[69] In this diagram I have purposely represented the right wing by a straight _rigid_ rod. The natural wing, however, is curved, _flexible_, and _elastic_. It likewise _moves in curves_, the curves being most marked towards the end of the up and down strokes, as shown at _m n_, _o p_. The curves, which are double figure-of-8 curves, are obliterated towards the middle of the strokes (_a r_). This remark holds true of all natural wings, and of all artificial wings properly constructed. The curves and the reversal thereof are necessary to give continuity of motion to the wing during its vibrations, and what is not less important, to enable the wing alternately to seize and dismiss the air.
_Rapidity of Wing Movements partly accounted for._--Much surprise has been expressed at the enormous rapidity with which some wings are made to vibrate. The wing of the insect is, as a rule, very long and narrow. As a consequence, a comparatively slow and very limited movement at the root confers great range and immense speed at the tip; the speed of each portion of the wing increasing as the root of the wing is receded from. This is explained on a principle well understood in mechanics, viz. that when a rod hinged at one end is made to move in a circle, the tip or free end of the rod describes a much wider circle _in a given time_ than a portion of the rod nearer the hinge. This principle is illustrated at fig. 56. Thus if _a b_ of fig. 56 be made to represent the rod hinged at _x_, it travels through the space _d b f_ in the same time it travels through _j k l_; and through _j k l_ in the same time it travels through _g h i_; and through _g h i_ in the same time it travels through _e a c_, which is the area occupied by the thorax of the insect. If, however, the part of the rod _b_ travels through the space _d b f_ in the same time that the part _a_ travels through the space _e a c_, it follows of necessity that the portion of the rod marked _a_ moves very much slower than that marked _b_. The muscles of the insect are applied at the point _a_, as short levers (the point referred to corresponding to the thorax of the insect), so that a comparatively slow and limited movement at the root of the wing produces the marvellous speed observed at the tip; the tip and body of the wing being those portions which occasion the blur or impression produced on the eye by the rapidly oscillating pinion (figs. 64, 65, and 66, p. 139), But for this mode of augmenting the speed originally inaugurated by the muscular system, it is difficult to comprehend how the wings could be driven at the velocity attributed to them. The wing of the blow-fly is said to make 300 strokes per second, _i.e._ 18,000 per minute. Now it appears to me that muscles to contract at the rate of 18,000 times in the minute would be exhausted in a very few seconds, a state of matters which would render the continuous flight of insects impossible. (The heart contracts only between sixty and seventy times in a minute.) I am, therefore, disposed to believe that the number of contractions made by the thoracic muscles of insects has been greatly overstated; the high speed at which the wing is made to vibrate being due less to the separate and sudden contractions of the muscles at its root than to the fact that the speed of the different parts of the wing is increased in a direct ratio as the several parts are removed from the driving point, as already explained. Speed is certainly a matter of great importance in wing movements, as the elevating and propelling power of the pinion depends to a great extent upon the rapidity with which it is urged. Speed, however, may be produced in two ways--either by a series of separate and opposite movements, such as is witnessed in the action of a piston, or by a series of separate and opposite movements acting upon an instrument so designed, that a movement applied at one part increases in rapidity as the point of contact is receded from, as happens in the wing. In the piston movement the motion is uniform, or nearly so; all parts of the piston travelling at very much the same speed. In the wing movements, on the contrary, the motion is gradually accelerated towards the tip of the pinion, where the pinion is most effective as an elevator, and decreased towards the root, where it is least effective--an arrangement calculated to reduce the number of muscular contractions, while it contributes to the actual power of the wing. This hypothesis, it will be observed, guarantees to the wing a very high speed, with comparatively few reversals and comparatively few muscular contractions.