64 BRIDGMAN. 



varies greatly over the pressure range of 12000 kgm. But in the case 

 of the solids to be studied here, it seems reasonable to assume a con- 

 siderably better approach to constancy of the three differences. For 

 instance, the compressibility of a liquid such as water has decreased 

 to I its initial value at 12000 kgm., whereas the compressibility of 

 steel does not vary more than a fraction of one per cent over the 

 same range. Steel is of course an extreme case, and the difference of 

 compressibility may change much more than the compressil)ility, 

 but in any event we would seem to be justified in presuming that Aoc 

 for two solids is more constant than for a solid and a liquid. A dis- 

 cussion of the above equation is of more \'alue here, therefore, than in 

 the case of the melting curves. It will not pay to completely discuss 

 all possible combinations of the constants. We will, however, show 

 that the curve may take a great variety of shapes according to the 

 relations between the constants, and that some of these shapes do not 

 seem to exist in practise. We infer, therefore, that in practise the con- 

 stants flo not assume all possible relations to each other; it will be our 

 problem in the latter part of this paper to determine these constants,, 

 and find within what relative range they are actually restricted. 



We notice in the first place that if Aa > 0, that is, if the high tempera- 

 ture phase is more compressible, as it is in many cases, that the curve 

 crosses the pressure axis twice. For we obtain immediately on put- 



2 Ac- 

 ting T = To that p — po = "T — • This means that when the pressure 



has been increased sufRciently to squeeze the high temperature phase 

 into a volimie as much smaller than the low temperature phase as it 

 was originally larger, the two phases can coexist again in equilil)rium. 

 This in itself indicates a rather unusual state of affairs; the only 

 example found so far is //f/Zi- But the equation furthermore indicates 

 that the curve may under proper conditions break up into two curves, 

 the second pressure just found lying on the second curve. This would 

 mean that the same phase may exist in two isolated regions of the 

 phase diagram, the two regions of stability being separated by the 

 region of stability of the second phase. Such cases, if they occur at 

 all in practise, are extremely rare; the only suggestion of such a thing 

 of which I know is concerning the modification of XHiNOs stable 

 below —16°, made by Wallerant.^ This however has not been 

 ^•erified in a more recent very careful investigation by Behn,^ although 



2 F. Wallerant, Bull. soc. fr. min. 133-374 (1905). 



3 U. Behn, Proc. Roy. Soc. 80, 444-4.57 (1907-08). 



