44 PHYSICS 



which Gibbs made the profoundest use. Unaware of this marshaling 

 of powerful mathematical forces, van 't Hoff (1886, 1888) consum- 

 mated his marvelously simple application of the second law; and 

 from interpretations 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 available for experi- 

 mental investigation. 



The highly generalized treatment of chemical statics by Gibbs 

 bore early fruit in its application to Deville's phenomenon of disso- 

 ciation (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 treat- 

 ment of dissociation 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 suc- 

 cinctly drawn in a profound paper by Helmholtz (1886), followed 

 with much skill by Duhem (1894, 1896) and Natanson (1896). 



Kinetic Theory of 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, of molecular velocity and of the ratio of 

 translational to total energy. He also introduced the mean free 

 path (1858). Closely after followed Maxwell (1860), adducing the 

 law for the distribution of velocity among molecules, later critically 

 and elaborately examined by Boltzmann (1868-81). Nevertheless, 

 the difficulties relating to the partition of energy have not yet been 

 surmounted. The subject is still under vigorous discussion, as the 

 papers of Burbury (1899) and others testify. 



To Maxwell (1860, 1868) is due the specifically kinetic interpret- 

 ation of viscosity, of diffusion, of heat conduction, subjects which 

 also engaged the attention of Boltzmann (1872-87). Rigorous data 

 for molecular velocity and mean free path have thus become avail- 

 able, and van der Waals (1873) added a final allowance for the size 

 of the molecules. Less satisfactory has been the exploration of the 

 character of molecular force for which Maxwell, Boltzmann (1872, 

 et seq.), Sutherland (1886, 1893), and others have put forward tenta- 

 tive investigations. 



The intrinsic equation of fluids discovered and treated in the 

 great paper of van der Waals (1873), though partaking of the charac- 



