If the centre of a revolving wheel be carried with a uniform velocity, along a line; and if a tracing-point be fixed to an arm of the wheel, that point will trace out a curved line; to which the general name cycloid or trochoid has been given; the former appellation being often restricted to those cases in which the centre of the wheel moves in a straight line, while the name epicycloid is given when the same centre moves along the circumference of a circle.

After placing on the table a series of three crania of the gorilla (Troglodytes gorilla), which he had a short time ago received from M. Du Chaillu, Dr Burt proceeded to relate to the Society several facts, recently come to light, in support of various of the statements of that traveller which had been called in question. He alluded to the doubts which had been cast on several of the statements of M. Du Chaillu, and to the uncourteous treatment he had received at the hands of some of his detractors, and enumerated some of the proofs since produced by that gentleman, which are now to be found in the British Museum, and in the possession of men of distinction in science, illustrative of the natural history and the habits of the people of Equatorial Africa, which confirmed the veracity of that gentleman's observations. The last letters received from M. Du Chaillu were written from Fernand Vaz previous to his departure for the interior.

The piece of amber, now on the table, was found in the kingdom of Ava, and sent to me from India by the late Mr George Swinton, to whom the Society was indebted for many interesting objects of natural history from that country. It weighs 2½ lbs., and in its general aspect seems to differ considerably from the ordinary specimens of amber. The remarkable fact, however, which distinguishes it from all the specimens of amber I have seen or read of, is, that it is intersected in various directions by thin veins of a crystallised mineral substance. These veins are in some parts of it as thin as a sheet of paper, and in other parts about the twentieth of an inch thick. In order to determine the nature of the mineral I extracted a portion of the thickest vein, and having obtained, by cleavage, a small rhomb, I succeeded in measuring the inclination of its planes, and found it to be carbonate of lime.

The author's attention was called to this subject in consequence of having had an attack of incipient cataract forty years ago. The laminæ of the lens had separated so much as to exhibit rays of light, and the prismatic colours, round every source of light. At the end of eight months the laminæ came into optical contact, the rays and colours disappeared, and the eye became as perfect as the other, —a proof that cataract, in its incipient stage, may be discovered optically, and may be cured. During a series of experiments on the changes in the crystalline lenses of animals after death, the author observed that the capsule of the lens transmitted water into the lens till it burst; and hence he concluded that cataract might arise from an unhealthy state of the aqueous humour,—hard cataract from too much albumen in the aqueous humour, and soft cataract from too much water.

The district referred to included Roxburghshire, Selkirkshire, and Peeblesshire, in which Mr Chambers had visited and examined about 200 hill forts. These ancient works are found on the tops of hills of moderate elevation, and are of different classes, shewing a progressive improvement in construction. Those of the smaller kind consist of one or two concentric rings of earth and stone, with a clear space in the centre, and measure from 150 to 250 feet across. Such are considered to be the earliest in construction, and are at the least 2000 years old, though they may have been kept in use later. Their first constructors were unquestionably the aboriginal Celtic tribes, to whom they served as places of refuge and defence in petty local wars, or on the occasion of invasion.

The author stated this to be the first of a series of papers, in which he intended to develop in detail a new theory of the molecular constitution of organic and inorganic compounds.

In this paper the author considers the constitution of the olefines C2nH2n, aldehyds C2nH2nO2, fatty acids, hydrides of alcohol radicles C2nH2n+2, alcohols C2nH2n+2O2, glycols C2nKn+2O4. (C = 6, 0 = 8.)

The object of the Geological Survey is to ascertain in detail the geological structure of the United Kingdom, and to publish the results in maps, sections, and descriptive memoirs. The Ordnance maps form the groundwork on which these geological investigations proceed; and as no district is examined until these maps are ready, the progress of the Geological Survey is guided in no small degree by that of the Ordnance engineers. In Scotland, the geological mapping has hitherto been conducted wholly upon the county maps on the scale of six inches to a mile, and the advantages of so large a scale are such, that although the work is finally reduced and published on the scale of one inch to a mile, no county is surveyed until its six-inch maps are ready for use.

This material was brought from Brazil to Liverpool, for the purpose of ascertaining its commercial value in this country. The importers submitted it to Dr Edwards, who reported that it yields a much larger percentage of oil than even the celebrated coal of Torbane Hill.

The crude oil of the first distillation has a sp. gr. of ·859.

On redistillation, a light and heavy oil are obtained from the crude oil.

This is a sequel to a paper read 28th April 1862 (See “Proceedings,” vol. iv. p. 607), and contains the results of the complete reduction of the observations on the conductivity of iron, by the application of the method there described. The thermometric readings are now rigorously corrected for scale errors, and for the difference of temperature between the bulb and the stem.

The methods of reduction, consisting of a combination of calculation and graphical projection, are the same as have been described in the first part of the paper. But the whole has beeen executed with minute attention to accuracy, and the avoidance of error of every kind.

These three firths denote different parts of an arm of the sea which has two constrictions;—one between Craigton Point and Longman Point, and the other between Fort George and the Chanonry Point. The upper part is known as the Beauly Firth, the intermediate portion as the Inverness Firth, and the outer part as the Moray Firth. Two rivers discharge their contents into this arm of the sea; the Beauly River, which flows in at the head of the Beauly Firth, and the Eiver Ness, which joins at the head of the Inverness Firth.

After describing the phenomena of hemiopsy, as observed by Dr Wollaston, M. Arago, and Mr Tyrrell, the author remarked that no attempt was made by these writers to ascertain the optical condition of the eye when it is said to be half blind, or to determine the locality and immediate cause of the complaint. Having experienced several attacks of hemiopsy, unaccompanied with any affections of the head or stomach, the author found that there was no insensibility to light, but merely an insensibility to the lines and shades of the object which disappeared. This insensibility commenced in both eyes, a little to the left of the foramen centrale, and extended itself irregularly to the margin of the retina on the left side. The parts of an object, or the letters of a word which disappear, are as bright as the ground around them, and are white if the ground is white, and always of the colour of the ground, so that the light of the ground has irradiated into the dark lines or shades of the picture on the retina, a phenomenon which can be produced in a sound eye by oblique vision.

In 1861–62 the author visited and examined several of the Tertiary coal-measures of New Zealand; and the paper, of which this is an abstract, contains, or consists of, an epitome of his observations thereon. The collections of specimens made during his excursions, with relative maps and other illustrations, were exhibited to the Society at their Conversazione of 25th February 1863. A suite of coal specimens was submitted to chemical analysis by Professor Murray Thomson, the results of which are included in the paper.

What is matter? has been the question of philosophy from the earliest times. The author of this paper referred to the speculations of Thales and other philosophers of the Ionic school six hundred years before Christ, and to the more profound views of the Eleatic school, which had its origin about fifty years later, and the questioning which then arose regarding the reality of the knowledge given us by the senses.

The Nudibranchs owe their prominence in British zoology to the late Dr Johnston of Berwick, and to the splendid monograph of Messrs Alder and Hancock.

Inhabitants for the most part of the laminarian and littoral zones, the rocks and rock-pools, by minute and continued search, produced the greater number of those met with at St Andrews, the few others being procured from fishing-boats and debris of storms. Almost all require to be sought for with care, and generally escape superficial notice altogether. Most have been kept for a longer or shorter period in confinement, and some are living even now, though with greatly diminished bodies, and less brilliant tints, the results of insufficient food and other unfavourable circumstances.

These observations are given in six sections.

In the first, “On the Action of Water on the Bed Corpuscles of the Blood” the results are stated of trials of different proportions of water on these corpuscles; from which it would appear, that two of water to one of cruor of the blood of the common fowl, sufficed to change the form of the corpuscles, and to render them globular. Other changes are described, which were witnessed when water in great excess was used,—changes referred by the author to endosmosis and exosmosis, and rupture of the corpuscles, and the exclusion of their nuclei.

On the revival of learning at the middle of the fifteenth century, the Hellenists of Europe took the pronunciation of Greek from their teachers, the learned Greek refugees who fled from Constantinople when that city was taken by the Turks in 1453, and who carried with them the Greek language, both as the living people who used it, and as the inheritors of the rich store of philological learning accumulated by an unbroken succession of Alexandrian, Roman, and Byzantine scholars.

The quantity represented by ∫vds, or its equivalent ∫v2dt, in any case of the motion of a particle, is known to possess important dynamical relations. The accidental discovery of a singularly simple geometrical representation of this quantity in the case of planetary motion led me to inquire whether the method involved might not be easily generalized. This note contains a sketch of some of the results of a hurried investigation of the point.

Graphical representations of the action in some common cases of motion readily suggest themselves.

Hamilton's beautiful theory of Varying Action reduces to the discovery of a single function any problem connected with motion under the action of a conservative system of forces, and with constraint by any system of smooth fixed surfaces.

It does not appear to have been applied to cases (such as the brachistochrone) in which the requisite constraint is the thing to be determined.

This paper contains upwards of seventy theorems, in great part new, with reference to the intersection of systems of lines. The demonstrations are based upon determinants.

This paper contains a demonstration of the theorem given in the fourth volume of the proceedings at p. 419.

The theorem in question was arrived at by the comparison of the well-known formula for the time of descent in a circular arc, with another formula given in the “Edinburgh Philosophical Magazine” for November 1828, by a writer under the signature T. W. L. Each of these series is reached by a long train of transformations, developments, and integrations, which require great familiarity with the most advanced branches of the higher calculus. Yet the theorem which results from their comparison has an aspect of extreme simplicity, and seems as if it could be reached by an easier road.