130 Dr. 0. J. Lodge on Intermittent Currents 



current itself. The temperature: of the spark at any time t 

 after the break is to be found, we may suppose, from such an 

 equation as this, 



mcO- 



C(r?-W)dt, 



where H is the cooling-constant. The mode in which the 

 resistance of air changes with temperature is unknown ; so we 

 may assume any simple and not improbable law, such as that 

 the decrement of resistance is proportional to the increment ..of 

 temperature, or 



dr=—kd0, 



where h is a constant. From these two equations r has to be 

 obtained as a function of the current i and of the time t ; and 

 then its value has to be substituted for S in equation (3). As 

 a first approximation, we may imagine the time too short for 

 cooling, or make H = 0. Then we get 



-k'\ iUt 



r=be Jo ; 



an expression which, as a coefficient in equation (3), to me 

 seems quite unmanageable. I will therefore assume for the 

 future that the change in the battery-circuit resistance is 

 always made suddenly from one finite value to another, no 

 spark or current across air-spaces being produced. 



8. Suppose the resistance of a battery-circuit oscillates rapidly 

 between the values R and S, each change being made suddenly 

 and lasting for the short time t; what is the strength of the cur- 

 rent after a few seconds ? . 



This may be assumed to be the sort of thing that happens 

 in a microphone or other arrangement for producing an inter- 

 mittent current. 



The strength of the current before the vibration begins is 



. E 



' * 0= R ; 



at the end of the first period t the strength is, by equation (4), 

 . E , E(S-B) -\t 



at the end of the second period t the current is 



E^E(S-R) » g+s 



13 I SR {e e h 



and so on— 



