The True Balance of a man's worth cannot be struck by a knowledge, however full, of only one of his activities.

I do not propose to confine myself to Cayley's aeronautical activities in this paper, for that would be to do much less than justice to a man whose interests, when known and understood, can only add to the stature of a great Yorkshireman and a great Englishman, one, to quote William Cobbett, “of the resident native gentry, attached to the soil, known to every farmer and labourer from their childhood, frequently mixing with them in those pursuits where all artificial distinctions are lost, practising hospitality without ceremony, from habit and not on calculation.”

Sir Walter Raleigh, in his introduction to the History of the War in the Air (1914-1918), referred to Cayley as one who “amused his leisure with science.” Raleigh was not aware and, indeed, very few who know something of Cayley's aeronautical work are aware, of how active was the interest Cayley took in scientific and engineering matters during his long life. I hope in this paper to add something to Cayley's stature, great as it is, in this respect.

The minimum weight approach to structural design was introduced by F. R. Shanley with reference to narrow and wide columns and shells subjected to bending, and was later dealt with more comprehensively in a book by the same author. This was further extended to structures like tapered round thin-walled columns and frames. In this paper expressions giving optimum sectional dimensions for long thin walled cells of circular, semi–circular, rectangular and triangular shapes and uniform wall thickness have been derived. The design criteria used to obtain the minimum necessary conditions are (1) failure by local buckling and (2) a limit on the twisting deformation of the cells. Working curves from which the optimum sectional dimensions can be read for given torque and limiting twist have been plotted. And finally, a method of approach to the problem of combined bending and torsion has also been indicated.

Some five years ago the author was privileged to deliver a Section Lecture to the Royal Aeronautical Society on the subject of reheat. The present paper attempts to summarise the problems which now arise and to give some idea of the progress which has been made in the intervening years.

In 1949, reheat was in its infancy in Great Britain. A certain amount of progress had been made in the United States but the information from that source was scanty and vague. Tests at the National Gas Turbine Establishment (N.G.T.E.) had given some engine data but this was in the nature of preliminary information only and was by no means complete. In fact the majority of the problems which now beset us were then completely unknown or were considered unimportant. The N.G.T.E. work was valuable, however, in that it demonstrated the practicability of reheat, although at the time the comments of many who saw this and other schemes in operation were somewhat sceptical and definitely unflattering.

Approximate Solutions obtained by the method of collocation are presented for the lowest critical buckling load of an isosceles triangular plate loaded as shown in Fig. 1. Also, the fundamental frequency is given. The base of the triangle is simply supported and the other equal edges are clamped. The usual assumptions regarding the bending of thin plates are made. The governing differential equation for the plate loaded as shown in Fig. 1 is

1

where D is the plate stiffness, N is axial load per unit length, w is deflection, positive downward, and the quantities a and h are dimensions shown in Fig.1.

In many engineering problems it is necessary, from time to time, to deduce from only a few characteristic values data which would ideally be obtained from a complete stress-strain curve. For instance many handbooks, used in design offices and published by materials manufacturers and others, contain values of Young's modulus and minimum guaranteed, or typical, values of various proof stresses for materials. From these, estimates of strain, tangent modulus or ratio of stress to tangent modulus appropriate to known stress values may be required, or various processes involving integration of the stress-strain curve may have to be carried out. Even when a complete stress-strain curve is available from a special test, the differentiation and integration of it, which may have to be repeated several times, are timeconsuming processes. Also, in analytical work involving the use of materials beyond the limit of proportionality, it is desirable to have available a generalised mathematical form of the stress-strain curve in order that the results obtained may be applied to a wide range of actual materials simply by the substitution of appropriate coefficients. These and many other applications will be familiar to the reader.