superior talents; and it seldom succeeds but in very short attempts. The verses, said to have been addressed to sir W. Young, with his answer

Dear madam, when ladies are willing,' &c.

were in reality composed by lady Hertford, to lord William Hamilton: the answer was a jeu d'esprit, written extempore by lady Mary on the back of a letter. As there are no marks to distinguish the lines now first printed, from those formerly given to the world, we cannot decide, from recollection, the quantity for which we are indebted to the present editor: we suspect he has given the larger portion.

ART. IX.-An Account of the astronomical Discoveries of Kepler: including an historical Review of the Systems which had successively prevailed before his Time. By Robert Small, D. D. &c. 8vo. 7s. 6d. Boards. Maw

man. 1801.

EVERY judicious attempt to elucidate the history of astronomy must be interesting and instructive; and, if not too prolix, must be also entertaining. To a cursory observer, the appearances of the heavenly bodies seem totally incompatible with every idea of order and regularity; and an attempt to reduce their motions to any fixed and precise rules might probably be considered as vain or enthusiastic. But unwearied assiduity triumphs over the most formidable obstacles; and the history of astronomy furnishes strong evidence of the success which attends the union of skill and perseverance.

In the volume now on our table, it is the chief object of Dr. Small to give a full and particular explanation of the doctrines and discoveries of Kepler, of the circumstances which produced them, and even of the mistakes committed in their prosecution. The design is unquestionably laudable: for, since that sagacious and indefatigable philosopher stands at the head of the modern or reformed astronomy, the establishment of which was in great measure effected by his grand discoveries, a specific statement of the steps he pursued, of the reasonings he adopted, and the operations he performed, cannot but be gratifying to the man of science; while, at the same time, the presentation of so singular and splendid an example of unceasing. application and fertile genius may stimulate others to exertion and ultimate success.

It is not merely on account of Kepler's more grand and striking 'discoveries, that he deserves to be celebrated: astronomers owe him other obligations than many are aware of. If he did not first give to astronomy the form of a science, he introduced into it many important principles and practices,. which, if previously known, were either known imperfectly, or

applied improperly: of this kind are his novel and numerous methods for ascertaining the places of the nodes, and the inclinations of the planetary orbits; his momentous doctrine of the permanency of those inclinations; his accurate principles for the proper reduction of any orbit to the ecliptic; and the first near determinations of the places and motions of nodes, apsides, &c.

The volume before us consists of eight chapters, with copious notes; of all which we shall speak in their order. In chapter I. are described the principal motions and inequalities of the celestial bodies. Here we have explications of the first or diurnal motion, and many peculiar actions; first and second inequalities; precession of the equinoxes; motion of the solar apsides; motions of the moon, with their inequalities; motions and inequalities of the planets; equations of the centre; nodes of the orbits, &c. The explanations in this chapter may be considered as preparatory to what follows: it teaches us what motions and inequalities were discovered by the ancients. But it would have been more satisfactory, if the processes, by which such discoveries were ascertained, had been more fully developed.

The most ancient theories and planetary systems, as the Platonic, the Egyptian, the concentric, and particularly the Ptolemaic system, form the subject of the second chapter. A system has been aptly compared to an imaginary machine, connecting together, in the fancy of the theorist, the different movements which should seem to be performed: as, therefore, in the infancy of astronomy, the motions and effects appeared complex, it is no wonder that their systems were complex also; but, as connecting principles were detected, which more closely connected discordant phænomena, the machines became gradually simplified; and at length a system was invented, which afforded the utmost satisfaction, both on account of its simplicity, and the facility with which it was applied to the solution of such phænomena. Dr. Small states both the natural difficulties and physical prejudices which prevented the rapid formation of a just system. The whole range of the celestial physics of the ancients, as this gentleman observes (p. 36), hinged on two principles, supposed to be unquestionable; first, that all the celestial motions were perfectly circular; and, secondly, that they were really uniform, when referred to their proper centres: and when an ancient astronomer had investigated the circles and epicycles which seemed best to agree with his observations, he rested satisfied that he had divined the true system of nature.' After giving an ample account of the Ptolemaic system, with its application to the motions of the moon and planets, our author states its imperfections; shows that its suppositions were dissimilar, and often inconsistent with

each other; that it was an assemblage of incongruous parts connected by no principle of union; and that the predictions made according to its rules were erroneous.

6

But' (says he) the objection which seems to have struck at the credit of the Ptolemaic theory, more than all its inaccuracy in representing the phenomena, was its contradiction to the sup posed inviolable law of circular and uniform motion, which it was the principal object of all systems to establish and confirm. Not only did its oscillations and librations produce perpetual deviations, both from the plane and the circumference of the circle; but also the uniformity aimed at by the equant itself was purely imaginary; for it took place in an orbit where the celestial body was hardly ever found; and, by the introduction of it, a real inequality of velocity was acknowledged in the orbit, which the body actually described. The position also of the centre of the equant was regulated by no general law: for, in the theories of Venus and the superior planets, its distance from the centre of the earth was bisected by the centre of the orbit; in the theory of Mercury, on the contrary, the mean excentricity of the orbit was bisected by it; in the lunar theory, it continually varied its position; and, in the solar theory, it coincided with the centre of the orbit.'

P. 79.

The third chapter is occupied in explaining the Copernican system; the author previously stating the original design, and probable motives, which induced Copernicus to frame a system of any kind, and his long hesitation in publishing it after he had completed it to his satisfaction. Much of this chapter is curious and interesting: but the author seems to have fallen into a common error in speaking of the phases of the inferior planets. When' (says he, p.125) in answer to another equally powerful objection, that no varieties of phase were seen in the planets, especially in Venus and Mercury, Copernicus could only express his hopes that such varieties would be discovered in future times, his reply, though it now raises admiration, could not, in his own times, make the least impression on those who opposed his system.' See also pp. 91. 142. Now, the fact is, that the mere changes in the discs of the inferior planets, as urged by the Ptolemaists, instead of being a powerful objection,' proved nothing as to the truth or falsehood of the Copernican hypothesis. For, from a little consideration, it will appear that, according to the Ptolemaic system, all the planets undergo mutations in their phases, similar to those of the moon; so that the objection (if it had any weight) would militate with more force against that system, than against the Copernican. It is somewhat singular, that a man of the acuteness of Copernicus did not detect the fallacy of this objection; and more extraordinary still, that, among the various writers on the science, we recollect only one or two who have exposed its inconsequence.

The system of the justly-celebrated Tycho Brahe, with its

awkward emendation, now known by the name of the Semi tychonic system, are explained in the fourth chapter. The great merit of this philosopher is justly insisted upon, as a zealous, indefatigable, and ingenious observer of the heavens ; and a proper tribute is paid to him for his diligence and care in determining the variable inclination of the moon's orbit. The causes which led to the temporary preference which the Tychonic system received, and those which produced the restoration and final triumph of the Copernican, are then related; particular notice being taken of the telescopic discoveries of Galileo.

In the fifth chapter are stated the original intentions of Kepler, and the facts which paved the way to his discoveries. This part, though very concise, contains some important information. In the following extract, we meet with a circumstance which is not generally known.

Though he' (Kepler) prosecuted his studies with success, and was a disciple of Mæstlinus, an astronomer of eminence, and of the Copernican school, he informs us, that he had no peculiar predi lection for astronomy. His passion was rather for studies more flattering to the ambition of a youthful mind; and when his prince selected him, in 1591, to fill the vacant astronomical chair at Gratz, in Stiria, it was purely from deference to his authority, and the persuasions of Mæstlinus, who had high expectations from his talents, that he reluctantly accepted of the office. He appears to have thought it unsuitable to his pretensions; and the state of astronomy was besides so low, uncertain, and in many respects visionary, that he had no hope of attaining to eminence in it. But what he undertook with reluctance, and as a temporary provision conferred on a dependant by his prince, soon engaged his ardour, and engrossed almost his whole attention.'

P. 145.

Kepler had not long attended to astronomic subjects before he meditated a considerable innovation. He conceived that the plane of every planetary orbit, and the line of its apsides, ought to pass through the centre of the sun, and not through the centre of the ecliptic, as had been previously taken for granted. The arguments he at first adduced were not fully conclusive; but, after many laborious operations, he at length struck upon a strict demonstration, which may be seen in page 266 of the volume before us. This was certainly an important discovery; but we think Dr. Small estimates its value too highly: it was scarcely necessary to give it a kind of superlative commendation in three distinct places, as the doctor has done in pp. 154, 266, and 269.

Many of the notes to this chapter exhibit striking evidences of the scrupulous precision with which Kepler examined the several parts of the ancient theories, before he ventured to introduce his own. Few persons have any notion of the

astonishing labour of a variety of his investigations: they equally excite our admiration and surprise. In note I, we could not help regarding some curious particulars, and especially the similarity between Kepler's solution of a problem, and one afterwards given by sir Isaac Newton to the same proposition-i. e. To describe a circle through two given points which shall touch another circle given in position.'

Chapter VI. treats of Kepler's theory, founded on apparent oppositions, which he distinguished by the name of the vicarious theory. Its refutation is likewise given, and the cause of Kepler's future discoveries stated. We agree with Dr. Small, that it is impossible to convey a just notion of the difficulties which attended the formation of Kepler's theory, or of his indefatigable patience in it, except by a repetition (or at least a close examination) of his procedure.' We therefore refer the reader to note N, page 330, for an example of that great astronomer's management of calculations, before the discovery of logarithms; and, if he should be fatigued by pursuing this single process, what must he think of the patience and perseverance of Kepler, who assures us he went over every step seventy times!! How painful to spend four years in such a manner and how much more painful to abandon the theory which had been the fruit of such incessant labour !

The last two chapters of Dr. Small's work describe Kepler's solar theory, or theory of the second inequalities, and the application of the physical method of equations to the theory of Mars, together with the important consequences of this application. Here we are made acquainted with the process by which Kepler concluded, from Tycho Brahe's observations, that the orbit of Mars could not be a circle; his reasons for supposing that the orbit must be some kind of oval, and probably an ellipse, as the most simple of all ovals; his precipitate theory concerning a peculiar kind of oval orbit, with the difficulties, vexations, and loss of time, in which he was thereby involved. Here, too, we have strong proofs of his unfeigned love of truth; in the pursuit of which, though old prejudices and misconceived theories would frequently conduct him into a wrong path, yet no disappointments could damp his ardour, no waste of time in tedious investigations could weaken the sagacity of his perception. No sooner was he convinced that the steps he had taken, however laborious, had led him astray, than he directed all his efforts into some new path, and pursued the course with redoubled energy. This indefatigable zeal and unabated ardour, in spite of every mistake and disappointment, greatly enhance his fame: to him may be applied, with strict propriety, the language of Martial

Si non errásset, fecerat ille minus.