1912-13.] On the Electron Theory of Thermo-electricity. 171 
= R retains its usual significance. The choice is, however, im- 
material, involving at most the introduction of a constant. In the 
evaporation (i) the gas expands isothermally, doing work of amount 
R 0 lo g^*A and (ii) it absorbs latent heat of amount q A , say. Now cause it 
to condense back isothermally into metal B. In this process, (i) work 
has to be done on the gas, of amount Rd log 2®, and (ii) the gas liberates 
latent heat of amount q B , say. Thus the nett effect of both changes has 
been an expenditure of work and heat on the gas of amount 
R6> log-^? - R 6 lo g^+g A - q B = R# log— +'|| A - 2 b)- 
P P Pa 
But as the process considered has merely resulted in the transfer from 
one side of the interface between A and B to the other side, against a 
potential-difference E (e.m.u.), of a quantity — (e.m.u.) of electricity, the 
above energy-expenditure must be balanced by the necessary electrical 
work E . — =E/x, say ; so that 
m 
E = — log — + -(?a— 2 b) ( 1) 
P Pa P 
gives the contact difference of potential at temperature d between the 
metals A, B. 
For the temperature-coefficient, since the electronic vapour-pressures 
and latent heats are functions of the temperature, we have 
R , p B Rd d 
log— +- 
Pa fA d6 
2 b)- 
Now the transfer of electrons took place in two distinct “evaporation” 
or “ condensation ” stages, to either of which accordingly Clapeyron’s 
equation will apply. Thus, for the evaporation out of A, 
a -v (P Pa 
qA ~ A °w 
assuming as usual that the volume of the vapour is large compared 
with that of the un-evaporated state, and writing v A for the volume-change, 
which is thus practically the whole vapour- volume. Or, 
2 a = 1 A 
PaVaO Pa 
a e 
log p A = 
2a_ 
R0 2 ' 
i.e. 
