118 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



upwards (in the direction in which f is measured) the states repre- 

 sented will be stable in respect to adjacent states. This also appears 

 directly from (162). But where the surface is concave upwards in 

 either of its principal curvatures the states represented will be un- 

 stable in respect to adjacent states. 



When the number of component substances is greater than unity, 

 it is not possible to represent the fundamental equation by a single 

 surface. We have therefore to consider how it may be represented 

 by an infinite number of surfaces. A natural extension of either of 

 the methods already described will give us a series of surfaces in 

 which every one is the v-ij-e surface, or every one the t-p- surface for 

 a body of constant composition, the proportion of the components 

 varying as we pass from one surface to another. But for a simul- 

 taneous view of the properties which are exhibited by compounds of 

 two or three components without change of temperature or pressure, 

 we may more advantageously make one or both of the quantities 

 t or p constant in each surface. 



Surfaces and Curves in which the Composition of the Body repre- 

 sented is Variable and its Temperature and Pressure are 

 Constant. 



When there are three components, the position of a point in the 

 X-Y plane may indicate the composition of a body most simply, 

 perhaps, as follows. The body is supposed to be composed of the 

 quantities m 1? m 2 , ra 3 of the substances S v S 2 , S B , the value of 

 r^-f m 2 +m 3 being unity. Let P I} P 2 , P 3 be any three points in the 

 plane, which are not in the same straight line. If we suppose masses 

 equal to m v ra 2 , m 3 to be placed at these three points, the center of 

 gravity of these masses will determine a point which will indicate 

 the value of these quantities. If the triangle is equiangular and has 

 the height unity, the distances of the point from the three sides will 

 be equal numerically to m v m 2 , m 3 . Now if for every possible phase 

 of the components, of a given temperature and pressure, we lay off 

 from the point in the X-Y plane which represents the composition 

 of the phase a distance measured parallel to the axis of Z and repre- 

 senting the value of f (when m 1 +m 2 -|-m 3 = l), the points thus 

 determined will form a surface, which may be designated us the 

 m 1 -i7i 2 -m 3 -f surface of the substances considered, or simply as their 

 m-f surface, for the given temperature and pressure. In like manner, 

 when there are but two component substances, we may obtain a 

 curve, which we will suppose in the X-Z plane. The coordinate y 

 may then represent temperature or pressure. But we will limit 

 ourselves to the consideration of the properties of the m-f surface 





