Chapter X: Part 10

In the helicopteric models made by MM. Nadar, Pontin d’Amécourt, and de la Landelle, the screws (_m n o p q r s t_ of figure) are arranged in tiers, _i.e._ the one screw is placed above the other. In this respect they resemble the aëroplanes recommended by Mr. Wenham, and tested by Mr. Stringfellow (compare _m n o p q r s t_ of fig. 112, with _a b c_ of fig. 110, p. 213). The superimposed screws, as already explained, were first figured and described by Sir George Cayley (p. 215). The French screws, and that employed by Mr. Phillips, are _rigid or unyielding_, and strike the air _at a given angle_, and herein, I believe, consists their principal defect. This arrangement results in a ruinous expenditure of power, and is accompanied by a great amount of slip. The aërial screw, and the machine to be elevated by it, can be set in motion without any preliminary run, and in this respect it has the advantage over the machine supported by mere sustaining planes. It has, in fact, a certain amount of inherent motion, its screws revolving, and supplying it with active or moving surfaces. It is accordingly more independent than the machine designed by Henson, Wenham, and Stringfellow.

I may observe with regard to the system of rigid inclined planes wedged forward at a given angle in a straight line or in a circle, that it does not embody the principle carried out in nature.

The wing of a flying creature, as I have taken pains to show, is _not rigid_; neither does it always strike the air _at a given angle_. On the contrary, it is capable of moving in all its parts, and attacks the air at _an infinite variety of angles_ (pp. 151 to 154). Above all, the surface exposed by a natural wing, when compared with the great weight it is capable of elevating, is remarkably small (fig. 89, p. 171). This is accounted for by the length and the great range of motion of natural wings; the latter enabling the wings to convert large tracts of air into supporting areas (figs. 64, 65, and 66, p. 139). It is also accounted for by the multiplicity of the movements of natural wings, these enabling the pinions to create and rise upon currents of their own forming, and to avoid natural currents when not adapted for propelling or sustaining purposes (fig. 67, 68, 69, and 70, p. 141).

If any one watches an insect, a bat, or a bird when dressing its wings, he will observe that it can incline the under surface of the wing at a great variety of angles to the horizon. This it does by causing the posterior or thin margin of the wing to rotate around the anterior or thick margin as an axis. As a result of this movement, the two margins are forced into double and opposite curves, and the wing converted into _a plastic helix_ or _screw_. He will further observe that the bat and bird, and some insects, have, in addition, the power of folding and drawing the wing towards the body during the up stroke, and of pushing it away from the body and extending it during the down stroke, so as alternately to diminish and increase its area; arrangements necessary to decrease the amount of resistance experienced by the wing during its ascent, and increase it during its descent. It is scarcely requisite to add, that in the aëroplanes and aërial screws, as at present constructed, no provision whatever is made for suddenly increasing or diminishing the flying surface, of conferring elasticity upon it, or of giving to it that infinite variety of angles which would enable it to seize and disentangle itself from the air with the necessary rapidity. Many investigators are of opinion that flight is a mere question of levity and power, and that if a machine could only be made light enough and powerful enough, it must of necessity fly, whatever the nature of its flying surfaces. A grave fallacy lurks here. Birds are not more powerful than quadrupeds of equal size, and Stringfellow’s machine, which, as we have seen, only weighed 12 lbs., exerted _one-third of a horse power_. The probabilities therefore are, that flight is dependent to a great extent on the nature of the flying surfaces, and the mode of applying those surfaces to the air.

_Artificial Wings_ (Borelli’s Views).--With regard to the production of _flight by the flapping of wings_, much may and has been said. Of all the methods yet proposed, it is unquestionably by far the most ancient. Discrediting as apocryphal the famous story of Dædalus and his waxen wings, we certainly have a very graphic account of artificial wings in the De Motu Animalium of Borelli, published as far back as 1680, _i.e._ nearly two centuries ago.[107]

[107] Borelli, De Motu Animalium. Sm. 4to, 2 vols. Romæ, 1680.

Indeed it will not be too much to affirm, that to this distinguished physiologist and mathematician belongs almost all the knowledge we possessed of artificial wings up till 1865. He was well acquainted with the properties of the wedge, as applied to flight, and he was likewise cognisant of the flexible and elastic properties of the wing. To him is to be traced the purely mechanical theory of the wing’s action. He figured a bird with artificial wings, each wing consisting of _a rigid rod in front_ and _flexible feathers_ behind. I have thought fit to reproduce Borelli’s figure both because of its great antiquity, and because it is eminently illustrative of his text.[108]

[108] De Motu Animalium, Lugduni Batavorum apud Petrum Vander. Anno
MDCLXXXV. Tab. XIII. figure 2. (New edition.)

The wings (_b c f_, _o e a_), are represented as striking vertically downwards (_g h_). They remarkably accord with those described by Straus-Durckheim, Girard, and quite recently by Professor Marey.[109]

[109] Revue des Cours Scientifiques de la France et de l’Etranger.
Mars 1869.

Borelli is of opinion that flight results from the application of an inclined plane, which beats the air, and which has a wedge action. He, in fact, endeavours to prove that a bird wedges itself forward upon the air by the perpendicular vibration of its wings, the wings during their action forming a wedge, the base of which (_c b e_) is directed towards the head of the bird; the apex (_a f_) being directed towards the tail. This idea is worked out in propositions 195 and 196 of the first part of Borelli’s book. In proposition 195 he explains how, if a wedge be driven into a body, the wedge will tend to separate that body into two portions; but that if the two portions of the body be permitted to react upon the wedge, they will communicate _oblique impulses_ to the sides of the wedge, and expel it, base first, in a straight line.

Following up the analogy, Borelli endeavours to show in his 196th proposition, “that if the air acts obliquely upon the wings, or the wings obliquely upon the air (which is, of course, a wedge action), the result will be _a horizontal transference of the body of the bird_.” In the proposition referred to (196) Borelli states--“If the expanded wings of a bird suspended in the air shall strike the undisturbed air beneath it with a motion _perpendicular to the horizon_, the bird will fly _with a transverse motion_ in a plane parallel with the horizon.” In other words, if the wings _strike vertically downwards_, the bird will fly _horizontally forwards_. He bases his argument upon the belief that the anterior margins of the wings are _rigid and unyielding_, whereas the posterior and after parts of the wings are _more or less flexible_, and readily give way under pressure. “If,” he adds, “the wings of the bird be expanded, and the under surfaces of the wings be struck by the air _ascending perpendicularly to the horizon_, with such a force as shall prevent the bird gliding downwards (_i.e._ with a tendency to glide downwards) from falling, it will be urged _in a horizontal direction_. This follows because the two osseous rods (virgæ) forming the anterior margins of the wings resist the upward pressure of the air, and so retain their original form (literally extent or expansion), whereas the flexible after-parts of the wings (posterior margins) are pushed up and approximated to form a cone, the apex of which (_vide_ _a f_ of fig. 113) is directed towards the tail of the bird. In virtue of the air playing upon and compressing the sides of the wedge formed by the wings, the wedge is driven forwards in the direction of its base (_c b e_), which is equivalent to saying that the wings carry the body of the bird to which they are attached _in a horizontal direction_.”

Borelli restates the same argument in different words, as follows:--

“If,” he says, “the air under the wings be struck by the flexible portions of the wings (_flabella_, literally fly-flaps or small fans) with a motion perpendicular to the horizon, the sails (vela) and flexible portions of the wings (flabella) will yield in an upward direction, and form a wedge, the point of which is directed towards the tail. Whether, therefore, the air strikes the wings from below, or the wings strike the air from above, the result is the same--the posterior or flexible margins of the wings _yield in an upward direction_, and in so doing urge the bird in a _horizontal direction_.”

In his 197th proposition, Borelli follows up and amplifies the arguments contained in propositions 195 and 196. “Thus,” he observes, “it is evident that the object of flight is to impel birds upwards, and keep them suspended in the air, and also to enable them to wheel round in a plane parallel to the horizon. The first (or upward flight) could not be accomplished unless the bird were impelled upwards by frequent leaps or vibrations of the wings, and its descent prevented. And because the downward tendency of heavy bodies is perpendicular to the horizon, the vibration of the plain surfaces of the wings must be made by striking the air beneath them in a direction perpendicular to the horizon, and in this manner nature produces the suspension of birds in the air.”

“With regard to the second or transverse motion of birds (_i.e._ horizontal flight) some authors have strangely blundered; for they hold that it is like that of boats, which, being impelled by oars, moved horizontally in the direction of the stern, and pressing on the resisting water behind, leaps with a contrary motion, and so are carried forward. In the same manner, say they, the wings vibrate towards the tail with a horizontal motion, and likewise strike against the undisturbed air, by the resistance of which they are moved forward by a reflex motion. But this is contrary to the evidence of our sight as well as to reason; for we see that the larger kinds of birds, such as swans, geese, etc., never vibrate their wings when flying towards the tail with a horizontal motion like that of oars, but always bend them downwards, and so describe circles raised perpendicularly to the horizon.[110]

[110] It is clear from the above that Borelli did not know that the
wings of birds strike _forwards_ as well as downwards during the down
stroke, and _forwards_ as well as upwards during the up stroke. These
points, as well as the twisting and untwisting figure-of-8 action of
the wing, were first described by the author. Borelli seems to have
been equally ignorant of the fact that the wings of insects vibrate
in a more or less horizontal direction.

“Besides, in boats the horizontal motion of the oars is easily made, and a perpendicular stroke on the water would be perfectly useless, inasmuch as their descent would be impeded by the density of the water. But in birds, such a horizontal motion (which indeed would rather hinder flight) would be absurd, since it would cause the ponderous bird to fall headlong to the earth; whereas it can only be suspended in the air by constant vibration of the wings _perpendicular to the horizon_. Nature was thus forced to show her marvellous skill in producing a motion which, by one and the same action, should suspend the bird in the air, and carry it forward in a horizontal direction. This is effected by striking the air below perpendicularly to the horizon, but with oblique strokes--an action which is rendered possible only by the flexibility of the feathers, for the fans of the wings in the act of striking acquire the form of a wedge, by the forcing out of which the bird is necessarily moved forwards in a horizontal direction.”

The points which Borelli endeavours to establish are these:--

First, That the action of the wing is a wedge action.

Second, That the wing consists of two portions--_a rigid_ anterior portion, and a _non-rigid_ flexible portion. The rigid portion he represents in his artificial bird (fig. 113, p. 220) as consisting of _a rod_ (_e r_), the yielding portion of _feathers_ (_a o_).

Third, That if the air strikes the under surface of the wing perpendicularly in a direction from below upwards, the flexible portion of the wing will yield in an upward direction, and form a wedge with its neighbour.

Fourth, Similarly and conversely, if the wing strikes the air perpendicularly from above, the posterior and flexible portion of the wing will yield and be forced in an upward direction.

Fifth, That this _upward yielding_ of the posterior or flexible margin of the wing results in and necessitates _a horizontal transference_ of the body of the bird.

Sixth, That to sustain a bird in the air the wings must strike _vertically downwards_, as this is the direction in which a heavy body, if left to itself, would fall.

Seventh, That to propel the bird in a horizontal direction, the wings must descend in a perpendicular direction, and the posterior or flexible portions of the wings _yield in an upward direction_, and in such a manner as virtually to communicate _an oblique action_ to them.

Eighth, That the feathers of the wing are _bent in an upward direction_ when the wing _descends_, the upward bending of the elastic feathers contributing to the horizontal travel of the body of the bird.

I have been careful to expound Borelli’s views for several reasons:--

_1st_, Because the purely mechanical theory of the wing’s action is clearly to be traced to him.

_2d_, Because his doctrines have remained unquestioned for nearly two centuries, and have been adopted by all the writers since his time, without, I regret to say in the majority of cases, any acknowledgment whatever.

_3d_, Because his views have been revived by the modern French school; and

_4th_, Because, in commenting upon and differing from Borelli, I will necessarily comment upon and differ from all his successors.

_As to the Direction of the Stroke, yielding of the Wing, etc._--The Duke of Argyll[111] agrees with Borelli in believing that the wing invariably strikes _perpendicularly downwards_. His words are--“Except for the purpose of arresting their flight birds can never strike except _directly downwards_; that is, against the opposing force of gravity.” Professor Owen in his Comparative Anatomy, Mr. Macgillivray in his British Birds, Mr. Bishop in his article “Motion” in the Cyclopedia of Anatomy and Physiology, and M. Liais “On the Flight of Birds and Insects” in the Annals of Natural History, all assert that the stroke is delivered _downwards_ and more or less _backwards_.

[111] “Reign of Law”--Good Words, 1865.

To obtain an _upward_ recoil, one would naturally suppose all that is required is a _downward_ stroke, and to obtain an _upward and forward_ recoil, one would naturally conclude a _downward and backward_ stroke alone is requisite. Such, however, is not the case.

In the first place, a natural wing, or a properly constructed artificial one, cannot be depressed either _vertically downwards_, or _downwards and backwards_. It will of necessity descend _downwards and forwards in a curve_. This arises from its being flexible and elastic throughout, and in especial from its being carefully graduated as regards thickness, the tip being thinner and more elastic than the root, and the posterior margin than the anterior margin.

In the second place, there is only one direction in which the wing could strike so at once _to support and carry the bird forward_. The bird, when flying, is a body in motion. It has therefore acquired momentum. If a grouse is shot on the wing _it does not fall vertically downwards_, as Borelli and his successors assume, but _downwards and forwards_. The flat surfaces of the wings are consequently made to strike downwards and forwards, as they in this manner act as kites to the falling body, which they bear, or tend to bear, _upwards and forwards_.

So much for the direction of the stroke during the descent of the wing.

Let us now consider to what extent the posterior margin of the wing yields in _an upward direction_ when the wing descends. Borelli does not state the exact amount. The Duke of Argyll, who believes with Borelli that the posterior margin of the wing is elevated during the down stroke, avers that, “whereas the air compressed in the hollow of the wing cannot pass through the wing owing to the closing upwards of the feathers against each other, or escape forwards because of the rigidity of the bones and of the quills in this direction, it passes backwards, and in so doing _lifts by its force the elastic ends of the feathers_. In passing backwards it communicates to the whole line of both wings a corresponding push forwards to the body of the bird. The same volume of air is thus made, in accordance with the law of action and reaction, _to sustain the bird and carry it forward_.”[112] Mr. Macgillivray observes that “to progress _in a horizontal direction_ it is necessary that the downward stroke should be modified _by the elevation in a certain degree of the free extremities of the quills_.”[113]

[112] “Reign of Law”--Good Words, February 1865, p. 128.

[113] History of British Birds. Lond. 1837, p. 43.

_Marey’s Views._--Professor Marey states that during _the down stroke_ the posterior or flexible margin of the wing yields in _an upward direction_ to such an extent as to cause the under surface of the wing _to look backwards_, and make a backward angle with the horizon of 45° _plus_ or _minus_ according to circumstances.[114] That the posterior margin of the wing yields in a slightly upward direction during the down stroke, I admit. By doing so it prevents shock, confers continuity of motion, and contributes in some measure to the elevation of the wing. The amount of yielding, however, is in all cases very slight, and the little upward movement there is, is in part the result of the posterior margin of the wing rotating around the anterior margin as an axis. That the posterior margin of the wing never yields in _an upward direction_ until the under surface of the pinion makes a backward angle of 45° with the horizon, as Marey remarks, is a matter of absolute certainty. This statement admits of direct proof. If any one watches the horizontal or upward flight of a large bird, he will observe that the posterior or flexible margin of the wing never rises during the down stroke to a perceptible extent, so that _the under surface of the wing_ on no occasion looks backwards, as stated by Marey. On the contrary, he will find that _the under surface of the wing_ (during the down stroke) invariably _looks forwards_--the posterior margin of the wing being inclined _downwards and backwards_; as shown at figs. 82 and 83, p. 158; fig. 103, p. 186; fig. 85 (_a b c_), p. 160; and fig. 88 (_c d e f g_), p. 166.

[114] “Méchanisme du vol chez les insectes. Comment se fait la
propulsion,” by Professor E. J. Marey. Revue des Cours Scientifiques
de la France et de l’Etranger, for 20th March 1869, p. 254.

The under surface of the wing, as will be seen from this account, not only always _looks forwards_, but it forms a true kite with the horizon, the angles made by the kite varying at every part of the down stroke, as shown more particularly at _d_, _e_, _f_, _g_; _j_, _k_, _l_, _m_ of fig. 88, p. 166. I am therefore opposed to Borelli, Macgillivray, Owen, Bishop, M. Liais, the Duke of Argyll, and Marey as to the direction and nature of the down stroke. I differ also as to the direction and nature of the up stroke.

Professor Marey states that not only does the posterior margin of the wing yield _in an upward direction_ during the _down stroke_ until the under surface of the pinion makes a backward angle of 45° with the horizon, but that during the _up stroke_ it yields to the same extent _in an opposite direction_. The posterior flexible margin of the wing, according to Marey, passes through a space of 90° every time the wing reverses its course, this space being dedicated to the mere adjusting of the planes of the wing for the purposes of flight. The planes, moreover, he asserts, are adjusted not by vital and vito-mechanical acts but by _the action of the air alone_; this operating on the under surface of the wing and forcing its posterior margin _upwards_ during _the down stroke_; the air during the _up stroke_ acting upon the posterior margin of the upper surface of the wing, and forcing it _downwards_. This is a mere repetition of Borelli’s view. Marey delegates to the air the difficult and delicate task of arranging the details of flight. The time, power, and space occupied in reversing the wing alone, according to this theory, are such as to render flight impossible. That the wing does not act as stated by Borelli, Marey, and others may be readily proved by experiment. It may also be demonstrated mathematically, as a reference to figs. 114 and 115, p. 228, will show.

Let _a b_ of fig. 114 represent the horizon; _m n_ the line of vibration; _x c_ the wing inclined at an upward backward angle of 45° in the act of making the down stroke, and _x d_ the wing inclined at a downward backward angle of 45° and in the act of making the up stroke. When the wing _x c_ descends it will tend to dive downwards in the direction _f_ giving very little of any horizontal support (_a b_); when the wing _x d_ ascends it will endeavour to rise in the direction _g_, as it darts up like a kite (the body bearing it being in motion). If we take the resultant of these two forces, we have at most propulsion in the direction _a b_. This, moreover, would only hold true if the bird was as light as air. As, however, gravity tends to pull the bird downwards as it advances, the real flight of the bird, according to this theory, would fall in a line between _b_ and _f_, probably in _x h_. It could not possibly be otherwise; the wing described and figured by Borelli and Marey is in one piece, and made to vibrate vertically on either side of a given line. If, however, a wing in one piece is elevated and depressed in a strictly perpendicular direction, it is evident that the wing will experience a greater resistance during _the up stroke_, when it is acting _against gravity_, than during _the down stroke_, when it is acting _with gravity_. As a consequence, the bird will be more vigorously depressed during the ascent of the wing than it will be elevated during its descent. That the mechanical wing referred to by Borelli and Marey is _not a flying wing_, but a mere propelling apparatus, seems evident to the latter, for he states that the winged machine designed by him has unquestionably _not motor power enough to support its own weight_.[115]

[115] Revue des Cours Scientifiques de la France et de l’Etranger.
8vo. March 20, 1869.

The manner in which the natural wing (and the artificial wing properly constructed and propelled) evades the resistance of the air during the up stroke, and gives continuous support and propulsion, is very remarkable. Fig. 115 illustrates the true principle. Let _a b_ represent the horizon; _m n_ the direction of vibration; _x s_ the wing ready to make the down stroke, and _x t_ the wing ready to make the up stroke. When the wing _x s_ descends, the posterior margin (_s_) is screwed _downwards_ and _forwards_ in the direction _s_, _t_; the forward angle which it makes with the horizon increasing as the wing descends (compare with fig. 85 (_a b c_), p. 160, and fig. 88 (_c d e f_), p. 166). The air is thus seized by a great variety of inclined surfaces, and as the under surface of the wing, which is a true kite, looks _upwards_ and _forwards_, it tends to carry the body of the bird _upwards_ and _forwards_ in the direction _x w_. When the wing _x t_ makes the _up stroke_, it rotates in the direction _t s_ to prepare for the second down stroke. It does not, however, ascend in the direction _t s_. On the contrary, it darts up like a true kite, which it is, in the direction _x v_, in virtue of the reaction of the air, and because the body of the bird, to which it is attached, has a forward motion communicated to it by the wing during the down stroke (compare with _g h i_ of fig. 88, p. 166). The resultant of the forces acting in the directions _x v_ and _x b_, is one acting in the direction _x w_, and if allowance be made for the operation of gravity, the flight of the bird will correspond to a line somewhere between _w_ and _b_, probably the line _x r_. This result is produced by the wing acting as an eccentric--by the upper concave surface of the pinion being always directed upwards, the under concave surface downwards--by the under surface, which is a true kite, darting forward in wave curves both during the down and up strokes, and never making a backward angle with the horizon (fig. 88, p. 166); and lastly, by the wing employing the air under it as a fulcrum during the down stroke, the air, on its own part, reacting on the under surface of the pinion, and when the proper time arrives, contributing to the elevation of the wing.

If, as Borelli and his successors believe, the posterior margin of the wing yielded to a marked extent in _an upward direction_ during the _down stroke_, and more especially if it yielded to such an extent as to cause the under surface of the wing to make _a backward angle with the horizon of 45°_, one of two things would inevitably follow--either the air on which the wing depends for support and propulsion would be permitted to escape before it was utilized; or the wing would dart rapidly _downward_, and carry the body of the bird with it. If the posterior margin of the wing yielded in an upward direction to the extent described by Marey during the down stroke, it would be tantamount to removing the fulcrum (the air) on which the lever formed by the wing operates.

If a bird flies in a horizontal direction the angles made by the under surface of the wing with the horizon _are very slight_, but they _always look forwards_ (fig. 60, p. 126). If a bird flies upwards the angles in question are increased (fig. 59, p. 126). In no instance, however, unless when the bird is everted and flying downwards, is the _posterior margin_ of the wing _on a higher level_ than the anterior one (fig. 106, p. 203). This holds true of natural flight, and consequently also of artificial flight.

These remarks are more especially applicable to the flight of the bat and bird where the wing is made to vibrate more or less perpendicularly (fig. 17, p. 36; figs. 82 and 83, p. 158. Compare with fig. 85, p. 160, and fig. 88, p. 166). If a bird or a bat wishes to fly upwards, its flying surfaces must always be inclined upwards. It is the same with the fish. A fish can only swim upwards if its body is directed upwards. In the insect, as has been explained, the wing is made to vibrate in a more or less horizontal direction. In this case the wing has not to contend directly against gravity (a wing which flaps vertically must). As a consequence it is made to tack upon the air obliquely zigzag fashion as horse and carriage would ascend a steep hill (_vide_ figs. 67 to 70, p. 141. Compare with figs. 71 and 72, p. 144). In this arrangement gravity is overcome by the wing reversing its planes and acting as a kite which flies alternately forwards and backwards. The kites formed by the wings of the bat and bird always fly forward (fig. 88, p. 166). In the insect, as in the bat and bird, the posterior margin of the wing never rises above the horizon so as to make an upward and backward angle with it, as stated by Borelli, Marey, and others (_c x a_ of fig. 114, p. 228).

While Borelli and his successors are correct as to the wedge-action of the wing, they have given an erroneous interpretation of the manner in which the wedge is produced. Thus Borelli states that when the wings descend their posterior margins ascend, the two wings forming a cone whose base is represented by _c b e_ of fig. 113, p. 220; its apex being represented by _a f_ of the same figure. The base of Borelli’s cone, it will be observed, is inclined forwards in the direction of the head of the bird. Now this is just the opposite of what ought to be. Instead of the two wings forming one cone, the base of which is directed _forwards_, each wing of itself forms two cones, the bases of which are directed _backwards_ and outwards, as shown at fig. 116.

In this figure the action of the wing is compared to the sculling of an oar, to which it bears a considerable resemblance.[116] The one cone, viz., that with its base directed outwards, is represented at _x b d_. This cone corresponds to the area mapped out by the tip of the wing in the process of _elevating_. The second cone, viz., that with its base directed backwards, is represented at _q p n_. This cone corresponds to the area mapped out by the posterior margin of the wing in the process of _propelling_. The two cones are produced in virtue of the wing rotating on its root and along its anterior margin as it ascends and descends (fig. 80, p. 149; fig. 83, p. 158). The present figure (116) shows the double twisting action of the wing, the tip describing the figure-of-8 indicated at _b e f g h d i j k l_; the posterior margin describing the figure-of-8 indicated at _p r n_. It is in this manner the cross pulsation or wave referred to at p. 148 is produced. To represent the action of the wing the sculling oar (_a b_, _x s_, _c d_) must have a small scull (_m n_, _q r_, _o p_) working at right angles to it. This follows because the wing has to elevate as well as propel; the oar of a boat when employed as a scull only propelling. In order to elevate more effectually, the oars formed by the wings are made to oscillate on a level with and under the volant animal rather than above it; the posterior margins of the wings being made to oscillate on a level with and below the anterior margins (pp. 150, 151).

[116] In sculling strictly speaking, it is the upper surface of the
oar which is most effective; whereas in flying it is the under.

Borelli, and all who have written since his time, are unanimous in affirming that the horizontal transference of the body of the bird is due to the perpendicular vibration of the wings, and to the yielding of the posterior or flexible margins of the wings in an upward direction as the wings descend. I am, however, as already stated, disposed to attribute the transference, _1st_, to the fact that the wings, both when elevated and depressed, _leap forwards in curves_, those curves uniting to form a continuous waved track; _2d_, to the tendency which the body of the bird has to swing forwards, in a more or less horizontal direction, when once set in motion; _3d_, to the construction of the wings (they are elastic helices or screws, which twist and untwist when they are made to vibrate, and tend to bear upwards and onwards any weight suspended from them); _4th_, to the reaction of the air on the under surfaces of the wings, which always act as kites; _5th_, to the ever-varying power with which the wings are urged, this being greatest at the beginning of the down stroke, and least at the end of the up one; _6th_, to the contraction of the voluntary muscles and elastic ligaments; _7th_, to the effect produced by the various inclined surfaces formed by the wings during their oscillations; _8th_, to the weight of the bird--weight itself, when acting upon inclined planes (wings), becoming a propelling power, and so contributing to horizontal motion. This is proved by the fact that if a sea bird launches itself from a cliff with expanded motionless wings, it sails along for an incredible distance before it reaches the water (fig. 103, p. 186).

The authors who have adopted Borelli’s plan of artificial wing, and who have indorsed his mechanical views of the action of the wing most fully, are Chabrier, Straus-Durckheim, Girard, and Marey. Borelli’s artificial wing, as already explained (p. 220, fig. 113), consists of _a rigid rod_ (_e_, _r_) in front, and _a flexible sail_ (_a_, _o_) composed of feathers, behind. It acts upon the air, and the air acts upon it, as occasion demands.

_Chabrier’s Views._--Chabrier states that the wing has only one period of activity--that, in fact, if the wing be suddenly lowered by the depressor muscles, it is elevated solely by the reaction of the air. There is one unanswerable objection to this theory--the bats and birds, and some, if not all the insects, have distinct elevator muscles. The presence of well-developed elevator muscles implies an elevating function, and, besides, we know that the insect, bat, and bird can elevate their wings when they are not flying, and when, consequently, no reaction of the air is induced.

_Straus-Durckheim’s Views._--Durckheim believes the insect abstracts from the air by means of _the inclined plane_ a component force (composant) which it employs _to support_ and _direct_ itself. In his Theology of Nature he describes a schematic wing as follows:--It consists of a _rigid ribbing_ in front, and _a flexible sail_ behind. A membrane so constructed will, according to him, be fit for flight. It will suffice if such a sail _elevates_ and _lowers_ itself successively. It will, of its own accord, dispose itself as an inclined plane, _and receiving obliquely the reaction of the air_, it transfers _into tractile force_ a part of the _vertical impulsion it has received_. These two parts of the wing are, moreover, equally indispensable to each other. If we compare the schematic wing of Durckheim with that of Borelli they will be found to be identical, both as regards their construction and the manner of their application.

Professor Marey, so late as 1869, repeats the arguments and views of Borelli and Durckheim, with very trifling alterations. Marey describes two artificial wings, the one composed of a _rigid rod_ and _sail_--the rod representing _the stiff anterior margin_ of the wing; the sail, which is made of paper bordered with card-board, _the flexible posterior portion_. The other wing consists of a _rigid nervure_ in front and behind of thin parchment which supports _fine rods of steel_. He states, that if the wing only elevates and depresses itself, “_the resistance of the air_ is sufficient to produce all the other movements. In effect the wing of an insect has not the power of equal resistance in every part. On the anterior margin the extended nervures make it _rigid_, while behind it is fine and _flexible_. During the vigorous depression of the wing the nervure has the power of _remaining rigid_, whereas the _flexible portion_, being pushed in _an upward direction_ on account of the resistance it experiences from the air, _assumes an oblique position_, which causes the upper surface of the wing _to look forwards_.” ... “At first the plane of the wing is parallel with the body of the animal. It lowers itself--the _front part_ of the wing _strongly resists_, the sail which follows it _being flexible yields_. Carried by the ribbing (the anterior margin of the wing) which lowers itself, the sail or posterior margin of the wing being raised meanwhile by the air, which sets it straight again, the sail will take an intermediate position, and _incline itself about 45° plus_ or _minus_ according to circumstances. The wing continues its movements of depression inclined to the horizon, but the impulse of the air which continues its effect, and naturally acts upon the surface which it strikes, has the power of resolving itself into two forces, _a vertical_ and _a horizontal force_, the first suffices _to raise_ the animal, the second to _move it along_.”[117] The reverse of this, Marey states, takes place during the elevation of the wing--the resistance of the air from above causing the upper surface of the wing _to look backwards_. The fallaciousness of this reasoning has been already pointed out, and need not be again referred to. It is not a little curious that Borelli’s artificial wing should have been reproduced in its integrity at a distance of nearly two centuries.

[117] Compare Marey’s description with that of Borelli, a translation
of which I subjoin. “Let a bird be suspended in the air with its
wings expanded, and first let the under surfaces (of the wings) be
struck by the air ascending perpendicularly to the horizon with such
a force that the bird gliding down is prevented from falling: I
say that it (the bird) will be impelled with _a horizontal forward
motion_, because the two osseous rods of the wings are able, owing
to the strength of the muscles, and because of their hardness, _to
resist the force of the air_, and therefore to retain the same form
(literally extent, expansion), but the total breadth of the fan
of each wing _yields to the impulse of the air_ when the flexible
feathers are permitted to rotate around the _manubria_ or osseous
axes, and hence it is necessary that the extremities of the wings
approximate each other: wherefore the wings acquire the form of a
wedge whose point is directed towards the tail of the bird, but whose
surfaces are compressed on either side by the ascending air in such
a manner that it is driven out in the direction of its base. Since,
however, the wedge formed by the wings cannot move forward unless it
carry the body of the bird along with it, it is evident that it (the
wedge) gives place to the air impelling it, and therefore the bird
_flies forward in a horizontal direction_. But now let the substratum
of still air be struck by the fans (feathers) of the wings with a
motion perpendicular to the horizon. Since the fans and sails of
the wings acquire the form of a wedge, the point of which is turned
towards the tail (of the bird), and since they suffer the same force
and compression from the air, whether the vibrating wings strike the
undisturbed air beneath, or whether, on the other hand, the expanded
wings (the osseous axes remaining rigid) receive the percussion of
the ascending air; in either case the _flexible feathers yield to the
impulse_, and hence approximate each other, and thus the bird moves
in _a forward direction_.”--De Motu Animalium, pars prima, prop. 196,
1685.

_The Author’s Views:--his Method of constructing and applying Artificial Wings as contra-distinguished from that of Borelli, Chabrier, Durckheim, Marey, etc._--The artificial wings which I have been in the habit of making for several years differ from those recommended by Borelli, Durckheim, and Marey in four essential points:--

_1st_, The mode of construction.

_2d_, The manner in which they are applied to the air.

_3d_, The nature of the powder employed.

_4th_, The necessity for adapting certain elastic substances to the root of the wing if in one piece, and to the root and the body of the wing if in several pieces.

And, first, as to the manner of construction.

Borelli, Durckheim, and Marey maintain that _the anterior margin of the wing_ should be _rigid_; I, on the other hand, believe that no part of the wing whatever should be rigid, _not even the anterior margin_, and that the pinion should be flexible and elastic throughout.

That the anterior margin of the wing should not be composed of a rigid rod may, I think, be demonstrated in a variety of ways. If a rigid rod be made to vibrate by the hand the vibration is not smooth and continuous; on the contrary, it is irregular and jerky, and characterized by two halts or pauses (dead points), the one occurring at the end of the _up stroke_, the other at the end of the _down stroke_. This mechanical impediment is followed by serious consequences as far as power and speed are concerned--the slowing of the wing at the end of the down and up strokes involving a great expenditure of power and a disastrous waste of time. The wing, to be effective as an elevating and propelling organ, should have no dead points, and should be characterized by a rapid winnowing or fanning motion. It should reverse and reciprocate with the utmost steadiness and smoothness--in fact, the motions should appear as continuous as those of a fly-wheel in rapid motion: they are so in the insect (figs. 64, 65, and 66, p. 139).

To obviate the difficulty in question, it is necessary, in my opinion, to employ _a tapering elastic rod_ or _series of rods_ bound together for the anterior margin of the wing.

If a longitudinal section of bamboo cane, ten feet in length, and one inch in breadth (fig. 117), be taken by the extremity and made to vibrate, it will be found that a wavy serpentine motion is produced, the waves being greatest when the vibration is slowest (fig. 118), and least when it is most rapid (fig. 119). It will further be found that at the extremity of the cane where the impulse is communicated there is _a steady reciprocating movement devoid of dead points_. The continuous movement in question is no doubt due to the fact that the different portions of the cane reverse at different periods--the undulations induced being to an interrupted or vibratory movement very much what the continuous play of a fly-wheel is to a rotatory motion.

_The Wave Wing of the Author._--If a similar cane has added to it, tapering rods of whalebone, which radiate in an outward direction to the extent of a foot or so, and the whalebones be covered by a thin sheet of india-rubber, an artificial wing, resembling the natural one in all its essential points, is at once produced (fig. 120). I propose to designate this wing, from the peculiarities of its movements, _the wave wing_ (fig. 121). If the wing referred to (fig. 121) be made to vibrate at its root, a series of longitudinal (_c d e_) and transverse (_f g h_) waves are at once produced; the one series running in the direction of _the length of the wing_, the other in the direction of _its breadth_ (_vide_ p. 148). This wing further _twists_ and _untwists_, figure-of-8 fashion, during the up and down strokes, as shown at fig. 122, p. 239 (compare with figs. 82 and 83, p. 158; fig. 86, p. 161; and fig. 103, p. 186). There is, moreover, a continuous play of the wing; the down stroke gliding into the up one, and _vice versâ_, which clearly shows that the down and up strokes are parts of one whole, and that neither is perfect without the other.

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
(_x x_), and appears as if it were in two places at the same time,
viz., _c_ and _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 more 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 at _j_, 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. _a b_ anterior margin of wing, _c
d_ 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 _c d e_, and the transverse waves by
the arrows _f g h_. A wing constructed on this principle gives a
continuous elevating and propelling power. It develops 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._]

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 humming-bird (_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.

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 neuræ or ribs are
affixed. _c_, _d_, Posterior 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. _r_,
_r_, Piston, with cross heads (_w_, _w_) and piston head (_s_).
_o_, _o_, 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 (_c d_) 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 (_g h i_ 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.