204 Mr. 0. Heaviside on the 



loud, then the minimum sound is also loud, and may be com- 

 parable to the original in intensity. We may also, by upset- 

 ting the resistance-balance by trial, still further approximate 

 to silence, and it may be a very good silence, with a false 

 resistance-balance. The question arises, Can these balances, 

 or any of them, be made of service and be as exact as the 

 previously described exact balances? and are the balances 

 easily interpretable, so that we may know what we are doing 

 when we employ them ? 



There are fifteen M's concerned, and therefore fifteen ways 

 of balancing by mutual induction when only two branches at 

 a time are allowed to influence one another, and in every case 

 three conditions are involved, because there are three degrees 

 of current-freedom in the six conductors involved. Owing 

 to this, and the fact that in allowing induction between a pair 

 of branches we use only one condition (i. e. giving a certain 

 value to the M concerned), whilst the resistance-balance makes 

 a second condition, I was of opinion, in writing on this sub- 

 ject before *, that all the balances by mutual induction, using 

 a true resistance-balance, were imperfect, although some of 

 them were far better than others. Thus, I observed experi- 

 mentally that when a ratio of equality (R 1 = E 2 , Li = L 2 ) was 

 taken, the balances by means of M 63 or M 64 were very good, 

 whilst that by M 65 was usually very bad, the minimum sound 

 being sometimes comparable in intensity to that which was 

 to be destroyed. 



I investigated the matter by direct calculation of the in- 

 tegral extra-current in branch 5 arising on breaking or 

 making branch 6, due to the momenta of the currents in the 

 various branches, making use of a principle I had previously 

 deduced from Maxwell's equations f , that when a coil is 

 discharged, through various paths, the integral current divides 

 as in steady flow, in spite of the electromotive forces of in- 

 duction set up during the discharge. This method gives us 

 the second condition of a true balance. 



But more careful observation, under various conditions, 

 showing a persistent departure from the true resistance- 

 balance in the M 65 method (due to Professor Hughes), and 

 that the M 63 and M 6i methods were persistently good and 

 were not to be distinguished from true balances, led me to 

 suspect that the second and third conditions united to form 

 one condition when a ratio of equality was used (just as in 

 (28c), (29c) above) in the M 63 and M 64 methods, but not in 

 the M 65 method. So I did what I should have done at the 



* < Electrician/ April 30, 1886. 



t Journal S. T. E. 1878, vol. vii. p. 303. 



