JOSIAE WILLARD GIBBS 483 



and great capacity for the rigors of formal logic, and the rapid move- 

 ment of his mind as he clears away the underbrush and covers the vast 

 area of his new territory is wearying and even confusing to the reader. 

 The intention of the present resume is frankly journalistic, aiming 

 only to emphasize such points in the Gibbsian theory as have been 

 thrown into strongest relief by their relation to recent science. These 

 are: 



The General Equation of Thermodynamics. — In applying the laws 

 of dynamics to thermal phenomena, Clausius had shown that if we dif- 

 ferentiate with respect to the volume of a body, we obtain its pressure 

 with reversed sign; if we differentiate with respect to its entropy we 

 obtain its temperature on the thermodynamic scale; the energy of the 

 body can then be expressed as a function of its volume and entropy, 

 the differential coefficients with respect to the latter being the pressure 

 (with negative sign) and the temperature. Gibbs has extended these 

 principles to the formulation of a fimdamental equation of thermo- 

 dynamics, in which the new departure is taken of introducing the 

 masses of the chemical components of a system as variables, the differ- 

 ential coefficients in this case being certain new conceptions which he 

 terms the " potentials " of the substances considered. From this equa- 

 tion most of the principles and formulae of thermodynamics can be 

 deduced. It lies at the basis of the new aggregate of sciences called 

 " eneigetics"^^ as well as of mathematical chemistry, in which all 

 spontaneous changes of substance or state are regarded as more or less 

 direct consequences of the second law. The equations of Clausius and 

 Gibbs, although exceedingly general and difficult of application to 

 chemistrj^, are exact, representing the physical facts.^^ 



The Chemical Potentials. — In the fundamental equation of Gibbs 

 we distinguish two classes of variables, of which the volume, entropy 

 and masses of the component substances are looked upon as magni- 

 tudes or capacities, while the temperature, the pressure and the poten- 

 tials are to be thought of as qualitative, being non-measurable, non- 

 additive physical intensities of the system considered. Thus the pres- 



" Tlioughout this paper, " energetics," thermodynamics and physical chem- 

 istry are regarded as practically identical in scope, in the original sense in 

 which Gibbs referred to all material systems as " actually thermodynamic," or 

 Ostwald to " das glanzendste Gebiet der heutigen Physik und Chemie, die reine 

 Thermodynamik, oder da dieser Name viel zu eng ist, die reine Energetik." 



^ If e, t, 77, p and v represent the energy, temperature, entropy, pressure 

 and volume of a homogeneous substance respectively, the equation of Clausius 

 may be written d e = tdi) — pdv. It is applicable to all one-component systems, 

 such as steam in a boiler. The equation of Gibbs, which is applicable to any 

 chemical system whatever, is Avritten 



de ^ tdr] — pdv + jx^^dm^ + fi^dnii ■ • • -\- fLndnin , 



where fi^, 112 • • • denote the chemical potentials, and wh, m^ ■ ■ ■ the masses of 

 the chemical components of the system. 



