( 194 } 
Physics. — “Ternary systems.” V. By Prof. J. D. van per WAALs. 
(Continued from pag. 21). 
If the temperature is so low that there is no question of eritical 
phenomena, and if therefore both liquid sheet and vapour sheet cover 
the whole triangle, »,, is for all points either positive or negative, 
and the given rules for the displacement of the curves of equal 
pressure will therefore be followed by all points of these curves. If 
on the other hand the temperature is chosen so high, that the surface 
of saturation does not cover any longer the whole triangle, and if 
therefore the liquid sheet and the vapour sheet pass into each other 
above a certain locus in the triangle, v,, vanishes for the phases 
represented by this locus. 
We may form an idea of the shape of the surface of saturation 
with the aid of fig. 11 (Cont. II, p. 185). Let us imagine that this 
figure represents a section by the vertical plane which contains the 
X-axis of the triangle and let us take a similar section by the 
vertical plane which contains the Y-axis. The value of 7’ is then 
chosen such that 77> (7), and also 7’ > (7), In the figure men- 
tioned P is the point, where a vertical tangent may be drawn, so 
this point represents a phasis which is in critical point-of-contact 
circumstance, and for which »,,=0. The point C represents the 
plaitpoint. If we now imagine different planes which contain the 
axis erected in the point 0 normal to the plane of the triangle, these 
planes will cut the surface of saturation, and the sections will be 
analogous figures, which however change their shape fluently from 
that which they have in the POX-plane to that which they have 
in the POY-plane. If the pressure is lower than the lowest pressure 
of the points Z, the two branches of the curves of equal pressure 
are perfectly separated lines which, if the pressure is increased, will 
be displaced according to the rules given above. If however the 
pressure has risen till the pressure of a point P has been reached, 
then the two branches are still separated, but on the vapour branch 
occurs a point for which »,,=— 0. Such a point is not displaced 
when the pressure increases. The locus of these points forms the 
limit of the mixtures which may be splitted up into two phases at 
the given temperature. From a geometrical point of view it is the 
envelope of the projections of the horizontal sections of the surface 
of saturation, or the envelope of the projections of the curves of equal 
pressure. If the pressure has been increased till it has attained the 
value of the lowest of the pressures of the point C, then the two 
branches of the curves of equal pressure pass continuously into one 
