( 23$ ) 
“longitudinal plait” two years ago, and owing to a new, parti¬ 
cular, chiefly geometrical method lie has arrived at a series of 
important results, which may be tested by experimental data; but 
the problem has proved to be so intricate that a treatment conclu¬ 
sive in all respects has not yet been reached. We mention some of 
the most important results. 
a . The miscibility or non-miscibilfly of two liquids depends in 
d*ip 
the first place on the presence and situation of the locus = 0. 
Non-miscibility occurs a good deal more frequently than was believed 
up to now, particularly at lower temperatures or in the critical 
region, and also when the components are perfectly normal. 
b. A sharp distinction must be made between the case that a 
branch plait, which has crossed the binodal curve, retreats again 
inside it, and the case of the splitting-up of a plait, in consequence 
of which the branch plait leaves the main plait altogether. Both 
cases may be found in an upper mixing point (Buchner’s upper 
critical end point), but in one case an increase of pressure promotes 
the miscibility, in the other it diminishes it. Kuenen, in his above- 
mentioned paper, had already pointed out this difference, without, 
however, more closely investigating the circumstances on which this 
difference depends, and which cause either one or the other pheno¬ 
menon to appear. 
. c. The case of the splitting up of a plait is only possible w en 
in the system also a minimum critical temperature and a maximum 
vapour pressure occur. 
A plait can retreat both when in the vapour-pressure line a maxi¬ 
mum occurs, and when this is not the case. 
d. When the region of non-miscibility extends as far as in e 
critical region proper (vapour-liquid) of the system, continuity fa es 
place of the plaitpoint-line proper and the plaitpoint-line o 
“longitudinal plait”, in consequence of which rathei compic 
forms may originate. nlait . 
e. Korteweg’s 1 2 ) general theory of plaits has shown t ‘ P 
point can only disappear from the surface either by coinci ^ 
with another plaitpoint or by leaving the surface along one 
boundary lines * = 0, « = 1 (critical point of the 
by leaving the surface through the line v — h. n lS . . { 
have to do with an “open” plait'), in that sense that even 
1) Archives n6erlandaises, I, 24, 295. 1889. Arch. N£erl* 
2) in physical sense; it is not an open plait in Korteweg s sense, 
XXIV p. 5. 
