The limited district of country which I am about to describe, is one of those which may rank amongst the least frequented in the civilized part of Europe, yet which might justly claim for France the character of romantic beauty which travellers on her beaten highways commonly, and not without reason, deny to her.

The modern department of the Ardêche, corresponding in part to the ancient province of the Vivarais, includes country of very dissimilar features, the southern and eastern part, forming the right bank of the Rhone near Viviers, being comparatively flat; whilst the north-western boundary is the irregular chain of the Cevennes, including the localities more immediately to be described. This chain is not so remarkable for its absolute height, although that be considerable, rising at the Mont Mezenc, in the neighbouring department of the Haute Loire, to an elevation of 5750 English feet above the sea, as from forming the separation of a remarkably elevated tract stretching to the north and west, and which suddenly subsides, at the point of which we now speak, into the wide champaign country of the Lower Rhone, possessing a very different aspect, soil, climate, and population.

[Extracted from a Letter addressed to Professor Kelland.]

My dear Sir,

In reading your paper in the Transactions of the Royal Society of Edinburgh, vol. xv., p. 315, some years ago, it occurred to me to try whether it would not be possible to give a general demonstration of the theorem, applying to apertures of all forms. I arrived at a proof, which I wrote out, but have never published. As I think it will interest you I will communicate it. You may make any use you please of it.

Case I. Aperture in front of a lens; light thrown on a screen at the focus, or received through an eye-piece, through which the luminous point is seen in focus.

The expression for the intensity is given in Airy's Tract, Prop. 20. If the intensity of the incident light at the distance of the aperture be taken for unity, and D be the quantity by which any element of the area of the aperture must be divided in forming the expression for the vibration, that expression becomes

the integration being extended over the whole aperture. If it should be necessary to suppose a change of phase to take place in the act of diffraction, such change may be included in the constant B.

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.

(33*.) In my paper on the Mechanical Action of Heat, published in the 1st Part of the 20th Volume of the Transactions of the Royal Society of Edinburgh, some of the numerical results depend upon the dynamical equivalent of a degree of temperature in liquid water. The value of that quantity which I then used, was calculated from the experiments of De la Roche and Bérard on the apparent specific heat of atmospheric air under constant pressure, as compared with liquid water.

The experiments of Mr Joule on the production of heat by friction, give, for the specific heat of liquid water, an equivalent about one-ninth part greater than that which is determined from those of De la Roche and Bérard. I was formerly disposed to ascribe this discrepancy in a great measure to the smallness of the differences of temperature measured by Mr Joule, and to unknown causes of loss of power in his apparatus, such as the production of sound and of electricity; but, subsequently to the publication of my paper, I have seen the detailed account of Mr Joule's last experiments in the Philosophical Transactions for 1850, which has convinced me, that the uncertainty arising from the smallness of the elevations of temperature, is removed by the multitude of experiments (being forty on water, fifty on mercury, and twenty on cast iron); that the agreement amongst the results from substances so different, shews that the error by unknown losses of power is insensible, or nearly so; and that the necessary conclusion is, that the dynamical value assigned by Mr Joule to the specific heat of liquid water, viz.:—772 feet per degree of Fahrenheit, does not err by more than two or at the utmost, three feet; and therefore, that the discrepancy originates chiefly in the experiments of De la Roche and Bérard.

The natural history of the Charr, especially as regards its generation and the early period of its life, is admitted to be very defective, partly, no doubt, arising from the peculiar habits of the fish withdrawing it from observation, and in part, and more, to the circumstance that it is comparatively of rare occurrence, being found only in a limited number of the deepest lakes of this country, and, with few exceptions, seldom taken by the angler, and consequently a good deal removed from the notice of the naturalist.

Residing for several years in the neighbourhood of Windermere,—a lake in which this fish, though decreasing in number, is still pretty abundant,—I endeavoured to collect information respecting its breeding, the time required for the hatching of its ova, and the peculiarities of the young fish after its exclusion, but in a great measure in vain. The fishermen of the lake were acquainted with its spawning season and the spawning localities; but none of them had ever seen a young charr after its quitting the egg, nor till it had attained a notable size.

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 facilities which are afforded by the introduction of the function into certain classes of Differential expressions are well known. This function has effected the combination and generalization of Problems, which, although found to be capable of solution in particular cases, were regarded rather as isolated and exceptional forms, than as integral parts of some comprehensive expression. But the subject is far from exhausted. Some of the most important Differential Equations have never as yet been solved by a general method. The present Memoir is intended to supply this defect. The process employed differs little from that which I have previously exhibited; but the range of Problems which it embraces is much more extensive, and the Problems themselves are of a more important character.

(34.) The objects of this paper are twofold: First, To compare the results of the formulæ and tables relative to the power of the steam-engine, which have been deduced from the Dynamical Theory of Heat, with those of experiments on the actual duty of a large Cornish engine at various rates of expansion; and, Secondly, To investigate and explain the method of determining the rate of expansion, and, consequently, the dimensions and proportions of a Cornish engine, which, with a given maximum pressure of steam in the cylinder, at a given velocity, shall perform a given amount of work at the least possible pecuniary cost, taking into account the expense of fuel, and the interest of the capital required for the construction of the engine.

During the last few years, great progress has been made in the study of the organic alkalies, and the discovery of methods by which these substances can be artificially produced, and the long train of investigations by which it has been followed, has greatly extended our previous information, and afforded us some definite ideas regarding their constitution. The advance made has, however, related entirely to the volatile bases produced by artificial processes, and our knowledge of the natural fixed alkaloids stands very much where it did some years since, and is still very imperfect, and in regard to many entirely fragmentary; so much so, indeed, that of all the alkaloids of this class described in chemical works, there are not perhaps a dozen of which the constitution can be considered as definitely fixed, and not half that number of which we know the products of decomposition. The fact is, that the interest attaching to the artificial bases has altogether diverted the attention of chemists from the natural alkalies, which have not hitherto proved a very productive field of inquiry; at least the researches to which many of them were subjected ten or fifteen years since, proved comparatively unfruitful in their results.

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.

Having long desired to witness a total eclipse of the sun, I resolved to proceed to some place in the line of the moon's shadow, for the purpose of observing that which took place on the 28th of last July.

Various reasons induced me to prefer the town of Göteborg in Sweden to any other station. It had interesting historical associations connected with eclipses: and there was something pleasing in the prospect of seeing the red prominences, which excited so much attention at the eclipse of 1842, at the very spot where they were observed, probably for the first time, in 1733; but a more important ground of preference, was its proximity to the central line of the moon's shadow, and its being directly accessible from England.

(39.) A machine working by expansive power consists essentially of a portion of some substance to which heat is communicated, so as to expand it, at a higher temperature, being abstracted from it, so as to condense it to its original volume, at a lower temperature. The quantity of heat given out by the substance is less than the quantity received; the difference disappearing as heat to appear in the form of expansive power.

The heat originally received by the working body may act in two ways: to raise its temperature, and to expand it. The heat given out may also act in two ways: to lower the temperature, and to contract the body. Now, as the conversion of heat into expansive power arises from changes of volume only, and not from changes of temperature, it is obvious, that the proportion of the heat received which is converted into expansive power will be the greatest possible, when the reception of heat, and its emission, each take place at a constant temperature.

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.

The following remarks, being the result of a careful examination of a small district of country characteristic of the relations of the trap formations, are perhaps worthy of being recorded; although the general features of the county of Roxburgh have been very clearly stated in a paper by Mr Milne, published in the 15th volume of the Edinburgh Transactions.

The outburst of porphyritic trap forming the conspicuous small group of the Eildon Hills, may be stated to be surrounded by the characteristic greywacke of the south of Scotland. It forms an elongated patch on the map, extending from the west end of Bowden Muir in the direction of the town of Selkirk, and running from west-south-west to east-north-east (true) towards Bemerside Hill, on the north bank of the Tweed. The breadth is variable, probably less than is generally supposed; but it cannot be accurately ascertained, owing to the accumulated diluvium which covers the whole south-eastern slope of this elevated ridge. On this account, my observations on the contact of rocks have been almost entirely confined to the northern and western boundaries of the trap, although the other side was examined with equal care.

There are few parts of mechanics in which theory has differed more from experiment than in the theory of elastic solids.

Mathematicians, setting out from very plausible assumptions with respect to the constitution of bodies, and the laws of molecular action, came to conclusions which were shewn to be erroneous by the observations of experimental philosophers. The experiments of Œersted proved to be at variance with the mathematical theories of Navier, Poisson, and Lamé and Clapeyron, and apparently deprived this practically important branch of mechanics of all assistance from mathematics.

Since the year 1803, when Desrone discovered the substance which afterwards received the name of Narcotine, the chemical investigation of opium has engaged the attention of many skilful and distinguished chemists, and in their hands has proved the source of a series of substances, unprecedented in their number and the variety of their properties. Up to the present time, there have been detected in it no less than eleven different substances, one acid, and ten, either basic or indifferent, all presenting definite characters and crystalline form, besides various imperfectly characterised substances, described under the names of caoutchouc of opium, resin of opium, extractive, and the like.

The following examination of capric acid and some of its salts, was made in the laboratory of Dr T. Anderson, to whom I am much indebted for his kindness in procuring for me the materials to work upon, and also for advice during the progress of this investigation. Capric acid has been found by Chevreul and Lerch in the butter of the cow and goat; by Redtenbacher, amongst the volatile oily acids he obtained by acting on oleic acid with nitric acid; by Gerhardt and Cahours, by the action of nitric acid on the oil of rue; and by Görgey in cocoa-nut oil;—from all these sources it has been obtained only in small quantities, and always along with other acids of the series to which capric acid belongs.

The attention which has of late years been paid to the elucidation of the manners and arts of the ancient inhabitants of America, has been productive of the most convincing proofs of the communication between the Eastern and Western Continents at remote but unknown epochs. The learned and highly-interesting researches of Humboldt on the antiquities of the New World, have irresistibly led him to this conclusion, which has farther been strengthened by the researches of later travellers. The comparison of the idioms of the Asiatic and American tongues, has hitherto not afforded very direct proof; because the philologist has not yet been put in possession of a sufficient number of materials to make the comparison with advantage. Our ignorance of the languages and customs of Central Asia is a great bar to such studies, and needs not any other illustration than the fact that a highly-polished nation, with a literature and arts hitherto almost unknown in Europe, should have existed for ages in Central Asia. Our countryman, Dr Gerard, stimulated by the humane desire of extending the blessings of vaccination to Thibet, has been for some time in that country, and has discovered in its language an Encyclopædia in forty-four volumes, of which the medical part alone fills five volumes; and he finds, that the art of Lithography, so new in Europe, has been practised from time immemorial in Kinnaour, a principal city in Thibet, where he found it employed to display the anatomy of the human body.

The oscillations of the barometer during gales of wind must have been noticed soon after the invention of the instrument by Torricelli 200 years ago. Every observer is familiar with the fact, that the barometric column is continually rising and falling during gales; and we frequently meet such observations as “Barometer very unsteady,” in Meteorological Registers.

In Sir William Reid's work on the Law of Storms, he says, “during the hardest part of the gale (the Bermuda hurricane of 1839) several persons observed remarkable oscillations of the mercury in the tubes of the barometers;” and in a letter which I had the honour to receive from the Astronomer-Royal, Professor Airy, in reply to one from myself on this subject, he says, “I think (but am not certain) that the depression of the barometer at every gust of a gale of wind is an ordinary phenomenon, without reference to the position of the barometer with regard to the direction of the wind. Many years ago I was in the observatory of Marseilles during the blowing of the Mistral (a wind well known there), and there I saw the drop of the barometer at every gust in great perfection. I do not remember the position of the barometer.”

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.