artes et scientiæ exultant, diligentius introspiciat, ubique inveniet ejusdem rei repetitiones infinitas, tractandi modis diversas, inventione præoccupatas, ut omnia primo intuitu numerosa, facto examine pauca reperiantur."

Far different now is the state of things: we have abundance of important memoirs, but great deficiency of those treatises which should collect, reduce to order, and systematize what has been written. The work of M. de la Lande (excluding other objections) has not been translated; and those of Street, Mercator, Whiston, Keil, Long, Ferguson, Leadbetter, Dune thorne, Hodgson, Costard, &c. do not suit the present maturity of the science.

Astronomy is now divided into two parts, plane and spheri cal: but in the time previous to that of Newton, the former only existed. The science then depended on observation alone; aided, corrected, and informed, by the sciences of geometry, algeura, and trigonometry. Its distinguished cultivators were Hipparchus, Ptolemy, Copernicus, Tycho Brahé, and Kepler. This last great man may be considered as the first founder of physical astronomy, and the forerunner of the greater Newton, He suspected gravity to be a principle in the universe, yet touched on it but lightly, " extremis digitis." The discoveries of Kepler prepared the way for that memorable epoch of philosophy, when

" Cælum ascendit ratio, cœpitque profundis Naturam rerum causis, viditque quod usquam est."

It was reserved for Newton to verify the suggestion of Kepler, and to prove how justly the antient philosophers had thought concerning the simplicity and unity of a principle which was to account for all phenomena, though they had constantly erred in assigning what that principle was. It is matter of curious speculation, to consider how strong the propensity has been, in all ages, and in all men, to establish a first cause or principle; to refer the infinite complication of effects, and the boundless variety of phænomena, to the varied operation of the same active cause, or to the different modifications of the same matter!-Thales of Miletus affirmed water to be the constituent principle of the universe; Anaxagoras thought that fire was the element by the activity of which Nature might be formed, was supported, and was animated; and at the distance of more than two thousand years, Democritus and Descartes agree in their system, and require only matter and motion to construct the universe. This idea of simplicity has probably been suggested by observing the constant effect of experiment and research; which has been to illustrate what at first appeared

con

confused, to find out effects which might properly be referred to the same class, to establish analogies, and to afford glimpses at least of a system dependent on certain general laws. Yet there is a precipitate propensity in man to form systems, a disposition to believe that an hypothesis which solves some few phænomena is competent to account for all, to leave too soon the severe inquisition of nature, and to follow the phantoms created by their own imagination *. A great philosopher has made an excellent remark which suits the present subject: "Hence (says he) it cometh that the mathematicians cannot satisfy themselves, except they reduce the motions of the celestial bodies to perfect circles, rejecting spiral lines, and labouring to be discharged of eccentrics.-Hence it cometh, that whereas there are many things in nature, as it were monodicą, sui juris s yet the cogitations of man do feign unto themselves relatives, parallels, and conjugates, whereas no such thing is; as they have feigned an element of fire to keep square with earth, water, and air, and the like," &c. Advancement of Learning, 4to. p. 79.

It is to be lamented that so much labour and ingenuity should have been thrown away by the antient philosophers ;that men, capable of adding to the substance and richness of science, should have been employed in spinning flimsy systems, the cobwebs of the mind, of fine thread and workmanship, indeed, but of no use nor profit. It is to be lamented that they wanted a Bacon, whose sagacity was to point out the true route in which science was to be followed; and that they were unable to use, like Newton, the balance of an exalted geometry, by which, after having discovered the cause and principle of the universe, he could ascertain its law and intensity. Hence it was that they suspected only, but could not prove, the simplicity of God's workmanship, as he doth hang the greatest weights upon the smallest wires."

If it should be thought remarkable that there exists in human nature a strong propensity to believe that one or a few principles and elements are competent to the production of effects in appearance unconnected, and endless in their variety, it may seem not less so that, in laying down an hypothesis and constructing on it a system, so great an inattention should be manifested towards those facts which may be called negative facts; those which no possible subtility nor wile of reasoning can

* M. Freret, speaking of the Greek philosophers who succeeded Aristotle, says; "On ne s'occupa plus de soin d'acquérir des connoissances nouvelles, mais de celui de ranger et de lier les unes aux autres, celles que l'on croyoit avoir, pour en former des systêmes."

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reduce within the limits of that system, and subject to its power. The constant endeavour is to bring affirmations, facts which support an hypothesis; and to keep out of sight any that are contrary to it: yet is the power of these two classes of facts immensely different. A thousand facts of the former class may support an hypothesis, yet one single ascertained fact of the latter is competent to its destruction, and to reduce the system founded on it to the rank of those baseless unsubstantial theories, which are destined to please the imagination without satisfying reason. To speak particularly to the point: -Newton, in order to verify his hypothesis (for in his time it 'was only an hypothesis) that gravity observed the law of the inverse square of the distance, applied to the investigation of the most sensible phænomena; and the results of his calculations agreed well with observation. This law of gravity therefore seemed to prevail in many cases; yet its universality was by no means completely established. The geometricians of the continent adopted the hypothesis of Newton: but, in investigating the theory of the moon, it appeared (at first sight) that the quantity, representing the mean motion of the moon's apogee, was only half of the quantity determined by actual observation: here, then, the theory seemed eminently defective:but an oversight had been committed: -Clairaut, summing more terms of the series, found that the quantity determined by calculation agreed to great nearness with observation.-Yet had this single instance, which manifested the disagreement of theory and observation, been after mature consideration clearly established, the Newtonian law of gravity must have been abandoned; and indeed, before the discovery of his mistake, Clairaut had proposed to alter the law of gravity from the inverse square to a law compounded of the inverse square and biquadratic. This law would have solved a great number of the phænomena of the universe, although not all, as was proved by D'Alembert:-it was attacked (perhaps successfully) by the metaphysical arguments of Buffon. To mention another instance: a single case solved by the doctrine of chances (such as is generally received) in the game of cross and pile, and of which the determination is plainly contradictory to our common conceptions, and most examined judgments, has subjected the whole doctrine to doubt'; and the sagacious D'Alembert has sufficiently proved that its principles need revision and correction. If, indeed, we examine the history of science, we shall find abundant argument for admitting with caution any principles, however recommended by their simplicity. It was well answered by Pythagoras, to one who objected to his system as confused, confused, " that it was not a confused system, but that man was a bad judge of what was simple."

Of like nature with the principles above mentioned, and of equal danger to philosophy, are those which may be called metaphysical; which ought perhaps to be entirely excluded in physical inquiries, and, if admitted into the pure science of quantity, should be received with great eircumspection. In the Elements of Euclid, we find a definition which is of a metaphysical nature, but of which no use is made. As far as Archimedes knew concerning the earth, he judged rightly when he determined its form to be spherical. The angles of incidence and reflection were proved formerly to be equal, on this principle, that a ray of light pursues the shortest course;" because, said they, "it is agreeable to the simplicity of nature to go in the shortest way." To solve the case in refraction, Leibnitz introduced another principle somewhat different from the former. -The "sufficient reason" of this last mentioned is well known. In fine, the errors of great men must reconcile us to the imperfection of our own knowlege, and create (what are of great use in philosophy) calmness, circumspection, and deliberation.

We have observed that physical astronomy properly dates itself from the time of Newton. -The name of this great man is pronounced by us with a kind of rapturous enthusiasm; and in thinking of him we indulge the feelings and exultation of national pride; yet in France has been made the most just estimate of his merit, and the noblest monument has been erected to his memory. The geometricians of the continent have done more to perpetuate his fame, than the pen of Pemberton, or the chissel of Roubilliac. -The rational and calm appreciation of genius, by men of science, is of more weight than the high-sounding panegyric of those who know that much has been done, yet have no distinct notion of what has been done. It is generally supposed that Newton completely, and beyond all doubt, established the truth and universality of his law of gravity: but such is not the case; to have done it, would have required a length of life as extraordinary as the powers with which he was endowed. Yet he lived in so fortunate a conjuncture, that the world of science experienced no darkness when its SUN SET!

“Sol occubuit, nox nulla secuta est."

The empire of Alexander (says M. Bailly) was divided among his successors; the sceptre of Newton passed into the hands of three geometricians*; and they were destined to esta

* Clairaut, Euler, D'Alembert.

blish the empire which their predecessor had founded. The problem of the two bodies Newton had completely resolved: but, if gravity was a quality essential to every particle of matter, mutual actions must take place throughout the system; and to calculate the effects of these mutual actions, the derangements, accelerations, variations, &c. which must happen in the motion of planets and in the forms of their orbits, required the solution of a problem called the problem of the three bodies. This solution was given by Clairaut, Euler, and D'Alembert *; and it is the glory and characteristic of the age which succeeded that of Newton. After this, the principle of gravity and its law were verified throughout the universe. Clairaut and Euler published their theories of the moon. The precession of the equinoxes was determined by D'Alembert; -a problem which Newton im perfectly solved, and of which he arrived only at a right conclu sion by a compensation of errors in the process of the solution. The phænomena of the tides were illustrated by D. Bernouilli. The derangements of Saturn and Jupiter were computed by Euler, as they have since been by de la Grange. The volumes of the Academies of Berlin, Paris, and Petersburgh, (contain a vast number of important memoirs, which may be considered as so many testimonies to the truth of the Newtonian system; and it may be now said to be nearly ascertained by that test which distinguishes the baseless and perishable fabrics of the imagination, from those that are built on the sure foundations of truth and nature: "Quæ enim in naturâ fundata sint, crescunt et augentur; quæ autem in opinione, variantur, non au gentur." Yet, although so much has been done, difficulties still remain; all is not luminous: we cannot yet exclaim " Venimus ad summam fortuna." It was formerly supposed that the acceleration of the mean motion of the planets might be explained by their mutual action: but Messrs. de la Place and de la Grange have shewn, and by different methods, that the mutual action of the several parts of the system can produce no acceleration in their mean motion. To account for this acceleration, two hypotheses have been formed, and consequent calculations instituted. M. Bossut supposes the resistance of the æther to be the cause; and M. de la Place has inquired whether the action of gravity be the same on a body in motion, as on one at rest, and whether its propagation be instantaneous or not? if not instantaneous, whether this cir

* We do not mean that a complete solution "hujus problematis enodatis completa [says Euler] omnes analyseos vires transcendere vide tur." The solution is by the method of approximation: the difficulty is, to integrate three differential equations of the second order.