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suits best is one which is made to act very suddenly and forcibly at the beginning of the down stroke, and which gradually abates in intensity until the end of the down stroke, where it ceases to act in a downward direction. The power is then made to act in an upward direction, and gradually to decrease until the end of the up stroke. The force is thus applied more or less continuously; its energy being increased and diminished according to the position of the wing, and the amount of resistance which it experiences from the air. The flexible and elastic nature of the wave wing, assisted by certain springs to be presently explained, insure a continuous vibration where neither halts nor dead points are observable. I obtain the varying power required by a direct piston action, and by working the steam expansively. The power employed is materially assisted, particularly during the up stroke, by the reaction of the air and the elastic structures about to be described. An artificial wing, propelled and regulated by the forces recommended, is in some respects as completely under control as the wing of the insect, bat, or bird.

Necessity for supplying the Root of Artificial Wings with Elastic Structures in imitation of the Muscles and Elastic Ligaments of Flying Animals.—Borelli, Durckheim, and Marey, who advocate the perpendicular vibration of the wing, make no allowance, so far as I am aware, for the wing leaping forward in curves during the down and up strokes. As a consequence, the wing is jointed in their models to the frame by a simple joint which moves only in one direction, viz., from above downwards, and vice versa. Observation and experiment have fully satisfied me that an artificial wing, to be effective as an elevator and propeller, ought to be able to move not only in an upward and downward direction, but also in a forward, backward, and oblique direction ; nay, more, that it should be free to rotate along its anterior margin in the direction of its length; in fact, that its movements should be universal. Thus it should be able to rise or fall, to advance or retire, to move at any degree of obliquity, and to rotate along its anterior margin. To secure the several movements referred to I furnish the root of the wing with a ball-and-socket joint, i.e., a universal joint (see x of fig. 122, p. 239). To regulate the several movements when the wing is vibrating, and to confer on the wing the various inclined surfaces requisite for flight, as well as to delegate as little as possible to the air, I employ a cross system of elastic bands. These bands vary in length, strength, and direction, and are attached to the anterior margin of the wing (near its root), and to the cylinder (or a rod extending from the cylinder) of the model (vide m, n of fig. 122, p. 239). The principal bands are four in number—a superior, inferior, anterior, and posterior. The superior band (m) extends between the upper part of the cylinder of the model, and the upper surface of the anterior margin of the wing; the inferior band (n) extending between the under part of the cylinder or the boiler and the inferior surface of the anterior margin of the pinion. The anterior and posterior bands are attached to the anterior and posterior portions of the wing and to rods extending from the centre of the anterior and posterior portions of the cylinder. Oblique bands are added, and these are so arranged that they give to the wing during its descent and ascent the precise angles made by the wing with the horizon in natural flight. The superior bands are stronger than the inferior ones, and are put upon the stretch during the down stroke. Thus they help the wing over the dead point at the end of the down stroke, and assist, in conjunction with the reaction obtained from the air, in elevating it. The posterior bands are stronger than the anterior ones to restrain within certain Jimits the great tendency which the wing has to leap forward in curves towards the end of the down and up strokes. The oblique bands, aided by the air, give the necessary degree of rotation to the wing in the direction of its length. This effect can, however, also be produced independently by the four principal bands. From what has been stated it will be evident that the elastic bands exercise a restraining influence, and that they act in unison with the driving power and with the reaction supplied by the air. They powerfully contribute to the continuous vibration of the wing, the vibration being peculiar in this that it varies in rapidity at every stage of the 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.

here bethe winge en partly

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

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Fig. 127.-Path described by artificial wave wing from right to left. 1,"

Horizon. m, n, o, Wave track traversed by wing from right to left. ,
Angle made by the wing with the horizon at beginning of struke, 9, Ditto.
made at middle of stroke. b, Ditto, towards end of stroke. e, 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. 2, X,

Horizon. u, v, w, Wave track traversed by wing from left to right. ,
Angle made by the wing with horizon at beginning of stroke. . Ditto.
at middle of stroke. 2, 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. 8, 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 (x ac) 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.

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 Inanner as to dissipate neither time nor power. It alternately seizes and evades the air so as to extract the maximum

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