of rotation to the wing in the direction of its length. This effect can, however, also be produced independently by the four principal bands. From what has been stated it will be evident that the elastic bands exercise a restraining influence, and that they act in unison with the driving power and with the reaction supplied by the air. They powerfully contribute to the continuous vibration of the wing, the vibration being peculiar in this that it varies in rapidity at every stage of the down and up strokes. I derive the motor power, as has been stated, from a direct piston action, the piston being urged either by steam worked expansively or by the hand, if it is merely a question of illustration. In the hand models the “_muscular sense_” at once informs the operator as to what is being done. Thus if one of the wave wings supplied with a ball-and-socket joint, and a cross system of elastic bands as explained, has a sudden vertical impulse communicated to it at the beginning of the down stroke, the wing darts _downwards and forwards in a curve_ (_vide a c_, of fig. 81, p. 157), and in doing so _it elevates_ and carries the piston and cylinder _forwards_. The force employed in depressing the wing is partly expended in stretching the superior elastic band, the wing being slowed towards the end of the down stroke. The instant the depressing force ceases to act, the superior elastic band contracts and the air reacts; the two together, coupled with the tendency which the model has to fall downwards and forwards during the up stroke, elevating the wing. The wing when it ascends describes an _upward and forward curve_ as shown at _c e_ of fig. 81, p. 157. The ascent of the wing stretches the inferior elastic band in the same way that the descent of the wing stretched the superior band. The superior and inferior elastic bands antagonize each other and reciprocate with vivacity. While those changes are occurring the wing is _twisting_ and _untwisting_ in the direction of its length and developing figure-of-8 curves along its margins (p. 239, fig. 122, _a b_, _c d_), and throughout its substance similar to what are observed under like circumstances in the natural wing (_vide_ fig. 86, p. 161; fig. 103, p. 186). The angles, moreover, made by the under surface of the wing with the horizon during the down and up strokes are continually varying--the wing all the while acting as a kite, which flies steadily _upwards and forwards_ (fig. 88, p. 166). As the elastic bands, as has been partly explained, are antagonistic in their action, the wing is constantly oscillating in some direction; there being no dead point either at the end of the down or up strokes. As a consequence, the curves made by the wing during the down and up strokes respectively, run into each other to form a continuous waved track, as represented at fig. 81, p. 157, and fig. 88, p. 166. A continuous movement begets a continuous buoyancy; and it is quite remarkable