1. It is familiar that the properties of the invariants and covariants of binary forms of the first four orders admit of elegant geometrical interpretations on rational normal curves and their projections. For forms of order higher than four the number of irreducible concomitants which appear in the complete system increases rapidly. It is the purpose of this note to exhibit geometrically the 23 irreducible concomitants of the binary quintic, using the rational normal curve R5 in space of five dimensions and its projection R′5 on to a prime as a foundation.

1. In this paper we consider the conditions at the surface of a semi-infinite elastic body due to the action of an external force applied, in a direction at right angles to the surface, to the interior of the body.

1. In this paper, a continuation of an earlier paper(1), we consider the two-dimensional motion of incompressible viscous liquid past a projection, the motion being one of uniform shear apart from the disturbance caused by the projection. A special form is assumed for the boundary, so that the area in the z-plane (Fig. 1) can be represented conformally on a circle in the ζ-plane by a rational function of ζ; this function contains a parameter a (0 < a ≤ 1), and by varying a the shape of the projection can be varied. Since a rational function is concerned in the conformal transformation a method lately developed by N. Muschelišvili(2) can be used in solving the biharmonic equation for the stream function, though the method actually used differs in some points of detail from that originally proposed by Muschelišvili and appears to be somewhat simpler.

1. The cosmical number N = . 136 . 2256 is most picturesquely described as ‘the number of protons and electrons in the universe’. This in itself would be a matter of idle curiosity. But N has a more general significance as a fundamental constant which enters into many physical formulae; it determines the ratio of the electrical to the gravitational forces between particles, the range and magnitude of the non-Coulombian forces in atomic nuclei, and the cosmical repulsion manifested in the recession of the nebulae. Its special interpretation as the number of particles in the universe arises in the following way. If we consider a distribution of hydrogen in equilibrium at zero temperature, the presence of the matter produces a curvature of space, and the curvature causes the space to close when the number of particles contained in it reaches a certain total; this total is N. We cannot say with the same confidence that the number of particles in the actual universe is precisely N, because the admission of radiation, complex nuclei, and unsteady conditions takes the problem outside the range of rigorously developed theory; but to the best of our belief these complications do not affect the total number of protons and electrons composing the matter of the universe.

The radiation from 198Au (half-value period 2·76 ± 0·02 day) have been studied, by absorption and coincidence methods, in a wide variety of experimental conditions. For the most part the results confirm those obtained by other investigators, but, in addition, a fairly intense γ-radiation of about 65 KeV. energy has been detected. This radiation has been distinguished from the weaker fluorescent K X-radiation of mercury, emitted as the result of internal conversion of one of the γ-rays of 198Au, and it has been shown that it is not the K X-radiation of platinum. Disintegration of 198Au by K-electron capture, if it occurs at all, cannot take place in more than about 15% of all disintegrations.

The absolute measurement of neutron flux density by ionization methods is discussed.

The relation Eυ = JυW ρ between the energy Eυ absorbed per unit volume of a solid medium and the ionization Jυ produced in a gas-filled cavity in the medium, the average energy W expended by the ionizing particles in producing a pair of ions in the gas, and ρ the stopping power of the solid relative to the gas for these particles, is critically examined from the point of view of the measurement of the rate of absorption of neutron energy at any point in a hydrogenous medium. The accuracy attainable is assessed, in so far as it depends on our knowledge of the quantities ρ and W.