270 ATTEACTION OF BODIES. 



other matter to the spherical bodies having manifestly no 

 effect in lessening the attraction. 



By similar methods we find the attraction of any portion or 

 segment of a sphere upon a particle placed in the centre, or 

 upon a particle placed in any other part of the axis. Thus in 

 the case of the particle being in the centre S, and the 

 particles of the segment E B G attracting with forces as the 



-th power of the distance S or S I, the curve A N B will by 



its area express the attraction of the spherical segment, if 



I O 8 (x of c* 

 D N or y be taken = ^- = *, - ^ , S being put = c, 



and A D = x, and AS = a, as before ; f y dx may be found as 



\ IT ^"~ CL 1 Cl SC """ (* U X 



before by integrating - - -r - - . The fluent is 



( oc ~* a ) 



(x - a) 3 "" (a? -a) 1 _ 2 c 3 -" 



s - - -- c 2 - - - -- H C ; and C = -; - - -- - ; and 

 3 - n 1 n* - 4 n + 3 



the whole attraction of the segment upon the particle at the 



a 3 -" c* a 1 "" 2 c 3 -* 



centre S is equal to - --- , -- h -5 - ; -- o- Ihus, it 

 3 n I n n* 4 + 3 



<a c) 2 

 n = 2 the attraction is as - - - , or as B 8 directly, and as 



S B inversely ; and if c = o, or the attraction is taken at the 

 centre, it is equal to a; and if the attraction is as the dis- 

 tance, or n = 1, then the attractive force of the segment is 



ii. Attractions of non-spherical bodies. The attractions of 

 two similar bodies upon two similar particles similarly situ- 

 ated with respect to them, if those attractions are as the same 



power of the distances -, are to one another as the masses 



directly, and the n th power of the distances inversely, or the 

 n th power of the homologous sides of the bodies ; and because 



