220 Prof. Thomson on the Dynamical Theory of Heat, 



strength of the current ; and, taking place equally with the 

 current in one direction 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-electric current, the strength of the current be infi- 

 nitely 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 electromotive force may fall short 

 of, or may exceed, by only an infijiitely small fraction of itself, 

 the amount required to balance the thermal electromotive force 

 of the battery, there will be only an infinitely 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, wasted on the fric- 

 tional 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 current 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 elsewhere in all actions 

 depending on heterogeneousness of the circuit, it appears that, 

 were there no propagation of heat through the battery by ordi- 

 nary conduction, Carnot's critei'ion 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 con- 

 sidering expansive engines fulfilling the same criterion, would 

 hold between the operative thermal agency and the mechanical 

 effect produced. It appears extremely probable that this rela- 

 tion does actually subsist between the part of the thermal agency 

 which is. reversed with the current and the mechanical effect pro- 

 duced by the engine, and that the ordinary conduction of heat 

 through the battery takes place independently of the electrical 

 circumstances. The following proposition is therefore assumed 

 as a fundamental hypothesis in the theory at present laid before 

 the Eoyal Society. 



106. The electromotive forces produced by inequalities of tem- 

 perature in a circuit of dijferent 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 dynamical 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 



