Gentlemen,—I find it recorded that in the year 1662, which was the first year of the incorporation of the Royal Society of London, the celebrated mathematician, Robert Hooke, drew up “Proposals for the good of the Royal Society,” the third article of which was as follows :— “That every member of the Society shall be equally obliged to promote the ends thereof by paying 52s. yearly, and by doing some one duty that shall be charged on him by the Council once a year, or, if his occasions will not permit, to pay 52s. more per annum.’ This proposed salutary rule does not seem ever to have been enacted by the Royal Society of London, nor do I believe that any analogous article forms part of the statutes of this Society, and yet it is in accordance with the spirit of such a rule that I appear before you this evening.

The day may even come when the general public is sufficiently instructed to receive with interest, in ordinary periodicals, the physieo-mathematical papers, which form the staple commodity of this Society, and then we shall have done our work. In the meantime I would venture, like Principal Forbes, to advocate “intellectual clubability.” All tentative essays, which are not yet ripe to form a book or an article, may fitly be contributed to this Society and embodied in its Transactions, and I should have thought that not a single professor of any department in the University could go through the teaching of a session, without coming across at least some one novel point, which it would be worth while to bring forward.

The Deputation appointed by the Council to represent the Society on the occasion of the 400th anniversary of the founding of the University of Upsala consisted of Mr Sprague and myself. Professor Balfour and Professor Sir Wyville Thomson, who represented the Edinburgh University, also joined the Deputation.

In this paper the author concludes that the measurement of the breaking-strain of liquids is the only universally applicable method of measuring their cohesion; and as dropping is the phenomenon in which the breaking-strain can be most easily measured, he examines the work already done in this direction. Dr Guthrie's theory that the increase in the size of drop, with the increase in the rate of dropping, is due to the attraction of the solid tearing more of the root of the drop in low than in high rates is put to a crucial test by an experiment in which mercury drops from a wide glass tube so arranged that the tube only acts as a support for a column of liquid from the end of which the drops fall.

(1.) The relation dσ = uqdρq–1 ensures that the tensor of dσ shall always be u times that of dρ Hence, if ρ be the common vector of three series of surfaces which together cut space into cubes, σ possesses the same property. (See § 6 of my paper On Orthogonal Isothermal Surfaces, Trans. R.S.E., 1873–4. In what follows this paper will be referred to as Ω.)

In “Trans. R.S.E.” (1864–5) Fox Talbot proved very simply, by means of a species of co-ordinates depending on confocal conics, the following theorem, at the same time asking for a simple geometrical proof.

If two sets of three concentric circles, with the same common difference of radii, intersect one another—the chords of the arcs intercepted on the mean circle of each series by the extremes of the other are equal.

Some time ago I made some experiments on “Suspension of Clay in Water, and in Acid and Saline Solutions.” These formed the subject of several communications to the Royal Physical Society of Edinburgh, and were afterwards published in the “Chemical News.” I shall describe some of these experiments as an introduction to this paper.

In § 25 of my paper on Green's and other Allied Theorems (“Trans. R. S. E.” 1869-70) I gave the following relation between a volume and a surface integral, the limits being determined by any simply continuous closed space:—

“I saw the ‘Phonograph’ the other day, and though it is very crude I was much interested. I would briefly describe the idea as follows:—

“To the centre of an iron diaphragm is attached a metallic point resting against a strip of paper or tinfoil. You speak against diaphragm through a mouthpiece, at same time the paper being drawn under the points. The vibration of diaphragm and point indent the paper to various depths, making an undulating (as it were) mark, &c. Now, if said paper is afterwards drawn under the point, the diaphragm vibrates exactly as your voice made it vibrate, and all the sounds are reproduced exactly as you said them, making a most astonishing effect—singing, laughing, and articulate words were all reproduced.

As the phenomenon of a colourless rainbow, which was seen here in the forenoon of Thursday the 10th January, seems to be very rare, never having been witnessed before either by myself or by any of my friends to whom I have mentioned the subject, I beg to offer the Society the following description:—

On my way that forenoon to the Botanic Garden, and arriving about a quarter-past eleven at the open view of the north at the bottom of Pitt Street, my attention, was arrested by the appearance of a magnificent white bow, visible in its entire arch from end to end in the northern sky.

Dr Ramsay Traquair,—The Neill prize for the triennial period 1874-77 has been awarded to you by the Council of this Society, nominally for your paper on the structures and affinities of Tristichopterus alatus (Egerton), communicated to this Society within the required period, and published in the 27th volume of the Transactions of the Society. The Council have, however, also taken into account, as they are entitled to do by the conditions of the prize, the many contributions which you have made during some years past to the knowledge of the structure of recent and fossil fishes.

In this third chapter Dr Heddle submits the results of his analyses of garnets from thirteen localities.

Notwithstanding the great frequency of the occurrence of the mineral, it is generally so largely contaminated with quartz that he was unable to procure, from many localities, specimens fit for examination.

Three varieties of garnet new to Scotland—one of these being altogether new—have, however, been the reward of the present investigation.

Perhaps the most singular fact connected with the telephone is the excessive feebleness of the currents which suffice to work it. I have had no opportunity of testing any but rough arrangements set up by present or former students of my own, so that I cannot judge how far my results may apply to the instrument as sold.

In the telephones used in these experiments the permanent magnets were of the ordinary horse-shoe form, about 4 inches long. No cores of soft iron were attached to the poles, the insulated wire, No. 26, being wound directly round both, in such a way that a current circulating through it followed the direction of Ampère's currents. The vibrating disc was the bottom of a shallow can of thin tinned iron, 2½ inches in diameter, supported directly above the poles of the magnet, and almost touching them.

The Telephone, invented by Mr Graham Bell, is an instrument by means of which any sounds, musical notes or spoken sentences, sounded into an instrument at the sending end of a telegraphic wire may be reproduced at the receiving end. The theory of the Telephone is two-fold. First, the mechanical theory of the nature of sounds and of speech; and secondly, the theory of the action of the instrument. The first part is well known. All sounds consist of a succession of waves propagated through the air, the rate and intensity of their succession determining the nature of the sound, in pitch, loudness, and tone. If the same succession of waves as a speaker makes in using his voice can be reproduced in the air in contact with the ear of any other person, by any means whatever, the latter person will hear a fac-simile of the sound uttered by the former.