of States of Aggregation.' 211 



§ 6. Discontinuity on crossing the principal edge. 



In general we may represent a given change of state by the 

 motion of a point along a definite line on the temperature- 

 surface, and the law followed by the mass in changing state 

 defines the form of the path-curve. 



If at every point of the temperature-surface the state of the 

 mass as well as the position of the point were defined without 

 ambiguity when the values of the three coordinates were given, 

 then might every line on the temperature-surface be consi- 

 dered as representing a continuous change of state, since to 

 the passage along an infinitely small element of the path cor- 

 responds only infinitely small variations in the magnitudes 

 that characterize the state of the mass. If the line were to cut 

 an edge of the temperature-surface, it might still serve to 

 represent a continuous change of state even at the points of 

 intersection, although the law of change would in general un- 

 dergo a sudden alteration as the edge was crossed. 



By § 4, the principal edge represents along its whole length 

 the singular cases of exception wherein the above condition is 

 not satisfied. To every given point of this edge indeed corre- 

 spond definite values of the coordinates p, v, T ; but to each 

 of these systems of values correspond an infinite number of 

 different values of the intrinsic energy U. Here, therefore, a 

 change of state can occur without any accompanying change 

 of coordinates. 



Considering the infinitely small line M N, cutting the prin- 

 cipal edge, to represent an element of the path that represents 

 the change of state, we see that in the passage from M to N 

 the magnitude U jumps discontinuously from a greater to a 

 smaller value, while the pressure, volume, and temperature 

 change only infinitesimally (fig. 12). The initial point M just 

 above the principal edge represents a mixture of water and 

 steam, and the point N just below the edge a mixture of ice and 

 steam. To each of these points corresponds a definite value of 

 U; and the difference between these values is finite, reaching 

 a maximum of more than 80 calories when the edge is crossed 

 at the point K. To a continuous variation of U would corre- 

 spond a discontinuous motion of the point representing the 

 state of the mass. On arriving at the principal edge it would 

 suddenly stop, remain there until the due variation of U was 

 accomplished, and then continue its motion along a line lying 

 at the other side of the edge. 



To represent this discontinuity we may consider the tempe- 

 rature-surface cut along the whole length of the principal 

 edge, and conceive this edge as a double edge made up of two 



P2 



