8Öl 



The quantities T:;rp etc. liere found arc related to those mentioned 

 above. And though a statistical deduction of the function ƒ enter- 

 ing into details may lead to difficulties, jet it is clear that 

 statistical mechanics yield a correlation analogous to that expressed 

 in cj. 



If we should wish to continne the deduction of the conditions of 

 the critical })oint, we should have to nse higher powers of t_, which 

 can be done without difticnlty; we then tiiid for the second condition 



— = 0. 



If we drop the supposition that the sphere of attraction is large, 

 we can use the function i>-, defined iji the quoted dissertation. In 

 order to take into account the correlation, we must suppose the 

 integrals 



} 



Ch\ . . dZn Ty ^= d- (Hy) 



defining Ö-, to depend on ??x- for the element in question and also 

 on the numbers of molecides in the surrounding elements. Therefore, 

 in general, the numbers of molecides of all elements will appear in 



{)ny. , but the influence of distant elements is so small that — — 



can be put zero. 



By considerations analogous to those used in the quoted disserta- 

 tion, we can show that i^iuy') has the form 



lly Vy, 



Vy (o) iix, c/, n/') 

 in which n/ n/- denote the densities (molecular), in the elements 

 with which Vy is in mutual action. The values of all n^ are equal 

 for the most frequent system. 

 Now we find for C 



g ^ C F" (to n, n, n, n . . .)" e~P 



where P is a quadratic form in the deviations for the various 

 elements, containing squares as well as double products. The form 

 might be easily indicated, but we will omit it, as it is only our 

 purpose to show how in general the statistic-mechanical considera- 

 tions, changed in the sense of a correlation of elemejits of volume, 

 lead to formulae analogous to those given in § 2. Here too the 

 mean square of deviation and the means of double products are 

 represented by quotients of minors of the discriminant of F and 



(//' 

 this qnanlitv itself. Here too for — =zO the discriminant vanishes. 



dv 



53* 



