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their master, when compared with the complex absurdity of the system of Ptolemy. But this very argument was wanting to the ancients : for the complexity of that system, as we find it in the hands of its last supporters, had not yet been introduced ; for the simple reason that observation had not yet become so nice as to show the necessity of the innumerable encumbrances with which, in a more advanced state of practical astronomy, it became necessary to load it.
We find, in truth, in ancient authors, but few traces of an opinion analogous to that of Copernicus ; and even had it been taught in the school of Pythagoras, of which we discover evidence in the works of Cicero and Vitruvius alone, it is evident that it had met with few followers, and had been finally entirely forgotten. If a true view of the subject had ever been brought forward, all traces of it had been obliterated, and it was left to Copernicus to discover it anew.
It is, then, by Copernicus, that the motion of the earth has been introduced as a fact in astronomy; he it is that first demonstrated how the revolution of our planet around the sun was capable of explaining the succession of the seasons, and the precession of the equinoxes ; who showed with what simplicity motions performed, at unequal rates, in orbits concentric at the sun, give rise to the phenomena of stations and retrogradations. He placed astronomy upon a new and consistent basis, and by the important change he introduced, opened the way for all subsequent investigations.
It is to the enthusiasm excited in the mind of Kepler, by the new truth given to the world by Copernicus, that we owe the discovery of the figure of the planetary orbits, and of the laws of their motions. The bare and naked idea of the earth's motion, had been unproductive among the ancients, because it had never been seriously entertained by astronomers. Its publication forms the epoch of modern astronomy.
But if Copernicus be entitled to the glory of being the founder of modern astronomy, that of being its legislator was reserved for a genius of even higher and more daring order. Copernicus seems to have been dismayed at his own boldness, and to have wanted the courage to put the finishing hand to his work. He in truth delayed its publication so long, that he did not receive a complete copy until the very day on which he died.
The system imagined by Copernicus, is one of extreme beauty and simplicity. By his introduction of circular orbits, supposed by him at first to be concentric at the sun, he suppressed at one blow all the epicycles with which Ptolemy and his followers had been compelled to load the path of their planets; the phenomena of stations and retrograde motions, become simple corollaries of the different radii of the orbits, and different rates of motion
of the planets. All the parts of the system are in close connexion with each other, the mutual relations are determinate, and all the distances are commensurable. On the other hand, in the ancient system, all is incoherent and vague ; each of the planets might be considered as nearer, or farther, indifferently, provided the order of distances were not inverted, by bringing closest to the earth a planet of the longest zodiacal revolution.
These advantages of the system of Copernicus, are of themselves highly important. Of them, none of the ancients had the least suspicion, for had they beerf aware of them, it is impossible they could have avoided dwelling upon them. If, however, in its general features, the system of Copernicus be thus brilliant and imposing, in its detail it was far less complete. The author lays down as an axiom, that all the motions are circular and uniform, while observation makes us acquainted with none that are not constantly varying. To account for this, Copernicus was finally compelled to give to each of his circular orbits a different centre ; the sun is enclosed within all the orbits, but does not occupy the centre of any ; it has no other apparent duty, but to distribute light, and appears unconnected with any of the motions. In fine, in order to reconcile the appearances with the theory, he · was compelled to recur again to new epicycles, after having suppressed those of Ptolemy.
An important step was however made by him, without which a farther progress was impracticable. But if the reformation had proceeded no farther, practical astronomy would have gained little by the change. The founder of modern astronomy was not in possession of a sufficient series of good and authentic observations ; he had not the taste or fitness for long calculations. To have done all, would have required more years than fall to the lot of man, and three whole lives were employed before the task begun by Copernicus was completed. Tycho Brache made the observations for which the life and strength of Copernicus were insufficient, and dying, left Kepler in possession of all that was necessary to complete the revolution in the system of astronomy.
Plutarch tells us, that an ancient philosopher had said, that the Greeks ought to have brought to trial as impious, him that had dared to disturb the sanctuary of Vesta, by ascribing motion to the earth. Such was the fate Copernicus feared for himself, and which caused him to defer for thirty-six years the publication of his book. .
Tycho, who is entitled to the gratitude of astronomers for his observations, made a retrograde step in the theory, by proposing a system intermediate between those of Copernicus and Ptolemy. It is uncertain whether he were actuated by the theological scruples of his day, or ambitious of the glory of creating a new
theory. Rich, and of one of the first families of Denmark, he devoted his whole life and fortune to the cultivation of astronomy His instruments were far superior to any used before him, and besides discovering several inequalities of motion previously unknown, he left to his successors a regular series of observations of all the known planets. These were made and recorded, for the purpose of proving the excellence of his own system ; but falling into the hands of Kepler, the latter made a more happy use of them, in establishing, on a secure and everlasting basis, that of Copernicus. Tycho had luckily completed all that his peculiar views would have permitted him to perform, when a persecution, the cause of which is ill understood, deprived him of the countenance of his sovereign, and forced him to expatriate himself. Lalande has devoted to infamy, and the execration of all future ages, the minister Walchendorp, who is named as the principal author of this persecution. In similar terms, probably, future historians of astronomy, will speak of those politicians of our country, who, from ill-judging economy, frustrated the survey of the coast, and prevented the establishment of a national observatory, after all the preliminary steps had been taken, and the greater part of the preparatory expenses incurred. Such acts frequently arise from ignorance rather than malice; they excite little attention at the moment, but are sure to be visited by the retributive sentence of posterity.
Before the time of Kepler, astronomers paid but little attention to physical causes. This was the case even with Copernicus himself. . They were content with imagining an hypothesis that might serve as the basis of their calculations. Kepler, on the other hand, was unwilling to admit any thing without a reason ; and having detected an error of 8' in the best predictions of the positions of a planet, he set himself to investigate a theory that should be more consistent with the phenomena. His course of inquiry was curious, and founded upon views of the harmony of numbers, and perfection of curves, that we know now to be incorrect, but which we cannot help rejoicing that he entertained.
He commenced by inquiring why the number of planets was limited to six, and upon what principle the ratios of their respective distances from the sun, in the system of Copernicus, were founded. In the course of this inquiry, he detected a series, to which the six planets conformed, with the exception of a single interval, where he inferred a planet was wanting. This gap has been filled by the modern discoveries, and besides, another planet has been discovered, which takes exactly the eighth place in the series of Kepler. Of this series, thus found consistent in all its parts, we yet want the physical reason.
He next sought the relations between the distances and the periodic times of the planets, and after seventeen years of labour
and research, discovered the famous law, which still goes by his name, viz. that the squares of the periodic times are proportioned to the cubes of the distances. He failed in giving a mathematical demonstration of this law, which depends on a principle he did not understand; but he showed, from its coincidence with the phenomena, that it was true of the earth and the five other planets then known. This relation has been verified in the case of the five planets since discovered ; and has been shown to be equally true of the satellites of Jupiter and Saturn.
The second law of the planetary motions discovered by him is, that their orbits are not circles, as had been always supposed before, but ellipses. The motions in them were therefore essentially unequal, and he thus refuted the ancient axiom, retained even by Copernicus, that ascribed to these bodies uniform circular motions. This law was demonstrated by Kepler in a most ingenious and original manner.
The theory of uniform and circular motion, had hitherto been the foundation of all the calculations used by astronomers. In acquiring, therefore, the knowledge of the true figure of the orbits, every existing mode of calculating the phenomena became useless. It was for this reason necessary to discover some new principle of uniformity, which was now shown not to exist either in the eccentrics or the equants of the ancient school. Kepler found this in the areas described by the radii veotores, which he made to vary in the proportion of the times of their description. This was at first deduced from observation alone, but he finally succeeded in demonstrating its necessity; and this demonstration, reproduced by Newton in a more rigorous form, is now universally received. By the aid of this principle, the direct calculation of elliptic motions becomes possible, but is still attended with great difficulty. These difficulties were removed by an artifice of Kepler's, who comprised the whole calculation in the determination of the elliptic from uniform circular motion, by means of three elegant and simple formulæ, sufficient for all the purposes of practical astronomy.
By these brilliant discoveries, the sun was at last brought to occupy the place Copernicus had wished to assign it, but whence, in consequence of an erroneous hypothesis in respect to the motions, he had himself been compelled to remove it. The sun cannot occupy the common centre of circular orbits, but it does a focus common to all the elliptical paths of the planets. To this point, as a centre, all the motions must be referred; from it, all the distances must be counted. The planes of these ellipses cut each other in lines passing through the centre of the sun, and all the lines of their nodes pass through the same centre.
It was in attempting to reduce all the motions to physical causes, that Kepler was led to the discovery of these fundament
al laws, of which no former astronomer or mathematician had even suspected the existence. When he found that the sun really occupied the common focus, and centre of motion of the system, he became aware that it must be the principal source and director of their motions. He ascribed to it a mass capable of attracting and moving all the planets. He even ventured to declare that the sun must revolve upon his own axis, and that in a space of time less than three months. He finally saw that Universal Gravitation, must be a law of nature, and thus wanted but one step of reaching the discovery of Newton. From some inadvertence, difficult at the present moment to conceive, he inferred that this attraction must decrease in the simple ratio of the distance ; and committed this error, even although he had established completely, that the intensity of light diminished in the ratio of the surfaces over which it is distributed, that is to say, as the squares of the distances.
Bouillaud, a French writer on astronomy, in a work published in 1643, pointed out the mistake of Kepler, but instead of avail. ing himself of this fortunate discovery to improve the theory, he used it as an argument against the laws of Kepler, with which, on the contrary, it is absolutely and completely consistent. Thus, for a second time, did the true law of attraction elude the grasp of astronomers; and it was not received nor appreciated until it was demonstrated by Newton.
While Kepler was thus correcting and completing the system of Copernicus, rendering it fit to form the basis of the future calculations of astronomers, and engaged in labours of which the whole value was long unappreciated, it was, almost at the same moment, receiving elucidation in another direction, to estimate the importance and consequences of which, required little more than the use of the faculty of sight. The telescope had been discovered in Holland, we hardly know whether by accident, or by the curiosity of an amateur of philosophy of the name of Metius. Galileo, a name so deservedly celebrated in the annals of philosophical discovery, hearing the news, sought to divine the mode of forming the instrument, and completed one within a day from the time he received the intelligence, equal in power, but different in composition, from the original. In the hands of the inventor it had been directed solely to terrestrial objects ; Galileo pointed it immediately to the heavens. He speedily detected phases of the planet Venus, precisely similar to those of the Moon. Copernicus, it is said, had announced that such phases were the necessary result of his system; adding, that they could not be observed, in consequence of the small apparent diameter of the planet, and the brilliancy of its light. Galileo's inference was the converse of this; from the phases he deduced that Venus revolves around the sun. On turning his instrument to Jupiter, he found
VOL. III.—NO. 6.