150 Prof. J. Zeleny on the Ratio of the Velocities of the 

 Integrating, 



where 



= — 4-7T 1 pdx 4- G, 



Jo 



dx 



o-(S 



dx/o ' 



dV 

 the value of -7- at x=0 : and 

 da? 



£ 



'0 



the total charge in a volume of unit cross-section extending 



from # = to x = x. 



Hence 



dV __ /dV\ 

 dx \ dx! 



Q,- 5~""" 



The value of 



dV _ /dY\ 

 dx \ dx)a 



4:7T 



can be obtained for any point a? from the curve in fig. 13 by 

 the equivalent expression 



tan — tan</> 



where and <£ are the angles indicated in the figure. 



From such values a curve can be plotted showing the 

 relation between Q c and x. 



If V and x (fig, 13) are measured in absolute units, then 

 the ordinates of the curve obtained will represent Q T in abso- 

 lute units of electrification. 



Fig. 14 shows such a curve derived from fig. 13. 



Since the ordinates represent the total quantity of electri- 

 fication for a unit cross-section between x = and x = x, the 

 quantity between any two points x x and x 2 is obtained from 

 the difference of the ordinates for these two points, and by 

 dividing this by x x x 2 the average density between the two 

 points is obtained. 



The curve shows that for such small potential gradients as 

 that used the free electrification is confined mostly to the 

 boundaries, the space between being almost free from any 

 charge. As the potential gradient is increased, electrification 

 is obtained farther from the plates, and with large voltages 



