It was pointed out in the earlier paper on this subject (Phil. Mag. xxxiii. p. 172) that the compounds investigated might be arranged in groups, and this is confirmed by the method of comparison now adopted. The twenty-two compounds appear to fall into four chief groups : I. Benzene and its halogen derivatives, carbon tetrachloride, stannic chloride, ether. II. The three alcohols (methyl alcohol differing, however, considerably from the others). III. Acetic acid. IV. The ten esters. Ratios of Absolute Temperatures at Corresponding Pressures to Absolute Critical Temperatures.-The ratios for the compounds in groups I. are the lowest; those for the esters are mostly higher; acetic acid comes next in order; whilst the values for the alcohols are much higher than for any of the other substances. In the first group the differences are not great, but the ratios for benzene and carbon tetrachloride are below, and those for stannic chloride and ether at low pressures are somewhat above the average. The influence of molecular weight and constitution on the ratios for the esters is fully discussed in the paper by Mr. Thomas and myself (Trans. Chem. Soc. lxiii. p. 1252), and it will be sufficient here to mention that there is a marked rise as the molecular weight increases. This is not the case, however, with the ratios of the volumes of liquid or of saturated vapour to the critical volumes. All the ratios appear to depend to some extent on the constitution of the esters. Ratios of Volumes of Liquid at Corresponding Pressures to Critical Volumes.-The differences in this case are small; in general the ratios for acetic acid are the highest, and those for the esters the lowest. At the lowest pressures the values for the alcohols are higher than for the esters, but at high pressures they are lower than for any of the other substances, and this is especially the case with methyl alcohol. Ratios of Volumes of Saturated Vapour at Corresponding Pressures to Critical Volumes.-The grouping of the compounds is well seen in this case, the differences being naturally most marked at low pressures. Acetic acid stands quite alone with the lowest ratios, whilst the alcohols, and especially methyl alcohol, have much higher ratios than the other compounds. Of the remaining substances the esters have higher values than the members of the first group. There is little doubt that the low ratios for acetic acid are due to the existence of complex molecules in the saturated Temperatures, Pressures, and Volumes. 7 vapour at low temperatures. The densities of the saturated vapours of the alcohols, on the other hand, are normal at low temperatures, and complex molecules cannot, therefore, be present; but there is considerable evidence of their existence in the liquid state. Ramsay and Shields (Phil. Trans. 184 A. p. 647; Trans. Chem. Soc. lxiii. p. 1089) have recently studied the surfaceenergy of a large number of compounds, and have described a method by which the molecular complexity of liquids may be ascertained. They show that most of the liquids investigated have the same molecular weight in the liquid as in the gaseous state, but that there is greater molecular complexity in the liquid state in the case of the fatty acids and alcohols. As regards homologous compounds-both acids and alcohols the complexity diminishes with rise of molecular weight, and as regards individual compounds it diminishes with rise of temperature; in order of complexity methyl alcohol comes next to acetic acid. These conclusions, based on totally different considerations, agree perfectly with those suggested in this paper and in the previous one on the same subject. An explanation of the relatively high molecular volumes of the saturated vapour of the alcohols at low temperatures would be afforded by the assumption that complex molecules exist to some extent at the critical points, an assumption which is supported by the high critical densities. It has been shown (Phil. Mag. Nov. 1890, p. 423) that if the generalizations of Van der Waals were strictly true, the following relation should be true for all substances : where v and v' are the molecular volumes of saturated vapour, V and V' those of liquid, and T and T the boiling-points on the absolute scale of temperature of any two substances at corresponding pressures p and p'. This relation should hold good at the critical point, or PV where P, V, and T are the critical pressure, the critical molecular volume, and the absolute critical temperature of any substance. As the critical volumes are now known, it is possible to test this relation at the critical points of the various comPV pounds, and the values of T are given in the table below. Again, the ratios of the actual to the theoretical density (for a perfect gas) at the critical point should be the same for all substances if Van der Waals's generalizations were strictly true: these ratios are also given in the table under D the heading Substance. Fluorbenzene D' 16270 3.80 Here, again, the grouping of the compounds is well marked acetic acid has by far the lowest value of (and PV T the highest density ratio); the alcohols come next in order, the values for methyl alcohol standing about midway between those for the other alcohols and acetic acid; the esters PV agree well together, the values of being in every case T lower than for the members of the first group. II. On the Separation of Three Liquids by Fractional Distillation. By Professor F. R. BARRELL, M.A., B.Sc., G. L. THOMAS, B.Sc., and Professor SYDNEY YOUNG, D.Sc., F.R.S., University College, Bristol*. IT Tis well known that the separation by fractional distillation of two substances which are miscible in all proportions and which do not-like propyl alcohol and water or formic acid and water-form mixtures of constant boiling-point, is usually a simple matter if there is a considerable difference in their boiling-points. The facility with which the separation can be effected depends, in fact, chiefly on this difference. Communicated by the Physical Society: read November 10, 1893. When, however, we have to deal with a mixture of three substances, the difficulty is greatly enhanced, and if the boiling-points are not far apart it may be almost, if not quite impossible to separate any quantity of the middle substance in a state of purity by the ordinary methods of fractional distillation. The variation in the composition of the distillate from a mixture of two substances, the boiling-point of which rises constantly during the distillation, has been carefully investigated by F. D. Brown (Trans. Chem. Soc. 1879, p. 550; 1880, pp. 49 & 304; 1881, p. 517)*; and his results may be briefly stated as follows:-Calling the relative weights of the two liquids at any instant in the still W, and W2, the relative weights at the same moment in the vapour (and therefore in the distillate at this instant coming over from the mixture W1+ W2) 1 and 2, and the vapour-pressures of the pure substances at the boiling-point of the mixture, P1 and P2, the composition of the instantaneous distillate is given approximately by the equation X1 W1 P1 = X2 2 but by substituting a constant, c, for the ratio *For an account of the experimental work and of the theoretical conclusions relating to the distillation of pairs of liquid that are (a) nonmiscible, (b) miscible within limits, (c) miscible in all proportions, the article by one of us on "Distillation" in Thorpe's 'Dictionary of Applied Chemistry' may be consulted. Pairs of liquids belonging to the first and second classes boil at a lower temperature than even the more volatile component when distilled alone, and no separation can be effected by fractional distillation. Among those in the third class there are some from which only one of the two substances can be so separated; in each case of this kind there is a particular mixture (the composition of which varies to some extent with the pressure) which distils at a constant temperature without change of composition, and it is this mixture that would be separated by fractional distillation from that one of the pure substances which is present in excess. In some cases-such as propyl alcohol and water—the mixture of constant boiling-point and composition boils at a lower temperature than either of the liquids when distilled alone; in other cases-for example, formic acid and water-this mixture has a higher boiling-point than either component. It is only when the boiling-point of every possible mixture lies between those of the components that both liquids can be separated by fractional distillation; it is only to such cases that Brown's law is applicable, and, in the case of three liquids, it is only such mixtures that are considered in this paper. The ratio P1 P 2 would, of course, vary to some extent during the distillation; the value of the constant, c, does not differ greatly from the mean value of the ratio P1 This equation of Brown's may be written in the form Taking L and M as the weights of A and B originally present, and L+M=1, we obtain by integration M Ly{c+(1—c)y}°~'=c°(1—x)^ ̄'(1—y)°, where y quantity of the more volatile liquid A in unit weight of the distillate coming over at the instant when x is the quantity of liquid distilled. By means of this equation we may trace the changes of composition that take place in the course of a distillation, and the variation in the composition of the distillate may be represented graphically. To take a very simple case, let us suppose that c=2, and that L=M=. In the diagram (fig. 1) the amounts of distillate that have |