﻿Electricity on Insulators and Metals. 273 



may be written 



where b is also a constant. The total charge existing on the 

 specimen will now be 



Q = e-e' (3) 



From these equations we find 



dQ , 

 a — aty 



which, on being integrated, gives 



Q=£(l-i-»-), (4) 



the constant of integration being determined by the fact 

 that Q and w vanish together. 



On this theory the frictional electricity reaches a constant 



maximum value, j ^ when the generation of charge is com- 

 pensated by the leakage. 



The constants, a/b and b, of (4) can be determined for any 

 particular case from two points on the experimental curve, 

 and Q can hence be calculated for any value of to. As a 

 rule, the theoretical curves so obtained show fair agreement 

 with the experimental curves, the chief difference being that 

 the calculated curve is generally rather steeper in the middle 

 part of the curve. Curves calculated in this way are shown 

 in broken lines in fig. 2, for quartz when rubbed by flannel, 

 silk, and leather. 



In order to account for the result that the maximum 

 charge is independent of the pressure, it is necessary to 

 suppose that a and b contain as factors the same function of 

 the pressure. In the case of the metallic specimens, where 

 Q = CV, if is the capacity and V the potential of the 

 specimen, the leakage in equation (2) should be assumed to 

 be proportional to V ; in other words, the coefficient b is 

 inversely proportional to the capacity. It follows by equa- 

 tion (4) that, in the case of two specimens of the same 

 material but of different capacities, the maximum charge 

 should be greater for the specimen of greater capacity, and 

 that the slope of the rising portion of the curve should be 

 steeper for this specimen. Less work should be necessary, 

 therefore, to produce any given charge in the case of the 



Phil. Mag. S. 6. Vol. 29. No. 170. Feb. 1915. T 



