304- I;E OF F FOR SIMM:I:I AI. SIIKI.L. 



V 

 a 



ce, A r =-,- = -, it or the attraction is the san 

 <la or 



if the mass of the shell were collected at its centre ; this was 

 proved in Art. 212. 



1 1. \Yhen Pis within the internal surface, the limits of r 

 are u a and w + a ; therefore 



4?r 



ru 



I pudu ........................ (2). 



u, 



Since this is independent of a, we have 



This is equivalent to the result found in Art. 213. 



III. By combining the, results contained in equations (1) 

 and (2), we see that it' P be between the bounding sui 

 of the shell, 



V= \ pifdu + 4-7T I puJn. 



From this we may deduce a result involved in Arts. iMi' and 

 LM:;. namely, that the resultant ati* the same as //'</// 



the matter which is nearer to the centre than P were collected at 

 the centre, and the rest of the matter neglected. 



. At any point (a, J, c) where tliere is no particle of the 

 mass, t/ie function V satisfies tlie partial differential 



<rv 



