1198 



bution-law of velocities in tlie calculation of t^ may have a certain 

 influence on the result. Unfortunately the computations referring to 

 this cannot he executed, because they will lead to a definite 

 integral which cannot be determined. In the third place it may be 

 alleged that with respect to the velocity of the moving molecule M 

 it is not quite justifiable to assume the molecules J/, and il/, to 

 be at rest on the strength of the fact that the movement may be 

 directed equally well towards the left as towards the right. It 

 should be pointed out here that when M^ e.g. is on the lefthand 

 side of its mean position, it will exert a stronger attractive 

 action on M than when it is on the righthand side. And there are 

 more similar remarks that might be made. 



In virtue of the above considerations we may, therefore, safely 

 apply the said correction, which is exceedingly slight with respect 

 to the logarithmically infinite chief term, and write : 



RT z= '' ' ...... (10a) 



log 





When we reverse this relation, we get: 



^— ^. =— -— ° — (II) 



HT 



Putting in this 

 we get finally : 



E, = ^ Nj{l-sY = *I^N .hv (12) 



^ Nhv 



E=z^Nhv^^^^ (11a) 



e^T" — I 



which is in agreement with Planck's relation (after muliplication by 

 3 on account of the transition from a linear to a spacial oscillator). 



Hence the quantity hv introduced by Planck would have been 

 given by : 



hv = ■IfjlsY (11a) 



fi-om which h could be calculated when r is (:/é/fr??imfc'c/ (this quantity 

 V would, accordingly, have lo contain the factor (/ — ó-)', hence it 

 would be dependent on the volume, as is, indeed, assumed), and 

 when ƒ, the constant of the attractive action introduced by us, is 

 known. We shall return to this special problem later on. 



We only still point out that our formula (11) or (11^), res p. (10) 

 or (10a) is only valid for lorv, and not for high temperatures, whereas 



