Laplace's theorem, &c. 417 



reasoning on this question, in order to make the 

 equation continuous, I must confess, has always 

 appeared to me to be difficult to comprehend. 

 The mode Poisson has adopted, is to divide the 

 attracting body into two parts, one of which is a 

 sphere surrounding the attracted point, and the 

 other of course is the remaining shell, for every 

 material point of which shell he supposes Laplace's 

 equation to be true, and he then calculates the 

 effects of the sphere upon the point P. This 

 mode of reasoning has conducted Poisson to the 

 equation 



d"^ , d^Y , d'Y . ,^,, 



d^' + JP + d?'=-''''P' (21) 



which he states to be true when the attracted 

 particle is a part of the attracting mass. I am 

 however, as before stated, unable to see the force 

 of Poisson's reasoning on this question, and cer- 

 tainly the conclusion to which he arrives is differ- 

 ent from the result which I have obtained in 

 equation (19) by means of a very different Ana- 

 lysis. The condition which must be complied 

 with, in order that Laplace's equation may be 

 true is, from equation (19), that the points 

 attracting must not be situated in any one of the 

 3 H 



