The ellipsoidal wave equation is the name given to the ordinary differential equation which arises when the wave equation (Helmholtz equation) is separated in ellipsoidal co-ordinates. In this paper, solutions of the equation are expressed as Neumann series (series of Bessel functions of increasing order).

A ring epimorphism θ:A →B extends in a natural way to a homomorphism γn: GLn(A)→GLn(B) and, when A is commutative, to a homomorphism σn:SLn(A)→SLn(B), where n ≧ 1. In this paper we consider the question: when are γn and σn surjective (or non-surjective)?

§1. The main object of this paper is to point out a method of applying hydrodynamic solutions already obtained to the solution of problems relating to flexural vibrations of thin elastic rods.

It is well known that pseudomorphic changes take place with many minerals. These changes may be either by alteration or displacement. In the case of carbonate of lime they are generally of the former order.

Among other work conducted at the Marine Station, Granton, during the past year, a number of experiments were instituted with the view of showing how far carbonate of lime was influenced in this direction by metallic and other salts.

Corals, preferably the more porous and soft varieties, were selected for this purpose, and these were exposed to the action of solutions of the following salts:–Chloride of manganese, sulphate of iron, chloride of zinc, chloride of chromium, nitrate of nickel, nitrate of cobalt, nitrate of copper, nitrate of lead, chloride of mercury, chloride of tin, nitrate of silver, phosphate of ammonia.

The pressure of ethylene in equilibrium with solid iodine and solid ethylene di-iodide was measured at temperatures between 10°C and 65°C.

The vapour pressure of undissociated ethylene di-iodide was measured at four temperatures between 15°C and 55° C.

From these results and the known vapour pressure of iodine equilibrium constants were calculated.

Some experiments were made on the rate of formation and decomposition of ethylene di-iodide.

We desire to thank Professor Sir James Walker and Professor Kendall for their interest in our work, and Imperial Chemical Industries, Ltd., for a grant towards the cost of apparatus.

This instrument consists of a close spiral of insulated copper wire bent into the form of an anchor ring, so as to form an endless solenoid. The spiral is placed in a rectangular groove turned on the edge of a wooden or brass ring of suitable thickness and diameter. Short lengths of wire at both ends of the copper spiral are left straight. These, after being well insulated, are twisted together and led to two terminals, which serve as electrodes. The ring containing the spiral is fixed on a base board with its plane vertical, and at right angles to the magnetic meridian, when the instrument is in use. A short magnet, rigidly attached at right angles to the lower end of a stiff wire, is suspended from a silk fibre, so that its centre is in the circular centre line of the anchor ring.

An opportunity for examining the Pituri of Australia was afforded to the author by Dr Bancroft of Brisbane, who, in 1877, gave him for that purpose specimens of dry broken leaves of the plant, in the form in which it is used by the natives, and also a small quantity of watery extract.

After describing its use by the natives of Australia, the author advanced reasons in support of Von Mueller's opinion, that Pituri is obtained from Duboisia Hopwoodii, and that this plant should be placed in the Solanaceæ.

In a recent paper on the fæcal pellets of the Anomura, pellets were described from a series of Galatheidea, Paguridea and Thalassinidea, but at that time no Hippidea were available. Since then, through Professor J. H. Orton, I have obtained specimens of Hippa asiatica from Madras and have prepared sections of their pellets. As the latter form an interesting addition to the series of curious pellets, apparently peculiar to the Anomura, a special description of their structure seems to be justified.

A few words in explanation are needed. In my summer course of lectures on Medical Psychology and Mental Diseases delivered in the University, I have to investigate the human mind in its practical relations to the body, and especially I have to teach how each influences the other, so that the physician, or any intelligent person, may be able to modify these relations beneficially. The starting-point in these inquiries is the fundamental fact of experience, that no changes in the mind or the consciousness of whatever kind can or do arise, or continue, without a corresponding series of changes somewhere in the brain-tissue.

During a visit to Scotland this autumn I had the opportunity of meeting Dr John B. Simpson and of discussing with him the desirability of definitively dating, by varve-measuring, the interesting ice-oscillation which he had described from the southern slope of the Scottish Highlands (1933).

The author stated that during summer, in neap tides, the stream flows from the Atlantic into the Minch all day, but from the Minch into the Atlantic all night. In winter this was reversed, the stream flowing through the Sound of Harris from the Minch into the Atlantic all day, but from the Atlantic into the Minch all night.

In spring tides, both during summer and winter, the stream comes in from the Atlantic during the greater part of the time the water is rising, and flows back into the Atlantic during the greater portion of the fall of the tide.

The taxonomic value of hair has long been recognised. The different types of human hair have been made use of as a basis for classification of the varieties of Man by Primer Bey and many others, while Waldeyer in his Atlas has described briefly the hair characters of well known members of the Mammalian orders. In the present paper it is proposed to deal with hair within the limits of a single family, that of the Equidæ, and to describe certain peculiarities in the hairs of members of that group, which the author is of opinion are probably of specific value. But before dealing with the hair characters by which the species may be distinguished from one another, something must be said about those of the group as a whole.

§ 1. Notation.—Suppose that a0, a1a2,… are real constants, such that, for some fixed p (≥1), the series is convergent. It is a consequence of the generalised Riesz-Fischer Theorem that there exists a function f(t) L1+p over ( – 1 , 1), of which

is the Fourier Series.

The first instalment of this part of my paper deals mainly with the theory of the behaviour of mixtures of CO2 and N, for which some remarkable experimental results were given by Andrews about 1874. His full paper, so far as he had drawn it up for press, was published posthumously in the Phil. Trans, for 1886, and is reprinted in his Scientific Papers, No. L. One special reaaon for the introduction of this question at the present stage of my work was the desire to attempt a correction of Amagat's numbers, for the (very small) admixture of air with his CO2. The virial equation for a mixture is formed on the same general principle as that I employed for a single gas. There are, of course, more undetermined constants :—and, unfortunately, the data for their determination are barely adequate. The general results, however, agree in character with those described by Andrews :—the particular phenomenon which is most closely studied being the increase of volume, at constant pressure, when the gases (originally separated by the liquefaction of one) were allowed to diffuse into one another.

Adolf Ritter von Baeyer was born on October 31, 1835, in Berlin. His interest in chemistry began at the early age of nine, when his father gave him a copy of Stöckhardt's Schule der Chemie. Subsequently he studied under Bunsen at Heidelberg, and also under Kekulé, whom he followed to Ghent, and whom he always considered to be his real teacher. In I860 he returned to Berlin, and became Privatdozenten at that University. From this day onwards he published numerous papers. After three years spent in Strassburg as Professor of Chemistry he finally settled at Munich, where most of his chemical researches reached maturity. The influence Baeyer exerted in the development of chemical science, and especially of organic chemistry, was greater probably than that of any other single man, for almost every professor of chemistry now in Germany passed through his laboratories at Munich and received a stimulus there from the enthusiastic head.

M. Melitensis is virulent to a greater or less degree for all the usual laboratory animals — guinea-pigs, rabbits, rats, mice, dogs, and monkeys — and by means of suitable passages its virulence for any particular species can be considerably exalted.

Dana, in his Report on the Crustacea of the North Atlantic Exploring Expedition, described a number of genera founded on larvae of various Crustacea. Of these genera Calyptopis, Furcilia and Cyrtopia were shown by Claus in 1863 to represent three stages in the development of the Euphausiidas. Metschnikoff, in 1869, described a still earlier stage under the name of Metanauplius; and in 1871 the same investigator was enabled to show that the young Euphausiidse are hatched as true Nauplii, having a rounded body and three pairs of swimming appendages.