232 THEORY OF NEWTONIAN FORCES. [PT. I. CH. V. 



[[{A cos (nx) 4- B cos (ny) 4- C cos (nz)} , ~ 



ia4 as a 



9a? 9y dz 



Integrating the volume integral by parts by Green's method, the 

 surface integral cancels the surface integral in F, leaving F as the 

 volume integral 



(2) 



If as usual we use x, y, z to denote the coordinates of the attracted 

 point, and a, b, c for the coordinates of the point of integration, 

 we must write 



Now since 



\r) I x a 1 



? l-6 1 



= cos (rz), 

 2 



^ 



dc r* r r 2 



the integrand is the geometrical product of the intensity of polariza- 

 tion and r the vector distance from the polarized element to the 

 attracted point, divided by the cube of the distance. We might 

 have obtained this result from the consideration of a doublet, or 

 pair of points of equal masses of opposite signs, placed at a distance 

 apart h, so that the moment of the doublet is M = mh. Then if 

 TI and r z are the distances of the attracted point from the positive 

 and negative ends of the doublet, we have 



.~ _ ra m _m(r^ r l ) 

 ~~~ 



