186 BRIDGMAN. 



spaces are to be thouj:jht of as playing an essential part in the phenom- 

 ena of polymorphism. In the face of such changes as that from ice 

 I to III with a change of volume of 17% and NH4C'l, I to II, with a 

 change of volume of 15%, it is most difficult to resist the conviction 

 that there are empty spaces of relatively large size and that they are 

 essentially concerned in polymorphic changes. Facts like these I 

 find it most difficult to reconcile with Professor T. W. Richards' 

 point of view that in a solid or a liquid nearly all the available space is 

 completely filled by the atoms, and that the changes of volume pro- 

 duced by pressure or changes of temperature are the result of changes 

 of volume of the atoms themselves. That the atoms are compressible, 

 and that the compressibility enters essentially into many phenomena 

 there can be no question, but it seems to me just as un([uestionable 

 that there must be vacant spaces aroimd the corners which also play 

 an important part in many phenomena, including preeminently the 

 phenomena of polymorphism. The difficulty of Professor Richards' 

 view seems to me increased by the fact that in many cases the phase of 

 smaller volume is the more comi)ressible. 



These suggestions are no more than very rough indications of what 

 may be the nature of the effects. The actual molecules are three 

 dimensional instead of two; this alone will cause profound differences 

 in the way in which a uniformly filled space can be built up from uni- 

 form elements. Furthermore, the elements in the diagrams ha\'e l)een 

 chosen so simply that the crystalline framework of both polymorphs is 

 the same, whereas only in isolated cases is tliis true in nature. It is 

 of interest, however, that we have here a suggestion as to why it is 

 that different phases may belong to the same system. We have also 

 considered only one kind of element, whereas the majoritv of crystals 

 are built up from tlifferent kinds of atoms. This alone will allow possi- 

 bilities of enormously greater complications. The actual shape of the 

 molecules are probably much more complicated and not so exaggerated 

 as those shown above, and there must be a greater multiplicity of 

 arrangements in which they can be piled. But the diagrams do illus- 

 trate the fertility of the fundamental idea; that by ascribing to the 

 molecules definite shapes as well as localized centers of force, systems 

 may be built up which show many of the complications of actual poly- 

 morphic forms. 



The bewildering complexity shown by various polymorphic transi- 

 tion throws light on a group of phenomena of another kind. In a 

 previous paper (G), I have described the eft'ect of high pressure on the 

 thermodynamic properties of a number of liquids. It appeared that 



