182 -T. W. Gibhs — Equilibrium of Heterogeneous Substances. 



But when the points of contact with the quadruple tangent plane 

 which represent the four coexistent phases can be joined so as to 

 form a quadrilateral ABCD (fig. 4) without reentrant angles, the 

 surface of dissipated energy will include this plane quadrilateral, 

 portions of the four sheets of the primitive surface which are tangent 

 to it, and portions of the four developable surfaces formed by double 



Fig. 4. 



Fig. 5. 



tangent planes rolling upon the four pairs of these sheets which corres- 

 pond to the four sides of the quadrilateral. To determine the gen- 

 eral eifect of a variation of temperature upon the surface of dissipated 

 energy, let us consider the composite states represented by the point 

 I at the intersection of the diagonals of the quadrilateral. Among 

 these states (which all relate to the same kind and quantity of matter) 

 there is one which is composed of the phases A and C, and another 

 which is composed of the phases B and D. Now if the entropy of 

 the first of these states is greater than that of the second, (i. e., if 

 heat is given ovit by a body in passing from the first to the second 

 state at constant temperature and pi'essure,) which we may suppose 

 without loss of generality, an elevation of temperature while the 

 pi'essure remains constant will cause the triple tangent planes to 

 (B), (D), and (A), and to (B), (D), and (C), to rise above the 

 triple tangent planes to (A), (C), and (B), and to (A), (C), 

 and (D), in the vicinity of the point I. The surface of dissipated 

 energy will therefore take the form indicated in figure 5, in which 

 there are two plane triangles and five developable surfaces besides 

 portions of the four primitive sheets. A diminution of temperature 

 wall give a different but entirely analogous form to the surface of dis- 

 sipated energy. The quadrilateral ABCD will in this case break 

 into two triangles along the diameter BD. The effects produced by 



