Mr. J. C. Glashan on Fractional Distillation. 275 



Formula (V.) shows distinctly that for p r nearly = 1 the 

 strength of the distillate is approximately proportional to that of 

 the mother-liquor for the same fraction of A distilled (observed 

 by Mr. Wanklyn). If r >1 or B volatile compared with A, for- 

 mula (IV.) shows that, with repeated distillations of the early- 

 passing-over distillate, the B strength of the distillate will 

 rapidly increase with the number of distillations, and formula 

 ("VI.) shows that, to a rude approximation, the rate of increase 

 is in geometrical progression. 



It has been assumed that the distillation is pure, i. e. that the 

 vapour does not carry over any liquor held in mechanical sus- 

 pension ; for in this case the coadhesive function of the liquids 

 will influence the result. Further, it is supposed that the whole 

 distillate has been separated from the still-liquor and, if it is 

 used, collected. This requires that no part of the distillate 

 (especially at the beginning) condenses on the sides of the still, 

 in time returning to the still-liquor. The following formulae 

 afford a test of the accuracy of the experiment (assuming the 

 theory to be true), and also a means of correctly calculating r, 

 even with a common still properly protected, although the 

 second of the above-mentioned difficulties tends to vitiate early- 

 made observations or those continuous from the beginning. 



1st still-liquor, a + b, (VII.) 



2nd „ „ ap + bp% (VIII.) 



3rd „ „ {ap)q+(bpr)q* (IX.) 



1st distillate from (VII.), 



a(l-p)+b(l-f), (X.) 



1st distillate from (VIII.), 



ap{l-q)+bf(l-cf) (XL) 



Let r be calculated from (X.) and (VII.), (VIII.) is determined 

 by observation for (X.) ; thus r may also be calculated from 

 (XI.) and (VIII.) . The latter value of r will be the more reli- 

 able if the elements of (X.) be accurately observed. The distil- 

 lation is supposed to be continuous. The value of r may also 

 be calculated very accurately from (II.), obtained, from (I.) by 

 evaporation under the air-pump. 



For simplicity of formulas I have assumed the mixture to be 

 homogeneous and to remain so throughout the operation ; but 

 the instant evaporation commences this condition is violated. 

 Thus in the deduction of the formulas through Mr. Wanklyir's 

 theory, the process is true only for the first infinitesimal distil- 

 lation, and all subsequent distillations will involve a function of 



T2 



