of the TJiennodynamic Properties of Su/>stances. 397 



We liave seen tliat in tlie ca!^e of such substances as can pass con- 

 tinuously from the state of liquid to that of vapor, unless the primi- 

 tive surface is abruptly terminated and that in a line which passes 

 through the critical point, a part of it must represent states which are 

 essentially unstable (i. e., unstable in rei>ard to continuous changes,) 

 and therefore cannot exist permanently unless in very limited spaces. 

 It does not necessarily follow that such states cannot be realized at 

 all. It appears quite probable, that a sul)stance initially in the criti- 

 cal state may be allowed to expand so rapidly, that, the time being 

 too short for appreciable conduction of heat, it will pass into some of 

 these states of essential instability. No other result is possible on 

 the supposition of no transmission of heat, which recjuires that the 

 points representing the states of all the parts of the body shall be 

 confined to the isenti'opic (adiabatic) line of the critical point upon 

 the primitive siirface. It will be observed that there is no insta- 

 bility in regard to changes of state thus limited, for this line (the 

 plane section of the primitive surface perpendicular to the axis of //) 

 is concave upward, as is evident from the fact that the primitive sur- 

 face lies entirely above the tangent plane for the critical point. 



We may sup])Ose waves of compression and expansion to be propa- 

 gated in a substance initially in the critical state. The velocity of 



propagation will depend upon the value of ( , I , i.e., of — ( -y;; — I . 



Now for a wave of compression the value of these expressions is 

 determined by the form of the isentropic on the primitive surface. 

 If a wave of expansion has the same velocity approximately as one 

 of compression, it follows that the substance wiien expanded under 

 the circumstaiu-es remains in a state represented by the primitive sur- 

 face, Avhich involves the realization of states of essential instability. 



The value of (-7— -I in the derived surface is, it Avill be observed. 



\<iiy- hi ' 



totally difterent from its value in the primitive surface, as the curva- 

 ture of these surfaces at the critical point is different. 



The case is different in regard to the part of the surface between 

 the limit of absolute stability and the limit of essential instability. 

 Here, we have experimental knowledge of some of the states repre- 

 sented. In water, for example, it is well known that liquid states can 

 be realized beyond the limit of absolute stability, — both beyond the 

 part of the limit where vaporization usually commences (LL' in figure 

 2), and beyond the part where congelation usually commences (LL'"). 

 That vapor may also exist beyt)nd the limit of absolute stability, i. e.. 



