A method is given for finding the reciprocal of a matrix which is triply partitioned horizontally and vertically in such a manner that the sub-matrices in the principal diagonal are square, but these matrices need not be of the same order. A preliminary rearrangement of the matrix may be helpful.

In theoretical work it is sometimes required to find the reciprocal of a matrix which can be so partitioned that some of the sub-matrices are of simple types, e.g. triangular or nul matrices, and the calculation of the reciprocal may then be facilitated by using formulae for the inversion of partitioned matrices. The same method will be often advantageous in numerical work also. In an earlier paper the reciprocation of doubly-partitioned matrices was treated in a general way and a method was given for triply-partitioned matrices subject to the restriction that the sub-matrices in the principal diagonal are square and of the same order.

Assuming the formation of plastic hinges at the quarter points of a ring subject to a diametral compressive force, a comparison is made between experimental collapse loads and those predicted by use of a simple expression based on the use of plastic rectangular stress blocks, for some common materials; good correlation is obtained with aluminium.

A member may be said to fail when it yields completely at several positions and so allows collapse as a mechanism to occur. The smallest load at which this happens marks the end of useful life of the member. In the case of very thin rings loaded at the ends of a diameter in compression, as shown in Fig. 1, it is obvious that the sections of greatest bending moment are at A, B, C and D. These moments will continue to increase with increasing diametral load.

Simple means of checking contractants has been devised which is considered essential to a computor.

In a recent paper Macmillan describes the method of contractants as applied to the evaluation of determinants. The method is essentially based on the extensional identity

Now, any determinant of order n may be expressed as a determinant of order n - 1, all of whose elements are third order determinants. This process is now repeated (n - 2) times until the value of the original determinant is obtained.

Recent interest has been shown in stability problems in which the parameters in the relevant characteristic equations are not constant. For instance, the coefficients in the characteristic equation for the stability of flutter of an aeroplane's wings are functions of the speed of the aircraft. When the aircraft is accelerating or decelerating it is therefore necessary to consider whether the resulting variation of the coefficients is sufficiently rapid to invalidate a calculation of stability which is based on the assumption that the coefficients are constant. Similar stability problems arise in connection with guided missiles.

The elastic stability of rectangular plates compressed in two perpendicular directions by forces uniformly distributed along the edges is considered. Edges x = 0 and x = a are simply supported, edge y = 0 is free and edge y = b is rigidly built-in (Fig. 1). Using the method described in a previous paper, after satisfying the boundary conditions at the edges of plate, the following transcendental equation is obtained:

It is usual when plotting characteristic diagrams for unsteady flow fields to assume a constant ratio of specific heats. In the general theory of characteristics developed by Guderley the variable specific heats are introduced into the calculation of the characteristic constants. In the following method the variation in the ratio of the specific heats is included directly into the slope of the state characteristics. The position diagram may then be plotted directly by the usual techniques.

In a recent article Lundberg has made reference to use of the “ Hydraulic Analogy ” for quantitative investigation of gas dynamics phenomena. This is quite feasible provided that the basic analogy and its limitations are properly understood. In fact, considerable progress has already been made and it has been proved possible to utilise the analogy for both supersonic and transonic research.

A study of the mathematical analogy indicates that the strongest physical analogy between a two-dimensional (inviscid) gas flow and a three-dimensional (viscous) water flow exists for the transonic case when the water depth is approximately one quarter inch and the model is towed. Only thin profiles with small incidence can be sensibly investigated. Under such conditions the analogous water flow may be considered as a distorted dissimilar model of a corresponding prototype gas flow.

In a recent paper the authors suggested that the minimum weight design of thin-walled cells in combined bending and torsion could be tackled by using the well-known concept of equivalent bending moment and torque. It is now felt that a more rational approach would be to base the analysis on the buckling behaviour of the walls of the cell under combined compression and shear and choose the dimensions such that the cell will just resist buckling. The second criterion for design is taken as a limit on the twist as adapted in the case of pure torsion. Two types of sections, rectangular and circular, are discussed in this note.

Unshrouded impellers of centrifugal compressors and centripetal turbines manifest an increase of the flow losses in comparison with the shrouded ones. Assuming that the controlling factor in such increase of loss is the leakage through the gap between wheel and casing, the author develops a simple theory leading to a formula for the volumetric efficiency. Only one experimental quantity is required for applying the formula; and tentative values, based on some experimental evidence, are presented.

The possibility of control of circulation around aircraft wings and gas turbine blades by ejection of air from the aerofoil into the main stream has drawn attention to the manifold problem. Discharge velocity distributions along the length of the wing or blade must be uniform, and it is important that the detailed nature of the flow in the supply manifolds should be understood. The distributions of velocity in manifolds supplying multicylinder internal combustion engines, in gas burners and in manifolds supplying canal locks are other allied problems.

An approximate method is shown for the estimation of the velocity and pressure distribution over the surface of circular annular aerofoils with thick symmetrical sections, at zero incidence.

Figure 1 shows an annular aerofoil or profiled ring obtained when an aerofoil with symmetrical section rotates about an axis.

From the theory of wing sections it is known that the aerodynamic effect of a symmetrical aerofoil section, at zero angle of attack, may be approximately replaced by the effect of sources and sinks distributed along the chord of the section.

In a previous note the authors gave a method of solution for the problem of a finite rectangular plate under constant skew and inclined loadings, two of the edges being rigidly held and the other two simply-supported. In this note the same problem is considered for a plate in the shape of a parallelogram.

The blow-down type of intermittent, supersonic tunnel is attractive because of its simplicity and because relatively high Reynolds numbers can be obtained for a given size of test section. An adverse characteristic, however, is the fall of stagnation temperature during runs, which can affect experiments in several ways. The Reynolds number varies and the absolute velocity is not constant, even if the Mach number and pressure are; heat-transfer cannot be studied under controlled conditions and the experimental errors arising from the effect of heat-transfer on the boundary layer vary in time. These effects can become significant in quantitative experiments if the tunnel is large and the variation of temperature very rapid; the expense required to eliminate them might then be justified.