The classical theory of small harmonic vibrations of a linear damped system embodies the notion of “ viscous damping.” The equations of motion which result are somewhat complicated and, when there are more than two degrees of freedom, they are usually too unwieldy to be of much practical value. When the damping is small, however, approximating assumptions may be made which permit the treatment of systems which are near resonance as if they possess but one degree of freedom. But the effects of making these assumptions are by no means easily assessed, and even their justification is tedious.

It is shown that these difficulties may be greatly diminished by postulating hysteretic damping instead of viscous damping; the concept of hysteretic damping has been dealt with in two previous papers. The equations then take a much simpler form and the justification for, and validity of, the foregoing approximations are more easily seen. Moreover, the effects of damping upon the principal modes which the system possesses in the absence of its damping may be elucidated in this way.

The non-linear theory of supersonic bangs, obtained in Part 1 for a body accelerating along a straight path, is extended to include curved paths. The basic theory remains the same. The important parameter, which appears in the theory, is the acceleration component along the ray, the rays being lines drawn from points on the flight path at an angle cos-1 (1/M) with the direction of motion. It is found that the only essential effect of the curvature of the path is in the modification of this acceleration component to include a term due to the transverse acceleration. With this modification the main results are formally the same as in Part I.

The strength of the bow shock is obtained, and it is found that the effect of the curvature of the path is more pronounced at points on the inside of the curve, and in general it becomes greater as the distance from the body increases. A simple asymptotic formula is obtained which predicts the strength of the shock with an error of less than five per cent, at distances of the order of a hundred body-lengths. Finally, the theory is compared and contrasted with the recent work by Warren.

One of the main problems associated with the “ Jet Flap ” concerns the discrepancy in thrust between idealised theory and the experimental results. This discrepancy is attributable to the mixing with the surrounding flow of the thin two-dimensional jet while still in close proximity to the aerofoil. The effect of the mixing may be calculated to a first approximation from a formula derivable from first principles, while certain second order effects, which can be significant, may be considered qualitatively.

It is concluded that.

• (i) the full thrust should be experienced by a jet flapped aircraft at cruise,

• (ii) it should be possible to attain a low form drag at cruise in comparison with a conventional aircraft,

• (iii) at take-off, an aircraft using a shrouded jet flap would have better thrust recovery than one using a pure jet flap (which shows appreciable losses),

• (iv) the use of by-pass engines would further improve the thrust characteristics,

• (v) the practical gains from thrust augmentation, as obtained by controllingthe mixing, seem likely to be small.

In the investigation of approximate numerical values of overtone frequencies of a turbine blade it is desirable to know formulae for certain integrals of the modes of vibration of an ordinary cantilever beam. The first object of this paper is to obtain such formulae and to arrange them in tabulated form. By proceeding along the lines of the calculus of perturbations, these results may then be used to obtain new formulae which give second order approximations for the effects of uniform breadth and thickness tapers on the overtone frequencies. The theory gives good agreement with experiments for tapers which do not exceed about 0·5, which is present-day practice for turbine blading.

The longitudinal stability derivatives and stability loci for a single-degree-of-freedom, pitching oscillation of a rectangular wing having an effective aspect ratio less than unity have been calculated from the results of a previous, analytical investigation. The results extend those previously available for a rectangular wing of effective aspect ratio greater than unity.

This paper is concerned with the solution of the creep buckling of columns. Instantaneous elastic and plastic deformations, as well as the transient and secondary creep, are considered. Formulae for the critical time at which a column fails are presented for integral values of the exponents appearing in the creep law.

The CHAIRMAN, in introducing the Author, said that Mr HARPER was educated at Latymer School, London, and at the London School of Economics in Sociology He spent seven years with I C I Ltd, in the Leather Cloth Division and Plastics Division in personnel management He became involved in work study problems and their application towards the end of the war and spent his last two years m I C I practising and teaching work study to management and other grades

The CHAIRMAN, in introducing the Author, said that Dr MORLEY, who was Forward Projects Fngineer, D Napier & Son Ltd, had been sixteen years on the scientific staff of the Engine Department of the Royal Aircraft Establishment, and at the end of the war was deputy head of the Gas Dynamics Division, which ultimately became the Supersonics Division For three years thereafter, he had lectured on aircraft propulsion at the College of Aeronautics, Cranfield In his present position as Forward Projects Engineer with D Napier & Son Ltd, he was engaged principally on technical investigations into developments in aeronautics