This paper contains the results of an investigation, on empirical and dynamical lines, into the following matters:—

(1) The origin of surfaces of discontinuity in the atmosphere;

(2) The precise processes occurring at such surfaces in well-defined cases;

(3) The physical processes which lead to the obliteration or movement of the discontinuities;

(4) The part played by the discontinuities in the development of the cyclones of temperate latitudes.

Balanus nubilis, one of the sessile Cirripedes, grows to a considerable size, a large specimen measuring some 10 to 11 cm. across the base and an equal distance in height. During a visit to Nanaimo Biological Station an opportunity was taken to study in this giant form a few features pertaining to the mechanism of movement of the operculum, which is attached within the cup of the shell by the opercular membrane. Peripherally the membrane is attached close to the downwardly directed sharp edge of an overhanging shelf formed by the inner wall of the shell; centrally it is attached to the free edge of the operculum on its basal aspect.

The function which is discussed in the greater part of this paper was introduced by Professor E. T. Whittaker in vol. xxxv (1915), pp. 181–194 of these Proceedings. A one-valued function, analytic in the finite part of the plane save possibly for poles, is taken and a table made of the values of f(x) for x = a, a + w, a — w, a + 2w, a — 2w, … The function

called the Cardinal Function, is then shown to be the simplest function satisfying the table of values so obtained, in that it is a function which, when analysed into its periodic constituents, has no rapid oscillations.

The highest member of the series of normal dibasic acids hitherto obtained by electrosynthesis is hexadecane dicarboxylic acid, HOOC.(CH2)16. COOH. In attempts to synthesise by this means dicarboxylic acids of still higher molecular weight, the following difficulties are encountered:—(1) The temperature of the liquid undergoing electrolysis must be kept above the melting point of the synthetic di-ester, in order that the latter may not solidify on the anode and prevent the passage of the current; (2) the alkali ethyl salts of the higher dibasic acids are of a soapy nature, and cannot readily be dealt with in concentrated solution. Two of the conditions favourable to electrosynthesis, high concentration of the electrolyte and low temperature, are thus unattainable.

The first experiments on this subject were suggested by the absorption effects associated with the “J” phenomenon. In a comparison of the absorbability in aluminium and in copper of the radiation emitted in one direction from an X-ray tube, it is found that in many cases, as the tube is hardened and a certain value of the mass-absorption coefficient reached, there is a sudden increase in the absorption by aluminium. Since the radiation is not strictly homogeneous, and since the above effect does not invariably take place, it is evident that the phenomenon is not to be explained simply in terms of a “J” series characteristic radiation similar to K and L characteristic radiations as regards the manner of its excitation. It is evident that certain critical conditions must obtain before the phenomenon occurs, and on account of the abruptness of the change it appears as though the whole wave-length range of the radiation were affected in respect of absorption by aluminium. This seems to be further substantiated by the fact that the discontinuous character of the change in absorption is preserved with a beam which is much more heterogeneous.

1. The rates of sedimentation of a kaolin suspension in presence of varying concentrations of a salt (sodium chloride, potassium chloride, sodium sulphate, di-sodium hydrogen phosphate, sodium citrate, calcium chloride, calcium sulphate, monocalcium phosphate, “superphosphate”, aluminium chloride, ferric chloride or lanthanum chloride) have been compared at various pH values. Abnormal results are obtained with sodium chloride, monocalcium phosphate, aluminium, ferric and lanthanum chlorides.

2. Sodium chloride increases the rate of sedimentation in alkaline solution, but actually inhibits it in acid solution.

3. In concentrations of monocalcium phosphate above 0·06 per cent, abnormal sedimentation in alkaline solution takes place, with the result that it is much more complete than at the corresponding concentrations in acid solution.

4. In acid solution the tervalent ions, aluminium, ferric and lanthanum have little effect, but a zone of very marked flocculation occurs at pH 7–8. This zone separates a region within which the unsedimented particles are negatively charged from a region within which they are positively charged.

Our knowledge of the anatomy of Dicksonia is mainly based on the description of D. Barometz given by Gwynne-Vaughan. The stem of this species possesses a radial dictyostele, which, on account of the shortness of the leaf gaps, is not far removed from the solenostelic condition. The leaf trace arises as a broad ribbon of tissue with inwardly folding margins, which soon, however, breaks up to form a horse-shoe of isolated strands.

About six years ago I communicated to the Society an account of some measurements made at Eskdalemuir Observatory of the more minute changes which are almost continually occurring in the vertical component of the earth's magnetic field. The method adopted was that of connecting the terminals of a coil of wire, whose axis is vertical, to a suitable galvanometer on which was measured the current induced in the coil by changes in the vertical component of the terrestrial field.

1. The properties of a colloidal sol of cholesterol have been investigated, more particularly in relation to the effect of pH in the presence of protein (gelatin) of various concentrations.

2. The cataphoretic P.D. between the particles of the sol and the medium has been determined in the presence of gelatin at various concentrations and at various pH values.

3. The effect of the presence of gelatin in preventing the precipitation of a cholesterol sol by sodium chloride at various pH values has been investigated. It has been shown that the amount of gelatin required to protect is approximately that required to cover the particles with a layer of gelatin from one to two atoms thick.

4. The mechanisms of precipitation and protection are discussed in the light of these results.

It has been pointed out in a previous paper (Wright and Kermack, 1923), that whereas the precipitation of colloidal gum benzoin by salts containing a uni- or bi-valent cation commences at a given concentration and continues to take place with increasing concentration, in the case of ferric chloride, there occurs with continuously increasing concentrations of this salt, first non-precipitation, second precipitation, then a range of concentrations where no precipitation occurs, and lastly precipitation again. Such a series of changes has been observed with other sols under the action of tervalent ions (cf. Burton, 1916).

It is now a thoroughly well-established fact that a satisfactory match to any coloured light observable in nature can be made by a combination, in suitable proportions, of three standard lights suitably chosen from a spectrum. It is customary to choose for the standards a red, a green, and a blue light of definite average wave-length in each case. The greatest deviation from the average is made so slight that there is no visible difference in colour between the extreme components present in any one standard. A simple way (used by Maxwell) of obtaining these standards would be by means of an ordinary spectroscopic arrangement in which light is focussed on a slit, and is parallelised by a collimating lens, after which it passes through a prism and the object glass of a telescope, on whose focal plane a spectrum is thus formed.

In this paper it is proposed to study the problem of the vibrations of a uniformly-stretched membrane whose superficial density σ depends upon the distance r from a fixed point in the membrane in accordance with the law

in which C and a are constants. The constant a will be known as the critical radius and the circle r = a as the critical circle.