HETEROGENEOUS EQUILIBRIUM 249 



per cent, the other of only one per cent. At the first boiling 

 point, addition of heat causes the solution to evaporate, liquid 

 changing into solid and vapor. At the boiling point at higher 

 temperature, called by Roozeboom, who discovered it, the 

 second boiling point, the solution boils on cooling. At the 

 second boiling point, the liquid changes into solid and vapor 

 with evolution of heat. If a melt of KNO3, saturated at its 

 melting point with water, be quickly cooled, it will be seen to 

 boil suddenly and violently, and at the same time to solidify. 

 This second boiling point has been observed in many systems,* 

 including silicate systems at high temperatures, and the phe- 

 nomenon has been made the basis of a theory of volcanism,t 

 which has been applied successfully to the activity of Mt. 

 Lassen, California.! 



10. The Equilibrium, Ice + Solution + Vapor. Of the four 

 univariant equilibria which proceed from the invariant point 

 we have considered but one, namely, the univariant equilib- 

 rium, solid KNO3 + solution + vapor. The univariant 

 equilibrium, ice + solution + vapor, is a second one in which 

 we have both liquid and vapor, and in this case solid and vapor 

 have the same composition. Our equation (8) becomes 



^V _^ /ytl 



X' — x' 

 and, since x^ = x* = 0, 



dp ^ ^^' - ''^ - ^^ ^^' - ^'^ ^ r - v' ^ 



dt , ,, - a;' ,x 2^" - v"' 



(y* — y') — ; (V — y') 



U — X 



But this equation refers to the vapor-pressure curve of ice; all 

 terms relating to the liquid have disappeared. This is a general 



* H. W. Bakhuis Roozeboom, Proc. Z2o?/. (Soc. Amsterdam, 4,371(1901). 

 t G. W. Morey, J. Wash. Acad. Sci., 12, 219 (1922). 

 t A. L. Day and E. T. Allen, Carnegie Inst. Wash., Publ. No. 360 

 (1925). A. L. Day, /. Franklin Inst., 200, 161 (1925). 



