178 BRIDGMAN. 



There is another interestuig point in connection with polymorphic 

 transitions at the absokite zero. If at the absolute zero a transition 

 runs irreversibly, in the metastable region, it is accompanied by 

 evolution of heat, according to the equation AH = {vi — v-y)^}^. This 

 is demanded by the law of the conservation of energy. The idea of 

 heat in finite quantities playing any essential or necessary part in 

 phenomena at absolute zero seems at first a little strange. It means 

 that in the mechanism of pol\'morphism there is something that 

 during the change converts potential into kinetic energy. 



At higher temperatures there is an interesting suggestion for the 

 quantum theory of solids in the fact that there are polymorphic phases 

 which are stable at the higher temperature, but have the lower specific 

 heat. That is, the modification of higher specific heat absorbs heat 

 and passes to a modification of lower Bpecific heat. If the total heat 

 (kinetic energy) content of either modification is equal to the heat 

 absorbed in warming from absolute zero {"^'jCpdr) then certainly the 

 specific heat curves of the two modifications cannot be of the same 

 character all the way down to the absolute zero, but one must cross 

 the other. Therefore the expression for the energy of the two phases 

 cannot be of a universal type, differing only by the numerical value 

 of a characteristic constant, as are the ordinary expressions of quan- 

 tum theory. This means that substances with polymorphs cannot be 

 treated like monatomic crystals, which is not surprising; but it also 

 means that the characteristic function of more complicated salts is a 

 function not only of the kinds of atoms, but also of their arrangement. 

 Of course we have applied considerations above to Cp which properly 

 apply only to Cv, but this can usually be done without sensible error. 



It is interesting to note in this connection that from the values which 

 we have given above for Aa, A/3, and ACp, we cannot calculate the 

 value of ACv. ACv cannot be obtained from the eciuation of the tran- 

 sition line and the difference of compressibility or Cp; to calculate it 

 we must know the absolute value of at least either the compressibility, 

 expansion, or Cp. 



The last part of this discussion is to be occupied with considerations 

 intended to make understandable how it is that there are polymorphic 

 changes, and that the phenomena are as complicated as we find them. 

 This will not be a theory of polymorphism in the proper sense of the 

 word. 



Brief mention should be first made of the recent theory of poly- 

 morphism of Smits *°. His theory is that any substance which shows 



40 A. Smits, Proc. Amst. Acad., numerous papers (1910-1915). 



