Here the arrows _r s_ indicate the range of the wing. At the beginning of the down stroke the upper or dorsal surface of the wing (_i d f_) is inclined slightly upwards and forwards. As the wing descends the posterior margin (_i f_) twists and rotates round the anterior margin (_i d_), and greatly increases the angle of inclination as seen at _i j_, _g h_. This rotation of the posterior margin (_i j_) round the anterior margin (_g h_) has the effect of causing the different portions of the under surface of the wing to assume various angles of inclination with the horizon, the wing attacking the air like a boy’s kite. The angles are greatest towards the root of the wing and least towards the tip. They accommodate themselves to the speed at which the different parts of the wing travel--a small angle with a high speed giving the same amount of buoying power as a larger angle with a diminished speed. The screwing of the under surface of the wing (particularly the posterior margin) in a downward direction during the down stroke is necessary to insure the necessary upward recoil; the wing being made to swing downwards and forwards pendulum fashion, for the purpose of elevating the body, which it does by acting upon the air as a long lever, and after the manner of a kite. During the down stroke the wing is active, the air passive. In other words, the wing is depressed by a purely vital act. The down stroke is readily explained, and its results upon the body obvious. The real difficulty begins with the up or return stroke. If the wing was simply to travel in an upward and backward direction from _c_ to _a_ of fig. 84, p. 160, it is evident that it would experience much resistance from the superimposed air, and thus the advantages secured by the descent of the wing would be lost. What really happens is this. The wing does not travel upwards and _backwards_ in the direction _c b a_ of fig. 84 (the body, be it remembered, is advancing) but upwards and _forwards_ in the direction _c d e f g_. This is brought about in the following manner. The wing is at right angles to the horizon (_x x´_) at _c_. It is therefore caught by the air at the point (2) because of the more or less horizontal travel of the body; the elastic ligaments and other structures combined with the resistance experienced from the air rotating the posterior or thin margin of the pinion in an upward direction, as shown at _d e f g_ and _d f g_ of figs. 84 and 85, p. 160. The wing by this partly vital and partly mechanical arrangement is rotated off the wind in such a manner as to keep its dorsal or non-biting surface directed upwards, while its concave or biting surface is directed downwards. The wing, in short, has its planes so arranged, and its angles so adjusted to the speed at which it is travelling, that it darts up a gradient like a true kite, as shown at _c d e f g_ of figs. 84 and 85, p. 160, or _g h i_ of fig. 88, p. 166. The wing consequently elevates and propels