 62, 65, 88, 119 + +Fabricius, D.,95, 120, 121 +Feil and Mantois, 88 +Fizeau, H. L., 85, 92, 99 +Flamsteed, J., 50, 58, 68, 78, 79, 93 +Fohi, 8 +Forbes, J. D., 52, 91 +Foucault, L., 85, 99 +Frauenhofer, J., 88, 90, 91 + +Galilei, G., 38, 46-49, 77, 93, 94, 95, 96, 107, 113, 115, 116, 133 +Galle, 71, 72 +Gascoigne, W., 45, 77 +Gauss, C. F., 65, 67 +Gauthier, 98 +Gautier, 89 +Gilbert, 44 +Gill, D., 84, 85, 128, 135, 139, 140 +Goodricke, J., 136 +Gould, B. A., 139 +Grant, R., 27, 47, 51, 86, 134 +Graham, 79 +Greek astronomy, 8-11 +Gregory, J. and D., 87 +Grimaldi, 113 +Groombridge, S., 139 +Grubb, 88, 89 +Guillemin, 122 +Guinand, 88 + +Hale, G. E., 101 +Hall, A., 112 +Hall, C. M., 88 +Halley, E., 19, 51, 58, 60, 61, 62, 63, 64, 79, 120, 122, 125, 129 +Halley’s comet, 62-64 +Halm, 85 +Hansen, P. A., 3, 65 +Hansky, A. P., 100 +Harding, C. L., 67 +Heliometer, 83 +Heller, 120 +Helmholtz, H. L. F., 35 +Henderson, T., 128 +Henry, P. and P., 139, 140, 143 +Heraclides, 16 +Heraclitus, 14 +Herodotus, 13 +Herschel, W., 65, 68, 97, 107, 110, 114, 115, 116, 117, 118, 126, 127, +130, 131, 132, 141, 142 +Herschel, J., 97, 111, 133, 134, 142 +Herschel, A. S., 125 +Hevelius, J., 178 +Hind, J. R., 5, 64, 120, 121, 122 +Hipparchus, 3, 18, 19, 20, 22, 23, 24, 26, 36, 55, 60, 74, 93, 137 +Hooke, R., 51, 111, 114 +Horrocks, J., 50, 56 +Howlett, 100 +Huggins, W., 92, 93, 99, 106, 120, 129, 137, 138, 142, 144 +Humboldt and Bonpland, 124 +Huyghens, C., 47, 77, 87, 110, 116, 117 + +Ivory, 65 + +Jansen, P. J. C., 105, 106 +Jansen, Z., 86 + +Kaiser, F., 111 +Kapteyn, J. C., 131, 138, 139 +Keeler, 117 +Kepler, J., 17, 23, 26, 29, 30, 36, 37, 38-46, 48, 49, 50, 52, 53, 63, +66, 77, 87, 93, 127, 137 +Kepler’s laws, 42 +Kirchoff, G.R., 91 +Kirsch, 9 +Knobel, E.B., 12, 13 +Ko-Show-King, 76 + +Lacaile, N.L., 139 +Lagrange, J.L., 61, 62, 65, 119 +La Hire, 114 +Lalande, J.J.L., 60, 63, 65, 66, 72, 139 +Lamont, J., 98 +Langrenus, 107 +Laplace, P.S. de, 50, 58, 61, 62, 65,66, 123, 146 +Lassel, 72, 88, 117, 118 +Law of universal gravitation, 53 +Legendre, 65 +Leonardo da Vinci, 46 +Lewis, G.C., 17 +Le Verrier, U.J.J., 65, 68, 70, 71,72, 110, 118, 125 +Lexell, 66, 123 +Light year, 128 +Lipperhey, H., 86 +Littrow, 121 +Lockyer, J.N., 103, 105, 146 +Logarithms invented, 50 +Loewy, 2, 100 +Long inequality of Jupiter and Saturn, 50, 62 +Lowell, P., 111, 112, 118 +Lubienietz, S. de, 122 +Luther, M., 38 +Lunar theory, 37, 50, 56, 64 + +Maclaurin, 65 +Maclear, T., 128 +Malvasia, 77 +Martin, 9 +Maxwell, J. Clerk, 117 +Maskelyne, N., 80, 130 +McLean, F., 89 +Medici, Cosmo di, 48 +Melancthon, 38 +Melotte, 83, 116 +Meteors, 123 +Meton, 15 +Meyer, 57, 65 +Michaelson, 85 +Miraldi, 110, 114 +Molyneux, 87 +Moon, physical observations, 107 +Mouchez, 139 +Moyriac de Mailla, 8 + +Napier, Lord, 50 +Nasmyth and Carpenter, 108 +Nebulae, 141, 146 +Neison, E., 108 +Neptune, discovery of, 68-72 +Newall, 89 +Newcomb, 85 +Newton, H.A., 124 +Newton, I., 5, 19, 43, 49, 51-60, 62, 64, 68, 77, 79, 87, 90, 93, 94, +114, 127, 133 +Nicetas, 16, 25 +Niesten, 115 +Nunez, P., 35 + +Olbers, H.W.M., 67 +Omar, 11, 24 +Oppolzer, 13, 125 +Oudemans, 129 + +Palitsch, G., 64 +Parallax, solar, 85, 86 +Parmenides, 14 +Paul III., 30 +Paul V., 48 +Pemberton, 51 +Peters, C.A.F., 125, 128, 135 +Photography, 99 +Piazzi, G., 67, 128, 129, 139 +Picard, 54, 77, 114 +Pickering, E.C., 118, 135 +Pingré, 13, 122 +Plana, 65 +Planets and satellites, physical observations, 109-119 +Plato, 17, 23, 26, 40 +Poisson, 65 +Pond, J., 80 +Pons, 122 +Porta, B., 86 +Pound, 87, 114 +Pontecoulant, 64 +Precession of the equinoxes, 19-21, 55, 57 +Proctor, R.A., 111 +Pritchett, 115 +Ptolemy, 11, 13, 21, 22, 23, 24, 93 +Puiseux and Loewy, 108 +Pulfrich, 131 +Purbach, G., 24 +Pythagoras, 14, 17, 25, 29 + +Ramsay, W., 106 +Ransome and May, 81 +Reflecting telescopes invented, 87 +Regiomontanus (Müller), 24 +Respighi, 82 +Retrograde motion of planets, 22 +Riccioli, 107 +Roberts, 137 +Römer, O.,78, 114 +Rosse, Earl of, 88, 142 +Rowland, H. A., 92, 102 +Rudolph H.,37, 39 +Rumker, C., 139 + +Sabine, E., 98 +Savary, 133 +Schaeberle, J. M., 135 +Schiaparelli, G. V., 110, 111, 124, 125 +Scheiner, C., 87, 95, 96 +Schmidt, 108 +Schott, 88 +Schröter, J. H., 107, 110, 111, 124, 125 +Schuster, 98 +Schwabe, G. H., 97 +Secchi, A., 93, 144 +Short, 87 +Simms, J., 81 +Slipher, V. M., 119 +Socrates, 17 +Solon, 15 +Souciet, 8 +South, J., 133 +Spectroscope, 89-92 +Spectroheliograph, 101 +Spoerer, G. F. W., 98 +Spots on the sun, 84; +periodicity of, 97 +Stars, Parallax, 127; +proper motion, 129; +double, 132; +binaries, 132, 135; +new, 19, 36, 137; +catalogues of, 19, 36, 139; +spectra of, 143 +Stewart, B., 2, 100 +Stokes, G. G., 91 +Stone, E. J., 139 +Struve, C. L., 130 +Struve, F. G. W,, 88, 115, 128, 133 + +Telescopes invented, 47, 86; +large, 88 +Temple, 115, 125 +Thales, 13, 16 +Theon, 60 +Transit circle of Römer, 78 +Timocharis, 17, 19 +Titius, 66 +Torricelli, 113 +Troughton, E., 80 +Tupman, G. L., 120 +Tuttle, 125 +Tycho Brahe, 23, 25, 30, 33-38, 39, 40, 44, 50, 75, 77, 93, 94, 129, +137 + +Ulugh Begh, 24 +Uranus, discovery of, 65 + +Velocity of light, 86, 128; +of earth in orbit, 128 +Verbiest, 75 +Vogel, H. C., 92, 129, 135, 136 +Von Asten, 122 + +Walmsley, 65 +Walterus, B., 24, 74 +Weiss, E., 125 +Wells, 122 +Wesley, 104 +Whewell, 112 +Williams, 10 +Wilson, A., 96, 100 +Winnecke, 120 +Witte, 86 +Wollaston, 90 +Wolf, M., 119, 125, 132 +Wolf, R., 98 +Wren, C., 51 +Wyllie, A., 77 + +Yao, 9 +Young, C. A., 103 +Yu-Chi, 8 + +Zenith telescopes, 79, 82 +Zöllner, 92 +Zucchi, 113 + + +End of the Project Gutenberg EBook of History of Astronomy, by George Forbes + +*** END OF THIS PROJECT GUTENBERG EBOOK HISTORY OF ASTRONOMY *** + +***** This file should be named 8172-0.txt or 8172-0.zip ***** +This and all associated files of various formats will be found in: + http://www.gutenberg.org/8/1/7/8172/ + +Produced by Jonathan Ingram, Dave Maddock, Charles Franks +and the Online Distributed Proofreading Team. + +Updated editions will replace the previous one--the old editions will +be renamed. + +Creating the works from print editions not protected by U.S. copyright +law means that no one owns a United States copyright in these works, +so the Foundation (and you!) can copy and distribute it in the United +States without permission and without paying copyright +royalties. 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Thus, we do not +necessarily keep eBooks in compliance with any particular paper +edition. + +Most people start at our Web site which has the main PG search +facility: www.gutenberg.org + +This Web site includes information about Project Gutenberg-tm, +including how to make donations to the Project Gutenberg Literary +Archive Foundation, how to help produce our new eBooks, and how to +subscribe to our email newsletter to hear about new eBooks. + diff --git a/8172-0.zip b/8172-0.zip Binary files differnew file mode 100644 index 0000000..7beb29c --- /dev/null +++ b/8172-0.zip diff --git a/8172-8.txt b/8172-8.txt new file mode 100644 index 0000000..0d1945e --- /dev/null +++ b/8172-8.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: ISO-8859-1 + +*** 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 CHALDANS + + 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 NEBUL + + 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 _ 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 Chaldans 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 Chaldan 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 Chaldans +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: CHALDAN 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 CHALDANS. + + +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, Chaldans, 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. + +_Chaldans_.--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 Chaldans, 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. Pingr and Oppolzer fix the date July 16th, 533 B.C. Thus +are the relations of the chronologies of Jews and Egyptians +established by these explorations. + + +FOOTNOTES: + +[1] These ancient dates are uncertain. + +[2] _R. A. S. Monthly Notices_, vol. lxviii., No. 5, March, 1908. + + + +3. ANCIENT GREEK ASTRONOMY. + + +We have our information about the earliest Greek astronomy from +Herodotus (born 480 B.C.). He put the traditions into writing. Thales +(639-546 B.C.) is said to have predicted an eclipse, which caused much +alarm, and ended the battle between the Medes and Lydians. Airy fixed +the date May 28th, 585 B.C. But other modern astronomers give +different dates. Thales went to Egypt to study science, and learnt +from its priests the length of the year (which was kept a profound +secret!), and the signs of the zodiac, and the positions of the +solstices. He held that the sun, moon, and stars are not mere spots on +the heavenly vault, but solids; that the moon derives her light from +the sun, and that this fact explains her phases; that an eclipse of +the moon happens when the earth cuts off the sun's light from her. He +supposed the earth to be flat, and to float upon water. He determined +the ratio of the sun's diameter to its orbit, and apparently made out +the diameter correctly as half a degree. He left nothing in writing. + +His successors, Anaximander (610-547 B.C.) and Anaximenes (550-475 +B.C.), held absurd notions about the sun, moon, and stars, while +Heraclitus (540-500 B.C.) supposed that the stars were lighted each +night like lamps, and the sun each morning. Parmenides supposed the +earth to be a sphere. + +Pythagoras (569-470 B.C.) visited Egypt to study science. He deduced +his system, in which the earth revolves in an orbit, from fantastic +first principles, of which the following are examples: "The circular +motion is the most perfect motion," "Fire is more worthy than earth," +"Ten is the perfect number." He wrote nothing, but is supposed to have +said that the earth, moon, five planets, and fixed stars all revolve +round the sun, which itself revolves round an imaginary central fire +called the Antichthon. Copernicus in the sixteenth century claimed +Pythagoras as the founder of the system which he, Copernicus, revived. + +Anaxagoras (born 499 B.C.) studied astronomy in Egypt. He explained +the return of the sun to the east each morning by its going under the +flat earth in the night. He held that in a solar eclipse the moon +hides the sun, and in a lunar eclipse the moon enters the earth's +shadow--both excellent opinions. But he entertained absurd ideas of +the vortical motion of the heavens whisking stones into the sky, there +to be ignited by the fiery firmament to form stars. He was prosecuted +for this unsettling opinion, and for maintaining that the moon is an +inhabited earth. He was defended by Pericles (432 B.C.). + +Solon dabbled, like many others, in reforms of the calendar. The +common year of the Greeks originally had 360 days--twelve months of +thirty days. Solon's year was 354 days. It is obvious that these +erroneous years would, before long, remove the summer to January and +the winter to July. To prevent this it was customary at regular +intervals to intercalate days or months. Meton (432 B.C.) introduced a +reform based on the nineteen-year cycle. This is not the same as the +Egyptian and Chaldean eclipse cycle called _Saros_ of 223 +lunations, or a little over eighteen years. The Metonic cycle is 235 +lunations or nineteen years, after which period the sun and moon +occupy the same position relative to the stars. It is still used for +fixing the date of Easter, the number of the year in Melon's cycle +being the golden number of our prayer-books. Melon's system divided +the 235 lunations into months of thirty days and omitted every +sixty-third day. Of the nineteen years, twelve had twelve months and +seven had thirteen months. + +Callippus (330 B.C.) used a cycle four times as long, 940 lunations, +but one day short of Melon's seventy-six years. This was more correct. + +Eudoxus (406-350 B.C.) is said to have travelled with Plato in +Egypt. He made astronomical observations in Asia Minor, Sicily, and +Italy, and described the starry heavens divided into constellations. +His name is connected with a planetary theory which as generally +stated sounds most fanciful. He imagined the fixed stars to be on a +vault of heaven; and the sun, moon, and planets to be upon similar +vaults or spheres, twenty-six revolving spheres in all, the motion of +each planet being resolved into its components, and a separate sphere +being assigned for each component motion. Callippus (330 B.C.) +increased the number to thirty-three. It is now generally accepted +that the real existence of these spheres was not suggested, but the +idea was only a mathematical conception to facilitate the construction +of tables for predicting the places of the heavenly bodies. + +Aristotle (384-322 B.C.) summed up the state of astronomical knowledge +in his time, and held the earth to be fixed in the centre of the +world. + +Nicetas, Heraclides, and Ecphantes supposed the earth to revolve on +its axis, but to have no orbital motion. + +The short epitome so far given illustrates the extraordinary deductive +methods adopted by the ancient Greeks. But they went much farther in +the same direction. They seem to have been in great difficulty to +explain how the earth is supported, just as were those who invented +the myth of Atlas, or the Indians with the tortoise. Thales thought +that the flat earth floated on water. Anaxagoras thought that, being +flat, it would be buoyed up and supported on the air like a kite. +Democritus thought it remained fixed, like the donkey between two +bundles of hay, because it was equidistant from all parts of the +containing sphere, and there was no reason why it should incline one +way rather than another. Empedocles attributed its state of rest to +centrifugal force by the rapid circular movement of the heavens, as +water is stationary in a pail when whirled round by a string. +Democritus further supposed that the inclination of the flat earth to +the ecliptic was due to the greater weight of the southern parts owing +to the exuberant vegetation. + +For further references to similar efforts of imagination the reader is +referred to Sir George Cornwall Lewis's _Historical Survey of the +Astronomy of the Ancients_; London, 1862. His list of authorities +is very complete, but some of his conclusions are doubtful. At p. 113 +of that work he records the real opinions of Socrates as set forth by +Xenophon; and the reader will, perhaps, sympathise with Socrates in +his views on contemporary astronomy:-- + +With regard to astronomy he [Socrates] considered a knowledge of it +desirable to the extent of determining the day of the year or month, +and the hour of the night, ... but as to learning the courses of the +stars, to be occupied with the planets, and to inquire about their +distances from the earth, and their orbits, and the causes of their +motions, he strongly objected to such a waste of valuable time. He +dwelt on the contradictions and conflicting opinions of the physical +philosophers, ... and, in fine, he held that the speculators on the +universe and on the laws of the heavenly bodies were no better than +madmen (_Xen. Mem_, i. 1, 11-15). + +Plato (born 429 B.C.), the pupil of Socrates, the fellow-student of +Euclid, and a follower of Pythagoras, studied science in his travels +in Egypt and elsewhere. He was held in so great reverence by all +learned men that a problem which he set to the astronomers was the +keynote to all astronomical investigation from this date till the time +of Kepler in the sixteenth century. He proposed to astronomers _the +problem of representing the courses of the planets by circular and +uniform motions_. + +Systematic observation among the Greeks began with the rise of the +Alexandrian school. Aristillus and Timocharis set up instruments and +fixed the positions of the zodiacal stars, near to which all the +planets in their orbits pass, thus facilitating the determination of +planetary motions. Aristarchus (320-250 B.C.) showed that the sun must +be at least nineteen times as far off as the moon, which is far short +of the mark. He also found the sun's diameter, correctly, to be half a +degree. Eratosthenes (276-196 B.C.) measured the inclination to the +equator of the sun's apparent path in the heavens--i.e., he +measured the obliquity of the ecliptic, making it 23 51', confirming +our knowledge of its continuous diminution during historical times. He +measured an arc of meridian, from Alexandria to Syene (Assuan), and +found the difference of latitude by the length of a shadow at noon, +summer solstice. He deduced the diameter of the earth, 250,000 +stadia. Unfortunately, we do not know the length of the stadium he +used. + +Hipparchus (190-120 B.C.) may be regarded as the founder of +observational astronomy. He measured the obliquity of the ecliptic, +and agreed with Eratosthenes. He altered the length of the tropical +year from 365 days, 6 hours to 365 days, 5 hours, 53 minutes--still +four minutes too much. He measured the equation of time and the +irregular motion of the sun; and allowed for this in his calculations +by supposing that the centre, about which the sun moves uniformly, is +situated a little distance from the fixed earth. He called this point +the _excentric_. The line from the earth to the "excentric" was +called the _line of apses_. A circle having this centre was +called the _equant_, and he supposed that a radius drawn to the +sun from the excentric passes over equal arcs on the equant in equal +times. He then computed tables for predicting the place of the sun. + +He proceeded in the same way to compute Lunar tables. Making use of +Chaldan eclipses, he was able to get an accurate value of the moon's +mean motion. [Halley, in 1693, compared this value with his own +measurements, and so discovered the acceleration of the moon's mean +motion. This was conclusively established, but could not be explained +by the Newtonian theory for quite a long time.] He determined the +plane of the moon's orbit and its inclination to the ecliptic. The +motion of this plane round the pole of the ecliptic once in eighteen +years complicated the problem. He located the moon's excentric as he +had done the sun's. He also discovered some of the minor +irregularities of the moon's motion, due, as Newton's theory proves, +to the disturbing action of the sun's attraction. + +In the year 134 B.C. Hipparchus observed a new star. This upset every +notion about the permanence of the fixed stars. He then set to work to +catalogue all the principal stars so as to know if any others appeared +or disappeared. Here his experiences resembled those of several later +astronomers, who, when in search of some special object, have been +rewarded by a discovery in a totally different direction. On comparing +his star positions with those of Timocharis and Aristillus he found no +stars that had appeared or disappeared in the interval of 150 years; +but he found that all the stars seemed to have changed their places +with reference to that point in the heavens where the ecliptic is 90 +from the poles of the earth--i.e., the equinox. He found that this +could be explained by a motion of the equinox in the direction of the +apparent diurnal motion of the stars. This discovery of _precession of +the equinoxes_, which takes place at the rate of 52".1 every year, was +necessary for the progress of accurate astronomical observations. It +is due to a steady revolution of the earth's pole round the pole of +the ecliptic once in 26,000 years in the opposite direction to the +planetary revolutions. + +Hipparchus was also the inventor of trigonometry, both plane and +spherical. He explained the method of using eclipses for determining +the longitude. + +In connection with Hipparchus' great discovery it may be mentioned +that modern astronomers have often attempted to fix dates in history +by the effects of precession of the equinoxes. (1) At about the date +when the Great Pyramid may have been built 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 and 27 to the horizon and in +the plane of the meridian. It also appears that 4,000 years +ago--i.e., about 2100 B.C.--an observer at the lower end of the +passage would be able to see 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 Chaldans 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 Botes 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 Mller, 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 _Astronomi Instaurat 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 _ 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. + ' " ' " +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 parabol, in which case they would +be seen more than once. He found two old comets whose orbits, in shape +and position, resembled the orbit of a comet observed by himself in +1682. Apian observed one in 1531; Kepler the other in 1607. The +intervals between these appearances is seventy-five or seventy-six +years. He then examined and found old records of similar appearance in +1456, 1380, and 1305. It is true, he noticed, that the intervals +varied by a year and a-half, and the inclination of the orbit to the +ecliptic diminished with successive apparitions. But he knew from +previous calculations that this might easily be due to planetary +perturbations. Finally, he arrived at the conclusion that all of these +comets were identical, travelling in an ellipse so elongated that the +part where the comet was seen seemed to be part of a parabolic +orbit. He then predicted its return at the end of 1758 or beginning of +1759, when he should be dead; but, as he said, "if it should return, +according to our prediction, about the year 1758, impartial posterity +will not refuse to acknowledge that this was first discovered by an +Englishman."[3] [_Synopsis Astronomiae Cometicae_, 1749.] + +Once again Halley's suggestion became an inspiration for the +mathematical astronomer. Clairaut, assisted by Lalande, found that +Saturn would retard the comet 100 days, Jupiter 518 days, and +predicted its return to perihelion on April 13th, 1759. In his +communication to the French Academy, he said that a comet travelling +into such distant regions might be exposed to the influence of forces +totally unknown, and "even of some planet too far removed from the sun +to be ever perceived." + +The excitement of astronomers towards the end of 1758 became intense; +and the honour of first catching sight of the traveller fell to an +amateur in Saxony, George Palitsch, on Christmas Day, 1758. It reached +perihelion on March 13th, 1759. + +This fact was a startling confirmation of the Newtonian theory, +because it was a new kind of calculation of perturbations, and also it +added a new member to the solar system, and gave a prospect of adding +many more. + +When Halley's comet reappeared in 1835, Pontecoulant's computations +for the date of perihelion passage were very exact, and afterwards he +showed that, with more exact values of the masses of Jupiter and +Saturn, his prediction was correct within two days, after an invisible +voyage of seventy-five years! + +Hind afterwards searched out many old appearances of this comet, going +back to 11 B.C., and most of these have been identified as being +really Halley's comet by the calculations of Cowell and Cromellin[4] +(of Greenwich Observatory), who have also predicted its next +perihelion passage for April 8th to 16th, 1910, and have traced back +its history still farther, to 240 B.C. + +Already, in November, 1907, the Astronomer Royal was trying to catch +it by the aid of photography. + + +FOOTNOTES: + +[1] Born 1736; died 1813. + +[2] Born 1749; died 1827. + +[3] This sentence does not appear in the original memoir communicated +to the Royal Society, but was first published in a posthumous reprint. + +[4] _R. A. S. Monthly Notices_, 1907-8. + + + +9. DISCOVERY OF NEW PLANETS--HERSCHEL, PIAZZI, ADAMS, AND LE VERRIER. + + +It would be very interesting, but quite impossible in these pages, to +discuss all the exquisite researches of the mathematical astronomers, +and to inspire a reverence for the names connected with these +researches, which for two hundred years have been establishing the +universality of Newton's law. The lunar and planetary theories, the +beautiful theory of Jupiter's satellites, the figure of the earth, and +the tides, were mathematically treated by Maclaurin, D'Alembert, +Legendre, Clairaut, Euler, Lagrange, Laplace, Walmsley, Bailly, +Lalande, Delambre, Mayer, Hansen, Burchardt, Binet, Damoiseau, Plana, +Poisson, Gauss, Bessel, Bouvard, Airy, Ivory, Delaunay, Le Verrier, +Adams, and others of later date. + +By passing over these important developments it is possible to trace +some of the steps in the crowning triumph of the Newtonian theory, by +which the planet Neptune was added to the known members of the solar +system by the independent researches of Professor J.C. Adams and of +M. Le Verrier, in 1846. + +It will be best to introduce this subject by relating how the +eighteenth century increased the number of known planets, which was +then only six, including the earth. + +On March 13th, 1781, Sir William Herschel was, as usual, engaged on +examining some small stars, and, noticing that one of them appeared to +be larger than the fixed stars, suspected that it might be a comet. +To test this he increased his magnifying power from 227 to 460 and +932, finding that, unlike the fixed stars near it, its definition was +impaired and its size increased. This convinced him that the object +was a comet, and he was not surprised to find on succeeding nights +that the position was changed, the motion being in the ecliptic. He +gave the observations of five weeks to the Royal Society without a +suspicion that the object was a new planet. + +For a long time people could not compute a satisfactory orbit for the +supposed comet, because it seemed to be near the perihelion, and no +comet had ever been observed with a perihelion distance from the sun +greater than four times the earth's distance. Lexell was the first to +suspect that this was a new planet eighteen times as far from the sun +as the earth is. In January, 1783, Laplace published the elliptic +elements. The discoverer of a planet has a right to name it, so +Herschel called it Georgium Sidus, after the king. But Lalande urged +the adoption of the name Herschel. Bode suggested Uranus, and this +was adopted. The new planet was found to rank in size next to Jupiter +and Saturn, being 4.3 times the diameter of the earth. + +In 1787 Herschel discovered two satellites, both revolving in nearly +the same plane, inclined 80 to the ecliptic, and the motion of both +was retrograde. + +In 1772, before Herschel's discovery, Bode[1] had discovered a curious +arbitrary law of planetary distances. Opposite each planet's name +write the figure 4; and, in succession, add the numbers 0, 3, 6, 12, +24, 48, 96, etc., to the 4, always doubling the last numbers. You +then get the planetary distances. + + Mercury, dist.-- 4 4 + 0 = 4 + Venus " 7 4 + 3 = 7 + Earth " 10 4 + 6 = 10 + Mars " 15 4 + 12 = 16 + -- 4 + 24 = 28 + Jupiter dist. 52 4 + 48 = 52 + Saturn " 95 4 + 96 = 100 + (Uranus) " 192 4 + 192 = 196 + -- 4 + 384 = 388 + +All the five planets, and the earth, fitted this rule, except that +there was a blank between Mars and Jupiter. When Uranus was +discovered, also fitting the rule, the conclusion was irresistible +that there is probably a planet between Mars and Jupiter. An +association of twenty-four astronomers was now formed in Germany to +search for the planet. Almost immediately afterwards the planet was +discovered, not by any member of the association, but by Piazzi, when +engaged upon his great catalogue of stars. On January 1st, 1801, he +observed a star which had changed its place the next night. Its motion +was retrograde till January 11th, direct after the 13th. Piazzi fell +ill before he had enough observations for computing the orbit with +certainty, and the planet disappeared in the sun's rays. Gauss +published an approximate ephemeris of probable positions when the +planet should emerge from the sun's light. There was an exciting hunt, +and on December 31st (the day before its birthday) De Zach captured +the truant, and Piazzi christened it Ceres. + + +The mean distance from the sun was found to be 2.767, agreeing with +the 2.8 given by Bode's law. Its orbit was found to be inclined over +10 to the ecliptic, and its diameter was only 161 miles. + +On March 28th, 1802, Olbers discovered a new seventh magnitude star, +which turned out to be a planet resembling Ceres. It was called +Pallas. Gauss found its orbit to be inclined 35 to the ecliptic, and +to cut the orbit of Ceres; whence Olbers considered that these might +be fragments of a broken-up planet. He then commenced a search for +other fragments. In 1804 Harding discovered Juno, and in 1807 Olbers +found Vesta. The next one was not discovered until 1845, from which +date asteroids, or minor planets (as these small planets are called), +have been found almost every year. They now number about 700. + +It is impossible to give any idea of the interest with which the first +additions since prehistoric times to the planetary system were +received. All of those who showered congratulations upon the +discoverers regarded these discoveries in the light of rewards for +patient and continuous labours, the very highest rewards that could be +desired. And yet there remained still the most brilliant triumph of +all, the addition of another planet like Uranus, before it had ever +been seen, when the analysis of Adams and Le Verrier gave a final +proof of the powers of Newton's great law to explain any planetary +irregularity. + +After Sir William Herschel discovered Uranus, in 1781, it was found +that astronomers had observed it on many previous occasions, mistaking +it for a fixed star of the sixth or seventh magnitude. Altogether, +nineteen observations of Uranus's position, from the time of +Flamsteed, in 1690, had been recorded. + +In 1790 Delambre, using all these observations, prepared tables for +computing its position. These worked well enough for a time, but at +last the differences between the calculated and observed longitudes of +the planet became serious. In 1821 Bouvard undertook a revision of the +tables, but found it impossible to reconcile all the observations of +130 years (the period of revolution of Uranus is eighty-four years). +So he deliberately rejected the old ones, expressing the opinion that +the discrepancies might depend upon "some foreign and unperceived +cause which may have been acting upon the planet." In a few years the +errors even of these tables became intolerable. In 1835 the error of +longitude was 30"; in 1838, 50"; in 1841, 70"; and, by comparing the +errors derived from observations made before and after opposition, a +serious error of the distance (radius vector) became apparent. + +In 1843 John Couch Adams came out Senior Wrangler at Cambridge, and +was free to undertake the research which as an undergraduate he had +set himself--to see whether the disturbances of Uranus could be +explained by assuming a certain orbit, and position in that orbit, of +a hypothetical planet even more distant than Uranus. Such an +explanation had been suggested, but until 1843 no one had the boldness +to attack the problem. Bessel had intended to try, but a fatal +illness overtook him. + +Adams first recalculated all known causes of disturbance, using the +latest determinations of the planetary masses. Still the errors were +nearly as great as ever. He could now, however, use these errors as +being actually due to the perturbations produced by the unknown +planet. + +In 1844, assuming a circular orbit, and a mean distance agreeing with +Bode's law, he obtained a first approximation to the position of the +supposed planet. He then asked Professor Challis, of Cambridge, to +procure the latest observations of Uranus from Greenwich, which Airy +immediately supplied. Then the whole work was recalculated from the +beginning, with more exactness, and assuming a smaller mean distance. + +In September, 1845, he handed to Challis the elements of the +hypothetical planet, its mass, and its apparent position for September +30th, 1845. On September 22nd Challis wrote to Airy explaining the +matter, and declaring his belief in Adams's capabilities. When Adams +called on him Airy was away from home, but at the end of October, +1845, he called again, and left a paper with full particulars of his +results, which had, for the most part, reduced the discrepancies to +about 1". As a matter of fact, it has since been found that the +heliocentric place of the new planet then given was correct within +about 2. + +Airy wrote expressing his interest, and asked for particulars about +the radius vector. Adams did not then reply, as the answer to this +question could be seen to be satisfactory by looking at the data +already supplied. He was a most unassuming man, and would not push +himself forward. He may have felt, after all the work he had done, +that Airy's very natural inquiry showed no proportionate desire to +search for the planet. Anyway, the matter lay in embryo for nine +months. + +Meanwhile, one of the ablest French astronomers, Le Verrier, +experienced in computing perturbations, was independently at work, +knowing nothing about Adams. He applied to his calculations every +possible refinement, and, considering the novelty of the problem, his +calculation was one of the most brilliant in the records of +astronomy. In criticism it has been said that these were exhibitions +of skill rather than helps to a solution of the particular problem, +and that, in claiming to find the elements of the orbit within certain +limits, he was claiming what was, under the circumstances, impossible, +as the result proved. + +In June, 1846, Le Verrier announced, in the _Comptes Rendus de +l'Academie des Sciences_, that the longitude of the disturbing planet, +for January 1st, 1847, was 325, and that the probable error did not +exceed 10. + +This result agreed so well with Adams's (within 1) that Airy urged +Challis to apply the splendid Northumberland equatoreal, at Cambridge, +to the search. Challis, however, had already prepared an exhaustive +plan of attack which must in time settle the point. His first work +was to observe, and make a catalogue, or chart, of all stars near +Adams's position. + +On August 31st, 1846, Le Verrier published the concluding +part of his labours. + +On September 18th, 1846, Le Verrier communicated his results to the +Astronomers at Berlin, and asked them to assist in searching for the +planet. By good luck Dr. Bremiker had just completed a star-chart of +the very part of the heavens including Le Verrier's position; thus +eliminating all of Challis's preliminary work. The letter was received +in Berlin on September 23rd; and the same evening Galle found the new +planet, of the eighth magnitude, the size of its disc agreeing with Le +Verrier's prediction, and the heliocentric longitude agreeing within +57'. By this time Challis had recorded, without reduction, the +observations of 3,150 stars, as a commencement for his search. On +reducing these, he found a star, observed on August 12th, which was +not in the same place on July 30th. This was the planet, and he had +also observed it on August 4th. + +The feeling of wonder, admiration, and enthusiasm aroused by this +intellectual triumph was overwhelming. In the world of astronomy +reminders are met every day of the terrible limitations of human +reasoning powers; and every success that enables the mind's eye to see +a little more clearly the meaning of things has always been heartily +welcomed by those who have themselves been engaged in like +researches. But, since the publication of the _Principia_, in 1687, +there is probably no analytical success which has raised among +astronomers such a feeling of admiration and gratitude as when Adams +and Le Verrier showed the inequalities in Uranus's motion to mean that +an unknown planet was in a certain place in the heavens, where it was +found. + +At the time there was an unpleasant display of international jealousy. +The British people thought that the earlier date of Adams's work, and +of the observation by Challis, entitled him to at least an equal share +of credit with Le Verrier. The French, on the other hand, who, on the +announcement of the discovery by Galle, glowed with pride in the new +proof of the great powers of their astronomer, Le Verrier, whose life +had a long record of successes in calculation, were incredulous on +being told that it had all been already done by a young man whom they +had never heard of. + +These displays of jealousy have long since passed away, and there is +now universally an _entente cordiale_ that to each of these great men +belongs equally the merit of having so thoroughly calculated this +inverse problem of perturbations as to lead to the immediate discovery +of the unknown planet, since called Neptune. + +It was soon found that the planet had been observed, and its position +recorded as a fixed star by Lalande, on May 8th and 10th, 1795. + +Mr. Lassel, in the same year, 1846, with his two-feet reflector, +discovered a satellite, with retrograde motion, which gave the mass of +the planet about a twentieth of that of Jupiter. + + +FOOTNOTES: + +[1] Bode's law, or something like it, had already been fore-shadowed +by Kepler and others, especially Titius (see _Monatliche +Correspondenz_, vol. vii., p. 72). + + + + +BOOK III. OBSERVATION + + + +10. INSTRUMENTS OF PRECISION--STATE OF THE SOLAR SYSTEM. + + +Having now traced the progress of physical astronomy up to the time +when very striking proofs of the universality of the law of +gravitation convinced the most sceptical, it must still be borne in +mind that, while gravitation is certainly the principal force +governing the motions of the heavenly bodies, there may yet be a +resisting medium in space, and there may be electric and magnetic +forces to deal with. There may, further, be cases where the effects of +luminous radiative repulsion become apparent, and also Crookes' +vacuum-effects described as "radiant matter." Nor is it quite certain +that Laplace's proofs of the instantaneous propagation of gravity are +final. + +And in the future, as in the past, Tycho Brahe's dictum must be +maintained, that all theory shall be preceded by accurate +observations. It is the pride of astronomers that their science stands +above all others in the accuracy of the facts observed, as well as in +the rigid logic of the mathematics used for interpreting these facts. + +It is interesting to trace historically the invention of those +instruments of precision which have led to this result, and, without +entering on the details required in a practical handbook, to note the +guiding principles of construction in different ages. + +It is very probable that the Chaldeans may have made spheres, like the +armillary sphere, for representing the poles of the heavens; and with +rings to show the ecliptic and zodiac, as well as the equinoctial and +solstitial colures; but we have no record. We only know that the tower +of Belus, on an eminence, was their observatory. We have, however, +distinct records of two such spheres used by the Chinese about 2500 +B.C. Gnomons, or some kind of sundial, were used by the Egyptians and +others; and many of the ancient nations measured the obliquity of the +ecliptic by the shadows of a vertical column in summer and winter. The +natural horizon was the only instrument of precision used by those who +determined star positions by the directions of their risings and +settings; while in those days the clepsydra, or waterclock, was the +best instrument for comparing their times of rising and setting. + +About 300 B.C. an observatory fitted with circular instruments for +star positions was set up at Alexandria, the then centre of +civilisation. We know almost nothing about the instruments used by +Hipparchus in preparing his star catalogues and his lunar and solar +tables; but the invention of the astrolabe is attributed to him.[1] + +In more modern times Nuremberg became a centre of astronomical +culture. Waltherus, of that town, made really accurate observations of +star altitudes, and of the distances between stars; and in 1484 +A.D. he used a kind of clock. Tycho Brahe tried these, but discarded +them as being inaccurate. + +Tycho Brahe (1546-1601 A.D.) made great improvements in armillary +spheres, quadrants, sextants, and large celestial globes. With these +he measured the positions of stars, or the distance of a comet from +several known stars. He has left us full descriptions of them, +illustrated by excellent engravings. Previous to his time such +instruments were made of wood. Tycho always used metal. He paid the +greatest attention to the stability of mounting, to the orientation of +his instruments, to the graduation of the arcs by the then new method +of transversals, and to the aperture sight used upon his +pointer. There were no telescopes in his day, and no pendulum +clocks. He recognised the fact that there must be instrumental +errors. He made these as small as was possible, measured their amount, +and corrected his observations. His table of refractions enabled him +to abolish the error due to our atmosphere so far as it could affect +naked-eye observations. The azimuth circle of Tycho's largest quadrant +had a diameter of nine feet, and the quadrant a radius of six feet. He +introduced the mural quadrant for meridian observations.[2] + +[Illustration: ANCIENT CHINESE INSTRUMENTS, Including quadrant, celestial +globe, and two armillae, in the Observatory at Peking. Photographed in +Peking by the author in 1875, and stolen by the Germans when the +Embassies were relieved by the allies in 1900.] + +The French Jesuits at Peking, in the seventeenth century, helped the +Chinese in their astronomy. In 1875 the writer saw and photographed, +on that part of the wall of Peking used by the Mandarins as an +observatory, the six instruments handsomely designed by Father +Verbiest, copied from the instruments of Tycho Brahe, and embellished +with Chinese dragons and emblems cast on the supports. He also saw +there two old instruments (which he was told were Arabic) of date +1279, by Ko Show-King, astronomer to Koblai Khan, the grandson of +Chenghis Khan. One of these last is nearly identical with the armillae +of Tycho; and the other with his "armillae quatori maxim," with +which he observed the comet of 1585, besides fixed stars and +planets.[3] + +The discovery by Galileo of the isochronism of the pendulum, followed +by Huyghens's adaptation of that principle to clocks, has been one of +the greatest aids to accurate observation. About the same time an +equally beneficial step was the employment of the telescope as a +pointer; not the Galilean with concave eye-piece, but with a +magnifying glass to examine the focal image, at which also a fixed +mark could be placed. Kepler was the first to suggest this. Gascoigne +was the first to use it. Huyghens used a metal strip of variable width +in the focus, as a micrometer to cover a planetary disc, and so to +measure the width covered by the planet. The Marquis Malvasia, in +1662, described the network of fine silver threads at right angles, +which he used in the focus, much as we do now. + +In the hands of such a skilful man as Tycho Brahe, the old open +sights, even without clocks, served their purpose sufficiently well to +enable Kepler to discover the true theory of the solar system. But +telescopic sights and clocks were required for proving some of +Newton's theories of planetary perturbations. Picard's observations at +Paris from 1667 onwards seem to embody the first use of the telescope +as a pointer. He was also the first to introduce the use of Huyghens's +clocks for observing the right ascension of stars. Olaus Romer was +born at Copenhagen in 1644. In 1675, by careful study of the times of +eclipses of Jupiter's satellites, he discovered that light took time +to traverse space. Its velocity is 186,000 miles per second. In 1681 +he took up his duties as astronomer at Copenhagen, and built the first +transit circle on a window-sill of his house. The iron axis was five +feet long and one and a-half inches thick, and the telescope was fixed +near one end with a counterpoise. The telescope-tube was a double +cone, to prevent flexure. Three horizontal and three vertical wires +were used in the focus. These were illuminated by a speculum, near the +object-glass, reflecting the light from a lantern placed over the +axis, the upper part of the telescope-tube being partly cut away to +admit the light. A divided circle, with pointer and reading +microscope, was provided for reading the declination. He realised the +superiority of a circle with graduations over a much larger +quadrant. The collimation error was found by reversing the instrument +and using a terrestrial mark, the azimuth error by star observations. +The time was expressed in fractions of a second. He also constructed a +telescope with equatoreal mounting, to follow a star by one axial +motion. In 1728 his instruments and observation records were destroyed +by fire. + +Hevelius had introduced the vernier and tangent screw in his +measurement of arc graduations. His observatory and records were burnt +to the ground in 1679. Though an old man, he started afresh, and left +behind him a catalogue of 1,500 stars. + +Flamsteed began his duties at Greenwich Observatory, as first +Astronomer Royal, in 1676, with very poor instruments. In 1683 he put +up a mural arc of 140, and in 1689 a better one, seventy-nine inches +radius. He conducted his measurements with great skill, and +introduced new methods to attain accuracy, using certain stars for +determining the errors of his instruments; and he always reduced his +observations to a form in which they could be readily used. He +introduced new methods for determining the position of the equinox and +the right ascension of a fundamental star. He produced a catalogue of +2,935 stars. He supplied Sir Isaac Newton with results of observation +required in his theoretical calculations. He died in 1719. + +Halley succeeded Flamsteed to find that the whole place had been +gutted by the latter's executors. In 1721 he got a transit instrument, +and in 1726 a mural quadrant by Graham. His successor in 1742, +Bradley, replaced this by a fine brass quadrant, eight feet radius, by +Bird; and Bradley's zenith sector was purchased for the observatory. +An instrument like this, specially designed for zenith stars, is +capable of greater rigidity than a more universal instrument; and +there is no trouble with refraction in the zenith. For these reasons +Bradley had set up this instrument at Kew, to attempt the proof of the +earth's motion by observing the annual parallax of stars. He certainly +found an annual variation of zenith distance, but not at the times of +year required by the parallax. This led him to the discovery of the +"aberration" of light and of nutation. Bradley has been described as +the founder of the modern system of accurate observation. He died in +1762, leaving behind him thirteen folio volumes of valuable but +unreduced observations. Those relating to the stars were reduced by +Bessel and published in 1818, at Knigsberg, 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 Zllner. + + +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. Kn. Bhm. 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 on each side of the equator, and that a +zone of equatoreal calms is free from spots. But it was +R. C. Carrington[4] who, by his continuous observations at Redhill, in +Surrey, established the remarkable fact that, while the rotation +period in the highest latitudes, 50, where spots are seen, is +twenty-seven-and-a-half days, near the equator the period is only +twenty-five days. His splendid volume of observations of the sun led +to much new information about the average distribution of spots at +different epochs. + +Schwabe, of Dessau, began in 1826 to study the solar surface, and, +after many years of work, arrived at a law of frequency which has been +more fruitful of results than any discovery in solar physics.[5] In +1843 he announced a decennial period of maxima and minima of sun-spot +displays. In 1851 it was generally accepted, and, although a period of +eleven years has been found to be more exact, all later observations, +besides the earlier ones which have been hunted up for the purpose, go +to establish a true periodicity in the number of sun-spots. But quite +lately Schuster[6] has given reasons for admitting a number of +co-existent periods, of which the eleven-year period was predominant +in the nineteenth century. + +In 1851 Lament, a Scotchman at Munich, found a decennial period in the +daily range of magnetic declination. In 1852 Sir Edward Sabine +announced a similar period in the number of "magnetic storms" +affecting all of the three magnetic elements--declination, dip, and +intensity. Australian and Canadian observations both showed the +decennial period in all three elements. Wolf, of Zurich, and Gauthier, +of Geneva, each independently arrived at the same conclusion. + +It took many years before this coincidence was accepted as certainly +more than an accident by the old-fashioned astronomers, who want rigid +proof for every new theory. But the last doubts have long vanished, +and a connection has been further traced between violent outbursts of +solar activity and simultaneous magnetic storms. + +The frequency of the Aurora Borealis was found by Wolf to follow the +same period. In fact, it is closely allied in its cause to terrestrial +magnetism. Wolf also collected old observations tracing the +periodicity of sun-spots back to about 1700 A.D. + +Spoerer deduced a law of dependence of the average latitude of +sun-spots on the phase of the sun-spot period. + +All modern total solar eclipse observations seem to show that the +shape of the luminous corona surrounding the moon at the moment of +totality has a special distinct character during the time of a +sun-spot maximum, and another, totally different, during a sun-spot +minimum. + +A suspicion is entertained that the total quantity of heat received by +the earth from the sun is subject to the same period. This would have +far-reaching effects on storms, harvests, vintages, floods, and +droughts; but it is not safe to draw conclusions of this kind except +from a very long period of observations. + +Solar photography has deprived astronomers of the type of Carrington +of the delight in devoting a life's work to collecting data. It has +now become part of the routine work of an observatory. + +In 1845 Foucault and Fizeau took a daguerreotype photograph of the +sun. In 1850 Bond produced one of the moon of great beauty, Draper +having made some attempts at an even earlier date. But astronomical +photography really owes its beginning to De la Rue, who used the +collodion process for the moon in 1853, and constructed the Kew +photoheliograph in 1857, from which date these instruments have been +multiplied, and have given us an accurate record of the sun's surface. +Gelatine dry plates were first used by Huggins in 1876. + +It is noteworthy that from the outset De la Rue recognised the value +of stereoscopic vision, which is now known to be of supreme +accuracy. In 1853 he combined pairs of photographs of the moon in the +same phase, but under different conditions regarding libration, +showing the moon from slightly different points of view. These in the +stereoscope exhibited all the relief resulting from binocular vision, +and looked like a solid globe. In 1860 he used successive photographs +of the total solar eclipse stereoscopically, to prove that the red +prominences belong to the sun, and not to the moon. In 1861 he +similarly combined two photographs of a sun-spot, the perspective +effect showing the umbra like a floor at the bottom of a hollow +penumbra; and in one case the facul 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 facul 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 facul 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. ngstrom 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-l en dehors des clipses_." And the next day he observed the +lines at the edge of the uneclipsed sun. Huggins had suggested this +observation in February, 1868, his idea being to use prisms of such +great dispersive power that the continuous spectrum reflected by our +atmosphere should be greatly weakened, while a bright line would +suffer no diminution by the high dispersion. On October 20th +Lockyer,[10] having news of the eclipse, but not of Jansen's +observations the day after, was able to see these lines. This was a +splendid performance, for it enabled the prominences to be observed, +not only during eclipses, but every day. Moreover, the next year +Huggins was able, by using a wide slit, to see the whole of a +prominence and note its shape. Prominences are classified, according +to their form, into "flame" and "cloud" prominences, the spectrum of +the latter showing calcium, hydrogen, and helium; that of the former +including a number of metals. + +The D line of sodium is a double line, and in the same eclipse (1868) +an orange line was noticed which was afterwards found to lie close to +the two components of the D line. It did not correspond with any known +terrestrial element, and the unknown element was called "helium." It +was not until 1895 that Sir William Ramsay found this element as a gas +in the mineral cleavite. + +The spectrum of the corona is partly continuous, indicating light +reflected from the sun's body. But it also shows a green line +corresponding with no known terrestrial element, and the name +"coronium" has been given to the substance causing it. + +A vast number of facts have been added to our knowledge about the sun +by photography and the spectroscope. Speculations and hypotheses in +plenty have been offered, but it may be long before we have a complete +theory evolved to explain all the phenomena of the storm-swept +metallic atmosphere of the sun. + +The proceedings of scientific societies teem with such facts and +"working hypotheses," and the best of them have been collected by Miss +Clerke in her _History of Astronomy during the Nineteenth Century_. As +to established facts, we learn from the spectroscopic researches (1) +that the continuous spectrum is derived from the _photosphere_ or +solar gaseous material compressed almost to liquid consistency; (2) +that the _reversing layer_ surrounds it and gives rise to black +lines in the spectrum; that the _chromosphere_ surrounds this, is +composed mainly of hydrogen, and is the cause of the red prominences +in eclipses; and that the gaseous _corona_ surrounds all of +these, and extends to vast distances outside the sun's visible +surface. + + +FOOTNOTES: + +[1] _Rosa Ursina_, by C. Scheiner, _fol_.; Bracciani, 1630. + +[2] _R. S. Phil. Trans_., 1774. + +[3] _Ibid_, 1783. + +[4] _Observations on the Spots on the Sun, etc.,_ 4; London and +Edinburgh, 1863. + +[5] _Periodicitt 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. Shrter supported this +opinion. W. Herschel opposed it. But Beer and Mdler 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 Schrter, Beer and Mdler (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 _Linn_, 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 (Msting 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. Shrter 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 Mdler, 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 Mdler 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, Rmer, 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. Shrter estimated its thickness at +500 miles. + +Many speculations have been advanced to explain the origin and +constitution of the ring. De Sejour said [6] that it was thrown off +from Saturn's equator as a liquid ring, and afterwards solidified. He +noticed that the outside would have a greater velocity, and be less +attracted to the planet, than the inner parts, and that equilibrium +would be impossible; so he supposed it to have solidified into a +number of concentric rings, the exterior ones having the least +velocity. + +Clerk Maxwell, in the Adams prize essay, gave a physico-mathematical +demonstration that the rings must be composed of meteoritic matter +like gravel. Even so, there must be collisions absorbing the energy of +rotation, and tending to make the rings eventually fall into the +planet. The slower motion of the external parts has been proved by the +spectroscope in Keeler's hands, 1895. + +Saturn has perhaps received more than its share of attention owing to +these rings. This led to other discoveries. Huyghens in 1655, and +J. D. Cassini in 1671, discovered the sixth and eighth satellites +(Titan and Japetus). Cassini lost his satellite, and in searching for +it found Rhea (the fifth) in 1672, besides his old friend, whom he +lost again. He added the third and fourth in 1684 (Tethys and +Dione). The first and second (Mimas and Encelades) were added by +Herschel in 1789, and the seventh (Hyperion) simultaneously by Lassel +and Bond in 1848. The ninth (Phoebe) was found on photographs, by +Pickering in 1898, with retrograde motion; and he has lately added a +tenth. + +The occasional disappearance of Cassini's Japetus was found on +investigation to be due to the same causes as that of Jupiter's fourth +satellite, and proves that it always turns the same face to the +planet. + +_Uranus and Neptune_.--The splendid discoveries of Uranus and two +satellites by Sir William Herschel in 1787, and of Neptune by Adams +and Le Verrier in 1846, have been already described. Lassel added two +more satellites to Uranus in 1851, and found Neptune's satellite in +1846. All of the satellites of Uranus have retrograde motion, and +their orbits are inclined about 80 to the ecliptic. + +The spectroscope has shown the existence of an absorbing atmosphere on +Jupiter and Saturn, and there are suspicions that they partake +something of the character of the sun, and emit some light besides +reflecting solar light. On both planets some absorption lines seem to +agree with the aqueous vapour lines of our own atmosphere; while one, +which is a strong band in the red common to both planets, seems to +agree with a line in the spectrum of some reddish stars. + +Uranus and Neptune are difficult to observe spectroscopically, but +appear to have peculiar spectra agreeing together. Sometimes Uranus +shows Frauenhofer lines, indicating reflected solar light. But +generally these are not seen, and six broad bands of absorption +appear. One is the F. of hydrogen; another is the red-star line of +Jupiter and Saturn. Neptune is a very difficult object for the +spectroscope. + +Quite lately [7] P. Lowell has announced that V. M. Slipher, at +Flagstaff Observatory, succeeded in 1907 in rendering some plates +sensitive far into the red. A reproduction is given of photographed +spectra of the four outermost planets, showing (1) a great number of +new lines and bands; (2) intensification of hydrogen F. and C. lines; +(3) a steady increase of effects (1) and (2) as we pass from Jupiter +and Saturn to Uranus, and a still greater increase in Neptune. + +_Asteroids_.--The discovery of these new planets has been +described. At the beginning of the last century it was an immense +triumph to catch a new one. Since photography was called into the +service by Wolf, they have been caught every year in shoals. It is +like the difference between sea fishing with the line and using a +steam trawler. In the 1908 almanacs nearly seven hundred asteroids are +included. The computation of their perturbations and ephemerides by +Euler's and Lagrange's method of variable elements became so laborious +that Encke devised a special process for these, which can be applied +to many other disturbed orbits. [8] + +When a photograph is taken of a region of the heavens including an +asteroid, the stars are photographed as points because the telescope +is made to follow their motion; but the asteroids, by their proper +motion, appear as short lines. + +The discovery of Eros and the photographic attack upon its path have +been described in their relation to finding the sun's distance. + +A group of four asteroids has lately been found, with a mean distance +and period equal to that of Jupiter. To three of these masculine names +have been given--Hector, Patroclus, Achilles; the other has not yet +been named. + + +FOOTNOTES: + +[1] Langrenus (van Langren), F. Selenographia sive lumina austriae +philippica; Bruxelles, 1645. + +[2] _Astr. Nach._, 2,944. + +[3] _Acad. des Sc._, Paris; _C.R._, lxxxiii., 1876. + +[4] _Mem. Spettr. Ital._, xi., p. 28. + +[5] _R. S. Phil. Trans_., No. 1. + +[6] Grant's _Hist. Ph. Ast_., p. 267. + +[7] _Nature_, November 12th, 1908. + +[8] _Ast. Nach_., Nos. 791, 792, 814, translated by G. B. Airy. +_Naut. Alm_., Appendix, 1856. + + + +14. COMETS AND METEORS. + + +Ever since Halley discovered that the comet of 1682 was a member of +the solar system, these wonderful objects have had a new interest for +astronomers; and a comparison of orbits has often identified the +return of a comet, and led to the detection of an elliptic orbit where +the difference from a parabola was imperceptible in the small portion +of the orbit visible to us. A remarkable case in point was the comet +of 1556, of whose identity with the comet of 1264 there could be +little doubt. Hind wanted to compute the orbit more exactly than +Halley had done. He knew that observations had been made, but they +were lost. Having expressed his desire for a search, all the +observations of Fabricius and of Heller, and also a map of the comet's +path among the stars, were eventually unearthed in the most unlikely +manner, after being lost nearly three hundred years. Hind and others +were certain that this comet would return between 1844 and 1848, but +it never appeared. + +When the spectroscope was first applied to finding the composition of +the heavenly bodies, there was a great desire to find out what comets +are made of. The first opportunity came in 1864, when Donati observed +the spectrum of a comet, and saw three bright bands, thus proving that +it was a gas and at least partly self-luminous. In 1868 Huggins +compared the spectrum of Winnecke's comet with that of a Geissler tube +containing olefiant gas, and found exact agreement. Nearly all comets +have shown the same spectrum.[1] A very few comets have given bright +band spectra differing from the normal type. Also a certain kind of +continuous spectrum, as well as reflected solar light showing +Frauenhofer lines, have been seen. + +[Illustration: COPY OF THE DRAWING MADE BY PAUL FABRICIUS. To define +the path of comet 1556. After being lost for 300 years, this drawing +was recovered by the prolonged efforts of Mr. Hind and Professor +Littrow in 1856.] + +When Wells's comet, in 1882, approached very close indeed to the sun, +the spectrum changed to a mono-chromatic yellow colour, due to sodium. + +For a full account of the wonders of the cometary world the reader is +referred to books on descriptive astronomy, or to monographs on +comets.[2] Nor can the very uncertain speculations about the structure +of comets' tails be given here. A new explanation has been proposed +almost every time that a great discovery has been made in the theory +of light, heat, chemistry, or electricity. + +Halley's comet remained the only one of which a prediction of the +return had been confirmed, until the orbit of the small, ill-defined +comet found by Pons in 1819 was computed by Encke, and found to have a +period of 3 1/3 years. It was predicted to return in 1822, and was +recognised by him as identical with many previous comets. This comet, +called after Encke, has showed in each of its returns an inexplicable +reduction of mean distance, which led to the assertion of a resisting +medium in space until a better explanation could be found.[3] + +Since that date fourteen comets have been found with elliptic orbits, +whose aphelion distances are all about the same as Jupiter's mean +distance; and six have an aphelion distance about ten per cent, +greater than Neptune's mean distance. Other comets are similarly +associated with the planets Saturn and Uranus. + +The physical transformations of comets are among the most wonderful of +unexplained phenomena in the heavens. But, for physical astronomers, +the greatest interest attaches to the reduction of radius vector of +Encke's comet, the splitting of Biela's comet into two comets in 1846, +and the somewhat similar behaviour of other comets. It must be noted, +however, that comets have a sensible size, that all their parts cannot +travel in exactly the same orbit under the sun's gravitation, and that +their mass is not sufficient to retain the parts together very +forcibly; also that the inevitable collision of particles, or else +fluid friction, is absorbing energy, and so reducing the comet's +velocity. + +In 1770 Lexell discovered a comet which, as was afterwards proved by +investigations of Lexell, Burchardt, and Laplace, had in 1767 been +deflected by Jupiter out of an orbit in which it was invisible from +the earth into an orbit with a period of 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 Pingr, 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 NEBUL. + + +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 nebul 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 +Lyr). 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 Vgel, 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; N. Decl. 25. This +grand discovery has been amply confirmed, and, though opinions differ +as to the exact direction, it happens that the point first indicated +by Herschel, from totally insufficient data, agrees well with modern +estimates. + +Comparing the proper motions and parallaxes to get the actual velocity +of each star relative to our system, C.L. Struve found the probable +velocity of the solar system in space to be fifteen miles a second, or +five astronomical units a year. + +The work of Herschel in this matter has been checked by comparing +spectroscopic velocities in the line of sight which, so far as the +sun's motion is concerned, would give a maximum rate of approach for +stars near Hercules, a maximum rate of recession for stars in the +opposite part of the heavens, and no effect for stars half-way +between. In this way the spectroscope has confirmed generally +Herschel's view of the direction, and makes the velocity eleven miles +a second, or nearly four astronomical units a year. + +The average proper motion of a first magnitude star has been found to +be 0".25 annually, and of a sixth magnitude star 0".04. But that all +bright stars are nearer than all small stars, or that they show +greater proper motion for that reason, is found to be far from the +truth. Many statistical studies have been made in this connection, and +interesting results may be expected from this treatment in the hands +of Kapteyn of Groningen, and others.[9] + +On analysis of the directions of proper motions of stars in all parts +of the heavens, Kapteyn has shown[10] that these indicate, besides the +solar motion towards Hercules, two general drifts of stars in nearly +opposite directions, which can be detected in any part of the +heavens. This result has been confirmed from independent data by +Eddington (_R.A.S., M.N._) and Dyson (_R.S.E. Proc._). + +Photography promises to assist in the measurement of parallax and +proper motions. Herr Pulfrich, of the firm of Carl Zeiss, has vastly +extended the applications of stereoscopic vision to astronomy--a +subject which De la Rue took up in the early days of photography. He +has made a stereo-comparator of great beauty and convenience for +comparing stereoscopically two star photographs taken at different +dates. Wolf of Heidelberg has used this for many purposes. His +investigations depending on the solar motion in space are remarkable. +He photographs stars in a direction at right angles to the line of the +sun's motion. He has taken photographs of the same region fourteen +years apart, the two positions of his camera being at the two ends of +a base-line over 5,000,000,000 miles apart, or fifty-six astronomical +units. On examining these stereoscopically, some of the stars rise out +of the general plane of the stars, and seem to be much nearer. Many of +the stars are thus seen to be suspended in space at different +distances corresponding exactly to their real distances from our solar +system, except when their proper motion interferes. The effect is most +striking; the accuracy of measurement exceeds that of any other method +of measuring such displacements, and it seems that with a long +interval of time the advantage of the method increases. + +_Double Stars._--The large class of double stars has always been much +studied by amateurs, partly for their beauty and colour, and partly as +a test for telescopic definition. Among the many unexplained stellar +problems there is one noticed in double stars that is thought by some +to be likely to throw light on stellar evolution. It is this: There +are many instances where one star of the pair is comparatively faint, +and the two stars are contrasted in colour; and in every single case +the general colour of the faint companion is invariably to be classed +with colours more near to the blue end of the spectrum than that of +the principal star. + +_Binary Stars._--Sir William Herschel began his observations of double +stars in the hope of discovering an annual parallax of the stars. In +this he was following a suggestion of Galileo's. The presumption is +that, if there be no physical connection between the stars of a pair, +the largest is the nearest, and has the greatest parallax. So, by +noting the distance between the pair at different times of the year, a +delicate test of parallax is provided, unaffected by major +instrumental errors. + +Herschel did, indeed, discover changes of distance, but not of the +character to indicate parallax. Following this by further observation, +he found that the motions were not uniform nor rectilinear, and by a +clear analysis of the movements he established the remarkable and +wholly unexpected fact that in all these cases the motion is due to a +revolution about their common centre of gravity.[11] He gave the +approximate period of revolution of some of these: Castor, 342 years; +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 Coron 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 "Nov" 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 Nov, 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. + +_Nebul and Star-clusters._--Our knowledge of nebul 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 nebul might be clusters of +innumerable minute stars at a great distance. Then he recognised the +different classes of nebul, and became convinced that there is a +widely-diffused "shining fluid" in space, though many so-called nebul +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 +nebul" might show a stage of evolution from the diffuse nebul, 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 nebul. + +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 nebul; 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 nebul, 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 or 5 square. Barnard asserts that the "nebular +hypothesis" would have been killed at its birth by a knowledge of +these photographs. Later he has used still more powerful instruments, +and extended his discoveries. + +The association of stars with planetary nebul, and the distribution +of nebul 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 _Systme 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 +ngstrom, 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 Mdler, 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 +Chaldan 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 +Pingr, 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 (Mller), 24 +Respighi, 82 +Retrograde motion of planets, 22 +Riccioli, 107 +Roberts, 137 +Rmer, 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 +Schrter, 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 Rmer, 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 +Zllner, 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 8172-8.txt or 8172-8.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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You may copy it, give it away or re-use it under the terms of +the Project Gutenberg License included with this eBook or online at +www.gutenberg.org. If you are not located in the United States, you'll have +to check the laws of the country where you are located before using this ebook. + +Title: History of Astronomy + +Author: George Forbes + +Release Date: June 25, 2003 [EBook #8172] +[Most recently updated: March 21, 2020] + +Language: English + +Character set encoding: UTF-8 + +*** START OF THIS PROJECT GUTENBERG EBOOK HISTORY OF ASTRONOMY *** + + + + +Produced by Jonathan Ingram, Dave Maddock, Charles Franks +and the Online Distributed Proofreading Team. + + + + + + +</pre> + +<div class="fig" style="width:60%;"> +<a name="illus01"></a> +<img src="images/001.jpg" style="width:100%;" alt="SIR ISAAC NEWTON +(From the bust by Roubiliac In Trinity College, Cambridge.)" /> +<p class="caption">S<small>IR</small> I<small>SAAC</small> +N<small>EWTON</small><br/>(From the bust by Roubiliac In Trinity College, +Cambridge.)</p> +</div> + +<h1>HISTORY OF ASTRONOMY</h1> + +<h3>BY</h3> + +<h2>GEORGE FORBES,<br/> +M.A., F.R.S., M. INST. C. E.,</h2> + +<p><b>(FORMERLY PROFESSOR OF NATURAL PHILOSOPHY, ANDERSON’S +COLLEGE, GLASGOW)</b></p> + +<p>AUTHOR OF “THE TRANSIT OF VENUS,” RENDU’S +“THEORY OF THE GLACIERS OF SAVOY,” ETC., ETC.</p> + +<p><br/><br/></p> + +<h2>CONTENTS</h2> + +<table summary="" style=""> + +<tr> +<td> <a href="#preface">PREFACE</a><br/><br/></td> +</tr> + +<tr> +<td> <a href="#book01"><b>BOOK I. THE GEOMETRICAL PERIOD</b></a></td> +</tr> + +<tr> +<td> <a href="#1">1. PRIMITIVE ASTRONOMY AND ASTROLOGY</a></td> +</tr> + +<tr> +<td> <a href="#2">2. ANCIENT ASTRONOMY—CHINESE AND CHALDÆANS</a></td> +</tr> + +<tr> +<td> <a href="#3">3. ANCIENT GREEK ASTRONOMY</a></td> +</tr> + +<tr> +<td> <a href="#4">4. THE REIGN OF EPICYCLES—FROM PTOLEMY TO COPERNICUS</a><br/><br/></td> +</tr> + +<tr> +<td> <a href="#book02"><b>BOOK II. THE DYNAMICAL PERIOD</b></a></td> +</tr> + +<tr> +<td> <a href="#5">5. DISCOVERY OF THE TRUE SOLAR SYSTEM—TYCHO BRAHE—KEPLER</a></td> +</tr> + +<tr> +<td> <a href="#6">6. GALILEO AND THE TELESCOPE—NOTIONS OF GRAVITY BY HORROCKS, ETC.</a></td> +</tr> + +<tr> +<td> <a href="#7">7. SIR ISAAC NEWTON—LAW OF UNIVERSAL GRAVITATION</a></td> +</tr> + +<tr> +<td> <a href="#8">8. NEWTON’S SUCCESSORS—HALLEY, EULER, LAGRANGE, +LAPLACE, ETC.</a></td> +</tr> + +<tr> +<td> <a href="#9">9. DISCOVERY OF NEW PLANETS—HERSCHEL, PIAZZI, ADAMS, +AND LE VERRIER</a><br/><br/></td> +</tr> + +<tr> +<td> <a href="#book03"><b>BOOK III. OBSERVATION</b></a></td> +</tr> + +<tr> +<td> <a href="#10">10. INSTRUMENTS OF PRECISION—SIZE OF THE SOLAR SYSTEM</a></td> +</tr> + +<tr> +<td> <a href="#11">11. HISTORY OF THE TELESCOPE—SPECTROSCOPE</a><br/><br/></td> +</tr> + +<tr> +<td> <a href="#book04"><b>BOOK IV. THE PHYSICAL PERIOD</b></a></td> +</tr> + +<tr> +<td> <a href="#12">12. THE SUN</a></td> +</tr> + +<tr> +<td> <a href="#13">13. THE MOON AND PLANETS</a></td> +</tr> + +<tr> +<td> <a href="#14">14. COMETS AND METEORS</a></td> +</tr> + +<tr> +<td> <a href="#15">15. THE STARS AND NEBULÆ</a><br/><br/></td> +</tr> + +<tr> +<td> <a href="#16">ILLUSTRATIONS</a></td> +</tr> + +<tr> +<td> <a href="#index">INDEX</a></td> +</tr> +</table> + +<hr /> + +<div class="chapter"> + +<h2><a name="preface"></a>PREFACE</h2> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p class="right"> +G. F. +</p> + +<p> +<i>August</i> 1<i>st</i>, 1909. +</p> + +</div><!--end chapter--> + +<div class="chapter"> + +<h2><a name="book01"></a>BOOK I. THE GEOMETRICAL PERIOD</h2> + +</div><!--end chapter--> + +<div class="chapter"> + +<h3><a name="1"></a>1. PRIMITIVE ASTRONOMY AND ASTROLOGY.</h3> + +<p> +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 <i>à priori</i> 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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +If the ancient Chaldæans gave to the planetary conjunctions an influence over +terrestrial events, let us remember that in our own time people have searched +for connection between terrestrial conditions and periods of unusual prevalence +of sun spots; while De la Rue, Loewy, and Balfour Stewart<a href="#linknote-1" name="linknoteref-1" id="linknoteref-1"><sup>[1]</sup></a> 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. +</p> + +<p> +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 <i>Soldier’s Pocket +Book</i>. +</p> + +<p> +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. +</p> + +<p> +So Hipparchus, about 150 B.C., and Ptolemy a little later, were able to use the +observations of Chaldæan astrologers, as well as those of Alexandrian +astronomers, and to make some discoveries which have helped the progress of +astronomy in all ages. So, also, Mr. Cowell<a href="#linknote-2" name="linknoteref-2" id="linknoteref-2"><sup>[2]</sup></a> has +examined the marks made on the baked bricks used by the Chaldæans for recording +the eclipses of 1062 B.C. and 762 B.C.; and has thereby been enabled, in the +last few years, to correct the lunar tables of Hansen, and to find a more +accurate value for the secular acceleration of the moon’s longitude and +the node of her orbit than any that could be obtained from modern observations +made with instruments of the highest precision. +</p> + +<p> +So again, Mr. Hind<a href="#linknote-3" name="linknoteref-3" id="linknoteref-3"><sup>[3]</sup></a> 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.<a href="#linknote-4" name="linknoteref-4" id="linknoteref-4"><sup>[4]</sup></a> +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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 <i>if</i> 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. +</p> + +<p> +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 <i>heliacal risings</i>—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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<hr /> + +<p> +<b>FOOTNOTES:</b> +</p> + +<p class="footnote"> +<a name="linknote-1" id="linknote-1"></a> <a href="#linknoteref-1">[1]</a> +Trans. R. S. E., xxiii. 1864, p. 499, <i>On Sun +Spots</i>, <i>etc</i>., by B. Stewart. Also Trans. R. S. 1860-70. Also Prof. +Ernest Brown, in <i>R. A. S. Monthly Notices</i>, 1900. +</p> + +<p class="footnote"> +<a name="linknote-2" id="linknote-2"></a> <a href="#linknoteref-2">[2]</a> +<i>R. A. S. Monthly Notices</i>, Sup.; 1905. +</p> + +<div class="fig" style="width:60%;"> +<a name="illus02"></a> +<img src="images/002.jpg" style="width:100%;" alt="CHALDÆAN BAKED BRICK OR +TABLET" /> +<p class="caption">C<small>HALDÆAN</small> B<small>AKED</small> B<small>RICK +OR</small> T<small>ABLET</small>,<br/> +<i>Obverse and reverse sides</i>,<br/> +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.) +</p> +</div> + +<p class="footnote"> +<a name="linknote-3" id="linknote-3"></a> <a href="#linknoteref-3">[3]</a> +<i>R. A. S. Monthly Notices</i>, vol. x., p. 65. +</p> + +<p class="footnote"> +<a name="linknote-4" id="linknote-4"></a> <a href="#linknoteref-4">[4]</a> +R. S. E. Proc., vol. x., 1880. +</p> + +</div><!--end chapter--> + +<div class="chapter"> + +<h3><a name="2"></a>2. ANCIENT ASTRONOMY—THE CHINESE AND CHALDÆANS.</h3> + +<p> +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. +</p> + +<p> +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 <i>Observations Astronomical, +Geographical, Chronological, and Physical</i>, drawn from ancient Chinese +books; and later by Father Moyriac-de-Mailla, who in 1777-1785 published +<i>Annals of the Chinese Empire, translated from Tong-Kien-Kang-Mou</i>. +</p> + +<p> +Bailly, in his <i>Astronomie Ancienne</i> (1781), drew, from these and other +sources, the conclusion that all we know of the astronomical learning of the +Chinese, Indians, Chaldæans, Assyrians, and Egyptians is but the remnant of a +far more complete astronomy of which no trace can be found. +</p> + +<p> +Delambre, in his <i>Histoire de l’Astronomie Ancienne</i> (1817), +ridicules the opinion of Bailly, and considers that the progress made by all of +these nations is insignificant. +</p> + +<p> +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. +</p> + +<p> +<i>China</i>.—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.).<a href="#linknote-5" name="linknoteref-5" id="linknoteref-5"><sup>[1]</sup></a> 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. +</p> + +<p> +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. +</p> + +<p> +It is also asserted, in the book called <i>Chu-King</i>, that in the time of +Yao the year was known to have 365¼ days, and that he adopted 365 days and +added an intercalary day every four years (as in the Julian Calendar). This may +be true or not, but the ancient Chinese certainly seem to have divided the +circle into 365 degrees. To learn the length of the year needed only patient +observation—a characteristic of the Chinese; but many younger nations got +into a terrible mess with their calendar from ignorance of the year’s +length. +</p> + +<p> +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 <i>Saros</i>. 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. +</p> + +<p> +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 <i>Observations of Comets from 611 B.C. to 1640 A.D., Extracted +from the Chinese Annals</i>. +</p> + +<p> +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. +</p> + +<p> +<i>Chaldæans</i>.—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. +</p> + +<p> +The Chaldæans, being the most ancient Babylonians, held the same station and +dignity in the State as did the priests in Egypt, and spent all their time in +the study of philosophy and astronomy, and the arts of divination and +astrology. They held that the world of which we have a conception is an eternal +world without any beginning or ending, in which all things are ordered by rules +supported by a divine providence, and that the heavenly bodies do not move by +chance, nor by their own will, but by the determinate will and appointment of +the gods. They recorded these movements, but mainly in the hope of tracing the +will of the gods in mundane affairs. Ptolemy (about 130 A.D.) made use of +Babylonian eclipses in the eighth century B.C. for improving his solar and +lunar tables. +</p> + +<p> +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. +</p> + +<p> +We have records of observations carried on under Asshurbanapal, who sent +astronomers to different parts to study celestial phenomena. Here is +one:— +</p> + +<p> +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.” +</p> + +<p> +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<a href="#linknote-6" name="linknoteref-6" id="linknoteref-6"><sup>[2]</sup></a> 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. +</p> + +<p> +Then again, Knobel reminds us of “the most interesting discovery a few +years ago by Father Strassmeier of a Babylonian tablet recording a partial +lunar eclipse at Babylon in the seventh year of Cambyses, on the fourteenth day +of the Jewish month Tammuz.” Ptolemy, in the Almagest (Suntaxis), says it +occurred in the seventh year of Cambyses, on the night of the seventeenth and +eighteenth of the Egyptian month Phamenoth. Pingré and Oppolzer fix the +date July 16th, 533 B.C. Thus are the relations of the chronologies of Jews and +Egyptians established by these explorations. +</p> + +<hr /> + +<p> +<b>FOOTNOTES:</b> +</p> + +<p class="footnote"> +<a name="linknote-5" id="linknote-5"></a> <a href="#linknoteref-5">[1]</a> +These ancient dates are uncertain. +</p> + +<p class="footnote"> +<a name="linknote-6" id="linknote-6"></a> <a href="#linknoteref-6">[2]</a> +<i>R. A. S. Monthly Notices</i>, vol. lxviii., No. 5, March, 1908. +</p> + +</div><!--end chapter--> + +<div class="chapter"> + +<h3><a name="3"></a>3. ANCIENT GREEK ASTRONOMY.</h3> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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.). +</p> + +<p> +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 +<i>Saros</i> 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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +Nicetas, Heraclides, and Ecphantes supposed the earth to revolve on its axis, +but to have no orbital motion. +</p> + +<p> +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. +</p> + +<p> +For further references to similar efforts of imagination the reader is referred +to Sir George Cornwall Lewis’s <i>Historical Survey of the Astronomy of +the Ancients</i>; 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:— +</p> + +<p> +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 +(<i>Xen. Mem</i>, i. 1, 11-15). +</p> + +<p> +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 <i>the problem of representing the courses of the +planets by circular and uniform motions</i>. +</p> + +<p> +Systematic observation among the Greeks began with the rise of the Alexandrian +school. Aristillus and Timocharis set up instruments and fixed the positions of +the zodiacal stars, near to which all the planets in their orbits pass, thus +facilitating the determination of planetary motions. Aristarchus (320-250 B.C.) +showed that the sun must be at least nineteen times as far off as the moon, +which is far short of the mark. He also found the sun’s diameter, +correctly, to be half a degree. Eratosthenes (276-196 B.C.) measured the +inclination to the equator of the sun’s apparent path in the +heavens—i.e., he measured the obliquity of the ecliptic, making it +23° 51’, confirming our knowledge of its continuous diminution +during historical times. He measured an arc of meridian, from Alexandria to +Syene (Assuan), and found the difference of latitude by the length of a shadow +at noon, summer solstice. He deduced the diameter of the earth, 250,000 stadia. +Unfortunately, we do not know the length of the stadium he used. +</p> + +<p> +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 <i>excentric</i>. The line from the earth to the +“excentric” was called the <i>line of apses</i>. A circle having +this centre was called the <i>equant</i>, 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. +</p> + +<p> +He proceeded in the same way to compute Lunar tables. Making use of Chaldæan +eclipses, he was able to get an accurate value of the moon’s mean motion. +[Halley, in 1693, compared this value with his own measurements, and so +discovered the acceleration of the moon’s mean motion. This was +conclusively established, but could not be explained by the Newtonian theory +for quite a long time.] He determined the plane of the moon’s orbit and +its inclination to the ecliptic. The motion of this plane round the pole of the +ecliptic once in eighteen years complicated the problem. He located the +moon’s excentric as he had done the sun’s. He also discovered some +of the minor irregularities of the moon’s motion, due, as Newton’s +theory proves, to the disturbing action of the sun’s attraction. +</p> + +<p> +In the year 134 B.C. Hipparchus observed a new star. This upset every notion +about the permanence of the fixed stars. He then set to work to catalogue all +the principal stars so as to know if any others appeared or disappeared. Here +his experiences resembled those of several later astronomers, who, when in +search of some special object, have been rewarded by a discovery in a totally +different direction. On comparing his star positions with those of Timocharis +and Aristillus he found no stars that had appeared or disappeared in the +interval of 150 years; but he found that all the stars seemed to have changed +their places with reference to that point in the heavens where the ecliptic is +90° from the poles of the earth—i.e., the equinox. He found that +this could be explained by a motion of the equinox in the direction of the +apparent diurnal motion of the stars. This discovery of <i>precession of the +equinoxes</i>, 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. +</p> + +<p> +Hipparchus was also the inventor of trigonometry, both plane and spherical. He +explained the method of using eclipses for determining the longitude. +</p> + +<p> +In connection with Hipparchus’ great discovery it may be mentioned that +modern astronomers have often attempted to fix dates in history by the effects +of precession of the equinoxes. (1) At about the date when the Great Pyramid +may have been built γ Draconis was near to the pole, and must have been +used as the pole-star. In the north face of the Great Pyramid is the entrance +to an inclined passage, and six of the nine pyramids at Gizeh possess the same +feature; all the passages being inclined at an angle between 26° and +27° to the horizon and in the plane of the meridian. It also appears that +4,000 years ago—i.e., about 2100 B.C.—an observer at the lower end +of the passage would be able to see γ Draconis, the then pole-star, at its +lower culmination.<a href="#linknote-7" name="linknoteref-7" id="linknoteref-7"><sup>[1]</sup></a> 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. +</p> + +<p> +(2) The Chaldæans gave names to constellations now invisible from Babylon which +would have been visible in 2000 B.C., at which date it is claimed that these +people were studying astronomy. +</p> + +<p> +(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 <i>Odyssey</i><a href="#linknote-8" name="linknoteref-8" id="linknoteref-8"><sup>[2]</sup></a> +(v. 272-5) and in the <i>Iliad</i> (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.<a href="#linknote-9" name="linknoteref-9" id="linknoteref-9"><sup>[3]</sup></a> +</p> + +<p> +(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<a href="#linknote-10" name="linknoteref-10" id="linknoteref-10"><sup>[4]</sup></a> 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. +</p> + +<p> +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 +<i>annual</i> 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 <i>deferent</i>), 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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<hr /> + +<p> +<b>FOOTNOTES:</b> +</p> + +<p class="footnote"> +<a name="linknote-7" id="linknote-7"></a> <a href="#linknoteref-7">[1]</a> +<i>Phil. Mag</i>., vol. xxiv., pp. 481-4. +</p> + +<p class="footnote"> +<a name="linknote-8" id="linknote-8"></a> <a href="#linknoteref-8">[2]</a> +<br/> +Plaeiadas t’ esoronte kai opse duonta bootaen<br/> +‘Arkton th’ aen kai amaxan epiklaesin kaleousin,<br/> +‘Ae t’ autou strephetai kai t’ Oriona dokeuei,<br/> +Oin d’ammoros esti loetron Okeanoio.<br/> +<br/> +“The Pleiades and Boötes that setteth late, and the Bear, which they +likewise call the Wain, which turneth ever in one place, and keepeth watch upon +Orion, and alone hath no part in the baths of the ocean.” +</p> + +<p class="footnote"> +<a name="linknote-9" id="linknote-9"></a> <a href="#linknoteref-9">[3]</a> +See Pearson in the Camb. Phil. Soc. Proc., vol. iv., +pt. ii., p. 93, on whose authority the above statements are made. +</p> + +<p class="footnote"> +<a name="linknote-10" id="linknote-10"></a> <a href="#linknoteref-10">[4]</a> +See p. 6 for definition. +</p> + +</div><!--end chapter--> + +<div class="chapter"> + +<h3><a name="4"></a>4. THE REIGN OF EPICYCLES—FROM PTOLEMY TO +COPERNICUS.</h3> + +<p> +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,<a href="#linknote-11" name="linknoteref-11" id="linknoteref-11"><sup>[1]</sup></a> and its ratio to that of the +epicycle,<a href="#linknote-12" name="linknoteref-12" id="linknoteref-12"><sup>[2]</sup></a> the distance of the excentric<a href="#linknote-13" name="linknoteref-13" id="linknoteref-13"><sup>[3]</sup></a> from the centre of the deferent, and the position of the +line of apses,<a href="#linknote-14" name="linknoteref-14" id="linknoteref-14"><sup>[4]</sup></a> 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. +</p> + +<p> +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. +</p> + +<p> +At the close of the fifteenth century King Alphonso of Spain employed computers +to produce the Alphonsine Tables (1488 A.D.), Purbach translated +Ptolemy’s book, and observations were carried out in Germany by +Müller, known as Regiomontanus, and Waltherus. +</p> + +<p> +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, <i>De Revolutionibus Orbium +Celestium</i>. 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. +</p> + +<p> +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. +</p> + +<p> +Copernicus could not sever himself from this obnoxious tradition.<a href="#linknote-15" name="linknoteref-15" id="linknoteref-15"><sup>[5]</sup></a> 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.<a href="#linknote-16" name="linknoteref-16" id="linknoteref-16"><sup>[6]</sup></a> 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. +</p> + +<p> +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,<a href="#linknote-17" name="linknoteref-17" id="linknoteref-17"><sup>[7]</sup></a> in drawing attention to the strange +conception, +</p> + +<p class="letter"> 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. +</p> + +<p> +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). +</p> + +<p> +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.<a href="#linknote-18" name="linknoteref-18" id="linknoteref-18"><sup>[8]</sup></a> He says:— +</p> + +<p class="letter"> 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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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.<a href="#linknote-19" name="linknoteref-19" id="linknoteref-19"><sup>[9]</sup></a> He says that whoever is not satisfied with this +explanation must be contented by being told that “mathematics are for +mathematicians” (Mathematicis mathematica scribuntur). +</p> + +<p> +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, <i>Tycho Brahe</i>) “proofs of the physical truth of +his system Copernicus had given none, and could give none,” any more than +Pythagoras or Aristarchus. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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 <i>Six Lectures on +Astronomy</i>, 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. +</p> + +<div class="fig" style="width:50%;"> +<a name="illus03"></a> +<img src="images/003.jpg" style="width:100%;" alt="“QUADRANS MURALIS SIVE +TICHONICUS.”" /> +<p class="caption">“Q<small>UADRANS</small> M<small>URALIS SIVE</small> +T<small>ICHONICUS</small>.”<br/> 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 +<i>Astronomiæ Instauratæ Mechanica</i>.) +</p> +</div> + +<hr /> + +<p> +<b>FOOTNOTES:</b> +</p> + +<p class="footnote"> +<a name="linknote-11" id="linknote-11"></a> <a href="#linknoteref-11">[1]</a> +For definition see p. 22. +</p> + +<p class="footnote"> +<a name="linknote-12" id="linknote-12"></a> <a href="#linknoteref-12">[2]</a> +<i>Ibid</i>. +</p> + +<p class="footnote"> +<a name="linknote-13" id="linknote-13"></a> <a href="#linknoteref-13">[3]</a> +For definition see p. 18. +</p> + +<p class="footnote"> +<a name="linknote-14" id="linknote-14"></a> <a href="#linknoteref-14">[4]</a> +For definition see p. 18. +</p> + +<p class="footnote"> +<a name="linknote-15" id="linknote-15"></a> <a href="#linknoteref-15">[5]</a> +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, <i>Ast. Mod. Hist</i>., pp. 86, +87). +</p> + +<p class="footnote"> +<a name="linknote-16" id="linknote-16"></a> <a href="#linknoteref-16">[6]</a> +Kepler tells us that Tycho Brahe was pleased with this device, and adapted it +to his own system. +</p> + +<p class="footnote"> +<a name="linknote-17" id="linknote-17"></a> <a href="#linknoteref-17">[7]</a> +<i>Hist. Ast.</i>, vol. i., p. 354. +</p> + +<p class="footnote"> +<a name="linknote-18" id="linknote-18"></a> <a href="#linknoteref-18">[8]</a> +<i>Hist. of Phys. Ast.</i>, p. vii. +</p> + +<p class="footnote"> +<a name="linknote-19" id="linknote-19"></a> <a href="#linknoteref-19">[9]</a> +“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.” +</p> + +</div><!--end chapter--> + +<div class="chapter"> + +<h2><a name="book02"></a>BOOK II. THE DYNAMICAL PERIOD</h2> + +</div><!--end chapter--> + +<div class="chapter"> + +<h3><a name="5"></a>5. DISCOVERY OF THE TRUE SOLAR SYSTEM—TYCHO +BRAHE—KEPLER.</h3> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +For a complete life of this great man the reader is referred to Dreyer’s +<i>Tycho Brahe</i>, 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. +</p> + +<p> +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.<a href="#linknote-20" name="linknoteref-20" id="linknoteref-20"><sup>[1]</sup></a> +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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 (<i>De Mundi</i>, <i>etc</i>.) that +</p> + +<p class="letter">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. +</p> + +<p> +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 <i>Tischreden</i>, pp. 22, 60) +derided him in his usual pithy manner, that Melancthon (<i>Initia doctrinae +physicae</i>) 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. +</p> + +<p> +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. +</p> + +<div class="fig" style="width:60%;"> +<a name="illus04"></a> +<img src="images/004.jpg" style="width:100%;" alt="PORTRAIT OF JOHANNES +KEPLER." /> +<p class="caption">P<small>ORTRAIT OF</small> J<small>OHANNES</small> +K<small>EPLER</small>.<br/> By F. Wanderer, from Reitlinger’s +“Johannes Kepler”<br/> (original in Strassburg). +</p> +</div> + +<p> +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 <i>à priori</i> +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. +</p> + +<p> +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.<a href="#linknote-21" name="linknoteref-21" id="linknoteref-21"><sup>[2]</sup></a> +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +His first law states that the planets describe ellipses with the sun at a focus +of each ellipse. +</p> + +<p> +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, <i>Astronomia Nova, sen. Physica Coelestis +tradita commentariis de Motibus Stelloe; Martis</i>, Prague, 1609. +</p> + +<p> +It took him nine years more<a href="#linknote-22" name="linknoteref-22" id="linknoteref-22"><sup>[3]</sup></a> to discover his third law, +that the squares of the periodic times are proportional to the cubes of the +mean distances from the sun. +</p> + +<p> +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. +</p> + +<p> +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 <i>Harmonics</i>, +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. +</p> + +<p> +The whole book, <i>Astronomia Nova</i>, 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. +</p> + +<p> + +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 +E<sub>3</sub> the date of the year gives the angle E<sub>3</sub>SM. And the +observation of Tycho gives the direction of Mars compared with the sun, +SE<sub>3</sub>M. So all the angles of the triangle SEM in any of these +positions of E are known, and also the ratios of SE<sub>1</sub>, +SE<sub>2</sub>, SE<sub>3</sub>, SE<sub>4</sub> to SM and to each other. +</p> + +<div class="fig" style="width:100%;"> +<img src="images/006.jpg" width="300" height="274" alt="" /> +</div> + +<p> +For the orbit of Mars observations were chosen at intervals of a year, when the +earth was always in the same place. +</p> + +<p> +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, <i>De Mundo Nostro Sublunari, Philosophia Nova</i>, +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 <i>De Magnete</i> was published in 1600.) +</p> + +<p> +A few of Kepler’s views on gravitation, extracted from the Introduction +to his <i>Astronomia Nova</i>, may now be mentioned:— +</p> + +<p> +1. Every body at rest remains at rest if outside the attractive power of other +bodies. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +5. If the earth and moon were not retained in their orbits by vital force +(<i>aut alia aligua aequipollenti</i>), the earth and moon would come together. +</p> + +<p> +6. If the earth were to cease to attract its waters, the oceans would all rise +and flow to the moon. +</p> + +<p> +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.” +</p> + +<p> +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. +</p> + +<p> +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? +</p> + +<hr /> + +<p> +<b>FOOTNOTES:</b> +</p> + +<p class="footnote"> +<a name="linknote-20" id="linknote-20"></a> <a href="#linknoteref-20">[1]</a> +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. +</p> + +<p class="footnote"> +<a name="linknote-21" id="linknote-21"></a> <a href="#linknoteref-21">[2]</a> +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 <i>foci</i>. Kepler found the sun to be in one +focus, say S. AB is the <i>major axis</i>. DE is the <i>minor axis</i>. C is +the <i>centre</i>. The direction of AB is the <i>line of apses</i>. The ratio +of CS to CA is the <i>excentricity</i>. The position of the planet at A is the +<i>perihelion</i> (nearest to the sun). The position of the planet at B is the +<i>aphelion</i> (farthest from the sun). The angle ASP is the <i>anomaly</i> +when the planet is at P. CA or a line drawn from S to D is the <i>mean +distance</i> of the planet from the sun. +</p> + +<div class="fig" style="width:100%;"> +<img src="images/005.jpg" width="300" height="252" alt="" /> +</div> + +<p class="footnote"> +<a name="linknote-22" id="linknote-22"></a> <a href="#linknoteref-22">[3]</a> +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. +</p> + +</div><!--end chapter--> + +<div class="chapter"> + +<h3><a name="6"></a> 6. GALILEO AND THE TELESCOPE—NOTIONS OF GRAVITY +BY HORROCKS, ETC.</h3> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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.” +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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 <i>evection</i> to +variations in the value of the eccentricity and in the direction of the line of +apses, at the same time correctly assigning <i>the disturbing force of the +Sun</i> 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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +</div><!--end chapter--> + +<div class="chapter"> + +<h3><a name="7"></a>7. SIR ISAAC NEWTON—LAW OF UNIVERSAL +GRAVITATION.</h3> + +<p> +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.<a href="#linknote-23" name="linknoteref-23" id="linknoteref-23"><sup>[1]</sup></a> +</p> + +<p> +Quite the most important event in the whole history of physical astronomy was +the publication, in 1687, of Newton’s <i>Principia (Philosophiae +Naturalis Principia Mathematica)</i>. 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. +</p> + +<p> +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. +</p> + +<p> +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:— +</p> + +<p> +The law of universal gravitation.—<i>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</i>.<a href="#linknote-24" name="linknoteref-24" id="linknoteref-24"><sup>[2]</sup></a> +</p> + +<p> +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 <i>Principia</i> +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.<a href="#linknote-25" name="linknoteref-25" id="linknoteref-25"><sup>[3]</sup></a> +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<pre> + Newton. Modern Tables. + ° ’ " ° ’ " +Mean monthly motion of Apses 1.31.28 3.4.0 +Mean annual motion of nodes 19.18.1,23 19.21.22,50 +Mean value of “variation” 36.10 35.47 +Annual equation 11.51 11.14 +Inequality of mean motion of apogee 19.43 22.17 +Inequality of mean motion of nodes 9.24 9.0 +</pre> + +<p> +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. +</p> + +<p> +Newton’s method of calculating the precession of the equinoxes, already +referred to, is as beautiful as anything in the <i>Principia</i>. 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. +</p> + +<p> +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. +</p> + +<p> +Laplace only expressed the universal opinion of posterity when he said that to +the <i>Principia</i> is assured “a pre-eminence above all the other +productions of the human intellect.” +</p> + +<p> +The name of Flamsteed, First Astronomer Royal, must here be mentioned as having +supplied Newton with the accurate data required for completing the theory. +</p> + +<p> +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 +<i>Principia</i> would never have been written; and but for his generosity in +supplying the means the Royal Society could not have published the book. +</p> + +<div class="fig" style="width:50%;"> +<a name="illus05"></a> +<img src="images/007.jpg" style="width:100%;" alt="DEATH MASK OF SIR ISAAC +NEWTON." /> +<p class="caption">D<small>EATH</small> M<small>ASK OF</small> +S<small>IR</small> I<small>SAAC</small> N<small>EWTON</small>.<br/> +Photographed specially for this work from the original, by kind permission of +the Royal Society, London.</p> +</div> + +<p> +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. +</p> + +<hr /> + +<p> +<b>FOOTNOTES:</b> +</p> + +<p class="footnote"> +<a name="linknote-23" id="linknote-23"></a> <a href="#linknoteref-23">[1]</a> +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! +</p> + +<p class="footnote"> +<a name="linknote-24" id="linknote-24"></a> <a href="#linknoteref-24">[2]</a> +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 <i>Principia</i>; +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.<br/> + With this exception the above statement of the law of universal gravitation +contains nothing that is not to be found in the <i>Principia</i>; and the +nearest approach to that statement occurs in the Seventh Proposition of Book +III.:—<br/> + Prop.: That gravitation occurs in all bodies, and that it is proportional to +the quantity of matter in each.<br/> + Cor. I.: The total attraction of gravitation on a planet arises, and is +composed, out of the attraction on the separate parts.<br/> + Cor. II.: The attraction on separate equal particles of a body is reciprocally +as the square of the distance from the particles. +</p> + +<p class="footnote"> +<a name="linknote-25" id="linknote-25"></a> <a href="#linknoteref-25">[3]</a> +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. +</p> + +</div><!--end chapter--> + +<div class="chapter"> + +<h3><a name="8"></a>8. NEWTON’S SUCCESSORS—HALLEY, EULER, LAGRANGE, +LAPLACE, ETC.</h3> + +<p> +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. +</p> + +<p> +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.” +</p> + +<p> +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.” +</p> + +<p> +The same subject was again proposed for a prize which was shared by Lagrange<a href="#linknote-26" name="linknoteref-26" id="linknoteref-26"><sup>[1]</sup></a> and Euler, neither finding a solution, while the latter +asserted the existence of a resisting medium in space. +</p> + +<p> +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. +</p> + +<p> +Laplace<a href="#linknote-27" name="linknoteref-27" id="linknoteref-27"><sup>[2]</sup></a> 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.) +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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.” +</p> + +<p> +Let us take one more discovery of Halley, furnishing directly a new triumph for +the theory. He noticed that Newton ascribed parabolic orbits to the comets +which he studied, so that they come from infinity, sweep round the sun, and go +off to infinity for ever, after having been visible a few weeks or months. He +collected all the reliable observations of comets he could find, to the number +of twenty-four, and computed their parabolic orbits by the rules laid down by +Newton. His object was to find out if any of them really travelled in elongated +ellipses, practically undistinguishable, in the visible part of their paths, +from parabolæ, in which case they would be seen more than once. He found two +old comets whose orbits, in shape and position, resembled the orbit of a comet +observed by himself in 1682. Apian observed one in 1531; Kepler the other in +1607. The intervals between these appearances is seventy-five or seventy-six +years. He then examined and found old records of similar appearance in 1456, +1380, and 1305. It is true, he noticed, that the intervals varied by a year and +a-half, and the inclination of the orbit to the ecliptic diminished with +successive apparitions. But he knew from previous calculations that this might +easily be due to planetary perturbations. Finally, he arrived at the conclusion +that all of these comets were identical, travelling in an ellipse so elongated +that the part where the comet was seen seemed to be part of a parabolic orbit. +He then predicted its return at the end of 1758 or beginning of 1759, when he +should be dead; but, as he said, “if it should return, according to our +prediction, about the year 1758, impartial posterity will not refuse to +acknowledge that this was first discovered by an Englishman.”<a href="#linknote-28" name="linknoteref-28" id="linknoteref-28"><sup>[3]</sup></a> [<i>Synopsis Astronomiae Cometicae</i>, 1749.] +</p> + +<p> +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.” +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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! +</p> + +<p> +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<a href="#linknote-29" name="linknoteref-29" id="linknoteref-29"><sup>[4]</sup></a> (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. +</p> + +<p> +Already, in November, 1907, the Astronomer Royal was trying to catch it by the +aid of photography. +</p> + +<hr /> + +<p> +<b>FOOTNOTES:</b> +</p> + +<p class="footnote"> +<a name="linknote-26" id="linknote-26"></a> <a href="#linknoteref-26">[1]</a> +Born 1736; died 1813. +</p> + +<p class="footnote"> +<a name="linknote-27" id="linknote-27"></a> <a href="#linknoteref-27">[2]</a> +Born 1749; died 1827. +</p> + +<p class="footnote"> +<a name="linknote-28" id="linknote-28"></a> <a href="#linknoteref-28">[3]</a> +This sentence does not appear in the original memoir communicated to the Royal +Society, but was first published in a posthumous reprint. +</p> + +<p class="footnote"> +<a name="linknote-29" id="linknote-29"></a> <a href="#linknoteref-29">[4]</a> +<i>R. A. S. Monthly Notices</i>, 1907-8. +</p> + +</div><!--end chapter--> + +<div class="chapter"> + +<h3><a name="9"></a>9. DISCOVERY OF NEW PLANETS—HERSCHEL, PIAZZI, ADAMS, +AND LE VERRIER.</h3> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +In 1787 Herschel discovered two satellites, both revolving in nearly the same +plane, inclined 80° to the ecliptic, and the motion of both was +retrograde. +</p> + +<p> +In 1772, before Herschel’s discovery, Bode<a href="#linknote-30" name="linknoteref-30" id="linknoteref-30"><sup>[1]</sup></a> 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, <i>etc</i>., to the 4, always doubling the last numbers. +You then get the planetary distances. +</p> + +<pre> + 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 +</pre> + +<p> +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. +</p> + +<p> +The mean distance from the sun was found to be 2.767, agreeing with the 2.8 +given by Bode’s law. Its orbit was found to be inclined over 10° to +the ecliptic, and its diameter was only 161 miles. +</p> + +<p> +On March 28th, 1802, Olbers discovered a new seventh magnitude star, which +turned out to be a planet resembling Ceres. It was called Pallas. Gauss found +its orbit to be inclined 35° to the ecliptic, and to cut the orbit of +Ceres; whence Olbers considered that these might be fragments of a broken-up +planet. He then commenced a search for other fragments. In 1804 Harding +discovered Juno, and in 1807 Olbers found Vesta. The next one was not +discovered until 1845, from which date asteroids, or minor planets (as these +small planets are called), have been found almost every year. They now number +about 700. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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°. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +In June, 1846, Le Verrier announced, in the <i>Comptes Rendus de +l’Academie des Sciences</i>, that the longitude of the disturbing planet, +for January 1st, 1847, was 325, and that the probable error did not exceed +10°. +</p> + +<p> +This result agreed so well with Adams’s (within 1°) that Airy urged +Challis to apply the splendid Northumberland equatoreal, at Cambridge, to the +search. Challis, however, had already prepared an exhaustive plan of attack +which must in time settle the point. His first work was to observe, and make a +catalogue, or chart, of all stars near Adams’s position. +</p> + +<p> +On August 31st, 1846, Le Verrier published the concluding part of his labours. +</p> + +<p> +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. +</p> + +<p> +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 <i>Principia</i>, 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. +</p> + +<p> +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. +</p> + +<p> +These displays of jealousy have long since passed away, and there is now +universally an <i>entente cordiale</i> 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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<hr /> + +<p> +<b>FOOTNOTES:</b> +</p> + +<p class="footnote"> +<a name="linknote-30" id="linknote-30"></a> <a href="#linknoteref-30">[1]</a> +Bode’s law, or something like it, had already been fore-shadowed by +Kepler and others, especially Titius (see <i>Monatliche Correspondenz</i>, vol. +vii., p. 72). +</p> + +</div><!--end chapter--> + +<div class="chapter"> + +<h2><a name="book03"></a>BOOK III. OBSERVATION</h2> + +</div><!--end chapter--> + +<div class="chapter"> + +<h3><a name="10"></a>10. INSTRUMENTS OF PRECISION—STATE OF THE SOLAR +SYSTEM.</h3> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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.<a href="#linknote-31" name="linknoteref-31" id="linknoteref-31"><sup>[1]</sup></a> +</p> + +<p> +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. +</p> + +<p> +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.<a href="#linknote-32" name="linknoteref-32" id="linknoteref-32"><sup>[2]</sup></a> +</p> + +<div class="fig" style="width:50%;"> +<a name="illus06"></a> +<img src="images/008.jpg" style="width:100%;" alt="ANCIENT CHINESE INSTRUMENTS" /> +<p class="caption">A<small>NCIENT</small> C<small>HINESE</small> +I<small>NSTRUMENTS</small>,<br/>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.</p> +</div> + +<p> +The French Jesuits at Peking, in the seventeenth century, helped the Chinese in +their astronomy. In 1875 the writer saw and photographed, on that part of the +wall of Peking used by the Mandarins as an observatory, the six instruments +handsomely designed by Father Verbiest, copied from the instruments of Tycho +Brahe, and embellished with Chinese dragons and emblems cast on the supports. +He also saw there two old instruments (which he was told were Arabic) of date +1279, by Ko Show-King, astronomer to Koblai Khan, the grandson of Chenghis +Khan. One of these last is nearly identical with the armillae of Tycho; and the +other with his “armillae æquatoriæ maximæ,” with which he observed +the comet of 1585, besides fixed stars and planets.<a href="#linknote-33" name="linknoteref-33" id="linknoteref-33"><sup>[3]</sup></a> +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +Flamsteed began his duties at Greenwich Observatory, as first Astronomer Royal, +in 1676, with very poor instruments. In 1683 he put up a mural arc of +140°, and in 1689 a better one, seventy-nine inches radius. He conducted +his measurements with great skill, and introduced new methods to attain +accuracy, using certain stars for determining the errors of his instruments; +and he always reduced his observations to a form in which they could be readily +used. He introduced new methods for determining the position of the equinox and +the right ascension of a fundamental star. He produced a catalogue of 2,935 +stars. He supplied Sir Isaac Newton with results of observation required in his +theoretical calculations. He died in 1719. +</p> + +<p> +Halley succeeded Flamsteed to find that the whole place had been gutted by the +latter’s executors. In 1721 he got a transit instrument, and in 1726 a +mural quadrant by Graham. His successor in 1742, Bradley, replaced this by a +fine brass quadrant, eight feet radius, by Bird; and Bradley’s zenith +sector was purchased for the observatory. An instrument like this, specially +designed for zenith stars, is capable of greater rigidity than a more universal +instrument; and there is no trouble with refraction in the zenith. For these +reasons Bradley had set up this instrument at Kew, to attempt the proof of the +earth’s motion by observing the annual parallax of stars. He certainly +found an annual variation of zenith distance, but not at the times of year +required by the parallax. This led him to the discovery of the +“aberration” of light and of nutation. Bradley has been described +as the founder of the modern system of accurate observation. He died in 1762, +leaving behind him thirteen folio volumes of valuable but unreduced +observations. Those relating to the stars were reduced by Bessel and published +in 1818, at Königsberg, in his well-known standard work, <i>Fundamenta +Astronomiae</i>. In it are results showing the laws of refraction, with tables +of its amount, the maximum value of aberration, and other constants. +</p> + +<p> +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 <i>circle</i>, 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. +</p> + +<p> +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. +</p> + +<p> +George Biddell Airy, Seventh Astronomer Royal,<a href="#linknote-34" name="linknoteref-34" id="linknoteref-34"><sup>[4]</sup></a> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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 <i>transit-circle</i> 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. +</p> + +<p> +Airy, like Bradley, was impressed with the advantage of employing stars in the +zenith for determining the fundamental constants of astronomy. He devised a +<i>reflex zenith tube</i>, 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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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>i.e.,</i> 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. +</p> + +<p> +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. +</p> + +<p> +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 (<i>Cape Obs</i>., Vol. +VI.). +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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.<a href="#linknote-35" name="linknoteref-35" id="linknoteref-35"><sup>[5]</sup></a> +</p> + +<p> +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<a href="#linknote-36" name="linknoteref-36" id="linknoteref-36"><sup>[6]</sup></a> +is 8".807 ± 0".0028.<a href="#linknote-37" name="linknoteref-37" id="linknoteref-37"><sup>[7]</sup></a> +</p> + +<hr /> + +<p> +<b>FOOTNOTES:</b> +</p> + +<p class="footnote"> +<a name="linknote-31" id="linknote-31"></a> <a href="#linknoteref-31">[1]</a> +In 1480 Martin Behaim, of Nuremberg, produced his <i>astrolabe</i> 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 <i>alhidada</i>, 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. +</p> + +<p class="footnote"> +<a name="linknote-32" id="linknote-32"></a> <a href="#linknoteref-32">[2]</a> +See illustration on p. 76. +</p> + +<p class="footnote"> +<a name="linknote-33" id="linknote-33"></a> <a href="#linknoteref-33">[3]</a> +See Dreyer’s article on these instruments in <i>Copernicus</i>, 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 +<i>Chinese Researches</i>, by Alexander Wyllie (Shanghai, 1897). +</p> + +<p class="footnote"> +<a name="linknote-34" id="linknote-34"></a> <a href="#linknoteref-34">[4]</a> +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. +</p> + +<p class="footnote"> +<a name="linknote-35" id="linknote-35"></a> <a href="#linknoteref-35">[5]</a> +<i>Annals of the Cape Observatory</i>, vol. x., part 3. +</p> + +<p class="footnote"> +<a name="linknote-36" id="linknote-36"></a> <a href="#linknoteref-36">[6]</a> +The parallax of the sun is the angle subtended by the earth’s radius at +the sun’s distance. +</p> + +<p class="footnote"> +<a name="linknote-37" id="linknote-37"></a> <a href="#linknoteref-37">[7]</a> +A. R. Hinks, R.A.S.; Monthly Notices, June, 1909. +</p> + +</div><!--end chapter--> + +<div class="chapter"> + +<h3><a name="11"></a>11. HISTORY OF THE TELESCOPE</h3> + +<p> +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, <i>Hist. Ph. Ast</i>.), 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 <i>camera obscura</i>, in which a lens throws an inverted image of +a landscape on the wall. +</p> + +<p> +The first telescopes were made in Holland, the originator being either Henry +Lipperhey,<a href="#linknote-38" name="linknoteref-38" id="linknoteref-38"><sup>[1]</sup></a> Zacharias Jansen, or James Metius, and the +date 1608 or earlier. +</p> + +<p> +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. +</p> + +<p> +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,<a href="#linknote-39" name="linknoteref-39" id="linknoteref-39"><sup>[2]</sup></a> of +Aberdeen and Edinburgh, in 1663, in his <i>Optica Promota</i>, 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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +In the nineteenth century gigantic <i>reflectors</i> 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. +</p> + +<p> +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. +</p> + +<p> +Cooke, of York, made an object-glass, 25-inch diameter, for Newall, of +Gateshead, which has done splendid work at Cambridge. We have the Washington +26-inch by Clark, the Vienna 27-inch by Grubb, the Nice 29½-inch by +Gautier, the Pulkowa 30-inch by Clark. Then there was the sensation of +Clark’s 36-inch for the Lick Observatory in California, and finally his +<i>tour de force</i>, the Yerkes 40-inch refractor, for Chicago. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<h4>SPECTROSCOPE.</h4> + +<p> +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. +</p> + +<p> +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.<a href="#linknote-40" name="linknoteref-40" id="linknoteref-40"><sup>[3]</sup></a> +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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.<a href="#linknote-41" name="linknoteref-41" id="linknoteref-41"><sup>[4]</sup></a> Iron, calcium, and other elements were +soon detected in the same way. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +In 1842 Doppler<a href="#linknote-42" name="linknoteref-42" id="linknoteref-42"><sup>[5]</sup></a> 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. +</p> + +<p> +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. +</p> + +<p> +In 1868 Huggins<a href="#linknote-43" name="linknoteref-43" id="linknoteref-43"><sup>[6]</sup></a> succeeded in thus measuring the +velocities of stars in the direction of the line of sight. +</p> + +<p> +In 1873 Vogel<a href="#linknote-44" name="linknoteref-44" id="linknoteref-44"><sup>[7]</sup></a> compared the spectra of the sun’s +East (approaching) limb and West (receding) limb, and the displacement of lines +endorsed the theory. This last observation was suggested by Zöllner. +</p> + +<hr /> + +<p> +<b>FOOTNOTES:</b> +</p> + +<p class="footnote"> +<a name="linknote-38" id="linknote-38"></a> <a href="#linknoteref-38">[1]</a> +In the <i>Encyclopaedia Britannica</i>, article “Telescope,” and in +Grant’s <i>Physical Astronomy</i>, good reasons are given for awarding +the honour to Lipperhey. +</p> + +<p class="footnote"> +<a name="linknote-39" id="linknote-39"></a> <a href="#linknoteref-39">[2]</a> +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, <i>Newton’s mathematics +were a little rusty</i>.” +</p> + +<p class="footnote"> +<a name="linknote-40" id="linknote-40"></a> <a href="#linknoteref-40">[3]</a> +<i>R. S. Phil. Trans</i>. +</p> + +<p class="footnote"> +<a name="linknote-41" id="linknote-41"></a> <a href="#linknoteref-41">[4]</a> +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. +</p> + +<p class="footnote"> +<a name="linknote-42" id="linknote-42"></a> <a href="#linknoteref-42">[5]</a> +<i>Abh. d. Kön. Böhm. d. Wiss</i>., Bd. ii., 1841-42, p. 467. See also Fizeau +in the <i>Ann. de Chem. et de Phys</i>., 1870, p. 211. +</p> + +<p class="footnote"> +<a name="linknote-43" id="linknote-43"></a> <a href="#linknoteref-43">[6]</a> +<i>R. S. Phil. Trans</i>., 1868. +</p> + +<p class="footnote"> +<a name="linknote-44" id="linknote-44"></a> <a href="#linknoteref-44">[7]</a> +<i>Ast. Nach</i>., No. 1, 864. +</p> + +</div><!--end chapter--> + +<div class="chapter"> + +<h2><a name="book04"></a>BOOK IV. THE PHYSICAL PERIOD</h2> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +</div><!--end chapter--> + +<div class="chapter"> + +<h3><a name="12"></a>12. THE SUN.</h3> + +<p> +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 <i>umbra</i> and the less dark, but more extensive, +<i>penumbra</i> 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. +</p> + +<p> +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. +</p> + +<div class="fig" style="width:60%;"> +<a name="illus07"></a> +<img src="images/009.jpg" style="width:100%;" alt="SOLAR SURFACE" /> +<p class="caption">S<small>OLAR</small> S<small>URFACE</small>.<br/>As +Photographed at the Royal Observatory, Greenwich, showing sun-spots with umbræ, +penumbræ, and faculæ.</p> +</div> + +<p> +Speculations as to the cause of sun-spots have never ceased from +Galileo’s time to ours. He supposed them to be clouds. Scheiner<a href="#linknote-45" name="linknoteref-45" id="linknoteref-45"><sup>[1]</sup></a> said they were the indications of tumultuous movements +occasionally agitating the ocean of liquid fire of which he supposed the sun to +be composed. +</p> + +<p> +A. Wilson, of Glasgow, in 1769,<a href="#linknote-46" name="linknoteref-46" id="linknoteref-46"><sup>[2]</sup></a> 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:— +</p> + +<p class="letter">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.<a href="#linknote-47" name="linknoteref-47" id="linknoteref-47"><sup>[3]</sup></a> +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +Sir John Herschel noticed that the spots are mostly confined to two zones +extending to about 35° on each side of the equator, and that a zone of +equatoreal calms is free from spots. But it was R. C. Carrington<a href="#linknote-48" name="linknoteref-48" id="linknoteref-48"><sup>[4]</sup></a> who, by his continuous observations at Redhill, in +Surrey, established the remarkable fact that, while the rotation period in the +highest latitudes, 50°, where spots are seen, is twenty-seven-and-a-half +days, near the equator the period is only twenty-five days. His splendid volume +of observations of the sun led to much new information about the average +distribution of spots at different epochs. +</p> + +<p> +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.<a href="#linknote-49" name="linknoteref-49" id="linknoteref-49"><sup>[5]</sup></a> 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<a href="#linknote-50" name="linknoteref-50" id="linknoteref-50"><sup>[6]</sup></a> has +given reasons for admitting a number of co-existent periods, of which the +eleven-year period was predominant in the nineteenth century. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +Spoerer deduced a law of dependence of the average latitude of sun-spots on the +phase of the sun-spot period. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +It is noteworthy that from the outset De la Rue recognised the value of +stereoscopic vision, which is now known to be of supreme accuracy. In 1853 he +combined pairs of photographs of the moon in the same phase, but under +different conditions regarding libration, showing the moon from slightly +different points of view. These in the stereoscope exhibited all the relief +resulting from binocular vision, and looked like a solid globe. In 1860 he used +successive photographs of the total solar eclipse stereoscopically, to prove +that the red prominences belong to the sun, and not to the moon. In 1861 he +similarly combined two photographs of a sun-spot, the perspective effect +showing the umbra like a floor at the bottom of a hollow penumbra; and in one +case the faculæ were discovered to be sailing over a spot apparently at some +considerable height. These appearances may be partly due to a proper motion; +but, so far as it went, this was a beautiful confirmation of Wilson’s +discovery. Hewlett, however, in 1894, after thirty years of work, showed that +the spots are not always depressions, being very subject to disturbance. +</p> + +<p> +The Kew photographs<a href="#linknote-51" name="linknoteref-51" id="linknoteref-51"><sup>[7]</sup></a> contributed a vast amount of +information about sun-spots, and they showed that the faculæ generally follow +the spots in their rotation round the sun. +</p> + +<p> +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. +</p> + +<p> +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.<a href="#linknote-52" name="linknoteref-52" id="linknoteref-52"><sup>[8]</sup></a> They have succeeded +in photographing the sun’s surface in monochromatic light, such as the +light given off as one of the bright lines of hydrogen or of calcium, by means +of the “Spectroheliograph.” The spectroscope is placed with its +slit in the focus of an equatoreal telescope, pointed to the sun, so that the +circular image of the sun falls on the slit. At the other end of the +spectroscope is the photographic plate. Just in front of this plate there is +another slit parallel to the first, in the position where the image of the +first slit formed by the K line of calcium falls. Thus is obtained a photograph +of the section of the sun, made by the first slit, only in K light. As the +image of the sun passes over the first slit the photographic plate is moved at +the same rate and in the same direction behind the second slit; and as +successive sections of the sun’s image in the equatoreal enter the +apparatus, so are these sections successively thrown in their proper place on +the photographic plate, always in K light. By using a high dispersion the +faculæ which give off K light can be correctly photographed, not only at the +sun’s edge, but all over his surface. The actual mechanical method of +carrying out the observation is not quite so simple as what is here described. +</p> + +<p> +By choosing another line of the spectrum instead of calcium K—for +example, the hydrogen line H<sub>(3)</sub>—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. +</p> + +<p> +The spectroscope has revealed the fact that, broadly speaking, the sun is +composed of the same materials as the earth. Ångstrom was the first to map +out all of the lines to be found in the solar spectrum. But Rowland, of +Baltimore, after having perfected the art of making true gratings with +equidistant lines ruled on metal for producing spectra, then proceeded to make +a map of the solar spectrum on a large scale. +</p> + +<p> +In 1866 Lockyer<a href="#linknote-53" name="linknoteref-53" id="linknoteref-53"><sup>[9]</sup></a> 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. +</p> + +<p> +<i>Total Solar Eclipses</i>.—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. +</p> + +<div class="fig" style="width:55%;"> +<a name="illus08"></a> +<img src="images/010.jpg" style="width:100%;" alt="SOLAR ECLIPSE, 1882." /> +<p class="caption">S<small>OLAR</small> E<small>CLIPSE</small>, 1882.<br/>From +drawing by W. H. Wesley, Secretary R.A.S.; showing the prominences, the corona, +and an unknown comet.</p> +</div> + +<p> +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: “<i>Je verrai ces lignes-là en dehors des +éclipses</i>.” 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,<a href="#linknote-54" name="linknoteref-54" id="linknoteref-54"><sup>[10]</sup></a> 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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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 <i>History of Astronomy during the Nineteenth Century</i>. As to +established facts, we learn from the spectroscopic researches (1) that the +continuous spectrum is derived from the <i>photosphere</i> or solar gaseous +material compressed almost to liquid consistency; (2) that the <i>reversing +layer</i> surrounds it and gives rise to black lines in the spectrum; that the +<i>chromosphere</i> surrounds this, is composed mainly of hydrogen, and is the +cause of the red prominences in eclipses; and that the gaseous <i>corona</i> +surrounds all of these, and extends to vast distances outside the sun’s +visible surface. +</p> + +<hr /> + +<p> +<b>FOOTNOTES:</b> +</p> + +<p class="footnote"> +<a name="linknote-45" id="linknote-45"></a> <a href="#linknoteref-45">[1]</a> +<i>Rosa Ursina</i>, by C. Scheiner, <i>fol</i>.; Bracciani, 1630. +</p> + +<p class="footnote"> +<a name="linknote-46" id="linknote-46"></a> <a href="#linknoteref-46">[2]</a> +<i>R. S. Phil. Trans</i>., 1774. +</p> + +<p class="footnote"> +<a name="linknote-47" id="linknote-47"></a> <a href="#linknoteref-47">[3]</a> +<i>Ibid</i>, 1783. +</p> + +<p class="footnote"> +<a name="linknote-48" id="linknote-48"></a> <a href="#linknoteref-48">[4]</a> +<i>Observations on the Spots on the Sun, etc.,</i> 4°; London and +Edinburgh, 1863. +</p> + +<p class="footnote"> +<a name="linknote-49" id="linknote-49"></a> <a href="#linknoteref-49">[5]</a> +<i>Periodicität der Sonnenflecken. Astron. Nach. XXI.</i>, 1844, P. 234. +</p> + +<p class="footnote"> +<a name="linknote-50" id="linknote-50"></a> <a href="#linknoteref-50">[6]</a> +<i>R.S. Phil. Trans.</i> (ser. A), 1906, p. 69-100. +</p> + +<p class="footnote"> +<a name="linknote-51" id="linknote-51"></a> <a href="#linknoteref-51">[7]</a> +“Researches on Solar Physics,” by De la Rue, Stewart and Loewy; +<i>R. S. Phil. Trans</i>., 1869, 1870. +</p> + +<p class="footnote"> +<a name="linknote-52" id="linknote-52"></a> <a href="#linknoteref-52">[8]</a> +“The Sun as Photographed on the K line”; <i>Knowledge</i>, London, +1903, p. 229. +</p> + +<p class="footnote"> +<a name="linknote-53" id="linknote-53"></a> <a href="#linknoteref-53">[9]</a> +<i>R. S. Proc.</i>, xv., 1867, p. 256. +</p> + +<p class="footnote"> +<a name="linknote-54" id="linknote-54"></a> <a href="#linknoteref-54">[10]</a> +<i>Acad. des Sc.</i>, Paris; <i>C. R.</i>, lxvii., 1868, p. 121. +</p> + +</div><!--end chapter--> + +<div class="chapter"> + +<h3><a name="13"></a>13. THE MOON AND PLANETS.</h3> + +<p> +<i>The Moon</i>.—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 <i>libration</i>, 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 <i>uniformly</i>, and that her revolution round +the earth is not uniform. +</p> + +<p> +Galileo said that the mountains on the moon showed greater differences of level +than those on the earth. Shröter supported this opinion. W. Herschel +opposed it. But Beer and Mädler measured the heights of lunar mountains by +their shadows, and found four of them over 20,000 feet above the surrounding +plains. +</p> + +<p> +Langrenus<a href="#linknote-55" name="linknoteref-55" id="linknoteref-55"><sup>[1]</sup></a> was the first to do serious work on +selenography, and named the lunar features after eminent men. Riccioli also +made lunar charts. In 1692 Cassini made a chart of the full moon. Since then we +have the charts of Schröter, Beer and Mädler (1837), and of Schmidt, +of Athens (1878); and, above all, the photographic atlas by Loewy and Puiseux. +</p> + +<p> +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, <i>Tycho</i>, 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. +</p> + +<p> +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. +</p> + +<p> +No certain changes have ever been observed; but several suspicions have been +expressed, especially as to the small crater <i>Linné</i>, in the <i>Mare +Serenitatis</i>. 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. +</p> + +<p> +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. +</p> + +<p> +The distance of the moon from the earth is just now the subject of +re-measurement. The base line is from Greenwich to Cape of Good Hope, and the +new feature introduced is the selection of a definite point on a crater +(Mösting A), instead of the moon’s edge, as the point whose distance +is to be measured. +</p> + +<p> +<i>The Inferior Planets</i>.—When the telescope was invented, the phases +of Venus attracted much attention; but the brightness of this planet, and her +proximity to the sun, as with Mercury also, seemed to be a bar to the discovery +of markings by which the axis and period of rotation could be fixed. Cassini +gave the rotation as twenty-three hours, by observing a bright spot on her +surface. Shröter made it 23h. 21m. 19s. This value was supported by +others. In 1890 Schiaparelli<a href="#linknote-56" name="linknoteref-56" id="linknoteref-56"><sup>[2]</sup></a> 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. +</p> + +<p> +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 <i>Vulcan</i>. 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<a href="#linknote-57" name="linknoteref-57" id="linknoteref-57"><sup>[3]</sup></a> 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. +</p> + +<p> +<i>Mars</i>.—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. +</p> + +<p> +Schroter attributed the other markings on Mars to drifting clouds. But Beer and +Mädler, in 1830-39, identified the same dark spots as being always in the +same place, though sometimes blurred by mist in the local winter. A spot +sketched by Huyghens in 1672, one frequently seen by W. Herschel in 1783, +another by Arago in 1813, and nearly all the markings recorded by Beer and +Mädler in 1830, were seen and drawn by F. Kaiser in Leyden during +seventeen nights of the opposition of 1862 (<i>Ast. Nacht.</i>, 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. +</p> + +<p> +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). +</p> + +<p> +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. +</p> + +<p> +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,<a href="#linknote-58" name="linknoteref-58" id="linknoteref-58"><sup>[4]</sup></a> +the second canal being always 200 to 400 miles distant from its fellow. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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). +</p> + +<div class="fig" style="width:60%;"> +<a name="illus09"></a> +<img src="images/011.jpg" style="width:100%;" alt="JUPITER." /> +<p class="caption">J<small>UPITER</small>.<br/>From a drawing by E. M. +Antoniadi, showing transit of a satellite’s shadow, the belts, and the +“great red spot” (<i>Monthly Notices</i>, R. A. S., vol. lix., pl. +x.).</p> +</div> + +<p> +<i>Jupiter.</i>—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<a href="#linknote-59" name="linknoteref-59" id="linknoteref-59"><sup>[5]</sup></a> 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. +</p> + +<p> +Jupiter’s rapid rotation ought, according to Newton’s theory, to be +accompanied by a great flattening at the poles. Cassini had noted an oval form +in 1691. This was confirmed by La Hire, Römer, and Picard. Pound measured +the ellipticity = 1/(13.25). +</p> + +<p> +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. +</p> + +<p> +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, <i>Gravitation</i>, has reduced these investigations to simple +geometrical explanations. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +In modern times much interest has been taken in watching a rival to +Cassini’s famous spot. The “great red spot” was first +observed by Niesten, Pritchett, and Tempel, in 1878, as a rosy cloud attached +to a whitish zone beneath the dark southern equatorial band, shaped like the +new war balloons, 30,000 miles long and 7,000 miles across. The next year it +was brick-red. A white spot beside it completed a rotation in less time by +5½ minutes than the red spot—a difference of 260 miles an hour. Thus +they came together again every six weeks, but the motions did not continue +uniform. The spot was feeble in 1882-4, brightened in 1886, and, after many +changes, is still visible. +</p> + +<p> +Galileo’s great discovery of Jupiter’s four moons was the last word +in this connection until September 9th, 1892, when Barnard, using the 36-inch +refractor of the Lick Observatory, detected a tiny spot of light closely +following the planet. This proved to be a new satellite (fifth), nearer to the +planet than any other, and revolving round it in 11h. 57m. 23s. Between its +rising and setting there must be an interval of 2½ Jovian days, and two or +three full moons. The sixth and seventh satellites were found by the +examination of photographic plates at the Lick Observatory in 1905, since which +time they have been continuously photographed, and their orbits traced, at +Greenwich. On examining these plates in 1908 Mr. Melotte detected the eighth +satellite, which seems to be revolving in a retrograde orbit three times as far +from its planet as the next one (seventh), in these two points agreeing with +the outermost of Saturn’s satellites (Phoebe). +</p> + +<p> +<i>Saturn.</i>—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. +</p> + +<p> +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 <i>De Saturni Luna Observatio Nova</i>, 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. +</p> + +<p> +In 1675 Cassini found the ring to be double, the concentric rings being +separated by a black band—a fact which was placed beyond dispute by +Herschel, who also found that the thickness of the ring subtends an angle less +than 0".3. Shröter estimated its thickness at 500 miles. +</p> + +<p> +Many speculations have been advanced to explain the origin and constitution of +the ring. De Sejour said<a href="#linknote-60" name="linknoteref-60" id="linknoteref-60"><sup>[6]</sup></a> 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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +<i>Uranus and Neptune</i>.—The splendid discoveries of Uranus and two +satellites by Sir William Herschel in 1787, and of Neptune by Adams and Le +Verrier in 1846, have been already described. Lassel added two more satellites +to Uranus in 1851, and found Neptune’s satellite in 1846. All of the +satellites of Uranus have retrograde motion, and their orbits are inclined +about 80° to the ecliptic. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +Quite lately<a href="#linknote-61" name="linknoteref-61" id="linknoteref-61"><sup>[7]</sup></a> 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. +</p> + +<p> +<i>Asteroids</i>.—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.<a href="#linknote-62" name="linknoteref-62" id="linknoteref-62"><sup>[8]</sup></a> +</p> + +<p> +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. +</p> + +<p> +The discovery of Eros and the photographic attack upon its path have been +described in their relation to finding the sun’s distance. +</p> + +<p> +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. +</p> + +<hr /> + +<p> +<b>FOOTNOTES:</b> +</p> + +<p class="footnote"> +<a name="linknote-55" id="linknote-55"></a> <a href="#linknoteref-55">[1]</a> +Langrenus (van Langren), F. Selenographia sive lumina austriae philippica; +Bruxelles, 1645. +</p> + +<p class="footnote"> +<a name="linknote-56" id="linknote-56"></a> <a href="#linknoteref-56">[2]</a> +<i>Astr. Nach.</i>, 2,944. +</p> + +<p class="footnote"> +<a name="linknote-57" id="linknote-57"></a> <a href="#linknoteref-57">[3]</a> +<i>Acad. des Sc.</i>, Paris; <i>C.R.</i>, lxxxiii., 1876. +</p> + +<p class="footnote"> +<a name="linknote-58" id="linknote-58"></a> <a href="#linknoteref-58">[4]</a> +<i>Mem. Spettr. Ital.</i>, xi., p. 28. +</p> + +<p class="footnote"> +<a name="linknote-59" id="linknote-59"></a> <a href="#linknoteref-59">[5]</a> +<i>R. S. Phil. Trans</i>., No. 1. +</p> + +<p class="footnote"> +<a name="linknote-60" id="linknote-60"></a> <a href="#linknoteref-60">[6]</a> +Grant’s <i>Hist. Ph. Ast</i>., p. 267. +</p> + +<p class="footnote"> +<a name="linknote-61" id="linknote-61"></a> <a href="#linknoteref-61">[7]</a> +<i>Nature</i>, November 12th, 1908. +</p> + +<p class="footnote"> +<a name="linknote-62" id="linknote-62"></a> <a href="#linknoteref-62">[8]</a> +<i>Ast. Nach</i>., Nos. 791, 792, 814, translated by G. B. Airy. <i>Naut. +Alm</i>., Appendix, 1856. +</p> + +</div><!--end chapter--> + +<div class="chapter"> + +<h3><a name="14"></a>14. COMETS AND METEORS.</h3> + +<p> +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. +</p> + +<p> +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.<a href="#linknote-63" name="linknoteref-63" id="linknoteref-63"><sup>[1]</sup></a> 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. +</p> + +<div class="fig" style="width:60%;"> +<a name="illus10"></a> +<img src="images/012.jpg" style="width:100%;" alt="COPY OF THE DRAWING MADE BY +PAUL FABRICIUS." /> +<p class="caption">C<small>OPY OF THE</small> D<small>RAWING</small> +M<small>ADE BY</small> P<small>AUL</small> F<small>ABRICIUS</small>.<br/>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.</p> +</div> + +<p> +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. +</p> + +<p> +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.<a href="#linknote-64" name="linknoteref-64" id="linknoteref-64"><sup>[2]</sup></a> 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. +</p> + +<p> +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.<a href="#linknote-65" name="linknoteref-65" id="linknoteref-65"><sup>[3]</sup></a> +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +In 1770 Lexell discovered a comet which, as was afterwards proved by +investigations of Lexell, Burchardt, and Laplace, had in 1767 been deflected by +Jupiter out of an orbit in which it was invisible from the earth into an orbit +with a period of 5½ years, enabling it to be seen. In 1779 it again +approached Jupiter closer than some of his satellites, and was sent off in +another orbit, never to be again recognised. +</p> + +<p> +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. +</p> + +<p> +A magnificent meteor shower was seen in America on November 12th-13th, 1833, +when the paths of the meteors all seemed to radiate from a point in the +constellation Leo. A similar display had been witnessed in Mexico by Humboldt +and Bonpland on November 12th, 1799. H. A. Newton traced such records back to +October 13th, A.D. 902. The orbital motion of a cloud or stream of small +particles was indicated. The period favoured by H. A. Newton was 354½ +days; another suggestion was 375½ days, and another 33¼ years. He +noticed that the advance of the date of the shower between 902 and 1833, at the +rate of one day in seventy years, meant a progression of the node of the orbit. +Adams undertook to calculate what the amount would be on all the five +suppositions that had been made about the period. After a laborious work, he +found that none gave one day in seventy years except the 33¼-year period, +which did so exactly. H. A. Newton predicted a return of the shower on the +night of November 13th-14th, 1866. He is now dead; but many of us are alive to +recall the wonder and enthusiasm with which we saw this prediction being +fulfilled by the grandest display of meteors ever seen by anyone now alive. +</p> + +<p> +The <i>progression</i> of the nodes proved the path of the meteor stream to be +retrograde. The <i>radiant</i> 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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<hr /> + +<p> +<b>FOOTNOTES:</b> +</p> + +<p class="footnote"> +<a name="linknote-63" id="linknote-63"></a> <a href="#linknoteref-63">[1]</a> +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. +</p> + +<p class="footnote"> +<a name="linknote-64" id="linknote-64"></a> <a href="#linknoteref-64">[2]</a> +Such as <i>The World of Comets</i>, by A. Guillemin; <i>History of Comets</i>, +by G. R. Hind, London, 1859; <i>Theatrum Cometicum</i>, by S. de Lubienietz, +1667; <i>Cometographie</i>, by Pingré, Paris, 1783; <i>Donati’s +Comet</i>, by Bond. +</p> + +<p class="footnote"> +<a name="linknote-65" id="linknote-65"></a> <a href="#linknoteref-65">[3]</a> +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. +</p> + +</div><!--end chapter--> + +<div class="chapter"> + +<h3><a name="15"></a>15. THE FIXED STARS AND NEBULÆ.</h3> + +<p> +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. +</p> + +<div class="fig" style="width:50%;"> +<a name="illus11"></a> +<img src="images/013.jpg" style="width:100%;" alt="SIR WILLIAM HERSCHEL, F.R.S.—1738-1822." /> +<p class="caption">S<small>IR</small> W<small>ILLIAM</small> +H<small>ERSCHEL</small>, F.R.S.—1738-1822.<br/>Painted by Lemuel F. +Abbott; National Portrait Gallery, Room XX.</p> +</div> + +<p> +In the field of telescopic discovery beyond our solar system there is no one +who has enlarged our knowledge so much as Sir William Herschel, to whom we owe +the greatest discovery in dynamical astronomy among the stars—viz., that +the law of gravitation extends to the most distant stars, and that many of them +describe elliptic orbits about each other. W. Herschel was born at Hanover in +1738, came to England in 1758 as a trained musician, and died in 1822. He +studied science when he could, and hired a telescope, until he learnt to make +his own specula and telescopes. He made 430 parabolic specula in twenty-one +years. He discovered 2,500 nebulæ and 806 double stars, counted the stars in +3,400 guage-fields, and compared the principal stars photometrically. +</p> + +<p> +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. +</p> + +<p> +<i>Parallax</i>.—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. +</p> + +<p> +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,<a href="#linknote-66" name="linknoteref-66" id="linknoteref-66"><sup>[1]</sup></a> +early in the nineteenth century, also failed. The first successes, afterwards +confirmed, were by Bessel and Henderson. Both used stars whose proper motion +had been found to be large, as this argued proximity. Henderson, at the Cape of +Good Hope, observed α Centauri, whose annual proper motion he found to +amount to 3".6, in 1832-3; and a few years later deduced its parallax 1".16. +His successor at the Cape, Maclear, reduced this to 0".92. +</p> + +<p> +In 1835 Struve assigned a doubtful parallax of 0".261 to Vega (α Lyræ). +But Bessel’s observations, between 1837 and 1840, of 61 Cygni, a star +with the large proper motion of over 5”, established its annual parallax +to be 0".3483; and this was confirmed by Peters, who found the value 0".349. +</p> + +<p> +Later determinations for α<sub>2</sub> Centauri, by Gill,<a href="#linknote-67" name="linknoteref-67" id="linknoteref-67"><sup>[2]</sup></a> make its parallax 0".75—This is the nearest known +fixed star; and its light takes 4 1/3 years to reach us. The lightyear is taken +as the unit of measurement in the starry heavens, as the earth’s mean +distance is “the astronomical unit” for the solar system.<a href="#linknote-68" name="linknoteref-68" id="linknoteref-68"><sup>[3]</sup></a> The proper motions and parallaxes combined tell us the +velocity of the motion of these stars across the line of sight: α Centauri +14.4 miles a second=4.2 astronomical units a year; 61 Cygni 37.9 miles a +second=11.2 astronomical units a year. These successes led to renewed zeal, and +now the distances of many stars are known more or less accurately. +</p> + +<p> +Several of the brightest stars, which might be expected to be the nearest, have +not shown a parallax amounting to a twentieth of a second of arc. Among these +are Canopus, α Orionis, α Cygni, β Centauri, and γ +Cassiopeia. Oudemans has published a list of parallaxes observed.<a href="#linknote-69" name="linknoteref-69" id="linknoteref-69"><sup>[4]</sup></a> +</p> + +<p> +<i>Proper Motion.</i>—In 1718 Halley<a href="#linknote-70" name="linknoteref-70" id="linknoteref-70"><sup>[5]</sup></a> detected +the proper motions of Arcturus and Sirius. In 1738 J. Cassinis<a href="#linknote-71" name="linknoteref-71" id="linknoteref-71"><sup>[6]</sup></a> 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”. +</p> + +<p> +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. +</p> + +<p> +When Huggins first applied the Doppler principle to measure velocities in the +line of sight,<a href="#linknote-72" name="linknoteref-72" id="linknoteref-72"><sup>[7]</sup></a> the faintness of star spectra +diminished the accuracy; but Vögel, in 1888, overcame this to a great +extent by long exposures of photographic plates. +</p> + +<p> +It has often been noticed that stars which seem to belong to a group of nearly +uniform magnitude have the same proper motion. The spectroscope has shown that +these have also often the same velocity in the line of sight. Thus in the Great +Bear, β, γ, δ, ε, ζ, all agree as to angular proper +motion. δ was too faint for a spectroscopic measurement, but all the +others have been shown to be approaching us at a rate of twelve to twenty miles +a second. The same has been proved for proper motion, and line of sight motion, +in the case of Pleiades and other groups. +</p> + +<p> +Maskelyne measured many proper motions of stars, from which W. Herschel<a href="#linknote-73" name="linknoteref-73" id="linknoteref-73"><sup>[8]</sup></a> came to the conclusion that these apparent motions are +for the most part due to a motion of the solar system in space towards a point +in the constellation Hercules, R.A. 257°; N. Decl. 25°. This grand +discovery has been amply confirmed, and, though opinions differ as to the exact +direction, it happens that the point first indicated by Herschel, from totally +insufficient data, agrees well with modern estimates. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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.<a href="#linknote-74" name="linknoteref-74" id="linknoteref-74"><sup>[9]</sup></a> +</p> + +<p> +On analysis of the directions of proper motions of stars in all parts of the +heavens, Kapteyn has shown<a href="#linknote-75" name="linknoteref-75" id="linknoteref-75"><sup>[10]</sup></a> 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 (<i>R.A.S., +M.N.</i>) and Dyson (<i>R.S.E. Proc.</i>). +</p> + +<p> +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. +</p> + +<p> +<i>Double Stars.</i>—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. +</p> + +<p> +<i>Binary Stars.</i>—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. +</p> + +<p> +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.<a href="#linknote-76" name="linknoteref-76" id="linknoteref-76"><sup>[11]</sup></a> He gave the approximate period of +revolution of some of these: Castor, 342 years; δ Serpentis, 375 years; +γ Leonis, 1,200 years; ε Bootis, 1,681 years. +</p> + +<p> +Twenty years later Sir John Herschel and Sir James South, after re-examination +of these stars, confirmed<a href="#linknote-77" name="linknoteref-77" id="linknoteref-77"><sup>[12]</sup></a> and extended the results, +one pair of Coronæ having in the interval completed more than a whole +revolution. +</p> + +<p> +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,<a href="#linknote-78" name="linknoteref-78" id="linknoteref-78"><sup>[13]</sup></a> 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 <i>History</i>: “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.” +</p> + +<p> +Latterly the best work on double stars has been done by S. W. Burnham,<a href="#linknote-79" name="linknoteref-79" id="linknoteref-79"><sup>[14]</sup></a> at the Lick Observatory. The shortest period he found +was eleven years (κ Pegasi). In the case of some of these binaries the +parallax has been measured, from which it appears that in four of the surest +cases the orbits are about the size of the orbit of Uranus, these being +probably among the smallest stellar orbits. +</p> + +<p> +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,<a href="#linknote-80" name="linknoteref-80" id="linknoteref-80"><sup>[15]</sup></a> 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. +</p> + +<p> +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. +</p> + +<p> +<i>Spectroscopic Binaries</i>.—On measuring the velocity of a star in the +line of sight at frequent intervals, periodic variations have been found, +leading to a belief in motion round an invisible companion. Vogel, in 1889, +discovered this in the case of Spica (α Virginis), whose period is 4d. 0h. +19m., and the diameter of whose orbit is six million miles. Great numbers of +binaries of this type have since then been discovered, all of short period. +</p> + +<p> +Also, in 1889, Pickering found that at regular intervals of fifty-two days the +lines in the spectrum of ζ of the Great Bear are duplicated, indicating a +relative velocity, equal to one hundred miles a second, of two components +revolving round each other, of which that apparently single star must be +composed. +</p> + +<p> +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. +</p> + +<p> +<i>Variable Stars.</i>—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. +</p> + +<p> +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,<a href="#linknote-81" name="linknoteref-81" id="linknoteref-81"><sup>[16]</sup></a> in 1783, explained variable stars +of this type. Algol (β Persei) completes the period of variable brightness +in 68.8 hours. It loses three-fifths of its light, and regains it in twelve +hours. In 1889 Vogel,<a href="#linknote-82" name="linknoteref-82" id="linknoteref-82"><sup>[17]</sup></a> 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. +</p> + +<p> +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. +</p> + +<p> +Roberts, in South Africa, has done splendid work on the periods of variables of +the Algol type. +</p> + +<p> +<i>New Stars</i>.—Extreme instances of variable stars are the new stars +such as those detected by Hipparchus, Tycho Brahe, and Kepler, of which many +have been found in the last half-century. One of the latest great +“Novæ” was discovered in Auriga by a Scotsman, Dr. Anderson, on +February 1st, 1892, and, with the modesty of his race, he communicated the fact +to His Majesty’s Astronomer for Scotland on an unsigned post-card.<a href="#linknote-83" name="linknoteref-83" id="linknoteref-83"><sup>[18]</sup></a> 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<a href="#linknote-84" name="linknoteref-84" id="linknoteref-84"><sup>[19]</sup></a> 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.<a href="#linknote-85" name="linknoteref-85" id="linknoteref-85"><sup>[20]</sup></a> +</p> + +<p> +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. +</p> + +<p> +The same may be said of the brilliant Nova Persei, brighter at its best than +Capella, and discovered also by Dr. Anderson on February 22nd, 1901. It +increased in brightness as it reached the densest part of the nebula, then it +varied for some weeks by a couple of magnitudes, up and down, as if passing +through separate nebular condensations. In February, 1902, it could still be +seen with an opera-glass. As with the other Novæ, when it first dashed into the +nebula it was vaporised and gave a continuous spectrum with dark lines of +hydrogen and helium. It showed no bright lines paired with the dark ones to +indicate a train left behind; but in the end its own luminosity died out, and +the nebular spectrum predominated. +</p> + +<p> +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. +</p> + +<p> +<i>Star Catalogues.</i>—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. +</p> + +<p> +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.<a href="#linknote-86" name="linknoteref-86" id="linknoteref-86"><sup>[21]</sup></a> 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. +</p> + +<div class="fig" style="width:60%;"> +<a name="illus12"></a> +<img src="images/014.jpg" style="width:100%;" alt="GREAT COMET, Nov. 14TH, 1882." /> +<p class="caption">G<small>REAT</small> C<small>OMET</small>, +N<small>OV</small>. 14<small>TH</small>, 1882. (Exposure 2hrs. 20m.)<br/>By +kind permission of Sir David Gill. From this photograph originated all stellar +chart-photography.</p> +</div> + +<p> +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. +</p> + +<p> +Then we have the Harvard College collection of photographic plates, always +being automatically added to; and their annex at Arequipa in Peru. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +<i>Nebulæ and Star-clusters.</i>—Our knowledge of nebulæ really dates +from the time of W. Herschel. In his great sweeps of the heavens with his giant +telescopes he opened in this direction a new branch of astronomy. At one time +he held that all nebulæ might be clusters of innumerable minute stars at a +great distance. Then he recognised the different classes of nebulæ, and became +convinced that there is a widely-diffused “shining fluid” in space, +though many so-called nebulæ could be resolved by large telescopes into stars. +He considered that the Milky Way is a great star cluster, whose form may be +conjectured from numerous star-gaugings. He supposed that the compact +“planetary nebulæ” might show a stage of evolution from the diffuse +nebulæ, and that his classifications actually indicate various stages of +development. Such speculations, like those of the ancients about the solar +system, are apt to be harmful to true progress of knowledge unless in the hands +of the ablest mathematical physicists; and Herschel violated their principles +in other directions. But here his speculations have attracted a great deal of +attention, and, with modifications, are accepted, at least as a working +hypothesis, by a fair number of people. +</p> + +<p> +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. +</p> + +<p> +Then his views were changed by the revelations due to the great discoveries of +Lord Rosse with his gigantic refractor,<a href="#linknote-87" name="linknoteref-87" id="linknoteref-87"><sup>[22]</sup></a> when one +nebula after another was resolved into a cluster of minute stars. At that time +the opinion gained ground that with increase of telescopic power this would +prove to be the case with all nebulæ. +</p> + +<p> +In 1864 all doubt was dispelled by Huggins<a href="#linknote-88" name="linknoteref-88" id="linknoteref-88"><sup>[23]</sup></a> in his +first examination of the spectrum of a nebula, and the subsequent extension of +this observation to other nebulæ; thus providing a certain test which increase +in the size of telescopes could never have given. In 1864 Huggins found that +all true nebulae give a spectrum of bright lines. Three are due to hydrogen; +two (discovered by Copeland) are helium lines; others are unknown. Fifty-five +lines have been photographed in the spectrum of the Orion nebula. It seems to +be pretty certain that all true nebulae are gaseous, and show almost exactly +the same spectrum. +</p> + +<p> +Other nebulæ, and especially the white ones like that in Andromeda, which have +not yet been resolved into stars, show a continuous spectrum; others are +greenish and give no lines. +</p> + +<p> +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. +</p> + +<p> +The light of the nebulas is remarkably actinic, so that photography has a +specially fine field in revealing details imperceptible in the telescope. In +1885 the brothers Henry photographed, round the star Maia in the Pleiades, a +spiral nebula 3’ long, as bright on the plate as that star itself, but +quite invisible in the telescope; and an exposure of four hours revealed other +new nebula in the same district. That painstaking and most careful observer, +Barnard, with 10¼ hours’ exposure, extended this nebulosity for +several degrees, and discovered to the north of the Pleiades a huge diffuse +nebulosity, in a region almost destitute of stars. By establishing a 10-inch +instrument at an altitude of 6,000 feet, Barnard has revealed the wide +distribution of nebular matter in the constellation Scorpio over a space of +4° or 5° square. Barnard asserts that the “nebular +hypothesis” would have been killed at its birth by a knowledge of these +photographs. Later he has used still more powerful instruments, and extended +his discoveries. +</p> + +<p> +The association of stars with planetary nebulæ, and the distribution of nebulæ +in the heavens, especially in relation to the Milky Way, are striking facts, +which will certainly bear fruit when the time arrives for discarding vague +speculations, and learning to read the true physical structure and history of +the starry universe. +</p> + +<p> +<i>Stellar Spectra.</i>—When the spectroscope was first available for +stellar research, the leaders in this branch of astronomy were Huggins and +Father Secchi,<a href="#linknote-89" name="linknoteref-89" id="linknoteref-89"><sup>[24]</sup></a> 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. +</p> + +<p> +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. +</p> + +<p> +The third class includes α Herculis, α Orionis (Betelgeux), Mira +Ceti, and about 500 red and variable stars. The spectrum has fluted bands +shaded from blue to red, and sharply defined at the more refrangible edge. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +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. +</p> + +<p> +<i>Nebular Hypothesis.</i>—The Nebular Hypothesis, which was first, as it +were, tentatively put forward by Laplace as a note in his <i>Système du +Monde</i>, 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. +</p> + +<p> +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 <i>History of Astronomy during the Nineteenth Century</i>. 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. +</p> + +<hr /> + +<p> +<b>FOOTNOTES:</b> +</p> + +<p class="footnote"> +<a name="linknote-66" id="linknote-66"></a> <a href="#linknoteref-66">[1]</a> +<i>R. S. Phil Trans</i>., 1810 and 1817-24. +</p> + +<p class="footnote"> +<a name="linknote-67" id="linknote-67"></a> <a href="#linknoteref-67">[2]</a> +One of the most valuable contributions to our knowledge of stellar parallaxes +is the result of Gill’s work (<i>Cape Results</i>, vol. iii., part ii., +1900). +</p> + +<p class="footnote"> +<a name="linknote-68" id="linknote-68"></a> <a href="#linknoteref-68">[3]</a> +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. +</p> + +<p class="footnote"> +<a name="linknote-69" id="linknote-69"></a> <a href="#linknoteref-69">[4]</a> +Ast. Nacht., 1889. +</p> + +<p class="footnote"> +<a name="linknote-70" id="linknote-70"></a> <a href="#linknoteref-70">[5]</a> +R. S. Phil. Trans., 1718. +</p> + +<p class="footnote"> +<a name="linknote-71" id="linknote-71"></a> <a href="#linknoteref-71">[6]</a> +Mem. Acad. des Sciences, 1738, p. 337. +</p> + +<p class="footnote"> +<a name="linknote-72" id="linknote-72"></a> <a href="#linknoteref-72">[7]</a> +R. S Phil. Trans., 1868. +</p> + +<p class="footnote"> +<a name="linknote-73" id="linknote-73"></a> <a href="#linknoteref-73">[8]</a> +<i>R.S. Phil Trans.</i>, 1783. +</p> + +<p class="footnote"> +<a name="linknote-74" id="linknote-74"></a> <a href="#linknoteref-74">[9]</a> +See Kapteyn’s address to the Royal Institution, 1908. Also Gill’s +presidential address to the British Association, 1907. +</p> + +<p class="footnote"> +<a name="linknote-75" id="linknote-75"></a> <a href="#linknoteref-75">[10]</a> +<i>Brit. Assoc. Rep.</i>, 1905. +</p> + +<p class="footnote"> +<a name="linknote-76" id="linknote-76"></a> <a href="#linknoteref-76">[11]</a> +R. S. Phil. Trans., 1803, 1804. +</p> + +<p class="footnote"> +<a name="linknote-77" id="linknote-77"></a> <a href="#linknoteref-77">[12]</a> +Ibid, 1824. +</p> + +<p class="footnote"> +<a name="linknote-78" id="linknote-78"></a> <a href="#linknoteref-78">[13]</a> +Connaisance des Temps, 1830. +</p> + +<p class="footnote"> +<a name="linknote-79" id="linknote-79"></a> <a href="#linknoteref-79">[14]</a> +<i>R. A. S. Mem.</i>, vol. xlvii., p. 178; <i>Ast. Nach.</i>, No. 3,142; +Catalogue published by Lick Observatory, 1901. +</p> + +<p class="footnote"> +<a name="linknote-80" id="linknote-80"></a> <a href="#linknoteref-80">[15]</a> +<i>R. A. S., M. N.</i>, vol. vi. +</p> + +<p class="footnote"> +<a name="linknote-81" id="linknote-81"></a> <a href="#linknoteref-81">[16]</a> +<i>R. S. Phil. Trans.</i>, vol. lxxiii., p. 484. +</p> + +<p class="footnote"> +<a name="linknote-82" id="linknote-82"></a> <a href="#linknoteref-82">[17]</a> +<i>Astr. Nach.</i>, No. 2,947. +</p> + +<p class="footnote"> +<a name="linknote-83" id="linknote-83"></a> <a href="#linknoteref-83">[18]</a> +<i>R. S. E. Trans</i>., vol. xxvii. In 1901 Dr. Anderson discovered Nova +Persei. +</p> + +<p class="footnote"> +<a name="linknote-84" id="linknote-84"></a> <a href="#linknoteref-84">[19]</a> +<i>Astr. Nach</i>., No. 3,079. +</p> + +<p class="footnote"> +<a name="linknote-85" id="linknote-85"></a> <a href="#linknoteref-85">[20]</a> +For a different explanation see Sir W. Huggins’s lecture, Royal +Institution, May 13th, 1892. +</p> + +<p class="footnote"> +<a name="linknote-86" id="linknote-86"></a> <a href="#linknoteref-86">[21]</a> +For the early history of the proposals for photographic cataloguing of stars, +see the <i>Cape Photographic Durchmusterung</i>, 3 vols. (<i>Ann. of the Cape +Observatory</i>, vols. in., iv., and v., Introduction.) +</p> + +<p class="footnote"> +<a name="linknote-87" id="linknote-87"></a> <a href="#linknoteref-87">[22]</a> +<i>R. S. Phil. Trans.</i>, 1850, p. 499 <i>et seq.</i> +</p> + +<p class="footnote"> +<a name="linknote-88" id="linknote-88"></a> <a href="#linknoteref-88">[23]</a> +<i>Ibid</i>, vol. cliv., p. 437. +</p> + +<p class="footnote"> +<a name="linknote-89" id="linknote-89"></a> <a href="#linknoteref-89">[24]</a> +<i>Brit. Assoc. Rep.</i>, 1868, p. 165. +</p> + +</div><!--end chapter--> + +<div class="chapter"> + +<h2><a name="16"></a>ILLUSTRATIONS</h2> + +<table summary="" > + +<tr> +<td> <a href="#illus01">S<small>IR</small> I<small>SAAC</small> N<small>EWTON</small></a><br/> +(From the bust by Roubiliac In Trinity College, Cambridge.)</td> +</tr> + +<tr> +<td> <a href="#illus02">C<small>HALDÆAN</small> B<small>AKED</small> B<small>RICK +OR</small> T<small>ABLET</small></a><br/> +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.)</td> +</tr> + +<tr> +<td> <a href="#illus03">“Q<small>UADRANS</small> M<small>URALIS SIVE</small> +T<small>ICHONICUS</small>.”</a><br/> 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 +<i>Astronomiæ Instauratæ Mechanica</i>.)</td> +</tr> + +<tr> +<td> <a href="#illus04">P<small>ORTRAIT OF</small> J<small>OHANNES</small> +K<small>EPLER</small>.</a><br/> By F. Wanderer, from Reitlinger’s +“Johannes Kepler” (Original in Strassburg).</td> +</tr> + +<tr> +<td> <a href="#illus05">D<small>EATH</small>-M<small>ASK OF</small> +S<small>IR</small> I<small>SAAC</small> N<small>EWTON</small>.</a><br/> +Photographed specially for this work from the original, by kind permission of +the Royal Society, London.</td> +</tr> + +<tr> +<td> <a href="#illus06">A<small>NCIENT</small> C<small>HINESE</small> +I<small>NSTRUMENTS</small>,</a><br/>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.</td> +</tr> + +<tr> +<td> <a href="#illus07">S<small>OLAR</small> S<small>URFACE</small>.</a><br/>As +Photographed at the Royal Observatory, Greenwich, showing sun spots with umbræ, +penumbræ, and faculæ.</td> +</tr> + +<tr> +<td> <a href="#illus08">S<small>OLAR</small> E<small>CLIPSE</small>, 1882.</a><br/> +From drawing by W. H. Wesley, Secretary R.A.S.; showing the prominences, the +corona, and an unknown comet.</td> +</tr> + +<tr> +<td> <a href="#illus09">J<small>UPITER</small>.</a><br/>From a drawing by E. M. +Antoniadi, showing transit of a satellite’s shadow, the belts, and the +“great red spot” (<i>Monthly Notices</i>, R. A. S., vol. lix., pl. +x.).</td> +</tr> + +<tr> +<td> <a href="#illus10">C<small>OPY OF THE</small> D<small>RAWING</small> +M<small>ADE BY</small> P<small>AUL</small> F<small>ABRICIUS</small>.</a><br/>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.</td> +</tr> + +<tr> +<td> <a href="#illus11">S<small>IR</small> W<small>ILLIAM</small> +H<small>ERSCHEL</small>, F.R.S.—1738-1822.</a><br/>Painted by Lemuel F. +Abbott; National Portrait Gallery, Room XX.</td> +</tr> + +<tr> +<td> <a href="#illus12">G<small>REAT</small> C<small>OMET</small>, +N<small>OV</small>. 14<small>TH</small>, 1882. (Exposure 2hrs. 20m.)</a><br/>By +kind permission of Sir David Gill. From this photograph originated all stellar +chart-photography.</td> +</tr> + +</table> + +</div><!--end chapter--> + +<div class="chapter"> + +<h2><a name="index"></a>INDEX</h2> + +<p class="noindent"> +Abul Wefa, 24<br/> +Acceleration of moon’s mean motion, 60<br/> +Achromatic lens invented, 88<br/> +Adams, J. C., 61, 65, 68, 69, 70, 87, 118, 124<br/> +Airy, G. B., 13, 30, 37, 65, 69, 70, 80, 81, 114, +119<br/> +Albetegnius, 24<br/> +Alphonso, 24<br/> +Altazimuth, 81<br/> +Anaxagoras, 14, 16<br/> +Anaximander, 14<br/> +Anaximenes, 14<br/> +Anderson, T. D., 137, 138<br/> +Ångstrom, A. J., 102<br/> +Antoniadi, 113<br/> +Apian, P., 63<br/> +Apollonius, 22, 23<br/> +Arago, 111<br/> +Argelander, F. W. A., 139<br/> +Aristarchus, 18, 29<br/> +Aristillus, 17, 19<br/> +Aristotle, 16, 30, 47<br/> +Arrhenius, 146<br/> +Arzachel, 24<br/> +Asshurbanapal, 12<br/> +Asteroids, discovery of, 67, 119<br/> +Astrology, ancient and modern, 1-7, 38<br/> +<br/> +Backlund, 122<br/> +Bacon, R., 86<br/> +Bailly, 8, 65<br/> +Barnard, E. E., 115, 143<br/> +Beer and Mädler, 107, 110, 111<br/> +Behaim, 74<br/> +Bessel, F.W., 65, 79, 128, 134, 139<br/> +Biela, 123<br/> +Binet, 65<br/> +Biot, 10<br/> +Bird, 79, 80<br/> +Bliss, 80<br/> +Bode, 66, 69<br/> +Bond, G. P., 99, 117, 122<br/> +Bouvard, A., 65, 68<br/> +Bradley, J., 79, 80, 81, 87, 127, 128, 139<br/> +Bredechin, 146<br/> +Bremiker, 71<br/> +Brewster, D., 52, 91, 112<br/> +Brinkley, 128<br/> +Bruno, G., 49<br/> +Burchardt, 65, 123<br/> +Burnham, S. W., 134<br/> +<br/> +Callippus, 15, 16, 31<br/> +Carrington, R. C., 97, 99, 114<br/> +Cassini, G. D., 107, 114, 115, 116, 117, 118<br/> +Cassini, J., 109, 129<br/> +Chacornac, 139<br/> +Chaldæan astronomy, 11-13<br/> +Challis, J., 69, 70, 71, 72<br/> +Chance, 88<br/> +Charles, II., 50, 81<br/> +Chinese astronomy, 8-11<br/> +Christie, W. M. H. (Ast. Roy.), 64, 82, 125<br/> +Chueni, 9<br/> +Clairaut, A. C., 56, 63, 65<br/> +Clark, A. G., 89, 135<br/> +Clerke, Miss, 106, 146<br/> +Comets, 120<br/> +Common, A. A., 88<br/> +Cooke, 89<br/> +Copeland, R., 142<br/> +Copernicus, N., 14, 24-31, 37, 38, 41, 42, 49, 128<br/> +Cornu, 85<br/> +Cowell, P. H., 3, 5, 64, 83<br/> +Crawford, Earl of, 84<br/> +Cromellin, A. C., 5, 64<br/> +<br/> +D’Alembert, 65<br/> +Damoiseau, 65<br/> +D’Arrest, H. L., 34<br/> +Dawes, W. R., 100, 111<br/> +Delambre, J. B. J., 8, 27, 51, 65, 68<br/> +De la Rue, W., 2, 94, 99, 100, 131<br/> +Delaunay, 65<br/> +Democritus, 16<br/> +Descartes, 51<br/> +De Sejour, 117<br/> +Deslandres, II., 101<br/> +Desvignolles, 9<br/> +De Zach, 67<br/> +Digges, L., 86<br/> +Dollond, J., 87, 90<br/> +Dominis, A. di., 86<br/> +Donati, 120<br/> +Doppler, 92, 129<br/> +Draper, 99<br/> +Dreyer, J. L. E., 29,77<br/> +Dunthorne, 60<br/> +Dyson, 131<br/> +<br/> +Eclipses, total solar, 103<br/> +Ecphantes, 16<br/> +Eddington, 131<br/> +Ellipse, 41<br/> +Empedocles, 16<br/> +Encke, J. F., 119, 122, 123, 133<br/> +Epicycles, 22<br/> +Eratosthenes, 18<br/> +Euclid, 17<br/> +Eudoxus, 15, 31<br/> +Euler, L., 60, 61, 62, 65, 88, 119<br/> +<br/> +Fabricius, D.,95, 120, 121<br/> +Feil and Mantois, 88<br/> +Fizeau, H. L., 85, 92, 99<br/> +Flamsteed, J., 50, 58, 68, 78, 79, 93<br/> +Fohi, 8<br/> +Forbes, J. D., 52, 91<br/> +Foucault, L., 85, 99<br/> +Frauenhofer, J., 88, 90, 91<br/> +<br/> +Galilei, G., 38, 46-49, 77, 93, 94, 95, 96, 107, 113, +115, 116, 133<br/> +Galle, 71, 72<br/> +Gascoigne, W., 45, 77<br/> +Gauss, C. F., 65, 67<br/> +Gauthier, 98<br/> +Gautier, 89<br/> +Gilbert, 44<br/> +Gill, D., 84, 85, 128, 135, 139, 140<br/> +Goodricke, J., 136<br/> +Gould, B. A., 139<br/> +Grant, R., 27, 47, 51, 86, 134<br/> +Graham, 79<br/> +Greek astronomy, 8-11<br/> +Gregory, J. and D., 87<br/> +Grimaldi, 113<br/> +Groombridge, S., 139<br/> +Grubb, 88, 89<br/> +Guillemin, 122<br/> +Guinand, 88<br/> +<br/> +Hale, G. E., 101<br/> +Hall, A., 112<br/> +Hall, C. M., 88<br/> +Halley, E., 19, 51, 58, 60, 61, 62, 63, 64, 79, 120, +122, 125, 129<br/> +Halley’s comet, 62-64<br/> +Halm, 85<br/> +Hansen, P. A., 3, 65<br/> +Hansky, A. P., 100<br/> +Harding, C. L., 67<br/> +Heliometer, 83<br/> +Heller, 120<br/> +Helmholtz, H. L. F., 35<br/> +Henderson, T., 128<br/> +Henry, P. and P., 139, 140, 143<br/> +Heraclides, 16<br/> +Heraclitus, 14<br/> +Herodotus, 13<br/> +Herschel, W., 65, 68, 97, 107, 110, 114, 115, 116, +117, 118, 126, 127,<br/> +130, 131, 132, 141, 142<br/> +Herschel, J., 97, 111, 133, 134, 142<br/> +Herschel, A. S., 125<br/> +Hevelius, J., 178<br/> +Hind, J. R., 5, 64, 120, 121, 122<br/> +Hipparchus, 3, 18, 19, 20, 22, 23, 24, 26, 36, 55, +60, 74, 93, 137<br/> +Hooke, R., 51, 111, 114<br/> +Horrocks, J., 50, 56<br/> +Howlett, 100<br/> +Huggins, W., 92, 93, 99, 106, 120, 129, 137, 138, +142, 144<br/> +Humboldt and Bonpland, 124<br/> +Huyghens, C., 47, 77, 87, 110, 116, 117<br/> +<br/> +Ivory, 65<br/> +<br/> +Jansen, P. J. C., 105, 106<br/> +Jansen, Z., 86<br/> +<br/> +Kaiser, F., 111<br/> +Kapteyn, J. C., 131, 138, 139<br/> +Keeler, 117<br/> +Kepler, J., 17, 23, 26, 29, 30, 36, 37, 38-46, 48, +49, 50, 52, 53, 63,<br/> +66, 77, 87, 93, 127, 137<br/> +Kepler’s laws, 42<br/> +Kirchoff, G.R., 91<br/> +Kirsch, 9<br/> +Knobel, E.B., 12, 13<br/> +Ko-Show-King, 76<br/> +<br/> +Lacaile, N.L., 139<br/> +Lagrange, J.L., 61, 62, 65, 119<br/> +La Hire, 114<br/> +Lalande, J.J.L., 60, 63, 65, 66, 72, 139<br/> +Lamont, J., 98<br/> +Langrenus, 107<br/> +Laplace, P.S. de, 50, 58, 61, 62, 65,66, 123, 146<br/> +Lassel, 72, 88, 117, 118<br/> +Law of universal gravitation, 53<br/> +Legendre, 65<br/> +Leonardo da Vinci, 46<br/> +Lewis, G.C., 17<br/> +Le Verrier, U.J.J., 65, 68, 70, 71,72, 110, 118, 125<br/> +Lexell, 66, 123<br/> +Light year, 128<br/> +Lipperhey, H., 86<br/> +Littrow, 121<br/> +Lockyer, J.N., 103, 105, 146<br/> +Logarithms invented, 50<br/> +Loewy, 2, 100<br/> +Long inequality of Jupiter and Saturn, 50, 62<br/> +Lowell, P., 111, 112, 118<br/> +Lubienietz, S. de, 122<br/> +Luther, M., 38<br/> +Lunar theory, 37, 50, 56, 64<br/> +<br/> +Maclaurin, 65<br/> +Maclear, T., 128<br/> +Malvasia, 77<br/> +Martin, 9<br/> +Maxwell, J. Clerk, 117<br/> +Maskelyne, N., 80, 130<br/> +McLean, F., 89<br/> +Medici, Cosmo di, 48<br/> +Melancthon, 38<br/> +Melotte, 83, 116<br/> +Meteors, 123<br/> +Meton, 15<br/> +Meyer, 57, 65<br/> +Michaelson, 85<br/> +Miraldi, 110, 114<br/> +Molyneux, 87<br/> +Moon, physical observations, 107<br/> +Mouchez, 139<br/> +Moyriac de Mailla, 8<br/> +<br/> +Napier, Lord, 50<br/> +Nasmyth and Carpenter, 108<br/> +Nebulae, 141, 146<br/> +Neison, E., 108<br/> +Neptune, discovery of, 68-72<br/> +Newall, 89<br/> +Newcomb, 85<br/> +Newton, H.A., 124<br/> +Newton, I., 5, 19, 43, 49, 51-60, 62, 64, 68, 77, +79, 87, 90, 93, 94,<br/> +114, 127, 133<br/> +Nicetas, 16, 25<br/> +Niesten, 115<br/> +Nunez, P., 35<br/> +<br/> +Olbers, H.W.M., 67<br/> +Omar, 11, 24<br/> +Oppolzer, 13, 125<br/> +Oudemans, 129<br/> +<br/> +Palitsch, G., 64<br/> +Parallax, solar, 85, 86<br/> +Parmenides, 14<br/> +Paul III., 30<br/> +Paul V., 48<br/> +Pemberton, 51<br/> +Peters, C.A.F., 125, 128, 135<br/> +Photography, 99<br/> +Piazzi, G., 67, 128, 129, 139<br/> +Picard, 54, 77, 114<br/> +Pickering, E.C., 118, 135<br/> +Pingré, 13, 122<br/> +Plana, 65<br/> +Planets and satellites, physical observations, 109-119<br/> +Plato, 17, 23, 26, 40<br/> +Poisson, 65<br/> +Pond, J., 80<br/> +Pons, 122<br/> +Porta, B., 86<br/> +Pound, 87, 114<br/> +Pontecoulant, 64<br/> +Precession of the equinoxes, 19-21, 55, 57<br/> +Proctor, R.A., 111<br/> +Pritchett, 115<br/> +Ptolemy, 11, 13, 21, 22, 23, 24, 93<br/> +Puiseux and Loewy, 108<br/> +Pulfrich, 131<br/> +Purbach, G., 24<br/> +Pythagoras, 14, 17, 25, 29<br/> +<br/> +Ramsay, W., 106<br/> +Ransome and May, 81<br/> +Reflecting telescopes invented, 87<br/> +Regiomontanus (Müller), 24<br/> +Respighi, 82<br/> +Retrograde motion of planets, 22<br/> +Riccioli, 107<br/> +Roberts, 137<br/> +Römer, O.,78, 114<br/> +Rosse, Earl of, 88, 142<br/> +Rowland, H. A., 92, 102<br/> +Rudolph H.,37, 39<br/> +Rumker, C., 139<br/> +<br/> +Sabine, E., 98<br/> +Savary, 133<br/> +Schaeberle, J. M., 135<br/> +Schiaparelli, G. V., 110, 111, 124, 125<br/> +Scheiner, C., 87, 95, 96<br/> +Schmidt, 108<br/> +Schott, 88<br/> +Schröter, J. H., 107, 110, 111, 124, 125<br/> +Schuster, 98<br/> +Schwabe, G. H., 97<br/> +Secchi, A., 93, 144<br/> +Short, 87<br/> +Simms, J., 81<br/> +Slipher, V. M., 119<br/> +Socrates, 17<br/> +Solon, 15<br/> +Souciet, 8<br/> +South, J., 133<br/> +Spectroscope, 89-92<br/> +Spectroheliograph, 101<br/> +Spoerer, G. F. W., 98<br/> +Spots on the sun, 84;<br/> +periodicity of, 97<br/> +Stars, Parallax, 127;<br/> +proper motion, 129;<br/> +double, 132;<br/> +binaries, 132, 135;<br/> +new, 19, 36, 137;<br/> +catalogues of, 19, 36, 139;<br/> +spectra of, 143<br/> +Stewart, B., 2, 100<br/> +Stokes, G. G., 91<br/> +Stone, E. J., 139<br/> +Struve, C. L., 130<br/> +Struve, F. G. W,, 88, 115, 128, 133<br/> +<br/> +Telescopes invented, 47, 86;<br/> +large, 88<br/> +Temple, 115, 125<br/> +Thales, 13, 16<br/> +Theon, 60<br/> +Transit circle of Römer, 78<br/> +Timocharis, 17, 19<br/> +Titius, 66<br/> +Torricelli, 113<br/> +Troughton, E., 80<br/> +Tupman, G. L., 120<br/> +Tuttle, 125<br/> +Tycho Brahe, 23, 25, 30, 33-38, 39, 40, 44, 50, 75, 77, 93, 94, 129, 137<br/> +<br/> +Ulugh Begh, 24<br/> +Uranus, discovery of, 65<br/> +<br/> +Velocity of light, 86, 128;<br/> +of earth in orbit, 128<br/> +Verbiest, 75<br/> +Vogel, H. C., 92, 129, 135, 136<br/> +Von Asten, 122<br/> +<br/> +Walmsley, 65<br/> +Walterus, B., 24, 74<br/> +Weiss, E., 125<br/> +Wells, 122<br/> +Wesley, 104<br/> +Whewell, 112<br/> +Williams, 10<br/> +Wilson, A., 96, 100<br/> +Winnecke, 120<br/> +Witte, 86<br/> +Wollaston, 90<br/> +Wolf, M., 119, 125, 132<br/> +Wolf, R., 98<br/> +Wren, C., 51<br/> +Wyllie, A., 77<br/> +<br/> +Yao, 9<br/> +Young, C. A., 103<br/> +Yu-Chi, 8<br/> +<br/> +Zenith telescopes, 79, 82<br/> +Zöllner, 92<br/> +Zucchi, 113 +</p> + +</div><!--end chapter--> + +<pre> + + + + + +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-h.htm or 8172-h.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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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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Be sure to check the +copyright laws for your country before downloading or redistributing +this or any other Project Gutenberg eBook. + +This header should be the first thing seen when viewing this Project +Gutenberg file. Please do not remove it. Do not change or edit the +header without written permission. + +Please read the "legal small print," and other information about the +eBook and Project Gutenberg at the bottom of this file. Included is +important information about your specific rights and restrictions in +how the file may be used. You can also find out about how to make a +donation to Project Gutenberg, and how to get involved. + + +**Welcome To The World of Free Plain Vanilla Electronic Texts** + +**eBooks Readable By Both Humans and By Computers, Since 1971** + +*****These eBooks Were Prepared By Thousands of Volunteers!***** + + +Title: History of Astronomy + +Author: George Forbes + +Release Date: May, 2005 [EBook #8172] +[Yes, we are more than one year ahead of schedule] +[This file was first posted on June 25, 2003] + +Edition: 10 + +Language: English + +Character set encoding: ASCII + +*** START OF THE 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 365-1/4 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 degrees 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 +degrees 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 degrees and 27 degrees +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 ophe 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 Bootes 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 Muller, 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. + degrees ' " degrees ' " +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 degrees 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 degrees 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 degrees 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 degrees. + +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 degrees. + +This result agreed so well with Adams's (within 1 degrees) 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 degrees, 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 Konigsberg, 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 +29-1/2-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 Zollner. + + +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. Kon. Bohm. 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 degrees 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 degrees, 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 degrees; London and +Edinburgh, 1863. + +[5] _Periodicitat 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. Shroter supported this +opinion. W. Herschel opposed it. But Beer and Madler 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 Schroter, Beer and Madler (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 (Mosting 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. Shroter 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 Madler, 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 Madler 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, Romer, 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 5-1/2 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 2-1/2 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. Shroter 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 degrees 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 5-1/2 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 354-1/2 days; another suggestion was 375-1/2 +days, and another 33-1/4 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 33-1/4-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 Vogel, 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 degrees; N. Decl. 25 +degrees. 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 +10-1/4 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 degrees or 5 degrees 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 Madler, 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 (Muller), 24 +Respighi, 82 +Retrograde motion of planets, 22 +Riccioli, 107 +Roberts, 137 +Romer, 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 +Schroter, 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 Romer, 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 +Zollner, 92 +Zucchi, 113 + + + + + +End of the Project Gutenberg EBook of History of Astronomy, by George Forbes + +*** END OF THE PROJECT GUTENBERG EBOOK HISTORY OF ASTRONOMY *** + +This file should be named 7hsrs10.txt or 7hsrs10.zip +Corrected EDITIONS of our eBooks get a new NUMBER, 7hsrs11.txt +VERSIONS based on separate sources get new LETTER, 7hsrs10a.txt + +Produced by Jonathan Ingram, Dave Maddock, Charles Franks +and the Online Distributed Proofreading Team. + +Project Gutenberg eBooks are often created from several printed +editions, all of which are confirmed as Public Domain in the US +unless a copyright notice is included. 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Do not change or edit the +header without written permission. + +Please read the "legal small print," and other information about the +eBook and Project Gutenberg at the bottom of this file. Included is +important information about your specific rights and restrictions in +how the file may be used. You can also find out about how to make a +donation to Project Gutenberg, and how to get involved. + + +**Welcome To The World of Free Plain Vanilla Electronic Texts** + +**eBooks Readable By Both Humans and By Computers, Since 1971** + +*****These eBooks Were Prepared By Thousands of Volunteers!***** + + +Title: History of Astronomy + +Author: George Forbes + +Release Date: May, 2005 [EBook #8172] +[Yes, we are more than one year ahead of schedule] +[This file was first posted on June 25, 2003] + +Edition: 10 + +Language: English + +Character set encoding: ISO-8859-1 + +*** START OF THE 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 CHALDANS + + 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 NEBUL + + 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 _ 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 Chaldans 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 Chaldan 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 Chaldans +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: CHALDAN 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 CHALDANS. + + +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, Chaldans, 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. + +_Chaldans_.--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 Chaldans, 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. Pingr and Oppolzer fix the date July 16th, 533 B.C. Thus +are the relations of the chronologies of Jews and Egyptians +established by these explorations. + + +FOOTNOTES: + +[1] These ancient dates are uncertain. + +[2] _R. A. S. Monthly Notices_, vol. lxviii., No. 5, March, 1908. + + + +3. ANCIENT GREEK ASTRONOMY. + + +We have our information about the earliest Greek astronomy from +Herodotus (born 480 B.C.). He put the traditions into writing. Thales +(639-546 B.C.) is said to have predicted an eclipse, which caused much +alarm, and ended the battle between the Medes and Lydians. Airy fixed +the date May 28th, 585 B.C. But other modern astronomers give +different dates. Thales went to Egypt to study science, and learnt +from its priests the length of the year (which was kept a profound +secret!), and the signs of the zodiac, and the positions of the +solstices. He held that the sun, moon, and stars are not mere spots on +the heavenly vault, but solids; that the moon derives her light from +the sun, and that this fact explains her phases; that an eclipse of +the moon happens when the earth cuts off the sun's light from her. He +supposed the earth to be flat, and to float upon water. He determined +the ratio of the sun's diameter to its orbit, and apparently made out +the diameter correctly as half a degree. He left nothing in writing. + +His successors, Anaximander (610-547 B.C.) and Anaximenes (550-475 +B.C.), held absurd notions about the sun, moon, and stars, while +Heraclitus (540-500 B.C.) supposed that the stars were lighted each +night like lamps, and the sun each morning. Parmenides supposed the +earth to be a sphere. + +Pythagoras (569-470 B.C.) visited Egypt to study science. He deduced +his system, in which the earth revolves in an orbit, from fantastic +first principles, of which the following are examples: "The circular +motion is the most perfect motion," "Fire is more worthy than earth," +"Ten is the perfect number." He wrote nothing, but is supposed to have +said that the earth, moon, five planets, and fixed stars all revolve +round the sun, which itself revolves round an imaginary central fire +called the Antichthon. Copernicus in the sixteenth century claimed +Pythagoras as the founder of the system which he, Copernicus, revived. + +Anaxagoras (born 499 B.C.) studied astronomy in Egypt. He explained +the return of the sun to the east each morning by its going under the +flat earth in the night. He held that in a solar eclipse the moon +hides the sun, and in a lunar eclipse the moon enters the earth's +shadow--both excellent opinions. But he entertained absurd ideas of +the vortical motion of the heavens whisking stones into the sky, there +to be ignited by the fiery firmament to form stars. He was prosecuted +for this unsettling opinion, and for maintaining that the moon is an +inhabited earth. He was defended by Pericles (432 B.C.). + +Solon dabbled, like many others, in reforms of the calendar. The +common year of the Greeks originally had 360 days--twelve months of +thirty days. Solon's year was 354 days. It is obvious that these +erroneous years would, before long, remove the summer to January and +the winter to July. To prevent this it was customary at regular +intervals to intercalate days or months. Meton (432 B.C.) introduced a +reform based on the nineteen-year cycle. This is not the same as the +Egyptian and Chaldean eclipse cycle called _Saros_ of 223 +lunations, or a little over eighteen years. The Metonic cycle is 235 +lunations or nineteen years, after which period the sun and moon +occupy the same position relative to the stars. It is still used for +fixing the date of Easter, the number of the year in Melon's cycle +being the golden number of our prayer-books. Melon's system divided +the 235 lunations into months of thirty days and omitted every +sixty-third day. Of the nineteen years, twelve had twelve months and +seven had thirteen months. + +Callippus (330 B.C.) used a cycle four times as long, 940 lunations, +but one day short of Melon's seventy-six years. This was more correct. + +Eudoxus (406-350 B.C.) is said to have travelled with Plato in +Egypt. He made astronomical observations in Asia Minor, Sicily, and +Italy, and described the starry heavens divided into constellations. +His name is connected with a planetary theory which as generally +stated sounds most fanciful. He imagined the fixed stars to be on a +vault of heaven; and the sun, moon, and planets to be upon similar +vaults or spheres, twenty-six revolving spheres in all, the motion of +each planet being resolved into its components, and a separate sphere +being assigned for each component motion. Callippus (330 B.C.) +increased the number to thirty-three. It is now generally accepted +that the real existence of these spheres was not suggested, but the +idea was only a mathematical conception to facilitate the construction +of tables for predicting the places of the heavenly bodies. + +Aristotle (384-322 B.C.) summed up the state of astronomical knowledge +in his time, and held the earth to be fixed in the centre of the +world. + +Nicetas, Heraclides, and Ecphantes supposed the earth to revolve on +its axis, but to have no orbital motion. + +The short epitome so far given illustrates the extraordinary deductive +methods adopted by the ancient Greeks. But they went much farther in +the same direction. They seem to have been in great difficulty to +explain how the earth is supported, just as were those who invented +the myth of Atlas, or the Indians with the tortoise. Thales thought +that the flat earth floated on water. Anaxagoras thought that, being +flat, it would be buoyed up and supported on the air like a kite. +Democritus thought it remained fixed, like the donkey between two +bundles of hay, because it was equidistant from all parts of the +containing sphere, and there was no reason why it should incline one +way rather than another. Empedocles attributed its state of rest to +centrifugal force by the rapid circular movement of the heavens, as +water is stationary in a pail when whirled round by a string. +Democritus further supposed that the inclination of the flat earth to +the ecliptic was due to the greater weight of the southern parts owing +to the exuberant vegetation. + +For further references to similar efforts of imagination the reader is +referred to Sir George Cornwall Lewis's _Historical Survey of the +Astronomy of the Ancients_; London, 1862. His list of authorities +is very complete, but some of his conclusions are doubtful. At p. 113 +of that work he records the real opinions of Socrates as set forth by +Xenophon; and the reader will, perhaps, sympathise with Socrates in +his views on contemporary astronomy:-- + +With regard to astronomy he [Socrates] considered a knowledge of it +desirable to the extent of determining the day of the year or month, +and the hour of the night, ... but as to learning the courses of the +stars, to be occupied with the planets, and to inquire about their +distances from the earth, and their orbits, and the causes of their +motions, he strongly objected to such a waste of valuable time. He +dwelt on the contradictions and conflicting opinions of the physical +philosophers, ... and, in fine, he held that the speculators on the +universe and on the laws of the heavenly bodies were no better than +madmen (_Xen. Mem_, i. 1, 11-15). + +Plato (born 429 B.C.), the pupil of Socrates, the fellow-student of +Euclid, and a follower of Pythagoras, studied science in his travels +in Egypt and elsewhere. He was held in so great reverence by all +learned men that a problem which he set to the astronomers was the +keynote to all astronomical investigation from this date till the time +of Kepler in the sixteenth century. He proposed to astronomers _the +problem of representing the courses of the planets by circular and +uniform motions_. + +Systematic observation among the Greeks began with the rise of the +Alexandrian school. Aristillus and Timocharis set up instruments and +fixed the positions of the zodiacal stars, near to which all the +planets in their orbits pass, thus facilitating the determination of +planetary motions. Aristarchus (320-250 B.C.) showed that the sun must +be at least nineteen times as far off as the moon, which is far short +of the mark. He also found the sun's diameter, correctly, to be half a +degree. Eratosthenes (276-196 B.C.) measured the inclination to the +equator of the sun's apparent path in the heavens--i.e., he +measured the obliquity of the ecliptic, making it 23 51', confirming +our knowledge of its continuous diminution during historical times. He +measured an arc of meridian, from Alexandria to Syene (Assuan), and +found the difference of latitude by the length of a shadow at noon, +summer solstice. He deduced the diameter of the earth, 250,000 +stadia. Unfortunately, we do not know the length of the stadium he +used. + +Hipparchus (190-120 B.C.) may be regarded as the founder of +observational astronomy. He measured the obliquity of the ecliptic, +and agreed with Eratosthenes. He altered the length of the tropical +year from 365 days, 6 hours to 365 days, 5 hours, 53 minutes--still +four minutes too much. He measured the equation of time and the +irregular motion of the sun; and allowed for this in his calculations +by supposing that the centre, about which the sun moves uniformly, is +situated a little distance from the fixed earth. He called this point +the _excentric_. The line from the earth to the "excentric" was +called the _line of apses_. A circle having this centre was +called the _equant_, and he supposed that a radius drawn to the +sun from the excentric passes over equal arcs on the equant in equal +times. He then computed tables for predicting the place of the sun. + +He proceeded in the same way to compute Lunar tables. Making use of +Chaldan eclipses, he was able to get an accurate value of the moon's +mean motion. [Halley, in 1693, compared this value with his own +measurements, and so discovered the acceleration of the moon's mean +motion. This was conclusively established, but could not be explained +by the Newtonian theory for quite a long time.] He determined the +plane of the moon's orbit and its inclination to the ecliptic. The +motion of this plane round the pole of the ecliptic once in eighteen +years complicated the problem. He located the moon's excentric as he +had done the sun's. He also discovered some of the minor +irregularities of the moon's motion, due, as Newton's theory proves, +to the disturbing action of the sun's attraction. + +In the year 134 B.C. Hipparchus observed a new star. This upset every +notion about the permanence of the fixed stars. He then set to work to +catalogue all the principal stars so as to know if any others appeared +or disappeared. Here his experiences resembled those of several later +astronomers, who, when in search of some special object, have been +rewarded by a discovery in a totally different direction. On comparing +his star positions with those of Timocharis and Aristillus he found no +stars that had appeared or disappeared in the interval of 150 years; +but he found that all the stars seemed to have changed their places +with reference to that point in the heavens where the ecliptic is 90 +from the poles of the earth--i.e., the equinox. He found that this +could be explained by a motion of the equinox in the direction of the +apparent diurnal motion of the stars. This discovery of _precession of +the equinoxes_, which takes place at the rate of 52".1 every year, was +necessary for the progress of accurate astronomical observations. It +is due to a steady revolution of the earth's pole round the pole of +the ecliptic once in 26,000 years in the opposite direction to the +planetary revolutions. + +Hipparchus was also the inventor of trigonometry, both plane and +spherical. He explained the method of using eclipses for determining +the longitude. + +In connection with Hipparchus' great discovery it may be mentioned +that modern astronomers have often attempted to fix dates in history +by the effects of precession of the equinoxes. (1) At about the date +when the Great Pyramid may have been built 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 and 27 to the horizon and in +the plane of the meridian. It also appears that 4,000 years +ago--i.e., about 2100 B.C.--an observer at the lower end of the +passage would be able to see 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 Chaldans 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 Botes 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 Mller, 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 _Astronomi Instaurat 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 _ 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. + ' " ' " +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 parabol, in which case they would +be seen more than once. He found two old comets whose orbits, in shape +and position, resembled the orbit of a comet observed by himself in +1682. Apian observed one in 1531; Kepler the other in 1607. The +intervals between these appearances is seventy-five or seventy-six +years. He then examined and found old records of similar appearance in +1456, 1380, and 1305. It is true, he noticed, that the intervals +varied by a year and a-half, and the inclination of the orbit to the +ecliptic diminished with successive apparitions. But he knew from +previous calculations that this might easily be due to planetary +perturbations. Finally, he arrived at the conclusion that all of these +comets were identical, travelling in an ellipse so elongated that the +part where the comet was seen seemed to be part of a parabolic +orbit. He then predicted its return at the end of 1758 or beginning of +1759, when he should be dead; but, as he said, "if it should return, +according to our prediction, about the year 1758, impartial posterity +will not refuse to acknowledge that this was first discovered by an +Englishman."[3] [_Synopsis Astronomiae Cometicae_, 1749.] + +Once again Halley's suggestion became an inspiration for the +mathematical astronomer. Clairaut, assisted by Lalande, found that +Saturn would retard the comet 100 days, Jupiter 518 days, and +predicted its return to perihelion on April 13th, 1759. In his +communication to the French Academy, he said that a comet travelling +into such distant regions might be exposed to the influence of forces +totally unknown, and "even of some planet too far removed from the sun +to be ever perceived." + +The excitement of astronomers towards the end of 1758 became intense; +and the honour of first catching sight of the traveller fell to an +amateur in Saxony, George Palitsch, on Christmas Day, 1758. It reached +perihelion on March 13th, 1759. + +This fact was a startling confirmation of the Newtonian theory, +because it was a new kind of calculation of perturbations, and also it +added a new member to the solar system, and gave a prospect of adding +many more. + +When Halley's comet reappeared in 1835, Pontecoulant's computations +for the date of perihelion passage were very exact, and afterwards he +showed that, with more exact values of the masses of Jupiter and +Saturn, his prediction was correct within two days, after an invisible +voyage of seventy-five years! + +Hind afterwards searched out many old appearances of this comet, going +back to 11 B.C., and most of these have been identified as being +really Halley's comet by the calculations of Cowell and Cromellin[4] +(of Greenwich Observatory), who have also predicted its next +perihelion passage for April 8th to 16th, 1910, and have traced back +its history still farther, to 240 B.C. + +Already, in November, 1907, the Astronomer Royal was trying to catch +it by the aid of photography. + + +FOOTNOTES: + +[1] Born 1736; died 1813. + +[2] Born 1749; died 1827. + +[3] This sentence does not appear in the original memoir communicated +to the Royal Society, but was first published in a posthumous reprint. + +[4] _R. A. S. Monthly Notices_, 1907-8. + + + +9. DISCOVERY OF NEW PLANETS--HERSCHEL, PIAZZI, ADAMS, AND LE VERRIER. + + +It would be very interesting, but quite impossible in these pages, to +discuss all the exquisite researches of the mathematical astronomers, +and to inspire a reverence for the names connected with these +researches, which for two hundred years have been establishing the +universality of Newton's law. The lunar and planetary theories, the +beautiful theory of Jupiter's satellites, the figure of the earth, and +the tides, were mathematically treated by Maclaurin, D'Alembert, +Legendre, Clairaut, Euler, Lagrange, Laplace, Walmsley, Bailly, +Lalande, Delambre, Mayer, Hansen, Burchardt, Binet, Damoiseau, Plana, +Poisson, Gauss, Bessel, Bouvard, Airy, Ivory, Delaunay, Le Verrier, +Adams, and others of later date. + +By passing over these important developments it is possible to trace +some of the steps in the crowning triumph of the Newtonian theory, by +which the planet Neptune was added to the known members of the solar +system by the independent researches of Professor J.C. Adams and of +M. Le Verrier, in 1846. + +It will be best to introduce this subject by relating how the +eighteenth century increased the number of known planets, which was +then only six, including the earth. + +On March 13th, 1781, Sir William Herschel was, as usual, engaged on +examining some small stars, and, noticing that one of them appeared to +be larger than the fixed stars, suspected that it might be a comet. +To test this he increased his magnifying power from 227 to 460 and +932, finding that, unlike the fixed stars near it, its definition was +impaired and its size increased. This convinced him that the object +was a comet, and he was not surprised to find on succeeding nights +that the position was changed, the motion being in the ecliptic. He +gave the observations of five weeks to the Royal Society without a +suspicion that the object was a new planet. + +For a long time people could not compute a satisfactory orbit for the +supposed comet, because it seemed to be near the perihelion, and no +comet had ever been observed with a perihelion distance from the sun +greater than four times the earth's distance. Lexell was the first to +suspect that this was a new planet eighteen times as far from the sun +as the earth is. In January, 1783, Laplace published the elliptic +elements. The discoverer of a planet has a right to name it, so +Herschel called it Georgium Sidus, after the king. But Lalande urged +the adoption of the name Herschel. Bode suggested Uranus, and this +was adopted. The new planet was found to rank in size next to Jupiter +and Saturn, being 4.3 times the diameter of the earth. + +In 1787 Herschel discovered two satellites, both revolving in nearly +the same plane, inclined 80 to the ecliptic, and the motion of both +was retrograde. + +In 1772, before Herschel's discovery, Bode[1] had discovered a curious +arbitrary law of planetary distances. Opposite each planet's name +write the figure 4; and, in succession, add the numbers 0, 3, 6, 12, +24, 48, 96, etc., to the 4, always doubling the last numbers. You +then get the planetary distances. + + Mercury, dist.-- 4 4 + 0 = 4 + Venus " 7 4 + 3 = 7 + Earth " 10 4 + 6 = 10 + Mars " 15 4 + 12 = 16 + -- 4 + 24 = 28 + Jupiter dist. 52 4 + 48 = 52 + Saturn " 95 4 + 96 = 100 + (Uranus) " 192 4 + 192 = 196 + -- 4 + 384 = 388 + +All the five planets, and the earth, fitted this rule, except that +there was a blank between Mars and Jupiter. When Uranus was +discovered, also fitting the rule, the conclusion was irresistible +that there is probably a planet between Mars and Jupiter. An +association of twenty-four astronomers was now formed in Germany to +search for the planet. Almost immediately afterwards the planet was +discovered, not by any member of the association, but by Piazzi, when +engaged upon his great catalogue of stars. On January 1st, 1801, he +observed a star which had changed its place the next night. Its motion +was retrograde till January 11th, direct after the 13th. Piazzi fell +ill before he had enough observations for computing the orbit with +certainty, and the planet disappeared in the sun's rays. Gauss +published an approximate ephemeris of probable positions when the +planet should emerge from the sun's light. There was an exciting hunt, +and on December 31st (the day before its birthday) De Zach captured +the truant, and Piazzi christened it Ceres. + + +The mean distance from the sun was found to be 2.767, agreeing with +the 2.8 given by Bode's law. Its orbit was found to be inclined over +10 to the ecliptic, and its diameter was only 161 miles. + +On March 28th, 1802, Olbers discovered a new seventh magnitude star, +which turned out to be a planet resembling Ceres. It was called +Pallas. Gauss found its orbit to be inclined 35 to the ecliptic, and +to cut the orbit of Ceres; whence Olbers considered that these might +be fragments of a broken-up planet. He then commenced a search for +other fragments. In 1804 Harding discovered Juno, and in 1807 Olbers +found Vesta. The next one was not discovered until 1845, from which +date asteroids, or minor planets (as these small planets are called), +have been found almost every year. They now number about 700. + +It is impossible to give any idea of the interest with which the first +additions since prehistoric times to the planetary system were +received. All of those who showered congratulations upon the +discoverers regarded these discoveries in the light of rewards for +patient and continuous labours, the very highest rewards that could be +desired. And yet there remained still the most brilliant triumph of +all, the addition of another planet like Uranus, before it had ever +been seen, when the analysis of Adams and Le Verrier gave a final +proof of the powers of Newton's great law to explain any planetary +irregularity. + +After Sir William Herschel discovered Uranus, in 1781, it was found +that astronomers had observed it on many previous occasions, mistaking +it for a fixed star of the sixth or seventh magnitude. Altogether, +nineteen observations of Uranus's position, from the time of +Flamsteed, in 1690, had been recorded. + +In 1790 Delambre, using all these observations, prepared tables for +computing its position. These worked well enough for a time, but at +last the differences between the calculated and observed longitudes of +the planet became serious. In 1821 Bouvard undertook a revision of the +tables, but found it impossible to reconcile all the observations of +130 years (the period of revolution of Uranus is eighty-four years). +So he deliberately rejected the old ones, expressing the opinion that +the discrepancies might depend upon "some foreign and unperceived +cause which may have been acting upon the planet." In a few years the +errors even of these tables became intolerable. In 1835 the error of +longitude was 30"; in 1838, 50"; in 1841, 70"; and, by comparing the +errors derived from observations made before and after opposition, a +serious error of the distance (radius vector) became apparent. + +In 1843 John Couch Adams came out Senior Wrangler at Cambridge, and +was free to undertake the research which as an undergraduate he had +set himself--to see whether the disturbances of Uranus could be +explained by assuming a certain orbit, and position in that orbit, of +a hypothetical planet even more distant than Uranus. Such an +explanation had been suggested, but until 1843 no one had the boldness +to attack the problem. Bessel had intended to try, but a fatal +illness overtook him. + +Adams first recalculated all known causes of disturbance, using the +latest determinations of the planetary masses. Still the errors were +nearly as great as ever. He could now, however, use these errors as +being actually due to the perturbations produced by the unknown +planet. + +In 1844, assuming a circular orbit, and a mean distance agreeing with +Bode's law, he obtained a first approximation to the position of the +supposed planet. He then asked Professor Challis, of Cambridge, to +procure the latest observations of Uranus from Greenwich, which Airy +immediately supplied. Then the whole work was recalculated from the +beginning, with more exactness, and assuming a smaller mean distance. + +In September, 1845, he handed to Challis the elements of the +hypothetical planet, its mass, and its apparent position for September +30th, 1845. On September 22nd Challis wrote to Airy explaining the +matter, and declaring his belief in Adams's capabilities. When Adams +called on him Airy was away from home, but at the end of October, +1845, he called again, and left a paper with full particulars of his +results, which had, for the most part, reduced the discrepancies to +about 1". As a matter of fact, it has since been found that the +heliocentric place of the new planet then given was correct within +about 2. + +Airy wrote expressing his interest, and asked for particulars about +the radius vector. Adams did not then reply, as the answer to this +question could be seen to be satisfactory by looking at the data +already supplied. He was a most unassuming man, and would not push +himself forward. He may have felt, after all the work he had done, +that Airy's very natural inquiry showed no proportionate desire to +search for the planet. Anyway, the matter lay in embryo for nine +months. + +Meanwhile, one of the ablest French astronomers, Le Verrier, +experienced in computing perturbations, was independently at work, +knowing nothing about Adams. He applied to his calculations every +possible refinement, and, considering the novelty of the problem, his +calculation was one of the most brilliant in the records of +astronomy. In criticism it has been said that these were exhibitions +of skill rather than helps to a solution of the particular problem, +and that, in claiming to find the elements of the orbit within certain +limits, he was claiming what was, under the circumstances, impossible, +as the result proved. + +In June, 1846, Le Verrier announced, in the _Comptes Rendus de +l'Academie des Sciences_, that the longitude of the disturbing planet, +for January 1st, 1847, was 325, and that the probable error did not +exceed 10. + +This result agreed so well with Adams's (within 1) that Airy urged +Challis to apply the splendid Northumberland equatoreal, at Cambridge, +to the search. Challis, however, had already prepared an exhaustive +plan of attack which must in time settle the point. His first work +was to observe, and make a catalogue, or chart, of all stars near +Adams's position. + +On August 31st, 1846, Le Verrier published the concluding +part of his labours. + +On September 18th, 1846, Le Verrier communicated his results to the +Astronomers at Berlin, and asked them to assist in searching for the +planet. By good luck Dr. Bremiker had just completed a star-chart of +the very part of the heavens including Le Verrier's position; thus +eliminating all of Challis's preliminary work. The letter was received +in Berlin on September 23rd; and the same evening Galle found the new +planet, of the eighth magnitude, the size of its disc agreeing with Le +Verrier's prediction, and the heliocentric longitude agreeing within +57'. By this time Challis had recorded, without reduction, the +observations of 3,150 stars, as a commencement for his search. On +reducing these, he found a star, observed on August 12th, which was +not in the same place on July 30th. This was the planet, and he had +also observed it on August 4th. + +The feeling of wonder, admiration, and enthusiasm aroused by this +intellectual triumph was overwhelming. In the world of astronomy +reminders are met every day of the terrible limitations of human +reasoning powers; and every success that enables the mind's eye to see +a little more clearly the meaning of things has always been heartily +welcomed by those who have themselves been engaged in like +researches. But, since the publication of the _Principia_, in 1687, +there is probably no analytical success which has raised among +astronomers such a feeling of admiration and gratitude as when Adams +and Le Verrier showed the inequalities in Uranus's motion to mean that +an unknown planet was in a certain place in the heavens, where it was +found. + +At the time there was an unpleasant display of international jealousy. +The British people thought that the earlier date of Adams's work, and +of the observation by Challis, entitled him to at least an equal share +of credit with Le Verrier. The French, on the other hand, who, on the +announcement of the discovery by Galle, glowed with pride in the new +proof of the great powers of their astronomer, Le Verrier, whose life +had a long record of successes in calculation, were incredulous on +being told that it had all been already done by a young man whom they +had never heard of. + +These displays of jealousy have long since passed away, and there is +now universally an _entente cordiale_ that to each of these great men +belongs equally the merit of having so thoroughly calculated this +inverse problem of perturbations as to lead to the immediate discovery +of the unknown planet, since called Neptune. + +It was soon found that the planet had been observed, and its position +recorded as a fixed star by Lalande, on May 8th and 10th, 1795. + +Mr. Lassel, in the same year, 1846, with his two-feet reflector, +discovered a satellite, with retrograde motion, which gave the mass of +the planet about a twentieth of that of Jupiter. + + +FOOTNOTES: + +[1] Bode's law, or something like it, had already been fore-shadowed +by Kepler and others, especially Titius (see _Monatliche +Correspondenz_, vol. vii., p. 72). + + + + +BOOK III. OBSERVATION + + + +10. INSTRUMENTS OF PRECISION--STATE OF THE SOLAR SYSTEM. + + +Having now traced the progress of physical astronomy up to the time +when very striking proofs of the universality of the law of +gravitation convinced the most sceptical, it must still be borne in +mind that, while gravitation is certainly the principal force +governing the motions of the heavenly bodies, there may yet be a +resisting medium in space, and there may be electric and magnetic +forces to deal with. There may, further, be cases where the effects of +luminous radiative repulsion become apparent, and also Crookes' +vacuum-effects described as "radiant matter." Nor is it quite certain +that Laplace's proofs of the instantaneous propagation of gravity are +final. + +And in the future, as in the past, Tycho Brahe's dictum must be +maintained, that all theory shall be preceded by accurate +observations. It is the pride of astronomers that their science stands +above all others in the accuracy of the facts observed, as well as in +the rigid logic of the mathematics used for interpreting these facts. + +It is interesting to trace historically the invention of those +instruments of precision which have led to this result, and, without +entering on the details required in a practical handbook, to note the +guiding principles of construction in different ages. + +It is very probable that the Chaldeans may have made spheres, like the +armillary sphere, for representing the poles of the heavens; and with +rings to show the ecliptic and zodiac, as well as the equinoctial and +solstitial colures; but we have no record. We only know that the tower +of Belus, on an eminence, was their observatory. We have, however, +distinct records of two such spheres used by the Chinese about 2500 +B.C. Gnomons, or some kind of sundial, were used by the Egyptians and +others; and many of the ancient nations measured the obliquity of the +ecliptic by the shadows of a vertical column in summer and winter. The +natural horizon was the only instrument of precision used by those who +determined star positions by the directions of their risings and +settings; while in those days the clepsydra, or waterclock, was the +best instrument for comparing their times of rising and setting. + +About 300 B.C. an observatory fitted with circular instruments for +star positions was set up at Alexandria, the then centre of +civilisation. We know almost nothing about the instruments used by +Hipparchus in preparing his star catalogues and his lunar and solar +tables; but the invention of the astrolabe is attributed to him.[1] + +In more modern times Nuremberg became a centre of astronomical +culture. Waltherus, of that town, made really accurate observations of +star altitudes, and of the distances between stars; and in 1484 +A.D. he used a kind of clock. Tycho Brahe tried these, but discarded +them as being inaccurate. + +Tycho Brahe (1546-1601 A.D.) made great improvements in armillary +spheres, quadrants, sextants, and large celestial globes. With these +he measured the positions of stars, or the distance of a comet from +several known stars. He has left us full descriptions of them, +illustrated by excellent engravings. Previous to his time such +instruments were made of wood. Tycho always used metal. He paid the +greatest attention to the stability of mounting, to the orientation of +his instruments, to the graduation of the arcs by the then new method +of transversals, and to the aperture sight used upon his +pointer. There were no telescopes in his day, and no pendulum +clocks. He recognised the fact that there must be instrumental +errors. He made these as small as was possible, measured their amount, +and corrected his observations. His table of refractions enabled him +to abolish the error due to our atmosphere so far as it could affect +naked-eye observations. The azimuth circle of Tycho's largest quadrant +had a diameter of nine feet, and the quadrant a radius of six feet. He +introduced the mural quadrant for meridian observations.[2] + +[Illustration: ANCIENT CHINESE INSTRUMENTS, Including quadrant, celestial +globe, and two armillae, in the Observatory at Peking. Photographed in +Peking by the author in 1875, and stolen by the Germans when the +Embassies were relieved by the allies in 1900.] + +The French Jesuits at Peking, in the seventeenth century, helped the +Chinese in their astronomy. In 1875 the writer saw and photographed, +on that part of the wall of Peking used by the Mandarins as an +observatory, the six instruments handsomely designed by Father +Verbiest, copied from the instruments of Tycho Brahe, and embellished +with Chinese dragons and emblems cast on the supports. He also saw +there two old instruments (which he was told were Arabic) of date +1279, by Ko Show-King, astronomer to Koblai Khan, the grandson of +Chenghis Khan. One of these last is nearly identical with the armillae +of Tycho; and the other with his "armillae quatori maxim," with +which he observed the comet of 1585, besides fixed stars and +planets.[3] + +The discovery by Galileo of the isochronism of the pendulum, followed +by Huyghens's adaptation of that principle to clocks, has been one of +the greatest aids to accurate observation. About the same time an +equally beneficial step was the employment of the telescope as a +pointer; not the Galilean with concave eye-piece, but with a +magnifying glass to examine the focal image, at which also a fixed +mark could be placed. Kepler was the first to suggest this. Gascoigne +was the first to use it. Huyghens used a metal strip of variable width +in the focus, as a micrometer to cover a planetary disc, and so to +measure the width covered by the planet. The Marquis Malvasia, in +1662, described the network of fine silver threads at right angles, +which he used in the focus, much as we do now. + +In the hands of such a skilful man as Tycho Brahe, the old open +sights, even without clocks, served their purpose sufficiently well to +enable Kepler to discover the true theory of the solar system. But +telescopic sights and clocks were required for proving some of +Newton's theories of planetary perturbations. Picard's observations at +Paris from 1667 onwards seem to embody the first use of the telescope +as a pointer. He was also the first to introduce the use of Huyghens's +clocks for observing the right ascension of stars. Olaus Romer was +born at Copenhagen in 1644. In 1675, by careful study of the times of +eclipses of Jupiter's satellites, he discovered that light took time +to traverse space. Its velocity is 186,000 miles per second. In 1681 +he took up his duties as astronomer at Copenhagen, and built the first +transit circle on a window-sill of his house. The iron axis was five +feet long and one and a-half inches thick, and the telescope was fixed +near one end with a counterpoise. The telescope-tube was a double +cone, to prevent flexure. Three horizontal and three vertical wires +were used in the focus. These were illuminated by a speculum, near the +object-glass, reflecting the light from a lantern placed over the +axis, the upper part of the telescope-tube being partly cut away to +admit the light. A divided circle, with pointer and reading +microscope, was provided for reading the declination. He realised the +superiority of a circle with graduations over a much larger +quadrant. The collimation error was found by reversing the instrument +and using a terrestrial mark, the azimuth error by star observations. +The time was expressed in fractions of a second. He also constructed a +telescope with equatoreal mounting, to follow a star by one axial +motion. In 1728 his instruments and observation records were destroyed +by fire. + +Hevelius had introduced the vernier and tangent screw in his +measurement of arc graduations. His observatory and records were burnt +to the ground in 1679. Though an old man, he started afresh, and left +behind him a catalogue of 1,500 stars. + +Flamsteed began his duties at Greenwich Observatory, as first +Astronomer Royal, in 1676, with very poor instruments. In 1683 he put +up a mural arc of 140, and in 1689 a better one, seventy-nine inches +radius. He conducted his measurements with great skill, and +introduced new methods to attain accuracy, using certain stars for +determining the errors of his instruments; and he always reduced his +observations to a form in which they could be readily used. He +introduced new methods for determining the position of the equinox and +the right ascension of a fundamental star. He produced a catalogue of +2,935 stars. He supplied Sir Isaac Newton with results of observation +required in his theoretical calculations. He died in 1719. + +Halley succeeded Flamsteed to find that the whole place had been +gutted by the latter's executors. In 1721 he got a transit instrument, +and in 1726 a mural quadrant by Graham. His successor in 1742, +Bradley, replaced this by a fine brass quadrant, eight feet radius, by +Bird; and Bradley's zenith sector was purchased for the observatory. +An instrument like this, specially designed for zenith stars, is +capable of greater rigidity than a more universal instrument; and +there is no trouble with refraction in the zenith. For these reasons +Bradley had set up this instrument at Kew, to attempt the proof of the +earth's motion by observing the annual parallax of stars. He certainly +found an annual variation of zenith distance, but not at the times of +year required by the parallax. This led him to the discovery of the +"aberration" of light and of nutation. Bradley has been described as +the founder of the modern system of accurate observation. He died in +1762, leaving behind him thirteen folio volumes of valuable but +unreduced observations. Those relating to the stars were reduced by +Bessel and published in 1818, at Knigsberg, 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 Zllner. + + +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. Kn. Bhm. 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 on each side of the equator, and that a +zone of equatoreal calms is free from spots. But it was +R. C. Carrington[4] who, by his continuous observations at Redhill, in +Surrey, established the remarkable fact that, while the rotation +period in the highest latitudes, 50, where spots are seen, is +twenty-seven-and-a-half days, near the equator the period is only +twenty-five days. His splendid volume of observations of the sun led +to much new information about the average distribution of spots at +different epochs. + +Schwabe, of Dessau, began in 1826 to study the solar surface, and, +after many years of work, arrived at a law of frequency which has been +more fruitful of results than any discovery in solar physics.[5] In +1843 he announced a decennial period of maxima and minima of sun-spot +displays. In 1851 it was generally accepted, and, although a period of +eleven years has been found to be more exact, all later observations, +besides the earlier ones which have been hunted up for the purpose, go +to establish a true periodicity in the number of sun-spots. But quite +lately Schuster[6] has given reasons for admitting a number of +co-existent periods, of which the eleven-year period was predominant +in the nineteenth century. + +In 1851 Lament, a Scotchman at Munich, found a decennial period in the +daily range of magnetic declination. In 1852 Sir Edward Sabine +announced a similar period in the number of "magnetic storms" +affecting all of the three magnetic elements--declination, dip, and +intensity. Australian and Canadian observations both showed the +decennial period in all three elements. Wolf, of Zurich, and Gauthier, +of Geneva, each independently arrived at the same conclusion. + +It took many years before this coincidence was accepted as certainly +more than an accident by the old-fashioned astronomers, who want rigid +proof for every new theory. But the last doubts have long vanished, +and a connection has been further traced between violent outbursts of +solar activity and simultaneous magnetic storms. + +The frequency of the Aurora Borealis was found by Wolf to follow the +same period. In fact, it is closely allied in its cause to terrestrial +magnetism. Wolf also collected old observations tracing the +periodicity of sun-spots back to about 1700 A.D. + +Spoerer deduced a law of dependence of the average latitude of +sun-spots on the phase of the sun-spot period. + +All modern total solar eclipse observations seem to show that the +shape of the luminous corona surrounding the moon at the moment of +totality has a special distinct character during the time of a +sun-spot maximum, and another, totally different, during a sun-spot +minimum. + +A suspicion is entertained that the total quantity of heat received by +the earth from the sun is subject to the same period. This would have +far-reaching effects on storms, harvests, vintages, floods, and +droughts; but it is not safe to draw conclusions of this kind except +from a very long period of observations. + +Solar photography has deprived astronomers of the type of Carrington +of the delight in devoting a life's work to collecting data. It has +now become part of the routine work of an observatory. + +In 1845 Foucault and Fizeau took a daguerreotype photograph of the +sun. In 1850 Bond produced one of the moon of great beauty, Draper +having made some attempts at an even earlier date. But astronomical +photography really owes its beginning to De la Rue, who used the +collodion process for the moon in 1853, and constructed the Kew +photoheliograph in 1857, from which date these instruments have been +multiplied, and have given us an accurate record of the sun's surface. +Gelatine dry plates were first used by Huggins in 1876. + +It is noteworthy that from the outset De la Rue recognised the value +of stereoscopic vision, which is now known to be of supreme +accuracy. In 1853 he combined pairs of photographs of the moon in the +same phase, but under different conditions regarding libration, +showing the moon from slightly different points of view. These in the +stereoscope exhibited all the relief resulting from binocular vision, +and looked like a solid globe. In 1860 he used successive photographs +of the total solar eclipse stereoscopically, to prove that the red +prominences belong to the sun, and not to the moon. In 1861 he +similarly combined two photographs of a sun-spot, the perspective +effect showing the umbra like a floor at the bottom of a hollow +penumbra; and in one case the facul 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 facul 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 facul 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. ngstrom 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-l en dehors des clipses_." And the next day he observed the +lines at the edge of the uneclipsed sun. Huggins had suggested this +observation in February, 1868, his idea being to use prisms of such +great dispersive power that the continuous spectrum reflected by our +atmosphere should be greatly weakened, while a bright line would +suffer no diminution by the high dispersion. On October 20th +Lockyer,[10] having news of the eclipse, but not of Jansen's +observations the day after, was able to see these lines. This was a +splendid performance, for it enabled the prominences to be observed, +not only during eclipses, but every day. Moreover, the next year +Huggins was able, by using a wide slit, to see the whole of a +prominence and note its shape. Prominences are classified, according +to their form, into "flame" and "cloud" prominences, the spectrum of +the latter showing calcium, hydrogen, and helium; that of the former +including a number of metals. + +The D line of sodium is a double line, and in the same eclipse (1868) +an orange line was noticed which was afterwards found to lie close to +the two components of the D line. It did not correspond with any known +terrestrial element, and the unknown element was called "helium." It +was not until 1895 that Sir William Ramsay found this element as a gas +in the mineral cleavite. + +The spectrum of the corona is partly continuous, indicating light +reflected from the sun's body. But it also shows a green line +corresponding with no known terrestrial element, and the name +"coronium" has been given to the substance causing it. + +A vast number of facts have been added to our knowledge about the sun +by photography and the spectroscope. Speculations and hypotheses in +plenty have been offered, but it may be long before we have a complete +theory evolved to explain all the phenomena of the storm-swept +metallic atmosphere of the sun. + +The proceedings of scientific societies teem with such facts and +"working hypotheses," and the best of them have been collected by Miss +Clerke in her _History of Astronomy during the Nineteenth Century_. As +to established facts, we learn from the spectroscopic researches (1) +that the continuous spectrum is derived from the _photosphere_ or +solar gaseous material compressed almost to liquid consistency; (2) +that the _reversing layer_ surrounds it and gives rise to black +lines in the spectrum; that the _chromosphere_ surrounds this, is +composed mainly of hydrogen, and is the cause of the red prominences +in eclipses; and that the gaseous _corona_ surrounds all of +these, and extends to vast distances outside the sun's visible +surface. + + +FOOTNOTES: + +[1] _Rosa Ursina_, by C. Scheiner, _fol_.; Bracciani, 1630. + +[2] _R. S. Phil. Trans_., 1774. + +[3] _Ibid_, 1783. + +[4] _Observations on the Spots on the Sun, etc.,_ 4; London and +Edinburgh, 1863. + +[5] _Periodicitt 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. Shrter supported this +opinion. W. Herschel opposed it. But Beer and Mdler 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 Schrter, Beer and Mdler (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 _Linn_, 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 (Msting 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. Shrter 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 Mdler, 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 Mdler 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, Rmer, 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. Shrter estimated its thickness at +500 miles. + +Many speculations have been advanced to explain the origin and +constitution of the ring. De Sejour said [6] that it was thrown off +from Saturn's equator as a liquid ring, and afterwards solidified. He +noticed that the outside would have a greater velocity, and be less +attracted to the planet, than the inner parts, and that equilibrium +would be impossible; so he supposed it to have solidified into a +number of concentric rings, the exterior ones having the least +velocity. + +Clerk Maxwell, in the Adams prize essay, gave a physico-mathematical +demonstration that the rings must be composed of meteoritic matter +like gravel. Even so, there must be collisions absorbing the energy of +rotation, and tending to make the rings eventually fall into the +planet. The slower motion of the external parts has been proved by the +spectroscope in Keeler's hands, 1895. + +Saturn has perhaps received more than its share of attention owing to +these rings. This led to other discoveries. Huyghens in 1655, and +J. D. Cassini in 1671, discovered the sixth and eighth satellites +(Titan and Japetus). Cassini lost his satellite, and in searching for +it found Rhea (the fifth) in 1672, besides his old friend, whom he +lost again. He added the third and fourth in 1684 (Tethys and +Dione). The first and second (Mimas and Encelades) were added by +Herschel in 1789, and the seventh (Hyperion) simultaneously by Lassel +and Bond in 1848. The ninth (Phoebe) was found on photographs, by +Pickering in 1898, with retrograde motion; and he has lately added a +tenth. + +The occasional disappearance of Cassini's Japetus was found on +investigation to be due to the same causes as that of Jupiter's fourth +satellite, and proves that it always turns the same face to the +planet. + +_Uranus and Neptune_.--The splendid discoveries of Uranus and two +satellites by Sir William Herschel in 1787, and of Neptune by Adams +and Le Verrier in 1846, have been already described. Lassel added two +more satellites to Uranus in 1851, and found Neptune's satellite in +1846. All of the satellites of Uranus have retrograde motion, and +their orbits are inclined about 80 to the ecliptic. + +The spectroscope has shown the existence of an absorbing atmosphere on +Jupiter and Saturn, and there are suspicions that they partake +something of the character of the sun, and emit some light besides +reflecting solar light. On both planets some absorption lines seem to +agree with the aqueous vapour lines of our own atmosphere; while one, +which is a strong band in the red common to both planets, seems to +agree with a line in the spectrum of some reddish stars. + +Uranus and Neptune are difficult to observe spectroscopically, but +appear to have peculiar spectra agreeing together. Sometimes Uranus +shows Frauenhofer lines, indicating reflected solar light. But +generally these are not seen, and six broad bands of absorption +appear. One is the F. of hydrogen; another is the red-star line of +Jupiter and Saturn. Neptune is a very difficult object for the +spectroscope. + +Quite lately [7] P. Lowell has announced that V. M. Slipher, at +Flagstaff Observatory, succeeded in 1907 in rendering some plates +sensitive far into the red. A reproduction is given of photographed +spectra of the four outermost planets, showing (1) a great number of +new lines and bands; (2) intensification of hydrogen F. and C. lines; +(3) a steady increase of effects (1) and (2) as we pass from Jupiter +and Saturn to Uranus, and a still greater increase in Neptune. + +_Asteroids_.--The discovery of these new planets has been +described. At the beginning of the last century it was an immense +triumph to catch a new one. Since photography was called into the +service by Wolf, they have been caught every year in shoals. It is +like the difference between sea fishing with the line and using a +steam trawler. In the 1908 almanacs nearly seven hundred asteroids are +included. The computation of their perturbations and ephemerides by +Euler's and Lagrange's method of variable elements became so laborious +that Encke devised a special process for these, which can be applied +to many other disturbed orbits. [8] + +When a photograph is taken of a region of the heavens including an +asteroid, the stars are photographed as points because the telescope +is made to follow their motion; but the asteroids, by their proper +motion, appear as short lines. + +The discovery of Eros and the photographic attack upon its path have +been described in their relation to finding the sun's distance. + +A group of four asteroids has lately been found, with a mean distance +and period equal to that of Jupiter. To three of these masculine names +have been given--Hector, Patroclus, Achilles; the other has not yet +been named. + + +FOOTNOTES: + +[1] Langrenus (van Langren), F. Selenographia sive lumina austriae +philippica; Bruxelles, 1645. + +[2] _Astr. Nach._, 2,944. + +[3] _Acad. des Sc._, Paris; _C.R._, lxxxiii., 1876. + +[4] _Mem. Spettr. Ital._, xi., p. 28. + +[5] _R. S. Phil. Trans_., No. 1. + +[6] Grant's _Hist. Ph. Ast_., p. 267. + +[7] _Nature_, November 12th, 1908. + +[8] _Ast. Nach_., Nos. 791, 792, 814, translated by G. B. Airy. +_Naut. Alm_., Appendix, 1856. + + + +14. COMETS AND METEORS. + + +Ever since Halley discovered that the comet of 1682 was a member of +the solar system, these wonderful objects have had a new interest for +astronomers; and a comparison of orbits has often identified the +return of a comet, and led to the detection of an elliptic orbit where +the difference from a parabola was imperceptible in the small portion +of the orbit visible to us. A remarkable case in point was the comet +of 1556, of whose identity with the comet of 1264 there could be +little doubt. Hind wanted to compute the orbit more exactly than +Halley had done. He knew that observations had been made, but they +were lost. Having expressed his desire for a search, all the +observations of Fabricius and of Heller, and also a map of the comet's +path among the stars, were eventually unearthed in the most unlikely +manner, after being lost nearly three hundred years. Hind and others +were certain that this comet would return between 1844 and 1848, but +it never appeared. + +When the spectroscope was first applied to finding the composition of +the heavenly bodies, there was a great desire to find out what comets +are made of. The first opportunity came in 1864, when Donati observed +the spectrum of a comet, and saw three bright bands, thus proving that +it was a gas and at least partly self-luminous. In 1868 Huggins +compared the spectrum of Winnecke's comet with that of a Geissler tube +containing olefiant gas, and found exact agreement. Nearly all comets +have shown the same spectrum.[1] A very few comets have given bright +band spectra differing from the normal type. Also a certain kind of +continuous spectrum, as well as reflected solar light showing +Frauenhofer lines, have been seen. + +[Illustration: COPY OF THE DRAWING MADE BY PAUL FABRICIUS. To define +the path of comet 1556. After being lost for 300 years, this drawing +was recovered by the prolonged efforts of Mr. Hind and Professor +Littrow in 1856.] + +When Wells's comet, in 1882, approached very close indeed to the sun, +the spectrum changed to a mono-chromatic yellow colour, due to sodium. + +For a full account of the wonders of the cometary world the reader is +referred to books on descriptive astronomy, or to monographs on +comets.[2] Nor can the very uncertain speculations about the structure +of comets' tails be given here. A new explanation has been proposed +almost every time that a great discovery has been made in the theory +of light, heat, chemistry, or electricity. + +Halley's comet remained the only one of which a prediction of the +return had been confirmed, until the orbit of the small, ill-defined +comet found by Pons in 1819 was computed by Encke, and found to have a +period of 3 1/3 years. It was predicted to return in 1822, and was +recognised by him as identical with many previous comets. This comet, +called after Encke, has showed in each of its returns an inexplicable +reduction of mean distance, which led to the assertion of a resisting +medium in space until a better explanation could be found.[3] + +Since that date fourteen comets have been found with elliptic orbits, +whose aphelion distances are all about the same as Jupiter's mean +distance; and six have an aphelion distance about ten per cent, +greater than Neptune's mean distance. Other comets are similarly +associated with the planets Saturn and Uranus. + +The physical transformations of comets are among the most wonderful of +unexplained phenomena in the heavens. But, for physical astronomers, +the greatest interest attaches to the reduction of radius vector of +Encke's comet, the splitting of Biela's comet into two comets in 1846, +and the somewhat similar behaviour of other comets. It must be noted, +however, that comets have a sensible size, that all their parts cannot +travel in exactly the same orbit under the sun's gravitation, and that +their mass is not sufficient to retain the parts together very +forcibly; also that the inevitable collision of particles, or else +fluid friction, is absorbing energy, and so reducing the comet's +velocity. + +In 1770 Lexell discovered a comet which, as was afterwards proved by +investigations of Lexell, Burchardt, and Laplace, had in 1767 been +deflected by Jupiter out of an orbit in which it was invisible from +the earth into an orbit with a period of 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 Pingr, 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 NEBUL. + + +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 nebul 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 +Lyr). 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 Vgel, 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; N. Decl. 25. This +grand discovery has been amply confirmed, and, though opinions differ +as to the exact direction, it happens that the point first indicated +by Herschel, from totally insufficient data, agrees well with modern +estimates. + +Comparing the proper motions and parallaxes to get the actual velocity +of each star relative to our system, C.L. Struve found the probable +velocity of the solar system in space to be fifteen miles a second, or +five astronomical units a year. + +The work of Herschel in this matter has been checked by comparing +spectroscopic velocities in the line of sight which, so far as the +sun's motion is concerned, would give a maximum rate of approach for +stars near Hercules, a maximum rate of recession for stars in the +opposite part of the heavens, and no effect for stars half-way +between. In this way the spectroscope has confirmed generally +Herschel's view of the direction, and makes the velocity eleven miles +a second, or nearly four astronomical units a year. + +The average proper motion of a first magnitude star has been found to +be 0".25 annually, and of a sixth magnitude star 0".04. But that all +bright stars are nearer than all small stars, or that they show +greater proper motion for that reason, is found to be far from the +truth. Many statistical studies have been made in this connection, and +interesting results may be expected from this treatment in the hands +of Kapteyn of Groningen, and others.[9] + +On analysis of the directions of proper motions of stars in all parts +of the heavens, Kapteyn has shown[10] that these indicate, besides the +solar motion towards Hercules, two general drifts of stars in nearly +opposite directions, which can be detected in any part of the +heavens. This result has been confirmed from independent data by +Eddington (_R.A.S., M.N._) and Dyson (_R.S.E. Proc._). + +Photography promises to assist in the measurement of parallax and +proper motions. Herr Pulfrich, of the firm of Carl Zeiss, has vastly +extended the applications of stereoscopic vision to astronomy--a +subject which De la Rue took up in the early days of photography. He +has made a stereo-comparator of great beauty and convenience for +comparing stereoscopically two star photographs taken at different +dates. Wolf of Heidelberg has used this for many purposes. His +investigations depending on the solar motion in space are remarkable. +He photographs stars in a direction at right angles to the line of the +sun's motion. He has taken photographs of the same region fourteen +years apart, the two positions of his camera being at the two ends of +a base-line over 5,000,000,000 miles apart, or fifty-six astronomical +units. On examining these stereoscopically, some of the stars rise out +of the general plane of the stars, and seem to be much nearer. Many of +the stars are thus seen to be suspended in space at different +distances corresponding exactly to their real distances from our solar +system, except when their proper motion interferes. The effect is most +striking; the accuracy of measurement exceeds that of any other method +of measuring such displacements, and it seems that with a long +interval of time the advantage of the method increases. + +_Double Stars._--The large class of double stars has always been much +studied by amateurs, partly for their beauty and colour, and partly as +a test for telescopic definition. Among the many unexplained stellar +problems there is one noticed in double stars that is thought by some +to be likely to throw light on stellar evolution. It is this: There +are many instances where one star of the pair is comparatively faint, +and the two stars are contrasted in colour; and in every single case +the general colour of the faint companion is invariably to be classed +with colours more near to the blue end of the spectrum than that of +the principal star. + +_Binary Stars._--Sir William Herschel began his observations of double +stars in the hope of discovering an annual parallax of the stars. In +this he was following a suggestion of Galileo's. The presumption is +that, if there be no physical connection between the stars of a pair, +the largest is the nearest, and has the greatest parallax. So, by +noting the distance between the pair at different times of the year, a +delicate test of parallax is provided, unaffected by major +instrumental errors. + +Herschel did, indeed, discover changes of distance, but not of the +character to indicate parallax. Following this by further observation, +he found that the motions were not uniform nor rectilinear, and by a +clear analysis of the movements he established the remarkable and +wholly unexpected fact that in all these cases the motion is due to a +revolution about their common centre of gravity.[11] He gave the +approximate period of revolution of some of these: Castor, 342 years; +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 Coron 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 "Nov" 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 Nov, 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. + +_Nebul and Star-clusters._--Our knowledge of nebul 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 nebul might be clusters of +innumerable minute stars at a great distance. Then he recognised the +different classes of nebul, and became convinced that there is a +widely-diffused "shining fluid" in space, though many so-called nebul +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 +nebul" might show a stage of evolution from the diffuse nebul, 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 nebul. + +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 nebul; 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 nebul, 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 or 5 square. Barnard asserts that the "nebular +hypothesis" would have been killed at its birth by a knowledge of +these photographs. Later he has used still more powerful instruments, +and extended his discoveries. + +The association of stars with planetary nebul, and the distribution +of nebul 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 _Systme 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 +ngstrom, 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 Mdler, 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 +Chaldan 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 +Pingr, 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 (Mller), 24 +Respighi, 82 +Retrograde motion of planets, 22 +Riccioli, 107 +Roberts, 137 +Rmer, 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 +Schrter, 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 Rmer, 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 +Zllner, 92 +Zucchi, 113 + + + + + +End of the Project Gutenberg EBook of History of Astronomy, by George Forbes + +*** END OF THE PROJECT GUTENBERG EBOOK HISTORY OF ASTRONOMY *** + +This file should be named 8hsrs10.txt or 8hsrs10.zip +Corrected EDITIONS of our eBooks get a new NUMBER, 8hsrs11.txt +VERSIONS based on separate sources get new LETTER, 8hsrs10a.txt + +Produced by Jonathan Ingram, Dave Maddock, Charles Franks +and the Online Distributed Proofreading Team. + +Project Gutenberg eBooks are often created from several printed +editions, all of which are confirmed as Public Domain in the US +unless a copyright notice is included. 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FOR PUBLIC DOMAIN EBOOKS*Ver.02/11/02*END* + diff --git a/old/8hsrs10.zip b/old/8hsrs10.zip Binary files differnew file mode 100644 index 0000000..513571b --- /dev/null +++ b/old/8hsrs10.zip diff --git a/old/8hsrs10h.htm b/old/8hsrs10h.htm new file mode 100644 index 0000000..d954fd7 --- /dev/null +++ b/old/8hsrs10h.htm @@ -0,0 +1,6444 @@ +<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> +<html> +<head> +<title>History of Astronomy, by George Forbes</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<style type="text/css"> +<!-- +body {margin:10%; text-align:justify} +--> +</style> +</head> +<body> + + +<pre> + +The Project Gutenberg EBook of History of Astronomy, by George Forbes + +Copyright laws are changing all over the world. 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You can also find out about how to make a +donation to Project Gutenberg, and how to get involved. + + +**Welcome To The World of Free Plain Vanilla Electronic Texts** + +**eBooks Readable By Both Humans and By Computers, Since 1971** + +*****These eBooks Were Prepared By Thousands of Volunteers!***** + + +Title: History of Astronomy + +Author: George Forbes + +Release Date: May, 2005 [EBook #8172] +[Yes, we are more than one year ahead of schedule] +[This file was first posted on June 25, 2003] + +Edition: 10 + +Language: English + +Character set encoding: ASCII + +*** START OF THE PROJECT GUTENBERG EBOOK HISTORY OF ASTRONOMY *** + + + + +Produced by Jonathan Ingram, Dave Maddock, Charles Franks +and the Online Distributed Proofreading Team. + + + + + +</pre> + + +<p align="center"><img src="001.jpg" alt="[Illustration: SIR ISAAC NEWTON (From the bust by Roubiliac In Trinity College, Cambridge.)]" /></p> + +<div align="center"> +<h1>HISTORY OF ASTRONOMY</h1> + +<h2>BY</h2> + +<h2>GEORGE FORBES,<br /> +M.A., F.R.S., M. INST. C. E.,</h2> + +<p><b>(FORMERLY PROFESSOR OF NATURAL PHILOSOPHY, ANDERSON’S +COLLEGE, GLASGOW)</b></p> + +<p>AUTHOR OF “THE TRANSIT OF VENUS,” RENDU’S +“THEORY OF THE GLACIERS OF SAVOY,” ETC., ETC.</p> +</div> + +<p><br /><br /></p> + +<h1>CONTENTS</h1> + +<blockquote> +<p><a href="#preface">PREFACE</a></p> +</blockquote> + +<h2>BOOK I. THE GEOMETRICAL PERIOD</h2> + +<blockquote> +<p><a href="#1">1. PRIMITIVE ASTRONOMY AND ASTROLOGY</a></p> + +<p><a href="#2">2. ANCIENT ASTRONOMY—CHINESE +AND CHALDÆANS</a></p> + +<p><a href="#3">3. ANCIENT GREEK ASTRONOMY</a></p> + +<p><a href="#4">4. THE REIGN OF EPICYCLES—FROM PTOLEMY TO COPERNICUS</a></p> +</blockquote> + +<h2>BOOK II. THE DYNAMICAL PERIOD</h2> + +<blockquote> +<p><a href="#5">5. DISCOVERY OF THE TRUE SOLAR SYSTEM—TYCHO BRAHE—KEPLER</a></p> + +<p><a href="#6">6. GALILEO AND THE TELESCOPE—NOTIONS OF GRAVITY BY HORROCKS, ETC.</a></p> + +<p><a href="#7">7. SIR ISAAC NEWTON—LAW OF UNIVERSAL GRAVITATION</a></p> + +<p><a href="#8">8. NEWTON’S SUCCESSORS—HALLEY, EULER, LAGRANGE, LAPLACE, ETC.</a></p> + +<p><a href="#9">9. DISCOVERY OF NEW PLANETS—HERSCHEL, PIAZZI, ADAMS, AND +LE VERRIER</a></p> +</blockquote> + +<h2>BOOK III. OBSERVATION</h2> + +<blockquote> + +<p><a href="#10">10. INSTRUMENTS OF PRECISION—SIZE +OF THE SOLAR SYSTEM</a></p> + +<p><a href="#11">11. HISTORY OF THE TELESCOPE—SPECTROSCOPE</a></p> +</blockquote> + +<h2>BOOK IV. THE PHYSICAL PERIOD</h2> + +<blockquote> +<p><a href="#12">12. THE SUN</a></p> + +<p><a href="#13">13. THE MOON AND PLANETS</a></p> + +<p><a href="#14">14. COMETS AND METEORS</a></p> + +<p><a href="#15">15. THE STARS AND NEBULÆ</a></p> + +<p><a href="#index">INDEX</a></p> +</blockquote> + +<hr width="75%" size="1" align="center" /> + +<p><br /><br /></p> + +<a name="preface"></a> +<h1>PREFACE</h1> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>G. F.<br /> +<i>August 1st, 1909.</i></p> + +<p><br /><br /></p> + +<h1>BOOK I. THE GEOMETRICAL PERIOD</h1> + +<p><br /><br /></p> + +<a name="1"></a> +<h2>1. PRIMITIVE ASTRONOMY AND ASTROLOGY.</h2> + +<p>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 <i>à priori</i> 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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>If the ancient Chaldæans gave to the planetary conjunctions +an influence over terrestrial events, let us remember +that in our own time people have searched for connection +between terrestrial conditions and periods of unusual +prevalence of sun spots; while De la Rue, Loewy, and +Balfour Stewart<a href="#fn1_1">[1]</a> 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.</p> + +<p>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 +<i>Soldier’s Pocket Book</i>.</p> + +<p>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.</p> + +<p>So Hipparchus, about 150 B.C., and Ptolemy a little +later, were able to use the observations of Chaldæan +astrologers, as well as those of Alexandrian astronomers, +and to make some discoveries which have helped the +progress of astronomy in all ages. So, also, +Mr. Cowell<a href="#fn1_2">[2]</a> has examined the marks made on the baked +bricks used by the Chaldæans for recording the eclipses +of 1062 B.C. and 762 B.C.; and has thereby been enabled, +in the last few years, to correct the lunar tables +of Hansen, and to find a more accurate value for the +secular acceleration of the moon’s longitude +and the node of her orbit than any that could be obtained +from modern observations made with instruments of the +highest precision.</p> + +<p>So again, Mr. Hind <a href="#fn1_3">[3]</a> 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. +<a href="#fn1_4">[4]</a></p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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 <i>if</i> 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.</p> + +<p>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 <i>heliacal +risings</i>—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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p><br /><br /></p> + +<p><b>FOOTNOTES:</b></p> + +<p><a name="fn1_1">[1]</a> Trans. R. S. E., xxiii. 1864, p. 499, <i>On +Sun Spots</i>, <i>etc</i>., by B. Stewart. Also +Trans. R. S. 1860-70. Also Prof. Ernest +Brown, in <i>R. A. S. Monthly Notices</i>, 1900.</p> + +<p><a name="fn1_2">[2]</a> <i>R. A. S. Monthly Notices</i>, Sup.; 1905.</p> + +<p align="center"><img src="002.jpg" alt="[Illustration: CHALDÆAN BAKED BRICK OR TABLET, <i>Obverse and reverse sides</i>, +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.)]" /></p> + +<p><a name="fn1_3">[3]</a> <i>R. A. S. Monthly Notices</i>, vol. x., +p. 65.</p> + +<p><a name="fn1_4">[4]</a> R. S. E. Proc., vol. x., 1880.</p> + +<p><br /><br /></p> + +<a name="2"></a> +<h2>2. ANCIENT ASTRONOMY—THE CHINESE AND CHALDÆANS.</h2> + +<p>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.</p> + +<p>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 <i>Observations +Astronomical, Geographical, Chronological, and Physical</i>, +drawn from ancient Chinese books; and later by Father +Moyriac-de-Mailla, who in 1777-1785 published <i>Annals +of the Chinese Empire, translated from Tong-Kien-Kang-Mou</i>.</p> + +<p>Bailly, in his <i>Astronomie Ancienne</i> (1781), +drew, from these and other sources, the conclusion +that all we know of the astronomical learning of the +Chinese, Indians, Chaldæans, Assyrians, and Egyptians +is but the remnant of a far more complete astronomy +of which no trace can be found.</p> + +<p>Delambre, in his <i>Histoire de l’Astronomie +Ancienne</i> (1817), ridicules the opinion of Bailly, +and considers that the progress made by all of these +nations is insignificant.</p> + +<p>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.</p> + +<p><i>China</i>.—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.).<a href="#fn2_1">[1]</a> 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.</p> + +<p>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.</p> + +<p>It is also asserted, in the book called <i>Chu-King</i>, +that in the time of Yao the year was known to have +365¼ days, and that he adopted 365 days and added +an intercalary day every four years (as in the Julian +Calendar). This may be true or not, but the ancient +Chinese certainly seem to have divided the circle +into 365 degrees. To learn the length of the +year needed only patient observation—a +characteristic of the Chinese; but many younger nations +got into a terrible mess with their calendar from +ignorance of the year’s length.</p> + +<p>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 <i>Saros</i>. 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.</p> + +<p>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 <i>Observations of Comets from 611 +B.C. to 1640 A.D., Extracted from the Chinese Annals</i>.</p> + +<p>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.</p> + +<p><i>Chaldæans</i>.—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.</p> + +<p>The Chaldæans, being the most ancient Babylonians, +held the same station and dignity in the State as +did the priests in Egypt, and spent all their time +in the study of philosophy and astronomy, and the +arts of divination and astrology. They held that +the world of which we have a conception is an eternal +world without any beginning or ending, in which all +things are ordered by rules supported by a divine +providence, and that the heavenly bodies do not move +by chance, nor by their own will, but by the determinate +will and appointment of the gods. They recorded +these movements, but mainly in the hope of tracing +the will of the gods in mundane affairs. Ptolemy +(about 130 A.D.) made use of Babylonian eclipses in +the eighth century B.C. for improving his solar and +lunar tables.</p> + +<p>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.</p> + +<p>We have records of observations carried on under Asshurbanapal, +who sent astronomers to different parts to study celestial +phenomena. Here is one:—</p> + +<p>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.”</p> + +<p>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<a href="#fn2_2">[2]</a> 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.</p> + +<p>Then again, Knobel reminds us of “the most interesting +discovery a few years ago by Father Strassmeier of +a Babylonian tablet recording a partial lunar eclipse +at Babylon in the seventh year of Cambyses, on the +fourteenth day of the Jewish month Tammuz.” + Ptolemy, in the Almagest (Suntaxis), says it occurred +in the seventh year of Cambyses, on the night of the +seventeenth and eighteenth of the Egyptian month Phamenoth. + Pingré and Oppolzer fix the date July 16th, 533 B.C. +Thus are the relations of the chronologies of Jews +and Egyptians established by these explorations.</p> + +<p><br /><br /></p> + +<p><b>FOOTNOTES:</b></p> + +<p><a name="fn2_1">[1]</a> These ancient dates are uncertain.</p> + +<p><a name="fn2_2">[2]</a> <i>R. A. S. Monthly Notices</i>, vol. lxviii., +No. 5, March, 1908.</p> + +<p><br /><br /></p> + +<a name="3"></a> +<h2>3. ANCIENT GREEK ASTRONOMY.</h2> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.).</p> + +<p>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 <i>Saros</i> 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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>Nicetas, Heraclides, and Ecphantes supposed the earth +to revolve on its axis, but to have no orbital motion.</p> + +<p>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.</p> + +<p>For further references to similar efforts of imagination +the reader is referred to Sir George Cornwall Lewis’s +<i>Historical Survey of the Astronomy of the Ancients</i>; +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:—</p> + +<p>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 (<i>Xen. +Mem</i>, i. 1, 11-15).</p> + +<p>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 <i>the problem +of representing the courses of the planets by circular +and uniform motions</i>.</p> + +<p>Systematic observation among the Greeks began with +the rise of the Alexandrian school. Aristillus +and Timocharis set up instruments and fixed the positions +of the zodiacal stars, near to which all the planets +in their orbits pass, thus facilitating the determination +of planetary motions. Aristarchus (320-250 B.C.) +showed that the sun must be at least nineteen times +as far off as the moon, which is far short of the +mark. He also found the sun’s diameter, +correctly, to be half a degree. Eratosthenes +(276-196 B.C.) measured the inclination to the equator +of the sun’s apparent path in the heavens—i.e., +he measured the obliquity of the ecliptic, making +it 23° 51’, confirming our knowledge of its +continuous diminution during historical times. +He measured an arc of meridian, from Alexandria to +Syene (Assuan), and found the difference of latitude +by the length of a shadow at noon, summer solstice. +He deduced the diameter of the earth, 250,000 stadia. +Unfortunately, we do not know the length of the stadium +he used.</p> + +<p>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 <i>excentric</i>. The line from +the earth to the “excentric” was called +the <i>line of apses</i>. A circle having this +centre was called the <i>equant</i>, 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.</p> + +<p>He proceeded in the same way to compute Lunar tables. +Making use of Chaldæan eclipses, he was able to get +an accurate value of the moon’s mean motion. + [Halley, in 1693, compared this value with his own +measurements, and so discovered the acceleration of +the moon’s mean motion. This was conclusively +established, but could not be explained by the Newtonian +theory for quite a long time.] He determined the plane +of the moon’s orbit and its inclination to the +ecliptic. The motion of this plane round the +pole of the ecliptic once in eighteen years complicated +the problem. He located the moon’s excentric +as he had done the sun’s. He also discovered +some of the minor irregularities of the moon’s +motion, due, as Newton’s theory proves, to the +disturbing action of the sun’s attraction.</p> + +<p>In the year 134 B.C. Hipparchus observed a new +star. This upset every notion about the permanence +of the fixed stars. He then set to work to catalogue +all the principal stars so as to know if any others +appeared or disappeared. Here his experiences +resembled those of several later astronomers, who, +when in search of some special object, have been rewarded +by a discovery in a totally different direction. +On comparing his star positions with those of Timocharis +and Aristillus he found no stars that had appeared +or disappeared in the interval of 150 years; but he +found that all the stars seemed to have changed their +places with reference to that point in the heavens +where the ecliptic is 90° from the poles of the earth—i.e., +the equinox. He found that this could be explained +by a motion of the equinox in the direction of the +apparent diurnal motion of the stars. This discovery +of <i>precession of the equinoxes</i>, 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.</p> + +<p>Hipparchus was also the inventor of trigonometry, +both plane and spherical. He explained the method +of using eclipses for determining the longitude.</p> + +<p>In connection with Hipparchus’ great discovery +it may be mentioned that modern astronomers have often +attempted to fix dates in history by the effects of +precession of the equinoxes. (1) At about the date +when the Great Pyramid may have been built γ Draconis +was near to the pole, and must have been used as the +pole-star. In the north face of the Great Pyramid +is the entrance to an inclined passage, and six of +the nine pyramids at Gizeh possess the same feature; +all the passages being inclined at an angle between +26° and 27° to the horizon and in the plane of the +meridian. It also appears that 4,000 years ago—i.e., +about 2100 B.C.—an observer at the lower +end of the passage would be able to see γ Draconis, +the then pole-star, at its lower culmination.<a href="#fn3_1">[1]</a> 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.</p> + +<p>(2) The Chaldæans gave names to constellations now +invisible from Babylon which would have been visible +in 2000 B.C., at which date it is claimed that these +people were studying astronomy.</p> + +<p>(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 <i>Odyssey</i> +<a href="#fn3_2">[2]</a> (v. 272-5) and in the <i>Iliad</i> (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. <a href="#fn3_3">[3]</a></p> + +<p>(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 +<a href="#fn3_4">[4]</a> 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.</p> + +<p>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 <i>annual</i> 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 <i>deferent</i>), 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.</p> + +<p>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.</p> + +<p>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.</p> + +<p><br /><br /></p> + +<p><b>FOOTNOTES:</b></p> + +<p><a name="fn3_1">[1]</a> <i>Phil. Mag</i>., vol. xxiv., pp. 481-4.</p> + +<p><a name="fn3_2">[2]</a></p> + +<p>Plaeiadas t’ esoronte kai opse duonta bootaen<br /> +‘Arkton th’ aen kai amaxan epiklaesin +kaleousin,<br /> +‘Ae t’ autou strephetai kai t’ Oriona +dokeuei,<br /> +Oin d’ammoros esti loetron Okeanoio.</p> + +<p>“The Pleiades and Boötes that setteth late, +and the Bear, which they likewise call the Wain, which +turneth ever in one place, and keepeth watch upon +Orion, and alone hath no part in the baths of the +ocean.”</p> + +<p><a name="fn3_3">[3]</a> See Pearson in the Camb. Phil. Soc. +Proc., vol. iv., pt. ii., p. 93, on whose authority +the above statements are made.</p> + +<p><a name="fn3_4">[4]</a> See p. 6 for definition.</p> + +<p><br /><br /></p> + +<a name="4"></a> +<h2>4. THE REIGN OF EPICYCLES—FROM PTOLEMY +TO COPERNICUS.</h2> + +<p>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,<a href="#fn4_1">[1]</a> and +its ratio to that of the epicycle,<a href="#fn4_2">[2]</a> the distance +of the excentric<a href="#fn4_3">[3]</a> from the centre of the deferent, +and the position of the line of apses,<a href="#fn4_4">[4]</a> 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.</p> + +<p>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.</p> + +<p>At the close of the fifteenth century King Alphonso +of Spain employed computers to produce the Alphonsine +Tables (1488 A.D.), Purbach translated Ptolemy’s +book, and observations were carried out in Germany +by Müller, known as Regiomontanus, and Waltherus.</p> + +<p>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, <i>De Revolutionibus Orbium +Celestium</i>. 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.</p> + +<p>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.</p> + +<p>Copernicus could not sever himself from this obnoxious +tradition.<a href="#fn4_5">[5]</a> 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.<a href="#fn4_6">[6]</a> 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.</p> + +<p>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,<a href="#fn4_7">[7]</a> in drawing attention +to the strange conception,</p> + +<blockquote>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.</blockquote> + +<p>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).</p> + +<p>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.<a href="#fn4_8">[8]</a> He says:—</p> + +<blockquote>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.</blockquote> + +<p>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.</p> + +<p>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.</p> + +<p>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.<a href="#fn4_9">[9]</a> +He says that whoever is not satisfied with this explanation +must be contented by being told that “mathematics +are for mathematicians” (Mathematicis mathematica +scribuntur).</p> + +<p>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, <i>Tycho +Brahe</i>) “proofs of the physical truth of +his system Copernicus had given none, and could give +none,” any more than Pythagoras or Aristarchus.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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 <i>Six Lectures on Astronomy</i>, 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.</p> + +<p align="center"><img src="003.jpg" alt="[Illustration: “QUADRANS MURALIS SIVE TICHONICUS.” + With portrait of Tycho Brahe, instruments, <i>etc</i>., +painted on the wall; showing assistants using the +sight, watching the clock, and recording. (From the +author’s copy of the <i>Astronomiæ Instauratæ +Mechanica.</i>)]" /></p> + +<p><br /><br /></p> + +<p><b>FOOTNOTES:</b></p> + +<p><a name="fn4_1">[1]</a> For definition see p. 22.</p> + +<p><a name="fn4_2">[2]</a> <i>Ibid</i>.</p> + +<p><a name="fn4_3">[3]</a> For definition see p. 18.</p> + +<p><a name="fn4_4">[4]</a> For definition see p. 18.</p> + +<p><a name="fn4_5">[5]</a> 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, <i>Ast. Mod. +Hist</i>., pp. 86, 87).</p> + +<p><a name="fn4_6">[6]</a> Kepler tells us that Tycho Brahe was pleased with +this device, and adapted it to his own system.</p> + +<p><a name="fn4_7">[7]</a> <i>Hist. Ast.</i>, vol. i., p. 354.</p> + +<p><a name="fn4_8">[8]</a> <i>Hist. of Phys. Ast.</i>, p. vii.</p> + +<p><a name="fn4_9">[9]</a> “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.”</p> + +<p><br /><br /></p> + +<h1>BOOK II. THE DYNAMICAL PERIOD</h1> + +<p><br /><br /></p> + +<a name="5"></a> +<h2>5. DISCOVERY OF THE TRUE SOLAR SYSTEM—TYCHO BRAHE—KEPLER.</h2> + +<p>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.</p> + +<p>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.</p> + +<p>For a complete life of this great man the reader is +referred to Dreyer’s <i>Tycho Brahe</i>, 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.</p> + +<p>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.<a href="#fn5_1">[1]</a></p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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 (<i>De Mundi</i>, <i>etc</i>.) +that</p> + +<blockquote>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.</blockquote> + +<p>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 +<i>Tischreden</i>, pp. 22, 60) derided him in his +usual pithy manner, that Melancthon (<i>Initia doctrinae +physicae</i>) 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.</p> + +<p>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.</p> + +<img src="004.jpg" alt="[Illustration: PORTRAIT OF JOHANNES KEPLER. + By F. Wanderer, from Reitlinger’s “Johannes +Kepler” (original in Strassburg).]" align="right" /> + +<p>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 <i>à priori</i> 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.</p> + +<p>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.<a href="#fn5_2">[2]</a></p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>His first law states that the planets describe ellipses +with the sun at a focus of each ellipse.</p> + +<p>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, <i>Astronomia +Nova, sen. Physica Coelestis tradita commentariis +de Motibus Stelloe; Martis</i>, Prague, 1609.</p> + +<p>It took him nine years more<a href="#fn5_3">[3]</a> to discover his third +law, that the squares of the periodic times are proportional +to the cubes of the mean distances from the sun.</p> + +<p>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.</p> + +<p>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 <i>Harmonics</i>, 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.</p> + +<p>The whole book, <i>Astronomia Nova</i>, 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.</p> + +<img src="006.png" alt="" align="right" /> + +<p>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 E<sub>3</sub> the date of the year +gives the angle E<sub>3</sub>SM. And the observation of +Tycho gives the direction of Mars compared with the +sun, SE<sub>3</sub>M. So all the angles of the triangle SEM +in any of these positions of E are known, and also +the ratios of SE<sub>1</sub>, SE<sub>2</sub>, SE<sub>3</sub>, SE<sub>4</sub> to SM and to each +other.</p> + +<p>For the orbit of Mars observations were chosen at +intervals of a year, when the earth was always in +the same place.</p> + +<p>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, <i>De +Mundo Nostro Sublunari, Philosophia Nova</i>, 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 <i>De Magnete</i> was published in 1600.)</p> + +<p>A few of Kepler’s views on gravitation, extracted +from the Introduction to his <i>Astronomia Nova</i>, +may now be mentioned:—</p> + +<p>1. Every body at rest remains at rest if outside +the attractive power of other bodies.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>5. If the earth and moon were not retained in +their orbits by vital force (<i>aut alia aligua aequipollenti</i>), +the earth and moon would come together.</p> + +<p>6. If the earth were to cease to attract its +waters, the oceans would all rise and flow to the +moon.</p> + +<p>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.”</p> + +<p>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.</p> + +<p>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?</p> + +<p><br /><br /></p> + +<p><b>FOOTNOTES:</b></p> + +<p><a name="fn5_1">[1]</a> 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.</p> + +<img src="005.png" alt="" align="right" /> + +<p><a name="fn5_2">[2]</a> 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 <i>foci</i>. +Kepler found the sun to be in one focus, say S. AB +is the <i>major axis</i>. DE is the <i>minor +axis</i>. C is the <i>centre</i>. The direction +of AB is the <i>line of apses</i>. The ratio of +CS to CA is the <i>excentricity</i>. The position +of the planet at A is the <i>perihelion</i> (nearest +to the sun). The position of the planet at B is +the <i>aphelion</i> (farthest from the sun). +The angle ASP is the <i>anomaly</i> when the planet +is at P. CA or a line drawn from S to D is the <i>mean +distance</i> of the planet from the sun.</p> + +<p><a name="fn5_3">[3]</a> 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.</p> + +<p><br /><br /></p> + +<a name="6"></a> +<h2>6. GALILEO AND THE TELESCOPE—NOTIONS OF GRAVITY BY HORROCKS, ETC.</h2> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.”</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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 <i>evection</i> +to variations in the value of the eccentricity and +in the direction of the line of apses, at the same +time correctly assigning <i>the disturbing force of +the Sun</i> 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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p><br /><br /></p> + +<a name="7"></a> +<h2>7. SIR ISAAC NEWTON—LAW OF UNIVERSAL +GRAVITATION.</h2> + +<p>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.<a href="#fn7_1">[1]</a></p> + +<p>Quite the most important event in the whole history +of physical astronomy was the publication, in 1687, +of Newton’s <i>Principia (Philosophiae Naturalis +Principia Mathematica)</i>. 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.</p> + +<p>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.</p> + +<p>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:—</p> + +<p>The law of universal gravitation.—<i>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</i>.<a href="#fn7_2">[2]</a></p> + +<p>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 <i>Principia</i> +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.<a href="#fn7_3">[3]</a></p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<pre>Newton. Modern Tables. +° ’ " ° ’ " +Mean monthly motion of Apses 1.31.28 3.4.0 +Mean annual motion of nodes 19.18.1,23 19.21.22,50 +Mean value of “variation” 36.10 35.47 +Annual equation 11.51 11.14 +Inequality of mean motion of apogee 19.43 22.17 +Inequality of mean motion of nodes 9.24 9.0</pre> + +<p>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.</p> + +<p>Newton’s method of calculating the precession +of the equinoxes, already referred to, is as beautiful +as anything in the <i>Principia</i>. 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.</p> + +<p>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.</p> + +<p>Laplace only expressed the universal opinion of posterity +when he said that to the <i>Principia</i> is assured +“a pre-eminence above all the other productions +of the human intellect.”</p> + +<p>The name of Flamsteed, First Astronomer Royal, must +here be mentioned as having supplied Newton with the +accurate data required for completing the theory.</p> + +<p>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 +<i>Principia</i> would never have been written; and +but for his generosity in supplying the means the +Royal Society could not have published the book.</p> + +<p align="center"><img src="007.jpg" alt="[Illustration: DEATH MASK OF SIR ISAAC NEWTON. +Photographed specially for this work from the original, +by kind permission of the Royal Society, London.]" /></p> + +<p>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.</p> + +<p><br /><br /></p> + +<p><b>FOOTNOTES:</b></p> + +<p><a name="fn7_1">[1]</a> 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!</p> + +<p><a name="fn7_2">[2]</a> 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 <i>Principia</i>; +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.</p> + +<p>With this exception the above statement of the law +of universal gravitation contains nothing that is +not to be found in the <i>Principia</i>; and the nearest +approach to that statement occurs in the Seventh Proposition +of Book III.:—</p> + +<p>Prop.: That gravitation occurs in all bodies, +and that it is proportional to the quantity of matter +in each.</p> + +<p>Cor. I.: The total attraction of gravitation +on a planet arises, and is composed, out of the attraction +on the separate parts.</p> + +<p>Cor. II.: The attraction on separate equal +particles of a body is reciprocally as the square +of the distance from the particles.</p> + +<p><a name="fn7_3">[3]</a> 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.</p> + +<p><br /><br /></p> + +<a name="8"></a> +<h2>8. NEWTON’S SUCCESSORS—HALLEY, +EULER, LAGRANGE, LAPLACE, ETC.</h2> + +<p>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.</p> + +<p>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.”</p> + +<p>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.”</p> + +<p>The same subject was again proposed for a prize which +was shared by Lagrange <a href="#fn8_1">[1]</a> and Euler, neither finding +a solution, while the latter asserted the existence +of a resisting medium in space.</p> + +<p>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.</p> + +<p>Laplace <a href="#fn8_2">[2]</a> 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.)</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.”</p> + +<p>Let us take one more discovery of Halley, furnishing +directly a new triumph for the theory. He noticed +that Newton ascribed parabolic orbits to the comets +which he studied, so that they come from infinity, +sweep round the sun, and go off to infinity for ever, +after having been visible a few weeks or months. +He collected all the reliable observations of comets +he could find, to the number of twenty-four, and computed +their parabolic orbits by the rules laid down by Newton. +His object was to find out if any of them really travelled +in elongated ellipses, practically undistinguishable, +in the visible part of their paths, from parabolæ, +in which case they would be seen more than once. +He found two old comets whose orbits, in shape and +position, resembled the orbit of a comet observed by +himself in 1682. Apian observed one in 1531; +Kepler the other in 1607. The intervals between +these appearances is seventy-five or seventy-six years. +He then examined and found old records of similar appearance +in 1456, 1380, and 1305. It is true, he noticed, +that the intervals varied by a year and a-half, and +the inclination of the orbit to the ecliptic diminished +with successive apparitions. But he knew from +previous calculations that this might easily be due +to planetary perturbations. Finally, he arrived +at the conclusion that all of these comets were identical, +travelling in an ellipse so elongated that the part +where the comet was seen seemed to be part of a parabolic +orbit. He then predicted its return at the end +of 1758 or beginning of 1759, when he should be dead; +but, as he said, “if it should return, according +to our prediction, about the year 1758, impartial posterity +will not refuse to acknowledge that this was first +discovered by an Englishman."<a href="#fn8_3">[3]</a> [<i>Synopsis Astronomiae +Cometicae</i>, 1749.]</p> + +<p>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.”</p> + +<p>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.</p> + +<p>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.</p> + +<p>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!</p> + +<p>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<a href="#fn8_4">[4]</a> +(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.</p> + +<p>Already, in November, 1907, the Astronomer Royal was +trying to catch it by the aid of photography.</p> + +<p><br /><br /></p> + +<p><b>FOOTNOTES:</b></p> + +<p><a name="fn8_1">[1]</a> Born 1736; died 1813.</p> + +<p><a name="fn8_2">[2]</a> Born 1749; died 1827.</p> + +<p><a name="fn8_3">[3]</a> This sentence does not appear in the original +memoir communicated to the Royal Society, but was +first published in a posthumous reprint.</p> + +<p><a name="fn8_4">[4]</a> <i>R. A. S. Monthly Notices</i>, 1907-8.</p> + +<p><br /><br /></p> + +<a name="9"></a> +<h2>9. DISCOVERY OF NEW PLANETS—HERSCHEL, +PIAZZI, ADAMS, AND LE VERRIER.</h2> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>In 1787 Herschel discovered two satellites, both revolving +in nearly the same plane, inclined 80° to the ecliptic, +and the motion of both was retrograde.</p> + +<p>In 1772, before Herschel’s discovery, Bode<a href="#fn9_1">[1]</a> +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, <i>etc</i>., to the 4, always +doubling the last numbers. You then get the +planetary distances.</p> + +<pre> + 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 +</pre> + +<p>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.</p> + +<p>The mean distance from the sun was found to be 2.767, +agreeing with the 2.8 given by Bode’s law. +Its orbit was found to be inclined over 10° to the +ecliptic, and its diameter was only 161 miles.</p> + +<p>On March 28th, 1802, Olbers discovered a new seventh +magnitude star, which turned out to be a planet resembling +Ceres. It was called Pallas. Gauss found +its orbit to be inclined 35° to the ecliptic, and +to cut the orbit of Ceres; whence Olbers considered +that these might be fragments of a broken-up planet. +He then commenced a search for other fragments. +In 1804 Harding discovered Juno, and in 1807 Olbers +found Vesta. The next one was not discovered until +1845, from which date asteroids, or minor planets +(as these small planets are called), have been found +almost every year. They now number about 700.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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°.</p> + +<p>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.</p> + +<p>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.</p> + +<p>In June, 1846, Le Verrier announced, in the <i>Comptes +Rendus de l’Academie des Sciences</i>, that +the longitude of the disturbing planet, for January +1st, 1847, was 325, and that the probable error did +not exceed 10°.</p> + +<p>This result agreed so well with Adams’s (within +1°) that Airy urged Challis to apply the splendid +Northumberland equatoreal, at Cambridge, to the search. + Challis, however, had already prepared an exhaustive +plan of attack which must in time settle the point. + His first work was to observe, and make a catalogue, +or chart, of all stars near Adams’s position.</p> + +<p>On August 31st, 1846, Le Verrier published the concluding +part of his labours.</p> + +<p>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.</p> + +<p>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 <i>Principia</i>, 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.</p> + +<p>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.</p> + +<p>These displays of jealousy have long since passed +away, and there is now universally an <i>entente cordiale</i> +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.</p> + +<p>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.</p> + +<p>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.</p> + +<p><br /><br /></p> + +<p><b>FOOTNOTES:</b></p> + +<p><a name="fn9_1">[1]</a> Bode’s law, or something like it, had already +been fore-shadowed by Kepler and others, especially +Titius (see <i>Monatliche Correspondenz</i>, vol. +vii., p. 72).</p> + +<p><br /><br /></p> + +<h1>BOOK III. OBSERVATION</h1> + +<p><br /><br /></p> + +<a name="10"></a> +<h2>10. INSTRUMENTS OF PRECISION—STATE +OF THE SOLAR SYSTEM.</h2> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.<a href="#fn10_1">[1]</a></p> + +<p>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.</p> + +<p>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.<a href="#fn10_2">[2]</a></p> + +<p align="center"><img src="008.jpg" alt="[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.]" /></p> + +<p>The French Jesuits at Peking, in the seventeenth century, +helped the Chinese in their astronomy. In 1875 +the writer saw and photographed, on that part of the +wall of Peking used by the Mandarins as an observatory, +the six instruments handsomely designed by Father +Verbiest, copied from the instruments of Tycho Brahe, +and embellished with Chinese dragons and emblems cast +on the supports. He also saw there two old instruments +(which he was told were Arabic) of date 1279, by Ko +Show-King, astronomer to Koblai Khan, the grandson +of Chenghis Khan. One of these last is nearly +identical with the armillae of Tycho; and the other +with his “armillae æquatoriæ maximæ,” with +which he observed the comet of 1585, besides fixed +stars and planets.<a href="#fn10_3">[3]</a></p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>Flamsteed began his duties at Greenwich Observatory, +as first Astronomer Royal, in 1676, with very poor +instruments. In 1683 he put up a mural arc of +140°, and in 1689 a better one, seventy-nine inches +radius. He conducted his measurements with great +skill, and introduced new methods to attain accuracy, +using certain stars for determining the errors of +his instruments; and he always reduced his observations +to a form in which they could be readily used. +He introduced new methods for determining the position +of the equinox and the right ascension of a fundamental +star. He produced a catalogue of 2,935 stars. +He supplied Sir Isaac Newton with results of observation +required in his theoretical calculations. He died +in 1719.</p> + +<p>Halley succeeded Flamsteed to find that the whole +place had been gutted by the latter’s executors. +In 1721 he got a transit instrument, and in 1726 a +mural quadrant by Graham. His successor in 1742, +Bradley, replaced this by a fine brass quadrant, eight +feet radius, by Bird; and Bradley’s zenith sector +was purchased for the observatory. An instrument +like this, specially designed for zenith stars, is +capable of greater rigidity than a more universal instrument; +and there is no trouble with refraction in the zenith. +For these reasons Bradley had set up this instrument +at Kew, to attempt the proof of the earth’s +motion by observing the annual parallax of stars. +He certainly found an annual variation of zenith distance, +but not at the times of year required by the parallax. +This led him to the discovery of the “aberration” +of light and of nutation. Bradley has been described +as the founder of the modern system of accurate observation. +He died in 1762, leaving behind him thirteen folio +volumes of valuable but unreduced observations. +Those relating to the stars were reduced by Bessel +and published in 1818, at Königsberg, in his well-known +standard work, <i>Fundamenta Astronomiae</i>. +In it are results showing the laws of refraction, +with tables of its amount, the maximum value of aberration, +and other constants.</p> + +<p>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 <i>circle</i>, +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.</p> + +<p>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.</p> + +<p>George Biddell Airy, Seventh Astronomer Royal,<a href="#fn10_4">[4]</a> +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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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 <i>transit-circle</i> +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.</p> + +<p>Airy, like Bradley, was impressed with the advantage +of employing stars in the zenith for determining the +fundamental constants of astronomy. He devised +a <i>reflex zenith tube</i>, 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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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>i.e.,</i> +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.</p> + +<p>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.</p> + +<p>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 (<i>Cape +Obs</i>., Vol. VI.).</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.<a href="#fn10_5">[5]</a></p> + +<p>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<a href="#fn10_6">[6]</a> is 8".807 ± 0".0028.<a href="#fn10_7">[7]</a></p> + +<p><br /><br /></p> + +<p><b>FOOTNOTES:</b></p> + +<p><a name="fn10_1">[1]</a> In 1480 Martin Behaim, of Nuremberg, produced +his <i>astrolabe</i> 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 <i>alhidada</i>, 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.</p> + +<p><a name="fn10_2">[2]</a> See illustration on p. 76.</p> + +<p><a name="fn10_3">[3]</a> See Dreyer’s article on these instruments +in <i>Copernicus</i>, 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 <i>Chinese Researches</i>, by Alexander Wyllie +(Shanghai, 1897).</p> + +<p><a name="fn10_4">[4]</a> 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.</p> + +<p><a name="fn10_5">[5]</a> <i>Annals of the Cape Observatory</i>, vol. x., +part 3.</p> + +<p><a name="fn10_6">[6]</a> The parallax of the sun is the angle subtended +by the earth’s radius at the sun’s distance.</p> + +<p><a name="fn10_7">[7]</a> A. R. Hinks, R.A.S.; <i>Monthly Notices</i>, June, +1909.</p> + +<p><br /><br /></p> + +<a name="11"></a> +<h2>11. HISTORY OF THE TELESCOPE</h2> + +<p>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, <i>Hist. Ph. Ast</i>.), 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 <i>camera obscura</i>, in +which a lens throws an inverted image of a landscape +on the wall.</p> + +<p>The first telescopes were made in Holland, the originator +being either Henry Lipperhey,<a href="#fn11_1">[1]</a> Zacharias Jansen, +or James Metius, and the date 1608 or earlier.</p> + +<p>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.</p> + +<p>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,<a href="#fn11_2">[2]</a> of Aberdeen +and Edinburgh, in 1663, in his <i>Optica Promota</i>, +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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>In the nineteenth century gigantic <i>reflectors</i> +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.</p> + +<p>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.</p> + +<p>Cooke, of York, made an object-glass, 25-inch diameter, +for Newall, of Gateshead, which has done splendid +work at Cambridge. We have the Washington 26-inch +by Clark, the Vienna 27-inch by Grubb, the Nice 29½-inch +by Gautier, the Pulkowa 30-inch by Clark. Then +there was the sensation of Clark’s 36-inch for +the Lick Observatory in California, and finally his +<i>tour de force</i>, the Yerkes 40-inch refractor, +for Chicago.</p> + +<p>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.</p> + +<p>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.</p> + +<p><b>SPECTROSCOPE.</b></p> + +<p>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.</p> + +<p>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. <a href="#fn11_3">[3]</a></p> + +<p>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.</p> + +<p>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.</p> + +<p>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.<a href="#fn11_4">[4]</a> +Iron, calcium, and other elements were soon detected +in the same way.</p> + +<p>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.</p> + +<p>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.</p> + +<p>In 1842 Doppler<a href="#fn11_5">[5]</a> 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.</p> + +<p>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.</p> + +<p>In 1868 Huggins<a href="#fn11_6">[6]</a> succeeded in thus measuring the +velocities of stars in the direction of the line of +sight.</p> + +<p>In 1873 Vogel<a href="#fn11_7">[7]</a> compared the spectra of the sun’s +East (approaching) limb and West (receding) limb, +and the displacement of lines endorsed the theory. +This last observation was suggested by Zöllner.</p> + +<p><br /><br /></p> + +<p><b>FOOTNOTES:</b></p> + +<p><a name="fn11_1">[1]</a> In the <i>Encyclopaedia Britannica</i>, article +“Telescope,” and in Grant’s <i>Physical +Astronomy</i>, good reasons are given for awarding +the honour to Lipperhey.</p> + +<p><a name="fn11_2">[2]</a> 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, <i>Newton’s mathematics +were a little rusty</i>.”</p> + +<p><a name="fn11_3">[3]</a> <i>R. S. Phil. Trans</i>.</p> + +<p><a name="fn11_4">[4]</a> 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.</p> + +<p><a name="fn11_5">[5]</a> <i>Abh. d. Kön. Böhm. d. Wiss</i>., +Bd. ii., 1841-42, p. 467. See also Fizeau in +the <i>Ann. de Chem. et de Phys</i>., 1870, p. 211.</p> + +<p><a name="fn11_6">[6]</a> <i>R. S. Phil. Trans</i>., 1868.</p> + +<p><a name="fn11_7">[7]</a> <i>Ast. Nach</i>., No. 1, 864.</p> + +<p><br /><br /></p> + +<h1>BOOK IV. THE PHYSICAL PERIOD</h1> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p><br /><br /></p> + +<a name="12"></a> +<h2>12. THE SUN.</h2> + +<p>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 <i>umbra</i> and the less dark, +but more extensive, <i>penumbra</i> 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.</p> + +<p align="center"><img src="009.jpg" alt="[Illustration: SOLAR SURFACE, As Photographed +at the Royal Observatory, Greenwich, showing sun-spots +with umbrae, penumbrae, and faculae.]" /></p> + +<p>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.</p> + +<p>Speculations as to the cause of sun-spots have never +ceased from Galileo’s time to ours. He +supposed them to be clouds. Scheiner<a href="#fn12_1">[1]</a> said +they were the indications of tumultuous movements occasionally +agitating the ocean of liquid fire of which he supposed +the sun to be composed.</p> + +<p>A. Wilson, of Glasgow, in 1769,<a href="#fn12_2">[2]</a> 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:—</p> + +<blockquote>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.<a href="#fn12_3">[3]</a></blockquote> + +<p>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.</p> + +<p>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.</p> + +<p>Sir John Herschel noticed that the spots are mostly +confined to two zones extending to about 35° on each +side of the equator, and that a zone of equatoreal +calms is free from spots. But it was R. C. Carrington<a href="#fn12_4">[4]</a> +who, by his continuous observations at Redhill, in +Surrey, established the remarkable fact that, while +the rotation period in the highest latitudes, 50°, +where spots are seen, is twenty-seven-and-a-half days, +near the equator the period is only twenty-five days. +His splendid volume of observations of the sun led +to much new information about the average distribution +of spots at different epochs.</p> + +<p>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.<a href="#fn12_5">[5]</a> 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<a href="#fn12_6">[6]</a> has given reasons for admitting a number +of co-existent periods, of which the eleven-year period +was predominant in the nineteenth century.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>Spoerer deduced a law of dependence of the average +latitude of sun-spots on the phase of the sun-spot +period.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>It is noteworthy that from the outset De la Rue recognised +the value of stereoscopic vision, which is now known +to be of supreme accuracy. In 1853 he combined +pairs of photographs of the moon in the same phase, +but under different conditions regarding libration, +showing the moon from slightly different points of +view. These in the stereoscope exhibited all +the relief resulting from binocular vision, and looked +like a solid globe. In 1860 he used successive +photographs of the total solar eclipse stereoscopically, +to prove that the red prominences belong to the sun, +and not to the moon. In 1861 he similarly combined +two photographs of a sun-spot, the perspective effect +showing the umbra like a floor at the bottom of a hollow +penumbra; and in one case the faculæ were discovered +to be sailing over a spot apparently at some considerable +height. These appearances may be partly due +to a proper motion; but, so far as it went, this was +a beautiful confirmation of Wilson’s discovery. +Hewlett, however, in 1894, after thirty years of work, +showed that the spots are not always depressions, +being very subject to disturbance.</p> + +<p>The Kew photographs <a href="#fn12_7">[7]</a> contributed a vast amount +of information about sun-spots, and they showed that +the faculæ generally follow the spots in their rotation +round the sun.</p> + +<p>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.</p> + +<p>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.<a href="#fn12_8">[8]</a> They +have succeeded in photographing the sun’s surface +in monochromatic light, such as the light given off +as one of the bright lines of hydrogen or of calcium, +by means of the “Spectroheliograph.” +The spectroscope is placed with its slit in the focus +of an equatoreal telescope, pointed to the sun, so +that the circular image of the sun falls on the slit. +At the other end of the spectroscope is the photographic +plate. Just in front of this plate there is another +slit parallel to the first, in the position where the +image of the first slit formed by the K line of calcium +falls. Thus is obtained a photograph of the section +of the sun, made by the first slit, only in K light. +As the image of the sun passes over the first slit +the photographic plate is moved at the same rate and +in the same direction behind the second slit; and +as successive sections of the sun’s image in +the equatoreal enter the apparatus, so are these sections +successively thrown in their proper place on the photographic +plate, always in K light. By using a high dispersion +the faculæ which give off K light can be correctly +photographed, not only at the sun’s edge, but +all over his surface. The actual mechanical method +of carrying out the observation is not quite so simple +as what is here described.</p> + +<p>By choosing another line of the spectrum instead of +calcium K—for example, the hydrogen line +H<sub>(3)</sub>—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.</p> + +<p>The spectroscope has revealed the fact that, broadly +speaking, the sun is composed of the same materials +as the earth. Ångstrom was the first to map out all +of the lines to be found in the solar spectrum. +But Rowland, of Baltimore, after having perfected +the art of making true gratings with equidistant lines +ruled on metal for producing spectra, then proceeded +to make a map of the solar spectrum on a large scale.</p> + +<p>In 1866 Lockyer<a href="#fn12_9">[9]</a> 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.</p> + +<p><i>Total Solar Eclipses</i>.—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.</p> + +<p align="center"><img src="010.jpg" alt="[Illustration: SOLAR ECLIPSE, 1882. From +drawing by W. H. Wesley, Secretary R.A.S.; showing +the prominences, the corona, and an unknown comet.]" /></p> + +<p>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: “<i>Je +verrai ces lignes-là en dehors des éclipses</i>.” +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,<a href="#fn12_10">[10]</a> 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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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 <i>History of Astronomy during the Nineteenth +Century</i>. As to established facts, we learn +from the spectroscopic researches (1) that the continuous +spectrum is derived from the <i>photosphere</i> or +solar gaseous material compressed almost to liquid +consistency; (2) that the <i>reversing layer</i> surrounds +it and gives rise to black lines in the spectrum; +that the <i>chromosphere</i> surrounds this, is composed +mainly of hydrogen, and is the cause of the red prominences +in eclipses; and that the gaseous <i>corona</i> surrounds +all of these, and extends to vast distances outside +the sun’s visible surface.</p> + +<p><br /><br /></p> + +<p><b>FOOTNOTES:</b></p> + +<p><a name="fn12_1">[1]</a> <i>Rosa Ursina</i>, by C. Scheiner, <i>fol</i>.; +Bracciani, 1630.</p> + +<p><a name="fn12_2">[2]</a> <i>R. S. Phil. Trans</i>., 1774.</p> + +<p><a name="fn12_3">[3]</a> <i>Ibid</i>, 1783.</p> + +<p><a name="fn12_4">[4]</a> <i>Observations on the Spots on the Sun, etc.,</i> +4°; London and Edinburgh, 1863.</p> + +<p><a name="fn12_5">[5]</a> <i>Periodicität der Sonnenflecken. Astron. +Nach. XXI.</i>, 1844, P. 234.</p> + +<p><a name="fn12_6">[6]</a> <i>R.S. Phil. Trans.</i> (ser. +A), 1906, p. 69-100.</p> + +<p><a name="fn12_7">[7]</a> “Researches on Solar Physics,” by +De la Rue, Stewart and Loewy; <i>R. S. Phil. +Trans</i>., 1869, 1870.</p> + +<p><a name="fn12_8">[8]</a> “The Sun as Photographed on the K line”; +<i>Knowledge</i>, London, 1903, p. 229.</p> + +<p><a name="fn12_9">[9]</a> <i>R. S. Proc.</i>, xv., 1867, p. 256.</p> + +<p><a name="fn12_10">[10]</a> <i>Acad. des Sc.</i>, Paris; <i>C. R.</i>, +lxvii., 1868, p. 121.</p> + +<p><br /><br /></p> + +<a name="13"></a> +<h2>13. THE MOON AND PLANETS.</h2> + +<p><i>The Moon</i>.—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 <i>libration</i>, +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 <i>uniformly</i>, +and that her revolution round the earth is not uniform.</p> + +<p>Galileo said that the mountains on the moon showed +greater differences of level than those on the earth. + Shröter supported this opinion. W. Herschel +opposed it. But Beer and Mädler measured the +heights of lunar mountains by their shadows, and found +four of them over 20,000 feet above the surrounding +plains.</p> + +<p>Langrenus <a href="#fn13_1">[1]</a> was the first to do serious work on +selenography, and named the lunar features after eminent +men. Riccioli also made lunar charts. In +1692 Cassini made a chart of the full moon. Since +then we have the charts of Schröter, Beer and Mädler +(1837), and of Schmidt, of Athens (1878); and, above +all, the photographic atlas by Loewy and Puiseux.</p> + +<p>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, <i>Tycho</i>, 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.</p> + +<p>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.</p> + +<p>No certain changes have ever been observed; but several +suspicions have been expressed, especially as to the +small crater <i>Linné</i>, in the <i>Mare Serenitatis</i>. +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.</p> + +<p>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.</p> + +<p>The distance of the moon from the earth is just now +the subject of re-measurement. The base line +is from Greenwich to Cape of Good Hope, and the new +feature introduced is the selection of a definite point +on a crater (Mösting A), instead of the moon’s +edge, as the point whose distance is to be measured.</p> + +<p><i>The Inferior Planets</i>.—When the telescope +was invented, the phases of Venus attracted much attention; +but the brightness of this planet, and her proximity +to the sun, as with Mercury also, seemed to be a bar +to the discovery of markings by which the axis and +period of rotation could be fixed. Cassini gave +the rotation as twenty-three hours, by observing a +bright spot on her surface. Shröter made it 23h. +21m. 19s. This value was supported by others. +In 1890 Schiaparelli<a href="#fn13_2">[2]</a> 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.</p> + +<p>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 <i>Vulcan</i>. 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<a href="#fn13_3">[3]</a> 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.</p> + +<p><i>Mars</i>.—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.</p> + +<p>Schroter attributed the other markings on Mars to drifting +clouds. But Beer and Mädler, in 1830-39, identified +the same dark spots as being always in the same place, +though sometimes blurred by mist in the local winter. +A spot sketched by Huyghens in 1672, one frequently +seen by W. Herschel in 1783, another by Arago in 1813, +and nearly all the markings recorded by Beer and Mädler +in 1830, were seen and drawn by F. Kaiser in Leyden +during seventeen nights of the opposition of 1862 +(<i>Ast. Nacht.</i>, 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.</p> + +<p>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).</p> + +<p>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.</p> + +<p>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,<a href="#fn13_4">[4]</a> the second +canal being always 200 to 400 miles distant from its +fellow.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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).</p> + +<p align="center"><img src="011.jpg" alt="[Illustration: JUPITER. From a drawing +by E. M. Antoniadi, showing transit of a satellite’s +shadow, the belts, and the “great red spot” +(<i>Monthly Notices</i>, R. A. S., vol. lix., pl. x.).]" /></p> + +<p><i>Jupiter.</i>—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<a href="#fn13_5">[5]</a> +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.</p> + +<p>Jupiter’s rapid rotation ought, according to +Newton’s theory, to be accompanied by a great +flattening at the poles. Cassini had noted an +oval form in 1691. This was confirmed by La Hire, +Römer, and Picard. Pound measured the ellipticity += 1/(13.25).</p> + +<p>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.</p> + +<p>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, <i>Gravitation</i>, has reduced these investigations +to simple geometrical explanations.</p> + +<p>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.</p> + +<p>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.</p> + +<p>In modern times much interest has been taken in watching +a rival to Cassini’s famous spot. The “great +red spot” was first observed by Niesten, Pritchett, +and Tempel, in 1878, as a rosy cloud attached to a +whitish zone beneath the dark southern equatorial band, +shaped like the new war balloons, 30,000 miles long +and 7,000 miles across. The next year it was +brick-red. A white spot beside it completed a +rotation in less time by 5½ minutes than the red spot—a +difference of 260 miles an hour. Thus they came +together again every six weeks, but the motions did +not continue uniform. The spot was feeble in +1882-4, brightened in 1886, and, after many changes, +is still visible.</p> + +<p>Galileo’s great discovery of Jupiter’s +four moons was the last word in this connection until +September 9th, 1892, when Barnard, using the 36-inch +refractor of the Lick Observatory, detected a tiny +spot of light closely following the planet. This +proved to be a new satellite (fifth), nearer to the +planet than any other, and revolving round it in 11h. +57m. 23s. Between its rising and setting there +must be an interval of 2½ Jovian days, and two or +three full moons. The sixth and seventh satellites +were found by the examination of photographic plates +at the Lick Observatory in 1905, since which time they +have been continuously photographed, and their orbits +traced, at Greenwich. On examining these plates +in 1908 Mr. Melotte detected the eighth satellite, +which seems to be revolving in a retrograde orbit three +times as far from its planet as the next one (seventh), +in these two points agreeing with the outermost of +Saturn’s satellites (Phoebe).</p> + +<p><i>Saturn.</i>—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.</p> + +<p>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 <i>De Saturni +Luna Observatio Nova</i>, 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.</p> + +<p>In 1675 Cassini found the ring to be double, the concentric +rings being separated by a black band—a +fact which was placed beyond dispute by Herschel, +who also found that the thickness of the ring subtends +an angle less than 0".3. Shröter estimated its +thickness at 500 miles.</p> + +<p>Many speculations have been advanced to explain the +origin and constitution of the ring. De Sejour +said <a href="#fn13_6">[6]</a> 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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p><i>Uranus and Neptune</i>.—The splendid +discoveries of Uranus and two satellites by Sir William +Herschel in 1787, and of Neptune by Adams and Le Verrier +in 1846, have been already described. Lassel added +two more satellites to Uranus in 1851, and found Neptune’s +satellite in 1846. All of the satellites of Uranus +have retrograde motion, and their orbits are inclined +about 80° to the ecliptic.</p> + +<p>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.</p> + +<p>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.</p> + +<p>Quite lately <a href="#fn13_7">[7]</a> 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.</p> + +<p><i>Asteroids</i>.—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. <a href="#fn13_8">[8]</a></p> + +<p>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.</p> + +<p>The discovery of Eros and the photographic attack +upon its path have been described in their relation +to finding the sun’s distance.</p> + +<p>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.</p> + +<p><br /><br /></p> + +<p><b>FOOTNOTES:</b></p> + +<p><a name="fn13_1">[1]</a> Langrenus (van Langren), F. Selenographia sive +lumina austriae philippica; Bruxelles, 1645.</p> + +<p><a name="fn13_2">[2]</a> <i>Astr. Nach.</i>, 2,944.</p> + +<p><a name="fn13_3">[3]</a> <i>Acad. des Sc.</i>, Paris; <i>C.R.</i>, lxxxiii., +1876.</p> + +<p><a name="fn13_4">[4]</a> <i>Mem. Spettr. Ital.</i>, xi., p. 28.</p> + +<p><a name="fn13_5">[5]</a> <i>R. S. Phil. Trans</i>., No. 1.</p> + +<p><a name="fn13_6">[6]</a> Grant’s <i>Hist. Ph. Ast</i>., +p. 267.</p> + +<p><a name="fn13_7">[7]</a> <i>Nature</i>, November 12th, 1908.</p> + +<p><a name="fn13_8">[8]</a> <i>Ast. Nach</i>., Nos. 791, 792, 814, translated +by G. B. Airy. <i>Naut. Alm</i>., Appendix, 1856.</p> + +<p><br /><br /></p> + +<a name="14"></a> +<h2>14. COMETS AND METEORS.</h2> + +<p>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.</p> + +<p>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.<a href="#fn14_1">[1]</a> +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.</p> + +<p align="center"><img src="012.jpg" alt="[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.]" /></p> + +<p>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.</p> + +<p>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.<a href="#fn14_2">[2]</a> 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.</p> + +<p>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.<a href="#fn14_3">[3]</a></p> + +<p>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.</p> + +<p>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.</p> + +<p>In 1770 Lexell discovered a comet which, as was afterwards +proved by investigations of Lexell, Burchardt, and +Laplace, had in 1767 been deflected by Jupiter out +of an orbit in which it was invisible from the earth +into an orbit with a period of 5½ years, enabling it +to be seen. In 1779 it again approached Jupiter +closer than some of his satellites, and was sent off +in another orbit, never to be again recognised.</p> + +<p>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.</p> + +<p>A magnificent meteor shower was seen in America on +November 12th-13th, 1833, when the paths of the meteors +all seemed to radiate from a point in the constellation +Leo. A similar display had been witnessed in +Mexico by Humboldt and Bonpland on November 12th, 1799. +H. A. Newton traced such records back to October 13th, +A.D. 902. The orbital motion of a cloud or stream +of small particles was indicated. The period +favoured by H. A. Newton was 354½ days; another suggestion +was 375½ days, and another 33¼ years. He noticed +that the advance of the date of the shower between +902 and 1833, at the rate of one day in seventy years, +meant a progression of the node of the orbit. + Adams undertook to calculate what the amount would +be on all the five suppositions that had been made +about the period. After a laborious work, he found +that none gave one day in seventy years except the +33¼-year period, which did so exactly. H. A. +Newton predicted a return of the shower on the night +of November 13th-14th, 1866. He is now dead; but +many of us are alive to recall the wonder and enthusiasm +with which we saw this prediction being fulfilled +by the grandest display of meteors ever seen by anyone +now alive.</p> + +<p>The <i>progression</i> of the nodes proved the path +of the meteor stream to be retrograde. The <i>radiant</i> +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.</p> + +<p>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.</p> + +<p>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.</p> + +<p><br /><br /></p> + +<p><b>FOOTNOTES:</b></p> + +<p><a name="fn14_1">[1]</a> 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.</p> + +<p><a name="fn14_2">[2]</a> Such as <i>The World of Comets</i>, by A. Guillemin; +<i>History of Comets</i>, by G. R. Hind, London, 1859; +<i>Theatrum Cometicum</i>, by S. de Lubienietz, 1667; +<i>Cometographie</i>, by Pingré, Paris, 1783; <i>Donati’s +Comet</i>, by Bond.</p> + +<p><a name="fn14_3">[3]</a> 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.</p> + +<p><br /><br /></p> + +<a name="15"></a> +<h2>15. THE FIXED STARS AND NEBULÆ.</h2> + +<p>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.</p> + +<img src="013.jpg" alt="[Illustration: SIR WILLIAM HERSCHEL, F.R.S.—1738-1822. + Painted by Lemuel F. Abbott; National Portrait Gallery, +Room XX.]" align="right" /> + +<p>In the field of telescopic discovery beyond our solar +system there is no one who has enlarged our knowledge +so much as Sir William Herschel, to whom we owe the +greatest discovery in dynamical astronomy among the +stars—viz., that the law of gravitation +extends to the most distant stars, and that many of +them describe elliptic orbits about each other. +W. Herschel was born at Hanover in 1738, came to England +in 1758 as a trained musician, and died in 1822. +He studied science when he could, and hired a telescope, +until he learnt to make his own specula and telescopes. +He made 430 parabolic specula in twenty-one years. +He discovered 2,500 nebulæ and 806 double stars, counted +the stars in 3,400 guage-fields, and compared the +principal stars photometrically.</p> + +<p>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.</p> + +<p><i>Parallax</i>.—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.</p> + +<p>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,<a href="#fn15_1">[1]</a> +early in the nineteenth century, also failed. +The first successes, afterwards confirmed, were by +Bessel and Henderson. Both used stars whose +proper motion had been found to be large, as this argued +proximity. Henderson, at the Cape of Good Hope, +observed α Centauri, whose annual proper motion +he found to amount to 3".6, in 1832-3; and a few years +later deduced its parallax 1".16. His successor +at the Cape, Maclear, reduced this to 0".92.</p> + +<p>In 1835 Struve assigned a doubtful parallax of 0".261 +to Vega (α Lyræ). But Bessel’s observations, +between 1837 and 1840, of 61 Cygni, a star with the +large proper motion of over 5”, established its +annual parallax to be 0".3483; and this was confirmed +by Peters, who found the value 0".349.</p> + +<p>Later determinations for α<sub>2</sub> Centauri, by Gill,<a href="#fn15_2">[2]</a> +make its parallax 0".75—This is the nearest +known fixed star; and its light takes 4 1/3 years +to reach us. The lightyear is taken as the unit +of measurement in the starry heavens, as the earth’s +mean distance is “the astronomical unit” +for the solar system.<a href="#fn15_3">[3]</a> The proper motions and parallaxes +combined tell us the velocity of the motion of these +stars across the line of sight: α Centauri +14.4 miles a second=4.2 astronomical units a year; +61 Cygni 37.9 miles a second=11.2 astronomical units +a year. These successes led to renewed zeal, and +now the distances of many stars are known more or less +accurately.</p> + +<p>Several of the brightest stars, which might be expected +to be the nearest, have not shown a parallax amounting +to a twentieth of a second of arc. Among these +are Canopus, α Orionis, α Cygni, β Centauri, +and γ Cassiopeia. Oudemans has published a +list of parallaxes observed.<a href="#fn15_4">[4]</a></p> + +<p><i>Proper Motion.</i>—In 1718 Halley<a href="#fn15_5">[5]</a> +detected the proper motions of Arcturus and Sirius. +In 1738 J. Cassinis<a href="#fn15_6">[6]</a> 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”.</p> + +<p>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.</p> + +<p>When Huggins first applied the Doppler principle to +measure velocities in the line of sight,<a href="#fn15_7">[7]</a> the faintness +of star spectra diminished the accuracy; but Vögel, +in 1888, overcame this to a great extent by long exposures +of photographic plates.</p> + +<p>It has often been noticed that stars which seem to +belong to a group of nearly uniform magnitude have +the same proper motion. The spectroscope has +shown that these have also often the same velocity +in the line of sight. Thus in the Great Bear, +β, γ, δ, ε, ζ, all agree as to +angular proper motion. δ was too faint for a spectroscopic +measurement, but all the others have been shown to +be approaching us at a rate of twelve to twenty miles +a second. The same has been proved for proper +motion, and line of sight motion, in the case of Pleiades +and other groups.</p> + +<p>Maskelyne measured many proper motions of stars, from +which W. Herschel<a href="#fn15_8">[8]</a> came to the conclusion that these +apparent motions are for the most part due to a motion +of the solar system in space towards a point in the +constellation Hercules, R.A. 257°; N. Decl. 25°. + This grand discovery has been amply confirmed, and, +though opinions differ as to the exact direction, +it happens that the point first indicated by Herschel, +from totally insufficient data, agrees well with modern +estimates.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.<a href="#fn15_9">[9]</a></p> + +<p>On analysis of the directions of proper motions of +stars in all parts of the heavens, Kapteyn has shown<a href="#fn15_10">[10]</a> +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 (<i>R.A.S., M.N.</i>) and Dyson +(<i>R.S.E. Proc.</i>).</p> + +<p>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.</p> + +<p><i>Double Stars.</i>—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.</p> + +<p><i>Binary Stars.</i>—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.</p> + +<p>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.<a href="#fn15_11">[11]</a> He gave the approximate +period of revolution of some of these: Castor, +342 years; δ Serpentis, 375 years; γ Leonis, 1,200 +years; ε Bootis, 1,681 years.</p> + +<p>Twenty years later Sir John Herschel and Sir James +South, after re-examination of these stars, confirmed<a href="#fn15_12">[12]</a> +and extended the results, one pair of Coronæ having +in the interval completed more than a whole revolution.</p> + +<p>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,<a href="#fn15_13">[13]</a> 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 <i>History</i>: +“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.”</p> + +<p>Latterly the best work on double stars has been done +by S. W. Burnham,<a href="#fn15_14">[14]</a> at the Lick Observatory. +The shortest period he found was eleven years (κ +Pegasi). In the case of some of these binaries +the parallax has been measured, from which it appears +that in four of the surest cases the orbits are about +the size of the orbit of Uranus, these being probably +among the smallest stellar orbits.</p> + +<p>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,<a href="#fn15_15">[15]</a> 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.</p> + +<p>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.</p> + +<p><i>Spectroscopic Binaries</i>.—On measuring +the velocity of a star in the line of sight at frequent +intervals, periodic variations have been found, leading +to a belief in motion round an invisible companion. +Vogel, in 1889, discovered this in the case of Spica +(α Virginis), whose period is 4d. 0h. 19m., and +the diameter of whose orbit is six million miles. +Great numbers of binaries of this type have since +then been discovered, all of short period.</p> + +<p>Also, in 1889, Pickering found that at regular intervals +of fifty-two days the lines in the spectrum of ζ +of the Great Bear are duplicated, indicating a relative +velocity, equal to one hundred miles a second, of +two components revolving round each other, of which +that apparently single star must be composed.</p> + +<p>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.</p> + +<p><i>Variable Stars.</i>—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.</p> + +<p>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,<a href="#fn15_16">[16]</a> in 1783, explained variable +stars of this type. Algol (β Persei) completes +the period of variable brightness in 68.8 hours. +It loses three-fifths of its light, and regains it +in twelve hours. In 1889 Vogel,<a href="#fn15_17">[17]</a> 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.</p> + +<p>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.</p> + +<p>Roberts, in South Africa, has done splendid work on +the periods of variables of the Algol type.</p> + +<p><i>New Stars</i>.—Extreme instances of +variable stars are the new stars such as those detected +by Hipparchus, Tycho Brahe, and Kepler, of which many +have been found in the last half-century. One +of the latest great “Novæ” was discovered +in Auriga by a Scotsman, Dr. Anderson, on February +1st, 1892, and, with the modesty of his race, he communicated +the fact to His Majesty’s Astronomer for Scotland +on an unsigned post-card.<a href="#fn15_18">[18]</a> 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<a href="#fn15_19">[19]</a> 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.<a href="#fn15_20">[20]</a></p> + +<p>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.</p> + +<p>The same may be said of the brilliant Nova Persei, +brighter at its best than Capella, and discovered +also by Dr. Anderson on February 22nd, 1901. +It increased in brightness as it reached the densest +part of the nebula, then it varied for some weeks +by a couple of magnitudes, up and down, as if passing +through separate nebular condensations. In February, +1902, it could still be seen with an opera-glass. +As with the other Novæ, when it first dashed into the +nebula it was vaporised and gave a continuous spectrum +with dark lines of hydrogen and helium. It showed +no bright lines paired with the dark ones to indicate +a train left behind; but in the end its own luminosity +died out, and the nebular spectrum predominated.</p> + +<p>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.</p> + +<p><i>Star Catalogues.</i>—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.</p> + +<p>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.<a href="#fn15_21">[21]</a> +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.</p> + +<p align="center"><img src="014.jpg" alt="[Illustration: GREAT COMET, Nov. 14TH, 1882. +(Exposure 2hrs. 20m.) By kind permission of Sir David +Gill. From this photograph originated all stellar +chart-photography.]" /></p> + +<p>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.</p> + +<p>Then we have the Harvard College collection of photographic +plates, always being automatically added to; and their +annex at Arequipa in Peru.</p> + +<p>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.</p> + +<p>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.</p> + +<p><i>Nebulæ and Star-clusters.</i>—Our knowledge +of nebulæ really dates from the time of W. Herschel. +In his great sweeps of the heavens with his giant +telescopes he opened in this direction a new branch +of astronomy. At one time he held that all nebulæ +might be clusters of innumerable minute stars at a +great distance. Then he recognised the different +classes of nebulæ, and became convinced that there +is a widely-diffused “shining fluid” in +space, though many so-called nebulæ could be resolved +by large telescopes into stars. He considered +that the Milky Way is a great star cluster, whose +form may be conjectured from numerous star-gaugings. +He supposed that the compact “planetary nebulæ” +might show a stage of evolution from the diffuse nebulæ, +and that his classifications actually indicate various +stages of development. Such speculations, like +those of the ancients about the solar system, are +apt to be harmful to true progress of knowledge unless +in the hands of the ablest mathematical physicists; +and Herschel violated their principles in other directions. +But here his speculations have attracted a great deal +of attention, and, with modifications, are accepted, +at least as a working hypothesis, by a fair number +of people.</p> + +<p>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.</p> + +<p>Then his views were changed by the revelations due +to the great discoveries of Lord Rosse with his gigantic +refractor,<a href="#fn15_22">[22]</a> when one nebula after another was resolved +into a cluster of minute stars. At that time +the opinion gained ground that with increase of telescopic +power this would prove to be the case with all nebulæ.</p> + +<p>In 1864 all doubt was dispelled by Huggins<a href="#fn15_23">[23]</a> in +his first examination of the spectrum of a nebula, +and the subsequent extension of this observation to +other nebulæ; thus providing a certain test which +increase in the size of telescopes could never have +given. In 1864 Huggins found that all true nebulae +give a spectrum of bright lines. Three are due +to hydrogen; two (discovered by Copeland) are helium +lines; others are unknown. Fifty-five lines have +been photographed in the spectrum of the Orion nebula. +It seems to be pretty certain that all true nebulae +are gaseous, and show almost exactly the same spectrum.</p> + +<p>Other nebulæ, and especially the white ones like that +in Andromeda, which have not yet been resolved into +stars, show a continuous spectrum; others are greenish +and give no lines.</p> + +<p>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.</p> + +<p>The light of the nebulas is remarkably actinic, so +that photography has a specially fine field in revealing +details imperceptible in the telescope. In 1885 +the brothers Henry photographed, round the star Maia +in the Pleiades, a spiral nebula 3’ long, as +bright on the plate as that star itself, but quite +invisible in the telescope; and an exposure of four +hours revealed other new nebula in the same district. +That painstaking and most careful observer, Barnard, +with 10¼ hours’ exposure, extended this nebulosity +for several degrees, and discovered to the north of +the Pleiades a huge diffuse nebulosity, in a region +almost destitute of stars. By establishing a 10-inch +instrument at an altitude of 6,000 feet, Barnard has +revealed the wide distribution of nebular matter in +the constellation Scorpio over a space of 4° or 5° +square. Barnard asserts that the “nebular +hypothesis” would have been killed at its birth +by a knowledge of these photographs. Later he +has used still more powerful instruments, and extended +his discoveries.</p> + +<p>The association of stars with planetary nebulæ, and +the distribution of nebulæ in the heavens, especially +in relation to the Milky Way, are striking facts, +which will certainly bear fruit when the time arrives +for discarding vague speculations, and learning to +read the true physical structure and history of the +starry universe.</p> + +<p><i>Stellar Spectra.</i>—When the spectroscope +was first available for stellar research, the leaders +in this branch of astronomy were Huggins and Father +Secchi,<a href="#fn15_24">[24]</a> 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.</p> + +<p>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.</p> + +<p>The third class includes α Herculis, α Orionis +(Betelgeux), Mira Ceti, and about 500 red and variable +stars. The spectrum has fluted bands shaded +from blue to red, and sharply defined at the more +refrangible edge.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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.</p> + +<p><i>Nebular Hypothesis.</i>—The Nebular +Hypothesis, which was first, as it were, tentatively +put forward by Laplace as a note in his <i>Système +du Monde</i>, 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.</p> + +<p>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 +<i>History of Astronomy during the Nineteenth Century</i>. +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.</p> + +<p><br /><br /></p> + +<p><b>FOOTNOTES:</b></p> + +<p><a name="fn15_1">[1]</a> <i>R. S. Phil Trans</i>., 1810 and 1817-24.</p> + +<p><a name="fn15_2">[2]</a> One of the most valuable contributions to our +knowledge of stellar parallaxes is the result of Gill’s +work (<i>Cape Results</i>, vol. iii., part ii., 1900).</p> + +<p><a name="fn15_3">[3]</a> 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.</p> + +<p><a name="fn15_4">[4]</a> Ast. Nacht., 1889.</p> + +<p><a name="fn15_5">[5]</a> R. S. Phil. Trans., 1718.</p> + +<p><a name="fn15_6">[6]</a> Mem. Acad. des Sciences, 1738, p. 337.</p> + +<p><a name="fn15_7">[7]</a> R. S Phil. Trans., 1868.</p> + +<p><a name="fn15_8">[8]</a> <i>R.S. Phil Trans.</i>, 1783.</p> + +<p><a name="fn15_9">[9]</a> See Kapteyn’s address to the Royal Institution, +1908. Also Gill’s presidential address +to the British Association, 1907.</p> + +<p><a name="fn15_10">[10]</a> <i>Brit. Assoc. Rep.</i>, 1905.</p> + +<p><a name="fn15_11">[11]</a> R. S. Phil. Trans., 1803, 1804.</p> + +<p><a name="fn15_12">[12]</a> Ibid, 1824.</p> + +<p><a name="fn15_13">[13]</a> Connaisance des Temps, 1830.</p> + +<p><a name="fn15_14">[14]</a> <i>R. A. S. Mem.</i>, vol. xlvii., p. 178; +<i>Ast. Nach.</i>, No. 3,142; Catalogue published +by Lick Observatory, 1901.</p> + +<p><a name="fn15_15">[15]</a> <i>R. A. S., M. N.</i>, vol. vi.</p> + +<p><a name="fn15_16">[16]</a> <i>R. S. Phil. Trans.</i>, vol. lxxiii., +p. 484.</p> + +<p><a name="fn15_17">[17]</a> <i>Astr. Nach.</i>, No. 2,947.</p> + +<p><a name="fn15_18">[18]</a> <i>R. S. E. Trans</i>., vol. xxvii. +In 1901 Dr. Anderson discovered Nova Persei.</p> + +<p><a name="fn15_19">[19]</a> <i>Astr. Nach</i>., No. 3,079.</p> + +<p><a name="fn15_20">[20]</a> For a different explanation see Sir W. Huggins’s +lecture, Royal Institution, May 13th, 1892.</p> + +<p><a name="fn15_21">[21]</a> For the early history of the proposals for photographic +cataloguing of stars, see the <i>Cape Photographic +Durchmusterung</i>, 3 vols. (<i>Ann. of the Cape Observatory</i>, +vols. in., iv., and v., Introduction.)</p> + +<p><a name="fn15_22">[22]</a> <i>R. S. Phil. Trans.</i>, 1850, p. +499 <i>et seq.</i></p> + +<p><a name="fn15_23">[23]</a> <i>Ibid</i>, vol. cliv., p. 437.</p> + +<p><a name="fn15_24">[24]</a> <i>Brit. Assoc. Rep.</i>, 1868, p. +165.</p> + +<p><br /><br /></p> + +<h1>INDEX</h1> + +<p>Abul Wefa, 24<br /> +Acceleration of moon’s mean motion, 60<br /> +Achromatic lens invented, 88<br /> +Adams, J. C., 61, 65, 68, 69, 70, 87, 118, 124<br /> +Airy, G. B., 13, 30, 37, 65, 69, 70, 80, 81, 114, +119<br /> +Albetegnius, 24<br /> +Alphonso, 24<br /> +Altazimuth, 81<br /> +Anaxagoras, 14, 16<br /> +Anaximander, 14<br /> +Anaximenes, 14<br /> +Anderson, T. D., 137, 138<br /> +Ångstrom, A. J., 102<br /> +Antoniadi, 113<br /> +Apian, P., 63<br /> +Apollonius, 22, 23<br /> +Arago, 111<br /> +Argelander, F. W. A., 139<br /> +Aristarchus, 18, 29<br /> +Aristillus, 17, 19<br /> +Aristotle, 16, 30, 47<br /> +Arrhenius, 146<br /> +Arzachel, 24<br /> +Asshurbanapal, 12<br /> +Asteroids, discovery of, 67, 119<br /> +Astrology, ancient and modern, 1-7, 38</p> + +<p>Backlund, 122<br /> +Bacon, R., 86<br /> +Bailly, 8, 65<br /> +Barnard, E. E., 115, 143<br /> +Beer and Mädler, 107, 110, 111<br /> +Behaim, 74<br /> +Bessel, F.W., 65, 79, 128, 134, 139<br /> +Biela, 123<br /> +Binet, 65<br /> +Biot, 10<br /> +Bird, 79, 80<br /> +Bliss, 80<br /> +Bode, 66, 69<br /> +Bond, G. P., 99, 117, 122<br /> +Bouvard, A., 65, 68<br /> +Bradley, J., 79, 80, 81, 87, 127, 128, 139<br /> +Bredechin, 146<br /> +Bremiker, 71<br /> +Brewster, D., 52, 91, 112<br /> +Brinkley, 128<br /> +Bruno, G., 49<br /> +Burchardt, 65, 123<br /> +Burnham, S. W., 134</p> + +<p>Callippus, 15, 16, 31<br /> +Carrington, R. C., 97, 99, 114<br /> +Cassini, G. D., 107, 114, 115, 116, 117, 118<br /> +Cassini, J., 109, 129<br /> +Chacornac, 139<br /> +Chaldæan astronomy, 11-13<br /> +Challis, J., 69, 70, 71, 72<br /> +Chance, 88<br /> +Charles, II., 50, 81<br /> +Chinese astronomy, 8-11<br /> +Christie, W. M. H. (Ast. Roy.), 64, 82, 125<br /> +Chueni, 9<br /> +Clairaut, A. C., 56, 63, 65<br /> +Clark, A. G., 89, 135<br /> +Clerke, Miss, 106, 146<br /> +Comets, 120<br /> +Common, A. A., 88<br /> +Cooke, 89<br /> +Copeland, R., 142<br /> +Copernicus, N., 14, 24-31, 37, 38, 41, 42, 49, 128<br /> +Cornu, 85<br /> +Cowell, P. H., 3, 5, 64, 83<br /> +Crawford, Earl of, 84<br /> +Cromellin, A. C., 5, 64</p> + +<p>D’Alembert, 65<br /> +Damoiseau, 65<br /> +D’Arrest, H. L., 34<br /> +Dawes, W. R., 100, 111<br /> +Delambre, J. B. J., 8, 27, 51, 65, 68<br /> +De la Rue, W., 2, 94, 99, 100, 131<br /> +Delaunay, 65<br /> +Democritus, 16<br /> +Descartes, 51<br /> +De Sejour, 117<br /> +Deslandres, II., 101<br /> +Desvignolles, 9<br /> +De Zach, 67<br /> +Digges, L., 86<br /> +Dollond, J., 87, 90<br /> +Dominis, A. di., 86<br /> +Donati, 120<br /> +Doppler, 92, 129<br /> +Draper, 99<br /> +Dreyer, J. L. E., 29,77<br /> +Dunthorne, 60<br /> +Dyson, 131</p> + +<p>Eclipses, total solar, 103<br /> +Ecphantes, 16<br /> +Eddington, 131<br /> +Ellipse, 41<br /> +Empedocles, 16<br /> +Encke, J. F., 119, 122, 123, 133<br /> +Epicycles, 22<br /> +Eratosthenes, 18<br /> +Euclid, 17<br /> +Eudoxus, 15, 31<br /> +Euler, L., 60, 61, 62, 65, 88, 119</p> + +<p>Fabricius, D.,95, 120, 121<br /> +Feil and Mantois, 88<br /> +Fizeau, H. L., 85, 92, 99<br /> +Flamsteed, J., 50, 58, 68, 78, 79, 93<br /> +Fohi, 8<br /> +Forbes, J. D., 52, 91<br /> +Foucault, L., 85, 99<br /> +Frauenhofer, J., 88, 90, 91</p> + +<p>Galilei, G., 38, 46-49, 77, 93, 94, 95, 96, 107, 113, +115, 116, 133<br /> +Galle, 71, 72<br /> +Gascoigne, W., 45, 77<br /> +Gauss, C. F., 65, 67<br /> +Gauthier, 98<br /> +Gautier, 89<br /> +Gilbert, 44<br /> +Gill, D., 84, 85, 128, 135, 139, 140<br /> +Goodricke, J., 136<br /> +Gould, B. A., 139<br /> +Grant, R., 27, 47, 51, 86, 134<br /> +Graham, 79<br /> +Greek astronomy, 8-11<br /> +Gregory, J. and D., 87<br /> +Grimaldi, 113<br /> +Groombridge, S., 139<br /> +Grubb, 88, 89<br /> +Guillemin, 122<br /> +Guinand, 88</p> + +<p>Hale, G. E., 101<br /> +Hall, A., 112<br /> +Hall, C. M., 88<br /> +Halley, E., 19, 51, 58, 60, 61, 62, 63, 64, 79, 120, +122, 125, 129<br /> +Halley’s comet, 62-64<br /> +Halm, 85<br /> +Hansen, P. A., 3, 65<br /> +Hansky, A. P., 100<br /> +Harding, C. L., 67<br /> +Heliometer, 83<br /> +Heller, 120<br /> +Helmholtz, H. L. F., 35<br /> +Henderson, T., 128<br /> +Henry, P. and P., 139, 140, 143<br /> +Heraclides, 16<br /> +Heraclitus, 14<br /> +Herodotus, 13<br /> +Herschel, W., 65, 68, 97, 107, 110, 114, 115, 116, +117, 118, 126, 127,<br /> +130, 131, 132, 141, 142<br /> +Herschel, J., 97, 111, 133, 134, 142<br /> +Herschel, A. S., 125<br /> +Hevelius, J., 178<br /> +Hind, J. R., 5, 64, 120, 121, 122<br /> +Hipparchus, 3, 18, 19, 20, 22, 23, 24, 26, 36, 55, +60, 74, 93, 137<br /> +Hooke, R., 51, 111, 114<br /> +Horrocks, J., 50, 56<br /> +Howlett, 100<br /> +Huggins, W., 92, 93, 99, 106, 120, 129, 137, 138, +142, 144<br /> +Humboldt and Bonpland, 124<br /> +Huyghens, C., 47, 77, 87, 110, 116, 117</p> + +<p>Ivory, 65</p> + +<p>Jansen, P. J. C., 105, 106<br /> +Jansen, Z., 86</p> + +<p>Kaiser, F., 111<br /> +Kapteyn, J. C., 131, 138, 139<br /> +Keeler, 117<br /> +Kepler, J., 17, 23, 26, 29, 30, 36, 37, 38-46, 48, +49, 50, 52, 53, 63,<br /> +66, 77, 87, 93, 127, 137<br /> +Kepler’s laws, 42<br /> +Kirchoff, G.R., 91<br /> +Kirsch, 9<br /> +Knobel, E.B., 12, 13<br /> +Ko-Show-King, 76</p> + +<p>Lacaile, N.L., 139<br /> +Lagrange, J.L., 61, 62, 65, 119<br /> +La Hire, 114<br /> +Lalande, J.J.L., 60, 63, 65, 66, 72, 139<br /> +Lamont, J., 98<br /> +Langrenus, 107<br /> +Laplace, P.S. de, 50, 58, 61, 62, 65,66, 123, 146<br /> +Lassel, 72, 88, 117, 118<br /> +Law of universal gravitation, 53<br /> +Legendre, 65<br /> +Leonardo da Vinci, 46<br /> +Lewis, G.C., 17<br /> +Le Verrier, U.J.J., 65, 68, 70, 71,72, 110, 118, 125<br /> +Lexell, 66, 123<br /> +Light year, 128<br /> +Lipperhey, H., 86<br /> +Littrow, 121<br /> +Lockyer, J.N., 103, 105, 146<br /> +Logarithms invented, 50<br /> +Loewy, 2, 100<br /> +Long inequality of Jupiter and Saturn, 50, 62<br /> +Lowell, P., 111, 112, 118<br /> +Lubienietz, S. de, 122<br /> +Luther, M., 38<br /> +Lunar theory, 37, 50, 56, 64</p> + +<p>Maclaurin, 65<br /> +Maclear, T., 128<br /> +Malvasia, 77<br /> +Martin, 9<br /> +Maxwell, J. Clerk, 117<br /> +Maskelyne, N., 80, 130<br /> +McLean, F., 89<br /> +Medici, Cosmo di, 48<br /> +Melancthon, 38<br /> +Melotte, 83, 116<br /> +Meteors, 123<br /> +Meton, 15<br /> +Meyer, 57, 65<br /> +Michaelson, 85<br /> +Miraldi, 110, 114<br /> +Molyneux, 87<br /> +Moon, physical observations, 107<br /> +Mouchez, 139<br /> +Moyriac de Mailla, 8</p> + +<p>Napier, Lord, 50<br /> +Nasmyth and Carpenter, 108<br /> +Nebulae, 141, 146<br /> +Neison, E., 108<br /> +Neptune, discovery of, 68-72<br /> +Newall, 89<br /> +Newcomb, 85<br /> +Newton, H.A., 124<br /> +Newton, I., 5, 19, 43, 49, 51-60, 62, 64, 68, 77, +79, 87, 90, 93, 94,<br /> +114, 127, 133<br /> +Nicetas, 16, 25<br /> +Niesten, 115<br /> +Nunez, P., 35</p> + +<p>Olbers, H.W.M., 67<br /> +Omar, 11, 24<br /> +Oppolzer, 13, 125<br /> +Oudemans, 129</p> + +<p>Palitsch, G., 64<br /> +Parallax, solar, 85, 86<br /> +Parmenides, 14<br /> +Paul III., 30<br /> +Paul V., 48<br /> +Pemberton, 51<br /> +Peters, C.A.F., 125, 128, 135<br /> +Photography, 99<br /> +Piazzi, G., 67, 128, 129, 139<br /> +Picard, 54, 77, 114<br /> +Pickering, E.C., 118, 135<br /> +Pingré, 13, 122<br /> +Plana, 65<br /> +Planets and satellites, physical observations, 109-119<br /> +Plato, 17, 23, 26, 40<br /> +Poisson, 65<br /> +Pond, J., 80<br /> +Pons, 122<br /> +Porta, B., 86<br /> +Pound, 87, 114<br /> +Pontecoulant, 64<br /> +Precession of the equinoxes, 19-21, 55, 57<br /> +Proctor, R.A., 111<br /> +Pritchett, 115<br /> +Ptolemy, 11, 13, 21, 22, 23, 24, 93<br /> +Puiseux and Loewy, 108<br /> +Pulfrich, 131<br /> +Purbach, G., 24<br /> +Pythagoras, 14, 17, 25, 29</p> + +<p>Ramsay, W., 106<br /> +Ransome and May, 81<br /> +Reflecting telescopes invented, 87<br /> +Regiomontanus (Müller), 24<br /> +Respighi, 82<br /> +Retrograde motion of planets, 22<br /> +Riccioli, 107<br /> +Roberts, 137<br /> +Römer, O.,78, 114<br /> +Rosse, Earl of, 88, 142<br /> +Rowland, H. A., 92, 102<br /> +Rudolph H.,37, 39<br /> +Rumker, C., 139</p> + +<p>Sabine, E., 98<br /> +Savary, 133<br /> +Schaeberle, J. M., 135<br /> +Schiaparelli, G. V., 110, 111, 124, 125<br /> +Scheiner, C., 87, 95, 96<br /> +Schmidt, 108<br /> +Schott, 88<br /> +Schröter, J. H., 107, 110, 111, 124, 125<br /> +Schuster, 98<br /> +Schwabe, G. H., 97<br /> +Secchi, A., 93, 144<br /> +Short, 87<br /> +Simms, J., 81<br /> +Slipher, V. M., 119<br /> +Socrates, 17<br /> +Solon, 15<br /> +Souciet, 8<br /> +South, J., 133<br /> +Spectroscope, 89-92<br /> +Spectroheliograph, 101<br /> +Spoerer, G. F. W., 98<br /> +Spots on the sun, 84;<br /> +periodicity of, 97<br /> +Stars, Parallax, 127;<br /> +proper motion, 129;<br /> +double, 132;<br /> +binaries, 132, 135;<br /> +new, 19, 36, 137;<br /> +catalogues of, 19, 36, 139;<br /> +spectra of, 143<br /> +Stewart, B., 2, 100<br /> +Stokes, G. G., 91<br /> +Stone, E. J., 139<br /> +Struve, C. L., 130<br /> +Struve, F. G. W,, 88, 115, 128, 133</p> + +<p>Telescopes invented, 47, 86;<br /> +large, 88<br /> +Temple, 115, 125<br /> +Thales, 13, 16<br /> +Theon, 60<br /> +Transit circle of Römer, 78<br /> +Timocharis, 17, 19<br /> +Titius, 66<br /> +Torricelli, 113<br /> +Troughton, E., 80<br /> +Tupman, G. L., 120<br /> +Tuttle, 125<br /> +Tycho Brahe, 23, 25, 30, 33-38, 39, 40, 44, 50, 75, +77, 93, 94, 129, 137</p> + +<p>Ulugh Begh, 24<br /> +Uranus, discovery of, 65</p> + +<p>Velocity of light, 86, 128;<br /> +of earth in orbit, 128<br /> +Verbiest, 75<br /> +Vogel, H. C., 92, 129, 135, 136<br /> +Von Asten, 122</p> + +<p>Walmsley, 65<br /> +Walterus, B., 24, 74<br /> +Weiss, E., 125<br /> +Wells, 122<br /> +Wesley, 104<br /> +Whewell, 112<br /> +Williams, 10<br /> +Wilson, A., 96, 100<br /> +Winnecke, 120<br /> +Witte, 86<br /> +Wollaston, 90<br /> +Wolf, M., 119, 125, 132<br /> +Wolf, R., 98<br /> +Wren, C., 51<br /> +Wyllie, A., 77</p> + +<p>Yao, 9<br /> +Young, C. A., 103<br /> +Yu-Chi, 8</p> + +<p>Zenith telescopes, 79, 82<br /> +Zöllner, 92<br /> +Zucchi, 113 </p> + + + + + + + + +<pre> + + + + + +End of the Project Gutenberg EBook of History of Astronomy, by George Forbes + +*** END OF THE PROJECT GUTENBERG EBOOK HISTORY OF ASTRONOMY *** + +This file should be named 8hsrs10h.htm or 8hsrs10h.zip +Corrected EDITIONS of our eBooks get a new NUMBER, 8hsrs11h.htm +VERSIONS based on separate sources get new LETTER, 8hsrs10ah.htm + +Produced by Jonathan Ingram, Dave Maddock, Charles Franks +and the Online Distributed Proofreading Team. + +Project Gutenberg eBooks are often created from several printed +editions, all of which are confirmed as Public Domain in the US +unless a copyright notice is included. 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Do not change or edit the +header without written permission. + +Please read the "legal small print," and other information about the +eBook and Project Gutenberg at the bottom of this file. Included is +important information about your specific rights and restrictions in +how the file may be used. You can also find out about how to make a +donation to Project Gutenberg, and how to get involved. + + +**Welcome To The World of Free Plain Vanilla Electronic Texts** + +**eBooks Readable By Both Humans and By Computers, Since 1971** + +*****These eBooks Were Prepared By Thousands of Volunteers!***** + + +Title: History of Astronomy + +Author: George Forbes + +Release Date: May, 2005 [EBook #8172] +[Yes, we are more than one year ahead of schedule] +[This file was first posted on June 25, 2003] + +Edition: 10 + +Language: English + +Character set encoding: Unicode UTF-8 + +*** START OF THE PROJECT GUTENBERG EBOOK HISTORY OF ASTRONOMY *** + + + + +Produced by Jonathan Ingram, Dave Maddock, Charles Franks +and the Online Distributed Proofreading Team. + + + + + + +[Illustration: SIR ISAAC NEWTON (From the bust by Roubiliac In Trinity +College, Cambridge.)] + +HISTORY OF ASTRONOMY + +BY + +GEORGE FORBES, +M.A., F.R.S., M. INST. C. E., + +(FORMERLY PROFESSOR OF NATURAL PHILOSOPHY, ANDERSON'S COLLEGE, GLASGOW) + +AUTHOR OF "THE TRANSIT OF VENUS," RENDU'S "THEORY OF THE GLACIERS OF +SAVOY," ETC., ETC. + + + + +CONTENTS + + PREFACE + + BOOK I. THE GEOMETRICAL PERIOD + + 1. PRIMITIVE ASTRONOMY AND ASTROLOGY + + 2. ANCIENT ASTRONOMY--CHINESE AND CHALDÆANS + + 3. ANCIENT GREEK ASTRONOMY + + 4. THE REIGN OF EPICYCLES--FROM PTOLEMY TO COPERNICUS + + BOOK II. THE DYNAMICAL PERIOD + + 5. DISCOVERY OF THE TRUE SOLAR SYSTEM--TYCHO BRAHE--KEPLER + + 6. GALILEO AND THE TELESCOPE--NOTIONS OF GRAVITY BY HORROCKS, ETC. + + 7. SIR ISAAC NEWTON--LAW OF UNIVERSAL GRAVITATION + + 8. NEWTON'S SUCCESSORS--HALLEY, EULER, LAGRANGE, LAPLACE, ETC. + + 9. DISCOVERY OF NEW PLANETS--HERSCHEL, PIAZZI, ADAMS, AND LE + VERRIER + + BOOK III. OBSERVATION + + + 10. INSTRUMENTS OF PRECISION--SIZE OF THE SOLAR SYSTEM + + 11. HISTORY OF THE TELESCOPE--SPECTROSCOPE + + BOOK IV. THE PHYSICAL PERIOD + + 12. THE SUN + + 13. THE MOON AND PLANETS + + 14. COMETS AND METEORS + + 15. THE STARS AND NEBULÆ + + 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 _à priori_ anticipations. +Experience alone, in both cases, leads to the idea of cause and effect +as a principle that seems to dominate our present universe, as a rule +for predicting the course of events, and as a guide to the choice of a +course of action. This idea of cause and effect is the most potent +factor in developing the history of the human race, as of the +individual. + +In no realm of nature is the principle of cause and effect more +conspicuous than in astronomy; and we fall into the habit of thinking +of its laws as not only being unchangeable in our universe, but +necessary to the conception of any universe that might have been +substituted in its place. The first inhabitants of the world were +compelled to accommodate their acts to the daily and annual +alternations of light and darkness and of heat and cold, as much as to +the irregular changes of weather, attacks of disease, and the fortune +of war. They soon came to regard the influence of the sun, in +connection with light and heat, as a cause. This led to a search for +other signs in the heavens. If the appearance of a comet was sometimes +noted simultaneously with the death of a great ruler, or an eclipse +with a scourge of plague, these might well be looked upon as causes in +the same sense that the veering or backing of the wind is regarded as +a cause of fine or foul weather. + +For these reasons we find that the earnest men of all ages have +recorded the occurrence of comets, eclipses, new stars, meteor +showers, and remarkable conjunctions of the planets, as well as +plagues and famines, floods and droughts, wars and the deaths of great +rulers. Sometimes they thought they could trace connections which +might lead them to say that a comet presaged famine, or an eclipse +war. + +Even if these men were sometimes led to evolve laws of cause and +effect which now seem to us absurd, let us be tolerant, and gratefully +acknowledge that these astrologers, when they suggested such "working +hypotheses," were laying the foundations of observation and deduction. + +If the ancient Chaldæans gave to the planetary conjunctions an +influence over terrestrial events, let us remember that in our own +time people have searched for connection between terrestrial +conditions and periods of unusual prevalence of sun spots; while De la +Rue, Loewy, and Balfour Stewart[1] thought they found a connection +between sun-spot displays and the planetary positions. Thus we find +scientific men, even in our own time, responsible for the belief that +storms in the Indian Ocean, the fertility of German vines, famines in +India, and high or low Nile-floods in Egypt follow the planetary +positions. + +And, again, the desire to foretell the weather is so laudable that we +cannot blame the ancient Greeks for announcing the influence of the +moon with as much confidence as it is affirmed in Lord Wolseley's +_Soldier's Pocket Book_. + +Even if the scientific spirit of observation and deduction (astronomy) +has sometimes led to erroneous systems for predicting terrestrial +events (astrology), we owe to the old astronomer and astrologer alike +the deepest gratitude for their diligence in recording astronomical +events. For, out of the scanty records which have survived the +destructive acts of fire and flood, of monarchs and mobs, we have +found much that has helped to a fuller knowledge of the heavenly +motions than was possible without these records. + +So Hipparchus, about 150 B.C., and Ptolemy a little later, were able +to use the observations of Chaldæan astrologers, as well as those of +Alexandrian astronomers, and to make some discoveries which have +helped the progress of astronomy in all ages. So, also, Mr. Cowell[2] +has examined the marks made on the baked bricks used by the Chaldæans +for recording the eclipses of 1062 B.C. and 762 B.C.; and has thereby +been enabled, in the last few years, to correct the lunar tables of +Hansen, and to find a more accurate value for the secular acceleration +of the moon's longitude and the node of her orbit than any that could +be obtained from modern observations made with instruments of the +highest precision. + +So again, Mr. Hind [3] was enabled to trace back the period during +which Halley's comet has been a member of the solar system, and to +identify it in the Chinese observations of comets as far back as 12 +B.C. Cowell and Cromellin extended the date to 240 B.C. In the same +way the comet 1861.i. has been traced back in the Chinese records to +617 A.D. [4] + +The theoretical views founded on Newton's great law of universal +gravitation led to the conclusion that the inclination of the earth's +equator to the plane of her orbit (the obliquity of the ecliptic) has +been diminishing slowly since prehistoric times; and this fact has +been confirmed by Egyptian and Chinese observations on the length of +the shadow of a vertical pillar, made thousands of years before the +Christian era, in summer and winter. + +There are other reasons why we must be tolerant of the crude notions +of the ancients. The historian, wishing to give credit wherever it may +be due, is met by two difficulties. Firstly, only a few records of +very ancient astronomy are extant, and the authenticity of many of +these is open to doubt. Secondly, it is very difficult to divest +ourselves of present knowledge, and to appreciate the originality of +thought required to make the first beginnings. + +With regard to the first point, we are generally dependent upon +histories written long after the events. The astronomy of Egyptians, +Babylonians, and Assyrians is known to us mainly through the Greek +historians, and for information about the Chinese we rely upon the +researches of travellers and missionaries in comparatively recent +times. The testimony of the Greek writers has fortunately been +confirmed, and we now have in addition a mass of facts translated from +the original sculptures, papyri, and inscribed bricks, dating back +thousands of years. + +In attempting to appraise the efforts of the beginners we must +remember that it was natural to look upon the earth (as all the first +astronomers did) as a circular plane, surrounded and bounded by the +heaven, which was a solid vault, or hemisphere, with its concavity +turned downwards. The stars seemed to be fixed on this vault; the +moon, and later the planets, were seen to crawl over it. It was a +great step to look on the vault as a hollow sphere carrying the sun +too. It must have been difficult to believe that at midday the stars +are shining as brightly in the blue sky as they do at night. It must +have been difficult to explain how the sun, having set in the west, +could get back to rise in the east without being seen _if_ it was +always the same sun. It was a great step to suppose the earth to be +spherical, and to ascribe the diurnal motions to its rotation. +Probably the greatest step ever made in astronomical theory was the +placing of the sun, moon, and planets at different distances from the +earth instead of having them stuck on the vault of heaven. It was a +transition from "flatland" to a space of three dimensions. + +Great progress was made when systematic observations began, such as +following the motion of the moon and planets among the stars, and the +inferred motion of the sun among the stars, by observing their +_heliacal risings_--i.e., the times of year when a star +would first be seen to rise at sunrise, and when it could last be seen +to rise at sunset. The grouping of the stars into constellations and +recording their places was a useful observation. The theoretical +prediction of eclipses of the sun and moon, and of the motions of the +planets among the stars, became later the highest goal in astronomy. + +To not one of the above important steps in the progress of astronomy +can we assign the author with certainty. Probably many of them were +independently taken by Chinese, Indian, Persian, Tartar, Egyptian, +Babylonian, Assyrian, Phoenician, and Greek astronomers. And we have +not a particle of information about the discoveries, which may have +been great, by other peoples--by the Druids, the Mexicans, and the +Peruvians, for example. + +We do know this, that all nations required to have a calendar. The +solar year, the lunar month, and the day were the units, and it is +owing to their incommensurability that we find so many calendars +proposed and in use at different times. The only object to be attained +by comparing the chronologies of ancient races is to fix the actual +dates of observations recorded, and this is not a part of a history of +astronomy. + +In conclusion, let us bear in mind the limited point of view of the +ancients when we try to estimate their merit. Let us remember that the +first astronomy was of two dimensions; the second astronomy was of +three dimensions, but still purely geometrical. Since Kepler's day we +have had a dynamical astronomy. + + +FOOTNOTES: + +[1] Trans. R. S. E., xxiii. 1864, p. 499, _On Sun Spots_, etc., by +B. Stewart. Also Trans. R. S. 1860-70. Also Prof. Ernest Brown, in +_R. A. S. Monthly Notices_, 1900. + +[2] _R. A. S. Monthly Notices_, Sup.; 1905. + +[Illustration: CHALDÆAN BAKED BRICK OR TABLET, _Obverse and reverse +sides_, Containing record of solar eclipse, 1062 B.C., used lately by +Cowell for rendering the lunar theory more accurate than was possible +by finest modern observations. (British Museum collection, +No. 35908.)] + +[3] _R. A. S. Monthly Notices_, vol. x., p. 65. + +[4] R. S. E. Proc., vol. x., 1880. + + + +2. ANCIENT ASTRONOMY--THE CHINESE AND CHALDÆANS. + + +The last section must have made clear the difficulties the way of +assigning to the ancient nations their proper place in the development +of primitive notions about astronomy. The fact that some alleged +observations date back to a period before the Chinese had invented the +art of writing leads immediately to the question how far tradition can +be trusted. + +Our first detailed knowledge was gathered in the far East by +travellers, and by the Jesuit priests, and was published in the +eighteenth century. The Asiatic Society of Bengal contributed +translations of Brahmin literature. The two principal sources of +knowledge about Chinese astronomy were supplied, first by Father +Souciet, who in 1729 published _Observations Astronomical, +Geographical, Chronological, and Physical_, drawn from ancient +Chinese books; and later by Father Moyriac-de-Mailla, who in 1777-1785 +published _Annals of the Chinese Empire, translated from +Tong-Kien-Kang-Mou_. + +Bailly, in his _Astronomie Ancienne_ (1781), drew, from these and +other sources, the conclusion that all we know of the astronomical +learning of the Chinese, Indians, Chaldæans, Assyrians, and Egyptians +is but the remnant of a far more complete astronomy of which no trace +can be found. + +Delambre, in his _Histoire de l'Astronomie Ancienne_ (1817), +ridicules the opinion of Bailly, and considers that the progress made +by all of these nations is insignificant. + +It will be well now to give an idea of some of the astronomy of the +ancients not yet entirely discredited. China and Babylon may be taken +as typical examples. + +_China_.--It would appear that Fohi, the first emperor, reigned +about 2952 B.C., and shortly afterwards Yu-Chi made a sphere to +represent the motions of the celestial bodies. It is also mentioned, +in the book called Chu-King, supposed to have been written in 2205 +B.C., that a similar sphere was made in the time of Yao (2357 +B.C.).[1] It is said that the Emperor Chueni (2513 B.C.) saw five +planets in conjunction the same day that the sun and moon were in +conjunction. This is discussed by Father Martin (MSS. of De Lisle); +also by M. Desvignolles (Mem. Acad. Berlin, vol. iii., p. 193), and by +M. Kirsch (ditto, vol. v., p. 19), who both found that Mars, Jupiter, +Saturn, and Mercury were all between the eleventh and eighteenth +degrees of Pisces, all visible together in the evening on February +28th 2446 B.C., while on the same day the sun and moon were in +conjunction at 9 a.m., and that on March 1st the moon was in +conjunction with the other four planets. But this needs confirmation. + +Yao, referred to above, gave instructions to his astronomers to +determine the positions of the solstices and equinoxes, and they +reported the names of the stars in the places occupied by the sun at +these seasons, and in 2285 B.C. he gave them further orders. If this +account be true, it shows a knowledge that the vault of heaven is a +complete sphere, and that stars are shining at mid-day, although +eclipsed by the sun's brightness. + +It is also asserted, in the book called _Chu-King_, that in the +time of Yao the year was known to have 365¼ days, and that he +adopted 365 days and added an intercalary day every four years (as in +the Julian Calendar). This may be true or not, but the ancient Chinese +certainly seem to have divided the circle into 365 degrees. To learn +the length of the year needed only patient observation--a +characteristic of the Chinese; but many younger nations got into a +terrible mess with their calendar from ignorance of the year's length. + +It is stated that in 2159 B.C. the royal astronomers Hi and Ho failed +to predict an eclipse. It probably created great terror, for they were +executed in punishment for their neglect. If this account be true, it +means that in the twenty-second century B.C. some rule for calculating +eclipses was in use. Here, again, patient observation would easily +lead to the detection of the eighteen-year cycle known to the +Chaldeans as the _Saros_. It consists of 235 lunations, and in +that time the pole of the moon's orbit revolves just once round the +pole of the ecliptic, and for this reason the eclipses in one cycle +are repeated with very slight modification in the next cycle, and so +on for many centuries. + +It may be that the neglect of their duties by Hi and Ho, and their +punishment, influenced Chinese astronomy; or that the succeeding +records have not been available to later scholars; but the fact +remains that--although at long intervals observations were made of +eclipses, comets, and falling stars, and of the position of the +solstices, and of the obliquity of the ecliptic--records become rare, +until 776 B.C., when eclipses began to be recorded once more with some +approach to continuity. Shortly afterwards notices of comets were +added. Biot gave a list of these, and Mr. John Williams, in 1871, +published _Observations of Comets from 611 B.C. to 1640 A.D., +Extracted from the Chinese Annals_. + +With regard to those centuries concerning which we have no +astronomical Chinese records, it is fair to state that it is recorded +that some centuries before the Christian era, in the reign of +Tsin-Chi-Hoang, all the classical and scientific books that could be +found were ordered to be destroyed. If true, our loss therefrom is as +great as from the burning of the Alexandrian library by the Caliph +Omar. He burnt all the books because he held that they must be either +consistent or inconsistent with the Koran, and in the one case they +were superfluous, in the other case objectionable. + +_Chaldæans_.--Until the last half century historians were +accustomed to look back upon the Greeks, who led the world from the +fifth to the third century B.C., as the pioneers of art, literature, +and science. But the excavations and researches of later years make us +more ready to grant that in science as in art the Greeks only +developed what they derived from the Egyptians, Babylonians, and +Assyrians. The Greek historians said as much, in fact; and modern +commentators used to attribute the assertion to undue modesty. Since, +however, the records of the libraries have been unearthed it has been +recognised that the Babylonians were in no way inferior in the matter +of original scientific investigation to other races of the same era. + +The Chaldæans, being the most ancient Babylonians, held the same +station and dignity in the State as did the priests in Egypt, and +spent all their time in the study of philosophy and astronomy, and the +arts of divination and astrology. They held that the world of which we +have a conception is an eternal world without any beginning or ending, +in which all things are ordered by rules supported by a divine +providence, and that the heavenly bodies do not move by chance, nor by +their own will, but by the determinate will and appointment of the +gods. They recorded these movements, but mainly in the hope of tracing +the will of the gods in mundane affairs. Ptolemy (about 130 A.D.) +made use of Babylonian eclipses in the eighth century B.C. for +improving his solar and lunar tables. + +Fragments of a library at Agade have been preserved at Nineveh, from +which we learn that the star-charts were even then divided into +constellations, which were known by the names which they bear to this +day, and that the signs of the zodiac were used for determining the +courses of the sun, moon, and of the five planets Mercury, Venus, +Mars, Jupiter, and Saturn. + +We have records of observations carried on under Asshurbanapal, who +sent astronomers to different parts to study celestial phenomena. Here +is one:-- + +To the Director of Observations,--My Lord, his humble servant +Nabushum-iddin, Great Astronomer of Nineveh, writes thus: "May Nabu +and Marduk be propitious to the Director of these Observations, my +Lord. The fifteenth day we observed the Node of the moon, and the moon +was eclipsed." + +The Phoenicians are supposed to have used the stars for navigation, +but there are no records. The Egyptian priests tried to keep such +astronomical knowledge as they possessed to themselves. It is probable +that they had arbitrary rules for predicting eclipses. All that was +known to the Greeks about Egyptian science is to be found in the +writings of Diodorus Siculus. But confirmatory and more authentic +facts have been derived from late explorations. Thus we learn from +E. B. Knobel[2] about the Jewish calendar dates, on records of land +sales in Aramaic papyri at Assuan, translated by Professor A. H. Sayce +and A. E. Cowley, (1) that the lunar cycle of nineteen years was used +by the Jews in the fifth century B.C. [the present reformed Jewish +calendar dating from the fourth century A.D.], a date a "little more +than a century after the grandfathers and great-grandfathers of those +whose business is recorded had fled into Egypt with Jeremiah" (Sayce); +and (2) that the order of intercalation at that time was not +dissimilar to that in use at the present day. + +Then again, Knobel reminds us of "the most interesting discovery a few +years ago by Father Strassmeier of a Babylonian tablet recording a +partial lunar eclipse at Babylon in the seventh year of Cambyses, on +the fourteenth day of the Jewish month Tammuz." Ptolemy, in the +Almagest (Suntaxis), says it occurred in the seventh year of Cambyses, +on the night of the seventeenth and eighteenth of the Egyptian month +Phamenoth. Pingré and Oppolzer fix the date July 16th, 533 B.C. Thus +are the relations of the chronologies of Jews and Egyptians +established by these explorations. + + +FOOTNOTES: + +[1] These ancient dates are uncertain. + +[2] _R. A. S. Monthly Notices_, vol. lxviii., No. 5, March, 1908. + + + +3. ANCIENT GREEK ASTRONOMY. + + +We have our information about the earliest Greek astronomy from +Herodotus (born 480 B.C.). He put the traditions into writing. Thales +(639-546 B.C.) is said to have predicted an eclipse, which caused much +alarm, and ended the battle between the Medes and Lydians. Airy fixed +the date May 28th, 585 B.C. But other modern astronomers give +different dates. Thales went to Egypt to study science, and learnt +from its priests the length of the year (which was kept a profound +secret!), and the signs of the zodiac, and the positions of the +solstices. He held that the sun, moon, and stars are not mere spots on +the heavenly vault, but solids; that the moon derives her light from +the sun, and that this fact explains her phases; that an eclipse of +the moon happens when the earth cuts off the sun's light from her. He +supposed the earth to be flat, and to float upon water. He determined +the ratio of the sun's diameter to its orbit, and apparently made out +the diameter correctly as half a degree. He left nothing in writing. + +His successors, Anaximander (610-547 B.C.) and Anaximenes (550-475 +B.C.), held absurd notions about the sun, moon, and stars, while +Heraclitus (540-500 B.C.) supposed that the stars were lighted each +night like lamps, and the sun each morning. Parmenides supposed the +earth to be a sphere. + +Pythagoras (569-470 B.C.) visited Egypt to study science. He deduced +his system, in which the earth revolves in an orbit, from fantastic +first principles, of which the following are examples: "The circular +motion is the most perfect motion," "Fire is more worthy than earth," +"Ten is the perfect number." He wrote nothing, but is supposed to have +said that the earth, moon, five planets, and fixed stars all revolve +round the sun, which itself revolves round an imaginary central fire +called the Antichthon. Copernicus in the sixteenth century claimed +Pythagoras as the founder of the system which he, Copernicus, revived. + +Anaxagoras (born 499 B.C.) studied astronomy in Egypt. He explained +the return of the sun to the east each morning by its going under the +flat earth in the night. He held that in a solar eclipse the moon +hides the sun, and in a lunar eclipse the moon enters the earth's +shadow--both excellent opinions. But he entertained absurd ideas of +the vortical motion of the heavens whisking stones into the sky, there +to be ignited by the fiery firmament to form stars. He was prosecuted +for this unsettling opinion, and for maintaining that the moon is an +inhabited earth. He was defended by Pericles (432 B.C.). + +Solon dabbled, like many others, in reforms of the calendar. The +common year of the Greeks originally had 360 days--twelve months of +thirty days. Solon's year was 354 days. It is obvious that these +erroneous years would, before long, remove the summer to January and +the winter to July. To prevent this it was customary at regular +intervals to intercalate days or months. Meton (432 B.C.) introduced a +reform based on the nineteen-year cycle. This is not the same as the +Egyptian and Chaldean eclipse cycle called _Saros_ of 223 +lunations, or a little over eighteen years. The Metonic cycle is 235 +lunations or nineteen years, after which period the sun and moon +occupy the same position relative to the stars. It is still used for +fixing the date of Easter, the number of the year in Melon's cycle +being the golden number of our prayer-books. Melon's system divided +the 235 lunations into months of thirty days and omitted every +sixty-third day. Of the nineteen years, twelve had twelve months and +seven had thirteen months. + +Callippus (330 B.C.) used a cycle four times as long, 940 lunations, +but one day short of Melon's seventy-six years. This was more correct. + +Eudoxus (406-350 B.C.) is said to have travelled with Plato in +Egypt. He made astronomical observations in Asia Minor, Sicily, and +Italy, and described the starry heavens divided into constellations. +His name is connected with a planetary theory which as generally +stated sounds most fanciful. He imagined the fixed stars to be on a +vault of heaven; and the sun, moon, and planets to be upon similar +vaults or spheres, twenty-six revolving spheres in all, the motion of +each planet being resolved into its components, and a separate sphere +being assigned for each component motion. Callippus (330 B.C.) +increased the number to thirty-three. It is now generally accepted +that the real existence of these spheres was not suggested, but the +idea was only a mathematical conception to facilitate the construction +of tables for predicting the places of the heavenly bodies. + +Aristotle (384-322 B.C.) summed up the state of astronomical knowledge +in his time, and held the earth to be fixed in the centre of the +world. + +Nicetas, Heraclides, and Ecphantes supposed the earth to revolve on +its axis, but to have no orbital motion. + +The short epitome so far given illustrates the extraordinary deductive +methods adopted by the ancient Greeks. But they went much farther in +the same direction. They seem to have been in great difficulty to +explain how the earth is supported, just as were those who invented +the myth of Atlas, or the Indians with the tortoise. Thales thought +that the flat earth floated on water. Anaxagoras thought that, being +flat, it would be buoyed up and supported on the air like a kite. +Democritus thought it remained fixed, like the donkey between two +bundles of hay, because it was equidistant from all parts of the +containing sphere, and there was no reason why it should incline one +way rather than another. Empedocles attributed its state of rest to +centrifugal force by the rapid circular movement of the heavens, as +water is stationary in a pail when whirled round by a string. +Democritus further supposed that the inclination of the flat earth to +the ecliptic was due to the greater weight of the southern parts owing +to the exuberant vegetation. + +For further references to similar efforts of imagination the reader is +referred to Sir George Cornwall Lewis's _Historical Survey of the +Astronomy of the Ancients_; London, 1862. His list of authorities +is very complete, but some of his conclusions are doubtful. At p. 113 +of that work he records the real opinions of Socrates as set forth by +Xenophon; and the reader will, perhaps, sympathise with Socrates in +his views on contemporary astronomy:-- + +With regard to astronomy he [Socrates] considered a knowledge of it +desirable to the extent of determining the day of the year or month, +and the hour of the night, ... but as to learning the courses of the +stars, to be occupied with the planets, and to inquire about their +distances from the earth, and their orbits, and the causes of their +motions, he strongly objected to such a waste of valuable time. He +dwelt on the contradictions and conflicting opinions of the physical +philosophers, ... and, in fine, he held that the speculators on the +universe and on the laws of the heavenly bodies were no better than +madmen (_Xen_. _Mem_, i. 1, 11-15). + +Plato (born 429 B.C.), the pupil of Socrates, the fellow-student of +Euclid, and a follower of Pythagoras, studied science in his travels +in Egypt and elsewhere. He was held in so great reverence by all +learned men that a problem which he set to the astronomers was the +keynote to all astronomical investigation from this date till the time +of Kepler in the sixteenth century. He proposed to astronomers _the +problem of representing the courses of the planets by circular and +uniform motions_. + +Systematic observation among the Greeks began with the rise of the +Alexandrian school. Aristillus and Timocharis set up instruments and +fixed the positions of the zodiacal stars, near to which all the +planets in their orbits pass, thus facilitating the determination of +planetary motions. Aristarchus (320-250 B.C.) showed that the sun must +be at least nineteen times as far off as the moon, which is far short +of the mark. He also found the sun's diameter, correctly, to be half a +degree. Eratosthenes (276-196 B.C.) measured the inclination to the +equator of the sun's apparent path in the heavens--i.e., he +measured the obliquity of the ecliptic, making it 23° 51', confirming +our knowledge of its continuous diminution during historical times. He +measured an arc of meridian, from Alexandria to Syene (Assuan), and +found the difference of latitude by the length of a shadow at noon, +summer solstice. He deduced the diameter of the earth, 250,000 +stadia. Unfortunately, we do not know the length of the stadium he +used. + +Hipparchus (190-120 B.C.) may be regarded as the founder of +observational astronomy. He measured the obliquity of the ecliptic, +and agreed with Eratosthenes. He altered the length of the tropical +year from 365 days, 6 hours to 365 days, 5 hours, 53 minutes--still +four minutes too much. He measured the equation of time and the +irregular motion of the sun; and allowed for this in his calculations +by supposing that the centre, about which the sun moves uniformly, is +situated a little distance from the fixed earth. He called this point +the _excentric_. The line from the earth to the "excentric" was +called the _line of apses_. A circle having this centre was +called the _equant_, and he supposed that a radius drawn to the +sun from the excentric passes over equal arcs on the equant in equal +times. He then computed tables for predicting the place of the sun. + +He proceeded in the same way to compute Lunar tables. Making use of +Chaldæan eclipses, he was able to get an accurate value of the moon's +mean motion. [Halley, in 1693, compared this value with his own +measurements, and so discovered the acceleration of the moon's mean +motion. This was conclusively established, but could not be explained +by the Newtonian theory for quite a long time.] He determined the +plane of the moon's orbit and its inclination to the ecliptic. The +motion of this plane round the pole of the ecliptic once in eighteen +years complicated the problem. He located the moon's excentric as he +had done the sun's. He also discovered some of the minor +irregularities of the moon's motion, due, as Newton's theory proves, +to the disturbing action of the sun's attraction. + +In the year 134 B.C. Hipparchus observed a new star. This upset every +notion about the permanence of the fixed stars. He then set to work to +catalogue all the principal stars so as to know if any others appeared +or disappeared. Here his experiences resembled those of several later +astronomers, who, when in search of some special object, have been +rewarded by a discovery in a totally different direction. On comparing +his star positions with those of Timocharis and Aristillus he found no +stars that had appeared or disappeared in the interval of 150 years; +but he found that all the stars seemed to have changed their places +with reference to that point in the heavens where the ecliptic is 90° +from the poles of the earth--i.e., the equinox. He found that this +could be explained by a motion of the equinox in the direction of the +apparent diurnal motion of the stars. This discovery of _precession of +the equinoxes_, which takes place at the rate of 52".1 every year, was +necessary for the progress of accurate astronomical observations. It +is due to a steady revolution of the earth's pole round the pole of +the ecliptic once in 26,000 years in the opposite direction to the +planetary revolutions. + +Hipparchus was also the inventor of trigonometry, both plane and +spherical. He explained the method of using eclipses for determining +the longitude. + +In connection with Hipparchus' great discovery it may be mentioned +that modern astronomers have often attempted to fix dates in history +by the effects of precession of the equinoxes. (1) At about the date +when the Great Pyramid may have been built γDraconis was near to the +pole, and must have been used as the pole-star. In the north face of +the Great Pyramid is the entrance to an inclined passage, and six of +the nine pyramids at Gizeh possess the same feature; all the passages +being inclined at an angle between 26° and 27° to the horizon and in +the plane of the meridian. It also appears that 4,000 years +ago--i.e., about 2100 B.C.--an observer at the lower end of the +passage would be able to see γDraconis, the then pole-star, at its +lower culmination.[1] It has been suggested that the passage was made +for this purpose. On other grounds the date assigned to the Great +Pyramid is 2123 B.C. + +(2) The Chaldæans gave names to constellations now invisible from +Babylon which would have been visible in 2000 B.C., at which date it +is claimed that these people were studying astronomy. + +(3) In the Odyssey, Calypso directs Odysseus, in accordance with +Phoenician rules for navigating the Mediterranean, to keep the Great +Bear "ever on the left as he traversed the deep" when sailing from the +pillars of Hercules (Gibraltar) to Corfu. Yet such a course taken now +would land the traveller in Africa. Odysseus is said in his voyage in +springtime to have seen the Pleiades and Arcturus setting late, which +seemed to early commentators a proof of Homer's inaccuracy. Likewise +Homer, both in the _Odyssey_ [2] (v. 272-5) and in the _Iliad_ +(xviii. 489), asserts that the Great Bear never set in those +latitudes. Now it has been found that the precession of the equinoxes +explains all these puzzles; shows that in springtime on the +Mediterranean the Bear was just above the horizon, near the sea but +not touching it, between 750 B.C. and 1000 B.C.; and fixes the date of +the poems, thus confirming other evidence, and establishing Homer's +character for accuracy. [3] + +(4) The orientation of Egyptian temples and Druidical stones is such +that possibly they were so placed as to assist in the observation of +the heliacal risings [4] of certain stars. If the star were known, +this would give an approximate date. Up to the present the results of +these investigations are far from being conclusive. + +Ptolemy (130 A.D.) wrote the Suntaxis, or Almagest, which includes a +cyclopedia of astronomy, containing a summary of knowledge at that +date. We have no evidence beyond his own statement that he was a +practical observer. He theorised on the planetary motions, and held +that the earth is fixed in the centre of the universe. He adopted the +excentric and equant of Hipparchus to explain the unequal motions of +the sun and moon. He adopted the epicycles and deferents which had +been used by Apollonius and others to explain the retrograde motions +of the planets. We, who know that the earth revolves round the sun +once in a year, can understand that the apparent motion of a planet is +only its motion relative to the earth. If, then, we suppose the earth +fixed and the sun to revolve round it once a year, and the planets +each in its own period, it is only necessary to impose upon each of +these an additional _annual_ motion to enable us to represent truly +the apparent motions. This way of looking at the apparent motions +shows why each planet, when nearest to the earth, seems to move for a +time in a retrograde direction. The attempts of Ptolemy and others of +his time to explain the retrograde motion in this way were only +approximate. Let us suppose each planet to have a bar with one end +centred at the earth. If at the other end of the bar one end of a +shorter bar is pivotted, having the planet at its other end, then the +planet is given an annual motion in the secondary circle (the +epicycle), whose centre revolves round the earth on the primary circle +(the _deferent_), at a uniform rate round the excentric. Ptolemy +supposed the centres of the epicycles of Mercury and Venus to be on a +bar passing through the sun, and to be between the earth and the +sun. The centres of the epicycles of Mars, Jupiter, and Saturn were +supposed to be further away than the sun. Mercury and Venus were +supposed to revolve in their epicycles in their own periodic times and +in the deferent round the earth in a year. The major planets were +supposed to revolve in the deferent round the earth in their own +periodic times, and in their epicycles once in a year. + +It did not occur to Ptolemy to place the centres of the epicycles of +Mercury and Venus at the sun, and to extend the same system to the +major planets. Something of this sort had been proposed by the +Egyptians (we are told by Cicero and others), and was accepted by +Tycho Brahe; and was as true a representation of the relative motions +in the solar system as when we suppose the sun to be fixed and the +earth to revolve. + +The cumbrous system advocated by Ptolemy answered its purpose, +enabling him to predict astronomical events approximately. He improved +the lunar theory considerably, and discovered minor inequalities which +could be allowed for by the addition of new epicycles. We may look +upon these epicycles of Apollonius, and the excentric of Hipparchus, +as the responses of these astronomers to the demand of Plato for +uniform circular motions. Their use became more and more confirmed, +until the seventeenth century, when the accurate observations of Tycho +Brahe enabled Kepler to abolish these purely geometrical makeshifts, +and to substitute a system in which the sun became physically its +controller. + + +FOOTNOTES: + +[1] _Phil. Mag_., vol. xxiv., pp. 481-4. + +[2] + +Πληιάδας τʽ ἐσορω̑ντε καὶ ὀψὲ δύοντα βοώτην +ʼΆρκτον θ̕, ἣν καὶ ἅμαξαν ἐπίκλησιν καλέουσιν, +ʽΉ τ̕ αὐτου̑ στρέφεται καὶ τ̕ ʼΩρίωνα δοκεύει, +Οἴη δ̕ἄμμορος ἐστι λοετρων ʽΩκεανοι̑ο. + +"The Pleiades and Boötes that setteth late, and the Bear, +which they likewise call the Wain, which turneth ever in one +place, and keepeth watch upon Orion, and alone hath no part in +the baths of the ocean." + +[3] See Pearson in the Camb. Phil. Soc. Proc., vol. iv., pt. ii., p. +93, on whose authority the above statements are made. + +[4] See p. 6 for definition. + + + +4. THE REIGN OF EPICYCLES--FROM PTOLEMY TO COPERNICUS. + + +After Ptolemy had published his book there seemed to be nothing more +to do for the solar system except to go on observing and finding more +and more accurate values for the constants involved--viz., the periods +of revolution, the diameter of the deferent,[1] and its ratio to that +of the epicycle,[2] the distance of the excentric[3] from the centre +of the deferent, and the position of the line of apses,[4] besides the +inclination and position of the plane of the planet's orbit. The only +object ever aimed at in those days was to prepare tables for +predicting the places of the planets. It was not a mechanical problem; +there was no notion of a governing law of forces. + +From this time onwards all interest in astronomy seemed, in Europe at +least, to sink to a low ebb. When the Caliph Omar, in the middle of +the seventh century, burnt the library of Alexandria, which had been +the centre of intellectual progress, that centre migrated to Baghdad, +and the Arabs became the leaders of science and philosophy. In +astronomy they made careful observations. In the middle of the ninth +century Albategnius, a Syrian prince, improved the value of +excentricity of the sun's orbit, observed the motion of the moon's +apse, and thought he detected a smaller progression of the sun's +apse. His tables were much more accurate than Ptolemy's. Abul Wefa, in +the tenth century, seems to have discovered the moon's "variation." +Meanwhile the Moors were leaders of science in the west, and Arzachel +of Toledo improved the solar tables very much. Ulugh Begh, grandson of +the great Tamerlane the Tartar, built a fine observatory at Samarcand +in the fifteenth century, and made a great catalogue of stars, the +first since the time of Hipparchus. + +At the close of the fifteenth century King Alphonso of Spain employed +computers to produce the Alphonsine Tables (1488 A.D.), Purbach +translated Ptolemy's book, and observations were carried out in +Germany by Müller, known as Regiomontanus, and Waltherus. + +Nicolai Copernicus, a Sclav, was born in 1473 at Thorn, in Polish +Prussia. He studied at Cracow and in Italy. He was a priest, and +settled at Frauenberg. He did not undertake continuous observations, +but devoted himself to simplifying the planetary systems and devising +means for more accurately predicting the positions of the sun, moon, +and planets. He had no idea of framing a solar system on a dynamical +basis. His great object was to increase the accuracy of the +calculations and the tables. The results of his cogitations were +printed just before his death in an interesting book, _De +Revolutionibus Orbium Celestium_. It is only by careful reading of +this book that the true position of Copernicus can be realised. He +noticed that Nicetas and others had ascribed the apparent diurnal +rotation of the heavens to a real daily rotation of the earth about +its axis, in the opposite direction to the apparent motion of the +stars. Also in the writings of Martianus Capella he learnt that the +Egyptians had supposed Mercury and Venus to revolve round the sun, and +to be carried with him in his annual motion round the earth. He +noticed that the same supposition, if extended to Mars, Jupiter, and +Saturn, would explain easily why they, and especially Mars, seem so +much brighter in opposition. For Mars would then be a great deal +nearer to the earth than at other times. It would also explain the +retrograde motion of planets when in opposition. + +We must here notice that at this stage Copernicus was actually +confronted with the system accepted later by Tycho Brahe, with the +earth fixed. But he now recalled and accepted the views of Pythagoras +and others, according to which the sun is fixed and the earth +revolves; and it must be noted that, geometrically, there is no +difference of any sort between the Egyptian or Tychonic system and +that of Pythagoras as revived by Copernicus, except that on the latter +theory the stars ought to seem to move when the earth changes its +position--a test which failed completely with the rough means of +observation then available. The radical defect of all solar systems +previous to the time of Kepler (1609 A.D.) was the slavish yielding to +Plato's dictum demanding uniform circular motion for the planets, and +the consequent evolution of the epicycle, which was fatal to any +conception of a dynamical theory. + +Copernicus could not sever himself from this obnoxious tradition.[5] +It is true that neither the Pythagorean nor the Egypto-Tychonic system +required epicycles for explaining retrograde motion, as the Ptolemaic +theory did. Furthermore, either system could use the excentric of +Hipparchus to explain the irregular motion known as the equation of +the centre. But Copernicus remarked that he could also use an +epicycle for this purpose, or that he could use both an excentric and +an epicycle for each planet, and so bring theory still closer into +accord with observation. And this he proceeded to do.[6] Moreover, +observers had found irregularities in the moon's motion, due, as we +now know, to the disturbing attraction of the sun. To correct for +these irregularities Copernicus introduced epicycle on epicycle in the +lunar orbit. + +This is in its main features the system propounded by Copernicus. But +attention must, to state the case fully, be drawn to two points to be +found in his first and sixth books respectively. The first point +relates to the seasons, and it shows a strange ignorance of the laws +of rotating bodies. To use the words of Delambre,[7] in drawing +attention to the strange conception, + + he imagined that the earth, revolving round the sun, ought always to + show to it the same face; the contrary phenomena surprised him: to + explain them he invented a third motion, and added it to the two + real motions (rotation and orbital revolution). By this third motion + the earth, he held, made a revolution on itself and on the poles of + the ecliptic once a year ... Copernicus did not know that motion in + a straight line is the natural motion, and that motion in a curve is + the resultant of several movements. He believed, with Aristotle, + that circular motion was the natural one. + +Copernicus made this rotation of the earth's axis about the pole of +the ecliptic retrograde (i.e., opposite to the orbital revolution), +and by making it perform more than one complete revolution in a year, +the added part being 1/26000 of the whole, he was able to include the +precession of the equinoxes in his explanation of the seasons. His +explanation of the seasons is given on leaf 10 of his book (the pages +of this book are not all numbered, only alternate pages, or leaves). + +In his sixth book he discusses the inclination of the planetary orbits +to the ecliptic. In regard to this the theory of Copernicus is unique; +and it will be best to explain this in the words of Grant in his great +work.[8] He says:-- + + Copernicus, as we have already remarked, did not attack the + principle of the epicyclical theory: he merely sought to make it + more simple by placing the centre of the earth's orbit in the centre + of the universe. This was the point to which the motions of the + planets were referred, for the planes of their orbits were made to + pass through it, and their points of least and greatest velocities + were also determined with reference to it. By this arrangement the + sun was situate mathematically near the centre of the planetary + system, but he did not appear to have any physical connexion with + the planets as the centre of their motions. + +According to Copernicus' sixth book, the planes of the planetary +orbits do not pass through the sun, and the lines of apses do not pass +through to the sun. + +Such was the theory advanced by Copernicus: The earth moves in an +epicycle, on a deferent whose centre is a little distance from the +sun. The planets move in a similar way on epicycles, but their +deferents have no geometrical or physical relation to the sun. The +moon moves on an epicycle centred on a second epicycle, itself centred +on a deferent, excentric to the earth. The earth's axis rotates about +the pole of the ecliptic, making one revolution and a twenty-six +thousandth part of a revolution in the sidereal year, in the opposite +direction to its orbital motion. + +In view of this fanciful structure it must be noted, in fairness to +Copernicus, that he repeatedly states that the reader is not obliged +to accept his system as showing the real motions; that it does not +matter whether they be true, even approximately, or not, so long as +they enable us to compute tables from which the places of the planets +among the stars can be predicted.[9] He says that whoever is not +satisfied with this explanation must be contented by being told that +"mathematics are for mathematicians" (Mathematicis mathematica +scribuntur). + +At the same time he expresses his conviction over and over again that +the earth is in motion. It is with him a pious belief, just as it was +with Pythagoras and his school and with Aristarchus. "But" (as Dreyer +says in his most interesting book, _Tycho Brahe_) "proofs of the +physical truth of his system Copernicus had given none, and could give +none," any more than Pythagoras or Aristarchus. + +There was nothing so startlingly simple in his system as to lead the +cautious astronomer to accept it, as there was in the later Keplerian +system; and the absence of parallax in the stars seemed to condemn his +system, which had no physical basis to recommend it, and no +simplification at all over the Egypto-Tychonic system, to which +Copernicus himself drew attention. It has been necessary to devote +perhaps undue space to the interesting work of Copernicus, because by +a curious chance his name has become so widely known. He has been +spoken of very generally as the founder of the solar system that is +now accepted. This seems unfair, and on reading over what has been +written about him at different times it will be noticed that the +astronomers--those who have evidently read his great book--are very +cautious in the words with which they eulogise him, and refrain from +attributing to him the foundation of our solar system, which is +entirely due to Kepler. It is only the more popular writers who give +the idea that a revolution had been effected when Pythagoras' system +was revived, and when Copernicus supported his view that the earth +moves and is not fixed. + +It may be easy to explain the association of the name of Copernicus +with the Keplerian system. But the time has long passed when the +historian can support in any way this popular error, which was started +not by astronomers acquainted with Kepler's work, but by those who +desired to put the Church in the wrong by extolling Copernicus. + +Copernicus dreaded much the abuse he expected to receive from +philosophers for opposing the authority of Aristotle, who had declared +that the earth was fixed. So he sought and obtained the support of +the Church, dedicating his great work to Pope Paul III. in a lengthy +explanatory epistle. The Bishop of Cracow set up a memorial tablet in +his honour. + +Copernicus was the most refined exponent, and almost the last +representative, of the Epicyclical School. As has been already +stated, his successor, Tycho Brahe, supported the same use of +epicycles and excentrics as Copernicus, though he held the earth to be +fixed. But Tycho Brahe was eminently a practical observer, and took +little part in theory; and his observations formed so essential a +portion of the system of Kepler that it is only fair to include his +name among these who laid the foundations of the solar system which we +accept to-day. + +In now taking leave of the system of epicycles let it be remarked that +it has been held up to ridicule more than it deserves. On reading +Airy's account of epicycles, in the beautifully clear language of his +_Six Lectures on Astronomy_, the impression is made that the +jointed bars there spoken of for describing the circles were supposed +to be real. This is no more the case than that the spheres of Eudoxus +and Callippus were supposed to be real. Both were introduced only to +illustrate the mathematical conception upon which the solar, +planetary, and lunar tables were constructed. The epicycles +represented nothing more nor less than the first terms in the Fourier +series, which in the last century has become a basis of such +calculations, both in astronomy and physics generally. + +[Illustration: "QUADRANS MURALIS SIVE TICHONICUS." With portrait of +Tycho Brahe, instruments, etc., painted on the wall; showing +assistants using the sight, watching the clock, and recording. (From +the author's copy of the _Astronomiæ Instauratæ Mechanica._)] + + +FOOTNOTES: + +[1] For definition see p. 22. + +[2] _Ibid_. + +[3] For definition see p. 18. + +[4] For definition see p. 18. + +[5] In his great book Copernicus says: "The movement of the heavenly +bodies is uniform, circular, perpetual, or else composed of circular +movements." In this he proclaimed himself a follower of Pythagoras +(see p. 14), as also when he says: "The world is spherical because the +sphere is, of all figures, the most perfect" (Delambre, +_Ast. Mod. Hist_., pp. 86, 87). + +[6] Kepler tells us that Tycho Brahe was pleased with this +device, and adapted it to his own system. + +[7] _Hist. Ast._, vol. i., p. 354. + +[8] _Hist. of Phys. Ast._, p. vii. + +[9] "Est enim Astronomi proprium, historiam motuum coelestium +diligenti et artificiosa observatione colligere. Deinde causas +earundem, seu hypotheses, cum veras assequi nulla ratione possit +... Neque enim necesse est, eas hypotheses esse veras, imo ne +verisimiles quidem, sed sufficit hoc usum, si calculum observationibus +congruentem exhibeant." + + + + +BOOK II. THE DYNAMICAL PERIOD + + + +5. DISCOVERY OF THE TRUE SOLAR SYSTEM--TYCHO BRAHE--KEPLER. + + +During the period of the intellectual and aesthetic revival, at the +beginning of the sixteenth century, the "spirit of the age" was +fostered by the invention of printing, by the downfall of the +Byzantine Empire, and the scattering of Greek fugitives, carrying the +treasures of literature through Western Europe, by the works of +Raphael and Michael Angelo, by the Reformation, and by the extension +of the known world through the voyages of Spaniards and Portuguese. +During that period there came to the front the founder of accurate +observational astronomy. Tycho Brahe, a Dane, born in 1546 of noble +parents, was the most distinguished, diligent, and accurate observer +of the heavens since the days of Hipparchus, 1,700 years before. + +Tycho was devoted entirely to his science from childhood, and the +opposition of his parents only stimulated him in his efforts to +overcome difficulties. He soon grasped the hopelessness of the old +deductive methods of reasoning, and decided that no theories ought to +be indulged in until preparations had been made by the accumulation of +accurate observations. We may claim for him the title of founder of +the inductive method. + +For a complete life of this great man the reader is referred to +Dreyer's _Tycho Brahe_, Edinburgh, 1890, containing a complete +bibliography. The present notice must be limited to noting the work +done, and the qualities of character which enabled him to attain his +scientific aims, and which have been conspicuous in many of his +successors. + +He studied in Germany, but King Frederick of Denmark, appreciating his +great talents, invited him to carry out his life's work in that +country. He granted to him the island of Hveen, gave him a pension, +and made him a canon of the Cathedral of Roskilde. On that island +Tycho Brahe built the splendid observatory which he called Uraniborg, +and, later, a second one for his assistants and students, called +Stjerneborg. These he fitted up with the most perfect instruments, and +never lost a chance of adding to his stock of careful observations.[1] + +The account of all these instruments and observations, printed at his +own press on the island, was published by Tycho Brahe himself, and the +admirable and numerous engravings bear witness to the excellence of +design and the stability of his instruments. + +His mechanical skill was very great, and in his workmanship he was +satisfied with nothing but the best. He recognised the importance of +rigidity in the instruments, and, whereas these had generally been +made of wood, he designed them in metal. His instruments included +armillae like those which had been used in Alexandria, and other +armillae designed by himself--sextants, mural quadrants, large +celestial globes and various instruments for special purposes. He +lived before the days of telescopes and accurate clocks. He invented +the method of sub-dividing the degrees on the arc of an instrument by +transversals somewhat in the way that Pedro Nunez had proposed. + +He originated the true system of observation and reduction of +observations, recognising the fact that the best instrument in the +world is not perfect; and with each of his instruments he set to work +to find out the errors of graduation and the errors of mounting, the +necessary correction being applied to each observation. + +When he wanted to point his instrument exactly to a star he was +confronted with precisely the same difficulty as is met in gunnery and +rifle-shooting. The sights and the object aimed at cannot be in focus +together, and a great deal depends on the form of sight. Tycho Brahe +invented, and applied to the pointers of his instruments, an +aperture-sight of variable area, like the iris diaphragm used now in +photography. This enabled him to get the best result with stars of +different brightness. The telescope not having been invented, he +could not use a telescopic-sight as we now do in gunnery. This not +only removes the difficulty of focussing, but makes the minimum +visible angle smaller. Helmholtz has defined the minimum angle +measurable with the naked eye as being one minute of arc. In view of +this it is simply marvellous that, when the positions of Tycho's +standard stars are compared with the best modern catalogues, his +probable error in right ascension is only ± 24", 1, and in declination +only ± 25", 9. + +Clocks of a sort had been made, but Tycho Brahe found them so +unreliable that he seldom used them, and many of his position-measurements +were made by measuring the angular distances from known stars. + +Taking into consideration the absence of either a telescope or a +clock, and reading his account of the labour he bestowed upon each +observation, we must all agree that Kepler, who inherited these +observations in MS., was justified, under the conditions then +existing, in declaring that there was no hope of anyone ever improving +upon them. + +In the year 1572, on November 11th, Tycho discovered in Cassiopeia a +new star of great brilliance, and continued to observe it until the +end of January, 1573. So incredible to him was such an event that he +refused to believe his own eyes until he got others to confirm what he +saw. He made accurate observations of its distance from the nine +principal stars in Casseiopeia, and proved that it had no measurable +parallax. Later he employed the same method with the comets of 1577, +1580, 1582, 1585, 1590, 1593, and 1596, and proved that they too had +no measurable parallax and must be very distant. + +The startling discovery that stars are not necessarily permanent, that +new stars may appear, and possibly that old ones may disappear, had +upon him exactly the same effect that a similar occurrence had upon +Hipparchus 1,700 years before. He felt it his duty to catalogue all +the principal stars, so that there should be no mistake in the +future. During the construction of his catalogue of 1,000 stars he +prepared and used accurate tables of refraction deduced from his own +observations. Thus he eliminated (so far as naked eye observations +required) the effect of atmospheric refraction which makes the +altitude of a star seem greater than it really is. + +Tycho Brahe was able to correct the lunar theory by his observations. +Copernicus had introduced two epicycles on the lunar orbit in the hope +of obtaining a better accordance between theory and observation; and +he was not too ambitious, as his desire was to get the tables accurate +to ten minutes. Tycho Brahe found that the tables of Copernicus were +in error as much as two degrees. He re-discovered the inequality +called "variation" by observing the moon in all phases--a thing which +had not been attended to. [It is remarkable that in the nineteenth +century Sir George Airy established an altazimuth at Greenwich +Observatory with this special object, to get observations of the moon +in all phases.] He also discovered other lunar equalities, and wanted +to add another epicycle to the moon's orbit, but he feared that these +would soon become unmanageable if further observations showed more new +inequalities. + +But, as it turned out, the most fruitful work of Tycho Brahe was on +the motions of the planets, and especially of the planet Mars, for it +was by an examination of these results that Kepler was led to the +discovery of his immortal laws. + +After the death of King Frederick the observatories of Tycho Brahe +were not supported. The gigantic power and industry displayed by this +determined man were accompanied, as often happens, by an overbearing +manner, intolerant of obstacles. This led to friction, and eventually +the observatories were dismantled, and Tycho Brahe was received by the +Emperor Rudolph II., who placed a house in Prague at his disposal. +Here he worked for a few years, with Kepler as one of his assistants, +and he died in the year 1601. + +It is an interesting fact that Tycho Brahe had a firm conviction that +mundane events could be predicted by astrology, and that this belief +was supported by his own predictions. + +It has already been stated that Tycho Brahe maintained that +observation must precede theory. He did not accept the Copernican +theory that the earth moves, but for a working hypothesis he used a +modification of an old Egyptian theory, mathematically identical with +that of Copernicus, but not involving a stellar parallax. He says +(_De Mundi_, etc.) that + + the Ptolemean system was too complicated, and the new one which that + great man Copernicus had proposed, following in the footsteps of + Aristarchus of Samos, though there was nothing in it contrary to + mathematical principles, was in opposition to those of physics, as + the heavy and sluggish earth is unfit to move, and the system is + even opposed to the authority of Scripture. The absence of annual + parallax further involves an incredible distance between the + outermost planet and the fixed stars. + +We are bound to admit that in the circumstances of the case, so long +as there was no question of dynamical forces connecting the members of +the solar system, his reasoning, as we should expect from such a man, +is practical and sound. It is not surprising, then, that astronomers +generally did not readily accept the views of Copernicus, that Luther +(Luther's _Tischreden_, pp. 22, 60) derided him in his usual pithy +manner, that Melancthon (_Initia doctrinae physicae_) said that +Scripture, and also science, are against the earth's motion; and that +the men of science whose opinion was asked for by the cardinals (who +wished to know whether Galileo was right or wrong) looked upon +Copernicus as a weaver of fanciful theories. + +Johann Kepler is the name of the man whose place, as is generally +agreed, would have been the most difficult to fill among all those who +have contributed to the advance of astronomical knowledge. He was born +at Wiel, in the Duchy of Wurtemberg, in 1571. He held an appointment +at Gratz, in Styria, and went to join Tycho Brahe in Prague, and to +assist in reducing his observations. These came into his possession +when Tycho Brahe died, the Emperor Rudolph entrusting to him the +preparation of new tables (called the Rudolphine tables) founded on +the new and accurate observations. He had the most profound respect +for the knowledge, skill, determination, and perseverance of the man +who had reaped such a harvest of most accurate data; and though Tycho +hardly recognised the transcendent genius of the man who was working +as his assistant, and although there were disagreements between them, +Kepler held to his post, sustained by the conviction that, with these +observations to test any theory, he would be in a position to settle +for ever the problem of the solar system. + +[Illustration: PORTRAIT OF JOHANNES KEPLER. By F. Wanderer, from +Reitlinger's "Johannes Kepler" (original in Strassburg).] + +It has seemed to many that Plato's demand for uniform circular motion +(linear or angular) was responsible for a loss to astronomy of good +work during fifteen hundred years, for a hundred ill-considered +speculative cosmogonies, for dissatisfaction, amounting to disgust, +with these _à priori_ guesses, and for the relegation of the +science to less intellectual races than Greeks and other Europeans. +Nobody seemed to dare to depart from this fetish of uniform angular +motion and circular orbits until the insight, boldness, and +independence of Johann Kepler opened up a new world of thought and of +intellectual delight. + +While at work on the Rudolphine tables he used the old epicycles and +deferents and excentrics, but he could not make theory agree with +observation. His instincts told him that these apologists for uniform +motion were a fraud; and he proved it to himself by trying every +possible variation of the elements and finding them fail. The number +of hypotheses which he examined and rejected was almost incredible +(for example, that the planets turn round centres at a little distance +from the sun, that the epicycles have centres at a little distance +from the deferent, and so on). He says that, after using all these +devices to make theory agree with Tycho's observations, he still found +errors amounting to eight minutes of a degree. Then he said boldly +that it was impossible that so good an observer as Tycho could have +made a mistake of eight minutes, and added: "Out of these eight +minutes we will construct a new theory that will explain the motions +of all the planets." And he did it, with elliptic orbits having the +sun in a focus of each.[2] + +It is often difficult to define the boundaries between fancies, +imagination, hypothesis, and sound theory. This extraordinary genius +was a master in all these modes of attacking a problem. His analogy +between the spaces occupied by the five regular solids and the +distances of the planets from the sun, which filled him with so much +delight, was a display of pure fancy. His demonstration of the three +fundamental laws of planetary motion was the most strict and complete +theory that had ever been attempted. + +It has been often suggested that the revival by Copernicus of the +notion of a moving earth was a help to Kepler. No one who reads +Kepler's great book could hold such an opinion for a moment. In fact, +the excellence of Copernicus's book helped to prolong the life of the +epicyclical theories in opposition to Kepler's teaching. + +All of the best theories were compared by him with observation. These +were the Ptolemaic, the Copernican, and the Tychonic. The two latter +placed all of the planetary orbits concentric with one another, the +sun being placed a little away from their common centre, and having no +apparent relation to them, and being actually outside the planes in +which they move. Kepler's first great discovery was that the planes +of all the orbits pass through the sun; his second was that the line +of apses of each planet passes through the sun; both were +contradictory to the Copernican theory. + +He proceeds cautiously with his propositions until he arrives at his +great laws, and he concludes his book by comparing observations of +Mars, of all dates, with his theory. + +His first law states that the planets describe ellipses with the sun +at a focus of each ellipse. + +His second law (a far more difficult one to prove) states that a line +drawn from a planet to the sun sweeps over equal areas in equal +times. These two laws were published in his great work, _Astronomia +Nova, sen. Physica Coelestis tradita commentariis de Motibus Stelloe; +Martis_, Prague, 1609. + +It took him nine years more[3] to discover his third law, that the +squares of the periodic times are proportional to the cubes of the +mean distances from the sun. + +These three laws contain implicitly the law of universal +gravitation. They are simply an alternative way of expressing that law +in dealing with planets, not particles. Only, the power of the +greatest human intellect is so utterly feeble that the meaning of the +words in Kepler's three laws could not be understood until expounded +by the logic of Newton's dynamics. + +The joy with which Kepler contemplated the final demonstration of +these laws, the evolution of which had occupied twenty years, can +hardly be imagined by us. He has given some idea of it in a passage +in his work on _Harmonics_, which is not now quoted, only lest +someone might say it was egotistical--a term which is simply grotesque +when applied to such a man with such a life's work accomplished. + +The whole book, _Astronomia Nova_, is a pleasure to read; the +mass of observations that are used, and the ingenuity of the +propositions, contrast strongly with the loose and imperfectly +supported explanations of all his predecessors; and the indulgent +reader will excuse the devotion of a few lines to an example of the +ingenuity and beauty of his methods. + +It may seem a hopeless task to find out the true paths of Mars and the +earth (at that time when their shape even was not known) from the +observations giving only the relative direction from night to +night. Now, Kepler had twenty years of observations of Mars to deal +with. This enabled him to use a new method, to find the earth's +orbit. Observe the date at any time when Mars is in opposition. The +earth's position E at that date gives the longitude of Mars M. His +period is 687 days. Now choose dates before and after the principal +date at intervals of 687 days and its multiples. Mars is in each case +in the same position. Now for any date when Mars is at M and the earth +at E₃ the date of the year gives the angle E₃SM. And the +observation of Tycho gives the direction of Mars compared with the +sun, SE₃M. So all the angles of the triangle SEM in any of these +positions of E are known, and also the ratios of SE₁, SE₂, SE₃, +SE₄ to SM and to each other. + +For the orbit of Mars observations were chosen at intervals of a year, +when the earth was always in the same place. + +[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. + ° ' " ° ' " +Mean monthly motion of Apses 1.31.28 3.4.0 +Mean annual motion of nodes 19.18.1,23 19.21.22,50 +Mean value of "variation" 36.10 35.47 +Annual equation 11.51 11.14 +Inequality of mean motion of apogee 19.43 22.17 +Inequality of mean motion of nodes 9.24 9.0 + +The only serious discrepancy is the first, which has been already +mentioned. Considering that some of these perturbations had never been +discovered, that the cause of none of them had ever been known, and +that he exhibited his results, if he did not also make the +discoveries, by the synthetic methods of geometry, it is simply +marvellous that he reached to such a degree of accuracy. He invented +the infinitesimal calculus which is more suited for such calculations, +but had he expressed his results in that language he would have been +unintelligible to many. + +Newton's method of calculating the precession of the equinoxes, +already referred to, is as beautiful as anything in the _Principia_. +He had already proved the regression of the nodes of a satellite +moving in an orbit inclined to the ecliptic. He now said that the +nodes of a ring of satellites revolving round the earth's equator +would consequently all regress. And if joined into a solid ring its +node would regress; and it would do so, only more slowly, if +encumbered by the spherical part of the earth's mass. Therefore the +axis of the equatorial belt of the earth must revolve round the pole +of the ecliptic. Then he set to work and found the amount due to the +moon and that due to the sun, and so he solved the mystery of 2,000 +years. + +When Newton applied his law of gravitation to an explanation of the +tides he started a new field for the application of mathematics to +physical problems; and there can be little doubt that, if he could +have been furnished with complete tidal observations from different +parts of the world, his extraordinary powers of analysis would have +enabled him to reach a satisfactory theory. He certainly opened up +many mines full of intellectual gems; and his successors have never +ceased in their explorations. This has led to improved mathematical +methods, which, combined with the greater accuracy of observation, +have rendered physical astronomy of to-day the most exact of the +sciences. + +Laplace only expressed the universal opinion of posterity when he said +that to the _Principia_ is assured "a pre-eminence above all the +other productions of the human intellect." + +The name of Flamsteed, First Astronomer Royal, must here be mentioned +as having supplied Newton with the accurate data required for +completing the theory. + +The name of Edmund Halley, Second Astronomer Royal, must ever be held +in repute, not only for his own discoveries, but for the part he +played in urging Newton to commit to writing, and present to the Royal +Society, the results of his investigations. But for his friendly +insistence it is possible that the _Principia_ would never have +been written; and but for his generosity in supplying the means the +Royal Society could not have published the book. + +[Illustration: DEATH MASK OF SIR ISAAC NEWTON. +Photographed specially for this work from the original, by kind +permission of the Royal Society, London.] + +Sir Isaac Newton died in 1727, at the age of eighty-five. His body +lay in state in the Jerusalem Chamber, and was buried in Westminster +Abbey. + + +FOOTNOTES: + +[1] The writer inherited from his father (Professor J. D. Forbes) a +small box containing a bit of wood and a slip of paper, which had been +presented to him by Sir David Brewster. On the paper Sir David had +written these words: "If there be any truth in the story that Newton +was led to the theory of gravitation by the fall of an apple, this bit +of wood is probably a piece of the apple tree from which Newton saw +the apple fall. When I was on a pilgrimage to the house in which +Newton was born, I cut it off an ancient apple tree growing in his +garden." When lecturing in Glasgow, about 1875, the writer showed it +to his audience. The next morning, when removing his property from the +lecture table, he found that his precious relic had been stolen. It +would be interesting to know who has got it now! + +[2] It must be noted that these words, in which the laws of +gravitation are always summarised in histories and text-books, do not +appear in the _Principia_; but, though they must have been composed by +some early commentator, it does not appear that their origin has been +traced. Nor does it appear that Newton ever extended the law beyond +the Solar System, and probably his caution would have led him to avoid +any statement of the kind until it should be proved. + +With this exception the above statement of the law of universal +gravitation contains nothing that is not to be found in the +_Principia_; and the nearest approach to that statement occurs in the +Seventh Proposition of Book III.:-- + +Prop.: That gravitation occurs in all bodies, and that it is +proportional to the quantity of matter in each. + +Cor. I.: The total attraction of gravitation on a planet arises, and +is composed, out of the attraction on the separate parts. + +Cor. II.: The attraction on separate equal particles of a body is +reciprocally as the square of the distance from the particles. + +[3] It is said that, when working out this final result, the +probability of its confirming that part of his theory which he had +reluctantly abandoned years before excited him so keenly that he was +forced to hand over his calculations to a friend, to be completed by +him. + + + +8. NEWTON'S SUCCESSORS--HALLEY, EULER, LAGRANGE, LAPLACE, ETC. + + +Edmund Halley succeeded Flamsteed as Second Astronomer Royal in +1721. Although he did not contribute directly to the mathematical +proofs of Newton's theory, yet his name is closely associated with +some of its greatest successes. + +He was the first to detect the acceleration of the moon's mean +motion. Hipparchus, having compared his own observations with those of +more ancient astronomers, supplied an accurate value of the moon's +mean motion in his time. Halley similarly deduced a value for modern +times, and found it sensibly greater. He announced this in 1693, but +it was not until 1749 that Dunthorne used modern lunar tables to +compute a lunar eclipse observed in Babylon 721 B.C., another at +Alexandria 201 B.C., a solar eclipse observed by Theon 360 A.D., and +two later ones up to the tenth century. He found that to explain +these eclipses Halley's suggestion must be adopted, the acceleration +being 10" in one century. In 1757 Lalande again fixed it at 10." + +The Paris Academy, in 1770, offered their prize for an investigation +to see if this could be explained by the theory of gravitation. Euler +won the prize, but failed to explain the effect, and said: "It appears +to be established by indisputable evidence that the secular inequality +of the moon's mean motion cannot be produced by the forces of +gravitation." + +The same subject was again proposed for a prize which was shared by +Lagrange [1] and Euler, neither finding a solution, while the latter +asserted the existence of a resisting medium in space. + +Again, in 1774, the Academy submitted the same subject, a third time, +for the prize; and again Lagrange failed to detect a cause in +gravitation. + +Laplace [2] now took the matter in hand. He tried the effect of a +non-instantaneous action of gravity, to no purpose. But in 1787 he +gave the true explanation. The principal effect of the sun on the +moon's orbit is to diminish the earth's influence, thus lengthening +the period to a new value generally taken as constant. But Laplace's +calculations showed the new value to depend upon the excentricity of +the earth's orbit, which, according; to theory, has a periodical +variation of enormous period, and has been continually diminishing for +thousands of years. Thus the solar influence has been diminishing, and +the moon's mean motion increased. Laplace computed the amount at 10" +in one century, agreeing with observation. (Later on Adams showed that +Laplace's calculation was wrong, and that the value he found was too +large; so, part of the acceleration is now attributed by some +astronomers to a lengthening of the day by tidal friction.) + +Another contribution by Halley to the verification of Newton's law was +made when he went to St. Helena to catalogue the southern stars. He +measured the change in length of the second's pendulum in different +latitudes due to the changes in gravity foretold by Newton. + +Furthermore, he discovered the long inequality of Jupiter and Saturn, +whose period is 929 years. For an investigation of this also the +Academy of Sciences offered their prize. This led Euler to write a +valuable essay disclosing a new method of computing perturbations, +called the instantaneous ellipse with variable elements. The method +was much developed by Lagrange. + +But again it was Laplace who solved the problem of the inequalities of +Jupiter and Saturn by the theory of gravitation, reducing the errors +of the tables from 20' down to 12", thus abolishing the use of +empirical corrections to the planetary tables, and providing another +glorious triumph for the law of gravitation. As Laplace justly said: +"These inequalities appeared formerly to be inexplicable by the law of +gravitation--they now form one of its most striking proofs." + +Let us take one more discovery of Halley, furnishing directly a new +triumph for the theory. He noticed that Newton ascribed parabolic +orbits to the comets which he studied, so that they come from +infinity, sweep round the sun, and go off to infinity for ever, after +having been visible a few weeks or months. He collected all the +reliable observations of comets he could find, to the number of +twenty-four, and computed their parabolic orbits by the rules laid +down by Newton. His object was to find out if any of them really +travelled in elongated ellipses, practically undistinguishable, in the +visible part of their paths, from parabolæ, in which case they would +be seen more than once. He found two old comets whose orbits, in shape +and position, resembled the orbit of a comet observed by himself in +1682. Apian observed one in 1531; Kepler the other in 1607. The +intervals between these appearances is seventy-five or seventy-six +years. He then examined and found old records of similar appearance in +1456, 1380, and 1305. It is true, he noticed, that the intervals +varied by a year and a-half, and the inclination of the orbit to the +ecliptic diminished with successive apparitions. But he knew from +previous calculations that this might easily be due to planetary +perturbations. Finally, he arrived at the conclusion that all of these +comets were identical, travelling in an ellipse so elongated that the +part where the comet was seen seemed to be part of a parabolic +orbit. He then predicted its return at the end of 1758 or beginning of +1759, when he should be dead; but, as he said, "if it should return, +according to our prediction, about the year 1758, impartial posterity +will not refuse to acknowledge that this was first discovered by an +Englishman."[3] [_Synopsis Astronomiae Cometicae_, 1749.] + +Once again Halley's suggestion became an inspiration for the +mathematical astronomer. Clairaut, assisted by Lalande, found that +Saturn would retard the comet 100 days, Jupiter 518 days, and +predicted its return to perihelion on April 13th, 1759. In his +communication to the French Academy, he said that a comet travelling +into such distant regions might be exposed to the influence of forces +totally unknown, and "even of some planet too far removed from the sun +to be ever perceived." + +The excitement of astronomers towards the end of 1758 became intense; +and the honour of first catching sight of the traveller fell to an +amateur in Saxony, George Palitsch, on Christmas Day, 1758. It reached +perihelion on March 13th, 1759. + +This fact was a startling confirmation of the Newtonian theory, +because it was a new kind of calculation of perturbations, and also it +added a new member to the solar system, and gave a prospect of adding +many more. + +When Halley's comet reappeared in 1835, Pontecoulant's computations +for the date of perihelion passage were very exact, and afterwards he +showed that, with more exact values of the masses of Jupiter and +Saturn, his prediction was correct within two days, after an invisible +voyage of seventy-five years! + +Hind afterwards searched out many old appearances of this comet, going +back to 11 B.C., and most of these have been identified as being +really Halley's comet by the calculations of Cowell and Cromellin[4] +(of Greenwich Observatory), who have also predicted its next +perihelion passage for April 8th to 16th, 1910, and have traced back +its history still farther, to 240 B.C. + +Already, in November, 1907, the Astronomer Royal was trying to catch +it by the aid of photography. + + +FOOTNOTES: + +[1] Born 1736; died 1813. + +[2] Born 1749; died 1827. + +[3] This sentence does not appear in the original memoir communicated +to the Royal Society, but was first published in a posthumous reprint. + +[4] _R. A. S. Monthly Notices_, 1907-8. + + + +9. DISCOVERY OF NEW PLANETS--HERSCHEL, PIAZZI, ADAMS, AND LE VERRIER. + + +It would be very interesting, but quite impossible in these pages, to +discuss all the exquisite researches of the mathematical astronomers, +and to inspire a reverence for the names connected with these +researches, which for two hundred years have been establishing the +universality of Newton's law. The lunar and planetary theories, the +beautiful theory of Jupiter's satellites, the figure of the earth, and +the tides, were mathematically treated by Maclaurin, D'Alembert, +Legendre, Clairaut, Euler, Lagrange, Laplace, Walmsley, Bailly, +Lalande, Delambre, Mayer, Hansen, Burchardt, Binet, Damoiseau, Plana, +Poisson, Gauss, Bessel, Bouvard, Airy, Ivory, Delaunay, Le Verrier, +Adams, and others of later date. + +By passing over these important developments it is possible to trace +some of the steps in the crowning triumph of the Newtonian theory, by +which the planet Neptune was added to the known members of the solar +system by the independent researches of Professor J.C. Adams and of +M. Le Verrier, in 1846. + +It will be best to introduce this subject by relating how the +eighteenth century increased the number of known planets, which was +then only six, including the earth. + +On March 13th, 1781, Sir William Herschel was, as usual, engaged on +examining some small stars, and, noticing that one of them appeared to +be larger than the fixed stars, suspected that it might be a comet. +To test this he increased his magnifying power from 227 to 460 and +932, finding that, unlike the fixed stars near it, its definition was +impaired and its size increased. This convinced him that the object +was a comet, and he was not surprised to find on succeeding nights +that the position was changed, the motion being in the ecliptic. He +gave the observations of five weeks to the Royal Society without a +suspicion that the object was a new planet. + +For a long time people could not compute a satisfactory orbit for the +supposed comet, because it seemed to be near the perihelion, and no +comet had ever been observed with a perihelion distance from the sun +greater than four times the earth's distance. Lexell was the first to +suspect that this was a new planet eighteen times as far from the sun +as the earth is. In January, 1783, Laplace published the elliptic +elements. The discoverer of a planet has a right to name it, so +Herschel called it Georgium Sidus, after the king. But Lalande urged +the adoption of the name Herschel. Bode suggested Uranus, and this +was adopted. The new planet was found to rank in size next to Jupiter +and Saturn, being 4.3 times the diameter of the earth. + +In 1787 Herschel discovered two satellites, both revolving in nearly +the same plane, inclined 80° to the ecliptic, and the motion of both +was retrograde. + +In 1772, before Herschel's discovery, Bode[1] had discovered a curious +arbitrary law of planetary distances. Opposite each planet's name +write the figure 4; and, in succession, add the numbers 0, 3, 6, 12, +24, 48, 96, etc., to the 4, always doubling the last numbers. You +then get the planetary distances. + + Mercury, dist.-- 4 4 + 0 = 4 + Venus " 7 4 + 3 = 7 + Earth " 10 4 + 6 = 10 + Mars " 15 4 + 12 = 16 + -- 4 + 24 = 28 + Jupiter dist. 52 4 + 48 = 52 + Saturn " 95 4 + 96 = 100 + (Uranus) " 192 4 + 192 = 196 + -- 4 + 384 = 388 + +All the five planets, and the earth, fitted this rule, except that +there was a blank between Mars and Jupiter. When Uranus was +discovered, also fitting the rule, the conclusion was irresistible +that there is probably a planet between Mars and Jupiter. An +association of twenty-four astronomers was now formed in Germany to +search for the planet. Almost immediately afterwards the planet was +discovered, not by any member of the association, but by Piazzi, when +engaged upon his great catalogue of stars. On January 1st, 1801, he +observed a star which had changed its place the next night. Its motion +was retrograde till January 11th, direct after the 13th. Piazzi fell +ill before he had enough observations for computing the orbit with +certainty, and the planet disappeared in the sun's rays. Gauss +published an approximate ephemeris of probable positions when the +planet should emerge from the sun's light. There was an exciting hunt, +and on December 31st (the day before its birthday) De Zach captured +the truant, and Piazzi christened it Ceres. + + +The mean distance from the sun was found to be 2.767, agreeing with +the 2.8 given by Bode's law. Its orbit was found to be inclined over +10° to the ecliptic, and its diameter was only 161 miles. + +On March 28th, 1802, Olbers discovered a new seventh magnitude star, +which turned out to be a planet resembling Ceres. It was called +Pallas. Gauss found its orbit to be inclined 35° to the ecliptic, and +to cut the orbit of Ceres; whence Olbers considered that these might +be fragments of a broken-up planet. He then commenced a search for +other fragments. In 1804 Harding discovered Juno, and in 1807 Olbers +found Vesta. The next one was not discovered until 1845, from which +date asteroids, or minor planets (as these small planets are called), +have been found almost every year. They now number about 700. + +It is impossible to give any idea of the interest with which the first +additions since prehistoric times to the planetary system were +received. All of those who showered congratulations upon the +discoverers regarded these discoveries in the light of rewards for +patient and continuous labours, the very highest rewards that could be +desired. And yet there remained still the most brilliant triumph of +all, the addition of another planet like Uranus, before it had ever +been seen, when the analysis of Adams and Le Verrier gave a final +proof of the powers of Newton's great law to explain any planetary +irregularity. + +After Sir William Herschel discovered Uranus, in 1781, it was found +that astronomers had observed it on many previous occasions, mistaking +it for a fixed star of the sixth or seventh magnitude. Altogether, +nineteen observations of Uranus's position, from the time of +Flamsteed, in 1690, had been recorded. + +In 1790 Delambre, using all these observations, prepared tables for +computing its position. These worked well enough for a time, but at +last the differences between the calculated and observed longitudes of +the planet became serious. In 1821 Bouvard undertook a revision of the +tables, but found it impossible to reconcile all the observations of +130 years (the period of revolution of Uranus is eighty-four years). +So he deliberately rejected the old ones, expressing the opinion that +the discrepancies might depend upon "some foreign and unperceived +cause which may have been acting upon the planet." In a few years the +errors even of these tables became intolerable. In 1835 the error of +longitude was 30"; in 1838, 50"; in 1841, 70"; and, by comparing the +errors derived from observations made before and after opposition, a +serious error of the distance (radius vector) became apparent. + +In 1843 John Couch Adams came out Senior Wrangler at Cambridge, and +was free to undertake the research which as an undergraduate he had +set himself--to see whether the disturbances of Uranus could be +explained by assuming a certain orbit, and position in that orbit, of +a hypothetical planet even more distant than Uranus. Such an +explanation had been suggested, but until 1843 no one had the boldness +to attack the problem. Bessel had intended to try, but a fatal +illness overtook him. + +Adams first recalculated all known causes of disturbance, using the +latest determinations of the planetary masses. Still the errors were +nearly as great as ever. He could now, however, use these errors as +being actually due to the perturbations produced by the unknown +planet. + +In 1844, assuming a circular orbit, and a mean distance agreeing with +Bode's law, he obtained a first approximation to the position of the +supposed planet. He then asked Professor Challis, of Cambridge, to +procure the latest observations of Uranus from Greenwich, which Airy +immediately supplied. Then the whole work was recalculated from the +beginning, with more exactness, and assuming a smaller mean distance. + +In September, 1845, he handed to Challis the elements of the +hypothetical planet, its mass, and its apparent position for September +30th, 1845. On September 22nd Challis wrote to Airy explaining the +matter, and declaring his belief in Adams's capabilities. When Adams +called on him Airy was away from home, but at the end of October, +1845, he called again, and left a paper with full particulars of his +results, which had, for the most part, reduced the discrepancies to +about 1". As a matter of fact, it has since been found that the +heliocentric place of the new planet then given was correct within +about 2°. + +Airy wrote expressing his interest, and asked for particulars about +the radius vector. Adams did not then reply, as the answer to this +question could be seen to be satisfactory by looking at the data +already supplied. He was a most unassuming man, and would not push +himself forward. He may have felt, after all the work he had done, +that Airy's very natural inquiry showed no proportionate desire to +search for the planet. Anyway, the matter lay in embryo for nine +months. + +Meanwhile, one of the ablest French astronomers, Le Verrier, +experienced in computing perturbations, was independently at work, +knowing nothing about Adams. He applied to his calculations every +possible refinement, and, considering the novelty of the problem, his +calculation was one of the most brilliant in the records of +astronomy. In criticism it has been said that these were exhibitions +of skill rather than helps to a solution of the particular problem, +and that, in claiming to find the elements of the orbit within certain +limits, he was claiming what was, under the circumstances, impossible, +as the result proved. + +In June, 1846, Le Verrier announced, in the _Comptes Rendus de +l'Academie des Sciences_, that the longitude of the disturbing planet, +for January 1st, 1847, was 325, and that the probable error did not +exceed 10°. + +This result agreed so well with Adams's (within 1°) that Airy urged +Challis to apply the splendid Northumberland equatoreal, at Cambridge, +to the search. Challis, however, had already prepared an exhaustive +plan of attack which must in time settle the point. His first work +was to observe, and make a catalogue, or chart, of all stars near +Adams's position. + +On August 31st, 1846, Le Verrier published the concluding +part of his labours. + +On September 18th, 1846, Le Verrier communicated his results to the +Astronomers at Berlin, and asked them to assist in searching for the +planet. By good luck Dr. Bremiker had just completed a star-chart of +the very part of the heavens including Le Verrier's position; thus +eliminating all of Challis's preliminary work. The letter was received +in Berlin on September 23rd; and the same evening Galle found the new +planet, of the eighth magnitude, the size of its disc agreeing with Le +Verrier's prediction, and the heliocentric longitude agreeing within +57'. By this time Challis had recorded, without reduction, the +observations of 3,150 stars, as a commencement for his search. On +reducing these, he found a star, observed on August 12th, which was +not in the same place on July 30th. This was the planet, and he had +also observed it on August 4th. + +The feeling of wonder, admiration, and enthusiasm aroused by this +intellectual triumph was overwhelming. In the world of astronomy +reminders are met every day of the terrible limitations of human +reasoning powers; and every success that enables the mind's eye to see +a little more clearly the meaning of things has always been heartily +welcomed by those who have themselves been engaged in like +researches. But, since the publication of the _Principia_, in 1687, +there is probably no analytical success which has raised among +astronomers such a feeling of admiration and gratitude as when Adams +and Le Verrier showed the inequalities in Uranus's motion to mean that +an unknown planet was in a certain place in the heavens, where it was +found. + +At the time there was an unpleasant display of international jealousy. +The British people thought that the earlier date of Adams's work, and +of the observation by Challis, entitled him to at least an equal share +of credit with Le Verrier. The French, on the other hand, who, on the +announcement of the discovery by Galle, glowed with pride in the new +proof of the great powers of their astronomer, Le Verrier, whose life +had a long record of successes in calculation, were incredulous on +being told that it had all been already done by a young man whom they +had never heard of. + +These displays of jealousy have long since passed away, and there is +now universally an _entente cordiale_ that to each of these great men +belongs equally the merit of having so thoroughly calculated this +inverse problem of perturbations as to lead to the immediate discovery +of the unknown planet, since called Neptune. + +It was soon found that the planet had been observed, and its position +recorded as a fixed star by Lalande, on May 8th and 10th, 1795. + +Mr. Lassel, in the same year, 1846, with his two-feet reflector, +discovered a satellite, with retrograde motion, which gave the mass of +the planet about a twentieth of that of Jupiter. + + +FOOTNOTES: + +[1] Bode's law, or something like it, had already been fore-shadowed +by Kepler and others, especially Titius (see _Monatliche +Correspondenz_, vol. vii., p. 72). + + + + +BOOK III. OBSERVATION + + + +10. INSTRUMENTS OF PRECISION--STATE OF THE SOLAR SYSTEM. + + +Having now traced the progress of physical astronomy up to the time +when very striking proofs of the universality of the law of +gravitation convinced the most sceptical, it must still be borne in +mind that, while gravitation is certainly the principal force +governing the motions of the heavenly bodies, there may yet be a +resisting medium in space, and there may be electric and magnetic +forces to deal with. There may, further, be cases where the effects of +luminous radiative repulsion become apparent, and also Crookes' +vacuum-effects described as "radiant matter." Nor is it quite certain +that Laplace's proofs of the instantaneous propagation of gravity are +final. + +And in the future, as in the past, Tycho Brahe's dictum must be +maintained, that all theory shall be preceded by accurate +observations. It is the pride of astronomers that their science stands +above all others in the accuracy of the facts observed, as well as in +the rigid logic of the mathematics used for interpreting these facts. + +It is interesting to trace historically the invention of those +instruments of precision which have led to this result, and, without +entering on the details required in a practical handbook, to note the +guiding principles of construction in different ages. + +It is very probable that the Chaldeans may have made spheres, like the +armillary sphere, for representing the poles of the heavens; and with +rings to show the ecliptic and zodiac, as well as the equinoctial and +solstitial colures; but we have no record. We only know that the tower +of Belus, on an eminence, was their observatory. We have, however, +distinct records of two such spheres used by the Chinese about 2500 +B.C. Gnomons, or some kind of sundial, were used by the Egyptians and +others; and many of the ancient nations measured the obliquity of the +ecliptic by the shadows of a vertical column in summer and winter. The +natural horizon was the only instrument of precision used by those who +determined star positions by the directions of their risings and +settings; while in those days the clepsydra, or waterclock, was the +best instrument for comparing their times of rising and setting. + +About 300 B.C. an observatory fitted with circular instruments for +star positions was set up at Alexandria, the then centre of +civilisation. We know almost nothing about the instruments used by +Hipparchus in preparing his star catalogues and his lunar and solar +tables; but the invention of the astrolabe is attributed to him.[1] + +In more modern times Nuremberg became a centre of astronomical +culture. Waltherus, of that town, made really accurate observations of +star altitudes, and of the distances between stars; and in 1484 +A.D. he used a kind of clock. Tycho Brahe tried these, but discarded +them as being inaccurate. + +Tycho Brahe (1546-1601 A.D.) made great improvements in armillary +spheres, quadrants, sextants, and large celestial globes. With these +he measured the positions of stars, or the distance of a comet from +several known stars. He has left us full descriptions of them, +illustrated by excellent engravings. Previous to his time such +instruments were made of wood. Tycho always used metal. He paid the +greatest attention to the stability of mounting, to the orientation of +his instruments, to the graduation of the arcs by the then new method +of transversals, and to the aperture sight used upon his +pointer. There were no telescopes in his day, and no pendulum +clocks. He recognised the fact that there must be instrumental +errors. He made these as small as was possible, measured their amount, +and corrected his observations. His table of refractions enabled him +to abolish the error due to our atmosphere so far as it could affect +naked-eye observations. The azimuth circle of Tycho's largest quadrant +had a diameter of nine feet, and the quadrant a radius of six feet. He +introduced the mural quadrant for meridian observations.[2] + +[Illustration: ANCIENT CHINESE INSTRUMENTS, Including quadrant, celestial +globe, and two armillae, in the Observatory at Peking. Photographed in +Peking by the author in 1875, and stolen by the Germans when the +Embassies were relieved by the allies in 1900.] + +The French Jesuits at Peking, in the seventeenth century, helped the +Chinese in their astronomy. In 1875 the writer saw and photographed, +on that part of the wall of Peking used by the Mandarins as an +observatory, the six instruments handsomely designed by Father +Verbiest, copied from the instruments of Tycho Brahe, and embellished +with Chinese dragons and emblems cast on the supports. He also saw +there two old instruments (which he was told were Arabic) of date +1279, by Ko Show-King, astronomer to Koblai Khan, the grandson of +Chenghis Khan. One of these last is nearly identical with the armillae +of Tycho; and the other with his "armillae æquatoriæ maximæ," with +which he observed the comet of 1585, besides fixed stars and +planets.[3] + +The discovery by Galileo of the isochronism of the pendulum, followed +by Huyghens's adaptation of that principle to clocks, has been one of +the greatest aids to accurate observation. About the same time an +equally beneficial step was the employment of the telescope as a +pointer; not the Galilean with concave eye-piece, but with a +magnifying glass to examine the focal image, at which also a fixed +mark could be placed. Kepler was the first to suggest this. Gascoigne +was the first to use it. Huyghens used a metal strip of variable width +in the focus, as a micrometer to cover a planetary disc, and so to +measure the width covered by the planet. The Marquis Malvasia, in +1662, described the network of fine silver threads at right angles, +which he used in the focus, much as we do now. + +In the hands of such a skilful man as Tycho Brahe, the old open +sights, even without clocks, served their purpose sufficiently well to +enable Kepler to discover the true theory of the solar system. But +telescopic sights and clocks were required for proving some of +Newton's theories of planetary perturbations. Picard's observations at +Paris from 1667 onwards seem to embody the first use of the telescope +as a pointer. He was also the first to introduce the use of Huyghens's +clocks for observing the right ascension of stars. Olaus Romer was +born at Copenhagen in 1644. In 1675, by careful study of the times of +eclipses of Jupiter's satellites, he discovered that light took time +to traverse space. Its velocity is 186,000 miles per second. In 1681 +he took up his duties as astronomer at Copenhagen, and built the first +transit circle on a window-sill of his house. The iron axis was five +feet long and one and a-half inches thick, and the telescope was fixed +near one end with a counterpoise. The telescope-tube was a double +cone, to prevent flexure. Three horizontal and three vertical wires +were used in the focus. These were illuminated by a speculum, near the +object-glass, reflecting the light from a lantern placed over the +axis, the upper part of the telescope-tube being partly cut away to +admit the light. A divided circle, with pointer and reading +microscope, was provided for reading the declination. He realised the +superiority of a circle with graduations over a much larger +quadrant. The collimation error was found by reversing the instrument +and using a terrestrial mark, the azimuth error by star observations. +The time was expressed in fractions of a second. He also constructed a +telescope with equatoreal mounting, to follow a star by one axial +motion. In 1728 his instruments and observation records were destroyed +by fire. + +Hevelius had introduced the vernier and tangent screw in his +measurement of arc graduations. His observatory and records were burnt +to the ground in 1679. Though an old man, he started afresh, and left +behind him a catalogue of 1,500 stars. + +Flamsteed began his duties at Greenwich Observatory, as first +Astronomer Royal, in 1676, with very poor instruments. In 1683 he put +up a mural arc of 140°, and in 1689 a better one, seventy-nine inches +radius. He conducted his measurements with great skill, and +introduced new methods to attain accuracy, using certain stars for +determining the errors of his instruments; and he always reduced his +observations to a form in which they could be readily used. He +introduced new methods for determining the position of the equinox and +the right ascension of a fundamental star. He produced a catalogue of +2,935 stars. He supplied Sir Isaac Newton with results of observation +required in his theoretical calculations. He died in 1719. + +Halley succeeded Flamsteed to find that the whole place had been +gutted by the latter's executors. In 1721 he got a transit instrument, +and in 1726 a mural quadrant by Graham. His successor in 1742, +Bradley, replaced this by a fine brass quadrant, eight feet radius, by +Bird; and Bradley's zenith sector was purchased for the observatory. +An instrument like this, specially designed for zenith stars, is +capable of greater rigidity than a more universal instrument; and +there is no trouble with refraction in the zenith. For these reasons +Bradley had set up this instrument at Kew, to attempt the proof of the +earth's motion by observing the annual parallax of stars. He certainly +found an annual variation of zenith distance, but not at the times of +year required by the parallax. This led him to the discovery of the +"aberration" of light and of nutation. Bradley has been described as +the founder of the modern system of accurate observation. He died in +1762, leaving behind him thirteen folio volumes of valuable but +unreduced observations. Those relating to the stars were reduced by +Bessel and published in 1818, at Königsberg, in his well-known +standard work, _Fundamenta Astronomiae_. In it are results showing the +laws of refraction, with tables of its amount, the maximum value of +aberration, and other constants. + +Bradley was succeeded by Bliss, and he by Maskelyne (1765), who +carried on excellent work, and laid the foundations of the Nautical +Almanac (1767). Just before his death he induced the Government to +replace Bird's quadrant by a fine new mural _circle_, six feet in +diameter, by Troughton, the divisions being read off by microscopes +fixed on piers opposite to the divided circle. In this instrument the +micrometer screw, with a divided circle for turning it, was applied +for bringing the micrometer wire actually in line with a division on +the circle--a plan which is still always adopted. + +Pond succeeded Maskelyne in 1811, and was the first to use this +instrument. From now onwards the places of stars were referred to the +pole, not to the zenith; the zero being obtained from measures on +circumpolar stars. Standard stars were used for giving the clock +error. In 1816 a new transit instrument, by Troughton, was added, and +from this date the Greenwich star places have maintained the very +highest accuracy. + +George Biddell Airy, Seventh Astronomer Royal,[4] commenced his +Greenwich labours in 1835. His first and greatest reformation in the +work of the observatory was one he had already established at +Cambridge, and is now universally adopted. He held that an observation +is not completed until it has been reduced to a useful form; and in +the case of the sun, moon, and planets these results were, in every +case, compared with the tables, and the tabular error printed. + +Airy was firmly impressed with the object for which Charles II. had +wisely founded the observatory in connection with navigation, and for +observations of the moon. Whenever a meridian transit of the moon +could be observed this was done. But, even so, there are periods in +the month when the moon is too near the sun for a transit to be well +observed. Also weather interferes with many meridian observations. To +render the lunar observations more continuous, Airy employed +Troughton's successor, James Simms, in conjunction with the engineers, +Ransome and May, to construct an altazimuth with three-foot circles, +and a five-foot telescope, in 1847. The result was that the number of +lunar observations was immediately increased threefold, many of them +being in a part of the moon's orbit which had previously been bare of +observations. From that date the Greenwich lunar observations have +been a model and a standard for the whole world. + +Airy also undertook to superintend the reduction of all Greenwich +lunar observations from 1750 to 1830. The value of this laborious +work, which was completed in 1848, cannot be over-estimated. + +The demands of astronomy, especially in regard to small minor planets, +required a transit instrument and mural circle with a more powerful +telescope. Airy combined the functions of both, and employed the same +constructors as before to make a _transit-circle_ with a telescope of +eleven and a-half feet focus and a circle of six-feet diameter, the +object-glass being eight inches in diameter. + +Airy, like Bradley, was impressed with the advantage of employing +stars in the zenith for determining the fundamental constants of +astronomy. He devised a _reflex zenith tube_, in which the zenith +point was determined by reflection from a surface of mercury. The +design was so simple, and seemed so perfect, that great expectations +were entertained. But unaccountable variations comparable with those +of the transit circle appeared, and the instrument was put out of use +until 1903, when the present Astronomer Royal noticed that the +irregularities could be allowed for, being due to that remarkable +variation in the position of the earth's axis included in circles of +about six yards diameter at the north and south poles, discovered at +the end of the nineteenth century. The instrument is now being used +for investigating these variations; and in the year 1907 as many as +1,545 observations of stars were made with the reflex zenith tube. + +In connection with zenith telescopes it must be stated that Respighi, +at the Capitol Observatory at Rome, made use of a deep well with a +level mercury surface at the bottom and a telescope at the top +pointing downwards, which the writer saw in 1871. The reflection of +the micrometer wires and of a star very near the zenith (but not quite +in the zenith) can be observed together. His mercury trough was a +circular plane surface with a shallow edge to retain the mercury. The +surface quickly came to rest after disturbance by street traffic. + +Sir W. M. H. Christie, Eighth Astronomer Royal, took up his duties in +that capacity in 1881. Besides a larger altazimuth that he erected in +1898, he has widened the field of operations at Greenwich by the +extensive use of photography and the establishment of large +equatoreals. From the point of view of instruments of precision, one +of the most important new features is the astrographic equatoreal, set +up in 1892 and used for the Greenwich section of the great +astrographic chart just completed. Photography has come to be of use, +not only for depicting the sun and moon, comets and nebulae, but also +to obtain accurate relative positions of neighbouring stars; to pick +up objects that are invisible in any telescope; and, most of all +perhaps, in fixing the positions of faint satellites. Thus Saturn's +distant satellite, Phoebe, and the sixth and seventh satellites of +Jupiter, have been followed regularly in their courses at Greenwich +ever since their discovery with the thirty-inch reflector (erected in +1897); and while doing so Mr. Melotte made, in 1908, the splendid +discovery on some of the photographic plates of an eighth satellite of +Jupiter, at an enormous distance from the planet. From observations in +the early part of 1908, over a limited arc of its orbit, before +Jupiter approached the sun, Mr. Cowell computed a retrograde orbit and +calculated the future positions of this satellite, which enabled +Mr. Melotte to find it again in the autumn--a great triumph both of +calculation and of photographic observation. This satellite has never +been seen, and has been photographed only at Greenwich, Heidelberg, +and the Lick Observatory. + +Greenwich Observatory has been here selected for tracing the progress +of accurate measurement. But there is one instrument of great value, +the heliometer, which is not used at Greenwich. This serves the +purpose of a double image micrometer, and is made by dividing the +object-glass of a telescope along a diameter. Each half is mounted so +as to slide a distance of several inches each way on an arc whose +centre is the focus. The amount of the movement can be accurately +read. Thus two fields of view overlap, and the adjustment is made to +bring an image of one star over that of another star, and then to do +the same by a displacement in the opposite direction. The total +movement of the half-object glass is double the distance between the +star images in the focal plane. Such an instrument has long been +established at Oxford, and German astronomers have made great use of +it. But in the hands of Sir David Gill (late His Majesty's Astronomer +at the Cape of Good Hope), and especially in his great researches on +Solar and on Stellar parallax, it has been recognised as an instrument +of the very highest accuracy, measuring the distance between stars +correctly to less than a tenth of a second of arc. + +The superiority of the heliometer over all other devices (except +photography) for measuring small angles has been specially brought +into prominence by Sir David Gill's researches on the distance of the +sun--_i.e.,_ the scale of the solar system. A measurement of the +distance of any planet fixes the scale, and, as Venus approaches the +earth most nearly of all the planets, it used to be supposed that a +Transit of Venus offered the best opportunity for such measurement, +especially as it was thought that, as Venus entered on the solar disc, +the sweep of light round the dark disc of Venus would enable a very +precise observation to be made. The Transit of Venus in 1874, in +which the present writer assisted, overthrew this delusion. + +In 1877 Sir David Gill used Lord Crawford's heliometer at the Island +of Ascension to measure the parallax of Mars in opposition, and found +the sun's distance 93,080,000 miles. He considered that, while the +superiority of the heliometer had been proved, the results would be +still better with the points of light shown by minor planets rather +than with the disc of Mars. + +In 1888-9, at the Cape, he observed the minor planets Iris, Victoria, +and Sappho, and secured the co-operation of four other heliometers. +His final result was 92,870,000 miles, the parallax being 8",802 +(_Cape Obs_., Vol. VI.). + +So delicate were these measures that Gill detected a minute periodic +error of theory of twenty-seven days, owing to a periodically +erroneous position of the centre of gravity of the earth and moon to +which the position of the observer was referred. This led him to +correct the mass of the moon, and to fix its ratio to the earth's mass += 0.012240. + +Another method of getting the distance from the sun is to measure the +velocity of the earth's orbital motion, giving the circumference +traversed in a year, and so the radius of the orbit. This has been +done by comparing observation and experiment. The aberration of light +is an angle 20" 48, giving the ratio of the earth's velocity to the +velocity of light. The velocity of light is 186,000 miles a second; +whence the distance to the sun is 92,780,000 miles. There seems, +however, to be some uncertainty about the true value of the +aberration, any determination of which is subject to irregularities +due to the "seasonal errors." The velocity of light was experimentally +found, in 1862, by Fizeau and Foucault, each using an independent +method. These methods have been developed, and new values found, by +Cornu, Michaelson, Newcomb, and the present writer. + +Quite lately Halm, at the Cape of Good Hope, measured +spectroscopically the velocity of the earth to and from a star by +observations taken six months apart. Thence he obtained an accurate +value of the sun's distance.[5] + +But the remarkably erratic minor planet, Eros, discovered by Witte in +1898, approaches the earth within 15,000,000 miles at rare intervals, +and, with the aid of photography, will certainly give us the best +result. A large number of observatories combined to observe the +opposition of 1900. Their results are not yet completely reduced, but +the best value deduced so far for the parallax[6] is 8".807 ± +0".0028.[7] + + +FOOTNOTES: + +[1] In 1480 Martin Behaim, of Nuremberg, produced his _astrolabe_ for +measuring the latitude, by observation of the sun, at sea. It +consisted of a graduated metal circle, suspended by a ring which was +passed over the thumb, and hung vertically. A pointer was fixed to a +pin at the centre. This arm, called the _alhidada_, worked round the +graduated circle, and was pointed to the sun. The altitude of the sun +was thus determined, and, by help of solar tables, the latitude could +be found from observations made at apparent noon. + +[2] See illustration on p. 76. + +[3] See Dreyer's article on these instruments in _Copernicus_, +Vol. I. They were stolen by the Germans after the relief of the +Embassies, in 1900. The best description of these instruments is +probably that contained in an interesting volume, which may be seen in +the library of the R. A. S., entitled _Chinese Researches_, by +Alexander Wyllie (Shanghai, 1897). + +[4] Sir George Airy was very jealous of this honourable title. He +rightly held that there is only one Astronomer Royal at a time, as +there is only one Mikado, one Dalai Lama. He said that His Majesty's +Astronomer at the Cape of Good Hope, His Majesty's Astronomer for +Scotland, and His Majesty's Astronomer for Ireland are not called +Astronomers Royal. + +[5] _Annals of the Cape Observatory_, vol. x., part 3. + +[6] The parallax of the sun is the angle subtended by the earth's +radius at the sun's distance. + +[7] A. R. Hinks, R.A.S.; _Monthly Notices_, June, 1909. + + + +11. HISTORY OF THE TELESCOPE + + +Accounts of wonderful optical experiments by Roger Bacon (who died in +1292), and in the sixteenth century by Digges, Baptista Porta, and +Antonio de Dominis (Grant, _Hist. Ph. Ast_.), have led some to +suppose that they invented the telescope. The writer considers that it +is more likely that these notes refer to a kind of _camera +obscura_, in which a lens throws an inverted image of a landscape +on the wall. + +The first telescopes were made in Holland, the originator being either +Henry Lipperhey,[1] Zacharias Jansen, or James Metius, and the date +1608 or earlier. + +In 1609 Galileo, being in Venice, heard of the invention, went home +and worked out the theory, and made a similar telescope. These +telescopes were all made with a convex object-glass and a concave +eye-lens, and this type is spoken of as the Galilean telescope. Its +defects are that it has no real focus where cross-wires can be placed, +and that the field of view is very small. Kepler suggested the convex +eye-lens in 1611, and Scheiner claimed to have used one in 1617. But +it was Huyghens who really introduced them. In the seventeenth century +telescopes were made of great length, going up to 300 feet. Huyghens +also invented the compound eye-piece that bears his name, made of two +convex lenses to diminish spherical aberration. + +But the defects of colour remained, although their cause was unknown +until Newton carried out his experiments on dispersion and the solar +spectrum. To overcome the spherical aberration James Gregory,[2] of +Aberdeen and Edinburgh, in 1663, in his _Optica Promota_, +proposed a reflecting speculum of parabolic form. But it was Newton, +about 1666, who first made a reflecting telescope; and he did it with +the object of avoiding colour dispersion. + +Some time elapsed before reflectors were much used. Pound and Bradley +used one presented to the Royal Society by Hadley in 1723. Hawksbee, +Bradley, and Molyneaux made some. But James Short, of Edinburgh, made +many excellent Gregorian reflectors from 1732 till his death in 1768. + +Newton's trouble with refractors, chromatic aberration, remained +insurmountable until John Dollond (born 1706, died 1761), after many +experiments, found out how to make an achromatic lens out of two +lenses--one of crown glass, the other of flint glass--to destroy the +colour, in a way originally suggested by Euler. He soon acquired a +great reputation for his telescopes of moderate size; but there was a +difficulty in making flint-glass lenses of large size. The first +actual inventor and constructor of an achromatic telescope was Chester +Moor Hall, who was not in trade, and did not patent it. Towards the +close of the eighteenth century a Swiss named Guinand at last +succeeded in producing larger flint-glass discs free from +striae. Frauenhofer, of Munich, took him up in 1805, and soon +produced, among others, Struve's Dorpat refractor of 9.9 inches +diameter and 13.5 feet focal length, and another, of 12 inches +diameter and 18 feet focal length, for Lamont, of Munich. + +In the nineteenth century gigantic _reflectors_ have been +made. Lassel's 2-foot reflector, made by himself, did much good work, +and discovered four new satellites. But Lord Rosse's 6-foot +reflector, 54 feet focal length, constructed in 1845, is still the +largest ever made. The imperfections of our atmosphere are against +the use of such large apertures, unless it be on high mountains. +During the last half century excellent specula have been made of +silvered glass, and Dr. Common's 5-foot speculum (removed, since his +death, to Harvard) has done excellent work. Then there are the 5-foot +Yerkes reflector at Chicago, and the 4-foot by Grubb at Melbourne. + +Passing now from these large reflectors to refractors, further +improvements have been made in the manufacture of glass by Chance, of +Birmingham, Feil and Mantois, of Paris, and Schott, of Jena; while +specialists in grinding lenses, like Alvan Clark, of the U.S.A., and +others, have produced many large refractors. + +Cooke, of York, made an object-glass, 25-inch diameter, for Newall, of +Gateshead, which has done splendid work at Cambridge. We have the +Washington 26-inch by Clark, the Vienna 27-inch by Grubb, the Nice +29½-inch by Gautier, the Pulkowa 30-inch by Clark. Then there was +the sensation of Clark's 36-inch for the Lick Observatory in +California, and finally his _tour de force_, the Yerkes 40-inch +refractor, for Chicago. + +At Greenwich there is the 28-inch photographic refractor, and the +Thompson equatoreal by Grubb, carrying both the 26-inch photographic +refractor and the 30-inch reflector. At the Cape of Good Hope we find +Mr. Frank McClean's 24-inch refractor, with an object-glass prism for +spectroscopic work. + +It would be out of place to describe here the practical adjuncts of a +modern equatoreal--the adjustments for pointing it, the clock for +driving it, the position-micrometer and various eye-pieces, the +photographic and spectroscopic attachments, the revolving domes, +observing seats, and rising floors and different forms of mounting, +the siderostats and coelostats, and other convenient adjuncts, besides +the registering chronograph and numerous facilities for aiding +observation. On each of these a chapter might be written; but the +most important part of the whole outfit is the man behind the +telescope, and it is with him that a history is more especially +concerned. + + +SPECTROSCOPE. + +Since the invention of the telescope no discovery has given so great +an impetus to astronomical physics as the spectroscope; and in giving +us information about the systems of stars and their proper motions it +rivals the telescope. + +Frauenhofer, at the beginning of the nineteenth century, while +applying Dollond's discovery to make large achromatic telescopes, +studied the dispersion of light by a prism. Admitting the light of the +sun through a narrow slit in a window-shutter, an inverted image of +the slit can be thrown, by a lens of suitable focal length, on the +wall opposite. If a wedge or prism of glass be interposed, the image +is deflected to one side; but, as Newton had shown, the images formed +by the different colours of which white light is composed are +deflected to different extents--the violet most, the red least. The +number of colours forming images is so numerous as to form a +continuous spectrum on the wall with all the colours--red, orange, +yellow, green, blue, indigo, and violet. But Frauenhofer found with a +narrow slit, well focussed by the lens, that some colours were missing +in the white light of the sun, and these were shown by dark lines +across the spectrum. These are the Frauenhofer lines, some of which +he named by the letters of the alphabet. The D line is a very marked +one in the yellow. These dark lines in the solar spectrum had already +been observed by Wollaston. [3] + +On examining artificial lights it was found that incandescent solids +and liquids (including the carbon glowing in a white gas flame) give +continuous spectra; gases, except under enormous pressure, give bright +lines. If sodium or common salt be thrown on the colourless flame of a +spirit lamp, it gives it a yellow colour, and its spectrum is a bright +yellow line agreeing in position with line D of the solar spectrum. + +In 1832 Sir David Brewster found some of the solar black lines +increased in strength towards sunset, and attributed them to +absorption in the earth's atmosphere. He suggested that the others +were due to absorption in the sun's atmosphere. Thereupon Professor +J. D. Forbes pointed out that during a nearly total eclipse the lines +ought to be strengthened in the same way; as that part of the sun's +light, coming from its edge, passes through a great distance in the +sun's atmosphere. He tried this with the annular eclipse of 1836, +with a negative result which has never been accounted for, and which +seemed to condemn Brewster's view. + +In 1859 Kirchoff, on repeating Frauenhofer's experiment, found that, +if a spirit lamp with salt in the flame were placed in the path of the +light, the black D line is intensified. He also found that, if he used +a limelight instead of the sunlight and passed it through the flame +with salt, the spectrum showed the D line black; or the vapour of +sodium absorbs the same light that it radiates. This proved to him the +existence of sodium in the sun's atmosphere.[4] Iron, calcium, and +other elements were soon detected in the same way. + +Extensive laboratory researches (still incomplete) have been carried +out to catalogue (according to their wave-length on the undulatory +theory of light) all the lines of each chemical element, under all +conditions of temperature and pressure. At the same time, all the +lines have been catalogued in the light of the sun and the brighter of +the stars. + +Another method of obtaining spectra had long been known, by +transmission through, or reflection from, a grating of equidistant +lines ruled upon glass or metal. H. A. Rowland developed the art of +constructing these gratings, which requires great technical skill, and +for this astronomers owe him a debt of gratitude. + +In 1842 Doppler[5] proved that the colour of a luminous body, like the +pitch or note of a sounding body, must be changed by velocity of +approach or recession. Everyone has noticed on a railway that, on +meeting a locomotive whistling, the note is lowered after the engine +has passed. The pitch of a sound or the colour of a light depends on +the number of waves striking the ear or eye in a second. This number +is increased by approach and lowered by recession. + +Thus, by comparing the spectrum of a star alongside a spectrum of +hydrogen, we may see all the lines, and be sure that there is hydrogen +in the star; yet the lines in the star-spectrum may be all slightly +displaced to one side of the lines of the comparison spectrum. If +towards the violet end, it means mutual approach of the star and +earth; if to the red end, it means recession. The displacement of +lines does not tell us whether the motion is in the star, the earth, +or both. The displacement of the lines being measured, we can +calculate the rate of approach or recession in miles per second. + +In 1868 Huggins[6] succeeded in thus measuring the velocities of stars +in the direction of the line of sight. + +In 1873 Vogel[7] compared the spectra of the sun's East (approaching) +limb and West (receding) limb, and the displacement of lines endorsed +the theory. This last observation was suggested by Zöllner. + + +FOOTNOTES: + +[1] In the _Encyclopaedia Britannica_, article "Telescope," and in +Grant's _Physical Astronomy_, good reasons are given for awarding the +honour to Lipperhey. + +[2] Will the indulgent reader excuse an anecdote which may encourage +some workers who may have found their mathematics defective through +want of use? James Gregory's nephew David had a heap of MS. notes by +Newton. These descended to a Miss Gregory, of Edinburgh, who handed +them to the present writer, when an undergraduate at Cambridge, to +examine. After perusal, he lent them to his kindest of friends, +J. C. Adams (the discoverer of Neptune), for his opinion. Adams's +final verdict was: "I fear they are of no value. It is pretty evident +that, when he wrote these notes, _Newton's mathematics were a little +rusty_." + +[3] _R. S. Phil. Trans_. + +[4] The experiment had been made before by one who did not understand +its meaning;. But Sir George G. Stokes had already given verbally the +true explanation of Frauenhofer lines. + +[5] _Abh. d. Kön. Böhm. d. Wiss_., Bd. ii., 1841-42, p. 467. See +also Fizeau in the _Ann. de Chem. et de Phys_., 1870, p. 211. + +[6] _R. S. Phil. Trans_., 1868. + +[7] _Ast. Nach_., No. 1, 864. + + + + +BOOK IV. THE PHYSICAL PERIOD + + +We have seen how the theory of the solar system was slowly developed +by the constant efforts of the human mind to find out what are the +rules of cause and effect by which our conception of the present +universe and its development seems to be bound. In the primitive ages +a mere record of events in the heavens and on the earth gave the only +hope of detecting those uniform sequences from which to derive rules +or laws of cause and effect upon which to rely. Then came the +geometrical age, in which rules were sought by which to predict the +movements of heavenly bodies. Later, when the relation of the sun to +the courses of the planets was established, the sun came to be looked +upon as a cause; and finally, early in the seventeenth century, for +the first time in history, it began to be recognised that the laws of +dynamics, exactly as they had been established for our own terrestrial +world, hold good, with the same rigid invariability, at least as far +as the limits of the solar system. + +Throughout this evolution of thought and conjecture there were two +types of astronomers--those who supplied the facts, and those who +supplied the interpretation through the logic of mathematics. So +Ptolemy was dependent upon Hipparchus, Kepler on Tycho Brahe, and +Newton in much of his work upon Flamsteed. + +When Galileo directed his telescope to the heavens, when Secchi and +Huggins studied the chemistry of the stars by means of the +spectroscope, and when Warren De la Rue set up a photoheliograph at +Kew, we see that a progress in the same direction as before, in the +evolution of our conception of the universe, was being made. Without +definite expression at any particular date, it came to be an accepted +fact that not only do earthly dynamics apply to the heavenly bodies, +but that the laws we find established here, in geology, in chemistry, +and in the laws of heat, may be extended with confidence to the +heavenly bodies. Hence arose the branch of astronomy called +astronomical physics, a science which claims a large portion of the +work of the telescope, spectroscope, and photography. In this new +development it is more than ever essential to follow the dictum of +Tycho Brahe--not to make theories until all the necessary facts are +obtained. The great astronomers of to-day still hold to Sir Isaac +Newton's declaration, "Hypotheses non fingo." Each one may have his +suspicions of a theory to guide him in a course of observation, and +may call it a working hypothesis. But the cautious astronomer does +not proclaim these to the world; and the historian is certainly not +justified in including in his record those vague speculations founded +on incomplete data which may be demolished to-morrow, and which, +however attractive they may be, often do more harm than good to the +progress of true science. Meanwhile the accumulation of facts has +been prodigious, and the revelations of the telescope and spectroscope +entrancing. + + + +12. THE SUN. + + +One of Galileo's most striking discoveries, when he pointed his +telescope to the heavenly bodies, was that of the irregularly shaped +spots on the sun, with the dark central _umbra_ and the less +dark, but more extensive, _penumbra_ surrounding it, sometimes +with several umbrae in one penumbra. He has left us many drawings of +these spots, and he fixed their period of rotation as a lunar month. + +[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° on each side of the equator, and that a +zone of equatoreal calms is free from spots. But it was +R. C. Carrington[4] who, by his continuous observations at Redhill, in +Surrey, established the remarkable fact that, while the rotation +period in the highest latitudes, 50°, where spots are seen, is +twenty-seven-and-a-half days, near the equator the period is only +twenty-five days. His splendid volume of observations of the sun led +to much new information about the average distribution of spots at +different epochs. + +Schwabe, of Dessau, began in 1826 to study the solar surface, and, +after many years of work, arrived at a law of frequency which has been +more fruitful of results than any discovery in solar physics.[5] In +1843 he announced a decennial period of maxima and minima of sun-spot +displays. In 1851 it was generally accepted, and, although a period of +eleven years has been found to be more exact, all later observations, +besides the earlier ones which have been hunted up for the purpose, go +to establish a true periodicity in the number of sun-spots. But quite +lately Schuster[6] has given reasons for admitting a number of +co-existent periods, of which the eleven-year period was predominant +in the nineteenth century. + +In 1851 Lament, a Scotchman at Munich, found a decennial period in the +daily range of magnetic declination. In 1852 Sir Edward Sabine +announced a similar period in the number of "magnetic storms" +affecting all of the three magnetic elements--declination, dip, and +intensity. Australian and Canadian observations both showed the +decennial period in all three elements. Wolf, of Zurich, and Gauthier, +of Geneva, each independently arrived at the same conclusion. + +It took many years before this coincidence was accepted as certainly +more than an accident by the old-fashioned astronomers, who want rigid +proof for every new theory. But the last doubts have long vanished, +and a connection has been further traced between violent outbursts of +solar activity and simultaneous magnetic storms. + +The frequency of the Aurora Borealis was found by Wolf to follow the +same period. In fact, it is closely allied in its cause to terrestrial +magnetism. Wolf also collected old observations tracing the +periodicity of sun-spots back to about 1700 A.D. + +Spoerer deduced a law of dependence of the average latitude of +sun-spots on the phase of the sun-spot period. + +All modern total solar eclipse observations seem to show that the +shape of the luminous corona surrounding the moon at the moment of +totality has a special distinct character during the time of a +sun-spot maximum, and another, totally different, during a sun-spot +minimum. + +A suspicion is entertained that the total quantity of heat received by +the earth from the sun is subject to the same period. This would have +far-reaching effects on storms, harvests, vintages, floods, and +droughts; but it is not safe to draw conclusions of this kind except +from a very long period of observations. + +Solar photography has deprived astronomers of the type of Carrington +of the delight in devoting a life's work to collecting data. It has +now become part of the routine work of an observatory. + +In 1845 Foucault and Fizeau took a daguerreotype photograph of the +sun. In 1850 Bond produced one of the moon of great beauty, Draper +having made some attempts at an even earlier date. But astronomical +photography really owes its beginning to De la Rue, who used the +collodion process for the moon in 1853, and constructed the Kew +photoheliograph in 1857, from which date these instruments have been +multiplied, and have given us an accurate record of the sun's surface. +Gelatine dry plates were first used by Huggins in 1876. + +It is noteworthy that from the outset De la Rue recognised the value +of stereoscopic vision, which is now known to be of supreme +accuracy. In 1853 he combined pairs of photographs of the moon in the +same phase, but under different conditions regarding libration, +showing the moon from slightly different points of view. These in the +stereoscope exhibited all the relief resulting from binocular vision, +and looked like a solid globe. In 1860 he used successive photographs +of the total solar eclipse stereoscopically, to prove that the red +prominences belong to the sun, and not to the moon. In 1861 he +similarly combined two photographs of a sun-spot, the perspective +effect showing the umbra like a floor at the bottom of a hollow +penumbra; and in one case the faculæ were discovered to be sailing +over a spot apparently at some considerable height. These appearances +may be partly due to a proper motion; but, so far as it went, this was +a beautiful confirmation of Wilson's discovery. Hewlett, however, in +1894, after thirty years of work, showed that the spots are not always +depressions, being very subject to disturbance. + +The Kew photographs [7] contributed a vast amount of information about +sun-spots, and they showed that the faculæ generally follow the spots +in their rotation round the sun. + +The constitution of the sun's photosphere, the layer which is the +principal light-source on the sun, has always been a subject of great +interest; and much was done by men with exceptionally keen eyesight, +like Mr. Dawes. But it was a difficult subject, owing to the rapidity +of the changes in appearance of the so-called rice-grains, about 1" in +diameter. The rapid transformations and circulations of these +rice-grains, if thoroughly studied, might lead to a much better +knowledge of solar physics. This seemed almost hopeless, as it was +found impossible to identify any "rice-grain" in the turmoil after a +few minutes. But M. Hansky, of Pulkowa (whose recent death is +deplored), introduced successfully a scheme of photography, which +might almost be called a solar cinematograph. He took photographs of +the sun at intervals of fifteen or thirty seconds, and then enlarged +selected portions of these two hundred times, giving a picture +corresponding to a solar disc of six metres diameter. In these +enlarged pictures he was able to trace the movements, and changes of +shape and brightness, of individual rice-grains. Some granules become +larger or smaller. Some seem to rise out of a mist, as it were, and to +become clearer. Others grow feebler. Some are split in two. Some are +rotated through a right angle in a minute or less, although each of +the grains may be the size of Great Britain. Generally they move +together in groups of very various velocities, up to forty kilometres +a second. These movements seem to have definite relation to any +sun-spots in the neighbourhood. From the results already obtained it +seems certain that, if this method of observation be continued, it +cannot fail to supply facts of the greatest importance. + +It is quite impossible to do justice here to the work of all those who +are engaged on astronomical physics. The utmost that can be attempted +is to give a fair idea of the directions of human thought and +endeavour. During the last half-century America has made splendid +progress, and an entirely new process of studying the photosphere has +been independently perfected by Professor Hale at Chicago, and +Deslandres at Paris.[8] They have succeeded in photographing the sun's +surface in monochromatic light, such as the light given off as one of +the bright lines of hydrogen or of calcium, by means of the +"Spectroheliograph." The spectroscope is placed with its slit in the +focus of an equatoreal telescope, pointed to the sun, so that the +circular image of the sun falls on the slit. At the other end of the +spectroscope is the photographic plate. Just in front of this plate +there is another slit parallel to the first, in the position where the +image of the first slit formed by the K line of calcium falls. Thus is +obtained a photograph of the section of the sun, made by the first +slit, only in K light. As the image of the sun passes over the first +slit the photographic plate is moved at the same rate and in the same +direction behind the second slit; and as successive sections of the +sun's image in the equatoreal enter the apparatus, so are these +sections successively thrown in their proper place on the photographic +plate, always in K light. By using a high dispersion the faculæ which +give off K light can be correctly photographed, not only at the sun's +edge, but all over his surface. The actual mechanical method of +carrying out the observation is not quite so simple as what is here +described. + +By choosing another line of the spectrum instead of calcium K--for +example, the hydrogen line H₍₃₎--we obtain two photographs, one +showing the appearance of the calcium floculi, and the other of the +hydrogen floculi, on the same part of the solar surface; and nothing +is more astonishing than to note the total want of resemblance in the +forms shown on the two. This mode of research promises to afford many +new and useful data. + +The spectroscope has revealed the fact that, broadly speaking, the sun +is composed of the same materials as the earth. Ångstrom was the first +to map out all of the lines to be found in the solar spectrum. But +Rowland, of Baltimore, after having perfected the art of making true +gratings with equidistant lines ruled on metal for producing spectra, +then proceeded to make a map of the solar spectrum on a large scale. + +In 1866 Lockyer[9] threw an image of the sun upon the slit of a +spectroscope, and was thus enabled to compare the spectrum of a spot +with that of the general solar surface. The observation proved the +darkness of a spot to be caused by increased absorption of light, not +only in the dark lines, which are widened, but over the entire +spectrum. In 1883 Young resolved this continuous obscurity into an +infinite number of fine lines, which have all been traced in a shadowy +way on to the general solar surface. Lockyer also detected +displacements of the spectrum lines in the spots, such as would be +produced by a rapid motion in the line of sight. It has been found +that both uprushes and downrushes occur, but there is no marked +predominance of either in a sun-spot. The velocity of motion thus +indicated in the line of sight sometimes appears to amount to 320 +miles a second. But it must be remembered that pressure of a gas has +some effect in displacing the spectral lines. So we must go on, +collecting data, until a time comes when the meaning of all the facts +can be made clear. + +_Total Solar Eclipses_.--During total solar eclipses the time is so +short, and the circumstances so impressive, that drawings of the +appearance could not always be trusted. The red prominences of jagged +form that are seen round the moon's edge, and the corona with its +streamers radiating or interlacing, have much detail that can hardly +be recorded in a sketch. By the aid of photography a number of records +can be taken during the progress of totality. From a study of these +the extent of the corona is demonstrated in one case to extend to at +least six diameters of the moon, though the eye has traced it +farther. This corona is still one of the wonders of astronomy, and +leads to many questions. What is its consistency, if it extends many +million miles from the sun's surface? How is it that it opposed no +resistance to the motion of comets which have almost grazed the sun's +surface? Is this the origin of the zodiacal light? The character of +the corona in photographic records has been shown to depend upon the +phase of the sun-spot period. During the sun-spot maximum the corona +seems most developed over the spot-zones--i.e., neither at the +equator nor the poles. The four great sheaves of light give it a +square appearance, and are made up of rays or plumes, delicate like +the petals of a flower. During a minimum the nebulous ring seems to +be made of tufts of fine hairs with aigrettes or radiations from both +poles, and streamers from the equator. + +[Illustration: SOLAR ECLIPSE, 1882. From drawing by W. H. Wesley, +Secretary R.A.S.; showing the prominences, the corona, and an unknown +comet.] + + +On September 19th, 1868, eclipse spectroscopy began with the Indian +eclipse, in which all observers found that the red prominences showed +a bright line spectrum, indicating the presence of hydrogen and other +gases. So bright was it that Jansen exclaimed: "_Je verrai ces +lignes-là en dehors des éclipses_." And the next day he observed the +lines at the edge of the uneclipsed sun. Huggins had suggested this +observation in February, 1868, his idea being to use prisms of such +great dispersive power that the continuous spectrum reflected by our +atmosphere should be greatly weakened, while a bright line would +suffer no diminution by the high dispersion. On October 20th +Lockyer,[10] having news of the eclipse, but not of Jansen's +observations the day after, was able to see these lines. This was a +splendid performance, for it enabled the prominences to be observed, +not only during eclipses, but every day. Moreover, the next year +Huggins was able, by using a wide slit, to see the whole of a +prominence and note its shape. Prominences are classified, according +to their form, into "flame" and "cloud" prominences, the spectrum of +the latter showing calcium, hydrogen, and helium; that of the former +including a number of metals. + +The D line of sodium is a double line, and in the same eclipse (1868) +an orange line was noticed which was afterwards found to lie close to +the two components of the D line. It did not correspond with any known +terrestrial element, and the unknown element was called "helium." It +was not until 1895 that Sir William Ramsay found this element as a gas +in the mineral cleavite. + +The spectrum of the corona is partly continuous, indicating light +reflected from the sun's body. But it also shows a green line +corresponding with no known terrestrial element, and the name +"coronium" has been given to the substance causing it. + +A vast number of facts have been added to our knowledge about the sun +by photography and the spectroscope. Speculations and hypotheses in +plenty have been offered, but it may be long before we have a complete +theory evolved to explain all the phenomena of the storm-swept +metallic atmosphere of the sun. + +The proceedings of scientific societies teem with such facts and +"working hypotheses," and the best of them have been collected by Miss +Clerke in her _History of Astronomy during the Nineteenth Century_. As +to established facts, we learn from the spectroscopic researches (1) +that the continuous spectrum is derived from the _photosphere_ or +solar gaseous material compressed almost to liquid consistency; (2) +that the _reversing layer_ surrounds it and gives rise to black +lines in the spectrum; that the _chromosphere_ surrounds this, is +composed mainly of hydrogen, and is the cause of the red prominences +in eclipses; and that the gaseous _corona_ surrounds all of +these, and extends to vast distances outside the sun's visible +surface. + + +FOOTNOTES: + +[1] _Rosa Ursina_, by C. Scheiner, _fol_.; Bracciani, 1630. + +[2] _R. S. Phil. Trans_., 1774. + +[3] _Ibid_, 1783. + +[4] _Observations on the Spots on the Sun, etc.,_ 4°; London and +Edinburgh, 1863. + +[5] _Periodicität der Sonnenflecken. Astron. Nach. XXI._, 1844, +P. 234. + +[6] _R.S. Phil. Trans._ (ser. A), 1906, p. 69-100. + +[7] "Researches on Solar Physics," by De la Rue, Stewart and Loewy; +_R. S. Phil. Trans_., 1869, 1870. + +[8] "The Sun as Photographed on the K line"; _Knowledge_, London, +1903, p. 229. + +[9] _R. S. Proc._, xv., 1867, p. 256. + +[10] _Acad. des Sc._, Paris; _C. R._, lxvii., 1868, p. 121. + + + +13. THE MOON AND PLANETS. + + +_The Moon_.--Telescopic discoveries about the moon commence with +Galileo's discovery that her surface has mountains and valleys, like +the earth. He also found that, while she always turns the same face to +us, there is periodically a slight twist to let us see a little round +the eastern or western edge. This was called _libration_, and the +explanation was clear when it was understood that in showing always +the same face to us she makes one revolution a month on her axis +_uniformly_, and that her revolution round the earth is not +uniform. + +Galileo said that the mountains on the moon showed greater differences +of level than those on the earth. Shröter supported this +opinion. W. Herschel opposed it. But Beer and Mädler measured the +heights of lunar mountains by their shadows, and found four of them +over 20,000 feet above the surrounding plains. + +Langrenus [1] was the first to do serious work on selenography, and +named the lunar features after eminent men. Riccioli also made lunar +charts. In 1692 Cassini made a chart of the full moon. Since then we +have the charts of Schröter, Beer and Mädler (1837), and of Schmidt, +of Athens (1878); and, above all, the photographic atlas by Loewy and +Puiseux. + +The details of the moon's surface require for their discussion a whole +book, like that of Neison or the one by Nasmyth and Carpenter. Here a +few words must suffice. Mountain ranges like our Andes or Himalayas +are rare. Instead of that, we see an immense number of circular +cavities, with rugged edges and flat interior, often with a cone in +the centre, reminding one of instantaneous photographs of the splash +of a drop of water falling into a pool. Many of these are fifty or +sixty miles across, some more. They are generally spoken of as +resembling craters of volcanoes, active or extinct, on the earth. But +some of those who have most fully studied the shapes of craters deny +altogether their resemblance to the circular objects on the moon. +These so-called craters, in many parts, are seen to be closely +grouped, especially in the snow-white parts of the moon. But there are +great smooth dark spaces, like the clear black ice on a pond, more +free from craters, to which the equally inappropriate name of seas has +been given. The most conspicuous crater, _Tycho_, is near the south +pole. At full moon there are seen to radiate from Tycho numerous +streaks of light, or "rays," cutting through all the mountain +formations, and extending over fully half the lunar disc, like the +star-shaped cracks made on a sheet of ice by a blow. Similar cracks +radiate from other large craters. It must be mentioned that these +white rays are well seen only in full light of the sun at full moon, +just as the white snow in the crevasses of a glacier is seen bright +from a distance only when the sun is high, and disappears at +sunset. Then there are deep, narrow, crooked "rills" which may have +been water-courses; also "clefts" about half a mile wide, and often +hundreds of miles long, like deep cracks in the surface going straight +through mountain and valley. + +The moon shares with the sun the advantage of being a good subject for +photography, though the planets are not. This is owing to her larger +apparent size, and the abundance of illumination. The consequence is +that the finest details of the moon, as seen in the largest telescope +in the world, may be reproduced at a cost within the reach of all. + +No certain changes have ever been observed; but several suspicions +have been expressed, especially as to the small crater _Linné_, in the +_Mare Serenitatis_. It is now generally agreed that no certainty can +be expected from drawings, and that for real evidence we must await +the verdict of photography. + +No trace of water or of an atmosphere has been found on the moon. It +is possible that the temperature is too low. In any case, no +displacement of a star by atmospheric refraction at occultation has +been surely recorded. The moon seems to be dead. + +The distance of the moon from the earth is just now the subject of +re-measurement. The base line is from Greenwich to Cape of Good Hope, +and the new feature introduced is the selection of a definite point on +a crater (Mösting A), instead of the moon's edge, as the point whose +distance is to be measured. + +_The Inferior Planets_.--When the telescope was invented, the phases +of Venus attracted much attention; but the brightness of this planet, +and her proximity to the sun, as with Mercury also, seemed to be a bar +to the discovery of markings by which the axis and period of rotation +could be fixed. Cassini gave the rotation as twenty-three hours, by +observing a bright spot on her surface. Shröter made it 23h. 21m. 19s. +This value was supported by others. In 1890 Schiaparelli[2] announced +that Venus rotates, like our moon, once in one of her revolutions, and +always directs the same face to the sun. This property has also been +ascribed to Mercury; but in neither case has the evidence been +generally accepted. Twenty-four hours is probably about the period of +rotation for each of these planets. + +Several observers have claimed to have seen a planet within the orbit +of Mercury, either in transit over the sun's surface or during an +eclipse. It has even been named _Vulcan_. These announcements would +have received little attention but for the fact that the motion of +Mercury has irregularities which have not been accounted for by known +planets; and Le Verrier[3] has stated that an intra-Mercurial planet +or ring of asteroids would account for the unexplained part of the +motion of the line of apses of Mercury's orbit amounting to 38" per +century. + +_Mars_.--The first study of the appearance of Mars by Miraldi led him +to believe that there were changes proceeding in the two white caps +which are seen at the planet's poles. W. Herschel attributed these +caps to ice and snow, and the dates of his observations indicated a +melting of these ice-caps in the Martian summer. + +Schröter attributed the other markings on Mars to drifting clouds. But +Beer and Mädler, in 1830-39, identified the same dark spots as being +always in the same place, though sometimes blurred by mist in the +local winter. A spot sketched by Huyghens in 1672, one frequently seen +by W. Herschel in 1783, another by Arago in 1813, and nearly all the +markings recorded by Beer and Mädler in 1830, were seen and drawn by +F. Kaiser in Leyden during seventeen nights of the opposition of 1862 +(_Ast. Nacht._, No. 1,468), whence he deduced the period of rotation +to be 24h. 37m. 22s.,62--or one-tenth of a second less than the period +deduced by R. A. Proctor from a drawing by Hooke in 1666. + +It must be noted that, if the periods of rotation both of Mercury and +Venus be about twenty-four hours, as seems probable, all the four +planets nearest to the sun rotate in the same period, while the great +planets rotate in about ten hours (Uranus and Neptune being still +indeterminate). + +The general surface of Mars is a deep yellow; but there are dark grey +or greenish patches. Sir John Herschel was the first to attribute the +ruddy colour of Mars to its soil rather than to its atmosphere. + +The observations of that keen-sighted observer Dawes led to the first +good map of Mars, in 1869. In the 1877 opposition Schiaparelli revived +interest in the planet by the discovery of canals, uniformly about +sixty miles wide, running generally on great circles, some of them +being three or four thousand miles long. During the opposition of +1881-2 the same observer re-observed the canals, and in twenty of them +he found the canals duplicated,[4] the second canal being always 200 +to 400 miles distant from its fellow. + +The existence of these canals has been doubted. Mr. Lowell has now +devoted years to the subject, has drawn them over and over again, and +has photographed them; and accepts the explanation that they are +artificial, and that vegetation grows on their banks. Thus is revived +the old controversy between Whewell and Brewster as to the +habitability of the planets. The new arguments are not yet generally +accepted. Lowell believes he has, with the spectroscope, proved the +existence of water on Mars. + +One of the most unexpected and interesting of all telescopic +discoveries took place in the opposition of 1877, when Mars was +unusually near to the earth. The Washington Observatory had acquired +the fine 26-inch refractor, and Asaph Hall searched for satellites, +concealing the planet's disc to avoid the glare. On August 11th he had +a suspicion of a satellite. This was confirmed on the 16th, and on the +following night a second one was added. They are exceedingly faint, +and can be seen only by the most powerful telescopes, and only at the +times of opposition. Their diameters are estimated at six or seven +miles. It was soon found that the first, Deimos, completes its orbit +in 30h. 18m. But the other, Phobos, at first was a puzzle, owing to +its incredible velocity being unsuspected. Later it was found that the +period of revolution was only 7h. 39m. 22s. Since the Martian day is +twenty-four and a half hours, this leads to remarkable results. +Obviously the easterly motion of the satellite overwhelms the diurnal +rotation of the planet, and Phobos must appear to the inhabitants, if +they exist, to rise in the west and set in the east, showing two or +even three full moons in a day, so that, sufficiently well for the +ordinary purposes of life, the hour of the day can be told by its +phases. + +The discovery of these two satellites is, perhaps, the most +interesting telescopic visual discovery made with the large telescopes +of the last half century; photography having been the means of +discovering all the other new satellites except Jupiter's fifth (in +order of discovery). + +[Illustration: JUPITER. From a drawing by E. M. Antoniadi, showing +transit of a satellite's shadow, the belts, and the "great red spot" +(_Monthly Notices_, R. A. S., vol. lix., pl. x.).] + +_Jupiter._--Galileo's discovery of Jupiter's satellites was followed +by the discovery of his belts. Zucchi and Torricelli seem to have seen +them. Fontana, in 1633, reported three belts. In 1648 Grimaldi saw but +two, and noticed that they lay parallel to the ecliptic. Dusky spots +were also noticed as transient. Hooke[5] measured the motion of one in +1664. In 1665 Cassini, with a fine telescope, 35-feet focal length, +observed many spots moving from east to west, whence he concluded that +Jupiter rotates on an axis like the earth. He watched an unusually +permanent spot during twenty-nine rotations, and fixed the period at +9h. 56m. Later he inferred that spots near the equator rotate quicker +than those in higher latitudes (the same as Carrington found for the +sun); and W. Herschel confirmed this in 1778-9. + +Jupiter's rapid rotation ought, according to Newton's theory, to be +accompanied by a great flattening at the poles. Cassini had noted an +oval form in 1691. This was confirmed by La Hire, Römer, and +Picard. Pound measured the ellipticity = 1/(13.25). + +W. Herschel supposed the spots to be masses of cloud in the +atmosphere--an opinion still accepted. Many of them were very +permanent. Cassini's great spot vanished and reappeared nine times +between 1665 and 1713. It was close to the northern margin of the +southern belt. Herschel supposed the belts to be the body of the +planet, and the lighter parts to be clouds confined to certain +latitudes. + +In 1665 Cassini observed transits of the four satellites, and also saw +their shadows on the planet, and worked out a lunar theory for +Jupiter. Mathematical astronomers have taken great interest in the +perturbations of the satellites, because their relative periods +introduce peculiar effects. Airy, in his delightful book, +_Gravitation_, has reduced these investigations to simple +geometrical explanations. + +In 1707 and 1713 Miraldi noticed that the fourth satellite varies much +in brightness. W. Herschel found this variation to depend upon its +position in its orbit, and concluded that in the positions of +feebleness it is always presenting to us a portion of its surface, +which does not well reflect the sun's light; proving that it always +turns the same face to Jupiter, as is the case with our moon. This +fact had also been established for Saturn's fifth satellite, and may +be true for all satellites. + +In 1826 Struve measured the diameters of the four satellites, and +found them to be 2,429, 2,180, 3,561, and 3,046 miles. + +In modern times much interest has been taken in watching a rival to +Cassini's famous spot. The "great red spot" was first observed by +Niesten, Pritchett, and Tempel, in 1878, as a rosy cloud attached to a +whitish zone beneath the dark southern equatorial band, shaped like +the new war balloons, 30,000 miles long and 7,000 miles across. The +next year it was brick-red. A white spot beside it completed a +rotation in less time by 5½ minutes than the red spot--a difference +of 260 miles an hour. Thus they came together again every six weeks, +but the motions did not continue uniform. The spot was feeble in +1882-4, brightened in 1886, and, after many changes, is still visible. + +Galileo's great discovery of Jupiter's four moons was the last word in +this connection until September 9th, 1892, when Barnard, using the +36-inch refractor of the Lick Observatory, detected a tiny spot of +light closely following the planet. This proved to be a new satellite +(fifth), nearer to the planet than any other, and revolving round it +in 11h. 57m. 23s. Between its rising and setting there must be an +interval of 2½ Jovian days, and two or three full moons. The sixth +and seventh satellites were found by the examination of photographic +plates at the Lick Observatory in 1905, since which time they have +been continuously photographed, and their orbits traced, at Greenwich. +On examining these plates in 1908 Mr. Melotte detected the eighth +satellite, which seems to be revolving in a retrograde orbit three +times as far from its planet as the next one (seventh), in these two +points agreeing with the outermost of Saturn's satellites (Phoebe). + +_Saturn._--This planet, with its marvellous ring, was perhaps the most +wonderful object of those first examined by Galileo's telescope. He +was followed by Dominique Cassini, who detected bands like Jupiter's +belts. Herschel established the rotation of the planet in 1775-94. +From observations during one hundred rotations he found the period to +be 10h. 16m. 0s., 44. Herschel also measured the ratio of the polar to +the equatoreal diameter as 10:11. + +The ring was a complete puzzle to Galileo, most of all when the planet +reached a position where the plane of the ring was in line with the +earth, and the ring disappeared (December 4th, 1612). It was not until +1656 that Huyghens, in his small pamphlet _De Saturni Luna Observatio +Nova_, was able to suggest in a cypher the ring form; and in 1659, in +his Systema Saturnium, he gave his reasons and translated the cypher: +"The planet is surrounded by a slender flat ring, everywhere distinct +from its surface, and inclined to the ecliptic." This theory explained +all the phases of the ring which had puzzled others. This ring was +then, and has remained ever since, a unique structure. We in this age +have got accustomed to it. But Huyghens's discovery was received with +amazement. + +In 1675 Cassini found the ring to be double, the concentric rings +being separated by a black band--a fact which was placed beyond +dispute by Herschel, who also found that the thickness of the ring +subtends an angle less than 0".3. Shröter estimated its thickness at +500 miles. + +Many speculations have been advanced to explain the origin and +constitution of the ring. De Sejour said [6] that it was thrown off +from Saturn's equator as a liquid ring, and afterwards solidified. He +noticed that the outside would have a greater velocity, and be less +attracted to the planet, than the inner parts, and that equilibrium +would be impossible; so he supposed it to have solidified into a +number of concentric rings, the exterior ones having the least +velocity. + +Clerk Maxwell, in the Adams prize essay, gave a physico-mathematical +demonstration that the rings must be composed of meteoritic matter +like gravel. Even so, there must be collisions absorbing the energy of +rotation, and tending to make the rings eventually fall into the +planet. The slower motion of the external parts has been proved by the +spectroscope in Keeler's hands, 1895. + +Saturn has perhaps received more than its share of attention owing to +these rings. This led to other discoveries. Huyghens in 1655, and +J. D. Cassini in 1671, discovered the sixth and eighth satellites +(Titan and Japetus). Cassini lost his satellite, and in searching for +it found Rhea (the fifth) in 1672, besides his old friend, whom he +lost again. He added the third and fourth in 1684 (Tethys and +Dione). The first and second (Mimas and Encelades) were added by +Herschel in 1789, and the seventh (Hyperion) simultaneously by Lassel +and Bond in 1848. The ninth (Phoebe) was found on photographs, by +Pickering in 1898, with retrograde motion; and he has lately added a +tenth. + +The occasional disappearance of Cassini's Japetus was found on +investigation to be due to the same causes as that of Jupiter's fourth +satellite, and proves that it always turns the same face to the +planet. + +_Uranus and Neptune_.--The splendid discoveries of Uranus and two +satellites by Sir William Herschel in 1787, and of Neptune by Adams +and Le Verrier in 1846, have been already described. Lassel added two +more satellites to Uranus in 1851, and found Neptune's satellite in +1846. All of the satellites of Uranus have retrograde motion, and +their orbits are inclined about 80° to the ecliptic. + +The spectroscope has shown the existence of an absorbing atmosphere on +Jupiter and Saturn, and there are suspicions that they partake +something of the character of the sun, and emit some light besides +reflecting solar light. On both planets some absorption lines seem to +agree with the aqueous vapour lines of our own atmosphere; while one, +which is a strong band in the red common to both planets, seems to +agree with a line in the spectrum of some reddish stars. + +Uranus and Neptune are difficult to observe spectroscopically, but +appear to have peculiar spectra agreeing together. Sometimes Uranus +shows Frauenhofer lines, indicating reflected solar light. But +generally these are not seen, and six broad bands of absorption +appear. One is the F. of hydrogen; another is the red-star line of +Jupiter and Saturn. Neptune is a very difficult object for the +spectroscope. + +Quite lately [7] P. Lowell has announced that V. M. Slipher, at +Flagstaff Observatory, succeeded in 1907 in rendering some plates +sensitive far into the red. A reproduction is given of photographed +spectra of the four outermost planets, showing (1) a great number of +new lines and bands; (2) intensification of hydrogen F. and C. lines; +(3) a steady increase of effects (1) and (2) as we pass from Jupiter +and Saturn to Uranus, and a still greater increase in Neptune. + +_Asteroids_.--The discovery of these new planets has been +described. At the beginning of the last century it was an immense +triumph to catch a new one. Since photography was called into the +service by Wolf, they have been caught every year in shoals. It is +like the difference between sea fishing with the line and using a +steam trawler. In the 1908 almanacs nearly seven hundred asteroids are +included. The computation of their perturbations and ephemerides by +Euler's and Lagrange's method of variable elements became so laborious +that Encke devised a special process for these, which can be applied +to many other disturbed orbits. [8] + +When a photograph is taken of a region of the heavens including an +asteroid, the stars are photographed as points because the telescope +is made to follow their motion; but the asteroids, by their proper +motion, appear as short lines. + +The discovery of Eros and the photographic attack upon its path have +been described in their relation to finding the sun's distance. + +A group of four asteroids has lately been found, with a mean distance +and period equal to that of Jupiter. To three of these masculine names +have been given--Hector, Patroclus, Achilles; the other has not yet +been named. + + +FOOTNOTES: + +[1] Langrenus (van Langren), F. Selenographia sive lumina austriae +philippica; Bruxelles, 1645. + +[2] _Astr. Nach._, 2,944. + +[3] _Acad. des Sc._, Paris; _C.R._, lxxxiii., 1876. + +[4] _Mem. Spettr. Ital._, xi., p. 28. + +[5] _R. S. Phil. Trans_., No. 1. + +[6] Grant's _Hist. Ph. Ast_., p. 267. + +[7] _Nature_, November 12th, 1908. + +[8] _Ast. Nach_., Nos. 791, 792, 814, translated by G. B. Airy. +_Naut. Alm_., Appendix, 1856. + + + +14. COMETS AND METEORS. + + +Ever since Halley discovered that the comet of 1682 was a member of +the solar system, these wonderful objects have had a new interest for +astronomers; and a comparison of orbits has often identified the +return of a comet, and led to the detection of an elliptic orbit where +the difference from a parabola was imperceptible in the small portion +of the orbit visible to us. A remarkable case in point was the comet +of 1556, of whose identity with the comet of 1264 there could be +little doubt. Hind wanted to compute the orbit more exactly than +Halley had done. He knew that observations had been made, but they +were lost. Having expressed his desire for a search, all the +observations of Fabricius and of Heller, and also a map of the comet's +path among the stars, were eventually unearthed in the most unlikely +manner, after being lost nearly three hundred years. Hind and others +were certain that this comet would return between 1844 and 1848, but +it never appeared. + +When the spectroscope was first applied to finding the composition of +the heavenly bodies, there was a great desire to find out what comets +are made of. The first opportunity came in 1864, when Donati observed +the spectrum of a comet, and saw three bright bands, thus proving that +it was a gas and at least partly self-luminous. In 1868 Huggins +compared the spectrum of Winnecke's comet with that of a Geissler tube +containing olefiant gas, and found exact agreement. Nearly all comets +have shown the same spectrum.[1] A very few comets have given bright +band spectra differing from the normal type. Also a certain kind of +continuous spectrum, as well as reflected solar light showing +Frauenhofer lines, have been seen. + +[Illustration: COPY OF THE DRAWING MADE BY PAUL FABRICIUS. To define +the path of comet 1556. After being lost for 300 years, this drawing +was recovered by the prolonged efforts of Mr. Hind and Professor +Littrow in 1856.] + +When Wells's comet, in 1882, approached very close indeed to the sun, +the spectrum changed to a mono-chromatic yellow colour, due to sodium. + +For a full account of the wonders of the cometary world the reader is +referred to books on descriptive astronomy, or to monographs on +comets.[2] Nor can the very uncertain speculations about the structure +of comets' tails be given here. A new explanation has been proposed +almost every time that a great discovery has been made in the theory +of light, heat, chemistry, or electricity. + +Halley's comet remained the only one of which a prediction of the +return had been confirmed, until the orbit of the small, ill-defined +comet found by Pons in 1819 was computed by Encke, and found to have a +period of 3⅓ years. It was predicted to return in 1822, and was +recognised by him as identical with many previous comets. This comet, +called after Encke, has showed in each of its returns an inexplicable +reduction of mean distance, which led to the assertion of a resisting +medium in space until a better explanation could be found.[3] + +Since that date fourteen comets have been found with elliptic orbits, +whose aphelion distances are all about the same as Jupiter's mean +distance; and six have an aphelion distance about ten per cent, +greater than Neptune's mean distance. Other comets are similarly +associated with the planets Saturn and Uranus. + +The physical transformations of comets are among the most wonderful of +unexplained phenomena in the heavens. But, for physical astronomers, +the greatest interest attaches to the reduction of radius vector of +Encke's comet, the splitting of Biela's comet into two comets in 1846, +and the somewhat similar behaviour of other comets. It must be noted, +however, that comets have a sensible size, that all their parts cannot +travel in exactly the same orbit under the sun's gravitation, and that +their mass is not sufficient to retain the parts together very +forcibly; also that the inevitable collision of particles, or else +fluid friction, is absorbing energy, and so reducing the comet's +velocity. + +In 1770 Lexell discovered a comet which, as was afterwards proved by +investigations of Lexell, Burchardt, and Laplace, had in 1767 been +deflected by Jupiter out of an orbit in which it was invisible from +the earth into an orbit with a period of 5½ years, enabling it to be +seen. In 1779 it again approached Jupiter closer than some of his +satellites, and was sent off in another orbit, never to be again +recognised. + +But our interest in cometary orbits has been added to by the discovery +that, owing to the causes just cited, a comet, if it does not separate +into discrete parts like Biela's, must in time have its parts spread +out so as to cover a sensible part of the orbit, and that, when the +earth passes through such part of a comet's orbit, a meteor shower is +the result. + +A magnificent meteor shower was seen in America on November 12th-13th, +1833, when the paths of the meteors all seemed to radiate from a point +in the constellation Leo. A similar display had been witnessed in +Mexico by Humboldt and Bonpland on November 12th, 1799. H. A. Newton +traced such records back to October 13th, A.D. 902. The orbital motion +of a cloud or stream of small particles was indicated. The period +favoured by H. A. Newton was 354½ days; another suggestion was 375½ +days, and another 33¼ years. He noticed that the advance of the date +of the shower between 902 and 1833, at the rate of one day in seventy +years, meant a progression of the node of the orbit. Adams undertook +to calculate what the amount would be on all the five suppositions +that had been made about the period. After a laborious work, he found +that none gave one day in seventy years except the 33¼-year period, +which did so exactly. H. A. Newton predicted a return of the shower on +the night of November 13th-14th, 1866. He is now dead; but many of us +are alive to recall the wonder and enthusiasm with which we saw this +prediction being fulfilled by the grandest display of meteors ever +seen by anyone now alive. + +The _progression_ of the nodes proved the path of the meteor +stream to be retrograde. The _radiant_ had almost the exact +longitude of the point towards which the earth was moving. This proved +that the meteor cluster was at perihelion. The period being known, the +eccentricity of the orbit was obtainable, also the orbital velocity of +the meteors in perihelion; and, by comparing this with the earth's +velocity, the latitude of the radiant enabled the inclination to be +determined, while the longitude of the earth that night was the +longitude of the node. In such a way Schiaparelli was able to find +first the elements of the orbit of the August meteor shower +(Perseids), and to show its identity with the orbit of Tuttle's comet +1862.iii. Then, in January 1867, Le Verrier gave the elements of the +November meteor shower (Leonids); and Peters, of Altona, identified +these with Oppolzer's elements for Tempel's comet 1866--Schiaparelli +having independently attained both of these results. Subsequently +Weiss, of Vienna, identified the meteor shower of April 20th (Lyrids) +with comet 1861. Finally, that indefatigable worker on meteors, +A. S. Herschel, added to the number, and in 1878 gave a list of +seventy-six coincidences between cometary and meteoric orbits. + +Cometary astronomy is now largely indebted to photography, not merely +for accurate delineations of shape, but actually for the discovery of +most of them. The art has also been applied to the observation of +comets at distances from their perihelia so great as to prevent their +visual observation. Thus has Wolf, of Heidelburg, found upon old +plates the position of comet 1905.v., as a star of the 15.5 magnitude, +783 days before the date of its discovery. From the point of view of +the importance of finding out the divergence of a cometary orbit from +a parabola, its period, and its aphelion distance, this increase of +range attains the very highest value. + +The present Astronomer Royal, appreciating this possibility, has been +searching by photography for Halley's comet since November, 1907, +although its perihelion passage will not take place until April, 1910. + + +FOOTNOTES: + +[1] In 1874, when the writer was crossing the Pacific Ocean in +H.M.S. "Scout," Coggia's comet unexpectedly appeared, and (while +Colonel Tupman got its positions with the sextant) he tried to use the +prism out of a portable direct-vision spectroscope, without success +until it was put in front of the object-glass of a binocular, when, to +his great joy, the three band images were clearly seen. + +[2] Such as _The World of Comets_, by A. Guillemin; _History of +Comets_, by G. R. Hind, London, 1859; _Theatrum Cometicum_, by S. de +Lubienietz, 1667; _Cometographie_, by Pingré, Paris, 1783; _Donati's +Comet_, by Bond. + +[3] The investigations by Von Asten (of St. Petersburg) seem to +support, and later ones, especially those by Backlund (also of +St. Petersburg), seem to discredit, the idea of a resisting medium. + + + +15. THE FIXED STARS AND NEBUL. + + +Passing now from our solar system, which appears to be subject to the +action of the same forces as those we experience on our globe, there +remains an innumerable host of fixed stars, nebulas, and nebulous +clusters of stars. To these the attention of astronomers has been more +earnestly directed since telescopes have been so much enlarged. +Photography also has enabled a vast amount of work to be covered in a +comparatively short period, and the spectroscope has given them the +means, not only of studying the chemistry of the heavens, but also of +detecting any motion in the line of sight from less than a mile a +second and upwards in any star, however distant, provided it be bright +enough. + +[Illustration: SIR WILLIAM HERSCHEL, F.R.S.--1738-1822. Painted by +Lemuel F. Abbott; National Portrait Gallery, Room XX.] + +In the field of telescopic discovery beyond our solar system there is +no one who has enlarged our knowledge so much as Sir William Herschel, +to whom we owe the greatest discovery in dynamical astronomy among the +stars--viz., that the law of gravitation extends to the most distant +stars, and that many of them describe elliptic orbits about each +other. W. Herschel was born at Hanover in 1738, came to England in +1758 as a trained musician, and died in 1822. He studied science when +he could, and hired a telescope, until he learnt to make his own +specula and telescopes. He made 430 parabolic specula in twenty-one +years. He discovered 2,500 nebulæ and 806 double stars, counted the +stars in 3,400 guage-fields, and compared the principal stars +photometrically. + +Some of the things for which he is best known were results of those +accidents that happen only to the indefatigable enthusiast. Such was +the discovery of Uranus, which led to funds being provided for +constructing his 40-feet telescope, after which, in 1786, he settled +at Slough. In the same way, while trying to detect the annual parallax +of the stars, he failed in that quest, but discovered binary systems +of stars revolving in ellipses round each other; just as Bradley's +attack on stellar parallax failed, but led to the discovery of +aberration, nutation, and the true velocity of light. + +_Parallax_.--The absence of stellar parallax was the great +objection to any theory of the earth's motion prior to Kepler's +time. It is true that Kepler's theory itself could have been +geometrically expressed equally well with the earth or any other point +fixed. But in Kepler's case the obviously implied physical theory of +the planetary motions, even before Newton explained the simplicity of +conception involved, made astronomers quite ready to waive the claim +for a rigid proof of the earth's motion by measurement of an annual +parallax of stars, which they had insisted on in respect of +Copernicus's revival of the idea of the earth's orbital motion. + +Still, the desire to measure this parallax was only intensified by the +practical certainty of its existence, and by repeated failures. The +attempts of Bradley failed. The attempts of Piazzi and Brinkley,[1] +early in the nineteenth century, also failed. The first successes, +afterwards confirmed, were by Bessel and Henderson. Both used stars +whose proper motion had been found to be large, as this argued +proximity. Henderson, at the Cape of Good Hope, observed α +Centauri, whose annual proper motion he found to amount to 3".6, in +1832-3; and a few years later deduced its parallax 1".16. His +successor at the Cape, Maclear, reduced this to 0".92. + +In 1835 Struve assigned a doubtful parallax of 0".261 to Vega (α +Lyræ). But Bessel's observations, between 1837 and 1840, of 61 Cygni, +a star with the large proper motion of over 5", established its annual +parallax to be 0".3483; and this was confirmed by Peters, who found +the value 0".349. + +Later determinations for α₂ Centauri, by Gill,[2] make its parallax +0".75--This is the nearest known fixed star; and its light takes 4⅓ +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: α Centauri 14.4 miles a second=4.2 +astronomical units a year; 61 Cygni 37.9 miles a second=11.2 +astronomical units a year. These successes led to renewed zeal, and +now the distances of many stars are known more or less accurately. + +Several of the brightest stars, which might be expected to be the +nearest, have not shown a parallax amounting to a twentieth of a +second of arc. Among these are Canopus, α Orionis, α Cygni, β +Centauri, and γ Cassiopeia. Oudemans has published a list of +parallaxes observed.[4] + +_Proper Motion._--In 1718 Halley[5] detected the proper motions +of Arcturus and Sirius. In 1738 J. Cassinis[6] showed that the former +had moved five minutes of arc since Tycho Brahe fixed its position. In +1792 Piazzi noted the motion of 61 Cygni as given above. For a long +time the greatest observed proper motion was that of a small star 1830 +Groombridge, nearly 7" a year; but others have since been found +reaching as much as 10". + +Now the spectroscope enables the motion of stars to be detected at a +single observation, but only that part of the motion that is in the +line of sight. For a complete knowledge of a star's motion the proper +motion and parallax must also be known. + +When Huggins first applied the Doppler principle to measure velocities +in the line of sight,[7] the faintness of star spectra diminished the +accuracy; but Vögel, in 1888, overcame this to a great extent by long +exposures of photographic plates. + +It has often been noticed that stars which seem to belong to a group +of nearly uniform magnitude have the same proper motion. The +spectroscope has shown that these have also often the same velocity in +the line of sight. Thus in the Great Bear, β, γ, δ, ε, ζ, all +agree as to angular proper motion. δ was too faint for a +spectroscopic measurement, but all the others have been shown to be +approaching us at a rate of twelve to twenty miles a second. The same +has been proved for proper motion, and line of sight motion, in the +case of Pleiades and other groups. + +Maskelyne measured many proper motions of stars, from which W. +Herschel[8] came to the conclusion that these apparent motions are for +the most part due to a motion of the solar system in space towards a +point in the constellation Hercules, R.A. 257°; N. Decl. 25°. This +grand discovery has been amply confirmed, and, though opinions differ +as to the exact direction, it happens that the point first indicated +by Herschel, from totally insufficient data, agrees well with modern +estimates. + +Comparing the proper motions and parallaxes to get the actual velocity +of each star relative to our system, C.L. Struve found the probable +velocity of the solar system in space to be fifteen miles a second, or +five astronomical units a year. + +The work of Herschel in this matter has been checked by comparing +spectroscopic velocities in the line of sight which, so far as the +sun's motion is concerned, would give a maximum rate of approach for +stars near Hercules, a maximum rate of recession for stars in the +opposite part of the heavens, and no effect for stars half-way +between. In this way the spectroscope has confirmed generally +Herschel's view of the direction, and makes the velocity eleven miles +a second, or nearly four astronomical units a year. + +The average proper motion of a first magnitude star has been found to +be 0".25 annually, and of a sixth magnitude star 0".04. But that all +bright stars are nearer than all small stars, or that they show +greater proper motion for that reason, is found to be far from the +truth. Many statistical studies have been made in this connection, and +interesting results may be expected from this treatment in the hands +of Kapteyn of Groningen, and others.[9] + +On analysis of the directions of proper motions of stars in all parts +of the heavens, Kapteyn has shown[10] that these indicate, besides the +solar motion towards Hercules, two general drifts of stars in nearly +opposite directions, which can be detected in any part of the +heavens. This result has been confirmed from independent data by +Eddington (_R.A.S., M.N._) and Dyson (_R.S.E. Proc._). + +Photography promises to assist in the measurement of parallax and +proper motions. Herr Pulfrich, of the firm of Carl Zeiss, has vastly +extended the applications of stereoscopic vision to astronomy--a +subject which De la Rue took up in the early days of photography. He +has made a stereo-comparator of great beauty and convenience for +comparing stereoscopically two star photographs taken at different +dates. Wolf of Heidelberg has used this for many purposes. His +investigations depending on the solar motion in space are remarkable. +He photographs stars in a direction at right angles to the line of the +sun's motion. He has taken photographs of the same region fourteen +years apart, the two positions of his camera being at the two ends of +a base-line over 5,000,000,000 miles apart, or fifty-six astronomical +units. On examining these stereoscopically, some of the stars rise out +of the general plane of the stars, and seem to be much nearer. Many of +the stars are thus seen to be suspended in space at different +distances corresponding exactly to their real distances from our solar +system, except when their proper motion interferes. The effect is most +striking; the accuracy of measurement exceeds that of any other method +of measuring such displacements, and it seems that with a long +interval of time the advantage of the method increases. + +_Double Stars._--The large class of double stars has always been much +studied by amateurs, partly for their beauty and colour, and partly as +a test for telescopic definition. Among the many unexplained stellar +problems there is one noticed in double stars that is thought by some +to be likely to throw light on stellar evolution. It is this: There +are many instances where one star of the pair is comparatively faint, +and the two stars are contrasted in colour; and in every single case +the general colour of the faint companion is invariably to be classed +with colours more near to the blue end of the spectrum than that of +the principal star. + +_Binary Stars._--Sir William Herschel began his observations of double +stars in the hope of discovering an annual parallax of the stars. In +this he was following a suggestion of Galileo's. The presumption is +that, if there be no physical connection between the stars of a pair, +the largest is the nearest, and has the greatest parallax. So, by +noting the distance between the pair at different times of the year, a +delicate test of parallax is provided, unaffected by major +instrumental errors. + +Herschel did, indeed, discover changes of distance, but not of the +character to indicate parallax. Following this by further observation, +he found that the motions were not uniform nor rectilinear, and by a +clear analysis of the movements he established the remarkable and +wholly unexpected fact that in all these cases the motion is due to a +revolution about their common centre of gravity.[11] He gave the +approximate period of revolution of some of these: Castor, 342 years; +δ Serpentis, 375 years; γ Leonis, 1,200 years; ε Bootis, 1,681 years. + +Twenty years later Sir John Herschel and Sir James South, after +re-examination of these stars, confirmed[12] and extended the results, +one pair of Coronæ having in the interval completed more than a whole +revolution. + +It is, then, to Sir William Herschel that we owe the extension of the +law of gravitation, beyond the limits of the solar system, to the +whole universe. His observations were confirmed by F.G.W. Struve (born +1793, died 1864), who carried on the work at Dorpat. But it was first +to Savary,[13] and later to Encke and Sir John Herschel, that we owe +the computation of the elliptic elements of these stars; also the +resulting identification of their law of force with Newton's force of +gravitation applied to the solar system, and the force that makes an +apple fall to the ground. As Grant well says in his _History_: +"This may be justly asserted to be one of the most sublime truths +which astronomical science has hitherto disclosed to the researches of +the human mind." + +Latterly the best work on double stars has been done by +S. W. Burnham,[14] at the Lick Observatory. The shortest period he +found was eleven years (κ Pegasi). In the case of some of +these binaries the parallax has been measured, from which it appears +that in four of the surest cases the orbits are about the size of the +orbit of Uranus, these being probably among the smallest stellar +orbits. + +The law of gravitation having been proved to extend to the stars, a +discovery (like that of Neptune in its origin, though unlike it in the +labour and originality involved in the calculation) that entrances the +imagination became possible, and was realised by Bessel--the discovery +of an unknown body by its gravitational disturbance on one that was +visible. In 1834 and 1840 he began to suspect a want of uniformity in +the proper motion of Sirius and Procyon respectively. In 1844, in a +letter to Sir John Herschel,[15] he attributed these irregularities in +each case to the attraction of an invisible companion, the period of +revolution of Sirius being about half a century. Later he said: "I +adhere to the conviction that Procyon and Sirius form real binary +systems, consisting of a visible and an invisible star. There is no +reason to suppose luminosity an essential quality of cosmical +bodies. The visibility of countless stars is no argument against the +invisibility of countless others." This grand conception led Peters to +compute more accurately the orbit, and to assign the place of the +invisible companion of Sirius. In 1862 Alvan G. Clark was testing a +new 18-inch object-glass (now at Chicago) upon Sirius, and, knowing +nothing of these predictions, actually found the companion in the very +place assigned to it. In 1896 the companion of Procyon was discovered +by Professor Schaeberle at the Lick Observatory. + +Now, by the refined parallax determinations of Gill at the Cape, we +know that of Sirius to be 0".38. From this it has been calculated that +the mass of Sirius equals two of our suns, and its intrinsic +brightness equals twenty suns; but the companion, having a mass equal +to our sun, has only a five-hundredth part of the sun's brightness. + +_Spectroscopic Binaries_.--On measuring the velocity of a star in the +line of sight at frequent intervals, periodic variations have been +found, leading to a belief in motion round an invisible +companion. Vogel, in 1889, discovered this in the case of Spica (α +Virginis), whose period is 4d. 0h. 19m., and the diameter of whose +orbit is six million miles. Great numbers of binaries of this type +have since then been discovered, all of short period. + +Also, in 1889, Pickering found that at regular intervals of fifty-two +days the lines in the spectrum of ζ of the Great Bear are +duplicated, indicating a relative velocity, equal to one hundred miles +a second, of two components revolving round each other, of which that +apparently single star must be composed. + +It would be interesting, no doubt, to follow in detail the +accumulating knowledge about the distances, proper motions, and orbits +of the stars; but this must be done elsewhere. Enough has been said to +show how results are accumulating which must in time unfold to us the +various stellar systems and their mutual relationships. + +_Variable Stars._--It has often happened in the history of different +branches of physical science that observation and experiment were so +far ahead of theory that hopeless confusion appeared to reign; and +then one chance result has given a clue, and from that time all +differences and difficulties in the previous researches have stood +forth as natural consequences, explaining one another in a rational +sequence. So we find parallax, proper motion, double stars, binary +systems, variable stars, and new stars all bound together. + +The logical and necessary explanation given of the cause of ordinary +spectroscopic binaries, and of irregular proper motions of Sirius and +Procyon, leads to the inference that if ever the plane of such a +binary orbit were edge-on to us there ought to be an eclipse of the +luminous partner whenever the non-luminous one is interposed between +us. This should give rise either to intermittence in the star's light +or else to variability. It was by supposing the existence of a dark +companion to Algol that its discoverer, Goodricke of York,[16] in +1783, explained variable stars of this type. Algol (β Persei) +completes the period of variable brightness in 68.8 hours. It loses +three-fifths of its light, and regains it in twelve hours. In 1889 +Vogel,[17] with the Potsdam spectrograph, actually found that the +luminous star is receding before each eclipse, and approaching us +after each eclipse; thus entirely supporting Goodricke's opinion. +There are many variables of the Algol type, and information is +steadily accumulating. But all variable stars do not suffer the sudden +variations of Algol. There are many types, and the explanations of +others have not proved so easy. + +The Harvard College photographs have disclosed the very great +prevalence of variability, and this is certainly one of the lines in +which modern discovery must progress. + +Roberts, in South Africa, has done splendid work on the periods of +variables of the Algol type. + +_New Stars_.--Extreme instances of variable stars are the new stars +such as those detected by Hipparchus, Tycho Brahe, and Kepler, of +which many have been found in the last half-century. One of the latest +great "Novæ" was discovered in Auriga by a Scotsman, Dr. Anderson, on +February 1st, 1892, and, with the modesty of his race, he communicated +the fact to His Majesty's Astronomer for Scotland on an unsigned +post-card.[18] Its spectrum was observed and photographed by Huggins +and many others. It was full of bright lines of hydrogen, calcium, +helium, and others not identified. The astounding fact was that lines +were shown in pairs, bright and dark, on a faint continuous spectrum, +indicating apparently that a dark body approaching us at the rate of +550 miles a second[19] was traversing a cold nebulous atmosphere, and +was heated to incandescence by friction, like a meteor in our +atmosphere, leaving a luminous train behind it. It almost disappeared, +and on April 26th it was of the sixteenth magnitude; but on August +17th it brightened to the tenth, showing the principal nebular band in +its spectrum, and no sign of approach or recession. It was as if it +emerged from one part of the nebula, cooled down, and rushed through +another part of the nebula, rendering the nebular gas more luminous +than itself.[20] + +Since 1892 one Nova after another has shown a spectrum as described +above, like a meteor rushing towards us and leaving a train behind, +for this seems to be the obvious meaning of the spectra. + +The same may be said of the brilliant Nova Persei, brighter at its +best than Capella, and discovered also by Dr. Anderson on February +22nd, 1901. It increased in brightness as it reached the densest part +of the nebula, then it varied for some weeks by a couple of +magnitudes, up and down, as if passing through separate nebular +condensations. In February, 1902, it could still be seen with an +opera-glass. As with the other Novæ, when it first dashed into the +nebula it was vaporised and gave a continuous spectrum with dark lines +of hydrogen and helium. It showed no bright lines paired with the dark +ones to indicate a train left behind; but in the end its own +luminosity died out, and the nebular spectrum predominated. + +The nebular illumination as seen in photographs, taken from August to +November, seemed to spread out slowly in a gradually increasing circle +at the rate of 90" in forty-eight days. Kapteyn put this down to the +velocity of light, the original outburst sending its illumination to +the nebulous gas and illuminating a spherical shell whose radius +increased at the velocity of light. This supposition seems correct, in +which case it can easily be shown from the above figures that the +distance of this Nova was 300 light years. + +_Star Catalogues._--Since the days of very accurate observations +numerous star-catalogues have been produced by individuals or by +observatories. Bradley's monumental work may be said to head the list. +Lacaille's, in the Southern hemisphere, was complementary. Then +Piazzi, Lalande, Groombridge, and Bessel were followed by Argelander +with his 324,000 stars, Rumker's Paramatta catalogue of the southern +hemisphere, and the frequent catalogues of national observatories. +Later the Astronomische Gesellschaft started their great catalogue, +the combined work of many observatories. Other southern ones were +Gould's at Cordova and Stone's at the Cape. + +After this we have a new departure. Gill at the Cape, having the comet +1882.ii. all to himself in those latitudes, wished his friends in +Europe to see it, and employed a local photographer to strap his +camera to the observatory equatoreal, driven by clockwork, and +adjusted on the comet by the eye. The result with half-an-hour's +exposure was good, so he tried three hours. The result was such a +display of sharp star images that he resolved on the Cape Photographic +Durchmusterung, which after fourteen years, with Kapteyn's aid in +reducing, was completed. Meanwhile the brothers Henry, of Paris, were +engaged in going over Chacornac's zodiacal stars, and were about to +catalogue the Milky Way portion, a serious labour, when they saw +Gill's Comet photograph and conceived the idea of doing the rest of +their work by photography. Gill had previously written to Admiral +Mouchez, of the Paris Observatory, and explained to him his project +for charting the heavens photographically, by combining the work of +many observatories. This led Admiral Mouchez to support the brothers +Henry in their scheme.[21] Gill, having got his own photographic work +underway, suggested an international astrographic chart, the materials +for different zones to be supplied by observatories of all nations, +each equipped with similar photographic telescopes. At a conference in +Paris, 1887, this was decided on, the stars on the charts going down +to the fourteenth magnitude, and the catalogues to the eleventh. + +[Illustration: GREAT COMET, Nov. 14TH, 1882. (Exposure 2hrs. 20m.) By +kind permission of Sir David Gill. From this photograph originated all +stellar chart-photography.] + +This monumental work is nearing completion. The labour involved was +immense, and the highest skill was required for devising instruments +and methods to read off the star positions from the plates. + +Then we have the Harvard College collection of photographic plates, +always being automatically added to; and their annex at Arequipa in +Peru. + +Such catalogues vary in their degree of accuracy; and fundamental +catalogues of standard stars have been compiled. These require +extension, because the differential methods of the heliometer and the +camera cannot otherwise be made absolute. + +The number of stars down to the fourteenth magnitude may be taken at +about 30,000,000; and that of all the stars visible in the greatest +modern telescopes is probably about 100,000,000. + +_Nebulæ and Star-clusters._--Our knowledge of nebulæ really dates from +the time of W. Herschel. In his great sweeps of the heavens with his +giant telescopes he opened in this direction a new branch of +astronomy. At one time he held that all nebulæ might be clusters of +innumerable minute stars at a great distance. Then he recognised the +different classes of nebulæ, and became convinced that there is a +widely-diffused "shining fluid" in space, though many so-called nebulæ +could be resolved by large telescopes into stars. He considered that +the Milky Way is a great star cluster, whose form may be conjectured +from numerous star-gaugings. He supposed that the compact "planetary +nebulæ" might show a stage of evolution from the diffuse nebulæ, and +that his classifications actually indicate various stages of +development. Such speculations, like those of the ancients about the +solar system, are apt to be harmful to true progress of knowledge +unless in the hands of the ablest mathematical physicists; and +Herschel violated their principles in other directions. But here his +speculations have attracted a great deal of attention, and, with +modifications, are accepted, at least as a working hypothesis, by a +fair number of people. + +When Sir John Herschel had extended his father's researches into the +Southern Hemisphere he was also led to the belief that some nebulae +were a phosphorescent material spread through space like fog or mist. + +Then his views were changed by the revelations due to the great +discoveries of Lord Rosse with his gigantic refractor,[22] when one +nebula after another was resolved into a cluster of minute stars. At +that time the opinion gained ground that with increase of telescopic +power this would prove to be the case with all nebulæ. + +In 1864 all doubt was dispelled by Huggins[23] in his first examination +of the spectrum of a nebula, and the subsequent extension of this +observation to other nebulæ; thus providing a certain test which +increase in the size of telescopes could never have given. In 1864 +Huggins found that all true nebulae give a spectrum of bright +lines. Three are due to hydrogen; two (discovered by Copeland) are +helium lines; others are unknown. Fifty-five lines have been +photographed in the spectrum of the Orion nebula. It seems to be +pretty certain that all true nebulae are gaseous, and show almost +exactly the same spectrum. + +Other nebulæ, and especially the white ones like that in Andromeda, +which have not yet been resolved into stars, show a continuous +spectrum; others are greenish and give no lines. + +A great deal has to be done by the chemist before the astronomer can +be on sure ground in drawing conclusions from certain portions of his +spectroscopic evidence. + +The light of the nebulas is remarkably actinic, so that photography +has a specially fine field in revealing details imperceptible in the +telescope. In 1885 the brothers Henry photographed, round the star +Maia in the Pleiades, a spiral nebula 3' long, as bright on the plate +as that star itself, but quite invisible in the telescope; and an +exposure of four hours revealed other new nebula in the same +district. That painstaking and most careful observer, Barnard, with +10¼ hours' exposure, extended this nebulosity for several degrees, +and discovered to the north of the Pleiades a huge diffuse nebulosity, +in a region almost destitute of stars. By establishing a 10-inch +instrument at an altitude of 6,000 feet, Barnard has revealed the wide +distribution of nebular matter in the constellation Scorpio over a +space of 4° or 5° square. Barnard asserts that the "nebular +hypothesis" would have been killed at its birth by a knowledge of +these photographs. Later he has used still more powerful instruments, +and extended his discoveries. + +The association of stars with planetary nebulæ, and the distribution +of nebulæ in the heavens, especially in relation to the Milky Way, are +striking facts, which will certainly bear fruit when the time arrives +for discarding vague speculations, and learning to read the true +physical structure and history of the starry universe. + +_Stellar Spectra._--When the spectroscope was first available for +stellar research, the leaders in this branch of astronomy were Huggins +and Father Secchi,[24] of Rome. The former began by devoting years of +work principally to the most accurate study of a few stars. The +latter devoted the years from 1863 to 1867 to a general survey of the +whole heavens, including 4,000 stars. He divided these into four +principal classes, which have been of the greatest service. Half of +his stars belonged to the first class, including Sirius, Vega, +Regulus, Altair. The characteristic feature of their spectra is the +strength and breadth of the hydrogen lines and the extreme faintness +of the metallic lines. This class of star is white to the eye, and +rich in ultra violet light. + +The second class includes about three-eighths of his stars, including +Capella, Pollux, and Arcturus. These stars give a spectrum like that +of our sun, and appear yellowish to the eye. + +The third class includes α Herculis, α Orionis (Betelgeux), Mira +Ceti, and about 500 red and variable stars. The spectrum has fluted +bands shaded from blue to red, and sharply defined at the more +refrangible edge. + +The fourth class is a small one, containing no stars over fifth +magnitude, of which 152 Schjellerup, in Canes Venatici, is a good +example. This spectrum also has bands, but these are shaded on the +violet side and sharp on the red side. They are due to carbon in some +form. These stars are ruby red in the telescope. + +It would appear, then, that all stars are suns with continuous +spectra, and the classes are differentiated by the character of the +absorbent vapours of their atmospheres. + +It is very likely that, after the chemists have taught us how to +interpret all the varieties of spectrum, it will be possible to +ascribe the different spectrum-classes to different stages in the +life-history of every star. Already there are plenty of people ready +to lay down arbitrary assumptions about the lessons to be drawn from +stellar spectra. Some say that they know with certainty that each star +begins by being a nebula, and is condensed and heated by condensation +until it begins to shine as a star; that it attains a climax of +temperature, then cools down, and eventually becomes extinct. They go +so far as to declare that they know what class of spectrum belongs to +each stage of a star's life, and how to distinguish between one that +is increasing and another that is decreasing in temperature. + +The more cautious astronomers believe that chemistry is not +sufficiently advanced to justify all of these deductions; that, until +chemists have settled the lately raised question of the transmutation +of elements, no theory can be sure. It is also held that until they +have explained, without room for doubt, the reasons for the presence +of some lines, and the absence of others, of any element in a stellar +spectrum; why the arc-spectrum of each element differs from its spark +spectrum; what are all the various changes produced in the spectrum of +a gas by all possible concomitant variations of pressure and +temperature; also the meanings of all the flutings in the spectra of +metalloids and compounds; and other equally pertinent matters--until +that time arrives the part to be played by the astronomer is one of +observation. By all means, they say, make use of "working hypotheses" +to add an interest to years of laborious research, and to serve as a +guide to the direction of further labours; but be sure not to fall +into the error of calling any mere hypothesis a theory. + +_Nebular Hypothesis._--The Nebular Hypothesis, which was first, as it +were, tentatively put forward by Laplace as a note in his _Système du +Monde_, supposes the solar system to have been a flat, disk-shaped +nebula at a high temperature in rapid rotation. In cooling it +condensed, leaving revolving rings at different distances from the +centre. These themselves were supposed to condense into the nucleus +for a rotating planet, which might, in contracting, again throw off +rings to form satellites. The speculation can be put in a really +attractive form, but is in direct opposition to many of the actual +facts; and so long as it is not favoured by those who wish to maintain +the position of astronomy as the most exact of the sciences--exact in +its facts, exact in its logic--this speculation must be recorded by +the historian, only as he records the guesses of the ancient Greeks--as +an interesting phase in the history of human thought. + +Other hypotheses, having the same end in view, are the meteoritic +hypothesis of Lockyer and the planetesimal hypothesis that has been +largely developed in the United States. These can best be read in the +original papers to various journals, references to which may be found +in the footnotes of Miss Clerke's _History of Astronomy during the +Nineteenth Century_. The same can be said of Bredichin's hypothesis of +comets' tails, Arrhenius's book on the applications of the theory of +light repulsion, the speculations on radium, the origin of the sun's +heat and the age of the earth, the electron hypothesis of terrestrial +magnetism, and a host of similar speculations, all combining to throw +an interesting light on the evolution of a modern train of thought +that seems to delight in conjecture, while rebelling against that +strict mathematical logic which has crowned astronomy as the queen of +the sciences. + + +FOOTNOTES: + +[1] _R. S. Phil Trans_., 1810 and 1817-24. + +[2] One of the most valuable contributions to our knowledge of stellar +parallaxes is the result of Gill's work (_Cape Results_, vol. iii., +part ii., 1900.) + +[3] Taking the velocity of light at 186,000 miles a second, and the +earth's mean distance at 93,000,000 miles, 1 light year=5,865,696,000,000 +miles or 63,072 astronomical units; 1 astronomical unit a year=2.94 +miles a second; and the earth's orbital velocity=18.5 miles a second. + +[4] Ast. Nacht., 1889. + +[5] R. S. Phil. Trans., 1718. + +[6] Mem. Acad. des Sciences, 1738, p. 337. + +[7] R. S Phil. Trans., 1868. + +[8] _R.S. Phil Trans._, 1783. + +[9] See Kapteyn's address to the Royal Institution, 1908. Also Gill's +presidential address to the British Association, 1907. + +[10] _Brit. Assoc. Rep._, 1905. + +[11] R. S. Phil. Trans., 1803, 1804. + +[12] Ibid, 1824. + +[13] Connaisance des Temps, 1830. + +[14] _R. A. S. Mem._, vol. xlvii., p. 178; _Ast. Nach._, No. 3,142; +Catalogue published by Lick Observatory, 1901. + +[15] _R. A. S., M. N._, vol. vi. + +[16] _R. S. Phil. Trans._, vol. lxxiii., p. 484. + +[17] _Astr. Nach._, No. 2,947. + +[18] _R. S. E. Trans_., vol. xxvii. In 1901 Dr. Anderson discovered +Nova Persei. + +[19] _Astr. Nach_., No. 3,079. + +[20] For a different explanation see Sir W. Huggins's lecture, Royal +Institution, May 13th, 1892. + +[21] For the early history of the proposals for photographic +cataloguing of stars, see the _Cape Photographic Durchmusterung_, 3 +vols. (_Ann. of the Cape Observatory_, vols. in., iv., and v., +Introduction.) + +[22] _R. S. Phil. Trans._, 1850, p. 499 _et seq._ + +[23] _Ibid_, vol. cliv., p. 437. + +[24] _Brit. Assoc. Rep._, 1868, p. 165. + + + +INDEX + + +Abul Wefa, 24 +Acceleration of moon's mean motion, 60 +Achromatic lens invented, 88 +Adams, J. C., 61, 65, 68, 69, 70, 87, 118, 124 +Airy, G. B., 13, 30, 37, 65, 69, 70, 80, 81, 114, 119 +Albetegnius, 24 +Alphonso, 24 +Altazimuth, 81 +Anaxagoras, 14, 16 +Anaximander, 14 +Anaximenes, 14 +Anderson, T. D., 137, 138 +Ångstrom, A. J., 102 +Antoniadi, 113 +Apian, P., 63 +Apollonius, 22, 23 +Arago, 111 +Argelander, F. W. A., 139 +Aristarchus, 18, 29 +Aristillus, 17, 19 +Aristotle, 16, 30, 47 +Arrhenius, 146 +Arzachel, 24 +Asshurbanapal, 12 +Asteroids, discovery of, 67, 119 +Astrology, ancient and modern, 1-7, 38 + +Backlund, 122 +Bacon, R., 86 +Bailly, 8, 65 +Barnard, E. E., 115, 143 +Beer and Mädler, 107, 110, 111 +Behaim, 74 +Bessel, F.W., 65, 79, 128, 134, 139 +Biela, 123 +Binet, 65 +Biot, 10 +Bird, 79, 80 +Bliss, 80 +Bode, 66, 69 +Bond, G. P., 99, 117, 122 +Bouvard, A., 65, 68 +Bradley, J., 79, 80, 81, 87, 127, 128, 139 +Bredechin, 146 +Bremiker, 71 +Brewster, D., 52, 91, 112 +Brinkley, 128 +Bruno, G., 49 +Burchardt, 65, 123 +Burnham, S. W., 134 + +Callippus, 15, 16, 31 +Carrington, R. C., 97, 99, 114 +Cassini, G. D., 107, 114, 115, 116, 117, 118 +Cassini, J., 109, 129 +Chacornac, 139 +Chaldæan astronomy, 11-13 +Challis, J., 69, 70, 71, 72 +Chance, 88 +Charles, II., 50, 81 +Chinese astronomy, 8-11 +Christie, W. M. H. (Ast. Roy.), 64, 82, 125 +Chueni, 9 +Clairaut, A. C., 56, 63, 65 +Clark, A. G., 89, 135 +Clerke, Miss, 106, 146 +Comets, 120 +Common, A. A., 88 +Cooke, 89 +Copeland, R., 142 +Copernicus, N., 14, 24-31, 37, 38, 41, 42, 49, 128 +Cornu, 85 +Cowell, P. H., 3, 5, 64, 83 +Crawford, Earl of, 84 +Cromellin, A. C., 5, 64 + +D'Alembert, 65 +Damoiseau, 65 +D'Arrest, H. L., 34 +Dawes, W. R., 100, 111 +Delambre, J. B. J., 8, 27, 51, 65, 68 +De la Rue, W., 2, 94, 99, 100, 131 +Delaunay, 65 +Democritus, 16 +Descartes, 51 +De Sejour, 117 +Deslandres, II., 101 +Desvignolles, 9 +De Zach, 67 +Digges, L., 86 +Dollond, J., 87, 90 +Dominis, A. di., 86 +Donati, 120 +Doppler, 92, 129 +Draper, 99 +Dreyer, J. L. E., 29,77 +Dunthorne, 60 +Dyson, 131 + +Eclipses, total solar, 103 +Ecphantes, 16 +Eddington, 131 +Ellipse, 41 +Empedocles, 16 +Encke, J. F., 119, 122, 123, 133 +Epicycles, 22 +Eratosthenes, 18 +Euclid, 17 +Eudoxus, 15, 31 +Euler, L., 60, 61, 62, 65, 88, 119 + +Fabricius, D.,95, 120, 121 +Feil and Mantois, 88 +Fizeau, H. L., 85, 92, 99 +Flamsteed, J., 50, 58, 68, 78, 79, 93 +Fohi, 8 +Forbes, J. D., 52, 91 +Foucault, L., 85, 99 +Frauenhofer, J., 88, 90, 91 + +Galilei, G., 38, 46-49, 77, 93, 94, 95, 96, 107, 113, 115, 116, 133 +Galle, 71, 72 +Gascoigne, W., 45, 77 +Gauss, C. F., 65, 67 +Gauthier, 98 +Gautier, 89 +Gilbert, 44 +Gill, D., 84, 85, 128, 135, 139, 140 +Goodricke, J., 136 +Gould, B. A., 139 +Grant, R., 27, 47, 51, 86, 134 +Graham, 79 +Greek astronomy, 8-11 +Gregory, J. and D., 87 +Grimaldi, 113 +Groombridge, S., 139 +Grubb, 88, 89 +Guillemin, 122 +Guinand, 88 + +Hale, G. E., 101 +Hall, A., 112 +Hall, C. M., 88 +Halley, E., 19, 51, 58, 60, 61, 62, 63, 64, 79, 120, 122, 125, 129 +Halley's comet, 62-64 +Halm, 85 +Hansen, P. A., 3, 65 +Hansky, A. P., 100 +Harding, C. L., 67 +Heliometer, 83 +Heller, 120 +Helmholtz, H. L. F., 35 +Henderson, T., 128 +Henry, P. and P., 139, 140, 143 +Heraclides, 16 +Heraclitus, 14 +Herodotus, 13 +Herschel, W., 65, 68, 97, 107, 110, 114, 115, 116, 117, 118, 126, 127, + 130, 131, 132, 141, 142 +Herschel, J., 97, 111, 133, 134, 142 +Herschel, A. S., 125 +Hevelius, J., 178 +Hind, J. R., 5, 64, 120, 121, 122 +Hipparchus, 3, 18, 19, 20, 22, 23, 24, 26, 36, 55, 60, 74, 93, 137 +Hooke, R., 51, 111, 114 +Horrocks, J., 50, 56 +Howlett, 100 +Huggins, W., 92, 93, 99, 106, 120, 129, 137, 138, 142, 144 +Humboldt and Bonpland, 124 +Huyghens, C., 47, 77, 87, 110, 116, 117 + +Ivory, 65 + +Jansen, P. J. C., 105, 106 +Jansen, Z., 86 + +Kaiser, F., 111 +Kapteyn, J. C., 131, 138, 139 +Keeler, 117 +Kepler, J., 17, 23, 26, 29, 30, 36, 37, 38-46, 48, 49, 50, 52, 53, 63, + 66, 77, 87, 93, 127, 137 +Kepler's laws, 42 +Kirchoff, G.R., 91 +Kirsch, 9 +Knobel, E.B., 12, 13 +Ko-Show-King, 76 + +Lacaile, N.L., 139 +Lagrange, J.L., 61, 62, 65, 119 +La Hire, 114 +Lalande, J.J.L., 60, 63, 65, 66, 72, 139 +Lamont, J., 98 +Langrenus, 107 +Laplace, P.S. de, 50, 58, 61, 62, 65,66, 123, 146 +Lassel, 72, 88, 117, 118 +Law of universal gravitation, 53 +Legendre, 65 +Leonardo da Vinci, 46 +Lewis, G.C., 17 +Le Verrier, U.J.J., 65, 68, 70, 71,72, 110, 118, 125 +Lexell, 66, 123 +Light year, 128 +Lipperhey, H., 86 +Littrow, 121 +Lockyer, J.N., 103, 105, 146 +Logarithms invented, 50 +Loewy, 2, 100 +Long inequality of Jupiter and Saturn, 50, 62 +Lowell, P., 111, 112, 118 +Lubienietz, S. de, 122 +Luther, M., 38 +Lunar theory, 37, 50, 56, 64 + +Maclaurin, 65 +Maclear, T., 128 +Malvasia, 77 +Martin, 9 +Maxwell, J. Clerk, 117 +Maskelyne, N., 80, 130 +McLean, F., 89 +Medici, Cosmo di, 48 +Melancthon, 38 +Melotte, 83, 116 +Meteors, 123 +Meton, 15 +Meyer, 57, 65 +Michaelson, 85 +Miraldi, 110, 114 +Molyneux, 87 +Moon, physical observations, 107 +Mouchez, 139 +Moyriac de Mailla, 8 + +Napier, Lord, 50 +Nasmyth and Carpenter, 108 +Nebulae, 141, 146 +Neison, E., 108 +Neptune, discovery of, 68-72 +Newall, 89 +Newcomb, 85 +Newton, H.A., 124 +Newton, I., 5, 19, 43, 49, 51-60, 62, 64, 68, 77, 79, 87, 90, 93, 94, + 114, 127, 133 +Nicetas, 16, 25 +Niesten, 115 +Nunez, P., 35 + +Olbers, H.W.M., 67 +Omar, 11, 24 +Oppolzer, 13, 125 +Oudemans, 129 + +Palitsch, G., 64 +Parallax, solar, 85, 86 +Parmenides, 14 +Paul III., 30 +Paul V., 48 +Pemberton, 51 +Peters, C.A.F., 125, 128, 135 +Photography, 99 +Piazzi, G., 67, 128, 129, 139 +Picard, 54, 77, 114 +Pickering, E.C., 118, 135 +Pingré, 13, 122 +Plana, 65 +Planets and satellites, physical observations, 109-119 +Plato, 17, 23, 26, 40 +Poisson, 65 +Pond, J., 80 +Pons, 122 +Porta, B., 86 +Pound, 87, 114 +Pontecoulant, 64 +Precession of the equinoxes, 19-21, 55, 57 +Proctor, R.A., 111 +Pritchett, 115 +Ptolemy, 11, 13, 21, 22, 23, 24, 93 +Puiseux and Loewy, 108 +Pulfrich, 131 +Purbach, G., 24 +Pythagoras, 14, 17, 25, 29 + +Ramsay, W., 106 +Ransome and May, 81 +Reflecting telescopes invented, 87 +Regiomontanus (Müller), 24 +Respighi, 82 +Retrograde motion of planets, 22 +Riccioli, 107 +Roberts, 137 +Römer, O.,78, 114 +Rosse, Earl of, 88, 142 +Rowland, H. A., 92, 102 +Rudolph H.,37, 39 +Rumker, C., 139 + +Sabine, E., 98 +Savary, 133 +Schaeberle, J. M., 135 +Schiaparelli, G. V., 110, 111, 124, 125 +Scheiner, C., 87, 95, 96 +Schmidt, 108 +Schott, 88 +Schröter, J. H., 107, 110, 111, 124, 125 +Schuster, 98 +Schwabe, G. H., 97 +Secchi, A., 93, 144 +Short, 87 +Simms, J., 81 +Slipher, V. M., 119 +Socrates, 17 +Solon, 15 +Souciet, 8 +South, J., 133 +Spectroscope, 89-92 +Spectroheliograph, 101 +Spoerer, G. F. W., 98 +Spots on the sun, 84; + periodicity of, 97 +Stars, Parallax, 127; + proper motion, 129; + double, 132; + binaries, 132, 135; + new, 19, 36, 137; + catalogues of, 19, 36, 139; + spectra of, 143 +Stewart, B., 2, 100 +Stokes, G. G., 91 +Stone, E. J., 139 +Struve, C. L., 130 +Struve, F. G. W,, 88, 115, 128, 133 + +Telescopes invented, 47, 86; + large, 88 +Temple, 115, 125 +Thales, 13, 16 +Theon, 60 +Transit circle of Römer, 78 +Timocharis, 17, 19 +Titius, 66 +Torricelli, 113 +Troughton, E., 80 +Tupman, G. L., 120 +Tuttle, 125 +Tycho Brahe, 23, 25, 30, 33-38, 39, 40, 44, 50, 75, 77, 93, 94, 129, 137 + +Ulugh Begh, 24 +Uranus, discovery of, 65 + +Velocity of light, 86, 128; + of earth in orbit, 128 +Verbiest, 75 +Vogel, H. C., 92, 129, 135, 136 +Von Asten, 122 + +Walmsley, 65 +Walterus, B., 24, 74 +Weiss, E., 125 +Wells, 122 +Wesley, 104 +Whewell, 112 +Williams, 10 +Wilson, A., 96, 100 +Winnecke, 120 +Witte, 86 +Wollaston, 90 +Wolf, M., 119, 125, 132 +Wolf, R., 98 +Wren, C., 51 +Wyllie, A., 77 + +Yao, 9 +Young, C. A., 103 +Yu-Chi, 8 + +Zenith telescopes, 79, 82 +Zöllner, 92 +Zucchi, 113 + + + + + +End of the Project Gutenberg EBook of History of Astronomy, by George Forbes + +*** END OF THE PROJECT GUTENBERG EBOOK HISTORY OF ASTRONOMY *** + +This file should be named 8hsrs10u.txt or 8hsrs10u.zip +Corrected EDITIONS of our eBooks get a new NUMBER, 8hsrs11u.txt +VERSIONS based on separate sources get new LETTER, 8hsrs10au.txt + +Produced by Jonathan Ingram, Dave Maddock, Charles Franks +and the Online Distributed Proofreading Team. + +Project Gutenberg eBooks are often created from several printed +editions, all of which are confirmed as Public Domain in the US +unless a copyright notice is included. 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