POLYMORPHIC TRANSFORMATIONS OF SOLIDS. 65 



he was not able to prove definitely that such was not the case. It is 

 interesting to bear in mind that this is at least a theoretical possi- 

 bility. For the present, then, we shall assume that Aa does not 

 remain constant over a wide enough range to allow curves with two 

 branches, and we shall consider only the nearer branch of the cur^'e 

 in the following. 



If the two phases have the same specific heats (ACp = 0) the equa- 

 tion becomes particularly simple, degenerating into a hyperbola. This 

 hyperbola has one vertical asvmptote and one inclined at an angle 



Aa . / * 



TTiri^- The hyperbolic form includes a number of types of behavior. 

 - '^P 



If Aa > 0, the curve may rise to a vertical asymptote, or may rise to a 

 maximum and fall to a vertical asymptote, or rise to a maximum and 

 fall to an inclined asymptote, or fall to a vertical asymptote, or fall 

 to a minimum and rise to a vertical asymptote, or fall to a minimum 

 and rise to an inclined asymptote. And if Aa<0, the curve may rise 

 to a vertical asymptote or rise to an inclined asymptote with con- 

 vexity either up or down, or may fall to a vertical asymptote, or may 

 fall to an inclined asymptote with convexity either up or down. Of 

 these cases, at least those with a vertical asymptote do not appear to 

 occur in practise. The hyperbola degenerates into one important 



special case. If ACp = 0, and Aa = 2A/3t^ the curve breaks up into 



two straight lines (we neglect the second line). Many of the transi- 

 tion lines actually found are nearly straight, so this condition is ap- 

 proximated to in practise. 



If now, in general, ACp 5^ 0, we see that the curve can ne\er have a 

 vertical asymptote. It may, howe^'er, have a vertical tangent, and 

 be double valued with respect to temperature, if ACp<0. This is a 

 case met in practise, benzol and ice for example. In general the 

 equation demands at high pressures either a maximum or a minimum, 

 or a curve with two branches. Since these are not actually of frequent 

 occurrence, the legitimate use of the equation must be restricted to a 

 comparatively narrow pressure range. We may perhaps say that very 

 roughly the usual type of the curve is one concave toward the pressure 

 axis, whether rising or falling. If the curvature is reversed, and there 

 are examples of this, it would imply in general either an exceptionally 

 large positive value of A/3, or a negative value of ACp. 



We discuss now the relations at a horizontal or vertical tangent. 

 W^e have seen in the previous paper that the transition data give us two 

 relations between Aa, A/3, and ACp. In general one other relation 



