( 819 ) 
not only the sign, but also the value of the abrupt change of direction 
in the course of the upper branch is determined. But this modification 
remains restricted between the two indicated temperatures — and 
neither of the lower sheet nor of the remaining part of the upper 
sheet does the shape change in any respect. Only the lower sheet 
undergoes some modification, but in sections of quite different values 
of x, namely those which are found between the values of « of the 
points Q’, and Q’,. And this modification occurs only for one single 
value of 7, at least so long as the curve Q’,Q’, has the property 
of being cut only once by a line normal to the «z-axis. 
The modification in the course of the lower branch consists in 
this that for certain value of 7’, to be derived from the curve Q’,Q.,, 
the lower branch begins to rise less steeply. The three-phase-pressure 
ascends then even more rapidly than the first direction of the lower 
branch did. Below the temperature at which this change in the course of 
the lower branch appears, the three-phase-pressure is. already found, 
but for the considered section it may be considered only as a parasitic 
branch. The part of the three-phase-pressure that belongs to higher 
temperatures lies and terminates in the unstable region, i.e. above 
the lower sheet of the surface of saturation. At least if Q',Q’, is not 
intersected for the second time at the same value of z. In this case 
a second, higher temperature occurs, for which the three-phase-curve 
runs below the lower sheet, and again a part of this curve becomes 
a parasitic part. But for all the sections between Q', and Q', the 
upper sheet is not subjected to any change. The proof of what was 
said here about the modification of the lower sheet, is again found. 
in the equations, which now with change of the indices, assume 
the form: 
dp (Op de, | Op 
Pee ee ede dT OT J an 
dp __(Op\ de, Op 
ere dx al dT a zn 
If, as is the case on the curve Q’, Q', the three-phase-pressure 
comes inside the heterogeneous region with ascending temperature then 
dp Op Op É | 
7 —>(s), and 5e): being negative on the whole lower sheet 
now that the second component is assumed to have higher 7% than 
and 
the first component, Dn is necessarily negative, as was drawn for 
( 
the curve QQ. But as we see from the properties of a pr or 
