Makerstoun, Kelso, 15th March 1830.

My Dear Sir,

Accompanying I beg leave to transmit you Mr Dunlop's paper on the distribution of the magnetic intensity over this country, which I formerly mentioned when I had the pleasure of seeing you, and which I request you will lay before the Royal Society.

Mr Dunlop has so fully and clearly detailed his mode of proceeding with these observations, that it would be unnecessary for me to enlarge upon them further, than to state, that, in point of number, extent of country, combined with precaution, accuracy, and consistency, I consider they are unrivalled in this or any other country.

An opinion has been entertained by some of the modern French philosophers, and, among others, by the late celebrated Marquis de La Place, that it was only when far advanced in years that Sir Isaac Newton turned his attention to the study of Theology; and it has been lately assumed by M. Biot, in an account of Newton and his discoveries, contained in the “Biographie Universelle,” as a fact which can scarcely be doubted, that, at one period of his life, he was actually in a state of mental derangement.

Il resterait à résoudre une problème plus générale, à trouver la courbe hectémoreale sur la sphère même, et sur un cadran quelconque.

Delambre, Conn. des Temps, an. 1820, p. 341.

The nature of these lines, though a subject of repeated investigation, has never been accurately determined. The loci of the points which divide the semi-diurnal arc into n equal parts, have almost invariably been considered as great circles, and their projections upon a plane, which are the dial-lines in question, in consequence viewed as straight lines. Clavius was the first to point out, and to prove, the error of this opinion; and Montucla (or rather Lalande) not only denied that they were circles at all, but affirmed they were curves of a very fantastical kind—“tres bizarre.” This latter opinion, which is partly true and partly false, seems rather to have been inconsiderately hazarded, than derived from any satisfactory course of reasoning. They are not great circles, it is true; but, as Delambre has replied, “il y a beaucoup d'exageration à donner une forme tres bizarre à des lignes qui, dans aucun des cadrons qu'on a tracées de cette manière, n'ont jamais pas s'ecarter sensiblement de la ligne droite.”

The decomposition of white light by prismatic refraction, as effected by Sir Isaac Newton, has, for more than a hundred and fifty years, been received as a demonstrated truth by the most distinguished philosophers of all nations. Various attempts indeed have been made, both in his day and in ours, to overturn this beautiful generalization, but they have been made by persons not only ignorant of the subject, but unacquainted with the first principles of physical research.

The analysis of light by the prism is perfect, in so far as it goes, and was demonstrated by Newton in the case of spectra produced by the single refracting medium which he employed. It was left, indeed, to his successors to discover the different dispersive powers of bodies, and the irrationality of the coloured spaces, and thus to establish the principles of the Achromatic and the Aplanatic Telescopes. These discoveries presented no points of objection to the views of Newton. They were entirely of a supplementary character, and were calculated to establish more firmly his general doctrine respecting the composition of light.

In the month of February 1829, I discovered accidentally that a bar of iron, when heated and placed with one end on a solid block of lead, in cooling vibrated considerably, and produced sounds similar to those of an Æolian harp.

1. I have lately made further experiments with bars of copper, zinc, brass, and bell-metal, which, when heated and placed on blocks of lead, tin, or pewter, produce the same effect as the iron.

2. The bars I generally used in making the experiments, were 4 inches long, 1½ inch wide, and 1½ inch thick, with a rod 7 inches long attached to one end, to serve as a handle. A ridge is formed along the centre of one side of the broad part, by its being bevelled off towards each edge; the other side is flat. The longitudinal ridge is the part that rests on the block.

In the month of November 1830, a small portion of a magnificent fossil stem was discovered in the quarry of Craigleith, in this vicinity, and more and more of it was brought into view as the working of the quarry proceeded.

In December following, I communicated to the Natural History Society of Northumberland a description of that part of the petrifaction which had then been uncovered. This description will appear in their Transactions.

At that period a considerable part of the stem had been brought into view, and since that time the remaining portion, and the roots, have been exposed.

1. The science of Meteorology must be ranked, at the present moment, among the most rising branches of natural knowledge. The transition from the hasty generalization which always marks the embryo state of science, to the application of sober inductive analysis, is one so important, and so truly interesting, as to repay amply the philosophical abstinence which it imposes. No more important lesson, indeed, can be learned, than from the very examples of crude speculation, which, for centuries, the progress of this subject has afforded among the multitudes whose scientific acquirements are limited to the art of consulting a weather-glass, or registering a thermometer, little imagining that the very science they affect to cultivate, ranks among its phenomena the interwoven effects of remote and recondite causes,—a science which, to use the words of Mr Herschel, is “one of the most complicated and difficult, but, at the same time, interesting subjects of physical research: one, however, which has of late begun to be studied with a diligence which promises the speedy disclosure of relations and laws, of which, at present, we can form but a very imperfect notion.”

In a paper which I communicated to this Society in 1815, and which was published in the Seventh volume of their Transactions, I described a new species of coloured fringes, produced between two plates of parallel glass. From a consideration of the theory of this class of phenomena, it was obvious that analogous, though much more complicated, systems of rings should be produced between plates with curved surfaces, but it was not till 1822 that I succeeded in detecting them; and so completely are these rings concealed by the superposition of similarly situated images, that, in consequence, of having forgotten my method of observation, I have experienced the greatest difficulty in rediscovering them.

My earliest experiments were performed with a double achromatic object-glass, made by Berge, having a diameter of inches, and 30 inches in focal length. The inner surfaces of the crown and flint glass lenses were ground to different radii, as shewn in the section of it at AB, CD, Fig. 5, Plate IX.; and the outer surface of the flint-glass lens was concave, so that there was left between the lenses a meniscus of air A 2, B 3 A.

Notwithstanding the intimate connexion which has long been known to exist between magnetism and electricity, we may safely say, that, only fifteen years ago, the announcement of the excitation of a luminous spark from a natural magnet would have been received with astonishment and even with incredulity.

After the great discovery of electro-magnetism, in 1819, by Professor Oersted, the extreme improbability of such a discovery was indeed removed; but, even after that period, until the recent researches of our distinguished countryman Mr Faraday, every attempt having failed to procure the feeblest trace of electricity from the obdurate magnetic mass, so striking a result, which comes home to the comprehension of those least accustomed to interest themselves in the less palpable results of scientific enquiry, could scarcely have been looked for with any degree of confidence.

1. In the course of some inquiries concerning the power of metallic substances to conduct intense electrical explosions, an account of which was honoured by a place in the Philosophical Transactions for the year 1827, I sought to obtain a comparative measure of the conducting power, in the heat evolved by the metal, at the time of transmitting the charge. The instrument employed for this purpose, was, in principle, that of a common air thermometer, the given metal, the subject of experiment, being drawn into a wire, and passed air-tight across its bulb. This simple contrivance, I have since extended to the general purposes of an electrometer, so as to estimate the force of any ordinary electrical accumulation. The results arrived at with voltaic combinations, seem, for the most part, of much practical utility; and therefore some account of them may, I trust, be found worthy of the attention of the Royal Society of Edinburgh.

It is the object of this paper tor establish with numerical exactness the following law of the Diffusion of Gases:

“The diffusion or spontaneous intermixture of two gases in contact, is effected by an interchange in position of indefinitely minute volumes of the gases, which volumes are not necessarily of equal magnitude, being, in the case of each gas, inversely proportional to the square root of the Density of that gas.”

These replacing volumes of the gases may be named equivalent volumes of diffusion, and are as follows: Air, 1; Hydrogen, 3.7947; Carbureted hydrogen, 1.3414; Water-vapour, 1.2649; Nitrogen, 1.0140; Oxygen, 0.9487 ; Carbonic acid, 0.8091; Chlorine, 0.6325, &c.; numbers which are inversely proportional to the square roots of the densities of these gases, being the reciprocals of the square roots of the densities, the density of air being assumed as unity.

The modern system of analytical geometry of three dimensions originated with Clairault, and received its final form from the hands of Monge. Descartes, it is true, had remarked, that the orthogonal projections of a curve anyhow situated in space, upon two given rectangular planes, determined the magnitude, species, and position of that curve; but this is, in fact, only an appropriation to scientific purposes of a principle which must have been employed from the earliest period of architectural delineation—the orthography and ichnography, or the ground-plan and section of the system of represented lines. Had Descartes, however, done more than make the suggestion—had he pointed out the particular aspect under which it could have been rendered available to geometrical research—had he furnished a suitable notation and methods of investigation—and, finally, had he given a few examples, calculated to render his analytical processes intelligible to other mathematicians;—then, indeed, this branch of science would have owed him deeper obligations than it can now be said to do.