Part 22

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.