The Focke helicopter presents the first successful solution of a problem which has occupied aeronautical science for a considerable time. Details of the record flights carried out last year caused a world sensation and with further development it is not too much to hope that this new type will open up fresh fields which up to now remained closed to orthodox aircraft.

I want this evening to present some reasons for believing- that we can build successful aeroplanes of enormous size, and, what is more important, that they will not be merely monuments to a desire for the gigantic.

In the past, bold computers have defined upper limits to the size of aeroplanes. Their prophecies have varied, and most of them have been belied by practical achievement. Their arguments were usually based on what has been called the “ Cube Law ” or the “ Square-Cube Rule.” This rule, though it has apparently proved misleading, is indeed correct when properly applied, and it forms a convenient point from which to begin an enquiry into the feasibility of the giant aeroplane.

Within recent years the subject of anodic oxidation has been very fully and minutely examined, notably by Bengough, Stuart, and Dr. Sutton, who was responsible for the large-scale experiments carried out at the Royal Aircraft establishment, Farnborough, and who, with his collaborators, has presented a number of excellent papers to the Royal Aeronautical Society, the Institute of Metals, and other bodies. In addition, scientists and industrialists at home and abroad are continuously adding to knowledge of aluminium, its uses and adaptability, and are giving a growing impetus to penetrations into spheres formerly exclusive to steel, brass, copper, tin and timber, each substitution calling for special consideration, so that it is well-nigh impossible for one to broach the subject without impinging somewhere upon the work ol others.

In recent years much attention has been devoted to what Professor Southwell has appropriately called relaxation (1) methods in the solution of structural problems. These methods are essentially physical applications of iteration processes for solving simultaneous equations. In this paper it is not intended to discuss the advantages or otherwise of physical relaxation as compared with analytical iteration. The object is to examine the mathematical basis of the relaxation methods and to investigate the conditions of their convergency.