POLYMORPHIC TRANSFORMATIONS OF SOLIDS. 67 



It is to be noticed that either a horizontal or a vertical tangent 

 demands properties that are in a certain sense abnormal. At a hori- 

 zontal tangent, to the right of the point of tangency, the phase with 

 the smaller volume has the higher compressibility, and immediately 

 below a vertical tangent the phase stable at the higher temperature 

 has the smaller specific heat. We have examples for both these cases. 



We have seen that it is not possible in general to determine Aa, Aj8, 

 and ACp from the data of the transition curve alone. (By the transi- 

 tion data we mean the curve giving the relation between pressure and 

 temperature, and the values of AV and AH along this curve.) It is 

 important to notice, however, that if the three phases come together 

 to a triple point, we do have enough to determine Aa, A/3, and ACp 

 completely on each of the three transition lines. The reason for this 



. , dAv , dAH . , ^ P , , , , ,. 



IS that —1 — and — r — are mdependent ot each other on the three Imes, 



whereas Aa, A|3, and ACp are not. We have evidently Aq;i3 = Aq!i2 + 

 Aq:23 etc. That is, at a triple point there are only six unknowns to 



dAv 

 determine, and six equations, one involving —7— and another mvolving 



— 1 — on each transition line. The six equations are obvious from the 



above; we need not bother to write them down. This information is 

 most important. In the following the results of the calculations are 

 given for those substances whose phase diagrams contain triple points. 

 In the case of those substances which do not have a triple point it 

 has been possible in a good manj^ cases to obtain some evidence as to 

 the value of Aa from the difference of slopes of the isothermal jj-v lines 

 above and below the transition point, and so, with the equations above, 

 to calculate AjS and ACp. It must be emphasized that the values so 

 found are in many cases very inaccurate. I have, however, thought 

 it worth while to give them, because this is a matter about which 

 absolutely nothing seems to be kno\\Ti, and is obviously one of ex- 

 treme importance for the understanding of polymorphic forms. In 

 fact, even the sign of these quantities does not seem to be known at 

 present; we do not know (except perhaps in a few cases) which of two 

 polymorphic forms has the greater compressibility or thermal expan- 

 sion or specific heat. The values given in the following would fully 

 justify themselves if they should even give the sign correctly. 



