266 PROFESSOR WILLIAM THOMSON ON THE 
derives more mechanical effect from the same quantity of heat, drawn from the 
source, than B, is false. Hence no engine whatever, with source and refrigerator 
at the same temperatures, can get more work froma given quantity of heat intro- 
duced than any engine which satisfies the condition of reversibility, which was to 
be proved. 
14. This proposition was first enunciated by Carnot, being the expression of 
his criterion of a perfect thermo-dynamic engine.* He proved it by demonstrat- 
ing that a negation of it would require the admission that there might be a self- 
acting machine constructed which would produce mechanical effect indefinitely, 
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 regard- 
ing the truth of this assumption, as a universal principle, is given by CarNnor 
himself ;+ 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 shew above) be considered 
to be perfectly certain. It must, then, be admitted that CarNnot’s original demon- 
stration utterly fails, but we cannot infer that the proposition concluded is false. 
The truth of the conclusion appeared to me, indeed, so probable, that I took it in 
connection 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 temperature, and obtained, 
about a year ago, results, of which the substance is given in the second part of 
the paper at present communicated to the Royal Society. It was not until the 
commencement 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 Ciausius, who published his demonstration 
of it in the month of May last year, in the second part of his paper on the Motive 
Power of Heat.{ I may be allowed to add, that I have given the demonstration 
exactly as it occurred to me before I knew that Crausius had either enunciated 
or demonstrated the proposition. The following is the axiom on which Ciausius’ 
demonstration is founded :— 
It is impossible for a self-acting machine, unaided by any external agency, to 
convey heat from one body to another at a higher temperature. 
It is easily shewn that, although this and the axiom I have used are different 
* “ Account of Carnor’s Theory,” § 13. t Ibid., § 6. 
+ Poccenporrr’s Annalen, referred to above. 
' 

ieee 
