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LVI. The Electron Theory of Metallic Conduction. — V. 

 Bg G. H. Livens*. 



1. Introduction. 



a^HE general theories of the conduction of heat and 

 electricity in metals based on the idea that they take 

 place by the tree electrons only, has been developed in 

 various different ways. In the original theories of Drude f , 

 Riecke J, and Thomson § the statistical motion of the electrons 

 is practically ignored except in so far as to assume that it 

 departs but slightly from the distribution of motion in the 

 undisturbed steady state. In the theory of Lorentz || the 

 complete specification of the statistical motion of the electrons 

 is fundamental. Whereas in the more recent generalization 

 of this theory given by Jeans % Wilson**, Bohr ft* and 

 others, a specification not of the velocity distribution but of 

 the momentum distribution is made the basis of all the 

 calculations of the theory. 



In the original theories of Lorentz, Thomson, Drude, and 

 Wilson, the electrons and atoms of the metal are regarded as 

 hard elastic spheres, at least as far as their interaction in 

 collision is concerned ; but in the more modern extensions 

 developed b}< Jeans and Bohr it has been found possible to 

 dispose of this restricting assumption and to formulate the 

 theory equally well for a more general type of metal. 



The object of the present note is to discuss certain aspects 

 mainly of the two earlier forms of the theory on the same 

 more general basis as that used by Jeans and Wilson. 

 Certain preliminary suggestions have already been made 

 independently concerning some of the points to be here 

 discussed, but their full analytical import has hardly been 

 realized : they will, therefore, in the main be repeated 

 together with their extension to the more general type of 

 theory. 



* Communicated by the Author. 



t Ann. d. Phys. Bd. i. p. 506, and Bd. iii. p. 369 (1900). 



T Wied. Ann. Bd. lxvi. pp. 353, o4o, & 1199 (1898). 



§ Rapp. d. Congres d. Physique, Paris, 1900, torn. iii. p. 138. 



|| Proc. Acad. Amsterdam, vol. vii. pp. 438, 585, & 684 (1905). 



f Phil. Mag. June, July 1909. 

 ** Phil. Mag. Nov. 1910. 



ft ' Studier over Metallernes Elektrontheori,' Dissertation. Copen- 

 hagen, 1911. 



