rooms which are most suitable for gas laboratories. The jar is therefore best charged by means of the simple and effectual arrangement represented in fig. 32. "It consists merely of a large porcelain tube, which, when held before the iron wire of the cylinder and rubbed with silk and amalgam*, evolves so much electricity that the jar is charged in a few seconds." One great advantage of Bunsen's mode of treating the subjects is, that he illustrates by numerous examples, and enters fully into the best and shortest modes of calculating the results. A considerable portion of the volume is devoted to the description of the methods required to meet special cases of gaseous analysis, the whole being copiously illustrated by examples, and even the most minute precautions being detailed. Much new and interesting matter of the highest value is contained in the portion treating of the "manipulation in the absorption of gases;" and having described the order of the processes, the author proceeds to develope a general formula, enabling the operator to calculate the relative volumes of the constituents of a mixture of known gases. The chapter on the specific gravities of gases strongly shows the neatness and ingenuity of the author as an operator. This is well seen in his illustration of the determination of the density of gaseous bromide of methyle, made with a flask of only 44 cubic centimetres capacity. Notwithstanding the small volume, the experiment gave 3.253, theory requiring 3.224. In addition to methods involving the necessity for weighings, he uses effusion as a mode of determining the densities of gases where only small quantities are at the operator's disposal. The gas effuses through a minute aperture in a thin platinum plate attached to an apparatus resembling an inverted Mohr's burette with a glass stopcock. The observations of time are made with a pendulum vibrating half-seconds. The contrivance by means of which the times of effusion of the gases are determined, and warning is given of the approach of the termination of the experiment, is both simple and ingenious. In fact, when we couple the simplicity of the mode of operating with the fact that an experiment can be made on so small a quantity of gas as two cubic inches, it is scarcely too much to say that in many researches it will entirely do away with the necessity of weighings. "The amalgam, by the aid of which a porcelain tube 3 feet long and 1} inch thick may be made to supply the place of a tolerably powerful electrical machine, is made as follows:-Two parts of mercury are heated in a common test-tube, and one part of thin zinc-foil, and one part of zinc added whilst the metal is well stirred. In order to make the amalgam more plastic, it is melted and stirred several times, and then placed in a piece of the thickest and best silk, which serves as a rubber. In rubbing the tube, the silk is so arranged that only half the surface in contact with the porcelain is covered with amalgam, the remainder being left free. The powerful action of the amalgam begins generally after it has been some time in use, and it preserves its activity often for months." A large portion of the work is devoted to the consideration of the laws of the absorption of gases in liquids, the methods of determining the coefficients of absorption, and numerous examples showing the coefficients of a considerable number of gases. A most valuable result of the perfection to which the determination of the coefficients of absorption can be carried, and one that cannot be too highly appreciated by chemists, is, that it enables us to ascertain whether a gas under examination is a mixture in atomic proportions or a truly chemical compound. It is well known to all who have paid any attention to this branch of chemistry, that Frankland and Kolbe have proved that eudiometric analysis (as might be expected) was incapable of showing the difference between two volumes of marsh-gas and equal volumes of hydrogen and methyle. Any process capable of throwing light on questions so difficult of solution will doubtless be thankfully received by chemists. In the work before us, Bunsen shows how perfectly the question may be solved by the method alluded to, even in cases like the present, where the greatest difficulty might have been anticipated, from the fact that the differences in the coefficients of absorption are very little. The result obtained by the absorptiometric method clearly indicates that marsh-gas, prepared by heating together the acetate with hydrate of potash, and purified by means of fuming sulphuric acid and potash, is not a mixture of methyle with hydrogen, nor an isomer of natural marsh-gas, but the same substance which is evolved by the mud volcanoes of Bulganak in the Crimea. The author has incorporated in his work the results of the researches which he made some years ago (in conjunction with Prof. Stegmann) on the laws of the diffusion of gases. As usual, the apparatus employed and the manipulation generally are both novel and ingenious. He deduces several facts from his experiments; among others, that the pores of the gypsum diaphragms do not act towards gases passing through them as a system of fine openings in thin plates, but as a system of capillary tubes. He has also made elaborate experiments to solve several other important questions, among which the following stands prominently forward:-"Do the volumes of two gases which have diffused into each other, stand to each other, as is universally admitted, inversely as the square roots of their densities?" To our surprise we find that a negative answer is returned to this question. We do not feel it necessary to enter into a detailed account of the author's experiments and deductions, as he admits this portion of the investigation to be still in an unfinished state. A very important portion of the volume, and one which will be read with interest by all who are engaged in eudiometry, is on the phænomena of the combustion of gases. The author considers in this, the last portion of the work,-the heat of combustion-the temperature of the combustion-the explosive force of gases-and the temperature of ignition of gases. Several other instructive and interesting properties of gases are studied incidentally, such as their diathermanous properties, and the influence of diluents; moreover, the author shows the bearings of the facts educed on the action of affinity. The volume concludes with copious and most valuable tables for the calculation of analyses. To the chemist who is engaged in investigations of this nature, such a volume as that before us is invaluable; unhappily their number in this country is so limited, that we fear the work is likely to have a less-extended sale than it deserves.. The translation has been entrusted to one of the author's pupils, Dr. H. E. Roscoe, and it appears to be most carefully made. XVI. Proceedings of Learned Societies. ROYAL SOCIETY. [Continued from p. 72.] January 8, 1857.-William Robert Grove, Esq., V.P., in the Chair. THEC In a previous paper on this subject (Philosophical Transactions, 1840), I had shown,-1st, that a long circular pillar, with its ends flat, was about three times as strong as a pillar of the same length and diameter with its ends rounded in such a manner that the pressure would pass through the axis, the ends being made to turn easily, but not so small as to be crushed by the weight; 2ndly, that if a pillar of the same length and diameter as the preceding had one end rounded and one flat, the strength would be twice as great as that of one with both ends rounded; 3rdly, if, therefore, three pillars be taken, differing only in the form of their ends, the first having both ends rounded, the second one end rounded and one flat, and the third both ends flat, the strength of these pillars will be as 1-2-3 nearly. The preceding properties having been arrived at experimentally, are here attempted to be demonstrated, at least approximately. The pillars referred to in my former paper were cast from Low Moor iron No. 3; they were very numerous, but usually much smaller than those used in the present trials. I felt desirous too of using the Low Moor iron in the hollow pillars employed on this occasion, not on account of its superior strength, but its other good qualities. The pillars from this iron were cast 10 feet long, and from 2 to 4 inches diameter, approaching in some degree, as to size, to the smaller ones used in practice. The results from the breaking weights of these were moderately consistent with the formula in the former paper, with a slight alteration of the constants, rendered necessary by the castings being of a larger size, and therefore softer than before, a matter which will be adverted to further on. The formulæ for the strength of a hollow pillar of Low Moor iron No. 2, where w is the breaking weight, in tons, of a pillar whose length is 7 in feet, and the external and internal diameters D and d in inches, the ends being flat and well bedded-are as below: from formula in present paper. To obtain some idea of the relative strengths of pillars of different British irons, I applied, at Mr. Stephenson's suggestion, to Messrs. Easton and Amos, who procured for me twenty-two solid pillars, each 10 feet long and 24 inches diameter, cast out of eleven kinds of iron (nine simple irons and two mixtures). The pillars were all from the same model, and were cast vertically in dry sand, and turned flat at the ends, as the hollow ones had been; two being cast from the same kind of iron in each case. The simple unmixed irons tried were as below, and all of No. 1. The mean strength of the pillars from the irons above varies from 20.05 to 29.50 tons; or as 2 to 3 nearly. The pillars formed of mixed irons were found to be weaker than the three strongest of the unmixed series. From many experiments, it was shown that the weight which would crush the pillars, if they were very short, would vary as 5 to 9 nearly. The pillars in general were broken of four different lengths, 10 feet, 7 feet 6 inches, 6 feet 3 inches, and 5 feet, the ends of all being turned flat, and perpendicular to the axis. It was found that when the length was the same, the strength varied as the 3'5 power of the diameter; and when the diameter was the same and the length varied, the strength was inversely as the 1.63 power of the length. Both of these were obtained from the mean results of many experiments. The formula for the strength of a solid pillar would therefore be where w is the breaking weight, d the diameter in inches, the length in feet, and m a weight which varied from 49.94 tons in the strongest iron we tried, to 33.60 tons in the weakest. The ultimate decrement of length, in pillars of various lengths but of the same diameter, varies inversely as the length nearly. Thus the ultimate decrements of pillars 10 feet, 7 feet 6 inches, 6 feet 3 inches, and 5 feet, vary as 2, 3, 3 and 4 nearly, according to the experiments, from which it appeared that the mean decrement of a 10-feet pillar was 176 inch. Irregularity in Cast Iron. The formulæ arrived at in this paper are on the supposition that the iron of which the pillars are composed is uniform throughout the whole section in every part; but this was not strictly the case in any of the solid pillars experimented upon. They were always found to be softer in the centre than in other parts. To ascertain the difference of strength in the sections of the pillars used, small cylinders inch in diameter and 11⁄2 inch high, were cut from the centre, and from the part between the centre and the circumference, and there was always found to be a difference in the crushing strength of the metal from the two parts, amounting perhaps to about one-sixth. The thin rings of hollow cylinders resisted in a much higher degree than the iron from solid cylinders. As an example, the central part of a solid cylinder of Low Moor iron No. 2, was crushed with 29.65 tons per square inch, and the part nearer to the circumference required 34.59 tons per square inch; cylinders out of a thin shell half an inch thick, of the same iron, required 39.06 tons per square inch; and other cylinders from still thinner shells of the same metal, required 50 tons per square inch, or upwards, to crush them. As these variations in cast iron have been little inquired into, except by myself, and have never, so far as I know, been subjected to computation, I have bestowed considerable trouble upon the matter, in an experimental point of view, and endeavoured to introduce into the formulæ previously given, changes which will in some degree include the irregularities observed. "Memoir on the Symmetric Functions of the Roots of certain Systems of two Equations." By Arthur Cayley, Esq., F.R.S. The author defines the term roots as applied to a system of n-1 equations =0,=0, &c., where p, 4, &c., are quantics (i. e. rational and integral homogeneous functions) of the n variables (x, y, z, . .) and the terms symmetric functions and fundamental symmetric functions of the roots of such a system; and he explains the process, given in Professor Schläfle's memoir, "Ueber die Resultante eines Systemes mehrerer algebraischer Gleichungen," Vienna Transactions, t. iv. (1852), whereby the determination of the symmetric functions of any system of (n-1) equations, and of the resultant of any system of n equations is made to depend upon the very simple question of the determination of the resultant of a system of n equations, all of them, except one, being linear. The object of the memoir is then stated to be the application of the process to two particular cases, viz. to obtaining the expressions for the simplest symmetric functions, after the fundamental ones of the following systems of two ternary equations, viz. first, a linear equation and a quadratic equation; and secondly, a linear equation and a cubic equation; and the author accordingly obtains expressions, as regards the first system, for the fundamental symmetric functions or symmetric functions of the first degree in respect to each set of roots, and for the symmetric |