12 Messrs. Barrell, Thomas, and Young on the 



fraction will be free from B, while the residue from the last 

 fraction will be free from A. 



Suppose now that our mixture contains a third substance, 

 C, the boiling-point of which is higher than that of B. 



It may be conjectured that in the progress of the distilla- 

 tion, the composition of the distillate at any instant will be 

 analogous to that determined experimentally by Brown in the 

 case of two liquids : namely, " the proportion of the three 

 substances in the vapour forming the instantaneous distillate 

 is the same as that of the weights of the three substances in 

 the residue in the still, each weight being multiplied by a 

 suitable constant which is roughly proportional to the vapour- 

 pressure of the corresponding liquid." 



With this assumption it is easy, as in the case of two liquids, 

 to calculate curves representing graphically the progress of 

 the distillation. 



Let f, w, f 5=5 weights of the three liquids in the still at 

 any instant ; 



.*. dl; j dv, d£ = weights of the three substances in the 

 instantaneous distillate. 



By hypothesis, 



d£ _drj _ dt, 



a% ~ on ~~ c£* 

 Integrate 



- log £ == 7 log 7j + k = - log f + k 1 . 



Let L, M, N be the original weights of the three liquids, 

 and (L + M + N=l); 



.-. ilogL = rlogM + * = -logN + *'. 

 a b ° c 



Subtract 



■■■&-(&-(&■ 



Let 



y x = weight of A 1 in unit weight of distillate 

 y 2 = }J B > coming over when x= weight 



t/ 3 = „ C J of liquid distilled ; 



