1185 



When calculating the differont time averages — which up to 

 now were too much neglected in this problem, the attention being 

 almost exclusively concentrated on all kinds ol' spacial mean values, 

 which can onl}' niodifv some numerical values already alluded to 

 above — it already soon appeared that the relation between the 

 mean Energy and the temperature was the same for small volumes 

 and low temperatures^) as the relation 



2E^ 



elil—l 

 which was drawn up by Planck on behalf of the theory of radiation 

 on assumption of the so-called hypothesis of quanta, in which only 

 7, -V/ii' would have to be substituted for E^ to find back Planck's 

 expression "). 



By a purely kinetic way, on the sole foundation of the ordinary 

 laws of cldssiC'd mechanics, we could therefore derive Pf-anck's 

 famous expression, which 1 think was only possible up to now on 

 the strength of very special suppositions, namely on the supposition 

 that the energy is emitted only in entire multiples of the quantity 

 hv ("energy quanta"). (The absorption can take place in arbitrary 

 quantities according to the last modification applied by Planck in 

 his theory). 



§ 2. General Considerations on the Nature of the 

 Attractive and Repulsive Forces. 



We shall suppose the molecules to be all ai-ranged along one 

 dimension, and assume every arbitrary molecule M to move con- 

 tinually to and fro between the two adjacent molecules 3J^ and M^. 

 Let the mean distance between the molecule centres be / (the ana- 

 logon of the volume v for three dimensions), the radius of the sphere 

 of attraction q, the diameter of the molecule vS'. As Af^ and J/, may 



J^ Uo 



&~^ ^ &^ £ ^ 



Fig. 1. 

 be found both on the lefthand side and on the righthand side of 

 the mean places A/, and J/.,, we may suppose them to be on an 

 average always in J/, and J/, ; besides we may assume .l/j and J/.^ 



ij With the ditïerence only of a small finite term, which may be neglected by 

 the side of the principal term, which becomes logaritlnnically infinite (see § 6). 

 2) I.e. multiplied by 3 on transition from a linear to a spacial oscillator. 



