62 BRIDGMAN. 



formula. Conversely, of course, the formula for the pressure shift 

 does not apply at a horizontal part of the transition line, where 



Vl — t'2 = 0. 



These formulas have been subjected to no restriction in the deriva- 

 tion except that the phase (1) is that in which the impurity is dissolved. 

 This might, if we liked, be the phase stable at the higher pressure or the 

 lower temperature, instead of as we have shown it. The formulas 

 show that in all cases the effect of impurity is to shift the transition 

 line into the region of the pure phase. For a given concentration of 

 the impurity, that is, for a given osmotic pressure, the displacement is 

 greatest for those substances with a small latent heat and a small 

 change of volume. These are much smaller for the solids investigated 

 here than for liquids, so that one would expect in general the displace- 

 ment of the transition lines to be greatest for the substances investi- 

 gated here. But as has been remarked, very few of these substances 

 contain dissolved impurities (form mixed crystals), so that most of the 

 transition lines are unaffected by what impurities there may be. 



If the impurity is soluble in both phases, we get for the pressure 

 shift 



^ ViApi — V2Ap2 • . 



Vi — ^2 



and for the temperature shift 



^^=-AH 



Ti Api — V2 Api 



This shows that if the total amount of impurity is slight, and if it is 

 so distributed between the two phases that Vi Ajh = % Ap2, then there 

 is no shift of the transition line. 



The phenomena in the neighborhood of a triple point offer no 

 particular difficulty. It may be shown directly by substitution that 

 the displaced transition lines must pass through a triple point as well 

 as the original lines, no matter what the relative amounts of impurity 

 dissolved in the three separate phases. This of course is what we 

 know must be the case from other considerations. 



It should be noticed that although these formulas are entirely valid 

 when the impurity is dissolved in more than one phase, nevertheless 

 the conditions under which they are derived are not always close to the 

 conditions of practise. We have assumed a knowledge of Api and 

 A;^. This demands that we know the way in which the impurity 

 is divided between the two phases. In practise this problem of the 

 distribution of the impurity must usually be solved first, since the 



