1912-13.] On the Electron Theory of Thermo-electricity. 173- 
passage across it of unit charge of electricity, and must accordingly be the 
Peltier effect ; 
i.e. 
_dE n 
e ~d0 ~ 0’ 
(5> 
which is the first of the two equations derived from purely thermodynamical 
considerations by Lord Kelvin.* The theories thus appear so far in con- 
sonance, but it has to be remarked that whereas the Kelvin result assumes 
reversibility of the thermo-electric processes and consequently neglects the 
irreversible heat conduction in the thermo-element — assumes, in fact, the 
equation J — 0 — the present treatment, though assuming reversibility of 
the individual “ evaporations,” does not require reversibility on the whole, 
but rests only upon the First Law. Further, “cTE” has not the same 
significance in the two cases. As obtained from (4) and (5) in the form 
dE = 
n 
0 
dO, it is obviously, for the case of a thermo-couple, only the difference 
of the E.M.F.’s at the junctions: in Kelvin’s expression of dE = ~dO,dEis 
u 
the whole E.M.F. over the whole circuit. Identity of the two expressions 
would therefore imply, as Kruger j- has pointed out for the case of his own 
result, the non-existence of any potential-difference due to the unequal 
heating of the conductors forming the couple, an implication quite at 
variance with the electron theory of metallic conduction. The result, 
therefore, only serves to cast further doubt on the justification for assuming 
reversibility in the thermo-electric problem. 
The variance in the meaning of E will prevent anything more than an 
approximation to the second Kelvin equation, 
de _ <r A - <r B 
dO 6 ’ 
being obtained. Thus, on differentiating (4) and again employing (3), we 
obtain 
( Il- ( r -r \ 
de no 2 y. de ' A B> ’ 
c c 
or, identifying — , — , the “ specific heats of unit charge of electricity ” in 
the two metals, with the Thomson effects cr A , era, 
de < 7 ab d 
dO 
/x6 2 dO 
(°a ~ 0b), 
• ( 6 ), 
an equation from which the proportionality of the difference of the Thomson 
* Kelvin, Math, and Phys. Papers, i., art. xlviii., part vi. p. 249. 
t Loc. cit., p. 805. 
