1088 



is reached, and passes therefore to the group for which f^vh, 

 whereas another part emits all the stored energy. For the chance 

 of emission we find another value than Planck. This is not astonishing 

 as we assumed that for e'^vh the function of probabilitj would be 

 continuous, whereas according to Planck it exhibits new disconti- 

 nuities at g = 2rA etc. At all events we see that Planck's hypothesis 

 concerning the zero-point energy can only be reconciled with the 

 thermodynomic law of the equilibrium change, when the function 

 of probability shows a discontinuity at s = vh, of entirely the same 

 nature as had already been assumed by Planck. 



In conclusion we will calculate /, as tiiis quantity occurs in the 

 formula for the equilibrium constant. Integration of (23«) with 



vh 1 

 U= -— 1 vh yields : 



vh ' 2 '^ 



.6> 



I = 



Ivh 



he~"^~^ 



vh 



This expression differs from tlie value whicli we found without 



1 vh 



9 n 



zero-point energy, and which we shall call 1' by the factor t^ '-' . 

 Hence we may write (20/>) iji the following form : 



Lf: 1 vh 



K~e ^ e ^^ ^ nr. 



And Q„ being = {Le f -5" - vli), we tind the same expression 



as without zero point energy, since then Q^ ^ Lf, and we may, 

 therefore, always write : 



K=e ^ nr. 



Chemistry. ■ — "A ncu- hi/drocarbon from the pinacone of methyU, 

 ethijlketone'. By Prof. P. van Romburgh and Miss D. W. Wknsink. 



(Communicated in the meeting of March 28, 1914). 



When studying the action of formic acid on this pinacone this 

 seemed to take a course quite contrary to expectation. Whereas in 

 this reaction tlie ordinary pinacone is almost completely converted 



