JOSIAH WILLARD GIBBS. xxiii 



Professor Gibbs returned to a theme closely connected with the 

 subjects of his earliest publications. In these he had been concerned 

 with the development of the consequences of the laws of thermo- 

 dynamics which are accepted as given by experience ; in this empirical 

 form of the science, heat and mechanical energy are regarded as two 

 distinct entities, mutually convertible of course with certain limita- 

 tions, but essentially different in many important ways. In accordance 

 with the strong tendency toward unification of causes, there have been 

 many attempts to bring these two things under the same category; 

 to show, in fact, that heat is nothing more than the purely mechanical 

 energy of the minute particles of which all sensible matter is supposed 

 to be made up, and that the extra-dynamical laws of heat are con- 

 sequences of the immense number of independent mechanical systems 

 in any body, a number so great that, to human observation, only 

 certain averages and most probable effects are perceptible. Yet in 

 spite of dogmatic assertions, in many elementary books and popular 

 expositions, that " heat is a mode of molecular motion," these attempts 

 have not been entirely successful, and the failure has been signalized 

 by Lord Kelvin as one of the clouds upon the history of science in 

 the nineteenth century. Such investigations must deal with the 

 mechanics of systems of an immense number of degrees of freedom 

 and (since we are quite unable in our experiments to identify or 

 follow individual particles), in order to compare the results of the 

 dynamical reasoning with observation, the processes must be statistical 

 in character. The difficulties of such processes have been pointed out 

 more than once by Maxwell, who, in a passage which Professor Gibbs 

 often quoted, says that serious errors have been made in such inquiries 

 by men whose competency in other branches of mathematics was un- 

 questioned. 



On account, then, of the difficulties of the subject and of the pro- 

 found importance of results which can be reached by no other known 

 method, it is of the utmost consequence that the principles and pro- 

 cesses of statistical mechanics should be put upon a firm and certain 

 foundation. That this has now been accomplished there can be no 

 doubt, and there will be little excuse in the future for a repetition of 

 the errors of which Maxwell speaks ; moreover, theorems have been 

 discovered and processes devised which will render easier the task of 

 every future student of this subject, as the work of Lagrange did in 

 the case of ordinary mechanics. 



The greater part of the book is taken up with this general develop- 

 ment of the subject without special reference to the problems of 

 rational thermodynamics. At the end of the twelfth chapter the 

 author has in his hands a far more perfect weapon for attacking such 

 problems than any previous investigator has possessed, and its 



