212 On the Self-induction of Wires. 



and M 24 are operative. That is, the self-induction balance is 

 independent of M 13 and M 24 . This corresponds to (81c) and 

 (82 c). 

 The other two are M 25 and M 45 . With M 25 we have 



0=L 2 -L 4 -2M 25 , .... (102c) 

 and with M 45 , 



= L 2 -L 4 -2M 45 (103c) 



The remaining eleven double conditions corresponding to 

 (85c) to (956) need not be written down. 



Several special balances of a comparatively simple kind 

 can be obtained from the preceding by means of induc- 

 tionless resistances, double-wound coils whose self-induction 

 is negligible under certain circumstances, allowing us to put 

 the I/s of one, two, or three of the four branches 1, 2, 3, 4 

 equal to zero. We may then usefully remove the ratio of 

 equality restriction if required. This vanishing of the L of a 

 branch of course also makes the induction between it and any 

 other branch vanish. 



For instance, let L 1 = L 2 = L 4 =0 ; then 



0=E s L 3 + M 36 (B 1 + B s ) .... (104c) 

 gives the induction-balance when M 36 is used, subject to 

 R^-EgR}. And 



0=B 2 L 3 -M 35 (R 2 + R 4 ) .... (105c) 



is the corresponding condition when M 35 is used. But M 56 

 will not give balance, except in the special case of S.H. cur- 

 rents, with a false resistance-balance. The method (104c) 

 is one of Maxwell's. His other two have been already 

 described. 



In the general theory of reciprocity, it is a force at one 

 place that produces the same flux at a second as the same 

 force at the second place does at the first. That the reciprocity 

 is between the force and the flux, it is sometimes useful to 

 remember in induction-balances. Thus the above-mentioned 

 second way of having a ratio of equality is merely equivalent 

 to exchanging the places of the force and the (vanishing) 

 flux. We must not, in making the exchange, transfer a coil 

 that is operative. For example, in the M 64 method (79c), 

 there is induction between branches 6 and 4 ; M 46 (equation 

 (88c)), on the other hand, fails to give balance. But if we 

 exchange the branches 5 and 6, it is the battery and telephone 

 that have to be exchanged ; so that we now use M 54 , which 

 gives silence, whilst M 64 will not. 



I have also employed the differential telephone sometimes, 

 having had one made some five years ago. But it is not so 



