206 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1912. 



the series of mental attitiules through which I have successively 

 passed. 



I asked myself first what was the value of the proposed demonstra- 

 tions. I saw that I could get the probabilities of the various distri- 

 butions of energy by simple enumeration, since the numbers were 

 fortunately finite according to the hypotheses, but I could not see 

 why they were all equally possible. Then I hitroduced the known 

 relations between the entropy, the temperature, and the probability. 

 That assumed the possibility oi a thermodynamic equilibrium since 

 the residts could be proved supposing that to be true. I knew that 

 such an equilibrium was possible, smce experiment has proved it. 

 But that did not satisfy m.e. I wished to show that it followed from 

 the hypothesis; indeed, that it would be a necessary consequence. I 

 really had no doubts, but I felt the necessity of seeing the matter a 

 little more clearly and for that I needed to examine the steps of the 

 process a little more in detail. 



In order that there may be a redistribution of the energy between 

 the resonators of difTerent wave lengths Vvdiose oscillations produce 

 radiation, it is necessary that they should be able to interchange 

 their energy; otherwise the initial distribution would pereist indefi- 

 nitely, and as that distribution was arbitrary there would result no 

 definite radiation law. Now a resonator can neither receive from 

 nor give to the ether light except of a perfectly definite wave length. 

 If, then, these resonators can not act upon each otlier mechanically, 

 that is, without the intervention of the ether, or if they are fixed and 

 immovable in a definite matrix, each of them could emit or absorb 

 only light of a definite color and it could exchange energy only v/ith a 

 resonator with which it was in perfect tune. The initial distribution 

 would remain unalterable. But we can conceive of two modes of 

 exchange which are not objectionable. First, some atoms, some free 

 electrons, might pass from one resonator to another, hit, and thus 

 communicate or receive energy; or, secondly, the light, reflected as 

 by a moving mirror, might change its wave length as recognized by 

 the Doppler-Fizeau principle. 



Are we free to choose between these two devices ? Surely both must 

 come into play, both should lead to the same result, the same lav/ of 

 radiation. What would we do if the results were contradictory, if 

 the mechanism of collisions working alone led to one law of radiation, 

 that of Planck, for instance, while the D6})pler-Fizeau effect to 

 another ? Very well, if both mechanisms came into play, one or the 

 other would alternate in preponderance according to chance, thus 

 causing an oscillation from one law to another, and there would be 

 no tendency to a final stable state, toward that thermal death where 

 there is no further change. Then the second law of thermodynamics 

 would be violated. 



