128 Dielectric Constant and Electrical Conductivity of Mica. 



It seems possible that the exponential term in the ex- 

 pression for the current in the strong fields may be due to 

 a distribution of electronic velocities in accordance with 

 Maxwell's law *. According to this the number of electrons 



3E 



possessing a given energy E should contain e ~ 2 ® as a factor,, 

 where E is the mean electronic energy. Now, in the case 

 of insulators, few, if any, electrons normally possess enough 

 energy to escape from the atoms to which they are attached, 

 and so take part in the conduction current. In a very 

 strong field, sufficient energy maybe contributed by the field 

 to enable some of the most energetic to escape. In order 

 that this may be possible, it is necessary that the electron 

 should possess energy not less than E 1 — E 2 , where E x is the 

 energy required to escape from the atom, and E 2 is the 

 energy contributed by the field during the escape. We may 

 write E 2 = Xe<i, where e is the electronic charge, and d some 

 distance of atomic magnitude. Hence the number of avail- 

 able electrons, and so the current, might be expected to 



SXed , 



contain e 2 ^ as a factor. Comparing this with the results 

 obtained, we find, after reducing X to E.S.U., that 



3ed 



-»=- = 5*5 x 10~ 4 . These results were obtained at about 



2E 



9° C, so, if we assume that the average electronic energy is 



the same as that for gaseous molecules |, we find that 



E = 2'8xl0- 14 , so as e = 4'8x 10" 10 we find that d is about 



2 xlO -8 , which is of the right order of magnitude. In the 



case of the strongest fields, the energy contributed by the 



field would be nearly four times the mean electronic 



energy J. 



If this explanation of the occurrence of the exponential 

 factor is correct, and if, as assumed above, the mean elec- 

 tronic energy is proportional to the absolute temperature, 

 the results obtained at different temperatures should vary 

 considerably. It is proposed to modify the arrangement so 

 as to enable determinations of the conduction current to be 

 made at varying temperatures. 



* See Richardson, Phil. Mag. August 1915. 



t Thomson, loc. eit. 



X The internal field due to the polarization is neglected here. As, 

 however, we may assume that it is proportional to X it will not affect 

 the form of the result. 



