This point has been fully investigated, so far as the square plane is concerned, by Joessel, Kummer, and Langley. It is found that for the normal plane the geometric and pressure centres are coincident, but that as the plane is inclined the latter is displaced towards the leading edge, the displacement of the centre of pressure increasing as the angle made by the plane to its line of flight becomes less and less. This is shown in the form of a diagram in Fig. 94, in which it is supposed that the plane is swung through a quadrant, from zero to 90 degrees, the locus of its centre of pressure, as determined by the different observers, being indicated in the figure, in which also are given the position of the plane at every 10 degrees angle, and one-tenth divisions from which the position of the centre of pressure may be read in terms of the width of the plane.
The general character of the curves of the square plane, both as to magnitude and location of pressure, are shared to a greater or less extent by planes of other proportions.
§ 149. Plausibility of the Sine2 Law.—The general acceptance of the experimental fact that the sine2 law is in error, has without doubt been delayed by the very plausibility of the law itself.
If we suppose (as is quite customary in dealing with physical problems) that the diagonal motion of the plane is compounded of its edgewise and normal components, then, as in the previous discussion (§ 145), we may, neglecting skin friction, regard the former as of no influence and the pressure as due entirely to the normal component. In greater detail, if we suppose the motion of the plane to take place in steps, i.e., alternate edgewise and normal movements, and if we assume the former to take place with infinite rapidity, and the steps to become infinitely numerous, then it would appear that the pressure due to the inclined motion has been demonstrated to be, in effect, exactly that due to the normal component of the whole motion.
The above reasoning is manifestly in error, since the result does not accord with experience. The fallacy has been pointed
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