down and up strokes. I derive the motor power, as has been stated, from a direct piston action, the piston being urged either by steam worked expansively or by the hand, if it is merely a question of illustration. In the hand models the "muscular sense at once informs the operator as to what is being done. Thus if one of the wave wings supplied with a ball-and-socket joint, and a cross system of elastic bands as explained, has a sudden vertical impulse communicated to it at the beginning of the down stroke, the wing darts downwards and forwards in a curve (vide a c, of fig. 81, p. 157), and in doing so it elevates and carries the piston and cylinder forwards. The force employed in depressing the wing is partly expended in stretching the superior elastic band, the wing being slowed towards the end of the down stroke. The instant the depressing force ceases to act, the superior elastic band contracts and the air reacts; the two together, coupled with the tendency which the model has to fall downwards and forwards during the up stroke, elevating the wing. The wing when it ascends describes an upward and forward curve as shown at ce of fig. 81, p. 157. The ascent of the wing stretches the inferior elastic band in the same way that the descent of the wing stretched the superior band. The superior and inferior elastic bands antagonize each other and reciprocate with vivacity. While those changes are occurring the wing is twisting and untwisting in the direction of its length and developing figure-of-8 curves along its margins (p. 239, fig. 122, a b, c d), and throughout its substance similar to what are observed under like circumstances in the natural wing (vide fig. 86, p. 161; fig. 103, p. 186). The angles, moreover, made by the under surface of the wing with the horizon during the down and up strokes are continually varying—the wing all the while acting as a kite, which flies steadily upwards and forwards (fig. 88, p. 166). As the elastic bands, as has been partly explained, are antagonistic in their action, the wing is constantly oscillating in some direction; there being no dead point either at the end of the down or up strokes. As a consequence, the curves made by the wing during the down and up strokes respectively, run into each other to form a continuous waved track, as represented at fig.

81, p. 157, and fig. 88, p. 166. A continuous movement begets a continuous buoyancy; and it is quite remarkable to what an extent, wings constructed and applied to the air on the principles explained, elevate and propel-how little power is required, and how little of that power is wasted in slip.

If the piston, which in the experiment described has been working vertically, be made to work horizontally, a series of essentially similar results are obtained. When the piston is worked horizontally, the anterior and posterior elastic bands require to be of nearly the same strength, whereas the inferior elastic band requires to be much stronger than the superior one, to counteract the very decided tendency the wing has to fly upwards. The power also requires

FIG. 127.-Path described by artificial wave wing from right to left. x, x, Horizon. m, n, o, Wave track traversed by wing from right to left. P, Angle made by the wing with the horizon at beginning of stroke, q, Ditto, made at middle of stroke. b, Ditto, towards end of stroke. c, Wing in the act of reversing; at this stage the wing makes an angle of 90° with the horizon, and its speed is less than at any other part of its course. d, Wing reversed, and in the act of darting up to u, to begin the stroke from left to right (vide u of fig. 128).—Original.

FIG. 128.-Path described by artificial wave wing from left to right. x, x', Horizon. u, v, w, Wave track traversed by wing from left to right. t, Angle made by the wing with horizon at beginning of stroke. y, Ditto, at middle of stroke. z, Ditto, towards end of stroke. r, Wing in the act of reversing; at this stage the wing makes an angle of 90° with the horizon, and its speed is less that at any other part of its course. s, Wing reversed, and in the act of darting up to m, to begin the stroke from right to left (vide m of fig. 127).-Original.

to be somewhat differently applied. Thus the wing must have a violent impulse communicated to it when it begins the stroke from right to left, and also when it begins the stroke from left to right (the heavy parts of the spiral line represented at fig. 71, p. 144, indicate the points where the impulse is communicated). The wing is then left to itself, the elastic bands and the reaction of the air doing the remainder of the work. When the wing is forced by the piston from right to

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 versâ. As a consequence, the angle is greatest when the speed is least.

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 c 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 a 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.

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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 represented 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. These experiments led me to conclude that when the wing descends, as in the bat and bird, it compresses and pushes before it, in a downward and forward