Josiah Willard Gibbs. 285 



The trend of Thomson's ideas had led him away towards other 

 problems, such as the cosmical results of his principle, and (1853) 

 the amount of mechanical energy that can be restored from an 

 unequally heated system of bodies in equalising their temperatures. 

 By taking one of the bodies to be of infinite thermal capacity and of 

 temperature #o> the energy so restorable would have been determined 

 immediately as H J dH/0 ; as it is necessarily the same for all rever- 

 sible paths of transformation, this formula leads directly to Clausius' 

 fundamental proposition about entropy. 



That function had, in fact, been introduced first of all, at a very early 

 period, by Rankine, who approached it through a special theory of 

 molecules and their atmospheres, and afterwards generalised the 

 argument, in his " Treatise on the Steam Engine," into a chain of 

 abstract propositions, which have never been satisfactorily interpreted 

 or understood. 



This sketch of the history of the first stage of the development of 

 abstract thermodynamics is outlined, for the sake of comparison with 

 the next stage of progress. It had been marked by the activity of two 

 great minds working contemporaneously at the same problems ; 

 questions of priority have naturally arisen ; but we are now far enough 

 removed from the period to appreciate that the merit of each is not 

 interfered with by the work of the other. 



Any want of balance in the account above given will be counteracted 

 by an extract from Willard Gibbs' obituary notice (1889) of Clausius, 

 whom he seems to have regarded as in a special sense his master ; the 

 extract is appropriate here, as conveying the attitude of mind of the 

 writer towards the history of the science which he had himself reduced 

 into its canonical form. 



" But it was with questions of quite another order of magnitude 

 that his [Clausius'] name was destined to be associated. The funda- 

 mental questions concerning the relation of heat to mechanical effect, 

 which had been raised by Eumford, Carnot, and others, to meet with 

 little response, were now everywhere pressing to the front. ' For more 

 than twelve years,' said Regnault, in 1853, 'I have been engaged in 

 collecting the materials for the solution of this question : Given a 

 certain quantity of heat, what is, theoretically, the amount of 

 mechanical effect which can be obtained by applying the heat to 

 evaporation, or the expansion of elastic fluids, in the various circum- 

 stances which can be realized in practice 1 ' The twenty-first volume of 

 the * Memoirs of the Academy of Paris,' describing the first part of the 

 magnificent series of researches which the liberality of the French 

 Government enabled him to carry out for the^sojution of this question, 

 was published in 1847. In the same^fear appeared Helmholtz's 

 celebrated memoir, * Ueber die Erhaltung der Kraft.' For some years 



C 



