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 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.

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.

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.

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.

Few poisons are of greater interest, in a historical or scientific point of view, than Hemlock. It has been known ever since the most classic periods of antiquity, being generally believed to have been the ϰωνϵιον of Nicander and Theophrastus, and commonly thought to have been the poison with which state-criminals were despatched in ancient Athens. Since that period it has occupied a prominent place in all works on Toxicology; and it has been immemorially familiar as a deadly poison to the vulgar in every part of Europe, where there is scarcely a country or even a province which does not produce it in abundance. For nearly a century, too, since the writings of Baron Storck of Vienna in 1762, it has been constantly in the hands of the physician as a remedy, and has been currently employed at different times in the treatment of some of the most common, as well as in some of the most malignant, of all the maladies to which the human body is liable.

I was led into the following train of investigation from observing, that, when minute quantities of certain substances were dissolved in alcohol, and the liquid was acted on by a moderate voltaic power, evident signs of decomposition were exhibited by the evolution of elastic fluid at the negative pole. In investigating the nature of the changes produced, I was farther led to examine the action of voltaic electricity on a variety of alcoholic solutions, and also the agency of more powerful galvanic batteries on pure alcohol and on ether; and, ultimately, I was conducted into a field, into which I should have hesitated voluntarily to enter, namely, the voltaic decomposition of aqueous solutions, which has recently been investigated with so much success by a distinguished cultivator of science. In the following paper, it will be my object to give some account of the experiments which I have made on these different subjects, and of the results and views to which I have been led.

Payne Knight, no mean name among philologers, after a masterly and convincing proof, that neither Zenodotus nor Aristarchus, the great critics of the Alexandrian school, could be acquitted of the charge of “scarcely credible ignorance” of the primitive form of the Homeric language, thus proceeds :—

“The grammarians and critics of Alexandria were all guilty of the same fault. They never investigated the original sources of the language, but classed among anomalous dialects and poetic licenses every thing that was not in unison with their own usual style of speaking. In their age there existed many clews to the inquiry, which have now disappeared, but which, at that time, might easily have been found in written records, and in the rude and semi-barbarous languages of Italy and other countries adjacent to Greece. Had any one, however, suggested to Aristarchus that the true form and character of the Homeric dialect was to be extracted from the Latin, Tuscan, or Oscan languages, he would in my opinion have been as much astonished as if he had heard of the claims of the Irish antiquary, who affirmed that the Homeric poems had been translated furtively from the “Gaelic into Greek.”

The power of making such a representation of any object, as shall give a distinct idea of its form, is a faculty which artists possess in different degrees of perfection. The principal difficulty is, to get a first delineation of any subject; from this a copy may be made in various ways, with less exertion of talent than was required for the composition of the original.

Various geometrical and optical inventions have been proposed to assist the artist in making an outline of an object which he wishes to represent. The Reticulated Square and other contrivances, for placing every point of the thing to be represented in its proper place in the picture, belong to the first class; the Camera Obscura and the Camera Lucida to the second. When a design is to be copied, a different kind of contrivances will in general be more convenient. It is only of these that I propose to treat here.

Among persons interesting themselves in the progress of British manufactures, it can scarce fail to be known, that Mr Neilson of Glasgow, manager of the Gas Works in that city, has taken out a patent for an important improvement in the working of such furnaces as, in the language of the patent, “are supplied with air by means of bellows, or other blowing apparatus.” In Scotland, Mr Neilson's invention has been extensively applied to the making of cast-iron, insomuch that there is only one Scotch iron-work where the invention is not in use, and in that work, apparatus is under construction to put the invention into operation.

1. The first series of these researches, in the exact form in which they are printed, were laid before the Royal Society on the 19th January 1835. The whole of the experiments there described were made, and the paper written and printed, within a space of time little exceeding two months. This haste, unfavourable to composition, I considered as a less evil than postponing for a period of time, which must have been considerable, the publication of a class of facts which might be said almost to embrace a new science. The professional duties which pressed upon me during the whole continuance of those experiments, then called imperatively on my attention, and during the remainder of the Session my time was devoted to them. The summer I devoted to a foreign excursion, some of the results of which I afterwards digested; and it was not till the commencement of the winter session which has just closed, that I prepared, with a fresh stock of health and spirits, to reinvestigate the whole subject of the Polarization of Heat, and to assign numerical values to the effects, whose existence I had before been contented to prove.

For a long time I was anxious to know the rate of expansion of the common building-stone of this neighbourhood, as it is not given in any of the tables of the expansions of substances, because I have sometimes thought that the vertical cracks frequently seen intersecting rubble walls might arise from the contraction caused by a diminution of temperature. During a long-continued and severe frost which occurred in 1826, I thought the rents in a considerable stretch of wall, which I passed at all seasons, appeared more open than usual. This, however, was merely conjectural, and I paid no more attention to the subject until 1830, when, as I mentioned in a notice on the commencement of my experiments read at the meeting of the British Association in September last, an interdict of the Dean of Guild Court of Edinburgh rendered the rate of expansion of stone a matter of more importance than merely a curious philosophical speculation.