400 



VIII. NEWTONIAN POTENTIAL FUNCTION. 



Picking out all the terms for which s -\- 1 = n we get for the 

 coefficient of f J 



p __ 



" 



2.4(2n-l)(2w-3) 

 The first polynomials have the values 



-30^+3), 



147. Development in Spherical Harmonics. We may use 



the formula 6), 128, for an internal point, to obtain the development 

 of a function of 9, <p, on the surface of a sphere in the same manner 

 as in 140 a for the case of a circle. Since the polynomials in the 

 development of the reciprocal distance involve only the cosine of the 

 angle between the radii to the fixed and variable points, we have 

 if r'<r, 



105) 



and differentiating this with respect to r, the internal normal , 



6) 



Inserting these values in 6), 128, namely 



&) 



-*//[ 



dn 



_10F 



d dn 



dS, 



