The title which I have given to this paper, is, perhaps, faulty, and apt to lead the imagination to expect a description of the various forms of those sea-weeds which clothe the channel of the deep;—the arrangement of the species, as depending on the soil and depth of water, the food which they yield to the various creatures that browse upon them, and the protection they afford to such as take refuge among their leaves and branches. Very different, however, is the scene which I propose to describe,—a bed of peat-moss, covered by the sea at every full tide, but indicating, by the appearances which it exhibits, that its present low level is different from its original position. In other words, it is a geological phenomenon, occurring in the Frith of Tay, similar to the one observed on the Lincolnshire coast, which, in 1796, was examined by the late Sir Joseph Banks and Dr Joseph Correa de Serra, and described by the latter in the Transactions of the Royal Society of London for 1799, p. 145, under the title, “On a Submarine Forest, on the East Coast of England.” I venture to prefix the same title to this paper, which I now offer to the consideration of the Royal Society of Edinburgh, aware of its impropriety, but urged by the wish to connect similar phenomena by the common terms employed in their description.

The questions which I propose to examine in the following paper, although not themselves dependent on chance, have arisen entirely from games in which it predominates. To determine some method of betting upon a number of successive events, (and the probability of each of which is either equal to, or less than one-half,) by which a profit shall be realised after a considerable number of them have been decided, is a problem which has occupied the attention, and exhausted the efforts, of one set of speculators, as completely as that of the quadrature of the circle has defeated the labours of another. The first and most simple plan, is that of doubling the stake whenever a loss occurs. This is well known, and has been so frequently practised, as to have acquired a peculiar name; it is technically called the martingal; it requires for its success, that the person who employs it have the power of leaving off whenever he please, and that he have the command of an unlimited capital. If the chance of the events happening is one-third instead of one-half, the stake must be tripled.

The various facts concerning the radiation of caloric present a very interesting subject of inquiry, and various theories have been formed, with a view to their explanation. The principal difficulty has been to explain the facts of the apparent radiation of cold. The most simple theory with respect to these, is that proposed by M. Prevost of Geneva. He supposes, that all bodies are always radiating caloric in proportion to their temperature, and that those surfaces, which radiate least, make up for the deficiency, by reflecting most; so that the combination of reflection and radiation from any surface, when in æquilibrio with the surrounding bodies, is the same. When a body is heated, its radiation is increased, and therefore, when placed near a thermometer, it radiates more to the thermometer than it receives from it, and therefore elevates its temperature. When, on the other hand, a body is cooled, it intercepts from the thermometer near it part of the radiation of the surrounding objects, and it radiates less than it receives. The thermometer must therefore sink.

In a Paper on Vision through coloured Glasses, which I had lately the honour of submitting to the Society, I pointed out the advantages of coloured media in Microscopical and Telescopical observations. Having experienced the great utility of Green and Red lenses, in developing vegetable structures that required to be examined with high powers, I was anxious to derive from this new principle all the advantages which it appeared to possess. In attempting to do this, it became necessary to ascertain the power of giving distinct vision, which belonged to each separate colour of the spectrum, and though I had stated in my former paper, ‘that it was difficult to discover ‘any reason why one coloured medium should be preferred ‘to another, provided each of them transmits equal quantities ‘of homogeneous light;’ yet it was desirable to put this theoretical opinion to the test of direct experiment.

The notice which, at the suggestion of Dr Brewster, is now to be laid before the Society, respecting a remarkable shower of hail which lately fell in Orkney, has been drawn up partly from conversations with Richard Caithness, a plain but intelligent country man, who possesses a small farm at Hunday in the island of Stronsa, and whose property suffered severely from the shower; and partly from subsequent correspondence with the Reverend William Taylor of Stronsa, whose house lay in the track of the cloud, and with Mr Robert Lindsay, Student of Divinity, who had an opportunity of witnessing the effects of the hail at Lopness, on the neighbouring island of Sanda, when the shower was nearly exhausted. They agree in all important particulars; but even at the risk of some repetition, their own words shall, as often as possible, be employed.

The morning of the 24th of July 1818, was, in Orkney, clear and warm, with a slight air of wind at due south.

My dear Sir,

As I see by a notice in your Journal, No. 13., which has just reached my hands, that your attention has been occupied by the phenomena of Coloured Flames, and the Absorption of Coloured Light by Diaphanous Bodies; and that you have been successful in the very valuable discovery of a manageable flame, discharging a homogeneous yellow light of an invariable character, I shall perhaps be excused, while the contents of your paper are unknown to me more particularly, for stating some phenomena Which I have myself observed, relative to this highly interesting department of physical optics.

If no provision has been made by the Great Author of Nature, for equalising the light and heat projected upon the different bodies of our system, we may consider the earth as receiving, from the direct action of the solar rays, a degree of heat, intermediate between the condensed radiations sustained by Mercury and Venus, and the attenuated warmth which reaches the remoter planets. The heat which our Globe thus acquires from its locality in the system, is again tempered by the obliquity of its axis, and is distributed over the same parallels of latitude by its daily rotation. When the Sun is in the Equator, his rays, beating on the Earth with a vertical influence, impart to it the full measure of their action; and as his meridian altitude decreases, their intensity suffers a corresponding diminution. The burning heat at the Equator becomes moderated in higher latitudes. In passing through the temperate zone, it declines with great rapidity, and between the Arctic Circle and the Pole, the rays of the Sun are unable even to temper the piercing cold which reigns in these inhospitable regions.

In compliance with your request, I send you a few notes of some of the principal geological facts I observed in Faroe, which may serve as a supplement to Sir George Mackenzie's and Mr Allan's accounts of these islands, which, as far as they extend, I found perfectly correct.

The Coal in Suderoe, which was not visited by them, is situated between two thick beds of hard clay, resembling the Clunch-clay of this country; to which succeed beds of trap. In some parts, pieces of petrified wood are very abundant in the superincumbent clay, and also nodules of ironstone; and in the coal, pieces of wood resembling charcoal. The coal has the same degree of inclination as the other beds, dipping towards the south-east, at an angle of about 4° or 5°; being the same as the dip in the other islands, excepting in part of Myggenæas, where it is much greater, being near 45°.

As it very frequently happens that an observation may not be obtained for the latitude, at the precise instant of noon, it becomes a most desirable object to supply that loss by every possible means. The method which I am about to detail, I have long practised, and from the experience of many hundred trials, I can recommend it, as combining much simplicity with the greatest accuracy; since one day's observations may be equal to those derived from the chances of three weeks of the ordinary course of weather in our climate. This method consists in merely reducing to noon these observations, the same as if made when the sun's centre was on the meridian, by the means of a very simple calculation, which I shall detail, and illustrate with the observations for two days, in order to shew the accuracy of the results thus obtained. Having previously ascertained the time of noon, either by equal altitudes, or from simple ones, in the manner I had the honour to detail in a former communication to the Society, “On the Mode of determining Time with the Sextant” I begin nearly 10′ from noon to observe the sun's altitude, from an artificial horizon of oil, or quicksilver, and continue making as many observations as I can accomplish until the sun has nearly the same altitude as when I began, which will be the case about as long past noon, during which an expert observer will easily take 20 altitudes, which, in most cases, will be sufficient to enable him to retain all those that appear to be consistent, and to reject those that differ much from the mean.

The interesting discoveries of Oersted, and the subsequent researches of Ampere, Arago, Davy, and Von Buch, which promise to throw a clearer light on the mysterious nature of Galvanism and Magnetism, induced us to undertake, and pursue conjunctly, a series of Electro-magnetic experiments. In prosecuting our inquiries in this new branch of scientific investigation, we have observed various interesting facts, some of which appeared to us new, while others did not seem to have been detailed so fully as their importance merited.

The following conjectures concerning the Analogy observed in the formation of some of the Tenses of the Greek Verb seem worthy of farther inquiry; for, if well founded, they may be useful towards establishing juster rules for the formation of the Tenses in some instances; and, particularly, they will account for certain forms of the Verb in Homer and Hesiod, which, being apparent violations of the usual analogy, have perplexed the grammarians, and reduced them to the necessity of assuming imaginary new Presents, without authority, and for no other reason, but to account for such anomalous forms.

I some time ago had the honour to present to the Royal Society, a specimen of a very singular fossil which had been found in the freestone quarry of Craigleith, near this city. It presented the appearance so commonly met with in the sandstone of the coal-formation,—an impression of what has always been considered as the bark of a vegetable connected with the Palm-tribe; but it differed from any thing I had ever before seen of the kind, by having circular marks ranged in a line along the surface, being apparently the impressions of flowers or fruit. As neither of these grow directly from the stem of any plant now known, except among the Cactus genus, this impression might have been referred to it, had not the regularity of distance between these supposed flowers, pointed out the improbability; and it consequently must be referred to some one, the prototype of which is no longer known.

The size of the specimen, of which the annexed engraving is a very exact representation, is twenty-one inches in length, and about fourteen broad; the widest part of the impression measures four inches, and the diameter of the circles a little more than three.

The Native Hydrate of Magnesia was first discovered, and ranked as a separate Mineral, by the late Dr Bruce of New York. It was found only at Hoboken in New Jersey, traversing serpentine in every direction, in veins from a few lines to two inches in thickness. Its specific gravity was 2.13, and it yielded upon analysis 70 parts of pure magnesia, and 30 of water.

In the year 1813, I received some fragments of this rare mineral from our late eminent countryman Dr John Murray, and though it exhibited no traces of a crystalline structure, I found it to be a regularly crystallised mineral, with one axis of double refraction perpendicular to the laminæ. The connection between the primitive form of minerals and their number of axes of double refraction, which I observed at a subsequent period, enabled me to determine that the Native Hydrate of Magnesia belonged either to the Rhomboidal or the Pyramidal system of Mohs.

About ten months ago, I had the honour of communicating to the Royal Society, a description of a new instrument for ascertaining the Magnetic Dip. Having made very considerable improvements in the apparatus, by means of which some curious results on the magnetic laws, especially those that relate to the production and annihilation of magnetism in iron, have been obtained,—I now beg leave to submit to the Society a drawing and description of my improved instrument, together with an outline of some of the most interesting experiments made with it. Many of the results appear to me to be new; if so, their importance will be my excuse for repeating some parts of the description given in the former paper. It has been long known that iron might be rendered magnetical by percussion; but I am not aware that the precise effect of position has ever been suggested, I remain, &c.

It is no doubt already known to you, that the late Alexander Keith, Esq. of Dunottar, bequeathed the sum of L. 1000 for the purpose of promoting the interests of Science in Scotland. Having been appointed Trustees for the Management of this Fund, wa have endeavoured to appropriate it in the most advantageous manner for the advancement of Science; and we have the satisfaction of stating, that the plan which has been adopted met with the special approbation of Mr Keith himself, to whom it was communicated previous to his death.

As the Royal Society of Edinburgh is the principal Scientific Establishment in Scotland, we hereby offer to its President and Council the sum of L 600; the principal of which shall on no account be encroached upon, while the interest shall form a Biennial Prize for the most important discoveries in Science, made in any part of the World, but communicated by their Author to the Royal Society, and published for the first time in their Transactions.