16 Messrs. Barrell, Thomas, and Young on the 



practically the same maximum value, viz. *45, the effect of 

 the varying richness of the fractions in regard to B being 

 merely to widen out or contract the B curve. 



III. a a, III, 8 "cd" III. eg represent the distillation of 

 those fractions of II. which are richest in A, B, and C 

 respectively, and give some indication of the processes going 

 on at the important stages of the third fractionation. In 

 these A rises from -7 to *82, B from *45 to *5, C from '9 to 

 *98. Here we notice that, owing to the small amount of C 

 present in III. aa (whose original composition is A '696, 

 B *239, and C '065), B attains a higher maximum (*525) than 

 it does ('496) in III. Bed, which is far richer in B originally 

 [A -182, B -44, C -378]. 



P represents a distillation at an advanced stage of the 

 fractionations — of a fraction rich in B. Its initial composi- 

 tion is A *02, B *96, C '02. B is only advanced from *96 to 

 *97 at the most favourable part of the curve, and is nowhere 

 very free from C ; this points to the difficulty of obtaining B 

 in a pure state by the ordinary method of fractionation. 



The calculations for III. 8 cd are appended as a specimen of 

 the system employed (see table opposite) : with the aid of the 

 slide-rule they are very quickly effected. 



Apart from the consideration of the above hypothesis and 

 formula^ it is clear that after five or six fractional distillations, 

 carried out in the ordinary manner (but with a larger number 

 of fractions than when only two substances are present), the 

 first fraction will contain a large excess of A, a little of B, 

 but very little, if any, of C ; the middle fraction will con- 

 tain an excess of B with moderate quantities of both A 

 and C ; the last fraction will consist almost entirely of C, the 

 quantity of A, if present at all, being much smaller than that 

 of B. 



Now let us suppose that these fractions are distilled sepa- 

 rately and completely. The first portion of the distillate 

 from the first fraction will consist of A in a nearly pure state, 

 and, even if it contains a little of B, will be free from C. Of 

 the middle fraction the middle portion (or probably a rather 

 later one) will be purest, but will contain a little of both A 

 and C. The purest part of the last fraction will be the last 

 portion (the residue in the still) and will be quite free from 

 A though it may contain a little of B. 



By proceeding with the fractionation in the usual manner 

 we could obtain A and in a pure state by separating each 

 time the first small portion of the first distillate and the 

 residue from the last distillate ; but we should have to carry 

 the fractionation a very great deal farther before we could 

 obtain B in a state of purity. We should, in fact, have to 



