29$ ATTRACTION ON A DISTANT I'AKTK I 



tide : let r 1 ^a, and ./. 



ordinates of any parti,-!,- <>f the l.ody, /> the density ot 

 part; 



i the distance between these two particles, or r, 



^ Let r< (r*) be the law of attraction ; then the whole attrae- 

 parallel to the axis of a; 



the limits being obtained from the equation to the sn 

 of the body. This attraction therefore 



...}, 

 dx dy d 





Jbf being the mass of the body, and fffpxdxdydz = 0, since a; 

 is measured from the centre of gravity of the body. 



Now supposes, y, z to be exceedingly small in mmpar 

 with c; then all the terms of (A) after the first an- xtremely 

 small in comparison with that term, it being nbsrrwd that 

 c*^' (c*) is of the same order as c<f> (c 2 ) in terms of r. Hence 

 the resultant attraction is very nearly ^fc<f> (c 2 ) ; that is, if is 

 vrry nearly the same as if the particles were c<.nd-n<, 

 their centre of gravity and attracted according to the, law 

 determined by the function r$ (r*). 



'. Frnin Art. 224, it appears that when the law of 

 attraction is that of the inverse square \' the distance, a 

 sphere composed of shells, each of which is hnmogen- 

 attracts an external particle with a resultant force, which is 

 the same as if the sphere were condensed at its centre. It 

 may be shewn also that two such spheres attract each other 



