TO A THERMO-ELECTRIC DIAGRAM. 131 
“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, 
>. (ka—hks) (Ta—t) =0. 
This holds for any number of separate materials in the conductor. As ¢ is the 
same throughout, the terms involving it evidently vanish identically; but there 
remains the equation 
2 .(ka— hy) m0 ? 
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, 
(Ka re ky) ii af (hy ae k) Ah + (k,— ka) 2 =0. 
From the direct experiments of LE Roux on “Veffet Thomson,” as he calls it, 
it appears that £ 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 
k=0. We may now construct 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 perpendicular to it give, for 
this substance employed with any other in a circuit of two metals, the values of 
Il 
aes Or 2 or (what comes to the same thing) the electro-motive force of a circuit 
whose junctions are both very nearly at ¢ but have a small constant temperattire 
difference. This quantity corresponds with what has been called the thermo- 
electric power of the circuit. 
“The two oblique straight lines in the diagram belong to the metals a, 3, 
respectively. The tangents of their inclination to the horizontal axis (the line 
of the supposed metal for which 4=0) are &,, /,—and they cut it at the points 
T,, T;, where they are neutral to it; cutting one another at a point A whose 
abscissa is their own neutral point T,,. The only change which would be intro- 
duced, by taking as horizontal axis the line corresponding to a metal for which 
* Annales de Chimie, 1867, vol. x. p. 277. 
