172 BRroCMAN. 



adjoins a known form, four are cases in which the trigonal form 

 adjoins another either of smaller volume and lower symmetry', or 

 larger volume and higher symmetr;s'. The general rule seems to be 

 the reverse of what we would expect, the phase of higher symmetry 

 in the majority of cases has the larger volume. 



In this connection it is also interesting to note that there are several 

 cases in which the same crystalline system occurs in more than one 

 phase of the same substance. NH4NO3 has two tetragonal forms 

 (possibly these are identical), RbNOs has two trigonal forms, probably 

 KHSO4 two rhombic, and of course NH4I, NHjBr, and NH4CI are a 

 striking series in which the different modifications belong to the same 

 sub-group. This shows that there is no restriction placed on the 

 total number of possible polymorphic forms of any one substance by 

 considerations of this character. As far as this goes, we might have 

 more than 32 modifications. 



It would seem that in our present state of knowledge the specifica- 

 tion of the crystalline system of different polymorphs is without special 

 significance, but is of value chiefly as a means of identification. And 

 probably when we are able to give a more detailed description of the 

 structure, specification of the crystalline system will be superfluous. 



We now turn from crystallographical considerations, and discuss 

 the general thermodynamic aspects of the phase diagrams. The enor- 

 mous complexity of the phase diagrams of solids as contrasted with the 

 melting diagrams is apparent. There are only two known melting 

 curves that fall in temperature with rising pressure, those of water 

 and bismuth; all others rise. The rising melting curves rise indefi- 

 nitely, with no suggestion of a maximum or a critical point. All the 

 melting curves, whether rising or falling, are concave toward the 

 pressure axis. On every one of the curves Av decreases with rising 

 temperature, and on every curve where accurate enough measurements 

 can be made, the curve plotting Av against pressure is convex toward 

 the pressure axis. Furthermore, the liquid is universally more com- 

 pressible, and of a higher specific heat than the solid, and only one case 

 is known in which the liquid has a smaller thermal expansion, that of 

 water over a restricted range. 



None of these uniformities hold for polymorphic changes. Retro- 

 gressive transition lines are of fairly common occurrence. Wallerant 

 makes the statement in his Cristallographie that there are only four 

 known transitions of this type; Agl, NH4NO3, Boracite, and Calcium 

 Chloraluminate. In all, sixteen such transitions have been examined 

 above, fourteen of them not known to Wallerant. It appears, then. 



