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 (f) 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 a b c d e f g h i j k l 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 cdefghijklm 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.

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 ƒ, ƒ 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

produce a continuous vibration. The wing is also practically hinged along its anterior margin, so that the posterior margin of the wing travels through a greater space in a given time than a portion nearer the anterior margin (fig. 80, p. 149). The compound rotation of the wing is greatly facilitated by the wing being flexible and elastic. This causes the pinion to twist upon its long axis during its vibration, as already stated. The twisting is partly a vital, and partly a mechanical act; that is, it is occasioned in part by the action of the muscles, in part by the reaction of the air, and in part by the greater momentum acquired by the tip and posterior margin of the wing, as compared with the root and anterior margin; the speed acquired by the tip and posterior margin causing them to reverse always subsequently to the root and anterior margin, which has the effect of throwing the anterior and posterior margins of the wing into figure-of-8 curves. It is in this way that the posterior margin of the outer portion of the wing is made to incline forwards at the end of the down stroke, when the anterior margin is inclined backwards; the posterior margin of the outer portion of the wing being made to incline backwards at the end of the up stroke, when a corresponding portion of the anterior margin is inclined forwards (figs. 69 and 70, g, a, p. 141; fig. 86, j, ƒ, p. 161).

The Angles formed by the Wing during its Vibrations.-Not the least interesting feature of the compound rotation of the wing of the varying degrees of speed attained by its different parts—and of the twisting or plaiting of the posterior margin around the anterior, is the great variety of kite-like surfaces developed upon its dorsal and ventral aspects. Thus the tip of the wing forms a kite which is inclined upwards, forwards, and outwards, while the root forms a kite which is inclined upwards, forwards, and inwards. The angles made by the tip and cuter portions of the wing with the horizon are less than those made by the body or central part of the wing, and those made by the body or central part less than those made by the root and inner portions. The angle of inclination peculiar to any portion of the wing increases as the speed peculiar to said portion decreases, and vice versa. The wing is consequently mechanically perfect; the angles made by its

several parts with the horizon being accurately adjusted to the speed attained by its different portions during its travel to and fro. From this it follows that the air set in motion by one part of the wing is seized upon and utilized by another; the inner and anterior portions of the wing supplying, as it were, currents for the outer and posterior portions. This results from the wing always forcing the air outwards and backwards. These statements admit of direct proof, and I have frequently satisfied myself of their exactitude by experiments made with natural and artificial wings.

In the bat and bird, the twisting of the wing upon its long axis is more of a vital and less of a mechanical act than in the insect; the muscles which regulate the vibration of the pinion in the former (bat and bird), extending quite to the tip of the wing (fig. 95, p. 175; figs. 82 and 83, p. 158).

The Body and Wings move in opposite Curves.-I have stated that the wing advances in a waved line, as shown at a cegi of fig. 81, p. 157; and similar remarks are to be made of the body as indicated at 1, 2, 3, 4, 5 of that figure. Thus, when the wing descends in the curved line a c, it elevates the body in a corresponding but minor curved line, as at 1, 2; when, on the other hand, the wing ascends in the curved line ce, the body descends in a corresponding but smaller curved line (2, 3), and so on ad infinitum. The undulations made by the body are so trifling when compared with those made by the wing, that they are apt to be overlooked. They are, however, deserving of attention, as they exercise an important influence on the undulations made by the wing; the body and wing swinging forward alternately, the one rising when the other is falling, and vice versû. Flight may be regarded as the resultant of three forces :-the muscular and elastic force, residing in the wing, which causes the pinion to act as a true kite, both during the down and up strokes; the weight of the body, which becomes a force the instant the trunk is lifted from the ground, from its tendency to fall downwards and forwards; and the recoil obtained from the air by the rapid action of the wing. These three forces may be said to be active and passive by turns.

When a bird rises from the ground it runs for a short