206] CONDUCTION IN DIELECTRICS. 399 



But in a dielectric, 

 (3) 



Differentiating (3) by t, and eliminating - from (2), we obtain for 

 a conducting dielectric 



3 f 1 d\ d f 1 dg)) 9 f 1 d3\ 



(4) ^-V-+T -^rr + o- \ V + T- -jfr + ^ -^ + -7- -^ = o. 



dx ( 4?r dt) dy ( 4>7r dt) dz ( 4?r dt ) 



If we put u, v, w, $, g), 3 m terms of the field, assuming that the 

 substance is homogeneous as regards both p and X, this becomes 



a f i 



a 4?r r dt d* 4?r r dt 



or in terms of the density 



Integrating this differential equation, we have 



-^t 

 (7) P = Pe - 



Accordingly whatever charge the body has originally decreases in 

 geometrical ratio as the time increases in arithmetical progression. 

 The constant T= //,/47rX, which is the time it takes for the density 

 at any point to fall to l/e of its original value, has been called by 

 Cohn* the relaxation-time, a term used by Maxwell in connection 

 with the Kinetic Theory of Gases. For ordinary metallic con- 

 ductors this time is so short as to have hitherto defied observation. 

 The importance of its discovery was recognized by the committee 

 setting subjects for an international prize competition in 1893, who 

 proposed this as one of the questions for investigation!. It appeared 

 that no experimenter ventured to attack the problem, it being 

 evidently considered too difficult. The finite relaxation-time was 

 determined for so good a conductor as water in some remarkable 

 experiments by Cohn and AronsJ, who are entitled to the credit of 

 discovering the finiteness of T for conductors. 



* Cohn, Wied. Ann. 40, p. 625, 1890. 

 t Elihu Thomson Prize, Electrician, 1892. 



J Cohn u. Arons. "Leitungsvermb'gen und Dielektricitatsconstante." Wied. 

 Ann. 28, p. 454, 1886. 



