According to this law, he also found, that the line described by bodies in their descent is an ellipse, of which the centre of the earth occupies one of the foci ; and considering afterwards, that the orbits of the planets are in like manner ellipses, having the centre of the sun in one of their foci, he had the satisfaction to perceive, that the solution which he had undertaken only from curiosity was applicable to some of the most sublime objects in nature. These discoveries gave birth to his cele brated work, which has justly ed his name, entitled " Philosophicx Na turalis Principia Mathematics." In generalising these researches, he showed that a projectile may describe any conic section whatsoever, by virtue of a force directed towards its focus, and act ing in proportion to the reciprocal squares of the distances. He also developed the various properties of motion in these kinds of curves, and determined the necessary conditions, so that the section should be a circle, an ellipse, or an hyperbola, which depend only upon the velocity and pri mitive position of the body, assigning in each case the conic section which the bo dy would describe.
He also applied these researches to the motion of the satellites and comets, show ing that the former move round their pri maries, and the latter round the sun, ac cording to the same law; and he pointed out the means of determining by observa tion the elements of these ellipses.
He also discovered the gravitation of the satellites towards the sun, as well as to wards the planets ; and that the sun gravi tates towards the planets and satellites, as well as that these gravitate towards each other: and afterwards extending, by ana logy, this property to all bodies, he este blished the principle, that every molecule ofmatter attracts everybody in proportion to its mass, and reciprocally as the square of the distance from the body attracted.
Having ascertained this principle, he from it determined, that the attractive force of a body on a point placed without it is the same as if the whole mass were united at the centre. He also proved, that the rotation of the earth upon its axis must occasion a flattening of it about the poles ; which has since been verified by actual measurement: and determined the law of the variation of the degrees in dif ferent latitudes, upon the supposition that the matter of the earth was homogeneous.
But, with the exdeption of what con.. cerns the elliptical motions of the planets and comets, and the attractions of the heavenly bodies, these discoveries were not wholly completed by Newton. His theory of the figures of the planets is limited by the supposition of their homo geneity ; and his solution of the problem of the precession of the equinoxes is de.
fective in several respects. He has per. fectly established the principle which he bad discovered ; but left the complete development of its consequences to the geometers that should succeed him.
The profound analysis also, of which he was the inventor, had not been sufficient ly perfected, to enable him to give com plete solutions to all the difficult problems which arise, in considering the theory of the system of the world ; so that he was oftentimes obliged to give only imperfect sketches or approximations, and leave them to be verified by a more rigorous calculation.
Attraction may be divided, with respect to the law it observes, into two kinds ; 1. That which extends to sensible distances ; such is the attraction of gravity, of which we have been treating, which is found in all bodies, and the attraction of magne tism and of electricity found in some par ticular bodies : 2. That which extends to very small or insensible distances.
The attractions belonging to the first class must be as numerous as there are bodies situated at sensible distances. It has been proved that their intensity varies with the mass and the distance of the at tracting bodies ; it increases with the mass of those bodies, but diminishes as the dis tance between them increases. The rate of variation has been demonstrated to be inversely as the square of the distance, in all cases of attraction belonging to the first class.
The nature of the attraction of gravity has been already discussed. It is, as far as the experience of man can extend, uni versal in all matter. The attractions of magnetism and of electricity are partial, being confined to certain sets of bodies, while the rest of matter is destitute of them ; for it is well known that all bodies are not electric, and that scarcely any bodies are magnetic, except iron, cobalt, nickel, and chromium ; and there is good reason to suspect that the magnetism of the three latter substances is caused by their containing some iron united to them.
The intensity of these three attractions increases as the mass of the attracting bo dies, and diminishes as the square of the distance.
'the first extends to the greatest dis tance at which bodies are known to be se parated from each other. How far elec tricity extends has not been ascertained ; but magnetism extends at least so far as the semidiameter of the earth. All bodies possess gravity ; but it has been suppos ed that the other two attractions are con fined to two or three subtile fluids, which constitute a part of all those bodies that exhibit the attractions of magnetism or of electricity.