498 INDUCTION. 



the ordinary electromotive forces at work in the circuit, the general 

 equation of induction will be 



(10) (E 



or 



519. COEFFICIENTS OF INDUCTION. If the inducing system is 

 a magnetic shell or a current, the flow Q is equal to the product of a 

 constant M, by the magnetic power of the shell or the strength of the 

 current. This constant is a function merely of the form and relative 

 position of the two circuits ; we know that it has the same value for 

 the two adjacent conductors (341), and that its value is defined 

 (353) by the integral 



(n) M=- I I Ads'. 



-IP 



This factor M is called the coefficient of reciprocal induction, or 

 of mutual induction of the two circuits. 



The constant L is an integral of the same form but with this 

 difference, that the two elements ds and ds' belong to the same 

 circuit. It is called the coefficient of self-induction. 



The value of the coefficient of self-induction L is the limit 

 towards which M tends when two equal circuits traversed by currents 

 in the same direction, and of the same strength I, nearly coincide. 

 For the total flow, which at this instant traverses the system of the 

 two circuits, is equal to the sum of the flows produced by each of 

 them that is to say, to 2 LI ; it may also be considered as the sum 

 2 MI of the equal flows, each one of which starts from one of the 

 circuits and traverses the positive face of the other. 



520. ELECTROMAGNETIC INDUCTION. The general formula, 

 applied to the case in which the inducing system is a shell of power 

 3>, gives 



(12) (E 



Suppose that while the magnetic power <3> is constant, the shell is 

 brought from an infinite distance to a determinate position in 

 presence of the induced circuit which we suppose fixed ; we have 

 then 



