ri 
DYNAMICAL THEORY OF HEAT. 135 
The general principles are most conveniently applied by restricting the num- 
ber of metals referred to in the general equations to two; a case which we accord- 
ingly proceed to consider. 
115. Let the principal conductor consist of two metals, one constituting the 
middle, and the other the two terminal portions. Let the junctions of these por- 
tions next the terminals E, E’ be denoted by A, A’ respectively, and let their tem- 
peratures be T, T’. Let also n(T),—1m (T’) be the quantities of heat absorbed at 
them per second by a current of unit strength. We should have 
m(T)=n(T), 
if the temperatures were equal, since the PeLTier phenomenon consists, as we 
hhave seen, of equal quantities of heat evolved or absorbed, according to the 
- direction of a current crossing the junction of two different metals; and if these 
quantities be not actually equal, we may consider them as particular values of a 
function 1 of the temperature, which depends on the particular relative thermo- 
electric quality of the two metals. Accordingly, the preceding notation is reduced 
ton=2, T,=T, T,=T’, 1,=(T), n,=—m(T); and we have 
m, 7, T, v 
* hs oats f o,dt+ a dtaf (o,—G,) dt, 
, T, T, T 
and similarly for the integral involving 2 . Hence the general equations become 
‘3 13 
F=J {0 (1)-n(1)+ : (7,—2,)at} (13) 
la 7 
“es : A= 7? 1t=0 ay SRN pec eee ace (18) 
If in the latter equation we substitute ¢ for T, and differentiate with reference to 
this variable, we have, as an equivalent equation, 
¢ +) o,-¢. 
pee ae d a . : - 15 
ime he Dvr e) 
I di 
or Cian amarilan ie . . . . (16) 
This last equation leads to a remarkably simple expression for the electro-motive 
force of a thermo-electric pair, solely in the terms of the PettiEer evolution of 
heat at any temperature intermediate between the temperatures of its junctions; 
for we have only to eliminate by means of it (¢,—c,) from (13), to find 
a} 
=i f OEE SS AR PNY Ole T5617) 
y it 
116. Let us first apply these equations to the case of a thermo-electric pair, 
VOL. XXI. PART I. 20 
b 
