1908] on the Scientific WorJc of Lord Kelvin. 223 



jidR/T) = 0, as above, the Carnot-Clausins equation. It would 

 provide the necessary complement to this nomenclature if his own 

 equation between ii\ e, and t, which is, in more usual notation, the 

 equation of energy A available at constant temperature T, 



a = b + t|.^, 



and is now the fundamental principle in chemical physics through 

 the far-reaching applications made by Clibbs, Helmholtz, van 't Hoif, 

 Nernst, and other investigators, were known as the Thomson equation. 

 His dominating position is indeed already widely, but not very 

 definitely, recognised. 



The question whether Thomson had prior knowledge of the 

 entropy principle has been matter of some controversy between 

 Clausius and Tait : on the view here taken it is relatively unimportant. 



We may now recall in general terms the form of the principle 

 developed into most varied applications by Willard Gibbs, with such 

 power and invention as to constitute him the creator of a new science. 

 The necessary increase of the entropy function S defines the trend of 

 adiabatic transformation ; the necessary decrease of the available 

 energy function A defines the trend of isothermal transformation. 



The two functions are immediately connected by noticing that 

 the S in the given configuration exceeds Sq, that in the standard con- 

 figuration at the same temperature T, by - 3A/9T. We can render 

 an isothermal transformation adiabatic by including in the system an 

 infinite reservoir of heat at its own temperature, in the manner 

 favoured by Planck : the change of total entropy is that of S - H/T, 

 so that this function must always increase in an isothermal system. 

 The reverse transition from adiabatic to isothermal would not be so 

 direct. In fact, the entropy S is the convenient analytical function 

 to employ when the temperature is different in different parts of the 

 system, as is illustrated by the complexity of the calculation (already 

 conducted in February 1853, in terms of Carnot's function /x) of the 

 energy available for mechanical effect in such a system when self- 

 contained,* which is mainly of cosmical interest, and has probably 

 drawn attention away from the principles of free energy, though the 

 latter were again emphasised in Thomson and Tait's 'Natural 

 Philosophy^' 



This analysis of available energy by Thomson had not escaped the 

 notice of Willard Gibbs (1876), though possibly only in its narrower 

 connection with elasticity. f " Such a method is evidently preferable 

 with regard to the directness with which the results are obtained. 

 The method of this paper shows more distinctly the role of energy and 



* Thomson, loc. cit., p. 554. The calculation of the final uniform tem- 

 perature is in fact based (p. 556) implicitly on constancy of the entropy. 

 t Scientific Papers of J. Willard Gibbs, i. p. 204. 



