this law. But the following values are the most accurate, and tend to prove the truth of the law. The apparent discordance in the case of iron is in part due to the variations in the qualities of that metal in different specimens. In calculating this table, the values of c from the experiments of M. Wersheim are used; those of a from the experiments of Mr Mathiessen (except iron); those of ẞ from the experiments quoted by Prof. Balfour Stewart in his Text-Book; and the assumed temperature is 18° C., or 283° absolute temperature. 2. Notice of the Completion of the Works designed by Sir Charles A. Hartley, F.R.S.E., for the Improvement of the Danube. By David Stevenson, Esq., V.P.R.S.E. In 1868 I presented to the Society, on behalf of Sir Charles A. Hartley, a memoir published by the European Commission of the Danube, on the improvement of that river, and at the same time gave a notice of the works designed by Sir Charles Hartley for effecting that important object. These works have now been completed, and Sir Charles Hartley has again asked me to present to the Society a second memoir published by the Commission, which brings the history of the works constructed under their charge down. to the time of their completion in 1873. In supplement of the notice formerly communicated, which referred to a work in progress, it may not be uninteresting, now that the work is completed, to state briefly what has been effected. by this most important and successful example of hydraulic engineering. The engineering problem to be solved by the European Commission was the removal of the bar which obstructed the Sulina mouth of the Danube, which, in 1856, had a varying depth of channel never exceeding 11 feet. The design of Sir Charles Hartley-the engineer to the Commission-consisted in piers so constructed as to confine the current of the river in its passage into the Black Sea. At the date of my last notice the north pier had been extended to the length of 4640 feet, and the south pier to feet instead of 11 feet had 3000 feet, and a maximum depth of 17 been obtained. I, however, suggested in that notice, that as the Danube must continue to bring down an enormous mass of detritus, so in course of time the works which had proved so successful must be extended; and it appears that this has been found necessary, as the south breakwater, completed in 1871, has been extended to 3457 feet in length, and even with this additional length it is, I think, not improbable that in the course of time still farther extension may be required, for the Sulina mouth of the Danube will still discharge the same amount of water, bearing with it the same amount of alluvial matter, estimated in high floods at about 70,000 tons in twenty-four hours, the deposit of which at the extremity of the piers will still have a tendency, though in deeper water, to form a bar. The works have, however, proved most successful, and reflect the highest credit on Sir Charles Hartley, by whom they were designed and executed, and the following is a summary of the results that have been obtained. The total length of piers executed is 8789 feet, at a cost of L.185,352, being L.21 per lineal foot, in an average depth of 14 feet at low water. The navigable depth of the channel over the bar has been increased from 11 feet in 1856, to 20 feet in 1873. In 1853, 2490 vessels, of 339,457 aggregate tonnage, left the port; in 1869 there were 2881 vessels, with a tonnage of 676,960. Thus, while the number of vessels increased only at the rate of 16 per cent., the tonnage, due to the greater draught, had been increased at the rate of 50 per cent., a good practical proof of the value of the improvements. The number of shipwrecks at the mouth of the Danube has also been greatly diminished. VOL. IX. Monday, 3d April 1876. SIR WILLIAM THOMSON, President, in the Chair. The following Communications were read: 1. Chapters on the Mineralogy of Scotland. By Professor Heddle. Chapter I. -On the Rhombohedral Carbonates. Communicated by Professor Tait. Professor Heddle read a paper on the "Rhombohedral Carbonates occurring in Scotland," the first of a series of Chapters intended to embrace the analytical results of an investigation of all unknown or insufficiently determined Scottish species. In this paper many analyses of the carbonates were submitted; and the pseudomorphic changes taking place in these were referred to in a special manner. 2. On Thermo-Dynamic Motivity. By Sir W. Thomson. 3. On the Vortex Theory of Gases, of the Condensation of Gases on Solids, and of the Continuity between the Gaseous and Liquid State of Matter. By Sir W. Thomson. 4. On two new Laboratory Apparatus. By William Dittmar. The object of this communication is to submit to the notice of the Society two little inventions of mine, which, whatever may be the degree of originality which they can claim, will, I venture to hope, prove useful additions to the catalogue of chemical-laboratory appliances. The one is a new form of the precision balance, which pretends to execute exact weighings with a hitherto unattained degree of rapidity; the other is a contrivance for maintaining a constant pressure in a supply of gas, and thus making it possible, with comparative facility, to keep, say an air-bath, for any length of time, at a constant temperature. The new balance differs from the instrument in its customary form only in two points, of which the more important is a modification of the centre of gravity "bob" arrangement, which enables one, at a moment's notice, to shift the centre of gravity of the instrument from a certain definite position, I., to a certain other (higher) position, II., matters being arranged so that in passing from I. to II., the sensibility, i.e. the deviation, corresponding to an overweight of, say 1 milligramme, is increased in an exactly pre-determined ratio, such as of 1: 10, for instance. For this purpose the "bob" is made very light, so that the distance through which it has to travel in order to effect the desired change of sensibility is not too small, and, instead of to a screw as usual, is fixed by mere friction to a vertical triangular steel rod forming part of the needle. The other new feature in the balance is, that the rider-principle, besides being discounted in a slightly different manner from the customary one, is extended to the determination of differences of weight up to 100 (instead of 10) milligrammes. ΔΟ Bob 10 A Fig. 1. The arrangement adopted is represented in the accompanying sketch, for the interpretation of which it is only necessary to say that C (10) and (10) O are equal to C (0), and (0), (10), respectively, and that both O(10) and 0, (10), are each divided into 10 equal parts, the former by notches filed into the beam, the latter by marks; and to add, that there are two riders, one weighing p centigrammes for the left arm, and another weighing p milligrammes for the right arm, the balance being adjusted so that, when both riders are at their zero-points, it is in equilibrium, and p being chosen so, that, supposing the large rider to be shifted to the n mark, and the small one to the m mark, this virtually amounts to the addition of 10n+m milligrammes to the charge in the right pan. There is no need of my explaining how the balance is meant to be used; I will rather avail myself of this opportunity for drawing the attention of readers interested in the subject to a few inferences from the theory of the balance, which, obvious as they are, have hitherto not been sufficiently appreciated by either the authors of our physical handbooks or by practical balance-makers. I. Given a balance in which everything is constant except the distance s of the centre of gravity of the empty instrument from the axis of rotation, and it is easily shown that (for a constant charge) the deviation a of the needle for a given over-weight A, and α consequently the "sensibility" a = is the greater the less A' 8. This, of course, is duly stated by all authors; but what is always forgotten to be pointed out are two things, viz.-1st, That the "sensibility" has nothing to do with the inherent precision of the instrument; and 2dly, That supposing the sensibility to be increased, all the other good qualities of the balance get less; we diminish the rate of vibration (this rate being proportional to ); we diminish the range of differences of weight deter minable by the method of vibration; we diminish the relative constancy (in opposition to variations in the charge) of the sensibility and the time of vibration. Considering now, II. The case of a balance to be constructed, the arm-length 7 and weight w of the empty beam also become variables, related to each other, according to some equation like w = const. l, and (assuming each of the pans to bear a certain medium charge p) we have t Ja i.e., by diminishing const.√√const. + const. l, we can increase the sensibility without diminishing the rate of vibration (or vice versa); but the other |