From the intimate connexion of the present subject with the improvement of the Achromatic Telescope, it must be admitted to be one of the most important in Optics; while, from the minuteness of the effects which are to be observed and compared, it is unquestionably one of the most difficult. From this cause very little progress has been made in the investigation. The irrationality of the coloured spaces, in prismatic spectra, formed by different substances, has not even been mentioned in any of our elementary treatises on Natural Philosophy, and there are some philosophers who have scrupled to receive it as a truth established in Physics.

In a paper which I had the honour of submitting to the Society, at the end of last session, I gave a detailed account of the effects of mechanical compression and dilatation, in communicating to glass and other uncrystallised bodies, all the properties of doubly refracting crystals. I had at that time attempted, without success, to alter the polarising structure of doubly refracting crystals, although I applied the force of powerful screws to Topaz, Rock-crystal, and Calcareous spar. All the specimens which I employed were crushed to pieces by the pressure, but exhibited no traces of the coloured rings when exposed to polarised light.

It will be readily admitted by every person who has been accustomed to solar observations, that an apparatus for diminishing the intensity of the sun's light, without distorting or colouring the resulting image, is still a desideratum in Practical Astronomy.

Dr Herschel is the only person who has given any degree of attention to this subject. When he applied his powerful telescopes to examine the surface of the sun, he found that the ordinary method of attenuating the light by smoked or coloured glasses, was of no avail; and it was in the prosecution of his experiments for determining the relative advantages of differently coloured glasses, or of combinations of differently coloured glasses, that he was conducted to those splendid discoveries respecting the invisible rays, which have formed an epoch both in Chemistry and Optics.

Some years ago I proposed, as decisive of the question which has been the subject of controversy on the nature of Oxymuriatic and Muriatic Acids, the experiment of procuring water from muriate of ammonia, formed by the combination of dry ammoniacal and muriatic acid gases. Muriatic acid gas being the sole product of the mutual action of oxymuriatic gas and hydrogen, it follows, that if oxymuriatic gas contain oxygen, muriatic acid gas must contain combined water; while, if the former be a simple body, the latter must be the real acid, free from water.

The Chloridic Theory, though more limited in its application to chemical phenomena, than the Antiphlogistic, may justly be regarded as of scarcely inferior importance. If established, it leads to the adoption of entirely new views concerning combustion and many of its products; it removes the muriates, a set of apparently well characterised saline bodies, from the class of salts altogether; and it has given birth, by analogy, to two new genera of compounds, in which iodine and fluorine, like chlorine, act a corresponding part with oxygen, in the system of Lavoisier.

Explosions in mines, from the kindling of the inflammable gas called Fire-Damp by the miners, have always occasionally occurred. Of late they have become more frequent in some of the coal-mines in this country, particularly those in the districts of the Tyne, and the Wear, in the North of England, and have been attended with such fatal consequences, as to have forcibly called public attention to the subject. In an explosion in one mine, about two years ago, ninety-two persons were killed; in another, which occurred soon after, thirty-two lost their lives; in one which happened within these few months, fifty-seven persons were destroyed; and recently, it has been affirmed, that several hundred lives are lost annually from this cause. From the state of the mines, particularly in the accumulation of wastes, the collection of water, and the increasing depth of the workings, there is reason to fear, too, that such accidents will become more frequent. Humanity loudly calls, therefore, on every effort being made to obviate the calamity; and even as a national concern, the immense loss of property in the mines, and the probability which has been suggested, that the working of them must ere long be abandoned, give to the subject the highest claims to consideration.

In the Philosophical Transactions for 1816, I have described at great length the various phenomena which are exhibited by glass and other substances to which the property of double refraction has been communicated by heat, by rapid cooling, by evaporation, or by mechanical compression and dilatation. In pursuing the same subject, I have observed many singular facts respecting the developement of new axes, by a change in the form and condition of the plates; and by submitting the phenomena to accurate measurement, I have succeeded in determining the laws which regulate the distribution of the polarising force. A brief account of these results will form the subject of the following paper.

The divisions of the day which different nations have employed, are denoted by hour-lines of various kinds on the sphere. Of these hour-lines, drawn on a supposition that neglects the inequalities of the Earth's motion, there are three kinds.

The first kind denotes hours counted from the meridian, equal to each other at all declinations of the sun. These lines are great circles on the sphere, passing through the poles of the equator, and every pair intercepting a similar arc on each of the parallels. Of this kind are the hour-lines of sidereal time, counted from the meridian, and the hour-lines of solar time, counted from the meridian.

The obligations of Experimental Physics to the labours of Lord Bacon, have been largely acknowledged by the generality of those who have treated of the History of Modern Science; insomuch, that the title of Father of experimental Philosophy has been oftener conferred upon him than upon any other of its benefactors. There are some, however, who seem to think, that there is no good ground for honouring him with this title, either on account of the merits or the effects of his writings. They do not indeed deny, that his views as to the proper objects and method of philosophizing were extensive and just; but they contend, that he had no peculiar merit in having stated these views; that all that he taught was virtually and more effectually taught by the discoveries of some of his contemporaries; and that, in fact, there are no traces of his agency to be found in the discoveries that followed.

As far as we can judge from historical records, the primeval mode of disposing of dead bodies, was by inhumation. It has been observed in another essay, that according to Pliny, the ancient Romans did not burn their dead, but consigned them to the earth. It must be admitted, however, that by some the mode of cremation had been preferred in a very early period of their history; as we cannot otherwise account for the prohibition, which Plutarch ascribes to Numa, as to the burning of his body.

The following circumstances respecting the Blind and Deaf Boy, James Mitchell, have come to my knowledge since the publication of Professor Stewart's Memoir; and I doubt not but the Society will think them worthy of being recorded. They are derived from the most accurate and authentic of all sources, the boy's sister, Miss Mitchell.

In the month of April 1814, Mr Parker, an English gentleman, (distinguished, as I have since learned, for his active benevolence,) did me the honour to wait upon me, to communicate a plan for the instruction of young Mitchell, which had some time before occurred to him, and which he was very desirous should be put to the test of experiment. This method seemed in no respect inconsistent with those principles which in all circumstances appear to regulate the acquisition of language; and I therefore expressed my willingness, to promote, by every means in my power, the object which Mr Parker had in view.

Nice is situated on the shore of the Mediterranean, in lat. 43° 41′ 16″ N. and long, east of Greenwich 7° 16′ 37″. The county of which Nice is the capital, was comprehended in the Roman province of the Maritime Alps: it was included, while under the influence of France, in a department to which the same name was given; and now, it is restored to the sovereignty of Piémont, it may be considered as bounded on the west by the Var, which separates it from France, on the north and east by the mountains of Dauphiné and Piémont, and on the south, it is washed by the Mediterranean.

The distribution of Heat over the surface of our Globe, is a capital object in the economy of Nature. The infusion of that active element communicates to bodies the principle of motion, and quickens the ceaseless revolution of the circle of generation and decay. But Heat, unlike air, water, or earth, appears never in a distinct and separate form: It exists onlv in a state of combination with other tangible substances; among which, it migrates from one to another. On the regulated tide of this transmission, depends the stability of the present order of things.

The practicability of instructing in any kind of language a person blind and deaf from infancy seems not to have occurred to the friends of James Mitchell till suggested by Dr Gordon, whose ideas on the subject are contained in Professor Stewart's account published in the Transactions of this Society. An attempt has been since made to put in practice a plan for the same purpose, proposed by Mr Parker, an English gentleman who resided for a short time in Scotland. This consisted in accustoming him to handle the letters of the alphabet, formed of pieces of wood or paste board, when placed together so as to compose different words significant of tangible objects, and making him handle the objects in order to learn their meaning.

It has long ago been remarked by the Abbé Hauy, that the property of Double Refraction is not possessed by any of those crystals the form of whose integrant molecule is distinguished by its symmetry, such as the Cube and the Regular Tetraedron. This class of minerals comprehends Fluate of Lime, Muriate of Soda, Spinelle Ruby, Muriate of Ammonia, Alum and the Diamond; and though M. Hauy had examined only a very small number of doubly refracting crystals, yet, with the exception of the Diamond, which I have found in many cases to possess the property of Double Refraction, his remark was confirmed by the experiments of Malus, Biot and myself, who considered all the crystals of this class as exercising no more action upon polarised light than a mass of water.

Having for a number of years been constantly moving about, in situations where I could not convey large astronomical instruments, I have repeatedly tried to what extent of accuracy and consistency I could arrive with the smaller ones. The results have convinced me, that a great deal of accuracy may in that way be obtained; and that the sextant is an instrument, which, if perfectly understood, would be in higher estimation, and more general use, than it is at present. The observations I am about to submit, were made with a ten inch sextant of Troughton's, divided on platina to 10″, (No 1200).

It has been long known to those who have studied the optical properties of Calcareous Spar, that there are numerous specimens of that mineral which form a multiplicity of images, affected with the most brilliant colours. These colours were considered by Malus, and other philosophers, as the colours of thin plates, and were supposed to be produced by a film of air, included in accidental fissures or fractures within the crystal. I have already shewn, from numerous experiments, that this opinion is erroneous, and that the various colours with which the images are affected, arise from the transmission of polarised light, through an extremely thin film or stratum of calcareous spar, which has different thicknesses in different specimens, but which has an invariable position, being always parallel to a plane passing through the longer diagonals of the rhomboidal faces.

It is possible, that the following observations may contain little that is new to those who are familiarly acquainted with the details of the science of Hydrostatics. But as I have not met with any remarks on the subject, in the course of my limited reading, the experiments which were performed, and the conclusions to which they lead, are here submitted to the consideration of the Royal Society.

The descriptions which historians and geographers have transmitted to us of the ancient world, are not generally deficient either in copiousness or accuracy. The theatre of those great events, which still interest mankind, may be commonly ascertained with sufficient precision. The distinct knowledge of the ancients, however, was limited to a certain sphere; after passing which, clouds always begin to envelope it. The almost total change of names, the uncertainty as to their itinerary measures, and the defects of their mathematical geography, leave no perfectly fixed point on which we can rest.

Alexander Tytler was born at Edinburgh, 15th October 1747. He was the eldest son of our late venerable associate William Tytler, Esq. of Woodhouselee, in the county of Mid-Lothian, and of Anne Craig, daughter of James Craig, Esq. of Costerton, in the same county.

If the most important education is that which is received beneath the paternal roof,—if it is there that the principles and tastes of future life are chiefly formed, the education of Mr Tytler began under fortunate auspices. His father was a man of high honour, of generous affections, of cultivated taste, and of distinguished eminence in his profession.