Self-induction of Wires . 189 



Consider the equations (24c) to (27c). Three conditions 

 have to be satisfied, in general, the resistance-balance (25c) 

 and the balance of integral extra-current (26c) not being 

 sufficient. To illustrate this in a simple manner, let 2 and 3 

 be equal coils, by previous adjustment, and 1 and 4 coils 

 having the same resistance as the others, but of lower induc- 

 tance, or else two coils whose total resistance in sequence is 

 that of each of the others, but of lower inductance when 

 separated. The resistance-balance is satisfied, of course. 

 Now, if the next condition were sufficient to make an 

 induction-balance, all we should have to do would be to make 

 L 1 + L 4 = 2L 3 . For instance, if L x is first adjusted to equal 

 L 2 and L 3 , then, by increasing either L x or L 4 to the right 

 amount, silence would result. It does result when it is L 4 

 that is increased, but not when it is L x . If the sound to be 

 quenched is slight, the residual sound in the Li case is feeble 

 and might be overlooked ; but if it be loud, then the residual 

 sound in the L x case is loud and is comparable with that to 

 be destroyed, whilst in the L 4 case there is perfect silence. 



The reason of this is that in the L x case we satisfy only the 

 second condition, whilst in the L 4 case we satisfy the third as 

 well. 



Another way to make the experiment is to make 1, 2, and 

 3 equal, and 4 of the same resistance but of lower inductance, 

 much lower. Then the insertion of a non-conducting iron 

 core in 1 will lead to a loud minimum, but if put in 4 will 

 bring us to silence, except as regards something to be men- 

 tioned later. 



Supposing, however, we should endeavour to get silence by 

 operating upon L,, although we cannot do it exactly, yet by 

 destroying the resistance-balance we may approximate to it. 

 Thus we have a false resistance- and a false induction-balance, 

 and the question would present itself, If we were to wilfully 

 go to work in this way in the presence of exact methods, 

 how should we interpret the results ? As neither (25c) nor 

 (26c) is true, it is suggested that we make use of the formula 

 based upon the assumption that the currents are sinusoidal 

 or pendulous, or S.H. functions of the time. Takep 2 =— n 1 

 in (24c), the frequency being n/27r, and we find 



E 1 B 4 (a' 1 + ^ 4 )=E 2 E 3 (^ 2 + ^3), . . . (34c) 

 (R 1 R 4 -E 2 E 3 )=n 2 (L 1 L 4 -L 2 L 3 ) . . (35c) 



are the two conditions to be satisfied; and we can undoubtedly, 

 if we take enough trouble, correctly interpret the results, if 

 the assumption that has been made is j ustifiable. 



I should have been fully inclined to admit (and have no 



