MEASURING SMALL TIME INTERVALS 345 



which the charging took place may be determined from the value of the 

 high resistance. 



The relationship between the interval of time of charging and the 

 value of resistance required to make the charges on the two condensers 

 equal is a direct proportion. This will be obvious from an inspection 

 of the general equation for the charge at any instant on a condenser 

 which is being charged through a high resistance. The equation is 



where 



g = (3(1 - g-wcfl)), (1) 



g — charge at time, t, 



t = elapsed time in seconds since the charging began, 

 Q = final or maximum charge on the condenser, 

 C = capacity of condenser in farads, 

 R = resistance in ohms in series with the condenser, 

 e = base of Naperian logarithms. 



Since q is always made equal to the charge on the comparison con- 

 denser and since the charging battery is common to the two condensers, 

 therefore, using the symbols shown in Fig. 1, C2E may be substituted 

 for q and CiE for Q. The equation then becomes 



C2 = Ci(l - e-('/ci«>)). (2) 



As mentioned above, the two condenser capacities are kept constant. 

 Therefore, any change in t requires a proportional change in Ri in 

 order to satisfy the equation. 



Fig. 2 is a schematic circuit diagram of the complete time measuring 

 bridge showing the manner in which it may be connected to a repre- 

 sentative type of circuit to be tested (shown by dotted lines). The 

 symbols used to designate the various circuit elements in this figure are 

 the same as those used in Fig. 1 and since the principles of operation 

 have already been explained in connection with the latter figure, a 

 comparison of the two figures will aid materially in understanding the 

 detailed circuit arrangements of the bridge. 



As shown in Fig. 2 the bridge is arranged to measure the operating 

 time of a voice operated switching device consisting of a detector and a 

 relay Z in the output circuit of the detector. The input circuit of the 

 detector is connected to the output circuit of an oscillator and may be 

 opened or closed by contacts on one of the bridge relays (relay W). 

 This relay is under the control of key K which, when closed, causes 

 relay W to operate and complete the oscillator connections to the 



