POLYMORPHISM AT HIGH PRESSURES. 183 



Another puzzling question is how we are to account for the phase at 

 the higher temperature having the smaller volume. The diagrams 

 above show how this may be. The localized centers of force are 

 situated on projections some distance from the center. At low^ tem- 

 peratures, when the energy of agitation is small, the molecules arrange 

 themselves in a form in Avhich the centers of force neutralize each other, 

 producing a crystal with large open framework. But with increased 

 temperature agitation, the forces at the apexes can no longer withstand 

 the disrupting efTect, and above a certain temperature the points are 

 shaken loose, and the molecules settle down to the arrangement of 

 smaller \olume. Evidently high pressure also tends to produce the 

 phase of smaller volume, so that at high pressure the temperature 

 need not be raised so high to shake the crystal into the phase of smaller 

 volimie. In other words, when the volume of the high temperature 

 phase is smaller, increased pressure lowers the transition point. 



In the summary of Table XIV we ha\'e found on falling transition 

 curves seven cases of abnormal compressibility, and only two of 

 normal. (By "abnormal" compressibility we mean that the phase of 

 larger Aolume is less compressible). The model of Figures 34 and 35 

 also suggests the reason for this. In general, two effects contribute 

 to the apparent compressibility of a substance; the actual change of 

 volume of the molecules under pressiu-e, and the closing up of the free 

 spaces which provide some of the possibility of temperature agitation. 

 Now e\idently in Figure 34 there can be ver^- little free space for 

 temperature agitation, because if the centers of the molecules are 

 separated by only a slight distance from the position of tight packing 

 a very small angular displacement suffices to carry the corners out of 

 register with each other, and the structure becomes unstable. In the 

 structure of Figure 35, however, much greater separation of the 

 centers from the position of actual contact is possible before a given 

 angular displacement carries the corners past each other. The phase 

 of smaller volume is more compressible, therefore, because in it there 

 is more free space from which the temperature agitation may be 

 excluded. One does not care to speculate much about the behavior 

 of the specific heats,- now that the theorem of equipartition is known 

 not to be valid, but it would seem in general as if the phase of smaller 

 volume would have the most freedom, and so the greater specific heat, 

 although it is conceivable that if the energy of temperature agitation 

 were chiefly energy of the nucleus, that the nucleus might have less 

 freedom at the smaller volume, and so the specific heat of the phase of 

 smaller volume be less. 



