CLAUSIUS' THEORY. 1 29 



zero of temperature, and the same definite form of Carnot's 

 function. Clausius then, for the first time, so expressed 

 Carnot's theory as to render its foundation consistent with 

 Joule's law. This partly hypothetical, partly general, 

 foundation led Clausius, in the mathematical development 

 of his mechanical theory of heat and its application almost, 

 though not quite, as far as Rankine had gone. 



These theories, coming as it were as "bolts from the blue," 

 caught Sir William Thomson still endeavouring to evolve the 

 perfectly general foundation of thermo-dynamics, from 

 Joule's discovery and Carnot's theorem. Rankine's was 

 the first, as after being read February 4th, 1850, Rankine's 

 paper was referred by the Royal Society of Edinburgh to 

 Thomson to report upon. This Sir William Thomson 

 did, suggesting certain improvements which the author 

 acknowledges and adopts, and for which he expresses 

 his thanks. The hypothetical foundation of Rankine's theory 

 (though exciting Sir William Thomson's admiration no less 

 than the mathematical development erected on this founda- 

 tion, and the novelty and importance of some of the results, 

 indicated in Rankine's initial application of it) afforded Sir 

 William no direct assistance in finding the general founda- 

 tion for which he was seeking ; though it could not but 

 have confirmed him in his view as to the possibility of such 

 a foundation. Clausius' paper, published in Pogendorff's 

 Annalen for March and April, 1850, reached Sir William 

 Thomson early in 185 1, just after he had succeeded in 

 proving Carnot's theorem on a foundation consistent with 

 Joule's discovery ; having previously determined the general 

 equations of the mathematical theory of heat founded on 

 the two principles — Joule's and Carnot's — and applied the 

 equation to Regnault's observations. Sir William Thomson 

 K 



