EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 129 



diagrams than they could be in words. It will be observed that a 

 knowledge of the lines which divide the various different portions of 

 the surface of dissipated energy and of the direction of the rectilinear 

 elements of the developable surfaces, as projected upon the X- Y plane, 

 without a knowledge of the form of the m-f surface in space, is 

 sufficient for the determination (in respect to the quantity and com- 

 position of the resulting masses) of the combinations and separations 

 of the substances, and of the changes in their states of aggregation, 

 which take place when the substances are exposed to the temperature 

 and pressure to which the projected lines relate, except so far as such 

 transformations are prevented by passive resistances to change. 



Critical Phases. 



It has been ascertained by experiment that the variations of two 

 coexistent states of the same substance are in some cases limited in 

 one direction by a terminal state at which the distinction of the 

 coexistent states vanishes.* This state has been called the critical 

 state. Analogous properties may doubtless be exhibited by com- 

 pounds of variable composition without change of temperature or 

 pressure. For if, at any given temperature and pressure, two liquids 

 are capable of forming a stable mixture in any ratio m^ : m 2 less than 

 a, and in any greater than b, a and b being the values of that ratio 

 for two coexistent phases, while either can form a stable mixture with 

 a third liquid in all proportions, and any small quantities of the first 

 and second can unite at once with a great quantity of the third to 

 form a stable mixture, it may easily be seen that two coexistent 

 mixtures of the three liquids may be varied in composition, the 

 temperature and pressure remaining the same, from initial phases 

 in each of which the quantity of the third liquid is nothing, to a 

 terminal phase in which the distinction of the two phases vanishes. 



In general, we may define a critical phase as one at which the 

 distinction between coexistent phases vanishes. We may suppose 

 the coexistent phases to be stable in respect to continuous changes, 

 for although relations in some respects analogous might be imagined 

 to hold true in regard to phases which are unstable in respect to 

 continuous changes, the discussion of such cases would be devoid 

 of interest. But if the coexistent phases and the critical phase are 

 unstable only in respect to the possible formation of phases entirely 

 different from the critical and adjacent phases, the liability to such 

 changes will in no respect affect the relations between the critical and 

 adjacent phases, and need not be considered in a theoretical discussion 



*See Dr. Andrews "On the continuity of the gaseous and liquid states of matter." 

 Phil Trans., vol. 159, p. 575. 



G. I. I 



