If we take off the wing of an insect, and holding it by the small joint which connects it with the thorax, expose it to a current of air, we see that the plane of the wing is inclined more and more as it is subjected to a more powerful impulse of the wind. The anterior nervure resists, but the membranous portion which is prolonged behind bends on account of its greater pliancy. The wings of insects may be regarded simply as vibrating wires, and hence the frequency of their movements can be calculated by the note produced. Their movements can be recorded directly on a revolving cylinder, previously blackened with smoke, the slightest touch of the tip of the wing removing the black and exposing the white paper beneath; Fig. 163 was obtained in this way. By this method it was calculated that in the common fly the wings made 330 strokes per second, the bee 190, the Macroglossus 72, the dragon-fly 28, and the butterfly (_Pieris rapæ_) 9. Thus the smaller the species, the more rapid are the movements of the wings. [Illustration: FIG. 164.—Appearance of a wasp flying in the sun: the extremity of the wing is gilded.—After Marey. ] The path or trajectory made by the tip of the wing is like a figure 8. Marey obtained this by fastening a spangle of gold-leaf to the extremity of a wasp’s wing. The insect was then seized with a pair of forceps and held in the sun in front of a dark background, the luminous trajectory shaping itself in the form of a lemniscate (Fig. 164). To determine with accuracy the direction taken by the wing at different stages of the trajectory, a small piece of capillary glass tubing was blackened in the smoke of a candle, so that the slightest touch on the glass was sufficient to remove the black coating and show the direction of movement in each limb of the lemniscate. This experiment was arranged as shown in Fig. 165. Different points on the path of movement were tested by the smoked rod, and from the track along which the black had been removed the direction of movement was deduced. This direction is represented in the figure by means of arrows. [Illustration: FIG. 165.—Experiment to test the direction of movement of an insect’s wing: _a_, _a′_, _b_, _b′_, different positions of the smoked rod. ] =Theory of insect flight.=—“The theory of insect flight,” says Marey, “may be completely explained from the preceding experiments. The wing, in its to-and-fro movement, is bent in various directions by the resistance of the air. Its action is always that of an inclined plane striking against a fluid and utilizing that part of the resistance which is favorable to its onward progression. “This mechanism is the same as that of a waterman’s scull, which as it moves backwards and forwards is obliquely inclined in opposite directions, each time communicating an impulse to the boat.”