Function of the Condenser in an Induction- Coil. 217 



and, of course, the intensity of the current. Thus we have at 

 the moment of breaking the primary circuit the time t = 0, 



and the intensity of the current is ? = y~ at the same time, 



E being the electromotive force of the battery, and R the 

 resistance of the circuit. The potential-difference being in 

 the condenser at the time £ = 0, we have for the oscillatory 

 charging and discharging the following equations: 



^^.C-^cos^+sin-^v/LC). \ * ( 



W 



4:1 



Here V is the potential -difference of the condenser and i 

 the intensity of the primary current ; L is the coefficient of 

 self-induction of the primary circuit and C the capacity of the 

 condenser. — « + /3v' —1 are the roots of the equation 



LCV 2 + RCr + l = 0. 



The capacity of the condenser is supposed to be at least as 

 great as is required for suppressing the spark. If this con- 

 dition were not satisfied, the above equations would have no 

 signification. 



Admitting that the maximum of the spark-length X in the 

 secondary circuit is proportional to the maximum of potential- 

 difference in the primary condenser, we have from equation (1) 

 approximately 



k.E _ ki 



x -tt7^~V()> (2) 



k being a constant so far as the coefficient of self-induction 

 in the primary circuit is not altered. 



By means of the equation (2), the maximum of spark- 

 length in the secondary circuit can be calculated for every 

 capacity of the condenser that is sufficient for suppression of 

 the spark at the interruptor of the primary. 



The lengths of the secondary sparks, observed by Mizuno, 

 and the values calculated from formula (2), are shown in 

 Tables I. and II. (pp 218, 219). 



The calculated values correspond to the observed as well as 

 can be expected considering the uncertainty of the propor- 

 tionality between spark-length and potential-difference. From 

 this agreement it can be concluded that each of the curves, 

 drawn up by Mizuno, is properly composed of two parts. 



