POLYIVIORPHIC TRANSFORMATIONS OF SOLIDS. 63 



practical conditions usually give us the total amount of impurity 

 present in the two phases together. The distribution problem is not 

 touched above; to solve it would require a knowledge of the heat and 

 volume effects of solution. 



The Equation of the Transition Lines. 



This equation has already been developed in a previous paper. ^ 

 The equation is 



(p - po) \Av + A^ (r - To) -i Aa (p - po)] - {Aso - ACp) (r - tq) 

 — ACp tIocj— = 



To 



For the slope of the line we find 



cIt Ai'o + A|3 (r — To) — Aa (p — po) 



dp 

 and for the second derivative 



Aso + ACp log A^{p — po) 



To 



"^^"^^Y-2A/3^ + Aa' 

 .dpj dp 



rfV _ _ ^^ dr 

 dp"^ Av dp 



The notation is as follows; A v is the difference of volume of the two 

 phases at the point po, tq of the transition line {Av = Vi — vo) ■ A|3 is 

 the difference of the thermal expansions. 



Aa is the difference of the compressibiHties considered as positive. 



''dvi\ fdi\ 



^dpjr \dp 



ACp is the difference of the specific heats (ACp = Cp^ — Cp), and A^o 

 is the difference of entropy between the two phases (A^o = AH/tq). 

 The equation presupposes that throughout the range of application 

 Aa, A/3, and ACp remain constant. 



In the preceding paper very little discussion was given of the shape 

 of the curve determined by the above equation, because the shape of 

 the melting curve is determined essentially by the variations with 

 pressure and temperature of Aa, A/3, and ACp. In particular, Aa 



