If U, V, &c, are rational and integral functions (٭)(x, y, z)r, all of the same degree r, in regard to the co-ordinates (x, y, z), then √U + √V + &c. is a polyzome, and the curve √U + √V + &c. = 0 a polyzomal curve. Each of the curves √U = 0, √V = 0, &c. (or say the curves U = 0, V = 0, &c.) is, on account of its relation of circumscription to the curve √U + √V + &c. = 0, considered as a girdle thereto (ζῶμα) and we have thence the term “zome” and the derived expressions “polyzome,” “zomal,” &c. If the number of the zomes √U, √V, &c. be = ν, then we have a ν-zome, and corresponding thereto a ν-zomal curve; the curves U = 0, V = 0, &c., are the zomal curves or zomals thereof.

I. On some Transformations in Films when brought in contact with Surfaces of Glass.

(1.) Let a film be formed on the rim of a cylindrical wine-glass, at or very near its margin; cover it immediately with a watch-glass, and holding the latter firmly in its place, invert the whole, so that the film is placed in a vertical position. The film will now attach itself to the watch-glass at the lowest point where it is in contact with the margin of the wine-glass, and will run up the concave surface of the former. At the same time, the film will leave the margin of the wine-glass at its upper edge, and retreat into the glass, running down its inner surface. A film of the form of the segment of a sphere will thus be produced, which, with the upper portions of the inner surfaces of the watch-glass and wine-glass, will form a hollow filled with air, as shown in fig. 1. This state of matters will remain the same, in whatever position we now place the wine-glass, the figure which has thus been produced being one of equilibrium. The phenomenon produced arises from the fact, that when the original film is first taken up on the margin of the wine-glass, a drop of liquid always remains in the bottom of the glass, and when the glass is inverted, so as to bring the film into the vertical position, this drop runs down the inner surface of the glass till, reaching its lowest point, it brings the film into close contact with the watch-glass; the film now attaches itself to and spreads itself over the surface of the latter in a similar way to what takes place when a bubble blown from a pipe is brought into contact with any smooth surface, whilst the original system of equilibrium being now disturbed, the upper part of the film is put in motion, and a new system of equilibrium is formed.

During the last three years I have made a large number of observations on the temperature of the common fowl under different circumstances, the results of which I now beg leave to submit to the Society, with the hope that they may be considered not altogether uninteresting to the physiologist.

The fowls tried were chiefly of the pure Dorking breed. At the time they appeared to be healthy, and all in good condition. They had all the run of a field adjoining the poultry yard.

In all the trials the same thermometer was used,—each degree of which, that of Fahrenheit, was divided into ten parts, and had been warranted correct by the makers after comparison with a standard.

As the reputed fact of Archimedes having burned the Roman ships engaged in the siege of Syracuse, by concentrating on them the solar rays, has not only been doubted but disbelieved by some of the most eminent scientific men, I shall briefly give the evidence on both sides.

The burning of the ships of Marcellus is mentioned by most of the ancient writers who refer to the machines which Archimedes employed in the defence of his native city, and their statements have been repeated by succeeding authors, without any doubts having been expressed until comparatively recent times. Our earliest authorities on the subject are Diodorus Siculus, Lucian, Galen, Dion, and Pappus.

There can be no reasonable doubt that a relation exists between the physiological action of a substance and its chemical composition and constitution, understanding by the latter term the mutual relations of the atoms in the substance. There are numerous indications of such a relation, and attempts have been made to express it formally in certain cases. Thus it has been long observed, that the salts of the same base have a common physiological action, and it has been pointed out by Mr Blake that, with some exceptions, the salts of isomorphous bases have a similar action. A corresponding likeness in physiological action may be traced in salts having the same acid, but beyond these generalisations we are not aware that any approach has been made to the statement of a law connecting the physiological action of a substance with its chemical constitution.

In the fourth part of these researches, I described a new base produced by the action of sodium upon picoline, to which I gave the name of Parapicoline, because it has the same composition as picoline, although the circumstances of its formation appeared to show that it had been produced by the combination of two molecules of that substance, so that its true formula would be C12H14N2. Unfortunately, its high boiling point, and tendency to decompose when distilled, made it impossible to determine its vapour density, which afforded the only means of ascertaining whether this hypothesis was correct; and it was only assumed, because similar cases of polymerisation had been established beyond a doubt in the case of other classes of organic compounds. In the hope of obtaining a similar base of lower boiling point, and therefore better adapted to the necessary experiments, I have submitted pyridine to the action of sodium, and the results of the inquiry are contained in the following pages.

1. The mathematical work of the present paper has been performed to illustrate the hypothesis, that space is continuously occupied by an incompressible frictionless liquid acted on by no force, and that material phenomena of every kind depend solely on motions created in this liquid. But I take, in the first place, as subject of investigation, a finite mass of incompressible frictionless fluid completely enclosed in a rigid fixed boundary.