When the disk of carbon dioxide is not very compact, no sound is produced, because the gas can escape in different ways through the little spaces left, otherwise the intensity of the sound is dependent on the conductivity for heat of the substance brought in contact. A silver coin, when touching the disk with the flat side, does not act, because it is uneven and little interstices are left, otherwise silver emits loud sounds, and so it is with copper, iron, aluminium; lead produces a dull note and bismuth none at all, as being a very bad conductor unless it has been heated, and then it sounds only for a moment. The carbon rods used in electric lamps remained silent, and also wood, but quartz and rock-salt gave an audible note when a lens of compressed carbon dioxide was applied on them with some pressure. Very beautiful sounds, of the character of those produced with the Trevelyan instrument, were heard when an iron rod was resting with one end on a horizontal cylinder of the compact solid substance and touching with the other a glass plate. As the escaping gas is the determining cause in all these cases, it is to be expected that other substances, when capable of rapid evaporation, on touching heated metals will also emit sound, and indeed I obtained this very loud when a brass sphere brought to incandescence was firmly pushed down on a piece of mercury bichloride or camphor, and especially on sal-ammoniac, all substances subliming at a red heat; accordingly dense vapours are evolved, when the metal came in contact, and sounded on perforating them. Crystallization of Mercury.—Though the freezing of this liquid metal with the mixture of solid carbon dioxide and sulphuric ether is easily effected, crystallization is not apparent, as the metal then solidifies too quickly. On trying the production of sound with this liquid, I found a very effective method to obtain it crystallized. A disk of slightly compressed carbon dioxide with a cavity was used, and still better was a little cup, 4 centim. high, such as could be formed in a convenient mould of wood, and this I filled with mercury, just as a crucible. A low and distinct sound was given off, and very regular undulations appeared on the bright metal surface, indicating the pulsations provoked by the escaping gas. Though the mercury does not actually touch the sides of the cup (or the cavity on the disk) as a gas layer keeps it away, yet its heat is dispersed by radiation towards the extremely cold surrounding matter, and gradually the vibrations cease. If at this moment the cup is emptied of its still liquid contents, it is seen to be covered inside with beautiful and sharply defined needles of solid mercury, resembling fern leaves, of more than one centim. in length; the whole mass is coherent and forms now a metal cup, of course with thin walls, that may easily be removed from its mould of solid carbon dioxide and maintains itself during some minutes. Effect of Gas and Vacuum Screens.-One of the most interesting experiments demonstrated by Prof. Dewar at his admirable lectures on liquid air, seems to me the property of a very high vacuum of preventing the access of heat from the surrounding medium to liquids placed inside. Lecturers on low temperatures will not likely have at command such splendid arrangements as Prof. Dewar could dispose of, but the principle of this fact may be illustrated, in a suitable way, with carbon dioxide. I had three glass tubes of 15 millim. diameter constructed, and of equal capacity, and according to Prof. Dewar's device. The first, A, was inside an oblong glass bulb, remaining open, and consequently filled with air that could be exchanged, when desired, for another gas; the second, B, had likewise this bulb, but rarefied with a mercurial pump, thus forming a vacuum-jacket; the third, C, was surrounded by two such concentric vacuum-jackets. Placing them in the same support, next to one another, I put in each the same amount by weight of a mixture of carbon dioxide with sulphuric ether; it is then soon observed, within the quarter of an hour, that A, provided with the air-jacket, is covered outside with a layer of hoar frost; B shows only a slight deposit of condensed aqueous vapour from the atmosphere; and C remains transparent, having no deposit outside. Thus the influence of convection and radiation with regard to a vacuum are visible even at great distances from the lecturer's table. With the first vessel, A, I carried out another experiment I found suggested in the report of Prof. Dewar's lecture, and bearing on the property of different gases transmitting heat, which they do not all possess to the same extent. In one experiment 1 put 3 grammes of compressed carbon dioxide in the inner tube of the vessel A, when air was in the bulb, and collected the gas, given off by evaporation at the ordinary temperature, in a glass jar above water. I noted 170 cub. centim. in five minutes. Supplying again the inner tube with the same amount of carbon dioxide and replacing the air by hydrogen, I could collect again in five minutes 250 cub. centim. This increasing proportion shows the great conductivity and convection that hydrogen possesses. On removing the hydrogen and taking carbon dioxide in gaseous form instead of it, and working also with 3 grammes of solid matter, I now collected only 150 cub. centim., and carbon dioxide in gaseous condition is considered a bad conductor of heat. But the difference in quantity of gas evolved depends also on the power for convection, which will not be equal in the three cases The following experiment, which is somewhat the reverse of the former, demonstrates the influence of convection in incandescent electric lamps in a striking way. Four similar lamps (16 candle-power and same voltage) were connected in parallel to a dynamo; the first was filled with gaseous carbon dioxide, the second with common coal-gas, the third with hydrogen, and the fourth was kept in normal condition, that is provided with its vacuum around the carbon filament. All carried a little piece of phosphorus at the top of the glass globe on the outside, and now admitting the current in all at the same time, it is observed that the phosphorus is set on fire at different rates; first it burns on the lamp with carbon dioxide, then on that containing coalgas, and shortly after on the hydrogen lamp, but on the vacuum lamp it remains for a long time intact. In the latter case it may be inferred that the dark heat-rays are very imperfectly transmitted by the vacuum, whilst convection of course must also be very reduced; hence the glass can only receive a small amount of heat, and as in Prof. Dewar's experiment the vacuum prevents the ready access of heat to the extremely cold liquid, in the incandescent lamp, on the contrary, it is an obstacle to the cooling of the filament of carbon. It can therefore attain a high temperature and convert the electric energy it receives, chiefly into radiant light. As for the other lamps, the difference in heat transferred in the same time outside may find its explanation in the well-known experiments of Grove† and the investigation of Clausius; yet it is a curious fact to see the carbon brightly * Prof. Kundt described, as long ago as 1877, an experiment of a similar character, employing three vessels of the same size, enclosing at a distance of 3 mm. little tubes each filled with the same volume of sulphuric ether. The vessels were filled respectively with hydrogen, air, and carbon dioxide acting as jackets. Putting all three together in boiling water, heat is transmitted in a different way, as appears when the ether vapour is lighted, and the flame of hydrogen is seen to be the longest, that of the carbon dioxide the smallest, but convection may also influence. + Grove published his paper on this subject in the Phil. Trans. in 1847, and he determined the amount of heat given off by a platinum wire in different gases to a surrounding mass of water; the experiments with the lamps are in accordance with his results. glowing in the lamp wherein the phosphorus does not burn, in the lamp with carbon dioxide the filament becomes only dull red, and in the others it remains obscure, but still the phosphorus burns there after a minute. Though the thermal conductive power interferes, I believe convection to play an important part here, and I venture to predict that, if the incandescent lamp, whilst glowing, could be intensely cooled, by being immersed in liquid oxygen or liquid air, that Prof. Dewar has so readily at hand, it would at once attain a higher illuminating power*; as convection would still more be lessened, the remaining particles of air and mercury vapour would have their motion almost entirely exhausted. And hence it may be concluded that such a lamp would absorb less electric energy for emitting the same amount of light, when the degree of rarefaction is made the highest possible. The Hague, April 1894. VII. On an Approximate Method of finding the Forces acting in Magnetic Circuits. By RICHARD THRELFALL, M.A., Professor of Physics, University of Sydney; assisted by FLORENCE MARTIN, Student in the University of Sydney †. DURING the last three years I have had occasion to design a good many reciprocating electromagnetic mechanisms, and have frequently felt the want of some simple method of making the necessary approximate calculations of magnetic forces. I have obtained very little satisfaction from the attempts I have made to calculate tractions, proceeding by the method of finding poles and applying the law of inverse squares. This ill success led me to investigate the applicability of the methods established by Maxwell in the chapter "On Energy and Stress in the Magnetic Field" (Electricity and Magnetism,' vol. ii. §§ 641-644), with the following results. 1. Theoretical Considerations. The problem for solution in its simplest form is as follows:"Given an iron anchor-ring uniformly wound and interrupted at one point by an air-gap of any given dimensions *I tried this effect with a mixture of solid carbon dioxide and ether on an incandescent lamp, but the globe becomes covered with frozen aqueous vapour and the mixture itself is a hindrance to judging the brightness acquired; a transparent cold liquid therefore is far more suitable. † Communicated by the Author. to calculate the forces tending to draw the ends of the iron ring together when the strength of current flowing in the magnetizing circuit and the data of winding are given. : § 2. The position established by Maxwell is as follows: (1) The laws of magnetic force are such that magnetic forces may be regarded as the expression of a state of stress in the magnetic medium. (2) The medium is stable under such a distribution of stresses. (3) A series of expressions may be found for the stresses at any point in the magnetic field. § 3. Maxwell's investigation does not explicitly include the case of a body with inconstant permeability; but I cannot find that this in any way vitiates the argument. Professor J. J. Thomson shows (Applications of Dynamics to Physics and Chemistry,' § 33) that Maxwell's results may be considered as being derived from the existence of a term HB in the 1 8π Lagrangian function for unit volume of a magnetic field. If the permeability is a function of the induction, however, in 1 any part of the field, the more general expression HdB 8. must be substituted for the above and the results modified accordingly. I have not succeeded in doing this. It appears, therefore, that Maxwell's system as applied to iron does not cover all the ground, because a modification must be introduced on account of the inconstancy of the permeability, and also on account of the Villari effect as shown by Professor Thomson. There may also be other undiscovered additions to make. § 4. A great step is necessary to pass from Maxwell's position that magnetic forces may be regarded as the expression of stresses in the field-to the position that magnetic forces are such an expression. There is all the difference that exists between a theory and a fact. Everything, however, tends to show that the fact is that the theory is probably true so far as it goes, and we will therefore provisionally adopt it, and see first what additional hypotheses are necessary. It is obvious at once that the stresses are "stresses in a medium," while the forces are mechanical forces acting on matter. We must therefore consider that the medium is "attached" to matter so as to allow the stresses to appear as forces. Now the stresses in the medium depend on the nature of the matter which is permeated by the medium. Thus in the cut anchor-ring |