PROGRESS IN NINETEENTH CENTURY 43 



conform to the second law has not been infrequent. Ideas of this 

 nature have been put forward by Boltzmann (1866, 1872), by Clau- 

 sius (1870, 1871), and more powerfully by Helmholtz (1884) in his 

 theory of cyclic systems, which in a measure suggested the hidden 

 mechanism at the root of Hertz's dynamics. Gibbs's (1902) element- 

 ary principles of statistical mechanics seem, however, to contain the 

 nearest approach to a logical justification of the second law an 

 approach which is more than a dynamical illustration. 



The applications of the first and second laws of thermodynamics 

 are ubiquitous. As interesting instances we may mention the con- 

 ception of an ideal gas and its properties; the departure of physical 

 gases from ideality as shown in Kelvin and Joule's plug experiment 

 (1854, 1862); the corrected temperature scale resulting on the one 

 hand, and the possibility of the modern liquid air refrigerator of 

 Linde and Hampson (1895) on the other. Difficulties encountered 

 in the liquefaction of incoercible gases by Cailletet and Pictet (1877) 

 have vanished even from the hydrogen coercions of Olezewski (1895) 

 and of Dewar and Travers. 



Again, the broad treatment of fusion and evaporation, beginning 

 with James Thomson's (1849) computation of the melting point of 

 ice under pressure, Kirchhoff's (1858) treatment of sublimation, the 

 extensive chapter of thermo-elastics set on foot by Kelvin's (1883) 

 equation, are further examples. 



To these must be added Andrews's (1869) discovery of the continu- 

 ity of the liquid and the gaseous states foreshadowed by Cagniard 

 de la Tour (1822, 1823); the deep insight into the laws of physical 

 gases furnished by the experimental prowess of Amagat (1881, 1893, 

 1896), and the remarkably close approximation amounting almost to 

 a prediction of the facts observed which is given by the great work 

 of van der Waals (1873). 



The further development of thermodynamics, remarkable for the 

 breadth, not to say audacity, of its generalizations, was to take 

 place in connection with chemical systems. The analytical power 

 of the conception of a thermodynamic potential was recognized 

 nearly at the same time by many thinkers: 1 by Gibbs (1876), who 

 discovered both the isothermal and the adiabatic potential; by 

 Massieu (1877), independently in his Fonctions characteristiques ; 

 by Helmholtz (1882), in his Freie Energie; by Duhem (1886) and by 

 Planck (1887, 1891), in their respective thermodynamic potentials. 

 The transformation of Lagrange's doctrine of virtual displacements of 

 infinitely more complicated systems than those originally contem- 

 plated, in other words the introduction of a virtual thermodynamic 

 modification in complete analogy with the virtual displacement of 

 the mecanique analytique, marked a new possibility of research of 

 1 Maxwell's available energy is accidentally overlooked in the text. 



