416 Sir W. Thomson. On Electrostatic Screening [Aj 



nected by an insulated wire with a quadrant electrometer in the 

 buildings. 



30. The problem of finding the distribution of electricity on a 

 spherical cage, of equal electric permeability, /t, in all parts of its 

 surface, formulated in (25) of 22, is easily solved by aid of spherical 

 harmonics. Confining ourselves for brevity to the case of external 

 influencing bodies, let their potential at any point, P, within S be 



(36) 



where Si denotes a given spherical surface-harmonic of order t, and r 

 the distance of P from the centre of S. And /,-, denoting an unknoi 

 surf ace- harmonic of order t, let 



be the harmonic expression for />, the required electric den 

 Going back to 20 for the definition of 0, we find, by the elements 

 spherical harmonics, 



Hence, by (25), 



K + So 



_(2t 

 pi= 



1 + 

 and = K + 2- 



(2t + l),i R< 

 IT" 



Jn (39) we have virtually the same result as in (33). The approxi- 

 mation on which we are founding in 17 29 is valid in (40) and 

 (41) only for values of t small in comparison 2-a-R/a: but, as in 

 virtue of greatness of the logarithm for the case formulated in (27), 

 /t may be great in comparison with a ; and therefore the denominator 

 of (40) need not be only infinitesimally greater than unity, and may 

 be any numeric however great. 



31. Taking S,r = x, S 2 = 0, S s = . . . . , we see by (41) that if an 

 insulated unelectrified spherical cage be brought into a uniform field 

 of electric force, X (that of atmospheric electricity, for example, at 

 any height above the ground exceeding five or six diameters of the 

 cage), the force within the cage is 



