164 COEFFICIENTS OF INDUCTION. 



Lastly, if the circles are concentric, we have also p = a, 

 fji = cos a = 0, which gives 



, / l)M ( 2n + *) 2 l -3-5 - 3 



In order to pass from this to the case of two coils with rectangular 

 channels, we shall multiply the value of given by equation (70) ex- 

 panded once, by nty^dxdydx' dy , and extend the two integrations to 

 the sections of the channels. 



If the sections of the channels are small, we shall have a first 

 approximation by multiplying the value of the couple calculated for 

 the mean radii m and a', by the product nn' of the numbers of 

 windings of the two coils. 



794. The preceding no longer holds if the revolution is about a 

 line oblique to the plane of the axes, or which does not pass through 

 their point of intersection. 



Let us consider, for instance, two circular currents S and S' with 

 radii a and a', having their axes on the same plane and at a right 

 angle, and such that the plane of the former passes through the 

 centre of the second ; and suppose that the second can turn about 

 the intersection of the two planes. 



Let X be the component parallel to the axis of the action of the 

 current S 15 given by equation (31), and d' an element of the sur- 

 face S', the expression of the couple will be 



= 



the integral being extended to the entire surface S'. 



a' a* 



Let r be the distance of the two centres ; if the ratios and - 



r H 



are of the same order a, and terms of a higher order than a 3 are 



