(707 ) 
indicates the sign of dz,. In the same way if we change 2 into 3. 
Now it is true that the surface of saturation has been greatly modi- 
fied by the existence of the three-phase-pressure. But this modifica- 
tion is restricted to values of 7’, between those at which this pres- 
sure begins and ends, and also within these limits of temperature, 
the surface of saturation consists only of a lower sheet and an 
upper sheet, if we leave the metastable and unstable coexisting 
phases out of account. So every section for given value of 2, is 
again, except for the modifications inside the said limits of tempe- 
rature, the well-known figure in which the lower branch passes 
continuously into the upper branch. Let us now think the line p,,, 
as function of 7’ traced in every section. Only for so far this line 
lies between the upper and the lower branch of the section of the 
modified surface of saturation, the mixture of the chosen value of 
« can split up into three phases. If this line intersects either the 
upper branch, or the lower branch, and if therefore part of the 
line p,., lies outside the surface of saturation, this must be considered 
as a parasitic branch, at least for the mixture chosen. So the dotted 
lines of fig. 39 and fig. 40 represent the values of 7’ for which the 
line p,,, intersects a chosen section of the surface of saturation. 
And so the question whether in fig. 40 the situation of point Q’, 
is such that another point occurs in the dotted curve for this value 
of zr, coincides with the question whether there exist sections for 
21 
which the line p,,, intersects the saturation curve twice. As 
U, = x, 
V 
and —— are negative on the vapour branch according to the formula 
L 3 alr 1 
da 
for the calculation of — a negative value of this quantity is attended 
a 
uf dp dp 
with a positive value of —— or with the line p,,, entering 
dE, Bd, 
the heterogeneous region with increasing 7. Reversely a positive 
value of shows that the line p,,, enters the homogeneous region 
TT 
ad 
with increasing temperature, and therefore appears further only as 
va ‚(dp 
parisitie branch. Now in the point Q’, the value of (35) is 
: 123 
dT 
saturation for the z of the point Q,, as follows if in the formula 
dp 
for = — we put xv, + de, for 7,, V.,tdV, for V,, and 7, + dy, 
G+ 138 
dp 
equal to the value of (4 ye as it is on the section of the surface of 
