600 
Proceedings of the Royal Society 
Now, it is an immediate consequence of the second law of thermo- 
dynamics that, as Peltier effects are reversible with the direction of 
the current, and are the only sensible thermal effects when a very 
feeble current passes through a thermo-electric circuit, all of whose 
parts are at one temperature, we must have 
or, assuming the parabolic law, 
^•fc-^)(T a6 -0 = 0. 
This holds for any number of separate materials in the conductor. 
As t is the same throughout, the terms involving it evidently 
vanish identically; but there remains the equation 
l.(k a -h b ) T a6 = 0, 
establishing a relation between the specific heats of electricity in a 
number of metals and the absolute temperatures of the neutral 
points of each junction of two of them. Other relations may be 
obtained by altering the order of the metals if there be more than 
three — but they are all virtually contained in the formula for three, 
which we write at full length, 
(ha ~ ^b) ^ab + d £ b ~ K) ^bc + (he ~ ^a) ^ca = 
From the direct experiments of Le Roux on “l’Effet Thomson,” as 
he calls it, it appears that h is null in lead.* At all events, 
since Thomson showed that it has opposite signs in iron and copper, 
we may imagine a substance for which h = 0. We may now con- 
struct an improved “ Thermo-electric diagram ” to represent these 
relations numerically, employing the line for this substance as 
our axis of absolute temperatures ; while the ordinates perpen- 
dicular to it give, for this substance employed with any other in a 
circuit of two metals, the values of or or (what comes 
to the same thing) the electro-motive force of a circuit whose 
junctions are both very nearly at t , but have a small constant 
temperature difference. This quantity corresponds with what has 
been called the thermo-electric power of the circuit. 
* Annales de Cljimie, 1867, vol. x. p. 277. 
