upward, downward, forward, or backward direction, but also at various intermediate degrees of obliquity. All wings obtain their leverage by presenting oblique surfaces to the air, the degree of obliquity gradually increasing in a direction. from behind forwards and downwards during extension and the down stroke, and gradually decreasing in an opposite direction during flexion and the up stroke.

In the insect the oblique surfaces are due to the conformation of the shoulder-joint, this being furnished with a system of check-ligaments, and with horny prominences or stops, set,

FIG. 63.-The Lowing, or Green Plover (Vanellus cristatus, Meyer), with one wing (c b, d' e' f') fully extended, and forming a long lever; the other (de f, cb) being in a flexed condition and forming a short lever. In the extended wing the anterior or thick margin (d' e' f') is directed upwards and forwards (vide arrow), the posterior or thin margin (c, b) downwards and backwards. The reverse of this happens during flexion, the anterior or thick margin (d, e, f) being directed downwards and forwards (vide arrow), the posterior or thin margin (c b) bearing the rowing-feathers upwards and backwards. The wings therefore twist in opposite directions during extension and flexion; and this is a point of the utmost importance in the action of all wings, as it enables the volant animal to rotate the wings on and off the air, and to present at one time (in extension) resisting, kite-like surfaces, and at another (in flexion) knife-like and comparatively non-resisting surfaces. It rarely happens in flight that the wing (d e f, c b) is so fully flexed as in the figure. As a consequence, the under surface of the wing is, as a rule, inclined upwards and forwards, even in flexion, so that it acts as a kite in extension and flexion, and during the up and down strokes.-Original.

as nearly as may be, at right angles to each other. The check-ligaments and horny prominences are so arranged that when the wing is made to vibrate, it is also made to rotate in the direction of its length, in the manner explained.

In the bat and bird the oblique surfaces are produced by the spiral configuration of the articular surfaces of the bones of

the wing, and by the rotation of the bones of the arm, forearm, and hand, upon their long axes. The reaction of the air also assists in the production of the oblique surfaces.

That the wing twists upon itself structurally, not only in the insect, but also in the bat and bird, any one may readily satisfy himself by a careful examination; and that it twists upon itself during its action I have had the most convincing and repeated proofs (figs. 64, 65, and 66). The twisting in question

FIG. 64 shows left wing (a, b) of wasp in the act of twisting upon itself, the tip of the wing describing a figure-of-8 track (a, c, b). From nature.-Original. FIGS. 65 and 66 show right wing of blue-bottle fly rotating on its anterior margin, and twisting to form double or figure-of-8 curves (a b, c d). From nature.-Original.

is most marked in the posterior or thin margin of the wing, the anterior and thicker margin performing more the part of an axis. As a result of this arrangement, the anterior or thick margin cuts into the air quietly, and as it were by stealth, the posterior one producing on all occasions a violent commotion, especially perceptible if a flame be exposed behind the vibrating wing. Indeed, it is a matter for surprise that the spiral conformation of the pinion, and its spiral mode of action, should have eluded observation so long; and I shall be pardoned for dilating upon the subject when I state my conviction that it

forms the fundamental and distinguishing feature in flight, and must be taken into account by all who seek to solve this most involved and interesting problem by artificial means. The importance of the twisted configuration or screw-like form of the wing cannot be over-estimated. That this shape is intimately associated with flight is apparent from the fact that the rowing feathers of the wing of the bird are every one of them distinctly spiral in their nature; in fact, one entire rowing feather is equivalent morphologically and physiologically to one entire insect wing. In the wing of the martin, where the bones of the pinion are short and in some respects rudimentary, the primary and secondary feathers are greatly developed, and banked up in such a manner that the wing as a whole presents the same curves as those displayed by the insect's wing, or by the wing of the eagle where the bones, muscles, and feathers have attained a maximum development. The conformation of the wing is such that it presents a waved appearance in every direction-the waves running longitudinally, transversely, and obliquely. The greater portion of the pinion may consequently be removed without materially affecting either its form or its functions. This is proved by making sections in various directions, and by finding, as has been already shown, that in some instances as much as two-thirds of the wing may be lopped off without visibly impairing the power of flight. The spiral nature of the pinion is most readily recognised when the wing is seen from behind and from beneath, and when it is foreshortened. It is also well marked in some of the long-winged oceanic birds when viewed from before (figs. 82 and 83, p. 158), and cannot escape detection under any circumstances, if sought for, the wing being essentially composed of a congeries of curves, remarkable alike for their apparent simplicity and the subtlety of their detail.

The Wing during its action reverses its Planes, and describes a Figure-of-8 track in space. The twisting or rotating of the wing on its long axis is particularly observable during extension and flexion in the bat and bird, and likewise in the insect, especially the beetle, cockroach, and such as fold their wings during repose. In these in extreme flexion

the anterior or thick margin of the wing is directed downwards, and the posterior or thin one upwards. In the act of extension, the margins, in virtue of the wing rotating upon its long axis, reverse their positions, the anterior or thick margins describing a spiral course from below upwards, the posterior or thin margin describing a similar but opposite course from above downwards. These conditions, I need scarcely observe, are reversed during flexion. The movements of the margins during flexion and extension may be represented with a considerable degree of accuracy by a figure-of-8 laid horizontally.

In the bat and bird the wing, when it ascends and descends, describes a nearly vertical figure-of-8. In the insect, the wing, from the more oblique direction of the stroke,

FIGS. 67, 68, 69, and 70 show the area mapped out by the left wing of the wasp when the insect is fixed and the wing made to vibrate. These figures illustrate the various angles made by the wing as it hastens to and fro, how the wing reverses and reciprocates, and how it twists upon itself and describes a figure-of-8 track in space. Figs. 67 and 69 represent the forward or down stroke; figs. 68 and 70 the backward or up stroke. The terms forward and back stroke are here employed with reference to the head of the insect.-Original.

describes a nearly horizontal figure-of-8. In either case the wing reciprocates, and, as a rule, reverses its planes. The down and up strokes, as will be seen from this account, cross each other, as shown more particularly at figs. 67, 68, 69, and 70.

In the wasp the wing commences the down or forward stroke at a of figs. 67 and 69, and makes an angle of some

thing like 45° with the horizon (xx). At b (figs. C7 and 69) the angle is slightly diminished, partly because of a rotation of the wing along its anterior margin (long axis of wing), partly from increased speed, and partly from the posterior margin of the wing yielding to a greater or less extent.

At c the angle is still more diminished from the same

causes.

At d the wing is slowed slightly, preparatory to reversing, and the angle made with the horizon (x) increased.

At e the angle, for the same reason, is still more increased; while at ƒ the wing is at right angles to the horizon. It is, in fact, in the act of reversing.

At g the wing is reversed, and the up or back stroke commenced.

The angle made at g is, consequently, the same as that made at a (45°), with this difference, that the anterior margin and outer portion of the wing, instead of being directed forwards, with reference to the head of the insect, are now directed backwards.

During the up or backward stroke all the phenomena are reversed, as shown at ghijkl of figs. 68 and 70 (p. 141); the only difference being that the angles made by the wing with the horizon are somewhat less than during the down or forward stroke- -a circumstance which facilitates the forward travel of the body, while it enables the wing during the back stroke still to afford a considerable amount of support. This arrangement permits the wing to travel backwards while the body is travelling forwards; the diminution of the angles made by the wing in the back stroke giving very much the same result as if the wing were striking in the direction of the travel of the body. The slight upward inclination of the wing during the back stroke permits the body to fall downwards and forwards to a slight extent at this peculiar juncture, the fall of the body, as has been already explained, contributing to the elevation of the wing.

The pinion acts as a helix or screw in a more or less horizontal direction from behind forwards, and from before backwards; but it likewise acts as a screw in a nearly vertical direction. If the wing of the larger domestic fly be viewed