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.
[Illustration: FIG. 114.]
[Illustration: FIG. 115.]
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.
[Illustration: 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.
[Illustration: FIG. 117.