1. The Council of the Royal Society of Edinburgh having, on my application in 1832, entrusted me with Hansteen's Magnetic Intensity Apparatus, in their possession, I feel it to be my duty to communicate to the Society the results then and subsequently obtained with it.

2. The instrument consists of a mahogany box 5 inches long, 4 broad, and 2 deep, with sides and top of glass, having also a wooden tube, screwing into the top, for containing a silk-worm's fibre about 5 inches long, by which the magnetic needle is suspended so as to place itself horizontally, and after being caused to deviate from its point of rest, the time of any given number of oscillations in a horizontal plane is measured,—whilst a graduated circle in the bottom of the box indicates its arc of vibration.

The following observations of the direction and force of the wind, were made with an anemometer lately invented by Professor Whewell of Cambridge.

In this instrument the only part that is fixed is a japanned cylinder, on which the points of the compass are marked by black lines dividing it in its whole length into compartments, corresponding to the spaces intervening between any two double points. On this the other parts are supported by means of a strong rod which runs down the centre of the cylinder, and, terminating in a sharp point, turns easily round as the wind changes. A single broad vane, having the rod running down the centre of the cylinder for its axis, presents to the wind a fly resembling the sails of a wind-mill, and causes the moveable part of the instrument to revolve round the fixed cylinder as the wind changes; so that the aërial current, come from what quarter it may, blows against the circular disk of the fly, and turns it with a velocity proportional to the force of the wind at the time.

The history of the newer sciences presents many instructive examples of the progress of the human mind in developing the germs of natural knowledge, and building on a single observation entire departments of science. Few pursuits indeed are more interesting, even to the student of immaterial nature, than in the perusal of such a history to trace the footsteps of the several investigators, and to mark how far, and by what means,—whether by new methods or by greater patience of research,—each successive observer advanced the inquiry. We see the human mind, as it were, set free from the trammels of time, and developing its resources on a large and continuous scale, not limited by the powers of one intellect, the length of one life, or the means of one station. We see, at the same time, what varied gifts and opportunities are necessary for the elucidation of a single subject; how these gifts, though not all imparted to one man or to one generation, are yet wisely and beneficently bestowed on the entire species; and how all are thus enabled to co-operate, either in unfolding abstract truth, or in drawing forth those practical results which directly conduce to the amelioration and comfort of all.

In the end of May, or beginning of June last, I happened to stand near a locomotive engine on the Greenwich Railway, which was discharging a vast quantity of high-pressure steam by its safety-valve. I chanced to look at the sun through the ascending column of vapour, and was struck by seeing it of a very deep orange-red colour, exactly similar to that of dense smoke, or the colour imparted to the sun when viewed through a common smoked glass.

I did not pay much attention to the fact at the moment, nor attempt to vary the experiment; but, reflecting on it afterwards, it seemed to me not only as in itself very singular, but as still more extraordinary, because I had never heard of a property of steam which must have been witnessed by thousands of persons. Some months after (in the end of October), being on the Newcastle and Carlisle Railway, I resolved to verify the fact, which I had no difficulty in doing, and I farther discovered a very important modification of it. For some feet or yards from the safety-valve at which the steam blows off, its colour for transmitted light is the deep orange-red I have described.

In the following Paper, it is proposed to illustrate more fully the hint explanatory of certain atmospheric colours, given in a notice of the remarkable red hue of condensing steam, communicated on the 21st January. Since that time, I have examined with care the principal authors who have adverted to the subject of the colour of the sky generally, and of the redness of sunset in particular; and since, in the course of that research, I have found much to confirm, and little to modify, the view which I have already taken of the subject, I hope that the present Paper may be considered as a fit appendix to my former experimental notice. It will be recollected that in it I stated the singular fact, that steam does not pass at once from the state of invisible pellucid vapour to that of a misty white cloud, such as issues from the spout of a tea-kettle; but that an intermediate stage occurs, in which it is coloured, even very highly, giving to transmitted light a hue varying from tawny yellow up to intense smoke-red. I then observed, that, since this phenomenon does not require steam of high tension for its production, it is very probable that the tints of sunset and of artificial lights seen through certain fogs, may be owing to the absorptive action of watery vapour in this critical condition.

In the summer of 1834, I was led to examine with considerable interest some of the phenomena of fluids, from the circumstance of having been consulted upon the means of improving a system of navigation to be conducted at unusually high velocities. Being well aware, however, of the very imperfect state of that part of Theoretical Hydrodynamics which relates to the Resistance of Fluids to the Motion of Floating Bodies, and that there had been found in its application to the solution of practical questions, discrepancies so wide between the predicted results and the observed phenomena, as to render the principles of the theory exceedingly false guides, when followed as maxims of art, I felt i t impossible to recommend conscientiously any mode of procedure founded on defective principles, and I therefore determined to undertake a series of investigations concerning the laws of the resistance of fluids, and the means of applying them to the formation of rules for the arts of practical navigation and naval architecture. In this investigation, I have now been engaged during the leisure of two summers, and I am still continuing to prosecute the investigation.

The following paper contains a continuation of the experiments on the action of the voltaic pile on alcohol, and some other liquids, of which experiments a considerable number was described to the Royal Society in a former memoir. At present it is intended, in the first place, to shew the perfect analogy between the electric action on pyroxylic spirit, and on alcohol, thereby confirming the interesting analogy already known to exist between these fluids in other respects: in the second place, to adduce a few farther illustrations of secondary voltaic actions in aqueous solutions; in the third place, to examine the nature of the changes produced in alcoholic solutions, under galvanic agency; in the fourth place, to inquire whether electric action does not throw light on the state in which the haloid salts are dissolved by water; and, lastly, to endeavour to suggest as a general law, regulating the electric decomposition of solutions of binary combinations of elementary substances in the principal solvents, that the dissolved body is not directly decomposed, but only the solvent, if itself an electrolyte.

It is well known, that when light is incident on a refracting surface, a portion of it is reflected, whilst both the transmitted and the reflected light undergo polarization. The obvious mode of accounting for this, is to attribute to the particles on whose motion light is supposed to depend, the property of transmitting one class of vibrations more freely than another, limited, however, by the direction and mode of action of the adjacent particles. M. Fresnel, in order to determine the intensity of light reflected and refracted under different circumstances, assumed that the density of the particles of ether is greater in refracting media than in vacuo. By means of this assumption, and other subsidiary ones, he deduced formulæ for the intensity of the reflected and refracted light, by means of which the amount of polarization, as well as the change which the plane of polarization undergoes, can be readily deduced. The obvious interpretation of the formulæ coincided precisely with discoveries which had been long known, and the more difficult deductions from them have been tested by numerous experiments of Sir David Brewster and others. It appears that, although for highly refractive media, they may be only approximations, yet, in most cases, they are so close as to deserve the most careful attention of those who endeavour to establish a correct mechanical theory.

The preparation of my Lectures on Medical Jurisprudence involved a consideration of the means of diminishing the chances of successful forgery, and again engaged me on a subject to which, many years ago, my attention had been very painfully turned by the frequency of executions for that crime. This will scarcely appear exaggeration, when it is stated, that, in the year 1809, there were no less than thirteen executions for forgery in the county of Lancaster, where I then resided: and when it is recollected that, in the fourteen years preceding 1819, two hundred and four individuals perished on the scaffold for that offence in England and Wales, every means of discouraging so fertile a source of misery and crime must be allowed to be a subject of no trifling importance.

The analogy between certain properties of the co-ordinates of elliptic and hyperbolic sectors, which forms the subject of this memoir, was observed by the early writers on the fluxional or differential calculus, and employed by them in its improvement. But, independently of this important application, the propositions in question are some of the most elegant theorems in geometry, and highly interesting as abstract truths.

Maclaurin, in the third chapter of the second book of his Treatise of Fluxions, has proved the truth of this theorem: “Supposing n to be any number, let E and n × E be elliptic sectors, which stand on arcs that begin at a vertex of either axis, and H and n × H hyperbolic sectors, which stand on arcs that begin at the extremity of the transverse axis: the algebraic equation which expresses the relation between x and z, ordinates drawn to the other axis from the extremities of the arcs, must be the very same in the two curves.”

Although a great number of Fishes have been described by naturalists as inhabiting the coast of Scotland, and though much has been done to increase its Fauna in other respects, yet in a field so extensive much must still remain to be done. Many lakes and estuaries in Scotland are still unexplored, and many fishes being merely local, a more thorough and accurate examination of these lakes and estuaries must take place, before the Ichthyology of Scotland can be fully ascertained.

In the beginning of July last, I obtained, from the Frith of Forth, a species of bream, which has not been mentioned by naturalists as inhabiting the British seas. A few days after, I procured, from the same quarter, a second specimen of the same species, each exhibiting a conspicuous dark violet-coloured spot at the base of the upper part of the pectoral fins. (See Plate VI.)

On consulting the continental works on Ichthyology, I find this bream to agree best with the description Baron Cuvier has given of the Pagellus acarne, an inhabitant of the Mediterranean; but, as no figure of the fish accompanies his description, the discrimination of the species is rendered somewhat uncertain.

The Teviot, Clyde, and Nith, are well known to be among the largest rivers in the south of Scotland. In the lower parts of their course they are navigable; and all along their banks, nearly up to their sources, there are innumerable mills and manufactories, dependent on the continuous flow of their waters.

On the morning of the 27th November 1838, the channels of these rivers were, in the upper and middle parts of their course, found almost entirely empty. The thousands of water wheels, many of which had for years, without interruption, been turned by their currents, suddenly stopped. Immense quantities of fish, inhabitants of their deep and rapid streams, were destroyed by being left dry, or being caught with the hand in deserted pools; and in places where it was usually difficult for even horses to ford, it was easy for children to walk across without wetting their feet.

Previously to the 25th and 26th November 1838, there had prevailed in Great Britain and Ireland, for more than a week, a steady wind from the NE., accompanied with frosts, a progressively rising barometer, and tolerably clear weather. The same sort of weather existed on the Continent, and over a large portion of northern Europe, both on sea and land.

This state of things was changed, by the arrival of two storms from southern latitudes, which passed over the British isles during the last week of November. These two storms, until they reached this part of the globe, were separate. The first one reached the British seas, about thirty-six hours before the other. But the second moved with about double the velocity of the first, and overtook the first somewhere about the north of Ireland and south-west of Scotland. Accordingly, in the southern parts of England, there were distinct indicia of two different storms, each having its own period of arrival, veering, and cessation;—whilst towards the north, these indicia became gradually less distinguishable, and were at length significant of only a general gale.

The object of the following paper is to put at rest a question which has been long agitated in Surgical Pathology, and which is intimately connected with some important points of Practical Surgery. An apology may seem due to the Society for bringing under its consideration a subject, which, though not exclusively professional, is still little studied except by those physiologists whose views are directed to surgery; but as the inquiry into which I propose to enter is neither long nor tedious, while it is quite intelligible without any previous knowledge of its details, I trust the patience of the members will not be exhausted; and if the question shall, as I hope, be decided to the conviction of those members who are conversant with surgical discussions, the prevailing diversity of sentiment relative to the point at issue will be more effectually composed than if I attempted to combat it through any other channel.

There is no branch of natural science about which we know so little as that which relates to the structure of crystalline bodies. By assuming the form of an integrant molecule, crystallographers have found no difficulty in building those geometrical solids which minerals and artificial crystals present to our observation. They conceive that these molecules unite by their homologous sides in the formation of the primitive crystal, and by supposing that they arrange themselves in plates on the faces of that crystal, each plate successively diminishing in size by the abstraction of a certain number of these molecules in lines of a given direction,—all the secondary forms of the crystal may be easily deduced.

In the year 1830, I succeeded in establishing a Register of the Thermometer at the Bonally Reservoir, which formerly supplied the city water-works, being at a distance of five miles in a direction south-west from Edinburgh. This station is on the northern acclivity of the Pentland Hills, at a height of 1100 feet above the sea. The following year I obtained corresponding observations at the village of Colinton, situated a mile and a half north of the preceding station, and above 700 feet lower. Although this difference of level be not very considerable, yet, as these comparative registers have been kept for nearly five years with pretty uniform results, some confidence is evidently due to the conclusions, even although considerable difficulties opposed themselves to obtaining registers quite free from exception. The interest attaching to them is the greater, that, although registers have been kept at Leadhills and other elevated stations, I do not recollect any strictly comparative observations in Scotland, perhaps not even in Great Britain, at two stations near one another, and differing considerably in level, from which the important meteorological element of the decrement of temperature in the atmosphere could be deduced.

It is my intention to undertake a series of Memoirs on that branch of Hydrodynamics which treats of the transmission of reciprocating motion. It may appear superfluous at first, that any further investigation should be bestowed on the general problem, when it is remembered that two of the most able mathematicians of the present age, M. Poisson and M. Cauchy, have devoted so much of their talents and attention to the subject. Yet, when advances are rapidly making in our experimental knowledge, we generally find that the complex and apparently general results, deduced by those who have paid the greatest attention to the science as it presented itself to their view, are in reality only particular cases, when they have to be applied to experiments in their actual form. This circumstance detracts greatly from the value of almost all general investigations; and in this instance it does so in a remarkable degree. The prosecution of the research has been extended in one direction—the prosecution of experimental knowledge has taken another; and thus, in order to meet the challenge of experimenters to keep pace with them, it behoves the theorist frequently to return on his path, and cross over to the line of their march.

1. The following paper is divided into three sections, containing three distinct yet intimately connected investigations. The two first on the Polarizability and Depolarization of Heat have arisen immediately out of the train of investigation contained in my two former papers, and the researches of others to which they gave rise. The third is on the Refrangibility of Heat, a point of the highest importance for theory.

2. The experiments on which these investigations are based have been performed almost exclusively during the past winter. Part of the experiments on Depolarization were, however, made in the winter 1836-7. The mode adopted for trying Refractive Indices I had long ago contemplated. It was not, however, put in practice until January last.