§ 1. The general problem in elasticity, as usually presented for solution, supposes the elastic substance to pass initially from a state without strain. But important cases exist where it must be conceived to start from a state already under considerable stress. When this is the case, the constitution of the solid undergoes great change, as is shown by the fact that strained glass loses its isotropic property, and becomes doubly refractive. This subject was long ago attacked by Cauchy, who, by means of the theory of molecular actions, deduced the existence, in the expressions for the stresses due to the secondary strains, of terms proportional to the initial or primary stresses. The problem has been since discussed by MM. De St Venant and Boussinesq, who have applied to it Green's expression for the energy stored up during the strain. But the question, in their hands, still retains traces of Cauchy's hypothetical element, inasmuch as their expression for the potential energy was deduced by means of the molecular theory. M. De St Venant even considers it a strong argument for the truth of the latter, that it is indispensable in the discussion of this problem. These authors have also failed to see in what way the remaining part of the potential depends on the original strain.

Musket-Bullets are occasionally found inclosed in ivory, and every anatomical museum contains specimens of this kind. Why bullets should be so frequently met with in this situation, it is not easy to say; the head of the animal appears to be generally aimed at, and foreign bodies when they enter the tusks, instead of being removed in the usual manner, are retained by the process, an investigation of which is to form the subject of the present paper.

Long after the arts of ancient Greece and Rome had been lost, and before any effectual attempt was made to revive them, a style of building, known among us by the name of Gothic Architecture, began to appear in Europe.

At first, a few only of its peculiar forms were employed, which, in some old buildings, are to be met with, intermixed with the remains of a still more ancient style. Afterwards, rising by degrees into favour, it supplanted, in all the departments of architecture, every other species of design, and maintained an unrivalled dominion during three hundred years.

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 immediate purpose of the present research was the investigation of the temperature at different pressures of boiling mixtures of steam and salts, analogous to the well-known freezing mixtures of ice and salt.

When steam is blown through common salt in coarse powder, it condenses to water, which dissolves some of the salt, and the resulting brine is kept boiling by the arrival of more steam. The temperature of this boiling mixture is quite constant so long as there is an abundant supply both of steam and of salt, and as the atmospheric pressure does not change, it is about 8·5° C. above the temperature of boiling water when the barometric pressure is the normal of 760 mm. When the barometric pressure is 560 mm. this excess has fallen to 8·0° C. Most other salts behave in a similar way.

At the close of the preceding session, the Council of the Society did me the honour of entrusting me with the chemical examination of several articles sent not long ago to the Society by Mr Swinton, Secretary to Government at Calcutta. The articles in question are, 1. Specimens of the black varnish used in different parts of Hindostan and the Burmese territories, with specimens of the juices of which these varnishes are said to be compounded; 2. Specimens of naphtha from Persia, and of petroleum from Rangoon; 3. Specimens of wood-oil, a variety of fluid turpentine; 4. Specimens of crude caoutchouc, and of solutions of it in wood-oil.

The only one of these articles which has hitherto yielded results of such interest as to induce me to lay them before the Society, is the petroleum of Rangoon, which appears to contain a compound inflammable principle hitherto unknown.

At the base of the wings of Anopheles maculipennis, Meig, is a small quadrilateral area (fig. 2, Plate) which has escaped the notice of the systematist, since the nervures in which he is interested lie almost entirely beyond the area in question, and which has escaped the notice of the morphologist, because it presents to him but a confused outline of meaningless ridges and intervening depressions of no structural importance. If, however, the well-preserved wing of a mosquito, whilst still attached to the thorax, be examined, a very curious apparatus can be made out, lying across the centre of the said quadrilateral area which is bounded posteriorly by the alula. This apparatus lies at about equal distances from the anterior and the posterior edge of the wing, and divides the base of the wings roughly into two halves.

Several of my friends have suggested to me the propriety of publishing something of the kind now offered to the Society, observing, that the great brevity with which the Antecedental Calculus is written, and the very concise form in which it is delivered to the public, may lead some to form erroneous opinions respecting the principles on which it is founded. In compliance partly with their request, I have drawn up this short paper, which I hope will remove even the possibility of misconception on that head, and convince every intelligent reader, that the antecedental calculus has the same geometrical principles for its ground-work, that the formulæ in the Universal Comparison themselves have, from which I originally derived it more than twenty years ago.

The singular appearances which were presented to my view by the Trap Rocks of Iceland, and the interest which they excited, made me resolve, as soon as I had given an account of that country to the public, to visit the Islands of Faroe. This expedition was undertaken, for the purpose of ascertaining, whether, in a Trap Country, where no traces of external volcanoes existed, any thing similar to the peculiar features of the rocks of Iceland was to be found. In the latter country were discovered a series of rocks, lying above the beds of Trap, which bore the most striking marks of igneous origin; in some instances having a perfect resemblance to ordinary Trap, and in others to the common Lavas of the country. The beds of Trap, and those above them, being separated by mechanical depositions of Tuffa (Trap-Tuff), led me to the conclusion, that the whole of the beds had been formed at the bottom of the sea, by successive eruptions of a submarine volcano.

When the Observatory on the summit of Ben Nevis was opened in 1883, arrangements were made with Mr Colin Livingston, of the Public School, Fort-William, whereby observations were made five times a day at the Schoolhouse for comparison with those on Ben Nevis. These observations, from December 1883 to December 1887, were published in vol. xxxiv. of the Transactions R.S.E., along with the Ben Nevis records; and three years more, up to December 1890, are given in this volume (see Introduction, p. 7). The Fort-William Observatory was opened in August 1890, but Mr Livingston kindly continued his observations till the end of 1891, so as to allow of a comparison between these two stations, which was the more desirable as Mr Livingston's observations had been used for the original determinations of the differences of pressure and temperature between Ben Nevis and sea-level, and any discrepancy between the observations made at the Schoolhouse and at the Observatory would necessitate a readjustment of these constants.

After having for many years felt with Professor Tait the want of a word “to express the Availability for work of the heat in a given magazine, a term for that possession the waste of which is called Dissipation” I now suggest the word Motivity to supply this want.

In my paper on the “Restoration of Energy from an Unequally Heated Space,” published in the Philosophical Magazine for January 1853, I gave the following expression for the amount of “mechanical energy” derivable from a body B, given with its different parts at different temperatures, by the equalisation of its temperature throughout to one common temperature T, by means of perfect thermodynamic engines,—

where t denotes the temperature of any point x, y, z of the body; c the thermal capacity of the body's substance at that point and that temperature; J, Joule's equivalent; and μ, Carnot's function of the temperature t.

In a paper which I communicated to this Society in 1815, and which was published in the Seventh volume of their Transactions, I described a new species of coloured fringes, produced between two plates of parallel glass. From a consideration of the theory of this class of phenomena, it was obvious that analogous, though much more complicated, systems of rings should be produced between plates with curved surfaces, but it was not till 1822 that I succeeded in detecting them; and so completely are these rings concealed by the superposition of similarly situated images, that, in consequence, of having forgotten my method of observation, I have experienced the greatest difficulty in rediscovering them.

My earliest experiments were performed with a double achromatic object-glass, made by Berge, having a diameter of inches, and 30 inches in focal length. The inner surfaces of the crown and flint glass lenses were ground to different radii, as shewn in the section of it at AB, CD, Fig. 5, Plate IX.; and the outer surface of the flint-glass lens was concave, so that there was left between the lenses a meniscus of air A 2, B 3 A.

The Reverend Dr William Richardson, late F. T. C. D., having sent to Dr Hope a collection of specimens from the northern coast of Antrim, with a catalogue, and observations, the specimens were exhibited, and the observations were read in the Royal Society, March 1803.

In the series of chapters of which the present is the first, I purpose to submit the results of an analytical examination of all the minerals of Scotland whose composition appeared doubtful; of such as had not previously been examined; or of such as appeared in any way to be of special geologic interest.

The Royal Society of Edinburgh having taken great interest in meteorological observations, it has occurred to me, that the accompanying Meteorological Journals would be acceptable to the Society. I therefore transmit them, in the hope that they may be of some service, in promoting the laudable object of the Society, the science of meteorology.

These journals include a period of twenty-four years, and were kept by the late Mr Pitt of Carlisle, who was long a careful and accurate observer of many atmospherical phenomena. Mr Pitt did not avail himself of the new instruments that are used in meteorology, but understood well the nature and application of those he employed. The thermometer, barometer, and rain-gauge, were the instruments he made use of, and they are probably more important than any other. For many years Mr Pitt had no particular occupation, and meteorology was his hobby. He devoted a great portion of his time to astronomical and meteorological observations, took great delight in keeping his journals, and was scrupulously accurate. From my personal knowledge of his diligence, of his habits of making correct observations, and the systematic fidelity with which he recorded them, I think I can with great safety vouch for the accuracy of the statements contained in his journals.

1. A compass needle, although freely suspended, will not always point with accuracy in the direction of the magnetic meridian, for its magnetic axis may not be strictly parallel to its axis of figure; and hence, when a rigidly exact value of the magnetic declination is required, it is necessary to take the mean of at least two observations of the needle, first, in its usual position, and next, inverted. Some time ago it occurred to me that the declination obtained in the manner now described, will only be approximately correct, unless the inversion is accomplished with perfect accuracy; and I wished to ascertain the greatest residual error which, in given circumstances, is likely to affect the mean of two observations of a magnet, first in an erect, and then in an inverted position. I failed, however, to find any allusion to such errors in those works on magnetism to which I had access; and I was therefore obliged to investigate the subject for myself.