In this paper it was shown that the usually received theorems concerning the faces of polyhedrons are true only of one class of solids. The theorem that “no solid can have every one of its faces more than pentagonal” was contradicted by the exhibitionof a solid bounded entirely by hexagons. Each corner of this solid is trihedral, and the sum of all its angles amounts to four times as many right angles as there are corners; whereas the usual theorem is, that “the angles of any solid amount to four times as many right angles as there are corners, lesseight.”

Professor Allman exhibited a portion of a pelvis of a seal, which had been recently obtained from the Pleistocene deposits in the neighbourhood of Kirkaldy, and sent to him for determination by Mr Martin Eigney of that place.

From a note received from Mr Rigney, it appears that the bone was found in the Tyrie clay field, about two miles west of Kirkaldy, and about a quarter of a mile from the shore of the Firth, and that it lay 18 or 19 feet below the surface of the soil, and about 30 feet above the present level of high-water. It was unaccompanied by any other remains.

The planet Saturn is surrounded by several concentric flattened rings, which appear to be quite free from any connection with each other, or with the planet, except that due to gravitation.

The exterior diameter of the whole system of rings is estimated at about 176,000 miles, the breadth from outer to inner edge of the entire system, 36,000 miles, and the thickness not more than 100 miles.

It is evident that a system of this kind, so broad and so thin, must depend for its stability upon the dynamical equilibrium between the motions of each part of the system, and the attractions which act on it, and that the cohesion of the parts of so large a body can have no effect whatever on its motions, though it were made of the most rigid material known on earth.

While examining the bones of a seal which had been for some time in maceration, the author observed that, in detaching one of the ribs from the vertebral column, a long ligament, connected to the head of the former, emerged from the intercostal foramen.

It was then found that the right and left rib in all the pairs articulating with two vertebræ were connected across the mesial plane by a ligament which was attached at each end to a depression on the lower part of the continuous convex cartilaginous surface of the head of the rib, and was lodged in a tube on the floor of the spinal canal, formed by a groove on the upper surface of the corresponding intervertebral disc covered by the superior longitudinal ligament, and lined by a synovial membrane common to the tube, the ligament contained in it, and the entire heads of both the ribs.

After alluding to the difficulty of determining the precise anatomical configuration of the condyles of the lower jaw, especially in the human subject, the temporo-maxillary articulation admitting of a multiplicity of movements, and these again being liable to modification by different accidental and other conditions of relative structures, such as the teeth, &c., the author stated that a general principle would nevertheless be found to prevail, and in general to be distinctly traceable in this joint, whatever might be the modifications existing either in its function or external form.

“During the last month of March. I made some experiments on the properties of ice near its melting point, with particular reference to those of Mr Faraday, published in the Athenæum and Literary Gazette for June 1850, to which attention has been more lately called by Dr Tyndall and Mr Huxley in relation to the phenomena of glaciers.

“Owing to indisposition, I have been obliged to leave my experiments for the present incomplete. But I am desirous, before the session of the Royal Society closes, to place on record some facts which I have observed, and also some conclusions which I deduce from these and other recent experiments and discussions.

During the vacation, I had looked forward with confidence to the pleasure of listening to-night to an address from one of the ablest experimenters and most vigorous writers that this Society has ever numbered amongst its members,—Sir David Brewster. And when, a short time since, I learnt that I had been indulging an ill-founded expectation, and that the duty of opening the session was to fall to my own lot, I experienced something more than disappointment. For, in addition to my imperfect knowledge of the past history and present position of the Society, is the fact that I had made no preparation, either in the way of collecting materials, or of providing a reserve of time, for drawing up an address. I must therefore come before you with an apology. I must crave your forbearance should some of the remarks which I make appear trite and unworthy of the occasion,—should others be traceable to what I have said elsewhere,—should all be found crude and lower in tone than beseems the position in which your kindness places me.

Dr Gregory, at the time of his death, which took place on the 24th of April last, was Professor of Chemistry in the University of Edinburgh, and one of the Secretaries of this Society. He was born on the 25th of December 1803. His father was the late Dr Gregory; for a long time professor of the practice of medicine in the University of Edinburgh. His brothers, James Crawford, who took the degree of medicine in 1824, and died in 1832, and Duncan, who, when he died, was a Fellow of Trinity College, Cambridge, were both so highly distinguished for their talents and acquirements as to be worthy representatives of a family of no small distinction in the science and literature of the country; but, in Dr Alison's opinion, Dr William Gregory was the member of the family who, in our day, had shown the greatest original talent and devotion to science for its own sake. His love of science manifested itself at an early period. He had been present at an introductory lecture by Dr Hope, which was illustrated by striking experiments. Several of these experiments he contrived to repeat by means of a rude apparatus which he constructed for the purpose.

In this communication the author called attention to the fact of his having discovered, in April last, in the Clyde, near Rothesay, numerous specimens of an Appendicularia, invested with the remarkable appendage, named “Haus” by Mertens, who originally described it in specimens captured in the North Pacific, near Behring's Straits, but which no one since his time had seen, though Appendicularia had become a subject of careful and elaborate investigation in the hands of several of the leading zoologists of the present day.

This communication was intended by the author to be in continuation of a former paper on the same subject, read before the Society during the previous session, and contained the following additional notices:—

The gonophore of Sertularia polyzonias consists of an oval capsule slightly corrugated transversely, with a short tubular, obscurely 4-toothed aperture, and having its axis occupied by a blastostyle, bearing in all the specimens examined a single sporosac.

The author commences by a vindication of the Scottish philosophy, that he may legitimately build upon substance as a reality as well as phenomenon. He then shows that just as the idea of substance presents, a priori, an alternative, viz., those which are wholly fixed, the subject of law imposed from without only, and those which possess a power of changing their mode of being from within themselves; so, in point of fact, common observation has recognised in all ages two orders of substances or beings characterized by this difference, and filling up in the sphere of reality this alternative given by pure thought; the one being the ground of all natural phenomena, and ordinarily designated body; the other the ground of all moral and intellectual phenomena, and designated spirit.

The chief portion of this paper is occupied with an inquiry into the truth of Milne Edwards' theory, that the branchial sac of the Ascidians is perforated throughout by apertures, or what he called branchial stigmata.

Some experiments and observations made by Mr Murray last season had induced him to regard this view with doubt. In considering the question, he first examined the evidence that was recorded in support of it. Putting aside those writers who had taken M. Edwards' theory on trust, he could only find four observers who seem to have critically tested it, viz.,—Dr Lister, with whom the idea originated: who, while stating that the walls of the sac appeared to be traversed by open spaces, yet states that at times he thought he saw something like a veil stretching across them, and that the particles in suspension in the water were observed to course past these spaces without entering; which would appear to be inconsistent with the idea of the water entering, for the course of the water, and of the particles floating in it, must necessarily be the same.

“In the course of last summer (1858) I became acquainted with a phenomenon described by Mr Gore in the Philosophical Magazine for June (Supplement, p. 519), of the following nature:—A metal cylinder, supported on two metallic rods or rails, the latter being in connection respectively with the poles of a battery, revolves in either direction, at will, under the action of an electric current copious in quantity. Also continuous rotation of a light copper ball, supported on two circular metallic rails, takes place in either direction at pleasure, depending on the first impulse. It appeared to me very probable that this interesting fact might be applied to explain what is still obscure in the experiment on heated metals, generally known as the “Trevelyan Experiment,” described by Mr Trevelyan, in the “Edinburgh Transactions,” vol. xii., where there is also a paper by myself on the same subject.

By a reference to observations made on the temperature of the air, of the sea, and the solid land, the author showed that the mean temperature of each of these in and around Scotland were within the fraction of a degree of each other. From observations made on the temperature of the air and of the sea at stations on the west coast, he showed that not only did the air and sea attain their respective minima and maxima at the same time, but that even in their fluctuations of temperature they bore a distinct accord with each other. He then pointed out that such fluctuations in the temperature of the sea were quite fatal to the theory of the mild winters of Britain being dependent on the influence of the Gulf-stream, as such fluctuations could not occur were the temperature of the sea dependent on the heated waters of the Gulf-stream.

This shower took place about the 10th of June. The following account of it is from the Inverness Courier; and, as showing the interest the phenomenon excited, it was republished in most of the English papers. The copy I give is from the Spectator of the 3d July.

“After the late thunder-storm, a deposit resembling sulphur was observed in several places in this neighbourhood (Inverness). At Freeburn it lay on the road and grass in some places to a depth of nearly half an inch. At Craigton Cottage, near Kissock, the deposit was observed on the top of water caught in a cask from the roof of the house, like a thick cream. The sulphurous substance was skimmed off, and dried in a piece of flannel. When dry it was a fine powder, and when thrown into the fire ignited exactly like gunpowder, making a slight fizzing noise. Unfortunately none was preserved beyond what was experimented on in this way.

Dr Lee commenced with a general account of the existing MSS. of the Greek Scriptures, and particularly of the Uncial MSS. These, though few in number in comparison of the Cursive MSS., are of peculiar value, on account of their greater antiquity and the superior purity of their text. Fac-similes of several of the most important of these interesting documents were exhibited. After making some remarks upon the Alexandrian, the Ephraem, the Beza, and Clermont MSS., Dr Lee remarked that all of these were now, and most of them had long been, available to Biblical scholars by means of the excellent copies which had been issued, the possessors of the documents having afforded every facility and encouragement. The only exception was the Vatican MS., of which he had now to speak, and which had hitherto been withheld from inspection, for reasons which might be guessed but could not be justified.

In this communication the author discusses the theory of the constitution of flame advanced by Professor Draper of New York, in his paper “On the Production of Light by Chemical Action,” which appeared in the Philosophical Magazine for 1848.

Professor Draper refers to experiments which prove that the higher the temperature of an incandescent body, the more refrangible are the rays of light emitted by it. He assumes that the temperature of the outer portions of a flame is greater than that of the interior regions; for outside there is a better supply of oxygen, and hence a more intense combustion is maintained.

This memoir commences by stating that it seemed desirable to arrange and preserve what memorials could still be found of one who had done very much to promote the study of natural science in Scotland, but whose memory had well-nigh perished.

Dr Skene's father and grandfather were both eminent physicians in Aberdeen, where he was born, on 13th August 1731.

His early education was conducted in Aberdeen. He spent the winter of 1751-2 in Edinburgh, attending various medical classes; and in the autumn of 1752 proceeded to London, where he studied under Hunter and Smellie, besides attending several of the hospitals.

In a newspaper printed at Shanghae, in the spring of 1857, a wonderful account was given of a poison, which was said to be employed in the interior of China for destroying the largest animals. Instant death was said to be produced, when an animal was struck in the trunk of the body with an arrow poisoned with it. Such was its potency, according to the opinion of the Chinese, that a scheme was said to have been set on foot for destroying the British army during the late war, by bringing down to Canton the natives who were in the practice of using it. But the scheme was frustrated by peace being unfortunately proclaimed too soon.