56 



Prof. R. A. Lehfeldt on the 



With regard to the other mixtures, alcohol with benzene 

 and toluene, the diagram shows the relations between log t and 

 log q to be very far from linear. I have not attempted to 

 find an equation to these curves, and will only make one or 

 two remarks as to their character. They are not drawn 

 directly from the experimental results on the composition of 

 the distillate, because when the percentage of alcohol is very 

 great or very small the observations lose considerably in 

 accuracy ; but on calculating the partial pressures, from the 

 observed composition of the vapour, and the total pressure, 

 smoothed curves could be drawn, the reliability of which is 

 enhanced by the fact that their end points (vapour-pressure 

 of the pure substances) are fixed. From these smoothed 

 curves of partial pressure the compositions were calculated 

 afresh, and it is the numbers so obtained that are represented 

 by the curves on fig. 4. The crosses on that figure stand 

 for the immediate results of observation, and it will be 

 noticed that they are regular enough in the middle parts of 

 the curves but not at the ends. 



At the maxima of vapour-pressure the composition of the 

 liquid and the vapour must be the same. That is shown, con- 

 sequently, by the intersection of the curves with the line 

 log g = \og t. The points of intersection form the most 

 reliable measure of the position of the maxima. They give 





log?. 



z. 



K- 



Alcohol-benzene 



Alcohol-toluene 



T-605 

 0170 



0-28-7 

 059-7 



0-406 

 0-74-7 



It will be seen that these results agree well with the 

 maxima shown in the vapour-pressure curves (fig. 2). 

 The differential equation referred to above is 



/ Bg s \l~ds 18^_ fl 



\Bq + A s + l/s -dg p~dq ' 

 or, as it may be written, 



, n d log s _ ;(! — £) dp 



For some purposes it is more convenient to express it in 

 terms of the partial pressures, when it assumes the more 

 symmetrical form adopted by Mar gules {loc. cit.) : 



„B]OgPA (1 



■)! 



d logy 

 3? 



'-=0. 



