591 



Physics. — "A mechanical theorem of Boltzmann a?id its relation 

 to the tlieory of enen/i/ quanta". By Prof. P. Ehrknfest. 

 (Communicated by Prof. H. A. IjOrentz). 



(Communicated in the meeting of November 29, 1913). 



Wlien black or also not black radiation is compressed re\^ersiblv 

 and adiabatically by compression of a perfectly reflecting enclosure, 

 it is known that the following takes place: The frequency Vj, and 

 the energy Ep of each of the principal modes of vibration of the 

 cavity increase during the compression in such a way that we get : 



df^^ = 0>=zl,2, ....,oc) . . . . ^. (1) 



for each of the infinitely many principal vibrations. 



Relation (1) is of fundamental importance for the purely 

 tliennodi/namic derivation of Wien's law; it is no less so for every 

 statistic theory of radiation, which is to remain in keeping with 

 the second law of thermodynamics ^). In particular it is also the 

 basis of Planck's assumption of differences of energy : ^) 



~ = 0,h,2h, (2) 



Of late Planck's supposition (2) ot the original region (Content 

 of energy of systems vibrating sinusoidally) has been applied to a 

 rapidly extending region. Of course tentatively. Two questions arise : 



1. Does there continue to exist an adiabatic relation analogous 

 to equation (1) in the transition of systems vibrating sinusoidally 

 (in which the motion is governed by linear differential equations 

 with constant coefficients) to general systems? 



. 1) P. Ehrenfest. Welche Züge der Lichtquantenhypothese spielen in der 

 Theorie der Warmestrahlung eine wesentliche RoUe? Ann. d. Phys. 36 (1911) 

 p. 91; §5. 



2) By way of elucidation: differences of energy e. g. of the form 



4 = 0, /^ , 2A , . . . . 



V 



would lead to a conflict with the second law of thermodynamics. It is known 

 that Planck arrived at (2) by first carrying out his combinatory calculation in 

 general on the assumption 



8 = , f{v) , 2f{v) , 3/(r) , . . . . 



and by then determining the form of fiv) from the condition that the formula of 

 radiation found by the combinatory way shall satisfy Wien's law. Thus he brought 

 his energy quanta implicite in liarmony both with relation (1) and willi the second 

 law of thermodynamics. 



3b* 



