(123) 
phasis coexists with a given phasis. It is true that we know that 
the pressure must be the same, and that therefore the second phasis 
will be found on the other sheet at the same height as the first 
phasis, but as the section of the second sheet by a plane ata height 
equal to p is a curve and not a point, the question is not yet per- 
feetly determined. Therefore, besides the series of curves of equal pres- 
sure, which are already given as the points which have the same 
height, still another series of curves must be traced on the surface 
of saturation which pass from lower to higher pressure and whose 
properties enable us to answer the question, which phasis of one 
of the sheets corresponds with a given phasis of the other sheet. 
We will again begin with treating the simplest case, in which 
maximum-pressures are excluded, as well for the pairs of components 
of which the ternary system consists, as for the ternary system itself, 
so the case for which the lowest pressure is equal to p, and the 
highest to p,. The question is then, what systems of curves, starting 
at the point where the pressure has the lowest value and ending in 
the point where the pressure has the highest value, may be traced 
on one of the sheets or on both sheets of the surface of saturation 
which enable us to find, what phases coexist with each other. Such 
a system of curves will be found in the course of a person who 
would climb the inclined sheet, e.g. the liquid sheet, always moving 
in such a direction that he has the phasis, coexisting with the point, 
where he is at the moment, just in front of him. If we now project 
the tangent to the way which he has followed ona horizontal plane, 
the point in which this projection cuts the vapour sheet will indicate 
the coexisting phasis. The projection of such curves on the plane of 
triangle OXY has therefore the property that the tangent passes 
through the conjugate point, and is therefore the chord, joining the 
points 1 and 2; from this follows again that these projections are the 
envelopes of these chords. If therefore in the plane of the triangle 
we have drawn the two branches of the curves of equal pressure, 
and if we have joined a pair of nodes by a chord, an element of 
the curve in question will be represented by an infinitely small part 
of this chord. Let the point from which we start represent a liquid 
phasis and be its coordinates x, and y,. The projections of the element 
of the way followed are then the quantities dr, and dy,. At the end 
of the elementary way the second phasis is also changed, of course, 
and the consequence of this will be that we have to follow a curve. 
But the direction of the infinitely small way will always be the same 
as that of the chord joining the nodes; and the differential equation 
will therefore be given by: 
