462 RUDOLF JULIUS EMANUEL CLAUSIUS. 



period in the history of the subject, of the ultimate form which the 

 theory was to take, shows a remarkable insight, which is by no 

 means to be lightly esteemed on account of the acknowledged want of 

 a rigorous demonstration. The propositions, indeed, as relating to 

 'quantities which escape direct measurement, belong to molecular 

 science, and seem to require for their complete and satisfactory 

 demonstration a considerable development of that science. This de- 

 velopment 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 

 which 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 Wiirrae 

 nennen," | 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 Liinge 

 der Wege, welche bei der Molecularbewegung gasformiger Korper 

 von den einzelnen Moleciilen zuriic.kgelegt werden, " $ and " Ueber die 

 Warrneleitung 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, " ^f 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 



* Nature, vol. xvii. p. 278. 

 t Ibid., vol. c. p. 353 (1857). 



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

 § Ibid., vol. cxv. p. 1 (1862). 



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

 1 Phil. Mag., vol. xix. p. 19 (1860). 



