The paper first discusses the analysis of a general vector field with the aid of the concept of the field line with its tangent, principal normal and binormal. Detailed applications are made to the motion of inviscid and of viscous fluids.

The influence of higher-harmonic deflection components on the creep-buckling characteristics of an idealised H-section column is investigated. The creep properties of the material of the column are defined by a simple power-function creep law. The results show that higher-harmonic deflection components reduce the column lifetime significantly only when their initial amplitudes, as well as the initial amplitude of the first harmonic component, are very large. Furthermore, it is shown that second-harmonic components have a much smaller effect on the column behaviour than do third-harmonic components.

The compressible flow past an oscillating two-dimensional aerofoil in a wind tunnel with porous walls is considered, using linearised theory. The porous wall is assumed to have the property that the ratio of the normal velocity at the wall to the pressure drop across the wall is constant. Transform theory is used to find the supersonic longitudinal stability derivatives, and an extension of Possio's integral equation for the quasi-stationary case in subsonic flow.

When a non-uniform stream flows through a cascade of compressor blades a three-dimensional secondary motion is generated in the outlet stream. This motion, which consists of a spanwise re-orientation of the Bernoulli planes, together with the effects of vorticity components in the stream direction, may be predicted theoretically. In this paper experimental results obtained on a 6 in. chord cascade are reported. The experimental and computed outlet angles are compared and the discrepancies are explained qualitatively. Additional particle track and visualisation experiments were designed to investigate the local blade flows and the effects of the nose vortices.

Some new solutions for steady incompressible laminar boundary layer flow, obtained by Gortler, have been used to test the accuracy of two methods which are commonly used to predict separation. A modification of Stratford's criterion for separation is given in this paper and is probably the most accurate and the simplest of all methods at present in use. Modified numerical functions are also given for Thwaites's method of predicting the main characteristics of the boundary layer over the whole surface, which improve the accuracy of the method.

The thrust magnitude programme of a rocket missile being supposed specified, the problem is solved of programming the thrust direction to achieve maximum range on the Earth's surface. Earth curvature and rotation, and variation of gravity with height are taken into account, but air resistance is neglected. Motion is assumed to take place in the Equatorial plane. Tables are included from which the optimal trajectories of missiles may be computed when two design parameters are known and these tables are used to assess the advantage to be gained at extreme ranges by firing in the sense of the Earth's rotation rather than against it.

In this work the co-ordinates of three-dimensional nozzles of several types have been obtained as explicit functions, and some shapes have been plotted. It is hoped that some of these might be of use in cases where smooth uniform fluid flow is desired. The design of a particular nozzle shape in the presence of a plane boundary is given: previously any equations obtained have been too intractable to use.

Modern turbine blades are generally twisted about their axes, the shape resembling that of a helicoid. This makes the determination of their overtone frequencies much more difficult. The equations governing the flexural vibrations may be obtained from the Clebsch-Kirchhoff theory for rods which are naturally twisted. By using these equations, this paper considers a first-order approximation for the effect of uniform twist.