242 THEORY OF NEWTONIAN FORCES. [FT. I. CH. V. 



we have 



L = a, Adr + flAafdr = M + L' t 



M = bojjlBdT+jjJBb'dr = b B + M', 



Xr = c (ffcdr + [((Cc'dr = c <7 + N'. 

 JJJ JJJ 



and if we choose 



the integrals L' y M' } N r vanish, and F_ 3 reduces to three terms. 

 The values of the integrals A, B, C, are not changed by this 

 change of origin, but those of all the others are. 



The new origin is called the center of the polarized distribu- 

 tion. If the polarization is uniform, it is the center of gravity 

 of the body. If we find a vector M whose components are 



A, B, C, we have 



., _ M (cos (Mx) cos (rx) + cos (My) cos (ry) + cos (Mz) cos (rz)} 



_ M cos (Mr) 



But this is equal to the potential due to a doublet of moment 

 M situated at the center. M is called the moment of the polarized 

 body, and since at great distances the first terms are relatively 

 the most important, we see that at great distances the body 

 acts as if concentrated at its center. The line through the center 

 having the direction of M is called the axis of the distribution. 



