146 NEWTON S PIUNCIPIA. 



logons sides of the bodies ; and because the masses are as 

 the cubes of these sides, S and s, the attractions are as 

 S 3 . s n : s 3 . S w , or as s n ~* : S M ~ 3 . Therefore, if n = 1, 

 the attraction is as S 2 : s 1 ; if the proportion is that of 

 the inverse square of the distance, the attraction is as 

 S : s; if that of the cube, the attraction is as 1 : 1, or 

 equal ; if as the biquadrate, the attraction is as s : S ; 

 and so on : and thus the law of the attractive force may 

 be ascertained from finding the action of bodies upon 

 particles similarly placed. 



Let us now consider the attraction of any body, of 

 what form soever, attracting with force proportioned to 

 the distance towards a particle situated beyond it. Any 

 two of its particles AB attract P, with forces as A x AP 

 and B x B P, and if G is their common centre of gravity, 

 their joint attraction is as (A-f B) x G P, because B P, 

 being resolved into B G and G P, and A P into A P 

 and G P, and (by the property of the centre of gravity) 



GPxA=APxG, therefore the forces in the line A P 

 destroy each other, and there remain only P G x B and 

 P G x A to draw P, that is ( A + B) x P G ; and the 

 same may be shown of any other particles C and the 



