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There is, moreover, a continuous play of the wing; the down stroke gliding into the up one, and vice versâ, which

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Fig. 117.-Represents a longitudinal section of bamboo cane ten feet long, and

one inch wide.- Original. FIG. 118.-The appearance presented by the same cane when made to vibrate

by the hand. The cane vibrates on either side of a given line (xx), and appears as if it were in two places at the same time, viz., cand f, g and d, e and h. It is thus during its vibration thrown into figures-of-8 or opposite

curves.--Original. FIG. 119.— The same cane when made to vibrate more rapidly. In this case

the waves made by the cane are less in size, but inore numerous. The cane is seen alternately on either side of the line x x, being now at i now at m, now at n now atj, now at k now at o, now at p now at l. The cane, when made to vibrate, has no dead points, a circumstance due to the fact that no two parts of it reverse or change their curves at precisely the same instant. This curious reciprocating motion enables the wing to seize and

disengage itself from the air with astonishing rapidity. Original. FIG. 120. - The same cane with a flexible elastic curtain or fringe added to it.

The curtain consists of tapering whalebone rods covered with a thin layer of india-rubber. ab anterior margin of wing. cd posterior ditto.-Original. Fig. 121.-Gives the appearance presented by the artificial wing (fig. 120)

when made to vibrate by the hand. It is thrown into longitudinal and transverse waves. The longitudinal waves are represented by the arrows cde, and the transverse waves by the arrows fgh. A wing constructed on this principle gives a continuous elevating and propelling power. It developes figure-of-8 curves during its action in longitudinal, transverse, and oblique directions. It literally floats upon the air. It has no dead points-is vibrated with amazingly little power, and has apparently no slip. It can fly in an upward, downward, or horizontal direction by merely altering its angle of inclination to the horizon. It is applied to the air by an irregular motion-the movement being most sudden and vigorous always at the beginning of the down stroke.- Original.

clearly shows that the down and up strokes are parts of one whole, and that neither is perfect without the other.

The wave wing is endowed with the very remarkable property that it will fly in any direction, demonstrating more or less clearly that flight is essentially a progressive movement, i.e. a horizontal rather than a vertical movement. Thus, if the anterior or thick margin of the wing be directed upwards, so that the under surface of the wing makes a forward angle with the horizon of 45°, the wing will, when made to vibrate by the hand, fly with an undulating motion in an upward direction, like a pigeon to its dovecot. If the under surface of the wing makes no angle, or a very small forward angle, with the horizon, it will dart forward in a series of curves in a horizontal direction, like a crow in rapid horizontal flight. If the anterior or thick margin of the wing be directed downwards, so that the under surface of the wing makes a backward angle of 45° with the horizon, the wing will describe a waved track, and fly downwards, as a sparrow from a house-top or from a tree (p. 230). In all those movements progression is a necessity. The movements are continuous gliding forward movements. There is no halt or pause between the strokes, and if the angle which the under surface of the wing makes with the horizon be properly regulated, the amount of steady tractile and buoying power developed is truly astonishing. This form of wing, which may be regarded as the realization of the figure-of-8 theory of flight, elevates and propels both during the down and up strokes, and its working is accompanied with almost no slip. It seems literally to float upon the air. No wing that is rigid in the anterior margin can twist and untwist during its action, and produce the figure-of-8 curves generated by the living wing. To produce the curves in question, the wing must be flexible, elastic, and capable of change of form in all its parts. The curves made by the artificial wing, as has been stated, are largest when the vibration is slow, and least when it is quick. In like manner, the air is thrown into large waves by the slow movement of a large wing, and into small waves by the rapid movement of a smaller wing. The size of the wing curves and air waves bear a fixed relation to each other, and both are dependent on the rapidity with

which the wing is made to vibrate. This is proved by the fact that insects, in order to fly, require, as a rule, to drive their small wings with immense velocity. It is further proved by the fact that the small humming-bird, in order to keep itself stationary before a flower, requires to oscillate its tiny wings with great rapidity, whereas the large hummingbird (Patagona gigas), as was pointed out by Darwin, can attain the same object by flapping its large wings with a very slow and powerful movement. In the larger birds the movements are slowed in proportion to the size, and more especially in proportion to the length of the wing; the cranes and vultures moving the wings very leisurely, and the large oceanic birds dispensing in a great measure with the flapping of the wings, and trusting for progression and support to the wings in the expanded position.

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FIG. 122.
Fig. 122.--Elastic spiral wing, which twists and untwists during its action, to

form a mobile helix or screw. This wing is made to vibrate by steam by a direct piston action, and by a slight adjustment can be propelled vertically, horizontally, or at any degree of obliquity. a, b, Anterior margin of wing, to which the neura or ribs are affixed. c, d, Pos

terior margin of wing crossing anterior one. X, Ball-and-socket joint at root of wing; the wing being attached to the side of the cylinder by the socket. t, Cylinder. rr, Piston, with cross heads (w, w) and piston head (s). 0, 0, Stuffing boxes. e, f, Driving chains. m, Superior elastic band, which assists in elevating the wing. n, Inferior elastic band, which antagonizes m. The alternate stretching of the superior and inferior elastic bands contributes to the continuous play of the wing, by preventing dead points at the end of the down and up strokes. The wing is free to move in a vertical and horizontal direction and at any degree of obliquity.-Original.

This leads me to conclude that very large wings may be driven with a comparatively slow motion, a matter of great importance in artificial flight secured by the flapping of wings.

How to construct an artificial Wave Wing on the Insect type.The following appear to me to be essential features in the construction of an artificial wing :

The wing should be of a generally triangular shape.

It should taper from the root towards the tip, and from the anterior margin in the direction of the posterior margin.

It should be convex above and concave below, and slightly twisted upon itself.

It should be flexible and elastic throughout, and should twist and untwist during its vibration, to produce figure-of-8 curves along its margins and throughout its substance.

Such a wing is represented at fig. 122, p. 239.

If the wing is in more than one piece, joints and springs require to be added to the body of the pinion.

In making a wing in one piece on the model of the insect wing, such as that shown at fig. 122 (p. 239), I employ one or more tapering elastic reeds, which arch from above downwards (a b) for the anterior margin. To this I add tapering elastic reeds, which radiate towards the tip of the wing, and which also arch from above downwards (g, h, i). These latter are so arranged that they confer a certain amount of spirality upon the wing; the anterior (a b) and posterior (cd) margins being arranged in different planes, so that they appear to cross each other. I then add the covering of the wing, which may consist of india-rubber, silk, tracing cloth, linen, or any similar substance.

If the wing is large, I employ steel tubes, bent to the proper shape. In some cases I secure additional strength by adding to the oblique ribs or stays (ghi of fig. 122) a series of very oblique stays, and another series of cross stays, as shown at m and a, n, o, p, q of fig. 123, p. 241.

This form of wing is made to oscillate upon two centres viz. the root and anterior margin, to bring out the peculiar eccentric action of the pinion.

If I wish to produce a very delicate light wing, I do so by selecting a fine tapering elastic reed, as represented at ab of fig. 124.

To this I add successive layers (i, h,g, f, e) of some flexible material, such as parchment, buckram, tracing cloth, or even

paper. As the layers overlap each other, it follows that there are five layers at the anterior margin (ab), and only one at the posterior (cd). This form of wing is not twisted upon itself structurally, but it twists and untwists, and becomes a true screw during its action.

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Fig. 123.- Artificial Wing with Perpendicular (rs) and Horizontal (tu) Elastic Bands attached to ferrule (w).

a, b, Strong elastic reed, which tapers towards the tip of the wing.

d, e, f, h, i, j, k, Tapering curved reeds, which run obliquely from the anterior to the posterior margin of the wing, and which radiate towards the

tip.

m, Similar curved reeds, which run still more obliquely.

a.'n, o.p.g, Tapering curved reeds, which run from the anterior margin of the wing, and at right angles to it. These support the two sets of oblique reeds, aud give additional strength to the anterior margin.

2, Ball-and-socket joint, by which the root of the wing is attached to the cylinder, as in fig. 122, p. 239.-Original FIG. 124.-Flexible elastic wing with tapering elastic reed (ah) running along anterior margin.

c, d, Posterior margin of wing. i, Portion of wing composed of one layer of flexible material. h, Portion of wing composed of two layers. g, Portion of wing composed of three layers. f, Portion of wing composed of four layers. e, Portion of wing composed of five layers. X, Ball-and-socket joint at root of wing.-Original. Fig. 125.-Flexible valvular wing with india-rubber springs attached to its root.

a, b, Anterior margin of wing, tapering and elastic. c, d, Posterior margin of wing, elastic. f. fif, Segments which open during the up stroke and close during the down, after the manner of valves. These are very narrow, and open and close instantly. 2, Universal joint. m, Superior elastic band. n, Ditto inferior. 0, Ditto anterior. p, q, Ditto oblique. r, Ring into which the elastic bands are fixed.-Original.

How to construct a Wave Wing which shall evade the superimposed Air during the Up Stroke.—To construct a wing which

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