COEFFICIENTS OF INDUCTION. 



The coefficient of mutual induction is equal and of opposite sign 

 (454) to the potential energy of the four magnetic layers A and B, 

 A' and B', the densities of which are respectively + n and - n v + n[ 

 and - n\. Let x be the distance of the bases A and B', P OT the mean 

 potential of the layer A for a mass equal to unity on the surface B' ; 

 the mean potential of this coil on the surface is 



The potential energy of the layer B' in respect of the coil C is 

 then, 



i-r 



C' 



Fig. 143. 



The potential energy of the layer A, where h' is the length of the 

 coil C', is in like manner 



From this follows for the coefficient of mutual induction of the 

 two coils, 



(36) M = ViS' [P m (*) ~ P m (* + h - P m (* + h') + P w (* + h + h'}} . 



The values P n might be calculated in various ways, according to 

 particular cases. 



771. Let us suppose the two coils concentric, the second having 

 a smaller radius and being shorter (Fig. 143), the distance of the 

 bases being x, 



The mean potential of the coil C on the base B', may be 

 expressed by 



TO (A - x) , 



