movement of a large wing, and into small waves by the rapid movement of a smaller wing. The size of the _wing curves_ and _air waves_ bear a fixed relation to each other, and both are dependent on the rapidity with which the wing is made to vibrate. This is proved by the fact that insects, in order to fly, require, as a rule, to drive their small wings with immense velocity. It is further proved by the fact that the small humming-bird, in order to keep itself stationary before a flower, requires to oscillate its tiny wings with great rapidity, whereas the large humming-bird (_Patagona gigas_), as was pointed out by Darwin, can attain the same object by flapping its large wings with a very slow and powerful movement. In the larger birds the movements are slowed in proportion to the size, and more especially in proportion to the length of the wing; the cranes and vultures moving the wings very leisurely, and the large oceanic birds dispensing in a great measure with the flapping of the wings, and trusting for progression and support to the wings in the expanded position. [Illustration: FIG. 122. FIG. 122.--Elastic spiral wing, which twists and untwists during its action, to form _a mobile helix or screw_. This wing is made to vibrate by steam by a direct piston action, and by a slight adjustment can be propelled vertically, horizontally, or at any degree of obliquity. _a_, _b_, Anterior margin of wing, to which the neuræ or ribs are affixed. _c_, _d_, Posterior margin of wing crossing anterior one. _x_, Ball-and-socket joint at root of wing; the wing being attached to the side of the cylinder by the socket. _t_, Cylinder. _r_, _r_, Piston, with cross heads (_w_, _w_) and piston head (_s_). _o_, _o_, Stuffing boxes. _e_, _f_, Driving chains. _m_, Superior elastic band, which assists in elevating the wing. _n_, Inferior elastic band, which antagonizes _m_. The alternate stretching of the superior and inferior elastic bands contributes to the continuous play of the wing, by preventing dead points at the end of the down and up strokes. The wing is free to move in a vertical and horizontal direction and at any degree of obliquity.--_Original._] This leads me to conclude that very large wings may be driven with a comparatively slow motion, a matter of great importance in artificial flight secured by the flapping of wings. _How to construct an artificial Wave Wing on the Insect type._--The following appear to me to be essential features in the construction of an artificial wing:-- The wing should be of a generally triangular shape. It should taper from the root towards the tip, and from the anterior margin in the direction of the posterior margin. It should be convex above and concave below, and slightly twisted upon itself. It should be flexible and elastic throughout, and should twist and untwist during its vibration, to produce figure-of-8 curves along its margins and throughout its substance.