a vertical direction, the horizontal and vertical motions being the horizontal and vertical components of the actual resultant motion of the fluid. We may regard the latter as in the main consisting of two parallel cylindrical vortices, having right and left-handed rotation respectively, which are being continually formed at the flank extremities (as in Fig. 61, reading this figure as an end-on presentation), whose energy is being continually dissipated in the wake of the advancing aerofoil.
From another point of view, this loss of energy may be looked upon as a gradual spreading out and dissipation of the wave (§ 116) on the crest of which the aerofoil rides, and it becomes necessary that the aerofoil should constantly renew the diminished wave energy in order to maintain sufficient amplitude and support the given load.
The first of these conceptions, i.e., that of the vortex cylinders, is not, for a perfect fluid, compatible with hydrodynamic theory, for such vortex motion would involve rotation, and could not be generated in a perfect fluid without involving a violation of Lagrange's theorem (§ 71). In an actual fluid this objection has but little weight, owing to the influence of viscosity, and it is worthy of note that the somewhat inexact method of reasoning adopted in the foregoing demonstration seems to be peculiarly adapted, qualitatively speaking, for exploring the behaviour of real fluids, though rarely capable of giving quantitative results. The problem in three dimensions will be again examined after reviewing the subject on more rigid lines.
§ 118. On the Sectional Form of the Aerofoil.—We are at the present juncture in a position to draw certain elementary inferences as to the form of aerofoil appropriate to the motion of the air in its vicinity. The two aspects of form which are of most interest are, firstly, cross-section by a vertical plane in the direction of motion; and secondly, plan-form or projection on a horizontal plane.
The immediate function performed by the sectional form of the
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