420 NEW INVESTIGATION OF 



where — j^ is the force arising from the shell 

 and ^ the force arising from the sphere — 



V C C C dx . dy , dz , , 



— - = I 1 1 f ^ where the 



r dx . dy , dz 



rectangular co-ordinates x y h z refers to any 

 point in the attracting mass — (See Poisson Traite 

 Mecanique, Nos. 96 and 10?) — and the limits of 

 integration depends upon the equation of the 

 surface of the attracting mass. Differentiate the 

 above equation with respect to a then we shall 

 have — 



-e?V CCC {a~x) dx dy dz 



oda 



(a-xf+ib-yf+ic-zy'^' 



consequently, 



rrr ia-x)d.dydz 



jJJ |("-^)'+(^-^)'+(''-^)y 



Similarly we have 



B _ r rr (h-y)dxdy dz 



P III ^(^a-xy+(b-yy+(c-zy'^' 



(25) 



