PIERCE. — THE COOPER HEWITT MERCURY INTERRUPTER. 409 



Now the current for the simplest case of a condenser discharge is given 



by the equation 



2 EC =» . 



% = . e 2L sin a) t . (2) 



V±LC-B 2 C 2 



vl 



If the resistance is negligible in comparison with 2V- the square root 



of the mean square value of i becomes (neglecting damping) 



I=^-E. (3) 



V2 Vl 



If the relations (1) and (3) were exact, we should have for a given 

 inductance 



VC R = constant, (4) 



and for different values of the inductance 



VC 



Vl 



X R = constant. (5) 



We should not expect the relations (4) and (5) to be exact, because, 

 first, equation (2) is obtained on the assumption that the resistance in 

 the discharge circuit is independent of the current, which is a contradic- 

 tion of (1), and, second, equation (1) is not true for small values of the 

 current. Especially is (5) inaccurate because we have neglected the 

 effect of the inductance on the damping. 



An examination of the experimental data of Table IV, V, and VI 

 shows that the inductance relation (5) is not verified. On the other hand, 

 with a constant inductance VCx /?, for an eight-fold variation of C, is 

 near enough to a constant to be of use, perhaps, in certain cases where 

 only a rough approximation is required.* 



For comparison with the resistance of the mercury interrupter, as 

 obtained in these experiments, the following tables VII and VIII for the 

 resistance of the ordinary spark in air are taken from the researches 

 respectively of Lindemann f and Battelli and Magri.t These experi- 



* This result is not to be confused with the apparently more exact relation 

 found by Lindemann for the dependence of spark-energy on capacity, 

 t Lindemann, Ann. derPhys., 12, 1012 (1903). 

 t Battelli and Magri, Phys. Zeit., 3, 5:10 (1901-1902), and 4, 181 (1903-4). 



