The Chairman delivered the following opening Address:—

Gentlemen, Fellows of The Royal Society of Edinburgh,—In compliance with a request of the Council, I have the honour to come before you this evening to give an address, on this the first night of our Winter Session, in pursuance of the custom prevalent in this and most other Societies.

Shortly after reading “Volcanic Eruptions in Iceland” (the “Scotsman,” May 21), and “An Appeal for Iceland” (the “Times” July 1), I made a trip to Arctis, partly with a view of inspecting and inquiring into the last outbreaks. Perhaps your energetic Society may not be unwilling to have an unprejudiced account of what was seen and heard.

The subject of this paper is steady motion of vortices.

1. Extended definition of “steady motion.” The motion of any system of solid or fluid or solid and fluid matter is said to be steady when its configuration remains equal and similar, and the velocities of homologous particles equal, however the configuration may move in space, and however distant individual material particles may at one time be from the points homologous to their positions at another time.

If an endless chain is hung over a pulley and the pulley driven at a great velocity, it is well known that the motion so communicated to the chain has almost no tendency to change the form of the curve in which the chain hangs, and that the principal effect of the motion is to confer on the chain a quasi-rigidity which enables it to resist any force tending to alter its curvature.

The apparatus which I used in a few experiments on silver wires was as follows:—To a beam, supported in stonework, a plate of copper was fastened, upon which a smaller plate could be tightly screwed. Between the two plates a very thick copper wire was secured, vertically. Its lower end was provided with a small plate of copper, fastened by screws. This plate served to make fast one end of the silver wire under investigation. The other end was joined in the same way to a second thick copper wire; this was provided with a horizontal round brass plate, through the centre of which it passed, and which acted as weight-carrier.

Faraday's discovery of the magnetic rotatory polarisation of light may be expressed in the following manner:—Let two electromagnets, in the form of iron tubes, surrounded by helices of wire, be placed end to end, so that in the space between them the lines of force are very intense. Let a rod of dense glass be placed in this space, so that a ray of light may pass through the two tubes and the rod of glass. Let such a ray on entrance be plane-polarised, so that the direction of vibration is in a vertical direction. If the electro-magnet be now magnetised, the emergent ray will be polarised, so that its vibrations are inclined to the vertical at a small angle. The direction in which the line of vibration has been rotated is the same as the direction of the positive current in the helices.

This paper contains the substance of investigations made for the most part many years ago, but recalled to me during last summer by a question started by Sir W. Thomson, connected with Laplace's theory of the tides.

A comparison is instituted between the results of various processes employed to reduce the general linear differential equation of the second order to a non-linear equation of the first order. The relation between these equations seems to be most easily shown by the following obvious process, which I lit upon while seeking to integrate the reduced equation by finding how the arbitrary constant ought to be involved in its integral.

Professor Blackie stated that though the origin of language might be considered by some more a metaphysical than a philological question, it was yet so closely connected with philology, that whatever opinions a philologer held on this question could not fail to exercise a strong secret influence on his philological procedure. The primary elements out of which language grew were admitted by all to be three, viz., cries or interjectional exclamation, mimetic reproduction of audible sounds, technically but stupidly called onomatopœia, and gesture.

“Formulæ like those you sent me are readily suggested by supposing the function operated on to be of the form ΣAxa, or say, for shortness, xa, with the understanding that no transformations are to be made which are not equally valid for ΣAxa.

In the year 1871, I read before this Society a memoir on the Gravid Uterus of Orca gladiator, in which I discussed the placentation of the Cetacea. This memoir was published in the Transactions for that year. On the present occasion I purpose describing the placenta in a Cetacean genus in which it has not hitherto been examined.

While engaged in cable work in the West Indies, I had, during the winter and early spring of 1875, a number of very favourable opportunities of examining the zodiacal light.

Before leaving this country I had, under the advice of Professor Tait, and with a note of recommendation from Professor Jenkin, applied to the Royal Society for the loan of a spectroscope, to make observations with during the voyage; but unfortunately I was unable to obtain one, and so had to content myself with a small pocket-spectroscope.

The late Transit of Venus Expedition gave the writer some opportunities of visiting several islands of the Hawaiian Archipelago, some details of which may prove interesting.

They form a group of islands about 10½ hours west longitude from Greenwich, and about 20° to 22° north of the equator, and differ in size from 10 miles long by 6 or 7 broad, to 90 miles by 60, which are about the dimensions of the most easterly and largest, viz., Hawaii (the Owyhee of Cook). The general lie of the islands is from north-west to south-east, those in the east displaying the most recent traces of volcanic activity.

Professor G. Forbes' paper, read at a late meeting of the Society, and some remarks made upon it by Professor Clerk-Maxwell, have once more recalled to me an experiment which I tried for the first time rather more than twenty years ago, in Queen's College, Belfast. I have since that time tried it again and again, whenever I succeeded in getting improved diamagnetics, a more powerful field of magnetic force, or a more powerful spectroscope. Hitherto it has led to no result, but it cannot yet be said to have been fairly tried. I mention it now because I may thus possibly be enabled to get a medium thoroughly suitable for a proper trial.

I am anxious to explain to the Society a kinematical device for the solution of the General Linear Differential Equation of the Second Order before I become acquainted with the principle of the integrating machine which, I understand, was described last Thursday by our President to the Royal Society.

Pure nickel foil, obtained in Paris by Dr Andrews, was cut into spiral about 20 inches long, and it was on this spiral that all the following experiments were made. During the month of November 1875 a large number of experiments were made as to its thermoelectric properties, and these were found to be almost identical with that of the specimen from observations on which the line was laid down on the “thermo-electric diagram.” (Trans. R.S.E., 1872–3.) This line, it will be remembered, is a peculiar one, and is very similar to that of iron, with this difference, that the peculiar changes take place at much lower temperatures in nickel than in iron.

In regard to external form, Nerine foliosa, Sars, is generally taken as the type of the family, and therefore it may be selected for structural examination in the first instance. Anteriorly the pointed snout is completed by the intricate interlacing of the muscular fibres beneath specially thickened cuticular and hypodermic layers. As soon as the body-wall assumes a rounded form, a layer of circular and oblique muscular fibres occurs beneath the hypoderm, the majority having the latter (i.e., the oblique) direction. In the centre of the area the oesophagus is suspended by strong muscular bundles (the most conspicuous of which are vertical) passing from the hypodermic basement-layer in the middle line superiorly to be attached to the œsophagal wall. A second series, as they descend to their insertion at the ventral surface, give lateral support to the tube; while a third group interlace in a complex manner, and, with the blood-vessels, fill up the space between the œsophagus and the wall of the body.