In a previous paper there had been given a general method of investigating the motions of elastic systems, when the redressing tendencies are proportional to the extents of the disturbance. The present paper contains the results of the application of this method to the oscillations of flexible pendulums, composed of weights attached by their centres of gravity to a thread. These results, though strictly applicable only to oscillations of infinitely small extent, may yet be held as indicating the general characters of oscillations of moderate dimensions.

The Royal Society of Edinburgh having been the arena wherein Professor W. Thomson first described his calculations and admirable extensions of Mr Waterston's meteoro-dynamic theory of solar light and heat, I beg leave to call the attention of the same learned Society to an apparent instance of confirmation which that theory appears to me to have received, by a phenomenon of very unique character, recently observed in an independent and most satisfactory manner, by either of two able scientific men—viz., Mr Carrington of the Observatory, Red Hill, and Mr Hodgson at Highgate.

In the Meteorological Tables for England, published at the public expense, viz., those of Greenwich Observatory, and those of the fifty-five meteorological stations in England, appended to the Registrar-General's Quarterly Reports, the mean temperature as given is not the true mean, but is an estimated mean, deduced from the united observations made with the self-registering and dry-bulb thermometers, the exact means of these instruments being first altered by certain tables, with the view of correcting them for diurnal and monthly range. The author objected to this mode of estimating the mean temperature, because the tables used for the purpose of correction were drawn up from insufficient data, and because the principle was bad of having observations made by one instrument, whose readings were liable to constant errors, made the basis for the correction of observations made by a more trustworthy instrument.

After noticing the various plants used in Africa as ordeal poisons, the author gave an account of the introduction of the Calabar Ordeal Bean into Scotland, by the Rev. W. Waddell, and mentioned its peculiar poisonous qualities, as determined by Dr Christison. To Dr Hewan, and the Rev. Zerub Baillie, who are connected with the United Presbyterian Mission in Old Calabar, he was indebted for some observations on actual cases of poisoning in Africa. The Rev. W. C. Thomson, another missionary, was the first who procured flowering specimens of the plant.

This paper was an account of a plan proposed and tried many years ago for poisoning whales, by introducing hydrocyanic acid into their bodies when struck with the harpoon.

In 1831, the author was consulted on the subject by the late Messrs G. and W. Young of Leith, at that time concerned in the northern whale-fishery. It appeared to the author that the idea was feasible; that it was sufficient to paralyse the animal, so that the boats could speedily come up with it; and that a quantity of concentrated hydrocyanic acid, adequate to produce that effect at least, could be introduced by means of two glass tubes, one on each side of the shank of the harpoon, where they would be protected by the barbs of the blade.

In a paper which I read last year before this Society, “On the Structure and Functions of the Branchial Sac of the Simple Ascidise,” I stated that I had fed and injected ascidiæ with indigo and other coloured sea-water, and that in those so fed, the coloured material was never found on the exterior of the sac, but always deposited on the inner wall, and that injection by the mouth into the sac failed to push the coloured matter through its walls, except by rupturing them.

These experiments were not isolated or few in number. I showed the results to various friends—among others, Professor Goodsir, Dr Wright, and Dr Cleland—and never, in any of the experiments which I made, did a single instance occur of the indigo passing through the stigmata of the sac; and, in that paper, I naturally reasoned from this fact.

Since the discovery of the polarisation of light by refraction, the action of a pile of transparent plates upon common and polarised light has not been studied by any of the writers on physical optics. It was believed that a pencil of common light was completely polarised in the plane of refraction when the plates were sufficiently numerous, no special notice having been taken of the light thrown back by reflexion into the transmitted and polarised beam. Sir John Herschel, indeed, had referred to it; but he remarks that “it mixes with the transmitted beam, and, being in an opposite plane, destroys a part of its polarisation.” So long ago as 1814, Sir David Brewster had shown that this reflected light is distinctly visible as light polarised by reflexion; but owing to the difficulty of procuring very thin plates of glass with perfectly parallel surfaces, it was impossible to ascertain the true character of the oppositely polarised pencils.

The position taken by Mr Darwin is, that all species have arisen by the natural process of ordinary generation. That the differences which we now see in them have arisen from slight variations in individuals having from time to time occurred, which have been perpetuated by inheritance, by successive stages and slow degrees, through unlimited spaces of time. Some of these slight variations he considers to originate in causes beyond our power of explanation, and which, although not the work of chance, we may call chance, for want of a better appellation—others to arise from habit, or from the excessive use or disuse of certain organs; but that when such a variation has once appeared, it is preserved by hereditary descent through a principle which he calls “natural selection,” and which he deduces as a corollary from the struggle for existence which we see constantly going on around us.

The method of investigation followed in this paper for finding the limit for a uniform chain, is to suppose a multitude of catenaries all having a common vertex, and to take, in each of them, that point at which the tension is fixed. The curve passing through all of these points has for its equation—

in which s is the tension, z the vertical, and x the horizontal ordinate.

The paper on the Climate of Edinburgh is divided into seven sections.

The First Section includes an account of the earliest records of the thermometer at Edinburgh which are to be found in the Edinburgh Medical Essays. They date from 1731. They were made with a thermometer having an arbitrary scale, which is described in Martine's Essays, and they appear to have been recorded with much care; but they cease in 1736. The next series, printed in the Essays of the Philosophical Society of Edinburgh, commence in 1764, and are continued till 1770. A parallel Register was begun at Hawkhill, near Edinburgh, and continued till 1776, and probably later.

The writer stated that this paper was the result of observations made while staying at the sea-coast for a few weeks in autumn. Near Ardross a bed of limestone had been discovered, with peculiar fossils, which promised geological results of some interest. To determine its stratigraphical position, it was necessary to reduce to order a portion of the coast, hitherto held to be in a state of hopeless confusion. This led to fuller inquiries, till the rocks underlying the coal-field had been examined from Burntisland to St Andrews.

The annual production of gold, in Europe, America, and Northern Asia, at the beginning of the present century, which was estimated by Baron Humboldt in round numbers at something over two and a half millions sterling, continued at about the same rate until additions began to be received from the renewed working of the Russian mines. These additions, which, for the period intervening between 1810 and 1822, are estimated by M. Michel Chevalier not to have exceeded in all one million and a half, gradually increased, until in 1847 they amounted to upwards of four millions per annum.

The first part of this paper contained a review of the existing nomenclature of trappean-rocks, and the following arrangement was given as that which the author had found to be most useful for practice in the field:—1st, Ash and volcanic conglomerate. 2d, Interbedded augitic traps (greenstones and basalts). 3d, Interbedded felspathic traps (felstones, porphyries). 4th, Intrusive augitic traps. 5th, Intrusive felspathic traps. By adopting a different colour for each of these classes, the general relations of an intricate trappean district could be shown at a glance.

My dear Dr Playfair,—We left England in April 1858, and up to this time we have not received a single private letter from home. This saves me the trouble of apologising to any of my friends whom I have neglected. So here goes into the middle of things. We have just traced this river up to its point of emergence from the hitherto undiscovered Lake of Nyassa or Nyinyessi. This discovery is of more importance than at first sight appears, for it opens a cotton-field superior, I imagine, to the American, inasmuch as there are no frosts to endanger or cut off the crops; and instead of the unmerciful toil required to raise the staple there, one sowing of foreign, probably American seed, introduced into several parts by the natives themselves, serves for three years' crops. Even when burned down, the plants spring up fresh again.

The paper was deduced from a series of experiments, made on the London Dock Works with blue lias and Dorking limes; and at Leith Docks with the limes in the neighbourhood of Edinburgh, and with cements both natural and artificial. A short account was first given of the nature of the experiments at the London Docks, with the points investigated. A longer and more professional account of these is to be found in the Transactions of the Institution of Civil Engineers for 1857–58.

Considerable difficulties attend the preparation of zinc-methyl. Frankland, who discovered the body, obtained it by heating pure iodide of methyl and zinc enclosed in small glass tubes. Owing to the high temperature at which reaction takes place, much gas is formed; hence the operation must be confined to very small quantities of materials.

No determination of the boiling-point, specific gravity, nor yet of the vapour density of zinc-methyl, was made by its discoverer; from which fact may be inferred how small was the product available for investigation.

In this paper the writer directed attention to the remarkably developed parotid glands of the beaver, which form a single large mass covering the whole front and sides of the neck, and cannot be separated from one another. He showed how the apparent disproportion between the anterior and posterior extremities of the beaver was increased by the way in which the parietes of the abdomen overhung the thighs, and the margin of the panniculus carnosus passed over the knees so as to include them in the muscular investment that enveloped the trunk.

The author, in the first instance, directed attention to the discrepant statements of various comparative anatomists respecting the thyroid gland in the Cetacea, quoting from the writings of John Hunter, Meckel, Cuvier, Carus, and Dr Martyn. He then related the result of his own dissections made on three specimens of the common porpoise (Phocœna communis), one being a fœtus, another a well grown male, the third an adult male. In each of these animals a well marked thyroid gland was found, lying on the anterior and lateral surfaces of the trachea at its upper end, and extending slightly upwards on each side over the outer surface of the cricoid cartilage. It presented no division into two lateral lobes, as described by Cuvier and Carus, but consisted of a single uniform mass extending across the middle line.

In this communication the author referred to the various theories advanced to account for the boring of the Pholadidæ in rocks.

The first hypothesis, which supposes that the molluscs perforate by means of the rotation of the valves acting as augers, he disproved by exhibiting old individuals of the Pholus crispata with the dentated costæ as sharp as in any young specimen. That these animals bore by silicious particles secreted by the foot, as suggested by Mr Hancock, has been disproved by microscopic observation; and that currents of water set in motion by vibratile cilia, seemed also insufficient to account for the phenomenon.

The author, having referred to the value of carefully prepared reports on the ornithology of particular districts, characterised the physical features of that part of Linlithgowshire in which his observations had mainly been made, and showed that it is well fitted for the support of a comparatively large number of species of birds. He stated that the following list had been gradually formed as the result of observations spread over fifteen years. Most of the species named had come under his own notice; for a few he had been indebted to Thomas Durham Weir, Esq. of Boghead, an accurate observer. The classification followed is that which he had found most helpful to his own studies. Species seldom met with are printed in italics.