Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/223

Rh Philosophy, 1822), that: “The resistances do by no means vary in the ratio of the squares of the sines of the angle of incidence; and for small angles the resistances are more nearly proportional to the sines than to their squares.” This is a very important statement, from which a vast amount of inference may be drawn; it has been fully justified by the subsequent work of Wenham, Dines, Langley, and others.

The most direct disproof of the Newtonian law is to be found in experiments with the falling plane. It is found that if a horizontal plane, suitably mounted in vertical guides, be allowed to fall freely, the time of fall may be increased almost indefinitely by imparting to it a simultaneous horizontal motion. This was pointed out by Wenham in the year 1866, and has more recently been brought into prominence by the experiments of the late Professor Langley. Langley employed an appliance which he termed a “plane dropper,” mounted upon the arm of his “whirling table” (§ 233), for making his determinations. It is of interest to note that although Langley took occasion more than once to comment upon the defects of the Newtonian law, as a deduction from his other experiments, he did not apparently appreciate that the falling plane really constitutes a direct disproof.

§ 147. The Square Plane.—The nature of the Newtonian discrepancy and the extent of agreement between the work of different investigators may be exemplified in the case of the plane of square form.

The square plane may be taken as the type of greatest simplicity which includes generally planes of square proportion; such planes are not affected seriously by considerations of “aspect,” although doubtless a square plane will not give exactly the same results in diagonal as in square presentation. The latter is always assumed in the absence of an explicit statement to the contrary.

In Fig. 93, in which ordinates represent the relative pressure