THE ETHER AND MATTER POINCAKE. 207 



I resolved lo exaniiiie one by one tiic two i)ioccsses, and I com- 

 menced with the one having mechanical action, colHsions. You know 

 why the old theories necessarily led lus to the law of equipartition. 

 It was because they assumed that all the equations of the mechanics 

 were of the Ilamiltonian form, and consequently made unity possible 

 as the last multiplier in the Jacobian sense. We must therefore sup- 

 pose that the laws of collision between a free electron and a resonator 

 are not of this form and that the equations then admit of a final mul- 

 tiplier other than unity; otherwise the second law of thermodjmamics 

 would not hold and then we would find ourselves in the dilliculty just 

 stated. However, it is not necessary that this multiplier be unity. 



It is exactly this last factor which is a measure of the probability 

 of the corresponding state of the system (or rather we might call it 

 the probability density). In the hypothesis of quanta, this factor 

 can not be a continuous function since the probability of a state must 

 be zero whenever the corresponding energy is not a multiple of a 

 quantum. That is an evident stumbling block, but one to which 

 we had to be resigned in advance. But I did not stop there. I 

 pushed the calculations to an end and came out with the law of 

 Planck, justifying fully the views of that German j)hysicist. 



I then passed to the Doppler-Fizeau mechanism. Let us imagin(^ 

 a recejitacle formed of the body and piston of a pump, the walls of 

 which are perfect reflectors and within which is inclosed a certain 

 quantity of energy in the form of light. This energy is distributetl 

 in any manner whatever among the various wave lengths. The re- 

 ceptacle contains no source of light. The luminous energy is inclosed 

 within the contrivance once forever. 



As long as the piston remains fixed, this distribution of the energy 

 among the wave lengths can not vary, for the light will retain the 

 same wave lengths each time it is reflected. However, if the piston 

 is moved, this distribution will vary. If the velocity of the piston is 

 very small, the phenomenon is reversible and the entropy must 

 remain constant. We would thus have the analysis of Wien and 

 come out with Wien's law. We would have made no advance, since 

 that law is common to both the old and the new theories. If the 

 velocity of the piston is not very small, the phenomenon is not revers- 

 ible, so that thermodynamic analysis would no longer lead to equali- 

 lies but to simple inequalities and we could draw no conclusions. 



However, it seems as if we could reason as follows: Let us suppose 

 the initial distribution of the energy to be that of black radiation, 

 evidently corresponding to a maximum of entropy. If we then give 

 several strokes to the piston, tlie final distribution nuist evidently be 

 the same, othei-wise the entropy would diminish. And, indeed, what- 

 ever the initial distribution, after a very great number of strokes of the 



