connected with the Theory of the Steam-Engine. 389 



loss of heat from the cylinder, steam-pipes, &c. ; nor could we 

 conclude that Mr. Rankine's proposition is false, if the steam 

 were observed in any case to issue dry from the steam-pipe, 

 and at a temperature above 212°, unless the expansive prin- 

 ciple were known to be pushed to the utmost in the actual work- 

 ing of the engine. It is however certain that if Mr. Rankine's 

 proposition be true, steam, after having passed through a high- 

 pressure engine in which the expansive principle is pushed to 

 the utmost, whether there be any " priming" or not, and whe- 

 ther there be any heat lost externally from the different parts 

 of the engine or not, will issue at the temperature of 212°, 

 and moist (and consequently scalding to the hand), from the 

 waste steam-pipe ; and, Regnault's modification of Wattes law 

 being considered as established, it is certain that steam issu- 

 ing immediately from a high-pressure boiler into the open air 

 will be above 212°, and dry. 



The demonstration which Mr. Rankine gives of his propo- 

 sition is partially founded on certain hypotheses regarding the 

 specific heats of gases and vapours. Rut, besides this propo- 

 sition, he derives another conclusion from the same investiga- 

 tion which is experimentally verified by Regnault's modifica- 

 tion of Watt's law : and hence, as it is easy lo show, if we are 

 contented to take Regnault's result as an experimental fact, 

 and if we adopt your mechanical equivalent for a thermal unit 

 (or Rankine's value, which is about Jths of yours), we may 

 demonstrate Mr. Rankine's remarkable theorem without any 

 other hypothesis than the convertibility of heat and mechani- 

 cal effect. 



In a paper by Clausius*, published in Poggendorff's Annalen 

 for last April and May, a similar conclusion to that which I 

 have quoted of Mr. Rankine's (whose paper was read before 

 the Royal Society of Edinburgh on the 4th of February), is 

 announced. I have not yet been able to make myself fully ac- 

 quainted with this paper; but, from the principles and methods 

 of reasoning explained at the commencement, which differ from 

 those of Carnot only in the adoption of your axiom instead of 

 Carnot's, I have no doubt but that the demonstration of the 

 proposition in question is the same in substance as Mr. Ran- 

 kine's modified in the manner I have suggested. 



I remain, dear Sir, yours most truly, 



J, P. Joule, Esq. William Thomson. 



[* A translation of this paper will appear in an early Number of this 

 Journal.— Ed.] 



