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inflection. The double point is always a point of intersection of the 
vapour branch and of the liquid branch; so it is never found on the 
branch of the unstable conditions. !) For a simpte substance it occurs, 
when the pressure is equal to the coexistence pressure at the chosen 
temperature. For a mixture it indicates the composition, for which 
at a chosen temperature the pressure which would be found by the 
criterium of MAXWELL if applied to the isothermal of the homoge- 
neous phases, would be exactly equal to the pressure for which the 
¢-curve has been drawn, or in other words: the place of the double 
point determines the mixture, for which the chosen pressure would 
be the maximum tension, if such a mixture continued to behave as 
a simple substance. I have proposed before (Arch. Néerl. Série IL 
Tome II, pag. 69) to call such a pressure coincidence pressure. 
When, therefore, the pressure, for which the S-curve has been drawn, 
is either smaller or greater than the coincidence pressure of any 
mixture at the assumed temperature, no point of intersection will 
occur. In such a case the f-curve consists of three branches, which 
keep quite separate and for which, when p is smaller than the 
smallest of the coincidence pressures would be, the vapour branch 
lies lowest. Above it we get the liquid branch, and still higher the 
unstable branch. If on the other hand p is greater than the highest 
of the coincidence pressures, the liquid branch lies lowest. 
As to the place of the points of inflection we have to observe 
that the relative position of # and E' (fig. 3) may be different. In 
the figure drawn Z' lies on the side of B and / on the side of B’. 
If, however, with increase of pressure the crest should disappear 
altogether, then Z' lies on the side of B' and & on the side of B. 
In a special case the transition of these two cases might take place, 
if the points ZE and E" have coincided in the point of intersection 
of the two branches. It appears from fig. 2 that for such a transition 
it is necessary that the two points & and £' are to be found at the 
same value of «. If E lies on the side of B, and £’ on the side 
of B', we shall call this the normal position. To determine the value 
of the plaitpoint-pressure and of the plaitpoint composition at a given 
temperature by means of the S-curve is: to seek for what value of 
p the two points of inflection, after they have assumed the normal 
position, coincide, and at what value of z this happens. To determine 
the composition and the pressure of the criticaltangent state 1s to 
seek at what pressure the point B' begins to retrograde and what 
the value of 2» is at the moment. 
') In some complicated cases an apparent exception may be found, 
