A start is made by considering why the subsonic propeller was abandoned when aircraft speeds approached the shock stall. It is true that the shock stall also occurs on the propeller blades under these conditions, causing a loss of lift and an increase of drag, but this is not the predominant effect which produces the marked decrease of propeller efficiency associated with high-speed aircraft. The main aerodynamic difficulty associated with the shock stall on the wings of an aircraft is due to the separation of flow caused by the shock wave rather than the presence of the shock wave itself. This difficulty is reduced on a propeller, as any separation of flow which might occur on a propeller blade due to the shock stall, would tend to cause the air to be stagnant relative to the blade, and would thus experience a large centrifugal force by virtue of the propeller rotation. Thus the propeller shock stall would never develop to the same degree that it does on the wings of an aircraft in steady flight.

It has almost become a tradition in recent years to begin a paper on boundary layer by paying a tribute to the great Prandtl and his famous paper in which he introduced the conception of boundary layer into Fluid Dynamics.

The year 1954 is, however, not only memorable to mark the passing of fifty years since Prandtl's classical demonstration of the effect of boundary layer suction on the flow pattern around a cylinder; it is also memorable because in 1954 most convincing demonstrations of practical applications of boundary layer control for aircraft have taken place. I am referring, in particular, to the demonstrations with the Attinello flap in the United States which mark the introduction of one form of boundary layer control as an engineering and practical reality.

A new method for evaluating determinants or matrices is given; it is rather tedious to describe and awkward to prove, but is very easy to use. The chief advantages this method is believed to possess are:

1. (i) It involves as few arithmetical manipulations as does the most rapid method of pivotal condensation currently used.

2. (ii) It is easier than any other known method to learn and to remember.

3. (iii) It can be adapted to routine computation, in such a way as to minimise the likelihood of error.

4. (iv) A digital computor can readily be programmed to use it.

The one-thousandth-and-fourth Lecture to be given before the Society, " London Airport," by Air Marshal Sir John D'Albiac, K.B.E., C.B., D.S.O., was given on 6th November 1956 at the Institution of Mechanical Engineers, London, S.W.I. Mr. E. T. Jones, C.B., O.B.E., F.R.Ae.S.. President of the Society, presided. Introducing the Lecturer, Mr. Jones said that they were to hear from the most competent man in England to give it, a talk on what he would say was the finest airport in the world. He did not think they had had a lecture on a modern airport before and it was worth while reflecting on previous means of transportation. Every previous vehicle of transport before the aeroplane had had to have tracks made for it to take it from one place to another, as well as terminal stations built for it on long distance journeys. Soma people commented on the costs of airports, the amount of concrete, etc., but when one realised that the air was provided free of charge and itself provided the means for the aircraft to go from one concrete patch to another, one appreciated that the airport was cheap compared with previous forms of transport. Air Marshal Sir John D'Albiac had, he thought, possibly one of the most interesting jobs in London; he met all the personalities, film stars, and so on. He had been there since 1946 when London Airport was converted from a small airfield. He therefore knew every little bit about it, control, runways, buildings and everything. Sir John started his career in the Army. He found that a little too slow for him and so he transferred to the Royal Naval Air Service. Whether he found that still not quite fast enough he did not know, but he later transferred to the Royal Air Force and he remained in that Service until about 1946 when he retired with the rank of Air Marshal.

During the past few years numerous developments in the hydrodynamic design of flying-boats have been brought about mainly by systematic model research. Although Germany deserves the credit for initiating research on the forces on planing plates and Vee wedges, we are indebted to various estabhshments in the U.S.A. for the multiplicity of data on both flying-boats and simple planing surfaces, which are now available.

It is known from both theoretical and experimental investigations that St. Venant's assumption on the constancy of the shape of the cross section of girders in pure bending does not hold true in case of thin-walled sections. The greater flexibility than calculated according to ordinary bending theory of initially curved tubes, as experimentally found by Professor Bantlin, was perfectly explained by Professor von Kármán in 1911 on the assumption of a flattening of the section.

In 1927 Brazier with the aid of the variational method determined exactly that the shape of an originally circular thin-walled bent cylinder corresponding to the least potential energy is quasi elliptical and that the cross section of the cylinder, therefore, must flatten, even if the centre line of the cylinder was originally straight. In consequence of the flattening St. Venant's linear law for the curvature loses its validity and the curvature increases more rapidly than the bending moment. For a certain value of the curvature the bending moment is a maximum, and after this value was reached the curvature increases even if the applied moment remains unchanged or decreases, fulfilling thereby the criterion of instability. This instability occurs when the rate of flattening, i.e., the maximum radial displacement of any point of the circumference of the tube divided by the original radius of the tube, will equal 2/9.

Unshrouded impellers of centrifugal compressors and centripetal turbines manifest an increase of the flow losses in comparison with the shrouded ones. Assuming that the controlling factor in such increase of loss is the leakage through the gap between wheel and casing, the author develops a simple theory leading to a formula for the volumetric efficiency. Only one experimental quantity is required for applying the formula; and tentative values, based on some experimental evidence, are presented.

In a recent paper, Yates has shown that it is convenient to distinguish between two main types of stimulus which induce torsional vibration in geared-shaft systems. The first, which is dealt with in detail in the literature, is “force excitation” by which periodic torques act upon the system and throw it into oscillation; for the purpose of this note, it will be convenient to refer to a previous article as dealing with this problem.

The second type of excitation to which Yates refers is “displacement excitation.” It may be thought of as arising from errors in the cutting of gears which cause periodic variations in the velocity ratio of mating components. A Hooke's joint which couples two rotating systems which are capable of torsional oscillation would give rise to this form of stimulus.