been collected are represented as abscissæ, and the relative quantities of the two liquids A and B in the distillate at any moment as ordinates.

It will be seen that the composition of the distillate alters slowly at first, then more and more rapidly, also that while the first portion of the distillate contains a considerable amount of the less volatile substance B, the last portion is very nearly free from the lower-boiling component A. These points are fully confirmed by experiment.

By fractionating a few times in the ordinary way, collecting the distillates in six or eight fractions, we shall have a very large excess of A in the first fraction, and of B in the last.

Suppose now that we have two of these fractions, one containing A and B in the ratio of 9: 1, and the other in the

ratio of 1: 9, and that we distil these fractions separately and completely; the results will then be represented by figs. 2

and 3.

In making use of this formula it is assumed that no condensation (and therefore no fractionation) goes on in the still-head, but that the vapour reaches the condenser in the same state as when first evolved from the liquid in the still. It is obvious that by using a long still-head or a dephlegmator a more rapid separation would be effected.

In any case it is evident that after a sufficient number of fractionations, the first portion of the distillate from the first

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 distillation, 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 vapourpressure 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, n,

=

=

weights of the three liquids in the still at any instant;

.. de, dn, de weights of the three substances in the instantaneous distillate.

Let L, M, N be the original weights of the three liquids, and (L+M+N=1);

.. 1-x=+n+} = L22+1+M2+1+Nz;

aLa

bM2"

aLz^+bM2+cN; 2 = aLe+bM+cN

y is

The elimination of z from the expressions for a and impracticable, but the curves may be readily traced by treating z as an independent variable.

In the following curves (figs. 4 & 5) we have taken

a=4, b=2, c=1, [and .. λ=3, μ=1],

these being nearly proportional to the vapour-pressures of methyl, ethyl, and propyl acetates.

I. represents the first distillation; in it L=M=N=}. II. a, II. B, II. y, II. 8, II. e represent what would take place if the five fractions into which I. is divided were separately distilled; the composition of these fractions being found from the curves I. to be :

It is to be noted that in II. a, which is richest in the lowboiling liquid A, the amount of A rises from 543 to an initial value 74, and in the first half (or at least) of the distillate the aggregate amount of A rises to 7.

In II. e, which is richest in the high-boiling liquid C, the amount of C rises from 687 to about 9 in the last fifth, or 82 in the last two-fifths of the distillate; whereas in II. 8,

which is richest in B, the middle liquid, the amount of B rises merely from 39, its initial value, to about 45, its value for the fifth which is collected just after the first half (5 to 7). It is curious that in each of these distillations B rises to