direction from behind forwards, and from before backwards; but it
likewise acts as a screw in a nearly vertical direction. If the wing of
the larger domestic fly be viewed during its vibrations from above,
it will be found that the blur or impression produced on the eye by
its action is more or less concave (fig. 66, p. 139). This is due to
the fact that the wing is spiral in its nature, and because during its
action it twists upon itself in such a manner as to describe a double
curve,--the one curve being directed upwards, the other downwards. The
double curve referred to is particularly evident in the flight of birds
from the greater size of their wings. The wing, both when at rest and
in motion, may not inaptly be compared to the blade of an ordinary
screw propeller as employed in navigation. Thus the general outline
of the wing corresponds closely with the outline of the blade of the
propeller, and the track described by the wing in space is twisted
upon itself propeller fashion. The great velocity with which the wing
is driven converts the impression or blur into what is equivalent to a
solid for the time being, in the same way that the spokes of a wheel
in violent motion, as is well understood, completely occupy the space
contained within the rim or circumference of the wheel (figs. 64, 65,
and 66, p. 139).
The figure-of-8 action of the wing explains how an insect, bat, or
bird, may fix itself in the air, the backward and forward reciprocating
action of the pinion affording support, but no propulsion. In these
instances, the backward and forward strokes are made to counterbalance
each other.
_The Wing, when advancing with the Body, describes a Looped and Waved
Track._--Although the figure-of-8 represents with considerable fidelity
the twisting of the wing upon its long axis during extension and
flexion, and during the down and up strokes when the volant animal
is playing its wings before an object, or still better, when it is
artificially fixed, it is otherwise when it is free and progressing
rapidly. In this case the wing, in virtue of its being carried forward
by the body in motion, describes first a looped and then a waved
track. This looped and waved track made by the wing of the insect is
represented at figs. 71 and 72, and that made by the wing of the bat
and bird at fig. 73, p. 144.
[Illustration: FIG. 71.]
[Illustration: FIG. 72.]
[Illustration: FIG. 73.]
The loops made by the wing of the insect, owing to the more oblique
stroke, are more horizontal than those made by the wing of the bat
and bird. The principle is, however, in both cases the same, the loops
ultimately terminating in a waved track. The impulse is communicated
to the insect wing at the heavy parts of the loops _a b c d e f g h i
j k l m n_ of fig. 71; the waved tracks being indicated at _p q r s t_
of the same figure. The recoil obtained from the air is represented
at corresponding letters of fig. 72, the body of the insect being
carried along the curve indicated by the dotted line. The impulse is
communicated to the wing of the bat and bird at the heavy part of the
loops _a b c d e f g h i j k l m n o_ of fig. 73, the waved track being
indicated at _p s t u v w_ of this figure. When the horizontal speed
attained is high, the wing is successively and rapidly brought into
contact with innumerable columns of undisturbed air. It, consequently,
is a matter of indifference whether the wing is carried at a high speed
against undisturbed air, or whether it operates upon air travelling
at a high speed (as, _e.g._ the artificial currents produced by the
rapidly reciprocating action of the wing). The result is the same
in both cases, inasmuch as a certain quantity of air is worked up
under the wing, and the necessary degree of support and progression
extracted from it. It is, therefore, quite correct to state, that as
the horizontal speed of the body increases, the reciprocating action
of the wing decreases; and _vice versâ_. In fact the reciprocating and
non-reciprocating action of the wing in such cases is purely a matter
of speed. If the travel of the wing is greater than the horizontal
travel of the body, then the figure-of-8 and the reciprocating power
of the wing will be more or less perfectly developed, according to
circumstances. If, however, the horizontal travel of the body is
greater than that of the wing, then it follows that no figure-of-8
will be described by the wing; that the wing will not reciprocate to
any marked extent; and that the organ will describe a waved track,
the curves of which will become less and less abrupt, _i.e._ longer
and longer in proportion to the speed attained. The more vertical
direction of the loops formed by the wing of the bat and bird will
readily be understood by referring to figs. 74 and 75 (p. 145), which
represent the wing of the bird making the down and up strokes, and in
the act of being extended and flexed. (Compare with figs. 64, 65, and
66, p. 139; and figs. 67, 68, 69, and 70, p. 141.)
[Illustration: FIG. 74. FIG. 75.
FIGS. 74 and 75 show the more or less perpendicular direction of the
stroke of the wing in the flight of the bird (gull)--how the wing
is gradually extended as it is elevated (_e f g_ of fig. 74)--how
it descends as a long lever until it assumes the position indicated
by _h_ of fig. 75--how it is flexed towards the termination of the
down stroke, as shown at _h i j_ of fig. 75, to convert it into a
short lever (_a b_), and prepare it for making the up stroke. The
difference in the length of the wing during flexion and extension is
indicated by the short and long levers _a b_ and _c d_ of fig. 75.
The sudden conversion of the wing from a long into a short lever at
the end of the down stroke is of great importance, as it robs the
wing of its momentum, and prepares it for reversing its movements.
Compare with figs. 82 and 83, p. 158.--_Original._]
The down and up strokes are compound movements,--the termination of the
down stroke embracing the beginning of the up stroke; the termination
of the up stroke including the beginning of the down stroke. This
is necessary in order that the down and up strokes may glide into
each other in such a manner as to prevent jerking and unnecessary
retardation.
_The Margins of the Wing thrown into opposite Curves during Extension
and Flexion._--The anterior or thick margin of the wing, and the
posterior or thin one, form different curves, similar in all respects
to those made by the body of the fish in swimming (see fig. 32,
p. 68). These curves may, for the sake of clearness, be divided into
axillary and distal curves, the former occurring towards the root
of the wing, the latter towards its extremity. The curves (axillary
and distal) found on the anterior margin of the wing are always the
converse of those met with on the posterior margin, _i.e._ if the
convexity of the anterior axillary curve be directed downwards, that
of the posterior axillary curve is directed upwards, and so of the
anterior and posterior distal curves. The two curves (axillary and
distal), occurring on the anterior margin of the wing, are likewise
antagonistic, the convexity of the axillary curve being always directed
downwards, when the convexity of the distal one is directed upwards,
and _vice versâ_. The same holds true of the axillary and distal curves
occurring on the posterior margin of the wing. The anterior axillary
and distal curves completely reverse themselves during the acts of
extension and flexion, and so of the posterior axillary and distal
curves (figs. 76, 77, and 78). This antagonism in the axillary and
distal curves found on the anterior and posterior margins of the wing
is referable in the bat and bird to changes induced in the bones of the
wing in the acts of flexion and extension. In the insect it is due to
a twisting which occurs at the root of the wing and to the reaction of
the air.
[Illustration:
FIG. 76.--Curves seen on the anterior (_d e f_) and posterior (c a b)
margin in the wing of the bird in flexion.--_Original._]
[Illustration:
FIG. 77.--Curves seen on the anterior margin (_d e f_) of the wing in
semi-extension. In this case the curves on the posterior margin (_b
c_) are obliterated.--_Original._]
[Illustration:
FIG. 78.--Curves seen on the anterior (_d e f_) and posterior (_c a
b_) margin of the wing in extension. The curves of this fig. are the
converse of those seen at fig. 76. Compare these figs. with fig. 79
and fig. 32, p. 68.--_Original._]
_The Tip of the Bat and Bird’s Wing describes an Ellipse._--The
movements of the wrist are always the converse of those occurring at
the elbow-joint. Thus in the bird, during extension, the elbow and
bones of the forearm are elevated, and describe one side of an ellipse,
while the wrist and bones of the hand are depressed, and describe the
side of another and opposite ellipse. These movements are reversed
during flexion, the elbow being depressed and carried backwards, while
the wrist is elevated and carried forwards (fig. 79).
[Illustration:
FIG. 79.--(_a b_) Line along which the wing travels during extension
and flexion. The body of the fish in swimming describes similar
curves to those described by the wing in flying.--(_Vide_ fig. 32,
p. 68.)]
_The Wing capable of Change of Form in all its Parts._--From this
description it follows that when the different portions of the anterior
margin are elevated, corresponding portions of the posterior margin
are depressed; the different parts of the wing moving in opposite
directions, and playing, as it were, at cross purposes for a common
good; the object being to rotate or screw the wing down upon the wind
at a gradually increasing angle during extension, and to rotate it
in an opposite direction and withdraw it at a gradually decreasing
angle during flexion. It also happens that the axillary and distal
curves co-ordinate each other and bite alternately, the distal curve
posteriorly seizing the air in extreme extension with its concave
surface (while the axillary curve relieves itself by presenting its
convex surface); the axillary curve, on the other hand, biting during
flexion with its concave surface (while the distal one relieves itself
by presenting its convex one). The wing may therefore be regarded as
exercising a fourfold function, the pinion in the bat and bird being
made to move from within outwards, and from above downwards in the down
stroke, during extension; and from without inwards, and from below
upwards, in the up stroke, during flexion.
_The Wing during its Vibration produces a Cross Pulsation._--The
oscillation of the wing on two separate axes--the one running
parallel with the body of the bird, the other at right angles to it
(fig. 80, _a b_, _c d_)--is well worthy of attention, as showing that
the wing attacks the air, on which it operates in every direction,
and at almost the same moment, viz. from within outwards, and from
above downwards, during the down stroke; and from without inwards,
and from below upwards, during the up stroke. As a corollary to the
foregoing, the wing may be said to agitate the air in two principal
directions, viz. from within outwards and downwards, or the converse;
and from behind forwards, or the converse; the agitation in question
producing two powerful pulsations, a vertical and a horizontal. The
wing when it ascends and descends produces artificial currents which
increase its elevating and propelling power. The power of the wing is
further augmented by similar currents developed during its extension
and flexion. The movement of one part of the wing contributes to
the movement of every other part in continuous and uninterrupted
succession. As the curves of the wing glide into each other when the
wing is in motion, so the one pulsation merges into the other by a
series of intermediate and lesser pulsations.
The vertical and horizontal pulsations occasioned by the wing in action
may be fitly represented by wave-tracks running at right angles to
each other, the vertical wave-track being the more distinct.
_Compound Rotation of the Wing._--To work the tip and posterior
margin of the wing independently and yet simultaneously, two axes are
necessary, one axis (the short axis) corresponding to the root of the
wing and running across it; the second (the long axis) corresponding
to the anterior margin of the wing, and running in the direction of
its length. The long and short axes render the movements of the wing
eccentric in character. In the wing of the bird the movements of the
primary or rowing feathers are also eccentric, the shaft of each
feather being placed nearer the anterior than the posterior margin; an
arrangement which enables the feathers to open up and separate during
flexion and the up stroke, and approximate and close during extension
and the down one.
[Illustration: FIG. 80.]
These points are illustrated at fig. 80, where _a b_ represents the
short axis (root of wing) with a radius _e f_; _c d_ representing the
long axis (anterior margin of wing) with a radius _g p_.
Fig. 80 also shows that, in the wing of the bird, the individual,
primary, secondary, and tertiary feathers have each what is equivalent
to a long and a short axis. Thus the primary, secondary, and tertiary
feathers marked _h_, _i_, _j_, _k_, _l_ are capable of rotating on
their long axes (_r s_), and upon their short axes (_m n_). The
feathers rotate upon their long axes in a direction from below upwards
during the down stroke, to make the wing impervious to air; and from
above downwards during the up stroke, to enable the air to pass
through it. The primary, secondary, and tertiary feathers have thus a
distinctly valvular action.[76] The feathers rotate upon their short
axes (_m n_) during the descent and ascent of the wing, the tip of the
feathers rising slightly during the descent of the pinion, and falling
during its ascent. The same movement virtually takes place in the
posterior margin of the wing of the insect and bat.
[76] The degree of valvular action varies according to circumstances.
_The Wing vibrates unequally with reference to a given Line._--The
wing, during its vibration, descends further below the body than it
rises above it. This is necessary for _elevating purposes_. In like
manner the posterior margin of the wing (whatever the position of the
organ) descends further below the anterior margin than it ascends
above it. This is requisite for _elevating and propelling purposes_;
the under surface of the wing being always presented at a certain
upward angle to the horizon, and acting as a true kite (figs. 82 and
83, p. 158. Compare with fig. 116, p. 231). If the wing oscillated
equally above and beneath the body, and if the posterior margin of the
wing vibrated equally above and below the line formed by the anterior
margin, much of its elevating and propelling power would be sacrificed.
The tail of the fish oscillates on either side of a given line, but it
is otherwise with the wing of a flying animal. The fish is of nearly
the same specific gravity as the water, so that the tail may be said
only to propel. The flying animal, on the other hand, is very much
heavier than the air, so that the wing requires both to propel and
_elevate_. The wing, to be effective as an _elevating organ_, must
consequently be vibrated rather below than above the centre of gravity;
at all events, the intensity of the vibration should occur rather
below that point. In making this statement, it is necessary to bear in
mind that the centre of gravity is _ever varying_, the body rising and
falling in a series of curves as the wings ascend and descend.
To _elevate_ and _propel_, the posterior margin of the wing must
rotate round the anterior one; the posterior margin being, as a rule,
always on a lower level than the anterior one. By the oblique and
more vigorous play of the wings _under_ rather than _above_ the body,
each wing expends its entire energy in pushing the body _upwards_
and _forwards_. It is necessary that the wings descend further than
they ascend; that the wings be _convex_ on their upper surfaces, and
_concave_ on their under ones; and that the concave or biting surfaces
be brought more violently in contact with the air during the down
stroke than the convex ones during the up stroke. The greater range of
the wing below than above the body, and of the posterior margin below
than above a given line, may be readily made out by watching the flight
of the larger birds. It is well seen in the upward flight of the lark.
In the hovering of the kestrel over its quarry, and the hovering of
the gull over garbage which it is about to pick up, the wings play
above and on a level with the body rather than below it; but these
are exceptional movements for special purposes, and as they are only
continued for a few seconds at a time, do not affect the accuracy of
the general statement.
_Points wherein the Screws formed by the Wings differ from those
employed in navigation._--1. In the blade of the ordinary screw the
integral parts are rigid and unyielding, whereas, in the blade of
the screw formed by the wing, they are mobile and plastic (figs. 93,
95, 97, pp. 174, 175, 176). This is a curious and interesting point,
the more especially as it does not seem to be either appreciated or
understood. The mobility and plasticity of the wing is necessary,
because of the tenuity of the air, and because the pinion is an
_elevating_ and _sustaining organ_, as well as a _propelling_ one.
2. The vanes of the ordinary two-bladed screw are short, and have a
comparatively limited range, the range corresponding to their area
of revolution. The wings, on the other hand, are long, and have a
comparatively wide range; and during their elevation and depression
rush through an extensive space, the slightest movement at the root or
short axis of the wing being followed by a gigantic up or down stroke
at the other (fig. 56, p. 120; figs. 64, 65, and 66, p. 139; figs. 82
and 83, p. 158). As a consequence, the wings as a rule act upon
successive and undisturbed strata of air. The advantage gained by this
arrangement in a thin medium like the air, where the quantity of air to
be compressed is necessarily great, is simply incalculable.
3. In the ordinary screw the blades follow each other in rapid
succession, so that they travel over nearly the same space, and operate
upon nearly the same particles (whether water or air), in nearly
the same interval of time. The limited range at their disposal is
consequently not utilized, the action of the two blades being confined,
as it were, to the same plane, and the blades being made to precede
or follow each other in such a manner as necessitates the work being
virtually performed only by one of them. This is particularly the case
when the motion of the screw is rapid and the mass propelled is in the
act of being set in motion, _i.e._ before it has acquired momentum.
In this instance a large percentage of the moving or driving power is
inevitably consumed in slip, from the fact of the blades of the screw
operating on nearly the same particles of matter. The wings, on the
other hand, do not follow each other, but have a distinct reciprocating
motion, _i.e._ they dart first in one direction, and then in another
and opposite direction, in such a manner that they make during the
one stroke the current on which they rise and progress the next.
The blades formed by the wings and the blur or impression produced
on the eye by the blades when made to vibrate rapidly are widely
separated,--the one blade and its blur being situated on the right
side of the body and corresponding to the right wing, the other on
the left and corresponding to the left wing. The right wing traverses
and completely occupies the right half of a circle, and compresses
all the air contained within this space; the left wing occupying and
working up all the air in the left and remaining half. The range or
sweep of the two wings, when urged to their extreme limits, corresponds
as nearly as may be to one entire circle[77] (fig. 56, p. 120). By
separating the blades of the screw, and causing them to reciprocate, a
double result is produced, since the blades always act upon independent
columns of air, and in no instance overlap or double upon each other.
The advantages possessed by this arrangement are particularly evident
when the motion is rapid. If the screw employed in navigation be
driven beyond a certain speed, it cuts out the water contained within
its blades; the blades and the water revolving as a solid mass. Under
these circumstances, the propelling power of the screw is diminished
rather than increased. It is quite otherwise with the screws formed by
the wings; these, because of their reciprocating movements, becoming
more and more effective in proportion as the speed is increased. As
there seems to be no limit to the velocity with which the wings may
be driven, and as increased velocity necessarily results in increased
elevating, propelling, and sustaining power, we have here a striking
example of the manner in which nature triumphs over art even in her
most ingenious, skilful, and successful creations.
[77] Of this circle, the thorax may be regarded as forming the
centre, the abdomen, which is always heavier than the head, tilting
the body slightly in an upward direction. This tilting of the trunk
favours flight by causing the body to act after the manner of a kite.
4. The vanes or blades of the screw, as commonly constructed, are
fixed at a given angle, and consequently always strike at the same
degree of obliquity. The speed, moreover, with which the blades are
driven, is, as nearly as may be, uniform. In this arrangement power
is lost, the two vanes striking after each other in the same manner,
in the same direction, and almost at precisely the same moment,--no
provision being made for increasing the angle, and the propelling
power, at one stage of the stroke, and reducing it at another, to
diminish the amount of slip incidental to the arrangement. The wings,
on the other hand, are driven at a varying speed, and made to attack
the air at a great variety of angles; the angles which the pinions
make with the horizon being gradually increased by the wings being
made to rotate on their long axes during the down stroke, to increase
the _elevating_ and _propelling_ power, and gradually decreased during
the up stroke, to reduce the resistance occasioned by the wings during
their ascent. The latter movement increases the _sustaining_ area by
placing the wings in a more horizontal position. It follows from this
arrangement that every particle of air within the wide range of the
wings is separately influenced by them, both during their ascent and
descent,--the elevating, propelling, and sustaining power being by this
means increased to a maximum, while the slip or waftage is reduced to
a minimum. These results are further secured by the undulatory or
waved track described by the wing during the down and up strokes. It
is a somewhat remarkable circumstance that the wing, when not actually
engaged as a propeller and elevator, acts as a _sustainer_ after the
manner of a parachute. This it can readily do, alike from its form and
the mode of its application, the double curve or spiral into which it
is thrown in action enabling it to lay hold of the air with avidity,
in whatever direction it is urged. I say “in whatever direction,”
because, even when it is being recovered or drawn off the wind during
the back stroke, it is climbing a gradient which arches above the
body to be elevated, and so prevents it from falling. It is difficult
to conceive a more admirable, simple, or effective arrangement, or
one which would more thoroughly economize power. Indeed, a study of
the spiral configuration of the wing, and its spiral, flail-like,
lashing movements, involves some of the most profound problems in
mathematics,--the curves formed by the pinion as a pinion anatomically,
and by the pinion in action, or physiologically, being exceedingly
elegant and infinitely varied; these running into each other, and
merging and blending, to consummate the triple function of _elevating_,
_propelling_, and _sustaining_.
Other differences might be pointed out; but the foregoing embrace the
more fundamental and striking. Enough, moreover, has probably been said
to show that it is to wing-structures and wing-movements the aëronaut
must direct his attention, if he would learn “the way of an eagle in
the air,” and if he would rise upon the whirlwind in accordance with
natural laws.