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.ee 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. 8 cd, which is far richer in B originally [A 182, B44, C 378].

P represents a distillation at an advanced stage of the fractionations-of a fraction rich in B. Its initial composition is A 02, B 96, C02. 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 formulæ, 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 contain 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 separately 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 C 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

Phil. Mag. S. 5. Vol. 37. No. 224. Jan. 1894.

C

reduce the quantitities of A and C in this fraction until they both disappeared from the middle portion of the distillate, and an idea of the difficulty of attaining such a result may be gathered from the diagram P.

With substances whose boiling-points are not very far apart the rise of temperature during such a distillation would be almost imperceptible, and in the fractionation it would be necessary to collect a large number of fractions above and below the true boiling-point of B with very small temperature-ranges. It would be necessary also to read the temperature with extreme care, and to make very accurate corrections for changes of the barometer (which would be impossible unless the vapour-pressures of the substance had previously been determined).

It has been pointed out, however, that after the mixture has been fractionated a few times, the first portion of the first distillate is free from C, while the residue from the last distillate is free from A. If, therefore, after the fifth or sixth fractionation we remove these first and last portions each time, we shall gradually accumulate two quantities of liquid, one (the first portions) containing only A and B, the other (the residues) only B and C, and these may be separately fractionated in the ordinary way.

It is to be noticed also that as a quantity of liquid is removed each time, the total amount to be distilled, and therefore the time required for the distillation, gradually diminishes.

In arranging the fractions—as regards temperature—it is advisable, if the true boiling-points of the liquids are known, to take these temperatures and also the middle temperatures between the boiling-points of A and B and of B and C as definite points, and to arrange the fractions as far as possible symmetrically about these points. There will thus be fractions of small and diminishing temperature-range above and below the boiling-point of B-and at the boiling-points of A and C after a few fractionations and until these substances are to a large extent eliminated-and fractions of large and increasing temperature-range above and below the two middle temperatures.

As the preliminary fractionation proceeds, more and more of A and C will be eliminated, so that after a time the boilingpoint of the first portion of the lowest fraction will gradually rise, while that of the residue from the last fraction will gradually fall until either A or C disappear, or, if we proceed still further, until we have nothing but B left. Much time

may therefore be saved if, instead of adding all the first portions of the lowest fractions together (and the same remark applies to the residues from the last fractions), we collect them in six or more different quantities. The final fractionations will then be in a forward state when the preliminary one is completed.

We shall in this manner obtain two quantities of B, one by the final fractionation of the first portions of the distillates from the lowest fractions of the preliminary fractionations, the other by that of the residues from the preliminary fractionations, and we can test the purity of the substance by comparing the boiling-points and the specific gravities of the two samples so obtained.

In order to test the value of this method, a mixture of 200 cub. cent. of methyl acetate (B.P. 57·1), 250 cub. cent. of ethyl acetate (B.P. 77·15), and 200 cub. cent. of propyl acetate (B.P. 101.55) was distilled from a flask provided with a still-head one metre in length. The distillate was collected in four approximately equal fractions, numbered 5, 8, 11, and 14 under F in the table (I.) below. The observed temperatures (reduced to 760 millim.), the range of temperature for each fraction (At), the weight of each fraction (Aw), and the ratio of the weight to the temperature-range

(Aw)

are also given in the tables. The second fractionation At (II.) was carried out in the following manner:-the first fraction from I. (No. 5, B. P. 63°8 to 71°3) was distilled and the distillate collected in a separate receiver (No. 4) until the temperature rose to 63°8 †, when receiver No. 5 was substituted for it and the distillation continued until the temperature rose to 71°.0. The gas was then turned out, and the second fraction from I. (No. 8, B. P. 71°3 to 77°-8) added to the residue in the flask. Heat was again applied and the

* The esters had previously been purified with great care, and were distilled separately from phosphorus pentoxide immediately before being mixed. Special precautions were also taken to avoid absorption of moisture during the fractionations. The methods of preparation and purification and proofs of the purity of the esters are fully described in the Trans. Chem. Soc. lxiii. p. 1194.

dp
dt

The actual temperature was 630-5, the barometric pressure being 751.1 millim.; the value of at the boiling-point is 27 millim. per degree for methyl acetate, 25 millim. for ethyl acetate, and 23 millim. for propyl acetate. All the temperatures are corrected to 760 millim. by means of these constants.