to what an extent, wings constructed and applied to the air on the principles explained, elevate and propel--how little power is required, and how little of that power is wasted in slip. [Illustration: FIG. 127. FIG. 127.--Path described by artificial wave wing from right to left. _x_, _x´_, Horizon. _m_, _n_, _o_, Wave track traversed by wing from right to left. _p_, Angle made by the wing with the horizon at beginning of stroke. _q_, Ditto, made at middle of stroke. _b_, Ditto, towards end of stroke. _c_, Wing in the act of reversing; at this stage the wing makes an angle of 90° with the horizon, and its speed is less than at any other part of its course. _d_, Wing reversed, and in the act of darting up to _u_, to begin the stroke from left to right (_vide u_ of fig. 128).--_Original._] [Illustration: FIG. 128. FIG. 128.--Path described by artificial wave wing from left to right. _x_, _x´_, Horizon. _u_, _v_, _w_, Wave track traversed by wing from left to right. _t_, Angle made by the wing with horizon at beginning of stroke. _y_, Ditto, at middle of stroke. _z_, Ditto, towards end of stroke. _r_, Wing in the act of reversing; at this stage the wing makes an angle of 90° with the horizon, and its speed is less that at any other part of its course. _s_, Wing reversed, and in the act of darting up to _m_, to begin the stroke from right to left (_vide m_ of fig. 127).--_Original._] If the piston, which in the experiment described has been working _vertically_, be made to work _horizontally_, a series of essentially similar results are obtained. When the piston is worked horizontally, the anterior and posterior elastic bands require to be of nearly the same strength, whereas the inferior elastic band requires to be much stronger than the superior one, to counteract the very decided tendency the wing has to fly upwards. The power also requires to be somewhat differently applied. Thus the wing must have a violent impulse communicated to it when it begins the stroke from right to left, and also when it begins the stroke from left to right (the _heavy parts_ of the spiral line represented at fig. 71, p. 144, indicate the points where the impulse is communicated). The wing is then left to itself, the elastic bands and the reaction of the air doing the remainder of the work. When the wing is forced by the piston from right to left, it darts forward in double curve, as shown at fig. 127; the various inclined surfaces made by the wing with the horizon changing at every stage of the stroke.