A simple exposition, using d'Alembert's principle and methods of virtual work, is given of the properties and applications of the normal modes of vibration of a linear elastic system. The use of the normal modes in problems of free and forced vibration and dynamic loading is discussed with the aid of simple examples, and it is shown that by these methods dynamical problems for any linear system may be solved without the use of the fundamental equations of motion, provided the natural frequencies and modes of the system are known. In most problems the solutions converge rapidly, so that only the first few modes of vibration need be considered, and in these cases the solution may be modified to give further improvement in convergence. Unsatisfactory convergence may be obtained, however, in problems where there is an exciting force of very high frequency, or an impact of short duration. An approximate allowance may be made for damping, provided this is small.

A Study of the air routes of the world brings out almost at once the fact that some of the most difficult route are also the most attractive. For instance, the North Atlantic route which couples North America with Europe is certainly one of the most difficult in the world, but also by the fact that it couples two of the most densely populated, as well as the most wealthy groups of people in the world, one of the most attractive.

The purpose which Air Transport should be designed to serve is, I suspect, all too often confused or ignored. I think that the essential contribution which Air Transport has to make to modern civilisation can be expressed, quite simply, in two words:—

Improved communications lead to traffic—both traffic robbed from older and less convenient forms of transport, and new traffic created by the new medium. Carriage of traffic is the fundamental task of all forms of transport. Air Transport, alone unimpeded by geographical barriers, has traffic-carrying potentials which are still largely unexplored, whether that traffic be passengers, freight or mails—businessmen to Brussels, honeymooners to Honolulu, or coals to Berlin. In the same way, estimates of traffic must form the basis of all operational planning and set the scale against which airline fleets and frequencies should be projected in terms of date as well as numbers.

My pleasure in accepting your invitation to lecture, which I treat as a great honour, has been somewhat overshadowed by doubt that I shall do justice to the occasion. This is but the second lecture to commemorate Captain Frank Barnwell. I am fully alive to the fact that the members of this Branch of the Society, many of whom were Captain Barnwell's personal friends, are very desirous of establishing, in these early lectures, a standard which is a worthy memorial.

Captain Barnwell was one of a small number—I suppose they can be counted on the fingers of two hands —who, by their courage and ability, made the barely flyable contraptions of 50 years ago into the aeroplanes we know today. The changes in aeronautical engineering have been so great that it is not easy to realise in 1955 the problems Barnwell and his colleagues faced in 1905, the year of the first Barnwell designs.