KUDOLF JULIUS EMANUEL CLAUSIUS. 265 



development naturally commenced with the simplest case involving 

 the characteristic problems of the subject, the case, namely, of gases. 



The origin of the kinetic theory of gases is lost in remote antiquity, 

 and its completion the most sanguine cannot hope to see. But a 

 single generation has seen it advance from the stage of vague sur- 

 mises to an extensive and well established body of doctrine. This is 

 mainly the work of three men, Clausius, Maxwell, and Boltzmann, of 

 whom Clausius was the earliest in the field, and has been called by 

 Maxwell the principal founder of the science.* We may regard his 

 paper (1857), "Ueber die Art der Bewegung, welche wir Warme 

 nennen,"t as marking his definite entrance into this field, although 

 many points were incidentally discussed in earlier papers. 



This was soon followed by his papers, " Ueber die mittlere Lange 

 der Wege, welche bei der Molecularbewegung gasformiger Korper 

 von den einzelnen Moleciilen zuriickgelegt werden," J and " Ueber die 

 Warmeleitung gasformiger Korper." 



A very valuable contribution to molecular science is the conception 

 of the virial, defined in his paper (1870), "Ueber einen auf die Warme 

 anwendbaren Satz,"|| where he shows that in any case of stationary 

 motion the mean vis viva of the system is equal to its virial. 



In the mean time, Maxwell and Boltzmann had entered the field. 

 Maxwell's first paper, " On the Motions and Collisions of perfectly 

 elastic Spheres," 1F was characterized by a new manner of proposing 

 the problems of molecular science. Clausius was concerned with the 

 mean values of various quantities which vary enormously in the 

 smallest time or space which we can appreciate. Maxwell occupied 

 himself with the relative frequency of the various values which these 

 quantities have. In this he was followed by Boltzmann. In reading 

 Clausius, we seem to be reading mechanics ; in reading Maxwell, and 

 in much of Boltzmann's most valuable work, we seem rather to be 

 reading in the theory of probabilities. There is no doubt that the 

 larger manner in which Maxwell and Boltzmann proposed the 

 problems of molecular science enabled them in some cases to get 

 a more satisfactory and complete answer, even for those questions 

 which do not at first sight seem to require so broad a treatment. 



Boltzmann's first work, however (1866), "Ueber die mechanische 

 Bedeutung des zweiten Hauptsatzes der Warmetheorie."** was in a 

 line in which no one had preceded him, although he was followed by 



* Nature, vol. xvii, p. 278. 



f Pogg. Ann., vol. c, p. 353 (1857). 



J Ibid., vol. cv, p. 239 (1858). See also Wied. Ann., vol. x, p. 92. 



/6id., vol. cxv, p. 1 (1862). 



|| Ibid., vol. cxli, p. 124. See also Jubelband, p. 411. 



IPhil. Mag., vol. xix, p. 19 (1860). 



** Sitzungsberichte Wien. Akad. vol. liii, p. 195. 



