Sel 
7 = 7 | = 1 3 
P= Pal p= a = (o, EH, + 6, B,) da .. ttl) 
P 
In the case of a closed circuit, which we get by making the points 
P and Q coincide, we shall integrate (55) along the circuit after 
3 ; da - dep 7 
having multiplied that equation by — and replaced / by — —. The 
a 5 
= 
— av 
intensity 7 being everywhere the same, the result takes the form 
> de 
lef RE en 
This is the mathematical expression of Oum’s law. 
§ 21. It must further be noticed that the equation (60) agrees 
with the law of the thermo-electric series. This may be shown as 
follows. If we suppose the temperature to be the same throughout 
a junction, we may easily infer from what has been said in § 19 
that the part of the integral corresponding to such a part of the 
circuit can be represented as the difference of two quantities, which 
are both functions of the temperature, but of which one depends 
solely on the nature of the first metal and the other on that of the 
second. Considering next a homogeneous part of the circuit between 
two junctions, we may remark that in this E, and E, have 
R ende ; 0, 0, 2 ; : 
the form / (7) a and that the rations — and — are functions of the 
da oO 0 
temperature. We may therefore write for the corresponding part 
of (60) 
7e 
| y (L) at. 
2 
This integral, which is to be taken between the temperatures 7” and 
7" of the junctions, may be considered as the difference of the values, 
for T= T7"' and 7 = 7", of a certain quantity depending on the 
nature of the metal. 
Combining these results, we see that the electromotive force in a 
given circuit is entirely determined by the temperatures of the 
junctions, and that, if there are two of these between the metals 
[and //, the electromotive force #7; we have examined in §10c¢ 
may still be represented by an equation of the form 
Fimo (2) = $1 2) = Sol) Sa 7); 
the function $/(7’) relating to the first, and the function $/,(7’) to 
