126, 127] POLARIZED DISTRIBUTIONS. 241 



Now inserting this value of \/d in the expression for the 

 potential in 122 (3), in which 1/r is to be replaced by 1/d, 



or performing the differentiations, x, y, z, r being constant, 





and collecting in powers of x, y, z, which can be taken out from 

 under the integral signs, we get the development in spherical 

 harmonics 



F=F_ 2 +F_ 3 +F_ 4 +..., 



where the coefficients are the definite integrals 



In like manner the coefficients in the harmonics of higher 

 orders are definite integrals throughout the polarized body of 

 the components of polarization multiplied by powers of the co- 

 ordinates of the point of integration. By a change of the origin 

 the integrals L, M, N may be made to vanish. For putting 



a = a + a', b = b + V, c = c + c', 



W. E. 16 



