THERMODYNAMIC PROPERTIES OF SUBSTANCES. 47 



We have seen that in the case 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 regard 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 substance initially in the 

 critical 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 requires that the 

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

 confined to the isentropic (adiabatic) line of the critical point upon 

 the primitive surface. It will be observed that there is no instability 

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

 section of the primitive surface perpendicular to the axis of rj) is con- 

 cave upward, as is evident from the fact that the primitive surface 

 lies entirely above the tangent plane for the critical point. 



We may suppose 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.e., of (-~) 



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 when expanded under 

 the circumstances remains in a state represented by the primitive 

 surface, which involves the realization of states of essential instability. 



/cZ 2 e\ 

 The value of (-r-) in the derived surface is. it will be observed, 



Vcfor/,, 



totally different from its value in the primitive surface, as the 

 curvature 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 (LI/ in figure 

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

 That vapor may also exist beyond the limit of absolute stability, i.e., 

 that it may exist at a given temperature at pressures greater than 

 that of equilibrium between the vapor and its liquid meeting in a 

 plane surface at that temperature, the considerations adduced by Sir 



