Josiah Wiltard Gibbs. 197 



in them would liave sufficed to firmly establish this theory even 

 if the experimental discoveries of Hertz had not rendered such 

 discussions forever unnecessary. 



In his last work, "Elementary Principles in Statistical 

 Mechanics," Professor Gibbs returned to a theme closely con- 

 nected with the subjects of his earliest publications. In these 

 he had been concerned with the development of the conse- 

 quences of the laws of thermodynamics 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 limitations, but 

 essentially different in many important Avays. In accordance 

 with the strong tendency toward unification of causes, there 

 have been many attem23ts 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 parti- 

 cles of which all sensible matter is supposed to be made up, 

 and that the extra-dynamical laws of heat are consequences 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 uj3on 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 indi- 

 vidual jDarticles), in order to compare the results of the dynami- 

 cal 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 unquestioned. 



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

 profound importance of results which can be reached by no 

 other known method, it is of the utmost consequence that the 

 principles and processes 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 



