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.

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.

In the month of September last (1822), when becalmed in my cutter in the Kyles of Bute, I accidently landed on the most northerly of the Burnt Isles, a small group that stretches across the Kyle or narrow channel between Bute and Argyleshire.

From the appearance of a ridge nearly covered with turf, I imagined at first that kelp had been formerly burnt here, but on examining it more narrowly I discovered that it was caused by the remains of a vitrified fort.

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.

My Dear Sir,

The Vertebra which I now send to you, was found about two years ago, on the property of Mr Mackenzie of Hilton, in Strathpeffer, county of Ross; and that gentleman desires me to present this interesting relic of some cetaceous animal to the Royal Society of Edinburgh.

About the end of the year 1821, when I was engaged in the examination of the Family of the Zeolites, Mr Heuland was so obliging as to send me a variety of Stilbite from a Calamine mine at Altenberg near Aix-la-Chapelle. Upon comparing its optical structure with that of the Stilbites, it was manifest that it had no connection with this class of crystals, and that it constituted a new mineral species. Upon mentioning this result to Mr Brooke, this acute mineralogist was of opinion that it was the Silicate of Zinc. Mr Heuland had been led to regard this substance as a Stilbite, in consequence of having received it as such from Major Petersen; but, particularly, from finding in the collection of Mr C. H. Turner, a single crystal of the same substance attached to Carbonate of Zinc, and bearing the annexed figure, with an inscription in the handwriting of the Abbé Hauy, stating it to be a new variety of Stilbite, to which he gave the name of Stilbite Duovigesimale.

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.

A box Chronometer having lately come into my possession, exhibiting remarkable proofs of strong and active Magnetism, I was induced to examine it particularly, and to ascertain the intensities of its different parts, by means of an apparatus resembling that employed by Coulomb, and which was capable, from its very delicate construction, of indicating the existence of the minutest traces of attraction.

The following paper contains the results of a series of inquiries, which lead to the conclusion, that the mineral called Smaragdite by Saussure, does not form a species of its own; but that this name has been given to a compound of certain varieties of two distinct species, Augite and Hornblende, the natural-historical species of paratomous and hemiprismatic Augite-spar.

Owing in part to the slight degree of resemblance prevailing among its varieties, the authors who have described them differ so essentially in opinion, that I am obliged to go into various details, both respecting the external appearance of the mineral itself, and of the opinions of mineralogists, in order to afford a correct view of the natural-historical species, to which these varieties belong, since this is the basis upon which every system, and, indeed, all accurate information in natural history, is founded, and the fixed point to which the one and the other must be referred.

The most simple and obvious use of the Trigonomentrical Tables, is to find the logarithmic sine, tangent, &c. corresponding to a given angle; and, reversely, the angle corresponding to a given sine or tangent. However, in their more general application, we have often to find a logarithmic cosine, having given the corresponding sine, or the contrary; also the sine or cosine from a given tangent, and, in these cases, it may be of no consequence to know the exact angle.

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.

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.

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.

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.

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.