[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.

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.

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.

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 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.”

Having expressed a decided opinion that there are, in all living bodies, chemical as well as mechanical phenomena, which, in the present state of our knowledge, ought to be designated as Vital, and referred to the operation of laws, distinct from those that regulate the chemical changes of inanimate matter, and observing that this opinion is controverted, and that the view of the chemical phenomena of life which I have maintained, is rejected as unphilosophical and delusive by two authors of high scientific reputation—Baron Humboldt and Dr Daubeny,—and that the judgment of other authors of acknowledged character on this subject is not clearly expressed, and seems to me to involve it in unnecessary obscurity, I am led to hope that some farther explanations may be of some use in establishing the first principles of a Science which, as it appears to me, has suffered, in several instances, not so much from want of facts, as from hypothetical and erroneous inferences, drawn from facts that are already known.

In a paper on Comenic Acid, read before this Society in April of last year, and since honoured with a place in its Transactions, I mentioned my being engaged in an investigation on Meconic Acid; the details of the experiments referred to form the matter of the present communication.

My object in undertaking this subject was to ascertain if products corresponding to those described as derived from comenic acid were formed under similar circumstances in the case of meconic acid. I also thought it probable, that as the former is itself a derivative of the latter, the changes undergone by meconic acid in some reactions, would be found to result in substances apparently the immediate derivatives of comenic acid. This remark refers to the action of heat on meconate of ammonia; and it will be seen that the expectation was realised. A similar result was found in other instances, where it had not been anticipated.

Having had the good fortune last autumn to get an antique marble bust of extreme beauty, the question naturally arose, of whom it might be the portrait, if, indeed, it was a portrait at all, and not an ideal head. I had proceeded some way in this inquiry, when it was suggested to me one day that it might interest the Society to know something of it, and that, though a little foreign no doubt to its usual topics, the change would be agreeable, and that ancient art was not without its charms. So urged I yielded,—perhaps too easily; but of this you will judge when I have done.

(1.) In February 1850, I laid before the Royal Society of Edinburgh a paper, in which the laws of the pressure and expansion of gases and vapours were deduced from the supposition, that that part of the elasticity of bodies which depends upon heat, arises from the centrifugal force of the revolutions of the particles of elastic atmospheres surrounding nuclei, or atomic centres. A summary of the results of this supposition, which I called the Hypothesis of Molecular Vortices, was printed in the Transactions of this Society, volume xx., as an introduction to a series of papers on the Mechanical Action of Heat; and the original paper has since appeared in detail in the Philosophical Magazine.

Correction of M. Regnault's Experiments for the Effect of Agitation.

The discovery by Mr Joule of the fact, that mechanical power expended in the agitation of liquids is converted into heat as the visible agitation subsides, renders a certain correction necessary in calculating the results of experiments on specific heat in which such agitation has occurred.

Of this kind are the experiments of M. Regnault on the apparent specific heat of liquid water at different temperatures. Water at a high temperature, T3, was emitted from a boiler into a calorimeter containing water at a low temperature, Tl, and the resulting intermediate temperature of the whole mass, T2, was used as the means of calculating the ratio of the mean specific heat of water between T3 and T2, to its mean specific heat between T2 and T1. Now, the upper part of the boiler contained steam at a high pressure, so that the hot water was expelled with great force.

The red prominences seen during total solar eclipses, are conspicuous rose-coloured objects which appear round the dark edge of the moon, as soon as the last rays of the sun have disappeared. In preparing my account of the total eclipse of the 28th July 1851, it was at first my intention to have stated some hypothetical views which I had formed regarding those remarkable objects, and other appearances I had observed during the total phase of the eclipse. I found, however, that the mere description of phenomena extended to so great a length, as to render such a course inexpedient; and I have since delayed resuming the subject, in order that by comparing a number of other observations with my own, I might be enabled, either to confirm or to modify my views.

In the first part of this paper, I have endeavoured to prove, that the red prominences seen during total solar eclipses, exist in the sun; and I now propose to state some views which have occurred to me as to the nature of those remarkable objects, and their possible connexion with other solar phenomena. It is not, however, without great misgivings that I venture on this subject; for we know so little of the sun, that any hypothesis regarding the constitution of his atmosphere, can amount only to a conjecture, possessing more or less probability according to the variety of the appearances it serves to explain, and the exactness with which theory and observation correspond in each case: and I am well aware that views which may seem probable to myself may not appear equally so to others, whose greater experience in observing the sun constitutes them better judges of such questions.

81. A body which is either emitting heat, or altering its dimensions against resisting forces, is doing work upon matter external to it. The mechanical effect of this work, in one case, is the excitation of thermal motions, and in the other, the overcoming of resistances. The body must itself be altering in its circumstances, so as to contain a less store of work within it, by an amount precisely equal to the aggregate value of the mechanical effects produced: and conversely, the aggregate value of the mechanical effects produced, must depend solely on the initial and final states of the body, and is therefore the same, whatever be the intermediate states through which the body passes, provided the initial and final states be the same.

In several communications made to this Society and to the British Association, I have announced the results of a series of observations on the distribution of Fluorine throughout the mineral, vegetable, and animal kingdoms. To myself, the least satisfactory part of these investigations has been the inquiry into the presence of fluorine in plants, for I have been more frequently foiled than successful in my attempts to detect it in them. Others have not, apparently, been more successful. Daubeny was as unable as Sprengel at an earlier period had been, to obtain evidence that the element under notice is present in vegetable structures; and Will of Giessen, the discoverer of fluorine in plants, speaks only of “traces” of it having been detected in barley. Later observers have not spoken more confidently concerning its abundance in vegetables; and in the many analyses of the ashes of plants which have recently been published, it seldom, if ever, finds a place.

When preparing to make a night journey over one of the plains of South Africa, in the month of June 1843, a friend called my attention to the peculiar appearance of the sky in the west, as offering a very decided proof, “agreeably with theory,” that there was no “Solar atmosphere” to be seen at that season of the year.

On looking in the direction mentioned, the last portion of the twilight was just visible, and forming a peculiarly level line above the place where the sun had set, for an extent in azimuth, of perhaps 40°, and at a height of about 5°. All the gorgeous colours which had attended the setting of the sun had long since vanished, and there only remained sufficient light within the flattened arc described, to make the space included between it and the horizon appear light blue, while all the rest of the sky had attained a deeper colour, nay was almost black, and thickly spangled with small as well as large stars.

Eclipses are still, as they have ever been, very important phenomena for the astronomical observer; partly on account of the crucial test which they afford for the examination of the truth of the theory and calculation of the motions, real and apparent, of the Sun and Moon, partly also for the special opportunities which they furnish of inquiring into some of the arcana of the physical characteristics of those bodies.

For the former purpose, a partial eclipse will serve almost as well as a total one; while the continued improvement of the observation of meridian passages is now raising these daily measures fully to the importance of the other occasional phenomena, as a test of the theory. But for inquiry into the physics of the Sun, a perfectly total eclipse of that body is necessary; revelations may then happily be procured, which no observation of any other phenomena at any other time, can hope to afford any suspicion of.