( 689 ) 
metal and having, for a given temperature, determinate values, whether 
the body be or not in contact with another metal. 
By the assumption E, = E,, (56) simplifies into 
and (57) becomes 
ien Paid A,pP 
Bq — Gp = (Ve — Via) +5 lon (F |= 
1 1 1Q 
1 2 al A 
== — (Vp mr Vg) = ba ( 2), > (59) 
x es e A,a 
a formula which is easily seen to imply the law of the tension-series. 
§ 20. The question now arises, whether, with a view to simplifying 
the theory of the thermo-electric current, we shall be allowed to con- 
sider E, and E, as equal, not only in the junctions, but also in the 
homogeneous parts of the circuit, in which the differences of tempe- 
rature come into play. This seems very improbable. Indeed, supposing 
for the sake of simplicity WV, and JV’, to be, for a given metal, inde- 
T r 
dV, 
dV, : 
== Wand —) 
ar ar 
pendent of 7, so that in a homogeneous conductor 
we find from (53), putting E, = E,, 
2 aT dlog A, 4 a dT 2 aT’ dlog A, 4 a dT 
= i 
3 ey dz ; 3 ë de = 33 e dr 3 es: dx : 
or, since e‚ = (Fe 
r d log (A, Ay) Bt ae = 
da da: 
which can hardly be true. It would imply that the product A, A, is 
inversely proportional to the fourth power of the absolute temperature 
and this would require in its turn, as may be seen by means of (13) 
and (14), that the product N, N, should be inversely proportional to 
T itself. 
We are therefore forced to admit inequality of E, and E,. Now, 
it may be shown that, whatever be the difficulties which then arise 
in other questions, the theory of the electromotive force remains 
nearly as simple as it was before. For an open circuit we have 
again to put #5 0; hence, the formula (56) will still hold, as may 
SA : dp Ek 
be inferred from (55), if we replace Z bv — —. The equation for 
det 
the electromotive force becomes therefore 
