Parts 1 to 5 of this paper (February, September and November 1947 issues of the JOURNAL) investigated the stresses and deformations of closed tubes in which the thicknesses were governed by the t s * and t * laws. In the present part, the analysis is extended to multi-cell tubes with openings, open tubes with or without St. Venant torsional stiffness, and to tubes formed by joining elements of different cross-sections. To illustrate the theory a numerical example of the stressing of a four-boom wing consisting of seven joined elements is fully worked out. Finally, an appendix gives practical methods of dealing with tubes which do not conform to the t s * and t * laws, and of finding approximate solutions for four-boom tubes with direct stress carrying covers.

Many types of detonation may be distinguished, and the causes are to be found in the engines as well as in the fuels. Obviously one single cause would not be expected to be found, but, on the contrary, quite a number of properties which will be more or less of influence under different engine conditions. These may differ widely, yet there is more unity in the multitude of causes of detonation than might be expected, and this the authors will endeavour to illustrate. They must apologise for mentioning many well-known, in addition to new, views, but it is necessary to do this for the general exposition of the material.

Two principal types of engines should be considered to-day :–

1. (1) That in which the fuel is added to the air at the end of compression (in air compressing or Diesel engines), and

2. (2) That in which the fuel is added to the air before compression (mixture compressing, e.g., petrol engines).

Most methods of increasing the output of petrol engines seem to attract the “ demon of knocking ” ; the reverse is true for Diesel engines, which is hopeful for their future development.

Investigations have been carried out in connection with the testing of a definite aeroplane type in order to ascertain the extent to which the safe take-off can be sufficiently ensured by prescribing certain practical requirements.

This led to inquiries into the question as to whether the qualities of the aeroplane in the take-off could be determined from individual tests, in such a way that it would be possible, from the results, to determine the take-off path when climbing in conformity with a definite previously established policy.

The present report consists of an analytical consideration of the safety in the take-off, which may be used as a practical guide for the predetermination of a safe take-off policy, and a means whereby the dimensions of an aerodrome, such as shall meet the rational requirements for a safe take-off (of a definite aeroplane type), can be determined.

I have, for the second time, the honour of addressing you. Four years ago I told you how I had had the good fortune to discover a new method of flying with characteristics altogether different from the conventional aeroplane.

To-day, taking advantage of your kind invitation, I come to tell you of how the crude experimental autogiros of 1925 have been developed into practical flying machines. I will also deal with a number of theoretical points in justification of the assertions I have often made about the qualities of the autogiro and in answer to the criticisms of which my system has been made the object from time to time.

In this paper an explanation is furnished as to why linear simultaneous equations arising in structural problems are, in certain circumstances, sensitive or “ill-conditioned,” and an indication is given concerning the physical significance of this sensitivity. Means are also discussed whereby difficulties of this kind may be overcome.

The free and forced vibrations of a multi-rotor system where one section of the shaft has a nonlinear elastic characteristic are considered in this paper. For any frequency of steady vibration the system is reduced to an equivalent rotor at either end of the nonlinear section. The vibrations at all points are assumed to be one-term approximate solutions and the amplitudes of steady forced vibration are determined by a method outlined by the author in an earlier paper.