722 BELL SYSTEM TECHNICAL JOURNAL 



Returning once more to the meaning of G, one sees that the placing 

 of the value 2 for G in equation (61) and all of its descendants amounts 

 to the making of the assumption that the electron-gas is really a 

 mixture of two equally numerous and entirely independent assemblages 

 of particles, each for itself obeying the Fermi statistics. This seems 

 a rather odd idea, but inevitable. 



Theory of Conduction 



The new theory of conduction developed by Houston and Bloch is 

 based upon the wave-theory of negative electricity, in which the 

 interior of a metal is conceived to be filled not with darting corpuscles, 

 but with stationary waves — as many distinct patterns of loops and 

 nodes, it may be, as in the corpuscle-picture there are free electrons. 

 It is not a consequence of the Fermi statistics alone, but of the Fermi 

 statistics plus the wave-theory. Of course, if we come to decide that 

 the Fermi statistics implies the wave-theory and vice versa, this warning 

 will seem superfluous; but it is not superfluous, so long as the new 

 statistics is used with reference to corpuscles. Now the corpuscle- 

 picture of negative electricity is not only familiar, but seems likely to 

 survive as the most convenient for describing most of the phenomena 

 in which electrons figure. I will therefore express as much as possible 

 of the new theory of conduction in the language of corpuscles, although 

 eventually I shall be forced to make an assumption which will come 

 to the same result as converting the corpuscles into waves. 



To realize the things to be explained, conceive a slab of metal, 

 having a thickness d measured along the :x;-axis; suppose a potential- 

 difference Fto exist between its faces, so that a field E = V/d directed 

 along the axis of x pervades it. 



If the electrons in the metal moved perfectly freely, then any 

 which was introduced without kinetic energy at the negative side of 

 the slab would fall forthwith to the positive side, arriving there with 

 the full kinetic energy eV and the full corresponding velocity of 

 magnitude (2eVlm)^'^ directed along the axis of x. Certainly nothing 

 of the sort occurs. When a potential-gradient exists along a wire, 

 for instance, heat is developed uniformly everywhere and there is 

 nothing to suggest that the electrons are moving mort rapidly at the 

 positive than at the negative end. 



We must then suppose that the free flight of the electron is inter- 

 rupted at frequent intervals, and that at every interruption it loses 

 the kinetic energy and the component of velocity up the potential 

 gradient which it has acquired from the field since the last one previous. 

 Or at least, the average loss of kinetic energy and of "drift-speed" 



