I32 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



Consider a mixture containing i kilogram of dry air, x kilograms 

 of the vapor of water, y kilograms of water and z kilograms of ice. 

 The sum x + y + z remains constant and we put 



x + y + z = £ 



Denoting by U" " the energy or specific heat of the ice and by L 

 the heat of fusion of the ice, we have 



U = U' + x U" + y U'" + z U"" 

 - U' + f U" + x (U" - U'") -z (U'" - U"") 



The temperature remaining constant, we have 



d U = (U" - U'") d x - (£/'" - U"") d z 

 We can neglect the volumes of the water and the ice and put 



V = x v" 

 p d V = (p - f) v" d x + / v" d x 



From the mechanical theory of heat we have approximately 



I = U" - U'" + A f v" 

 L = U'" - U"" 



By the aid of equation (i) we find 



= / d x - L d z + A (p - f) v" d x 



Introducing from equation (7) the value of p — f and observing that 

 at the temperature of zero we have 



e a 

 f v" = - 273 

 g 

 we shall find 



A a d x 



= Idx - Ldz + — 273 (8) 



g ^ 



At the commencement we have 



x = x , y = y , z = 

 and when all the water has disappeared (by congelation) we have 



x = x; ^ = 0; z = x + y — x 

 By integration and substituting / = 606.5 arR l L = 79-°6 we have 



log - = 1.822 7 - 15.80 (x - x ) (9) 



Xq 



