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



liquid A of volatility w, and b units of a liquid B of volatility v. 

 Distil till there remains a t -\- fy, giving a distillate {a—a t ) -f {b—b t ); 

 then b=(a l :a) v:u '; or putting p for # y : a, and r for v : w, we 

 have the very simple formulae: 



1st still-liquor, a-' r b, (I.) 



2nd „ } , ap + bp r , (II.) 



Distillate, a (l-p) + b(l-p'), . . . (III.) 

 (Distillate)*, a(l—p) n + b(l— p r )\ . . (IV.) 



(Distillate)" means that it is the distillate of (distillate)"" 1 . 

 Solutions of (III.) "and (IV.) of 1 degree of approximation are 

 * ( a + ftr)(l^p), (V.) 



{a + br n ){l-p) n . ...... (VI.) 



As stated above, these formulae may be obtained by Mr. 

 Wanklyn/s theory. Thus, ratio of liquids in original liquor, 



a : b ; « 



in first infinitesimal distillate, 



da : br — : 

 a 



in remaining liquor, 



da\ T /.. da' 



(i-i)-i^-i> 



Continue distillation to the separation of n distillates. Ratio of 

 remaining liquor, 



This for a finite distillation, or n infinitely large, becomes 



for limit ll—r — j = limit f 1— — j , and, by definition of p, 



Mr. WanMyn uses (V.) and obtains r^9'6 for ammonia 

 (water =1); but from consideration of the composition of the re- 

 maining (or rather last distilling) liquor he concludes r>13< 14. 

 The correct value as found from (III.) is 



