288 Obituary Notices of Fellows deceased. 



not stated whether this novel and direct mode of argument was 

 suggested by the extreme simplicity of the result already obtained 

 through more complex considerations. This investigation, expounded 

 later by Maxwell* in terms of entropy, went far towards completing 

 the doctrine of thermodynamics for interacting gaseous systems, and 

 its results are naturally referred to by Gibbs in that connexion. 



The investigations of Gibbs began in 1873, with two papers on the 

 graphical expression of thermodynamic relations, energy and entropy 

 appearing explicitly as variables ; of these papers, the later one 

 described the well-known thermodynamic surface, afterwards constructed 

 to scale by Maxwell for water-substance, and gracefully presented by him 

 to its discoverer. It would seem as if it was the study of these 

 surfaces that directed Gibbs towards his general thermodynamic 

 functions, whose minima at any given temperature determine the 

 phases of stable equilibrium of a physical or chemical system at that 

 temperature. Next appeared his great memoir, or rather treatise, 

 published in instalments in the "Transactions of the Connecticut 

 Academy," in 1875 and the three following years, in which this 

 property of minimum in these functions is applied to the most general 

 material systems going, in his theoretical deductions, far ahead of any 

 experimental procedure that was then contemplated. Thus, advancing 

 beyond Rayleigh's postulated separator of gaseous mixtures by 

 reversible chemical absorption, he introduces into physics, by a stroke 

 of pure theory, the so-called semi-permeable membrane, and the 

 osmotic pressure against it, which has more recently played so funda- 

 mental a part in theory, and to some extent in practice, as a mode of 

 expression of the reversible energy-relations between solutions. 



The specification of a definite formula for the available energy in a 

 thermodynamic system, in Lord Kelvin's original order of ideas, proved 

 to be a subject not devoid of perplexity. It has been noticed above 

 that the addition to the system of a condenser, or sink of heat, of 

 unlimited capacity at a fixed temperature leads to a simple expression 

 for the energy which can be available in this composite system in the 

 process of reversibly reducing all its heat to this temperature, namely 

 E - #o<A) the quantity afterwards termed " motivity " by Lord Kelvin ; 

 and that this involves as a corollary that <, the entropy of Clausius, is 

 a definite analytical function of the actual state of the system, which 

 cannot spontaneously increase provided the system is isolated. A 

 hasty confusion between entropy and availability, which occurred in 

 the first edition of Maxwell's " Theory of Heat," was corrected by 

 Gibbs in his early memoir on the thermodynamic surface ; and it is, 

 perhaps, not unlikely that he was thereby led to reflect on the question as 

 to the true measure of available energy of the system considered by itself- 



* " Ency. Brit.," Article " Diffusion." 



