510 CONSTANTS OF COILS. 



the principal current, requires, besides the condition for the per- 

 manent state, that we have (951) 



^b _ -L&' _ *-*a -^a' 



T~~V~~a~~j~' 



Moreover, any given variations are in equilibrium if the resist- 

 ance of each branch is proportional to its current of self-induction. 

 In order to make use of this property, the two coils to be compared, 

 whose coefficients are L and L', are placed in the two branches 

 a and a', for instance, the other branches being supposed to have no 

 induction. Complete equilibrium requires that the two conditions 



be simultaneously realised. 



Two resistance-boxes, which have no induction of their own, are 

 necessary ; one is placed in the same branch as one of the coils, the 

 other on one of the free branches. The experiment is a long one, 

 for the equilibrium of the permanent currents must first be realised, 

 before trying the effect of the transient currents ; we must also see if 

 the conditions for the permanent and for the variable state are not 

 independent. The final result can only be attained after a series of 

 trials. 



1098. COMPARISON OF A COEFFICIENT OF SELF - INDUCTION 

 AND A COEFFICIENT OF MUTUAL INDUCTION.* The coil of co- 

 efficient L is introduced in the branch AC of Wheatstone's bridge 

 (Fig. 234), and the second coil is introduced in the circuit of the 

 battery, near the first. Let M be their coefficient of mutual in- 

 duction. Two electromotive forces of induction are thus introduced 

 in the branch AC, which, if made equal and opposite, the equili- 

 brium of the bridge for the permanent condition will also satisfy the 

 variable state, for each branch of the bridge is conjugate in respect 

 of the battery, and therefore indifferent to the variations of the 

 principal current. 



In "the variable state, the difference of potential between the 

 summits A and C is 



- dl 



* MAXWELL. Electricity and Magnetism, Vol. n., p. 356. 



