124 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



form a quadrilateral ABCD (fig. 4) without re-entrant 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 

 tangent planes rolling upon the four pairs of these sheets which 

 correspond to the four sides of the quadrilateral. To determine the 

 general effect of a variation of temperature upon the surface of dis- 

 sipated 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 out by a body in passing from the first to the second 



Fig. 4. Fig. 5. 



state at constant temperature arid pressure), which we may suppose 

 without loss of generality, an elevation of temperature while the 

 pressure 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 

 will give a different but entirely analogous form to the surface of 

 dissipated energy. The quadrilateral ABCD will in this case break 

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

 variation of the pressure while the temperature remains constant will 

 of course be similar to those described. By considering the difference 

 of volume instead of the difference of entropy of the two states 

 represented by the point I in the quadruple tangent plane, we may 

 distinguish between the effects of increase and diminution of pressure. 

 It should be observed that the points of contact of the quadruple 



