Whaling companies have for some years successfully conducted a whale fishery off the shores of the South Shetlands, Graham Land, South Orkneys, and South Georgia, where the waters of the Antarctic mingle with the South Atlantic Ocean.

The optical rotation of a solution of sucrose in water was first measured by Biot (Mém., 1819, ii, 41) in 1819. He introduced the term “optical saccharimetry” for the method of estimation of sugar by measurement of its optical rotation.

In 1846, Dubrunfaut (Ann. Chim. Phys., 1846, xviii, 99) observed that the specific rotation of a freshly prepared aqueous solution of glucose decreased from an initial value of about + 110° to a constant value of +52°. The initial value being approximately double the constant value, he called the phenomenon “bi-rotation.” This term proved unsuitable in the case of other substances where a similar change of rotation took place, the initial and final values being rarely in the proportion of 2: 1; hence the expression “multi-rotation” came into use.

Part I of this work on Growth Periodicity (Proc. Roy. Soc. Edin., vol. xxxiii, Part I (No. 8), p. 85) dealt with the occurrence of a four-day periodicity in plant organs and with rhythm in roots. With reference to the latter, the following conclusions were deduced from various observations made up to that time:—

1. “Roots exhibit a periodicity under ordinary conditions of environment which differs from that of shoots.

2. “Owing to correlation, the root periodicity is affected by changes in the root rhythm, but to what extent has yet to be determined.”

Since then, numerous experiments have been performed to find out whether any correlation exists between the growth of the root and the shoot, and if so, the nature of such a correlation.

(1) If we seek to extend the definition of an orthogonant by making the square of each row equal to σ instead of 1, this fixed quantity will naturally be found to appear in the statement of almost all the properties of the determinant in question. It is therefore convenient and appropriate to call it the base of the orthogonant, and to speak of an orthogonant to the base σ or an orthogonant of base σ.

It is a simple matter to ascertain what modifications are necessary in the statement of the known properties of the ordinary orthogonant to make them applicable to the extended definition.

When a function has been expressed as a series of spherical harmonics with constant coefficients, the determination of these coefficients from given values of the function is in the general case one of the most complicated operations which can be set before the calculator.

Since Gauss first carried out these operations in a calculation of this kind, efforts have not been wanting to simplify them and make their frequent application possible. The most successful of all in this respect was Franz Neumann, who showed that by a suitable choice of the argument the calculation could be materially shortened.

§ 1. Object of Paper.—The chief object of the present paper is to establish the following theorem:

The functions of Lamé [that is to say, the doubly-periodic solutions of the differential equation

are the solutions of the homogeneous integral-equation

where η denotes an arbitrary constant.

(1) Homarus vulgáris, Eupagurus bernhardus, and Carcinus mœnas all form limb-buds or papillæ in the process of limb regeneration. These are covered by a chitinous envelope, and the observations here recorded show that their outer form and size are adaptations to the requirements of the animal. That of the lobster is straight, that of the hermit crab curved, while the shore crab has a papilla which may be folded on itself three times inside the envelope.

(2) Valvular action of the diaphragm at the breaking plane plays a greater part in the stopping of haemorrhage after self-amputation than clotting, and the dilatation of small vessels which pass beneath the epidermis detaches a layer of cells. This layer of epidermis proliferates from its free edges to form the new limb.

(3) A new diaphragm is the first structure laid down, and differentiation takes place from the base outwards. Muscle arises at the growing tip from cells proliferated from the old epidermis (an ectodermal structure), and the nerve grows outwards from the torn end by cell proliferation.

(4) Muscle-fibres are anatomically complete immediately before moulting. The fibrillæ are cross-striated and enclosed in a sarcolemma, but full functional activity does not come till several days after moulting, beginning with slow rhythmic movements. Sarcoplasm seems to be less plentiful than in the normal fibre.

(5) When moulting occurs the papilla is at once expanded to several times its previous size by valvular action, and the epidermis, previously composed of several layers of cells, now thins to a single layer, as is seen in the normal limb.

A necessary condition in any hydrodynamical problem is that the pressure exerted by the fluid at any point must always be positive, and be given by

C being a constant determined by the boundary conditions of the problem, ν the velocity, and ρ the density of the fluid, provided there are no external forces involved. Should the velocity at any point, however, be so great that the expression C — ρν2/2 becomes negative, the problem in this respect at least loses its validity as an approximation to actual fact. Now it can easily be shown that, in any form of potential streaming about a body with sharp edges, the velocity at the sharp edges becomes infinite, and the pressure therefore negative. The equations of motion of the fluid having been obtained on the assumption of continuity of motion, this suggests at once that some form of discontinuity of the fluid probably exists near the sharp edges.

The work embraces the results of the systematic examination, for fossil micro-organisms, of slides prepared from ironstones and ferruginous limestones from various districts of Great Britain.

Abundant traces were found in the Frodingham Ironstone of a fossil fungus allied to the modern Phycomycetes. This is named Phycomycites Frodinghamii. The traces include hyphæ, sporangia, and spores. These are described, measured, and photographed, and details of the life-history, so far as ascertainable, are given.

In some experiments on sodamide carried out at 200°, in which an attempt was made to use hydrogen as an indifierent atmosphere, it was found that a slow but constant evolution of ammonia took place. The sodamide being isolated from the glass tube in which it was heated, by silver foil, the formation of ammonia could not be due to a reaction between the glass and the sodamide.

(1) Determinations have been made, at 18° C, of:—(a) the specific electrical conductivity, (b) the percentage composition by weight, of a series of mixtures made by saturating, with sodium chloride, solutions of hydrochloric acid containing from 16 to 27 per cent, of hydrogen chloride.

(2) Within this range of concentration the salt-saturated acid has lower specific conductivity than the aqueous solution of hydrogen chloride alone, from which it may be supposed to be derived. Of the salt-saturated acid mixtures, that one has maximum conductivity which could be prepared by adding salt to hydrochloric acid containing 2·9 per cent, of hydrogen chloride. Of solutions of hydrogen chloride alone, in water, that containing 19·1 per cent, hydrogen chloride has maximum conductivity.

(3) The critical concentration of hydrogen chloride at which hydrochloric acid is able to affect the colour of cobalt chloride is changed, in the same sense as the concentration of hydrogen chloride corresponding to maximum conductivity is changed, by saturating the solution with salt.

(4) A new form of conductivity cell is described. It is specially suitable for solutions which are saturated with dissolved solid, or contain a volatile solvent.

The eye is sensitive only to light of wave-length 7600 to 4000 A.U. With the ordinary dry photographic plate and glass lenses we can get an effect down to wave-length 3300 A.U.; with the same plate and quartz lenses we can get an effect from a wave-length as short as 2000 A.U. The gelatine of the plate absorbs the wave-lengths immediately above this limit, and their effect is very faint. A camera fitted with a quartz lens can take a picture in which all the wave-lengths down to 2000 A.U. produce their share, and hence can extend the range of the eye another octave, but the disadvantage of this picture is that it integrates all the different colours. We cannot, for example, tell whether a mark is due to light of wave-length 3500 A.U. or 2500 A.U. Such a picture makes the ultraviolet appear the same as the visible would appear to a man with monochromatic vision. All the detail due to variety and wealth of colour is lost. Now if we could photograph the same objects in succession with monochromatic light of wave-length say 3500 A.U., 3000 A.U., 2500 A.U., and 2000 A.U., it is possible that a great amount of new detail might be obtained of the utmost value to science. It was with the purpose of obtaining monochromatic photographs in the ultraviolet that the present research was undertaken.

The object of this note is to obtain briefly the intrinsic equations of motion of a gyroscope, and to show how they lead immediately to the solution of a number of problems. So much has been written on the subject of the gyroscope that these equations are hardly likely to be new, but I do not remember to have met with them in their explicit form. Apart from their use as a basis for calculation, they have a simple interpretation which enables us to foresee the general character of the motion in cases where the actual calculation would be difficult.

The published determinations of the vapour densities of ammonium chloride are not consistent. Thus the percentage dissociation calculated from the observations at 300° to 323° ranges from 87 to 100; at 350°, from 83 to 100; and at 445°, from 89 to 99. The results also lack quantitative significance because they were nearly all obtained by the Dumas or the V. Meyer method. When the former method was used, the density was that at atmospheric pressure, although the temperature corresponded to a much higher vapour pressure. When the latter method was used, in most cases, for the same reason, the vapour was highly unsaturated. In a few instances the vapour pressure was less than one atmosphere, and the vaporisation could proceed only by diffusion of the vapour into the air contained in the apparatus.

Pelouze, as early as 1847, employed a method for determining nitrates in the commercial potassium and sodium salts, in which weighed quantities of the latter were boiled with ferrous chloride solution (obtained by treating a definite weight of iron wire with excess of hydrochloric acid), and afterwards the remainder of the ferrous salt was determined by titration of the diluted solution with potassium permanganate.

1. If a plastic body be subjected to a uniform change of shape, any two equal, similarly placed cubes become equal, similarly placed parallelepipeds. It is well known that the character of the deformation may be determined by a set of nine constants; but the physicist naturally prefers to regard the strain as an operator, and to represent it by a single symbol. The resulting operational algebra may even react favourably on the mathematical aspect of the question, and give us new methods of attack for old problems.

Let ƒ(x) be a given function of a variable x. We shall suppose that ƒ(x) is a one-valued analytic function, so that its Taylor's expansion in any part of the plane of the complex variable x can be derived from its Taylor's expansion in any other part of the plane by the process of analytic continuation.

The various factors which are supposed to influence the composition of milk have already been the subject of numerous investigations. The general result of these has been to show that within very wide limits the composition of milk is very little affected by the nature of the food supplied. As regards the mineral constituents the results of some of the investigations are rather conflicting, and while there is a general consensus of opinion that the composition and amount of the mineral constituents are independent of the food-supply, certain investigators claim to have been able to increase both the calcium and phosphoric acid in the milk by slight amounts.

In the course of a large inquiry on the inter-relations between the meteorological conditions in Antarctica and the Southern Ocean, on the one hand, and those prevailing in the southern continents, more especially South America, on the other, there has come to light an interesting see-saw between the barometric pressure, air temperature, and wind velocity in the Weddell and the Boss Seas. The above inquiry, which I hope to lay before this Society shortly, refers to the eight-year period 1902–09; and since the present paper deals with the years 1902, 1903, 1911, and 1912, I have thought it better to make it the subject of a separate communication. The positions of these stations and others where observations have been made are shown on the accompanying map, for which I am indebted to Dr H. R. Mill. The figures within the rings give the number of years covered by the records at the various places.