1087 

 6' dl 



.o ai i 



2 = ::£ hrh +^ c,dT = :s 



= 2: U . . . . (23a) 



In all these summations the quantities must have the sign -|- or 

 — according as they relate to the righthand or the lefthand member 

 of the reaction equation. The equations having to hold for every 

 chemical reaction, independent of the values of the r's, we shall 

 be allowed to omit the 2 signs in (23r/), and write such an equation 

 for every coordinate separately. 



or 



I {vhr- F{0,v) + ƒ . ^ ^{,,v)d, = 0^ j ƒ ^ de 4 J|, e <^ ^{,,v)d, 



v/i vA 



or 



1 dFW.v) 



2 ^ ^ ^ -^ dO 



from which follows 



vh 

 W 



F{6v)=C Xe ^^ (2-1) 



It is evidently not impossible to assign such a value to the C 



e 



tiiat F{0,v) and e / (f,r) continuously pass into each other at 



more than a single temperature. In general a discontinuity will occur 



in the function of probability at s = vli. I do not know a way to 



determine C. The value /(^'^O suggests itself most naturally. 



8 = v/i 



Then the function of probability becomes continuous at 6* = go , 



which is in accordance with the fact that at high temperatures the 



deviations from classical mechanics become smaller. With this 



value of C we see that the number of molecules having an energy 



slightly smaller than rh, is greater that the number having a some- 



hv 



what greater energy. The ratio is e-'^. This is in harmony with 

 Pl.anck's theory according to which for vibrators which are absorbing 

 energy of radiation, only a part continues to absorb when e = vh 



7J 

 Proceedings Royal Acad. Amsterdam. Vol. XVI. 



