308 APPLICATION TO THE SPIII 



shall di-n-'t.- l>y /-,. ';< attraction ought evidently 



to vanish when r = 0, we must Iwve C Q; therefore =0. 



the attraction always vanishes. ami the partiel.- is in 

 equilibrium whatever be its ]> within tin- unoccupied 



part of the sphere. 



Suppose next that tin- particle forms part of the mass of 

 the sphere ; we have, by Art. 239, 



d*V ZdV 



p being a given function of r. 



Multiply by r 2 , and integrate from the value ?-, of r; BJ 

 = for all points in the interior, it is so at the limit ?-, ; 



thus 



dV 



^ 



[ r 

 4?r I pr'dr. 



But I Tn*pdr is the mass comprised within that surface of 



J r\ 



the sphere which passes through the attracted particle. It we 

 call it M' , we have 



dV M' 



K/f' 

 The absolute value of the attraction will therefore fr- 



it is the same as if the mass M' acted alone and were coll- 

 at its centiv. 



If tin- attracted particle is on the exterior surface having 

 its radius =r,, we nave, if J/be the whole mass of the hollow 

 sphere. 



dr ~ r^ 



and tin- attraction exercised upon this particle will hav 

 its value 



M 



