, ( 135 ) 



not develop tlie conseqiieiiees of lliis decreasing value of !> but 



it appears already in my paper on "The equation of state and the 

 theory of cyclic motions" and in the i)aper in the "Livre Jub. dédié 

 a LoRENTz" quoted above that I still regarded the (|iiestioii from the 

 same point of vie\\ . 



^\\ tirst sut)positi()n concerning the cause of the deci-ease of h 

 witli the volume was not that the smaller value of h correst)onded 

 to smaller volume of the molecules, h,, being ecpial to four times 

 the molecular volume, I supposed smaller values of h to be lower 

 multiples of this volume. In this way of considering tiie question 

 the decrease of h does not indicate a real decrease of the volume 

 of the molecules. We will therefore call it a quasi-decrease. 



It can scarcely be doubted that such a quasi-decrease of the 

 voluiiie of the molecules exists. In his "-Vorlesungen" Boltzmann 

 started from the fundamental supposition that the state of equilibrium 

 i.e. the state of maximum-entropy is at the same time the "most 

 probable state" : in doing which he w^as obliged to take into account 

 the chance that two distance spheres partially coiiicide. And conqiarino- 

 the expression which he found in this way for the maximum-entrojiy 



r dv 

 with the expression R I (i.e. the entropy in the state of equi- 

 librium according to the equation of state) it was possible for Iiim 

 to determine the values of some of the coefficients of the expix^ssion : 



This method is indirect. I myself had tried to find these coeffi- 

 cients by investigating directly the influence of the coincidence of 

 the distance spheres on the value of the pressure. According to 

 these two different methods different values for the coefficients were 

 found. My son has afterwards pointed out (see these Proceedino-s 

 1902) that also according to the direct method a \-alue of « equal 

 to that calculated In 1j0T.tz.maxn is found, if we form another 

 conception of the influence on the pressure than I had formed and 

 since then I am inclined to adopt the coefficients calculated accordin»- to 

 the method of Boltzmann as accurate. 



But these values apply only to spherical molecules and oiiiv in 

 the case of monatomic gases we may suppose molecules with such 

 a shape. It is not impossible that for complex molecules these coef- 

 ficients will be found to be much smaller. Moreover for the determina- 



C ^^' 

 tion oi I knowledge of all the coefficients is required — and 



