. MEASUREMENT OF DISCHARGES. 533 



If the inducing current has been reversed, the resistance of the 

 induced circuit is 



H^-tan/3 



R = 27rM , 



h G Ta 



and we should calculate, by the dimensions of the coils, the value 

 of their coefficient of mutual induction M. 



Most of the experiments were made with equal coils of small 

 section of the channel, compared with the mean radius, and placed 

 at a certain distance from each other, the axes coinciding. In 

 these conditions M is calculated by elliptic functions. The relative 

 resultant error is a function of relative errors made on the mean 

 radius a, and on the distance x of the two mean planes. 



Apart from the terms of correction, the value of M (763) is 

 equal to the product of ^irjaa', by a function of the angle y 

 defined by the equation 



sin 7 = 



As the coefficient M is a length, or a homogeneous function of 

 the first degree of the variables #, a', and jr, making a = a', we 

 may put 



d?M v da dx 

 - =\ +fj. , 

 M * ' 



with the condition 



Equation 



M =/(*,*) 



being in fact homogeneous, and of the first degree, we have 

 M =** = 



da xf' x dx 



' 



