left, it darts forward in double curve, as shown at fig. 127; the various inclined surfaces made by the wing with the horizon changing at every stage of the stroke.

At the beginning of the stroke from right to left, the angle made by the under surface of the wing with the horizon (xx) is something like 45° (p), whereas at the middle of the stroke it is reduced to 20° or 25° (q). At the end of the stroke the angle gradually increases to 45° (b), then to 90° (c), after which the wing suddenly turns a somersault (d), and reverses precisely as the natural wing does at e, f, g of figs. 67 and 69, p. 141. The artificial wing reverses with amazing facility, and in the most natural manner possible. The angles made by its under surface with the horizon depend chiefly upon the speed with which the wing is urged at different stages of the stroke; the angle always decreasing as the speed increases, and vice versa. As a consequence, the angle is greatest when the speed is least.

с

When the wing reaches the point b its speed is much less than it was at q. The wing is, in fact, preparing to reverse. At e the wing is in the act of reversing (compare c of figs. 84 and 85, p. 160), and, as a consequence, its speed is at a minimum, and the angle which it makes with the horizon at a maximum. At d the wing is reversed, its speed being increased, and the angle which it makes with the horizon diminished. Between the letters d and u the wing darts suddenly up like a kite, and at u it is in a position to commence the stroke from left to right, as indicated at u of fig. 128, p. 250. The course described and the angles made by the wing with the horizon during the stroke from left to right are represented at fig. 128 (compare with figs. 68 and 70, p. 141). The stroke from left to right is in every respect the converse of the stroke from right to left, so that a separate description is unnecessary.

The Artificial Wave Wing can be driven at any speedit can make its own currents, or utilize existing ones.-The remarkable feature in the artificial wave wing is its adaptability. It can be driven slowly, or with astonishing rapidity. It has no dead points. It reverses instantly, and in such a manner as to dissipate neither time nor power. It alternately seizes and evades the air so as to extract the maximum

of support with the minimum of slip, and the minimum. of force. It supplies a degree of buoying and propelling power which is truly remarkable. Its buoying area is nearly equal to half a circle. It can act upon still air, and it can create and utilize its own currents. I proved this in the following manner. I caused the wing to make horizontal sweep from right to left over a candle; the wing rose steadily as a kite would, and after a brief interval, the flame of the candle was persistently blown from right to left. I then waited until the flame of the candle assumed its normal perpendicular position, after which I caused the wing to make another and opposite sweep from left to right. The wing again rose kite fashion, and the flame was a second time affected, being blown in this case from left to right. I now caused the wing to vibrate steadily and rapidly above the candle, with this curious result, that the flame did not incline alternately from right to left and from left to right. On the contrary, it was blown steadily away from me, i.e. in the direction of the tip of the wing, thus showing that the artificial currents made by the wing, met and neutralized each other always at mid stroke. I also found that under these circumstances the buoying power of the wing was remarkably increased.

Compound rotation of the Artificial Wave Wing: the different parts of the Wing travel at different speeds.-The artificial wave wing, like the natural wing, revolves upon two centres (a b, cd of fig. 80, p. 149; fig. 83, p. 158, and fig. 122, p. 239), and owes much of its elevating and propelling, seizing, and disentangling power to its different portions travelling at different rates of speed (see fig. 56, p. 120), and to its storing up and giving off energy as it hastens to and fro. Thus the tip of the wing moves through a very much greater space in a given time than the root, and so also of the posterior margin as compared with the anterior. This is readily understood by bearing in mind that the root of the wing forms the centre or axis of rotation for the tip, while the anterior margin is the centre or axis of rotation for the posterior margin. The momentum, moreover, acquired by the wing during the stroke from right to left is expended in

reversing the wing, and in preparing it for the stroke from left to right, and vice versâ; a continuous to-and-fro movement devoid of dead points being thus established. If the artificial wave wing be taken in the hand and suddenly depressed in a more or less vertical direction, it immediately springs up again, and carries the hand with it. It, in fact, describes a curve whose convexity is directed downwards, and in doing so, carries the hand upwards and forwards. If a second down stroke be added, a second curve is formed; the curves running into each other, and producing a progressive waved track similar to what is represen ted at a, c, e, g, i, of fig. 81, p. 157. This result is favoured if the operator runs forward so as not to impede or limit the action of the wing.

How the Wave Wing creates currents, and rises upon them, and how the Air assists in elevating the Wing.-In order to ascertain in what way the air contributes to the elevation of the wing, I made a series of experiments with natural

and artificial wings.

that when the wing

FIG. 129.

These experiments led me to conclude descends, as in the bat and bird, it

compresses and pushes before it, in a downward and forward

direction, a column of air represented by a, b, c of fig. 129, p. 253.1 The air rushes in from all sides to replace the displaced air, as shown at d, e, f, g, h, i, and so produces a circle of motion indicated by the dotted line s, t, v, w. The wing rises upon the outside of the circle referred to, as more particularly seen at d, e, v, w. The arrows, it will be observed, are all pointing upwards, and as these arrows indicate the direction of the reflex or back current, it is not difficult to comprehend how the air comes indirectly to assist in elevating the wing. A similar current is produced to the right of the figure, as indicated by l, m, o, p, q, r, but seeing the wing is always advancing, this need not be taken into

account.

If fig. 129 be made to assume a horizontal position, instead of the oblique position which it at present occupies, the manner in which an artificial current is produced by one sweep of the wing from right to left, and utilized by it in a subsequent sweep from left to right, will be readily understood. The artificial wave wing makes a horizontal sweep from right to left, i.e. it passes from the point a to the point c of fig. 129. During its passage it has displaced a column of air. To fill the void so created, the air rushes in from all sides, viz. from d, e, f, g, h, i; l, m, o, p, q, r. The currents marked g, h, i; p, q, r, represent the reflex or artificial currents. These are the currents which, after a brief interval, force the flame of the candle from right to left. It is those same currents which the wing encounters, and which contribute so powerfully to its elevation, when it sweeps from left to right. The wing, when it rushes from left to right, produces a new series of artificial currents, which are equally powerful in elevating the wing when it passes a second time from right to left, and thus the process of making and utilizing currents goes on so long as the wing is made to oscillate. In waving the artificial wing to and fro, I found

1 The artificial currents produced by the wing during its descent may be readily seen by partially filling a chamber with steam, smoke, or some impalpable white powder, and causing the wing to descend in its midst. By a little practice, the eye will not fail to detect the currents represented at d, e, f, g, h, i, l, m, o, p, q, r of fig. 129, p. 253.

the best results were obtained when the range of the wing and the speed with which it was urged were so regulated as to produce a perfect reciprocation. Thus, if the range of the wing be great, the speed should also be high, otherwise the air set in motion by the right stroke will not be utilized by the left stroke, and vice versa. If, on the other hand, the range of the wing be small, the speed should also be low, as the short stroke will enable the wing to reciprocate as perfectly as when the stroke is longer and the speed quicker. When the speed attained is high, the angles made by the under surface of the wing with the horizon are diminished; when it is low, the angles are increased. From these remarks it will be evident that the artificial wave wing reciprocates in the same way that the natural wing reciprocates; the reciprocation being most perfect when the wing is vibrating in a given spot, and least perfect when it is travelling at a high horizontal speed.

The Artificial Wing propelled at various degrees of speed during the Down and Up Strokes.-The tendency which the artificial wave wing has to rise again when suddenly and vigorously depressed, explains why the elevator muscles of the wing should be so small when compared with the depressor muscles-the latter being something like seven times larger than the former. That the contraction of the elevator muscles is necessary to the elevation of the wing, is abundantly proved by their presence, and that there should be so great a difference between the volume of the elevator and depressor muscles is not to be wondered at, when we remember that the whole weight of the body is to be elevated by the rapid descent of the wings-the descent of the wing being entirely due to the vigorous contraction of the powerful pectoral muscles. If, however, the wing was elevated with as great a force as it was depressed, no advantage would be gained, as the wing, during its ascent (it acts against gravity) would experience a much greater resistance from the air than it did during its descent. The wing is consequently elevated more slowly than it is depressed; the elevator muscles exercising a controlling and restraining influence. By slowing the wing during the up stroke