Distillation of Binary Mixtures. 527 



of alcohol by weight has a minimum boiling-point, and ac- 

 cordingly distils without change. It may be noted that the 

 curve given by Konowalow himself would point to the 

 contrary conclusion. 



In the practical conduct of distillation it is the pressure 

 that is constant rather than the temperature. Inasmuch, 

 however, as pressure always rises with temperature, a maxi- 

 mum or minimum pressure when temperature is given 

 necessarily corresponds with a minimum or maximum tem- 

 perature when pressure is given. In the case of a solution 

 of hydrochloric acid, for example, the thermometer marks a 

 maximum temperature at the point where the solution distills 

 without chancre. 



Calculation of Residue. 



Before proceeding to the experimental part of this paper 

 it may be well to explain further the significance of the 

 curves exhibiting the relative compositions of liquid and 

 vapour. If iv represent the whole quantity (weight) of 

 liquid, say alcohol and water, remaining in the retort at any 

 time, y the quantity of one ingredient (alcohol), the abscissa 

 f of the curve is y/iv. As the distillation proceeds for a short 

 time w becomes w + div, and y becomes y + dy*\ and the 

 composition of the vapour, that is the ordinate rj of the 

 diagram, is dy/dw. Thus 



Z=y! w , y = dy/dw, 



while the functional relation between £ and t) is given by the 

 curve, and may be analytically expressed by ?? =/(£). Thus 



dw J ™> 

 whence 



w f* dS 



^'05 £o being corresponding values of w and £. 



When f is small the curve is often approximately straight. 

 If we set /(f) = a;£ we find 



e/e.-w-O'- 1 - 



For example, in the case of alcohol and water, we have for 

 very weak mixtures >? = 12f approximately, so that # = 12. 

 As the distillation proceeds, id diminishes and f soon becomes 

 exceedingly small. The halving of iv implies a diminution 



* die and dy being negative. 



log 



