86 PROCEEDINGS OF THE AMERICAN ACADEMY. 



Returning, then, to equation (18) and putting 



x=k x T K , (20) 



with k x and k as positive constants, we get 



e L 2 



+ t,Tf'-« kjc v (k + tt) r<« + *- « 



(21) 



If we take the point of view of thermal effusion, according to which 



dF 4- dT= - R (| + ^ + v), we get from (18) 



1 



a = - 

 e 



k r {l + p-v)T»+ k x k r (1+K + p) Tl* + "> 



(210 



+ k v irT(« ~ 1) - ftjfe, (* + tt) T ^ + - ~ 1) • 



Neither equation (21) nor equation (21') would permit us to have 

 a strictly proportional to T; but we are not sure that a is strictly 

 proportional to T in any metal. If the terms beyond the first in the 

 second member are small compared with this first term, we may have 

 approximately straight lines on the thermo-electric diagram, — that 

 is, have a nearly proportional to T, if p = 1. 



Moreover, the presence of (— v) in the coefficient of this first term 

 provides for possible negative values of a, if the first term is really the 

 dominating part of this quantity. Of the other terms, the second and 

 third are positive, according to the assumptions already made, while 

 the fourth may be negative, if tt, which is supposed negative, can be 

 numerically greater than k. I shall assume, for the present at least, 

 that k x is very small, thus making the second and fourth terms very 

 small. To make k x small is to make x small, so that I am here assuming 

 that the greater part of the electric conductivity is due to the (^1) 

 electrons. This assumption accords well with what we know in 

 regard to the temperature coefficient of conductivity. For even with 

 equation (21) we cannot get a negative value of cr proportional to T, 

 a condition approached very closely by several metals, without 

 making p = 1 and v greater than 1, so that the K^ term in the value 

 of the conductivity, equation (2), will still increase with rise of temper- 

 ature. The K a term in (2) must apparently he the prevailing term, 

 at least so far as the temperature coefficient of conductivity is con- 

 cerned, in some metals, if not in all. 



