they most exactly and wonderfully accounted.

astronomer must undoubtedly have seen, as he was particularly conversant with every thing that came from or through the hands of Dr. Wallis.

This philosopher was the first who, in 1639, after detecting the fallacies of the Lansbergian tables and correcting them, by the use of Kepler's, which he improved, calculated and took the observation of that rare and decisive phenomenon, the transit of Venus, in which Kepler had failed. This important observation, by which the sun's parallax and distance from the earth are more justly ascertained, he published in a work entitled De Venere in Sole Visa, a few weeks before his death; and he had a much greater work in hand, in which he had made considerable progress. The subject of this was, in the first part, to refute the hypothesis of Lansberg, by which he had been misled; which is the work collected and published by Dr. Wallis: and the second part was still more important, intending to found a new philosophy upon the basis of sound experiment and accurate observation, in which he adopted the Keplerian hypothesis corrected and improved. But though he had made such advances in this new philosophy, as from it to calculate and construct an ephemeris, he had not so adjusted his materials and committed them to paper, that they could be collected and arranged for publication. An idea of his general scope may however be collected from what is incidentally said in the tract De Motu Siderum, inserted in the publication mentioned above. "Causa vera est physica, sol nempe conversione sui corporis reliquos planetas legibus magneticis secum rapit in gyrum, non aliter quam terra lunam, nubes, et reliqua in altum projecta, magnetica hac virtute secum circumvehit, ut doctissime probat Keplerus. Causam autem excentricitatis male (ut mihi videtur) tradit. Illam ego fibris magneticis quas ille in corpore planetarum fingit tribuendam non censeo, sed inertiæ eorum corporali, qua locum suum tueri conantur adversus fortiorem solis

By this theory founded and established in projectile motion, and thence by a vast ex

virtutem. Philosophiam hanc alio tempore fusius exponam, ejusque ope sperare ausim, ipsum creationis momentum ex motibus cœlestibus (saltem probabilissime) demonstrare. In presens hoc ago, ut studiosiorum animos a vanis illis et fictitiis circulorum somniis, ad naturalem et physicam magis causarum disquisitionem revocarem.-Exempla multa dari possunt eorum quæ per leges naturales et magneticas in circuitum rapiuntur.-Videmus terram magnetica sua vi nubes et reliqua sursum projecta abripere in gyrum.-Docet igitur hic nos experientia figuram circularem per leges magneticas generari posse, cur illud de stellis dubitemus, quod in aliis verum cernimus?-Ostendimus nos philosophiæ nostræ familiare exemplum.-Philosophiam nostram ab ipsa natura ultro oblatam nos grati accepimus: frustra illi ad causas fictitias, et pro lubitu commentas confugiunt." That every philosopher has an absolute right to avail himself of the labours and discoveries of his predecessors, as a legacy freely given him, is a privilege which philosophy always claims. It is however a tribute justly due to the memory of this extraordinary genius, whilst we regret the loss of his more valuable works, to acknowledge from what has been saved, that he was principally instrumental in calling philosophy out of the regions of fictitious invention, and putting her on the investigation of the physical causes of things from experiments and observations; that he not only made the application of projectile motion to the analo. gical illustration of celestial, but also assigned the forces both projective and attractive on which all geometrical calculations are founded; and that, without injuring the immortal fame of his great successor, he may be fairly considered as the forerunner of Newton. He mentions the vis inertiæ of matter in totidem verbis; and as to the attractive force, whether it be that of magnetism or gravitation, is immaterial; and indeed Sir Isaac himself, in the beginning of his Principia, is quite indifferent both as to its name and

ertion of mind translated to celestial, he confirmed the observations of these philosophers; demonstrated their hypotheses and conjectures"; and enacted on a sound

nature: (vel vi gravitatis, si modo gravis sit luna, vel alia quacunque vi, quâ in terram urgeatur).

That all bodies in reference to the earth as their centre, and all bodies in reference to the sun as their centre and moving in a sphere, are acted upon and varied in their motions and spheres, according to their respective distance, by some physical cause or causes from which their phenomena could be geometrically demonstrated, was the general doctrine of Horrox. Halley, observing the surfaces of the planetary spheres to be as the squares of their radii, found the force at several distances to act reciprocally as the squares. And Newton demonstrated, that a planet must revolve in an ellipsis about the centre of force in the lower focus acting reciprocally as the square of the distance, and that with a radius drawn to that centre, it must describe areas proportionable to the times; particularizing and completing the mathematical calculation, and carrying it through all the celestial phenomena. All which might probably have been done by Horrox, had he lived to execute his work; but this admirable young man of illustrious genius though humble birth died in the year 1641, at the age of twentythree!

32 It is Kepler's first rule, "That the same planets describe equal areas in equal times ;" and Sir Isaac Newton demonstrated from thence, " that the planets are attracted towards the sun as their centre." Kepler's second rule is, “That the squares of the periodical times are as the cubes of the transverse axis of their orbits;" and Sir Isaac demonstrated "that the force is reciprocally as the squares of the distance;" from which duplicate ratio he demonstrated the rule. It is Kepler's third rule, "That the orbits of the planets are oval and probably elliptical, having the sun in the

foundation the laws of the whole planetary system, which, on finding their truth confirmed by repeated facts and continued experience, he called the mathematical principles of astronomy".

From these principles or general laws of motion, by the same geometrical calculations, he deduced the stupendous theory of the elliptical orbits of the planets both primary and secondary, of the spaces through which they pass, of the different velocity with which they move, both in respect of each other and of themselves in the different stages of their ethereal journey, of their relative times and respective situations; and crowned this amazing system of the heavens, by his new philosophy of the motion of the comets, the moon and the tides.

For the mathematical foundation of his astronomy, as the effects and motions were the same or similar, he assigned the same or

focus;" and Sir Isaac demonstrated "that the orbits are really elliptical, and that the sun is in the lower focus."

33

Principia tradidi a mathematicis recepta et experientia multiplici confirmata.-Newton. Præf. in Princip.

similar forces existing in nature, as the efficient causes both of mechanical and celestial motion 34. And truly whether in the act of deriving his principles from the projectile phenomena, or subsequently for the purpose of applying them to the planetary, it was necessary to analyze the elliptical motion of the heavenly bodies into a compound of two simple motions in right lines produced by

35

See his Regulæ Philosophandi prefixed to the third book of the Principia.

Having founded his astronomy on the analogy between the phenomena of projectile and planetary motion, from the phenomena he pushed the analogy to the forces as the efficient causes of both. "Despiciamus," says Mr. Cotes in his preface, "qualis sit in terrestribus natura gravitatis, ut deinde tutius progrediamur ubi ad corpora cœlestia longissime a sedibus nostris remota perventum fuerit;" which is more fully explained in the following words: "Videamus jam comparatione instituta inter planetarum vires centripetas et vim gravitatis, annon ejusdem forte sint generis. Ejusdem vero generis erunt, si deprehendantur hinc et inde leges eædem, eædemque affectiones."

35 The projective impulse given to a stone being the cause of its ascent in the air, and its own weight that of its descent to the earth, he adopted projection and gravitation or the centrifugal and centripetal forces, in their compound operation both on the projectile and planet, as the causes of their similar motions: and these forces he made the mechanical foundation of his Principia. "Mechanica rationalis erit scientia motuum qui a viribus quibuscunque resultant, accurate proposita ac demonstrata." And, after his Principia were formed, these and similar forces are the subjects upon