14 Prof. Thomson on the Dynamical Theory of Heat. 



gine*. He proved it by demonstrating that a negation of it 

 would require the admission that there might be a self-acting 

 machine constructed which would produce mechanical effect inde- 

 finitely, without any source either in heat or the consumption of 

 materials, or any other physical agency ; but this demonstration 

 involves, fundamentally, the assumption that, in " a complete 

 cycle of operations," the medium parts with exactly the same 

 quantity of heat as it receives. A very strong expression of doubt 

 regarding the truth of this assumption, as a universal principle, is 

 given by Caruot himselff ; and that it is false, where mechanical 

 work is, on the whole, either gained or spent in the operations, 

 may (as I have tried to show above) be considered to be perfectly 

 certain. It must then be admitted that Carnot's original de- 

 monstration utterly fails, but wc cannot infer that the proposition 

 concluded is false. The truth of the conclusion appeared to me, 

 indeed, so probable, that I took it in connexion with Joule's 

 principle, on account of which Carnot's demonstration of it fails, 

 as the foundation of an investigation of the motive power of heat 

 in air-engines or steam-engines through finite ranges of tempe- 

 rature, and obtained about a year ago results, of which the sub- 

 stance is given in the second part of the paper at present com- 

 municated to the Royal Society. It was not until the com- 

 mencement of the present year that I found the demonstration 

 given above, by which the truth of the proposition is established 

 upon an axiom (§ 12) which I think will be generally admitted. 

 It is with no wish to claim priority that I make these statements, 

 as the merit of first establishing the proposition upon correct 

 principles is entirely due to Clausius, who published his demon- 

 stration of it in the month of May last year, in the second part 

 of his paper on the motive power of heat J. I may be allowed 

 to add, that I have given the demonstration exactly as it occurred 

 to me before I knew that Clausius had either enunciated or de- 

 monstrated the proposition. Tlie following is the axiom on 

 which Clausius' demonstration is founded : — 



It is impossible for a self-acting machine, unaided by any ex- 

 ternal agency, to convey heat from one body to another at a higher 

 temperature. 



It is easily shown, that, although this and the axiom I have 

 used are different in form, either is a consequence of the other. 

 The reasoning in each demonstration is strictly analogous to that 

 which Carnot originally gave. 



15. A complete theory of the motive power of heat would 

 consist of the application of the two propositions demonstrated 

 above, to every possible method of producing mechanical effect 



* Account of Caniot's Theory, § 13. f Ibid. § 6. 



X Poggentlorff'8 Annalen, referred to above. 



