The first part (5) of a study of the quantitative distribution of the bottom-fauna in Scottish waters, and of the natural faunistic divisions of the North Sea and adjacent areas, dealt with the distribution of the molluscs in the North Sea. In this paper the echinoderms from the same area are treated on similar lines. In addition the natural faunistic divisions, as shown by the distribution of the dominant species of molluscs and echinoderms, and the validity of Petersen's community concept as applied to the North Sea, are discussed.

Reference should be made to the earlier paper for information concerning the methods of collecting, the area covered by the Scottish surveys, similar surveys carried out by other workers in the remaining parts of the North Sea, the number of hauls in each square, and other introductory matters.

1. The method for the solution of questions in the theory of probabilities applied in this paper, is that which was developed by the author in a treatise entitled, “An Investigation of the Laws of Thought, on which are founded the Mathematical Theories of Logic and Probabilities.” The practical object of the paper is to deduce from that method certain conclusions relating to the combination of testimonies or judgments. Beside this, however, it will have a speculative reference to some more general questions connected with the theory of probabilities; and especially to the following question, viz.: To what extent the different modes in which the human mind proceeds, in the estimation of probability, may be considered as mutually confirming each other,—as manifestations of a central unity of thought amid the diversity of the forms in which that unity is developed.

§ 1. A short description of some temperature observations in the Madüsee has been published in the Scottish Geographical Magazine for December 1910, and this communication aims at giving a more complete description of the observations with a first attempt at the mathematical discussion of oscillations at the surface of separation of two liquids in a basin of varying depth and cross-section.

In Scotland, the base of the Ballagan Formation has traditionally been placed at the first grey mudstone within a contiguous Late Devonian to Carboniferous succession. This convention places the Devonian–Carboniferous boundary within the Old Red Sandstone (ORS) Kinnesswood Formation. The consequences of this placement are that tetrapods from the Ballagan Formation were dated as late Tournaisian in age and that the ranges of typically Devonian fish found in the Kinnesswood Formation continued into the Carboniferous. The Pease Bay specimen of the fish Remigolepis is from the Kinnesswood Formation. Comparisons with its range in Greenland, calibrated against spores, show it was Famennian in age. Detailed palynological sampling at Burnmouth from the base of the Ballagan Formation proves that the early Tournaisian spore zones (VI and HD plus Cl 1) are present. The Schopfites species that occurs through most of the succession is Schopfites delicatus rather than Schopfites claviger. The latter species defines the late Tournaisian CM spore zone. The first spore assemblage that has been found in Upper ‘ORS' strata underlying the Ballagan Formation (Preston, Whiteadder Water), contains Retispora lepidophyta and is from the early latest Famennian LL spore zone. The spore samples are interbedded with volcaniclastic debris, which shows that the Kelso Volcanic Formation is, in part, early latest Famennian in age. These findings demonstrate that the Ballagan Formation includes most of the Tournaisian with the Devonian–Carboniferous boundary positioned close to the top of the Kinnesswood Formation. The Stage 6 calcrete at Pease Bay can be correlated to the equivalent section at Carham, showing that it represents a time gap equivalent to the latest Famennian glaciation(s). Importantly, some of the recently described Ballagan Formation tetrapods are older than previously dated and now fill the key early part of Romer's Gap.

The economic importance of the leaf-roll disease of potatoes has been recognised for a number of years owing to the fact that its incidence leads to a heavy reduction in marketable ware. The annual loss to potato growers in England and on the Continent from leaf-roll amounts to a high figure, but the disease is not of such prime importance to the Scottish cultivator as certain other diseases of the virus class to which the potato is prone, namely, mosaic and crinkle.

Many Ordovician trilobites possess morphological structures on the cephalon, the pygidium and sometimes also on the thoracic segments, which interlock during enrolment. These coaptative devices, also known in living arthropods, are functional, inherited, and seem to remain stable at the species level. Significant evolutionary changes in coaptative devices occur throughout time within the genera Placoparia (Pliomeridae) and Crozonaspis (Dalmanitidae). New data are presented which have relevance for the details of the coaptative structures in Placoparia (Coplacoparia), and for the classification of the dalmanitid species morenensis and dujardini. In some species of Crozonaspis and in Placoparia (Coplacoparia), interlocking structures prevent the possibility of shearing between cephalon and post-cephalic exoskeleton.

Many of the earlier accounts of the group of Crustacea, known as Isopoda, suffer from want of more detailed diagnoses and figures. To some extent this has been remedied during recent years by the authors of different monographs, but there are still many families which remain somewhat obscure, or only partially understood, owing to the above-mentioned cause. Such a family is the Idoteidæ.

In the present communication I propose to revise the diagnoses of the British genera and species, to set forth in greater detail than has hitherto been done their structure, illustrating the same, and to discuss the classification and affinities of the family as a whole.

Triarthrinid trilobites are described from the Middle Ordovician Andersön Shale and Örån Shale of Jämtland, central Sweden. The faunas include at least five species, belonging to two genera, Porterfieldia Cooper 1953 and Triarthrus Green 1832. Porterfieldia is represented by a single species, Porterfieldia humilis (Hadding 1913), while at least four species belong to Triarthrus: T. freji Thorslund, 1940, T. jemtlandicus Linnarsson, 1875, T. latissimus nom. nov. and T. linnarssoni Thorslund, 1940. P. humilis is found only in the lower Andersön Shale, equivalent to the Hustedograptus teretiusculus Zone. T. freji, T. jemtlandicus and T. latissimus occur frequently in the upper part of the Anderson Shale, which comprises the Nemagraptus gracilis Zone, and probably also the lower part of the Diplograptus multidens Zone. T. linnarssoni occurs throughout the Örån Shale (mainly Dicranograptus clingani Zone). T. jemtlandicus and T. aff. linnarssoni are also sporadically present in the lower and middle parts of the Oran Shale. Almost all growth stages of T. latissimus, from the anaprotaspid stage and onwards, are represented and the ontogeny is described. The early stages are, however, comparatively uncommon.

The exact horizon occupied by the Shetland strata of Old Red Sandstone age, and their relation to the corresponding series in the north of Scotland, have long been subjects of considerable speculation and much uncertainty. While their resemblance to the flag-stones of Caithness and Orkney was generally recognised, more definite palæontological evidence was required for correlation purposes, and the barrenness of the islands in this respect has been commented on again and again. Up to quite recent years the only fossils found in Shetland were fragmentary plant remains of doubtful affinities, and the small crustacean Estheria membranacea; the abundant ichthyolites which characterise the beds of Caithness and Orkney seemed here to be wanting, and the dearth of fossil evidence is reflected in the conservative and guarded opinions as to the position to be assigned to the series.

The fossils dealt with in this part of our memoir should have been included in the first paper of the series had it been possible to treat the plants described in the order of the complexity of their structure. Unfortunately, however, the specimens did not reach our hands until Part I. was already published; and since we were no longer able to place them in their proper position in the sequence already embarked upon, it was decided to defer their treatment until the conclusion of the memoir.

While collecting specimens of Diplolabis römeri (Solms) at Pettycur about three years ago, I discovered several blocks of stone containing numerous petrified fragments of another Zygopterid fern—Metaclepsydropsis duplex (Williamson). Two of the blocks were found to be parts of one large mass, and the petrifactions could be traced from the one block into the other. In size the complete mass must have been about 3 feet × 2 feet × 2 feet. The larger portion had to be broken into two before it was possible to remove it. Another block containing similar specimens was obtained later, but the preservation was so poor that the whole of the material was discarded.

The material brought home by the Scotia and available for examination consists in all of fifty-five samples of deposits from the floor of the ocean. The majority of these consist of true “deep-sea” deposits, i.e. material from depths of over 100 fathoms; but, for convenience, the description of a few samples from shallow waters (mostly in the neighbourhood of the S. Orkneys) is also included in this report.

The number of deposits is considerably less than the number of soundings taken by the Expedition, because, for various reasons, a sample of deposit was not obtained in every case where a sounding was taken.

The investigations recorded in the present paper have been carried out at various times during the last six years. A number of the observations on aquatic Oligochæta were made some time ago in India, and, along with some of the theoretical conclusions, formed Part IV. of a Thesis (“Studies on the Aquatic Oligochæta of the Punjab”) presented in 1909 for the D.Sc. degree of the London University. This division of the paper has been considerably extended as a result of further investigations on Indian freshwater forms, and on the littoral Oligochæta of the Clyde, the latter carried out at Millport in 1909. The portion of the present paper which is concerned with the Polychæta and smaller groups represents work done in 1909 at Millport, and in 1912, during my occupancy of the London University table, at the Plymouth Laboratory.

The ensuing paper forms part of a series of researches respecting the consequences of an hypothesis called that of Molecular Vortices, the object of which is to deduce the laws of elasticity, and of heat as connected with elasticity, by means of the principles of mechanics, from a physical supposition consistent and connected with the theory which deduces the laws of radiant light and heat from the hypothesis of undulations. Those researches were commenced in 1842, and after having been laid aside for nearly seven years, from the want of experimental data, were resumed in consequence of the appearance of the experiments of M. Regnault on gases and vapours.

The investigation which I have now to describe, relates to the mutual conversion of heat and mechanical power by means of the expansion and contraction of gases and vapours.

Rare remains of tyrannosauroid dinosaurs from the Aguja Formation in West Texas indicate the presence here of a relatively gracile species, comparable in form and adult size to Appalachiosaurus or subadult albertosaurines, Gorgosaurus and Albertosaurus. Histologic analysis of one of the specimens indicates that the Aguja tyrannosaur attained an adult size substantially smaller than adult albertosaurines (700 kg, 6·5 m body length). The frontal bone is narrow with a wide orbital slot and a bipartite joint for the postorbital, features thought to be diagnostic of Albertosaurinae; but there is a tall sagittal crest and reduced parietal wedge separating the frontals on the midline, features thought to be diagnostic of Tyrannosaurinae. The tall sagittal crest may be a synapomorphy of Tyrannosaurinae, and the Aguja tyrannosaur is herein referred to that clade. However, the unique combination of character states exhibited by the frontal prevents confident attribution to any known species. The Aguja tyrannosaur provides further evidence that North American Campanian tyrannosauroids were remarkably diverse for such large predators, and that each species was apparently endemic to a relatively small geographic province.

Byne Hill, two miles south of Girvan, Ayrshire, is composed of Lower Ordovician igneous rocks which form partof the Girvan-Ballantrae igneous series. Byne Hill consists of serpentinized harzburgite, gabbro, diorite and trondhjemite which probably form a N.E.–S.W. elongated dome with trondhjemite occupying the core. There are transitional passages from gabbro into dioritic gabbro, diorite, quartz diorite and trondhjemite with no sharp contacts, and gabbroidal minerals and textures persist into the marginal hornblendic phases of the trondhjemite. The mineralogical changes are mainly progressive amphibolization and albitization of the gabbro accompanied by increases in SiO2 and Na2O. Geochemical culminations of FeO, MnO and P2O5 occur in the intermediate dioritic gabbro and diorites. Comparing the intermediate rocks with similar rock series from other areas suggests that mineralogical and chemical criteria do not always distinguish intermediate rocks of metasomatic origin from those produced by fractional crystallization. On Byne Hill the textural evidence suggests that the intermediate rocks are hybrids produced by reaction between crystalline gabbro and silicic sodium-rich solutions related to the trondhjemite, although there is evidence that the trondhjemite is itself metasomatic in origin. Serpentinization and rodingitization of the Byne Hill gabbro at contacts with serpentinite are described, and it is concluded that the gabbro was emplaced into the ultrabasic rocks prior to their serpentinization.

The present report deals with the whole of the Schizopoda and Stomatopoda in the Scotia collections, and with those Isopoda which were taken in localities outside the limits of Antarctica. I am indebted to the courtesy of Dr W. S. Bruce for the opportunity of examining and reporting on these collections. The report on the Antarctic Isopoda is being prepared by Mr T. V. Hodgson.

I also include a few notes on a small collection of Schizopoda which were taken by the Discovery on its outward journey to the South Pole, for the opportunity of examining which I am indebted to the kindness of Dr W. T. Calman, of the British Museum. These latter records are most appropriately included here along with those of the species which the Scotia captured on her outward journey, over very nearly the same ground.

Although only about 20m thick, the Andersö Shale contains one of the most diverse, if not the most diverse, late Middle-early Late Ordovician faunas known in Baltoscandia. It includes more than 20 trilobite species, more than 20 species of other shelly fossils, about 10 graptolite species, and about 20 conodont species. Based on its lithology, its geographical position near the foreland basin margin, and the presence of trilobites of the raphiophorid association and conodonts of the Periodon-Pygodus biofacies, this formation is interpreted to represent an outer shelf-upper slope (ramp) deposit laid down in moderately deep water. The co-occurrence of some widespread and biostratigraphically diagnostic conodonts, graptolites and trilobites makes it possible directly to compare distribution patterns of these fossils, establish ties between graptolite and conodont zones, and correlate the formation with units elsewhere in Europe, North America and China. Stratigraphically and faunally, the Andersö Shale is of particular interest in straddling the Middle-Upper Ordovician Series boundary as this boundary is recognised in the new global classification of the Ordovician System.

The fossiliferous bed in the Upper Comley Sandstone, described by Cobbold & Pocock (in 1934) as the ‘Paradoxides forchhammeri Grit’ and correlated by them with the Andrarum Limestone of the late Middle Cambrian (P. forchhammeri Stage) in Scandinavia, is shown to be a shallow-water development of the older punctuosus Zone (medial Middle Cambrian, P. paradoxissimus Stage). It is here re-named the ‘Rushton Brook Bed’. The trilobite fauna, formerly considered comparable with that of the Andrarum Limestone, is reviewed and found taxonomically distinct, the supposed similarities being attributable to facial and preservational factors.

1. A year ago last April, Prof. Tait proposed that I should undertake to derive from Mr Kirkman's polyhedral drawings the alternate ± knots of eleven crossings, thus doing for order 11 what had been done so admirably by himself in orders 8, 9, and 10.

2. The work has been a very protracted one, because of the great number of forms involved—more than three times as many as in all preceding orders combined. Mr Kirkman's manuscript contains 1581 forms, of which 22 are bifilar and 16 duplicates. I find from the remainder 357 knots with 1595 forms as shown in the following table:—

As this is an odd order, perversion doubles these numbers, making 714 elevenfold knots, with crossings alternately over and under.

3. It has been thought unnecessary to show upon the Plates more than one form of each knot; all, however, have been drawn. Knots of each class having the same number of forms are grouped together to make more simple the identification of a particular elevenfold. A small figure following the series number upon the plates indicates how many distinct forms each knot can assume. Knots 84, 357, and 2386 are misplaced.