In offering to this Society a few remarks which have occurred to me on this fundamental department of Mental Physiology, I beg in the first place to explain, that my reason for doing so is merely this, that in consequence of certain unguarded expressions, and, as I think, hasty reflections, the opinions of Dr Brown, and likewise of Sir James Mackintosh, and of Lord Jeffrey, and other more recent writers on this subject, have been supposed to be irreconcileably at variance with those of Dr Reid and Mr Stewart; i. e., with those which are usually called the leading doctrines, or essential characteristics, of the Scotch School of Metaphysics, in this fundamental department of the science. And when such difference of opinion is believed to exist among men of generally acknowledged talent, who have studied this subject, and nothing like an experimentum crucis can be pointed out, to compel us to adopt one opinion and reject another,—the natural inference is, that there is something in the study itself, which renders it unfit for scientific inquiry,—that what is called the study of the Mental Faculties granted to our species is, in fact, only a record of the vacillations of human fancy and ingenuity, in the invention and demolition of hypotheses,—and that the subject is one on which it is in vain for our minds to dwell, with any hope of applying the principles of Inductive Science, and acquiring any insight into the laws of Nature, regulating the phenomena presented by the last and greatest of her works, similar to that which is the object and the reward of all other scientific inquiries.

The series propossed for solution in the follwing paper is—

The law of this series is manifest. Each term is the product of two factorials, the first consisting of p, and the latter of q factors. And in each successive term, the factors of the first factorial are each diminished by one, and those of the latter increased by one.

The existence of certain minerals imbedded in others,—the optical phenomena which they exhibit,—their form and mode of distribution, and the mechanical influence which has been exerted during their formation on the mineral that contains them, are among the most curious and instructive facts in physical science.

The dissemination of perfectly-formed crystals of titanium, both in the form of titanite and anatase, in Brazilian crystals of quartz, is a fact so well known that I shall take no farther notice of it, but shall proceed to give an account of a series of facts of a much more general and interesting character, which I have had occasion to observe, during an extensive examination of minerals, undertaken with a different object.

The influence of compression and dilatation in producing the doubly refracting structure in solids of all kinds, whether crystallised or uncrystallised, which do not possess it, and in modifying that structure in all crystals which do possess it, has been long known; but with this class of phenomena, those which I am about to describe have no connection whatever.

In the course of experiments on the double reflexion and polarisation of light which I discovered in the chrysammates of potash and magnesia, murexide, and other crystals, I was surprised to find that these substances could be spread out upon glass by hard pressure, like grease or soft wax, and that in the case of chrysammate of potash and other bodies, when the powder could scarcely be distinguished from snuff, I obtained a transparent film, exhibiting the phenomena of double reflexion and polarisation from its surface, as perfectly as if I had been using a large crystal.

Temperature being measured by the pressure of a perfect gas at constant density, the absolute zero of temperature is that point on the thermometric scale at which, if it were possible to maintain a perfect gas at so low a temperature, the pressure would be null.

The position of this point is of great importance, both theoretically and practically; for by reckoning temperatures from it, the laws of phenomena depending on heat are reduced to a more simple form than they are when any other zero is adopted.

Section VI.—A Review of the Fundamental Principles of the Mechanical Theory of Heat; with Remarks on the Thermic Phenomena of Currents of Elastic Fluids, as illustrating those Principles.

(Article 46.) I have been induced to write this Section, in continuation of a paper on the Mechanical Action of Heat, by the publication (in the Philosophical Magazine for December 1852, Supplementary Number) of a series of experiments by Mr Joule and Professor William Thomson, on the Thermal Effects experienced by Air in rushing through small Apertures. Although those authors express an intention to continue the experiments on a large scale, so as to obtain more precise results; yet the results already obtained are sufficient to constitute the first step towards the experimental determination of that most important function in the theory of the mechanical action of heat, which has received the name of Carnot's Function.

The source from which plants obtain nitrogen, which is now recognised as one of their most important elements, has, from the first recognition of its importance, been matter of dispute. Latterly, however, chemists and physiologists have pretty unanimously come to the conclusion, that a large (perhaps the largest) part of the nitrogen of vegetables is derived from ammonia; whilst much discussion has been carried on as to the question, Is any part of their nitrogen yielded by nitric acid?

The most able advocate in this country of the claims of ammonia is Dr Gregory. The most able advocate of the claims of nitric acid is Professor Johnston of Durham, and the opposite conclusions to which accomplished chemists like these have come in reference to the point in dispute, have perplexed botanists, who know not which view to prefer. The extent to which they are pressed by this dilemma, has been so strongly represented to me by Dr Balfour, that I have engaged to bring the subject, as I now do, before this Society. I shall sedulously avoid discussing the question in a polemical spirit; and, as the shortest and most satisfactory way of doing justice to the rival views, I shall select Dr Gregory's clear and concise statement, as representing the opinions of those who deny that nitric acid is part of the food of plants; and then proceed to state what appear to me conclusive proofs that nitric acid does supply plants with nitrogen.

What are the nutritive qualities of fish, compared with other kinds of animal food? Do different species of fish differ materially in degree in nutritive power? Have fish, as food, any peculiar or special properties? These are questions, amongst many others, which may be asked, but which, in the present state of our knowledge, I apprehend it would be difficult to answer in a manner at all satisfactory.

On the present occasion, I shall attempt little more than an opening of the inquiry, and that directed to a few points,—chiefly those alluded to in the foregoing queries.

In 1836, Mr Fox Talbot communicated to the Royal Society a paper “On the Optical Phenomena of certain Crystals” which he obtained by dissolving a crystal of Borax in a drop of somewhat diluted Phosphoric acid. When the acid and the salt are in proper proportions, “the field of view of the microscope is seen covered with minute circular spots, each of which is like a tuft of silk radiating from a centre, and is composed of a close assemblage of delicate acicular crystals forming a star.” Among these crystals are seen interspersed “a number of circular transparent bodies, which are tufts or stars of acicular crystals, in such close assemblage as to be in optical contact with each other, and to produce the appearance of a single individual.”