of Edinburgh, Session 1870 - 71 . 
309 
My hypothetical result was to the effect that what Thomson 
(Trans. R.S.E. 1854, Phil. Trans. 1856) calls the specific heat of 
electricity, should he, like thermal and electric resistance, directly 
proportional in pure metals to the absolute temperature, the coeffi¬ 
cient of proportionality being, for some substances, negative. 
Hence, using Thomson’s notation as in Trans. R.S.E., we have 
for any two metals 
J <Ti = hf , J = \t , 
where Jc x and k. 2 are constants, whose sign as well as value depends 
on the properties of each metal, crq , <r > 2 are the specific heats of 
electricity, and J is Joule’s Equivalent. 
Thus, introducing these values into Thomson’s formulae, we have 
where n is the Peltier effect at a junction at absolute tempera¬ 
ture t. Integrating, we have 
c - (k - k)t = J? , 
£ 
or 
J y = (K ~ K) (t 0 - t) , 
where t 0 is the constant of integration, obviously in this case the 
temperature at which the two metals are thermo-electrically neutral 
to one another. Hence the Peltier effect may be represented by 
the ordinates of a parabola of which temperatures are the abscissse; 
the ordinates being parallel to the axis of the curve. 
The electromotive force in a circuit whose junctions are at ab¬ 
solute temperatures t and V is then represented by 
E = Z S* T dt = “ r) - & - <,2) ] 
= (&, - k 2 ) (t - f) n„ - i ±t . 
This, of course, is again the equation of a parabola. That t - t' is 
a factor of E has long been known, and Thomson has given the 
t t' 
results of many experiments tending to show that t 0 -is also 
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