604 



the requh-ed value of - bk. By means of (7) and (8) we find easily : 



(9) 



or when Ab =^ 



8 /Tz. s\ I— '1.8 



(9«) 



When therefore the value of /? has been found from (7) and (7(j!), 

 it can be substituted in (9) or (9^), and V/? ^i is known. 



According- to van der Waals, {b) would be = 6,52 :1,2 = 5,43 

 for metliylalcohol, whereas (for Lb = 0) the more accurate value 

 with ^ = 0,'S5 (see above) would amoujit to 5,43X1,084 = 5,89. 



This ^'alue is still larger than that found by van dp.r Waals, and 

 would yield 7,55 — 5,89 = 1,66 for CH„ instead of 2,12. And when 

 Ab = is assumed, the accurate value of (/>) will be lai-ger than 

 the approximate one for every value of ^, because 1 — V4 is always 



>(i - V. i^r- 



It is, however, easy to see that when not (7^/) and (9c/) are used 

 for the calculation resp. of ^ and [b), a value <^ 1, e.g. 0,88 can 

 very well be found for the factor (3??r — 2?i) : in' in (9), through 

 which 5,43 would diminish to 4,78, so that 7,55 — 4,78 = 2,77 

 would be found for OH^, in good harmony with the value found 

 for ethylalcohol. 



Now (3??i^ — '2n):rif becomes <[ 1, when 



2n 

 3 ^1 or nv <^n. 



I. e. with a view to (3) 



[1 + V. ^ (1 -.?) ( 1 + ^fYv < 1 + V. i^ (1 m + <f) + 



+ 73/?(l-^)(l-3^^)(l-f ^)' 

 must be, i. e. 



/3(i -/3) ( 1 + <fy + V. i^^ (1 -ii}' (I + ^Y < 



< V4 f^a-pf) a + y) + Vs ^(1 -/3) (1-3^^) (1 + <f)\ 



or 



(1 + ^f) + V. i^ (1 -^) (1 + <fy < \'. + Vs (1-3/5^) (1 + cpY, 



or also 



6 - 8 (1 + 90) + (1 _ 3/3') (1 + cfY - 2/ï(l -/?)(! + y)^ > 0. 



If i? were = 0, then cp would have to be <^ 3 — [/ 10, i. e. 

 < — 0,162. If [3 were ='/„ then fp ought to be < about — 0,25. 

 And if ^ were = 1, then (f would have to be <^ — 3 -|- [/7, i. e. 



