The author of this paper confined himself entirely to the use of contemporary data; and amongst these, the only kinds found available for the very earliest ages, were buildings of one kind or another.

Examining these again, after their first approximate arrangement in chronological relative order by well-known archæologists, it was discovered that there resided a peculiar astronomical opposition between the chief structures in the valley of the Euphrates and those in the valley of the Nile.

In this paper the authors communicate the first results of an attempt to discover the relation which must exist between the chemical constitution and the physiological action of a substance. As the chemical constitution of the majority of physiologically active substances is unknown, they investigate the subject by examining the physiological action of a substance before and after the performance upon it of a definite chemical operation, introducing a known change into its constitution. The question is thus reduced to a problem in what may be called a chemico-physical calculus of finite variations.

That the Roman ships were destroyed by burning glasses invented by Archimedes, is mentioned as a fact by most of the ancient writers, especially those who treat on mechanics, and their statements have been repeated by succeeding authors, without any doubts having been suggested until comparatively recent times. The earliest authorities on the subject are Diodorus Siculus, Lucian, Galen, Dion Cassius, and Pappus. It is much to be regretted that a work by the last named author on the Siege of Syracuse is now lost; but Zonares and Tzetzes, writers of the 12th century, in whose time it was extant, give quotations from it. That of the latter, translated pretty literally, runs thus:—“When Marcellus had placed the ships a bow shot off, the old man (Archimedes) constructed a sort of hexagonal mirror. He placed at proper distances from the mirror other smaller mirrors of the same kind, which were moved by means of their hinges and certain plates of metal. He placed it amid the rays of the sun at noon, both in summer and winter. The rays being reflected by this, a frightful fiery kindling was excited on the ships, and it reduced them to ashes, from the distance of a bow shot. Thus the old man baffled Marcellus, by means of his inventions.”

The author gives a detailed statement of the theories of Professor Smyth, as given in the Transactions of this Society, Vol. XXIII. Part III. He then, after heartily commending the zeal and diligence of the Professor, brings forward objections to some of his views. 1. As to the metron or unit of linear measure. Mr Wackerbarth objects that this measure was utterly unknown to the ancient Egyptians—appearing in no Egyptian document or monument whatever, nor in any ancient writer who describes the condition of the Egyptians.

In experiments on the spectrum, it is usual to employ a slit through which the light is admitted, a prism to analyse the light, and one or more lenses to bring the rays of each distinct kind to a distinct focus on the screen. The most perfect arrangement is that adopted by M. Kirchhoff, in which two achromatic lenses are used, one before and the other after the passage of the light through the prism, so that every pencil consists of parallel rays while passing through the prism.

But when the observer has not achromatic lenses at his command, or when, as in the case of the highly refrangible rays, or the rays of heat, he is restricted in the use of materials, it may still be useful to be able to place the lenses and prism in such a way as to bring the rays of all colours to their foci at approximately the same distance from the prism.

After considering the many proposed derivations of the word Pyramid, it was pointed out that the origin of the name suggested by the distinguished Egyptologist, Mr Birch, from two Coptic words, “pouro” “the king,” and “emahau” or “maha,” “tomb,”—the two in combination signifying “the king's tomb,”—was probably correct. “Men,” in Coptic, signifies “monument,” “memorial;” and “pouro-men” or “king's monument” may possibly also be the original form of the word. Various authors, as Pope, Pownall, Daniel Wilson, Burton, had long applied the term pyramid to the larger forms of conical and round sepulchral mounds, cairns, or barrows—such as are found in Ireland, Brittany, Orkney, &c., and in numerous districts of the New World as well as the Old; and which are all characterised by containing in their interior, chambers or cells, constructed usually of large stones, and with megalithic galleries leading into them.

During the last winter session, I communicated to the Society a paper on the “Musculus Sternalis,” in which I argued that the longitudinally arranged muscle, occasionally found superficial to the sternal fibres of origin of the pectoralis major, was not, as anatomists have usually described it, homologous with the anterior or thoracic fibres of the mammalian rectus, but belonged to another group of muscles.

Since that time I have met with two subjects in the dissecting-room, in each of which a longitudinal muscle occurred, lying in contact with the outer surface of the anterior extremities of the upper true ribs, and beneath the fibres of the pectoral muscle, which is, from the position, direction, and connection of its fibres, I believe to be regarded as homologous with the thoracic end of the mammalian rectus.

Notwithstanding the intense interest of the topography of Palestine, and above all else of the Holy City itself, yet it is only within the life-time of the present generation that any attempt has been made, systematically and scientifically, to explore its sacred and historical sites.

Centuries after the foundations of ancient Rome had been traced, years after the temples of Attica had been searched and rifled by Lord Elgin of their fairest ornaments, we knew no more of the topography of Jerusalem than could be gathered from the monkish chroniclers, or from Reland and Maundrell, and dreamt not that a buried city lay beneath the streets of modern Zion, as little revealed by the contour of the buildings on the surface as were the palaces beneath the sand mounds of Assyria.

In the month of September last (1867), when visiting the Great Exhibition in Paris, I was particularly struck with the fine appearance of the obelisk of Luxor in the Place de la Concorde, and I thought that as the French had taken the trouble and gone to the expense of moving this highly interesting monolith, it was a reflection on our nation and on the engineering skill of Britain that the prostrate obelisk at Alexandria (one of Cleopatra's needles, as it is commonly termed), was not occupying a place of honour in England or Scotland.

This obelisk was presented to George IV. many years ago by Mahomed Ali Pacha, who also generously offered to move it on rollers to the sea, from which it is 200 or 300 yards distant, and embarking it on rafts and lighters, convey it to a vessel for transport to England.

Before proceeding to read Dr Davy's paper, Professor Allman made the following remarks:—

The duty has devolved on me of being the medium through which the paper just announced should be communicated to the Society—a duty not unmixed with melancholy; for when the distinguished author of that paper had placed it in the hands of the Council, there was nothing to prevent our looking forward to a continuance of those labours with whose results the pages of your Transactions have been so often enriched. But the pen which had worked unwearyingly for nearly sixty years is at last still; and the paper now before you closes in for ever the earthly labours of its author.

The tendency of the air contained in a soap-bubble is to expand in bulk, while that of the film is to contract in surface. Hence it becomes a curious question to decide whether both of these tendencies are not satisfied when two or more bubbles unite into one.

The excess of pressure inside a bubble, of radius r, over the pressure of the external air, is

where T is the contractile force of the film.

In this paper the author alluded to the spore as the ultimate germinating cell of cryptogamic plants. The true spore is the product of impregnation, but there are also bodies called spores which, so far as known, do not depend on the process of fertilisation. Occasionally the term spore includes both the spore and the spore-case or sporangium. The structure of the spore was described, and its resemblance to the pollen grain, both as regards its anatomy and germination, was shown. Ciliated moving spores were considered, and reference was specially made to the movements of the non-ciliated spores of Helminthora, which, when discharged, continue to change their form for several hours like the Amœba, becoming in turn oblong, pyriform, rhomboidal, &c.,—lengthening and contracting, swelling at one point and shrinking at another.

The greatest height to which the tide has ever been known to rise at any given place is of the utmost consequence to the marine engineer. It forms an important element in the design and in the estimate for any works in the sea; and any error on this point might lead to the most lamentable results both to life and property, especially in the construction of embankments for the reclamation of land.

I have therefore thought that a notice of the tide of the 8th of last month might not be uninteresting to the Society, as it is one of the highest, if not indeed the highest, that has ever been recorded with accuracy on the east coast of Britain, and the most remarkable example with which I am acquainted of the effect of wind in raising the level of high water on that coast.

The three charts which were exhibited, showing, by isobarometric lines, the mean atmospheric pressure over the globe, during January, July, and the year, were constructed from observations made at 358 places thus distributed over the earth,—167 in Europe; 51 in Asia; 22 in Africa and adjoining islands; 35 in South America, West Indian Islands, and Atlantic; 63 in North America; and 20 in Australasia and Antarctic Ocean. Of the European stations, 12 are in Scotland, 14 in England, 27 in Austria, 12 in Italy, 10 in France, 10 in the Netherlands, 9 in Norway, and 57 in the Russian empire, &c. The list might have been largely increased; thus a larger number might have been given from the 80 Scottish stations; but the 12 given were judged sufficient to represent the mean atmospheric pressure of this country.

This paper was accompanied by two diagrams, one of them representing more particularly the features attending on space, and the probable errors of several modern determinations therein; and the other representing the chronological order of the events, or progress made by man from the earliest times, down to the present, in ascertaining that most important of all questions in astronomy and general physics, viz., the true mean distance of the earth from the sun.

If a number of equal masses of the same material be given, at different temperatures, and enclosed in an envelope impervious to heat, they will finally assume a common temperature; which is the arithmetic mean of the initial temperatures, if the material be one whose specific heat does not vary with temperature.

But they may be brought to a common temperature by means of reversible thermodynamic engines employed to obtain the utmost amount of work from the initial unequal distribution. This question was first investigated by Thomson (Phil. Mag. 1853, “On the Restoration of Energy from an unequally heated Space”), and the application of his method to the present problem shows that the final common temperature of the masses, when as much work as possible has been obtained from them, is the geometric mean of the initial temperatures; but this investigation introduces the condition that the temperatures must be measured from the absolute zero.

The paper contains some curious applications of the principle of dissipation to the conduction of heat, the connection of heat and electricity, thermo-electric currents, the electric convection of heat, &c. But in this abstract we confine ourselves to one very simple case of the conduction of heat, as the hypothesis on which it is investigated is fundamentally assumed in all the other applications.

This paper is a continuation of that read on 4th February 1867, and already published in the Transactions. Instead, however, of the liquid films being formed within systems of wires, hollow glass vessels are here employed. By using a single or double cone of glass open at both ends, and inserting within it small bubbles blown from a quill or tube with a small aperture, regular binary, ternary, or quaternary systems of films are produced. Thus, by first obtaining a plane film within the conical vessel, and then inserting upon it four small bubbles, a system is produced consisting of four hollow films, of curious curvature, united to one another respectively by vertical plane surfaces, and connected in their centres by a common plane film, which, by adopting certain precautions, may, with a little care, be made to assume either a horizontal or a vertical position.