The degree of convexity given to the upper surface of the wing can be increased or diminished at pleasure by causing a cord (ij; A, A') and elastic band (k) to extend between two points, which may vary according to circumstances. The wing is supplied with vertical springs, which assist in slowing and reversing it towards the end of the down and up strokes, and these, in conjunction with the elastic properties of the wing itself, contribute powerfully to its continued play. The compound wave wing produces the currents on which it rises. Thus during the up stroke it draws after it a current, which being met by the wing during its descent, confers additional elevating and propelling power. During the down stroke the wing in like manner draws after it a current which forms an eddy, and on this eddy the wing rises, as explained at p. 253, fig. 129. The ascent of the wing is favoured by the superimposed air playing on the upper surface of the posterior margin of the organ, in such a manner as to cause the wing to assume a more and more oblique position with reference to the horizon. This change in the plane of the wing enables its upper surface to avoid the superincumbent air during the up stroke, while it, confers upon its under surface a combined kite and parachute action. The compound wave wing leaps forward in a curve both during the down and up strokes, so that the wing during its vibration describes a waved track, as shown at a, c, e, g, i of fig. 81, p. 157. The compound wave wing possesses most of the peculiarities of single wings when made to vibrate separately. It forms a most admirable elevator and propeller, and has this advantage over ordinary wings, that it can be worked without injury to itself, when the machine which it is intended to elevate is resting on the ground. Two or more compound wave wings may be arranged on the same plane, or superimposed, and made to act in concert. They may also by a slight modification be made to act horizontally instead of vertically. The length of the stroke of the compound wave wing is determined in part, though not entirely by the stroke of the piston-the extremities of the wing, because of their elasticity, moving through a greater space than the centre of the wing. By fixing the wing to the head of the piston all

gearing apparatus is avoided, and the number of joints and working points reduced—a matter of no small importance when it is desirable to conserve the motor power and keep down the weight.

How to apply Artificial Wings to the Air-Borelli, Durckheim, Marey, and all the writers with whom I am acquainted, assert that the wing should be made to vibrate vertically. I believe that if the wing be in one piece it should be made to vibrate obliquely and more or less horizontally. If, however, the wing be made to vibrate vertically, it is necessary to supply it with a ball-and-socket joint, and with springs at its root (m n of fig. 125, p. 241), to enable it to leap forward in a curve when it descends, and in another and opposite curve when it ascends (vide a, c, e, g, i of fig. 81, p. 157). This arrangement practically converts the vertical vibration into an oblique one. If this plan be not adopted, the wing is apt to foul at its tip. In applying the wing to the air it ought to have a figure-of-8 movement communicated to it either directly or indirectly. It is a peculiarity of the artificial wing properly constructed (as it is of the natural wing), that it twists and untwists and makes figure-of-8 curves during its action (see a b, c d of fig. 122, p. 239), this enabling it to seize and let go the air with wonderful rapidity, and in such a manner as to avoid dead points. If the wing be in several pieces, it may be made to vibrate more vertically than a wing in one piece, from the fact that the outer half of the pinion moves forwards and backwards when the wing ascends and descends so as alternately to become a short and a long lever; this arrangement permitting the wing to avoid the resistance experienced from the air during the up stroke, while it vigorously seizes the air during the down stroke.

If the body of a flying animal be in a horizontal position, a wing attached to it in such a manner that its under surface shall look forwards, and make an upward angle of 45° with the horizon is in a position to be applied either vertically (figs. 82 and 83, p. 158), or horizontally (figs. 67, 68, 69, and 70, p. 141). Such, moreover, is the conformation of the shoulder-joint in insects, bats, and birds, that the wing can be applied vertically, horizontally, or at any degree of obliquity

without inconvenience.1 It is in this way that an insect which may begin its flight by causing its wings to make figure-of-8 horizontal loops (fig. 71, p. 144), may gradually change the direction of the loops, and make them more and more oblique until they are nearly vertical (fig. 73, p. 144). In the beginning of such flight the insect is screwed nearly vertically upwards; in the middle of it, it is screwed upwards and forwards; whereas, towards the end of it, the insect advances in a waved line almost horizontally (see q',r', s', t' of fig. 72, p. 144). The muscles of the wing are so arranged that they can propel it in a horizontal, vertical, or oblique direction. It is a matter of the utmost importance that the direction of the stroke and the nature of the angles made by the surface of the wing during its vibration with the horizon be distinctly understood; as it is on these that all flying creatures depend when they seek to elude the upward resistance of the air, and secure a maximum of elevating and propelling power with a minimum of slip.

As to the nature of the Forces required for propelling Artificial Wings.-Borelli, Durckheim, and Marey affirm that it suffices if the wing merely elevates and depresses itself by a rhythmical movement in a perpendicular direction; while Chabrier is of opinion that a movement of depression only is required. All those observers agree in believing that the details of flight are due to the reaction of the air on the surface of the wing. Repeated experiment has, however, convinced me that the artificial wing must be thoroughly under control, both during the down and up strokes-the details of flight being in a great measure due to the movements communicated to the wing by an intelligent agent. In order to reproduce flight by the aid of artificial wings, I find it necessary to employ a power which varies in intensity at every stage of the down and up strokes. The power which

1 The human wrist is so formed that if a wing be held in the hand at an upward angle of 45°, the hand can apply it to the air in a vertical or horizontal direction without difficulty. This arises from the power which the hand has of moving in an upward and downward direction, and from side to side with equal facility. The hand can also rotate on its long axis, so that it virtually represents all the movements of the wing at its root.

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 limits 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