Laplace's theorem, &c. 421 



&-^= {{{ ^ ('^-^)^^<^^^ ^26) 



See Poisson's Mecanique, No. 96. The limits 

 of these integrations in the case of the shell V 

 are functions of a , b , c , the co-ordinates of the 

 attracted point. Hence the differential of A with 

 respect to a cannot be performed, in the case of 

 V\ before the integration with respect to <r , j/ , z . 

 These reasons have induced me to believe that 

 Poisson's correction of Laplace's theorem is 

 wrong. 



And for the limits of integration in the equa- 

 tions (24), (25), and (26) to be independent of 

 the co-ordinates of P , which must be the case if 

 Laplace's equation is true, we must have the 

 following conditions — 



If, f(^, j^, z)-0 (27) 



be the equation to the surface of the attracting 

 mass 



.-. f(« , J/ , ^) = 



& ((x,b,z) =zO \ (28) 



& f(x ,t/,c)=0 



