I have been deputed by your President to address you to-night from this chair, and so to attempt a task which would have been much better performed by one who possesses all the requisite scientific acquirements which I want, and without which, I fear, justice can only be imperfectly done to the work which I have undertaken.

It is usual at this meeting to give some notice of those of our Members who have died during the preceding year, and the list on this occasion contains so many, and some of them such distinguished names, that it will leave me no space for touching on other topics.

In this paper the author reviewed the arguments by which the geologists of Switzerland endeavour to prove that the so-called, “orographic” lakes are essential parts of the architecture of the Alps. He showed from detailed sections of one or two lakes, particularly of the Lake of the Four Cantons, that the amount of denudation, which the surrounding rocks had suffered, demonstrated that the lakes must be greatly younger than the plication of the strata of the Alpine chain; that from the known effects of subaerial denudatoni, the lakes must be, in a geological sense, quite modern; and that the Alpine lakes possessed no distinctive features which entitled them to be considered apart from the numerous lakes which are scattered over northern Europe and America. He regarded the enormous development of lakes at the present period in northern latitudes as a fact which could not be explained by reference to subterranean movements.

This communication was preliminary to a more extended memoir which the author hopes to lay before the Society during the Session.

The colour, general form, and dimensions of the animal, were taken when the whale was lying on the shore at Longniddry. The observations on its internal structure were made whilst it was undergoing the operation of flensing at Kirkcaldy, or on specimens which were brought over to the Anatomical Museum of the University. These specimens it was his intention to preserve in the Museum. In conducting the examination he had been ably and willingly seconded by the thoroughly cordial and enthusiastic co-operation of his assistant Mr Stirling, and his pupils Mr Millen Coughtrey, and Mr James Foulis.

In this paper it is pointed out that deliveries are a better means of arriving at an estimate of the healthiness of an hospital than amputations; that the deliveries in the Dublin Hospital are remarkably valuable because of their great number (nearly 200,000), and of the length of time of the hospital's operation (above 100 years); and that the evidence derivable from them relative to the danger of confinement, as regulated by the amount of aggregation, or number brought together at the same time, has never been properly taken.

In the outset, it was stated that the currency consisted mainly of a large mass of paper, whose convertibility had been provided for by Sir Robert Peel's Bank Bill of 1844–45, with which paper, and the gold set aside for it, the author did not propose to meddle. But alongside of the paper there circulated a large quantity of gold, and the object of his paper was to economise it. Now, gold having only three uses—as currency, in the arts, and to discharge debts abroad—it was desirable that some arrangement should be thought of which might relieve it of the first mentioned service, in which it suffers much waste, and set it free for the two others.

The author described the circumstances which led him, in 1863, to begin the investigation of these terraces, and showed he had traced their course along the Earn from Loch Earn to where they meet the tide. He had also examined the valley of the Teith, and had found the same deposits from the head of Loch Lubnaig to near Stirling. There are three different levels on which the terraces lie at different heights above the river bed. The lowest consists of the present banks of the stream and haughs or meadows; above this there is an intermediate terrace, which, in its turn, is surmounted by the highest. Owing to the effects of denudation, one or other of these levels is frequently interrupted or obstructed, but they are ever again found recurring, and the whole three present themselves so frequently as to show that this threefold terrace system is the true key to these valley deposits.

The author's paper consists mainly of a Table exhibiting certain of the positive results of many hundred experiments on the colouring matters contained in or educible from Lichens. The experiments in question are partly a repetition, and partly an extension on a more systematic and complete scale, of a series of researches made by the author between 1852 and 1855, the results of which were originally submitted to the Botanical Society of Edinburgh. The present series of experiments includes the whole family of the Lichens. The Table represents mainly the effects of chemical reagents on solutions of the lichen colouring-matters, or colorific principles, in boiling alcohol or water. The nomenclature of the Colour-reactions is that of Werner and Syme.

Professor Blackie commenced by saying that, of all the branches of interesting and curious learning, there was none which had been so systematically neglected in this country by English scholars as mythology—a subject closely connected both with theology and philosophy, and on which those grand intellectual pioneers and architects, the Germans, had expended a vast amount of profitable and unprofitable labour. The consequence of this neglect was that of the few British books we had on the subject, the most noticeable were not free from the dear seduction of favourite ideas which possessed the minds of the writers as by a juggling witchcraft, and prevented them from looking on a rich and various subject with that many-sided sympathy and catholic receptiveness which it required.

The reciprocal figures treated of in this paper are plane rectilinear figures, such that every line in one figure is perpendicular to the corresponding line in the other, and lines which meet in a point in one figure correspond to lines which form a closed polygon in the other.

By turning one of the figures round 90°, the corresponding lines become parallel, and are more easily recognised. The practical use of these figures depends on the proposition known as the “Polygon of Forces.” If we suppose one of the reciprocal figures to represent a system of points acted on by tensions or pressures along the lines of the figure, then, if the forces which act along these lines are represented in magnitude, as they are in direction, by the corresponding lines of the other reciprocal figure, every point of the first figure will be in equilibrium.

The operation in use by the ancient geometers for finding the numerical expression for the ratio of two quantities, was to repeat each of them until some multiple of the one agreed with a multiple of the other; the numbers of the repetitions being inversely proportional to the magnitudes.

The modern process, introduced by Lord Brouncker, under the name of continued fractions, is to seek for that submultiple of the one which may be contained exactly in the other; the numbers being then directly proportional to the quantities compared.

On applying this method to the roots of quadratic equations, the integer parts of the denominators were found to recur in periods; and Lagrange showed that, while all irrational roots of quadratics give recurring chain-fractions, every recurring chain-fraction expresses the root of a quadratic; and hence it was argued that this phenomenon of recurrence is exhibited by quadratic equations alone.

Cyclic irrotational motion, [§ 60 (z)] once established through an aperture or apertures, in a movable solid immersed in a liquid, continues for ever after with circulation or circulations unchanged, [§60 (a)] however the solid be moved, or bent, and whatever influences experienced from other bodies. The solid, if rigid and left at rest, must clearly continue at rest relatively to the fluid surrounding it to an infinite distance, provided there be no other solid within an infinite distance from it. But if there be any other solid or solids at rest within any finite distance from the first, there will be mutual forces between them, which, if not balanced by proper application of force, will cause them to move.

In a closed vessel containing only a liquid and its vapour, all at one temperature, the liquid rests, with its free surface raised or depressed in capillary tubes and in the neighbourhood of the solid boundary, in permanent equilibrium according to the same law of relation between curvature and pressure as in vessels open to the air. The permanence of this equilibrium implies physical equilibrium between the liquid and the vapour in contact with it at all parts of its surface. But the pressure of the vapour at different levels differs according to hydrostatic law. Hence the pressure of saturated vapour in contact with a liquid differs according to the curvature of the bounding surface, being less when the liquid is concave, and greater when it is convex.

On the 26th of January, about noon, I observed the appearance of a coloured bow on the frozen surface of the ditch which surrounds S. John's College, Cambridge. Its appearance and position seemed to correspond with those of an ordinary primary rainbow. I at once made a rough measurement of the angle on the board of a book which I had with me, and then borrowed from Dr Parkinson, President of S. John's College, a sextant, with which I found that the angle between the bright red and the shadow of the large mirror was 41° 50′, and that for bright blue 40° 30′. The angle for the extreme red of the primary bow, as given in Parkinson's Optics, is 42° 20′, and that for violet 40° 32′. The bows formed by ice crystals are seen on the same side as the sun, and not on the opposite side.

The investigation of the volume retained by different elementary substances, when combined in the solid condition, has attracted the attention of many chemists. We have only to look at the laborious memoirs of Schröter, Kopp, Playfair and Joule, Boullay, Filhol, and others, to be convinced of the great amount of labour expended on the subject. Nor is it at all remarkable that so many workers should take to this field of research, when we remember the simplicity of the laws regulating the combining volumes of gaseous substances, and the probable extension of some such similar law to the solid condition of matter. Emboldened by analogy, the forementioned workers endeavoured to find some constant to which volumes of elements and compounds held the relation of some simple multiple, and thus extend the apparent simplicity of Prout's law of combining weights to combining volumes.

For some time past an animated discussion has been going on in the columns of the “Comptes Rendus de l'Académie des Sciences” between MM. Dubranfaut and Maumené regarding the nature of inverted sugar. M. Dubranfaut, many years ago, made many valuable additions to our knowledge concerning the composition and reactions of various sugars, especially in explaining the result of the action of dilute acids on cane sugar. He explained the levo-rotatory action of inverted sugar, and its rapidly varying power with the temperature, as the result of a molecule of water in reacting with a molecule of cane sugar, generating one molecule of glucose and one of lævulose. Dubranfaut believed that inverted sugar consisted of a mixture of glucose and lævulose in equal weights; and although he did not make a direct analysis of the product, yet he was justly entitled to assume that it was so constituted, seeing that, generally, it agreed with a mean of the properties of inulin sugar and dextrose.

The conditions of a steady flow of electricity in a conducting surface are completely determined, if we know either the nature of the electrical distribution throughout the surface, or the direction and intensity of the flow at every point. On the first of these ways of considering the question, the problem is solved if we can express the potential v at any point as a function of the co-ordinates, and the nature of the distribution will be indicated to the eye by forming the equipotential curves

In nearly every narrative of exploration in uncivilised tropical regions, accounts are given, often no doubt somewhat fanciful, of poisonous substances which are said to possess the most remarkable properties. Usually these poisons are of vegetable origin; and the great majority may be included in the two divisions of ordeal and of arrow poisons, according as they are applied to one or other of these purposes. Among the most remarkable of the ordeal poisons are the Tanghinia venifera of Madagascar, the Physostigma venenosum of Old Calabar, and the Akazga poison of the Gaboon; and of the arrow-poisons, the famous Curara or Wourali of South America, and the Antiaris toxicaria of Java.

Thebo-lactic acid was discovered in Turkey opium by Messrs T. & H. Smith, the eminent morphia manufacturers of this city. It was examined by Stenhouse, and found to have the same composition as lactic acid, from which, however, it was supposed by the Messrs Smith to differ in the crystalline form of its copper and morphia salts. At present we are acquainted with three isomerie lactic acids, two of them differing from each other chemically, whilst the third is distinguished by its power of rotating the plane of polarisation of light. The last named acid, having been but recently discovered, it is impossible to say whether it possesses any decidedly distinctive chemical properties or not. The other two, namely, the ordinary or ethyliden—and the ethylen-lactic acids, possess perfectly distinct chemical properties, determined by the different relative position in each of the alcoholic hydroxyl.

Towards the end of last autumn, one of my pupils, Mr William Stirling, B.Sc., requested me to determine some bones which had been found whilst sinking a new shaft for a pit in the Grangemouth coal-field. On examination, I found these bones to be the two halves of the lower jaw, a fragment of the upper jaw with some loose teeth, the right temporal bone, the atlas with fragments of other vertebræ, the glenoid part of the left scapula, the right astragalus and femur, and small fragments of other bones of the skeleton of a seal. The animal had not reached the adult state, for the epiphyses of the femur were not united to the shaft. The bones were imbedded in a stiff red clay.

The mortality of assured lives is introduced by a short statement of the process followed in the obtainment of the rate of mortality among the male population of England and Wales during seven teen years, and in which the results are compared with the rate obtained by following the same process with the male population of Scotland during ten years. A statement is given of the method employed for collecting the facts referring to assured lives, and of tabulating the results with the view of extracting, not only the total numbers entering upon and dying in each year of life, but of exhibiting the experience of several highly interesting and important sections of risks, and more especially with the view of showing the nature and benefits accruing from the assurance of selected healthy lives.