7 

 Measurement of Small Capacities and Inductances. 49 



the ampere value of a steady current which will make the 

 same deflexion. This can be accomplished by putting the 

 galvanometer in series with a variable resistance, and placing 

 the two as a shunt on a known small resistance in series with 

 another variable resistance, and then placing on the terminals 

 of this circuit a cell o£ known electromotive force. 



In the case of most movable coil galvanometers, the scale 

 deflexions are by no means proportional to the current, and 

 hence when measuring a series of capacities it is desirable 

 afterwards to plot a calibration curve of the galvanometer 

 scale, from which the condenser currents can be read off 

 directly in microamperes. This, however, is always easily 

 accomplished. In addition, we have to measure the potential 

 of the discharging battery. For most practical purposes 

 this can be done by a Weston voltmeter. 



Thus let V represent the voltage of the battery charging 

 the condenser or aerial, C the capacity of the condenser in 

 microfarads, A the current in microamperes through the 

 galvanometer, n the number of charges per second, then 



A = nCY 

 or C = A/nV, 



In order to avoid the necessity for standardizing the 

 Galvanometer and measuring the voltage of the charging 

 battery, we have devised a method employing a differential 

 galvanometer which in principle is as follows : — The condenser 

 discharges, as above described., pass through one coil of the 

 differential galvanometer, the other coil being traversed by a 

 current taken from the same battery, and therefore having 

 the same voltage. This second coil is shunted by means of 

 a shunt R and has in series with it a high resistance r. If 

 then these resistances are arranged so that the galvanometer 

 shows no deflexion, we have the following equation for the 

 capacitv : — 



nVG V _ 



10 6 GS 



r + G + S 



( G + S)10 c 



™<G + S) + >*GS' 



This determines the capacity in terms of a conductance 1 and 

 the reciprocal of a time, thus reducing the number of dimen- 

 sional quantities to be measured to the minimum. 



In carrying out this method, it is perfectly impossible 10 

 use any ordinary differential galvanometer, because with an 



