The area lying between the north of Britain and the Faeröe Islands is classical in the annals of Marine Zoology, not only from the fact that the first systematic deep-sea investigations undertaken by this country were carried out there, but also from the number of new and remarkable types of animal life which have been first found in that region. Speaking only of the Echinoderm fauna, in justification of these remarks, it will suffice to mention the discovery of such forms as Phormosoma and Porocidaris amongst Echinoids, and of Hymenaster, Korethraster and Zoroaster amongst Asteroids.

It is a singular fact in the history of science, that, after all the attempts of the most eminent modern mathematicians, to obtain a simple and satisfactory demonstration of the fundamental property of the lever, the solution of this problem given by Archimedes, should still be considered as the most legitimate and elementary. Galileo, Huygens, De la Hire, Sir Isaac Newton, Maclaurin, Landen, and Hamilton, have directed their attention to this important part of mechanics; but their demonstrations are in general either tedious and abstruse, or founded on assumptions too arbitrary to be recognised as a proper basis for mathematical reasoning. Even the demonstration given by Archimedes is not free from objections, and is applicable only to the lever, considered as a physical body.

We consider the reinterpretation of Bethia by Bassett et al. (2008) to be flawed in several regards. Details of the pedicle rootlets and wrinkles strongly imply a soft-tissue structure rather than calcified sheath. The ornament is unusual, but equally so under either an orthide or a plectambonitoidean model. The reinterpretation of the ‘deltial plates’ as ‘chilidial plates’ is likely correct, but argues against a plectambonitoidean affinity by implying that the pedicle emerges between the valves. Other arguments presented in favour of a plectambonitoidean affinity are also discussed; we consider them unpersuasive. Finally, we contend that Bethia is sufficiently well characterised to deserve a taxonomic name.

In the Geology of Scotland, no feature comes at once more prominently before the observer than the number and variety of the trap-rocks. From the Sheant Isles to the Cheviot Hills the map is dotted over with trappean patches, which occur sometimes as long, narrow dykes, and often as irregular sheets, that extend almost over entire counties. The appearance of the rocks on the face of the country is scarcely less marked than on the map, and to their ever-changing varieties, we owe not a little of the characteristic scenery of Scotland. Throughout the wilds of the Inner Hebrides it is the trap-rocks which form many of the precipitous cliff-lines, and the craggy irregular hills. The soft pastoral valleys of the Ochils and the Pentlands lie among trappean rocks, while the hill-ranges, which break up the great central valley of Scotland, more especially the abrupt solitary crags that form such prominent landmarks, owe their existence to the permanence of the trap-rocks of which they consist. In short, there is no group of rocks more constantly found throughout the length and breadth of the island, and none, therefore, which so frequently obtrudes on the geologist or more imperatively demands his attention.

For a number of years I have been collecting specimens and conducting an investigation into the craniological characters of the native inhabitants of our great Indian Empire, and several hundred skulls have now been under examination, and almost all have been measured. The sources to which I have been indebted for material are in part the collection of crania belonging to the Henderson Trustees, long known as the Edinburgh Phrenological Museum, and now deposited by the Trustees in the Anatomical Museum of the University; in part, a few specimens belonging to the University collected by my predecessors in office; in part, the valuable series of Indian crania belonging to the Indian Museum, Calcutta, which through the intercession of Dr John Anderson, F.R.S., the former Director, the Trustees of that Museum, with great liberality, most courteously permitted me to have the loan of for purposes of study; and lastly, a number of crania which have been forwarded to me by friends and former pupils, engaged in the public service in India, to whom I take this opportunity of expressing my indebtedness for the valuable material which I have received from them.

One of the grandest steps which has ever been made in Dynamical Science is contained in two papers, “On a General Method in Dynamics” contributed to the Philosophical Transactions for 1834 and 1835 by Sir W. R. Hamilton. It is there shown that the complete solution of any kinetical problem, involving the action of a given conservative system of forces, and constraint depending upon the reaction of smooth guiding curves or surfaces, also given, is reducible to the determination of a single quantity called the Characteristic Function of the motion. This quantity is to be found from a partial differential equation of the first order, and second degree; and it has been shown that, from any complete integral of this equation, all the circumstances of the motion may be deduced by differentiation. So far as I can discover, this method has not been applied to inverse problems, of the nature of the Brachistochrone for instance, where the object aimed at is essentially the determination of the constraint requisite to produce a given result. It is easy to see, however, that a large class of such questions may be treated successfully by a process perfectly analogous to that of Hamilton; though the characteristic function in such cases is not the same function (of the quantities determining the motion) as that of the Method of Varying Action.

Coal and hydrocarbons have been exploited from the Carboniferous rocks of the Midland Valley for over 200 years. This work characterises organic matter from the Mississippian black shales of the Midland Valley from Wardie, Scotland. Biomarker analysis allowed the estimation of the degree of microbial transformation of organic matter, type of kerogen and thermal maturity during hydrocarbon generation. Parameters based on the biomarker indicators confirm a generally mixed type II/III kerogen. However, some samples contain mostly terrestrial organic matter, whilst others contain predominantly marine organic matter, which shows that the sedimentary environment varied greatly throughout the basin. The presence of gammacerane suggests water column stratification and anoxic conditions. Organic matter was much better protected from post-depositional alteration within the concretions, where higher TOC (total organic carbon) and TS (total sulphur) contents occur, than in the surrounding sediments. This can be induced by very early diagenetic formation of these concretions which protected organic matter from late diagenetic degradation.

Estimated values of vitrinite reflectance (Rc, Rcs) show that the sedimentary rocks reached the catagenesis stage. Most samples exhibit maximum organic matter maturation temperatures of around c60–90°C. However, stable isomers of phenyldibenzo[b,d]thiophene detected in some samples indicate that in some cases post-depositional hydrothermal activity affected maturation of organic matter increasing temperatures to as high as c174°C.

Brachiopod taxonomy is based on descriptions of shell morphology and key characters, but diagenesis generally modifies or erases some of them, hindering brachiopod identification. Brachiopods that are taxonomically related usually present shells with similar appearance but can differ in size (i.e., Rhynchonellata). Some aspects of morphology – for example the angular measurement of the curvature of the shell or details of shell microstructure – could aid taxonomic identification. Gigantoproductids, which lack a robust taxonomy, have the largest shells among brachiopods and are ideal for this kind of study because of their gigantic size and morphological variability. Furthermore, they have a great abundance and worldwide distribution during the mid-Carboniferous. More than 700 samples have been collected from Sierra Morena (Spain), Montagne Noire (France) and Adarouch (Morocco) identifying up to six gigantoproductid genera: Globosoproductus, Semiplanus, Kansuella?, Latiproductus, Gigantoproductus and Datangia. Microstructural features from 170 thin sections belonging to gigantoproductid ventral valves have been studied, and six crystal morphologies have been distinguished within the tertiary layer: subhorizontal, imbricated, crenulated, acicular, short and long columnar morphologies. Moreover, 23 complete shells from all genera have been selected to investigate shell size and curvature. Results from this study emphasise that shell size, curvature and crystal shape are taxa-related. Finally, a remarkable morphological change in the gigantoproductid populations from the western Palaeo-Tethys occurred during the Viséan–Serpukhovian, from thin-shelled genera with subhorizontal morphology (Viséan) to thick-shelled genera with a tertiary layer consisting of long columnar crystals (Serpukhovian). This study proves that microstructure, maximum thickness and shell spiral characterisation are robust characters when applied to gigantoproductid taxonomy, but also have great potential in other brachiopod groups.

Hydrocarbon migration mechanism into a reservoir is one of the most controversial in oil and gas geology. The research aimed to study the effect of supercritical carbon dioxide (СО2) on the permeability of sedimentary rocks (carbonates, argillite, oil shale), which was assessed by the yield of chloroform extracts and gas permeability (carbonate, argillite) before and after the treatment of rocks with supercritical СО2. An increase in the permeability of dense potentially oil-source rocks has been noted, which is explained by the dissolution of carbonates to bicarbonates due to the high chemical activity of supercritical СО2 and water dissolved in it. Similarly, in geological processes, the introduction of deep supercritical fluid into sedimentary rocks can increase the permeability and, possibly, the porosity of rocks, which will facilitate the primary migration of hydrocarbons and improve the reservoir properties of the rocks. The considered mechanism of hydrocarbon migration in the flow of deep supercritical fluid makes it possible to revise the time and duration of the formation of gas–oil deposits decreasingly, as well as to explain features in the formation of various sources of hydrocarbons and observed inflow of oil into operating and exhausted wells.

Byronids are problematic fossils of possible cnidarian affinity, only rarely reported from the Devonian, but never previously studied in the Barrandian area, Czech Republic. Two new species Prestephanoscyphus branzovensis sp. nov. and Prestephanoscyphus robustus sp. nov. are erected from the Lochkovian and the Eifelian, respectively. Four poorly known species referred to Byronia are described in open nomenclature from the Emsian and Eifelian. The new genus Parabyronia gen. nov. with the type species Parabyronia elegans sp. nov. is closely related to other sphenothallids but is distinguished by transverse ridges on its theca and short spines at the apertural end of the theca. Definite identification of phosphatic rings as the attachment structure of byronids was proved by new material of the Lochkovian age. A dwarf conularia Pidiconularia gen. nov. with the type species Pidiconularia tubulata sp. nov. is remarkable by its minute size and very fine ornament; its conulariid affinity is proved by subrectangular cross-section and four internal carinae. Microstructure of theca of Prestephanoscyphus is characterised by alternation of compact laminae of aligned columnar microcrystallites and chambered laminae with isometric microcrystallites of apatite. Accretionary growth of byronid theca and structure of the holdfast with basal opening for the adhesive pedal disc support their cnidarian affinity although they likely display the bilateral instead of tetramerous symmetry. The protective function of bilaterally symmetrical whorls of internal apophyses in Prestephanoscyphus is suggested and their role in strengthening of thecal wall or supporting function of gastric septa are disputed. The byronids are regarded as epibionts rather than attached to the rocks. They are representatives of benthic groups with phosphatic shells that declined with decreasing availability of phosphorus in seas and oceans.

The St David's Head Intrusion, exposed in North Pembrokeshire, is a tholeiitic sill up to 570 m thick, comprising principally mafic gabbros, which are in part layered. Layering varies from the centimetre to the metre scale. A range of gabbroic compositions is present, defining seven major petrological types, which are cut by thin silicic (aplitic) veins.

Log–log plots of incompatible elements from the various lithological units indicate that all of the rocks in the intrusion are petrogenetically linked, although a variety of processes has been operative. Roach (1969) considered the quartz gabbros and dolerites, which form an envelope around the other units, to relate most closely to the parental composition. However, the least evolved compositions in the intrusion are from the xenolithic laminated olivine gabbros, although these mafic compositions are due primarily to the presence of abundant, mafic, cognate xenoliths. These xenoliths are thought to relate to an earlier episode of crystal accumulation in a high-level magma chamber. The various laminated gabbros reflect crystal accumulation in situ after magma emplacement, leading in certain layers to extreme enrichments in Fe, Ti, and V, related to high modal proportions of cumulus ilmenite. Further in situ crystallisation led to differentiation of the residual liquid, producing more silicic gabbros with well-developed granophyric textures, the granophyre reflecting the silicic residuum. Extreme differentiation, possibly combined with expulsion of silicic residual liquid during crystal accumulation and compaction, resulted in the cross-cutting aplite veins.

Three different types of layering are present in the intrusion. Firstly, preferred orientation of tabular minerals in the laminated gabbro units is thought to result from discrete sedimentation episodes from a convecting magma chamber. Secondly, macrorhythmic modal layering up to 1 m thick consists of an alternation of relatively ilmenite-rich and ilmenite-poor layers in the laminated gabbro units, although the reason for the modal variation is not certain. Thirdly, a centimetre-scale felsic–mafic microrhythmic layering is present in the envelope quartz gabbros and dolerites, which is similar to the inch-scale layering in the Stillwater Igneous Complex. This layering is thought to relate to metasomatic reaction in the gabbro in the presence of water at a late magmatic stage. Overall, these various lithological units themselves define a large-scale layering in the intrusion.

Combined, the petrological and geochemical data suggest that the St David's Head Intrusion was not emplaced in a single event. Rather, a series of magma pulses, of contrasting compositions but petrogenetically linked, was intruded. Some of the chemical variations now seen existed prior to emplacement, indicating the former presence of high-level crustal magma chambers, while other variations developed as a result of in situ crystallisation processes and related chemical differentiation.

Sir George Clerk-Maxwell of Pennycuik, Baronet, one of the Presidents of the Physical Class of this Society, was born at Edinburgh, on the last day of October 1715. He was the fourth son of Sir John Clerk of Pennycuik, one of the Barons of Exchequer in Scotland: His mother was a daughter of Sir James Inglis of Cramond.

His more early studies were carried on at the University of Edinburgh, under the eye of his father, who was himself a man of letters, and from whom he appears very early to have caught a strong taste for Natural History, Antiquities and the Theory of Commerce, particularly in so far as these branches of knowledge related to his own country. He afterwards went to Leyden, where he finished his studies under the immediate inspection of the celebrated Boerhaave, who had been the friend of his father; and, before his return home, he visited several parts of France and Germany.

Before entering on the main subject of this paper, the composition of rainwater, I shall give a brief account of the rain that has fallen in the Lake-District during the year just past; and this I shall do chiefly by means of tables. The quantity of rain registered has been so greatly in excess of any former year, that of itself it is deserving of record, and the more so, comparing the weather which has prevailed here with the weather in the south, for the most part, happily for the harvest, as remarkable for an opposite state, an excess of dryness.

Before commencing the discussion of the subject, it is necessary to make some definitions, with a view to avoiding the confusion which extensively prevails, from the neglect of the all-important definition of terms. I might be even more exact than I shall be, and excuse myself from adopting such a seeming improvement, on the ground that further refinement of definition would itself cause confusion in the present stage of advancement of our knowledge.

Absolute sterility, I shall hold to mean the condition of a woman who, under ordinary favourable cirumstances for breeding, produces no living or dead child, nor any kind of abortion.

Sterility, I shall hold to mean the condition of a woman who, under ordinary favourable circumstances for breeding, adds not even one to the population, or produces no living and viable child.

Relative sterility, I shall hold to mean the condition of a woman who, while she may or may not be absolutely sterile, while she may or may not be sterile, is, under ordinary favourable circumstances for breeding, sterile in relation to the circumstance of time; or, in other words, in relation to her age, and the duration of her married life.

In preparing solutions of various salts with a view to determine their electrical conductivity, we found it of importance to know both the amount of salt in each solution, and its density. We prepared the solutions by mixing known weights of the salt under examination with known volumes of distilled water, and then measured their densities as soon as solution was complete by weighing a glass bulb in the liquid. We employed a balance which weighed to a milligramme with a kilogramme in each pan, and to give the results as great accuracy as possible we corrected for the upward pressure of the air displaced by the weights. The weight of the bulb itself was about eighty grammes. When not in use it was kept immersed in distilled water, in order to prevent change in its weight or volume being caused by impurities adhering to it. The temperature at which the densities were taken was 10° centigrade.

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.

The causes of the peculiarities of the solar rotation exhibited by the superficial layers of the sun's body must still be considered unknown, notwithstanding recent interesting attempts at explanation. This is no doubt partly due to the difficulties of the hydrodynamical problem placed before the mathematician in an investigation of such complexity as the movements of particles in a rotating fluid subject to energetic convection. But it must also be conceded that the observational data available for a basis of mathematical, or even speculative, research are still so scanty, that for this reason alone we may perhaps not feel surprised at the failure so far of theoretical attempts.

The observations which have been made to determine the magnitude and figure of the earth, have not hitherto led to results completely satisfactory. They have indeed demonsrated the compression or oblateness of the terrestrial spheroid, but they have left an uncertainty as to the quantity of that compression, extending from about the one hundred and seventieth, to the three hundred and thirtieth part of the radius of the equator. Between these two quantities, the former of which is nearly double of the latter, most of the results are placed, but in such a manner that those best entitled to credit are much nearer to the least extreme than to the greatest.