and the Theory of the Induction-balance. 129 



tact-breaker, or clock -ticking microphone, or some other ar- 

 rangement for producing an intermittent current is inserted. 

 I shall therefore leave the consideration of the induction- 

 balance for the present, and examine the case of a primary 

 circuit in space by itself and having a break and make in 

 some part of it. Then we will consider the case of an inter- 

 mittent primary in the neighbourhood of a closed secondary; 

 and after this it will be easy to apply our results to the induction- 

 balance. 



On the Law of Variation of a Battery-current in a solitary 



Circuit. 



6. Let a battery of constant electromotive force E act in a 

 circuit whose total resistance may be suddenly changed from 

 the value R to the value S, and let L be the coefficient of self- 

 induction of this circuit. Then the current i at any time t 

 after the change of resistance has occurred is to be found from 

 the equation 



L I +S *= E > ^ 



with the initial condition *=4 when £=0. This gives us in 

 the integral form 



Putting R=co, we get the well-known expression for the 

 current at " make," 



feg(l-<fL>) (5 ) 



Putting S very large, we get an expression for the current at 

 partial break, provided there is no extra-current spark at the 

 surface of separation, 



. E -s 



*=R« L («) 



It will not do to put S = co , because it is impossible to make 

 the resistance suddenly infinite, i. e. to stop the current instan- 

 taneously. 



7. It is difficult to get a reasonably correct expression for 

 the value of the current at break. We may suppose that, by 

 separation of two portions of the circuit, the resistance is sud- 

 denly changed from R to a quantity which would be 8 if the 

 current instantaneously ceased, but which is much less than 

 S for a very short time, owing to the heat generated by the 



Phil Mag. S. 5. Vol. 9. No. 54. Feb. 1880. K 



