122 THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 



a definite amount of " non-compensated work." It is not 

 difficult to obtain a mathematical expression for this work 

 involving the change of entropy (under reversible conditions) 

 the " internal energy/' the (constant) temperature of the body 

 in question, and the external work done during the transforma- 

 tion. Finally, after assuming limitations to the character of 

 the external work conformable with the conditions under 

 which an investigation of this kind would commonly be 

 pursued, it becomes possible to regard the "non-compensated 

 work " as the difference between the values at the end and 

 the beginning of the operation of a special function which its 

 inventor, Duhem, calls "the thermodynamic potential."* In 

 this function we have, for a large number of important cases 

 in which " physical phenomena affect one another," the desired 

 means of specifying the state of equilibrium. For <: lorsque le 

 potentiel thermodynamique est minimum, le systeme est dans 

 un etat d'equilibre stablest 



It would be unsuitable to follow in these pages the extremely 

 technical development and applications of this principle. It 

 must suffice to note that by means which are equivalent to the 

 use of the thermodynamic potential, but before Duhem had 

 published his systematic theory of the processes, Willard Gibbs 

 had shown how to reduce to intelligibility large areas of pre- 

 viously intractable chemical and physical phenomena; while 

 Helmholtz had explained, by thermodynamical reasoning, the 

 astonishing discovery that the heat developable in an electric 

 circuit is only a fraction of the heat equivalent of the chemical 

 decompositions occurring in the cell a fact which he showed 

 to be a particular case of the law that only part of the heat 

 drawn from any source is available for transformation into 

 useful work. This part, to which he gave the name of 

 "free energy," is identical (in this case) with Duhem's 

 thermodynamic potential. Upon the work of these pioneers 



* Op. tit., p. 8. 

 t Op. cit., p. 9. 



