notions had often been imposed on the world as notions stately and magnificent, they could not refrain from throwing an air of mystery over their discoveries; and they sought an unworthy triumph by perplexing and bewildering, when they ought simply and plainly to have instructed.

Much then is to be found in the writings of these patriarchs in science, that may be retrenched and altered; and the author who has skill and patience to pierce through light and darkness, through truth and error, and to separate them, is intitled to the thanks of the community. In such a situation, the present writer stands :-to sufficient patience for the task, we congratulate ourselves that Dr. Small added the requisite ability; and possessing the requisite ability, we must strongly applaud his patience.

Of the plan of this work, we cannot give a better account than is contained in the author's own words:

My principal intention, in the present publication, is to give a more full and particular account of Kepler's discoveries, than any to be found in the usual systems, or the general histories of Astronomy; and to extract the account from his own investigations. These are chiefly contained in his Commentary on the Motions of Mars; and I have often regretted that a work, containing such invaluable discoveries, should not be more generally and distinctly known. This work claims attention for another reason, that it exhibited, even prior to the publication of Bacon's Novum Organum, a more perfect example, than perhaps ever was given, of legitimate connection between theory and experiment; of experiments suggested by theory, and of theory submitted without prejudice to the test and decision of experiments. But, in order to form a just estimate of those discoveries, nay, perhaps, a distinct conception of the investigations by which they were produced, it seemed absolutely necessary to prefix an account of the more ancient astronomical theories, and of the principal phenomena which they were contrived and supposed to explain.'

In Chapter 1, on the Principal Motions and Inequalities of the Celestial Bodies, will be found a very precise and perspicuous statement of some of the ordinary phænomena of the heavenly bodies; together with the method of computing the mean motions of the planets, &c. Since the writings of Kepler and their merits cannot be properly appreciated without a knowlege of the antient systems, Dr. Small devotes his second chapter to explain those systems, and particularly that of Ptolemy. We do not force ourselves into panegyric, when we say that this explanation is conveyed in a very masterly manner. Dr. S. clearly represents the concentric and excentric theories, and shews the alteration, (or rather complication,) which such theories received, in order that the heavenly phanomena might be reduced under their laws. He does not

in a rough and general manner exhibit Ptolemy's system, but gives the method by which that great Astronomer found the excentricity of the equant, the equations of the centre, the semi diameters of the epicycle, &c. He likewise points out the defects under which Ptolemy's system laboured; not defects originating in physical absurdity, or absence of simplicity and analogy, but on an inadequate explanation of phænomena; and this is the true ground for rejecting theories: since in the most perfect, something must always be left to conjecture, and much must rest on probability.-The author concludes the 2d chapter with these sensible observations:

• Notwithstanding the labour employed, and the ingenuity displayed in the formation of this system, its imperfections were so great and numerous, that it was impossible it should always continue to maintain its credit. Though the original introduction of excentric orbits by Hipparchus banished some of the ancient epicycles, and promised greater simplicity than had been attained in the ancient concentric theory, the more extensive application, which Ptolemy and his followers made of the excentric theory, rendered it at last almost as perplexed and intricate as the theory which it had displaced. Its suppositions were often dissimilar, and even inconsistent with one another; and instead of answering to the title of a system, it was an assemblage of parts connected by no general principle of union, and between which there subsisted no known mutual relations; for, though the ratio of an epicycle to its peculiar orbit might be determined, those of the orbits to one another were entirely arbitrary. In many respects it was destitute of the authority even of sense, to which it principally appealed; and, notwithstanding the pretensions of reducing the celestial phenomena to the rules of geometrical calculation, it was not uncommon to find differences of hours and days, and even of months, between the calculation and the fact; nay, it frequently happened, that the predictions, made according to its rules, entirely failed. But 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 supposed 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. Finally, by the complicated motions ascribed to some of the circles, especially in the theories of the moon and Mercury, those bodies were brought, in some parts of their orbits, so near to the earth, that their position was wholly incon sistent with all observations of diurnal parallax.'

With our present advantages of science, improved and confirmed by multiplied observations, the system of Ptolemy appears monstrous and incongruous: by the multiplication of epicycles, it might explain the inequalities in the motions of the heavenly bodies, but it could never adequately account for the alterations of their distances: besides, the planets' motions in latitude caused new perplexities to the system; and (which was a great argument, at least against its simplicity,) it was found necessary continually to increase the number of the epicycles, with the advancing accuracy of observations. Yet these real defects of the Ptolemaic system were not the cause of its overthrow; since the motives which happily induced Copernicus to revolt against antient authority were not founded in reason. He was displeased, not with the complication of the epicycles, (for he himself did not reject their use,) but with the violation of what he thought was a law of nature, the principle of uniform motion in perfect circles:-but now, relying on an astronomy established by numerous and accurate observations, we teach that the motions of the heavenly bodies are neither uniform nor performed in circles. If, however, the cause of Copernicus's revolt was unjustifiable, the revolt itself was most fortunate, and opened a road for the explanation of the true system of the world.

By a happy temerity, or by a wonderful sagacity, Copernicus at one blow demolished a multitude of epicycles, by making the earth to revolve round the sun, like other planets, and its orbit to become a great epicycle. All astronomers know that, by this simple hypothesis, he plainly and adequately accounted for what are called the second inequalities; and it became immediately obvious, with the help of a diagram, why a planet must sometimes appear retrograde, and sometimes stationary. By this hypothesis he was enabled, with the aid of geometry, to assign the ratio subsisting between the distances of the planets from the sun, and to account for the variations of the planets' latitudes. In other explanations, however, Copernicus failed:in that of the lunar theory, and of the first inequalities of the planets. He exerted, like his predecessors, much ingenuity and much geometry, to no purpose.-The author of the present treatise thus neatly concludes his account of the Coperni can system:

The principal cause which engaged Copernicus in all this waste of labour and ingenuity, was the unhappy prejudices so often mentioned

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tioned in favour of uniform and circular motion, joined to his excessive deference for Ptolemy. This deference was indeed the sole cause of that most vexatious part of his labour, which regarded the motions of Mercury: for his situation on the low and foggy banks of the Vistula, rendered it impossible for him to make observations himself on that excentric planet; and he had not presumed, like Kepler, to suspect that Ptolemy, instead of deducing his theory from. observations, had sometimes corrected the observations to suit the theory. When he introduced therefore such a complication of circles, and perplexed compositions of their motions, to account for the singular phenomenon of Mercury's greatest digressions taking place at 60° on each side of his least distance from the earth, it was because he had no opportunity of discovering that the phenomenon was imaginary; and the observations, from which it was inferred, either inaccurately made, or unfaithfully transmitted.

The system of Copernicus was not received, on its appearance, with any degree of that approbation which it deserved, and which it now universally obtains. Its cold reception, indeed, fully justified the hesitation and tardiness of its author, to communicate it to the world. Yet, his want of success in explaining the latitudes and first inequalities of the planets in longitude, and the intricacy of his theories on these subjects, were not the principal causes of rejecting his opinions. On the contrary, those were the parts of bis labours which, on their first publication, were chiefly valued and his theory of Mercury, especially, notwithstanding its being encumbered with more epicycles than his explanation of the second inequalities had banished, excited the admiration of many eminent astronomers. But his system was chiefly opposed, on account of all in it that was valuable and distinguishing and the substitution of the diurnal and annual motions of the earth, for the apparent diurnal revolution of the heavens, and the annual motion of the sun, was such a violent contradiction, both of the philosophical principles of the age, and the immediate evidence of sense, that all its advantages were undervalued, and proved insufficient to procure to it general credit. The conception of Copernicus, which represented the distance of the fixed stars from the sun to be so immense, that in comparison with it, the whole diameter of the terrestrial orbit shrunk into an imperceptible point, was too great to be adopted suddenly by men accustomed to refer all magnitudes to the earth, and to consider the earth as the principal object in the universe. Instead of being reckoned an answer to the objection against the annual revolution of the earth, that her axis was not found directed to different stars, it was rather considered as the subterfuge of one who had invented, and therefore tried to vindicate, an absurdity and, when 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. The earth was universly supposed to be so immense and ponderous as to be incapable of any kind of motion: and the diurnal rotation, in particular, was

thought

thought to be decisively confuted by the consideration of centrifugal force; which would throw off all bodies, animate and inanimate, from its surface. These objections, and many others of no force in themselves, but in that age deemed irresistible, by reason of the low state of human knowledge, prevented the Copernican system from being generally considered in any other light than as a mere hypothesis, and were the principal causes of the celebrity for some time maintained by the system of T. Brahć.'

In pursuance of his plan, Dr. Small next gives an account of Tycho Brahé, with his system and discoveries. The former has shared the fate of the Ptolemaic, and is rejected as false : but his discoveries of the lunar inequality, called the Variation, -of the inequalities of the motions of the nodes, and of the inclination of the lunar orbit,-and lastly his numerous observations which proved so useful to Kepler,must for ever assign to Tycho Brahé a distinguished place among the founders of astronomical science. His system was favourably received by his contemporaries: for the Danish astronomer shocked not vulgar prejudices, nor was guilty of Galileo's heresy, by ascribing motion to the earth.

Great, however, as the ingenuity and merits of T. Brahé appear to be, we can hardly fail to perceive the inferiority of his system to the Copernican, in perspicuity, simplicity, and symmetry of parts. The periodical motions which he ascribed to the planets were double, and performed round two different centres; for, considering the orbits of the planets as epicycles, a planet had first to move in the circumference of its epicycle round the sun, and then the sun, carrying along with him all the planetary epicycles, had to move round the centre of the ecliptic: and, if we also take into consideration the diurnal revolution, the system of T. Brahé will be found more complex than that of Ptolemy, who gave one common centre to all the revolutions, both periodical and diurnal. But, notwithstanding the perplexed nature of this system, and that it gave no account why the sun, moon, and planets, should obey the diurnal revolution of a sphere, in which they did not move: or why the planets should obey the annual revolution of the solar sphere, from which the distance of some was immense; or why the earth, though placed. between the spheres of Mars and Venus, should alone resist the influence, whatever it might be, which carried these bodies and so many others on each side of it round the sun; such was the difficulty of conceiving and admitting the motion of the earth, that this intricate and incoherent system was preferred to the simple and beautiful system of Copernicus, by all the vulgar; and for a long time rivalled, and even surpassed it, in reputation, among the learned.'

The 5th chapter presents a brief relation of Kepler's studies, of his first publication, of his introduction to Tycho Brahé, and of his original intentions. Kepler soon found that all existing theories were defective; and his first projected innovation was

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suggested