The theory of the knotting of curves, except for a few elementary theorems due to Listing, was entirely neglected until Tait was led to a consideration of knots by Sir W. Thomson's (Lord Kelvin's) work on the Theory of Vortex Atoms. He attacked chiefly the problem of constructing knots with any number of crossings, and obtained a census of the knots of not more than ten crossings. Those knots which exhibit a special kind of symmetry—the amphicheiral knots—offer certain points of interest.

The numerical taxonomic analysis of encrinurine trilobites by Temple and Tripp (1979) is extended to 28 described Chinese species, 35 other Chinese samples, and 13 non-Chinese species, in addition to 56 species analysed previously. The 132 entities are coded for 34 cranidial and pygidial attributes, and are ordinated on the eigenvectors of the interattribute correlation matrix for 32 attributes. Chinese material falls into four clusters informally compared with Coronocephalus, Kailia, Encrinuroides and Encrinurus. The Encrinurus-like Chinese species occur mainly in Northern China and have links with non-Chinese species.

The immense amount that has been written on the subject of dew renders it extremely difficult for one to state anything regarding it which has not been previously expressed in some form. It has been examined over and over by minds of every type, and from every point of view; so that every possible explanation of the different phenomena seems to have been given, and so many passing thoughts recorded, that from the literary point of view the whole subject seems exhausted. As a necessary result, these different treatises are in many respects contradictory; and it would be quite impossible to construct anything like a consistent explanation and account of our subject, from the very voluminous writings of those who have treated it from the purely literary point of view, and whose ideas have been evolved from their inner consciousness, according to what seemed to them the fitness of things, and without questioning nature as to the truth of their conclusions. On the scientific side of the subject, however, the writings are not so voluminous, and additions to it are still required to enable us to determine which of the many conflicting opinions are correct.

The 119 subsolids (marked ss) and the 244 unsolids (marked us), of these unifilars are here arranged in lists according to their flaps. Fe is the number of flaps of e loops upon a knot; and the headings of the lists, as, e.g.10I, F2 = 1, F1 = 3, describe so far all the knots in the lists. Thus in 10I each has one 2-ple flap and three single ones. After the number in the list comes always the base on which the knot is constructed by the rules of my paper, XVII. in vol. xxxii. part ii. of the Trans. R. S. E.; and the reader who has that paper before him will find it easy to draw any knot on its base, nearly always there figured, by the first given flap, which is the leading one of the knot described; thus in 10I the first written flap is the double one, and in 10P, F3 = 1, F1 = 2, it is the triple one. The leading flap of a subsolid is always followed by a colon.

Alexander Wilson, M. D., late Professor of Practical Astronomy in Glasgow College, was a younger son of Patrick Wilson, town-clerk of St Andrew's, and was born there in 1714. He was very young when his father died, and was afterwards brought up by the care of his mother, Clara Fairfoul, a person much respected for her prudence, virtue, and piety.

Having received the usual education at the different schools, he entered to the College of St Andrew's, where he made great proficiency in literature and the sciences, and, after completing a regular course of studies, was admitted to the degree of Master of Arts in his 19th year.

The genus Cephalodiscus was instituted by M'Intosh for a species, C. dodecalophus, which had been obtained by the Challenger Expedition. After the publication of the full account of this species, by M'Intosh and Harmer (87) in the Challenger Report, succeeding papers for nearly twenty years were all based on the original Challenger material. The subject was in particular re-investigated by Masterman in a series of papers (971, 972, 98, 99, 03). The Siboga report, published by Hakmer (05) in 1905, added three Oriental species to the genus. Schepotieff (05, 07, 08) devoted several papers to a further description of the Challenger material; while, more recently (09), he has described an interesting new species, C. indicus, from Ceylon. In 1906 Ridewood (06) described C. gilchristi from South Africa; and in the following year he gave an account (071) of the two species which had been dredged by the Discovery Expedition; and (072) of the development of the plumes in four species of Cephalodiscus. One of the Discovery species, C. nigrescens, had been described two years earlier by Lankester (05), in a preliminary paper; and Ridewood (12) has recently brought forward evidence to show that this species had been dredged by the Erebus and Terror Expedition in 1841 or 1842. In 1907 Andersson (07) added no less than six species to the genus, in describing the results of the Swedish South Polar Expedition, though we give some evidence (pp. 559–563) to show that one of them, C. inæquatus, is synonymous with C. hodgsoni, which had been described by Ridewood (071) earlier in the same year, from the Discovery collection. The most recent addition to the list of species has been given by Gravier (12), who has published an account of C. anderssoni, a new species which was obtained by the second French Antarctic Expedition.

Arthropods were the first known animals to colonise land habitats, with myriapods and arachnids having done so at least by the Silurian. Much later, several lineages of Pancrustacea (hexapods and the paraphyletic crustaceans) also ventured onto land; the hexapods by the Early Devonian, and later at least four other groups of crustaceans, namely isopods, amphipods, ostracods and decapods, most of which generally colonised the continental water bodies. All faced a series of challenges (in particular: gas exchange; desiccation; reproduction; osmoregulation; and exposure to ultraviolet radiation), resulting in many morphological, physiological and ecological adaptations. Nonetheless, whether they reached land via saltwater or freshwater remains poorly documented, mainly because relevant localities are few. The Famennian (Late Devonian) Strud locality in Belgium provided an exceptional source of information on early aquatic continental ecosystems and their plant, vertebrate and arthropod colonisers at a crucial step in the terrestrialisation process. Here, we review and update its crustacean fauna, which inhabited floodplain and temporary pool waters. New anatomical details of the notostracan Strudops goldenbergi Lagebro et al., 2015, as well as a new genus and species of spinicaudatan, are described. We also discuss the ecology of this unique, early continental ecosystem and the insights it gives into the terrestrialisation process.

The Psilotaceæ constitute one of the most interesting of existing Pteridophyte groups. This interest is mainly due to their phylogenetic isolation. They are perhaps the most isolated of existing types—showing no close affinity to other Pteridophytes. They are very highly specialised in their anatomy, habit, and habitat, and limited to a comparatively narrow geographical distribution. They include two probably monotypic genera—Tmesipteris and Psilotum—which are closely related. Although both genera are limited to the tropics and sub-tropics, Psilotum has a much wider distribution than Tmesipteris. The latter is confined to the South Sea Islands, Australia, New Zealand, and parts of Polynesia. Up till recent years they have been classed with the Lycopodiales, but this has been more a matter of convenience than an indication of close relationship, and has only served as a temporary classification until more knowledge has been obtained regarding them. The peculiar nature of these plants, as shown in their structure and in their habitat, suggests that they are highly specialised remnants of a much larger group which has practically become extinct. Recent inquiry into the structure of the sporophyte of both plants has made this much more than a suggestion. As a result of the careful investigations of Scott (1908), Boodle (1904), Bower (1894-1908), Ford (1904), and others, there has been a marked tendency to remove the Psilotaceæ from their temporary position among the Lycopodiales and associate them with the extinct Sphenophyllales. Scott (p. 631) states that it seems best to regard the Psilotaceæ as forming a class of their own, the Psilotales, under the main division Sphenopsida—their closest affinity under this class being the Sphenophyllales. This probable affinity of the Psilotaceæ to such an ancient and long extinct race as the Sphenophylls, and the great uncertainty of their relationship to other existing types, have awakened a great interest in these two specialised and isolated genera. When, in addition to this, we consider that the Psilotaceæ is the only group of Pteridophytes in which the gametophyte generation and embryo are not yet definitely known, our interest in these plants becomes twofold, and any new information throwing additional light on their life-histories will be welcomed.

Since the liver is an organ whose due activity is indispensable for the maintenance of health; since it is frequently the subject of disorder, and consequently receives a large share of attention from the physician, it is obviously of great importance that he should possess precise knowledge of the manner in which it is affected by medicinal agents.

The Bail Hill Volcanic Group (Caradoc) represents the largest, single volcanic complex exposed within the Ordovician turbidite succession of the Northern Belt in the Southern Uplands of Scotland. The group comprises a heterogeneous sequence of submarine lavas, volcaniclastic and intrusive rocks (up to 2 km thick), and crops out in a small area (c. 4 km2) around Bail Hill, north of Sanquhar. The Cat Cleuch Formation (older) is dominated by a sequence of autobrecciated basaltic lavas which contain large, zoned diopsidic clinopyroxene. The overlying Peat Rig Formation comprises a more mixed sequence of plagioclase-amphibole-phyric lavas, volcaniclastic rocks and contemporaneous volcaniclastic sedimentary rocks. The Cat Cleuch and lower part of the Peat Rig formations are cut by a vent breccia, the Bught Craig vent breccia, which formed part of the feeder to the upper part of the Peat Rig Formation. The Bail Hill volcanic rocks are alkaline in character, ranging from alkali basalt to trachyandesite in composition, possessing trace element characteristics and enrichment patterns typical of oceanic within-plate basalts. The Bail Hill Volcanic Group, although geochemically distinct, forms part of a mixed assemblage of tholeiitic and alkaline withinplate lavas within the Southern Uplands which are of broadly similar age, some of which are intercalated within the greywacke sandstone sequence. This assemblage clearly indicates that a period of extension and within-plate volcanism occurred during the early stages of the development of the Southern Uplands sedimentary basin.

Major and trace element, including REE, analytical data are used as bases for interpreting the petrogenesis of the major igneous components of the northern part of the Ballantrae complex which occurs in the southwestern part of the Midland Valley of Scotland. Most of the peridotite, now serpentinised, is similar to ultramafic rocks in other ophiolite complexes. Mean crystallisation conditions, determined on the basis of co-existing orthopy-roxenes and clinopyroxenes for the dominant peridotite and minor pyroxenite were 1060 (±60)°C—20 (±2) kb and 1240 (±89)°C—25 (±25) kb, respectively. These rocks, of mantle provenance, have compositions consistent with being residues after the extraction of 20–30% of tholeiitic material from the mantle. The presence among them of a rock whose REE contents indicate that it is a plagioclase peridotite, point to the tectonic incorporation of the products of a high level magma chamber.

The mafic parts of the complex have tholeiitic characteristics and developed between 1300° and 1100°C. They do not represent primary mantle melt but fractionated material. Clinopyroxene was the main fractionating phase and more than 10% fractional crystallisation is indicated with increase from gabbros, through beerbachites (metadolerites) of a sheeted dyke complex and pillow lavas, to microgabbros and pyroxene diorites. Biotite diorites and trondhjemites represent the most fractionated products, the latter having affinities with ophiolitic plagiogranites.

The beerbachites of the sheeted dyke complex do not all represent the same stage of fractionation. The pillow lavas have REE patterns similar to rocks found in marginal basins but are markedly different from pillow lavas from the Highland Border Complex in Arran, near the northern margin of the Midland Valley.

That phase of the nucleus just preceding the heterotype mitosis, and which was first called Synapsis by Moore (1895), has come to be regarded as an important and critical period in the life-cycle. It was called synapsis because of the apparent condensation and contraction of the chromatin at one side of the nuclear cavity. This discovery at first received scant support, the synaptic contraction being considered by many investigators to be nothing more than an artifact—an artificial contraction caused by imperfect fixation. In 1897, however, Moore's discovery was confirmed by Miss Sargant, who not only observed it in fixed material, but also found it in the living pollen-mother-cells of Lilium.

The genus Amphioxus was instituted by Mr Yarrell for the reception of a singular little animal which he received from Mr Couch. The characters of this genus, as given in the History of British Fishes, are, “Body compressed, the surface without scales, both ends pointed; a single dorsal fin extending the whole length of the back; no pectoral, ventral, anal, or caudal fins; mouth on the under part of the head, narrow, elongated, each lateral margin furnished with a row of slender filaments.”

While an endodermis in the leaf is a relatively rare occurrence amongst the Angiosperms, its presence has been noted as being fairly constant in a number of families; but it is only in the case of a few of these families that it has been treated in sufficient detail to indicate its representation generically. Mylius (8), in particular, has examined the foliar endodermis of the Myrtaceæ, the Onagraceæ, and the Rosaceæ; especially the latter family, in which he makes a comprehensive investigation of the genera Spiræa, Alchemilla, Fragaria, Potentilla, Rosa, Agrimonia, and Sanguisorba (Poterium) from this standpoint. An endodermis has also been recorded as present in the leaves of certain Monocotyledonous families of which the Bromeliaceæ, Orchidaceæ, and Gramineæ (tribe Festuceæ) are examples quoted by Haberlandt (4, p. 368 sqq.) from the work of Rimbach, Schwendener, and van Wisselingh.

Svecokarelian migmatites in the Jussarö area of the southern Finnish archipelago comprise tonalitic gneiss, amphibolite, metagabbro, microgranite, the metamorphosed derivatives of sediments, including carbonates and graded argillites, together with later-emplaced potassic granite, and basic and acidic pegmatites. The rock assemblage shows evidence of repeated deformation; a succession of 15 sets of folds (and fold-related structures) is identified and documented. There are two sets of early intraf oliai isoclinal folds (Faa and Fab), isoclinal folds (Fbr), recumbent folds (Fx), upright open folds (Fy), tight upright folds (Fbb), two sets of asymmetrical folds (Fc and Fd), ‘scar’ folds (Fb1, Fcb Fd1), slip folds Fb, conjugate shear folds (Fe), angular folds (Fn), open warps (Fw) and tight ductile shears (Fds). From isotopie evidence reported elsewhere, the evolution of this crustal segment of the Svecokarelides is known to have spread over a period of approximately 200 m.y. from c. 1900 m.y. to c. 1700 m.y.

The following Memoir contains the results of researches made during the last three years. My investigations were originally directed to British lichens only, but they have subsequently and gradually embraced lichens from all parts of the world. The majority of Scotch species examined were collected by myself while on botanical tours in various parts of Scotland during the last ten years. Lowland species were collected chiefly in the counties of Perth, Edinburgh, and Dumfries; but also in Forfar, Fife, and others of the midland counties. In order to study alpine species I made a special tour among the highest of our Scotch mountains in the summer of 1856. I then visited the Braemar Highlands, Ben Lawers, Ben Nevis, and the Coollin Hills, in Skye. I have likewise studied the lichens of Don, now in the possession of Mr M'Nab, of the Ptoyal Botanic Garden, Edinburgh; the lichens collected by Maughan, M'Millan, and others, in the Herbarium of the Botanical Society of Edinburgh; those collected by the late Alexander Menzies, in the Menziesian Herbarium belonging to the Botanic Garden of Edinburgh; those collected by Borrer, Hooker, Carmichael, Gardiner, and others, in the magnificent Hookerian Herbarium at Kew; and I have also examined the valuable herbarium of the University of Edinburgh, under the care of Professor Balfour, and the herbarium of Dr Greville.

Comparative Anatomists have long been desirous to obtain detailed information on the Placentation of the Sloths. The only observations on this subject which appear to have been made up to this time have been recorded by Professor Rudolphi of Berlin, and Dr C. G. Carus of Dresden. Rudolphi in the course of some remarks on the structure of the umbilical cord in Bradypus tridactylus incidentally mentions that the placenta was cotyledonary as in the Ruminants. Carus figures the placenta and an almost mature fœtus of a B. tridactylus which came into his possession in 1830. He gives no description, however, of the specimen, but contents himself with a brief explanation of his engraved figures; in the course of which he says, that the specimen seemed to him important on account of the length of the umbilical cord, and the form of the cotyledons, which did not project, as is usual, outwards, but towards the inner face of the ovum, a peculiarity which had not yet been observed and described.

Hauy, and other mineralogists, observed the two colours which are visible in several varieties of fluor-spar. He regarded the two tints as complementary, and explained them, as he did every other analogous phenomenon, by a reference to the colours of thin plates. In describing a species of dichroism noticed by Dr Prout in the purpurates of ammonia and potash, Sir John Herschel ascribes the green reflected lights “to some peculiar conformation of the green surfaces producing what may be best termed a superficial colour, or one analogous to the colour of thin plates, and striated or dotted surfaces.” And he adds—“A remarkable example of such superficial colour, differing from the transmitted tints, is met with in the green fluor of Alston Moor, which, on its surfaces, whether natural or artificial, exhibits, in certain lights, a deep blue tint, not to be removed by any polishing.”

Detached petioles and their branches are described under the name Lyginorachis arberi sp. nov. In their anatomy they resemble the petioles of Rhetinangium arberi Gordon, a presumed Pteridosperm. Two specimens show preparation for dichotomy. Others are interpreted as rachides probably formed by dichotomy of petioles. In cross section such rachides show the presence of pinna-traces arising alternately and marginally from the V-shaped vascular bundle. The pinna bundles are also V-shaped but have only three corrugations in section. Cylindrical pinnules are borne on the pinnæ.

L. kidstoni sp. nov. is a smaller petiole with a less corrugated and C-shaped vascular bundle. Both species are associated with seeds of Genomosperma.

There are several problems of great practical importance in electro-magnetic measurements, in which the value of a quantity has to be calculated by taking the sum of the logarithms of the distances of a system of parallel wires from a given point. The calculation is in some respects analogous to that in which we find the potential at a point due to a given system of equal particles, by adding the reciprocals of the distances of the particles from the given point. There is this difference, however, that whereas the reciprocal of a line is completely defined when we know the unit of length, the logarithm of a line has no meaning till we know not only the unit of length, but the modulus of the system logarithms.