The Project Gutenberg EBook of Great Astronomers, by R. S. Ball Copyright laws are changing all over the world. 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: Great Astronomers Author: R. S. Ball Release Date: August 2000 [EBook #2298] [grast10.txt was first posted on August 8, 2000] [Two variations of this ebook, derived from the same source, were posted in the year 2000. strnm10.txt was posted on May 9, 2000. grast10.txt was posted on August 9, 2000. strnm10 was, overall, the better of the two, although some minor errors, not present in grast10, were introduced into strnm10 during rewrapping of the text. grast10 made it into GUTINDEX, thus becoming the "primary" version. strnm10 has since been taken offline.] [grast11.txt, an improved edition of strnm10.txt, was first posted on May 23, 2004] Edition: 11 Language: English Character set encoding: ASCII *** START OF THIS PROJECT GUTENBERG EBOOK GREAT ASTRONOMERS *** This etext was prepared by Chris Brennen cbrennen@freenet.co.uk Jill R. Diffendal Barb Grow pebareka@iexpress.net.au Christine L. Hall Goleta, CA. USA Pamela L. Hall pamhall@www.edu GREAT ASTRONOMERS by SIR ROBERT S. BALL D.Sc. LL.D. F.R.S. Lowndean Professor of Astronomy and Geometry in the University of Cambridge Author of "In Starry Realms" "In the High Heavens" etc. [PLATE: GREENWICH OBSERVATORY.] PREFACE. It has been my object in these pages to present the life of each astronomer in such detail as to enable the reader to realise in some degree the man's character and surroundings; and I have endeavoured to indicate as clearly as circumstances would permit the main features of the discoveries by which he has become known. There are many types of astronomers--from the stargazer who merely watches the heavens, to the abstract mathematician who merely works at his desk; it has, consequently, been necessary in the case of some lives to adopt a very different treatment from that which seemed suitable for others. While the work was in progress, some of the sketches appeared in "Good Words." The chapter on Brinkley has been chiefly derived from an article on the "History of Dunsink Observatory," which was published on the occasion of the tercentenary celebration of the University of Dublin in 1892, and the life of Sir William Rowan Hamilton is taken, with a few alterations and omissions, from an article contributed to the "Quarterly Review" on Graves' life of the great mathematician. The remaining chapters now appear for the first time. For many of the facts contained in the sketch of the late Professor Adams, I am indebted to the obituary notice written by my friend Dr. J. W. L. Glaisher, for the Royal Astronomical Society; while with regard to the late Sir George Airy, I have a similar acknowledgment to make to Professor H. H. Turner. To my friend Dr. Arthur A. Rambaut I owe my hearty thanks for his kindness in aiding me in the revision of the work. R.S.B. The Observatory, Cambridge. October, 1895 CONTENTS. INTRODUCTION. PTOLEMY. COPERNICUS. TYCHO BRAHE. GALILEO. KEPLER. ISAAC NEWTON. FLAMSTEED. HALLEY. BRADLEY. 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Another objection, however, appeared to him to possess the gravest moment. It was argued that if the earth were rotating, there is nothing to make the air participate in this motion, mankind would therefore be swept from the earth by the furious blasts which would arise from the movement of the earth through an atmosphere at rest. Even if we could imagine that the air were carried round with the earth, the same would not apply, so thought Ptolemy, to any object suspended in the air. So long as a bird was perched on a tree, he might very well be carried onward by the moving earth, but the moment he took wing, the ground would slip from under him at a frightful pace, so that when he dropped down again he would find himself at a distance perhaps ten times as great as that which a carrier-pigeon or a swallow could have traversed in the same time. Some vague delusion of this description seems even still to crop up occasionally. I remember hearing of a proposition for balloon travelling of a very remarkable kind. The voyager who wanted to reach any other place in the same latitude was simply to ascend in a balloon, and wait there till the rotation of the earth conveyed the locality which happened to be his destination directly beneath him, whereupon he was to let out the gas and drop down! Ptolemy knew quite enough natural philosophy to be aware that such a proposal for locomotion would be an utter absurdity; he knew that there was no such relative shift between the air and the earth as this motion would imply. It appeared to him to be necessary that the air should lag behind, if the earth had been animated by a movement of rotation. In this he was, as we know, entirely wrong. There were, however, in his days no accurate notions on the subject of the laws of motion. Assiduous as Ptolemy may have been in the study of the heavenly bodies, it seems evident that he cannot have devoted much thought to the phenomena of motion of terrestrial objects. Simple, indeed, are the experiments which might have convinced a philosopher much less acute than Ptolemy, that, if the earth did revolve, the air must necessarily accompany it. If a rider galloping on horseback tosses a ball into the air, it drops again into his hand, just as it would have done had he been remaining at rest during the ball's flight; the ball in fact participates in the horizontal motion, so that though it really describes a curve as any passer-by would observe, yet it appears to the rider himself merely to move up and down in a straight line. This fact, and many others similar to it, demonstrate clearly that if the earth were endowed with a movement of rotation, the atmosphere surrounding it must participate in that movement. Ptolemy did not know this, and consequently he came to the conclusion that the earth did not rotate, and that, therefore, notwithstanding the tremendous improbability of so mighty an object as the celestial sphere spinning round once in every twenty-four hours, there was no course open except to believe that this very improbable thing did really happen. Thus it came to pass that Ptolemy adopted as the cardinal doctrine of his system a stationary earth poised at the centre of the celestial sphere, which stretched around on all sides at a distance so vast that the diameter of the earth was an inappreciable point in comparison therewith. Ptolemy having thus deliberately rejected the doctrine of the earth's rotation, had to make certain other entirely erroneous suppositions. It was easily seen that each star required exactly the same period for the performance of a complete revolution of the heavens. Ptolemy knew that the stars were at enormous distances from the earth, though no doubt his notions on this point came very far short of what we know to be the reality. If the stars had been at very varied distances, then it would be so wildly improbable that they should all accomplish their revolutions in the same time, that Ptolemy came to the conclusion that they must be all at the same distance, that is, that they must be all on the surface of a sphere. This view, however erroneous, was corroborated by the obvious fact that the stars in the constellations preserved their relative places unaltered for centuries. Thus it was that Ptolemy came to the conclusion that they were all fixed on one spherical surface, though we are not informed as to the material of this marvellous setting which sustained the stars like jewels. Nor should we hastily pronounce this doctrine to be absurd. The stars do appear to lie on the surface of a sphere, of which the observer is at the centre; not only is this the aspect which the skies present to the untechnical observer, but it is the aspect in which the skies are presented to the most experienced astronomer of modern days. No doubt he knows well that the stars are at the most varied distances from him; he knows that certain stars are ten times, or a hundred times, or a thousand times, as far as other stars. Nevertheless, to his eye the stars appear on the surface of the sphere, it is on that surface that his measurements of the relative places of the stars are made; indeed, it may be said that almost all the accurate observations in the observatory relate to the places of the stars, not as they really are, but as they appear to be projected on that celestial sphere whose conception we owe to the genius of Ptolemy. This great philosopher shows very ingeniously that the earth must be at the centre of the sphere. He proves that, unless this were the case, each star would not appear to move with the absolute uniformity which does, as a matter of fact, characterise it. In all these reasonings we cannot but have the most profound admiration for the genius of Ptolemy, even though he had made an error so enormous in the fundamental point of the stability of the earth. Another error of a somewhat similar kind seemed to Ptolemy to be demonstrated. He had shown that the earth was an isolated object in space, and being such was, of course, capable of movement. It could either be turned round, or it could be moved from one place to another. We know that Ptolemy deliberately adopted the view that the earth did not turn round; he had then to investigate the other question, as to whether the earth was animated by any movement of translation. He came to the conclusion that to attribute any motion to the earth would be incompatible with the truths at which he had already arrived. The earth, argued Ptolemy, lies at the centre of the celestial sphere. If the earth were to be endowed with movement, it would not lie always at this point, it must, therefore, shift to some other part of the sphere. The movements of the stars, however, preclude the possibility of this; and, therefore, the earth must be as devoid of any movement of translation as it is devoid of rotation. Thus it was that Ptolemy convinced himself that the stability of the earth, as it appeared to the ordinary senses, had a rational philosophical foundation. Not unfrequently it is the lot of the philosophers to contend against the doctrines of the vulgar, but when it happens, as in the case of Ptolemy's researches, that the doctrines of the vulgar are corroborated by philosophical investigation which bear the stamp of the highest authority, it is not to be wondered at that such doctrines should be deemed well-nigh impregnable. In this way we may, perhaps, account for the remarkable fact that the theories of Ptolemy held unchallenged sway over the human intellect for the vast period already mentioned. Up to the present we have been speaking only of those primary motions of the heavens, by which the whole sphere appeared to revolve once every twenty-four hours. We have now to discuss the remarkable theories by which Ptolemy endeavoured to account for the monthly movement of the moon, for the annual movement of the sun, and for the periodic movements of the planets which had gained for them the titles of the wandering stars. Possessed with the idea that these movements must be circular, or must be capable, directly or indirectly, of being explained by circular movements, it seemed obvious to Ptolemy, as indeed it had done to previous astronomers, that the track of the moon through the stars was a circle of which the earth is the centre. A similar movement with a yearly period must also be attributed to the sun, for the changes in the positions of the constellations in accordance with the progress of the seasons, placed it beyond doubt that the sun made a circuit of the celestial sphere, even though the bright light of the sun prevented the stars in its vicinity, from being seen in daylight. Thus the movements both of the sun and the moon, as well as the diurnal rotation of the celestial sphere, seemed to justify the notion that all celestial movements must be "perfect," that is to say, described uniformly in those circles which were the only perfect curves. The simplest observations, however, show that the movements of the planets cannot be explained in this simple fashion. Here the geometrical genius of Ptolemy shone forth, and he devised a scheme by which the apparent wanderings of the planets could be accounted for without the introduction of aught save "perfect" movements. To understand his reasoning, let us first set forth clearly those facts of observation which require to be explained. I shall take, in particular, two planets, Venus and Mars, as these illustrate, in the most striking manner, the peculiarities of the inner and the outer planets respectively. The simplest observations would show that Venus did not move round the heavens in the same fashion as the sun or the moon. Look at the evening star when brightest, as it appears in the west after sunset. Instead of moving towards the east among the stars, like the sun or the moon, we find, week after week, that Venus is drawing in towards the sun, until it is lost in the sunbeams. Then the planet emerges on the other side, not to be seen as an evening star, but as a morning star. In fact, it was plain that in some ways Venus accompanied the sun in its annual movement. Now it is found advancing in front of the sun to a certain limited distance, and now it is lagging to an equal extent behind the sun. [FIG. 1. PTOLEMY'S PLANETARY SCHEME.] These movements were wholly incompatible with the supposition that the journeys of Venus were described by a single motion of the kind regarded as perfect. It was obvious that the movement was connected in some strange manner with the revolution of the sun, and here was the ingenious method by which Ptolemy sought to render account of it. Imagine a fixed arm to extend from the earth to the sun, as shown in the accompanying figure (Fig. 1), then this arm will move round uniformly, in consequence of the sun's movement. At a point P on this arm let a small circle be described. Venus is supposed to revolve uniformly in this small circle, while the circle itself is carried round continuously by the movement of the sun. In this way it was possible to account for the chief peculiarities in the movement of Venus. It will be seen that, in consequence of the revolution around P, the spectator on the earth will sometimes see Venus on one side of the sun, and sometimes on the other side, so that the planet always remains in the sun's vicinity. By properly proportioning the movements, this little contrivance simulated the transitions from the morning star to the evening star. Thus the changes of Venus could be accounted for by a Combination of the "perfect" movement of P in the circle which it described uniformly round the earth, combined with the "perfect" motion of Venus in the circle which it described uniformly around the moving centre. In a precisely similar manner Ptolemy rendered an explanation of the fitful apparitions of Mercury. Now just on one side of the sun, and now just on the other, this rarely-seen planet moved like Venus on a circle whereof the centre was also carried by the line joining the sun and the earth. The circle, however, in which Mercury actually revolved had to be smaller than that of Venus, in order to account for the fact that Mercury lies always much closer to the sun than the better-known planet. [FIG. 2. PTOLEMY'S THEORY OF THE MOVEMENT OF MARS.] The explanation of the movement of an outer planet like Mars could also be deduced from the joint effect of two perfect motions. The changes through which Mars goes are, however, so different from the movements of Venus that quite a different disposition of the circles is necessary. For consider the facts which characterise the movements of an outer planet such as Mars. In the first place, Mars accomplishes an entire circuit of the heaven. In this respect, no doubt, it may be said to resemble the sun or the moon. A little attention will, however, show that there are extraordinary irregularities in the movement of the planet. Generally speaking, it speeds its way from west to east among the stars, but sometimes the attentive observer will note that the speed with which the planet advances is slackening, and then it will seem to become stationary. Some days later the direction of the planet's movement will be reversed, and it will be found moving from the east towards the west. At first it proceeds slowly and then quickens its pace, until a certain speed is attained, which afterwards declines until a second stationary position is reached. After a due pause the original motion from west to east is resumed, and is continued until a similar cycle of changes again commences. Such movements as these were obviously quite at variance with any perfect movement in a single circle round the earth. Here, again, the geometrical sagacity of Ptolemy provided him with the means of representing the apparent movements of Mars, and, at the same time, restricting the explanation to those perfect movements which he deemed so essential. In Fig. 2 we exhibit Ptolemy's theory as to the movement of Mars. We have, as before, the earth at the centre, and the sun describing its circular orbit around that centre. The path of Mars is to be taken as exterior to that of the sun. We are to suppose that at a point marked M there is a fictitious planet, which revolves around the earth uniformly, in a circle called the DEFERENT. This point M, which is thus animated by a perfect movement, is the centre of a circle which is carried onwards with M, and around the circumference of which Mars revolves uniformly. It is easy to show that the combined effect of these two perfect movements is to produce exactly that displacement of Mars in the heavens which observation discloses. In the position represented in the figure, Mars is obviously pursuing a course which will appear to the observer as a movement from west to east. When, however, the planet gets round to such a position as R, it is then moving from east to west in consequence of its revolution in the moving circle, as indicated by the arrowhead. On the other hand, the whole circle is carried forward in the opposite direction. If the latter movement be less rapid than the former, then we shall have the backward movement of Mars on the heavens which it was desired to explain. By a proper adjustment of the relative lengths of these arms the movements of the planet as actually observed could be completely accounted for. The other outer planets with which Ptolemy was acquainted, namely, Jupiter and Saturn, had movements of the same general character as those of Mars. Ptolemy was equally successful in explaining the movements they performed by the supposition that each planet had perfect rotation in a circle of its own, which circle itself had perfect movement around the earth in the centre. It is somewhat strange that Ptolemy did not advance one step further, as by so doing he would have given great simplicity to his system. He might, for instance, have represented the movements of Venus equally well by putting the centre of the moving circle at the sun itself, and correspondingly enlarging the circle in which Venus revolved. He might, too, have arranged that the several circles which the outer planets traversed should also have had their centres at the sun. The planetary system would then have consisted of an earth fixed at the centre, of a sun revolving uniformly around it, and of a system of planets each describing its own circle around a moving centre placed in the sun. Perhaps Ptolemy had not thought of this, or perhaps he may have seen arguments against it. This important step was, however, taken by Tycho. He considered that all the planets revolved around the sun in circles, and that the sun itself, bearing all these orbits, described a mighty circle around the earth. This point having been reached, only one more step would have been necessary to reach the glorious truths that revealed the structure of the solar system. That last step was taken by Copernicus. COPERNICUS [PLATE: THORN, FROM AN OLD PRINT.] The quaint town of Thorn, on the Vistula, was more than two centuries old when Copernicus was born there on the 19th of February, 1473. The situation of this town on the frontier between Prussia and Poland, with the commodious waterway offered by the river, made it a place of considerable trade. A view of the town, as it was at the time of the birth of Copernicus, is here given. The walls, with their watch-towers, will be noted, and the strategic importance which the situation of Thorn gave to it in the fifteenth century still belongs thereto, so much so that the German Government recently constituted the town a fortress of the first class. Copernicus, the astronomer, whose discoveries make him the great predecessor of Kepler and Newton, did not come from a noble family, as certain other early astronomers have done, for his father was a tradesman. Chroniclers are, however, careful to tell us that one of his uncles was a bishop. We are not acquainted with any of those details of his childhood or youth which are often of such interest in other cases where men have risen to exalted fame. It would appear that the young Nicolaus, for such was his Christian name, received his education at home until such time as he was deemed sufficiently advanced to be sent to the University at Cracow. The education that he there obtained must have been in those days of a very primitive description, but Copernicus seems to have availed himself of it to the utmost. He devoted himself more particularly to the study of medicine, with the view of adopting its practice as the profession of his life. The tendencies of the future astronomer were, however, revealed in the fact that he worked hard at mathematics, and, like one of his illustrious successors, Galileo, the practice of the art of painting had for him a very great interest, and in it he obtained some measure of success. By the time he was twenty-seven years old, it would seem that Copernicus had given up the notion of becoming a medical practitioner, and had resolved to devote himself to science. He was engaged in teaching mathematics, and appears to have acquired some reputation. His growing fame attracted the notice of his uncle the bishop, at whose suggestion Copernicus took holy orders, and he was presently appointed to a canonry in the cathedral of Frauenburg, near the mouth of the Vistula. To Frauenburg, accordingly, this man of varied gifts retired. Possessing somewhat of the ascetic spirit, he resolved to devote his life to work of the most serious description. He eschewed all ordinary society, restricting his intimacies to very grave and learned companions, and refusing to engage in conversation of any useless kind. It would seem as if his gifts for painting were condemned as frivolous; at all events, we do not learn that he continued to practise them. In addition to the discharge of his theological duties, his life was occupied partly in ministering medically to the wants of the poor, and partly with his researches in astronomy and mathematics. His equipment in the matter of instruments for the study of the heavens seems to have been of a very meagre description. He arranged apertures in the walls of his house at Allenstein, so that he could observe in some fashion the passage of the stars across the meridian. That he possessed some talent for practical mechanics is proved by his construction of a contrivance for raising water from a stream, for the use of the inhabitants of Frauenburg. Relics of this machine are still to be seen. [PLATE: COPERNICUS.] The intellectual slumber of the Middle Ages was destined to be awakened by the revolutionary doctrines of Copernicus. It may be noted, as an interesting circumstance, that the time at which he discovered the scheme of the solar system has coincided with a remarkable epoch in the world's history. The great astronomer had just reached manhood at the time when Columbus discovered the new world. Before the publication of the researches of Copernicus, the orthodox scientific creed averred that the earth was stationary, and that the apparent movements of the heavenly bodies were indeed real movements. Ptolemy had laid down this doctrine 1,400 years before. In his theory this huge error was associated with so much important truth, and the whole presented such a coherent scheme for the explanation of the heavenly movements, that the Ptolemaic theory was not seriously questioned until the great work of Copernicus appeared. No doubt others, before Copernicus, had from time to time in some vague fashion surmised, with more or less plausibility, that the sun, and not the earth, was the centre about which the system really revolved. It is, however, one thing to state a scientific fact; it is quite another thing to be in possession of the train of reasoning, founded on observation or experiment, by which that fact may be established. Pythagoras, it appears, had indeed told his disciples that it was the sun, and not the earth, which was the centre of movement, but it does not seem at all certain that Pythagoras had any grounds which science could recognise for the belief which is attributed to him. So far as information is available to us, it would seem that Pythagoras associated his scheme of things celestial with a number of preposterous notions in natural philosophy. He may certainly have made a correct statement as to which was the most important body in the solar system, but he certainly did not provide any rational demonstration of the fact. Copernicus, by a strict train of reasoning, convinced those who would listen to him that the sun was the centre of the system. It is useful for us to consider the arguments which he urged, and by which he effected that intellectual revolution which is always connected with his name. The first of the great discoveries which Copernicus made relates to the rotation of the earth on its axis. That general diurnal movement, by which the stars and all other celestial bodies appear to be carried completely round the heavens once every twenty-four hours, had been accounted for by Ptolemy on the supposition that the apparent movements were the real movements. As we have already seen, Ptolemy himself felt the extraordinary difficulty involved in the supposition that so stupendous a fabric as the celestial sphere should spin in the way supposed. Such movements required that many of the stars should travel with almost inconceivable velocity. Copernicus also saw that the daily rising and setting of the heavenly bodies could be accounted for either by the supposition that the celestial sphere moved round and that the earth remained at rest, or by the supposition that the celestial sphere was at rest while the earth turned round in the opposite direction. He weighed the arguments on both sides as Ptolemy had done, and, as the result of his deliberations, Copernicus came to an opposite conclusion from Ptolemy. To Copernicus it appeared that the difficulties attending the supposition that the celestial sphere revolved, were vastly greater than those which appeared so weighty to Ptolemy as to force him to deny the earth's rotation. Copernicus shows clearly how the observed phenomena could be accounted for just as completely by a rotation of the earth as by a rotation of the heavens. He alludes to the fact that, to those on board a vessel which is moving through smooth water, the vessel itself appears to be at rest, while the objects on shore seem to be moving past. If, therefore, the earth were rotating uniformly, we dwellers upon the earth, oblivious of our own movement, would wrongly attribute to the stars the displacement which was actually the consequence of our own motion. Copernicus saw the futility of the arguments by which Ptolemy had endeavoured to demonstrate that a revolution of the earth was impossible. It was plain to him that there was nothing whatever to warrant refusal to believe in the rotation of the earth. In his clear-sightedness on this matter we have specially to admire the sagacity of Copernicus as a natural philosopher. It had been urged that, if the earth moved round, its motion would not be imparted to the air, and that therefore the earth would be uninhabitable by the terrific winds which would be the result of our being carried through the air. Copernicus convinced himself that this deduction was preposterous. He proved that the air must accompany the earth, just as his coat remains round him, notwithstanding the fact that he is walking down the street. In this way he was able to show that all a priori objections to the earth's movements were absurd, and therefore he was able to compare together the plausibilities of the two rival schemes for explaining the diurnal movement. [PLATE: FRAUENBURG, FROM AN OLD PRINT.] Once the issue had been placed in this form, the result could not be long in doubt. Here is the question: Which is it more likely--that the earth, like a grain of sand at the centre of a mighty globe, should turn round once in twenty-four hours, or that the whole of that vast globe should complete a rotation in the opposite direction in the same time? Obviously, the former is far the more simple supposition. But the case is really much stronger than this. Ptolemy had supposed that all the stars were attached to the surface of a sphere. He had no ground whatever for this supposition, except that otherwise it would have been well-nigh impossible to have devised a scheme by which the rotation of the heavens around a fixed earth could have been arranged. Copernicus, however, with the just instinct of a philosopher, considered that the celestial sphere, however convenient from a geometrical point of view, as a means of representing apparent phenomena, could not actually have a material existence. In the first place, the existence of a material celestial sphere would require that all the myriad stars should be at exactly the same distances from the earth. Of course, no one will say that this or any other arbitrary disposition of the stars is actually impossible, but as there was no conceivable physical reason why the distances of all the stars from the earth should be identical, it seemed in the very highest degree improbable that the stars should be so placed. Doubtless, also, Copernicus felt a considerable difficulty as to the nature of the materials from which Ptolemy's wonderful sphere was to be constructed. Nor could a philosopher of his penetration have failed to observe that, unless that sphere were infinitely large, there must have been space outside it, a consideration which would open up other difficult questions. Whether infinite or not, it was obvious that the celestial sphere must have a diameter at least many thousands of times as great as that of the earth. From these considerations Copernicus deduced the important fact that the stars and the other celestial bodies must all be vast objects. He was thus enabled to put the question in such a form that it could hardly receive any answer but the correct one. Which is it more rational to suppose, that the earth should turn round on its axis once in twenty-four hours, or that thousands of mighty stars should circle round the earth in the same time, many of them having to describe circles many thousands of times greater in circumference than the circuit of the earth at the equator? The obvious answer pressed upon Copernicus with so much force that he was compelled to reject Ptolemy's theory of the stationary earth, and to attribute the diurnal rotation of the heavens to the revolution of the earth on its axis. Once this tremendous step had been taken, the great difficulties which beset the monstrous conception of the celestial sphere vanished, for the stars need no longer be regarded as situated at equal distances from the earth. Copernicus saw that they might lie at the most varied degrees of remoteness, some being hundreds or thousands of times farther away than others. The complicated structure of the celestial sphere as a material object disappeared altogether; it remained only as a geometrical conception, whereon we find it convenient to indicate the places of the stars. Once the Copernican doctrine had been fully set forth, it was impossible for anyone, who had both the inclination and the capacity to understand it, to withhold acceptance of its truth. The doctrine of a stationary earth had gone for ever. Copernicus having established a theory of the celestial movements which deliberately set aside the stability of the earth, it seemed natural that he should inquire whether the doctrine of a moving earth might not remove the difficulties presented in other celestial phenomena. It had been universally admitted that the earth lay unsupported in space. Copernicus had further shown that it possessed a movement of rotation. Its want of stability being thus recognised, it seemed reasonable to suppose that the earth might also have some other kinds of movements as well. In this, Copernicus essayed to solve a problem far more difficult than that which had hitherto occupied his attention. It was a comparatively easy task to show how the diurnal rising and setting could be accounted for by the rotation of the earth. It was a much more difficult undertaking to demonstrate that the planetary movements, which Ptolemy had represented with so much success, could be completely explained by the supposition that each of those planets revolved uniformly round the sun, and that the earth was also a planet, accomplishing a complete circuit of the sun once in the course of a year. [PLATE: EXPLANATION OF PLANETARY MOVEMENTS.] It would be impossible in a sketch like the present to enter into any detail as to the geometrical propositions on which this beautiful investigation of Copernicus depended. We can only mention a few of the leading principles. It may be laid down in general that, if an observer is in movement, he will, if unconscious of the fact, attribute to the fixed objects around him a movement equal and opposite to that which he actually possesses. A passenger on a canal-boat sees the objects on the banks apparently moving backward with a speed equal to that by which he is himself advancing forwards. By an application of this principle, we can account for all the phenomena of the movements of the planets, which Ptolemy had so ingeniously represented by his circles. Let us take, for instance, the most characteristic feature in the irregularities of the outer planets. We have already remarked that Mars, though generally advancing from west to east among the stars, occasionally pauses, retraces his steps for awhile, again pauses, and then resumes his ordinary onward progress. Copernicus showed clearly how this effect was produced by the real motion of the earth, combined with the real motion of Mars. 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