1912-13.] On the Electron Theory of Thermo-electricity. 175 
and, differentiating (1) and inserting this value, we have 
dYj R , R 6 d , p v> \ d, 
— = -los- B + Th ]o %—+- 37#ab 
fi, d(j Px p dO 
Pa - Pb l _ Pa~ Pb 
) u 
d0~ g 
R 
log a ^ + '^ T 
/xi a A V 
6 2 
dE , , ,v 1 d 
— = (a constant) + 
dO p da 
1 d 
+ r .d0 q ^’ 
Avenarius’s law, however, gives — it is obviously impossible to attempt 
a deduction of the law from the above equation, in view of the presently 
indefinite character of q A B as given by (3) — 
^? = A + B6> + C0 2 + .... 
dO 
(or, to a first approximation, -^=A + B$), whence, in the differential 
identity 
A + B0 + C0 2 + . . . . = (a constant) + — 
ad /x 
a 
it is only necessary that should be of the form pd + gd 2 -}-rd 3 -f . . . . 
fX 
(or, to a first approximation, pG)* and so from equation (3), written 
(a A - <r B ), 
we require an equality of the form 
o- a -<x b = A 1 6> + B 1 0 2 + C 1 0 3 + (10) 
or, to a first approximation, cta — <x B = A 1 #, i.e., in view of the certainly 
extremely small coefficients B 1 , C 1 , .... we may say that the difference of 
the Thomson effects is approximately simply proportional to the absolute 
temperature. 
We conclude accordingly that the theory is essentially reconcilable 
with the standard Kelvin equations, with the exception of small divergences 
to be traced to the irreversible nature of the heat flow along the conductors, 
a consideration omitted in the Kelvin treatment. Whether the present 
theory will give more information as to the actual physical processes 
involved in the action of a thermo-couple is another question. It certainly 
.seems to indicate the positive existence of potential-differences, however 
small, due solely to unequal heating of conductors. Experimental results 
cannot help us much so far ; it has, for example, proved impossible, even 
* Gf. Preston’s Heat , p. 316 (1894 edition) : “It has been suggested that . . . the 
molecular latent heat is proportional to the absolute temperature.” 
