carnot's theory of the motive power of heat. 545 



11. On the measurement of Thermal Agency, considered with reference to its 

 equivalent of mechanical affect. 



12. A perfect thermo-dynamic engine of any kind, is a machine by means of 

 which the greatest possible amount of mechanical effect can be obtained from a 

 given thermal agency ; and, therefore, if in any manner we can construct or ima- 

 gine a perfect engine which may be applied for the transference of a given quan- 

 tity of heat from a body at any given temperature, to another body, at a lower 

 given temperature, and if we can evaluate the mechanical effect thus obtained, 

 we shall be able to answer the question at present under consideration, and so to 

 complete the theory of the motive power of heat. But whatever kind of engine 

 we may consider with this view, it will be necessary for us to prove that it is a 

 perfect engine ; since the transference of the heat from one body to the other may 

 be wholly, or partially, effected by conduction through a solid,* without the de- 

 velopment of mechanical effect ; and, consequently, engines may be constructed 

 in which the whole, or any portion of the thermal agency is wasted. Hence it is 

 of primary importance to discover the criterion of a perfect engine. This has 

 been done by Carnot, who proves the following proposition : — 



13. A perfect thermo-dynamic engine is such that, whatever amount of mecha- 

 nical effect it can derive from a certain thermal agency ; if an equal amount be spent 

 in working it backwards, an equal reverse thermal effect will be produced.^ 



14. This proposition will be made clearer by the applications of it which 

 are given below (§ 29), in the cases of the air-engine and the steam-engine, than it 

 could be by any general explanation ; and it will also appear, from the nature 

 of the operations described in those cases, and the principles of Carnot's reason- 

 ing, that a perfect engine may be constructed with any substance of an in- 

 destructible texture as the alternately expanding and contracting medium. 

 Thus we might conceive thermo-dynamic engines founded upon the expansions 



* When " thermal agency" is thus spent in conducting heat through a solid, what becomes of 

 the mechanical effect which it might produce ? Nothing can be lost in the operations of nature — 

 no energy can be destroyed. What effect then is produced in place of the mechanical effect which is 

 lost ? A perfect theory of heat imperatively demands an answer to this question ; yet no answer can 

 be given in the present state of science. A few years ago, a similar confession must have been made 

 with reference to the mechanical effect lost in a fluid set in motion in the interior of a rigid closed 

 vessel, and allowed to come to rest by its own internal friction ; but in this case, the foundation of a 

 solution of the difficulty has been actually found, in Mr Joule's discovery of the generation of heat, 

 by the internal friction of a fluid in motion. Encouraged by this example, we may hope that the 

 very perplexing question in the theory of heat, by which we are at present arrested, will, before long, 

 be cleared up. 



It might appear, that the difficulty would be entirely avoided, by abandoning Carnot's funda- 

 mental axiom ; a view which is strongly urged by Mr Joule (at the conclusion of his paper " On 

 the Changes of Temperature produced by the Rarefaction and Condensation of Air." Phil. Mag., 

 May 1845, vol. xxvi.) If we do so. however, we meet with innumerable other difficulties — insuper- 

 able without farther experimental investigation, and an entire reconstruction of the theory of heat, 

 from its foundation. It is in reality to experiment that we must look — either for a verification of 

 Caknot's axiom, and an explanation of the difficulty we have been considering ; or for an entirely new 

 basis of the Theory of Heat. 



t For a demonstration, see § 29, below. 



VOL. XVI. PART V. 7 B 



