799 



Of course, tlie potential energies will not strictlv be the same for 

 different configurations within the elements, but we shall neglect this 

 complication. Further we will represent the mutual potential energy 

 for the two elements a and o by 



— {v + r,) (v + T.) (f^, 

 dv 

 all elements of volume being put equal. 



For the total potential energy we find, in this way 



Zciv 

 For the frequency ^ of a system with the given distribution of 

 molecules we find 



(r+TJ/(^'+TJ.^.> ' ^ ^ ' ^ 



Here to is the function defined in the quoted dissertation on p. 48. 



Supposing r <^ 1' and developing, we get, 



1 ,,^ ^ ^ /^ 1 1 ^ d log io «)„„ ~\ 



— na:S,(p,, + iJSJS" \ a"' ^- + ^^ r,^4- 



g=(7 tt>" a-'^e'^® ' V ï^ V da da &dv J 



+ ^^^'^,= + (12) 



0dv 



The number of molecules per unit of volume represented there 

 by n, has been put a in this paper. The function w and the faculties 

 are developed in the same way as in the quoted dissertation. The 

 double sum in the exponent gives the forms ^^r^jTcT-p and -^'r.r-S'ryp,. 

 These forms are identical, as they consist of the same terms differ- 

 ently arranged, further ^ffp^ is the same for all molecules and 

 St^ = 0, consequently both sums vanish. 



The constant 6' contains the factor Ne^^'l® along with quantities which 

 do not de[)end on the volume by summing up ('J 2) over all possible 

 Values of r (and taking into account that ^r-, = 0) we get ^V, the 

 total number of systems in the ensemble. So we find 



llie quantity A being the disöriminant of the quadratic form in the 

 exponent. 



dip 

 When we write -S';7';7 = «, we find for the pressure w = — — - 



53 



Proceedings Royal Acad. Amsterdam. Vol. XVII. 



