284 Obituary Notices of Fellows deceased. 



fact have been quite well developed in a form which would leave open 

 the question as to Joule's principle. Carnot himself before his death 

 in 1832, long previous to this time, had already advanced further; 

 continued reflexion on the phenomena and properties of gases had 

 impelled him to recognise the law of conservation in total energy, 

 as appears very clearly in his manuscript remains published to the 

 world in 1882. 



The first suggestion that a dynamical scale of temperature more 

 convenient than Thomson's original one would be gained by taking 

 Carnot's function to be the reciprocal of the temperature, measured 

 from absolute zero by the expansion of any ideal gas, came to him 

 from Joule himself in 1848, who, in reasoning on this subject, pre- 

 sumably attended to his own principle.* In the procedure of Clausius'' 

 memoir, the value of Carnot's function was derived from the discussion 

 of an ideal gas, including in its definition Joule's property of absence of 

 internal work, or rather the indications thereof deducible from 

 general considerations and from Regnault's results. It was shown to be 

 the reciprocal of absolute temperature as measured by this ideal body as 

 thermometric substance ; and he thence advanced at once to the funda- 

 mental simple formula for the efficiency with finite range of temperature. 

 But the precise practical determination of this ideal absolute scale in terms 

 of practical scales based on known actual thermometric substances was 

 a great effort of genius, entirely the work of Joule and Thomson, which 

 amply atoned for Thomson's earlier slip. 



The final general form toward which Carnot's principle was to 

 crystallize was first adumbrated by W. Thomson, in 1852, in the state- 

 ment that the trend of spontaneous change is towards the dissipation 

 01 irrecoverable diffusion of the sources of mechanical power. In 1854 

 Clausius contributed to placing the matter on a simple and quan- 

 titative basis by introducing the scalar quantity which he afterwards, 

 called the entropy of a system and in 1865f the law of trend of changes 

 took the final form that in spontaneous change in a system with given 

 energy the entropy must tend always to increase. In this form, 

 viz., expressed by means of entropy, the proposition, quoted from 

 Clausius, is placed by Gibbs at the head of his great memoir, as virtually 

 constituting the culmination of the creative ideas in this subject, what 

 remained being the application of the principle, re-stated by him in- 

 far more manageable form, in the ramifications of change of state in 

 actual matter. 



* Lord Kelvin, under date February 19, 1852 (Joule's " Collected Papers," 

 i, p. 353) describes Joule's letter to him of December 9, 1848 as giving this result 

 " as the expression of Mayer's hypothesis in terms of the notation of my account of 

 Carnot's theory." 



f The passages may be readily found in Hirst's translation of Clausius' 

 earlier Memoirs, published by Van Voorst, 1867. 



