Graduation of the Sonometer, 63 



plate of radius b, at a point distant b from the plate along its 

 axis, 



'-^-^ 



a flZ> 2 1.35 ^ 1.3.56 6 . \ 



If we introduce zonal harmonics as coefficients, this becomes 

 jib' 1.3&* , 1.3.5 5% . \ 



This is now the potential at any point in space where b < c. 



If there be a second circular circuit of radius /3 on the same 

 axis, we may suppose it replaced by a magnetic shell bounded 

 by the current and lying on the sphere, with centre at the 

 centre of the first current, the radius of the sphere being c. 



This shell may be considered to consist of two layers of 

 matter of equal and opposite densities, ft and — fi, at distances 

 c and c + dc from the centre. The potential on the second 

 layer is 



I j fttodB, 



where the integration is taken over the shell. The potential 

 on the second layer is 



the sum being 



but since the strength =1, /nde = l, and we have the mutual 

 potential 



-JJ: 



I J is. 



Keplacmg the element cZS by c'd/j, dcf), the limits will be for <£ 

 from to 27r, and for \x from 1 to [m. 



Integrating with respect to 0, and remembering that c is 

 constant in integrating for //,, we have 



= -4 w v{^J'p 1 ^-^|.4gJ , p 3 ^+&o.}. 



