I Had last winter the honour of laying before the Royal Society a few hasty remarks on what are called the Parallel Roads of Glen Roy, suggested to me by an accidental ramble through that valley, in the course of a pedestrian tour in the West Highlands, during the previous August. My curiosity having been much excited by what I then saw, I was induced to revisit the highly interesting district of Lochaber, in the beginning of last June, and had thus an opportunity of devoting three whole days to a more complete inspection of these remarkable shelves, which I was surprised to find, were to be traced through a much more extensive stretch of country than former observation had led me to imagine. My first visit to Glen Roy was accidental; but upon this late occasion, I went with the purpose of endeavouring to put myself in possession of all the facts I could possibly collect, regarding these curious appearances; and in doing this, I had several advantages which I did not formerly enjoy.

The subject of poisonous fish has long been a source of puzzle and speculation to the inhabitants of the West Indies. Much has been conjectured upon it, and numerous tests and theories been proposed, which have had for a time their believers and advocates; but all have been found to be equally baseless. The author of this paper, by a narrative of what he has himself seen and observed on the subject, proposes rather to shew to the Society what it is not, than what it actually is, and thereby to clear the way for the future successful investigation of this curious and interesting phenomenon, by dissipating many erroneous notions that stand in the way of the discovery of truth.

Throughout the greater part of the West Indies, the accident of meeting a poisonous fish is a rare and extraordinary occurrence. At Barbadoes, for instance, it happens so seldom, that the majority of even the best informed inhabitants can scarcely be made to believe, that it has ever taken place amongst them.

While examining an abandoned lead-mine in the vicinity of Stromness, in the year 1803, I found a mineral which, from its weight and appearance, I supposed to be carbonate of barytes. A few hasty experiments soon convinced me that it was a different substance; but circumstances occurring which prevented a more accurate investigation, the mineral lay neglected among the duplicates of my collection till last autumn, when having mentioned my doubts and conjectures respecting it to my friend Dr Murray of Edinburgh, I was strongly urged by that gentleman to undertake its analysis. During his short visit to Liverpool, a few preliminary experiments were begun, from which it appeared, that the mineral contained carbonate of strontia, and I have since completed its chemical examination.

Having heard at Port-of-Spain of an appearance that went by the name of the Mud Volcanoes, we took the opportunity when surveying the southern quarter of Trinidad, to examine them. They are situated near Point Icaque, the southern extremity of the island, on an alluvial tongue of land, that has been appended to the primitive rocks, where no doubt the land originally terminated. This appendage is several miles in length, and points directly into one of the mouths of the Oronoko, on the mainland, about twelve or fifteen miles off.

We landed nearly opposite to where we were told we should find the mud volcanoes, and after making our way about five miles through the woods, across the sandy isthmus, we came upon two plantations very pleasantly situated, amidst a group of remarkable round little hills, each from eighty to a hundred feet in height.

Having had frequent opportunities, during my residence in France, of seeing a great many Repeating Reflecting Circles, several of which I have observed with, and having found much consistency in the results deduced from observations made with them, it occurred to me, that if I could engage Mr Troughton to execute one for me, it would be a most perfect instrument. This he accordingly did; and I trust that the observations made with it, which I am about to communicate, will perfectly justify the opinion I had formed of its precision. The instrument is only of about six inches radius, divided in gold to 20″. I have always been in the habit of choosing for latitudes 30 repetitions, when the weather would permit, divided into three series of 10 each, and reading the angle or arc run through during the series, which completely destroys every imperfection of the division, or reading. In order to determine the time, I have always found six repetitions quite sufficient to give it as correct as equal altitudes.

The quarry of Niteshill, from which this very interesting petrifaction was taken, lies about three miles south-east of Paisley, and is part of a coal formation. It consists of white sandstone, which in many parts is deeply stained by an impregnation of iron. Two very thin seams of excellent coal occur immediately under the sandstone, with the intervention of a few feet of till or blaize. The strata dip to the south, and crop out about a hundred yards north of the spot from whence the tree was taken. At this spot the face of rock is about sixteen feet; fourteen feet above the tree, and one under; another foot being occupied by the stem itself.

The part which has been detached from the rock consists of stem and roots, five feet of stem, and two of roots, different views of which I have endeavoured to represent in figures 1, 2, & 3.

When I lately mentioned to you in conversation, the disease in the eyes of horses in India, occasioned by the presence of a worm within the ball of the eye, I thought that you might probably have heard of it before; but as you had not, and are desirous of further information upon the subject, I now take this method of mentioning the circumstances to you, so far as I know them.

The animal occasioning this disease, is termed by the natives about Madras, the “Worm” in the Horse's Eye, by using the corresponding words in their respective languages. I have been told that in Bengal it is called the “Sānp” or the Snake in the Horse's Eye. As it seems more to resemble a fish or an aquatic insect, it might perhaps with more propriety be regarded as an eel.

The author of the Naval Tactics is one of those men who, by the force of their own genius, have carried great improvements into professions which were not properly their own. The history both of the sciences and of the arts furnishes several remarkable examples of a similar nature. Fermat the rival, sometimes the superior of Descartes, one of the most inventive mathematicians of a most inventive age, was by profession a lawyer, and had only devoted to science the time that could be spared from the duties of a counsellor or a judge: about fifty years earlier, also, his countryman Vieta had made a like digression from the same employment, and hardly with inferior success.

Perrault, who, in the façade of the Louvre, has left behind him so splendid a monument of architectural skill and taste, was a physician, and not only practised, but wrote books on medicine. Dr Herschell too, who has made more astronomical discoveries than any individual of the present age, betook himself to the study of the heavens as a relaxation from professional pursuits.

In plates of Rock-Crystal cut perpendicular to the axis of the prism, an unusual kind of polarisation had been observed in the colours seen along the axis. The phenomena were subsequently analysed by M. Biot, who remarked, that in some specimens of quartz, the succession of tints appeared by turning the doubly refracting prism from right to left, while in other specimens the same succession was developed by turning the prism from left to right; and he concluded from his experiments, that the quartz impressed upon the particles of light a rotatory motion, and that this property belonged to the ultimate particles of silex, and was independent of their mode of aggregation.

The same species of colours was afterwards observed, about the same time, by MM. Biot and Seebeck, in transmitting polarised light through considerable thicknesses of some essential oils, and solutions of sugar and camphor; and this new fact seemed to confirm the supposition that the colours were not dependent upon crystallisation.

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.

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.

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.

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.

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.