[CLARK] CAPILLARY ELECTROMETER 75 



change in capacity of tiie electrometer due to the changed position of 

 the meniscus. 



If the original potential of the standard condenser of capacity 

 Ci is Vi and after mixture is V, we have for the total charge 



Qi = CiVx=(Ci + C)V=CiV+Q 



where C is the capacity of the electrometer in the final position. Q is 

 the charge in the electrometer after mixture. From these equations 



or Q = Ci(Vi-V). • • 



Using the first we may get the value of C, but for comparison of results, 

 we may plot Q against V, i.e., the charge in the electrometer against 

 the potential. Then, if the capacity is constant the graph will be 

 straight, if variable it will be curved. 



If the capacity is not constant it should be defined as — , or as the 

 ^ ^ dV 



slope of the Q-V curve. The ordinary definition of capacity at any 



given potential difference gives the average value over the interval of 



potential from zero to the final value. 



Figure 1 shows the general character of the results of capacity 

 measurement. In most cases for direct charging, with mercury as 

 the cathode, the capacity decreases as the potential difference increases 

 and becomes nearly constant. For reverse charging th° capacity 

 always increases and for the larger potentials becomes very large. 

 The slope of the curve is continuous through the origin. In a few 

 cases, the curve for direct charging was conca\'e upward and the 

 capacity increased a little and became constant. In either case the 

 capacity seems to approach a steady value. In all cases where the 

 curve for direct charge is concave upward, the capacity is very high. 

 This form of curve is easily interpreted. 



We may regard the electrometer as a system composed of two 

 condensers in series, one at the surface of the mercury in the capil- 

 lary tube, the other at the surface in the larger vessel. If we call the 

 capacity of the first Ci and that of the second C2, the combined 

 capacity is given by 



1 _ 1 , 1 



— = h — or 



C Ci C2 



r = ^^^^ 



C1+C2 



