44 



REPRESENTATION BY SURFACES OF THE 



entirely above it, except the single point of contact. A tangent plane 

 at any point of the primitive surface within these lines will cut the 

 surface. These lines, therefore, taken together may be called the 

 limit of absolute stability, and the surface outside of them, the surface 

 of absolute stability. That part of the envelop of the rolling plane, 

 which lies between the pair of lines which the plane traces on the 

 surface, is a part of the derived surface, and represents a mixture of 

 two states of the substance. 



The relations of these lines and surfaces are roughly represented in 

 horizontal projection* in figure 2, in which the full lines represent lines 

 on the primitive surface, and the dotted lines those on the derived 

 surface. S, L, and V are the points which have a common tangent 



Fig. 2. 



plane and represent the states of solid, liquid, and vapor which can 

 exist in contact. The plane triangle SLV is the derived surface 

 representing compounds of these states. LL' and VV are the pair of 

 lines traced by the rolling double tangent plane, between which lies 

 the derived surface representing compounds of liquid and vapor. 

 VV" and SS" are another such pair, between which lies the derived 

 surface representing compounds of vapor and solid. SS'" and LI/" 

 are the third pair, between which lies the derived surface representing 

 a compound of solid and liquid. L"'LL', V'VV" and S"SS"' are the 

 boundaries of the surfaces which represent respectively the absolutely 

 stable states of liquid, vapor, and solid. 



The geometrical expression of the results which Dr. Andrews, 



* A horizontal projection of the thermodynamic surface is identical with the diagram 

 described on pages 20-28 of this volume, under the name of the volume-entropy 

 diagram. 



