444: Theory and Measurement of Residual Charges. 



v = \n 2 (n— Nlogn + A), 

 or (dn\ 2 



(-J = 2Xn 2 (n - N log n + A) , 



where A is a constant. Since this equation is true for every 

 uniform field of force, we must have 



A-NlogN-N, 

 and, therefore, 



(£T= 2 ^("- N - Nlo 4> 



,£ = -4 2 x(„-N-N,o g |)] 4 , 



it being clearly negative at every point. P is therefore 

 determined, and is equal to 



-X-27rNe(2^--a) + 47r* [|(w- N-Klog^)]*. 



The experiment on the sulphur plate shows that, very 

 probably, n never differs very much from N. 



^ = 1 +/3, where /3 is small. 



Then dn XT/1 , ~ K /3 2 ~l* 



2=-N(l + «[ 2 X.f]% 



^ = -*/XN./3(l +/ 3). 



•* 1 + 



where C is a constant.' 



Hence N 





The constant C must be determined by experiment. In 

 the experiment above described, when q/Q was # 05, or when 

 the electric force applied was 80 volts per '153 cm., 



n x — n 1 

 n, ~20' 



