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IN these articles an attempt will be made to provide an introduction to a large subject specially serviceable to engineers. Restrictions on space make themselves felt in various ways. Proper acknowledgments cannot be given for the sources of information beyond mention of the books of Bairstow, Lamb, Cowley and Levy, and Glauert, to which frequent reference has been made. No account can be included of the fascinating and often instructive historical development of the science; it must be assumed that proofs of various essential theorems will be sought in text‐books of Engineering, Mathematics and Physics; lastly, there can occur little opportunity for the working of illustrative examples upon which a proper grip of the subject greatly depends. The engineer of experience will detect much that, with slight generalisation, could be made capable of important use in other branches of his profession, but in this treatment we shall keep closely in view the scientific aspect of aircraft design, structural strength apart.

Examination in Article I of the nature of the force arising on a body in steady motion through the atmosphere, showed it to depend upon the shape and size of the body, the density and viscosity of the air, and the relative velocity. No other factor enters which cannot be traced to these variables until, at velocities approaching that of sound, compressibility makes itself felt. Mathematical difficulties compel us to leave the question of shape to the laboratory, where smallscale models may be suspended in an artificial wind, and aerodynamical details determined by practical means. The design of aircraft from experimental data, with regard to shape, may involve, however, large changes in the other variables, and it is essential to investigate at the outset what means and justification exist for the transition.

Each form of normal, steady aeroplane flight dictates a particular setting of the control surfaces and engine throttle. In whatever circumstances a desired steady motion may be pre‐arranged in this way, a completely stable aeroplane will establish of its own devices the speed and other conditions necessary for equilibrium. No help is demanded from the pilot, or from automatic operation of the controls, which are supposed to remain fixed, but only a sulficient space for transitional manoeuvring. It follows that if the aeroplane be subsequently disturbed, whether by accident or design, left to itself it will return to its arranged motion.

IT is a common experience, and by no means confined to engineers, to fail to understand the general theory of non‐rectilinear flow of air. An investigation culminates, of course, in the well ‐ known equations of viscous motion. But, as Dr. Prescott remarked recently when introducing his new proof, many derivations of these are cither unsatisfying or else difficult to follow. Indeed, the equations are usually taken for granted. Yet the disadvantage is obvious: even the mathematician can do very little with them in the end, and fundamental ideas on which the proof rests, though likely to be of general service to engineers, lie buried. An example is perhaps worth while. Consider the problem of determining the viscosity of an oil from measurement of the torque required slowly to revolve a circular cylinder in a tank or pot of it. The equations of motion can be solved in this case, but it is not necessary to go so far; there is a well‐known treatment much more to the heart of an engineer. On the other hand, the usual theory of rectilinear viscous flow is without avail, and if the engineer can solve this simple problem without the equations then he understands the bulk of the proof of them.

WE found, on experimental grounds in Article I, that the field of air‐flow past a short body of low resistance shape, such as an aerofoil, comprises two dissimilar parts: (a) a thin boundary layer enveloping the body and dominated by viscous effects, and (b) a motion outside the boundary layer in which viscosity is much less important. It will be remembered that in the external motion occur the large pressure changes, which, transmitted through the boundary layer, account for nearly all the lift and for part of the drag. These pressures we observed to be calculable from the velocities without appreciable error by Bernoulli's equation. In the present Article we confine attention to this external flow, assuming it to be steady, incompressible, and inviscid. Its dependence upon (a), already discussed to some extent, we ignore; the boundary layer is conceived to be everywhere very thin, so that the only role it plays is to allow of relative velocity at the surface of the body. The assumptions made, excepting that of incompressibility, will appear drastic, and it will not be surprising if some of our deductions prove discordant with experimental fact. Nevertheless, they lead to a theory which finds many applications and uses in real fluid motion, and, in particular, gives an intimate view of aerofoil flow that is very close to the truth. It is convenient to develop our reasoning in analytical terms and for simplicity to restrict the flow to two dimensions (Article 1, §5). But the engineer will find special scope in this part of aerodynamics for graphical methods in the solution of particular problems.

The two volumes recording the work of the Congress together run to some 1,700 pages. The presentation is good, and several lecturers have graciously met our peculiar national difficulty by giving their papers in English. The summaries in French are also a great help.

THE recently developed families of mathematical wing profiles have already been investigated theoretically in two papers. It is hoped, however, that these sections will not be confined to purely scientific work, but will find a place in design. A description in more practical terms is therefore of interest.

(1) An aircraft in steady, straight‐line motion can have no resultant force or couple acting upon it. This condition is never continuously maintained in flight, and the craft proceeds in a series of oscillations or wide, corrected curves. Continuous adjustment takes place in the direction of its flight through either an inherent stability or a judicious use of the controls by the pilot, but the motion may be regarded mostly without error as steady for purposes of design. Calculations carried out on the basis of steady equilibrium have for objects the determination of optimum lay‐out; the selection of most suitable component parts; the provision of adequate and easeful control; the specification of loading for strength design; and the prediction and testing of performance. In practice, such calculations go hand in hand with others concerned with statical and dynamical stability; with accel‐erated motions; with strength and weight; and with a host of purely practical considerations. Deductions drawn from the principles discussed in this Article may not be decisive in a given case till set in proper perspective. In this connection we note, without straying from our subject matter, that many secondary factors are here neglected, whose effect the engineer has, on occasion, to take carefully into account.

THE greatly increased transition Reynolds numbers now attained in the boundary layers of cylinders having favourably shaped sections have renewed interest in the solution of the equations of steady flow in a thin boundary layer. It is familiar that the scries solutions of Blasius and Hiemenz, improved by Howarth (ref. 1), and of Falkner (ref. 2) become severely restricted in range when applied to cylinders having other than bluff sections. But it appears that a series solution of substantially greater range is possible, at least for symmetrical flow, provided that the nose of the section is rounded. This problem forms the subject of Section I of the present paper.

TWENTY years ago, engineering youth emerging from apprenticeship often had reason for regarding the possession of a university degree as an invidious distinction, on the whole rather better concealed. Nowadays, it is difficult for universities to cope with the demand from certain branches of the engineering industry for young men of suitable education with talent for work.