ON THE PHYSICAL VIEW OF NATURE. 173 



ture remaining constant), he gave the name of free energy. 47. 



8J Helmholtz'a 



He showed that in a state of equilibrium the free or " free 



energy. 



available energy must be a minimum. He also showed 

 the connection in which the available or free energy 

 stands to the quantity introduced by Eankine and 

 Clausius, the entropy which measures the unavailable or 

 hidden energy. By making chemical changes depend 

 on the increase or decrease of a definite measurable 

 quantity a parallel was established between chemical and 

 mechanical processes, the latter always taking place in 

 the direction of a decrease of potential energy. Free 

 energy has thus been appropriately termed by M. Duhem 

 the thermo-dynamic potential. 



Helmholtz did not apply this fruitful view to chemical 

 processes on any extensive scale, but his explanations 

 have done much to establish that correcter and more 

 comprehensive way of treating such questions which has 

 since become general. Horstmann had indeed led up 

 to this view, Willard Gibbs had applied it before, and 

 Lord Kayleigh had suggested it. 1 The conception of 



1 The general use of the concep- 

 tion of useful or free energy must 

 be dated from the remarkably lucid 

 expositions of Helmholtz, though 

 it is now recognised by all who 

 have studied the history of this 

 fertile conception that the physi- 

 cal notion of available energy goes 

 back to Thomson (see Tait, ' Ther- 

 modynamics,' 1868, p. 100) and 

 Maxwell (' Heat,' p. 187, 8th ed. ; 

 Duhem, ' Me"canique chimique,' 

 vol. i. p. 92 ; Le Chatelier in 

 'Journal de Physique,' 1894, p. 

 291) ; that the mathematical 

 formulae were given by Massieu 

 (quoted by Duhem, ' Le Potential 

 Thermodynamique,' 1886, pp. v 



and 11), and more definitely ex- 

 plained and applied to the phys- 

 ical phenomena of dissociation by 

 Gibbs ('Thermodynamische Stud- 

 ien,' ed. Ostwald, p. 66, &c. ; 

 ' Amer. Journ. of Sciences and 

 Arts,' 1879) ; and that it is es- 

 pecially owing to the labours of 

 Duhem that the subject has 

 received the attention of chemists. 

 M. Duhem, in the introduction to 

 the work of 1886, gives a very 

 valuable and lucid historical ex- 

 position, and subsequently in his 

 large work in four volumes ('Me"- 

 canique chimique,' 1897-1900) a 

 vast number of applications. For 

 the history of thought the import- 



