viii PREFACE. 



Such inquiries have been called by Maxwell statistical. 

 They belong to a branch of mechanics which owes its origin to 

 the desire to' explain the laws of thermodynamics on mechan- 

 ical principles, and of which Clausius, Maxwell, and Boltz- 

 mann are to be regarded as the principal founders. The first 

 inquiries in this field were indeed somewhat narrower in their 

 scope than that which has been mentioned, being applied to 

 the particles of a system, rather than to independent systems. 

 Statistical inquiries were next directed to the phases (or con- 

 ditions with respect to configuration and velocity) which 

 succeed one another in a given system in the course of time. 

 The explicit consideration of a great number of systems and 

 their distribution in phase, and of the permanence or alteration 

 of this distribution in the course of time is perhaps first found 

 in Boltzmann's paper on the " Zusammenhang zwischen den 

 Satzen iiber das Verhalten mehratomiger Gasmolekiile mit 

 Jacobi's Princip des letzten Multiplicators " (1871). 



But although, as a matter of history, statistical mechanics 

 owes its origin to investigations in thermodynamics, it seems 

 eminently worthy of an independent development, both on 

 account of the elegance and simplicity of its principles, and 

 because it yields new results and places old truths in a new 

 light in departments quite outside of thermodynamics. More- 

 over, the separate study of this branch of mechanics seems to 

 afford the best foundation for the study of rational thermody- 

 namics and molecular mechanics. 



The laws of thermodynamics, as empirically determined, 

 express the approximate and probable behavior of systems of 

 a great number of particles, or, more precisely, they express 

 the laws of mechanics for such systems as they appear to 

 beings who have not the fineness of perception to enable 

 them to appreciate quantities of the order of magnitude of 

 those which relate to single particles, and who cannot repeat 

 their experiments often enough to obtain any but the most 

 probable results. The laws of statistical mechanics apply to 

 conservative systems of any number of degrees of freedom, 



