fin and tail of the fish, whale, porpoise, etc.; and the wing of the
penguin (a bird which is incapable of flight, and can only swim and
dive) with the wing of the insect, bat, and bird, I have been able
to show that a close analogy exists between the flippers, fins, and
tails of sea mammals and fishes on the one hand, and the wings of
insects, bats, and birds on the other; in fact, that theoretically and
practically these organs, one and all, form flexible helices or screws,
which, in virtue of their rapid reciprocating movements, operate upon
the water and air by a wedge-action after the manner of twisted or
double inclined planes. The twisted inclined planes act upon the air
and water by means of curved surfaces, the curved surfaces reversing,
reciprocating, and engendering a wave pressure, which can be continued
indefinitely at the will of the animal. The wave pressure emanates in
the one instance mainly from the tail of the fish, whale, porpoise,
etc., and in the other from the wing of the insect, bat, or bird--_the
reciprocating and opposite curves_ into which the tail and wing are
thrown in swimming and flying constituting _the mobile helices, or
screws_, which, during their action, produce the precise kind and
degree of pressure adapted to fluid media, and to which they respond
with the greatest readiness.
In order to prove that sea mammals and fishes swim, and insects, bats,
and birds fly, by the aid of curved figure-of-8 surfaces, which exert
an intermittent wave pressure, I constructed artificial fish-tails,
fins, flippers, and wings, which curve and taper in every direction,
and which are flexible and elastic, particularly towards the tips
and posterior margins. These artificial fish-tails, fins, flippers,
and wings are slightly twisted upon themselves, and when applied to
the water and air by a sculling or figure-of-8 motion, curiously
enough reproduce the curved surfaces and movements peculiar to real
fish-tails, fins, flippers, and wings, in swimming, and flying.
Propellers formed on the fish-tail and wing model are, I find, the
most effective that can be devised, whether for navigating the water
or the air. To operate efficiently on fluid, _i.e._ yielding media,
the propeller itself must yield. Of this I am fully satisfied from
observation and experiment. The propellers at present employed in
navigation are, in my opinion, faulty both in principle and application.
The observations and experiments recorded in the present volume date
from 1864. In 1867 I lectured on the subject of animal mechanics at
the Royal Institution of Great Britain:[7] in June of the same year
(1867) I read a memoir “On the Mechanism of Flight” to the Linnean
Society of London;[8] and in August of 1870 I communicated a memoir “On
the Physiology of Wings” to the Royal Society of Edinburgh.[9] These
memoirs extend to 200 pages quarto, and are illustrated by 190 original
drawings. The conclusions at which I arrived, after a careful study of
the movements of walking, swimming, and flying, are briefly set forth
in a letter addressed to the French Academy of Sciences in March 1870.
This the Academy did me the honour of publishing in April of that year
(1870) in the Comptes Rendus, p. 875. In it I claim to have been the
first to describe and illustrate the following points, viz.:--
[7] “On the various modes of Flight in relation to
Aëronautics.”--Proceedings of the Royal Institution of Great Britain,
March 22, 1867.
[8] “On the Mechanical Appliances by which Flight is attained in the
Animal Kingdom.”--Transactions of the Linnean Society, vol. xxvi.
[9] “On the Physiology of Wings.”--Transactions of the Royal Society
of Edinburgh, vol. xxvi.
That quadrupeds walk, and fishes swim, and insects, bats, and birds fly
by figure-of-8 movements.
That the flipper of the sea bear, the swimming wing of the penguin, and
the wing of the insect, bat, and bird, are screws _structurally_, and
resemble the blade of an ordinary screw-propeller.
That those organs are screws _functionally_, from their twisting and
untwisting, and from their rotating in the direction of their length,
when they are made to oscillate.
That they have a reciprocating action, and reverse their planes more or
less completely at every stroke.
That the wing describes _a figure-of-8 track_ in space when the flying
animal is artificially fixed.
That the wing, when the flying animal is progressing at a high speed
in a horizontal direction, describes _a looped_ and then _a waved
track_, from the fact that the figure of 8 is gradually opened out or
unravelled as the animal advances.
That the wing acts after the manner of a kite, both during the down and
up strokes.
I was induced to address the above to the French Academy from finding
that, nearly two years after I had published my views on the figure
of 8, looped and wave movements made by the wing, etc., Professor
E. J. Marey (College of France, Paris) published a course of lectures,
in which the peculiar figure-of-8 movements, first described and
figured by me, were put forth as a new discovery. The accuracy of this
statement will be abundantly evident when I mention that my first
lecture, “On the various modes of Flight in relation to Aëronautics,”
was published in the Proceedings of the Royal Institution of Great
Britain on the 22d of March 1867, and translated into French (Revue
des cours scientifiques de la France et de l’Étranger) on the 21st
of September 1867; whereas Professor Marey’s first lecture, “On the
Movements of the Wing in the Insect” (Revue des cours scientifiques de
la France et de l’Étranger), did not appear until the 13th of February
1869.
Professor Marey, in a letter addressed to the French Academy in reply
to mine, admits my claim to priority in the following terms:--
“J’ai constaté qu’effectivement M. Pettigrew a vu avant moi, et
représenté dans son Mémoire, la forme en 8 du parcours de l’aile de
l’insecte: que la méthode optique à laquelle j’avais recours est à peu
près identique à la sienne.... Je m’empresse de satisfaire à cette
demande légitime, et de laisser entièrement la priorité sur moi à M.
Pettigrew relativement à la question ainsi restreinte.”--(Comptes
Rendus, May 16, 1870, p. 1093).
The figure-of-8 theory of walking, swimming, and flying, as originally
propounded in the lectures, papers, and memoirs referred to, has been
confirmed not only by the researches and experiments of Professor
Marey, but also by those of M. Senecal, M. de Fastes, M. Ciotti, and
others. Its accuracy is no longer a matter of doubt. As the limits
of the present volume will not admit of my going into the several
arrangements by which locomotion is attained in the animal kingdom as
a whole, I will only describe those movements which illustrate in a
progressive manner the several kinds of progression on the land, and on
and in the water and air.
I propose first to analyse the natural movements of walking, swimming,
and flying, after which I hope to be able to show that certain of these
movements may be reproduced artificially. The locomotion of animals
depends upon mechanical adaptations found in all animals which change
locality. These adaptations are very various, but under whatever guise
they appear they are substantially those to which we resort when we
wish to move bodies artificially. Thus in animal mechanics we have
to consider the various orders of levers, the pulley, the centre of
gravity, specific gravity, the resistance of solids, semi-solids,
fluids, etc. As the laws which regulate the locomotion of animals are
essentially those which regulate the motion of bodies in general, it
will be necessary to consider briefly at this stage the properties of
matter when at rest and when moving. They are well stated by Mr. Bishop
in a series of propositions which I take the liberty of transcribing:--
“_Fundamental Axioms._--First, every body continues in a state of rest,
or of uniform motion in a right line, until a change is effected by
the agency of some mechanical force. Secondly, any change effected in
the quiescence or motion of a body is in the direction of the force
impressed, and is proportional to it in quantity. Thirdly, reaction
is always equal and contrary to action, or the mutual actions of two
bodies upon each other are always equal and in opposite directions.
“_Of uniform motion._--If a body moves constantly in the same manner,
or if it passes over equal spaces in equal periods of time, its motion
is uniform. The velocity of a body moving uniformly is measured by the
space through which it passes in a given time.
“The velocities generated or impressed on different masses by the same
force are reciprocally as the masses.
“_Motion uniformly varied._--When the motion of a body is uniformly
accelerated, the space it passes through during any time whatever is
proportional to the square of the time.
“In the leaping, jumping, or springing of animals in any direction
(except the vertical), the paths they describe in their transit from
one point to another in the plane of motion are parabolic curves.
“_The legs move by the force of gravity as a pendulum._--The Professor,
Weber, have ascertained, that when the legs of animals swing forward in
progressive motion, they obey the same laws as those which regulate the
periodic oscillations of the pendulum.
“_Resistance of fluids._--Animals moving in air and water experience
in those media a sensible resistance, which is greater or less in
proportion to the density and tenacity of the fluid, and the figure,
superficies, and velocity of the animal.
“An inquiry into the amount and nature of the resistance of air and
water to the progression of animals will also furnish the data for
estimating the proportional values of those fluids acting as fulcra to
their locomotive organs, whether they be fins, wings, or other forms of
lever.
“The motions of air and water, and their directions, exercise very
important influences over velocity resulting from muscular action.
“_Mechanical effects of fluids on animals immersed in them._--When a
body is immersed in any fluid whatever, it will lose as much of its
weight relatively as is equal to the weight of the fluid it displaces.
In order to ascertain whether an animal will sink or swim, or be
sustained without the aid of muscular force, or to estimate the amount
of force required that the animal may either sink or float in water, or
fly in the air, it will be necessary to have recourse to the specific
gravities both of the animal and of the fluid in which it is placed.
“The specific gravities or comparative weights of different substances
are the respective weights of equal volumes of those substances.
“_Centre of gravity._--The centre of gravity of any body is a
point about which, if acted upon only by the force of gravity, it
will balance itself in all positions; or, it is a point which, if
supported, the body will be supported, however it may be situated in
other respects; and hence the effects produced by or upon any body
are the same as if its whole mass were collected into its centre of
gravity.
“The attitudes and motions of every animal are regulated by the
positions of their centres of gravity, which, in a state of rest, and
not acted upon by extraneous forces, must lie in vertical lines which
pass through their basis of support.
“In most animals moving on solids, the centre is supported by variously
adapted organs; during the flight of birds and insects it is suspended;
but in fishes, which move in a fluid whose density is nearly equal
to their specific gravity, the centre is acted upon equally in all
directions.”[10]
[10] Cyc. of Anat. and Phy., Art. “Motion,” by John Bishop, Esq.
As the locomotion of the higher animals, to which my remarks more
particularly apply, is in all cases effected by levers which differ in
no respect from those employed in the arts, it may be useful to allude
to them in a passing way. This done, I will consider the bones and
joints of the skeleton which form the levers, and the muscles which
move them.
“_The Lever._--Levers are commonly divided into three kinds, according
to the relative positions of the prop or fulcrum, the power, and the
resistance or weight. The straight lever of each order is equally
balanced when the power multiplied by its distance from the fulcrum
equals the weight, multiplied by its distance, or P the power, and
W the weight, are in equilibrium when they are to each other in the
inverse ratio of the arms of the lever, to which they are attached. The
pressure on the fulcrum however varies.
[Illustration: FIG. 1.]
“In straight levers of the _first kind_, the fulcrum is between the
power and the resistance, as in fig. 1, where F is the fulcrum of the
lever AB; P is the power, and W the weight or resistance. We have
P : W :: BF : AF, hence P.AF = W.BF, and the pressure on the fulcrum is both
the power and resistance, or P + W.
“In the second order of levers (fig. 2), the resistance is between
the fulcrum and the power; and, as before, P : W :: BF : AF, but the
pressure of the fulcrum is equal to W - P, or the weight less the power.
[Illustration: FIG. 2.]
“In the third order of lever the power acts between the prop and the
resistance (fig. 3), where also P : W :: BF : AF, and the pressure on
the fulcrum is P - W, or the power less the weight.
[Illustration: FIG. 3.]
“In the preceding computations the weight of the lever itself is
neglected for the sake of simplicity, but it obviously forms a part of
the elements under consideration, especially with reference to the arms
and legs of animals.
“To include the weight of the lever we have the following equations:
P.AF + {AF}.1/2AF = W.BF + {BF}.1/2BF; in the first order, where
{AF} and {BF} represent the weights of these portions of the lever
respectively. Similarly, in the second order P.AF = W.BF + {AF}.(AF)/2,
and in the third order P.AF = W.BF + {BF}.(BF)/2.
“In this outline of the theory of the lever, the forces have been
considered as acting vertically, or parallel to the direction of the
force of gravity.
“_Passive Organs of Locomotion. Bones._--The solid framework or
skeleton of animals which supports and protects their more delicate
tissues, whether chemically composed of entomoline, carbonate, or
phosphate of lime; whether placed internally or externally; or whatever
may be its form or dimensions, presents levers and fulcra for the
action of the muscular system, in all animals furnished with earthy
solids for their support, and possessing locomotive power.”[11] The
levers and fulcra are well seen in the extremities of the deer, the
skeleton of which is selected for its extreme elegance.
[11] Bishop, _op. cit._
[Illustration:
FIG. 4. Skeleton of the Deer (after Pander and D’Alton). The bones
in the extremities of this the fleetest of quadrupeds are inclined
very obliquely towards each other, and towards the scapular and
iliac bones. This arrangement increases the leverage of the muscular
system and confers great rapidity on the moving parts. It augments
elasticity, diminishes shock, and indirectly begets continuity of
movement, _a._ Angle formed by the femur with the ilium, _b._ Angle
formed by the tibia and fibula with the femur, _c._ Angle formed by
the cannon bone with the tibia and fibula, _d._ Angle formed by the
phalanges with the cannon bone. _e._ Angle formed by the humerus
with the scapula. _f._ Angle formed by the radius and ulna with the
humerus.]
While the bones of animals form levers and fulcra for portions of the
muscular system, it must never be forgotten that the earth, water, or
air form fulcra for the travelling surfaces of animals as a whole.
Two sets of fulcra are therefore always to be considered, viz. those
represented by the bones, and those represented by the earth, water,
or air respectively. The former when acted upon by the muscles produce
motion in different parts of the animal (not necessarily progressive
motion); the latter when similarly influenced produce locomotion.
Locomotion is greatly favoured by the tendency which the body once
set in motion has to advance in a straight line. “The form, strength,
density, and elasticity of the skeleton varies in relation to the bulk
and locomotive power of the animal, and to the media in which it is
destined to move.
“The number of moveable articulations in a skeleton determines the
degree of its mobility within itself; and the kind and number of
the articulations of the locomotive organs determine the number and
disposition of the muscles acting upon them.
“The bones of vertebrated animals, especially those which are
entirely terrestrial, are much more elastic, hard, and calculated by
their chemical elements to bear the shocks and strains incident to
terrestrial progression, than those of the aquatic vertebrata; the
bones of the latter being more fibrous and spongy in their texture, the
skeleton is more soft and yielding.
“The bones of the higher orders of animals are constructed according
to the most approved mechanical principles. Thus they are convex
externally, concave within, and strengthened by ridges running across
their discs, as in the scapular and iliac bones; an arrangement which
affords large surfaces for the attachment of the powerful muscles of
locomotion. The bones of birds in many cases are not filled with marrow
but with air,--a circumstance which insures that they shall be very
strong and very light.
“In the thigh bones of most animals an angle is formed by the head
and neck of the bone with the axis of the body, which prevents the
weight of the superstructure coming vertically upon the shaft, converts
the bone into an elastic arch, and renders it capable of supporting
the weight of the body in standing, leaping, and in falling from
considerable altitudes.
“_Joints._--Where the limbs are designed to move to and fro simply
in one plane, the ginglymoid or hinge-joint is applied; and where
more extensive motions of the limbs are requisite, the enarthrodial,
or ball-and-socket joint, is introduced. These two kinds of joints
predominate in the locomotive organs of the animal kingdom.
“The enarthrodial joint has by far the most extensive power of
motion, and is therefore selected for uniting the limbs to the trunk.
It permits of the several motions of the limbs termed pronation,
supination, flexion, extension, abduction, adduction, and revolution
upon the axis of the limb or bone about a conical area, whose apex is
the axis of the head of the bone, and base circumscribed by the distal
extremity of the limb.”[12]
[12] Bishop, _op. cit._
The ginglymoid or hinge-joints are for the most part spiral in their
nature. They admit in certain cases of a limited degree of lateral
rocking. Much attention has been paid to the subject of joints
(particularly human ones) by the brothers Weber, Professor Meyer
of Zürich, and likewise by Langer, Henke, Meissner, and Goodsir.
Langer, Henke, and Meissner succeeded in demonstrating the “screw
configuration” of the articular surfaces of the elbow, ankle, and
calcaneo-astragaloid joints, and Goodsir showed that the articular
surface of the knee-joint consist of “a double conical screw
combination.” The last-named observer also expressed his belief “that
articular combinations with opposite windings on opposite sides of
the body, similar to those in the knee-joint, exist in the ankle and
tarsal, and in the elbow and carpal joints; and that the hip and
shoulder joints consist of single threaded couples, but also with
opposite windings on opposite sides of the body.” I have succeeded
in demonstrating a similar spiral configuration in the several bones
and joints of the wing of the bat and bird, and in the extremities of
most quadrupeds. The bones of animals, particularly the extremities,
are, as a rule, twisted levers, and act after the manner of screws.
This arrangement enables the higher animals to apply their travelling
surfaces to the media on which they are destined to operate at any
degree of obliquity so as to obtain a maximum of support or propulsion
with a minimum of slip. If the travelling surfaces of animals did not
form screws structurally and functionally, they could neither seize
nor let go the fulcra on which they act with the requisite rapidity to
secure speed, particularly in water and air.
“_Ligaments._--The office of the ligaments with respect to locomotion,
is to restrict the degree of flexion, extension, and other motions of
the limbs within definite limits.
“_Effect of Atmospheric pressure on Limbs._--The influence of
atmospheric pressure in supporting the limbs was first noticed by Dr.
Arnott, though it has been erroneously ascribed by Professor Müller
to Weber. Subsequent experiments made by Dr. Todd, Mr. Wormald, and
others, have fully established the mechanical influence of the air in
keeping the mechanism of the joints together. The amount of atmospheric
pressure on any joint depends upon the area or surface presented to its
influence, and the height of the barometer. According to Weber, the
atmospheric pressure on the hip-joint of a man is about 26 lbs. The
pressure on the knee-joint is estimated by Dr. Arnott at 60 lbs.”[13]
[13] Bishop, _op. cit._
[Illustration:
FIG. 5. Shows the muscular cycle formed by the biceps (_a_) or flexor
muscle, and the triceps (_b_) or extensor muscle of the human arm. At
_i_ the centripetal or shortening action of the biceps is seen, and
at _j_ the centrifugal or elongating action of the triceps (_vide_
arrows). The present figure represents the forearm as flexed upon
the arm. As a consequence, the long axes of the sarcous elements or
ultimate particles of the biceps (_i_) are arranged in a more or less
horizontal direction; the long axes of the sarcous elements of the
triceps (_j_) being arranged in a nearly vertical direction. When
the forearm is extended, the long axes of the sarcous elements of
the biceps and triceps are reversed. The present figure shows how
the bones of the extremities form levers, and how they are moved
by muscular action. If, _e.g._, the biceps (_a_) shortens and the
triceps (_b_) elongates, they cause the forearm and hand (_h_) to
move towards the shoulder (_d_). If, on the other hand, the triceps
(_b_) shortens and the biceps (_a_) elongates, they cause the forearm
and hand (_h_) to move away from the shoulder. In these actions the
biceps (_a_) and triceps (_b_) are the power; the elbow-joint (_g_)
the fulcrum, and the forearm and hand (_h_) the weight to be elevated
or depressed. If the hand represented a travelling surface which
operated on the earth, the water, or the air, it is not difficult to
understand how, when it was made to move by the action of the muscles
of the arm, it would in turn move the body to which it belonged, _d_
Coracoid process of the scapula, from which the internal or short
head of the biceps (_a_) arises, _e_ Insertion of the biceps into
the radius. _f_ Long head of the triceps (_b_). _g_ Insertion of the
triceps into the olecranon process of the ulna.--_Original._]