164 



SCIENCE. 



[N. S. Vol. XXIII. No. 579. 



In the domain of optics, also, there has 

 been considerable progress, of which a very 

 important part is due to- our lamented 

 friend, whose work I have already consid- 

 ered. In other parts of our science, the 

 work which has been done is not of so con- 

 secutive a character, nor has it been pro- 

 ductive of such important results as to call 

 for particular mention. 



The subject upon which I wish to speak 

 to you to-day is that of the partition of 

 energy. As is well understood, the energy 

 here referred to is the kinetic energy of the 

 moving particles, which, according to the 

 kinetic theory of matter, constitute a body. 

 The general theorem which I wish to dis- 

 cuss may be stated by saying that the kin- 

 etic energy of the body is so distributed 

 among the degrees of freedom, by which 

 the state of the body as a dynamical system 

 is described, that an equal share is, on the 

 average, allotted to each degree of freedom 

 of each type of molecule. 



Since the enunciation of this theorem as 

 applied to gases, by Maxwell, in 1859, it 

 has from time to time attracted the atten- 

 tion of the mathematical physicists. Lately 

 it has again been brought forward, and the 

 difficulties which surround it very consid- 

 erably removed, by the work of Jeans. 

 This author has collected the results of his 

 own researches, in combination with a his- 

 torical and critical study of previous work 

 on the question, in a recently published 

 book, which covers the ground so com- 

 pletely as to supersede any independent 

 study of the subject which I could have 

 made; but I trust that the exposition of it 

 which I shall give will be of interest as an 

 introduction to the experimental matter 

 which I shall adduce ; and that this will at 

 least indicate a way in which we may hope 

 to obtain some confirmation of the theorem 

 of equipartition. 



The questions which have ahA'ays been 

 raised about this important theorem of the 



kinetic theory at once come to our minds. 

 First, is the theorem true, or rather, does 

 it state what would be true for an ideal 

 system of particles moving freely ■within a 

 containing vessel? second, is the proof of 

 the theorem impeccable ? third, is there any 

 experimental evidence that it applies to 

 real bodies? 



I would remark abovxt the first question 

 that the theorem is so distinguished by its 

 simplicity, and by its aspect as a sort of 

 unifying principle in nature, that few men 

 can set it fairly before their minds without 

 at least desiring to believe it true. Most 

 of those who have recognized that Max- 

 well's original demonstration was not flaw- 

 less are still convinced of the truth of his 

 conclusion, or at least believe his conclusion 

 to be so probable as to make it worth while 

 to try for a more accurate demonstration. 

 Their state of mind is like that of Clausius 

 and of Lord Kelvin, when they perceived 

 that Carnot's theorem respecting the effi- 

 ciency of a reversible engine could not be 

 proved in the way in which Carnot tried 

 to prove it. 



"With respect to the second question, it 

 was very soon pointed out that Maxwell 

 had made in his proof an assumption that 

 could not be justified by immediate inspec- 

 tion, and which was itself in need of demon- 

 stration or of avoidance. The later dem- 

 onstrations of Maxwell and Boltzmann have 

 been likewise subjected to criticism, and 

 can be shown to involve assumptions that 

 will not be granted on inspection. The 

 difficulties that arise in these proofs come 

 from the necessity of applying in them the 

 calculus of probabilities, and center around 

 the question of the legitimacy of the appli- 

 cation of that- calcuhis. It is commonly 

 agreed that Maxwell and Boltzmann have 

 assumed a condition of the system of mov- 

 ing particles, as a requisite for the applica- 

 tion of the calculus of probabilities, which 

 is contradicted by many systems of which 



