Although many proposals have been made to obtain a series of hourly meteorological observations by mechanical means, this desideratum has not, from various causes, been completely attained. The chief obstacle to be overcome, in such self-registering instruments, is the great amount of friction, which necessarily vitiates all the results, more especially in delicate instruments, such as the barometer and thermometer.

Dr Robert Hooke was the first to propose a self-registered series of meteorological observations, by an instrument, which he quaintly called a Weather-wiser; but no further notice is taken of this contrivance than a short description in one of his tracts, bearing the date 5th December 1678, which would lead us to believe that the instrument was never used. The late Alexander Keith, Esq. of Ravelston also proposed a similar contrivance, a description of which is contained in this Society's Transactions, Vol. 4th. This contrivance, from the constant friction excited by the marker on the revolving paper, seems likewise to have been abandoned.

In certain investigations which I have presented to the Society, relative to the modifications which light undergoes when it meets with a medium more dense than that in which it is travelling, the law of force has been supposed to be that of the inverse square of the distance. On re-examination of this subject, I find that there is no necessity for restricting the computations by the hypothesis of any particular law. The conclusions are perfectly independent of the law, provided one of the equations of reduction, the value of which it is not possible to compute by any known methods of analysis, be admitted as an experimental result. The object of the present Memoir is twofold : 1st, To present the analysis of the general theorem of vibrations at the surface of an interrupted medium in its most simple form; and, 2d, To apply the results to the case of reflection unaccompanied by refraction.

This remarkable seed or nut is now well known in London, as a substance extensively carved into a variety of ornaments, and capable of receiving as high a polish as the finest ivory; which it also greatly resembles in colour. I lately obtained various specimens both of the nut in its natural state and of the fine turnings produced in the process of working it, being desirous of submitting them to a chemical examination.

The nuts in my possession vary in size from a pigeon's to a hen's egg, and have a somewhat angular shape. They are covered with a brown epidermis, and have an outer shell of an inch thick, and consisting of an outer white and an inner brown layer. The inner mass of the nut is remarkably close grained and homogeneous to the naked eye; and when cut and polished exactly resembles animal ivory. The hardness is considerable; the white mass yielding with some difficulty to a knife. Thin portions are translucent. The density of the white mass is 1.376, at 53° F.

The object of the following paper is to lay before the Royal Society the results of a repetition of several of Dr Samuel Brown's processes for the conversion of carbon into silicon. The greater number of these processes were published in the Society's Transactions for 1840–41; and certain additional ones have since appeared in a separate form. The latter were much simpler, and more readily performed, than those made public at an earlier period; and to one of these we first directed our attention.

The Acephalocyst, or simple Hydatid, is composed of a vesicle, containing a watery fluid, which, in the normal state of the creature, is quite transparent and colourless (Pl. XIV., fig. 1.) The internal surface of the vesicle is generally studded with numerous cells of various sizes, many of which are found detached and floating loose in the fluid contained in the vesicle. These are the young Hydatids. Their development will be described when we come to that portion of the present paper, which has been set apart for that purpose.

During the century which has nearly elapsed since Dr Matthew Stewart published his General Theorems, many eminent geometers, both English and Foreign, have attempted to discover their solutions. Those attempts have, however, been rewarded with but limited success, and by far the most general and the most difficult of them remain still without a single published remark in the way of discussion or solution. Dr Stewart did not, as far as I know, make allusion to them himself in any of his subsequent writings, though he describes them as “of considerable use in the higher parts of mathematics;” and we learn from the preface to Mr Glenie's Demonstration of the 42d Proposition (Tract, 1813), that in conversation, Professor Dugald Stewart, in 1805, stated that, “he had not been able to find amongst his father's posthumous papers one word respecting them; that he had, oftener than once, observed mention made of them, in terms of admiration and respect, by some of the first mathematicians on the continent of Europe; but that as both they and the geometers in this country had tried their strength on them without success, and they had so long remained without demonstrations, he never expected to see them demonstrated.” This circumstance, of neither any demonstrations nor even memoranda, on the subject being found amongst Dr Stewart's papers, is readily accounted for by Professor Playfair, in his biography of that distinguished geometer (Edin. Trans. vol. i. p. 74), in the description which he gives of the habits of study of Dr Stewart. “He rarely wrote down any of his investigations till it became necessary to do so for the purpose of publication. When he discovered any proposition, he would put down the enunciation with great accuracy, and on the same piece of paper would construct very neatly the figure to which it referred. To these he trusted for recalling to his mind, at any future period, the demonstration or the analysis, however complicated it might be.”

This phenomenon presented a remarkable interference with those laws which govern the ordinary movements of the ocean. It occurred at one place whilst the tide was flowing, at another whilst it was ebbing; in some cases, producing a sudden retrocession of the waters,—and in others, as sudden an impulse of them on the shore.

The period during which the sea thus continued to retreat and rise respectively, was generally from ten to fifteen minutes. It then made a momentary halt—after which, it began to flow in the opposite direction, and which it continued to do, for about the same period which characterised its previous movement.

In this state of alternate flux and reflux, the sea was at most places observed to continue, for three or four hours together.

The volatile oil commonly known as Indian-Grass Oil, is supposed by Professor Royle to be produced from a peculiar species of Andropogon. This species he considers identical with the Καλαμος αςωματιχος of the ancient Greeks, an he has therefore called it A. calamus aromaticus.

For the specimen of the oil which I have examined I am indebted to Dr Christison, by whom it was received from Mr Key, of the Madras Medical Service. This gentleman obtained it while resident in the Nizam's territories, not far from Ellichpoor, where the plant grows freely on hilly ground. The oil is there called Roossah-oil.

In the course of an investigation into the structure and composition of the solid frame-work of vertebrated animals, I remarked, in the vertebral column of cartilaginous fishes, an important peculiarity of structure, which seems to have almost entirely escaped the notice of writers on ichthyology and on comparative anatomy.

Under the name Conversion of Relief, an expression first used by Mr Wheatstone, I include all those optical illusions which take place in the vision of cameos and intaglios, of elevations and depressions, whether they are produced with opaque or transparent bodies,—on surfaces with or without shadows,—in reflected or transmitted light,—while using one or both eyes,—or by erect or inverted vision. In these various forms of the phenomenon, the illusion is modified by certain secondary causes, which were regarded both by Mr Wheatstone and myself as primary causes; so that we were led away, each in a different direction, from the right path of inquiry.

In analysing Mr Wheatstone's beautiful discovery, that in binocular vision we see all objects of three dimensions by means of two dissimilar pictures on the retina, I trust I have satisfied the Society that the dissimilarity of these two pictures is in no respect the cause of our vivid perception of such objects, but, on the contrary, an unavoidable accompaniment of binocular vision, which renders it less perfect than vision with one eye. On the other hand, it is quite true that, in Mr Wheatstone's experiment of producing the perception of objects of three dimensions by the apparent coalescence of two dissimilar representations of such objects in plano, the dissimilarity of the pictures is necessary in the exhibition of that beautiful phenomenon.