In this fig. _f f´_ represent the moveable fulcra furnished by the air; _p p´_ the power residing in the wing, and _b_ the body to be flown. In order to make the problem of flight more intelligible, I have prolonged the lever formed by the wing beyond the body (_b_), and have applied to the root of the wing so extended the weight _w w´_. _x_ represents the universal joint by which the wing is attached to the body. When the wing ascends, as shown at _p_, the air (= fulcrum _f_) resists its upward passage, and forces the body (_b_), or its representative (_w_), slightly downwards. When the wing descends, as shown at _p´_, the air (= fulcrum _f´_) resists its downward passage, and forces the body (_b_), or its representative (_w´_), slightly upwards. From this it follows, that when the wing rises the body falls, and _vice versâ_; the wing describing the arc of a large circle (_f f´_), the body (_b_), or the weights representing it (_w w´_) describing the arc of a much smaller circle. The body, therefore, as well as the wing, rises and falls in flight. When the wing descends it elevates the body, the wing being active and the body passive; when the body descends it elevates the wing, the body being active and the wing passive. The elevator muscles, and the reaction of the air on the under surface of the wing, contribute to its elevation. It is in this manner that weight forms a factor in flight, the wing and the weight of the body reciprocating and mutually assisting and relieving each other. This is an argument for employing four wings in artificial flight, the wings being so arranged that the two which are up shall always by their fall mechanically elevate the two which are down. Such an arrangement is calculated greatly to conserve the driving power, and, as a consequence, to reduce the weight. It is the upper or dorsal surface of the wing which more especially operates upon the air during the up stroke, and the under or ventral surface which operates during the down stroke. The wing, which at the beginning of the down stroke has its surfaces and margins (anterior and posterior) arranged in nearly the same plane with the horizon,[62] rotates upon its anterior margin as an axis during its descent and causes its under surface to make a gradually increasing angle with the horizon, the posterior margin (fig. 53, _c_) in this movement descending beneath the anterior one. A similar but opposite rotation takes place during the up stroke. The rotation referred to causes the wing to twist on its long axis screw-fashion, and to describe a figure-of-8 track in space, one-half of the figure being described during the ascent of the wing, the other half during its descent. The twisting of the wing and the figure-of-8 track described by it when made to vibrate, are represented at fig. 53. The rotation of the wing on its long axis as it ascends and descends causes the under surface of the wing to act as a kite, both during