X PREFACE. 



phenomena distinctively thermodynamic, we do not escape 

 difficulties in as simple a matter as the number of degrees 

 of freedom of a diatomic gas. It is well known that while 

 theory would assign to the gas six degrees of freedom per 

 molecule, in our experiments on specific heat we cannot ac- 

 count for more than five. Certainly, one is building on an 

 insecure foundation, who rests his work on hypotheses con- 

 cerning the constitution of matter. 



Difficulties of this kind have deterred the author from at- 

 tempting to explain the mysteries of nature, and have forced 

 him to be contented with the more modest aim of deducing 

 some of the more obvious propositions relating to the statis- 

 tical branch of mechanics. Here, there can be no mistake in 

 regard to the agreement of the hypotheses with the facts of 

 nature, for nothing is assumed in that respect. The only 

 error into which one can fall, is the want of agreement be- 

 tween the premises and the conclusions, and this, with care, 

 one may hope, in the main, to avoid. 



The matter of the present volume consists in large measure 

 of results which have been obtained by the investigators 

 mentioned above, although the point of view and the arrange- 

 ment may be different. These results, given to the public 

 one by one in the order of their discovery, have necessarily, 

 in their original presentation, not been arranged in the most 

 logical manner. 



In the first chapter we consider the general problem which 

 has been mentioned, and find what may be called the funda- 

 mental equation of statistical mechanics. A particular case 

 of this equation will give the condition of statistical equi- 

 librium, i. e., the condition which the distribution of the 

 systems in phase must satisfy in order that the distribution 

 shall be permanent. In the general case, the fundamental 

 equation admits an integration, which gives a principle which 

 may be variously expressed, according to the point of view 

 from which it is regarded, as the conservation of density-in- 

 phase, or of extension-in-phase, or of probability of phase. 



