94 DISSERTATION SECOND. [fart if. 



years afterwards, that the conversation of Dr. Halley, who 

 made him a visit at Cambridge, induced him to resume 

 and extend his researches. 



He then found, that the three great facts in astronomy, 

 which form the laws of Kepler, gave the most complete 

 evidence to the system of gravitation. The first of them, 

 the proportionality of the areas described by the radius vec- 

 tor to the times in which they are described, is the peculiar 

 character of the motions produced by an original impulse 

 impressed on a body, combined with a centripetal force 

 continually urging it to a given centre. The second law, 

 that the planets describe ellipses, having the sun in one of 

 the foci, common to them all, coincides with this proposi- 

 tion, that a body under the influence of a centripetal force, 

 varying as the square of the distance inversely, and having any 

 projectile force whatever originally impressed on it, must 

 describe a conic section having one focus in the centre of 

 force, which section, if the projectile force does not exceed 

 a certain limit, will become an ellipse. The third law, 

 that the squares of the periodic times are as the cubes of 

 the distances, is a property which belongs to the bodies de- 

 scribing elliptic orbits under the conditions just stated. 

 Thus the three great truths to which the astronomy of the 

 planets had been reduced by Kepler, were all explained in 

 the most satisfactory manner, by the supposition, that the 

 planets gravitate to the sun with a force, which varies in 

 the inverse ratio of the square of the distances. It added 

 much to this evidence,, that the observations of Cassini had 

 proved the same laws to prevail among the satellites of 

 Jupiter. 



But did the principle which appeared thus to unite the 

 great bodies of the universe act only on those bodies? 

 Did it reside merely in their centres, or was it a force 

 common to all the particles of matter ? Was it a fact that 



