If light, emanating from a fixed source, be reflected to the eye, also fixed, from the surface of a polished cylinder, which cylinder changes its position in some definite manner, the point of reflection moves in some curve or locus whose nature may be made the subject of investigation.

In the present paper I propose to examine that case in which an indefinitely thin cylinder is restricted to pass through a fixed point. The locus of the point of reflection is then a curved surface, For the present I shall still farther restrict the polished line to the plane passing through the vertex, the source of light, and the eye ; the locus being then a plane curve.

Let then a fine polished straight line, extended indefinitely both ways, turn on the vertex O, while light emanating from the source A is reflected to the eye at B; it is required to investigate the locus of the point C at which the reflection takes place.

The reflection is only possible while the polished line passes outside of the angle AOB. When the wire lies along AO, the point of reflection is at A ; when along OB, at B; and when it is equally inclined, outwards, to OA and OB, the reflection occurs at O, wherefore the curve must pass through the three points O, A, and B.

Although the osteology of Antarctic seals has been very completely discussed, notably by the late Dr J. E. Gray, Sir William Turner, and Professor Robert Thomson, yet the literature regarding the subject is somewhat scattered. I have therefore considered that it might be important from the point of view, as it were, of an index to publish a complete series of photographs of a set of the skulls of seals taken by the naturalists of the Scotia during the Antarctic voyage of 1902–1904.

The mines of Joachimsthal in Bohemia, have long been celebrated for their riches. They were successfully worked at an early period, and though their produce has been exceedingly fluctuating, yet the mining district, in which they occur, continues one of the most important of that country. They seem to have been particularly lucrative and important while they belonged to the house of the Counts Schlick, and when, in the beginning of the sixteenth century, a larger kind of silver coin was introduced into Germany, it took the name of Joachimsthaler, from the place of its coinage, a name which was afterwards changed into thaler, talaro, and dollar.

These mines are not less remarkable for the variety of the species, and for the beauty of the specimens which they have produced. The ancient collections of minerals at Vienna, the Imperial cabinet, that of Von der Nüll, that of Von Morgenbesser, and others, contain magnificent suites of sulphuret of silver, of red silver, &c. chiefly crystallised. The finest specimens, however, of the red silver, and perhaps the finest that ever were known in the species, were dug up so late as 1817 and 1822. The National Museum at Prague possesses one of them, consisting of a group of crystals several inches long, without having any rock attached to it, and weighing about twelve marks, or upwards of six pounds Avoirdupois, the value of the silver of which is more than L. 16 Sterling.

The following communication is intended to be the first of a series, in which I propose to consider the results of observations made at Makerstoun, near Kelso, Roxburghshire, in the Observatory of the President of this Society. These observations, and the tabular results, will be found ultimately in the volumes of Makerstoun Observations, constituting volumes of the Society's Transactions.

Trace element abundances in garnet from a polyphase migmatite were measured by secondary ion mass spectrometry (SIMS) in order to identify some of the effective variables on the trace element distribution between garnet and melanosome or leucosome. In general, garnet is zoned with respect to REE, in which garnet cores are enriched by a factor of 2–3 relative to the rims. For an inclusion-rich garnet from the melanosome, equilibrium distribution following a simple Rayleigh fractionation is responsible for the decreasing concentrations in REE from core to rim. Inclusion-poor garnet from the same melanosome located in the vicinity of the leucosomes shows distinct enrichment and depletion patterns for REE from core to rim. These features suggest disequilibrium between garnet and the host rock which, in this case, could have been an in-situ derived melt. This would probably indicate a period of open-system behaviour at a time when the garnet, originally nucleated in the metamorphic environment reacted with the melt. In addition, non-gradual variation in trace element abundances between core and rim may suggest variable garnet growth rates. Inclusion-free garnet from the leucosome, interpreted to have crystallised in the presence of a melt, has a small core with high REE abundances and a broad rim with lower REE abundances. Here, crystal-liquid diffusion-controlled partitioning is a likely process to explain the trace element variation.

Mauna Kea in Hawaii is the world’s tallest mountain — about 1000 m taller than Mount Everest (Science, volume 313, 22 September 2006, p. 1732). Near the summit, at an altitude of 4092 m, is the James Clerk Maxwell Telescope (JCMT) — the largest astronomical telescope designed to operate in the sub-millimetre wavelength region of the spectrum. In 1987 the JCMT was dedicated by HRH Prince Philip, Duke of Edinburgh, and named for the physicist James Clerk Maxwell (1831-1879). Sir John Dutton Clerk of Penicuik Bt, CBE, VRD, DL FRSE (1917-2002) represented the family.

The following report deals with the systematics and distribution of molluscs collected in and around certain lakes in Jasper National Park, Alberta, Canada. For the sake of completeness some records published by Baker (2) are also included. The investigations of which this forms a part were made under the direction of Professor Charles H. O'Donoghue at the request of the Biological Board of Canada, and I desire to thank him for his encouragement and help throughout.

Alderia modesta (class Gastropoda, order Sacoglossa) has a central nervous system of a type common in the Stiligeridae and Limapontiidae. The visceral loop is short and bears two ganglia, the abdominal and supra-intestinal.

Medio-dorsal bodies, probably neurosecretory in function, are present on the cerebral ganglia. They were also found in eight other species of Sacoglossa and latero-dorsal bodies were noted in Oxynoe viridis (Pease) and Lobiger viridis (Pease).

Dissections of sixteen species of Sacoglossa showed that the order may be arranged on the length of the visceral loop and the number of ganglia on it. The evolution of medio-dorsal bodies is discussed.

In following out the principle formerly laid down—that the study of the organization and functions of the part to which the nerve is distributed, will explain the peculiarities of its origin and connections—I have in this paper entered on a subject of great extent and difficulty.

As the Facial Nerve is one of a distinct class, it will be necessary to shew in what that class is peculiar—that it essentially belongs to the act of breathing—that the act of respiration being, in its ordinary condition, independent of the will, there are nerves appropriated to that function. At the same time, it must be shewn, as the apparatus of breathing is made subservient to other purposes in the economy, by what relations it is brought under the influence of the will.

Recent water-undersaturated phase equilibrium data on the subsystems of the granite-H2O system have provided important new constraints on the topology of the cotectic surfaces and hence on the compositional evolution of felsic magmas. The effect of water on phase relations can be deduced from a comparison of anhydrous and H2O-saturated data or from data obtained in the presence of a CO2-bearing fluid. However, although new experimental evidence indicates that the silica enrichment of evolving H2O-undersaturated, H2O-unbuffered melts during the co-precipitation of quartz and feldspar is as previously thought for orthoclase-rich compositions, it suggests that such a trend is considerably less for Ab-rich compositions. For water-poor trachytic melts, the newly recognised strong destabilisation of the sanidine melt component relative to the anorthite melt component with increasing water content indicates that the co-precipitation of two feldspars will result in saturation of the melt with ternary alkali feldspar at an earlier stage (i.e. higher melt anorthite content) than previously thought. This, in turn, implies that the melt differentiation path will have a greater component of anorthite depletion during the equilibrium co-precipitation of ternary feldspars and that the melt will remain in the peritectic region of the two feldspar plus liquid surface over a greater interval of crystallisation, thereby enhancing the possibility that the resoption of plagioclase during the early stages of equilibrium with alkali feldspar may go to completion. Comparison of CO2-free and CO2-bearing haplogranitic phase equilibrium data suggests that CO2 may be playing an independent part in the modification of phase equilibria and may induce a significant destabilisation of the orthoclase melt component.

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.

The mineral to which I have given the name of Sodalite, was also put into my hands by Mr Allan. In the Greenland collection which he purchased, there were several specimens of a rock, obviously primitive. In the composition of these, the substance of which I am about to treat, formed a constituent, and, at first appearance, was taken for felspar, to which it bears a very striking resemblance.

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.

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.

Nearly six years ago, I presented to the Society two Memoirs on the subject of Differentiation, with fractional indices. The method which I adopted to extend the signification of a differential coefficient consisted in assuming that the function , which enters into the value of the coefficient deduced from a particular hypothesis, is limited only by the definition . This generalization appears to be perfectly satisfactory, and promises to offer, if not the only, certainly the best extension of the Differential Calculus. Considering the length of the interval which has elapsed since the publication of my former Memoirs, it is remarkable that so little addition has been made to our knowledge of this branch of analysis. With the exception of one or two papers in Liouville's Journal, and a few remarks by Professor De Morgan, in his Treatise on the Differential Calculus (pp. 598–600), I am not aware that anything has been written on this subject since that time. Seeing, therefore, that others are not willing to enter on this very promising field, I consider it not improper that I should make known a number of extensions of this science to which I have been subsequently led, many of which have been in my possession a considerable time.