( 906 ) 
Physics. — “On the course of the tsobars in: binary systems” HL. 
By Prof. Dr. Pa. Konystamm. (Communicated by Prof. J. D. 
VAN DER WAALS.) 
18. We showed in $ 3 of the first communication (These Proc. 
of Jan. 1909, p. 599) that the equation 6=0O has always two real 
roots; whether the equation @—O will have real roots or not will 
depend on this whether a*,, is greater or smaller than a,a,. We 
shall get all possible cases for the isobars when we give the line 
which represents @ as function of « (and which we shall briefly 
call the «-line) all possible positions with respect to the 6-lne. Let 
us first investigate the supposition «°,, <0, We first consider the 
case that the minimum of the «-line lies on the right side of 4,. 
(We call the two points where 5 0, from the right to the left 4, 
and 5, and shall afterwards apply the same notation also for a). 
Then we have the position of the two lines represented by fig. 187), 
That in this case there is always a minimum critical temperature, 
Wid Al 
7 
. . - x C “4 
follows from the considerations of § 11. For these teach that a 
Ck 
must always be positive for vr — + %, as soon as the minimum of 
the a-line lies on the righthand of that of the 4-line. We need not 
dwell on the course of the isobars in this case; it is the usual ease, 
further illustrated for low temperatures by the figs. 16 and 17. 
If the a-line moves to the left, so that the minimum gets on the 
left of 6, but sull continues to be on the right of the minimum of 
the d-line, we shall only notice a difference in the shape of the 
isobars at lower temperatures. There we shall namely get the course 
of the figs. 12 and 10 instead of that of fig. 16 or 17 aceording as 
the maximum and the minimum of the critical pressure drawn in 
fig 18 is present or not. At higher temperature — viz. that tem- 
‚db das d : 
perature for which MAT eer for the point 6, — the modifica- 
Av LY 
a dp Paitin 
tion in the course of the line — == O sets in, in consequence of 
av 
which these figures pass into those of the first case. This transition 
may take place both above the minimum critical temperature of the 
system and not above it, hence figures as figs. 13 and 14 will be 
possible, but it is just as well possible that already before the line 
1) Gf. preceding communication. In the diagram the minimum of a lies more 
to the left than we intended; this is, however, not of influence on the course of 
the other lines. 
