The author stated, that the paper consisted principally of communications made by members of this society, which had been placed in his hands. Many points in the statistics of the storm had been noticed with great accuracy; and it is important, in the present promising condition of our knowledge of the statistics and philosophy of this branch of meteorology, that such communications should be arranged and preserved, for the purpose of furnishing materials for its improvement. The author went on to explain the views of the nature of storms which had been successively propounded by Franklin, Espy, Redfield, and Reid. He then read various communications of observations, from Sir John Robison, Professor Christison, Mr Nichol, Mr Stevenson, Professor Wallace, Mr Hunter of Thurston, Mr Scott, Sir David Brewster, Mr Russell, Mr Bald, and other gentlemen, who had, with himself, taken an interest in the subject. The paper concluded with deductions of a general nature from the facts observed.

The object of this paper was to develope an application of the fact communicated by the author on the 21st January. It was then remarked, that the discovery that steam in a certain stage of condensation is deeply red-coloured for transmitted light, seemed to offer a probable solution of a difficulty which has never yet been fairly met, namely, the red colour of clouds at sunset, and the redness of light transmitted through certain kinds of fogs.

A-pretty full history of theories proposed to account for the colours of the atmosphere was first given; it was obtained in almost every case from an examination of the original authorities.

The object of this memoir was to remove from the molecular theory, difficulties in which the recent investigations of Mr Green appear to involve it. The question at issue is the ratio of the densities of the ether within and without a refracting medium. The usual mechanical hypotheses would appear to lead to the conclusion that the former density is the greater; whilst from the molecular hypothesis the latter appears to be the truth.

Electrical observers have experienced three important defects in the common galvanic trough battery, as constructed by Cruickshanks, namely, that the zinc is deposited on the copper plates, that the zinc plates become gradually covered with a coating of oxide of zinc, and that the hydrogen formed by the decomposition of water adheres in globules to the surface of the copper; the result of all which circumstances is, that the galvanic action quickly decreases in force. These inconveniences have been in part removed in the battery of Professor Daniell, in which the zinc plates are covered by an animal membrane, and sulphate of copper is substituted for acids to form an exciting solution.

Various accounts have been given of the alcoholic strength of wines by Mr Brande, Julia-Fontenelle, and others. The author has been engaged for some time in experiments for determining the proportion of alcohol contained in various wines of commerce, and also the circumstances which occasion a variety in this respect. The present paper is an interim notice of the results.

The method of analysis consisted in the mode by distillation, which was applied with such contrivances for accuracy that nearly the whole spirit and water were distilled over without a trace of empyreuma, and without the loss of more than between 2 and 6 grains in 2000. From the quantity and density of the spirit, the weight of absolute alcohol of the density 793.9, as well as the volume of proof spirit of the density 920, was calculated from the tables of Richter founded on those of Gilpin.

The phenomenon was in the first instance described, and certain views were afterwards offered explanatory of it.

It appears that, betwixt 10 P.M. on the 26th November, and 6 A. M. on the 27th November, the channels of the Teviot, Clyde, and Nith, became nearly dry for a great part or their course, so that scarcely any current flowed in them. All the mills on the Clyde, as far down as several miles below New Lanark, were stopped from want of water. The Nith was nearly dry as far down as Enterkinefoot; and the mills on it, and on its tributaries, were stopped. This was the case also on the Teviot. The phenomenon was most strikingly manifested in the higher parts of the rivers, near their sources. The small streams from which they derive their supplies, were in general completely dried up. The rivers, in the lower parts of their course, were not entirely deprived of their current; nor were the rivulets, which there supplied them, nearly so much affected as the rivulets in more elevated districts.

“At the meeting of the Society on the 4th February, I remarked, on the occasion of Professor Kelland's paper on the Intensity of Reflected Light, that it was almost without a parallel in science, that a quantitative physical law like that of the intensity of the reflection of light at different angles, should have first been divined by the rare sagacity of Fresnel, and confirmed by the very different but elaborate mathematical investigations which Mr Green of Cambridge and Professor Kelland have applied to the subject, whilst scarcely any attempt has been made towards its verification by direct experiment.

The author proposes, in a series of memoirs on this subject, to investigate the different problems of Hydrodynamics, in a manner which shall carry theory along with experiment. From the great attention that has been of late years bestowed on the question of the motion of the tide-wave, any mathematical investigation which does not assume some process of approximation, is extremely interesting. Whilst the more recondite problems of motion derived from impulses, &c. have been carefully examined by the greatest philosophers of the present day, the more simple and easy ones have been left almost untouched.

This method is founded on the expedient devised by Mitscherlich, of obtaining two images of a minute distant object from a section of a hemitrope crystal of selenite, which is flat when cold, but is composed of two inclined surfaces when heated. By throwing the sun's image, reflected from such a surface, on a distant wall, the gradual formation of the double image during heating may be seen by any number of persons.

The results communicated to the Society were obtained from nearly five years of simultaneous observations, made twice a-day at Colinton and at the Bonally reservoir five miles south-west from Edinburgh. The height of the former station above the level of the sea is 364 feet, of the latter 1100 feet exactly; the difference 736 feet. The mean annual difference of temperature amounted to 3°.22, giving 229 feet of ascent for a diminution of temperature of 1° Fahr. The influence of the seasons is briefly shewn by the following numbers:

That the decrement of temperature is most rapid in summer, and least so in winter, has been long known.

While conducting some galvanic experiments, the author accidentally used an iron-wire as a positive electrode, and was surprised to find it was not oxidated, but, on the contrary, retained its original brightness, and gave out oxygen-gas from water placed under its action, in the same quantity as a platinum electrode would have done in the same situation.

Struck by this fact, he followed it up by a course of experiments, and arrived at the conclusion that iron is in a singularly anomalous electric condition, being positive when compared with copper, and yet far more highly negative than copper when compared in their electric relation with zinc: and that although copper and iron form a galvanic combination in which the iron is positive to the copper, yet, when iron is associated with zinc as a galvanic pair, it produces a more powerful current of electricity than a galvanic pair of equal-size, consisting of copper and zinc.

Mr Smith of Jordanhill stated the general results of his observations on the newest tertiary or pliocene deposites of Scotland. In every one of the maritime counties, elevated marine beds containing shells, of which about one-tenth are no longer to be found in the British seas, have been discovered. Some of the shells appear to have become altogether extinct, others occur in crag and Sicilian tertiary beds, and others in the Arctic seas,—indicating that the climate was probably colder at the period of their deposition.

The object of this paper is to investigate, for the ellipse and hyperbola, a series of propositions analogous to those which, in the circle, constitute the calculus of sines.

Any diameter of an ellipse, or a transverse diameter of a hyperbola, is expressed by a, its conjugate diameter by b, and the ratio of these diameters, viz. by c. The nature of the curves is exbpressed by this formula, In the ellipse, c has the sign +, but in the hyperbola the sign −.

The author described in this paper certain anomalous appearances presented by venous blood when left in contact with coloured porcelain. When blood drawn from a vein is either allowed to coagulate in a porcelain cup, or after coagulation is left in it for some hours, the dark purple tint characteristic of venous blood is found to be altered to the bright arterial hue, wherever it was in contact with any elevated device of the green colour, which is communicated by means of protoxide of chrome. In one instance the same effect was produced by a device of a crimson tint; but in more than sixty trials with this and every other variety of colour used in ornamenting porcelain, the author could observe no such effect as was invariably produced by patterns of a green tint.

It was stated, that the first indication of the advent of these two storms to the British islands was given by the barometer. On the 25th and 26th November, the barometer in all parts of the United Kingdom began to sink; and it is important to observe, that, not only when this sinking began, but likewise for nearly two days after, the wind was blowing E. or NE., and was accompanied by a severe frost, circumstances which of themselves cause the mercurial column to rise.

The functional equation to be resolved is this—

In this equation xo° and x′ denote any two values of the indefinite variable x, and c is a constant quantity. The object of inquiry is the forms of the function.

It is proved that there are two forms of the function, which alike satisfy the proposed equation: viz.

In the first of these functions x increases, while f(x) decreases; and in the second, x and f(x) increase together. The first of these functions is applied in the paper to the theorem of the Parallelogram of Forces, whilst the theory of Curves of Equilibration is deduced from the second function: these last, in their most general form, have two parameters. The curve of equilibration is formed by a perfectly flexible chain suspended in a vertical plane between two fixed points.

“As early as the time of Leibnitz, it was suggested that a general form might be discovered for differential coefficients, somewhat in the same way as that which applies to expansions. Notwithstanding this suggestion, the difficulty of the subject appears to have deterred mathematicians from engaging in it, until a few years since M. Liouville published a series of memoirs, in which its principles are developed, and theorems deduced applicable to the solution of a variety of difficult and important problems. Amongst a mass of particular results, the generalization of each of which would probably give a distinct aspect to the science, M. Liouville appears to have selected that one which is the most readily applicable to practice, and which, at the same time, affords conclusions remarkably convincing of its completeness.

The author, in this paper, gives an account of the continuance and confirmation of his experimental observations on the growth of salmon fry, as formerly communicated to the Society. He considers the objections made to his artificial ponds, in so far as they were supposed to afford an insufficient supply of food, to be without reasonable foundation, as these ponds actually abound with the ordinary insect food of fishes, and the young broods themselves correspond in every way to those of the same age in the natural streams and pools of the river. He had previously ascertained and stated, that young salmon remain in their native river for two years (under the names of parrs, pinks, fingerlings, &c), and during that period, or till near its close, he applies to them the name of parr, as that by which they arc usually designated in Scotland.

“It appears to the author, that the only fact established by the experiments of MM. Dulong and Petit is the following:—That the scale of measurement by which we express our knowledge of the state of heat within a body, is not applicable to the expression of the flow of heat within or from the surface of the body. Proceeding upon this supposition, he deduces the thermometric temperature of a body, from the formulæ in v, given by M. Fourier, taking the formulæ as finally obtained, believing them to be accurate expressions of physical conditions. As, however, the letter v cannot, consistently with MM. Dulong and Petit's experiments, denote the thermometric temperature, but some exponential function of it, the author proposes, in order to prevent confusion, to employ the word “thermature” to denote that to which the flow of heat is proportional.