November 23, 1893J 



NATURE 



.93 



liilobite by Mr. W. D. Matthew, it has been possible, with the 

 new material supplied to the Yale Museum, to trace its develop- 

 ment back to the earlier stages. Larval specimens have been 

 found in which the thorax is undeveloped and the cephalon pre- 

 dominates, while the other parts are not clearly differentiated. 

 The larva is ovate in outline. The frontal ma'-gin is marked by 

 a convex fold of the test. The axis is annulaied. Near the 

 lateral anterior margins are two slight elevations which may 

 represent the palpebral lobes of the eyes. 



American Joitnial of Mathematics, vol. xv. No. 4. — On 

 toroidal functions, by A. B. Basset (pp. 287-302). The 

 theory of these functions was first investigated by Prof. W. M. 

 Ilicks, in his discussion of the motion of circular vortex rings 

 i/'/i//. Trans. 1881). The author considers that Prof. Hicks 

 jiresented the subject in a somewhat complicated form, and the 

 oi)ject of his own communication i^ to develop the subject, and 

 to correct errors which he attributes to Prof. Hicks. The 

 memoir appears to be on the lines of a communication Mr. 

 Basset made to the London Mathematical Society (April 13, 

 1S93'). — Simple groups as far as order 660, by F. N. Cole (pp. 

 303-315). This is a continuation of a paper in vol. xiv., in 

 which it was shown that the orders of simple groups between 

 the limits 200 and 500 are restricted to two possibilities, 360 and 

 432. Tn the present memoir the order 432 is shown to be inad- 

 missible, and the order 360 to furnish only one type of a simple 

 group. Two other simple groups are shown to present them- 

 selves, of orders 504 and 660 respectively. The order 504 

 '• seems hardly to have been recognised hitherto." It was a 

 singular fact, pointed out at the November meeting of the 

 London Mathematical Society, that this memoir anticipated 

 some results in Prof. W. Buniside's notes on the theory 

 of groups of finite order. The latter had evidently ar- 

 rived at his result quite independently of Dr. Cole. — On the 

 expansion of functions in infinite series, by W. H. Echols (pp. 

 316-320).— The elliptic inequalities in the lunar theory, by E. 

 W. Brown (pp. 321-338). This is. a resumption of the author's 

 paper from p. 263. — On the multiplication of semi-convergent 

 series, by F. Cajori (j p. 339-343)- The writer's object is to 

 extend results given by A. Voss, in the JMath. Aim. (vol. xxiv. 

 p. 44). — On certain ruled surfaces of the fourth order, by T. 

 F. Holijate (pp. 344-386). An introductory section is histori- 

 cal, and refers to previous memi)irs on the subject. The author 

 considers those species of the surface of the fourth order which 

 may be generated by two projective sheaves of planes of the 

 second order. These admit of a trinodal quartic section, and 

 are consequently of deficiency zero. The volume concludes 

 with a note on the so-called quotient G/H in the theory of 

 groups by Prof. Cayley, (pp 387-8), and the index of contents. 



SOCIETIES AND ACADEMIES. 



London. 



Physical Society, November 10. — Prof. A. W. Riicker, 

 F.R.S., President, in the chair. — A paper on the separation of 

 three liquids by fractional distillation, by Prof. F. R. Barrell, 

 G. L. Thomas, and Prof. Sydney Young, F.R.S., was read by 

 Prof. Young. Accepting the results obtained by F. D. Brown 

 in his experiments on the variation in the composition of the 

 distillate from a mixture of two liquids, viz. that the relative 

 quantities of the two substances in the vapour at any instant are 

 proportional to the weights of the substances in the still, multi- 

 plied by the ratio of their vapour pressures, the authors write 



Brown's equation in the form ' - = c^, where | and 77 are the 



weights of the two liquids in the still, and c the ratio of their 

 vapour pressures. Taking c as constant, the above equation is 

 integrated, and from the resulting expressions curves are plotted 

 showing the changes in composition that take place during the 

 distillation. Assuming that a similar law holds for three 



liquids, A, B, and C, viz. i -^ ^^I'^^l = 1 ''}>, the composi- 

 I a i, b f) c i 



ition of the distillate at any instant is calculated. Taking a = 

 i4, /■ = 2, and c = I (numbers nearly i^roportional to the vapour 

 'pressures of methyl, ethyl, and propyl acetates), numerous curves 

 jare plotted showing the progress of the separation at various 

 stages of fractionation. These curves show distinctly that 

 lahhough fractions containing large proportions of the liquids 



I NO. 1256, VOL. 49J 



A and C, of lowest and highest boiling points respectively, can 

 be easily separated, the middle substance, B, is much more 

 difficult to obtain in a state of purity. Consideration of these 

 curves led the authors to see that by carrying out the fraction- 

 ation in a particular way, it was possible to separate the mixture 

 into two portions, one containing only A and P., and the other 

 B and C. These mixtures of two liquids could then be frac- 

 tionated in the usual manner. Ttiis process was cirried out on 

 a mixture of methyl, ethyl, and propyl acetates, the results of 

 which are given in considerable detail in the paper. The 

 remarkable agreement between the densities of the ethyl acetates 

 obtained respectively from the mixtures A and B, and B and 

 C, as well as the fact that the densities of the separated liquids 

 were the same as before the mixing, show conclusively that the 

 method employed was highly successful. Prof. Ramsay said 

 the paper was a most valuable one, and would be a great aid to 

 chemists. Distillations were usually carried out by mere " rule- 

 of-thumb," with the result that absolutely pure liquids could 

 rarely be obtained. The President inquired whether curves 

 representing the progress of distillation could be constructe<l 

 from the very complete experiments made, and so test the 

 assumed law. Prof. Young thought this not possible from th-e 

 numbers obtained. To test the law in this way would be very 

 laborious. — A note on the generalisations of Van der Waals re- 

 garding " corresponding " temperatures, pressures, ani volumes, 

 was read by Prof. S. Young. In November 1891 the nuthor 

 read a paper on the same subject {Fhil. Mag. February 1892)^ 

 and gave the critical molecular voluines of some twelve sub,tances 

 as calculated by M. Mathias. Since then a few small errors 

 have been found in the calculation, and the authors' corrected 

 values are now given. The vapour pressures, molecular 

 volumes and critical constants of ten esters (methyl formate, 

 acetate, propionate, butyrate, and isobutyrate, ethyl formate, 

 acetate and propionate, and propyle formate and acetate) have 

 recently been detennined (Trans. Chem. Soc. Ixiii. p. 1191). In 

 the present paper the absolute temperatures and volumes of the 

 twelve substances are given in terms of their critical constants, 

 and tables given showing, respectively, the ratios of boiling points 

 (abs. temps.) at corresponding pressures, to absolute critical tem- 

 peratures; theratios of volumes of liquid at corresponding pres- 

 sures to the critical volumes, and ratios of volumes of saturaiei 

 vapours at corresponding pressures to critical volumes, for the 

 halogen derivatives of benzene, carbon tetrachloride, stannic 

 chloride, ether; methyl, ethyl, and propyl alcohols, and acetic 

 acid : and the extreme values for the ten esters previously men- 

 tioned. Whilst showing fair agreement with each other, the dif- 

 ferences between them exceed errors of experiment. The rati'is 

 also indicate that the substances can be arranged in four grou]is, 

 thus tending to show that molecular weight and chemical con- 

 stitution have some influence on the results. The differences 

 found would probably result from the presence of complex 

 molecules, such as are known to exist in acetic acid. If 



. P "^ 

 Van der Waals's generalisations were strictly true, the ratio 77, 



at the critical point should be constant for all substances, as 



also the ratio — ^ of the actual to the theoretical density (for a 



perfect gas) at the critical point. On comparing these quan- 

 tities only a rough approximation is found, but the grouping of 

 the compounds is again well marked. Prof Ramsay was not 

 sure that the existence of complexes would alter the molecular- 

 volume in the liquid state, for liquids seem very compact. 

 Experiments on the surface energy of liquids had proved that 

 complex molecules do exist in the alcohols and acetic acid. Dr. 

 Young's conclusions were therefore confirmed by experiments of 

 an entirely different nature. Prof. Herschel was gratified to 

 see Van der Waals's theory so well borne out in liquids, and 

 hoped to see it extended to solids. The recent researches of 

 Prof. Robert Austen on alloys seemed to point in this direction. 

 Mr. Rogers said molecular complexes do exert an influence on 

 the properties of substances, as had been shown by Prof. 

 Thorpe's viscosity experiments. Van der Waals's generalisa- 

 tions should therefore be looked at from a chemical as well as a 

 physical point of view. The President thought the numl)er 

 brought forward showed fair agreements, especially when it 

 was remembered that Van der Waals took no account of 

 complex molecules. Contrary to Prof. Ramsay, he would 

 rather expect aggregation to affect the molecular volumes in the 

 liquid state, for only about one- fifth the space was supposed to 

 be occupied by matter. On the other hand, the relatively 



