( 92 ) 



If we, namely put 7\''7\. z= \i.^, (32") becomes, vvlieJi /^i 4" ^/> is 

 substituted for nh., in it : 



1 _21 rLF 

 ~2 ~~~%\h 



"((■%■') 



So we get : 



log 



1 



27 



when .1' is written for the ratio Lb-.b^. From this we calculate then 

 the following values of n^' for x =z — 0,5, — 0,3 and — 0,1: 



4 _ 27 

 ^^^' ~ 16 



log 

 log 

 loq 



1 



243 



0,49n,i' 400 

 1 27 



log'' = 0,733 

 log'' = 0,264 

 log'" = 0,0293 



= ; lo<i'" = 



//(.r = 0,74 



Jliï = 1.11 



)i^ï =1,15 

 {n^' = 1) 



0,81n/3' 4i;0 

 1 



So if ^' is not to be greater than e.g. 0,07 (see p. 462 loc. cit.), 

 n must be at least =11 for .i- =: — 0,5 ; at least =: 16 for .v = — 03, 

 at least =z=17 for .v = — 0,1, this number verging to about 14 

 according as .v approaches to 0. In his first paper on Quasi asvsocia- 

 tion in liquids (These Proc. June 1910 p. 129) van der Waals found 

 already ?i ^ 6 ; so it is by no means remarkable that we find 

 n ^ 10 (for negative values of A6, so for retrogressive melting-point 

 lines), the more so as we have included Jiot only the liquid state, 

 but more particularly the solid state, in our considerations. 



Repeating the above calculation for positive values of Lb, we find 

 for V =: 0,5, 0,3 and 0,1 successively : 



X z= 0,5 

 X = 0,3 

 X = 0,1 

 {x = 0) 



1 _ 27 

 ^^ 2.25MJ' ~ To 



log 

 log 



243 



l,Q9nii' 400 

 1 27 



l,2bij?' 400 



iog -^, = ^ 



7i^ï = 0,082 

 n^' = 0,322 

 n^ï = 0,770 

 (n/?' = 1 



