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.

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.

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.”

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.

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.

That the facts which I communicate regarding the natural history of the salmon in its earlier stages, may not appear altogether undeserving of consideration, I may premise that my remarks have not proceeded from hasty or imperfect observation, but from the experience of many years sedulously devoted to the subject, the whole of my life, with the exception of a few seasons, having been spent on the banks of streams where salmon are in the habit of depositing their spawn, and where of course the parr is likewise abundant. My opportunities of observation have thus been as ample, as my efforts have been unremitting and laborious, to discover the true history of this invaluable species. I shall here present a brief abstract of my earlier proceedings in relation to the subject.

We owe to Leibnitz the first suggestion of Differentiation, with fractional and negative indices, but no definite notion of the theory was attained until Euler expounded it in the Petersburgh Commentaries for 1731. Still Euler wrote only a few pages on the subject, so that the theory could scarcely be said to have come into existence, until Laplace, in his Théorie des Probabilités, and Fourier, in his Théorie de la Propagation de la Chaleur, shewed how general differential coefficients might be deduced by means of definite integrals, provided we assume or prove, by means of some elementary definition, that the differential coefficient of a circular or of an exponential function has a certain form. The formula given by M. Fourier is a very simple one; and our astonishment is great, when we reflect on the time which elapsed from its announcement to the first application that was made of it. This took place in 1832, in a memoir by M. Liouville, entitled Questions of Geometry and Mechanics resolved by a new analysis, which memóir is followed by two others on the more immediate theory of the analysis itself. Although M. Liouville regards his analysis as a new invention, we have no doubt that the idea is due to Fourier; but still to M. Liouville belongs the honour of moulding it into a shape capable of being made use of in the solution of problems.

In a former memoir on this subject, it was my endeavour to exhibit the principles of the science of General Differentiation in a simple, at the same time in a general, point of view. I endeavoured to deduce, from one general formula, results easy of application in all instances; and thus to exhibit the unity of the different parts of the science, and the completeness of its fundamental formulæ, shewing at the same time the facility of their adaptation to particular and varied cases. With the exception of certain expansions by means of a theorem analogous to the series of Taylor, I gave no application of the principles to problems of any kind. It is my intention in the present memoir to supply this branch of the subject, without which, indeed, however interesting may be the details, as a portion of pure analysis, they will offer little to interest any but those who attach themselves to the study of analytical combination. We hope, by the exhibition of a few simple mechanical problems, solved by this process, to give to our subject an interest in the eyes of all, derived not from its intrinsic beauty, but from its use as a medium of demonstration. It is well known that considerable difficulty hangs over several very simple inverse mechanical problems; from the generality of their statement, a direct solution is sometimes impossible by the ordinary methods. We shall shew that by our process such solutions are attainable with the greatest readiness. By this means we hope to give a value to our subject as a branch of knowledge, independent of that value which it must possess from its curious and elegant structure.

This mineral is found embedded in small crystals in prehnite, at Bishop town, in Renfrewshire. It had been long supposed by mineralogists to be a variety of zinc-blende; but it was first distinguished from that mineral by Lord Greenock, who communicated his opinion to Professor Jameson; and two small crystals, together less than a grain in weight, were sent to me for chemical examination by the latter, who concurred in the supposition that it was a new mineral.

Article 1. The introduction of the notion of a function of a variable quantity into the mathematics, without any regard to its particular form, has given vast extension to the science, and been the germ of some of its most important theories. The doctrine of curve lines, no doubt, produced that of functions, for the former may be made the visible expression of the latter: thus, either of the coordinates of a curve being taken as the representation of the variable, the other co-ordinate is a function of the variable; so also are the arc of the curve, and its area. Indeed, in contemplating functions, and discussing their properties, it is convenient to substitute in our reasonings the geometrical representation for the abstract notion of the function.

Avant de parler des dykes contenus dans la portion d'Arran au midi de la baye de Lamlash, portion que, vu l'augmentation du nombre des dykes et le peu de temps que j'avois à donner à leur étude, je n'ai pu examiner que très rapidement et incomplètement, je vais rassembler ici en une sorte de résumé, les résultats généraux de l'examen des faits consignés dans les tableaux suivants.

The ancient Greeks have laid claim to the earliest discovery of the method of manufacturing iron, but it will appear that the art was known in Persia at least as early as among the Greeks. The method of producing malleable-iron by a single process directly from the ore, is not indeed quite unknown at the present day, but it is believed to be altogether disused in Great Britain and throughout Europe; but there is no doubt that, in Britain, particularly at Castle Cough, Glamorganshire, and at Furness, near Ulverston, in Lancashire, as well as elsewhere, malleable-iron must have been known long before the discovery of cast-iron. In the 17th century, malleable-iron appears to have been made directly from the ore, in preference to the method now practised. In the Philosophical Transactions (for 1693, vol. xvii. p. 695), there is the following short notice by Mr Sturdy, of the method as then practised at Milthorpe-forge in Lancashire. “The forge is like a common blacksmith's, with a hearth made of sow-iron, in which they make a charcoal fire, and put in ore, first broken into pieces like a pigeon's egg; it is melted by the blast, leaving the iron in a lump, which is never in a perfect fusion; this is taken out and beaten under great hammers, played with water, and, after several heatings in the same furnace, it is brought into bars. They get about one hundredweight of metal at one melting, being the produce of about three times as much ore; no limestone or any other flux is used.” It has been doubted by an intelligent author (Farey on the Steam-Engine, p. 271), whether, by the process here described, the iron was really made directly from the ore, or only from pig metal. The existence, however, of a similar process at the present day in Persia, evidently the same which has been practised in that country from a very remote period, will make it appear not the least improbable that iron may have been thus produced from the rich hematite or fibrous red iron-ore of Lancashire.