Table of contents

This paper discusses various proposals which have been made to accelerate the convergence of the relaxation method as applied to the solution of some of the well-known differential equations of physics and engineering. It is shown that a very high accuracy can easily be achieved in simple cases where the differential equation is of the second order.

In the case of the biharmonic (fourth order) equation, which occurs in the analysis of plane stress and plane strain, a method is proposed by which, in suitable cases, a high accuracy can be achieved by employing two second-order equations successively. It is suggested that where this can be done a given accuracy can be achieved with relatively little labour, though it is recognized that the method proposed has only a limited application.

An analysis is made of the effect of orientation of the fibres on the stiffness and strength of paper and other fibrous materials. It is shown that these effects may be represented completely by the first few coefficients of the distribution function for the fibres in respect of orientation, the first three Fourier coefficients for a planar matrix and the first fifteen spherical harmonics for a solid medium. For the planar case it is shown that all possible types of elastic behaviour may be represented by composition of four sets of parallel fibres in appropriate ratios. The means of transfer of load from fibre to fibre are considered and it is concluded that the effect of short fibres may be represented merely by use of a reduced value for their modulus of elasticity. The results of the analysis are applied to certain samples of resin bonded fibrous filled materials and moderately good agreement with experimental results is found.

The temperature distribution in a solid of infinite area bounded by two parallel planes in which heat is being uniformly generated and the surfaces of which are maintained at an elevated temperature is evaluated for the case in which the solid is initially at a uniform temperature throughout. A comparison is made between platten and combined heating which shows that the heating time can be divided by a factor which depends on the tolerable temperature variation, but which is of the order of 10 for a variation of 19% and 2.5 for a variation of 1.2%. Some consideration is given to the optimum conditions required for the setting of synthetic resins and like materials for which the setting time is a function of the temperature. Practical considerations which restrict the choice of some of the parameters are mentioned.

A theory of the action of Helmholtz resonators as sound absorbers is presented, covering both the isolated resonator and regular arrays. Experiments in reverberation rooms and acoustically treated studios are described and general recommendations for design are given. Regular arrays are preferable to single resonators, openings being made more resistive by covering with a fabric. It is concluded that great variations in design to suit architectural requirements may be made without loss of effectiveness, and the widths of the frequency band over which absorption takes place may be varied between wide limits.

Oscillations which are critically dependent on anode voltage have been obtained over a wavelength range of 6 to 20 cm in disk seal triodes. The oscillations occur when the cathode-grid transit time is about five-quarters of the alternating period. They are closely analogous to the negative resistance oscillations obtained in diodes

This paper describes a method of calculating the design of a solenoid with any number of compensating end coils to produce an approximately uniform magnetic field along a large portion of the solenoid length. The design of a solenoid with two end coils at each end is given in a numerical example and its estimated performance compared with experimental results.

A method has been described for the rapid determination of the total emissivity of metals and oxides in the temperature range 300-800° C. Values have been obtained for lampblack and polished platinum and also for Nimonic 75, pure nickel, and stainless steel, with various surface conditions. The total emissivities of the pure oxides ceria, zirconia, thoria, magnesia, alumina and fused silica have also been determined. The effect of particle size of the oxides and the variation of emissivity with angle of emission have been studied.