ON THE MOLECULAR THEORY AND LAWS OF ELECTRICITY. BY L. LORENZ OF COPENHAGEN. In a paper on the mechanical theory of heat*, M. A. Dupré has given a lower limit for the number N of molecules contained in a milligramme of water, namely N> 125 x 1018; that is, that the number is greater than 125 trillions. A similar though somewhat higher limit may, I think, be deduced in an entirely different and, as I think, very simple manner. For measuring the intensity of an electrical current I will choose the electromagnetic unit, and as unit of the quantity of electricity that which passes in a second through the section of a conductor when its intensity is equal to unity. I take, as electricity which has passed through, the sum of the positive quantities passing in the direction of the current, and of the negative in the opposite direction. The repulsion, F, of two electrical bodies with the quantities of electricity e and e' and the distance r is then expressed in absolute units by in which F=a2 ee1 a=31074 × 107. Further, let the electrical tension of a body be that quantity which is required to impart to the body the unit of the quantity of electricity. If p is the electrical tension, e the quantity of electricity, pde is the work required for the communication of the electricity de, and the whole work A of the tension p and the corresponding quantity e is determined by A= S'pode If, for instance, the quantity e is uniformly distributed upon the surface of a sphere whose radius is r, the tension is The decomposition of a milligramme of water requires an amount * Annales de Chimie et de Physique, vol. vii. (1866). of work which can be exerted by a certain quantity of electricity; for the tension is diminished by a certain amount. According to Weber and others, a milligramme of water is decomposed by 107 units of current in a second, and therefore by 107 units of electricity. If we denote by N the number of molecules contained in a milligramme, and by e the quantity of electricity which each must receive and give up in order to be decomposed, then Ne=107. Further, according to Bosscha, the electromotive force of a Daniell's element in electromagnetic units (or, what is the same thing, the tension of the positive pole of such an element whose negative pole is connected with the earth) is equal to 10258 x 10", a number which may also be deduced from Favre and Silbermann's experiments. The decomposition of water requires a tension 1.46 as great; if this is denoted by P, we have P=15 x 101o. Let us suppose that the molecule of water has a tetrahedral arrangement, then in which ♪ is the distance of two adjacent molecules of water, and the quantity of electricity e which a molecule has received must somehow have spread inside a spherical surface the diameter of which is d. The work e corresponding to this quantity of electricity will have now its smallest value if the electricity is uniformly diffused over the surface of this sphere; for any other arrangement of the electricity would require an increased work. The tension corresponding to this order will be 2a2e and this magnitude must therefore be smaller than the actual tension P resulting from another distribution of the same quantity of electricity. Thus we get From these equations we find 2a2e <P. This limit to the number sought is eleven times as great, and that for the distance & half as great as that found by Dupré. We readily see moreover that the limit for N may be put higher, if we assume that the quantity of electricity e is distributed on the surface of each of the atoms of which a molecule of water consists. The same result is obtained from the consideration of other more easily decom. posable bodies; and the same calculation made for oxide of silver (AgO) shows that the limit for N may be put twenty-seven times as great, and that for d one-third as great, if it be assumed that the molecule of silver oxide contains two atoms, and that an equivalent of silver oxide consists of the same number of molecules as an equivalent of water. It seems remarkable also that while the quantity of electricity e of a source of electricity P performs the work Pe, in a molecule with the same quantity of electricity e and the same tension P only half this quaniity of work (that is, Pe) is present as work when it passes from the tension P to 0. It is possible, therefore, that the amount of the work of the electricity may disappear for chemical action to the extent of one half to occur in another form (as heat).—Poggendorff's Annalen, No. 8, 1870. EASY PREPARATION OF A LIQUID FOR PRODUCING PLATEAU'S FIGURES. BY RUDOLPH BÖTTGER. For producing these figures, as well as for the formation of soapbubbles which last for hours and have the most magnificent play of colours, a liquid may advantageously be used which is readily and quickly prepared in the following manner. In a pretty large flask parings of palm-oil soap are placed along with cold distilled water, and a solution as saturated as possible prepared by constant agitation. This is filtered through porous grey paper, and is mixed with about a third of its volume of chemically pure concentrated glycerine. Each time before using, it is convenient to agitate it gently. By the aid of a small glass funnel about 2 inches in diameter, provided with an india-rubber tube, soap-bubbles of unusual permanence and continually varying splendour of colour may be prepared, provided that immediately after their production they are carefully deposited upon a slightly oxidized iron ring moistened with the soap solution in question. Bubbles of 1 foot diameter, and more, last, when suitably protected against agitation and draught, frequently for five, or even ten minutes; others of 2 or 3 inches diameter for hours, in most cases as long as ten, sometimes twenty hours. Poggendorff's Annalen, No. 8, 1870. Lectures on Mineralogy applied to Geology and the Arts are given by Professor TENNANT, F.G.S., at his residence, 149 Strand, London, W.C. The Course commences with a description of the Physical and Chemical characters of Minerals in general, and includes a minute description of all the substances entering into the composition of Rocks, and of those Minerals which are also used in the Arts; illustrated by an extensive collection of characteristic specimens, and diagrams of the principal crystalline forms, &c. The Students are accompanied by the Professor to the Museum of Practical Geology, the British Museum, and other public institutions, and also on excursions into the country. TO GEOLOGISTS. Professor TENNANT has received instructions to dispose of, by private contract, the extensive and valuable Collection of Tertiary and other Fossils the property of N. T. WETHERELL, Esq., F.G.S., of Highgate. This Collection (well known as the North London) consists principally of a very large series of London-Clay Fossils and Minerals from Highgate and its vicinity, as also from Bognor, Bracklesham Bay, Hampshire, and Sheppy. The fossils are for the most part carefully arranged and named. Many of the specimens are the originals which have been figured in various works, while others are quite new to science. In addition to the above-named, there is an extensive series of Fossils and Minerals from the Boulder Clay of Muswell Hill and Finchley. Also numerous Fossils from the Chalk, the Greensand, Oolite, Lias, &c. MR. TENNANT, 149 Strand, London, W.C., has for sale two Cabinets, measuring 9 feet 3 inches long, 2 feet 4 inches wide, and 3 feet 10 inches high; each containing 45 drawers, with a Glass Case on the top of each Cabinet, 4 feet 11 inches high, and 15 inches from back to front. One Cabinet is filled with 2600 Minerals, the other with 3400 Fossils. The Collection consists of six thousand specimens, many very select. The first Gold Nugget received from Australia, which was exhibited in the Exhibition of 1851, is in the Collection; it cost £37, and contains about 8 ounces of gold: also a fine series of Diamonds, illustrating crystalline form and colour. The specimens have been used to illustrate the Lectures on Mineralogy and Geology at King's College, London, and at the Royal Military Academy, Woolwich. Price THREE THOUSAND GUINEAS. Any person wishing to become practically acquainted with the interesting and important study of Mineralogy and Geology will find this a good opportunity to obtain an instructive and valuable Museum, the specimens having been collected with care and at great expense during the last thirty years. Elementary Geological Collections at 2, 5, 10, 20, 50, to 100 guineas each, and every requisite to assist those commencing the study of this interesting branch of Science, a knowledge of which affords so much pleasure to the traveller in all parts of the world. A collection for Five Guineas, to illustrate the recent works on Geology, by Ansted, Buckland, Lyell, Mantell, Murchison, Page, Phillips, and others, contains 200 specimens, in a plain Mahogany Cabinet, with five trays, comprising the following specimens. viz. :-MINERALS which are either the components of Rocks, or occasionally imbedded in them-Quartz, Agate, Chalcedony, Jasper, Garnet, Zeolite, Hornblende, Augite, Asbestos, Felspar, Mica, Talc, Tourmaline, Calcite, Fluor, Selenite, Baryta, Strontia, Salt, Sulphur, Plumbago, Bitumen, &c. NATIVE METALS, or METALLIFEROUS MINERALS; these are found in masses or beds, in veins, and occasionally in the beds of rivers. Specimens of the following Metallic Ores are put in the Cabinet:-Iron, Manganese, Lead, Tin, Zinc, Copper, Antimony, Silver, Gold, Platina, &c. Rocks: Granite, Gneiss, Mica-slate, Clay-slate, Porphyry, Serpentine, Sandstones, Limestones, Basalt, Lavas, &c. PALEOZOIC FOSSILS from the Cambrian, Silurian, Devonian, Carboniferous, and Permian Rocks. SECONDARY FOSSILS from the Rhætic, Lias, Oolite, Wealden, and Cretaceous Groups. TERTIARY FOSSILS from the Plastic Clay, London Clay, Crag, &c. In the more expensive collections some of the specimens are rare, and all more select. JAMES TENNANT, Mineralogist (by appointment) to Her Majesty, 149 Strand, London, W.C. November 1870. XLI. On the Temperature and Physical Constitution of the Sun. XLII. On a Salt that is invisible in its Mother-liquor. By CHARLES XLIII. On the Geodesic Lines on an Oblate Spheroid. By Pro- XLIV. Reply to Mr. Templeton's "Remarks suggested by Mr. Douglas's Account of a New Optometer." By J. C. DoOUGLAS, Government Science Teacher, Assistant Superintendent East-India XLV. On Approach caused by Vibration. By FREDERICK GUTHRIE. XLVI. Experimental and Theoretical Researches into the Figures of Equilibrium of a Liquid Mass without Weight.-Ninth, Tenth, ROYAL SOCIETY:-The EARL OF ROSSE on the Construction of Thermopiles, and on the Radiation of Heat from the Moon; Mr. A. LE SUEUR'S Observations with the Great Melbourne |