364 



SCIENCE. 



[N. S. Vol. XXII. No. ^60. 



of OlezeAvski (1895) and of Dewar and 

 Travers. 



Again, the broad treatment of fusion and 

 evaporation, beginning with James Thom- 

 son's (1849) computation of the melting 

 point of ice under pressure, Kirchhoif's 

 (1858) treatment of sublimation, the ex- 

 tensive chapter of thermo-elastics set on 

 foot by Kelvin's (1883) equation, are fur- 

 ther examples. 



To these must be added Andrews's 

 (1869) discovery of the continuity 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 re- 

 markably 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 thermody- 

 namics, remarkable for the breadth, not to 

 say audacity, of its generalizations, was to 

 take place in connection with chemical sys- 

 tems. The analytical power of the concep- 

 tion of a thermodynamic potential was 

 recognized nearly at the same time by 

 many thinkers: by Gibbs (1876), who dis- 

 covered both the isothermal and the adia- 

 batic potential; by Massieu (1877), inde- 

 pendently in his 'functions characteris- 

 tiques'; by Helmholtz (1882), in his 'Freie 

 Energie'; by Duhem (1886) and by Planck 

 (1887, 1891), in their respective thermo- 

 dynamic potentials. The transformation 

 of Lagrange's doctrine of virtual displace- 

 ments of indefinitely more complicated sys- 

 tems than those originally contemplated, 

 in other words the introduction of a virtual 

 thermodj^namic modification in complete 

 analogy with the virtual displacement of 

 the 'mecanique analytique,' marked a new 

 possibility of research of which Gibbs 

 made the profoundest use. Unaware of 



this marshaling of powerful mathematical 

 forces, van't Ploff (1886, 1888) consum- 

 mated his marvelously simple application 

 of the second law; and from interpreta- 

 tions of the experiments of Pfeffer (1877) 

 and of Raoult (1883, 1887) propounded a 

 new theory of solution, indeed a basis for 

 chemical physics in a form at once avail- 

 able for experimental investigation. 



The highly generalized treatment of 

 chemical statics by Gibbs bore early fruit 

 in its application to E)eville's phenomenon 

 of dissociation (1857), and in succession 

 Gibbs (1878, 1879), Duhem (1886), Planck 

 (1887), have deduced adequate equations, 

 while the latter in case of dilute solutions 

 gave a theoretical basis for Guldberg and 

 Waage's law of mass action (1879). An 

 earlier independent treatment of dissocia- 

 tion is due to Horstmann (1869, 1873). 



In comparison with the brilliant advance 

 of chemical statics which followed Gibbs, 

 the progress of chemical dynamics has been 

 less obvious ; but the outlines of the subject 

 have, nevertheless, been succinctly drawn 

 in a profound paper by Helmholtz (1886), 

 followed with much skill by Duhem (1894, 

 1896) andNatanson (1896). 



KINETIC THEORY OP GASES. 



The kinetic theory of gases at the outset, 

 and as suggested by Herapath (1821), Joule 

 (1851, 1857), Kronig (1856), virtually re- 

 affirmed the classic treatise of Bernoulli 

 (1738). Clausius in 1857-62 gave to the 

 theory a modern aspect in his derivation 

 of Boyle's law in its thermal relations, 

 molecular velocity and of the ratio of trans- 

 lational to total energy. He also intro- 

 duced the mean free path (1858). Closely 

 after followed Maxwell (1860), adducing 

 the law for the distribution of velocity 

 among molecules, later critically and elab- 

 orately examined by Boltzmann (1868-81). 

 Nevertheless, the difficulties relating to the 

 partition of energy have not yet been sur- 



