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 (" s), 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.1 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.

3. In the ordinary screw the blades follow each other in rapid succession, so that they travel over nearly the same space, and operate upon nearly the same particles (whether water or air), in nearly the same interval of time. The limited range at their disposal is consequently not utilized, the action of the two blades being confined, as it were, to the same plane, and the blades being made to precede or follow each other in such a manner as necessitates the work being virtually performed only by one of them. This is particularly the case when the motion of the screw is rapid and the mass propelled is in the act of being set in motion, i.e. before it has acquired momentum. In this instance a large percentage of the moving or driving power is inevitably consumed in slip, from the fact of the blades of the screw operating on nearly the same particles of matter. The wings, on the other hand, do not follow each other, but have a distinct reciprocating motion, i.e. they dart first in one direction, and then in another and opposite direction, in such a manner that they make during the one stroke the current on which they rise and progress the next. The blades formed by the wings and the blur or impression produced on the eye by the blades when made to vibrate rapidly are widely separated,—the one blade and its blur being situated on the right side of the body and corresponding to the right wing, the other on the left and corresponding to the left wing. The right wing traverses and completely occupies the right half of a circle, and compresses all the air contained within this space; the left wing occupying and working up all the air in the left and remaining half. The range or sweep of the two wings, when urged to their extreme limits, corresponds as nearly as may be to one entire circle1 (fig. 56, p. 120). By separating the blades of the screw, and causing them to reciprocate, a double result is produced, since the blades always act upon independent columns of air, and in no instance overlap or double upon each other. The advantages possessed by this

1 Of this circle, the thorax may be regarded as forming the centre, the abdomen, which is always heavier than the head, tilting the body slightly in an upward direction. This tilting of the trunk favours flight by causing the body to act after the manner of a kite.

arrangement are particularly evident when the motion is rapid. If the screw employed in navigation be driven beyond a certain speed, it cuts out the water contained within its blades ; the blades and the water revolving as a solid mass. Under these circumstances, the propelling power of the screw is diminished rather than increased. It is quite otherwise with the screws formed by the wings; these, because of their reciprocating movements, becoming more and more effective in proportion as the speed is increased. As there seems to be no limit to the velocity with which the wings may be driven, and as increased velocity necessarily results in increased elevating, propelling, and sustaining power, we have here a striking example of the manner in which nature triumphs over art even in her most ingenious, skilful, and successful creations.

4. The vanes or blades of the screw, as commonly constructed, are fixed at a given angle, and consequently always strike at the same degree of obliquity. The speed, moreover, with which the blades are driven, is, as nearly as may be, uniform. In this arrangement power is lost, the two vanes striking after each other in the same manner, in the same direction, and almost at precisely the same moment,-no provision being made for increasing the angle, and the propelling power, at one stage of the stroke, and reducing it at another, to diminish the amount of slip incidental to the arrangement. The wings, on the other hand, are driven at a varying speed, and made to attack the air at a great variety of angles; the angles which the pinions make with the horizon being gradually increased by the wings being made to rotate on their long axes during the down stroke, to increase the elevating and propelling power, and gradually decreased during the up stroke, to reduce the resistance occasioned by the wings during their ascent. The latter movement increases the sustaining area by placing the wings in a more horizontal position. It follows from this arrangement that every particle of air within the wide range of the wings is separately influenced by them, both during their ascent and descent, the elevating, propelling, and sustaining power being by this means increased to a maximum, while the slip or waftage is reduced to a minimum.