128 PROFESSOR W. THOMSON ON THE 
strength of the current; and taking place equally with the current in one direc- 
tion or in the contrary, is obviously of an irreversible kind. Any other thermal 
action that can take place must depend on the heterogeneousness of the circuit, 
and must be of a kind reversible with the current. 
105. Now if in an unbroken circuit with an engine driven by a thermo-elec- 
tric current, the strength of the current be infinitely small compared with what 
it would be were the engine held at rest, or, which is the same, if the engine be 
kept at some such speed that its inductive electro-motive force may fall short of, 
or may exceed, by only an infinitely small fraction of itself, the amount required 
to balance the thermal electro-motive force of the battery, there will only an infi- 
nitely small fraction of the work done by the current in the former case, or of 
the work done in turning the engine in the latter, be wasted on the frictional 
generation of heat through the electric circuit. In these circumstances, it is 
clear, that whatever mechanical effect would be produced in any time by the 
engine from a direct current of a certain strength, an equal amount of work would 
have to be spent in forcing it to move faster and keeping up an equal reverse cur- 
rent for the same length of time; and as the direct and reverse currents would 
certainly produce equal and opposite thermal effects at the junctions, and else- 
where in all actions depending on heterogeneousness of the circuit, it appears that, 
were there no propagation of heat through the battery by ordinary conduction, 
Carnor’s criterion of a perfect thermo-dynamic engine would be completely 
fulfilled, and a definite relation, the same as that which has been investigated 
(§ 25) already by considering expansive engines fulfilling the same criterion, 
would hold between the operative thermal agency and the mechanical effect pro- 
duced. It appears extremely probable that this relation does actually subsist 
between the part of the thermal agency which is reversed with the current and the 
mechanical effect produced by the engine, and that the ordinary conduction of 
heat through the battery takes place independently of the electrical circum- 
stances. The following proposition is therefore assumed as a fundamental hypo- 
thesis in the Theory at present laid before the Royal Society. 
106. The electro-motive forces produced by inequalities of temperature in a cir- 
cuit of different metals, and the thermal effects of electric currents circulating in it, 
are subject to the laws which would follow from the general principles of the dynami- 
cal theory of heat if there were no conduction of heat from one part of the circuit to 
another. 
In adopting this hypothesis, it must be distinctly understood that it is only a 
hypothesis, and that, however probable it may appear, experimental evidence in 
the special phenomena of thermo-electricity is quite necessary to prove it. Not 
only are the conditions prescribed in the second Law of the Dynamical Theory 
not completely fulfilled, but the part of the agency which does fulfil them is in all 
