during its vibrations from above, it will be found that the blur or impression produced on the eye by its action is more or less concave (fig. 66, p. 139). This is due to the fact that the wing is spiral in its nature, and because during its action it twists upon itself in such a manner as to describe a double curve, the one curve being directed upwards, the other downwards. The double curve referred to is particularly evident in the flight of birds from the greater size of their wings. The wing, both when at rest and in motion, may not inaptly be compared to the blade of an ordinary screw propeller as employed in navigation. Thus the general outline of the wing corresponds closely with the outline of the blade of the propeller, and the track described by the wing in space is twisted upon itself propeller fashion. The great velocity with which the wing is driven converts the impression or blur into what is equivalent to a solid for the time being, in the same way that the spokes of a wheel in violent motion, as is well understood, completely occupy the space contained within the rim or circumference of the wheel (figs. 64, 65, and 66, p. 139).

The figure-of-8 action of the wing explains how an insect, bat, or bird, may fix itself in the air, the backward and forward reciprocating action of the pinion affording support, but no propulsion. In these instances, the backward and forward strokes are made to counterbalance each other.

The Wing, when advancing with the Body, describes a Looped and Waved Track.-Although the figure-of-8 represents with considerable fidelity the twisting of the wing upon its long axis during extension and flexion, and during the down and up strokes when the volant animal is playing its wings before an object, or still better, when it is artificially fixed, it is otherwise when it is free and progressing rapidly. In this case the wing, in virtue of its being carried forward by the body in motion, describes first a looped and then a waved track. This looped and waved track made by the wing of the insect is represented at figs. 71 and 72, and that made by the wing of the bat and bird at fig. 73, p. 144.

The loops made by the wing of the insect, owing to the more oblique stroke, are more horizontal than those made by

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

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 b c d e f g h i j k l m n o 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 versa. 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

h

j

bd

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 (efg 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

K

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.

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 (def) 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 j) and posterior (ca b) margin of the wing in extension. The curves of this fig. are the converse of those see 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