The Mineral called Analcime or Cubizite has been ranked by Haüy among those crystals which have the Cube for their primitive form; an opinion which has been adopted by all succeeding mineralogists. No distinct cleavage-planes, however, so far as I can learn, have been observed in it. Crystallographers presumed that such planes must exist, and, allowing conjecture to supply the place of observation, they considered Analcime as differing in no respect from other crystals of the same series. This opinion was first rendered doubtful by the observation, that at thicknesses of of an inch, it displayed a considerable action upon polarised light; but though, from the tessular form of the mineral, this fact indicated something singular in its organization, yet, owing to the great difficulty of obtaining proper specimens, I have been baffled in repeated attempts to investigate its structure.

It is universally admitted, that, in the present advanced stage of Meteorological Science, nothing would be more desirable than complete and accurate registers of the indications of Meteorological Instruments,—more especially of the Thermometer, Barometer, and Hygrometer, such registers being cotemporaneously kept at numerous places, and at various elevations on the earth's surface. Many are the obstacles, however, which have been found opposed to such an acquisition.

My dear Sir,

I request you will do me the favour of submitting to the Royal Society the accompanying observations made at Paramatta and Sydney. Those of the Comet, together with the elements inferred from them, are exclusively Mr Rumker's, to whom it is impossible for me to give adequate praise, either for zeal, assiduity, or intelligence. In order to have a better chance of observing the transit of Mercury over the Sun's disk, I proceeded to Sydney, about 15 miles from hence, and I am happy to say that we had a most propitious day throughout for the observations, and that the near agreement of them at both places tends to confirm their accuracy, as well as to increase their value.

Although I possess a collection of specimens of Chalcedony, made expressly with the view to enable me to form some plausible theory of its formation; and; although my cabinet contains a variety of forms, perhaps unequalled in any other collection, I have, for many years, refrained from describing them, because the oftener I contemplated my specimens, the less able I found myself to apply any single agent, so that its operations alone could account for their forms. It is, indeed, very long since I entertained the opinion, that no hypothesis founded on the separate agency of heat or of water, could be satisfactory to speculative minds; and that geologists could never account for the formation of individual minerals, or of the rocks containing them, without combining the power of heat with that of water. But even this combination, though it can be easily conceived capable of forming many of the productions of the mineral kingdom, leaves numerous phenomena unexplained.

The following observations, which I have the honour to present to the Society, have arisen out of an inquiry into the structure and distribution of the nervous system throughout the animal creation. It will readily be imagined, that the nerves supplied to the organs of sense, did not fail strongly to attract my attention, and that those belonging to so important an organ as the eye, were considered by me as worthy of the most minute investigation. It was impossible to proceed in this inquiry without submitting the organ itself to a very careful examination, in executing which, several important facts presented themselves, which I believed to be novel, at least, to lead to views respecting the physiology of the eye, different from those generally adopted. It became my duty to search into authors of the present and of the past age, and to collect into view whatever had been previously written on the subject; but leisure being altogether wanting for such an undertaking, I have thought it best to describe what I have myself seen.

Since the perfecting of a Natural Arrangement has become the grand object of scientific pursuit, it has been found necessary to enter more minutely than was required by an artificial system, into modifications of structure and function. Botanists have no longer rested satisfied with observing plants in their fully developed forms, but have also had recourse to several other periods in the existence of vegetable life, the observance of which gives much insight into the organisation of the individual. Of these there is none more important than germination, which is often the only means afforded for ascertaining the structure of the seed. This is the case with all the cryptogamic tribes, the seeds of which are generally so minute, that many of them must be brought together before they be distinctly visible.

In the year 1818, my attention was accidentally directed to the subject of water in crystallised bodies, by the explosion of a crystal of Topaz, which I had exposed to a red heat, for the purpose of expelling its colouring matter. This violent disruption of the specimen, which was shivered into a thousand films, of extreme tenuity, arose from the expansion of the imprisoned fluid, and induced me to institute a series of experiments, for the purpose of determining the nature of the fluid, the form of the cavities which contained it, and the arrangement of these cavities in reference to the crystalline form of the mineral.

As it is my intention soon to publish, in various works on Natural History, the observations on the Botany of India which I made during my residence there, I wish to place on record an account of the opportunities which I enjoyed of making such observations, with the view of explaining to the Botanist where he may find the various collections which I made in different parts. I also wish to explain the geographical terms that I shall employ, in giving an account of the places where I found each species. For this purpose I prefer using the ancient Sanscrita names, both as being more scientific, and as being more likely to remain permanent; for, after a lapse of many ages, they continue to be known to all Hindus of learning, while each new invasion or revolution sinks into immediate oblivion the mushroom appellations imposed by modern rulers, whether Muhammedans or Christians.

In the present state of mathematical science, cultivated as it has been, with assiduity, during the two preceding centuries, it can hardly be expected that any considerable improvement remains to be made in Plane Trigonometry, one of its most elementary theories. There is, however, one case in the resolution of oblique-angled triangles, which appears to me to admit of a solution somewhat more simple and convenient than those which are commonly known; it is that in which two sides and the included angle are given to find the third side.

The history of the progress of discovery in the Natural Sciences, records innumerable instances, where the different ways of considering the same subject have created apparent contradictions, which have subsequently been reconciled by more accurate examination. The first observation of facts is very often far from being accurate; and, in most cases, this inaccuracy cannot be corrected, till the science itself has attained a higher degree of perfection. The optical and crystallographic inquiries into the nature of mineral substances, refer equally to the regular forms which these bodies present. The object of Crystallography is to ascertain this regular form from direct observations; and that of the department of Optics, which relates to this subject, is to determine the action of regularly crystallised bodies upon light. According to certain general laws, it has been found possible to argue from the optical phenomena to the external forms of minerals, and inversely from these forms to the actions dependent upon them, which affect light in its passage through crystallised substances.

The experiments which I now submit to the Royal Society are repetitions of those I made many months ago, for the purpose of ascertaining the Specific Heats of the Gases. The importance of the subject so impressed my mind, that I determined to spare no pains in the prosecution of the inquiry, and therefore I willingly withheld my first experiments from the public eye, until, by a fresh series, I might present them with the greater confidence. The apparatus employed in these experiments was calculated to operate upon greater quantities of the Gases than the former one, and as every precaution which had been suggested was adopted, they have, perhaps, given even more decisive results than the last. The results themselves, however, are in every important particular exactly the same. It is also but justice to myself to state, that the conclusions which the former experiments led to, were exactly the reverse of what I had anticipated, and that they seemed at the time totally opposed to the doctrines of Black and Crawford, which I am still disposed to credit to a limited degree.

In the Paper which I had the honour of submitting to the Society, on the Two New Fluids in mineral bodies, I have given the index of refraction for the most expansible of the two, as it exists in the cavities of Amethyst; but as I had not then ascertained the refractive power of the second fluid, and as the principal phenomena of the two fluids, especially those which related to their properties when taken out of the cavities, were observed in specimens of Topaz, it became desirable to have an approximate measure of the refractive power of both of them, as they exist in that mineral. As the fluid in Amethyst had never been examined in the open air, its identity with that in Topaz was inferred solely from the equality of their expansion by heat, so that the determination of the refractive power of the latter was necessary to establish either a difference between these two substances, or their perfect identity.

In the course of some inquiries into the affinity and structure of the Greek and Latin languages, I was led to analyse the superlative degree of both, and to trace, as I thought, some connection between it and the word Sublimis. While engaged in the investigation, I was naturally led to examine the common theories respecting the etymology of this remarkable word, and, in particular, the origin assigned to it by the late Dr Parr, and to weigh, with more attention than I had previously done, the arguments and proofs he had advanced in support of his opinions. All that I knew of them, till lately, was by verbal report, as I had not seen the abridged statement of them in an Appendix to the Notes of the 2d edition of Mr Stewart's Essays.

The public attention, animated by scientific controversy, has of late years been much directed to Geological subjects; and the certainty of many important facts, has in consequence been ascertained beyond dispute, which were formerly unknown, or at least involved in such obscurity, that no person could have ventured to assert them, without being charged with extravagance. But though, no doubt, many branches of this science still remain to be investigated, such inquiries may now be said to have acquired a considerable degree of consistency and interest, from the substantial basis upon which they have been found to rest.

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.