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. [Illustration: FIG. 80.] 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 (_r 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 downwards during the up stroke, to enable the air to pass through it. The primary, secondary, and tertiary feathers have thus a distinctly valvular action.[76] The feathers rotate upon their short axes (_m n_) 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. [76] The degree of valvular action varies according to circumstances.