necessary degree of resistance and non-resistance. 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, i.e. when the fulcrum, as happens with the air, is elastic and yielding. In this case a very slight movement at the root of the pinion, or that end of the lever directed towards the body, is succeeded by an immense sweep of the extremity of the wing, where its elevating and propelling power is greatest. This arrangement insures that the large quantity of air necessary for propulsion and support shall be compressed under the most favourable conditions.

It follows from this that those insects and birds are endowed with the greatest powers of flight whose wings are the longest. The dragon-fly and albatross furnish examples. The former on some occasions dashes along with amazing velocity and wheels with incredible rapidity; at other times it suddenly checks its headlong career and hovers or fixes itself in the air after the manner of the kestrel and humming-birds. The flight of the albatross is also remarkable. This magnificent bird, I am informed on reliable authority, sails about with apparent unconcern for hours together, and rarely deigns to flap its enormous pinions, which stream from its body like ribbons to the extent, in some cases, of seven feet on either side.

The manner in which the wing levers the body upwards and forwards in flight is shown at fig. 52.

In this fig. ƒƒ' represent the moveable fulcra furnished by the air; pp' the power residing in the wing, and b the body to be flown. In order to make the problem of flight more intelligible, I have prolonged the lever formed by the wing beyond the body (b), and have applied to the root of the wing so extended the weight w w'. represents the universal joint by which the wing is attached to the body. When the wing ascends, as shown at p, the air (= fulcrum f) resists its upward passage, and forces the body (b), or its representative (w), slightly downwards. When the wing descends, as shown at p', the air (= fulcrum f') resists its downward passage, and forces the body (b), or its representative (w), slightly upwards. From this it follows, that when the wing rises the

body falls, and vice versâ; the wing describing the arc of a large circle (ff'), the body (b), or the weights representing it (ww) describing the arc of a much smaller circle. The body,

therefore, as well as the wing, rises and falls in flight. When the wing descends it elevates the body, the wing being active and the body passive; when the body descends it elevates the wing, the body being active and the wing passive. The elevator muscles, and the reaction of the air on the under surface of the wing, contribute to its elevation. It is in this manner that weight forms a factor in flight, the wing and the weight of the body reciprocating and mutually assisting and relieving each other. This is an argument for employing four wings in artificial flight, the wings being so arrranged that the two which are up shall always by their fall mechanically elevate the two which are down. Such an arrangement is calculated greatly to conserve the driving power, and, as a consequence, to reduce the weight. It is the upper or dorsal surface of the wing which more especially operates upon the air during the up stroke, and the under or ventral surface which operates during the down stroke. The wing, which at the beginning of the down stroke has its surfaces and margins (anterior and posterior) arranged in nearly the same plane with

the horizon,1 rotates upon its anterior margin as an axis during its descent and causes its under surface to make a gradually increasing angle with the horizon, the posterior margin (fig. 53, c) in this movement descending beneath the anterior one. A similar but opposite rotation takes place during the up stroke. The rotation referred to causes the wing to twist on its long axis screw-fashion, and to describe a figure-of-8 track in space, one-half of the figure being described during the ascent of the wing, the other half during its descent. The twisting of the wing and the figure-of-8 track described by it when made to vibrate, are represented at fig. 53. The rotation of the wing on its long axis as it ascends and descends causes the under surface of the wing to act as a kite, both during the up and down strokes, provided always the body bearing the wing is in forward motion. But the upper surface of the wing, as has been explained, acts when the wing is being elevated, so that both the upper and under surfaces of the wing are efficient during the up stroke. When the wing ascends, the upper surface impinges against the air; the under surface impinging at the same time from its being carried obliquely forward, after the manner of a kite, by the body, which is in motion. During the down stroke, the under surface only acts. The wing is consequently effective both during its ascent and descent, its slip being nominal in amount. The wing acts as a kite, both when it ascends and descends. It acts more as a propeller than an elevator during its ascent; and more as an elevator than a propeller during its descent. It is, however, effective both in an upward and downward direction. The efficiency of the wing is greatly increased by the fact that when it ascends it draws a current of air up after it, which current being met by the wing during its descent, greatly augments the power of the down stroke. In like manner, when the wing descends it draws a current of air down after it, which being met by the wing during its ascent, greatly augments the power of the up stroke. These induced currents are to the wing what a stiff autumn breeze is to the boy's kite. The wing is endowed with this very re

1 In some cases the posterior margin is slightly elevated above the horizon (fig. 53, g).

markable property, that it creates the current on which it rises and progresses. It literally flies on a whirlwind of its own forming.

These remarks apply more especially to the wings of bats and birds, and those insects whose wings are made to vibrate in a more or less vertical direction. The action of the wing is readily imitated, as a reference to fig. 53 will show.

If, for example, I take a tapering elastic reed, as represented at a b, and supply it with a flexible elastic sail (cd), and a ball-and-socket joint (x), I have only to seize the reed at a and cause it to oscillate upon x to elicit all the wing movements. By depressing the root of the reed in the direction ne, the wing flies up as a kite in the direction j f. During the upward movement the wing flies upwards and forwards, and describes a double curve. By elevating the root of the reed in the direction m a, the wing flies down as a kite in the direction i b. During the downward movement the wing flies downwards and forwards, and describes a double curve. These curves, when united, form a waved track, which represents progressive flight. During the rise and fall of the wing a large amount of tractile force is evolved, and if the wings and the body of the flying creature are inclined slightly upwards, kite-fashion, as they invariably are in ordinary flight, the whole mass of necessity moves upwards and

a

107) does the same, cd

forwards. To this there is no exception. A sheet of paper or a card will float along if its anterior margin is slightly raised, and if it be projected with sufficient velocity. The wings of all flying creatures when made to vibrate, twist and untwist, the posterior thin margin of each wing twisting round the anterior thick one, like the blade of a screw. The artificial wing represented at fig. 53 (p. twisting round a b, and g h round e f. The natural and artificial wings, when elevated and depressed, describe a figure-of-8 track in space when the bodies to which they are attached are stationary. When the bodies advance, the figure-of-8 is opened out to form first a looped and then a waved track. I have shown how those insects, bats, and birds which flap their wings in a more or less vertical direction evolve tractile or propelling power, and how this, operating on properly constructed inclined surfaces, results in flight. I wish now to show that flight may also be produced by a very oblique and almost horizontal stroke of the wing, as in some insects, e.g. the wasp, blue-bottle, and other flies. In those insects. the wing is made to vibrate with a figure-of-8 sculling

motion in a very oblique direction, and with immense energy. This form of flight differs in no respect from the other, unless in the direction of the stroke, and can be readily imitated, as a reference to fig. 54 will show.