VOLTAIC POTENTIAL DIFFERENCE BETWEEN CONDUCTORS. 



79 



If the potential V = V w at / = t, 



two equations from which both N and V c may be found, if the limiting 

 potentials V^.V'^ and the electrometer current l^are severally observed. 

 If V M is not obtainable, it may be computed from observations at t and 

 t l = 2t as 



V ao = ( 2 V- V,) I V 2 and V = (2 V - V\) / V* 



Here, however, there is a difficulty, as the curves begin with a double 

 inflection not yet explained. The times t l = 2t must therefore be esti- 

 mated from the observations beyond the double inflections, or the rear- 

 ward prolongation of the curve for those observations, to meet the time 

 axis. The initial tangents may be found in the same way, but this is not 

 necessary, since their values are, respectively, 



while 



and V a (i + kN) 

 ~ Kt 



V=V a (i-kN) 



i-e 



K 



,etc. 



A few other relations are often useful, as, for instance, 



V 



v r = v v = v d -V iv 



a V -V c ^ a ' c 



' 00 V C 



all of which, however, have limited application because of the initial 

 double inflection of the curves. 



To solve the transcendental equations the times of two observations 

 may be chosen, so that if V and /, V and t' correspond, /' = 2t. Thus, 



Kt 



e~ Kt = 



V '~ V 



- 

 V 



from which N = K follows. Similarly, 



I 2V -V 



V 



V 



00 



V 2 



If t' = 2t and t / l = 2t l , the initial double inflection may in a measure be 

 ignored in 



,-,->_ .V_-VL I, 



V,-V\ V 



