Many complex machines and mechanical systems have an ideal and abstract form which has been evolved from fundamental theory without reference to those engineering principles that are so essential in practice. Thus the heat engine has its Carnot cycle and the propeller its actuator disc. With these, and numerous other examples, the object is to provide a standard of reference, to give an ideal which can be approached but never reached and, most important, to indicate the fundamental limitations imposed by theory and prevent profitless investigations.

Whereas a body of theoretical research is available on the conditions of supersonic flow through Laval nozzles and around aerofoils, such is lacking for turbo-machinery in general, with the exception of some researches by Stodola, confined to axial steam turbines. The present paper investigates some important questions relating to the flow at supersonic velocity through centrifugal machines of the general type.

I want first of all to pay my very sincere thanks to the Council of the Royal Aeronautical Society for having invited me to give the Wilbur Wright Memorial Lecture. It is a high honour to be chosen, and I have derived pleasure and instruction from listening to, I think, nearly all of them.

It is everywhere acknowledged that the Wright brothers were the first to make sustained flights in a heavier-than-air machine at Kitty Hawk, North Carolina, on December 17, 1903.

Mainly because of acts and statements of former officers of the Smithsonian Institution, arising from tests made with the reconditioned Langley plane of 1903 at Hammondsport, New York, in 1914, Dr. Orville Wright feels that the Institution adopted an unfair and injurious attitude. He therefore sent the original Wright Kitty Hawk plane to England in 1928.

It is a well known fact that the (simple) Engineers’ Theory of Bending is based on the assumption of the Law of Proportionality, that is to say that the stress-strain characteristic of the material concerned is a straight line, and it accordingly follows that stress values determined by the formulæ: , for the stress at any station on the section, and M/Z for the maximum fibre stress can be correct only when the M/Z value lies within the limit of proportionality of the material.

In 1917–19, Barling and Webb, Berry, Cowley and Levy, and Webb and Lang discussed the elastic stability of struts of various tapers, but it appears to have escaped notice that one of the few cases in which formal integration is possible is that in which the tapered profile of axial longitudinal sections is part of a parabola; this gives a “ homogeneous linear “ differential equation, i.e., a linear equation of the form f (xd/dx) y = F (x).