Molecules of a Gas in a Field of Force, 637 



Under these circumstances equations (2), (3), and (13) 

 reduce to 



64 o /l -| 75 -U 



„ 2 = NV,- 1 = dTh- et + 7f c3V * r3 , ( 1 6) 



where 



4tt /3gMR\l 

 5N / ' 



_4tt / 



~9A 3 V 



(17) 



In any actual case the term in V 2 on the right can 

 always be regarded as negligible. The term in T 3 is also o£ 

 little importance unless T is considerable. In considering 

 thermionic phenomena, however, the last-named term cannot 

 be disregarded, and the same statement is true of some o£ 

 the other terms which have been dropped in arriving at (16). 

 Another treatment suitable for such cases will be considered 

 later (p. 642). 



From the way in which M enters into equation (3), it will 

 be seen that a small molecular weight has the same effect as 

 a low temperature or a large density. Thus the deviations 

 from the results of the classical dynamics will be much more 

 marked the lower the molecular weight of the gas. For 

 an atmosphere of electrons such deviations will become 

 important at concentrations so small and temperatures so 

 high that the deviations would be inappreciable with ordinary 

 gases. One result of this is that if the number of free 

 electrons present in metals is comparable with the number of 

 atoms, a result which is indicated by a number of lines of 

 reasoning, equations (2) and (3) show that they will give 

 rise only to a very small fraction of the specific heats of 

 metals at ordinary temperatures. These points have already 

 been made by Keesom *. According to the present theory, 

 both the numbers per unit volume and the thermal energy of 

 the free electrons in metals approach constant values at low 

 temperatures. Indeed, if the numbers per unit volume are 

 of the order just supposed, this approach to constancy takes 

 place at temperatures which are not at all low. It follows 

 tha,fc the rapid temperature change of the resistance of metals 

 at low temperatures must be attributed entirely either to a 

 change in the mean free path of the electrons or, what may 

 come to the same thing, to the strength of the centres with 

 which they collide. One consequence is that it is necessary 

 to suppose that the atoms at rest have no influence on the 

 rectilinear motion of the free electrons; their paths are 

 deflected only in so far as the atoms are in motion. It is 



* Loc. cit. 



