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.

It has always appeared to me, that the study of the stratification of rocks and of mountain masses, ought to be one of the principal objects of a geological observer. Many of the most important facts in geology have been ascertained by the consideration of the position of strata. Among these facts, the relation existing between the direction and the inclination of the strata and the unstratified rocks, to whose presence the change in the position of the beds from an horizontal to an inclined, and sometimes even to a vertical situation, is now generally attributed, is one of the most conspicuous. It is only by an accurate determination of the position of the strata in any mountain-chain that the real direction of the line of elevation of that chain or its mineralogical axis may be determined.

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.

During the researches which I have made upon this subject since the composition of my former paper, printed in the first Part of this Volume, so many and so varied inquiries arising out of it, and essentially connected with it, have presented themselves, that I have been compelled to make a total change in the plan I had then laid down for the completion of the present section of my communication. I found that many subjects to which I there alluded might, with propriety, be omitted in the present case, as constituting little more, in reference to principles, than illustrations, however interesting they might be when viewed as properties of geometrical figures. On this ground, therefore, I have cancelled a considerable number of properties of the Spherical Conic Sections, and retained only one or two for the purpose of illustrating the method of discussing the properties of those curves. The remarks I intended to make upon the singular points of spherical curves, the geometrical signification of certain symbols, and other inquiries collateral to these, have grown into systems of themselves, or been attached to other dissertations (either wholly or partially completed), to which they seemed to be as closely allied as even to the present subject.

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.”

1. On the 17th January 1831, Mr Arthur Trevelyan communicated to the Royal Society of Edinburgh a paper, entitled “Notice regarding some phenomena observed during the Cooling of certain Metals placed in contact with Lead.” This was the first account published of the remarkable discovery made by that gentleman, of a most curious class of phenomena, which till then was unknown to the scientific world. This paper was afterwards published, with some additions, in the 12th volume of the Transactions of that body, under the title of “Notice regarding some Observations on the Vibrations of Heated Metals.”

2. Mr Trevelyan had, in February 1829, first observed the phenomena just alluded to, which consist in certain tremulous motions accompanied by sounds, often highly musical, excited in many metals while hot, placed in contact with lead or tin, at a lower temperature.

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.

The inquiries of scientific persons into the various departments of knowledge, have very generally for their sole object the investigation of truth, and the progress of science, without any reference to trade or the usual business of life. Hence to the practical man they seem generally dry and without interest, his mind being directed towards immediate utility, public or individual. Should I in the course of the present inquiry, (which in its essential nature is strictly anatomical and physiological, and can be investigated with advantage only by the anatomist and physiologist,) seem to the strictly scientific to have paid too much attention to practical details, apparently unconnected with the scientific part, and consequently out of the line of my vocation, my apology is, that in the course of the observations, I found this to be unavoidable, although my utmost efforts were made to prevent the inquiry running into this laborious and expensive train; and I entertain a firm belief, that, on a careful perusal of the observations, taking all matters into consideration, it will be found that I could not have done otherwise.

In a paper on the Monochromatic Lamp, &c., read before this Society on the 15th April 1822, and published in their Transactions, I recorded some of my earliest experiments on the action of coloured media on the Solar Spectrum. These experiments were continued at irregular intervals, with the view of obtaining distinguishing characters of coloured media, of investigating the cause of the colours of natural bodies, and of examining more correctly the phenomena of the overlapping colours of equal refrangibility, the discovery of which I had announced in the paper already referred to. The results to which I was conducted on the two last of these subjects, have been already communicated to the Society in two papers, one on the Analysis of Solar light, and the other on the Colours of Natural Bodies.

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.

Having frequently had the pleasure of examining the very interesting and highly valuable collection of volcanic specimens brought from Iceland, and presented to the Royal Society by Sir George Mackenzie, I was gratified in an opportunity which was afforded me, at the close of 1830, of visiting the Lipari Islands, the only other great repository of obsidian in Europe, and of there collecting the suite of specimens which I have now the honour of presenting to the society. Unfortunately, it is far from complete as a geological series; for the difficulties occasioned by the tempestuous state of the weather, and the impossibility of getting to the more remote islands in a small boat during the month of December, limited my movements extremely, and forced me to confine my observations to the two principal islands of the group, viz. Lipari and Vulcano. I do not therefore pretend to give any geological account of these islands, or even of the two on which I landed. My object in collecting, and consequently also in presenting to the Society, this series of specimens, was to afford the means of comparing with each other the productions of the two great obsidian districts of Europe; those from Lipari, which are now on their table, with the Iceland suite already in their possession.

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.

There are few of the applications of optical science so universally interesting as that which has for its object the explanation of the colours of natural bodies. Sir Isaac Newton was the first person who ventured to refer to one general principle all the variety of colours which are found in nature; and he has maintained his opinions on this subject with a confidence in their accuracy which seems to have confounded his adversaries: For while his analysis of light, the most perfect of all his labours, exposed him to the most harassing controversies, his theory of natural colours, the least perfect of his speculations, was allowed to pass without examination or censure.

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.