DYNAMICAL THEORY OF HEAT. 139 
heat amounting to ©, at the cold junction, and of mechanical effect by the current 
amounting to F units of work. If we estimate the value of F,”*° as half what it 
would be were the electro-motive force the same for all equal differences of 
temperature as for small differences near the freezing point,* that is, if we take 
F,?8°=1 x 40m x 280, the preceding equation becomes — 
140 xmx40=I(_ fo sar— @, i 
0 
But we found mx 40= pe. 
280 140 pu 140 3 
Hence df 3 dt =o (1+ i = 0) (1 a7) = %x5 nearly . . .(b); 
or, according to (a), 
280 3 
J) Saige tee pode -cstd do, waiting tutecrsiioc-deril- sage 
results, of which (4) shows how the difference of the aggregate amount of the theo- 
retically indicated convective effect in the two metals is related to the PELTIER 
effect at the cold junction; and (c) shows that its absolute value is rather more 
than one-third of a thermal unit per second per unit strength of current. 
120. If the specific heats of current electricity either vanished or were equal 
in the different metals, we should have, by (15) and (16), 
a = constant : : ME hoe - (20), 
0 
and Fa} @=T) BOL su stingy (210). 
or, the PeLTIER thermal effect at a junction of two metals would be proportional 
to the absolute temperature at which it takes place, and the electro-motive force 
_in a circuit of any two metals would vary in the simple ratio of the difference of 
temperature on the new absolute scale between their junctions.+ Whatever 
thermometric system be followed, the second of these conclusions would require 
the same law of variation of electro-motive force with the temperatures of the 
junctions, in every pair of metals used as a thermo-electric element. 
121. Before the existence of a convective effect of electricity in an unequally 
heated metal had even been conjectured, I arrived at the preceding conclusions by 
a theory in which the Pettier effect was taken as the only thermal effect reversible 
with the current in a thermo-electric circuit, and found them at variance with 
* See § 122, below. 
+ When the Theory was first communicated to the Royal Society, I stated these conclusions with 
reference to temperature by the air thermometer, and therefore in terms of Carno7’s absolute function 
of the temperature, not simply as now in terms of absolute temperature. At the same time, I gave as 
consequences of Mayerr’s hypothesis, the same statement in terms of air thermometer temperatures, 
as is now made absolutely. See Proceedings, Dec. 15, 1851 ; or Philosophical Magazine, June 1852, 
p. 532. 
VOL. XXI. PART I. Qp *# 
