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and empty air, but this was worse. “Get out, get out!”

release time：2023-12-07 09:04:06 source：complement each other author：{typename type="name"/}

NEW BEGINNINGS IN GENERAL SCIENCE We have dwelt thus at length on the subject of medical science, because it was chiefly in this field that progress was made in the Western world during the mediaeval period, and because these studies furnished the point of departure for the revival all along the line. It will be understood, however, from what was stated in the preceding chapter, that the Arabian influences in particular were to some extent making themselves felt along other lines. The opportunity afforded a portion of the Western world--notably Spain and Sicily --to gain access to the scientific ideas of antiquity through Arabic translations could not fail of influence. Of like character, and perhaps even more pronounced in degree, was the influence wrought by the Byzantine refugees, who, when Constantinople began to be threatened by the Turks, migrated to the West in considerable numbers, bringing with them a knowledge of Greek literature and a large number of precious works which for centuries had been quite forgotten or absolutely ignored in Italy. Now Western scholars began to take an interest in the Greek language, which had been utterly neglected since the beginning of the Middle Ages. Interesting stories are told of the efforts made by such men as Cosmo de' Medici to gain possession of classical manuscripts. The revival of learning thus brought about had its first permanent influence in the fields of literature and art, but its effect on science could not be long delayed. Quite independently of the Byzantine influence, however, the striving for better intellectual things had manifested itself in many ways before the close of the thirteenth century. An illustration of this is found in the almost simultaneous development of centres of teaching, which developed into the universities of Italy, France, England, and, a little later, of Germany. The regular list of studies that came to be adopted everywhere comprised seven nominal branches, divided into two groups--the so-called quadrivium, comprising music, arithmetic, geometry, and astronomy; and the trivium comprising grammar, rhetoric, and logic. The vagueness of implication of some of these branches gave opportunity to the teacher for the promulgation of almost any knowledge of which he might be possessed, but there can be no doubt that, in general, science had but meagre share in the curriculum. In so far as it was given representation, its chief field must have been Ptolemaic astronomy. The utter lack of scientific thought and scientific method is illustrated most vividly in the works of the greatest men of that period--such men as Albertus Magnus, Thomas Aquinas, Bonaventura, and the hosts of other scholastics of lesser rank. Yet the mental awakening implied in their efforts was sure to extend to other fields, and in point of fact there was at least one contemporary of these great scholastics whose mind was intended towards scientific subjects, and who produced writings strangely at variance in tone and in content with the others. This anachronistic thinker was the English monk, Roger Bacon.



ROGER BACON Bacon was born in 1214 and died in 1292. By some it is held that he was not appreciated in his own time because he was really a modern scientist living in an age two centuries before modern science or methods of modern scientific thinking were known. Such an estimate, however, is a manifest exaggeration of the facts, although there is probably a grain of truth in it withal. His learning certainly brought him into contact with the great thinkers of the time, and his writings caused him to be imprisoned by his fellow-churchmen at different times, from which circumstances we may gather that he was advanced thinker, even if not a modern scientist. Although Bacon was at various times in durance, or under surveillance, and forbidden to write, he was nevertheless a marvellously prolific writer, as is shown by the numerous books and unpublished manuscripts of his still extant. His master-production was the Opus Majus. In Part IV. of this work he attempts to show that all sciences rest ultimately on mathematics; but Part V., which treats of perspective, is of particular interest to modern scientists, because in this he discusses reflection and refraction, and the properties of mirrors and lenses. In this part, also, it is evident that he is making use of such Arabian writers as Alkindi and Alhazen, and this is of especial interest, since it has been used by his detractors, who accuse him of lack of originality, to prove that his seeming inventions and discoveries were in reality adaptations of the Arab scientists. It is difficult to determine just how fully such criticisms are justified. It is certain, however, that in this part he describes the anatomy of the eye with great accuracy, and discusses mirrors and lenses. The magnifying power of the segment of a glass sphere had been noted by Alhazen, who had observed also that the magnification was increased by increasing the size of the segment used. Bacon took up the discussion of the comparative advantages of segments, and in this discussion seems to show that he understood how to trace the progress of the rays of light through a spherical transparent body, and how to determine the place of the image. He also described a method of constructing a telescope, but it is by no means clear that he had ever actually constructed such an instrument. It is also a mooted question as to whether his instructions as to the construction of such an instrument would have enabled any one to construct one. The vagaries of the names of terms as he uses them allow such latitude in interpretation that modern scientists are not agreed as to the practicability of Bacon's suggestions. For example, he constantly refers to force under such names as virtus, species, imago, agentis, and a score of other names, and this naturally gives rise to the great differences in the interpretations of his writings, with corresponding differences in estimates of them. The claim that Bacon originated the use of lenses, in the form of spectacles, cannot be proven. Smith has determined that as early as the opening years of the fourteenth century such lenses were in use, but this proves nothing as regards Bacon's connection with their invention. The knowledge of lenses seems to be very ancient, if we may judge from the convex lens of rock crystal found by Layard in his excavations at Nimrud. There is nothing to show, however, that the ancients ever thought of using them to correct defects of vision. Neither, apparently, is it feasible to determine whether the idea of such an application originated with Bacon. Another mechanical discovery about which there has been a great deal of discussion is Bacon's supposed invention of gunpowder. It appears that in a certain passage of his work he describes the process of making a substance that is, in effect, ordinary gunpowder; but it is more than doubtful whether he understood the properties of the substance he describes. It is fairly well established, however, that in Bacon's time gunpowder was known to the Arabs, so that it should not be surprising to find references made to it in Bacon's work, since there is reason to believe that he constantly consulted Arabian writings. The great merit of Bacon's work, however, depends on the principles taught as regards experiment and the observation of nature, rather than on any single invention. He had the all-important idea of breaking with tradition. He championed unfettered inquiry in every field of thought. He had the instinct of a scientific worker--a rare instinct indeed in that age. Nor need we doubt that to the best of his opportunities he was himself an original investigator.



LEONARDO DA VINCI The relative infertility of Bacon's thought is shown by the fact that he founded no school and left no trace of discipleship. The entire century after his death shows no single European name that need claim the attention of the historian of science. In the latter part of the fifteenth century, however, there is evidence of a renaissance of science no less than of art. The German Muller became famous under the latinized named of Regio Montanus (1437-1472), although his actual scientific attainments would appear to have been important only in comparison with the utter ignorance of his contemporaries. The most distinguished worker of the new era was the famous Italian Leonardo da Vinci--a man who has been called by Hamerton the most universal genius that ever lived. Leonardo's position in the history of art is known to every one. With that, of course, we have no present concern; but it is worth our while to inquire at some length as to the famous painter's accomplishments as a scientist. From a passage in the works of Leonardo, first brought to light by Venturi,[1] it would seem that the great painter anticipated Copernicus in determining the movement of the earth. He made mathematical calculations to prove this, and appears to have reached the definite conclusion that the earth does move--or what amounts to the same thing, that the sun does not move. Muntz is authority for the statement that in one of his writings he declares, "Il sole non si mouve"--the sun does not move.[2] Among his inventions is a dynamometer for determining the traction power of machines and animals, and his experiments with steam have led some of his enthusiastic partisans to claim for him priority to Watt in the invention of the steam-engine. In these experiments, however, Leonardo seems to have advanced little beyond Hero of Alexandria and his steam toy. Hero's steam-engine did nothing but rotate itself by virtue of escaping jets of steam forced from the bent tubes, while Leonardo's "steam-engine" "drove a ball weighing one talent over a distance of six stadia." In a manuscript now in the library of the Institut de France, Da Vinci describes this engine minutely. The action of this machine was due to the sudden conversion of small quantities of water into steam ("smoke," as he called it) by coming suddenly in contact with a heated surface in a proper receptacle, the rapidly formed steam acting as a propulsive force after the manner of an explosive. It is really a steam-gun, rather than a steam-engine, and it is not unlikely that the study of the action of gunpowder may have suggested it to Leonardo. It is believed that Leonardo is the true discoverer of the camera-obscura, although the Neapolitan philosopher, Giambattista Porta, who was not born until some twenty years after the death of Leonardo, is usually credited with first describing this device. There is little doubt, however, that Da Vinci understood the principle of this mechanism, for he describes how such a camera can be made by cutting a small, round hole through the shutter of a darkened room, the reversed image of objects outside being shown on the opposite wall. Like other philosophers in all ages, he had observed a great number of facts which he was unable to explain correctly. But such accumulations of scientific observations are always interesting, as showing how many centuries of observation frequently precede correct explanation. He observed many facts about sounds, among others that blows struck upon a bell produced sympathetic sounds in a bell of the same kind; and that striking the string of a lute produced vibration in corresponding strings of lutes strung to the same pitch. He knew, also, that sounds could be heard at a distance at sea by listening at one end of a tube, the other end of which was placed in the water; and that the same expedient worked successfully on land, the end of the tube being placed against the ground. The knowledge of this great number of unexplained facts is often interpreted by the admirers of Da Vinci, as showing an almost occult insight into science many centuries in advance of his time. Such interpretations, however, are illusive. The observation, for example, that a tube placed against the ground enables one to hear movements on the earth at a distance, is not in itself evidence of anything more than acute scientific observation, as a similar method is in use among almost every race of savages, notably the American Indians. On the other hand, one is inclined to give credence to almost any story of the breadth of knowledge of the man who came so near anticipating Hutton, Lyell, and Darwin in his interpretation of the geological records as he found them written on the rocks. It is in this field of geology that Leonardo is entitled to the greatest admiration by modern scientists. He had observed the deposit of fossil shells in various strata of rocks, even on the tops of mountains, and he rejected once for all the theory that they had been deposited there by the Deluge. He rightly interpreted their presence as evidence that they had once been deposited at the bottom of the sea. This process he assumed bad taken hundreds and thousands of centuries, thus tacitly rejecting the biblical tradition as to the date of the creation. Notwithstanding the obvious interest that attaches to the investigations of Leonardo, it must be admitted that his work in science remained almost as infertile as that of his great precursor, Bacon. The really stimulative work of this generation was done by a man of affairs, who knew little of theoretical science except in one line, but who pursued that one practical line until he achieved a wonderful result. This man was Christopher Columbus. It is not necessary here to tell the trite story of his accomplishment. Suffice it that his practical demonstration of the rotundity of the earth is regarded by most modern writers as marking an epoch in history. With the year of his voyage the epoch of the Middle Ages is usually regarded as coming to an end. It must not be supposed that any very sudden change came over the aspect of scholarship of the time, but the preliminaries of great things had been achieved, and when Columbus made his famous voyage in 1492, the man was already alive who was to bring forward the first great vitalizing thought in the field of pure science that the Western world had originated for more than a thousand years. This man bore the name of Kopernik, or in its familiar Anglicized form, Copernicus. His life work and that of his disciples will claim our attention in the succeeding chapter.



IV. THE NEW COSMOLOGY--COPERNICUS TO KEPLER AND GALILEO We have seen that the Ptolemaic astronomy, which was the accepted doctrine throughout the Middle Ages, taught that the earth is round. Doubtless there was a popular opinion current which regarded the earth as flat, but it must be understood that this opinion had no champions among men of science during the Middle Ages. When, in the year 1492, Columbus sailed out to the west on his memorable voyage, his expectation of reaching India had full scientific warrant, however much it may have been scouted by certain ecclesiastics and by the average man of the period. Nevertheless, we may well suppose that the successful voyage of Columbus, and the still more demonstrative one made about thirty years later by Magellan, gave the theory of the earth's rotundity a certainty it could never previously have had. Alexandrian geographers had measured the size of the earth, and had not hesitated to assert that by sailing westward one might reach India. But there is a wide gap between theory and practice, and it required the voyages of Columbus and his successors to bridge that gap. After the companions of Magellan completed the circumnavigation of the globe, the general shape of our earth would, obviously, never again be called in question. But demonstration of the sphericity of the earth had, of course, no direct bearing upon the question of the earth's position in the universe. Therefore the voyage of Magellan served to fortify, rather than to dispute, the Ptolemaic theory. According to that theory, as we have seen, the earth was supposed to lie immovable at the centre of the universe; the various heavenly bodies, including the sun, revolving about it in eccentric circles. We have seen that several of the ancient Greeks, notably Aristarchus, disputed this conception, declaring for the central position of the sun in the universe, and the motion of the earth and other planets about that body. But this revolutionary theory seemed so opposed to the ordinary observation that, having been discountenanced by Hipparchus and Ptolemy, it did not find a single important champion for more than a thousand years after the time of the last great Alexandrian astronomer. The first man, seemingly, to hark back to the Aristarchian conception in the new scientific era that was now dawning was the noted cardinal, Nikolaus of Cusa, who lived in the first half of the fifteenth century, and was distinguished as a philosophical writer and mathematician. His De Docta Ignorantia expressly propounds the doctrine of the earth's motion. No one, however, paid the slightest attention to his suggestion, which, therefore, merely serves to furnish us with another interesting illustration of the futility of propounding even a correct hypothesis before the time is ripe to receive it--particularly if the hypothesis is not fully fortified by reasoning based on experiment or observation. The man who was destined to put forward the theory of the earth's motion in a way to command attention was born in 1473, at the village of Thorn, in eastern Prussia. His name was Nicholas Copernicus. There is no more famous name in the entire annals of science than this, yet posterity has never been able fully to establish the lineage of the famous expositor of the true doctrine of the solar system. The city of Thorn lies in a province of that border territory which was then under control of Poland, but which subsequently became a part of Prussia. It is claimed that the aspects of the city were essentially German, and it is admitted that the mother of Copernicus belonged to that race. The nationality of the father is more in doubt, but it is urged that Copernicus used German as his mother-tongue. His great work was, of course, written in Latin, according to the custom of the time; but it is said that, when not employing that language, he always wrote in German. The disputed nationality of Copernicus strongly suggests that he came of a mixed racial lineage, and we are reminded again of the influences of those ethnical minglings to which we have previously more than once referred. The acknowledged centres of civilization towards the close of the fifteenth century were Italy and Spain. Therefore, the birthplace of Copernicus lay almost at the confines of civilization, reminding us of that earlier period when Greece was the centre of culture, but when the great Greek thinkers were born in Asia Minor and in Italy. As a young man, Copernicus made his way to Vienna to study medicine, and subsequently he journeyed into Italy and remained there many years, About the year 1500 he held the chair of mathematics in a college at Rome. Subsequently he returned to his native land and passed his remaining years there, dying at Domkerr, in Frauenburg, East Prussia, in the year 1543. It would appear that Copernicus conceived the idea of the heliocentric system of the universe while he was a comparatively young man, since in the introduction to his great work, which he addressed to Pope Paul III., he states that he has pondered his system not merely nine years, in accordance with the maxim of Horace, but well into the fourth period of nine years. Throughout a considerable portion of this period the great work of Copernicus was in manuscript, but it was not published until the year of his death. The reasons for the delay are not very fully established. Copernicus undoubtedly taught his system throughout the later decades of his life. He himself tells us that he had even questioned whether it were not better for him to confine himself to such verbal teaching, following thus the example of Pythagoras. Just as his life was drawing to a close, he decided to pursue the opposite course, and the first copy of his work is said to have been placed in his hands as he lay on his deathbed. The violent opposition which the new system met from ecclesiastical sources led subsequent commentators to suppose that Copernicus had delayed publication of his work through fear of the church authorities. There seems, however, to be no direct evidence for this opinion. It has been thought significant that Copernicus addressed his work to the pope. It is, of course, quite conceivable that the aged astronomer might wish by this means to demonstrate that he wrote in no spirit of hostility to the church. His address to the pope might have been considered as a desirable shield precisely because the author recognized that his work must needs meet with ecclesiastical criticism. Be that as it may, Copernicus was removed by death from the danger of attack, and it remained for his disciples of a later generation to run the gauntlet of criticism and suffer the charges of heresy. The work of Copernicus, published thus in the year 1543 at Nuremberg, bears the title De Orbium Coelestium Revolutionibus. It is not necessary to go into details as to the cosmological system which Copernicus advocated, since it is familiar to every one. In a word, he supposed the sun to be the centre of all the planetary motions, the earth taking its place among the other planets, the list of which, as known at that time, comprised Mercury, Venus, the Earth, Mars, Jupiter, and Saturn. The fixed stars were alleged to be stationary, and it was necessary to suppose that they are almost infinitely distant, inasmuch as they showed to the observers of that time no parallax; that is to say, they preserved the same apparent position when viewed from the opposite points of the earth's orbit. But let us allow Copernicus to speak for himself regarding his system, His exposition is full of interest. We quote first the introduction just referred to, in which appeal is made directly to the pope. "I can well believe, most holy father, that certain people, when they hear of my attributing motion to the earth in these books of mine, will at once declare that such an opinion ought to be rejected. Now, my own theories do not please me so much as not to consider what others may judge of them. Accordingly, when I began to reflect upon what those persons who accept the stability of the earth, as confirmed by the opinion of many centuries, would say when I claimed that the earth moves, I hesitated for a long time as to whether I should publish that which I have written to demonstrate its motion, or whether it would not be better to follow the example of the Pythagoreans, who used to hand down the secrets of philosophy to their relatives and friends only in oral form. As I well considered all this, I was almost impelled to put the finished work wholly aside, through the scorn I had reason to anticipate on account of the newness and apparent contrariness to reason of my theory. "My friends, however, dissuaded me from such a course and admonished me that I ought to publish my book, which had lain concealed in my possession not only nine years, but already into four times the ninth year. Not a few other distinguished and very learned men asked me to do the same thing, and told me that I ought not, on account of my anxiety, to delay any longer in consecrating my work to the general service of mathematicians. "But your holiness will perhaps not so much wonder that I have dared to bring the results of my night labors to the light of day, after having taken so much care in elaborating them, but is waiting instead to hear how it entered my mind to imagine that the earth moved, contrary to the accepted opinion of mathematicians--nay, almost contrary to ordinary human understanding. Therefore I will not conceal from your holiness that what moved me to consider another way of reckoning the motions of the heavenly bodies was nothing else than the fact that the mathematicians do not agree with one another in their investigations. In the first place, they are so uncertain about the motions of the sun and moon that they cannot find out the length of a full year. In the second place, they apply neither the same laws of cause and effect, in determining the motions of the sun and moon and of the five planets, nor the same proofs. Some employ only concentric circles, others use eccentric and epicyclic ones, with which, however, they do not fully attain the desired end. They could not even discover nor compute the main thing--namely, the form of the universe and the symmetry of its parts. It was with them as if some should, from different places, take hands, feet, head, and other parts of the body, which, although very beautiful, were not drawn in their proper relations, and, without making them in any way correspond, should construct a monster instead of a human being. "Accordingly, when I had long reflected on this uncertainty of mathematical tradition, I took the trouble to read again the books of all the philosophers I could get hold of, to see if some one of them had not once believed that there were other motions of the heavenly bodies. First I found in Cicero that Niceties had believed in the motion of the earth. Afterwards I found in Plutarch, likewise, that some others had held the same opinion. This induced me also to begin to consider the movability of the earth, and, although the theory appeared contrary to reason, I did so because I knew that others before me had been allowed to assume rotary movements at will, in order to explain the phenomena of these celestial bodies. I was of the opinion that I, too, might be permitted to see whether, by presupposing motion in the earth, more reliable conclusions than hitherto reached could not be discovered for the rotary motions of the spheres. And thus, acting on the hypothesis of the motion which, in the following book, I ascribe to the earth, and by long and continued observations, I have finally discovered that if the motion of the other planets be carried over to the relation of the earth and this is made the basis for the rotation of every star, not only will the phenomena of the planets be explained thereby, but also the laws and the size of the stars; all their spheres and the heavens themselves will appear so harmoniously connected that nothing could be changed in any part of them without confusion in the remaining parts and in the whole universe. I do not doubt that clever and learned men will agree with me if they are willing fully to comprehend and to consider the proofs which I advance in the book before us. In order, however, that both the learned and the unlearned may see that I fear no man's judgment, I wanted to dedicate these, my night labors, to your holiness, rather than to any one else, because you, even in this remote corner of the earth where I live, are held to be the greatest in dignity of station and in love for all sciences and for mathematics, so that you, through your position and judgment, can easily suppress the bites of slanderers, although the proverb says that there is no remedy against the bite of calumny."

In chapter X. of book I., "On the Order of the Spheres," occurs a more detailed presentation of the system, as follows: "That which Martianus Capella, and a few other Latins, very well knew, appears to me extremely noteworthy. He believed that Venus and Mercury revolve about the sun as their centre and that they cannot go farther away from it than the circles of their orbits permit, since they do not revolve about the earth like the other planets. According to this theory, then, Mercury's orbit would be included within that of Venus, which is more than twice as great, and would find room enough within it for its revolution. "If, acting upon this supposition, we connect Saturn, Jupiter, and Mars with the same centre, keeping in mind the greater extent of their orbits, which include the earth's sphere besides those of Mercury and Venus, we cannot fail to see the explanation of the regular order of their motions. He is certain that Saturn, Jupiter, and Mars are always nearest the earth when they rise in the evening--that is, when they appear over against the sun, or the earth stands between them and the sun--but that they are farthest from the earth when they set in the evening--that is, when we have the sun between them and the earth. This proves sufficiently that their centre belongs to the sun and is the same about which the orbits of Venus and Mercury circle. Since, however, all have one centre, it is necessary for the space intervening between the orbits of Venus and Mars to include the earth with her accompanying moon and all that is beneath the moon; for the moon, which stands unquestionably nearest the earth, can in no way be separated from her, especially as there is sufficient room for the moon in the aforesaid space. Hence we do not hesitate to claim that the whole system, which includes the moon with the earth for its centre, makes the round of that great circle between the planets, in yearly motion about the sun, and revolves about the centre of the universe, in which the sun rests motionless, and that all which looks like motion in the sun is explained by the motion of the earth. The extent of the universe, however, is so great that, whereas the distance of the earth from the sun is considerable in comparison with the size of the other planetary orbits, it disappears when compared with the sphere of the fixed stars. I hold this to be more easily comprehensible than when the mind is confused by an almost endless number of circles, which is necessarily the case with those who keep the earth in the middle of the universe. Although this may appear incomprehensible and contrary to the opinion of many, I shall, if God wills, make it clearer than the sun, at least to those who are not ignorant of mathematics. "The order of the spheres is as follows: The first and lightest of all the spheres is that of the fixed stars, which includes itself and all others, and hence is motionless as the place in the universe to which the motion and position of all other stars is referred. "Then follows the outermost planet, Saturn, which completes its revolution around the sun in thirty years; next comes Jupiter with a twelve years' revolution; then Mars, which completes its course in two years. The fourth one in order is the yearly revolution which includes the earth with the moon's orbit as an epicycle. In the fifth place is Venus with a revolution of nine months. The sixth place is taken by Mercury, which completes its course in eighty days. In the middle of all stands the sun, and who could wish to place the lamp of this most beautiful temple in another or better place. Thus, in fact, the sun, seated upon the royal throne, controls the family of the stars which circle around him. We find in their order a harmonious connection which cannot be found elsewhere. Here the attentive observer can see why the waxing and waning of Jupiter seems greater than with Saturn and smaller than with Mars, and again greater with Venus than with Mercury. Also, why Saturn, Jupiter, and Mars are nearer to the earth when they rise in the evening than when they disappear in the rays of the sun. More prominently, however, is it seen in the case of Mars, which when it appears in the heavens at night, seems to equal Jupiter in size, but soon afterwards is found among the stars of second magnitude. All of this results from the same cause--namely, from the earth's motion. The fact that nothing of this is to be seen in the case of the fixed stars is a proof of their immeasurable distance, which makes even the orbit of yearly motion or its counterpart invisible to us."[1]

The fact that the stars show no parallax had been regarded as an important argument against the motion of the earth, and it was still so considered by the opponents of the system of Copernicus. It had, indeed, been necessary for Aristarchus to explain the fact as due to the extreme distance of the stars; a perfectly correct explanation, but one that implies distances that are altogether inconceivable. It remained for nineteenth-century astronomers to show, with the aid of instruments of greater precision, that certain of the stars have a parallax. But long before this demonstration had been brought forward, the system of Copernicus had been accepted as a part of common knowledge. While Copernicus postulated a cosmical scheme that was correct as to its main features, he did not altogether break away from certain defects of the Ptolemaic hypothesis. Indeed, he seems to have retained as much of this as practicable, in deference to the prejudice of his time. Thus he records the planetary orbits as circular, and explains their eccentricities by resorting to the theory of epicycles, quite after the Ptolemaic method. But now, of course, a much more simple mechanism sufficed to explain the planetary motions, since the orbits were correctly referred to the central sun and not to the earth. Needless to say, the revolutionary conception of Copernicus did not meet with immediate acceptance. A number of prominent astronomers, however, took it up almost at once, among these being Rhaeticus, who wrote a commentary on the evolutions; Erasmus Reinhold, the author of the Prutenic tables; Rothmann, astronomer to the Landgrave of Hesse, and Maestlin, the instructor of Kepler. The Prutenic tables, just referred to, so called because of their Prussian origin, were considered an improvement on the tables of Copernicus, and were highly esteemed by the astronomers of the time. The commentary of Rhaeticus gives us the interesting information that it was the observation of the orbit of Mars and of the very great difference between his apparent diameters at different times which first led Copernicus to conceive the heliocentric idea. Of Reinhold it is recorded that he considered the orbit of Mercury elliptical, and that he advocated a theory of the moon, according to which her epicycle revolved on an elliptical orbit, thus in a measure anticipating one of the great discoveries of Kepler to which we shall refer presently. The Landgrave of Hesse was a practical astronomer, who produced a catalogue of fixed stars which has been compared with that of Tycho Brahe. He was assisted by Rothmann and by Justus Byrgius. Maestlin, the preceptor of Kepler, is reputed to have been the first modern observer to give a correct explanation of the light seen on portions of the moon not directly illumined by the sun. He explained this as not due to any proper light of the moon itself, but as light reflected from the earth. Certain of the Greek philosophers, however, are said to have given the same explanation, and it is alleged also that Leonardo da Vinci anticipated Maestlin in this regard.[2] While, various astronomers of some eminence thus gave support to the Copernican system, almost from the beginning, it unfortunately chanced that by far the most famous of the immediate successors of Copernicus declined to accept the theory of the earth's motion. This was Tycho Brahe, one of the greatest observing astronomers of any age. Tycho Brahe was a Dane, born at Knudstrup in the year 1546. He died in 1601 at Prague, in Bohemia. During a considerable portion of his life he found a patron in Frederick, King of Denmark, who assisted him to build a splendid observatory on the Island of Huene. On the death of his patron Tycho moved to Germany, where, as good luck would have it, he came in contact with the youthful Kepler, and thus, no doubt, was instrumental in stimulating the ambitions of one who in later years was to be known as a far greater theorist than himself. As has been said, Tycho rejected the Copernican theory of the earth's motion. It should be added, however, that he accepted that part of the Copernican theory which makes the sun the centre of all the planetary motions, the earth being excepted. He thus developed a system of his own, which was in some sort a compromise between the Ptolemaic and the Copernican systems. As Tycho conceived it, the sun revolves about the earth, carrying with it the planets-Mercury, Venus, Mars, Jupiter, and Saturn, which planets have the sun and not the earth as the centre of their orbits. This cosmical scheme, it should be added, may be made to explain the observed motions of the heavenly bodies, but it involves a much more complex mechanism than is postulated by the Copernican theory. Various explanations have been offered of the conservatism which held the great Danish astronomer back from full acceptance of the relatively simple and, as we now know, correct Copernican doctrine. From our latter-day point of view, it seems so much more natural to accept than to reject the Copernican system, that we find it difficult to put ourselves in the place of a sixteenth-century observer. Yet if we recall that the traditional view, having warrant of acceptance by nearly all thinkers of every age, recorded the earth as a fixed, immovable body, we shall see that our surprise should be excited rather by the thinker who can break away from this view than by the one who still tends to cling to it. Moreover, it is useless to attempt to disguise the fact that something more than a mere vague tradition was supposed to support the idea of the earth's overshadowing importance in the cosmical scheme. The sixteenth-century mind was overmastered by the tenets of ecclesiasticism, and it was a dangerous heresy to doubt that the Hebrew writings, upon which ecclesiasticism based its claim, contained the last word regarding matters of science. But the writers of the Hebrew text had been under the influence of that Babylonian conception of the universe which accepted the earth as unqualifiedly central--which, indeed, had never so much as conceived a contradictory hypothesis; and so the Western world, which had come to accept these writings as actually supernatural in origin, lay under the spell of Oriental ideas of a pre-scientific era. In our own day, no one speaking with authority thinks of these Hebrew writings as having any scientific weight whatever. Their interest in this regard is purely antiquarian; hence from our changed point of view it seems scarcely credible that Tycho Brahe can have been in earnest when he quotes the Hebrew traditions as proof that the sun revolves about the earth. Yet we shall see that for almost three centuries after the time of Tycho, these same dreamings continued to be cited in opposition to those scientific advances which new observations made necessary; and this notwithstanding the fact that the Oriental phrasing is, for the most part, poetically ambiguous and susceptible of shifting interpretations, as the criticism of successive generations has amply testified. As we have said, Tycho Brahe, great observer as he was, could not shake himself free from the Oriental incubus. He began his objections, then, to the Copernican system by quoting the adverse testimony of a Hebrew prophet who lived more than a thousand years B.C. All of this shows sufficiently that Tycho Brahe was not a great theorist. He was essentially an observer, but in this regard he won a secure place in the very first rank. Indeed, he was easily the greatest observing astronomer since Hipparchus, between whom and himself there were many points of resemblance. Hipparchus, it will be recalled, rejected the Aristarchian conception of the universe just as Tycho rejected the conception of Copernicus. But if Tycho propounded no great generalizations, the list of specific advances due to him is a long one, and some of these were to prove important aids in the hands of later workers to the secure demonstration of the Copernican idea. One of his most important series of studies had to do with comets. Regarding these bodies there had been the greatest uncertainty in the minds of astronomers. The greatest variety of opinions regarding them prevailed; they were thought on the one hand to be divine messengers, and on the other to be merely igneous phenomena of the earth's atmosphere. Tycho Brahe declared that a comet which he observed in the year 1577 had no parallax, proving its extreme distance. The observed course of the comet intersected the planetary orbits, which fact gave a quietus to the long-mooted question as to whether the Ptolemaic spheres were transparent solids or merely imaginary; since the comet was seen to intersect these alleged spheres, it was obvious that they could not be the solid substance that they were commonly imagined to be, and this fact in itself went far towards discrediting the Ptolemaic system. It should be recalled, however, that this supposition of tangible spheres for the various planetary and stellar orbits was a mediaeval interpretation of Ptolemy's theory rather than an interpretation of Ptolemy himself, there being nothing to show that the Alexandrian astronomer regarded his cycles and epicycles as other than theoretical. An interesting practical discovery made by Tycho was his method of determining the latitude of a place by means of two observations made at an interval of twelve hours. Hitherto it had been necessary to observe the sun's angle on the equinoctial days, a period of six months being therefore required. Tycho measured the angle of elevation of some star situated near the pole, when on the meridian, and then, twelve hours later, measured the angle of elevation of the same star when it again came to the meridian at the opposite point of its apparent circle about the polestar. Half the sum of these angles gives the latitude of the place of observation. As illustrating the accuracy of Tycho's observations, it may be noted that he rediscovered a third inequality of the moon's motion at its variation, he, in common with other European astronomers, being then quite unaware that this inequality had been observed by an Arabian astronomer. Tycho proved also that the angle of inclination of the moon's orbit to the ecliptic is subject to slight variation. The very brilliant new star which shone forth suddenly in the constellation of Cassiopeia in the year 1572, was made the object of special studies by Tycho, who proved that the star had no sensible parallax and consequently was far beyond the planetary regions. The appearance of a new star was a phenomenon not unknown to the ancients, since Pliny records that Hipparchus was led by such an appearance to make his catalogue of the fixed stars. But the phenomenon is sufficiently uncommon to attract unusual attention. A similar phenomenon occurred in the year 1604, when the new star--in this case appearing in the constellation of Serpentarius--was explained by Kepler as probably proceeding from a vast combustion. This explanation--in which Kepler is said to have followed. Tycho--is fully in accord with the most recent theories on the subject, as we shall see in due course. It is surprising to hear Tycho credited with so startling a theory, but, on the other hand, such an explanation is precisely what should be expected from the other astronomer named. For Johann Kepler, or, as he was originally named, Johann von Kappel, was one of the most speculative astronomers of any age. He was forever theorizing, but such was the peculiar quality of his mind that his theories never satisfied him for long unless he could put them to the test of observation. Thanks to this happy combination of qualities, Kepler became the discoverer of three famous laws of planetary motion which lie at the very foundation of modern astronomy, and which were to be largely instrumental in guiding Newton to his still greater generalization. These laws of planetary motion were vastly important as corroborating the Copernican theory of the universe, though their position in this regard was not immediately recognized by contemporary thinkers. Let us examine with some detail into their discovery, meantime catching a glimpse of the life history of the remarkable man whose name they bear.

JOHANN KEPLER AND THE LAWS OF PLANETARY MOTION Johann Kepler was born the 27th of December, 1571, in the little town of Weil, in Wurtemburg. He was a weak, sickly child, further enfeebled by a severe attack of small-pox. It would seem paradoxical to assert that the parents of such a genius were mismated, but their home was not a happy one, the mother being of a nervous temperament, which perhaps in some measure accounted for the genius of the child. The father led the life of a soldier, and finally perished in the campaign against the Turks. Young Kepler's studies were directed with an eye to the ministry. After a preliminary training he attended the university at Tubingen, where he came under the influence of the celebrated Maestlin and became his life-long friend. Curiously enough, it is recorded that at first Kepler had no taste for astronomy or for mathematics. But the doors of the ministry being presently barred to him, he turned with enthusiasm to the study of astronomy, being from the first an ardent advocate of the Copernican system. His teacher, Maestlin, accepted the same doctrine, though he was obliged, for theological reasons, to teach the Ptolemaic system, as also to oppose the Gregorian reform of the calendar. The Gregorian calendar, it should be explained, is so called because it was instituted by Pope Gregory XIII., who put it into effect in the year 1582, up to which time the so-called Julian calendar, as introduced by Julius Caesar, had been everywhere accepted in Christendom. This Julian calendar, as we have seen, was a great improvement on preceding ones, but still lacked something of perfection inasmuch as its theoretical day differed appreciably from the actual day. In the course of fifteen hundred years, since the time of Caesar, this defect amounted to a discrepancy of about eleven days. Pope Gregory proposed to correct this by omitting ten days from the calendar, which was done in September, 1582. To prevent similar inaccuracies in the future, the Gregorian calendar provided that once in four centuries the additional day to make a leap-year should be omitted, the date selected for such omission being the last year of every fourth century. Thus the years 1500, 1900, and 2300, A.D., would not be leap-years. By this arrangement an approximate rectification of the calendar was effected, though even this does not make it absolutely exact. Such a rectification as this was obviously desirable, but there was really no necessity for the omission of the ten days from the calendar. The equinoctial day had shifted so that in the year 1582 it fell on the 10th of March and September. There was no reason why it should not have remained there. It would greatly have simplified the task of future historians had Gregory contented himself with providing for the future stability of the calendar without making the needless shift in question. We are so accustomed to think of the 21st of March and 21st of September as the natural periods of the equinox, that we are likely to forget that these are purely arbitrary dates for which the 10th might have been substituted without any inconvenience or inconsistency. But the opposition to the new calendar, to which reference has been made, was not based on any such considerations as these. It was due, largely at any rate, to the fact that Germany at this time was under sway of the Lutheran revolt against the papacy. So effective was the opposition that the Gregorian calendar did not come into vogue in Germany until the year 1699. It may be added that England, under stress of the same manner of prejudice, held out against the new reckoning until the year 1751, while Russia does not accept it even now. As the Protestant leaders thus opposed the papal attitude in a matter of so practical a character as the calendar, it might perhaps have been expected that the Lutherans would have had a leaning towards the Copernican theory of the universe, since this theory was opposed by the papacy. Such, however, was not the case. Luther himself pointed out with great strenuousness, as a final and demonstrative argument, the fact that Joshua commanded the sun and not the earth to stand still; and his followers were quite as intolerant towards the new teaching as were their ultramontane opponents. Kepler himself was, at various times, to feel the restraint of ecclesiastical opposition, though he was never subjected to direct persecution, as was his friend and contemporary, Galileo. At the very outset of Kepler's career there was, indeed, question as to the publication of a work he had written, because that work took for granted the truth of the Copernican doctrine. This work appeared, however, in the year 1596. It bore the title Mysterium Cosmographium, and it attempted to explain the positions of the various planetary bodies. Copernicus had devoted much time to observation of the planets with reference to measuring their distance, and his efforts had been attended with considerable success. He did not, indeed, know the actual distance of the sun, and, therefore, was quite unable to fix the distance of any planet; but, on the other hand, he determined the relative distance of all the planets then known, as measured in terms of the sun's distance, with remarkable accuracy. With these measurements as a guide, Kepler was led to a very fanciful theory, according to which the orbits of the five principal planets sustain a peculiar relation to the five regular solids of geometry. His theory was this: "Around the orbit of the earth describe a dodecahedron--the circle comprising it will be that of Mars; around Mars describe a tetrahedron--the circle comprising it will be that of Jupiter; around Jupiter describe a cube--the circle comprising it will be that of Saturn; now within the earth's orbit inscribe an icosahedron--the inscribed circle will be that of Venus; in the orbit of Venus inscribe an octahedron --the circle inscribed will be that of Mercury."[3] Though this arrangement was a fanciful one, which no one would now recall had not the theorizer obtained subsequent fame on more substantial grounds, yet it evidenced a philosophical spirit on the part of the astronomer which, misdirected as it was in this instance, promised well for the future. Tycho Brahe, to whom a copy of the work was sent, had the acumen to recognize it as a work of genius. He summoned the young astronomer to be his assistant at Prague, and no doubt the association thus begun was instrumental in determining the character of Kepler's future work. It was precisely the training in minute observation that could avail most for a mind which, like Kepler's, tended instinctively to the formulation of theories. When Tycho Brahe died, in 1601, Kepler became his successor. In due time he secured access to all the unpublished observations of his great predecessor, and these were of inestimable value to him in the progress of his own studies. Kepler was not only an ardent worker and an enthusiastic theorizer, but he was an indefatigable writer, and it pleased him to take the public fully into his confidence, not merely as to his successes, but as to his failures. Thus his works elaborate false theories as well as correct ones, and detail the observations through which the incorrect guesses were refuted by their originator. Some of these accounts are highly interesting, but they must not detain us here. For our present purpose it must suffice to point out the three important theories, which, as culled from among a score or so of incorrect ones, Kepler was able to demonstrate to his own satisfaction and to that of subsequent observers. Stated in a few words, these theories, which have come to bear the name of Kepler's Laws, are the following: 1. That the planetary orbits are not circular, but elliptical, the sun occupying one focus of the ellipses. 2. That the speed of planetary motion varies in different parts of the orbit in such a way that an imaginary line drawn from the sun to the planet--that is to say, the radius vector of the planet's orbit--always sweeps the same area in a given time.

These two laws Kepler published as early as 1609. Many years more of patient investigation were required before he found out the secret of the relation between planetary distances and times of revolution which his third law expresses. In 1618, however, he was able to formulate this relation also, as follows: 3. The squares of the distance of the various planets from the sun are proportional to the cubes of their periods of revolution about the sun.

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