We owe to Leibnitz the first suggestion of Differentiation, with fractional and negative indices, but no definite notion of the theory was attained until Euler expounded it in the Petersburgh Commentaries for 1731. Still Euler wrote only a few pages on the subject, so that the theory could scarcely be said to have come into existence, until Laplace, in his Théorie des Probabilités, and Fourier, in his Théorie de la Propagation de la Chaleur, shewed how general differential coefficients might be deduced by means of definite integrals, provided we assume or prove, by means of some elementary definition, that the differential coefficient of a circular or of an exponential function has a certain form. The formula given by M. Fourier is a very simple one; and our astonishment is great, when we reflect on the time which elapsed from its announcement to the first application that was made of it. This took place in 1832, in a memoir by M. Liouville, entitled Questions of Geometry and Mechanics resolved by a new analysis, which memóir is followed by two others on the more immediate theory of the analysis itself. Although M. Liouville regards his analysis as a new invention, we have no doubt that the idea is due to Fourier; but still to M. Liouville belongs the honour of moulding it into a shape capable of being made use of in the solution of problems.

The material to be described here was taken from individuals of a school of Pseudorca crassidens, forty-one of which were stranded at Buddon Ness in the estuary of the Tay in November 1935. There is very little published work on this species beyond reports on the occurrence of stranded individuals. Beebe (1924) refers to six skeletons found on the shores of the Galapagos Archipelago, and West (1935) gave a preliminary account of a male fœtus taken from a female stranded in Wales. More recently, Peacock, Comrie, and Greenshields (1936) gave an account of the Tay specimens, while Fraser (1936) published a review of various strandings around our British coasts, and Gill (1935) has dealt with those stranded in South Africa (see abstract in Nature, September 1936). With regard to the reproductive system valuable assistance has been obtained from recent researches on other species by MacIntosh and Wheeler (1929), Wheeler (1930), Ommanney (1932), and Laurie (1937), published in Discovery Reports, while earlier papers, also on other species, by Schulte (1916) and Meek (1918) have also been consulted.

The interpretation of pedicle soft tissue preservation in a unique brachiopod specimen of Wenlock (Silurian) age from Herefordshire, western England, is re-assessed. Bethia serraticulma, assigned originally to the Orthida, is more probably a member of the Strophomenida (Plectambonitoidea). The supposed pedicle structure is more plausibly a weakly mineralised pedicle sheath, which is a common morphological and functional development in the early ontogeny of a number of Palaeozoic brachiopod lineages.

The following paper contains the results of an inquiry which has occupied me at intervals for somewhere about ten years. It was carried out in part at the expense of the British Association, and I have already reported results to that body in 1869 and 1871. But these provisional reports referred to very short ranges of temperature only, and the experiments were made with faulty thermometers, for which I had not the corrections which had been carefully determined by Welsh at Kew.

The inquiry arose from my desire to extend to other metals the very beautiful and original method which Principal Forbes devised, and which the state of his health prevented him from applying to any substance but iron. Forbes' experiments gave a result so very remarkable, and (as it seemed to me) so theoretically suggestive, that I wished to extend them to other pure metals, and also, in one or two cases at least, to alloys.

I believe that Principal Forbes had at least two reasons for undertaking his investigations:—(1.) When he commenced his inquiry, there was no really accurate or trustworthy determination of the absolute conductivity of any body whatever for heat. (2.) FORBES had himself, in 1833 and subsequent years, pointed out a very remarkable analogy between the conducting powers of metals for electricity and for heat, and had shown that these were almost precisely proportional to one another—that is to say, that the list of the average relative conductivities of different metals for electricity differed, from that of their relative conductivities with regard to heat, certainly not more than did the several electric lists furnished by different experimenters, and certainly less than the corresponding thermal lists. Hence it was natural to suppose that temperature might have a marked effect on thermal conductivity, as it was known to have such an effect on electric conductivity.

The worms which form the subject of the present communication were forwarded to me, in a living condition, from Kew Gardens.

I have received lately a considerable number of living Oligochæta from those Gardens, through the kindness of Mr Dyer, who permitted me to have the earth arriving from different parts of the world in the Wardian cases, in which plants are packed for travelling, thoroughly sifted, with a view to preserving the worms which had been accidentally included. By these means I have succeeded in obtaining some very interesting new forms, as well as a number of others which are still imperfectly known. The species which I describe in the present paper appears to be a new species of Eisen's genus Ocnerodrilus. The genus Ocnerodrilus was formed by Eisen in 1878 [1] for a small worm found in Fresno County, California. The specimens were all met with in “an irrigation box,” where they were found crawling among the algæ which covered the boards. It is evidently, therefore, aquatic in its habits, but Eisen contrasts its slow movements with the rapid swimming of Lumbriculus and Rhynchelmis, comparing it in general appearance with a small species of Lumbricus.

A two-parameter Margules method has been developed for modelling the thermodynamic mixing properties and hypersolidus phase relations of albite-water (ab-w) melts. The method is based largely on phase-equilibrium and calorimetric data that are either currently available or readily obtainable; P-V-T data are not required.

The new modelling method has been applied to calculate: (1) thermodynamic mixing properties for ab-w melts at 2-5 kbar, 815°C; and (2) hypersolidus phase relations for the ab-w system at 2·5 kbar. Results are uniformly positive—activity-composition relations are similar to those predicted by equations based on P-V-T data, excess enthalpies are in good agreement with data obtained from calorimetry, and calculated phase relations are fully compatible with phase-equilibrium data for ab-w melts acquired at 2·5 kbar.

It is concluded that the Margules method for thermodynamic modelling of ab-w melts is a practical alternative to the P-V-T modelling method.

In the determination of the effects of stress upon different materials, the investigator has several methods of attack open to him, each of which has its own particular advantages. In the great majority of cases the material under investigation obeys the generalised Hooke's law, and the effects of a stress are therefore most easily followed and measured by observations of the strains produced. The strains being usually exceedingly minute, it is necessary to magnify them sufficiently to allow of accurate measurement. To this end many instruments have been devised for measuring the strains obtained by the action of different stresses, and in fact the great majority of our experimental knowledge has been obtained in this way. The application of polarised light to the determination of stress was first suggested by Brewster, and he applied it to many problems, particularly the determination of the neutral axis of a glass beam. Neumann, with a full knowledge of the work of Brewster, developed a theory of the analysis of strain by polarised light, and Maxwell also independently developed a theory. A third method, which has assumed great prominence in recent years, is the microscopic examination of metals under stress, as developed by Ewing, and Rosenhain, and others.

In September 1903 I received a bottle containing twelve specimens of a large parasite presented to me by Mr Chr. Castberg, the manager of a Norwegian whaling company which has established a fishing station at Ronasvoe in the north of Shetland. In his letters Mr Castberg stated that the parasites were attached to a Finner whale, which, from its size, the mottled character of the whalebone and the pointed head, was obviously a Razorback—Balænoptera musculus. The parasites were numerous, and were fixed to the back of the whale, and the attached end penetrated through the skin into the blubber. Although Mr Castberg had seen many hundred whales, this is the first occasion on which he had met with this form of parasite.

The Cape Granites are a granitic suite intruded into Neoproterozoic greywackes and slates, and unconformably overlain by early Palaeozoic Table Mountain Group orthoquartzites. They were first recognised at Paarl in 1776 by Francis Masson, and by William Anderson and William Hamilton in 1778. Studies of the Cape Granites were central to some of the early debates between the Wernerian Neptunists (Robert Jameson and his former pupils) and the Huttonian Plutonists (John Playfair, Basil Hall, Charles Darwin), in the first decades of the 19th Century, since it is at the foot of Table Mountain that the first intrusive granites outside of Scotland were described by Hall in 1812. The Neptunists believed that all rocks, including granite and basalt, were precipitated from the primordial oceans, whereas the Plutonists believed in the intrusive origin of some igneous rocks, such as granite. In this paper, some of the early descriptions and debates concerning the Cape Granites are reviewed, and the history of the development of ideas on granites (as well as on contact metamorphism and sea level changes) at the Cape in the late 18th Century and early to mid 19th Century, during the emerging years of the discipline of geology, is presented for the first time.

Foraminifers, calcareous algae and incertae sedis Algospongia of late Asbian to late Brigantian age in limestones from East Fife, East Lothian and Northumberland, enable the base of the late Brigantian to be recognised in all these areas. Preservation of the late Asbian and early Brigantian limestones in cyclothemic successions is generally poor. The St Monans White Limestone (St Monans, Fife), First Abden Limestone (Kirkcaldy, Fife), Middle Longcraig Limestone (East Lothian) and Lower Bath-House Wood/Middle Bath-House Wood (Northumberland) were confidently correlated by their foraminiferal assemblages. These limestones are all assigned to the top of the Assemblage 6 in northern England (Single Post Limestone). The St Monans Brecciated/St Monans Little/Charlestown Main limestones (St Monans, Fife) and the Second Abden/Seafield Tower limestones (Kirkcaldy, Fife), Upper Longcraig/Lower Skateraw limestones (East Lothian), Upper Bath-House Wood/Shotto Wood limestones and Eelwell Limestone (Northumberland) are assigned to the Assemblage 7 in northern England (Scar Limestone and Five Yard Limestone). The paired Middle/Upper Skateraw limestones (East Lothian) and the Acre Limestone (Northumberland) contain representatives of the Assemblage 8 from northern England (Three Yard Limestone). Higher up in the succession, in Northumberland, the foraminiferal assemblage in the Sandbanks Limestone can be compared with Assemblage 9 in northern England (Four Fathom Limestone). Above the Great Limestone and Little Limestone, with their characteristic Pendleian assemblages, the Sugar Sands Limestone and Corbridge Limestone contain Arnsbergian foraminiferal assemblages, typical of the Lower Felltop Limestone in northern England. The Lower Foxton Limestone is correlated with the Upper Felltop Limestone, whereas the Thornbrough Limestone in Northumberland lacks diagnostic Arnsbergian taxa.

The following research was undertaken chiefly with the object of furnishing a complete memoir on the morphology and physiology of Patella vulgata. A number of isolated observations on various organs are recorded, but no systematic account has as yet been written, so far as the writer is aware. He has endeavoured to incorporate these observations in such a general account, having first convinced himself of their accuracy so far as lay in his power.

That there is a decided need for the ecological study of insects and other animals was first brought home to the mind of the author whilst engaged upon the subject of a “General Survey of the Insect Fauna of the Soil” (vide Jour. Econ. Biol., vol. viii, part 3, 1913). Much information has been collected at various times by numerous authors, and especially those who have treated of the habits and behaviour of animals, but very little attempt has been made to systematise the data variously gathered, to explain the cause and effect of many obscure phenomena, or to make important observations accessible for the use of the animal ecologist. Thus, at present, we find ourselves on the threshold of practically a new and undisputed field, with opportunities for original and interesting research extending in innumerable directions. Dr C. C. Adams, now of Syracuse University, New York, who has written a most useful work, “the outgrowth of the effort as it has developed in the study and teaching of animal ecology,” in which is listed most of the literature applicable to the science, says (p. 10): “The associational is the phase of animal activity which may be considered as the form of animal behaviour which has developed into the human social relations,” and concludes that, because of the social character of human society, those interested in matters pertaining to the welfare of mankind, such as the sociologist, the physician, the sanitarian, and the agriculturist, will ultimately participate in a keener appreciation of the associational aspect.

Our knowledge of the earliest stages of blood-vascular development in the human embryo suffers from a dearth of suitable material. Early human specimens are not frequently available for examination; many are pathological; some, although of value for other purposes, are not sufficiently well preserved to furnish observations on angiogenesis; direct microscopic observation of the tissues while undergoing development cannot be carried out as is possible, say, in the chick embryo. Our knowledge of the process must be based on descriptions of separate specimens representing different stages. Individual specimens, therefore, are worthy of careful record.

This paper describes a terebratelloid articulate brachiopod, Gyrothyris williamsi sp. nov., based on 95 specimens from seamounts on the Lord Howe Rise, Coral Sea, SW Pacific Ocean. The new species is attributed to Gyrothyris on the basis of (a) morphological and growth trajectory similarities; (b) phylogenetic analyses of an alignment of DNA sequence (∼2900-sites) obtained from nuclear-encoded small- and large-subunit ribosomal RNA genes (SSU and LSU); and (c) the presence of a distinctive, two-part deletion in the LSU gene. It is distinguished morphologically from Gyrothyris mawsoni and its subspecies by both internal and external morphology and by its isolated geographical distribution, which extends the patchy, known range of this genus to an area some 2000 km north of its previous northern limit around New Zealand. Phylogenetic analyses of the rDNAs and of mitochondrial cox1 gene sequences (663 sites) confirm previous indications that the New Zealand endemic terebratelloid genera form a clade (Neothyris (Calloria, Gyrothyris, Terebratella), but the position of Terebratella with respect to Calloria and Gyrothyris remains weakly established. These sequences disagree inexplicably about the closeness of the relationship between Neothyris parva and N. lenticularis. Analyses of the first sequences from Calloria variegata, a species restricted to the Hauraki Gulf, New Zealand, are consistent with the possibility that it originated locally, and recently, from C. inconspicua. Magellania venosa from S. America/Falklands joins with Antarctic Magellania fragilis and M. joubini to form an rDNA clade that excludes Terebratalia as the putative sister-group of the New Zealand terebratelloid clade. The cox1 (but not the rDNA) sequences of the New Zealand clade pass a test for clock-like rates of evolution, and maximum likelihood pairwise distances suggest that if genetic isolation between the ancestor of Antarctic Magellania and the last common ancestor of the New Zealand terebratelloid clade was initiated by separation of the Antarctic and New Zealand plates ∼90 Mya, isolation from M. venosa was initiated earlier, perhaps ∼145 Mya. However, in the simple phylogenetic reconstruction presented here from cox1 sequences, S. American and Antarctic Magellania spp. do not yield a well-supported clade, perhaps because of differences in base composition.

Ultrastructural examination of the brachiopod Thecidellina from three different locations in the Caribbean and the Atlantic revealed that at least three cryptic species are present. One is the type species of the genus, Thecidellina barretti, which may only occur in Jamaica. The other two, previously lumped into T. barretti, are new to science, viz T. bahamiensis Lüter & Logan sp. nov. from the Bahamas and T. williamsi Lüter & Logan sp. nov. from Cape Verde. All three species clearly differ not only in their provenance, but also in specific shell characters, such as spiculation of the ventral valve, presence of a ventral median ridge, shape of two holes in the intrabrachial ridge of the dorsal valve and the structure of the interbrachial lobes. The identification of three instead of a single species and their supposed allopatric speciation is discussed with regard to the thecideide life cycle and independent models of larval dispersal in the Caribbean, based on oceanographic data.

The special features of interest attaching to the Tertiary igneous rocks of Mull have been made known to geologists mainly through the classic descriptions of Professor J. W. Judd and Sir Archibald Geikie. The point of view of these two investigators is, however, essentially geological, and they refer but little to the occurrence of minerals and rarely give precise localities. It is clear, too, that the late Professor M. F. Heddle did not make an exhaustive examination of many localities in Mull, for his collection in the Royal Scottish Museum contains very few specimens from that island. With a view to filling up this gap I have paid several visits to Mull, and this paper deals with some of the material which I collected. The officers of the Geological Survey who are at present mapping the island have helped me considerably with information and material; and to Mr J. B. Richey, B.A., who has surveyed the area from which a large part of the material was obtained, I am particularly indebted for assistance in collecting specimens from somewhat inaccessible localities.

It is the object of this paper tor establish with numerical exactness the following law of the Diffusion of Gases:

“The diffusion or spontaneous intermixture of two gases in contact, is effected by an interchange in position of indefinitely minute volumes of the gases, which volumes are not necessarily of equal magnitude, being, in the case of each gas, inversely proportional to the square root of the Density of that gas.”

These replacing volumes of the gases may be named equivalent volumes of diffusion, and are as follows: Air, 1; Hydrogen, 3.7947; Carbureted hydrogen, 1.3414; Water-vapour, 1.2649; Nitrogen, 1.0140; Oxygen, 0.9487 ; Carbonic acid, 0.8091; Chlorine, 0.6325, &c.; numbers which are inversely proportional to the square roots of the densities of these gases, being the reciprocals of the square roots of the densities, the density of air being assumed as unity.

The consequences of urbanisation for Earth's biogeochemical cycles are largely unexplored. Copper (Cu) in urban soils is being accumulated mainly due to anthropogenic activities under rapid urbanisation. The increasing Cu concentrations may contribute to altering soil nitrogen (N) cycling in urban ecosystems through modulating denitrification processes. This research aims to identify how Cu impacts urban soil denitrification functions and denitrifier abundance. An urban park soil with a background total Cu concentration of 7.9μgg–1 was incubated anaerobically with different Cu amendments (10, 20, 40, 80 and 160μg Cu g–1 soil), similar to prevalent Cu contents in urban soils. We evaluated the soil denitrification functions using the acetylene (C2H2) inhibition method and assessed the denitrifier abundance by quantitative polymerase chain reaction (qPCR) analyses of denitrifying marker genes (nirK, nirS and nosZ). At the function level, we observed that both the potential soil denitrification activity and the N2O emission rate due to denitrification were significantly (P<0.05) inhibited by Cu; even the lowest Cu addition (10μg Cu g–1 soil) drastically affected the denitrification function. Moreover, Cu significantly (P<0.05) decreased the abundance of nirK and nirS genes at the additions of 160μg Cu g–1 soil and 40μg Cu g–1 soil, respectively, whereas it had no clear impact on nosZ gene copies. Further correlation analyses revealed that the potential denitrification activity was positively correlated to the copy numbers of nirK and nirS genes, but it was not correlated to nosZ gene abundance. These findings indicate that Cu additions inhibited soil denitrification function and decreased denitrifier abundance in the investigated urban park soil. Our results suggest that Cu accumulation in urban soils, resulting from urbanisation, may generally influence denitrification in urban ecosystems.

A preliminary account of an earlier investigation of this nature has been given in a previous paper (Redington and Priestley, 1925), and it is intended to record here the results of further work, with particular reference to questions of growth and development. The new data that are presented are the result of two series of experiments, which will be called Series B and C, whilst the earlier work will be referred to as Series A. A critical review of the relevant literature has recently been published (Redington, 1929), so reference will only be made to such work when it has a direct, positive, or negative bearing on the results recorded here.

In 1917 I published an account (16) of the so-called pharyngeal gland-cells of earthworms, unevenly but intensely staining cells (whence the name “chromophil” which I gave to them) which form lobular masses on the pharynx, and smaller aggregations in other places in the anterior segments. I came to the conclusion that the cells were not, as was usually held, epithelial in origin—were not cells which had fallen out of the epithelial layer while still retaining their connection with the pharyngeal cavity by means of a long neck functioning as a ductule. On the contrary, they were, I believed, mesoblastic in origin, and congeneric with the peritoneum; and were devoid of ducts leading into the pharynx.