592 



2. If so — how can it be applied heuristicallj, when Pi.anck's 

 assuni[)tion (2) is extended to systems vibrating not sinusoidallj ? 



The answer to the first question is in the affirmative. In the 

 search for the extension of the adiabatic rehition (1) I perceived 

 that such an extension, and indeed a surprisingly far-reaching one, 

 follows immediately from a mechanic theorem found by Boltzmann 

 and Clavsius independently of each other (see § 1). 



For the present I can only answer the second question by giving 

 an example (§ 3). The difficulties which in general present them- 

 selves in this — Prof. Einstein drew my attention to the most 

 troublesome one (^ 4) in a conversation — I have stated in § ?, 

 3, 4, without being able to remove them. 



Another objection may be raised against the whole viz. : there is 

 no sense — it may be argued — in combining a thesis, which is 

 derived on the premise of the mechanical equations with the anti- 

 mechanical hypothesis of energy quanta. Answer : Wien's law holds 

 out the hope to us that results which may be derived from classical 

 mechanics and electrodynamics by the consideration of macroscopic- 

 adiabatic processes, will continue to be valid in the future mechanics 

 of energy quanta. 



§ 



§ J. Let q^ , . . . , q,i be the coordinates of a mechanic system. 

 The potential energy *I* may depend, besides on the coordinates q, 

 also on some "slowly variable parameters" 7\, )\, . . . Let the kinetic 

 energy T of the system be an homogeneous, quadratic function of 

 the velocities q^, and contain in its coefficients besides the q's, even- 

 tually also the r's. 



Let farther the system possess the following properties : For definite 

 but arbitrarily chosen values of the parameters rj, r^,.--- all the motions 

 of the system are periodical, no matter with what initial phase 

 {q^,....,qn, 7?i,...,p,0 the system begins. The period P will in general 

 not only depend on the values of )\, )\,...., but also on the phase 

 (<Zo' Po)> with which the system begins. 



By changing the parameters )\, )\,.... infinitely slowly we can 

 transform every original motion (.4) of the system into another {B). 

 This particular mode of inüuencing the system is called "adiabatic 

 influencing" of the motion. 



If moreovei' the respective periods of the motion are indicated by 

 P\ and Pb, or their reciprocal values (the ''frequencies") by va 

 and vjj, and further the temporal mean of the kinetic energy by 



I's and Tb , tlien 



