ATTRACTION. 



riican system, yet acknowledged an at- 

 tractive power in matter. 



In France, also, we find Ferinat and Ro- 

 bcrval, mathematicians of great eminence, 

 maintaining the same opinion. The lat- 

 ter, in particular, made it the fundamental 

 principle of his system of physical astro- 

 nomy, which he published in 1644, under 

 the title of " Arist. Samii de Mundi Sys- 

 tema." 



Dr. Hooke, however, was the person 

 who conceived the most just and clear no- 

 tions of the doctrine of gravitation, of any 

 before Newton, in his work, called " An 

 Attempt to prove the Motion of the 

 Earth :" 1674. He observes, that the hy- 

 pothesis on which he explains the system 

 of the world, is in many respects different 

 from all others ; and that it is founded on 

 the following principles . 1. That all the 

 heavenly bodies have not only an attrac- 

 tion or gravitation towards their own cen- 

 tres, but that they mutually attract each 

 other within the sphere of their activity. 

 2. That all bodies which have a simple or 

 direct motion continue to move in a right 

 line, if some force operating without in- 

 cessantly, does not constrain them to de- 

 scribe a circle, an ellipse, or some other 

 more complicated curve. 3. That attrac- 

 tion is so much the more powerful, as the 

 attracting bodies are nearer to each other. 



But the precise determination of the 

 laws and limits of the doctrine of attrac- 

 tion was reserved for the genius of New- 

 ton : in the year 1666, he first began to 

 turn his attention to this subject, when, to 

 avoid the plague, he had retired from Lon- 

 don into the country ; but, on account of 

 the incorrectness of the measures of the 

 terrestrial meridian, made before this pe- 

 riod, he was unable to bring his calcula- 

 tions on the subject to perfection at first. 



Some years afterwards, his attention 

 was again called to attraction by a letter 

 of Dr. Hooke's ; and Picard having about 

 this time measured a degree of the earth, 

 in France, with great exactness, he em- 

 ployed this measure in his calculations, 

 instead of the one he had before used, and 

 found, by that means, that the moon is 

 retained in her orbit by the sole power 

 of gravity, sup posed to be reciprocally pro- 

 portional to the squares of the distances. 



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 ot 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 immortall;: 

 ed his name, entitled " Philosophic^ Na- 

 turalis Principia Mathematical' 



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, whicli 

 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 esta- 

 blished the principle, that every molecule 

 of matter 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 exception 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 do- 

 fective in several respects. He has per- 

 fectly established the principle which he 



