FIG. 57.--Shows a butterfly with comparatively very large wings. The nervures are seen to great advantage in this specimen; and the enormous expanse of the pinions readily explains the irregular flight of the insect on the principle of recoil. _a_ Anterior wing. _b_ Posterior wing. _e_ Anterior margin of wing. _f_ Ditto posterior margin. _g_ Ditto outer margin. Compare with beetle, fig. 58.--_Original._] [Illustration: FIG. 58.--Under-surface of large beetle (_Goliathus micans_), with deeply concave and comparatively small wings (compare with butterfly, fig. 57), shows that the nervures (_r_, _d_, _e_, _f_, _n_, _n_, _n_) of the wings of the beetle are arranged along the anterior margins and throughout the substance of the wings generally, very much as the bones of the arm, forearm, and hand, are in the wings of the bat, to which they bear a very marked resemblance, both in their shape and mode of action. The wings are folded upon themselves at the point _e_ during repose. Compare letters of this figure with similar letters of fig. 17, p. 36.--_Original._] The apparent inconsistencies in the dimensions of the body and wings are readily explained by the greater muscular development of the heavy-bodied short-winged insects and birds, and the increased power and rapidity with which the wings in them are made to oscillate. In large-winged animals the movements are slow; in small-winged ones comparatively very rapid. This shows that flight may be attained by a heavy, powerful animal with comparatively small wings, as well as by a lighter one with enormously enlarged wings. While there is apparently no fixed relation between the area of the wings and the animal to be raised, there is, unless in the case of sailing birds,[70] an unvarying relation between the weight of the animal, the area of its wings, and the number of oscillations made by them in a given time. The problem of flight thus resolves itself into one of weight, power, velocity, and small surfaces; _versus_ buoyancy, debility, diminished speed, and extensive surfaces,--weight in either case being a _sine quâ non_. In order to utilize the air as a means of transit, the body in motion, whether it moves in virtue of the life it possesses, or because of a force superadded, must be heavier than the air. It must tread and rise upon the air as a swimmer upon the water, or as a kite upon the wind. It must act against gravity, and elevate and carry itself forward at the expense of the air, and by virtue of the force which resides in it. If it were rescued from the law of gravity on the one hand, and bereft of independent movement on the other, it would float about uncontrolled and uncontrollable, as happens in the ordinary gas-balloon.