Resistance of Compound Conductors. 495 



value obtained by galvanometric observation of the transition 

 from a state of things in which all the currents are zero to 

 one in which they have steady values under the action of a 

 constant electromotive force. In the ordinary theory of Max- 

 well's method for determining self-induction from the throw 

 of the galvanometer-needle in a Wheatstone's bridge (a resist- 

 ance-balance having been already secured), the conductor 

 under test is supposed to be simple. The general case of an 

 arbitrary combination of conductors can only be treated by a 

 general method. An. investigation founded upon the equa- 

 tions of my former paper* shows that the result which would 

 be obtained by Maxwell's method corresponds to the self- 

 induction of the combination for infinitely slow vibrations. 



We have supposed that the behaviour of the compound 

 conductor is not influenced by electrostatic phenomena ; other- 

 wise the representation of the part of the electromotive force 

 in the same phase as dQ / dt as due merely to self-induction 

 would be unnatural. So far as experiment is concerned, we 

 have no means of distinguishing between an effect dependent 

 upon dO /dt and one dependent upon §Cdt, for the phase of 

 both is the same. We may contrast two extreme cases — (1) a 

 simple conductor with resistance and self-induction, (2) a 

 simple condenser with resisting leads. In the first case the 

 electromotive force at the terminals is written 



L.*>C + R.C; 

 in the second 



where yJ represents the " stiffness " of the condenser. If we 

 persisted in regarding the imaginary part in the second case 

 as due to (negative) self-induction, we should have to face the 

 fact that the coefficient becomes infinite as p diminishes with- 

 out limit. 



A number of combinations in which the induction of coils 

 is balanced by condensers are considered by Chrystal in his 

 valuable memoir on the differential telephone!. 



.In a pap erf already referred to I have shown that when 

 two conductors in parallel exercise a powerful reciprocal 



* Phil. Mag., May 1886, p. 372. The analysis may be simplified by 

 choosing the first type so as to correspond to steady flow. The coeffi- 

 cients b 12 , b 13 . . . , as well as the final values of yjr 2 , \jr 3 . . , are then zero, 

 and the result may be expressed, 



t Edinburgh Transactions, 1879. J Phil. Mag. May 1886, p. 378. 



