70 PKOCEEDINGS OF THE AMERICAN ACADEMY. 



with freedom to make p and v any constants whatever for any given 

 metal, we should be able to represent the facts with considerable 

 accuracy through moderate ranges of temperature, and we have 

 under these conditions a field of possibilities which seems to be worth 

 exploring. 



Electric Conduction. 



According to the ideas set forth in the preceding pages the specific 

 conductivity of a metal is the sum of two parts, one due to the (A) 

 electrons, the other to the (B), or "gas-kinetic," electrons. The 

 first of these parts I shall represent as 



K a = F 1 (8 t T), • 



where F x is some function of 8, the mean distance between the centres 

 of adjacent atoms of the metal, and of T, the absolute temperature 

 of the metal. 



I shall assume that previous discussions 6 of free electron theory 

 have been correct in taking that part of the conductivity which 

 depends on the free electrons as proportional to n (in equation (1)) 

 and to r, the mean time between collisions of a free electron with the 

 atoms. Evidently r is equal to the free mean path, between such 

 collisions, divided by the mean heat-velocity of the electrons. The 

 mean free path is some function of 8, — F 2 (8), let us say, which increases 

 with rise of temperature under ordinary conditions, while the mean 

 velocity 7 is proportional to (RT) h ; so that t*F 2 (8)+(RT) h ; with 

 R = k r T p , as in equation (1). Accordingly we get, as the part of the 

 specific conductivity which depends on (B), 



K b = h T" F 2 (8) -4- rKH-D = kb f 2 ((5 ) T (—M). (2)6 



For the total specific conductivity we now have 



K = Fi (8, T) + h F 2 (8) rt— i "-*>. (2) 



When a metal is heated under ordinary conditions, — that is, at 

 constant pressure with increase of volume, we have as the temperature 

 coefficient of K 



= J*L 1 fdFA eft J_ fdF{\ 

 ap KdT = '' K\d8J T dT + K\dTj 6 



h dF 2 cl8 J w -* pr ~fih P / s w t n Tf „_, _ 3) /0 , 

 + R-l8-df' T +K' F2( - S){v - ip - i)Ti " ^ (3) 



6 For example, see p. 303 of Tunzelmann's Electrical Theory. 



7 See footnote, p. 69. 



