176 BRIDGMAN. 



ence of crystals. It is easy to prove that if Neumann's law holds, that 

 is, if all the other physical properties possess all the elements of sym- 

 metry of the crystalline form, then a uniform hydrostatic pressure or a 

 uniform change of temperature cannot so change the dimensions of 

 the crystal as to alter its crystalline system. The existence of a 

 critical point is not compatible with Neumann's law. If Neumann's 

 law expresses some fundamental fact of crystal structure, as it probably 

 does, then we are morally certain that a critical point does not exist, 

 and if a critical point should be discoyered, this alone would be suffi- 

 cient to dethrone Neumann's law from a position of yitally funda- 

 mental importance. 



There is another possibility. Instead of suddenly stopping at a 

 critical point, where the volumes of the two phases become equal, the 

 transition line might suddenly stop at a point where the volumes were 

 different, and spread out into a fan shaped region occupied by a con- 



FiGTJRE 33. Showing a conceivable degeneration of a transition line into a 

 region of mixed crystals. 



tinuous series of mixed crystals of the two phases as shown in Figure 33. 

 But although this sort of thing is possible thermodynamically, such a 

 phenomenon would be even more foreign to our experience than a 

 critical point, and in all probability does not exist. Such an effect 

 would be detected experimentally by a continuous change of volume 

 throughout the shaded region. Never in any of my work have I 

 found anything to suggest such an effect. 



It is interesting to inquire whether the theory of solids derived 

 from quantum hypothesis has any restrictions to impose on the 

 shape of the transition lines. The quantum hypothesis when applied 

 to solids demands that in the neighborhood of the absolute zero Cv 

 and the thermal expansion are proportional to the third power of the 

 temperature, and that the compressibility is constant. That is, 



^) = a, ( ) = 0T^, and Cv = 77^, where a, /S, and 7 are con- 



dpjr \OT/p 



