RUDOLF JULIUS EMANUEL CLAUSIUS. 463 



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

 iu much of Boltzmanu's most valuable work, we seem rather to be 

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

 larger manner in which Maxwell and Boltzmann proposed the prob- 

 lems 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, (186G,) " 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 

 some of the most distinguished names among his contemporaries. 

 Somewhat later (1870) Clausius, whose attention had not been called 

 to Boltzmann's work, wrote his paper, " Ueber die Zuruckfuhrung des 

 zweiten Hauptsatzes der mechauischen "Warmetheorie auf allgemeine 

 meclianische Principien." f 



The point of departure of these investigations, and others to which 

 they gave rise, is the consideration of the mean values of the force- 

 function and of the vis viva of a system in which the motions are 

 periodic, and of the variations of these mean values when the exter- 

 nal influences are changed. The theorems developed belong to the 

 same general category as the principle of least action, and the prin- 

 ciple or principles known as Hamilton's, which have to do, explicitly 

 or implicitly, with the variations of these mean values. 



Among other papers of Clausius on this subject, we may mention 

 the two followinor: "Ueber einen neuen mechauischen Satz in Bezus: 

 auf stationiire Bewegung/'t (1873,) and "Ueber den Satz vom mit- 

 tleren Ergal und seine Anwendung auf die Molecularbewegungen der 

 Gase"§ (1874). 



The first problem of molecular science is to derive from the ob- 

 served properties of bodies as accurate a notion as possible of their 

 molecular constitution. The knowledge we may gain of their molecu- 

 lar constitution may then be utilized in the search for formulas to 

 represent their observable properties. A most notable achievement 

 in this direction is that of van der Waals, in his celebrated memoir 

 "On the Continuity of the Gaseous and Liquid States." To this part 

 of the subject belong the following papers of Clausius : " Ueber das 

 Verhalten der Kohlensiiure in Bezug auf Druck, Volumen und Tem- 



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



t Pogg. Ann., vol. cxiii. p. 43.3. 



I Ibid., vol. cl. p. 106. 



§ Ibid., Erganzungsband vii. p. 215. 



