DYNAMICAL THEORY OF HEAT. 127 
This equation may be considered as the mathematical expression of the Second 
fundamental Law of the Dynamical Theory of Heat. The corresponding expres- 
sion of the First Law is 
W+J (H+ Hy+ iwi). + He» + Hy) =0 . : . . (2), 
where W denotes the aggregate amount of work spent in producing the operations, 
and J the mechanical equivalent of the thermal unit. 
§§ 102-106. Lnitial examination of Thermo-dynamic circumstances regarding 
Electric Currents in Linear Conductors. 
102. Prttier’s admirable discovery that an electric current in a metallic cir- 
cuit of antimony and bismuth produces cold where it passes from bismuth to 
antimony, and heat where it passes from antimony to bismuth, shows how an 
evolution of mechanical effect, by means of thermo-electric currents, involves trans- 
ference of heat from a body at a higher temperature to a body at a lower temper- 
ature, and how a reverse thermal effect may be produced, by thermo-electric 
means, from the expenditure of work. For if a galvanic engine be kept in motion 
doing work, by a thermo-electric battery of bismuth and antimony; the current 
by means of which this is effected passing, as it does, from bismuth to antimony 
through the hot junctions, and from antimony to bismuth through the cold 
junctions, must cause absorption of heat in each of the former, and evolution of 
heat in each of the latter; and to sustain the difference of temperature required for 
the excitation of the electro-motive force, even were there no propagation of 
heat by conduction through the battery, it would be necessary continually, during 
the existence of the current, to supply heat from a source to the hot junctions, 
and to draw off heat from the cold junctions by a refrigerator :—Or, if work be 
spent to turn the engine faster than the rate at which its inductive reaction 
balances the electro-motive force of the battery, there will be a reverse current 
sent through the circuit, producing absorption of heat at the cold junctions, and 
evolution of heat at the hot junctions, and consequently effecting the transference 
of some heat from the refrigerator to the source. 
103. We see then, that in PeLtier’s phenomenon we have a reversible thermal 
agency of exactly the kind supposed in the second Law of the Dynamical Theory 
of Heat. Before, however, we can apply either this or the first Law, we must 
consider other thermal actions which are involved in the circumstances of a 
thermo-electric current; and with reference to the second Law we shall have to 
examine whether there are any such of an essentially irreversible kind. 
104. It is to be remarked, in the first place, that a current cannot pass through 
a homogeneous conductor without generating heat in overcoming resistance. 
This effect, which we shall call the frictional generation of heat, has been dis- 
covered by Joute to be produced at a rate proportional to the square of the 
VOl.. XXI. PART. I. 2M 
a 
