( 520 ) 
n a 5 : 
The term with /og— was introduced some time ago by VAN DER 
v 5 5 
Waats'); in the original theory this term was neglected, and so the 
ik 
equation (4) was simply R7’= aw (1—.) 43 (5) 
a a 
In consequence of the relations — = RT, pes where ac- 
v v 
cording to the variability of the liquid-volume v, the coefficients f 
and y will still vary slowly with the temperature (fis the well 
known factor of the vapour-tension, which may be put circa 7), we 
can also write for (4): 
Ske 
mr TE Ow? 
JSS Be (A) 
0? log pe 
1+.a4(1—z2) eae 
i 
We see, that only in the case, that the critical pressures of the two 
components differ little, the term with Log p. can be omitted. This 
will be also the case, when w is in the neighbourhood of 1 and 0. 
But in all other cases if would be inaccurate to omit a priori the 
designed term. 
Further we write: 
a = (l—«)? a, 4- 24 (le) a,, + 27 a, 
v= (l—a) v, + av, 
since for liquids at low temperatures ¢ can be supposed dependent on 
wv in entirely the same manner ash = (1—v) 6, + «b,. The molecular 
volumes 7, and v, must then be regarded, just as >, and 5,, as constant 
or as slowly varying with the temperature *). We then find after some 
reductions : 
1) These Proceedings, in Ternary Systems, specially IV, p. 96—100. (June 12, 
1902); see also July 13, 1904, p. 145 sequ. 
2) If we substitute in the case of liquids v by b, and then write 6 = (1—.r) bj + «bz, 
the difficulty arises, that in that way quantities of order v—b are neglected 
against those of order 7, and the question would present itself, if this is only 
upon very definite conditions no¢ in contradiction with omitting p by the side of 
a 
ye 
(This observation was kindly made to me by Prof. Lorentz). 
{ hope to escape this difficulty by not substituting » by 6, but by simply 
supposing the volume v linearly variable with « in the case of liquids at 
low temperatures; by writing therefore for 7, analogous to the expression for b, 
b= (1—2) 1, Her. As 1 remarked, vj and #7 still vary slowly with the tempe- 
rature, whereas bj and », of course would be perfectly constant. Now it 
