314 FLIGHT efficiency of the down stroke. This statement can be readily verified by experiment both with natural and arti ficial wings. Neither the up nor the down strokes are com plete iu themselves. The wing to act efficiently must be driven at a certain speed, and in such a manner that the down and up strokes shall glide into each other. It is only in this way that the air can be made to pulsate, and that the rhythm of the wing and the air waves can be made to correspond. The air must be seized and let go in a certain order and at a certain speed to extract a maximum recoil. The rapidity of the wing movements is regulated by the size of the wing, small wings being driven at a very much higher speed than larger ones. The different parts of the wing, moreover, are made to travel at different degrees of velocity the tip and posterior margin of the wing always rushing through a much greater space, in a given time, than the root and anterior margin. The rapidity of travel of the insect wing is in some cases enormous. The wasp, for instance, is said to ply its wings at the rate of 110, and the common house fly at the rate of 330 beats per second. Quick as are the vibrations of natural wings, the speed of certain parts of the wing is amazingly increased. Wings as a rule are 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 wing or rod hinged at one end is made to move in a circle, the tip or free end of the wing or rod describes a much wider circle in a given time than a portion of the wing or rod nearer the hinge (fig. 25). FIG. 25 shows how different portions of the wing travel at different degrees of speed. In this figure the rod aft, hinged at x, represents the wing. When the wing is made to vihrate, its several portions travel through the spaces dbf,jkl,g/nSi n(l enc in exactly the same interval of time. The part of the wing marked ft, and which corresponds with the tip, consequently travels very much more rapidly than the part marked a, which corresponds with the root. jnn,op, curves made by the wing at the end of the up and down strokes ; r, position of the wing at the middle of the stroke. (Pettigrew, 1870.) One naturally inquires why the high speed of wings, and why the progressive increase of speed at their tips aud posterior margins 1 The answer is not far to seek. If the wingp were not driven at a high speed, and if they were not eccentrics made to revolve upon two separate axes, they would of necessity be large cumbrous structures ; but large heavy wings would bs difficult to work, and what is worse, they would (if too large), instead of controlling the air, be controlled by it, and so cease to be flying organs. There is, however, another reason why wings should be made to vibrate at high speeds. The air, as explained, is a very light, thin, elastic medium, which yields on the slightest pressure, and unless the wings attacked it with great violence the necessary recoil or resistance could not be obtained. The atmosphere, because of its great tenuity, mobility, and comparative imponderability, presents little resistance to bodies passing through it at low velocities. If, however, the speed be greatly accelerated, the action of even an ordinary cane is sufficient to elicit a recoil. This comes of the action aad reaction of matter, the resistance experienced varying according to the density of the atmo sphere and the shape, extent, and velocity of the body acting upon it. While, therefore, scarcely any impediment is offered to the progress of an animal in motion in tho air, it is often exceedingly difficult to compress the air with sufficient rapidity aud energy to convert it into a suitable fulcrum for securing the onward impetus. This arises from the fact that bodies moving in air experience a minimum of resistance and occasion a maximum of dis placement. Another and very obvious difficulty is traceable to the great disparity in the weight of air as compared with any known solid, and the consequent want of buoy ing or sustaining power which that disparity involves. If we compare air with water we find it is nearly 1000 times lighter. To meet these peculiarities the insect, bat, and bird are furnished with extensive flying surfaces in the shape of wings, which they apply with singular velocity and power to the air, as levers of the third order. In this form of lever, as the reader is aware, the power is applied between the fulcrum and the weight to be raised. The power is represented by the wing, the fulcrum by the air, and the weight by the body of the flying animal. Although the third order of lever is particularly inefficient when the fulcrum is rigid and immobile, it possesses singular advantages when these conditions are reversed, that is, when the fulcrum, as happens with the air, is elastic and yielding. In this instance a very slight movement at the root of the pinion, or that end of the lever directed towards the body, is followed by an immense sweep of the extremity of the wing, where its elevating and propelling power is greatest, this arrangement ensuring that the large quantity of air necessary for propulsion and support shall be compressed under the most favourable conditions. In this process the weight of the body performs an im portant part, by acting upon the inclined planes formed by the wings in the plane of progression, The power aud the FIG. 2(i In this figure f,.f represent the movable fulcra furnished by the air, p p the power residing in the wing, and 6 the body to be moved. In order to make the problem of flight more intelligible, the lever formed by the wing is prolonged beyond the body (4), and to the root of the wing so extended the weight (ic,w ) is attached; x represents the universal joint by which the wing is attached to the body. When the wing ascends as shown at ;>, the air (ful crum/) resists its tipward passage, and forces the body (ft) or its representa tive () slightly downwards. When the wing descends as shown dtp , the air (fulcrum/ ) resists its downward passage, and forces the body (ft) or its represen tative (> ) slightly upwards. From this it follows that when the wing rises the body falls, and vice versa, the wing describing the arc of a large circle (ff), tho body (6), or the weights (, ) representing it, describing the arc of a small circle. (Pettigrew, 1873.) weight may thus be said to reciprocate, the two sitting as it were side by side and blending their peculiar influences to produce a common result, as indicated at fig. 26.
