422 NEW INVESTIGATION, &C. 



will be the equations to three plane sections of 

 the attracting mass passing through P, the at- 

 tracted point, and parallel to the co-ordinate 

 \-)]anes ^z, xz, xy respectively. If the first of 

 equation (28) for instance, gives impossible values 

 for y^ when z takes any value whatever &c. with 

 the second and third, then Laplace's equation is 

 true, if to the contrary it is not necessarily true. 



