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XIjV. The Electron Theory of Metallic Conductors applied to 

 Electrostatic Distribution Problems. By L. Silberstein, 

 Ph.D.* 



TI^HE electron theory of metallic conductors, as propounded 

 A by Riecke and Drude, and developed by J. J . Thomson, 

 Lorentz, and others, has almost exclusively been treated in 

 connexion with problems of current-conduction and allied 

 questions, this being undoubtedly the most vital and 

 promising field of application of the theory, especially for 

 the experimentalist. From a more theoretical standpoint, 

 however, electrostatic applications may not be devoid of 

 interest. As far as I could gather, investigations of this 

 kind are limited to an incidental rough estimate of " the 

 thickness " of the layer of electricity in a conductor, due to 

 J. J. Thomson "f. 



It has seemed, therefore, worth while to represent the 

 general problem of electrostatic distribution in terms of 

 the electron theory. This, together with a full solution 

 in the case of some of the most simple illustrative problems, 

 is the object of the present paper. 



1. Consider a metallic conductor or, more generally, any 

 system of insulated conductors at uniform absolute tempera- 

 ture T. The latter will enter into our formulae through a 

 magnitude fundamental in every kinetic theory, viz. the 

 average kinetic energy of a molecule or of a free electron, 

 per degree of freedom, 



fc=±*T, (1) 



where a is the " universal " constant, equal to § of the gas 

 constant divided byAvogadro's number, i. e. about 2. 10~ 16 erg 

 per degree centigrade -j. The classical problem of distri- 

 bution can be put as follows : Given the total charge of each 

 conductor and the potential <b e of the external field, due to 

 charges fixed outside the conducting masses, find the electro- 

 static or equilibrium distribution of electricity over each of 

 the conductors. The solution of the problem in its classical 



* Communicated by the A uthor. 



t 'The Corpuscular Theory of Matter' (1907), p. 82. The example 

 treated by Thomson, which concerns an infinite plane as boundary of the 

 conductor, has more recently been taken up again and dealt with on 

 almost identical lines by Lorentz, who does not seem to have noticed 

 Thomson's estimate ; cf. Vortraege ueber die kinet. Theorie d. Materie fy 

 Elektr. Leipzig (1914), pp. 191-192. 



% The symbol k used by some authors stands for foe. 



Phil. Mag. S. 6. Vol. 36. No. 215. Nov. 1918. 2 F 



