

AN 



^= 1 + 

 N 



— i —i 



I I \ 9 i'^ll^) <^'^(^yd:: — 3 111^5' (Ixdydz 



'' \\\^9d<''<^y dz— \\\ ^g dx dydz. 



+ 3 I I I — ,a c?A- dy d 



— l ^ — / 



Every integral in this formula is always smaller than the prece- 

 ding one. If / is large with respect to the distance for which g has 

 an appreciable value, there remains only the first integral. For 

 any great volume we have 



^ +^ 



^ = 1 + fff gdx dydz (11) 



— x 



3. In trying to determine the function ƒ by means of statistical 

 mechanics, we meet with difticulties. Still something may be found 

 about the quantities i\v^ by applying the statistic-mechanical method 

 to oui- problem. Indeed statistical mechanics permit to introduce a 

 mutual action of the elements of volume. 



We will avail ourselves of a canonical ensemble. We suppose the 

 molecules to be spherical and rigid, and to attract each other for 

 distances which are great with respect to their size. Elements small 

 with respect to the sphere of attraction therefore may still contain a 

 great number of molecules. But now we drop tlie supposition of the 

 sphere of attraction being homogeneously filled for all systems (or 

 at least for by far the greater part of them) ^). 



In calculating the number of the various distributions, we 

 must, for the potential energy of attraction, take into account the 

 mutual action of the elements ; whereas, in calculating the exclusion 

 of definite configurations of centres, we may neglect the fact that 

 there is some correlation on the borders of the elements. For the 

 dimensions of the elements have been supposed large with respect 

 to the molecular diameter. 



The mutual potential energy of the r -j- t molecules contained in 

 an element dv, will be represented by 



dv 

 in this formula v represents the number of molecules contained in 

 the volume dv for the most frequent system. In this system the 

 distribution is homogeneous. 



■) Gf Ornsteix, Toepassing der Statistische mechanica van GIbbs op molekulair- 

 theoretische vraagstukken. Diss. Leiden 1908, p. 43 and p. 110. 



