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the wing of the bat and bird. The principle is, however, in both cases the same, the loops ultimately terminating in a waved track. The impulse is communicated to the insect wing at the heavy parts of the loops a b c d e f g h i j k l m n of fig. 71; the waved tracks being indicated at p q r s t of the same figure. The recoil obtained from the air is represented at corresponding letters of fig. 72, the body of the

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insect being carried along the curve indicated by the dotted line. The impulse is communicated to the wing of the bat and bird at the heavy part of the loops a bcdefghijklmno of fig. 73, the waved track being indicated at p s t u v w of this figure. When the horizontal speed attained is high, the wing is successively and rapidly brought into contact with innumerable columns of undisturbed air. It, consequently, is a matter of indifference whether the wing is carried at a high speed against undisturbed air, or whether it operates upon air

travelling at a high speed (as, e.g. the artificial currents produced by the rapidly reciprocating action of the wing). The result is the same in both cases, inasmuch as a certain quantity of air is worked up under the wing, and the necessary degree of support and progression extracted from it. It is, therefore, quite correct to state, that as the horizontal speed of the body increases, the reciprocating action of the wing decreases; and vice versâ. In fact the reciprocating and nonreciprocating action of the wing in such cases is purely a matter of speed. If the travel of the wing is greater than the horizontal travel of the body, then the figure-of-8 and the reciprocating power of the wing will be more or less perfectly developed, according to circumstances. If, however, the

horizontal travel of the body is greater than that of the wing, then it follows that no figure-of-8 will be described by the wing; that the wing will not reciprocate to any marked

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FIG. 74.

FIG. 75.

Figs. 74 and 75 show the more or less perpendicular direction of the stroke of the wing in the flight of the bird (gull)-how the wing is gradually extended as it is elevated (e f g of fig. 74)-how it descends as a long lever until it assumes the position indicated by h of fig. 75-how it is flexed towards the termination of the down stroke, as shown at hij of tig. 75, to convert it into a short lever (a b), and prepare it for making the up stroke. The difference in the length of the wing during flexion and extension is indicated by the short and long levers a b and c d of fig. 75. The sudden conversion of the wing from a long into a short lever at the end of the down stroke is of great importance, as it robs the wing of its momentum, and prepares it for reversing its movements. Compare with figs. 82 and 83, p. 158.-Original.

extent; and that the organ will describe a waved track, the curves of which will become less and less abrupt, i.e. longer and longer in proportion to the speed attained. The more

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vertical direction of the loops formed by the wing of the bat and bird will readily be understood by referring to figs. 74 and 75 (p. 145), which represent the wing of the bird making the down and up strokes, and in the act of being extended and flexed. (Compare with figs. 64, 65, and 66, p. 139; and figs. 67, 68, 69, and 70, p. 141.)

The down and up strokes are compound movements,—the termination of the down stroke embracing the beginning of the up stroke; the termination of the up stroke including the beginning of the down stroke. This is necessary in order that the down and up strokes may glide into each other in such a manner as to prevent jerking and unnecessary retardation.

The Margins of the Wing thrown into opposite Curves during Extension and Flexion.-The anterior or thick margin of the wing, and the posterior or thin one, form different curves, similar in all respects to those made by the body of the fish in swimming (see fig. 32, p. 68). These curves may, for the sake of clearness, be divided into axillary and distal curves, the former occurring towards the root of the wing, the latter towards its extremity. The curves (axillary and distal) found on the anterior margin of the wing are always the converse of those met with on the posterior margin, i.e. if the convexity of the anterior axillary curve be directed downwards, that of the posterior axillary curve is directed upwards, and so of the anterior and posterior distal curves. The two curves (axillary and distal), occurring on the anterior margin of the wing, are likewise antagonistic, the convexity of the axillary curve being always directed downwards, when the convexity of the distal one is directed upwards, and vice versa. The same holds true of the axillary and distal curves occurring on the posterior margin of the wing. The anterior axillary and distal curves completely reverse themselves during the acts of extension and flexion, and so of the posterior axillary and distal curves (figs. 76, 77, and 78). This antagonism in the axillary and distal curves found on the anterior and posterior margins of the wing is referable in the bat and bird to changes induced in the bones of the wing in the acts of flexion and extension. In the

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

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FIG. 76.

FIG. 77.

FIG. 78.

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 (d e f) of the wing in semi-extension. In this case the curves on the posterior margin (b e) are obliterated.-Original.

FIG. 78. Curves seen on the anterior (de f) and posterior (c 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).

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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

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