THE lyrHER AND MATTER POINCARE. 205 



eqiiijmrlition ol enei-gy should be supreme outside the chased little 

 world save at the inoment the door opened; but that is not true. 



The specific heat of solid bodies diminishes rapidly with decreasing 

 temperatures as if some of the degrees of freedom of the atoms were 

 successively paralyzed — frozen, so to speak — or, if you prefer, have 

 lost connection wdth the exterior world, witlidrawn within the 

 interior in some unknown manner. 



Furtliermore, tlie law of "black" radiation is not what would be 

 expected from the theory of equipartition. The law wliich results 

 from that theorj^ is the one derived by Rayleigh, and that law, 

 besides involving an evident contradiction, since it gives an infinite 

 total radiation, is absolutely at variance with experimental results. 

 In the emission of a black body there is much less light of short wave 

 lengths than would be requu^ed by the equipartition hypothesis. 



Planck consequently devised his quanta theory, according to which 

 the exchange of energ}^ between the matter and the ether — or rather 

 between ordinary matter and the small resonators whose vibrations 

 furnish the light of incandescent matter— can take place only inter- 

 mittently. A resonator can not gain energy or lose it in a continu- 

 ous manner. It can not gain a fraction of a quantum; it must acquire 

 a whole quantum or none at all. 



Why, tlien, does the specific heat of a solid diminish at low temperei- 

 tures ? Why do its atoms seem to lose certain degrees of freedom ? 

 It is because the supply of energy ofl'ered to them at low temperatures 

 is not great enough to give to each a quantum. Certain ones could 

 get only a fraction of a quantum and, as they will take a whole one 

 or none, they remain without. 



It is just so in the case of radiation wdiere certain resonatoi-s 

 which can not have a whole quantum take none and remain inactive. 

 Consequently there is much less radiation at low temperatures than 

 there would otherwise be. Since the required quantity becomes 

 greater as the wave length becomes shorter, it is especially the 

 sho]-t wave-length resonators which remain inactive, so that the 

 pro]:>ortion of short wave-length light is much less than that indicated 

 by Rayleigh's formula. 



To say that a plausible theory should remove all difficulties would 

 be somewhat naive. When a somewhat daring theory is launched, 

 difiicultios are expected. If we upset all the accepted notions, we 

 must not be surprised at some obstacles. vSucli difficulties do not 

 count as valid objections. 



I take the courage, therefore, to indicate some of these difficulties, 

 and I will not choose those which are the greatest, nor the most 

 evident, those which occur to everyone; that would be futile indeed, 

 since you all recognize them immiediately. I wash to state to you 



