﻿for Measurement of Resistances and Capacities. 305 

 is constant, the integration of (5) gives 



C=0-*)J+A e -*>, 



where A is an arbitrary constant. This shows that the ex- 

 pression for the current is different during the contact period 

 ab (tig. 2) of the battery commutator, where E/F lias a finite 

 constant value, and during he, where E/F is zero. Let t be 

 the time reckoned from the instant a at which the battery 

 commutator just begins to make contact, t the reversal period 

 ac, the contact period ah. We may then put 



C = C 1 = (p-&)~+A*-^ between *=0and t = 0l 



* C > ( b ) 



C = C 2 = B *-*('-*) „ t = and t=r) 



where B is another arbitrary constant. 



The constants A and B may be determined on the assump- 

 tion that the state is steady. Integrate (5) between two 

 times infinitely close together which include any sudden 

 finite variation in E/F, and we see at oncp, since the only 

 finite terms are those which contain I) as a factor, that 



J Sudden increase \ f . f Sudden increase 1 

 I in current J =yP" r ) x \ m E/F J ■ 



Applying this formula to the sudden variations of E/F which 

 occur at the instants t — and t = 0, we get 



F 

 [C 2 -C 1 ] f==e =-( j p-r) T 



and rn n ,_ , . E 



where C 2 ' is the final value of the current during the break 

 period just preceding the instant £ = 0. But from the con- 

 sideration that the state is steady we must have 



[c 2 '] fc0 =-[c 2 L =r . 



These equations determine A and B. Substituting the 

 resulting values in (6), and putting = %t (p. 300) we get 



Phil Maa. S. 6. Vol. 12. No. 70. Oct. 1906, X 



