(1.) On the Values of μ derived from Observations on the Vapours of various Liquids.

An important test of the truth of the axiom on which Carnot's Theory is founded, will be afforded by comparing the values of μ deduced from observations on various liquids. I am informed by Mons. Regnault, that, by the end of this year, data as complete as those which we at present possess for water, will be supplied for five or six different liquids, from certain investigations with which he is now occupied. Carnot gives values of μ for the temperatures of the boiling of sulphuric ether, alcohol, water, and essence of turpentine, derived from various observations upon those liquids.

In his memoir of Dr Chalmers, lately read to this Society, Mr Ramsay has referred to an experiment which Dr Chalmers was anxious to have performed on the tide-wave in the Bay of Fundy. The object was to determine the earth's density by the attraction of the tide-wave on a plummet or spirit-level, on the same principle as Maskelyne's experiment on Schiehallion, but with the superior advantages arising from the perfect homogeneity of the attracting mass, and from the circumstance that all the observations might be made at a single station. The experiment might, in short, appear to unite the advantages both of Maskelyne's and Cavendish's methods of determining the earth's density.

In this paper were given descriptions of alluvial formations of a terassiform character in the valley of the Lir river, near Drammen, in Norway, and of similar objects in valleys near the foot of the Miösen lake. The author then described a remarkable terrace which runs for fully fourteen miles at one elevation along the upper part of the valley of the Logan, in the Dovre field. It is composed on the left side of the valley of water-laid sand, and is believed to be about 2150 feet above the level of the sea. On the Dovre field, several hundred feet higher, are morasses containing the remains of much greater trees than are now growing in that district, the highest vegetation of which is a dwarf birch; and Mr Chambers remarks, that when the terrace was on the sea-level this district would enjoy a temperature fit for the production of such large timber. Mr Chambers next described some remarkable terraces in the valleys near Trondhiem, and particularly the great terrace of erosion which overlooks that city at an elevation of 522 feet above the sea.

“Whilst lecturing lately on the subject of Vision, I consulted some recent authorities on the dimensions and curvatures of the refracting apparatus of the eye; and having calculated from them the convergence of rays within the eye, it may save trouble to others to put them on record.

“The measures of the eye given in almost every English work on the subject, are those given by Young on his own authority, or that of Petit. In the fifth volume of Dove's Repertorium, I find a series of measures collected by Treviranus from his own and preceding observations, which I have converted below from French lines into decimals of an English inch. In these the curvatures are supposed spherical. In the same work of Dove. I find a series of measures by Dr Krause of Hanover, on eight recent human eyes, which seem to have been made with uncommon care, and in which the deviation of the surfaces from sphericity is noticed.

The author, after referring to a communication made to this Society, on the 18th March 1839, on this subject, and noticed in the “Proceedings” of that date, stated, that being about to recommence his observations on radiant heat, so long and unavoidably interrupted, he had carefully examined the unpublished observations on which the previous notice was founded, with a view to ascertain what might be the numerical discrepancy which they present from Fresnel's Theoretical Law. The variation in the results of experiment for each of the angles was very considerable, arising from a multitude of causes as yet imperfectly estimated, but which appear to have been encountered by other observers, who, since that time, have undertaken the same research. Under the circumstances, the mean of the whole observations made between November 1838 and March 1839, have been taken for each angle of incidence; and the results being projected in the usual manner, the angles of incidence forming the line of abscissæ, and the intensities the ordinates, an interpolating curve was drawn through the whole. The numbers thus obtained (which are presented as only a rude first approximation), are shewn in the following table, and compared with Fresnel's Formula, calculated for an index of refraction of 1·50.

Until recently, general solutions of several classes of equations, such as that which occurs in the theory of the figure of the earth, could not be arrived at. An ingenious transformation lately rendered it a matter of comparative ease to arrive at a solution of these equations in those forms in which they are presented in the solution of physical problems; but still much remains to be done. The object of the present paper is to supply some portion of the deficiency in this respect, by the introduction of a new transformation, and the adoption of the function Γ. The solutions thus obtained are perfectly general, and are arrived at with the greatest facility.

Professor Goodsir communicated an abstract of a paper by Mr Zaglus on the muscular structure of the tongue. The author of the paper had found the muscular substance of the tongue to consist of a cortical layer, which surrounds the organ on all sides, except its posterior attachment, and in the middle line of its inferior surface.

The author thus sums up the general results of his memoir:—

“In the first place, it appears that the Alban volcano (for it is essentially one) has acted throughout a great period of time; for not only has it evidently repeatedly changed its form and materials of eruption, but it is surrounded by knolls of basaltic formations which seem to indicate very ancient and very repeated ejections, without taking the regular form of craters. Such are probably Monte Algido, Civita Lavinia, Monte Giove (Corioli), the Capuccini of Albano, Rocca Priore, Colonna, and perhaps even Capo di Bove, and several open craters, such as one a little below Albano, the Lago Cornufelle near Frascati, the Lake of Gabii, and one near Colonna which, on the authority of Ponzi, appear to have ejected peperino. The horse-shoe form of the old crater of the Alban Mount, which, whether formed by the elevation process or not, appears to be composed of beds of basalt, lapilli, tuff, or peperino, and here and there of the lava called Sperone, gave way, like that of Somma, on the western or seaward side, and I cannot but think it in no small degree probable, that the vast lava beds which lie under Nemi and Genzano, and which dip at a small angle under Monte Cavo, are part of the dislocated walls of the ancient crater displaced by the convulsion which rent it on the western side, and which was accompanied by a prodigious fluid discharge of peperino, which then formed the strata of La Riccia and Albano, and which, overwhelming the broken-down wall of the ancient crater, formed at the same time the Monte Gentile, and the peperino beds above Nemi.

Although Gamboge has been known in European commerce for nearly two centuries and a half, and its applications in the arts have been extended in recent times, the tree which produces it is still unknown to botanists.

The late Dr Graham, in 1836, was the first to describe accurately a species of Garcinia, which inhabits Ceylon, and which is well known there to produce a sort of Gamboge, not, however, known in the commerce of Europe. Resting on a peculiarity in the structure of the anthers, which are circumscissile, or open transversely by the separation of a lid on the summit, he constituted a new genus for this plant, and called it Hebradendron cambogioides. At the same period the Author examined the properties of this Gamboge, and found that it possesses the purgative action of the commercial drug in full intensity, and that the two kinds agree closely also, though not absolutely, in chemical constitution.

This deposit of shells is situated about a mile and a half west from Borrowstounness, where the Carse of Falkirk terminates in a strip of flat land a furlong in breadth. The shells are exposed in two openings, each about 300 feet long, made in the soil to procure limestone for Mr Wilson's iron-works. The bed can be traced in these openings along lines having an aggregate length of 1000 feet. Over all that spare the shells form an unbroken stratum of very uniform depth (nearly three inches), and almost perfectly horizontal.

On the 2d of January 1849, a communication, entitled “Theoretical Considerations on the Effect of Pressure in Lowering the Freezing-Point of Water, by James Thomson, Esq., of Glasgow,” was laid before the Royal Society, and it has since been published in the Transactions, Vol. XVI., Part V. In that paper it was demonstrated that, if the fundamental axiom of Carnot's Theory of the Motive Power of Heat be admitted, it follows, as a rigorous consequence, that the temperature at which ice melts will be lowered by the application of pressure; and the extent of this effect due to a given amount of pressure was deduced by a reasoning analogous to that of Carnot from Regnault's experimental determination of the latent heat, and the pressure of saturated aqueous vapour at various temperatures differing very little from the ordinary freezing-point of water.

In a letter dated Madras, November 1849, Captain Jacob says, “I have been much interested in reading, lately, Professor Forbes's paper in the Philosophical Transactions, 1842, Part 2, on the Extinction of Light and Heat in the Atmosphere.” As his results agree very closely with those of my experience on the Trigonometrical Survey of India, and which, though not founded on any precise measures, being still the conclusions of some years' experience, are perhaps worth noticing, particularly when they agree with the results of more exact measures.

The object of this paper is to shew how the laws of the phenomena of Elasticity and Expansion, as connected with heat, may be reduced to mechanical principles by means of an hypothesis called that of Molecular Vortices.

The author ascribes the first distinct statement of an hypothesis of this kind to Sir Humphrey Davy, and refers to Mr Joule as having supported it; but he states that its consequences, to the best of his knowledge, have not hitherto been developed by means of the principles of Analytical Mechanics.

The paper commenced with a suggestion, that, as the inferences of ordinary logic admitted no premises but such as were absolutely certain, and as the premises with which we have to deal in the business of life were not certain, but only probable, therefore it was highly desirable that we should have a logic, or rules for drawing inferences on the case of probable premises.

The attention of the Society was then drawn to the 15th section of the article Probabilities, in the Encyclopœdia Metropolitana, and especially to the following passage: “It is an even chance that A is B, and the same that B is C; and therefore, 1 to 3 from these grounds only that A is C. But other considerations of themselves give an even chance that A is C. What is the resulting degree of evidence that A is C?” To which query the answer in the Encyclopœdia is .

The object proposed by Dr Elton, is a summary of the knowledge we possess on the discovery of the Continent of America, by several adventurous European voyagers, anterior to the time of Columbus.

This subject, which has been for almost a century and a half well known to the students of northern history, was first made known to the rest of Europe by the publication of the Vinlandia Antiqua of the celebrated Torfœus in 1705; and most of the facts given by Dr Elton are extracted from that work. Torfœus proved from existing Icelandic MSS., that America was discovered, and even attempted to be colonized, by his enterprising countrymen, in the end of the tenth and beginning of the eleventh century; and the descriptions transmitted to us prove that they landed on what are now Newfoundland, Nova Scotia, Massachusetts, and Rhode Island.

This paper commenced by pointing out the insufficiency of all theories of elastic solids, in which the equations do not contain two independent constants deduced from experiments. One of these constants is common to liquids and solids, and is called the modulus of cubical elasticity. The other is peculiar to solids, and is here called the modulus of linear elasticity. The equations of Navier, Poisson, and Lamé and Clapeyron, contain only one coefficient; and Professor G. G. Stokes of Cambridge, seems to have formed the first theory of elastic solids which recognised the independence of cubical and linear elasticity, although M. Cauchy seems to have suggested a modification of the old theories, which made the ratio of linear to cubical elasticity the same for all substances. Professor Stokes has deduced the theory of elastic solids from that of the motion of fluids, and his equations are identical with those of this paper, which are deduced from the two following assumptions.

These letters were dated in August 1846 and September 1847. Earl Cathcart intended himself to have read them to the Society, but, having been prevented by his official duties from coming to Edinburgh, had sent them, to be communicated in his name.

In the first letter, the author, who had been sent to examine the geology of Canada, describes a visit which he made, on his way to Fort-William, Lake Superior, to the silver and copper mines on the south side of the lake, in the territory of the United States.

1. On the Purification of Sulphuric Acid.

The author, after describing the different methods, recommended for purifying sulphuric acid from nitric acid, namely, boiling with a little sugar, and heating with sulphate of ammonia, both of which had proved troublesome and imperfect, stated, that after trying various plans, the only one which he found to answer well, was the action of sulphurous acid on the oil of vitriol, after diluting it to the sp. gr. of 1·715, or lower. He adds one volume of water to three of the oil of vitriol, passes sulphurous acid gas through the hot liquid till it is in excess, and then boils off the excess of sulphurous acid; or, still better, three volumes of oil of vitriol are added to or diluted with, one of a saturated solution of sulphurous acid in pure water, and boiled. The acid is thus so perfectly purified from nitric acid, that when used for making hydrochloric acid, it yields a product quite colourless, which was not the case with the oil of vitriol purified by any other process.

Dr Wilson reminded the Society that he had announced to them in 1846 the occurrence of fluorine in the water of the Frith of Forth, and mentioned, that, in the preceding summer, he had found it in deposits obtained during the evaporation of sea-water from the Frith of Clyde, and the German Ocean. Professor Forchammer had made similar observations on the Baltic, and had furnished Dr Wilson with the account of them which follows. Before reading this, he wished to add, that he had recently examined incrustations from the boiler of a steam-vessel sailing between Liverpool and Dublin, and similar deposits from the Canada Transatlantic steamer, and H.M. war-steamer Sidon, which had been three years on the Mediterranean station. The different crusts were, without preliminary treatment, except reduction to powder, heated with oil of vitriol, and were found to yield an acid vapour which etched glass. Specimens of glass, in illustration, were shewn to the Society. From these observations, Dr Wilson inferred the presence of fluorine in the Friths of Forth and Clyde, in the German Ocean, the Irish Sea, the Atlantic, and the Mediterranean. He then proceeded to read Professor Forchammer's communication, which follows. It is dated, Copenhagen, 20th December 1849.