Mr Sang briefly explained an application of the method of continued fractions to the resolution of the exponential equation, and illustrated it by exhibiting the computation of the logarithm of the prime number 27073 directly.

The urinary secretion of fishes, the author believes, has hitherto received so little attention owing to certain difficulties attending its investigation. He brings forward the few and imperfect observations he has made, with the hope of inducing others more favourably situated to prosecute the inquiry.

The fishes he has examined in quest of their urinary secretion have been fifteen; of those with a urinary bladder he found a fluid only in three, the Perch, Ling, and Ray; and in those without this organ, only in two, in their ureters—those of the Pike and Turbot.

In a recent work, entitled “Wahre Parthenogenesis bei Schmetterlingen und Bienen”—Real Parthenogenesis in Butterflies and Bees, Von Siebold, after reviewing the present condition of the subject, distinguishes the so-called alternate generation from parthenogenesis, and limits Professor Owen's term to reproduction by unimpregnated females.

He has ascertained that this real parthenogenetic mode of reproduction occurs in certain moths—Solenobia lichenella and triquetrella, the larvæ of which are sac-bearers; and in Psyche helix, the larva of which constructs one of those remarkable spiral sacs which have been mistaken for the shells of molluscs.

After exhibiting Crania of these races recently received from South Africa, along with two British crania of normal size and form, and stating their respective measurements, facial angles, and principal diameters, the author reviewed the observations of Natural Historians and Anatomists on the skulls and physical characteristics of the races above mentioned. Camper's facial angle was compared with that of Blumenbach, showing the differences, and how far the adult Negro and the orangoutang receded from the higher cranial types; and also how, according to Mr Owen, the facial angle depends upon whether it is taken in the young or adult state.

Polished and rounded surfaces of rock are, under their more ordinary conditions, of very frequent occurrence in Argyllshire. By “their more ordinary conditions,” I mean principally two—viz., Where they occur on the existing coast-line, either at, or not far above the present level of the sea; secondly, Where they occur in valleys, or the lower flanks of the hills,—whether under the boulder clay, or on surfaces naturally exposed.

I am very reluctant to occupy the time of this meeting with a personal matter, but as I am necessitated to defend my priority in reference to certain researches which, in greater part, were first communicated to this Society, and first made public through its “Transactions,” it seems the proper tribunal, at least in this country, to adjudicate on a question liable to dispute.

The object of Dr Bennett's communication was to unite two separate kinds of research, which of late had been directed towards advancing our knowledge of the structure and functions of the spinal cord. From these it would, he thought, appear, that the views considered to be so firmly established by the genius and labours of Charles Bell, required great modification. Dr Bennett then gave a sketch of these views, and of the present opinions of physiologists regarding the functions of the spinal cord.

Little is known of the course of the Irrawaddy River above Ava, and as it is joined by no large tributary near its mouth, its sectional area differs very little for hundreds of miles. At Prome, a distance of 190 miles in a direct line from the sea, the river is confined between two ranges of hills. The eastern range passes through the Tharawaddy district, separates the Irrawaddy from the Sittang Valley, and is lost in low undulating hills at Rangoon.

In this paper the author reported the progress made by the committee appointed to select and purchase a series of chartagraphic works for the library of the Royal Society, and the means adopted for their arrangement and classification. The collection already comprises 534 separate sheets of the best existing maps, chiefly of the several countries of Europe, but embracing the survey of India, in so far as published. The maps are placed in cases resembling volumes, so indexed as to admit of being indefinitely extended, and easily consulted. Specimens of the different works were exhibited, and the author presented a rapid sketch of the progress of surveying and mapping, from the sixteenth century to the present time.

A friend, who returned lately from Rome, has sent me some copies of a pamphlet by Father Secchi of the Collegio Romano, one of which I lay on the table of the Society.

It describes a barometer stated to be on a new construction. The barometric tube is suspended from one arm of a balance, and counterpoised. It is filled with mercury in the usual way; but the cistern into which it opens is fixed apart, and does not move with the beam of the balance. It is evident, therefore, that the varying pressure of the air on the exterior of the tube will require a changing counterpoise, and that the magnitude of the change may be increased by enlarging the section of the tube, so that the alteration of pressure may be indicated with any required delicacy.

The object of this paper was to show that where sulphuric acid combines with water, distinct reference is made to certain definite compounds or hydrates of sulphuric acid.

In his astronomical visit to Teneriffe last summer, the author was instructed to inquire into the lateral oscillation of stars, as seen by Baron Von Humboldt in his ascent of the mountain. During a month's residence on the place of the alleged observation no approach to anything of the sort was ever noticed, although a powerful equatorial, with a twelve-foot telescope and high magnifying powers, was employed to detect any irregularity in the motions of the stars. The author concluded, therefore, that the anomalous movements described by Humboldt could not have been produced by any general or cosmical action of the atmosphere, or of light or heat, which astronomers were bound to consider.

The author maintained that the genus Pedicellina, notwithstanding the circular arrangement of its tentacula, does not properly belong to the infundibulate Polyzoa at all, but is in reality hippocrepian, of which type, however, it presents a remarkable modification. The intestine at first sight appears to terminate within the margin of a orbicular lophophore, and, consequently, within the circle of tentacula, and thus to present a striking exception to the admitted plan of the Polyzoa. It was shown, however, that the anomaly which thus seems to exist was only apparent, for the lophophore, when carefully examined, is found to be constructed on the hippocrepian type, with the tentacula confined to the outer or convex margin, and the arms of the crescent united at their extremities so as to enclose a space, around which the tentacula will then be arranged in an uninterrupted circle, and within which the intestine opens, its termination being thus quite normal, and properly external to the lophophore.

Mr Murray commences with a resumé of what is known regarding the growth of eyes in insects, from the first stage in the larva, when many are without eyes, till their exclusion from the chrysalis, when they usually appear well provided with compound eyes. He reviews the nervous system in different species, and gives some details as to those species which live in dark places, and which have small eyes and a less-developed optic nerve, contrary to what one would at first suppose. The next portion of his paper is devoted to explaining his views of the structure of the eye in insects, and its relation to the eye in vertebrate animals.

Since the publication in 1826, of Joh. Müller's Vergleichende Physiologie des Gesichtssinnes, Physiologists have admitted three fundamental forms of the organ of vision. 1st, The eye-spot, organized for the mere perception of light. 2d, The compound eye, in which the picture on the nervous surface is a mosaic. 3d, The simple eye, in which the retinal picture is continuous. The difference between the simple and compound eye, as explained by Mülier, and since generally admitted, consists in this, that the formation of the picture in the simple eye is the result of the convergence of all the pencils diverging from the visible points of the object on corresponding points of the retina, by means of the crystalline lenticular structure of the organ; while, in the compound eye, the picture is formed by the stopping off, by means of the constituent crystalline columns of the eye, all rays except those which pass in or near the axes of the columns.

It will be remembered that, when the cutting was made, early in 1846, athwart the shoulder of Arthur's Seat above Samson's Ribs, for the formation of the Queen's Drive, the rock was found hollowed in a trough-form for a space of about eighty yards, and smoothed and striated in the manner of a glacier-bed of the Alps. The striæ were in the direction of the hollow, pointing to east 20° south. The whole was covered over with a brown tenacious clay, containing fragments of rocks of the district, along with some supposed to have come from a distance.

The top is an instrument similar to that exhibited by the author at the meeting of the British Association in 1856. It differs from it in being of smaller size and entirely of brass, except the ends of the axle; and in having six horizontal adjusting screws and three vertical ones, instead of four of each kind.