1 208 



no pi-actieal objection, though the probabilitj' to such a behaviour 

 may not he great. 



The theory of the factor of distribution (?^A- (or (1 + Pr)--, 

 etc. etc.) rests in inj opinion on nothing but a misunderstanding, 

 and the theory of the virial of attraction and collision should be 

 built up on entb^ehj new grounds. 



XIV. More Accurate Theory of the Virial of Attraction 



and Collision. 



The method of calculation followed up to now (Reinganum, 

 Van Laar, Kkksoai) might in a certain sense be called the ''static" 

 method. In this it is assumed thai the molecules are distributed 

 according to a certain law round the considered molecule, in which their 

 motion, i-esp. velocity and direction, is entirely eliminated (disregard- 

 ing the mean final velocity at the collision). In the place of this 

 Boltzmann's factor of distribution e~^'^r is then substituted, which is 

 to set everything right again. But in my opinion Boltzmann's con- 

 siderations are no longer valid for separate micro-complexes, as molecules 

 in collision, and immediately before impact, or* passing each other 

 at a small distance in the sphere of attraction. 



It is easily seen that the effect of the attraction will be this, that 

 the at first rectilinear path (at least for large vohnne) will be mc7m^t/ 

 more or less towards the molecule under the influence of the attraction 

 in the sphere of attraction, and that therefore molecules which would 

 otherwise remain further from the molecule under consideration, 

 will now get into spheres where the attraction is greater. And the' 

 smaller the velocity with which the molecules will pass, the stronger 

 this enlarging influence will be. If the temperature is exceedingly 

 low, all the molecules that pass the border of the sphere of attraction 

 (?' = r„) with their centres, will collide with the molecule under 

 consideration, through which for all the maximum value M is obtained 

 for — Pr, a-nd a maximum value will therefore be found for a — but 

 not an exponentially infinitely large one, as with Boltzmann's factor 

 of distribution. 



The same thing holds for b. Molecules that would not collide 

 under other circumstances, will now collide under the influence of 

 the attraction that causes them to deflect, and the number of 

 colliding molecules will therefore be increased, in more or less 

 degree as the temperature will be higher or lower. And it is easy 

 to see that here too the value of h,, will approach to a maximum 

 for T z= (as the radius of the sphere of attraction Vn remains 



