Throughout this paper a ring will mean a commutative ring with identity element. If A is an ideal of the ring R and P is a minimal prime ideal of A, then the intersection Q of all P-primary ideals which contain A is called the isolated primary component of A belonging to P. The ideal Q can also be described as the set of all elements x∈R such that xr∈A for some r∈R\P. If {Pα} is the collection of all minimal prime ideals of A and Qα is the isolated primary component of A belonging to Pα, then is called the kernel of A.

A general theory of an elastic-plastic continuum which is valid for non-isothermal deformation and which includes explicit restrictions derived from thermodynamics has been given recently by Green and Naghdi [2]. In the development of this theory, the analysis was carried out for a symmetric plastic strain tensor, although it was noted that it is possible to use instead a plastic strain tensor which is nonsymmetric and this would require only a slight modification of the results.

The paper discusses the advantages of solving boundaryvalue problems by the use of eigen-function expansions of suitable fourth order differential equations instead of those of second order equations. Some such expansions are constructed, their convergence properties studied and their use in different types of boundary-value problems are discussed.

A “roughness parameter”, first used by the author in 1953 (Feather 1953 b) has been re-calculated for 348 points on the mass surface. Systematic features are identified in relation to the variation of this parameter with charge number (Z) and isotopie number (D). In the region of small Z these regularities provide evidence for the persistence of some degree of alpha-unit structure at least as far as Ca. In the region of greater Z (20 < Z < 50) they provide evidence for neutron-proton interactions among the last-added nucleons. Overall, they indicate that the “residuals” characterizing the various semi-empirical mass equations currently in use very probably arise in large part from sub-shell effects which it would be impracticable to attempt to include in the equations.

The paper describes an investigation of the terminal velocity of uniformly dispersed particles of various shapes, sizes and densities falling through water.

It is concluded that for concentrations above 0–5 per cent by weight, the suspension as a whole behaves as though it were viscous even though the individual particles lie well outside the Stokes range. The shape of the particles has a significant effect only when the concentration is less than 0·5 per cent, and for concentrations between 0·5 and 7·0 per cent, the relative changes in velocity of descent are adequately described for a range of particle shapes from highly angular to spherical and for sizes at least up to 0·65 mm. nominal diameter, by the power series

in which U is the velocity of the suspension, U0 that of a single particle, d the nominal diameter (i.e. that of a sphere having the same volume) and s the mean spacing of the particles.

If the concentration is lower than 4 per cent, the equation may be assumed linear in (d/s) without serious error.

Many results concerning real orthogonal matrices have their counterparts in the theory of orthogonal Boolean matrices. In particular, the analogues for Boolean matrices of certain theorems due to Kronecker are established. The structure of the group of orthogonal Boolean matrices of order n is determined in the case where the underlying Boolean algebra is finite.

The distribution of stress in the neighbourhood of an infinite row of collinear cracks in an elastic body is calculated for general distributions of internal pressure. The case in which each of the cracks is opened out by the same constant pressure is considered in detail; the variation with the ratio of the width of the crack to the distance between two cracks of quantities of physical interest is shown in a series of diagrams.