418 NEW INVESTIGATION OF 



three planes, passing through the point P attracted, 

 parallel to the co-ordinate planes. 



And if the attracted point P be a part of the 

 attracting mass, then equation (19) will give the 

 relation between the three partial differential co- 

 efficients of V with respect to the co-ordinates of 

 the attracted point. I state these conclusions 

 with great diffidence and respect for the high 

 authority of Poisson, whose results on this subject 

 appear to me to be different from those which the 

 foregoing investigation has enabled me to obtain ; 

 and I cannot refrain from thinking, in consequence 

 of being unable to alter the above researches, that 

 Poisson's correction of Laplace's equation when 

 the attracted point is a part of the attracting mass 

 is not strictly right. The error which I conceive 

 Poisson has made is, in stating that the shell into 

 which he divides the attracting body will satisfy 

 Laplace's equation. 



Thus suppose V =: V -|- U , where V refers 

 to the shell and U to the sphere which surrounds 

 the attracted point. 



da^ da^ da'' 



