Josiah Willard Gills. 295 



antiquity, and its completion the most sanguine cannot hope to see. 

 But a single generation has seen it advance from the stage of vague 

 surmises 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. 



" In the meantime, Maxwell and Boltzmann had entered the field. 

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

 Elastic Spheres,' 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 

 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 Zuruckfiihrung des 

 zweiten Hauptsatzes der mechanischen Warmetheorie auf allgemeine 

 mechanische Principien.' The point of departure of these investiga- 

 tions, 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 external influences are changed. The theorems 

 developed belong to the same general category as the principle of 

 least action, and the principle or principles known as Hamilton's, 

 which have to do, explicitly or implicitly, with the variations of these 

 mean values 



" The first problem of molecular science is to derive from the 

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

 molecular constitution. The knowledge we may gain of their 

 molecular constitution may then be utilized in the search for formulas 

 to represent their observable properties " 



