1. The Council of the Royal Society of Edinburgh having, on my application in 1832, entrusted me with Hansteen's Magnetic Intensity Apparatus, in their possession, I feel it to be my duty to communicate to the Society the results then and subsequently obtained with it.

2. The instrument consists of a mahogany box 5 inches long, 4 broad, and 2 deep, with sides and top of glass, having also a wooden tube, screwing into the top, for containing a silk-worm's fibre about 5 inches long, by which the magnetic needle is suspended so as to place itself horizontally, and after being caused to deviate from its point of rest, the time of any given number of oscillations in a horizontal plane is measured,—whilst a graduated circle in the bottom of the box indicates its arc of vibration.

The history of the newer sciences presents many instructive examples of the progress of the human mind in developing the germs of natural knowledge, and building on a single observation entire departments of science. Few pursuits indeed are more interesting, even to the student of immaterial nature, than in the perusal of such a history to trace the footsteps of the several investigators, and to mark how far, and by what means,—whether by new methods or by greater patience of research,—each successive observer advanced the inquiry. We see the human mind, as it were, set free from the trammels of time, and developing its resources on a large and continuous scale, not limited by the powers of one intellect, the length of one life, or the means of one station. We see, at the same time, what varied gifts and opportunities are necessary for the elucidation of a single subject; how these gifts, though not all imparted to one man or to one generation, are yet wisely and beneficently bestowed on the entire species; and how all are thus enabled to co-operate, either in unfolding abstract truth, or in drawing forth those practical results which directly conduce to the amelioration and comfort of all.

In the summer of 1834, I was led to examine with considerable interest some of the phenomena of fluids, from the circumstance of having been consulted upon the means of improving a system of navigation to be conducted at unusually high velocities. Being well aware, however, of the very imperfect state of that part of Theoretical Hydrodynamics which relates to the Resistance of Fluids to the Motion of Floating Bodies, and that there had been found in its application to the solution of practical questions, discrepancies so wide between the predicted results and the observed phenomena, as to render the principles of the theory exceedingly false guides, when followed as maxims of art, I felt i t impossible to recommend conscientiously any mode of procedure founded on defective principles, and I therefore determined to undertake a series of investigations concerning the laws of the resistance of fluids, and the means of applying them to the formation of rules for the arts of practical navigation and naval architecture. In this investigation, I have now been engaged during the leisure of two summers, and I am still continuing to prosecute the investigation.

The following paper contains a continuation of the experiments on the action of the voltaic pile on alcohol, and some other liquids, of which experiments a considerable number was described to the Royal Society in a former memoir. At present it is intended, in the first place, to shew the perfect analogy between the electric action on pyroxylic spirit, and on alcohol, thereby confirming the interesting analogy already known to exist between these fluids in other respects: in the second place, to adduce a few farther illustrations of secondary voltaic actions in aqueous solutions; in the third place, to examine the nature of the changes produced in alcoholic solutions, under galvanic agency; in the fourth place, to inquire whether electric action does not throw light on the state in which the haloid salts are dissolved by water; and, lastly, to endeavour to suggest as a general law, regulating the electric decomposition of solutions of binary combinations of elementary substances in the principal solvents, that the dissolved body is not directly decomposed, but only the solvent, if itself an electrolyte.

Although a great number of Fishes have been described by naturalists as inhabiting the coast of Scotland, and though much has been done to increase its Fauna in other respects, yet in a field so extensive much must still remain to be done. Many lakes and estuaries in Scotland are still unexplored, and many fishes being merely local, a more thorough and accurate examination of these lakes and estuaries must take place, before the Ichthyology of Scotland can be fully ascertained.

In the beginning of July last, I obtained, from the Frith of Forth, a species of bream, which has not been mentioned by naturalists as inhabiting the British seas. A few days after, I procured, from the same quarter, a second specimen of the same species, each exhibiting a conspicuous dark violet-coloured spot at the base of the upper part of the pectoral fins. (See Plate VI.)

On consulting the continental works on Ichthyology, I find this bream to agree best with the description Baron Cuvier has given of the Pagellus acarne, an inhabitant of the Mediterranean; but, as no figure of the fish accompanies his description, the discrimination of the species is rendered somewhat uncertain.

The object of the following paper is to put at rest a question which has been long agitated in Surgical Pathology, and which is intimately connected with some important points of Practical Surgery. An apology may seem due to the Society for bringing under its consideration a subject, which, though not exclusively professional, is still little studied except by those physiologists whose views are directed to surgery; but as the inquiry into which I propose to enter is neither long nor tedious, while it is quite intelligible without any previous knowledge of its details, I trust the patience of the members will not be exhausted; and if the question shall, as I hope, be decided to the conviction of those members who are conversant with surgical discussions, the prevailing diversity of sentiment relative to the point at issue will be more effectually composed than if I attempted to combat it through any other channel.

There is no branch of natural science about which we know so little as that which relates to the structure of crystalline bodies. By assuming the form of an integrant molecule, crystallographers have found no difficulty in building those geometrical solids which minerals and artificial crystals present to our observation. They conceive that these molecules unite by their homologous sides in the formation of the primitive crystal, and by supposing that they arrange themselves in plates on the faces of that crystal, each plate successively diminishing in size by the abstraction of a certain number of these molecules in lines of a given direction,—all the secondary forms of the crystal may be easily deduced.

1. The following paper is divided into three sections, containing three distinct yet intimately connected investigations. The two first on the Polarizability and Depolarization of Heat have arisen immediately out of the train of investigation contained in my two former papers, and the researches of others to which they gave rise. The third is on the Refrangibility of Heat, a point of the highest importance for theory.

2. The experiments on which these investigations are based have been performed almost exclusively during the past winter. Part of the experiments on Depolarization were, however, made in the winter 1836-7. The mode adopted for trying Refractive Indices I had long ago contemplated. It was not, however, put in practice until January last.

The following attempt to investigate the real nature of Symbolical Algebra, as distinguished from the various branches of analysis which come under its dominion, took its rise from certain general considerations, to which I was led in following out the principle of the separation of symbols of operation from those of quantity. I cannot take it on me to say that these views are entirely new, but at least I am not aware that any one has yet exhibited them in the same form. At the same time, they appear to me to be important, as clearing up in a considerable degree the obscurity which still rests on several parts of the elements of symbolical algebra. Mr Peacock is, I believe, the only writer in this country who has attempted to write a system of algebra founded on a consideration of general principles, for the subject is not one which has much attraction for the generality of mathematicians. Much of what follows will be found to agree with what he has laid down, as well as with what has been written by the Abbé Buee and Mr Warren; but as I think that the view I have taken of the subject is more general than that which they have done, I hope that the following pages will be interesting to those who pay attention to such speculations.

The series l(1+ x) = M (x—½ x2 + ⅓ x3—¼ x4+&c.), discovered by Mercator, seems to be the origin from which, directly or indirectly, all the series may be derived which are usually employed in the computation of logarithms. A series, which affords remarkable facilities for such computations, and which lately occurred to me, may be investigated in the following manner.

It is not a little remarkable, that in an age which assumes to itself the character of devotion to science, in anatomy, a science which embraces the best interests of humanity, this question should remain unanswered; What is the meaning of the nerves of the spinal marrow being in regular order and perfectly symmetrical: whilst the ten nerves arising from the brain present no similarity one to another, and agree neither in origin, size, nor distribution?

It is plain that we must be in the dark, not only with respect to the knowledge of the nervous system, but of the animal frame generally, whilst such a question is open and courts inquiry, and yet remains without an effort being made towards its solution. We must, I fear, attribute this neglect in part only to the difficulty of the inquiry, and much to the indifference to all that does not tend directly to profit; on which account it has the better demand on the attention of a learned and philosophical Society.

In following out the principle formerly laid down—that the study of the organization and functions of the part to which the nerve is distributed, will explain the peculiarities of its origin and connections—I have in this paper entered on a subject of great extent and difficulty.

As the Facial Nerve is one of a distinct class, it will be necessary to shew in what that class is peculiar—that it essentially belongs to the act of breathing—that the act of respiration being, in its ordinary condition, independent of the will, there are nerves appropriated to that function. At the same time, it must be shewn, as the apparatus of breathing is made subservient to other purposes in the economy, by what relations it is brought under the influence of the will.

Interesting as theoptical properties of the eye have been to philosophers in every age, there are conditions of this organ which are no less curious, and which have not had their share of attention.

In the year 1823, I introduced the subject to the Royal Society of London, nearly in the terms I am now using, but there is much more in the subject than I then conceived, although I see no reason to change the mode of contemplating it.

The eight muscles of the eye, and the five nerves, exclusive of the optic nerve, which pass to them, imply the complex nature of the apparatus exterior to the globe, and I fear it is too plain that the subject has not been satisfactorily treated.

It is chiefly with respect to the protecting motions of the eye that the difficulty occurs, for I hope the dependence of the proper organ of vision on the voluntary muscles of the eye, has been proved and acknowledged.

Permit me to draw the attention of the Society to what appears a very simple piece of anatomy, the circular muscle which closes the eyelids, orbicularis palpebrarum.

Sir Charles Blagden concludes a memoir in the Philosophical Transactions of London, vol. lxxviii., for the year 1788, “On the Effect of various substances in lowering the Point of Congelation in Water,” with the account of an experiment to determine the effect of salt upon the expansion of water by cold.

From that experiment, he imagined that he had reason to conclude, as far as one experiment goes, that the combination of a salt with water has no other effect upon its quality of expanding by cold, than to depress the point at which that quality begins to be sensible, just as much as it depresses the point of congelation.

The scientific world appear to have admitted this general deduction of Blagden, and, trusting to the result of a single experiment, extended it so far as to lay it down as a general law, that, as pure water has its maximum of density at 7½° above its freezing point, so every saline solution has a maximum of density at a temperature above its point of congelation, and that this temperature will be exactly 7½° distant from the freezing point of the solution.

I am not aware of any account having been published of the Coal-fields in East and Mid Lothian, or of any attempt to institute a geological survey of the country in which they are situated. Sinclair, the author of a well known work intituled “Satan's Invisible World,” published also in 1672 a treatise on Hydrostatics, in which he takes notice of the Prestongrange coals, and of the whinstone-dike that intersects them. Williams, in his “Mineral Kingdom” (published) in 1810, gives some information regarding the direction of the Gilmerton and Loanhead coal-seams. But the information contained in both these works, even respecting the coal-strata,—which alone they professed to treat of, is extremely vague, and generally very erroneous. Dr Hibbert was the first geologist who with a scientific eye entered on the district, in order to describe with fulness and accuracy any of its rocks. His discovery of the Saurian remains in the limestone-quarries of Burdiehouse, led him to a minute inspection of the strata in which they were imbedded, and to a consideration of the relative position of these particular strata in the Mid-Lothian coal-field.