The author stated in some prefatory remarks, that a belief in the operation of the laws of numerical harmonic ratio in the constitution of beautiful forms had long existed, although those laws had not been systematised so as to render them applicable in the formative arts. In proof of this, Mr Hay quoted a correspondence upon the subject of harmonic ratio, between Sir John Harrington and Sir Isaac Newton, in which the latter expresses his belief in such laws in the following words: “I am inclined to believe some general laws of the Creator prevailed with respect to the agreeable or unpleasing affections of all our senses; at least the supposition does not derogate from the power or wisdom of God, and seems highly consonant to the simplicity of the macrocosm in general.” The belief of this great philosopher, the author trusted, would form some apology to men of science for the repeated attempts he has made to establish the fact. These attempts he had hitherto made with reference to architecture, to ornamental design, and latterly to the human head and countenance; but on the present occasion he intended to shew the operation of these laws in constituting the symmetrical beauty of the entire human figure.

The object of this communication was chiefly to exhibit a specimen of the register of the electric chronograph, wherein the second's beats of two clocks were marked side by side, one going nearly to sidereal time, and the other to solar; and the length of a second's interval on the paper was so great, and the accuracy of the punctuation such, that the minute acceleration of the one clock on the other could be registered almost from second to second.

The electric register can be applied with ease to any clock, and at any distance from the recording apparatus; and two or more clocks, or they may be simple pendulums, can be made to register their vibrations on the same slip of paper.

“On the evening of the 19th December 1849, whilst walking near the southern part of Edinburgh, about fifteen minutes past five. Greenwich time (as I afterwards estimated), I observed a meteor, fully brighter than Venus at her average brilliancy, moving from W. towards N., parallel to the horizon, elevated 15° above it, and followed by a distinct luminous train. This angle was subsequently taken by estimation by daylight, with the aid of a theodolite; and the compass-bearing of the meteor, when first seen, ascertained in the same way, must have been 47° W. of N. When it bore 29° E. of magnetic north, it was observed to have divided into two, the one part following the other at some distance; and I soon after lost sight of it in the obscurity of the smoke of the town. When it split, its altitude was estimated at 6°. It thus described an arc of no less than 76°, in doing which it occupied, as I roughly estimated, about 15 seconds, or possibly more.

Chloroform has been prepared both from alcohol and from wood-spirit. The latter has been used for the sake of cheapness; but as it is a mixture of several liquids, all of which do not yield chloroform, it gives an impure product, in a proportion which varies much, but is always below that obtained from alcohol. There is therefore not only no advantage, but the contrary, in using woodspirit, which is not, after all, much cheaper than alcohol.

The author prefaced his description of the instrument, by a few general remarks on the communication, in very remote epochs, between the inhabitants of the old and new worlds, as deducible from affinities in their traditions, their cosmogenies, their religious rites and structures, their astronomical cycles, and their determination of the length of the year.

The Peruvian instrument was discovered, some years ago, in a huaco, or vast tumulus, that was believed to cover the remains of an Inca of Peru. It is not of unequal reeds, like the Greek syrinx, but is cut out of a piece of potstone, of a trapezoidal form, in which are cut eight tubular holes of unequal depths.

That theories of the physical appearances of comets have generally failed, appeared to the author to arise from the facts having been misunderstood or misinterpreted in general by the observers themselves. As a particular instance of this, the wide-spread notion of comets shooting forth their tails, at, or a little before the perihelion passage, and drawing them in again afterwards, so as to be larger at that period of their orbits than at any other, was mentioned; and in place of which, the author shewed that the comets were at the perihelion, of their smallest size; the tails becoming then more visible, not from being actually produced at that time, but from being more dense, and illumined by a stronger solar light, as well as being in general seen from a smaller terrestrial distance.

The fundamental hypothesis of the author was stated to be this:— That the eye is capable of appreciating the exact subdivision of spaces, just as the ear is capable of appreciating the exact subdivisions of intervals of time; so that tho division of space into an exact number of equal parts will affect the eye agreeably in the same way that the division of the time of vibration in music, into an exact number of equal parts, agreeably affects the ear. But the question now arises, What spaces does the eye most readily divide? It was stated that the author supposes those spaces to be angles, not lines; believing that the eye is more affected by direction than by distance. The basis of his theory, accordingly, is, that bodies are agreeable to the eye, so far as symmetry is concerned, whenever the principal angles are exact submultiples of some common fundamental angle.

The author commenced his paper by referring to the analysis of codeine made by different chemists. On these analyses four different formulæ had been founded; but two only, those of Regnault and of Gerhardt, required special mention, the others being now known certainly not to represent the constitution of the base. Regnault had deduced from his analysis the formula C35 H20 NO5, while Gerhardt gives C36 H21 NO6 as the expression of his results.

Dr Fleming directed the attention of the Society, in the first instance, to the characteristic features of sea and river proper; and then proceeded to consider the peculiarities of that common space, alternately sea and river, to which he restricted the term estuary. He then considered the nature of the space between high and low water, and pointed out the mean level, or mid-tide mark, as the only constant and universally applicable boundary plane. The influence of the tidal wave in reversing the current, checking the velocity, and increasing the depth of the river, was next brought under notice, and an experiment exhibited, illustrating the conservation of force, which causes the waters at the head of an estuary, and the connected river, in certain circumstances, to attain a higher level than the high-water mark of the neighbouring sea-shore.

When a steel needle or rod is so constructed that its centre of gravity is in a finely-turned axle at right angles to its length, it will rest in any position when the axle is placed upon polished planes; when, however, we magnetize the needle, it assumes a position which is that of the direction of the magnetic force at the place: in this way we obtain the ordinary dipping-needle. The dipping-needle can obviously move only in one plane, that to which the axle is at right angles; were it possible to suspend it freely, so that it could move in every plane with every variation of the direction of the magnetic force, we should then be able, by observing the variations of its position, to determine at once the laws which a magnet in its true position obeys; this, however, we have not been able to do; even the small variations in the vertical plane, which we might expect to obtain from the ordinary dipping-needle, are nearly or altogether destroyed by the friction of the axle upon its supports; and there are many mechanical difficulties in the way of the other methods of suspension. It has been found convenient, then, to make use of the simplest methods of suspending magnets in a horizontal plane; and to endeavour to deduce, from the composition of their motions, the laws both of the variation of the force with which a truly suspended magnet is directed, and of the direction of that force itself.

For “These data are (1.),” &c., read “These data are (1.), The known expansion of water in freezing; (2.), The known quantity of heat which becomes latent in the melting of ice ; and (3.), The quantity of work given out,” &c.