wing during the down stroke is well seen in the dragon-fly, represented at fig. 86, p. 161.

Here the arrows rs indicate the range of the wing. At the beginning of the down stroke the upper or dorsal surface of the wing (i d ƒ) is inclined slightly upwards and forwards. As the wing descends the posterior margin (if) twists and rotates round the anterior margin (i d), and greatly increases the angle of inclination as seen at ij, gh. This rotation of the posterior margin (ij) round the anterior margin (gh) 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 cba 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 (xx) 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 defg and dfg 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 nonbiting 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 ghi of fig. 88, p. 166. The wing consequently elevates and propels during its ascent as well as during its descent. It is, in fact, a kite during both the down and up strokes. The ascent of the wing is greatly assisted by the forward travel, and downward and forward fall of the body. This view will be readily understood by supposing, what is really the case, that the wing is more or less fixed by the air in space at the point indicated by 2 of figs. 84 and 85, p. 160; the body, the instant the wing is fixed, falling downwards and forwards in a curve, which, of course, is equivalent to placing the wing above, and, so to speak, behind the volant. animal-in other words, to elevating the wing preparatory to a second down stroke, as seen at g of the figures referred to (figs. 84 and 85). The ascent and descent of the wing is always very much greater than that of the body, from the fact of the pinion acting as a long lever. The peculiarity of the wing consists in its being a flexible lever which acts upon yielding fulcra (the air), the body participating in, and to a certain extent perpetuating, the movements originally produced

by the pinion. The part which the body performs in flight is indicated at fig. 87. At a the body is depressed, the wing being elevated and ready to make the down stroke at b. The

wing descends in the direction cd, but the moment it begins to descend the body moves upwards and forwards (see arrows) in a curved line to e. As the wing is attached to the body the wing is made gradually to assume the position f. The body (e), it will be observed, is now on a higher level than the wing (f); the under surface of the latter being so adjusted that it strikes upwards and forwards as a kite. It is thus that the wing sustains and propels during the up stroke. The body (e) now falls downwards and forwards in a curved line to g, and in doing this it elevates or assists in elevating the wing to j. The pinion is a second time depressed in the direction kl, which has the effect of forcing the body along a waved track and in an upward direction until it reaches the point m. The ascent of the body and the descent of the wing take place simultaneously (mn). The body and wing, are alternately above and beneath a given line x x'.

A careful study of figs. 84, 85, 86, and 87, pp. 160, 161, and 163, shows the great importance of the twisted configuration and curves peculiar to the natural wing. If the wing was not curved in every direction it could not be rolled on and off the wind during the down and up strokes, as seen more particularly at fig. 87, p. 163. This, however, is a vital point in progressive flight. The wing (b) is rolled on to the wind in the direction ba, its under concave or biting surface being crushed hard down with the effect of elevating the body to e. The body falls to g, and the wing (ƒ) is rolled off the wind in the direction fj, and elevated until it assumes the position j. The elevation of the wing is effected partly by the fall of the body, partly by the action of the elevator muscles and elastic ligaments, and partly by the reaction of the air, operating on its under or concave biting surface. The wing is therefore to a certain extent resting during the up stroke.

The concavo-convex form of the wing is admirably adapted for the purposes of flight. In fact, the power which the wing possesses of always keeping its concave or under surface directed downwards and forwards enables it to seize the air at every stage of both the up and down strokes so as to supply a persistent buoyancy. The action of the natural wing is accompanied by remarkably little slip-the elasticity of the

organ, the resiliency of the air, and the shortening and elongating of the elastic ligaments and muscles all co-operating and reciprocating in such a manner that the descent of the wing elevates the body; the descent of the body, aided by the reaction of the air and the shortening of the elastic ligaments and muscles, elevating the wing. The wing during the up stroke arches above the body after the manner of a parachute, and prevents the body from falling. The sympathy which exists between the parts of a flying animal and the air on which it depends for support and progress is consequently of the most intimate character.

The up stroke (B, D of figs. 84 and 85, p. 160), as will be seen from the foregoing account, is a compound movement due in some measure to recoil or resistance on the part of the air; to the shortening of the muscles, elastic ligaments, and other vital structures; to the elasticity of the wing; and to the falling of the body in a downward and forward direction. The wing may be regarded as rotating during the down stroke upon 1 of figs. 84 and 85, p. 160, which may be taken to represent the long and short axes of the wing; and during the up stroke upon 2, which may be taken to represent the yielding fulcrum furnished by the air. A second pulsation is indicated by the numbers 3 and 4 of the same figures (84, 85).

The Wing acts upon yielding Fulcra.-The chief peculiarity of the wing, as has been stated, consists in its being a twisted flexible lever specially constructed to act upon yielding fulcra (the air). The points of contact of the wing with the air are represented at abcdefghijkl respectively of figs. 84 and 85, p. 160; and the imaginary points of rotation of the wing upon its long and short axes at 1, 2, 3, and 4 of the same figures. The assumed points of rotation advance from 1 to 3 and from 2 to 4 (vide arrows marked r and s, fig. 85); these constituting the steps or pulsations of the wing. The actual points of rotation correspond to the little loops a b c d fghijl of fig. 85. The wing descends at A and C, and ascends at B and D.

The Wing acts as a true Kite both during the Down and Up Strokes. If, as I have endeavoured to explain, the wing, even when elevated and depressed in a strictly vertical direction, inevitably and invariably darts forward, it follows as a con

sequence that the wing, as already partly explained, flies forward as a true kite, both during the down and up strokes, as shown at c d e f g h i j k l m of fig. 88; and that its under concave or biting surface, in virtue of the forward travel communicated to it by the body in motion, is closely applied to the air, both during its ascent and descent-a fact hitherto overlooked, but one of considerable importance, as showing how the wing furnishes a persistent buoyancy, alike when it rises and falls.

b

k

m

FIG. 88.

f

In fig. 88 the greater impulse communicated during the down stroke is indicated by the double dotted lines. The angle made by the wing with the horizon (a b) is constantly varying, as a comparison of c with d, d with e, e with f, f with g, g with h, and h with i will show; these letters having reference to supposed transverse sections of the wing. This figure also shows that the convex or non-biting surface of the wing is always directed upwards, so as to avoid unnecessary resistance on the part of the air to the wing during its ascent; whereas the concave or biting surface is always directed downwards, so as to enable the wing to contend successfully with gravity.

Where the Kite formed by the Wing differs from the Boy's Kite. -The natural kite formed by the wing differs from the artificial kite only in this, that the former is capable of being moved in all its parts, and is more or less flexible and elastic, the latter being comparatively rigid. The flexibility and elasticity of the kite formed by the natural wing is rendered necessary by the fact that the wing is articulated or hinged at its root; its different parts travelling at various degrees of speed in proportion as they are removed from the axis of rotation. Thus the tip of the wing travels through a much greater space in a given time than a portion nearer the root. If the wing was not flexible and elastic, it would be impossible to reverse it at the end of the up and down strokes, so as to