1 62 COEFFICIENTS OF INDUCTION. 



For a suitable value of x, the value of f is a maximum which 

 corresponds to the condition 



m 

 or -%=() 



The reciprocal action varies then only by a term of the fourth 

 order, and may be regarded as constant. 



Let us suppose, first of all, that the coils A, B, and A' are 

 reduced to their mean circumferences of radii a and a, the con- 

 dition of the maximum for is 



d^u a' 2 flu a* 



Ct 



When the ratio of the two radii is very small, we get from 



a 



equations (32) of (736) 



If the powers of the ratio higher than the square may be 

 neglected, we have in the same manner 



i 0' 2 ^a 4 



or, replacing x in the second member by its approximate value, 



x = 



2 



Lastly, if the radii a and a are but little different, we may take 

 the expression (65). 



Considering the first term only, which is the most important, the 



d* 

 condition -HJ^O gives then 



or 



