82 THE ROYAL SOCIETY OF CANADA 



keys with a short interval of time between and the electrometer shows 

 the final potential of the condenser. This time interval may be 

 changed at will over a wide range and a series of readings taken for 

 different times of charge or discharge. 



Figure 3 shows the result using for R = 100 ohms. The standard 

 condenser had a capacity of 1 microfarad and the electrometer about 

 • 27 microfarads with normal charging. 



It will be noticed that the minima are much nearer the mean 

 positions on which would be a logarithmic curve than the maxima, 

 and the curvature is much less also. This is the result of the condenser 

 having different capacities in the different directions. 



Non-Oscillatory Discharge Curves 



It was easy to obtain charge and discharge curves with the above 

 mentioned chronograph, but the efïects of varying resistance and 

 capacity are best seen by plotting the results semi-logarithmically. 

 If the resistance of the electrometer is mainly that of the mercury 

 and acid column in the small tube, the changes will be relatively small 

 when the meniscus is not too near the open end of the tube, but may 



be large if the meniscus is near the end. In the first case, the discharge 



t_ 



curve is represented well by V = Vo e ^^ and the semi-logarithmic 

 plot is straight. On the other hand, if the meniscus is near the end 

 the resistance of the column depends on the position of the meniscus, 

 thus on the potential difference V. We may treat the resistance as 

 though made up of two parts, one approximately constant, and the 

 other approximately proportional to V, so R = aV-fb and the current 

 at any instant is 



. _ V _ dq çdV 



aV+b dt dt • 



which is satisfied by 



Ca(V-Vo)+Cblog^= -t. 

 Vo 



Both of these equations are well satisfied by observations taken under 



the proper circumstances. 



Since the capacity increases a little with the increase of potential 



difference the effect on the discharge curve is of the same general 



nature as that of the increase in resistance, so all curves plotted as 



described show a slight curvature. 



