Chapter XI: Part 11

If I wish to produce a very delicate light wing, I do so by selecting a fine tapering elastic reed, as represented at _a b_ 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 (_a b_), and only one at the posterior (_c d_). This form of wing is not twisted upon itself structurally, but it twists and untwists, and becomes a true screw during its action.

FIG. 123.--_Artificial Wing with Perpendicular (r s) and Horizontal
(t u) 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_, _q_, 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, and give additional strength to the
anterior margin.

_x_, 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 (_a b_)
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_, _f_, _f_, 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. _x_,
Universal joint. _m_, Superior elastic band. _n_, Ditto inferior.
_o_, 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 shall elude the air during the up stroke, it is necessary to make it valvular, as shown at fig. 125, p. 241.

This wing, as the figure indicates, is composed of _numerous narrow segments_ (_f f f_), so arranged that the air, when the wing is made to vibrate, opens or separates them at the beginning of the up stroke, and closes or brings them together at the beginning of the down stroke.

The time and power required for opening and closing the segments is comparatively trifling, owing to their extreme narrowness and extreme lightness. The space, moreover, through which they pass in performing their valvular action is exceedingly small. The wing under observation is flexible and elastic throughout, and resembles in its general features the other wings described.

I have also constructed a wing which is self-acting in another sense. This consists of two parts--the one part being made of an elastic reed, which tapers towards the extremity; the other of a flexible sail. To the reed, which corresponds to the anterior margin of the wing, delicate tapering reeds are fixed at right angles; the principal and subordinate reeds being arranged on the same plane. The flexible sail is attached to the under surface of the principal reed, and is stiffer at its insertion than towards its free margin. When the wing is made to ascend, the sail, because of the pressure exercised upon its upper surface by the air, assumes a very oblique position, so that the resistance experienced by it during the _up stroke_ is very slight. When, however, the wing descends, the sail instantly flaps in an upward direction, the subordinate reeds never permitting its posterior or free margin to rise above its anterior or fixed margin. The under surface of the wing consequently descends in such a manner as to present a nearly flat surface to the earth. It experiences much resistance from the air during the _down stroke_, the amount of buoyancy thus furnished being very considerable. The above form of wing is more effective during the down stroke than during the up one. It, however, elevates and propels during both, the forward travel being greatest during the down stroke.

_Compound Wave Wing of the Author._--In order to render the movements of the wing as simple as possible, I was induced to devise a form of pinion, which for the sake of distinction I shall designate the _Compound Wave Wing_. This wing consists of two wave wings united at the roots, as represented at fig. 126. It is impelled by steam, its centre being fixed to the head of the piston by a compound joint (_x_), which enables it to move in a circle, and to rotate along its anterior margin (_a b c d_; _A_, _A´_) in the direction of its length. The circular motion is for steering purposes only. The wing rises and falls with every stroke of the piston, and the movements of the piston are quickened during the down stroke, and slowed during the up one.

During the up stroke of the piston the wing is very decidedly convex on its upper surface (_a b c d_; _A_, _A´_), its under surface being deeply concave and inclined obliquely upwards and forwards. It thus evades the air during the up stroke. During the down stroke of the piston the wing is flattened out in every direction, and its extremities twisted in such a manner as to form two screws, as shown at _a´ b´ c´ d´_; _e´ f´ g´ h´_; _B_, _B´_ of figure. The active area of the wing is by this means augmented, the wing seizing the air with great avidity during the down stroke. The area of the wing may be still further increased and diminished during the down and up strokes by adding joints to the body of the wing. The degree of convexity given to the upper surface of the wing can be increased or diminished at pleasure by causing a cord (_i j_; _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.[118] 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.

[118] 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.

_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 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 versâ_. 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 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 _c e_ 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.

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._]

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 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 x´_) 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 speed--it 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.

_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_, _c d_ 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 direction, a column of air represented by _a_, _b_, _c_ of fig. 129, p. 253.[119] 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.

[119] 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.

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 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 versâ_. 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, the air has an opportunity of reacting on its under surface.

_The Artificial Wave Wing as a Propeller._--The wave wing makes an admirable propeller if its tip be directed _vertically downwards_, and the wing lashed from side to side with a sculling figure-of-8 motion, similar to that executed by the tail of the fish. Three wave wings may be made to act in concert, and with a very good result; two of them being made to vibrate figure-of-8 fashion in a more or less horizontal direction with a view to elevating; the third being turned in a downward direction, and made to act vertically for the purpose of propelling.

FIG. 130.--Aërial wave screw, whose blades are slightly twisted (_a
b_, _c d_; _e f_, _g h_), so that those portions nearest the root (_d
h_) make a greater angle with the horizon than those parts nearer
the tip (_b f_). The angle is thus adjusted to the speed attained
by the different portions of the screw. The angle admits of further
adjustment by means of the steel springs _z_, _s_, these exercising
a restraining, and to a certain extent a regulating, influence which
effectually prevents shock.

It will be at once perceived from this figure that the portions of
the screw marked _m_ and _n_ travel at a much lower speed than those
portions marked _o_ and _p_, and these again more slowly than those
marked _q_ and _r_ (compare with fig. 56, p. 120). As, however, the
angle which a wing or a portion of a wing, as I have pointed out,
varies to accommodate itself to the speed attained by the wing, or a
portion thereof, it follows, that to make the wave screw mechanically
perfect, the angles made by its several portions must be accurately
adapted to the travel of its several parts as indicated above.

_x_, Vertical tube for receiving driving shaft. _v_, _w_, Sockets
in which the roots of the blades of the screw rotate, the degree of
rotation being limited by the steel springs _z_, _s_. _a b_, _e f_,
Tapering elastic reeds forming anterior or thick margins of blades of
screw. _d c_, _h g_, Posterior or thin elastic margins of blades of
screw. _m n_, _o p_, _q r_, Radii formed by the different portions of
the blades of the screw when in operation. The arrows indicate the
direction of travel.--_Original._]

_A New Form of Aërial Screw._--If two of the wave wings represented at fig. 122, p. 239, be placed end to end, and united to a vertical portion of tube to form a two-bladed screw, similar to that employed in navigation, a most powerful elastic aërial screw is at once produced, as seen at fig. 130.

This screw, which for the sake of uniformity I denominate _the aërial wave screw_, possesses advantages for aërial purposes to which no form of _rigid_ screw yet devised can lay claim. The way in which it clings to the air during its revolution, and the degree of buoying power it possesses, are quite astonishing. It is a self-adjusting, self-regulating screw, and as its component parts are flexible and elastic, it accommodates itself to the speed at which it is driven, and gives a uniform buoyancy. The slip, I may add, is nominal in amount. This screw is exceedingly light, and owes its efficacy to its shape and the graduated nature of its blades; the anterior margin of each blade being comparatively rigid, the posterior margin being comparatively flexible and more or less elastic. The blades are kites in the same sense that natural wings are kites. They are flown as such when the screw revolves. I find that the aërial wave screw flies best and elevates most when its blades are inclined at a certain upward angle as indicated in the figure (130). The aërial wave screw may have the number of its blades increased by placing the one above the other; and two or more screws may be combined and made to revolve in opposite directions so as to make them reciprocate; the one screw producing the current on which the other rises, as happens in natural wings.

_The Aërial Wave Screw operates also upon Water._--The form of screw just described is adapted in a marked manner for water, if the blades be reduced in size and composed of some elastic substance, which will resist the action of fluids, as gutta-percha, carefully tempered finely graduated steel plates, etc. It bears the same relation to, and produces the same results upon, water, as the tail and fin of the fish. It throws its blades during its action into double figure-of-8 curves, similar in all respects to those produced on the anterior and posterior margins of the natural and artificial flying wing. As the speed attained by the several portions of each blade varies, so the angle at which each part of the blade strikes varies; the angles being always greatest towards the root of the blade and least towards the tip. The angles made by the different portions of the blades are diminished in proportion as the speed, with which the screw is driven, is increased. The screw in this manner is self-adjusting, and extracts a large percentage of propelling power, with very little force and surprisingly little slip.

A similar result is obtained if two finely graduated angular-shaped gutta-percha or steel plates be placed end to end and applied to the water (vertically or horizontally matters little), with a slight sculling figure-of-8 motion, analogous to that performed by the tail of the fish, porpoise, or whale. If the thick margin of the plates be directed forwards, and the thin ones backwards, an unusually effective propeller is produced. This form of propeller is likewise very effective in air.

CONCLUDING REMARKS.

From the researches and experiments detailed in the present volume, it will be evident that a remarkable analogy exists between walking, swimming, and flying. It will further appear that the movements of the tail of the fish, and of the wing of the insect, bat, and bird can be readily imitated and reproduced. These facts ought to inspire the pioneer in aërial navigation with confidence. The land and water have already been successfully subjugated. The realms of the air alone are unvanquished. These, however, are so vast and so important as a highway for the nations, that science and civilisation equally demand their occupation. The history of artificial progression indorses the belief that the fields etherean will one day be traversed by a machine designed by human ingenuity, and constructed by human skill. In order to construct a successful flying machine, it is not necessary to reproduce the filmy wing of the insect, the silken pinion of the bat, or the complicated and highly differentiated wing of the bird, where every feather may be said to have a peculiar function assigned to it; neither is it necessary to reproduce the intricacy of that machinery by which the pinion in the bat, insect, and bird is moved: all that is required is to distinguish the properties, form, extent, and manner of application of the several flying surfaces, a task attempted, however imperfectly executed, in the foregoing pages. When Vivian and Trevithick devised the locomotive, and Symington and Bell the steamboat, they did not seek to reproduce a quadruped or a fish; they simply aimed at producing motion adapted to the land and water, in accordance with natural laws, and in the presence of living models. Their success is to be measured by an involved labyrinth of railway which extends to every part of the civilized world; and by navies whose vessels are despatched without trepidation to navigate the most boisterous seas at the most inclement seasons. The aëronaut has a similar but more difficult task to perform. In attempting to produce a flying-machine he is not necessarily attempting an impossible thing. The countless swarms of flying creatures testify as to the practicability of such an undertaking, and nature supplies him at once with models and materials. If artificial flight were not attainable, the insects, bats, and birds would furnish the only examples of animals whose movements could not be reproduced. History, analogy, observation, and experiment are all opposed to this view. The success of the locomotive and steamboat is an earnest of the success of the flying machine. If the difficulties to be surmounted in its construction are manifold, the triumph and the reward will be correspondingly great. It is impossible to over-estimate the boon which would accrue to mankind from such a creation. Of the many mechanical problems before the world at present, perhaps there is none greater than that of aërial navigation. Past failures are not to be regarded as the harbingers of future defeats, for it is only within the last few years that the subject of artificial flight has been taken up in a true scientific spirit. Within a comparatively brief period an enormous mass of valuable data has been collected. As societies for the advancement of aëronautics have been established in Britain, America, France, and other countries, there is reason to believe that our knowledge of this most difficult department of science will go on increasing until the knotty problem is finally solved. If this day should ever come, it will not be too much to affirm, that it will inaugurate a new era in the history of mankind; and that great as the destiny of our race has been hitherto, it will be quite out-lustred by the grandeur and magnitude of coming events.

INDEX.

PAGE

Aerial creatures not stronger than terrestrial ones, 13

Aërial flight as distinguished from sub-aquatic flight, 92

Aëronautics, 209

Air cells in insects and birds not necessary to flight, 115

Albatross, flight of, compared to compass set upon gimbals, 199

Amphibia have larger travelling surfaces than land animals, but less
than aërial ones, 8

Artificial fins, flippers, and wings, how constructed, 14

Artificial wings, Borelli, 219

Do. Marey, 226

Do. Chabrier, 233

Do. Straus-Durckheim, 233

Do. how to apply to the air, 245

Do. nature of forces required to propel, 246

Artificial _wave_ wing of Pettigrew, 236

Do. how to construct on insect type, 240

Do. how to construct to evade the superimposed air during the up
stroke, 241

Do. can create currents and rise upon them, 253

Do. can be driven at any speed; can make new currents and utilize
old ones, 251, 255

Do. as a propeller and aërial screw, 256

Do. compound rotation of: the different parts of the wing travel at
different speeds, 252

Do. necessity for supplying root of, with elastic structures, 247

Artificial _compound wave_ wing of Pettigrew, 242

Atmospheric pressure, effects of, on limbs, 24

Axioms, fundamental, 17

Balancing, how effected in flight, 118

Balloon, 210

Bats and birds, lax condition of shoulder-joint in, 190

Birds, lifting capacity of, 205

Body and wing reciprocate in flight, and each describes a waved
track, 12

Bones, 21

Bones of the extremities twisted and spiral, 28, 29

Bones of wing of bat--spiral configuration of their articular
surfaces, 176

Bones of wing of bird--their articular surfaces, movements,
etc., 178

Borelli’s artificial bird, 220

Chabrier’s artificial wings, 233

Elytra or wing cases and membranous wings, 170

Feathers, primary, secondary, and tertiary, 180

Fins, flippers, and wings form mobile helices or screws, 14

Flight, weight necessary to, 3, 4, 110, 111, 112, 113

Flight the poetry of motion, 6

Flight the least fatiguing kind of motion, 13

Flight under water, 90

Flight of the flying-fish, 98

Flight, horizontal, in part due to weight of flying mass, 110

Flight--the regular and irregular, 201

Flight--how to ascend, descend, and turn, 201

Flight of birds referrible to muscular exertion and weight, 204

Fluids, mechanical effects of, on animals immersed in them, 18

Fluids, resistance of, 18

Flying machine, Henson, 212

Do. Stringfellow, 213

Do. Cayley, 215

Do. Phillips, 216

Do. M. de la Landelle, 217

Do. Borelli, 219

A flying machine possible, 2, 3

Forces which propel the wings of insects, bats, and birds, 186, 189

Fulcra, yielding, 8, 104, 165

Gravity, the legs move by the force of, 18

Gravity, centre of, 18

History of the figure-of-8 theory of walking, swimming, and
flying, 15

Joints, 23

Kite-like action of the wings, 98

Kite--how kite formed by wing differs from boy’s kite, 166

Laws of natural and artificial progression the same, 4, 17

Legs, moved by the force of gravity, 18

Lever--the wing one of the third order, 103

Levers, the three orders of, 19

Life linked to motion, 3

Lifting capacity of birds, 205

Ligaments, 24

Ligaments, elastic, position and action of, in wing of pheasant,
snipe, crested crane, swan, etc., 191

Ligaments, elastic, more highly differentiated in wings which
vibrate quickly, 193

Locomotion, the active organs of, 24

Locomotion, the passive organs of, 21

Locomotion of the horse, 39

Locomotion of the ostrich, 45

Locomotion of man, 51

Marey’s artificial wings, 233

Membranous wings, 170

Motion associated with the life and well-being of animals, 1

Motion not confined to the animal kingdom, 2

Motion, natural and artificial, 4

Motion, of uniform, 17

Motion uniformly varied, 17

Muscles, their properties, mode of action, etc., 24

Muscles arranged in longitudinal, transverse, and oblique spiral
lines, 28

Muscles, oblique spiral, necessary for spiral bones and joints, 31

Muscles take precedence of bones in animal movements, 29

Muscular cycles, 26

Muscular waves, 26

Pendulums, the extremities of animals act as, in walking,
9, 18, 56, 57

Plane, inclined, as applied to the air, 211

Pettigrew’s method of constructing and applying artificial wings as
contradistinguished from that of Borelli, Chabrier, Durckheim,
Marey, etc., 235

Pettigrew’s _wave_ wing, 236

Pettigrew’s _compound wave_ wing, 242

Progression on the land, 37

Do. on or in the water, 64

Do. in or through the air, 103

Quadrupeds walk, fishes swim, and insects, bats, and birds fly, by
figure-of-8 movements, 15, 16

Screws--the wing of the bird and the extremity of the biped and
quadruped screws, structurally and functionally, 12

Screws--difference between those formed by the wings and those
employed in navigation, 151

Sculling action of the wing, 231

Speed attained by insects, 188

Speed of wing movements partly accounted for, 120

Spine, spiral movements of, transferred to the extremities, 33

Straus-Durckheim’s artificial wings, 233

Swimming of the fish, whale, porpoise, etc., 66

Swimming of the seal, sea-bear, and walrus, 74

Swimming of man, 78

Swimming of the turtle, triton, crocodile, etc., 89

Terrestrial animals have smaller travelling surfaces than amphibia,
amphibia than fishes, and fishes than insects, bats, and birds, 8

The travelling surfaces of animals increase as the density of the
media traversed decreases, 7, 8

The travelling surfaces of animals variously modified and adapted
to the media on or in which they move, 34

Walking, swimming, and flying correlated, 5

Walking of the quadruped, biped, etc., 9, 10, 11

_Wave_ wing of Pettigrew, 236

Do. how to construct on insect type, 240

Do. how to construct to evade the superimposed air during the up
stroke, 241

Do. can be driven at any speed, 251, 255

Do. can create currents and rise upon them, 253

Do. can make new currents and utilize existing ones, 251, 255

Do. as a propeller, 256

Do. as an aërial screw, 256

Do. forces required to apply to the air, 245, 246

Do. necessity for supplying root of, with elastic structures, 247

Wave wing, _compound_, 242

Weight necessary to flight, 110

Weight contributes to flight, 112

Weight, momentum, and power to a certain extent synonymous in
flight, 114

Wing of the bird and the extremity of the biped and quadruped are
screws, structurally and functionally, 12, 136

Wing in flight describes figure-of-8 curves, 12

Wing during its action reverses its planes and describes a
figure-of-8 track in space, 140

Wing when advancing with the body describes looped and waved
tracks, 143

Wing, margins of, thrown into opposite curves during extension and
flexion, 146

Wing, tip of, describes an ellipse, 147

Wing and body reciprocate in flight, and each describes a wave
track, 12

Wing moves in opposite curves to body, 168

Wing ascends when body descends, and _vice versâ_, 159

Wing during its vibrations produces a cross pulsation, 148

Wing vibrates unequally with reference to a given line, 150, 231

Wing, compound rotation of, 149

Wing a lever of the third order, 103

Wing acts on yielding fulcra, 8, 104, 165

Wings, their form, etc., all wings screws, structurally and
functionally, 136

Wing capable of change of form in all its parts, 147

Wing-area variable and in excess, 124

Wing-area decreases as the size and weight of the volant animal
increases, 132

Wing, natural, when elevated and depressed must move forwards, 156

Wing, angles formed by, when in action, 167

Wing acts as true kite both during down and up strokes, 165

Wing, traces of design in, 180

Wing of bird not always opened up to same extent in up stroke, 182

Wing, flexion of, necessary to flight of birds, 183

Wing flexed and partly elevated by action of elastic ligaments, 191

Wing, power of, to what owing, 194

Wing, effective stroke of, why delivered downwards and forwards, 195

Wing acts as an elevator, propeller, and sustainer both during
extension and flexion, 197

Wings, points wherein the screws formed by, differ from those in
ordinary use, 151

Wings at all times thoroughly under control, 154

Wings of insects, consideration of forces which propel, 186

Wings of bats and birds, consideration of forces which propel, 189

PRINTED BY T. AND A. CONSTABLE, PRINTERS TO HER MAJESTY, AT THE
EDINBURGH UNIVERSITY PRESS.