416 NEW INVESTIGATION OF 



And equation (17) will become — 



rf^ ^ jz^ _y^ 1 



X Z J Y Z I 



+S--7 n+^'c 71 (19) 



— = sum of every point in the mass of the 



attracting body multiplied by the reciprocal of its 

 distance from P. 



If the point P which is attracted, be exterior 

 to all the attracting points, and such that none of 

 the attracting bodies are in the planes passing 

 through P, and parallel to the co-ordinate planes. 

 Then we shall have from (19). 



^v d^\ r/^V 



^ + W + 4J = (20) 



This equation was first given by the justly 

 celebrated mathematical philosopher Laplace, 

 (See Pratt's Mechanical Philosophy, page 155,) 

 and Poisson was the first to show that the theorem 

 was not true when the attracted point P was 

 surrounded by the attracting particles, and his 



