Between Crinan Bay on the north and the head of Loch Fyne on the south, there is a trough or hollow now occupied by the Crinan Canal. The highest point along this trough, is about 150 feet above the sea. A series of locks occur at this summit-level, to allow of the passage of vessels between the two sea-lochs.

At the summit-level, the rocks form a sort of ridge across the valley, with smooth surfaces towards the north, and rough surfaces towards the south.

On both sides of this rocky ridge, there are large boulders; on the north side, I counted between forty and fifty, on the south side, there are not more than two or three. The boulders are a syenitic gneiss; the rocks in situ, are shivery clay slate, nearly vertical, dipping steeply towards the south.

The Chairman closed the session with the following remarks:—

I have now, in a very few words, to close this session, and in so doing I beg to remind you that it is the ninety-ninth session of the Royal Society of Edinburgh. This Society, which was originally an offshoot of the University of Edinburgh, was first started, on the suggestion of Principal Robertson, towards the close of 1782. So that in the latter part of next year you will be able to announce your hundredth birthday. The Society came into existence just one year after its late distinguished President, Sir David Brewster, who was born in December 1781. While individuals pass away, age brings no decrepitude, but rather the reverse, to universities and scientific bodies.

§ 1. Every one may readily notice that the collection of statistical information goes on around us to a vast and constantly increasing extent; not simply in the periodic census, but in the daily labours of the Registrar-General's Department, of the Board of Trade, and the like. Such functions are carried on in every civilised country by many special statistical bureaux; a statistical society exists in almost every great intellectual centre, and an International Statistical Congress, which has proposed to itself the vast object of accumulating, co-ordinating, and comparing the whole body of national statistics, has met periodically since 1853.

§ 1. The method by which Hamilton has established the symbolical cubic

and more particularly the relation

is founded on a generalisation of the result

where ϕ represents a linear and vector function, and ϕ' its conjugate according to the definition

In the most general case of ϕρ the expression of this function is reducible to a vector sum of three terms of the form αSα1ρ, and the directions which ϕρ is susceptible of representing are generally not limited in space.

While seeking for a good elementary illustration of Hamilton's general methods in optics, the author was led to consider, from a somewhat novel point of view, the path of light in a medium whose refractive index is a function of the distance from a plane. This is, at least approximately, the case of the peculiar atmospheric arrangements to which are due the phenomena of Mirage, so long as the curvature of the earth can be neglected.

A considerable improvement in the usual theoretical treatment of this subject was introduced by Professor J. Thomson in 1872, and afterwards developed by Professor Everett in Phil. Mag., 1873.

The main feature of this improvement is the study of the curvature of the ray in terms of the rate of change of refractive index in the medium.

The Council having awarded the Makdougall-Brisbane Prize, for the biennial period 1879–80, to Professor Piazzi Smyth, Astronomer-Royal for Scotland, for his Memoir, entitled “The Solar Spectrum in 1877–78, with some practical idea of its probable temperature of origination,” published in the Society's Transactions, vol. xxix. p. 285, the Medal was presented to him by the Chairman, with the following remarks:—

The first matter of public business for to-night is to present the Makdougall-Brisbane prize to Professor Piazzi Smyth, Astronomer Royal for Scotland.

Many hundred tourists annually climb Ben Nevis, and shudder when they cast their eyes down its profound precipices; but no one seems to bethink him that, to view a great precipice aright, he should behold it from below, rather than from above, and consequently that the great North-Eastern Precipice should be seen from the valley opposite its base. No one, tourist or guide, visits the narrow rugged glen into which it descends; few of the neighbouring gentry—of my acquaintance at least—have made the excursion; and the only visitors I have heard of have been a few solitary geologists at long intervals of time. Nevertheless, in the year 1810, in the first volume of the Edinburgh Wernerian Society Transactions, the late Reverend Dr. Macknight, one of the ministers of this city,—a gentleman of many accomplishments, and, among these, skilled in geology,—has interspersed his geological account of the rocks of the mountain with a description, in the most glowing language, of many magnificent scenes in its great North-Eastern Precipice. But he appears to have thus encouraged only his geological successors to follow his example.

This paper first treats of the composition and properties of the different kinds of iron, known as wrought iron, steel, and cast iron, and especially of the changes which steel undergoes on being heated to redness and then suddenly cooled by plunging it into water, mercury, or oil, and known as hardening; also of the peculiar property known as tempering, by which the hardness and brittleness can be removed.

When the circulation of the blood is observed in the transparent tissues of an animal, it is noticed that the coloured corpuscles run in the axial part of the stream, while the colourless mostly keep in the peripheral still current. The coloured corpuscles move much faster than the colourless; they have also a gliding, while the colourless have a rotatory, motion. Further, if the frog's web be examined in the upright position, with the microscope inclined so as to be horizontal with the table on which it is placed, it is noticed that the great majority of the leucocytes not only flow in the peripheral stream, but on the upper surface of the vessel. From a number of observations of blood-vessels in the frog's web, examined in this position, it was found that for every 13 leucocytes which are seen running along the lower surface, there is an average of 92 on the upper. In fact, the only time, apparently, in which a leucocyte gets to the lower surface, is in passing round a curved capillary, where, in changing its position, the stream of coloured corpuscles prevents it from gaining the upper surface of the vessel for some distance. If followed along the stream, sufficiently far, such a leucocyte is eventually found to make its way through the stream of coloured blood-corpuscles and to gain the upper surface of the vessel.

It is now nearly forty years since the presence of chlorophyll in certain species of Planarians was recognised by Schultze. Later observers recognised that the green colour of certain Infusorians, of the common fresh-water hydra (Hydra viridis), and of the freshwater sponge (Spongilla fluviatilis), was due to the same pigment, but little more attention was paid to the subject until Ray Lankester applied the spectroscope to its investigation.

It has long been known, having been first, I believe, pointed out by Kant, and more recently brought very near to a practical conclusion by Delaunay, that the earth's rotational velocity is diminished by tidal agency, in virtue of the imperfect fluidity of the ocean. An integral effect of all the consumption of energy by fluid friction (or more properly speaking by continued deformation of fluid matter) in the tidal motions, is to cause the time of high water on an average for the whole earth to be not exactly either transit, or 6 o'clock, as it would be were the ocean a perfect fluid, but to be some time after transit, and before 6 o'clock.

The station of Parkhill, on the Great North of Scotland Railway, is seven and a half miles from Aberdeen, and the cist which is the subject of these notes was situated in a mound of gravel and sand to the north-east of, and within one or two hundred yards of, the station. This is the second which has been uncovered at the same spot,—a previous one having been disclosed in 1867, the contents of which—a vase and some bones—are preserved in the Anatomical Museum, Marischal College, University of Aberdeen.

By Cauchy the word “symmetric,” as applied to functions, was used in a more general sense than that in which we ordinarily use it now, or than that in which it was used before his time. He spoke of “fonctions symétriques permanentes” and “fonctions symétriques alternées:” we apply the word symmetric only to certain of the first of these; the second we call simply “alternating functions.” Thus the expression

was called by him a permanent symmetric function, since if a1, a2, a3 are interchanged in order with b1, b2, b3, the function remains unaltered. It would be more definite to say that it is a permanent symmetric function with respect to a1, a2, a3 and b1, b2, b3.

The second figure in Professor Everett's note (ante, p. 360) has reminded me of my explanation of a phenomenon which I have repeatedly seen for more than twenty years in the College. When sunlight enters my apparatus-room through a vertical chink between the edge of the blind and the window-frame, the line of light formed on the wall or floor shows a well-marked kink. Similar phenomena, though not usually so well marked, are often seen in old houses, when the sun shines through the chinks of a Venetian blind. They are obviously due to inequalities (bull's-eyes) in the glass which was used more than a generation ago for window-panes. Professor Everett's figure, which was drawn for a cylindrical lens, represents the general form of a central section of such a bull's-eye.