264 ATTEACTION OF BODIES. 



and formed by the revolution of I H K L I round the diameter 



IP 2 



A B, and which is proportional to I H x I q, is as ^ =-- ; 



Pp x P S 



and if the attraction upon the particle P is as the surface 

 directly, and the square of the distance inversely, or -^-^, that 



attraction will be as ' -. But if the force acting in 

 Pp X PS 



the line P I is resolved into one acting in P S and another 



P<7 



acting in SD, the force upon P will be as =j^, or (because of 



P 



the similar triangles PIQ, PS^) as -. The attraction, 



therefore, of the infinitely small curvilinear surface formed 

 by the revolution of I H is as rp7 2 or as ^-^ ; that is 



inversely as the square of the distance from the centre of the 

 sphere. And the same may be shown of the surface formed 

 by the revolution of K L, and so of every part of the spherical 

 surface. Therefore the whole attraction of the spherical sur- 

 face will be in the same inverse duplicate ratio. 



In like manner, because the attraction of a homogeneous 

 sphere is the attraction of all its particles, and the mass of 

 these is as the cube of the sphere's diameter D, if a particle 

 be placed at a distance from it in any given ratio to the 

 diameter, as ra.D, and the attraction be inversely as the 

 square of that distance, it will be directly as D 3 , and also as 



g -p^, and therefore will be in the simple proportion of D, 



the diameter. Hence if two similar solids are composed of 

 equally dense matter, and have an attraction inversely as the 

 square of the distance, their attraction on any particle simi- 

 larly placed with respect to them will be as their diameters. 

 Thus, also, a particle placed within a hollow spheroid, or in a 

 solid, produced by the revolution of an ellipsis, will not be 



