carbonic acid and water under the influence of light, and consequent purification of the atmosphere; and he insisted chiefly on the following points: 1. That this change is probably gradual; the carbonic acid being taken into the juices of the plant and slowly decomposed there, more or less completely, according to circumstances, whence result not only starch or its allied compounds, but likewise different organic acids and various oils. 2. That the formation of sugar in plants is probably to be regarded rather as a simply chemical action than as a result of vital affinities; or that it is a first product of the decomposition of starch by the agency of water and oxygen. 3. That, on the other hand, the formation of lignin, containing more carbon and less oxygen, from starch or from cellulose, and from the carbonic acid and water brought into the cells, appears to be the result of a strictly vital affinity, strongest at the period of greatest vigour of the plant. 4. That in this, as in other of the metamorphoses which take place in living beings, and which he proposes farther to examine, the carbon, thus originally fixed on the earth's surface from the atmosphere, appears to be the chief material employed by nature for the formation of all organized structures, and to be invested, for that purpose, with peculiar and transient vital affinities, while oxygen hardly appears to exert any chemical powers in living bodies, different from those which it manifests elsewhere; but is taken into the interior of all living bodies, only that it may support the excretions which are continually going on in them, and resolving organized into inorganic matter; and thus, that it gradually resumes its power over the carbon which had been temporarily separated from it for the formation of the animated part of creation. The following Donations to the Society's Library were announced: The Journal of Agriculture, and the Transactions of the Highland and Agricultural Society of Scotland, for March 1846.—By the Society. Journal of the Asiatic Society of Bengal. No. 160, for 1845.—By the Society. Life and Correspondence of David Hume. queathed by his Nephew to the Royal From the Papers be Society of Edinburgh, and other original sources. By John Hill Burton, Esq., Advocate. 2 vols. 8vo. By the Author. Natural History of New York. 10 vols., 4to. Geological Map of New York, published by Legislative authority in 1842.-By the Governor and Secretary of State of New York. Monday, 16th March 1846. The RIGHT REV. BISHOP TERROT, Vice-President, in the Chair. The following Communications were read : 1. On the Personal Nomenclature of the Romans, with an especial reference to the Nomen of Caius Verres. By the Rev. J. W. Donaldson, Author of the New Cratylus. Communicated by Bishop Terrot. 2. On the appearance of the Great Comet of 1843, at the Cape of Good Hope, with illustrative Drawings. By Professor C. P. Smyth. Communicated by the Secretary. This comet attracted much attention from its excessive brightness at and near its perihelion passage, as well as from the length and form of its tail. The drawings were intended to represent these particulars, and the changes which occurred during the time that the comet remained visible from the Cape Observatory. It was seen for a short time, but not generally, before the perihelion passage, which took place on the 27th February 1843; and it ceased to be visible by the naked eye towards the end of March, though it could be discerned with the telescope till the 19th April. After passing the perihelion, this object was seen on the 3d March, about a quarter of an hour after sunset. The head then glistened like a star of the second magnitude, and had a well-defined planetary disc, about 20" in diameter, having an envelope of rays, the brightest of which came out like wings on both sides. The tail, which was 40° long, was in form bifid; its two sides were very narrow, bright and straight, the space between the sides almost as dark as the neighbouring sky. There were also two faint streamers on either side of the tail. On the 4th March, one of the streamers had disappeared, and the space between the central streamers had become less dark. The planetary disc was also less defined. On the 9th March, the planetary disc had disappeared, in place of which there was a mere coma, having a thickening towards the middle. Both streamers of the tail had disappeared, and the dark axial space was filled with a faint luminosity. The tail, however, had become longer. The tail, which was at this time preceding the head, was curved slightly towards the aphelion, and was also in advance of a line joining the sun with the comet's head. With a small telescope of low power, indications of a nucleus often appeared, but were as often dispelled by the employment of more powerful instruments. When the tail appeared to the naked eye upwards of 40° long, nothing like a solid or stellar nucleus could be discovered. There was only a mass of vapour, which, though condensed in certain parts, was still permeable to the rays of the mi nutest stars. 3. On the Existence of Fluorine in the Bones from Arthur's Seat. By Dr G. Wilson. 4. On the Composition of the Bones from Arthur's Seat. By Dr Christison. The author found that the bones of animals lately disinterred in the course of the new drive, contained of the quantity of gelatine common in recent bones. The following Gentlemen were duly elected Ordinary Fellows of the Society: GEORGE TURNBULL, Esq., W.S. The following Donations to the Society's Library were announced: : The London University Kalendar, 1846.-By the University. Journal of the Asiatic Society of Bengal, No. 159.-By the Society. The Electrical Magazine. Conducted by Mr Charles V. Walker. January 1846.-By the Editor. Twenty-fifth Report of the Council of the Leeds Philosophical and Literary Society for Session 1844-45.-By the Society. Biographical Notice of the late Sir John Robison, K.H., Sec. R.S. Ed. By Professor Forbes.-By the Author. Il Cimento; Giornale di Fisica, Chimica e Storia Naturale. 1844 and 1845, January to Aug.-By Professor Forbes. Nieuwe Verhandelingen der Eerste Klasse von het KoninklijkNederlansche Instituut van Wetenschappen, Letterkunde en Schoone Kunsten te Amsterdam. Deel XII., Stuk 1.— By the Institut. Monday, 6th April 1846. SIR THOMAS M. BRISBANE, Bart., President, in the Chair. The following Communications were read :— 1. On the Description of Oval Curves, and those having a plurality of Foci. By Mr Clerk Maxwell junior; with remarks by Professor Forbes. Communicated by Professor Forbes. Mr Clerk Maxwell ingeniously suggests the extension of the common theory of the foci of the conic sections to curves of a higher degree of complication in the following manner : = (1.) As in the ellipse and hyperbola, any point in the curve has the sum or difference of two lines drawn from two points or foci a constant quantity, so the author infers, that curves to a certain degree analogous, may be described and determined by the condition that the simple distance from one focus plus a multiple distance from the other, may be a constant quantity; or more generally, m times the one distance + n times the other constant. (2.) The author devised a simple mechanical means, by the wrapping of a thread round pins, for producing these curves. See Figs. 1 & 2 (Plate II.) He then thought of extending the principle to other curves, whose property should be, that the sum of the simple or multiple distances of any point of the curve from three or more points or foci, should be a constant quantity; and this, too, he has effected mechanically, by a very simple arrangement of a string of given length passing round three or more fixed pins, and constraining a tracing point, P. See Fig. 3. Farther, the author regards curves of the first kind as constituting a particular class of curves of the second kind, two or more foci coinciding in one, a focus in which two strings meet being considered a double focus; when three strings meet a treble focus, &c. Professor Forbes observed that the equation to curves of the first class are easily found, having the form √ x2 + y2 = a + b√(x−c)2 + y2, which is that of the curve known under the name of the First Oval of Descartes.* Mr Maxwell had already observed that when one of the foci was at an infinite distance, (or the thread moved parallel to itself, and was confined in respect of length by the edge of a board,) a curve resembling an ellipse was traced; from which property Professor Forbes was led first to infer the identity of the oval with the Cartesian oval, which is well known to have this property. But the simplest analogy of all is that derived from the method of description, and being the radients to any point of the curve from the two foci; m r + n r = constant, which in fact at once expresses on the undulatory theory of light the optical character of the surface in question, namely, that light diverging from one focus F without the medium, shall be correctly convergent at another point ƒ within it; and in this case the ratio n m expresses the index of refraction of the medium.† If we denote by the power of either focus the number of strings leading to it by Mr Maxwell's construction, and if one of the foci be removed to an infinite distance, if the powers of the two foci be equal the curve is a parabola; if the power of the nearer focus be greater than the other, the curve is an ellipse; if the power of the infinitely distant focus be the greater, the curve is a hyperbola. The first case evidently corresponds to the case of the reflection of parallel rays to a focus, the velocity being unchanged after reflection; the second, to the refraction of parallel rays to a focus in a dense medium (in which light moves slower); the third case to refraction into a rarer medium. The ovals of Descartes were described in his Geometry, where he has also given a mechanical method of describing one of them, but only in a particular case, and the method is less simple than Mr Maxwell's. The demonstration of the optical properties was given by Newton in the Principia, Book I., prop. 97, by the law of the sines; and by Huyghens in 1690, on the Theory of Undulations in his Traité de la Lumière. It probably has not been suspected that so easy and elegant a method exists of describing these curves by the use of a thread and pins whenever the powers of the foci are com * Herschel on Light, Art. 232; Lloyd on Light and Vision, Chap. vii. This was perfectly well shewn by Huyghens in his Traité de la Lumière, p. 111. (1690.) Edit. 1683. Geometria, Lib. II., p. 54. |