210 ELECTRICAL MEASUREMENTS 



differ greatly from V , and consequently the ratio " will be 



seriously affected by errors of observation. By observing F 

 and the fall of potential, much more accurate results may be 

 obtained. Let the fall from V in time t be denoted by v, then 



Fo = V t + v, 



and 



J0.4343 



R 



Clog, 



Vo-V 



Only the ratio of voltages enters the formula, and it is possible to 

 use a ballistic galvanometer instead of an electrometer or elec- 

 trostatic voltmeter in the work. Connections are made so that 

 the condenser is charged from the battery through the ballistic 

 galvanometer. Let the elongation be D = KQ = KCV Q . After 

 the cable has leaked for t seconds, it is again connected to the 

 battery through the galvanometer and the elongation due to 

 the quantity which is necessary to replace that which has leaked 

 out is observed. Call this elongation D t , then 



D t = KQ t = KCv 

 consequently 



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R = - 



Clog 



Do- D t 



In this formula an error in D does not seriously affect the results, 

 as it occurs both in the numerator and denominator, and D t is a 

 comparatively small quantity directly observed, so inaccuracies 

 in it will not greatly affect the results. The ballistic galvanometer 

 should be so sensitive that D t will be large, and conse- 

 quently can be read with accuracy. This will probably mean 

 that the instrument is used with the Aryton shunt adjusted 

 for m = 1. When D is observed, it will be necessary to shunt 

 the galvanometer (the Ayrton shunt is used as it keeps the damp- 

 ing constant) in order to keep the deflection on the scale. In 

 this case D and D t are the deflections corrected for the multiply- 

 ing power of the shunts; that is, both are reduced to the value 

 they would have if m = 1. 



