804 



even then only an approximaUon can be obtained. Therefore we 

 will take another way. As remarked in § 1, the exact value of v' 

 for verij yrent voUunes was already known. In our notation we have 



_ RT a' 



N dp 



V — 



dv 



where N is the number of Avogrado, v the molecular volume. 

 According to formula (4) we have 



Putting these results equal, we get 



v'^ dp 

 ^ ~ ^ ~~R7'd^' 



In the critical point F=l.^) 



The formula of opalescence tirst arrived at by Keesom and Einstein 



1) There appears to exist a closer correspondence between the given slatistic- 

 mechanical method and the method using general considerations of probabihty, than 

 perhaps might be expected. The elements of the discriminant (which is an infinite 

 determinant in the former) agree with the function f in the latter. The former finds 

 from this the value of v^ vr as the quotient of a minor with that discriminant, 

 the latter deduces this value from an integral-equation. In the critical point the 

 discriminant vanishes, corresponding to tliis the Fredholm determinant of the 

 integral-equation is likewise zero. That this is the case when F= 1, appears by 

 more closely studying tlie equation 



g (§7i?) — X ig (5>jC) ƒ (,^■ + §,// + % ~ + ?) d^dyid^ = 



which only permits appropriate solutions if ). = --, (i e. this is the only proper 



value). For F= 1 this is therefore the case ^w'dh. the equation (6) without second 

 member. 



From the formula (15) it will be seen that form. (G; can be solved by a Fourier 

 integral. Putting 



+ ^, 

 I 1 I cos m.v cos ny cos lzf{.vyz) dxdydz =^ cf [m, n, I) 



we have 



1 rrr cf{m, n,i) i , , v 



g [xyz) z=. I I I cos nuv cos ny cos iz amancU. 



