insect it is due to a twisting which occurs at the root of the wing and to the reaction of the air.

FIG. 76. Curves seen on the anterior (de f) and posterior (ca b) margin in the wing of the bird in flexion.- Original.

FIG. 77.-Curves seen on the anterior margin (de f) of the wing in semi-extension. In this case the curves on the posterior margin (b c) are obliterated.-Original.

FIG. 78.-Curves seen on the anterior (de f) and posterior (e a b) margin of the wing in extension. The curves of this fig. are the converse of those seen at fig. 76. Compare these figs. with fig. 79 and fig. 32, p. 68.-Original.

The Tip of the Bat and Bird's Wing describes an Ellipse.The movements of the wrist are always the converse of those occurring at the elbow-joint. Thus in the bird, during extension, the elbow and bones of the forearm are elevated, and describe one side of an ellipse, while the wrist and bones of the hand are depressed, and describe the side of another and opposite ellipse. These movements are reversed during flexion, the elbow being depressed and carried backwards, while the wrist is elevated and carried forwards (fig. 79).

FIG. 79.-(a b) Line along which the wing travels during extension and flexion. The body of the fish in swimming describes similar curves to those described by the wing in flying.-(Vide fig. 32, p. 68.)

The Wing capable of Change of Form in all its Parts-From this description it follows that when the different portions of the anterior margin are elevated, corresponding portions of the posterior margin are depressed; the different parts of the wing moving in opposite directions, and playing, as it were, at cross purposes for a common good; the object being to rotate or screw the wing down upon the wind at a gradually increasing angle during extension, and to rotate it in an

opposite direction and withdraw it at a gradually decreasing angle during flexion. It also happens that the axillary and distal curves co-ordinate each other and bite alternately, the distal curve posteriorly seizing the air in extreme extension with its concave surface (while the axillary curve relieves itself by presenting its convex surface); the axillary curve, on the other hand, biting during flexion with its concave surface (while the distal one relieves itself by presenting its convex one). The wing may therefore be regarded as exercising a fourfold function, the pinion in the bat and bird being made to move from within outwards, and from above downwards in the down stroke, during extension; and from without inwards, and from below upwards, in the up stroke, during flexion.

The Wing during its Vibration produces a Cross Pulsation.-The oscillation of the wing on two separate axes-the one running parallel with the body of the bird, the other at right angles to it (fig. 80, a b, c d)-is well worthy of attention, as showing that the wing attacks the air, on which it operates in every direction, and at almost the same moment, viz. from within outwards, and from above downwards, during the down stroke; and from without inwards, and from below upwards, during the up stroke. As a corollary to the foregoing, the wing may be said to agitate the air in two principal directions, viz. from within outwards and downwards, or the converse; and from behind forwards, or the converse; the agitation in question producing two powerful pulsations, a vertical and a horizontal. The wing when it ascends and descends produces artificial currents which increase its elevating and propelling power. The power of the wing is further augmented by similar currents developed during its extension and flexion. The movement of one part of the wing contributes to the movement of every other part in continuous and uninterrupted succession. As the curves of the wing glide into each other when the wing is in motion, so the one pulsation merges into the other by a series of intermediate and lesser pulsations.

The vertical and horizontal pulsations occasioned by the wing in action may be fitly represented by wave-tracks running

at right angles to each other, the vertical wave-track being the more distinct.

Compound Rotation of the Wing.-To work the tip and posterior margin of the wing independently and yet simultaneously, two axes are necessary, one axis (the short axis) corresponding to the root of the wing and running across it; the second (the long axis) corresponding to the anterior margin of the wing, and running in the direction of its length. The long and short axes render the movements of the wing eccentric in character. In the wing of the bird the movements of the primary or rowing feathers are also eccentric, the shaft of each feather being placed nearer the anterior than the posterior margin; an arrangement which enables the feathers to open up and separate during flexion and the up stroke, and approximate and close during extension and the down one. These points are illustrated at fig. 80, where a b represents

the short axis (root of wing) with a radius e f; c d representing the long axis (anterior margin of wing) with a radius g p. Fig. 80 also shows that, in the wing of the bird, the individual, primary, secondary, and tertiary feathers have each what is equivalent to a long and a short axis. Thus the primary, secondary, and tertiary feathers marked h, i, j, k,l are capable of rotating on their long axes (rs), and upon their short axes (m n). The feathers rotate upon their long axes in a direction from below upwards during the down stroke, to make the wing impervious to air; and from above down

wards during the up stroke, to enable the air to pass through it. The primary, secondary, and tertiary feathers have thus a distinctly valvular action. The feathers rotate upon their short axes (mn) during the descent and ascent of the wing, the tip of the feathers rising slightly during the descent of the pinion, and falling during its ascent. The same movement virtually takes place in the posterior margin of the wing of the insect and bat.

The Wing vibrates unequally with reference to a given Line.— The wing, during its vibration, descends further below the body than it rises above it. This is necessary for elevating purposes. In like manner the posterior margin of the wing (whatever the position of the organ) descends further below the anterior margin than it ascends above it. This is requisite for elevating and propelling purposes; the under surface of the wing being always presented at a certain upward angle to the horizon, and acting as a true kite (figs. 82 and 83, p. 158. Compare with fig. 116, p. 231). If the wing oscillated equally above and beneath the body, and if the posterior margin of the wing vibrated equally above and below the line formed by the anterior margin, much of its elevating and propelling power would be sacrificed. The tail of the fish oscillates on either side of a given line, but it is otherwise with the wing of a flying animal. The fish is of nearly the same specific gravity as the water, so that the tail may be said only to propel. The flying animal, on the other hand, is very much heavier than the air, so that the wing requires both to propel and elevate. The wing, to be effective as an elevating organ, must consequently be vibrated rather below than above the centre of gravity; at all events, the intensity of the vibration should occur rather below that point. In making this statement, it is necessary to bear in mind that the centre of gravity is ever varying, the body rising and falling in a series of curves as the wings ascend and descend.

To elevate and propel, the posterior margin of the wing must rotate round the anterior one; the posterior margin being, as a rule, always on a lower level than the anterior one. By the oblique and more vigorous play of the wings under rather than above the body, each wing expends its entire energy in

1 The degree of valvular action varies according to circumstances.

pushing the body upwards and forwards. It is necessary that the wings descend further than they ascend; that the wings be convex on their upper surfaces, and concave on their under ones; and that the concave or biting surfaces be brought more violently in contact with the air during the down stroke than the convex ones during the up stroke. The greater range of the wing below than above the body, and of the posterior margin below than above a given line, may be readily made out by watching the flight of the larger birds. It is well seen in the upward flight of the lark. In the hovering of the kestrel over its quarry, and the hovering of the gull over garbage which it is about to pick up, the wings play above and on a level with the body rather than below it; but these are exceptional movements for special purposes, and as they are only continued for a few seconds at a time, do not affect the accuracy of the general statement.

Points wherein the Screws formed by the Wings differ from those employed in navigation.-1. In the blade of the ordinary screw the integral parts are rigid and unyielding, whereas, in the blade of the screw formed by the wing, they are mobile and plastic (figs. 93, 95, 97, pp. 174, 175, 176). This is a curious and interesting point, the more especially as it does not seem to be either appreciated or understood. The mobility and plasticity of the wing is necessary, because of the tenuity of the air, and because the pinion is an elevating and sustaining organ, as well as a propelling one.

2. The vanes of the ordinary two-bladed screw are short, and have a comparatively limited range, the range corresponding to their area of revolution. The wings, on the other hand, are long, and have a comparatively wide range; and during their elevation and depression rush through an extensive space, the slightest movement at the root or short axis of the wing being followed by a gigantic up or down stroke at the other (fig. 56, p. 120; figs. 64, 65, and 66, p. 139; figs. 82 and 83, p. 158). As a consequence, the wings as a rule act upon successive and undisturbed strata of air. The advantage gained by this arrangement in a thin medium like the air, where the quantity of air to be compressed is necessarily great, is simply incalculable.