395-397] Passage of Electricity through Dielectrics 349 



Thus we have 



f/7fl /9 2 F 9 2 F9 2 F\ dp[, 



III \~ 3-T + ^-T+-^r ~?:\dxdydz = Q, 



JJj [T V9# 2 dy* 9^ 2 / at) 



and since this is true whatever surface is taken, each integrand must vanish 

 separately, and we must have, at every point of the dielectric, 



e^F 3*F 



dx* + df + 



We have also, as in equation (326), 



e^F 3*F d*V_ dp 



dx* + d + a* 2 ~ T dt m 



4t7Tp 



df~*~!w~ "IT' 



dp _ 4-7T 



The integral of this equation is 



dp 



so that 



Kr 



where p is the value of p at time t = 0. 



Thus the charge at every point in the dielectric falls off exponentially 

 with the time, the modulus of decay being -==- . The time -. - , in which 



xx T 4?T 



all the charges in the dielectric are reduced to l/e times their original 

 value, is called the "time of relaxation," being analogous to the corresponding 

 quantity in the Dynamical Theory of Gases *. 



The relaxation-time admits of experimental determination, and as r is 

 easily determined, this gives us a means of determining K experimentally 

 for conductors. In the case of good conductors, the relaxation-time is too 

 small to be observed with any accuracy, but the method has been employed 

 by Cohn and Arons-f- to determine the inductive capacity of water. The 

 value obtained, K= 73*6, does not, however, appear to be consistent with the 

 molecular theory of dielectrics explained in Chap. V. 



Discharge of a Condenser. 



397. Let us suppose that a condenser is charged up to a certain 

 potential, and that a certain amount of leakage takes place through the 

 dielectric between the two plates. Then, as we have just seen, the dielectric 

 will, except in very special cases, become charged with electricity. 



Now suppose that the two plates are connected by a wire, so that, in 

 ordinary language, the condenser is discharged. Conduction through the 

 wire is a very much quicker process than conduction through the dielectric, 



* Cf. Maxwell, Collected Works, n. p. 681, or Jeans, Dynamical Theory of Gases, p. 294. 

 t Wied. Ann, xxvni. p. 454. 



