Professor Andrews, in the “Philosophical Magazine” for 1852, recalled the attention of physicists to the method originally devised by Davy of making a vacuum so perfect, that the residual gas exercised no appreciable pressure as registered by the depression of a barometric column. This he effected by filling the vessel to be exhausted with carbonic acid gas, having previously inserted a cup containing a concentrated solution of caustic potash. On rapidly exhausting with an air-pump, and leaving time for the absorption of the residual carbonic acid by the caustic potash, he obtained a vacuum as perfect as a Torricellian. Andrews' method was afterwards employed by Gassiot in his well-known investigations on the passage of electricity through attenuated media.

I owe to Mr Dewar's skill in manipulation the means of determining the line of sodium in the thermo-electric diagram. He constructed for me a long quill tube of German glass, with platinum wires inserted near the ends; exhausted it by means of a Sprengel pump, and drew in melted sodium from a bath of paraffin. Exact determinations will require considerable time, even with this excellent apparatus; but in the meantime I may state (as a first approximation) that the line of sodium is nearly parallel to that of palladium, and somewhat above it in the diagram.

For some days past I have been in the habit of observing atmospheric electricity about one o'clock, with the view of ascertaining whether the concussion produced by the time-gun has, as I suspected from an experiment of ten years ago, an effect on the amount collected by the water dropper. For several successive days the atmospheric charge was small and only slowly variable, and uniformly on these occasions I found a sudden slight increase of the deflection of the electrometer (whether it was originally positive or negative) to occur simultaneously with the sound, precisely the result obtained in the single experiment of date 21st May 1864. It appears to be most probably due to mere shaking of the instruments.

The design of this paper is to describe the results of some experiments on “the Resistance of the Air,” which I made under the superintendence of Professor Forbes, in the physical laboratory of the Andersonian University, Glasgow. The apparatus employed resembles somewhat that used by M. le Chevalier de Borda, whose experiments on “the Resistance of Fluids” are recorded in the “Mémoires de l'Académie Royale des Sciences.” It consists essentially of a wooden frame, which was firmly secured to the floor, and supporting a horizontal axis, at one extremity of which is fixed a wooden arm, on to which were bolted the vanes of different forms and sizes, the resistance of which it was desired to ascertain. A cylinder or barrel, about 3 inches in diameter, is fastened to the axis, whereon was wound a cord, which, being acted on by weights, gave a circular motion to the axis, and consequently to the arm, thereby carrying the vanes in the circumference of a circle of 3 feet diameter, and causing them to impinge upon the air with velocities due to the force applied.

The idea of this class of curves arose during an attempt to resolve an important problem in the doctrine of wheel-work; a statement of the conditions of that problem is thus the natural introduction to the subject.

When the shape of the tooth of one wheel A has been assumed, the shape of the tooth of another wheel B, to work along with it, may be deduced by a very simple graphic process; and when these two wheels are made to turn together, the points of contact describe a certain line or path.

Farther experiments with the apparatus described in the “Proceedings” of 2d March 1874, and with a similar one containing potassium, have led to the following values of the tangent of the inclination of the corresponding lines in the thermo-electric diagram. I have added its value in palladium for comparison—

Na – ·00212

K – ·00066

Pd – ·00182

The facts to be explained were observed by Messrs Gore and Barrett, and were described by the latter gentleman in the “Philosophical Magazine” for 1873.

The experiments are performed on an iron or steel wire of no great thickness. When this is heated to an intense white heat and allowed to cool, the following facts appear at the instant it has cooled down to a dull-red heat:—

1. The wire expands for an instant, and then continues its normal contraction.

2. The glow from the wire is at the same instant seen to increase.

The following facts appear to have been conclusively established by universal experience:—

1. Nearly all, if not all, solid substances become self-luminous at the same temperature.

2. The red rays are the first to become visible, and, on increasing the temperature, colours of less wave-lengths are successively added in the order of their wave-lengths.

3. While colours of shorter wave-lengths are being added, those which were previously visible become more intense.

The author had laid before the Society, on the 19th January, a preliminary note containing an outline of a theory of the function of the semicircular canals of the internal ear. In that note it was stated that the six semicircular canals form three pairs—the members of each pair being parallel, and having their ampullæ at opposite ends. In this paper the author communicates the results of measurements of the position of the bony canals in a large number of animals.

Now fifty years ago, while engaged with some heavy calculations connected with engineering work, I became impressed with the advantage of having logarithmic tables much more extensive than those in use. The trouble of the interpolations at the early part of the table, contrasted with the convenience of the small additional part from 100,000 to 108,000 printed in Hutton, gave rise to the idea of carrying the table onwards even so far as to one million. Although the bulk of such a table appears to be an objection, and the turning of so many leaves a toil, the ease to the habitual computer of finding at once the number of which he is in search is so great as far to outweigh the opposite considerations. Thus, though working only to five places, we prefer to use the extensive seven-place tables rather than to take up Lalande's small volume; and so, while working to seven places, we should gladly avail ourselves of a nine-place million table, the construction of which I proposed to myself, notwithstanding the vast amount of the labour.

It may interest those who are acquainted with the history, structure, and composition of the Craigleith fossil trees, described in the two papers recently read to this Society, to learn that an opportunity has occurred for examining comparatively specimens from the submerged fossil trees of Granton Quarry. The specimens were preserved by Mr Hawkins, engineer of the Granton harbour, and have been, through his kindness, not only subjected to examination, but also presented for preservation to the Botanic Garden collection.

The result of the author's examination of diseased birds has been to confirm the statements of Drs Cobbold and Crisp, lately published in the “British Medical Journal,” that diseased grouse, or at least the emaciated birds commonly known as “piners,” owe their depraved condition to a small thread-like worm (Strongylus pergracilis, Cobbold) which infests the cæca. The author concurs in the opinion entertained by most of those who have written on the subject, that the tape-worm (Tœnia calva), which is well known to infest the grouse, is not the cause of the disease. The Tœnia is undoubtedly often present along with the Strongylus in diseased birds, but is often found by itself in plump healthy grouse. The worst cases seem to be those in which both are present in quantity, as in one examined by the author, whose cæca was crowded with Strongyli, whilst the intestine contained ten tape-worms, the whole weight of the bird, a full-grown cock, being only 15½ ounces.

In my paper on Continuants, recently communicated to the Royal Society, it was shown that the order of a continuant may be depressed if the first element of the main diagonal be unity, viz., thus:—

and from the definition it is evident that

Hence we have

In this paper the authors describe in detail compounds of dimethyl-thetine, some of which were enumerated in an earlier communication. Hydrobromate of dimethyl-thetine is readily obtained as a colourless crystalline body by the action of sulphide of methyl on bromacetic acid at ordinary temperatures. Its analysis shows that it contains quantities of the different elements agreeing with the formula C4H9BrSO2, and its mode of formation and reaction lead to the constitutional formula—

This peculiar iridescent pinkish Annelid was dredged in 1871 in Bressay Sound, in four or five fathoms, on a bottom of coarse sand and gravel, which abounded with finely-branched Melobesia calcarea, Ell. and Soland.