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When two solid bodies are pressed together without at any point exceeding the elastic limit, their common area of contact is frequently circular, and in such cases the normal stress at each point of this area may be calculated by a simple approximate method giving results correct, as a rule, to within 1 or 2 per cent. The approximation makes use of two principles: (a) The displacement at the centre of the circle of contact is twice that at its edge, and (b) for the purpose of calculating the stresses we may replace the two bodies by a single sphere of which the circle of contact is a diametral section, and write the strain at any point as the ratio of the displacement of that point to the length of the line drawn from the point to the sphere in the direction of displacement. When the elastic modulus with which this is multiplied is taken as that appropriate to a rod with sides fixed, the agreement with accurate theory is close. It is shown that the principle (a) remains nearly true for elliptical areas of contact.

This paper, which describes the continuation of a research upon the impact of soft metallic bodies, contains the results of four investigations, as follows: (1) Impact of equal spheres for low values of the velocity of approach ν. The duration of contact is found to vary inversely as νfraction one-fifth, while the coefficients of restitution e in the same cases are found to be unity for all speeds below a value characteristic of each material, as though the metals were perfectly elastic for smaller speeds. (2) The effect of duration of contact upon the size of the permanent deformations. No effect was observed. (3) The variation of duration of contact t with mass of sphere at high speeds of approach. Within the limits of experimental error, t varies as the square root of the mass, as theory predicts. (4) The impact of crossed cylinders. No important new phenomena are found.

The formation of percussion figures by the pressure of a steel ball on glass blocks is here traced out, and an investigation suggested by this exploration elicits the following facts: (1) The diameter of the innermost circular or part-circular crack remains constant for one specimen of glass, and is independent of the maximum pressure exerted by the ball on the glass. (2) The diameter of the outermost circular or part-circular crack varies with the maximum pressure in a manner which suggests that the crack tends to keep to the outer edge of the area of contact. (3) No crack is formed until the pressure exceeds a value characteristic of the glass. A method of testing the fragility of glass is developed: and finally some observations on percussion figures upon spherical surfaces are mentioned.

The absorption of monochromatic radiation from the sun in an atmosphere of which the density varies exponentially with height is considered; the energy of the radiation, or a definite fraction of it, is supposed to dissociate or ionize the air, and the dissociation products are supposed to recombine with one another only, and not to diffuse away from the element in which they were formed. The resulting distribution of density of the dissociation products is determined, a constant recombination coefficient being assumed, while account is taken of the variation in rate of dissociation due to the earth's rotation. The results are illustrated by numerous diagrams, showing the density of the dissociation-products as a function of height, time, latitude and season.

The flow of fluid through long straight tubes of circular section was experimented on, at speeds in the neighbourhood of the lower critical velocity, in an attempt to detect any trace of periodicity in the turbulent motion. The experimental methods included (a) an aural method; (b) photography of the motion of a deflected vane; and (c) injection of colour-streamers about halfway along the tube. Intermittent turbulence was investigated at speeds near the critical speed, and measurements of the critical speed were made. It was shown that the velocity parallel to the tube-axis is sometimes almost uniform momentarily over the transverse section.

No trace was found of a simple frequency, but evidence was obtained of a predominant wave-length in the turbulent motion at the critical speed. Both these observations seem to agree with the approximate theory for flow between a pair of parallel planes given by Heisenberg.

The spectrum of the condensed spark of cerium has been investigated in the ultra-violet, and doublet combinations in Ce IV, in addition to those given by Gibbs and White, have been found. The 6²P - 6²D combination of La III also has been identified. Term values and ionization potentials of La III and Ce IV are calculated.

The photographic action of γ-rays from radium and radon in equilibrium with their short-lived products has been investigated, the rays being filtered with lead screens of thicknesses 0, 0.19, 1.42, 2.61 and 4.03 cm. The variations of photographic density both with time and with intensity have been examined. The shape of the characteristic (C) curves (D - log I) have been found to be independent of the filtering, and the same holds for the Hurter-Driffield (H.D.) curves (D - log t), except when no lead filter is used. The value of p in the Schwarzschild relation, D = f (It^p), has been found to be unity for all the lead filters. The absorption coefficient of lead for γ-rays from the sources used has been found to be 0.533 cm^-1 for thicknesses of lead from 1 to 7 cm.

The doublet system of As III published by R. J. Lang has been amended and extended in the light of fresh observations which have been made, and a scheme of terms has been evaluated.

A method is described for measuring the damping-coefficients and conductances of the orifices of the small resonators used in the construction of hot-wire microphones. Observations show that resonant microphones with cylindrical necks of diameter between 0.5 and 0.64 cm. and length between 1.2 and 2.25 cm. have damping-coefficients which are about 23 per cent. greater than the values indicated by theory. The observed conductances of the necks agree very closely with those calculated from a formula in which allowance is made for the added inertia due to viscosity.

Attention is directed to the fact that at least three temperatures may require to be specified in a description of the magnetic behaviour of a ferromagnetic substance. These are respectively termed the ferromagnetic critical point, the ferromagnetic Curie point, and the paramagnetic Curie point. The significance of the relative positions of the last two points is discussed, and it is shown that a slight extension of the view that ferromagnetism is due to a magnetic particle consisting of a group of associated atoms may account for the paramagnetic behaviour of iron, nickel and cobalt, and for that of more complicated substances such as the ferrocobalts, magnetite and manganese arsenide.

The effect of temperature on spark-potential in hydrogen and nitrogen at ordinary pressures has been studied up to 860° C., over 6000 voltmeter-readings having been taken. The spark-potential is found to depend on the density of the gas and to be independent of temperature and pressure for a given density. Additional ionization of limited amount does not lower the spark-potential at ordinary densities.