At the opening of another session it seems to me not inappropriate to refer to the question of the relation of science to industries and to education. Not much that is new can be said on this theme. The neglect of science by the Government and the people and the persistent indifference to scientific training and methods have been exposed by prominent scientists for many years. Repeated appeals and warnings have had little or no effect. But this world war has, at last, aroused the Government and the practical Briton to realise that success in war and prosperity in peace under modern conditions depend upon the application of scientific methods, and the development of research in relation to the industries.

Emil Clement Jungfleisch was born in Paris in 1839. He devoted himself to chemistry and pharmacy, and in 1869 became Assistant to Berthelot, whom he succeeded in 1876. He has made numerous contributions to organic chemistry, and for his work on the different forms of tartaric acid was awarded the Jecker Prize of the Academy of Sciences. One of his latest contributions was a study of gutta-percha, in which he showed that the leaves of the plant could be used as a source of the material instead of the stem.

The solution of the common quadratic

which is usually written

is, when expanded,

This expansion will be found to be the work of the operator each term being derived from its predecessor by this operator's agency, so that the whole solution may be written

Descended from marine ancestors, Ligia oceanica, like other members of the sub-order (Oniscoidea or “slaters”) to which it belongs, has adopted a terrestrial mode of life. The other Oniscoidea have spread inland, invading regions far from the sea. Ligia, known as the sea-slater, is confined to the coastal fringe, and may possibly form a link between marine isopods and the more truly terrestrial forms.

(1) Ligia, like other iposods, moults in two stages. First the coverin of the abdomen with that of the posterior three thoracic segments is es uviated. About four days later the anterior covering is thrown off. Th external changes that occur in the cuticle as it ages, and the behaviou of the animal during moult, are described.

(2) At the moult the cuticle splits in two main directions: (i) transvers between the fourth and fifth (free) thoracic segments; (ii) longitudina at the coxotergal junctions of (free) thoracic segments 2 to 7, there being no coxotergal split in segment 1. Coxotergal splitting is an arthrostracai if not a peracaridan, feature.

(3) Ligiæ that have fasted for many weeks in sea-water may still moult normally. It follows that onset of the moult is determined by an underlying cyclic change, not as Réaumur suggested by simple growth of the animal. A second moult during the period of fast was not observed.

1. Each walking leg of Ligia shows three prominent flexures arranged alternately in one plane. Generally speaking, the planes of flexure of the whole series of seven limbs are transverse to the body, the basipodites flexing medially; this arrangement, here called isopodan limb-taxis, is associated with clinging power.

2. In Amphipoda and in Tanaidacea there are likewise three chief flexures in the limb, which are also arranged tri-alternately and in one plane. In the Tanaidacea the basipodites project laterally not medially. In the Amphipoda the basipodites flex antero-posteriorly. Tanaidacean limb-taxis seems to be the primitive form.

3. The tri-alternate flexion-complex in each limb of these Peracarida, as well as in certain limbs of Cumacea, is a reptant feature; so is the separation of the seven limbs into two opposing groups: an analogy with the limbs of reptant vertebrates is here traced. By simple inspection it is usually possible to say if a crustacean limb used for swimming has been secondarily modified from a reptant limb.

4. The flexion-complex in the limbs of reptant Eucarida is neither tri-alternate nor uniplanar as in the limbs of reptant Peracarida. This distinction is of more importance than that suggested by Boas, which relies upon the amount of flexion possible at the mero-carpal and at the carpo-propodal articulation respectively.

5. The Peracarida, like the Decapoda, may be divided into natant and reptant forms, with intermediate links. Of the reptant forms only those with isopodan or amphipodan limb-taxis have shown themselves capable of adopting a land life.

6. It is suggested that Phreatoicus may in progression employ its posterior peraeopods or its pleon in the same way as a Gammarus. Should it be found that the animal does so, one could formulate additional correlations between structure and function; these would involve vertical pleural plates, uropods, and the number of free segments in the pleon.

7. Considerations relating to limb flexures and limb-taxis have been tentatively applied to the classification of the Isopoda.

8. The different forms of limb-taxis in the Peracarida and certain features involving the flexion-complex, present problems analogous to the rotation and torsion that occur in the fore-limb of a developing mammal.

9. In a discussion on homology and analogy it is pointed out that homology in the sense of homoplasy (Lankester) cannot be effectively distinguished from analogy. The systematic study of analogies would appear to be more worthy of consideration than is generally acknowledged.

§ 1. Ordinary and singular periodic solutions of a dynamical system. — The present paper is concerned with the motion of dynamical systems which possess an integral of energy. To fix ideas, we shall suppose that the system has two degrees of freedom, so that the equations of motion in generalised co-ordinates may be written in Hamilton's form

where (q1q2) are the generalised co-ordinates, (p1, p2) are the generalised momenta, and where H is a function of (q1, q2, p1, p2) which represents the sum of the kinetic and potential energies.

The following study of the diet of labouring class families in Glasgow was made as part of an investigation upon the etiology of rickets at present being carried out in the Physiological Department of the University of Glasgow. But the information gathered by Miss Lindsay in her study of the diet of the same class in 1911–1912 makes possible a very interesting comparison between the conditions of living then and under the present war conditions, and the fact that these studies extended over three periods—(1) Summer of 1915, (2) Winter of 1915, (3) Spring of 1916 —enables some idea of the progressive effects of war conditions to be obtained. Forty families have been studied.

The following is a summary of the more important conclusions which have been put forward in this paper:—

1. The Nature and Distribution of Stratus in Anticyclones.

(1) Stratus clouds have an adiabatic temperature gradient below them, and a reversed gradient above them; within the cloud the gradient is usually adiabatic. The same relations hold for well-defined layers of haze.

(2) On the northern and eastern sides of anticyclones there is nearly always a layer of stratus, or of haze with cloud patches; the height of this layer varies between 3000 and 6000 feet above the surface, but the level is usually the same over a very large area.

(3) Stratus is common in winter on the southern sides of anticyclones.

In 1859 the scientific world was startled by the publication of Charles Darwin's book on the Origin of Species, a work in which he advocated the doctrine that the various species of animals and plants, now inhabiting the globe, have been evolved by means of secondary causes from pre-existing and less differentiated forms of life—a process which he designated by the name of “Natural Selection.” This theory is founded mainly on the struggle for existence which all living organisms have to undergo, not only against their natural enemies, but the overcrowding of their own species. The intensity of this contest becomes apparent to any careful observer who takes the trouble to look beneath the surface of his environment at the marvellous activity of the agencies at work in producing the countless living organisms which now tenant the earth. The most striking feature of these genetic operations, besides the astonishing number of seeds, fruits, eggs, young animals, etc., which come so profusely into existence, but of which so few come to maturity, is that those who survive have apparently no higher purpose in life than the propagation of their own species. Notwithstanding the activity of the never-ending agencies by which life is thus kept up as a going concern, the stock of wild animals, i.e. animals not in a state of domestication, seldom vary from year to year. The consequence of so profusely overcrowding the environment with the offspring of plants and animals is the premature death of the vast majority.

(1) The adsorption of sulphur dioxide by blood charcoal at –10° C. was studied, and measurements were taken of the amount adsorbed, the pressure, and the isothermal heat of adsorption at constant volume.

(2) The adsorption isotherm is a typical vapour adsorption curve, and runs the same course as that found by Trouton for the adsorption of water vapour.

(3) The heat of adsorption curve passes through a minimum and a maximum, and finally runs parallel to the adsorption axis. A tentative explanation of this is offered.

In conclusion, the author would seek to express his thanks to Professor F. G. Donnán, F.R.S., for his advice given in the course of these experiments which were performed in 1913–14 in the Chemical Laboratories, University College, London.

In this communication an attempt is made to correlate the different members of the Lower Carboniferous Limestone Series of the East of Scotland with what has been chosen as the type section at Hurlet, near Paisley. For close on fifty years Scottish geologists have been endeavouring to correlate the Lower Carboniferous Limestones of Fife and the Lothians, and in general the Carboniferous Rocks of Scotland, with the Hurlet Section, but up till the present time the various attempts have only met with a partial success, the reason for this being, that our knowledge of the Hurlet section has by no means been either sufficiently detailed or accurate enough to admit of comparison with other widely separated Scottish sections. The important question also arises as to what extent the Hurlet Section can be considered as typical of the group of deposits as a whole.

The arithmetical mean of similar meteorological observations is usually regarded as their representative value. The object of this paper is to show that in a certain case this assumption is not borne out by observations.

In communications to this Society in 1893 and in 1912, and in other papers, I have shown that some of the nuclei in the atmosphere have a power of condensing water vapour even when the air is unsaturated, owing to the material of which they are composed having an affinity for water. All kinds of nuclei have an affinity for water vapour, and by their surface action condense some water at all degrees of humidity, so causing increase in their size and hazing effect; but the particles having an affinity for water condense very much more and cause fogs in. unsaturated air. In the present communication I intend to deal with the more common form of nuclei—that is, those which have little or no chemical affinity for water—and with those nuclei which require supersaturation to cause condensation; the reason for this investigation being some statements which have appeared in scientific journals in this country and abroad regarding the nuclei counted by the condensation method. It has been definitely stated that the greater number of the nuclei counted are not dust particles but only ions, or aggregations of them. It therefore seemed desirable that further investigation should be made into the subject to see if there was anything to support this ionic theory of the condensation nuclei in the air, and at the same time to inquire into their origin.

1. Advantage has been taken of the large size of Glyptonotus to study certain structural features, especially skeletal, which cannot be so readily investigated in smaller isopods. Where possible, an attempt has been made to correlate structural peculiarities with functional use.

2. The Legs.—The peculiar articulation, analogous to a spheroidal bony joint, between the coxopodites and basipodites of the thoracic limbs, is described in detail. A comparison is instituted between the full flexion-complex of the isopodan and of the brachyuran walking limb. The peræopods are contrasted with the gnathopods of Glyptonotus, and functional peculiarities pertaining to each group of limbs are discussed.

3. The Peræon.—The medial split in the thoracic sternites is interpreted as a device for allowing of distension of the body, say, after a meal. The arched thoracic somites articulate with each other in a special way, not by a crossed articulation, like that in a pair of scissors, but by a rocker articulation, like that in a spring clothes-pin; this combination of arch and rocker articulation is interpreted as a means of preventing change of internal volume in body flexion. The phenomena pertaining to the moulting process throw light upon the numerical grouping of the successive fusions of coxæ with somites which have occurred in isopods.

4. The Pleon.—The pleon consists of four movable portions, the last four of the seven constituent pieces being welded together. Of the four fused segments, only the first has a complete sternite, like those of somites 1, 2, and 3. In the skeleton of the pleonic floor a wide opening is thus left posteriorly, which is closed by a diaphragm of soft cuticle; part of this diaphragm is elevated into two long parallel folds or valves, one on each side of the anus.

5. The Pleonic Appendages.—The protopodite of each of the anterior three pleopods is composed of two complete pieces; a third piece more proximally situated is interpreted, not as evidence of an additional primitive segment, but as a secondary development in the articular membrane. The uropods have acquired their present position by a forward rotation of the sternite of the sixth primitive somite, and the gill-directed surface of the uropod corresponds to the posterior surface of the pleopods. It follows that what has commonly been called the exopodite of the uropod is a real exopodite. In addition to the pleopods, the internal walls of the whole uropodal chamber subserve a respiratory function.

6. The Cephalosome.—Two thoracic somites are fused with the head to form a cephalosome. By welded inturnings of the anterior border of these two and of the posterior border of the mandibular cephalic somite a strong internal bracing is formed. The tergites of the maxillary somites have apparently disappeared from the dorsal aspect of the cephalon; the endo-skeletal structures described by Lloyd in Bathynomus, and by him named “sternal alæ,” functionally correspond to these tergites in so far as they serve for attachment of muscles for the maxillæ. These “sternal alæ” (which also appear to form a covering for the maxillary excretory gland) with other ventral endoskeletal structures are described in detail. All are rigidly fixed to the maxillo-sternal framework, which is capable of independent movement.

7. The Alimentary Canal.—The foregut of Glyptonotus is not a gastric mill; the muscle-provided involutions of its wall (exactly analogous to those in Bathynomus) are concerned simply with onward propulsion of the food, i.e. with swallowing. Between the midgut and the hindgut, the two opposed ends of which are not in exact alignment, is a strongly contractile part of the gut, which acts as a sphincter. The hepatic cæca could not be examined. Glyptonotus is carnivorous.

8. The Eyes and the Chromatophore-System.—By experiment on colour change of Idotea it has been shown that the eye of this animal acts as a double mechanism, the ventral half being functionally separable from the dorsal. Glyptonotus has retractile chromatophores, and probably undergoes colour change in accordance with différent modes of eye illumination. Its eye is divided into two entirely separate parts, one lying on the dorsal the other on the ventral aspect of the cephalon.

The cost of providing the illustrations which accompany this paper was defrayed by a grant from the Earl of Moray Endowment for the promotion of research in the University of Edinburgh; and the expense of preparing the blocks was defrayed by a grant from the Carnegie Trust.

I have to record my thanks to Dr W. S. Bruce, not only for the material provided, but for information relating to the quarters inhabited by Glyptonotus.

In the last paper of the present series it was pointed out that the articulations between the thoracic somites of Glyptonotus are so designed as to minimise change of internal volume during flexion and extension of the body. The pleon of the long-tailed Decapoda forms a system comparable to the series of thoracic somites of Glyptonotus; and as the macrurous decapods execute very rapid strokes of the pleon, one might expect that change of volume during movement is slight, for otherwise there would be waste of energy owing to inertia. It was decided to examine the matter experimentally.

1. In cases of gas poisoning in which symptoms persist there is an increase in the number of lymphocytes, relative and absolute, in the circulating blood. In slight cases this may not be beyond the normal limits, or in excess of what may be met with from other causes. In any marked case, however, the change is sufficiently striking to be of some importance in cases where the medical officer is in doubt as to the reliance to be placed upon the statements of men complaining of having been gassed.

2. The blood change is elicited by a differential count of the leucocytes, and it may be taken that a count in which the percentage of lymphocytes approaches that of the polymorpho-nuclear leucocytes indicates that the patient is still suffering from the effects of gassing, provided always that there is no other complicating disease present which might produce a similar change. A slight relative lymphocytosis is not an uncommon finding, and particularly in men from overseas, so that no great reliance can be placed upon the sign unless it is marked, i.e. unless the percentage of lymphocytes approaches closely that of the polymorpho-nuclear cells.

3. The cell which is increased is the ordinary small lymphocyte of the blood. There may be, in some cases, a diminution in the number of polymorpho-nuclear leucocytes which will, of course, accentuate the sign, but the increase of lymphocytes is an absolute one. Moreover, it appears in cases with a high leucocyte count.

4. The change is one which develops early, probably within a month of the gassing, and continues for a long time, in cases with persistent symptoms for at least eighteen months.

5. The change appears to be independent of the kind of gas, and it is shown by patients exhibiting many varieties of symptoms.

6. It is not clear what the change is due to, but from analogy with other conditions exhibiting a lymphocytosis it is probable that chronic inflammatory change in respiratory and gastric mucous membranes is at least a factor.

In 1888 Dr Thomas Muir gave the following theorem:—

Theorem A.—If any two determinants A and B of the nth order be taken, and from these two sets of determinants be formed, namely, first, a set of nCr determinants, each of which is in r rows identical with A and in the remaining rows with B; and, secondly, a set of the same number of determinants each of which is in r columns identical with A and in the remaining columns with B, then the sum of the first set of determinants is equal to the sum of the second set.

A characteristic feature of the plateau of Cambrian Limestone in the neighbourhood of Inchnadamff is the occurrence in it of swallow-holes, caves, and subterranean channels which are intimately associated with the geological history of the region. The valley of Allt nan Uamh (Burn of the Caves), locally known as the Coldstream Burn, furnishes striking examples of these phenomena. One of the caves in this valley yielded an interesting succession of deposits, from which were collected abundant remains of mammals and birds. The discovery of bones of the Northern Lynx, the Arctic Lemming, and the Northern Vole among these relics, and the collateral evidence of the materials forming some of these layers, seem to link the early history of this bone-cave with late glacial time, or at least with a period before the final disappearance of local glaciers in that region.

The equation in linear vector functions

was proposed by Tait, and an elegant solution was obtained by him which does not require a determination of the axes of ω. He showed that upon this equation depends the separation of the pure and the rotational parts of a homogeneous strain. The problem appears to be interesting also from the point of view of algebraic analysis. The number and character of the solutions is more varied, given different types of the function ω, than we might at first suppose. In fact there are two forms which may be assigned to M such that the equation does not permit of solution. Otherwise the number of solutions.