56 BRIDGMAN. 



range of this paper is from 0° to 200°, and from 1 to 12000 kgm. The 

 measurements to be given here must be regarded as only the beginning 

 of an attack on an immense field. The most important immediate 

 task would seem to be the collection of a large mass of data, so that 

 we may become familiar with the general types of phenomena. About 

 the only discussion that can be attempted is a thermodynamic one, 

 and even from this narrow point of view the measurements are not 

 sufficient to completely determine the behavior of the several phases. 

 We can go only a little way toward the solution of the general problem, 

 which is to predict from the properties of any one phase when to expect 

 new polymorphic phases, and what their properties will be. We may 

 perhaps expect more definite results when methods such as are used 

 here are taken in conjunction with recent X-ray methods for determin- 

 ing crystal structure. 



Thermodynamically, the transition between two solids is charac- 

 terized by the same elements as determine the melting and the vapori- 

 zation curves, and from this point of view the discussion of previous 

 papers ^ is applicable. As a matter of fact, however, the character 

 of the solid-solid curves may vary much more widely than that of 

 the melting or vaporization curves. For instance, all vaporization or 

 melting curves, absolutely without exception, either rise or fall over 

 their entire length, while solid-solid curves may have either a maxi- 

 mum temperature or pressure. In the previous discussion it was not 

 necessary, therefore, to consider certain special relations between the 

 thermodynamic constants at the maximum points, but now these 

 relations become of importance. A discussion of these is given in the 

 following. Another matter that needs reconsideration is that of 

 the effect of impurities at a point of maximum pressure. Evidently 

 the usual statement of the effect of impurity as causing a displaced 

 temperature of equilibrium will not serve here. In the following are 

 given the slight modifications necessary in the usual discussion to find 

 the pressure shift of the equilibrium line. 



It has been possible to give a much more thorough investigation of 

 the difference of compressibility, thermal expansion, and specific heat 

 between the several phases than was possible in the case of melting. 

 The reason for this is the much greater relial)ility of the experimental 

 measurements of the difference of compressibility between the separate 

 phases, because, except in those cases where the impurity forms mixed 

 crystals, there is absolutely no rounding of the corners of the volume- 



1 P. W. Bridgman, Phys. Rev. 3, 126-203 (1914), and 6, 1-33 (1915). 



