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Transcriber’s notes:

The text of this e-book has been preserved in its original form
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developes → develops). Inconsistent use of accents and hyphenation, and
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[Illustration:

_C. Berjeau_     _W. Ballingall_

WALKING, SWIMMING, AND FLYING.]




                           ANIMAL LOCOMOTION

                                  OR

                    WALKING, SWIMMING, AND FLYING,

                        WITH A DISSERTATION ON

                             AËRONAUTICS.


                                  BY

          J. BELL PETTIGREW, M.D. F.R.S. F.R.S.E. F.R.C.P.E.

    PATHOLOGIST TO THE ROYAL INFIRMARY OF EDINBURGH; CURATOR OF THE
         MUSEUM OF THE ROYAL COLLEGE OF SURGEONS OF EDINBURGH;

  Extraordinary Member and late President of the Royal Medical Society
   of Edinburgh; Croonian Lecturer to the Royal Society of London for
  1860; Lecturer to the Royal Institution of Great Britain and Russell
     Institution, 1867; Lecturer to the Royal College of Surgeons of
  Edinburgh, 1872; Author of numerous Memoirs on Physiological Subjects
       in the Philosophical and other Transactions, etc. etc. etc.

               _ILLUSTRATED BY 130 ENGRAVINGS ON WOOD._

                          HENRY S. KING & CO.

             65 CORNHILL, AND 12 PATERNOSTER ROW, LONDON.

                                 1873.




[Illustration:

  (_All Rights reserved._)]




PREFACE.


In the present volume I have endeavoured to explain, in simple
language, some difficult problems in “Animal Mechanics.” In order to
avoid elaborate descriptions, I have introduced a large number of
original Drawings and Diagrams, copied for the most part from my Papers
and Memoirs “On Flight,” and other forms of “Animal Progression.” I
have drawn from the same sources many of the facts to be found in
the present work. My best thanks are due to Mr. W. Ballingall, of
Edinburgh, for the highly artistic and effective manner in which he has
engraved the several subjects. The figures, I am happy to state, have
in no way deteriorated in his hands.

  ROYAL COLLEGE OF SURGEONS OF EDINBURGH,
               _July 1873_.




[Illustration]




CONTENTS.


  ANIMAL LOCOMOTION.

  INTRODUCTION.

                                                                  PAGE

  Motion associated with the life and well-being of animals,         1

  Motion not confined to the animal kingdom; all matter in motion;
  natural and artificial motion; the locomotive, steamboat, etc.
  A flying machine possible,                                         2

  Weight necessary to flight,                                        3

  The same laws regulate natural and artificial progression,         4

  Walking, swimming, and flying correlated,                          5

  Flight the poetry of motion,                                       6

  Flight a more unstable movement than that of walking and
  swimming; the travelling surfaces and movements of animals
  adapted to the earth, the water, and the air,                      7

  The earth, the water, and the air furnish the fulcra for the
  levers formed by the travelling surfaces of animals,               8

  Weight plays an important part in walking, swimming, and flying,   9

  The extremities of animals in walking act as pendulums, and
  describe figure-of-8 curves,                                       9

  In swimming, the body of the fish is thrown into figure-of-8
  curves,                                                           10

  The tail of the fish made to vibrate pendulum fashion,            11

  The tail of the fish, the wing of the bird, and the extremity
  of the biped and quadruped are screws structurally and
  functionally. They describe figure-of-8 and waved tracks,         12

  The body and wing reciprocate in flight; the body rising when
  the wing is falling, and _vice versâ_,                            12

  Flight the least fatiguing kind of motion. Aërial creatures not
  stronger than terrestrial ones,                                   13

  Fins, flippers, and wings form mobile helics or screws,           14

  Artificial fins, flippers, and wings adapted for navigating the
  water and air,                                                    14

  History of the figure-of-8 theory of walking, swimming, and
  flying,                                                           15

  Priority of discovery on the part of the Author. Admission to
  that effect on the part of Professor Marey,                       16

  Fundamental axioms. Of uniform motion. Motion uniformly
  varied,                                                           17

  The legs move by the force of gravity. Resistance of fluids.
  Mechanical effects of fluids on animals immersed in them.
  Centre of gravity,                                                18

  The three orders of lever,                                        19

  Passive organs of locomotion. Bones,                              21

  Joints,                                                           23

  Ligaments. Effects of atmospheric pressure on limbs. Active
  organs of locomotion. Muscles; their properties, arrangement,
  modes of action, etc.,                                            24

  Muscular cycles. Centripetal and centrifugal movements of
  muscles; muscular waves. Muscles arranged in longitudinal,
  transverse, and oblique spiral lines,                          25–27

  The bones of the extremities twisted and spiral,                  28

  Muscles take precedence of bones in animal movements,             29

  Oblique spiral muscles necessary for spiral bones and joints,     31

  The spiral movements of the spine transferred to the
  extremities,                                                      33

  The travelling surfaces of animals variously modified and
  adapted to the media on or in which they move,                 34–36


  PROGRESSION ON THE LAND.

  Walking of the Quadruped, Biped, etc.,                            37

  Locomotion of the Horse,                                          39

  Locomotion of the Ostrich,                                        45

  Locomotion of Man,                                                51


  PROGRESSION ON AND IN THE WATER.

  Swimming of the Fish, Whale, Porpoise, etc.,                      66

  Swimming of the Seal, Sea-Bear, and Walrus,                       74

  Swimming of Man,                                                  78

  Swimming of the Turtle, Triton, Crocodile, etc.,                  89

  Flight under water,                                               90

  Difference between sub-aquatic and aërial flight,                 92

  Flight of the Flying-fish; the kite-like action of the wings,     98


  PROGRESSION IN OR THROUGH THE AIR.

  The wing a lever of the third order,                             103

  Weight necessary to flight,                                      110

  Weight contributes to horizontal flight,                         112

  Weight, momentum and power to a certain extent synonymous
  in flight,                                                       114

  Air-cells in insects and birds not necessary to flight,          115

  How balancing is effected in flight,                             118

  Rapidity of wing movements partly accounted for,                 120

  The wing area variable and in excess,                            124

  The wing area decreases as the size and weight of the volant
  animal increases,                                                132

  Wings, their form, etc. All wings screws, structurally and
  functionally,                                                    136

  The wing, during its action, reverses its planes, and describes
  a figure-of-8 track in space,                                    140

  The wing, when advancing with the body, describes a looped
  and waved track,                                                 143

  The margins of the wing, thrown into opposite curves during
  extension and flexion,                                           146

  The tip of the bat and bird’s wing describes an ellipse,         147

  The wing capable of change of form in all its parts,             147

  The wing during its vibration produces a cross pulsation,        148

  Compound rotation of the wing,                                   149

  The wing vibrates unequally with reference to a given line,      150

  Points wherein the screws formed by the wings differ from
  those in common use,                                             151

  The wing at all times thoroughly under control,                  154

  The natural wing when elevated and depressed must move
  forwards,                                                        156

  The wing ascends when the body descends, and _vice versâ_,       159

  The wing acts upon yielding fulcra,                              165

  The wing acts as a true kite both during the down and up
  strokes,                                                         165

  Where the kite formed by the wing differs from the boy’s kite,   166

  The angles formed by the wing during its vibrations,             167

  The body and wings move in opposite curves,                      168


  THE WINGS OF INSECTS, BATS, AND BIRDS.

  Elytra or wing cases and membranous wings; their shape and
  uses,                                                            170


  THE WINGS OF BATS.

  The bones of the wing of the bat; the spiral configuration of
  their articular surfaces,                                        176


  THE WINGS OF BIRDS.

  The bones of the wing of the bird; their articular surfaces,
  movements, etc.,                                                 178

  Traces of design in the wing of the bird; the arrangement of
  the primary, secondary, and tertiary feathers, etc.,             18O

  The wing of the bird not always opened up to the same extent
  in the up stroke,                                                182

  Flexion of the wing necessary to the flight of birds,            183

  Consideration of the forces which propel the wings of insects,   186

  Speed attained by insects,                                       188

  Consideration of the forces which propel the wings of bats and
  birds,                                                           189

  Lax condition of the shoulder-joint in bats and birds,           190

  The wing flexed and partly elevated by the action of elastic
  ligaments; the nature and position of said ligaments in
  the Pheasant, Snipe, Crested Crane, Swan, etc.,                  191

  The elastic ligaments more highly differentiated in wings which
  vibrate rapidly,                                                 193

  Power of the wing, to what owing,                                194

  Reasons why the effective stroke should be delivered downwards
  and forwards,                                                    195

  The wing acts as an elevator, propeller, and sustainer, both
  during extension and flexion,                                    197

  Flight divisible into four kinds,                                197

  The flight of the Albatross compared to the movements of a
  compass set upon gimbals,                                        199

  The regular and irregular in flight,                             201

  Mode of ascending, descending, turning, etc.,                    201

  The flight of birds referable to muscular exertion and weight,   204

  Lifting capacity of birds,                                       205


  AËRONAUTICS.

  The balloon,                                                     210

  The inclined plane,                                              211

  The aërial screw,                                                215

  Artificial wings (Borelli’s views),                              219

  Marey’s views,                                                   226

  Chabrier’s views,                                                233

  Straus-Durckheim’s views,                                        233

  The Author’s views; his method of constructing and applying
  artificial wings, as contra-distinguished from that of Borelli,
  Chabrier, Durckheim, and Marey,                                  235

  The wave wing of the Author,                                     236

  How to construct an artificial wave wing on the insect type,     240

  How to construct a wave wing which shall evade the superimposed
  air during the up stroke,                                        241

  Compound wave wing of the Author,                                242

  How to apply artificial wings to the air,                        245

  As to the nature of the forces required for propelling
  artificial wings,                                                246

  Necessity for supplying the roots of artificial wings with
  elastic structures in imitation of the muscles and elastic
  ligaments of flying animals,                                     247

  The artificial wave wing can be driven at any speed--it can
  make its own currents or utilize existing ones,                  251

  Compound rotation of the artificial wave wing. The different
  parts of the wing travel at different speeds,                    252

  How the wave wing creates currents and rises upon them, and
  how the air assists in elevating the wing,                       253

  The artificial wing propelled at various degrees of speed
  during the down and up strokes,                                  255

  The artificial wave wing as a propeller,                         256

  A new form of aërial screw,                                      256

  The aërial wave screw operates upon water,                       257

  The sculling action of the wing,                                 231

  CONCLUDING REMARKS,                                              258




[Illustration]




LIST OF ILLUSTRATIONS.

  The Engravings are, with few exceptions, from Photographs, Drawings,
  and Designs by Mr. Charles Berjeau and the Author. Such as are not
  original are duly acknowledged.


  FRONTISPIECE.                                                   PAGE

  In the clutch of the enemy--(_The Graphic_).

  The three orders of lever--(_Bishop_),                        19, 20

  The skeleton of a Deer--(_Pander and D’Alton_),                   21

  Muscular cycle in the act of flexing the arm,                     25

  Screws formed by the bones of the wing of the bird, the bones
  of the anterior extremity of the Elephant, and the cast of the
  interior of the left ventricle of the heart,                      28

  The muscular system of the Horse--(_Bagg_),                       30

  The feet of the Deer, Ornithorhynchus, Otter, Frog, and Seal,     34

  The Red-throated Dragon,                                          35

  The Flying Lemur,                                                 35

  The Bat,                                                          36

  Chillingham Bull with extremities describing figure-of-8
  movements,                                                        37

  Double waved tracks described by Man in walking,                  39

  Horse in the act of trotting,                                     41

  Footprints of the Horse in the walk, trot, and gallop--
  (_Gamgee_),                                                       43

  Skeleton of the Ostrich--(_Dallas_),                              47

  Ostriches pursued by a hunter,                                    48

  Skeleton of Man,                                                  55

  The positions assumed by the extremities and feet in walking--
  (_Weber_),                                                        59

  Preparing to run--(_Flaxman_),                                    62

  The skeleton of a Perch--(_Dallas_),                              65

  The Salmon swimming leisurely,                                    65

  Swimming of the fish according to Borelli,                        67

  Swimming of the fish according to the Author,                     68

  The Porpoise and Manatee,                                         73

  The skeleton of the Dugong--(_Dallas_),                           74

  The Seal,                                                         74

  The Sea-Bear,                                                     76

  The elliptical, looped, and spiral tracks made in swimming,       81

  The several attitudes assumed by the extremities in swimming
  in the prone position,                                            82

  Overhand swimming,                                                85

  Side swimming,                                                    86

  Swimming of the Turtle and Triton,                                89

  Swimming of the Little Penguin,                                   91

  Sub-aquatic flight or diving,                                     94

  The feet of the Swan as seen in the open and closed condition,    96

  The foot of the Grebe with swimming membrane--(_Dallas_),         97

  Double waved track described by the feet of swimming birds,       97

  The flight of the Flying-fish,                                    98

  The wing a lever of the third order,                             105

  Figure-of-8 vertical track made by the wing in flight,           107

      Do.     horizontal track,                                    108

  Feathers and cork flying forward,                                112

  Diagram illustrating how wings obtain their high speed,          120

  Butterfly with large wings,                                      124

  Beetle with small wings,                                         125

  Partridge with small wings; Heron with large wings,              126

  The wings of the Hawk and Albatross,                        136, 137

  The Green Plover with one wing flexed and the other extended,    138

  Blur or impression produced on the eye by the rapidly
  oscillating wing of the insect,                                  139

  Diagram in which the down and up strokes of the wing of the
  insect are analysed,                                             141

  Diagrams illustrating the looped and waved tracks described
  by the wing of the insect, bat, and bird,                        144

  Figures showing the positions assumed by the wing of the bird
  during the up and down strokes (side view),                      145

  The positions assumed by the wing of the insect as it hastens
  to and fro and describes a figure-of-8 track,                    147

  The figure-of-8 curves made by the wing of the bird in flexion
  and extension,                                                   147

  The long and short axes of the wing,                             149

  The waved tracks described by the wing and body of the
  bird as they alternately rise and fall,                     157, 163

  The positions assumed by the wing of the bird during the
  down and up strokes (front view),                                158

  Analysis of the movements of the wing,                      160, 161

  The kite-like action and waved movements of the wing,            166

  The Centaur Beetle and Water Bug,                                171

  The Dragon Fly,                                                  172

  The screws formed by the wing of the insect, bat,
  and bird,                                              174, 175, 176

  The muscles, elastic ligaments, and feathers of the wing
  of the bird,                                                     181

  The flight of the King-fisher,                                   183

  The flight of the Gull,                                          186

  The flight of the Owl,                                           198

  The flight of the Albatross,                                     200

  Pigeon and Duck alighting,                                  203, 204

  Hawk and quarry--(_The Graphic_),                                206

  The Vauxhall Balloon of Mr. Green,                               208

  Mr. Henson’s Flying Machine,                                     212

  Mr. Stringfellow’s Flying Machine,                               213

  Sir George Cayley’s Flying Apparatus,                            215

  Flying Machine designed by De la Landelle,                       217

  Borelli’s Artificial Bird,                                       220

  Diagrams illustrating the true and false action of the wing,     228

  The sculling action of the wing as seen in the bird,             231

  The artificial wave wing of the Author,                          237

        Do.         do.     with driving apparatus,                239

  Various forms of artificial wings by the Author,                 241

  The compound wave wing of the Author,                            243

  Diagrams illustrative of artificial wing movements,              250

  Diagram illustrating the currents produced by the movements
  of artificial wings,                                             253

  The aërial wave screw of the Author,                             256

  Swallow in pursuit of insects,                                   260

[Illustration]

[Illustration]




ANIMAL LOCOMOTION.




[Illustration:

  _Engraved by W. Ballingall._

  IN THE CLUTCH OF THE ENEMY.]




ANIMAL LOCOMOTION.

INTRODUCTION.


The locomotion of animals, as exemplified in walking, swimming, and
flying, is a subject of permanent interest to all who seek to trace
in the creature proofs of beneficence and design in the Creator.
All animals, however insignificant, have a mission to perform--a
destiny to fulfil; and their manner of doing it cannot be a matter of
indifference, even to a careless observer. The most exquisite form
loses much of its grace if bereft of motion, and the most ungainly
animal conceals its want of symmetry in the co-adaptation and exercise
of its several parts. The rigidity and stillness of death alone are
unnatural. So long as things “live, move, and have a being,” they are
agreeable objects in the landscape. They are part and parcel of the
great problem of life, and as we are all hastening towards a common
goal, it is but natural we should take an interest in the movements
of our fellow-travellers. As the locomotion of animals is intimately
associated with their habits and modes of life, a wide field is opened
up, teeming with incident, instruction, and amusement. No one can see a
bee steering its course with admirable precision from flower to flower
in search of nectar; or a swallow darting like a flash of light along
the lanes in pursuit of insects; or a wolf panting in breathless haste
after a deer; or a dolphin rolling like a mill-wheel after a shoal of
flying fish, without feeling his interest keenly awakened.

Nor is this love of motion confined to the animal kingdom. We admire a
cataract more than a canal; the sea is grander in a hurricane than in
a calm; and the fleecy clouds which constantly flit overhead are more
agreeable to the eye than a horizon of tranquil blue, however deep
and beautiful. We never tire of sunshine and shadow when together: we
readily tire of either by itself. Inorganic changes and movements are
scarcely less interesting than organic ones. The disaffected growl of
the thunder, and the ghastly lightning flash, scorching and withering
whatever it touches, forcibly remind us that everything above, below,
and around is in motion. Of absolute rest, as Mr. Grove eloquently
puts it, nature gives us no evidence. All matter, whether living or
dead, whether solid, liquid, or gaseous, is constantly changing form:
in other words, is constantly moving. It is well it is so; for those
incessant changes in inorganic matter and living organisms introduce
that fascinating variety which palls not upon the eye, the ear, the
touch, the taste, or the smell. If an absolute repose everywhere
prevailed, and plants and animals ceased to grow; if day ceased to
alternate with night and the fountains were dried up or frozen; if the
shadows refused to creep, the air and rocks to reverberate, the clouds
to drift, and the great race of created beings to move, the world would
be no fitting habitation for man. In change he finds his present solace
and future hope. The great panorama of life is interesting because it
moves. One change involves another, and everything which co-exists,
co-depends. This co-existence and inter-dependence causes us not only
to study ourselves, but everything around us. By discovering natural
laws we are permitted in God’s good providence to harness and yoke
natural powers, and already the giant Steam drags along at incredible
speed the rumbling car and swiftly gliding boat; the quadruped has been
literally outraced on the land, and the fish in the sea; each has been,
so to speak, beaten in its own domain. That the tramway of the air may
and will be traversed by man’s ingenuity at some period or other, is,
reasoning from analogy and the nature of things, equally certain. If
there were no flying things--if there were no insects, bats, or birds
as models, artificial flight (such are the difficulties attending its
realization) might well be regarded an impossibility. As, however, the
flying creatures are legion, both as regards number, size, and pattern,
and as the bodies of all are not only manifestly heavier than the
air, but are composed of hard and soft parts, similar in all respects
to those composing the bodies of the other members of the animal
kingdom, we are challenged to imitate the movements of the insect,
bat, and bird in the air, as we have already imitated the movements
of the quadruped on the land and the fish in the water. We have made
two successful steps, and have only to make a third to complete that
wonderfully perfect and very comprehensive system of locomotion which
we behold in nature. Until this third step is taken, our artificial
appliances for transit can only be considered imperfect and partial.
Those authors who regard artificial flight as impracticable sagely
remark that the land supports the quadruped and the water the fish.
This is quite true, but it is equally true that the air supports the
bird, and that the evolutions of the bird on the wing are quite as safe
and infinitely more rapid and beautiful than the movements of either
the quadruped on the land or the fish in the water. What, in fact,
secures the position of the quadruped on the land, the fish in the
water, and the bird in the air, is the life; and by this I mean that
prime moving or self-governing power which co-ordinates the movements
of the _travelling surfaces_ (whether feet, fins, or wings) of all
animals, and adapts them to the medium on which they are destined to
operate, whether this be the comparatively unyielding earth, the mobile
water, or the still more mobile air. Take away this life suddenly--the
quadruped falls downwards, the fish (if it be not specially provided
with a swimming bladder) sinks, and the bird gravitates of necessity.
There is a sudden subsiding and cessation of motion in either case,
but the quadruped and fish have no advantage over the bird in this
respect. The _savans_ who oppose this view exclaim not unnaturally
that there is no great difficulty in propelling a machine either
along the land or the water, seeing that both these media support it.
There is, I admit, no great difficulty now, but there were apparently
insuperable difficulties before the locomotive and steam-boat were
invented. _Weight_, moreover, instead of being a barrier to artificial
flight is absolutely necessary to it. This statement is quite opposed
to the commonly received opinion, but is nevertheless true. No bird is
lighter than the air, and no machine constructed to navigate it should
aim at being specifically lighter. What is wanted is a reasonable but
not cumbrous amount of weight, and a duplicate (in principle if not
in practice) of those structures and movements which enable insects,
bats, and birds to fly. Until the structure and uses of wings are
understood, the way of “an eagle in the air” must of necessity remain
a mystery. The subject of flight has never, until quite recently, been
investigated systematically or rationally, and, as a result, very
little is known of the laws which regulate it. If these laws were
understood, and we were in possession of trustworthy data for our
guidance in devising artificial pinions, the formidable Gordian knot of
flight, there is reason to believe, could be readily untied.

That artificial flight is a possible thing is proved beyond
doubt--_1st_, by the fact that flight is a natural movement; and _2d_,
because the natural movements of walking and swimming have already been
successfully imitated.

The very obvious bearing which natural movements have upon artificial
ones, and the relation which exists between organic and inorganic
movements, invest our subject with a peculiar interest.

It is the blending of natural and artificial progression in theory
and practice which gives to the one and the other its chief charm.
The history of artificial progression is essentially that of natural
progression. The same laws regulate and determine both. The wheel of
the locomotive and the screw of the steam-ship apparently greatly
differ from the limb of the quadruped, the fin of the fish, and the
wing of the bird; but, as I shall show in the sequel, the curves which
go to form the wheel and the screw are found in the travelling surfaces
of all animals, whether they be limbs (furnished with feet), or fins,
or wings.

It is a remarkable circumstance that the undulation or wave made by
the wing of an insect, bat, or bird, when those animals are fixed
or hovering before an object, and when they are flying, corresponds
in a marked manner with the track described by the stationary and
progressive waves in fluids, and likewise with the waves of sound.
This coincidence would seem to argue an intimate relation between the
instrument and the medium on which it is destined to operate--the wing
acting in those very curves into which the atmosphere is naturally
thrown in the transmission of sound. Can it be that the animate and
inanimate world reciprocate, and that animal bodies are made to impress
the inanimate in precisely the same manner as the inanimate impress
each other? This much seems certain:--The wind communicates to the
water similar impulses to those communicated to it by the fish in
swimming; and the wing in its vibrations impinges upon the air as an
ordinary sound does. The extremities of quadrupeds, moreover, describe
waved tracks on the land when walking and running; so that one great
law apparently determines the course of the insect in the air, the fish
in the water, and the quadruped on the land.

We are, unfortunately, not taught to regard the travelling surfaces and
movements of animals as correlated in any way to surrounding media,
and, as a consequence, are apt to consider walking as distinct from
swimming, and walking and swimming as distinct from flying, than which
there can be no greater mistake. Walking, swimming, and flying are in
reality only modifications of each other. Walking merges into swimming,
and swimming into flying, by insensible gradations. The modifications
which result in walking, swimming, and flying are necessitated by the
fact that the earth affords a greater amount of support than the water,
and the water than the air.

That walking, swimming, and flying represent integral parts of the
same problem is proved by the fact that most quadrupeds swim as well
as walk, and some even fly; while many marine animals walk as well as
swim, and birds and insects walk, swim, and fly indiscriminately. When
the land animals, properly so called, are in the habit of taking to
the water or the air; or the inhabitants of the water are constantly
taking to the land or the air; or the insects and birds which are
more peculiarly organized for flight, spend much of their time on
the land and in the water; their organs of locomotion must possess
those peculiarities of structure which characterize, as a class,
those animals which live on the land, in the water, or in the air
respectively.

In this we have an explanation of the gossamer wing of the insect,--the
curiously modified hand of the bat and bird,--the webbed hands and
feet of the Otter, Ornithorhynchus, Seal, and Walrus,--the expanded
tail of the Whale, Porpoise, Dugong, and Manatee,--the feet of the
Ostrich, Apteryx, and Dodo, exclusively designed for running,--the feet
of the Ducks, Gulls, and Petrels, specially adapted for swimming,--and
the wings and feet of the Penguins, Auks, and Guillemots, especially
designed for diving. Other and intermediate modifications occur in the
Flying-fish, Flying Lizard, and Flying Squirrel; and some animals, as
the Frog, Newt, and several of the aquatic insects (the Ephemera or
May-fly for example[1]) which begin their career by swimming, come
ultimately to walk, leap, and even fly.[2]

  [1] The Ephemeræ in the larva and pupa state reside in the water
  concealed during the day under stones or in horizontal burrows which
  they form in the banks. Although resembling the perfect insect in
  several respects, they differ materially in having longer antennæ, in
  wanting ocelli, and in possessing horn-like mandibles; the abdomen
  has, moreover, on each side a row of plates, mostly in pairs, which
  are a kind of false branchiæ, and which are employed not only in
  respiration, _but also as paddles_.--Cuvier’s Animal Kingdom, p. 576.
  London, 1840.

  [2] Kirby and Spence observe that some insects which are not
  naturally aquatic, do, nevertheless, swim very well if they fall
  into the water. They instance a kind of grasshopper (_Acrydium_),
  which can paddle itself across a stream with great rapidity by the
  powerful strokes of its hind legs.--(Introduction to Entomology, 5th
  edit., 1828, p. 360.) Nor should the remarkable discovery by Sir John
  Lubbock of a swimming insect (_Polynema natans_), which uses its
  wings _exclusively as fins_, be overlooked.--Linn. Trans. vol. xxiv.
  p. 135.

Every degree and variety of motion, which is peculiar to the land, and
to the water- and air-navigating animals as such, is imitated by others
which take to the elements in question secondarily or at intervals.

Of all animal movements, flight is indisputably the finest. It may be
regarded as the poetry of motion. The fact that a creature as heavy,
bulk for bulk, as many solid substances, can by the unaided movements
of its wings urge itself through the air with a speed little short of
a cannon-ball, fills the mind with wonder. Flight (if I may be allowed
the expression) is a more unstable movement than that of walking and
swimming; the instability increasing as the medium to be traversed
becomes less dense. It, however, does not essentially differ from the
other two, and I shall be able to show in the following pages, that the
materials and forces employed in flight are literally the same as those
employed in walking and swimming. This is an encouraging circumstance
as far as artificial flight is concerned, as the same elements and
forces employed in constructing locomotives and steamboats may, and
probably will at no distant period, be successfully employed in
constructing flying machines. Flight is a purely mechanical problem. It
is warped in and out with the other animal movements, and forms a link
of a great chain of motion which drags its weary length over the land,
through the water, and, notwithstanding its weight, through the air. To
understand flight, it is necessary to understand walking and swimming,
and it is with a view to simplifying our conceptions of this most
delightful form of locomotion that the present work is mainly written.
The chapters on walking and swimming naturally lead up to those on
flying.

In the animal kingdom the movements are adapted either to the land,
the water, or the air; these constituting the three great highways of
nature. As a result, the instruments by which locomotion is effected
are specially modified. This is necessary because of the different
densities and the different degrees of resistance furnished by the
land, water, and air respectively. On the land the extremities of
animals encounter the _maximum_ of _resistance_, and occasion the
_minimum_ of _displacement_. In the air, the pinions experience the
_minimum_ of _resistance_, and effect the _maximum_ of _displacement_;
the water being intermediate both as regards the degree of resistance
offered and the amount of displacement produced. The speed of an animal
is determined by its shape, mass, power, and the density of the medium
on or in which it moves. It is more difficult to walk on sand or snow
than on a macadamized road. In like manner (unless the travelling
surfaces are specially modified), it is more troublesome to swim than
to walk, and to fly than to swim. This arises from the displacement
produced, and the consequent want of support. The land supplies the
fulcrum for the levers formed by the extremities or travelling surfaces
of animals with terrestrial habits; the water furnishes the fulcrum for
the levers formed by the tail and fins of fishes, sea mammals, etc.;
and the air the fulcrum for the levers formed by the wings of insects,
bats, and birds. The fulcrum supplied by the land is immovable; that
supplied by the water and air movable. The mobility and immobility
of the fulcrum constitute the principal difference between walking,
swimming, and flying; the travelling surfaces of animals increasing in
size as the medium to be traversed becomes less dense and the fulcrum
more movable. Thus terrestrial animals have smaller travelling surfaces
than amphibia, amphibia than fishes, and fishes than insects, bats, and
birds. Another point to be studied in connexion with unyielding and
yielding fulcra, is the resistance offered to forward motion. A land
animal is supported by the earth, and experiences little resistance
from the air through which it moves, unless the speed attained is
high. Its principal friction is that occasioned by the contact of
its travelling surfaces with the earth. If these are few, the speed
is generally great, as in quadrupeds. A fish, or sea mammal, is of
nearly the same specific gravity as the water it inhabits; in other
words, it is supported with as little or less effort than a land
animal. As, however, the fluid in which it moves is more dense than
air, the resistance it experiences in forward motion is greater than
that experienced by land animals, and by insects, bats, and birds.
As a consequence fishes are for the most part elliptical in shape;
this being the form calculated to cleave the water with the greatest
ease. A flying animal is immensely heavier than the air. The support
which it receives, and the resistance experienced by it in forward
motion, are reduced to a minimum. Flight, because of the rarity of
the air, is infinitely more rapid than either walking, running, or
swimming. The flying animal receives support from the air by increasing
the size of its travelling surfaces, which act after the manner of
twisted inclined planes or kites. When an insect, a bat, or a bird is
launched in space, its weight (from the tendency of all bodies to fall
vertically downwards) presses upon the inclined planes or kites formed
by the wings in such a manner as to become converted directly into a
_propelling_, and indirectly into a _buoying_ or supporting power. This
can be proved by experiment, as I shall show subsequently. But for the
share which the weight or mass of the flying creature takes in flight,
the protracted journeys of birds of passage would be impossible. Some
authorities are of opinion that birds even sleep upon the wing. Certain
it is that the albatross, that prince of the feathered tribe, can sail
about for a whole hour without once flapping his pinions. This can only
be done in virtue of the weight of the bird acting upon the inclined
planes or kites formed by the wings as stated.

The weight of the body plays an important part in walking and swimming,
as well as in flying. A biped which advances by steps and not by leaps
may be said to roll over its extremities,[3] the foot of the extremity
which happens to be upon the ground for the time forming the centre
of a circle, the radius of which is described by the trunk in forward
motion. In like manner the foot which is off the ground and swinging
forward pendulum fashion in space, may be said to roll or rotate upon
the trunk, the head of the femur forming the centre of a circle the
radius of which is described by the advancing foot. A double rolling
movement is thus established, the body rolling on the extremity the
one instant, the extremity rolling on the trunk the next. During these
movements the body rises and falls. The double rolling movement is
necessary not only to the progression of bipeds, but also to that of
quadrupeds. As the body cannot advance without the extremities, so
the extremities cannot advance without the body. The double rolling
movement is necessary to continuity of motion. If there was only one
movement there would be dead points or halts in walking and running,
similar to what occur in leaping. The continuity of movement necessary
to progression in some bipeds (man for instance) is further secured
by a pendulum movement in the arms as well as in the legs, the right
arm swinging before the body when the right leg swings behind it, and
the converse. The right leg and left arm advance simultaneously, and
alternate with the left leg and right arm, which likewise advance
together. This gives rise to a double twisting of the body at the
shoulders and loins. The legs and arms when advancing move in curves,
the convexities of the curves made by the right leg and left arm, which
advance together when a step is being made, being directed outwards,
and forming, when placed together, a more or less symmetrical ellipse.
If the curves formed by the legs and arms respectively be united,
they form waved lines which intersect at every step. This arises from
the fact that the curves formed by the right and left legs are found
alternately on either side of a given line, the same holding true
of the right and left arms. Walking is consequently to be regarded
as the result of a twisting diagonal movement in the trunk and in
the extremities. Without this movement, the momentum acquired by the
different portions of the moving mass could not be utilized. As the
momentum acquired by animals in walking, swimming, and flying forms an
important factor in those movements, it is necessary that we should
have a just conception of the value to be attached to weight when in
motion. In the horse when walking, the stride is something like five
feet, in trotting ten feet, but in galloping eighteen or more feet. The
stride is in fact determined by the speed acquired by the mass of the
body of the horse; the momentum at which the mass is moving carrying
the limbs forward.[4]

  [3] This is also true of quadrupeds. It is the posterior part of the
  feet which is set down first.

  [4] “According to Sainbell, the celebrated horse Eclipse, when
  galloping at liberty, and with its greatest speed, passed over the
  space of twenty-five feet at each stride, which he repeated 2-1/3
  times in a second, being nearly four miles in six minutes and two
  seconds. The race-horse Flying Childers was computed to have passed
  over eighty-two feet and a half in a second, or nearly a mile in a
  minute.”

In the swimming of the fish, the body is thrown into double or
figure-of-8 curves, as in the walking of the biped. The twisting of
the body, and the continuity of movement which that twisting begets,
reappear. The curves formed in the swimming of the fish are never
less than two, a caudal and a cephalic one. They may and do exceed
this number in the long-bodied fishes. The tail of the fish is made to
vibrate pendulum fashion on either side of the spine, when it is lashed
to and fro in the act of swimming. It is made to rotate upon one or
more of the vertebræ of the spine, the vertebra or vertebræ forming the
centre of a lemniscate, which is described by the caudal fin. There
is, therefore, an obvious analogy between the tail of the fish and the
extremity of the biped. This is proved by the conformation and swimming
of the seal,--an animal in which the posterior extremities are modified
to resemble the tail of the fish. In the swimming of the seal the hind
legs are applied to the water by a sculling figure-of-8 motion, in the
same manner as the tail of the fish. Similar remarks might be made with
regard to the swimming of the whale, dugong, manatee, and porpoise,
sea mammals, which still more closely resemble the fish in shape. The
double curve into which the fish throws its body in swimming, and
which gives continuity of motion, also supplies the requisite degree
of steadiness. When the tail is lashed from side to side there is a
tendency to produce a corresponding movement in the head, which is
at once corrected by the complementary curve. Nor is this all; the
cephalic curve, in conjunction with the water contained within it,
forms the _point d’appui_ for the caudal curve, and _vice versa_.
When a fish swims, the anterior and posterior portions of its body
(supposing it to be a short-bodied fish) form curves, the convexities
of which are directed on opposite sides of a given line, as is the case
in the extremities of the biped when walking. The mass of the fish,
like the mass of the biped, when once set in motion, contributes to
progression by augmenting the rate of speed. The velocity acquired by
certain fishes is very great. A shark can gambol around the bows of a
ship in full sail; and a sword-fish (such is the momentum acquired by
it) has been known to thrust its tusk through the copper sheathing of
a vessel, a layer of felt, four inches of deal, and fourteen inches of
oaken plank.[5]

  [5] A portion of the timbers, etc., of one of Her Majesty’s ships,
  having the tusk of a sword-fish imbedded in it, is to be seen in the
  Hunterian Museum of the Royal College of Surgeons of England.

The wing of the bird does not materially differ from the extremity
of the biped or the tail of the fish. It is constructed on a similar
plan, and acts on the same principle. The tail of the fish, the wing
of the bird, and the extremity of the biped and quadruped, are screws
structurally and functionally. In proof of this, compare the bones of
the wing of a bird with the bones of the arm of a man, or those of
the fore-leg of an elephant, or any other quadruped. In either case
the bones are twisted upon themselves like the screw of an augur. The
tail of the fish, the extremities of the biped and quadruped, and the
wing of the bird, when moving, describe waved tracks. Thus the wing
of the bird, when it is made to oscillate, is thrown into double or
figure-of-8 curves, like the body of the fish. When, moreover, the wing
ascends and descends to make the up and down strokes, it rotates within
the _facettes_ or depressions situated on the scapula and coracoid
bones, precisely in the same way that the arm of a man rotates in the
glenoid cavity, or the leg in the acetabular cavity in the act of
walking. The ascent and descent of the wing in flying correspond to the
steps made by the extremities in walking; the wing rotating upon the
body of the bird during the down stroke, the body of the bird rotating
on the wing during the up stroke. When the wing descends it describes
a downward and forward curve, and elevates the body in an upward and
forward curve. When the body descends, it describes a downward and
forward curve, the wing being elevated in an upward and forward curve.
The curves made by the wing and body in flight form, when united, waved
lines, which intersect each other at every beat of the wing. The wing
and the body act upon each other alternately (the one being active
when the other is passive), and the descent of the wing is not more
necessary to the elevation of the body than the descent of the body is
to the elevation of the wing. It is thus that the weight of the flying
animal is utilized, slip avoided, and continuity of movement secured.

As to the actual waste of tissue involved in walking, swimming, and
flying, there is much discrepancy of opinion. It is commonly believed
that a bird exerts quite an enormous amount of power as compared with
a fish; a fish exerting a much greater power than a land animal. This,
there can be no doubt, is a popular delusion. A bird can fly for a
whole day, a fish can swim for a whole day, and a man can walk for a
whole day. If so, the bird requires no greater power than the fish, and
the fish than the man. The speed of the bird as compared with that of
the fish, or the speed of the fish as compared with that of the man, is
no criterion of the power exerted. The speed is only partly traceable
to the power. As has just been stated, it is due in a principal
measure to the shape and size of the travelling surfaces, the density
of the medium traversed, the resistance experienced to forward motion,
and the part performed by the mass of the animal, when moving and
acting upon its travelling surfaces. It is erroneous to suppose that a
bird is stronger, weight for weight, than a fish, or a fish than a man.
It is equally erroneous to assume that the exertions of a flying animal
are herculean as compared with those of a walking or swimming animal.
Observation and experiment incline me to believe just the opposite. A
flying creature, when fairly launched in space (because of the part
which weight plays in flight, and the little resistance experienced in
forward motion), sweeps through the air with almost no exertion.[6]
This is proved by the sailing flight of the albatross, and by the fact
that some insects can fly when two-thirds of their wing area have been
removed. (This experiment is detailed further on.) These observations
are calculated to show the grave necessity for studying the media to
be traversed; the fulcra which the media furnish, and the size, shape,
and movements of the travelling surfaces. The travelling surfaces of
animals, as has been already explained, furnish the levers by whose
instrumentality the movements of walking, swimming, and flying are
effected.

  [6] A flying creature exerts its greatest power when rising. The
  effort is of short duration, and inaugurates rather than perpetuates
  flight. If the volant animal can launch into space from a height, the
  preliminary effort may be dispensed with as in this case, the weight
  of the animal acting upon the inclined planes formed by the wings
  gets up the initial velocity.

By comparing the flipper of the seal, sea-bear, and walrus with the
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._]

_Active organs of Locomotion. Muscles, their Properties, Arrangement,
Mode of Action, etc._--If time and space had permitted, I would have
considered it my duty to describe, more or less fully, the muscular
arrangements of all the animals whose movements I propose to analyse.
This is the more desirable, as the movements exhibited by animals of
the higher types are directly referable to changes occurring in their
muscular system. As, however, I could not hope to overtake this task
within the limits prescribed for the present work, I shall content
myself by merely stating the properties of muscles; the manner in
which muscles act; and the manner in which they are grouped, with a
view to moving the osseous levers which constitute the bony framework
or skeleton of the animals to be considered. Hitherto, and by common
consent, it has been believed that whereas a flexor muscle is situated
on one aspect of a limb, and its corresponding extensor on the other
aspect, these two muscles must be opposed to and antagonize each other.
This belief is founded on what I regard as an erroneous assumption,
viz., that muscles have only the power of shortening, and that when
one muscle, say the flexor, shortens, it must drag out and forcibly
elongate the corresponding extensor, and the converse. This would be a
mere waste of power. Nature never works against herself. There are good
grounds for believing, as I have stated elsewhere,[14] that there is
no such thing as antagonism in muscular movements; the several muscles
known as flexors and extensors; abductors and adductors; pronators
and supinators, being simply correlated. Muscles, when they act,
operate upon bones or something extraneous to themselves, and not upon
each other. The muscles are folded round the extremities and trunks
of animals with a view to operating in masses. For this purpose they
are arranged in cycles, there being what are equivalent to extensor
and flexor cycles, abductor and adductor cycles, and pronator and
supinator cycles. Within these muscular cycles the bones, or extraneous
substances to be moved, are placed, and when one side of a cycle
shortens, the other side elongates. Muscles are therefore endowed with
a centripetal and centrifugal action. These cycles are placed at every
degree of obliquity and even at right angles to each other, but they
are so disposed in the bodies and limbs of animals that they always
operate consentaneously and in harmony. _Vide_ fig. 5, p. 25.

  [14] “Lectures on the Physiology of the Circulation in Plants, in the
  Lower Animals, and in Man.”--Edinburgh Medical Journal for January
  and February 1873.

There are in animals very few simple movements, _i.e._ movements
occurring in one plane and produced by the action of two muscles.
Locomotion is for the most part produced by the consentaneous action
of a great number of muscles; these or their fibres pursuing a variety
of directions. This is particularly true of the movements of the
extremities in walking, swimming, and flying.

Muscles are divided into the voluntary, the involuntary, and the
mixed, according as the will of the animal can wholly, partly, or in
no way control their movements. The voluntary muscles are principally
concerned in the locomotion of animals. They are the power which moves
the several orders of levers into which the skeleton of an animal
resolves itself.

The movements of the voluntary and involuntary muscles are essentially
wave-like in character, _i.e._ they spread from certain centres,
according to a fixed order, and in given directions. In the extremities
of animals the centripetal or converging muscular wave on one side of
the bone to be moved, is accompanied by a corresponding centrifugal or
diverging wave on the other side; the bone or bones by this arrangement
being perfectly under control and moved to a hair’s-breadth. The
centripetal or converging, and the centrifugal or diverging waves of
force are, as already indicated, correlated.[15] Similar remarks may
be made regarding the different parts of the body of the serpent
when creeping, of the body of the fish when swimming, of the wing of
the bird when flying, and of our own extremities when walking. In all
those cases the moving parts are thrown into curves or waves definitely
correlated.

  [15] Muscles virtually possess a pulling and pushing power; the
  pushing power being feeble and obscured by the flaccidity of the
  muscular mass. In order to push effectually, the pushing substance
  must be more or less rigid.

It may be broadly stated, that in every case locomotion is the result
of the opening and closing of opposite sides of muscular cycles. By
the closing or shortening, say of the flexor halves of the cycles, and
the opening or elongation of the extensor halves, the angles formed by
the osseous levers are diminished; by the closing or shortening of the
extensor halves of the cycles, and the opening or elongation of the
flexor halves, the angles formed by the osseous levers are increased.
This alternate diminution and increase of the angles formed by the
osseous levers produce the movements of walking, swimming, and flying.
The muscular cycles of the trunk and extremities are so disposed with
regard to the bones or osseous levers, that they in every case produce
a maximum result with a minimum of power. The origins and insertions of
the muscles, the direction of the muscles and the distribution of the
muscular fibres insure, that if power is lost in moving a lever, speed
is gained, there being an apparent but never a real loss. The variety
and extent of movement is secured by the obliquity of the muscular
fibres to their tendons; by the obliquity of the tendons to the bones
they are to move; and by the proximity of the attachment of the muscles
to the several joints. As muscles are capable of shortening and
elongating nearly a fourth of their length, they readily produce the
precise kind and degree of motion required in any particular case.[16]

  [16] The extensor muscles preponderate in mass and weight over the
  flexors, but this is readily accounted for by the fact, that the
  extensors, when limbs are to be straightened, always work at a
  mechanical disadvantage. This is owing to the shape of the bones,
  the conformation of the joints, and the position occupied by the
  extensors.

[Illustration:

  FIG. 6.--Wing of bird. Shows how the bones of the arm (_a_), forearm
  (_b_), and hand (_c_), are twisted, and form a conical screw. Compare
  with Figs. 7 and 8.--_Original._]

[Illustration: FIG. 7.  FIG. 8.

  FIG. 7.--Anterior extremity of elephant. Shows how the bones
  of the arm (_q_), forearm (_q´x_), and foot (_o_), are twisted to
  form an osseous screw. Compare with Figs. 6 and 8.--_Original._

  FIG. 8.--Cast or mould of the interior of the left ventricle of the
  heart of a deer. Shows that the left ventricular cavity is conical
  and spiral in its nature. _a_ Portion of right ventricular cavity;
  _b_, base of left ventricular cavity; _x_, _y_, spiral grooves
  occupied by the spiral _musculi papillares_; _j_, _q_, spiral ridges
  projecting between the _musculi papillares_. Compare with Figs. 6 and
  7.--_Original._]

The force of muscles, according to the experiments of Schwann,
increases with their length, and _vice versa_. It is a curious
circumstance, and worthy the attention of those interested in
homologies, that the voluntary muscles of the superior and inferior
extremities, and more especially of the trunk, are arranged in
longitudinal, transverse, and oblique spiral lines, and in layers or
strata precisely as in the ventricles of the heart and hollow muscles
generally.[17] If, consequently, I eliminate the element of bone from
these several regions, I reproduce a typical hollow muscle; and what is
still more remarkable, if I compare the bones removed (say the bones of
the anterior extremity of a quadruped or bird) with the cast obtained
from the cavity of a hollow muscle (say the left ventricle of the heart
of the mammal), I find that the bones and the cast are twisted upon
themselves, and form elegant screws, the threads or ridges of which run
in the same direction. This affords a proof that the involuntary hollow
muscles supply the type or pattern on which the voluntary muscles are
formed. Fig. 6 represents the bones of the wing of the bird; fig. 7 the
bones of the anterior extremity of the elephant; and fig. 8 the cast
or mould of the cavity of the left ventricle of the heart of the deer.

  [17] “On the Arrangement of the Muscular Fibres in the Ventricles
  of the Vertebrate Heart, with Physiological Remarks,” by the
  Author.--Philosophical Transactions, 1864.

  “On the Muscular Arrangements of the Bladder and Prostate, and
  the manner in which the Ureters and Urethra are closed,” by the
  Author.--Philosophical Transactions, 1867.

  “On the Muscular Tunics in the Stomach of Man and other Mammalia,” by
  the Author.--Proceedings Royal Society of London, 1867.

[Illustration: FIG. 9.--The Superficial Muscles in the Horse, (after
Bagg).]

It has been the almost invariable custom in teaching anatomy, and
such parts of physiology as pertain to animal movements, to place
much emphasis upon the configuration of the bony skeleton as a whole,
and the conformation of its several articular surfaces in particular.
This is very natural, as the osseous system stands the wear and tear
of time, while all around it is in a great measure perishable. It is
the link which binds extinct forms to living ones, and we naturally
venerate and love what is enduring. It is no marvel that Oken, Goethe,
Owen, and others should have attempted such splendid generalizations
with regard to the osseous system--should have proved with such cogency
of argument that the head is an expanded vertebra. The bony skeleton
is a miracle of design very wonderful and very beautiful in its way.
But when all has been said, the fact remains that the skeleton, when
it exists, forms only an adjunct of locomotion and motion generally.
All the really essential movements of an animal occur in its soft
parts. The osseous system is therefore to be regarded as secondary
in importance to the muscular, of which it may be considered a
differentiation. Instead of regarding the muscles as adapted to the
bones, the bones ought to be regarded as adapted to the muscles. Bones
have no power either of originating or perpetuating motion. This begins
and terminates in the muscles. Nor must it be overlooked, that bone
makes its appearance comparatively late in the scale of being; that
innumerable creatures exist in which no trace either of an external
or internal skeleton is to be found; that these creatures move freely
about, digest, circulate their nutritious juices and blood when
present, multiply, and perform all the functions incident to life.
While the skeleton is to be found in only a certain proportion of the
animals existing on our globe, the soft parts are to be met with in
all; and this appears to me an all-sufficient reason for attaching
great importance to the movements of soft parts, such as protoplasm,
jelly masses, involuntary and voluntary muscles, etc.[18] As the
muscles of vertebrates are accurately applied to each other, and to
the bones, while the bones are rigid, unyielding, and incapable of
motion, it follows that the osseous system acts as a break or boundary
to the muscular one,--and hence the arbitrary division of muscles
into extensors and flexors, pronators and supinators, abductors and
adductors. This division although convenient is calculated to mislead.
The most highly organized animal is strictly speaking to be regarded as
a living mass whose parts (hard, soft, and otherwise) are accurately
adapted to each other, every part reciprocating with scrupulous
exactitude, and rendering it difficult to determine where motion begins
and where it terminates. Fig. 9 shows the more superficial of the
muscular masses which move the bones or osseous levers of the horse,
as seen in the walk, trot, gallop, etc. A careful examination of these
carneous masses or muscles will show that they run longitudinally,
transversely, and obliquely, the longitudinal and transverse muscles
crossing each other at nearly right angles, the oblique ones tending to
cross at various angles, as in the letter X. The crossing is seen to
most advantage in the deep muscles.

  [18] Lectures “On the Physiology of the Circulation in Plants, in the
  Lower Animals, and in Man,” by the Author.--Edinburgh Medical Journal
  for September 1872.

In order to understand the twisting which occurs to a greater or less
extent in the bodies and extremities (when present) of all vertebrated
animals, it is necessary to reduce the bony and muscular systems
to their simplest expression. If motion is desired in a dorsal,
ventral, or lateral direction only, a dorsal and ventral or a right
and left lateral set of longitudinal muscles acting upon straight
bones articulated by an ordinary ball-and-socket joint will suffice.
In this case the dorsal, ventral, and right and left lateral muscles
form _muscular cycles_; contraction or shortening on the one aspect
of the cycle being accompanied by relaxation or elongation on the
other, the bones and joints forming as it were the diameters of the
cycles, and oscillating in a backward, forward, or lateral direction
in proportion to the degree and direction of the muscular movements.
Here the motion is confined to two planes intersecting each other at
right angles. When, however, the muscular system becomes more highly
differentiated, both as regards the number of the muscles employed,
and the variety of the directions pursued by them, the bones and
joints also become more complicated. Under these circumstances, the
bones, as a rule, are twisted upon themselves, and their articular
surfaces present various degrees of spirality to meet the requirements
of the muscular system. Between the straight longitudinal muscles,
therefore, arranged in dorsal and ventral, and right and left lateral
sets, and those which run in a more or less transverse direction, and
between the simple joint whose motion is confined to one plane and the
ball-and-socket joints whose movements are universal, every degree of
obliquity is found in the direction of the muscles, and every possible
modification in the disposition of the articular surfaces. In the fish
the muscles are for the most part arranged in dorsal, ventral, and
lateral sets, which run longitudinally; and, as a result, the movements
of the trunk, particularly towards the tail, are from side to side
and sinuous. As, however, oblique fibres are also present, and the
tendons of the longitudinal muscles in some instances cross obliquely
towards the tail, the fish has also the power of tilting or twisting
its trunk (particularly the lower half) as well as the caudal fin. In
a mackerel which I examined, the oblique muscles were represented by
the four lateral masses occurring between the dorsal, ventral, and
lateral longitudinal muscles--two of these being found on either side
of the fish, and corresponding to the myocommas or “_grand muscle
latéral_” of Cuvier. The muscular system of the fish would therefore
seem to be arranged on a fourfold plan,--there being four sets of
longitudinal muscles, and a corresponding number of slightly oblique
and oblique muscles, the oblique muscles being spiral in their nature
and tending to cross or intersect at various angles, an arrest of the
intersection, as it appears to me, giving rise to the myocommas and to
that concentric arrangement of their constituent parts so evident on
transverse section. This tendency of the muscular fibres to cross each
other at various degrees of obliquity may also be traced in several
parts of the human body, as, for instance, in the deltoid muscle of
the arm and the deep muscles of the leg. Numerous other examples
of penniform muscles might be adduced. Although the fibres of the
myocommas have a more or less longitudinal direction, the myocommas
themselves pursue an oblique spiral course from before backwards and
from within outwards, _i.e._ from the spine towards the periphery,
where they receive slightly oblique fibres from the longitudinal
dorsal, ventral, and lateral muscles. As the spiral oblique myocommas
and the oblique fibres from the longitudinal muscles act directly and
indirectly upon the spines of the vertebræ, and the vertebræ themselves
to which they are specially adapted, and as both sets of oblique fibres
are geared by interdigitation to the fourfold set of longitudinal
muscles, the lateral, sinuous, and rotatory movements of the body and
tail of the fish are readily accounted for. The spinal column of the
fish facilitates the lateral sinuous twisting movements of the tail and
trunk, from the fact that the vertebræ composing it are united to each
other by a series of modified universal joints--the vertebræ supplying
the cup-shaped depressions or sockets, the intervertebral substance,
the prominence or ball.

The same may be said of the general arrangement of the muscles in the
trunk and tail of the Cetacea, the principal muscles in this case
being distributed, not on the sides, but on the dorsal and ventral
aspects. The lashing of the tail in the whales is consequently from
above downwards or vertically, instead of from side to side. The spinal
column is jointed as in the fish, with this difference, that the
vertebræ (especially towards the tail) form the rounded prominences or
ball, the meniscus or cup-shaped intervertebral plates the receptacles
or socket.

When limbs are present, the spine may be regarded as being ideally
divided, the spiral movements, under these circumstances, being thrown
upon the extremities by typical ball-and-socket joints occurring at the
shoulders and pelvis. This is peculiarly the case in the seal, where
the spirally sinuous movements of the spine are transferred directly to
the posterior extremities.[19]

  [19] That the movements of the extremities primarily emanate from
  the spine is rendered probable by the remarkable powers possessed by
  serpents. “It is true,” writes Professor Owen (_op. cit._ p. 261),
  “that the serpent has no limbs, yet it can outclimb the monkey,
  outswim the fish, outleap the jerboa, and, suddenly loosing the close
  coils of its crouching spiral, it can spring into the air and seize
  the bird upon the wing.” ... “The serpent has neither hands nor
  talons, yet it can outwrestle the athlete, and crush the tiger in the
  embrace of its ponderous overlapping folds.” The peculiar endowments,
  which accompany the possession of extremities, it appears to me,
  present themselves in an undeveloped or latent form in the trunk of
  the reptile.

The extremities, when present, are provided with their own muscular
cycles of extensor and flexor, abductor and adductor, pronator and
supinator muscles,--these running longitudinally and at various
degrees of obliquity, and enveloping the hard parts according to their
direction--the bones being twisted upon themselves and furnished
with articular surfaces which reflect the movements of the muscular
cycles, whether these occur in straight lines anteriorly, posteriorly,
or laterally, or in oblique lines in intermediate situations. The
straight and oblique muscles are principally brought into play in the
movements of the extremities of quadrupeds, bipeds, etc. in walking;
in the movements of the tails and fins of fishes, whales, etc. in
swimming; and in the movements of the wings of insects, bats, and
birds in flying. The straight and oblique muscles are usually found
together, and co-operate in producing the movements in question; the
amount of rotation in a part always increasing as the oblique muscles
preponderate. The combination of ball-and-socket and hinge-joints, with
their concomitant oblique and longitudinal muscular cycles (the former
occurring in their most perfect forms where the extremities are united
to the trunk, the latter in the extremities themselves), enable the
animal to present, when necessary, an extensive resisting surface the
one instant, and a greatly diminished and a comparatively non-resisting
one the next. This arrangement secures the subtlety and nicety of
motion demanded by the several media at different stages of progression.

[Illustration: FIG. 10.  FIG. 11.  FIG. 12.  FIG. 13.  FIG. 14.

  FIG. 10.--Extreme form of compressed foot, as seen in the deer, ox,
  etc., adapted specially for land transit.--_Original._

  FIG. 11.--Extreme form of expanded foot, as seen in the
  _Ornithorhynchus_, etc., adapted more particularly for
  swimming.--_Original._

  FIGS. 12 and 13.--Intermediate form of foot, as seen in the otter
  (fig. 12), frog (fig. 13), etc. Here the foot is equally serviceable
  in and out of the water.--_Original._

  FIG. 14.--Foot of the seal, which opens and closes in the act of
  natation, the organ being folded upon itself during the non-effective
  or return stroke, and expanded during the effective or forward
  stroke. Due advantage is taken of this arrangement by the seal when
  swimming, the animal rotating on its long axis, so as to present the
  lower portion of the body and the feet obliquely to the water during
  the return stroke, and the flat, or the greatest available surface of
  both, during the effective or forward stroke.--_Original._]

_The travelling surfaces of Animals modified and adapted to the medium
on or in which they move._--In those land animals which take to the
water occasionally, the feet, as a rule, are furnished with membranous
expansions extending between the toes. Of such the Otter (fig. 12),
Ornithorhynchus (fig. 11), Seal (fig. 14), Crocodile, Sea-Bear
(fig. 37, p. 76), Walrus, Frog (fig. 13), and Triton, may be cited.
The crocodile and triton, in addition to the membranous expansion
occurring between the toes, are supplied with a powerful swimming-tail,
which adds very materially to the surface engaged in natation. Those
animals, one and all, walk awkwardly, it always happening that when
the extremities are modified to operate upon two essentially different
media (as, for instance, the land and water), the maximum of speed is
attained in neither. For this reason those animals which swim the best,
walk, as a rule, with the greatest difficulty, and _vice versâ_, as the
movements of the auk and seal in and out of the water amply testify.

In addition to those land animals which run and swim, there are
some which precipitate themselves, parachute-fashion, from immense
heights, and others which even fly. In these the membranous expansions
are greatly increased, the ribs affording the necessary support in
the Dragon or Flying Lizard (fig. 15), the anterior and posterior
extremities and tail, in the Flying Lemur (fig. 16) and Bat (fig. 17,
p. 36).

[Illustration: FIG. 15. FIG. 16.

  FIG. 15.--The Red-throated Dragon (_Draco hæmatopogon_, Gray) shows
  a large membranous expansion (_b b_) situated between the anterior
  (_d d_) and posterior extremities, and supported by the ribs. The
  dragon by this arrangement can take extensive leaps with perfect
  safety.--_Original._

  FIG. 16.--The Flying Lemur _Galeopithecus volans_, Shaw. In the
  flying lemur the membranous expansion (_a b_) is more extensive than
  in the Flying Dragon (fig. 15). It is supported by the neck, back,
  and tail, and by the anterior and posterior extremities. The flying
  lemur takes enormous leaps; its membranous tunic all but enabling it
  to fly. The Bat, _Phyllorhina gracilis_ (fig. 17), flies with a very
  slight increase of surface. The surface exposed by the bat exceeds
  that displayed by many insects and birds. The wings of the bat are
  deeply concave, and so resemble the wings of beetles and heavy-bodied
  short-winged birds. The bones of the arm (_r_), forearm (_d_), and
  hand (_n, n, n_) of the bat (fig. 17) support the anterior or thick
  margin and the extremity of the wing, and may not inaptly be compared
  to the nervures in corresponding positions in the wing of the
  beetle.--_Original._]

[Illustration:

  FIG. 17.--The Bat (_Phyllorhina gracilis_, Peters). Here the
  travelling-surfaces (_r d e f_, _a n n n_) are enormously increased
  as compared with that of the land and water animals generally.
  Compare with figures from 10 to 14, p. 34. _r_ Arm of bat; _d_
  forearm of bat; _e f_, _n n n_ hand of bat.--_Original._]

Although no lizard is at present known to fly, there can be little
doubt that the extinct Pterodactyles (which, according to Professor
Huxley, are intermediate between the lizards and crocodiles) were
possessed of this power. The bat is interesting as being the only
mammal at present endowed with wings sufficiently large to enable it to
fly.[20] It affords an extreme example of modification for a special
purpose,--its attenuated body, dwarfed posterior, and greatly elongated
anterior extremities, with their enormous fingers and outspreading
membranes, completely unfitting it for terrestrial progression. It is
instructive as showing that flight may be attained, without the aid of
hollow bones and air-sacs, by purely muscular efforts, and by the mere
diminution and increase of a continuous membrane.

  [20] The Vampire Bat of the Island of Bonin, according to Dr.
  Buckland, can also swim; and this authority was of opinion that the
  Pterodactyle enjoyed similar advantages.--Eng. Cycl. vol. iv. p. 495.

As the flying lizard, flying lemur, and bat (figs. 15, 16, and
17, pp. 35 and 36), connect terrestrial progression with aërial
progression, so the auk, penguin (fig. 46, p. 91), and flying-fish
(fig. 51, p. 98), connect progression in the water with progression in
the air. The travelling surfaces of these anomalous creatures run the
movements peculiar to the three highways of nature into each other,
and bridge over, as it were, the gaps which naturally exist between
locomotion on the land, in the water, and in the air.




PROGRESSION ON THE LAND.


_Walking of the Quadruped, Biped, etc._--As the earth, because of
its solidity, will bear any amount of pressure to which it may be
subjected, the size, shape, and weight of animals destined to traverse
its surface are matters of little or no consequence. As, moreover, the
surface trod upon is rigid or unyielding, the extremities of quadrupeds
are, as a rule, terminated by small feet. Fig. 18 (contrast with
fig. 17).

[Illustration:

  FIG. 18.--Chillingham Bull (_Bos Scoticus_). Shows powerful heavy
  body, and the small extremities adapted for land transit. Also the
  figure-of-8 movements made by the feet and limbs in walking and
  running. _u_, _t_ Curves made by right and left anterior extremities.
  _r_, _s_ Curves made by right and left posterior extremities. The
  right fore and the left hind foot move together to form the waved
  line (_s_, _u_); the left fore and the right hind foot move together
  to form the waved line (_r_, _t_). The curves formed by the anterior
  (_t_, _u_) and posterior (_r_, _s_) extremities form ellipses.
  Compare with fig. 19, p. 39.--_Original._]

In this there is a double purpose--the limited area presented to the
ground affording the animal sufficient support and leverage, and
enabling it to disentangle its feet with the utmost facility, it
being a condition in rapid terrestrial progression that the points
presented to the earth be few in number and limited in extent, as
this approximates the feet of animals most closely to the wheel in
mechanics, where the surface in contact with the plane of progression
is reduced to a minimum. When the surface presented to a dense
resisting medium is increased, speed is diminished, as shown in the
tardy movements of the mollusc, caterpillar, and slowworm, and also,
though not to the same extent, in the serpents, some of which move
with considerable celerity. In the gecko and common house-fly, as
is well known, the travelling surfaces are furnished with suctorial
discs, which enable those creatures to walk, if need be, in an inverted
position; and “the tree-frogs (_Hyla_) have a concave disc at the end
of each toe, for climbing and adhering to the bark and leaves of trees.
Some toads, on the other hand, are enabled, by peculiar tubercles or
projections from the palm or sole, to clamber up old walls.”[21] A
similar, but more complicated arrangement, is met with in the arms of
the cuttle-fish.

  [21] Comp. Anat. and Phys. of Vertebrates, by Professor Owen, vol. i.
  pp. 262, 263. Lond. 1866.

The movements of the extremities in land animals vary considerably.

In the kangaroo and jerboa,[22] the posterior extremities only are
used, the animals advancing _per saltum_, _i.e._ by a series of
leaps.[23]

  [22] The jerboa when pursued can leap a distance of nine feet, and
  repeat the leaps so rapidly that it cannot be overtaken even by the
  aid of a swift horse. The bullfrog, a much smaller animal, can, when
  pressed, clear from six to eight feet at each bound, and project
  itself over a fence five feet high.

  [23] The long, powerful tail of the kangaroo assists in maintaining
  the equilibrium of the animal prior to the leaps; the posterior
  extremities and tail forming a tripod of support.

The deer also bounds into the air in its slower movements; in its
fastest paces it gallops like the horse, as explained at pp. 40–44.
The posterior extremities of the kangaroo are enormously developed
as compared with the anterior ones; they are also greatly elongated.
The posterior extremities are in excess, likewise, in the horse,
rabbit,[24] agouti, and guinea pig. As a consequence these animals
descend declivities with difficulty. They are best adapted for slightly
ascending ground. In the giraffe the anterior extremities are longer
and more powerful, comparatively, than the posterior ones, which is
just the opposite condition to that found in the kangaroo.

  [24] The rabbit occasionally takes several short steps with the fore
  legs and one long one with the hind legs; so that it walks with the
  fore legs, and leaps with the hind ones.

In the giraffe the legs of opposite sides move together and alternate,
whereas in most quadrupeds the extremities move diagonally--a remark
which holds true also of ourselves in walking and skating, the right
leg and left arm advancing together and alternating with the left leg
and right arm (fig. 19).

[Illustration:

  FIG. 19.--Diagram showing the figure-of-8 or double-waved track
  produced by the alternating of the extremities in man in walking
  and running; the right leg (_r_) and left arm (_s_) advancing
  simultaneously to form one step; and alternating with the left
  leg (_t_) and right arm (_u_), which likewise advance together to
  form a second step. The continuous line (_r_, _t_) gives the waved
  track made by the legs; the interrupted line (_s_, _u_) that made
  by the arms. The curves made by the right leg and left arm, and by
  the left leg and right arm, form ellipses. Compare with fig. 18,
  p. 37.--_Original._]

In the hexapod insects, according to Müller, the fore and hind foot
of the one side and the middle one of the opposite side move together
to make one step, the three corresponding and opposite feet moving
together to form the second step. Other and similar combinations are
met with in the decapods.

The alternating movements of the extremities are interesting as
betokening a certain degree of flexuosity or twisting, either in the
trunk or limbs, or partly in the one and partly in the other.

This twisting begets the figure-of-8 movements observed in walking,
swimming, and flying. (Compare figs. 6, 7, and 26 _x_, pp. 28 and
55; figs. 18 and 19, pp. 37 and 39; figs. 32 and 50, pp. 68 and 97;
figs. 71 and 73, p. 144; and fig. 81, p. 157.)

_Locomotion of the Horse._--As the limits of the present volume
forbid my entering upon a consideration of the movements of all the
animals with terrestrial habits, I will describe briefly, and by
way of illustration, those of the horse, ostrich, and man. In the
horse, as in all quadrupeds endowed with great speed, the bones of
the extremities are inclined obliquely towards each other to form
angles; the angles diminishing as the speed increases. Thus the angles
formed by the bones of the extremities with each other and with the
scapulæ and iliac bones, are less in the horse than in the elephant.
For the same reason they are less in the deer than in the horse. In
the elephant, where no great speed is required, the limbs are nearly
straight, this being the best arrangement for supporting superincumbent
weight. The angles formed by the different bones of the wing of the
bird are less than in the fleetest quadruped, the movements of wings
being more rapid than those of the extremities of quadrupeds and
bipeds. These are so many mechanical adaptations to neutralize shock,
to increase elasticity, and secure velocity. The paces of the horse
are conveniently divided into the walk, the trot, the amble, and the
gallop. If the horse begins his walk by raising his near fore foot,
the order in which the feet are lifted is as follows:--first the left
fore foot, then the right or diagonal hind foot, then the right fore
foot, and lastly the left or diagonal hind foot. There is therefore
a twisting of the body and spiral overlapping of the extremities of
the horse in the act of walking, in all respects analogous to what
occurs in other quadrupeds[25] and in bipeds (figs. 18 and 19, pp. 37
and 39). In the slowest walk Mr. Gamgee observes “that three feet are
in constant action on the ground, whereas in the free walk in which
the hind foot passes the position from which the parallel fore foot
moves, there is a fraction of time when only two feet are upon the
ground, but the interval is too short for the eye to measure it. The
proportion of time, therefore, during which the feet act upon the
ground, to that occupied in their removal to new positions, is as
three to one in the slow, and a fraction less in the fast walk. In the
fast gallop these proportions are as five to three. In all the paces
the power of the horse is being exerted mainly upon a fore and hind
limb, with _the feet implanted in diagonal positions_. There is also a
constant parallel line of positions kept up by a fore and hind foot,
_alternating sides_ in each successive move. These relative positions
are renewed and maintained. Thus each fore limb assumes, as it alights,
the advanced position parallel with the hind, just released and moving;
the hind feet move by turns, in sequence to their diagonal fore, and
in priority to their parallel fellows, which following they maintain
for nearly half their course, when the fore in its turn is raised and
carried to its destined place, the hind alighting midway. All the feet
passing over equal distances and keeping the same time, no interference
of the one with the other occurs, and each successive hind foot as it
is implanted forms a new diagonal with the opposite fore, the latter
forming the front of the parallel in one instant, and one of the
diagonal positions in the next: while in the case of the hind, they
assume the diagonal on alighting and become the terminators of the
parallel in the last part of their action.”

  [25] If a cat when walking is seen from above, a continuous wave
  of movement is observed travelling along its spine from before
  backwards. This movement closely resembles the crawling of the
  serpent and the swimming of the eel.

[Illustration:

  FIG. 20.--Horse in the act of trotting. In this, as in all the
  other paces, the body of the horse is levered forward by a diagonal
  twisting of the trunk and extremities, the extremities describing a
  figure-of-8 track (_s u_, _r t_). The figure-of-8 is produced by the
  alternate play of the extremities and feet, two of which are always
  on the ground (_a_, _b_). Thus the right fore foot describes the
  curve marked _t_, the left hind foot that marked _r_, the left fore
  foot that marked _u_, and the right hind foot that marked _s_. The
  feet on the ground in the present instance are the left fore and the
  right hind. Compare with figs. 18 and 19, pp. 37 and 39.--_Original._]

In the trot, according to Bishop, the legs move in pairs diagonally.
The same leg moves rather oftener during the same period in trotting
than in walking, or as six to five. The velocity acquired by moving the
legs in pairs, instead of consecutively, depends on the circumstance
that in the trot each leg rests on the ground during a short interval,
and swings during a long one; whilst in walking each leg swings a
short, and rests a long period. The undulations arising from the
projection of the trunk in the trot are chiefly in the vertical plane;
in the walk they are more in the horizontal.

The gallop has been erroneously believed to consist of a series of
bounds or leaps, the two hind legs being on the ground when the two
fore legs are in the air, and _vice versâ_, there being a period when
all four are in the air. Thus Sainbell in his “Essay on the Proportions
of Eclipse,” states “that the gallop consists of a repetition of
bounds, or leaps, more or less high, and more or less extended in
proportion to the strength and lightness of the animal.” A little
reflection will show that this definition of the gallop cannot be the
correct one. When a horse takes a ditch or fence, he gathers himself
together, and by a vigorous effort (particularly of the hind legs),
throws himself into the air. This movement requires immense exertion
and is short-lived. It is not in the power of any horse to repeat these
bounds for more than a few minutes, from which it follows that the
gallop, which may be continued for considerable periods, must differ
very materially from the leap.

The pace known as the amble is an artificial movement, produced by the
cunning of the trainer. It resembles that of the giraffe, where the
right fore and right hind foot move together to form one step; the
left fore and left hind foot moving together to form the second step.
By the rapid repetition of these movements the right and left sides of
the body are advanced alternately by a lateral swinging motion, very
comfortable for the rider, but anything but graceful. The amble is a
defective pace, inasmuch as it interferes with the diagonal movements
of the limbs, and impairs the continuity of motion which the twisting,
cross movement begets. Similar remarks might be made of the gallop if
it consisted (which it does not) of a series of bounds or leaps, as
each bound would be succeeded by a halt, or dead point, that could not
fail seriously to compromise continuous forward motion. In the gallop,
as in the slower movements, the horse has never less than two feet on
the ground at any instant of time, no two of the four feet being in
exactly the same position.

Mr. Gamgee, who has studied the movements of the horse very carefully,
has given diagrams of the walk, trot, and gallop, drawn to a scale of
the feet of a two-year-old colt in training, which had been walked,
trotted, and galloped over the ground for the purpose. The point he
sought to determine was the exact distance through which each foot was
carried from the place where it was lifted to that where it alighted.
The diagrams are reproduced at figures 21, 22, and 23. In figure 23
I have added a continuous waved line to indicate the alternating
movements of the extremities; Mr. Gamgee at the time he wrote[26]
being, he informs me, unacquainted with the figure-of-8 theory of
animal progression as subsequently developed by me. Compare fig. 23
with figs. 18 and 19, pp. 37 and 39; with fig. 50, p. 97; and with
figs. 71 and 73, p. 144.

  [26] “On the Breeding of Hunters and Roadsters.” Prize
  Essay.--Journal of Royal Agricultural Society for 1863.

[Illustration: FIG. 21. WALK.]

[Illustration: FIG. 22. TROT.]

[Illustration: FIG. 23. GALLOP.]

In examining figures 21, 22, and 23, the reader will do well to
remember that the _near_ fore and hind feet of a horse are the _left_
fore and hind feet; the _off_ fore and hind feet being the _right_ fore
and hind feet. The terms _near_ and _off_ are technical expressions,
and apply to the left and right sides of the animal. Another point to
be attended to in examining the figures in question, is the relation
which exists between the fore and hind feet of the near and off sides
of the body. In slow walking the near hind foot is planted behind the
imprint made by the near fore foot. In rapid walking, on the contrary,
the near hind foot is planted from six to twelve or more inches in
advance of the imprint made by the near fore foot (fig. 21 represents
the distance as eleven inches). In the trot the near hind foot is
planted from twelve to eighteen or more inches in advance of the
imprint made by the near fore foot (fig. 22 represents the distance
as nineteen inches). In the gallop the near hind foot is planted 100
or more inches in advance of the imprint made by the near fore foot
(fig. 23 represents the distance as 110-1/2 inches). The distance by
which the near hind foot passes the near fore foot in rapid walking,
trotting, and galloping, increases in a progressive ratio, and is due
in a principal measure to the velocity or momentum acquired by the mass
of the horse in rapid motion; the body of the animal carrying forward
and planting the limbs at greater relative distances in the trot than
in the rapid walk, and in the gallop than in the trot. I have chosen to
speak of the near hind and near fore feet, but similar remarks may of
course be made of the off hind and off fore feet.

“At fig. 23, which represents the gallop, the distance between two
successive impressions produced, say by the near fore foot, is eighteen
feet one inch and a half. Midway between these two impressions is
the mark of the near hind foot, which therefore subdivides the space
into nine feet and six-eighths of an inch, but each of these is again
subdivided into two halves by the impressions produced by the off fore
and off hind feet. It is thus seen that the horse’s body instead of
being propelled through the air by bounds or leaps even when going at
the highest attainable speed, acts on a system of levers, the mean
distance between the points of resistance of which is four feet six
inches. The exact length of stride, of course, only applies to that of
the particular horse observed, and the rate of speed at which he is
going. In the case of any one animal, the greater the speed the longer
is the individual stride. In progression, the body moves before a limb
is raised from the ground, as is most readily seen when the horse is
beginning its slowest action, as in traction.”[27]

  [27] Gamgee in Journal of Anatomy and Physiology, vol. iii. pp. 375,
  376.

At fig. 22, which represents the trot, the stride is ten feet one
inch. At fig. 21, which represents the walk, it is only five feet five
inches. The speed acquired, Mr. Gamgee points out, determines the
length of stride; the length of stride being the effect and evidence of
speed and not the cause of it. The momentum acquired in the gallop, as
already explained, greatly accelerates speed.

“In contemplating length of strides, with reference to the fulcra,
allowance has to be made for the length of the feet, which is to be
deducted from that of the strides, because the apex, or toe of the
horse’s hind foot forms the fulcrum in one instant, and the heel of
the fore foot in the next, and _vice versâ_. This phenomenon is very
obvious in the action of the human foot, and is remarkable also for the
range of leverage thus afforded in some of the fleetest quadrupeds, of
different species. In the hare, for instance, between the point of its
hock and the termination of its extended digits, there is a space of
upwards of six inches of extent of leverage and variation of fulcrum,
and in the fore limb from the _carpus_ to the toe-nails (whose function
in progression is not to be underrated) upwards of three inches of
leverage are found, being about ten inches for each lateral biped, and
the double of that for the action of all four feet. Viewed in this
way the stride is not really so long as would be supposed if merely
estimated from the space between the footprints.

“Many interesting remarks might be made on the length of the stride of
various animals; the full movement of the greyhound is, for instance,
upwards of sixteen feet; that of the hare at least equal; whilst that
of the Newfoundland dog is a little over nine feet.”[27]

_Locomotion of the Ostrich._--Birds have been divided by naturalists
into eight orders:--the _Natatores_, or Swimming Birds; the
_Grallatores_, or Wading Birds; the _Cursores_, or Running Birds; the
_Scansores_, or Climbers; the _Rasores_, or Scrapers; the _Columbæ_,
or Doves; the _Passeres_; and the _Raptores_, or Birds of Prey.

The first five orders have been classified according to their habits
and modes of progression. The _Natatores_ I shall consider when I come
to speak of swimming as a form of locomotion, and as there is nothing
in the movements of the wading, scraping, and climbing birds,[28] or
in the _Passeres_[29] or _Raptores_, requiring special notice, I shall
proceed at once to a consideration of the _Cursores_, the best examples
of which are the ostrich, emu, cassowary, and apteryx.

  [28] The woodpeckers climb by the aid of the stiff feathers of their
  tails; the legs and tail forming a firm basis of support.

  [29] In this order there are certain birds--the sparrows and
  thrushes, for example--which advance by a series of vigorous leaps;
  the leaps being of an intermitting character.

The ostrich is remarkable for the great length and development of
its legs as compared with its wings (fig. 24). In this respect it is
among birds what the kangaroo is among mammals. The ostrich attains
an altitude of from six to eight feet, and is the largest living bird
known. Its great height is due to its attenuated neck and legs. The
latter are very powerful structures, and greatly resemble in their
general conformation the posterior extremities of a thoroughbred
horse or one of the larger deer--compare with fig. 4, p. 21. They
are expressly made for speed. Thus the bones of the leg and foot are
inclined very obliquely towards each other, the femur being inclined
very obliquely to the ilium. As a consequence the angles made by the
several bones of the legs are comparatively small; smaller in fact than
in either the horse or deer.

[Illustration:

  FIG. 24.--Skeleton of the Ostrich. Shows the powerful legs, small
  feet, and rudimentary wings of the bird; the obliquity at which the
  bones of the legs and wings are placed, and the comparatively small
  angles which any two bones make at their point of junction. _a_ Angle
  made by femur with ilium. _b_ Angle made by tibia and fibula with
  femur. _c_ Angle made by tarso-metatarsal bone with tibia and fibula.
  _d_ Angle made by bones of foot with tarso-metatarsal bone. _r_ Bones
  of wing inclined to each other at nearly right angles. Compare with
  fig. 4, p. 21, fig. 26, p. 55, and fig. 27, p. 59.--Adapted from
  Dallas.]

The feet of the ostrich, like those of the horse and deer, are reduced
to a minimum as regards size; so that they occasion very little
friction in the act of walking and running. The foot is composed of two
jointed toes,[30] which spread out when the weight of the body comes
upon them, in such a manner as enables the bird to seize and let go
the ground with equal facility. The advantage of such an arrangement
in rapid locomotion cannot be over-estimated. The elasticity and
flexibility of the foot contribute greatly to the rapidity of movement
for which this celebrated bird is famous. The limb of the ostrich, with
its large bones placed very obliquely to form a system of powerful
levers, is the very embodiment of speed. The foot is quite worthy of
the limb, it being in some respects the most admirable structure of its
kind in existence. The foot of the ostrich differs considerably from
that of all other birds, those of its own family excepted. Thus the
under portion of the foot is flat, and specially adapted for acting
on plane surfaces, particularly solids.[31] The extremities of the
toes superiorly are armed with powerful short nails, the tips of which
project inferiorly to protect the toes and confer elasticity when the
foot is leaving the ground. The foot, like the leg, is remarkable
for its great strength. The legs of the ostrich are closely set,
another feature of speed.[32] The wings of the ostrich are in a very
rudimentary condition as compared with the legs.[33] All the bones are
present, but they are so dwarfed that they are useless as organs of
flight. The angles which the bones of the wing make with each other,
are still less than the angles made by the bones of the leg. This
is just what we would _a priori_ expect, as the velocity with which
wings are moved greatly exceeds that with which legs are moved. The
bones of the wing of the ostrich are inclined towards each other at
nearly right angles. The wings of the ostrich, although useless as
flying organs, form important auxiliaries in running. When the ostrich
careers along the plain, he spreads out his wings in such a manner that
they act as balancers, and so enable him to maintain his equilibrium
(fig. 25). The wings, because of the angle of inclination which their
under surfaces make with the horizon, and the great speed at which
the ostrich travels, act like kites, and so elevate and carry forward
by a mechanical adaptation a certain proportion of the mass of the
bird already in motion. The elevating and propelling power of even
diminutive inclined planes is very considerable, when carried along
at a high speed in a horizontal direction. The wings, in addition
to their elevating and propelling power, contribute by their short,
rapid, swinging movements, to continuity of motion in the legs. No bird
with large wings can run well. The albatross, for example, walks with
difficulty, and the same may be said of the vulture and eagle. What,
therefore, appears a defect in the ostrich, is a positive advantage
when its habits and mode of locomotion are taken into account.

  [30] The toes in the emu amount to three.

  [31] Feet designed for swimming, grasping trees, or securing prey, do
  not operate to advantage on a flat surface. The awkward waddle of the
  swan, parrot, and eagle when on the ground affords illustrations.

  [32] In draught horses the legs are much wider apart than in racers;
  the legs of the deer being less widely set than those of the racer.

  [33] In the apteryx the wings are so very small that the bird is
  commonly spoken of as the “wingless bird.”

[Illustration: FIG. 25.--Ostriches pursued by a Hunter.]

Professional runners in many cases at matches reduce the length of
their anterior extremities by flexing their arms and carrying them
on a level with their chest (fig. 28, p. 62). It would seem that in
rapid running there is not time for the arms to oscillate naturally,
and that under these circumstances the arms, if allowed to swing
about, <DW44> rather than increase the speed. The centre of gravity
is well forward in the ostrich, and is regulated by the movements of
the head and neck, and the obliquity of the body and legs. In running
the neck is stretched, the body inclined forward, and the legs moved
alternately and with great rapidity. When the right leg is flexed and
elevated, it swings forward pendulum-fashion, and describes a curve
whose convexity is directed towards the right side. When the left leg
is flexed and elevated, it swings forward and describes a curve whose
convexity is directed towards the left side. The curves made by the
right and left legs form when united a waved line (_vide_ figs. 18, 19,
and 20, pp. 37, 39, and 41). When the right leg is flexed, elevated,
and advanced, it rotates upon the iliac portion of the trunk of the
bird, the trunk being supported for the time being by the left leg,
which is extended, and in contact with the ground. When the left leg
is flexed, elevated, and advanced, it in like manner rotates upon the
trunk, supported in this instance by the extended right leg. The leg
which is on the ground for the time being supplies the necessary lever,
the ground the fulcrum. When the right leg is flexed and elevated, it
rotates upon the iliac portion of the trunk in a forward direction,
the right foot describing the arc of a circle. When the right leg and
foot are extended and fixed on the ground, the trunk rotates upon the
right foot in a forward direction to form the arc of a circle, which is
the converse of that formed by the right foot. If the arcs alternately
supplied by the right foot and trunk are placed in opposition, a more
or less perfect circle is produced, and thus it is that the locomotion
of animals is approximated to the wheel in mechanics. Similar remarks
are to be made of the left foot and trunk. The alternate rolling of the
trunk on the extremities, and the extremities on the trunk, utilizes
or works up the inertia of the moving mass, and powerfully contributes
to continuity and steadiness of action in the moving parts. By
advancing the head, neck, and anterior parts of the body, the ostrich
inaugurates the rolling movement of the trunk, which is perpetuated by
the rolling movements of the legs. The trunk and legs of the ostrich
are active and passive by turns. The movements of the trunk and limbs
are definitely co-ordinated. But for this reciprocation the action of
the several parts implicated would neither be so rapid, certain, nor
continuous. The speed of the ostrich exceeds that of every other land
animal, a circumstance due to its long, powerful legs and great stride.
It can outstrip without difficulty the fleetest horses, and is only
captured by being simultaneously assailed from various points, or run
down by a succession of hunters on fresh steeds. If the speed of the
ostrich, which only measures six or eight feet, is so transcending,
what shall we say of the speed of the extinct _Æpyornis maximus_ and
_Dinornis giganteus_, which are supposed to have measured from sixteen
to eighteen feet in height? Incredible as it may appear, the ostrich,
with its feet reduced to a minimum as regards size, and peculiarly
organized for walking and running on solids, can also swim. Mr. Darwin,
that most careful of all observers, informs us that ostriches take to
the water readily, and not only ford rapid rivers, but also cross from
island to island. They swim leisurely, with neck extended, and the
greater part of the body submerged.

_Locomotion in Man._--The speed attained by man, although considerable,
is not remarkable. It depends on a variety of circumstances, such as
the height, age, sex, and muscular energy of the individual, the nature
of the surface passed over, and the resistance to forward motion due to
the presence of air, whether still or moving. A reference to the human
skeleton, particularly its inferior extremities, will explain why the
speed should be moderate.

On comparing the inferior extremities of man with the legs of birds,
or the posterior extremities of quadrupeds, say the horse or deer, we
find that the bones composing them are not so obliquely placed with
reference to each other, neither are the angles formed by any two
bones so acute. Further, we observe that in birds and quadrupeds the
tarsal and metatarsal bones are so modified that there is an actual
increase in the number of the angles themselves. In the extremities
of birds and quadrupeds there are four angles, which may be increased
or diminished in the operations of locomotion. Thus, in the quadruped
and bird (fig. 4, p. 21, and fig. 24, p. 47), the femur forms with the
ilium one angle (_a_); the tibia and fibula with the femur a second
angle (_b_); the cannon or tarso-metatarsal bone with the tibia and
fibula a third angle (_c_); and the bones of the foot with the cannon
or tarso-metatarsal bone a fourth angle (_d_). In man three angles only
are found, marked respectively _a_, _b_, and _c_ (figs. 26 and 27,
pp. 55 and 59). The fourth angle (_d_ of figs. 4 and 24) is absent. The
absence of the fourth angle is due to the fact that in man the tarsal
and metatarsal bones are shortened and crushed together; whereas in the
quadruped and bird they are elongated and separated.

As the speed of a limb increases in proportion to the number and
acuteness of the angles formed by its several bones, it is not
difficult to understand why man should not be so swift as the majority
of quadrupeds. The increase in the number of angles increases the power
which an animal has of shortening and elongating its extremities, and
the levers which the extremities form. To increase the length of a
lever is to increase its power at one end, and the distance through
which it moves at the other; hence the faculty of bounding or leaping
possessed in such perfection by many quadrupeds.[34] If the wing be
considered as a lever, a small degree of motion at its root produces an
extensive sweep at its tip. It is thus that the wing is enabled to work
up and utilize the thin medium of the air as a buoying medium.

  [34] “The posterior extremities in both the lion and tiger are
  longer, and the bones inclined more obliquely to each other than the
  anterior, giving them greater power and elasticity in springing.”

Another drawback to great speed in man is his erect position. Part of
the power which should move the limbs is dedicated to supporting the
trunk. For the same reason the bones of the legs, instead of being
obliquely inclined to each other, as in the quadruped and bird, are
arranged in a nearly vertical spiral line. This arrangement increases
the angle formed by any two bones, and, as a consequence, decreases
the speed of the limbs, as explained. A similar disposition of the
bones is found in the anterior extremities of the elephant, where
the superincumbent weight is great, and the speed, comparatively
speaking, not remarkable. The bones of the human leg are beautifully
adapted to sustain the weight of the body and neutralize shock.[35]
Thus the femur or thigh bone is furnished at its upper extremity with
a ball-and-socket joint which unites it to the cup-shaped depression
(acetabulum) in the ilium (hip bone). It is supplied with a neck which
carries the body or shaft of the bone in an oblique direction from
the ilium, the shaft being arched forward and twisted upon itself
to form an elongated cylindrical screw. The lower extremity of the
femur is furnished with spiral articular surfaces accurately adapted
to the upper extremities of the bones of the leg, viz. the tibia and
fibula, and to the patella. The bones of the leg (tibia and fibula) are
spirally arranged, the screw in this instance being split up. At the
ankle the bones of the leg are applied to those of the foot by spiral
articular surfaces analogous to those found at the knee-joint. The
weight of the trunk is thus thrown on the foot, not in straight lines,
but in a series of curves. The foot itself is wonderfully adapted to
receive the pressure from above. It consists of a series of small bones
(the tarsal, metatarsal, and phalangeal bones), arranged in the form
of a double arch; the one arch extending from the heel towards the
toes, the other arch across the foot. The foot is so contrived that
it is at once firm, elastic, and moveable,--qualities which enable
it to sustain pressure from above, and exert pressure from beneath.
In walking, the heel first reaches and first leaves the ground. When
the heel is elevated the weight of the body falls more and more on
the centre of the foot and toes, the latter spreading out[36] as in
birds, to seize the ground and lever the trunk forward. It is in this
movement that the wonderful mechanism of the foot is displayed to most
advantage, the multiplicity of joints in the foot all yielding a little
to confer that elasticity of step which is so agreeable to behold, and
which is one of the characteristics of youth. The foot may be said to
roll over the ground in a direction from behind forwards. I have stated
that the angles formed by the bones of the human leg are larger than
those formed by the bones of the leg of the quadruped and bird. This is
especially true of the angle formed by the femur with the ilium, which,
because of the upward direction given to the crest of the ilium in man,
is so great that it virtually ceases to be an angle.

  [35] “The pelvis receives the whole weight of the trunk and
  superposed organs, and transmits it to the heads of the femurs.”

  [36] The spreading action of the toes is seen to perfection in
  children. It is more or less destroyed in adults from a faulty
  principle in boot and shoemaking, the soles being invariably too
  narrow.

The bones of the superior extremities in man merit attention from the
fact that in walking and running they oscillate in opposite directions,
and alternate and keep time with the legs, which oscillate in a similar
manner. The arms are articulated at the shoulders by ball-and-socket
joints to cup-shaped depressions (glenoid cavities) closely resembling
those found at the hip-joints. The bone of the arm (humerus) is carried
away from the shoulder by a short neck, as in the thigh-bone (femur).
Like the thigh-bone it is twisted upon itself and forms a screw. The
inferior extremity of the arm bone is furnished with spiral articular
surfaces resembling those found at the knee. The spiral articular
surfaces of the arm bone are adapted to similar surfaces existing on
the superior extremities of the bones of the forearm, to wit, the
radius and ulna. These bones, like the bones of the leg, are spirally
disposed with reference to each other, and form a screw consisting of
two parts. The bones of the forearm are united to those of the wrist
(carpal) and hand (metacarpal and phalangeal) by articular surfaces
displaying a greater or less degree of spirality. From this it follows
that the superior extremities of man greatly resemble his inferior
ones; a fact of considerable importance, as it accounts for the part
taken by the superior extremities in locomotion. In man the arms do
not touch the ground as in the brutes, but they do not on this account
cease to be useful as instruments of progression. If a man walks with
a stick in each hand the movements of his extremities exactly resemble
those of a quadruped.

The bones of the human extremities (superior and inferior) are seen to
advantage in fig. 26; and I particularly direct the attention of the
reader to the ball-and-socket or universal joints by which the arms are
articulated to the shoulders (_x_, _x´_), and the legs to the pelvis
(_a_, _a´_), as a knowledge of these is necessary to a comprehension of
the oscillating or pendulum movements of the limbs now to be described.
The screw configuration of the limbs is well depicted in the left arm
(_x_) of the present figure. Compare with the wing of the bird, fig. 6,
and with the anterior extremity of the elephant, fig. 7, p. 28. But
for the ball-and-socket joints, and the spiral nature of the bones and
articular surfaces of the extremities, the undulating, sinuous, and
more or less continuous movements observable in walking and running,
and the twisting, lashing, flail-like movements necessary to swimming
and flying, would be impossible.

[Illustration: FIG. 26.--Skeleton of Man. Compare with fig. 4, p. 21,
and fig. 24, p. 47.--_Original._]

The leg in the human subject moves by three joints, viz., the hip,
knee, and ankle joints. When standing in the erect position, the
hip-joint only permits the limb to move forwards, the knee-joint
backwards, and the ankle-joint neither backwards nor forwards. When the
body or limbs are inclined obliquely, or slightly flexed, the range
of motion is increased. The greatest angle made at the knee-joint
is equal to the sums of the angles made by the hip and ankle joints
when these joints are simultaneously flexed, and when the angle of
inclination made by the foot with the ground equals 30°.

From this it follows that the trunk maintains its erect position during
the extension and flexion of the limbs. The step in walking was divided
by Borelli into two periods, the one corresponding to the time when
both limbs are on the ground; the other when only one limb is on the
ground. In running, there is a brief period when both limbs are off the
ground. In walking, the body is alternately supported by the right and
left legs, and advanced by a sinuous movement. Its forward motion is
quickened when one leg is on the ground, and slowed when both are on
the ground. When the limb (say the right leg) is flexed, elevated, and
thrown forward, it returns if left to itself (_i.e._ if its movements
are not interfered with by the voluntary muscles) to the position from
which it was moved, viz. the vertical, unless the trunk bearing the
limb is inclined in a forward direction at the same time. The limb
returns to the vertical position, or position of rest, in virtue of the
power exercised by gravity, and from its being hinged at the hip by a
ball-and-socket joint, as explained. In this respect the human limb
when allowed to oscillate exactly resembles a pendulum,--a fact first
ascertained by the brothers Weber. The advantage accruing from this
arrangement, as far as muscular energy is concerned, is very great, the
muscles doing comparatively little work.[37] In beginning to walk, the
body and limb which is to take the first step are advanced together.
When, however, the body is inclined forwards, a large proportion
of the step is performed mechanically by the tendency which the
pendulum formed by the leg has to swing forward and regain a vertical
position,--an effect produced by the operation of gravity alone. The
leg which is advanced swings further forward than is required for the
step, and requires to swing back a little before it can be deposited on
the ground. The pendulum movement effects all this mechanically. When
the limb has swung forward as far as the inclination of the body at the
time will permit, it reverses pendulum fashion; the back stroke of the
pendulum actually placing the foot upon the ground by a retrograde,
descending movement. When the right leg with which we commenced is
extended and firmly placed upon the ground, and the trunk has assumed
a nearly vertical position, the left leg is flexed, elevated, and the
trunk once more bent forward. The forward inclination of the trunk
necessitates the swinging forward of the left leg, which, when it has
reached the point permitted by the pendulum movement, swings back again
to the extent necessary to place it securely upon the ground. These
movements are repeated at stated and regular intervals. The retrograde
movement of the limb is best seen in slow walking. In fast walking the
pendulum movement is somewhat interrupted from the limb being made to
touch the ground when it attains a vertical position, and therefore
before it has completed its oscillation.[38] The swinging forward of
the body may be said to inaugurate the movement of walking. The body
is slightly bent and inclined forwards at the beginning of each step.
It is straightened and raised towards the termination of that act.
The movements of the body begin and terminate the steps, and in this
manner regulate them. The trunk rises vertically at each step, the head
describing a slight curve well seen in the walking of birds. The foot
on the ground (say the right foot) elevates the trunk, particularly
its right side, and the weight of the trunk, particularly its left
side, depresses the left or swinging foot, and assists in placing it
on the ground. The trunk and limbs are active and passive by turns. In
walking, a spiral wave of motion, most marked in an antero-posterior
direction (although also appearing laterally), runs through the
spine. This spiral spinal movement is observable in the locomotion
of all vertebrates. It is favoured in man by the antero-posterior
curves (cervical, dorsal, and lumbar) existing in the human vertebral
column. In the effort of walking the trunk and limbs oscillate on the
ilio-femoral articulations (hip-joints). The trunk also rotates in
a forward direction on the foot which is placed upon the ground for
the time being. The rotation begins at the heel and terminates at the
toes. So long as the rotation continues, the body rises. When the
rotation ceases and one foot is placed flat upon the ground, the body
falls. The elevation and rotation of the body in a forward direction
enables the foot which is off the ground for the time being to swing
forward pendulum fashion; the swinging foot, when it can oscillate no
further in a forward direction, reversing its course and retrograding
to a slight extent, at which juncture it is deposited on the ground,
as explained. The retrogression of the swinging foot is accompanied
by a slight retrogression on the part of the body, which tends at
this particular instant to regain a vertical position. From this it
follows that in slow walking the trunk and the swinging foot advance
together through a considerable space, and retire through a smaller
space; that when the body is swinging it rotates upon the ilio-femoral
articulations (hip-joints) as an axis; and that when the leg is not
swinging, but fixed by its foot upon the ground, the trunk rotates upon
the foot as an axis. These movements are correlated and complementary
in their nature, and are calculated to relieve the muscles of the legs
and trunk engaged in locomotion from excessive wear and tear.

  [37] The brothers Weber found that so long as the muscles exert the
  general force necessary to execute locomotion, the velocity depends
  on the size of the legs and on external forces, but _not on the
  strength of the muscles_.

  [38] “In quick walking and running the swinging leg never passes
  beyond the vertical which cuts the head of the femur.”

Similar movements occur in the arms, which, as has been explained,
are articulated to the shoulders by ball-and-socket joints (fig. 26,
_x_ _x_´, p. 55). The right leg and left arm advance together to make
one step, and so of the left leg and right arm. When the right leg
advances the right arm retires, and _vice versâ_. When the left leg
advances the left arm retires, and the converse. There is therefore a
complementary swinging of the limbs on each side of the body, the leg
swinging always in an opposite direction to the arm on the same side.
There is, moreover, a diagonal set of movements, also complementary
in character: the right leg and left arm advancing together to form
one step; the left leg and right arm advancing together to form the
next. The diagonal movements beget a lateral twisting of the trunk and
limbs; the oscillation of the trunk upon the limbs or feet, and the
oscillation of the feet and limbs upon the trunk, generate a forward
wave movement, accompanied by a certain amount of vertical undulation.
The diagonal movements of the trunk and extremities are accompanied
by a certain degree of lateral curvature; the right leg and left
arm, when they advance to make a step, each describing a curve, the
convexity of which is directed to the right and left respectively.
Similar curves are described by the left leg and right arm in making
the second or complementary step. When the curves formed by the right
and left legs or the right and left arms are joined, they form waved
tracks symmetrically arranged on either side of a given line. The
curves formed by the legs and arms intersect at every step, as shown
at fig. 19, p. 39. Similar curves are formed by the quadruped when
walking (fig. 18, p. 37), the fish when swimming (fig. 32, p. 68), and
the bird when flying (figs. 73 and 81, pp. 144 and 157).

[Illustration:

  FIG. 27 shows the simultaneous positions of both legs during a step,
  divided into four groups. The first group (_A_), 4 to 7, gives the
  different positions which the legs simultaneously assume while both
  are on the ground; the second group (_B_), 8 to 11, shows the various
  positions of both legs at the time when the posterior leg is elevated
  from the ground, but behind the supported one; the third group (_C_),
  12 to 14, shows the positions which the legs assume when the swinging
  leg overtakes the standing one; and the fourth group (_D_), 1 to 3,
  the positions during the time when the swinging leg is propelled in
  advance of the resting one. The letters _a_, _b_, and _c_ indicate
  the angles formed by the bones of the right leg when engaged in
  making a step. The letters _m_, _n_, and _o_, the positions assumed
  by the right foot when the trunk is rolling over it. _g_ Shows the
  rotating forward of the trunk upon the left foot (_f_) as an axis.
  _h_ Shows the rotating forward of the left leg and foot upon the
  trunk (_a_) as an axis. Compare with fig. 4, p. 21; with fig. 24,
  p. 47; and with fig. 26, p. 55.--After Weber.]

The alternate rotation of the trunk upon the limb and the limb upon the
trunk is well seen in fig. 27, p. 59.

At _A_ of fig. 27 the trunk (_g_) is observed rotating on the left foot
(_f_). At _D_ of fig. the left leg (_h_) is seen rotating on the trunk
(_a_, _i_): these, as explained, are complementary movements. At _A_
of fig. the right foot (_c_) is firmly placed on the ground, the left
foot (_f_) being in the act of leaving it. The right side of the trunk
is on a lower level than the left, which is being elevated, and in the
act of rolling over the foot. At _B_ of fig. the right foot (_m_) is
still upon the ground, but the left foot having left it is in the act
of swinging forward. At _C_ of fig. the heel of the right foot (_n_)
is raised from the ground, and the left foot is in the act of passing
the right. The right side of the trunk is now being elevated. At _D_
of fig. the heel of the right foot (_o_) is elevated as far as it can
be, the toes of the left foot being depressed and ready to touch the
ground. The right side of the trunk has now reached its highest level,
and is in the act of rolling over the right foot. The left side of the
trunk, on the contrary, is subsiding, and the left leg is swinging
before the right one, preparatory to being deposited on the ground.

From the foregoing it will be evident that the trunk and limbs have
pendulum movements which are natural and peculiar to them, the extent
of which depends upon the length of the parts. A tall man and a short
man can consequently never walk in step if both walk naturally and
according to inclination.[39]

  [39] “The number of steps which a person can take in a given time in
  walking depends, first, on the length of the leg, which, governed
  by the laws of the pendulum, swings from behind forwards; secondly,
  on the earlier or later interruption which the leg experiences in
  its arc of oscillation by being placed on the ground. The weight of
  the swinging leg and the velocity of the trunk serve to give the
  impulse by which the foot attains a position vertical to the head
  of the thigh-bone; but as the latter, according to the laws of the
  pendulum, requires in the quickest walking a given time to attain
  that position, or _half_ its entire curve of oscillation, it follows
  that every person has a certain measure for his steps, and a certain
  number of steps in a given time, which, in his natural gait in
  walking, he cannot exceed.”

In traversing a given distance in a given time, a tall man will take
fewer steps than a short man, in the same way that a large wheel will
make fewer revolutions in travelling over a given space than a smaller
one. The relation is a purely mechanical one. The nave of the large
wheel corresponds to the ilio-femoral articulation (hip-joint) of the
tall man, the spokes to his legs, and portions of the rim to his feet.
The nave, spokes, and rim of the small wheel have the same relation to
the ilio-femoral articulation (hip-joint), legs and feet of the small
man. When a tall and short man walk together, if they keep step, and
traverse the same distance in the same time, either the tall man must
shorten and slow his steps, or the short man must lengthen and quicken
his.

The slouching walk of the shepherd is more natural than that of the
trained soldier. It can be kept up longer, and admits of greater speed.
In the natural walk, as seen in rustics, the complementary movements
are all evoked. In the artificial walk of the trained army man, the
complementary movements are to a great extent suppressed. Art is
consequently not an improvement on nature in the matter of walking.
In walking, the centre of gravity is being constantly changed,--a
circumstance due to the different attitudes assumed by the different
portions of the trunk and limbs at different periods of time. All
parts of the trunk and limbs of a biped, and the same may be said of a
quadruped, move when a change of locality is effected. The trunk of the
biped and quadruped when walking are therefore in a similar condition
to that of the body of the fish when swimming.

In running, all the movements described are exaggerated. Thus the steps
are more rapid and the strides greater. In walking, a well-proportioned
six-feet man can nearly cover his own height in two steps. In running,
he can cover without difficulty a third more.

In fig. 28 (p. 62), an athlete is represented as bending forward prior
to running.

The left leg and trunk, it will be observed, are advanced beyond the
vertical line (_x_), and the arms are tucked up like the rudimentary
wings of the ostrich, to correct undue oscillation at the shoulders,
occasioned by the violent oscillation produced at the pelvis in the act
of running.

[Illustration:

  FIG. 28.--Preparing to run, from a design by Flaxman. Adapted. In the
  original of this figure the right arm is depending and placed on the
  right thigh.]

In order to enable the right leg to swing forward, it is evident that
it must be flexed, and that the left leg must be extended, and the
trunk raised. The raising of the trunk causes it to assume a more
vertical position, and this prevents the swinging leg from going too
far forwards; the swinging leg tending to oscillate in a slightly
backward direction as the trunk is elevated. The body is more inclined
forwards in running than in walking, and there is a period when both
legs are off the ground, no such period occurring in walking. “In
quick walking, the propelling leg acts more obliquely on the trunk,
which is more inclined, and forced forwards more rapidly than in slow
walking. The time when both legs are on the ground diminishes as the
velocity increases, and it vanishes altogether when the velocity is
at a maximum. In quick running the length of step rapidly increases,
whilst the duration slowly diminishes; but in slow running the length
diminishes rapidly, whilst the time remains nearly the same. The time
of a step in quick running, compared to that in quick walking, is
nearly as two to three, whilst the length of the steps are as two to
one; consequently a person can run in a given time three times as fast
as he can walk. In running, the object is to acquire a greater velocity
in progression than can be attained in walking. In order to accomplish
this, instead of the body being supported on each leg alternately, the
action is divided into two periods, during one of which the body is
supported on one leg, and during the other it is not supported at all.

“The velocity in running is usually at the rate of about ten miles an
hour, but there are many persons who, for a limited period, can exceed
this velocity.”[40]

  [40] Cyc. of Anat. and Phy., article “Motion.”




PROGRESSION ON AND IN THE WATER.


If we direct our attention to the water, we encounter a medium less
dense than the earth, and considerably more dense than the air. As
this element, in virtue of its fluidity, yields readily to external
pressure, it follows that a certain relation exists between it and the
shape, size, and weight of the animal progressing along or through it.
Those animals make the greatest headway which are of the same specific
gravity, or are a little heavier, and furnished _with extensive
surfaces_, which, by a dexterous tilting or twisting (for the one
implies the other), or by a sudden contraction and expansion, they
apply wholly or in part to obtain the maximum of resistance in the one
direction, and the minimum of displacement in the other. The change
of shape, and the peculiar movements of the swimming surfaces, are
rendered necessary by the fact, first pointed out by Sir Isaac Newton,
that bodies or animals moving in water and likewise in air experience
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.

To obtain the degree of resistance and non-resistance necessary
for progression in water, Nature, never at fault, has devised some
highly ingenious expedients,--the Syringograde animals advancing
by alternately sucking up and ejecting the water in which they are
immersed--the Medusæ by a rhythmical contraction and dilatation of
their mushroom-shaped disk--the Rotifera or wheel-animalcules by a
vibratile action of their cilia, which, according to the late Professor
Quekett, twist upon their pedicles so as alternately to increase and
diminish the extent of surface presented to the water, as happens
in the feathering of an oar. A very similar plan is adopted by the
Pteropoda, found in countless multitudes in the northern seas,
which, according to Eschricht, use the wing-like structures situated
near the head after the manner of a double paddle, resembling in
its general features that at present in use among the Greenlanders.
The characteristic movement, however, and that adopted in by far
the greater number of instances, is that commonly seen in the fish
(figs. 29 and 30).

[Illustration:

  FIG. 29.--Skeleton of the Perch (_Perca fluviatilis_). Shows the
  jointed nature of the vertebral column, and the facilities afforded
  for lateral motion, particularly in the tail (_d_), dorsal (_e_,
  _f_), ventral (_b_, _c_), and pectoral (_a_), fins, which are
  principally engaged in swimming. The extent of the travelling
  surfaces required for water greatly exceed those required for land.
  Compare the tail and fins of the present figure with the feet of the
  ox, fig. 18, p. 37.--(After Dallas.)]

[Illustration:

  FIG. 30.--The Salmon (_Salmo salar_) swimming leisurely. The body,
  it will be observed, is bent in two curves, one occurring towards
  the head, the other towards the tail. The shape of the salmon is
  admirably adapted for cleaving the water.--_Original._]

This, my readers are aware, consists of a lashing, curvi-linear, or
flail-like movement of the broadly expanded tail, which oscillates from
side to side of the body, in some instances with immense speed and
power. The muscles in the fish, as has been explained, are for this
purpose arranged along the spinal column, and constitute the bulk of
the animal, it being a law that when the extremities are wanting, as
in the water-snake, or rudimentary, as in the fish, lepidosiren,[41]
proteus, and axolotl, the muscles of the trunk are largely developed.
In such cases the onus of locomotion falls chiefly, if not entirely,
upon the tail and lower portion of the body. The operation of this law
is well seen in the metamorphosis of the tadpole, the muscles of the
trunk and tail becoming modified, and the tail itself disappearing as
the limbs of the perfect frog are developed. The same law prevails in
certain instances where the anterior extremities are comparatively
perfect, but too small for swimming purposes, as in the whale,
porpoise, dugong, and manatee, and where both anterior and posterior
extremities are present but dwarfed, as in the crocodile, triton, and
salamander. The whale, porpoise, dugong, and manatee employ their
anterior extremities in balancing and turning, the great organ of
locomotion being the tail. The same may be said of the crocodile,
triton, and salamander, all of which use their extremities in quite a
subordinate capacity as compared with the tail. The peculiar movements
of the trunk and tail evoked in swimming are seen to most advantage in
the fish, and may now be briefly described.

  [41] The _lepidosiren_ is furnished with two tapering flexible
  stem-like bodies, which depend from the anterior ventral aspect
  of the animal, the _siren_ having in the same region two pairs of
  rudimentary limbs furnished with four imperfect toes, while the
  _proteus_ has anterior extremities armed with three toes each, and a
  very feeble posterior extremity terminating in two toes.

_Swimming of the Fish, Whale, Porpoise, etc._--According to
Borelli,[42] and all who have written since his time, the fish in
swimming causes its tail to vibrate on either side of a given line,
very much as a rudder may be made to oscillate by moving its tiller.
The line referred to corresponds to the axis of the fish when it is at
rest and when its body is straight, and to the path pursued by the fish
when it is swimming. It consequently represents the axis of the fish
and the axis of motion. According to this theory the tail, when flexed
or curved to make what is termed the back or non-effective stroke, is
forced away from the imaginary line, its curved, concave, or biting
surface being directed outwards. When, on the other hand, the tail is
extended to make what is termed the effective or forward stroke, it
is urged towards the imaginary line, its convex or non-biting surface
being directed inwards (fig. 31).

  [42] Borelli, “De motu Animalium,” plate 4, fig. 5, sm. 4to, 2 vols.
  Romæ, 1680.

[Illustration: FIG. 31.--Swimming of the Fish.--(After Borelli.)]

When the tail strikes in the direction _a i_, the head of the fish
is said to travel in the direction _c h_. When the tail strikes in
the direction _g e_, the head is said to travel in the direction
_c b_; these movements, when the tail is urged with sufficient
velocity, causing the body of the fish to move in the line _d c f_.
The explanation is apparently a satisfactory one; but a careful
analysis of the swimming of the living fish induces me to believe
it is incorrect. According to this, the commonly received view, the
tail would experience a greater degree of resistance during the back
stroke, _i.e._ when it is flexed and carried away from the axis of
motion (_d c f_) than it would during the forward stroke, or when it is
extended and carried towards the axis of motion. This follows, because
the concave surface of the tail is applied to the water during what
is termed the back or non-effective stroke, and the convex surface
during what is termed the forward or effective stroke. This is just the
opposite of what actually happens, and led Sir John Lubbock to declare
that there was a period in which the action of the tail dragged the
fish backwards, which, of course, is erroneous. There is this further
difficulty. When the tail of the fish is urged in the direction _g e_,
the head does not move in the direction _c b_ as stated, but in the
direction _c h_, the body of the fish describing the arc of a circle,
_a c h_. This is a matter of observation. If a fish when resting
suddenly forces its tail to one side and curves its body, the fish
describes a curve in the water corresponding to that described by the
body. If the concavity of the curve formed by the body is directed
to the right side, the fish swims in a curve towards that side. To
this there is no exception, as any one may readily satisfy himself,
by watching the movements of gold fish in a vase. Observation and
experiment have convinced me that when a fish swims it never throws its
body into a single curve, as represented at fig. 31, p. 67, but always
into a double or figure-of-8 curve, as shown at fig. 32.[43]

  [43] It is only when a fish is turning that it forces its body into a
  single curve.

[Illustration:

  FIG. 32.--Swimming of the Sturgeon. From Nature. Compare with
  figs. 18 and 19, pp. 37 and 39; fig. 23, p. 43; and figs. 64 to 73,
  pp. 139, 141, and 144.--_Original._]

The double curve is necessary to enable the fish to present a convex
or non-biting surface (_c_) to the water during flexion (the back
stroke of authors), when the tail is being forced away from the axis of
motion (_a b_), and a concave or biting surface (_s_) during extension
(the forward or effective stroke of authors), when the tail is being
forced with increased energy towards the axis of motion (_a b_); the
resistance occasioned by a concave surface, when compared with a convex
one, being in the ratio of two to one. The double or complementary
curve into which the fish forces its body when swimming, is necessary
to correct the tendency which the head of the fish has to move in the
same direction, or to the same side as that towards which the tail
curves. In swimming, the body of the fish describes a waved track,
but this can only be done when the head and tail travel in opposite
directions, and on opposite sides of a given line, as represented at
fig. 32. The anterior and posterior portions of the fish alternately
occupy the positions indicated at _d_ _c_ and _w_ _v_; the fish
oscillating on either side of a given line, and gliding along by a
sinuous or wave movement.

I have represented the body of the fish as forced into two curves
when swimming, as there are never less than two. These I designate
the cephalic (_d_) and caudal (_c_) curves, from their respective
positions. In the long-bodied fishes, such as the eels, the number
of the curves is increased, but in every case the curves occur in
pairs, and are complementary. The cephalic and caudal curves not
only complement each other, but they act as fulcra for each other,
the cephalic curve, with the water seized by it, forming the _point
d’appui_ for the caudal one, and _vice versâ_. The fish in swimming
lashes its tail from side to side, precisely as an oar is lashed from
side to side in sculling. It therefore describes a figure-of-8 track
in the water (_e_ _f_ _g_ _h_ _i_ _j_ _k_ _l_ of fig. 32). During each
sweep or lateral movement the tail is both extended and flexed. It is
extended and its curve reduced when it approaches the line _a b_ of
fig. 32, and flexed, and a new curve formed, when it recedes from the
line in question. The tail is effective as a propeller both during
flexion and extension, so that, strictly speaking, the tail has no back
or non-effective stroke. The terms effective and non-effective employed
by authors are applicable only in a comparative and restricted sense;
the tail always operating, but being a less effective propeller, when
in the act of being flexed or curved, than when in the act of being
extended or straightened. By always directing the concavity of the tail
(_s_ and _t_) towards the axis of motion (_a b_) during extension, and
its convexity (_c_ and _v_) away from the axis of motion (_a b_) during
flexion, the fish exerts a maximum of propelling power with a minimum
of slip. In extension of the tail the caudal curve (_s_) is reduced
as the tail travels _towards_ the line _a b_. In flexion a new curve
(_v_) is formed as the tail travels _from_ the line _a b_. While the
tail travels from _s_ in the direction _t_, the head travels from _d_
in the direction _w_. There is therefore a period, momentary it must
be, when both the cephalic and caudal curves are reduced, and the body
of the fish is straight, and free to advance without impediment. The
different degrees of resistance experienced by the tail in describing
its figure-of-8 movements, are represented by the different-sized
curves _e f_, _g h_, _i j_, and _k l_ of fig. 32, p. 68. The curves
_e f_ indicate the resistance experienced by the tail during flexion,
when it is being carried away from and to the right of the line _a b_.
The curves _g h_ indicate the resistance experienced by the tail when
it is extended and carried towards the line _a b_. This constitutes a
half vibration or oscillation of the tail. The curves _i j_ indicate
the resistance experienced by the tail when it is a second time flexed
and carried away from and to the left of the line _a b_. The curves _k
l_ indicate the resistance experienced by the tail when it is a second
time extended and carried towards the line _a b_. This constitutes a
complete vibration. These movements are repeated in rapid succession
so long as the fish continues to swim forwards. They are only varied
when the fish wishes to turn round, in which case the tail gives single
strokes either to the right or left, according as it wishes to go to
the right or left side respectively. The resistance experienced by the
tail when in the positions indicated by _e f_ and _i j_ is diminished
by the tail being slightly compressed, by its being moved more slowly,
and by the fish rotating on its long axis so as to present the tail
obliquely to the water. The resistance experienced by the tail when
in the positions indicated by _g h_, _k l_, is increased by the tail
being divaricated, by its being moved with increased energy, and by
the fish re-rotating on its long axis, so as to present the flat of
the tail to the water. The movements of the tail are slowed when the
tail is carried away from the line _a b_, and quickened when the tail
is forced towards it. Nor is this all. When the tail is moved slowly
away from the line _a b_, it draws a current after it which, being
met by the tail when it is urged with increased velocity towards the
line _a b_, enormously increases the hold which the tail takes of the
water, and consequently its propelling power. The tail may be said to
work without slip, and to produce the precise kind of currents which
afford it the greatest leverage. In this respect the tail of the fish
is infinitely superior as a propelling organ to any form of screw yet
devised. The screw at present employed in navigation ceases to be
effective when propelled beyond a given speed. The screw formed by
the tail of the fish, in virtue of its reciprocating action, and the
manner in which it alternately eludes and seizes the water, becomes
more effective in proportion to the rapidity with which it is made to
vibrate. The remarks now made of the tail and the water are equally
_apropos_ of the wing and the air. The tail and the wing act on a
common principle. A certain analogy may therefore be traced between
the water and air as media, and between the tail and extremities as
instruments of locomotion. From this it follows that the water and
air are acted upon by curves or wave-pressure emanating in the one
instance from the tail of the fish, and in the other from the wing of
the bird, the reciprocating and opposite curves into which the tail and
wing are thrown in swimming and flying constituting _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. The whole body of the fish is thrown into
action in swimming; but as the tail and lower half of the trunk are
more free to move than the head and upper half, which are more rigid,
and because the tendons of many of the trunk-muscles are inserted into
the tail, the oscillation is greatest in the direction of the latter.
The muscular movements travel in spiral waves from before backwards;
and the waves of force react upon the water, and cause the fish to
glide forwards in a series of curves. Since the head and tail, as has
been stated, always travel in opposite directions, and the fish is
constantly alternating or changing sides, it in reality describes a
waved track. These remarks may be readily verified by a reference to
the swimming of the sturgeon, whose movements are unusually deliberate
and slow. The number of curves into which the body of the fish is
thrown in swimming is increased in the long-bodied fishes, as the eels,
and decreased in those whose bodies are short or are comparatively
devoid of flexibility. In proportion as the curves into which the body
is thrown in swimming are diminished, the degree of rotation at the
tail or in the fins is augmented, some fishes, as the mackerel, using
the tail very much after the manner of a screw in a steam-ship. The
fish may thus be said to drill the water in two directions, viz. from
behind forwards by a twisting or screwing of the body on its long axis,
and from side to side by causing its anterior and posterior portions
to assume opposite curves. The pectoral and other fins are also thrown
into curves when in action, the movement, as in the body itself,
travelling in spiral waves; and it is worthy of remark that the wing
of the insect, bat, and bird obeys similar impulses, the pinion, as I
shall show presently, being essentially a spiral organ.

The twisting of the pectoral fins is well seen in the common perch
(_Perca fluviatilis_), and still better in the 15-spined Stickleback
(_Gasterosteus spinosus_), which latter frequently progresses by their
aid alone.[44] In the stickleback, the pectoral fins are so delicate,
and are plied with such vigour, that the eye is apt to overlook them,
particularly when in motion. The action of the fins can be reversed
at pleasure, so that it is by no means an unusual thing to see the
stickleback progressing tail first. The fins are rotated or twisted,
and their free margins lashed about by spiral movements which closely
resemble those by which the wings of insects are propelled.[45] The
rotating of the fish upon its long axis is seen to advantage in the
shark and sturgeon, the former of which requires to turn on its
side before it can seize its prey,--and likewise in the pipefish,
whose motions are unwontedly sluggish. The twisting of the tail is
occasionally well marked in the swimming of the salamander. In those
remarkable mammals, the whale,[46] porpoise, manatee, and dugong
(figs. 33, 34, and 35), the movements are strictly analogous to those
of the fish, the only difference being that the tail acts from above
downwards or vertically, instead of from side to side or laterally. The
anterior extremities, which in those animals are comparatively perfect,
are rotated on their long axes, and applied obliquely and non-obliquely
to the water, to assist in balancing and turning. Natation is performed
almost exclusively by the tail and lower half of the trunk, the tail of
the whale exerting prodigious power.

  [44] The _Syngnathi_, or Pipefishes, swim chiefly by the undulating
  movement of the dorsal fin.

  [45] If the pectoral fins are to be regarded as the homologues of
  the anterior extremities (which they unquestionably are), it is not
  surprising that in them the spiral rotatory movements which are
  traceable in the extremities of quadrupeds, and so fully developed
  in the wings of bats and birds, should be clearly foreshadowed. “The
  muscles of the pectoral fins,” remarks Professor Owen, “though, when
  compared with those of the homologous members in higher vertebrates,
  they are very small, few, and simple, yet suffice for all the
  requisite movements of the fins--elevating, depressing, advancing,
  and again laying them prone and flat, by an oblique stroke, upon the
  sides of the body. The rays or digits of both pectorals and ventrals
  (the homologues of the posterior extremities) can be divaricated
  and approximated, and the intervening webs spread out or folded
  up.”--_Op. cit._ vol. i. p. 252.

  [46] _Vide_ “Remarks on the Swimming of the Cetaceans,” by Dr. Murie,
  Proc. Zool. Soc., 1865, pp. 209, 210.

[Illustration:

  FIG. 33.--The Porpoise (_Phocœna communis_). Here the tail is
  principally engaged in swimming, the anterior extremities being
  rudimentary, and resembling the pectoral fins of fishes. Compare with
  fig. 30, p. 65.--_Original._]

[Illustration:

  FIG. 34.--The Manatee (_Manatus Americanus_). In this the anterior
  extremities are more developed than in the porpoise, but still the
  tail is the great organ of natation. Compare with fig. 33, p. 73,
  and with fig. 30, p. 65. The shape of the manatee and porpoise is
  essentially that of the fish.--_Original._]

It is otherwise with the Rays, where the hands are principally
concerned in progression, these flapping about in the water very much
as the wings of a bird flap about in the air. In the beaver, the tail
is flattened from above downwards, as in the foregoing mammals, but in
swimming it is made to act upon the water laterally as in the fish. The
tail of the bird, which is also compressed from above downwards, can be
twisted obliquely, and when in this position may be made to perform the
office of a rudder.

[Illustration:

  FIG. 35.--Skeleton of the Dugong. In this curious mammal the anterior
  extremities are more developed than in the manatee and porpoise,
  and resemble those found in the seal, sea-bear, and walrus. They
  are useful in balancing and turning, the tail being the effective
  instrument of propulsion. The vertebral column closely resembles
  that of the fish, and allows the tail to be lashed freely about in a
  vertical direction. Compare with fig. 29, p. 65.--(After Dallas.)]

_Swimming of the Seal, Sea-Bear, and Walrus._--In the seal, the
anterior and posterior extremities are more perfect than in the whale,
porpoise, dugong, and manatee; the general form, however, and mode of
progression (if the fact of its occasionally swimming on its back be
taken into account), is essentially fish-like.

[Illustration:

  FIG. 36.--The Seal (_Phoca fœtida_, Müll.), adapted principally for
  water. The extremities are larger than in the porpoise and manatee.
  Compare with figs. 33 and 34, p. 73.--_Original._]

A peculiarity is met with in the swimming of the seal, to which I think
it proper to direct attention. When the lower portion of the body
and posterior extremities of these creatures are flexed and tilted,
as happens during the back and least effective stroke, the naturally
expanded feet are more or less completely closed or pressed together,
in order to diminish the extent of surface presented to the water,
and, as a consequence, to reduce the resistance produced. The feet are
opened to the utmost during extension, when the more effective stroke
is given, in which case they present their maximum of surface. They
form powerful propellers, both during flexion and extension.

The swimming apparatus of the seal is therefore more highly
differentiated than that of the whale, porpoise, dugong, and manatee;
the natatory tail in these animals being, from its peculiar structure,
incapable of lateral compression.[47] It would appear that the
swimming appliances of the seals (where the feet open and close as in
swimming-birds) are to those of the sea-mammals generally, what the
feathers of the bird’s wing (these also open and close in flight) are
to the continuous membrane forming the wing of the insect and bat.

  [47] In a few instances the caudal fin of the fish, as has been
  already stated, is more or less pressed together during the back
  stroke, the compression and tilting or twisting of the tail taking
  place synchronously.

The anterior extremities or flippers of the seal are not engaged in
swimming, but only in balancing and in changing position. When so
employed the fore feet open and close, though not to the same extent
as the hind ones; the resistance and non-resistance necessary being
secured by a partial rotation and tilting of the flippers. By this
twisting and untwisting, the narrow edges and broader portions of the
flippers are applied to the water alternately. The rotating and tilting
of the anterior and posterior extremities, and the opening and closing
of the hands and feet in the balancing and swimming of the seal, form a
series of strictly progressive and very graceful movements. They are,
however, performed so rapidly, and glide into each other so perfectly,
as to render an analysis of them exceedingly difficult.

In the Sea-Bear (_Otaria jubata_) the anterior extremities attain
sufficient magnitude and power to enable the animal to progress by
their aid alone; the feet and the lower portions of the body being
moved only sufficiently to maintain, correct, or alter the course
pursued (fig. 73). The anterior extremities are flattened out, and
greatly resemble wings, particularly those of the penguin and auk,
which are rudimentary in character. Thus they have a thick and
comparatively stiff anterior margin; and a thin, flexible, and more
or less elastic posterior margin. They are screw structures, and when
elevated and depressed in the water, twist and untwist, screw-fashion,
precisely as wings do, or the tails of the fish, whale, dugong, and
manatee.

[Illustration:

  FIG. 37.--The Sea-Bear (_Otaria jubata_), adapted principally for
  swimming and diving. It also walks with tolerable facility. Its
  extremities are larger than those of the seal, and its movements,
  both in and out of the water, more varied.--_Original._]

This remarkable creature, which I have repeatedly watched at the
Zoological Gardens[48] (London), appears to fly in the water, the
universal joints by which the arms are attached to the shoulders
enabling it, by partially rotating and twisting them, to present the
palms or flat of the hands to the water the one instant, and the edge
or narrow parts the next. In swimming, the anterior or thick margins
of the flippers are _directed downwards_, and similar remarks are to
be made of the anterior extremities of the walrus, great auk, and
turtle.[49]

  [48] The unusual opportunities afforded by this unrivalled collection
  have enabled me to determine with considerable accuracy the movements
  of the various land-animals, as well as the motions of the wings and
  feet of birds, both in and out of the water. I have also studied
  under the most favourable circumstances the movements of the otter,
  sea-bear, seal, walrus, porpoise, turtle, triton, crocodile, frog,
  lepidosiren, proteus, axolotl, and the several orders of fishes.

  [49] This is the reverse of what takes place in flying, the anterior
  or thick margins of the wings being invariably _directed upwards_.

The flippers are advanced alternately; and the twisting, screw-like
movement which they exhibit in action, and which I have carefully noted
on several occasions, bears considerable resemblance to the motions
witnessed in the pectoral fins of fishes. It may be remarked that the
twisting or spiral movements of the anterior extremities are calculated
to utilize the water to the utmost--the gradual but rapid operation of
the helix enabling the animal to lay hold of the water and disentangle
itself with astonishing facility, and with the minimum expenditure of
power. In fact, the insinuating motion of the screw is the only one
which can contend successfully with the liquid element; and it appears
to me that this remark holds even more true of the air. It also applies
within certain limits, as has been explained, to the land. The otaria
or sea-bear swims, or rather flies, under the water with remarkable
address and with apparently equal ease in an upward, downward, and
horizontal direction, by muscular efforts alone--an observation which
may likewise be made regarding a great number of fishes, since the
swimming-bladder or float is in many entirely absent.[50] Compare with
figs. 33, 34, 35, and 36, pp. 73 and 74. The walrus, a living specimen
of which I had an opportunity of frequently examining, is nearly allied
to the seal and sea-bear, but differs from both as regards its manner
of swimming. The natation of this rare and singularly interesting
animal, as I have taken great pains to satisfy myself, is effected by
a mixed movement--the anterior and posterior extremities participating
in nearly an equal degree. The anterior extremities or flippers of the
walrus, morphologically resemble those of the seal, but physiologically
those of the sea-bear; while the posterior extremities possess many
of the peculiarities of the hind legs of the sea-bear, but display the
movements peculiar to those of the seal. In other words, the anterior
extremities or flippers of the walrus are moved alternately, and
reciprocate, as in the sea-bear; whereas the posterior extremities are
lashed from side to side by a twisting, curvilinear motion, precisely
as in the seal. The walrus may therefore, as far as the physiology of
its extremities is concerned, very properly be regarded as holding
an intermediate position between the seals on the one hand, and the
sea-bears or sea-lions on the other.

  [50] The air-bladder is wanting in the dermopteri, plagiostomi, and
  pleuronectidæ.--Owen, _op. cit._ p. 255.

_Swimming of Man._--The swimming of man is artificial in its nature,
and consequently does not, strictly speaking, fall within the scope of
the present work. I refer to it principally with a view to showing that
it resembles in its general features the swimming of animals.

The human body is lighter than the water, a fact of considerable
practical importance, as showing that each has in himself that which
will prevent his being drowned, if he will only breathe naturally, and
desist from struggling.

The catastrophe of drowning is usually referrible to nervous agitation,
and to spasmodic and ill-directed efforts in the extremities. All
swimmers have a vivid recollection of the great difficulty experienced
in keeping themselves afloat, when they first resorted to aquatic
exercises and amusements. In especial they remember the short,
vigorous, but flurried, misdirected, and consequently futile strokes
which, instead of enabling them to skim the surface, conducted them
inevitably to the bottom. Indelibly impressed too are the ineffectual
attempts at respiration, the gasping and puffing and the swallowing of
water, inadvertently gulped instead of air.

In order to swim well, the operator must be perfectly calm. He must,
moreover, know how to apply his extremities to the water with a view to
propulsion. As already stated, the body will float if left to itself;
the support obtained is, however, greatly increased by projecting it
along the surface of the water. This, as all swimmers are aware, may be
proved by experiment. It is the same principle which prevents a thin
flat stone from sinking when projected with force against the surface
of water. A precisely similar result is obtained if the body be placed
slantingly in a strong current, and the hands made to grasp a stone or
branch. In this case the body is raised to the surface of the stream
by the action of the running water, the body remaining motionless. The
quantity of water which, under the circumstances, impinges against
the body in a given time is much greater than if the body was simply
immersed in still water. To increase the area of support, either
the supporting medium or the body supported must move. The body is
supported in water very much as the kite is supported in air. In both
cases the body and the kite are made to strike the water and the air
at a slight upward angle. When the extremities are made to move in a
horizontal or slightly downward direction, they at once propel and
support the body. When, however, they are made to act in an upward
direction, as in diving, they submerge the body. This shows that the
movements of the swimming surfaces may, according to their direction,
either augment or destroy buoyancy. The swimming surfaces enable the
seal, sea-bear, otter, ornithorhynchus, bird, etc., to disappear from
and regain the surface of the water. Similar remarks may be made of the
whale, dugong, manatee, and fish.

Man, in order to swim, must learn the art of swimming. He must serve
a longer or shorter apprenticeship to a new form of locomotion, and
acquire a new order of movements. It is otherwise with the majority
of animals. Almost all quadrupeds can swim the first time they are
immersed, as may readily be ascertained by throwing a newly born kitten
or puppy into the water. The same may be said of the greater number
of birds. This is accounted for by the fact that quadrupeds and birds
are lighter, bulk for bulk, than water, but more especially, because
in walking and running the movements made by their extremities are
precisely those required in swimming. They have nothing to learn, as
it were. They are buoyant naturally, and if they move their limbs
at all, which they do instinctively, they swim of necessity. It is
different with man. The movements made by him in walking and running
are not those made by him in swimming; neither is the position resorted
to in swimming that which characterizes him on land. The vertical
position is not adapted for water, and, as a consequence, he requires
to abandon it and assume a horizontal one; he requires, in fact, to
throw himself flat upon the water, either upon his side, or upon
his dorsal or ventral aspect. This position assimilates him to the
quadruped and bird, the fish, and everything that swims; the trunks
of all swimming animals, being placed in a prone position. Whenever
the horizontal position is assumed, the swimmer can advance in any
direction he pleases. His extremities are quite free, and only require
to be moved in definite directions to produce definite results. The
body can be propelled by the two arms, or the two legs; or by the
right arm and leg, or the left arm and leg; or by the right arm and
left leg, or the left arm and right leg. Most progress is made when
the two arms and the two legs are employed. An expert swimmer can
do whatever he chooses in water. Thus he can throw himself upon his
back, and by extending his arms obliquely above his head until they
are in the same plane with his body, can float without any exertion
whatever; or, maintaining the floating position, he can fold his arms
upon his chest and by alternately flexing and extending his lower
extremities, can propel himself with ease and at considerable speed;
or, keeping his legs in the extended position and motionless, he can
propel himself by keeping his arms close to his body, and causing his
hands to work like sculls, so as to make figure-of-8 loops in the
water. This motion greatly resembles that made by the swimming wings of
the penguin. It is most effective when the hands are turned slightly
upwards, and a greater or less backward thrust given each time the
hands reciprocate. The progress made at first is slow, but latterly
very rapid, the rapidity increasing according to the momentum acquired.
The swimmer, in addition to the foregoing methods, can throw himself
upon his face, and by alternately flexing and extending his arms and
legs, can float and propel himself for long periods with perfect
safety and with comparatively little exertion. He can also assume
the vertical position, and by remaining perfectly motionless, or by
treading the water with his feet, can prevent himself from sinking;
nay more, he can turn a somersault in the water either in a forward or
backward direction. The position most commonly assumed in swimming
is the prone one, where the ventral surface of the body is directed
towards the water. In this case the anterior and posterior extremities
are simultaneously flexed and drawn towards the body slowly, after
which they are simultaneously and rapidly extended. The swimming of
the frog conveys an idea of the movement.[51] In ordinary swimming,
when the anterior and posterior extremities are simultaneously flexed,
and afterwards simultaneously extended, the hands and feet describe
four ellipses; an arrangement which, as explained, increases the area
of support furnished by the moving parts. The ellipses are shown at
fig. 38; the continuous lines representing extension, the dotted lines
flexion.

  [51] The frog in swimming leisurely frequently causes its extremities
  to move diagonally and alternately. When, however, pursued and
  alarmed, it folds its fore legs, and causes its hind ones to move
  simultaneously and with great vigour by a series of sudden jerks,
  similar to those made by man when swimming on his back.

[Illustration: Fig. 38.]

[Illustration: Fig. 39.]

[Illustration: Fig. 40.]

Thus when the arms and legs are pushed away from the body, the arms
describe the inner sides of the ellipses (fig. 38, _a a_), the legs
describing the outer sides (_c c_). When the arms and legs are drawn
towards the body, the arms describe the outer sides of the ellipses (_b
b_), the legs describing the inner sides (_d d_). As the body advances,
the ellipses are opened out and loops formed, as at _e e_, _f f_ of
fig. 39. If the speed attained is sufficiently high, the loops are
converted into waved lines, as in walking and flying.--(_Vide_ _g g_,
_h h_ of fig. 40, p. 81, and compare with fig. 18, p. 37, and figs. 71
and 73, p. 144.) The swimming of man, like the walking, swimming, and
flying of animals, is effected by alternately flexing and extending the
limbs, as shown more particularly at fig. 41, _A_, _B_, _C_.

[Illustration:

  FIG. 41.--_A_ shows the arms and legs folded or flexed and drawn
  towards the mesial line of the body.--_Original._

  _B_ shows the arms and legs opened out or extended and carried away
  from the mesial line of the body.--_Original._

  _C_ shows the arms and legs in an intermediate position, _i.e._ when
  they are neither flexed nor extended. The arms and legs require to be
  in the position shown at _A_ before they can assume that represented
  at _B_, and they require to be in the position shown at _B_ before
  they can assume that represented at _C_. When the arms and legs are
  successively assuming the positions indicated at _A_, _B_, and _C_,
  they move in ellipses, as explained.--_Original._]

By alternately flexing and extending the limbs, the angles made by
their several parts with each other are decreased and increased,--an
arrangement which diminishes and augments the degree of resistance
experienced by the swimming surfaces, which by this means are made to
elude and seize the water by turns. This result is further secured by
the limbs being made to move more slowly in flexion than in extension,
and by the limbs being made to rotate in the direction of their length
in such a manner as to diminish the resistance experienced during the
former movement, and increase it during the latter. When the arms are
extended, the palms of the hands and the inner surfaces of the arms
are directed downwards, and assist in buoying up the anterior portion
of the body. The hands are screwed slightly round towards the end of
extension, the palms acting in an outward and backward direction
(fig. 41, _B_). In this movement the posterior surfaces of the arms
take part; the palms and posterior portions of the arms contributing to
the propulsion of the body. When the arms are flexed, the flat of the
hands is directed downwards (fig. 41, _C_). Towards the end of flexion
the hands are slightly depressed, which has the effect of forcing the
body upwards, and hence the bobbing or vertical wave-movement observed
in the majority of swimmers.[52]

  [52] The professional swimmer avoids bobbing, and rests the side of
  his head on the water to diminish its weight and increase speed.

During flexion the posterior surfaces of the arms act powerfully as
propellers, from the fact of their striking the water obliquely in a
backward direction. I avoid the terms _back_ and _forward_ strokes,
because the arms and hands, so long as they move, support and propel.
There is no period either in extension or flexion in which they are not
effective. When the legs are pushed away from the body, or extended
(a movement which is effected rapidly and with great energy, as shown
at fig. 41, _B_), the soles of the feet, the anterior surfaces of the
legs, and the posterior surfaces of the thighs, are directed outwards
and backwards. This enables them to seize the water with great avidity,
and to propel the body forward. The efficiency of the legs and feet
as propelling organs during extension is increased by their becoming
more or less straight, and by their being moved with greater rapidity
than in flexion; there being a general back-thrust of the limbs as a
whole, and a particular back-thrust of their several parts.[53] In this
movement the inner surfaces of the legs and thighs act as sustaining
organs and assist in floating the posterior part of the body. The
slightly inclined position of the body in the water, and the forward
motion acquired in swimming, contribute to this result. When the legs
and feet are drawn towards the body or flexed, as seen at fig. 41, _C_,
_A_, their movements are slowed, an arrangement which reduces the
degree of friction experienced by the several parts of the limbs when
they are, as it were, being drawn off the water preparatory to a second
extension.

  [53] The greater power possessed by the limbs during extension, and
  more especially towards the end of extension, is well illustrated by
  the kick of the horse; the hind feet dealing a terrible blow when
  they have reached their maximum distance from the body. Ostlers are
  well aware of this fact, and in grooming a horse keep always very
  close to his hind quarters, so that if he does throw up they are
  forced back but not injured.

There are several grave objections to the ordinary or old method of
swimming just described. _1st_, The body is laid prone on the water,
which exposes a large resisting surface (fig. 41, _A_, _B_, _C_,
p. 82). _2d_, The arms and legs are spread out on either side of the
trunk, so that they are applied very indirectly as propelling organs
(fig. 41, _B_, _C_). _3d_, The most effective part of the stroke of the
arms and legs corresponds to something like a quarter of an ellipse,
the remaining three quarters being dedicated to getting the arms and
legs into position. This arrangement wastes power and greatly increases
friction; the attitudes assumed by the body at _B_ and _C_ of fig. 41
being the worst possible for getting through the water. _4th_, The arms
and legs are drawn towards the trunk the one instant (fig. 41, _A_),
and pushed away from it the next (fig. 41, _B_). This gives rise to
dead points, there being a period when neither of the extremities are
moving. The body is consequently impelled by a series of jerks, the
swimming mass getting up and losing momentum between the strokes.

In order to remedy these defects, scientific swimmers have of late
years adopted quite another method. Instead of working the arms and
legs together, they move first the arm and leg of one side of the body,
and then the arm and leg of the opposite side. This is known as the
_overhand_ movement, and corresponds exactly with the natural walk of
the giraffe, the amble of the horse, and the swimming of the sea-bear.
It is that adopted by the Indians. In this mode of swimming the body
is thrown more or less on its side at each stroke, the body twisting
and rolling in the direction of its length, as shown at fig. 42,
an arrangement calculated greatly to reduce the amount of friction
experienced in forward motion.

[Illustration: FIG. 42.--Overhand Swimming.--_Original._]

The overhand movement enables the swimmer to throw himself forward on
the water, and to move his arms and legs in a nearly vertical instead
of a horizontal plane; the extremities working, as it were, above and
beneath the trunk, rather than on either side of it. The extremities
are consequently employed in the best manner possible for developing
their power and reducing the friction to forward motion caused by their
action. This arrangement greatly increases the length of the effective
stroke, both of the arms and legs, this being equal to nearly half an
ellipse. Thus when the left arm and leg are thrust forward, the arm
describes the curve _a b_ (fig. 42), the leg _e_ describing a similar
curve. As the right side of the body virtually recedes when the left
side advances, the right arm describes the curve _c d_, while the left
arm is describing the curve _a b_; the right leg _f_ describing a curve
the opposite of that described by _e_ (compare arrows). The advancing
of the right and left sides of the body alternately, in a nearly
straight line, greatly contributes to continuity of motion, the impulse
being applied now to the right side and now to the left, and the limbs
being disposed and worked in such a manner as in a great measure to
reduce friction and prevent dead points or halts. When the left arm and
leg are being thrust forward (_a b_, _e_ of fig. 42), the right arm and
leg strike very nearly directly backward (_c d_, _f_ of fig. 42). The
right arm and leg, and the resistance which they experience from the
water consequently form a _point d’appui_ for the left arm and leg; the
two sides of the body twisting and screwing upon a moveable fulcrum
(the water)--an arrangement which secures a maximum of propulsion with
a minimum of resistance and a minimum of slip. The propulsive power is
increased by the concave surfaces of the hands and feet being directed
backwards during the back stroke, and by the arms being made to throw
their back water in a slightly outward direction, so as not to impede
the advance of the legs. The overhand method of swimming is the most
expeditious yet discovered, but it is fatiguing, and can only be
indulged in for short distances.

[Illustration: FIG. 43.--Side-stroke Swimming.--_Original._]

An improvement on the foregoing for long distances is that known as
the _side_ stroke. In this method, as the term indicates, the body
is thrown more decidedly upon the side. Either side may be employed,
some preferring to swim on the right side, and some on the left;
others swimming alternately on the right and left sides. In swimming
by the side stroke (say on the left side), the left arm is advanced
in a curve, and made to describe the upper side of an ellipse, as
represented at _a b_ of fig. 43. This done, the right arm and legs
are employed as propellers, the right arm and legs making a powerful
backward stroke, in which the concavity of the hand is directed
backwards and outwards, as shown at _c d_ of the same figure.[54] The
right arm in this movement describes the under side of an ellipse,
and acts in a nearly vertical plane. When the right arm and legs are
advanced, some swimmers lift the right arm out of the water, in order
to diminish friction--the air being more easily penetrated than the
water. The lifting of the arm out of the water increases the speed, but
the movement is neither graceful nor comfortable, as it immerses the
head of the swimmer at each stroke. Others keep the right arm in the
water and extend the arm and hand in such a manner as to cause it to
cut straight forward. In the side stroke the left arm (if the operator
swims on the left side) acts as a cutwater (fig. 43, _b_). It is made
to advance when the right arm and legs are forced backwards (fig. 43,
_c d_). The right arm and legs move together, and alternate with the
left arm, which moves by itself. The right arm and legs are flexed and
carried forwards, while the left arm is extended and forced backwards,
and _vice versâ_. The left arm always moves in an opposite direction
to the right arm and legs. We have thus in the side stroke three limbs
moving together in the same direction and keeping time, the fourth
limb always moving in an opposite direction and out of time with the
other three. The limb which moves out of time is the left one if the
operator swims on the left side, and the right one if he swims on the
right side. In swimming on the left side, the right arm and legs are
advanced slowly the one instant, and forced in a backward direction
with great energy and rapidity the next. Similar remarks are to be made
regarding the left arm. When the right arm and legs strike backwards
they communicate to the body a powerful forward impulse, which, seeing
the body is tilted upon its side and advancing as on a keel, transmits
it to a considerable distance. This arrangement reduces the amount of
resistance to forward motion, conserves the energy of the swimmer, and
secures in a great measure continuity of movement, the body being in
the best possible position for gliding forward between the strokes.

  [54] The outward direction given to the arm and hand enables them to
  force away the back water from the body and limbs, and so reduce the
  friction to forward motion.

In good side swimming the legs are made to diverge widely when they
are extended or pushed away from the body, so as to include within
them a fluid wedge, the apex of which is directed forwards. When
fully extended, the legs are made to converge in such a manner that
they force the body away from the wedge, and so contribute to its
propulsion. By this means the legs in extension are made to give what
may be regarded a double stroke, viz. an outward and inward one. When
the double move has been made, the legs are flexed or drawn towards
the body preparatory to a new stroke. In swimming on the left side,
the left or cutwater arm is extended or pushed away from the body in
such a manner that the concavity of the left hand is directed forwards,
and describes the upper half of a vertical ellipse. It thus meets with
comparatively little resistance from the water. When, however, the left
arm is flexed and drawn towards the body, the concavity of the left
hand is directed backwards and made to describe the under half of the
ellipse, so as to scoop and seize the water, and thus contribute to the
propulsion of the body. The left or cutwater arm materially assists
in floating the anterior portions of the body. The stroke made by the
left arm is equal to a quarter of a circle, that made by the right arm
to half a circle. The right arm, when the operator swims upon the left
side, is consequently the more powerful propeller. The right arm, like
the left, assists in supporting the anterior portion of the body. In
swimming on the left side the major propelling factors are the right
arm and hand and the right and left legs and feet. Swimming by the side
stroke is, on the whole, the most useful, graceful, and effective yet
devised. It enables the swimmer to make headway against wind, wave,
and tide in quite a remarkable manner. Indeed, a dexterous side-stroke
swimmer can progress when a powerful breast-swimmer would be driven
back. In still water an expert non-professional swimmer ought to make
a mile in from thirty to thirty-five minutes. A professional swimmer
may greatly exceed this. Thus, Mr. J. B. Johnson, when swimming against
time, August 5th, 1872, in the fresh-water lake at Hendon, near London,
did the full mile in twenty-six minutes. The first half-mile was done
in twelve minutes. _Cæteris paribus_, the shorter the distance, the
greater the speed. In August 1868, Mr. Harry Parker, a well-known
professional swimmer, swam 500 yards in the Serpentine in seven minutes
fifty seconds. Among non-professional swimmers the performance of Mr.
J. B. Booth is very creditable. This gentleman, in June 1871, swam 440
yards in seven minutes fourteen seconds in the fresh-water lake at
Hendon, already referred to. I am indebted for the details regarding
time to Mr. J. A. Cowan of Edinburgh, himself acknowledged to be one
of the fastest swimmers in Scotland. The speed attained by man in the
water is not great when his size and power are taken into account. It
certainly contrasts very unfavourably with that of seals, and still
more unfavourably with that of fishes. This is due to his small hands
and feet, the slow movements of his arms and legs, and the awkward
manner in which they are applied to and withdrawn from the water.

[Illustration:

  FIG. 44.--The Turtle (_Chelonia imbricata_), adapted for swimming and
  diving, the extremities being relatively larger than in the seal,
  sea-bear, and walrus. The anterior extremities have a thick anterior
  margin and a thin posterior one, and in this respect resemble wings.
  Compare with figs. 36 and 37, pp. 74 and 76.--_Original._]

[Illustration:

  FIG. 45.--The Crested Newt (_Triton cristatus_, Laur.) In the newt a
  tail is superadded to the extremities, the tail and the extremities
  both acting in swimming.--_Original._]

_Swimming of the Turtle, Triton, Crocodile, etc._--The swimming of
the turtle differs in some respects from all the other forms of
swimming. While the anterior extremities of this quaint animal move
alternately, and tilt or partially rotate during their action, as in
the sea-bear and walrus, the posterior extremities likewise move by
turns. As, moreover, the right anterior and left posterior extremities
move together, and reciprocate with the left anterior and right
posterior ones, the creature has the appearance of walking in the water
(fig. 44).

The same remarks apply to the movements of the extremities of the
triton (fig. 45, p. 89) and crocodile, when swimming, and to the feebly
developed corresponding members in the lepidosiren, proteus, and
axolotl, specimens of all of which are to be seen in the Zoological
Society’s Gardens, London. In the latter, natation is effected
principally, if not altogether, by the tail and lower half of the body,
which is largely developed and flattened laterally for this purpose, as
in the fish.

The muscular power exercised by the fishes, the cetaceans, and the
seals in swimming, is conserved to a remarkable extent by the momentum
which the body rapidly acquires--the velocity attained by the mass
diminishing the degree of exertion required in the individual or
integral parts. This holds true of all animals, whether they move on
the land or on or in the water or air.

The animals which furnish the connecting link between the water and
the air are the diving-birds on the one hand, and the flying-fishes on
the other,--the former using their wings for flying above and through
the water, as occasion demands; the latter sustaining themselves for
considerable intervals in the air by means of their enormous pectoral
fins.

_Flight under water, etc._--Mr. Macgillivray thus describes a flock
of red mergansers which he observed pursuing sand-eels in one of the
shallow sandy bays of the Outer Hebrides:--“The birds seemed to move
under the water with almost as much velocity as in the air, and often
rose to breathe at a distance of 200 yards from the spot at which they
had dived.”[55]

  [55] History of British Birds, vol. i. p. 48.

[Illustration:

  FIG. 46.--The Little Penguin (_Aptenodytes minor_, Linn.), adapted
  exclusively for swimming and diving. In this quaint bird the wing
  forms a perfect screw, and is employed as such in swimming and
  diving. Compare with fig. 37, p. 76, and fig. 44, p. 89.--_Original._]

In birds which fly indiscriminately above and beneath the water, the
wing is provided with stiff feathers, and reduced to a minimum as
regards size. In subaqueous flight the wings may act by themselves,
as in the guillemots, or in conjunction with the feet, as in the
grebes.[56] To convert the wing into a powerful oar for swimming,
it is only necessary to extend and flex it in a slightly backward
direction, the mere act of extension causing the feathers to roll down,
and giving to the back of the wing, which in this case communicates the
more effective stroke, the angle or obliquity necessary for sending
the animal forward. This angle, I may observe, corresponds with that
made by the foot during extension, so that, if the feet and wings are
both employed, they act in harmony. If proof were wanting that it is
the back or convex surface of the wing which gives the more effective
stroke in subaquatic flight, it would be found in the fact that in the
penguin and great auk, which are totally incapable of flying out of the
water, the wing is actually twisted round in order that the concave
surface, which takes a better hold of the water, may be directed
backwards (fig. 46).[57] The thick margin of the wing when giving the
effective stroke is turned downwards, as happens in the flippers of
the sea-bear, walrus, and turtle. This, I need scarcely remark, is
precisely the reverse of what occurs in the ordinary wing in aërial
flight. In those extraordinary birds (great auk and penguin) the wing
is covered with short, bristly-looking feathers, and is a mere rudiment
and exceedingly rigid, the movement which wields it emanating, for
the most part, from the shoulder, where the articulation partakes of
the nature of a universal joint. The wing is beautifully twisted upon
itself, and when it is elevated and advanced, it rolls up from the side
of the bird at varying degrees of obliquity, till it makes a right
angle with the body, when it presents a _narrow_ or _cutting edge_ to
the water. The wing when fully extended, as in ordinary flight, makes,
on the contrary, an angle of something like 30° with the horizon. When
the wing is depressed and carried backwards,[58] the angles which
its under surface make with the surface of the water are gradually
increased. The wing of the penguin and auk propels both when it is
elevated and depressed. It acts very much after the manner of a screw;
and this, as I shall endeavour to show, holds true likewise of the wing
adapted for aërial flight.

  [56] The guillemots in diving do not use their feet; so that they
  literally fly under the water. Their wings for this purpose are
  reduced to the smallest possible dimensions consistent with flight.
  The loons, on the other hand, while they employ their feet, rarely,
  if ever, use their wings. The subaqueous progression of the grebe
  resembles that of the frog.--Cuvier’s Animal Kingdom, Lond. 1840,
  pp. 252, 253.

  [57] In the swimming of the crocodile, turtle, triton, and frog, the
  concave surfaces of the feet of the anterior extremities are likewise
  turned backwards.

  [58] The effective stroke is also delivered during flexion in the
  shrimp, prawn, and lobster.

_Difference between Subaquatic and Aërial Flight._--The difference
between subaquatic flight or diving, and flight proper, may be briefly
stated. In aërial flight, the most effective stroke is delivered
_downwards_ and _forwards_ by the under, concave, or biting surface
of the wing which is turned in this direction; the less effective
stroke being delivered in an upward and forward direction by the upper,
convex, or non-biting surface of the wing. In subaquatic flight, on
the contrary, the most effective stroke is delivered _downwards_ and
_backwards_, the least effective one upwards and forwards. In aërial
flight the long axis of the body of the bird and the short axis of the
wings are inclined slightly upwards, and make a _forward_ angle with
the horizon. In subaquatic flight the long axis of the body of the
bird, and the short axis of the wings are inclined slightly downwards
and make a _backward_ angle with the surface of the water. The wing
acts more or less efficiently in every direction, as the tail of the
fish does. The difference noted in the direction of the down stroke
in flying and diving, is rendered imperative by the fact that a bird
which flies in the air is heavier than the medium it navigates, and
must be supported by the wings; whereas a bird which flies under the
water or dives, is lighter than the water, and must force itself into
it to prevent its being buoyed up to the surface. However paradoxical
it may seem, _weight_ is necessary to aërial flight, and _levity_ to
subaquatic flight. A bird destined to fly above the water is provided
with travelling surfaces, so fashioned and so applied (they strike
_from above_, _downwards_ and _forwards_), that if it was lighter than
the air, they would carry it off into space without the possibility of
a return; in other words, the action of the wings would carry the bird
obliquely upwards, and render it quite incapable of flying either in a
horizontal or downward direction. In the same way, if a bird destined
to fly under the water (auk and penguin) was not lighter than the
water, such is the configuration and mode of applying its travelling
surfaces (they strike _from above_, _downwards_ and _backwards_), they
would carry it in the direction of the bottom without any chance of
return to the surface. In aërial flight, weight is the power which
nature has placed at the disposal of the bird for regulating its
altitude and horizontal movements, a cessation of the play of its
wings, aided by the inertia of its trunk, enabling the bird to approach
the earth. In subaquatic flight, levity is a power furnished for a
similar but opposite purpose; this, combined with the partial slowing
or stopping of the wings and feet, enabling the diving bird to regain
the surface at any moment. Levity and weight are auxiliary forces, but
they are necessary forces when the habits of the aërial and aquatic
birds and the form and mode of applying their travelling surfaces are
taken into account. If the aërial flying bird was lighter than the air,
its wings would require _to be twisted round_ to resemble the diving
wings of the penguin and auk. If, on the other hand, the diving bird
(penguin or auk) was heavier than the water, its wings would require to
resemble aërial wings, and they would require to strike in an opposite
direction to that in which they strike normally. From this it follows
that _weight_ is necessary to the bird (as at present constructed)
destined to navigate the air, and _levity_ to that destined to navigate
the water. If a bird was made very large and very light, it is obvious
that the diving force at its disposal would be inadequate to submerge
it. If, again, it was made very small and very heavy, it is equally
plain that it could not fly. Nature, however, has struck the just
balance; she has made the diving bird, which flies under the water,
relatively much heavier than the bird which flies in the air, and
has curtailed the travelling surfaces of the former, while she has
increased those of the latter. For the same reason, she has furnished
the diving bird with a certain degree of buoyancy, and the flying
bird with a certain amount of weight--levity tending to bring the one
to the surface of the water, weight the other to the surface of the
earth, which is the normal position of rest for both. The action of the
subaquatic or diving wing of the king penguin is well seen at p. 94,
fig. 47.

[Illustration:

  FIG. 47.--At _A_ the penguin is in the act of diving, and it will be
  observed that the anterior or thick margin of the wing is directed
  downwards and forwards, while the posterior margin is directed
  upwards and backwards. This has the effect of directing the under
  or ventral concave surface of the wing _upwards_ and _backwards_,
  the most effective stroke being delivered in a downward and backward
  direction. The efficacy of the wing in counteracting _levity_ is thus
  obvious. At _B_ the penguin is in the act of regaining the surface of
  the water, and in this case the wing is maintained in one position,
  or made to strike downwards and forwards like the aërial wing, the
  margins and under surface of the pinion being reversed for this
  purpose. The object now is not to depress but to elevate the body.
  Those movements are facilitated by the alternate play of the feet.
  (Compare fig. 47 with fig. 37, p. 76.)]

From what has been stated it will be evident that the wing acts very
differently in and out of the water; and this is a point deserving of
attention, the more especially as it seems to have hitherto escaped
observation. In the water the wing, when most effective, strikes
_downwards_ and _backwards_, and acts as an auxiliary of the foot;
whereas in the air it strikes _downwards_ and _forwards_. The oblique
surfaces, spiral or otherwise, presented by animals to the water and
air are therefore made to act in opposite directions, as far as the
down strokes are concerned. This is owing to the greater density of
the water as compared with the air,--the former supporting or nearly
supporting the animal moving upon or in it; the latter permitting the
creature to fall through it in a downward direction during the ascent
of the wing. To counteract the tendency of the bird in motion to fall
downwards and forwards, the down stroke is delivered in this direction;
the kite-like action of the wing, and the rapidity with which it is
moved causing the mass of the bird to pursue a more or less horizontal
course. I offer this explanation of the action of the wing in and out
of the water after repeated and careful observation in tame and wild
birds, and, as I am aware, in opposition to all previous writers on the
subject.

The rudimentary wings or paddles of the penguin (the movements of which
I had an opportunity of studying in a tame specimen) are principally
employed in swimming and diving. The feet, which are of moderate size
and strongly webbed, are occasionally used as auxiliaries. There
is this difference between the movements of the wings and feet of
this most curious bird, and it is worthy of attention. The wings act
together, or synchronously, as in flying birds; the feet, on the
other hand, are moved alternately. The wings are wielded with great
energy, and, because of their semi-rigid condition, are incapable of
expansion. They therefore present their maximum and minimum of surface
by a partial rotation or tilting of the pinion, as in the walrus,
sea-bear, and turtle. The feet, which are moved with less vigour,
are, on the contrary, rotated or tilted to a very slight extent, the
increase and diminution of surface being secured by the opening and
closing of the membranous expansion or web between the toes. In this
latter respect they bear a certain analogy to the feet of the seal, the
toes of which, as has been explained, spread out or divaricate during
extension, and the reverse. The feet of the penguin entirely differ
from those of the seal, in being worked separately, the foot of one
side being flexed or drawn towards the body, while its fellow is being
extended or pushed away from it. The feet, moreover, describe definite
curves in opposite directions, the right foot proceeding from within
outwards, and from above downwards during extension, or when it is
fully expanded and giving the effective stroke; the left one, which is
moving at the same time, proceeding from without inwards and from below
upwards during flexion, or when it is folded up, as happens during the
back stroke. In the acts of extension and flexion the legs are slightly
rotated, and the feet more or less tilted. The same movements are
seen in the feet of the swan, and in those of swimming birds generally
(fig. 48).

[Illustration:

  FIG. 48.--Swan, in the act of swimming, the right foot being fully
  expanded, and about to give the effective stroke, which is delivered
  outwards, downwards, and backwards, as represented at _r_ of fig. 50;
  the left foot being closed, and about to make the return stroke,
  which is delivered in an inward, upward, and forward direction,
  as shown at _s_ of fig. 50. In rapid swimming the swan flexes its
  legs simultaneously and somewhat slowly; it then vigorously extends
  them.--_Original._]

[Illustration:

  FIG. 49.--Foot of Grebe (_Podiceps_). In this foot each toe is
  provided with its swimming membrane; the membrane being closed when
  the foot is flexed, and expanded when the foot is extended. Compare
  with foot of swan (fig. 48), where the swimming membrane is continued
  from the one toe to the other.--(After Dallas.)]

One of the most exquisitely constructed feet for swimming and diving
purposes is that of the grebe (fig. 49). This foot consists of three
swimming toes, each of which is provided with a membranous expansion,
which closes when the foot is being drawn towards the body during the
back stroke, and opens out when it is being forced away from the body
during the effective stroke.

[Illustration:

  FIG. 50.--Diagram representing the double waved track described by
  the feet of swimming birds. Compare with figs. 18 and 19, pp. 37 and
  39, and with fig. 32, p. 68.--_Original._]

In swimming birds, each foot describes one side of an ellipse when it
is extended and thrust from the body, the other side of the ellipse
being described when the foot is flexed and drawn towards the body.
The curve described by the right foot when pushed from the body is
seen at the arrow _r_ of fig. 50; that formed by the left foot when
drawn towards the body, at the arrow _s_ of the same figure. The curves
formed by the feet during extension and flexion produce, when united
in the act of swimming, waved lines, these constituting a chart for the
movements of the extremities of swimming birds.

There is consequently an obvious analogy between the swimming of birds
and the walking of man (compare fig. 50, p. 97, with fig. 19, p. 39);
between the walking of man and the walking of the quadruped (compare
figs. 18 and 19, pp. 37 and 39); between the walking of the quadruped
and the swimming of the walrus, sea-bear, and seal; between the
swimming of the seal, whale, dugong, manatee, and porpoise, and that of
the fish (compare fig. 32, p. 68, with figs. 18 and 19, pp. 37 and 39);
and between the swimming of the fish and the flying of the insect, bat,
and bird (compare all the foregoing figures with figs. 71, 73, and 81,
pp. 144 and 157).

[Illustration:

  FIG. 51.--The Flying-fish (_Exocœtus exsiliens_, Linn.), with wings
  expanded and elevated in the act of flight (_vide_ arrows). This
  anomalous and interesting creature is adapted both for swimming
  and flying. The swimming-tail is consequently retained, and the
  pectoral fins, which act as wings, are enormously increased in
  size.--_Original._]

_Flight of the Flying-fish; the kite-like action of the Wings,
etc._--Whether the flying-fish uses its greatly expanded pectoral fins
as a bird its wings, or only as parachutes, has not, so far as I am
aware, been determined by actual observation. Most observers are of
opinion that these singular creatures glide up the wind, and do not
beat it after the manner of birds; so that their flight (or rather
leap) is indicated by the arc of a circle, the sea supplying the
chord. I have carefully examined the structure, relations, and action
of those fins, and am satisfied in my own mind that they act as true
pinions within certain limits, their inadequate dimensions and limited
range alone preventing them from sustaining the fish in the air for
indefinite periods. When the fins are fully flexed, as happens when
the fish is swimming, they are arranged along the sides of the body;
but when it takes to the air, they are raised above the body and make
a certain angle with it. In being raised they are likewise inclined
forwards and outwards, the fins rotating on their long axes until they
make an angle of something like 30° with _the horizon_--this being, as
nearly as I can determine, the greatest angle made by the wings during
the down stroke in the flight of insects and birds.

The pectoral fins, or pseudo-wings of the flying-fish, like all other
wings, act after the manner of kites--the angles of inclination
which their under surfaces make with the horizon varying according
to the degree of extension, the speed acquired, and the pressure to
which they are subjected by being carried against the air. When the
flying-fish, after a preliminary rush through the water (in which it
acquires initial velocity), throws itself into the air, it is supported
and carried forwards by the kite-like action of its pinions;--this
action being identical with that of the boy’s kite when the boy runs,
and by pulling upon the string causes the kite to glide upwards and
forwards. In the case of the boy’s kite _a pulling force_ is applied
to the kite in front. In the case of the flying-fish (and everything
which flies) _a similar force_ is applied to the kites formed by the
wings by the weight of the flying mass, which always tends to fall
vertically downwards. Weight supplies a motor power in flight similar
to that supplied by the leads in a clock. In the case of the boy’s
kite, the hand of the operator furnishes the power; in flight, a large
proportion of the power is furnished by the weight of the body of the
flying creature. It is a matter of indifference how a kite is flown, so
long as its under surface is made to impinge upon the air over which
it passes.[59] A kite will fly effectually when it is neither acted
upon by the hand nor a weight, provided always there is a stiff breeze
blowing. In flight one of two things is necessary. Either the under
surface of the wings must be carried rapidly against still air, or
the air must rush violently against the under surface of the expanded
but motionless wings. Either the wings, the body bearing them, or the
air, must be in rapid motion; one or other must be active. To this
there is no exception. To fly a kite in still air the operator must
run. If a breeze is blowing the operator does not require to alter
his position, the breeze doing the entire work. It is the same with
wings. In still air a bird, or whatever attempts to fly, must flap
its wings energetically until it acquires initial velocity, when the
flapping may be discontinued; or it must throw itself from a height,
in which case the initial velocity is acquired by the weight of the
body acting upon the inclined planes formed by the motionless wings.
The flapping and gliding action of the wings constitute the difference
between ordinary flight and that known as skimming or sailing flight.
The flight of the flying-fish is to be regarded rather as an example
of the latter than the former, the fish transferring the velocity
acquired by the vigorous lashing of its tail in the water to the
air,--an arrangement which enables it to dispense in a great measure
with the flapping of the wings, which act by a combined parachute and
wedge action. In the flying-fish the flying-fin or wing attacks the
air _from beneath_, whilst it is being raised above the body. It has
no downward stroke, the position and attachments of the fin preventing
it from descending beneath the level of the body of the fish. In this
respect the flying-fin of the fish differs slightly from the wing of
the insect, bat, and bird. The gradual expansion and raising of the
fins of the fish, coupled with the fact that the fins never descend
below the body, account for the admitted absence of beating, and have
no doubt originated the belief that the pectoral fins are merely
passive organs. If, however, they do not act as true pinions within
the limits prescribed, it is difficult, and indeed impossible, to
understand how such small creatures can obtain the momentum necessary
to project them a distance of 200 or more yards, and to attain, as they
sometimes do, an elevation of twenty or more feet above the water.
Mr. Swainson, in crossing the line in 1816, zealously attempted to
discover the true action of the fins in question, but the flight of the
fish is so rapid that he utterly failed. He gives it as his opinion
that flight is performed in two ways,--first by a spring or leap, and
second by the spreading of the pectoral fins, which are employed in
propelling the fish in a forward direction, either by flapping or by a
motion analogous to the skimming of swallows. He records the important
fact, that the flying-fish can change its course after leaving the
water, which satisfactorily proves that the fins are not simply passive
structures. Mr. Lord, of the Royal Artillery,[60] thus writes of those
remarkable specimens of the finny tribe:--“There is no sight more
charming than the flight of a shoal of flying-fish, as they shoot forth
from the dark green wave in a glittering throng, like silver birds in
some gay fairy tale, gleaming brightly in the sunshine, and then, with
a mere touch on the crest of the heaving billow, again flitting onward
reinvigorated and refreshed.”

  [59] “On the Various Modes of Flight in relation to Aëronautics.” By
  the Author.--Proceedings of the Royal Institution of Great Britain,
  March 1867.

  [60] Nature and Art, November 1866, p. 173.

Before proceeding to a consideration of the graceful and, in some
respects, mysterious evolutions of the denizens of the air, and
the far-stretching pinions by which they are produced, it may not
be out of place to say a few words in recapitulation regarding the
extent and nature of the surfaces by which progression is secured
on land and on or in the water. This is the more necessary, as the
travelling-surfaces employed by animals in walking and swimming bear
a certain, if not a fixed, relation to those employed by insects,
bats, and birds in flying. On looking back, we are at once struck with
the fact, remarkable in some respects, that the travelling-surfaces,
whether feet, flippers, fins, or pinions, are, as a rule, increased
in proportion to the tenuity of the medium on which they are destined
to operate. In the ox (fig. 18, p. 37) we behold a ponderous body,
slender extremities, and unusually small feet. The feet are slightly
expanded in the otter (fig. 12, p. 34), and considerably so in the
ornithorhynchus (fig. 11, p. 34). The travelling-area is augmented
in the seal (fig. 14, p. 34; fig. 36, p. 74), penguin (figs. 46 and
47, pp. 91 and 94), sea-bear (fig. 37, p. 76), and turtle (fig. 44,
p. 89). In the triton (fig. 45, p. 89) a huge swimming-tail is added
to the feet--the tail becoming larger, and the extremities (anterior)
diminishing, in the manatee (fig. 34, p. 73) and porpoise (fig. 33,
p. 73), until we arrive at the fish (fig. 30, p. 65), where not only
the tail but _the lower half of the body_ is actively engaged in
natation. Turning from the water to the air, we observe a remarkable
modification in the huge pectoral fins of the flying-fish (fig. 51,
p. 98), these enabling the creature to take enormous leaps, and serving
as pseudo-pinions. Turning in like manner from the earth to the air,
we encounter the immense tegumentary expansions of the flying-dragon
(fig. 15, p. 35) and galeopithecus (fig. 16, p. 35), the floating
or buoying area of which greatly exceeds that of some of the flying
beetles.

In those animals which fly, as bats (fig. 17, p. 36), insects (figs. 57
and 58, p. 124 and 125), and birds (figs. 59 and 60, p. 126), the
travelling surfaces, because of the extreme tenuity of the air, are
prodigiously augmented; these in many instances greatly exceeding the
actual area of the body. While, therefore, the movements involved in
walking, swimming, and flying are to be traced in the first instance
to the shortening and lengthening of the muscular, elastic, and other
tissues operating on the bones, and their peculiar articular surfaces;
they are to be referred in the second instance to the extent and
configuration of the travelling areas--these on all occasions being
accurately adapted to the capacity and strength of the animal and the
density of the medium on or in which it is intended to progress. Thus
the land supplies the resistance, and affords the support necessary
to prevent the small feet of land animals from sinking to dangerous
depths, while the water, immensely less resisting, furnishes the
peculiar medium requisite for buoying the fish, and for exposing,
without danger and to most advantage, the large surface contained in
its ponderous lashing tail,--the air, unseen and unfelt, furnishing
that quickly yielding and subtle element in which the greatly expanded
pinions of the insect, bat, and bird are made to vibrate with lightning
rapidity, discoursing, as they do so, a soft and stirring music very
delightful to the lover of nature.




PROGRESSION IN OR THROUGH THE AIR.


The atmosphere, because of its great tenuity, mobility, and comparative
imponderability, presents little resistance to bodies passing through
it at low velocities. If, however, the speed be greatly accelerated,
the passage of even an ordinary cane is sensibly impeded.

This comes of the action and reaction of matter, the resistance
experienced varying according to the density of the atmosphere and
the shape, extent, and velocity of the body acting upon it. While,
therefore, scarcely any impediment is offered to the progress of an
animal in motion, it is often exceedingly difficult to compress the
air with sufficient rapidity and energy to convert it into a suitable
fulcrum for securing the onward impetus. This arises from the fact
that bodies moving in the air experience the _minimum of resistance_
and occasion the _maximum of displacement_. Another and very obvious
difficulty is traceable to the great disparity in the weight of air as
compared with any known solid, this in the case of water being nearly
as 1000 to 1. According to the density of the medium so is its buoying
or sustaining power.

_The Wing a Lever of the Third Order._--To meet the peculiarities
stated above, the insect, bat, and bird are furnished with extensive
surfaces in the shape of pinions or wings, which they can apply
with singular velocity and power, as levers of the third order
(fig. 3, p. 20),[61] at various angles, or by alternate slow and
sudden movements, to obtain the necessary degree of resistance and
non-resistance. Although the third order of lever is particularly
inefficient when the fulcrum is _rigid_ and _immobile_, it possesses
singular advantages when these conditions are reversed, _i.e._ when the
fulcrum, as happens with the air, is _elastic_ and _yielding_. In this
case a very slight movement at the root of the pinion, or that end of
the lever directed towards the body, is succeeded by an immense sweep
of the extremity of the wing, where its elevating and propelling power
is greatest. This arrangement insures that the large quantity of air
necessary for propulsion and support shall be compressed under the most
favourable conditions.

  [61] In this form of lever the power is applied between the fulcrum
  and the weight to be raised. The mass to be elevated is the body of
  the insect, bat, or bird,--the force which resides in the living
  pinion (aided by the inertia of the trunk) representing the power,
  and the air the fulcrum.

It follows from this that those insects and birds are endowed with the
greatest powers of flight whose wings are the longest. The dragon-fly
and albatross furnish examples. The former on some occasions dashes
along with amazing velocity and wheels with incredible rapidity; at
other times it suddenly checks its headlong career and hovers or fixes
itself in the air after the manner of the kestrel and humming-birds.
The flight of the albatross is also remarkable. This magnificent
bird, I am informed on reliable authority, sails about with apparent
unconcern for hours together, and rarely deigns to flap its enormous
pinions, which stream from its body like ribbons to the extent, in some
cases, of seven feet on either side.

The manner in which the wing levers the body upwards and forwards in
flight is shown at fig. 52.

[Illustration: FIG. 52.]

In this fig. _f f´_ represent the moveable fulcra furnished by the
air; _p p´_ the power residing in the wing, and _b_ the body to be
flown. In order to make the problem of flight more intelligible, I
have prolonged the lever formed by the wing beyond the body (_b_), and
have applied to the root of the wing so extended the weight _w w´_.
_x_ represents the universal joint by which the wing is attached to
the body. When the wing ascends, as shown at _p_, the air (= fulcrum
_f_) resists its upward passage, and forces the body (_b_), or its
representative (_w_), slightly downwards. When the wing descends, as
shown at _p´_, the air (= fulcrum _f´_) resists its downward passage,
and forces the body (_b_), or its representative (_w´_), slightly
upwards. From this it follows, that when the wing rises the body
falls, and _vice versâ_; the wing describing the arc of a large circle
(_f f´_), the body (_b_), or the weights representing it (_w w´_)
describing the arc of a much smaller circle. The body, therefore, as
well as the wing, rises and falls in flight. When the wing descends it
elevates the body, the wing being active and the body passive; when
the body descends it elevates the wing, the body being active and the
wing passive. The elevator muscles, and the reaction of the air on
the under surface of the wing, contribute to its elevation. It is in
this manner that weight forms a factor in flight, the wing and the
weight of the body reciprocating and mutually assisting and relieving
each other. This is an argument for employing four wings in artificial
flight, the wings being so arranged that the two which are up shall
always by their fall mechanically elevate the two which are down. Such
an arrangement is calculated greatly to conserve the driving power,
and, as a consequence, to reduce the weight. It is the upper or dorsal
surface of the wing which more especially operates upon the air during
the up stroke, and the under or ventral surface which operates during
the down stroke. The wing, which at the beginning of the down stroke
has its surfaces and margins (anterior and posterior) arranged in
nearly the same plane with the horizon,[62] rotates upon its anterior
margin as an axis during its descent and causes its under surface to
make a gradually increasing angle with the horizon, the posterior
margin (fig. 53, _c_) in this movement descending beneath the anterior
one. A similar but opposite rotation takes place during the up stroke.
The rotation referred to causes the wing to twist on its long axis
screw-fashion, and to describe a figure-of-8 track in space, one-half
of the figure being described during the ascent of the wing, the other
half during its descent. The twisting of the wing and the figure-of-8
track described by it when made to vibrate, are represented at fig. 53.
The rotation of the wing on its long axis as it ascends and descends
causes the under surface of the wing to act as a kite, both during
the up and down strokes, provided always the body bearing the wing
is in forward motion. But the upper surface of the wing, as has been
explained, acts when the wing is being elevated, so that both the upper
and under surfaces of the wing are efficient during the up stroke.
When the wing ascends, the upper surface impinges against the air;
the under surface impinging at the same time from its being carried
obliquely forward, after the manner of a kite, by the body, which is in
motion. During the down stroke, the under surface only acts. The wing
is consequently effective both during its ascent and descent, its slip
being nominal in amount. The wing acts as a kite, both when it ascends
and descends. It acts more as a propeller than an elevator during its
ascent; and more as an elevator than a propeller during its descent.
It is, however, effective both in an upward and downward direction.
The efficiency of the wing is greatly increased by the fact that when
it ascends it draws a current of air up after it, which current being
met by the wing during its descent, greatly augments the power of the
down stroke. In like manner, when the wing descends it draws a current
of air down after it, which being met by the wing during its ascent,
greatly augments the power of the up stroke. These induced currents
are to the wing what a stiff autumn breeze is to the boy’s kite. The
wing is endowed with this very remarkable property, that it creates
the current on which it rises and progresses. It literally flies on a
whirlwind of its own forming.

  [62] In some cases the posterior margin is slightly elevated above
  the horizon (fig. 53, _g_).

These remarks apply more especially to the wings of bats and birds,
and those insects whose wings are made to vibrate in a more or less
vertical direction. The action of the wing is readily imitated, as a
reference to fig. 53 will show.

[Illustration: FIG. 53.]

If, for example, I take a tapering elastic reed, as represented at
_a b_, and supply it with a flexible elastic sail (_c d_), and a
ball-and-socket joint (_x_), I have only to seize the reed at _a_
and cause it to oscillate upon _x_ to elicit all the wing movements.
By depressing the root of the reed in the direction _n e_, the wing
flies up as a kite in the direction _j f_. During the upward movement
the wing flies upwards and forwards, and describes a double curve. By
elevating the root of the reed in the direction _m a_, the wing flies
down as a kite in the direction _i b_. During the downward movement the
wing flies downwards and forwards, and describes a double curve. These
curves, when united, form a waved track, which represents progressive
flight. During the rise and fall of the wing a large amount of tractile
force is evolved, and if the wings and the body of the flying creature
are inclined slightly upwards, kite-fashion, as they invariably are
in ordinary flight, the whole mass of necessity moves upwards and
forwards. To this there is no exception. A sheet of paper or a card
will float along if its anterior margin is slightly raised, and if
it be projected with sufficient velocity. The wings of all flying
creatures when made to vibrate, twist and untwist, the posterior thin
margin of each wing twisting round the anterior thick one, like the
blade of a screw. The artificial wing represented at fig. 53 (p. 107)
does the same, _c d_ twisting round _a b_, and _g h_ round _e f_. The
natural and artificial wings, when elevated and depressed, describe a
figure-of-8 track in space when the bodies to which they are attached
are stationary. When the bodies advance, the figure-of-8 is opened out
to form first a looped and then a waved track. I have shown how those
insects, bats, and birds which flap their wings in a more or less
vertical direction evolve tractile or propelling power, and how this,
operating on properly constructed inclined surfaces, results in flight.
I wish now to show that flight may also be produced by a very oblique
and almost horizontal stroke of the wing, as in some insects, _e.g._
the wasp, blue-bottle, and other flies. In those insects the wing is
made to vibrate with a figure-of-8 sculling motion in a very oblique
direction, and with immense energy. This form of flight differs in no
respect from the other, unless in the direction of the stroke, and can
be readily imitated, as a reference to fig. 54 will show.

[Illustration: FIG. 54.]

In this figure (54) the conditions represented at fig. 53 (p. 107)
are exactly reproduced, the only difference being that in the present
figure the wing is applied to the air in a more or less horizontal
direction, whereas in fig. 53 it is applied in a more or less vertical
direction. The letters in both figures are the same. The insects whose
wings tack upon the air in a more or less horizontal direction, have an
extensive range, each wing describing nearly half a circle, these half
circles corresponding to the area of support. The body of the insect
is consequently the centre of a circle of motion. It corresponds to
_x_ of the present figure (fig. 54). When the wing is seized by the
hand at _a_, and the root made to travel in the direction _n e_, the
body of the wing travels in the direction _j f_. While so travelling,
it flies upwards in a double curve, kite-fashion, and elevates the
weight _l_. When it reaches the point _f_, it reverses suddenly to
prepare for a return stroke, which is produced by causing the root of
the wing to travel in the direction _m a_, the body and tip travelling
in the direction _i b_. During the reverse stroke, the wing flies
upwards in a double curve, kite-fashion, and elevates the weight _k_.
The more rapidly these movements are repeated, the more powerful the
wing becomes, and the greater the weight it elevates. This follows
because of the reciprocating action of the wing,--the wing, as already
explained, always drawing a current of air after it during the one
stroke, which is met and utilized by it during the next stroke. The
reciprocating action of the wing here referred to is analogous in
all respects to that observed in the flippers of the seal, sea-bear,
walrus, and turtle; the swimming wing of the penguin; and the tail
of the whale, dugong, manatee, porpoise, and fish. If the muscles
of the insect were made to act at the points _a e_, the body of the
insect would be elevated as at _k l_, by the reciprocating action of
the wings. The amount of tractile power developed in the arrangement
represented at fig. 53 (p. 107), can be readily ascertained by fixing a
spring or a weight acting over a pulley to the anterior margin (_a b_
or _e f_) of the wing; weights acting over pulleys being attached to
the root of the wing (_a_ or _e_).

The amount of elevating power developed in the arrangement represented
at fig. 54, can also be estimated by causing weights acting over
pulleys to operate upon the root of the wing (_a_ or _e_), and watching
how far the weights (_k_ or _l_) are raised. In these calculations
allowance is of course to be made for friction. The object of the two
sets of experiments described and figured, is to show that the wing can
exert a tractile power either in a nearly horizontal direction or in a
nearly vertical one, flight being produced in both cases. I wish now to
show that a body not supplied with wings or inclined surfaces will, if
left to itself, fall vertically downwards; whereas, if it be furnished
with wings, its vertical fall is converted into oblique downward
flight. These are very interesting points. Experiment has shown me that
a wing when made to vibrate vertically produces horizontal traction;
when made to vibrate horizontally, vertical traction; the vertical fall
of a body armed with wings producing oblique traction. The descent
of weights can also be made to propel the wings either in a vertical
or horizontal direction; the vibration of the wings upon the air in
natural flight causing the weights (body of flying creature) to move
forward. This shows the very important part performed by weight in all
kinds of flight.

_Weight necessary to Flight._--However paradoxical it may seem, a
certain amount of weight is indispensable in flight.

In the first place, it gives peculiar efficacy and energy to the up
stroke, by acting upon the inclined planes formed by the wings in the
direction of the plane of progression. The power and the weight may
thus be said to reciprocate, the two sitting, as it were, side by side,
and blending their peculiar influences to produce a common result.

Secondly, it adds momentum,--a heavy body, when once fairly under
weigh, meeting with little resistance from the air, through which it
sweeps like a heavy pendulum.

Thirdly, the mere act of rotating the wings on and off the wind during
extension and flexion, with a slight downward stroke, apparently
represents the entire exertion on the part of the volant animal, the
rest being performed by weight alone.

This last circumstance is deserving of attention, the more especially
as it seems to constitute the principal difference between a living
flying thing and an aërial machine. If a flying-machine was constructed
in accordance with the principles which we behold in nature, the weight
and the propelling power of the machine would be made to act upon the
sustaining and propelling surfaces, whatever shape they assumed, and
these in turn would be made to operate upon the air, and _vice versâ_.
In the aërial machine, as far as yet devised, there is no sympathy
between the weight to be elevated and the lifting power, whilst in
natural flight the wings and the weight of the flying creature act in
concert and reciprocate; the wings elevating the body the one instant,
the body by its fall elevating the wings the next. When the wings
elevate the body they are active, the body being passive. When the body
elevates the wings it is active, the wings being passive. The force
residing in the wings, and the force residing in the body (weight is a
force when launched in space and free to fall in a vertical direction)
cause the mass of the volant animal to oscillate vertically on either
side of an imaginary line--this line corresponding to the path of the
insect, bat, or bird in the air. While the wings and body act and
react upon each other, the wings, body, and air likewise act and react
upon each other. In the flight of insects, bats, and birds, _weight_
is to be regarded as an independent moving power, this being made to
act upon the oblique surfaces presented by the wings in conjunction
with the power expended by the animal--the latter being, by this
arrangement, conserved to a remarkable extent. Weight, assisted by
the elastic ligaments or springs, which recover all wings in flexion,
is to be regarded as the mechanical expedient resorted to by nature
in supplementing the efforts of all flying things.[63] Without this,
flight would be of short duration, laboured, and uncertain, and the
almost miraculous journeys at present performed by the denizens of the
air impossible.

[63] Weight, as is well known, is the sole moving power in the
clock--the pendulum being used merely to regulate the movements
produced by the descent of the leads. In watches, the onus of motion
is thrown upon a _spiral spring_; and it is worthy of remark that the
mechanician has seized upon, and ingeniously utilized, two forces
largely employed in the animal kingdom.

_Weight contributes to Horizontal Flight._--That the weight of the body
plays an important part in the production of flight may be proved by a
very simple experiment.

[Illustration: FIG. 55.]

If I take two primary feathers and fix them in an ordinary cork, as
represented at fig. 55, and allow the apparatus to drop from a height,
I find the cork does not fall vertically downwards, but _downwards_
and _forwards_ in a curve. This follows, because the feathers _a_,
_b_ are twisted flexible inclined planes, which arch in an upward
direction. They are in fact true wings in the sense that an insect
wing in one piece is a true wing. (Compare _a_, _b_, _c_ of fig. 55,
with _g_, _g´_, _s_ of fig. 82, p. 158.) When dragged downwards by
the cork (_c_), which would, if left to itself, fall vertically, they
have what is virtually a down stroke communicated to them. Under these
circumstances a struggle ensues between the cork tending to fall
vertically and the feathers tending to travel in an upward direction,
and, as a consequence, the apparatus describes the curve _d e f g_
before reaching the earth _h_, _i_. This is due to the action and
reaction of the feathers and air upon each other, and to the influence
which gravity exerts upon the cork. The forward travel of the cork and
feathers, as compared with the space through which they fall, is very
great. Thus, in some instances, I found they advanced as much as a yard
and a half in a descent of three yards. Here, then, is an example of
flight produced by purely mechanical appliances. The winged seeds fly
in precisely the same manner. The seeds of the plane-tree have, _e.g._
two wings which exactly resemble the wings employed for flying; thus
they taper from the root towards the tip, and from the anterior margin
towards the posterior margin, the margins being twisted and disposed
in different planes to form true screws. This arrangement prevents the
seed from falling rapidly or vertically, and if a breeze is blowing
it is wafted to a considerable distance before it reaches the ground.
Nature is uniform and consistent throughout. She employs the same
principle, and very nearly the same means, for flying a heavy, solid
seed which she employs for flying an insect, a bat, or a bird.

When artificial wings constructed on the plan of natural ones, with
stiff roots, tapering semi-rigid anterior margins, and thin yielding
posterior margins, are allowed to drop from a height, they describe
double curves in falling, the roots of the wings reaching the ground
first. This circumstance proves the greater buoying power of the tips
of the wings as compared with the roots. I might refer to many other
experiments made in this direction, but these are sufficient to show
that weight, when acting upon wings, or, what is the same thing, upon
elastic twisted inclined planes, must be regarded as an independent
moving power. But for this circumstance flight would be at once the
most awkward and laborious form of locomotion, whereas in reality
it is incomparably the easiest and most graceful. The power which
rapidly vibrating wings have in sustaining a body which tends to
fall vertically downwards, is much greater than one would naturally
imagine, from the fact that the body, which is always beginning to
fall, is never permitted actually to do so. Thus, when it has fallen
sufficiently far to assist in elevating the wings, it is at once
elevated by the vigorous descent of those organs. The body consequently
never acquires the downward momentum which it would do if permitted
to fall through a considerable space uninterruptedly. It is easy to
restrain even a heavy body when beginning to fall, while it is next to
impossible to check its progress when it is once fairly launched in
space and travelling rapidly in a downward direction.

_Weight, Momentum, and Power, to a certain extent, synonymous in
Flight._--When a bird rises it has little or no momentum, so that if
it comes in contact with a solid resisting surface it does not injure
itself. When, however, it has acquired all the momentum of which it
is capable, and is in full and rapid flight, such contact results in
destruction. My friend Mr. A. D. Bartlett informed me of an instance
where a wild duck terminated its career by coming violently in contact
with one of the glasses of the Eddystone Lighthouse. The glass, which
was fully an inch in thickness, was completely smashed. Advantage is
taken of this circumstance in killing sea-birds, a bait being placed
on a board and set afloat with a view to breaking the neck of the
bird when it stoops to seize the carrion. The additional power due to
momentum in heavy bodies in motion is well illustrated in the start
and progress of steamboats. In these the _slip_, as it is technically
called, decreases as the speed of the vessel increases; the strength of
a man, if applied by a hawser attached to the stern of a moderate-sized
vessel, being sufficient to <DW44>, and, in some instances prevent, its
starting. In such a case the power of the engine is almost entirely
devoted to “slip” or in giving motion to the fluid in which the screw
or paddle is immersed. It is consequently not the power residing in the
paddle or screw which is cumulative, but the momentum inhering in the
mass. In the bird, the momentum, _alias_ weight, is made to act upon
the inclined planes formed by the wings, these adroitly converting it
into sustaining and propelling power. It is to this circumstance, more
than any other, that the prolonged flight of birds is mainly due, the
inertia or dead weight of the trunk aiding and abetting the action
of the wings, and so relieving the excess of exertion which would
necessarily devolve on the bird. It is thus that the power which in
living structures resides in the mass is conserved, and the mass itself
turned to account. But for this reciprocity, no bird could retain its
position in the air for more than a few minutes at a time. This is
proved by the comparatively brief upward flight of the lark and the
hovering of the hawk when hunting. In both these cases the body is
exclusively sustained by the action of the wings, the weight of the
trunk taking no part in it; in other words, the weight of the body does
not contribute to flight by adding its momentum and the impulse which
momentum begets. In the flight of the albatross, on the other hand,
the momentum acquired by the moving mass does the principal portion
of the work, the wings for the most part being simply rotated on and
off the wind to supply the proper angles necessary for the inertia or
mass to operate upon. It appears to me that in this blending of active
and passive power the mystery of flight is concealed, and that no
arrangement will succeed in producing flight artificially which does
not recognise and apply the principle here pointed out.

_Air-cells in Insects and Birds not necessary to Flight._--The boasted
levity of insects, bats, and birds, concerning which so much has been
written by authors in their attempts to explain flight, is delusive in
the highest degree.

Insects, bats, and birds are as heavy, bulk for bulk, as most other
living creatures, and flight can be performed perfectly by animals
which have neither air-sacs nor hollow bones; air-sacs being found in
animals never designed to fly. Those who subscribe to the heated-air
theory are of opinion that the air contained in the cavities of
insects and birds is so much lighter than the surrounding atmosphere,
that it must of necessity contribute materially to flight. I may
mention, however, that the quantity of air imprisoned is, to begin
with, so infinitesimally small, and the difference in weight which
it experiences by increase of temperature so inappreciable, that it
ought not to be taken into account by any one endeavouring to solve
the difficult and important problem of flight. The Montgolfier or
fire-balloons were constructed on the heated-air principle; but as
these have no analogue in nature, and are apparently incapable of
improvement, they are mentioned here rather to expose what I regard a
false theory than as tending to elucidate the true principles of flight.

When we have said that cylinders and hollow chambers increase the area
of the insect and bird, and that an insect and bird so constructed
is stronger, weight for weight, than one composed of solid matter, we
may dismiss the subject; flight being, as I shall endeavour to show
by-and-by, not so much a question of levity as one of weight and power
intelligently directed, upon properly constructed flying surfaces.

The bodies of insects, bats, and birds are constructed on strictly
mechanical principles,--lightness, strength, and durability of frame
being combined with power, rapidity, and precision of action. The
cylindrical method of construction is in them carried to an extreme,
the bodies and legs of insects displaying numerous unoccupied spaces,
while the muscles and solid parts are tunnelled by innumerable
air-tubes, which communicate with the surrounding medium by a series of
apertures termed spiracles.

A somewhat similar disposition of parts is met with in birds, these
being in many cases furnished not only with hollow bones, but also
(especially the aquatic ones) with a liberal supply of air-sacs. They
are likewise provided with a dense covering of feathers or down,
which adds greatly to their bulk without materially increasing their
weight. Their bodies, moreover, in not a few instances, particularly
in birds of prey, are more or less flattened. The air-sacs are well
seen in the swan, goose, and duck; and I have on several occasions
minutely examined them with a view to determine their extent and
function. In two of the specimens which I injected, the material
employed had found its way not only into those usually described,
but also into others which ramify in the substance of the muscles,
particularly the pectorals. No satisfactory explanation of the purpose
served by these air-sacs has, I regret to say, been yet tendered.
According to Sappey,[64] who has devoted a large share of attention to
the subject, they consist of a membrane which is neither serous nor
mucous, but partly the one and partly the other; and as blood-vessels
in considerable numbers, as my preparations show, ramify in their
substance, and they are in many cases covered with muscular fibres
which confer on them a rhythmic movement, some recent observers (Mr.
Drosier[65] of Cambridge, for example) have endeavoured to prove that
they are adjuncts of the lungs, and therefore assist in aërating the
blood. This opinion was advocated by John Hunter as early as 1774,[66]
and is probably correct, since the temperature of birds is higher
than that of any other class of animals, and because they are obliged
occasionally to make great muscular exertions both in swimming and
flying. Others have viewed the air-sacs in connexion with the hollow
bones frequently, though not always, found in birds,[67] and have come
to look upon the heated air which they contain as being more or less
essential to flight. That the air-cells have absolutely nothing to do
with flight is proved by the fact that some excellent fliers (take the
bats, _e.g._) are destitute of them, while birds such as the ostrich
and apteryx, which are incapable of flying, are provided with them.
Analogous air-sacs, moreover, are met with in animals never intended
to fly; and of these I may instance the great air-sac occupying the
cervical and axillary regions of the orang-outang, the float or
swimming-bladder in fishes, and the pouch communicating with the
trachea of the emu.[68]

  [64] Sappey enumerates fifteen air-sacs,--the _thoracic_, situated
  at the lower part of the neck, behind the sternum; _two cervical_,
  which run the whole length of the neck to the head, which they supply
  with air; _two pairs of anterior_, and _two pairs of posterior
  diaphragmatic_; and _two pairs of abdominal_.

  [65] “On the Functions of the Air-cells and the Mechanism of
  Respiration in Birds,” by W. H. Drosier, M.D., Caius College.--Proc.
  Camb. Phil. Soc., Feb. 12, 1866.

  [66] “An Account of certain Receptacles of Air in Birds which
  communicate with the Lungs, and are lodged among the Fleshy Parts and
  in the Hollow Bones of these Animals.”--Phil. Trans., Lond. 1774.

  [67] According to Dr. Crisp the swallow, martin, snipe, and many
  birds of passage have no air in their bones (Proc. Zool. Soc., Lond.
  part xxv. 1857, p. 13). The same author, in a second communication
  (pp. 215 and 216), adds that the glossy starling, spotted flycatcher,
  whin-chat, wood-wren, willow-wren, black-headed bunting, and canary,
  five of which are birds of passage, have likewise no air in their
  bones. The following is Dr. Crisp’s summary:--Out of ninety-two birds
  examined he found “air in many of the bones, five (_Falconidæ_);
  air in the humeri and not in the inferior extremities, thirty-nine;
  no air in the extremities and probably none in the other bones,
  forty-eight.”

  [68] Nearly allied to this is the great gular pouch of the bustard.
  Specimens of the air-sac in the orang, emu, and bustard, and likewise
  of the air-sacs of the swan and goose, as prepared by me, may be seen
  in the Museum of the Royal College of Surgeons of England.

The same may be said of the hollow bones,--some really admirable
fliers, as the swifts, martins, and snipes, having their bones filled
with marrow, while those of the wingless running birds alluded to have
air. Furthermore and finally, a living bird weighing 10 lbs. weighs the
same when dead, plus a very few grains; and all know what effect a few
grains of heated air would have in raising a weight of 10 lbs. from the
ground.

_How Balancing is effected in Flight, the Sound produced by the Wing,
etc._--The manner in which insects, bats, and birds balance themselves
in the air has hitherto, and with reason, been regarded a mystery,
for it is difficult to understand how they maintain their equilibrium
when the wings are beneath their bodies. Figs. 67 and 68, p. 141,
throw considerable light on the subject in the case of the insect. In
those figures the space (_a_, _g_) mapped out by the wing during its
vibrations is entirely occupied by it; _i.e._ the wing (such is its
speed) is in every portion of the space at nearly the same instant, the
space representing what is practically a solid basis of support. As,
moreover, the wing is jointed to the upper part of the body (thorax)
by a universal joint, which admits of every variety of motion, the
insect is always suspended (very much as a compass set upon gimbals is
suspended); the wings, when on a level with the body, vibrating in such
a manner as to occupy a circular area (_vide_ _r d b f_ of fig. 56,
p. 120), in the centre of which the body (_a e c_) is placed. The
wings, when vibrating above and beneath the body occupy a conical area;
the apex of the cone being directed upwards when the wings are below
the body, and downwards when they are above the body. Those points
are well seen in the bird at figs. 82 and 83, p. 158. In fig. 82 the
inverted cone formed by the wings when above the body is represented,
and in fig. 83 that formed by the wings when below the body is given.
In these figures it will be observed that the body, from the insertion
of the roots of the wings into its upper portion, is always suspended,
and this, of course, is equivalent to suspending the centre of gravity.
In the bird and bat, where the stroke is delivered more vertically
than in the insect, the _basis of support_ is increased by the tip of
the wing folding inwards and backwards in a more or less horizontal
direction at the end of the down stroke; and outwards and forwards at
the end of the up stroke. This is accompanied by the rotation of the
outer portion of the wing upon the wrist as a centre, the tip of the
wing, because of the ever varying position of the wrist, describing
an ellipse. In insects whose wings are broad and large (butterfly),
and which are driven at a comparatively low speed, the balancing power
is diminished. In insects whose wings, on the contrary, are long and
narrow (blow-fly), and which are driven at a high speed, the balancing
power is increased. It is the same with short and long winged birds, so
that the function of balancing is in some measure due to the form of
the wing, and the speed with which it is driven; the long wing and the
wing vibrated with great energy increasing the capacity for balancing.
When the body is light and the wings very ample (butterfly and heron),
the reaction elicited by the ascent and descent of the wing displaces
the body to a marked extent. When, on the other hand, the wings are
small and the body large, the reaction produced by the vibration of
the wing is scarcely perceptible. Apart, however, from the shape and
dimensions of the wing, and the rapidity with which it is urged, it
must never be overlooked that all wings (as has been pointed out) are
attached to the bodies of the animals bearing them by some form of
universal joint, and in such a manner that the bodies, whatever the
position of the wings, are accurately balanced, and swim about in a
more or less horizontal position, like a compass set upon gimbals. To
such an extent is this true, that the position of the wing is a matter
of indifference. Thus the pinion may be above, beneath, or on a level
with the body; or it may be directed forwards, backwards, or at right
angles to the body. In either case the body is balanced mechanically
and without effort. To prove this point I made an artificial wing and
body, and united the one to the other by a universal joint. I found,
as I had anticipated, that in whatever position the wing was placed,
whether above, beneath, or on a level with the body, or on either side
of it, the body almost instantly attained a position of rest. The body
was, in fact, equally suspended and balanced from all points.

[Illustration: FIG. 56.[69]]

  [69] In this diagram I have purposely represented the right wing
  by a straight _rigid_ rod. The natural wing, however, is curved,
  _flexible_, and _elastic_. It likewise _moves in curves_, the curves
  being most marked towards the end of the up and down strokes, as
  shown at _m n_, _o p_. The curves, which are double figure-of-8
  curves, are obliterated towards the middle of the strokes (_a r_).
  This remark holds true of all natural wings, and of all artificial
  wings properly constructed. The curves and the reversal thereof
  are necessary to give continuity of motion to the wing during its
  vibrations, and what is not less important, to enable the wing
  alternately to seize and dismiss the air.

_Rapidity of Wing Movements partly accounted for._--Much surprise has
been expressed at the enormous rapidity with which some wings are made
to vibrate. The wing of the insect is, as a rule, very long and narrow.
As a consequence, a comparatively slow and very limited movement at
the root confers great range and immense speed at the tip; the speed
of each portion of the wing increasing as the root of the wing is
receded from. This is explained on a principle well understood in
mechanics, viz. that when a rod hinged at one end is made to move in a
circle, the tip or free end of the rod describes a much wider circle
_in a given time_ than a portion of the rod nearer the hinge. This
principle is illustrated at fig. 56. Thus if _a b_ of fig. 56 be made
to represent the rod hinged at _x_, it travels through the space _d b
f_ in the same time it travels through _j k l_; and through _j k l_ in
the same time it travels through _g h i_; and through _g h i_ in the
same time it travels through _e a c_, which is the area occupied by
the thorax of the insect. If, however, the part of the rod _b_ travels
through the space _d b f_ in the same time that the part _a_ travels
through the space _e a c_, it follows of necessity that the portion of
the rod marked _a_ moves very much slower than that marked _b_. The
muscles of the insect are applied at the point _a_, as short levers
(the point referred to corresponding to the thorax of the insect), so
that a comparatively slow and limited movement at the root of the wing
produces the marvellous speed observed at the tip; the tip and body of
the wing being those portions which occasion the blur or impression
produced on the eye by the rapidly oscillating pinion (figs. 64, 65,
and 66, p. 139), But for this mode of augmenting the speed originally
inaugurated by the muscular system, it is difficult to comprehend how
the wings could be driven at the velocity attributed to them. The wing
of the blow-fly is said to make 300 strokes per second, _i.e._ 18,000
per minute. Now it appears to me that muscles to contract at the rate
of 18,000 times in the minute would be exhausted in a very few seconds,
a state of matters which would render the continuous flight of insects
impossible. (The heart contracts only between sixty and seventy times
in a minute.) I am, therefore, disposed to believe that the number of
contractions made by the thoracic muscles of insects has been greatly
overstated; the high speed at which the wing is made to vibrate being
due less to the separate and sudden contractions of the muscles at its
root than to the fact that the speed of the different parts of the wing
is increased in a direct ratio as the several parts are removed from
the driving point, as already explained. Speed is certainly a matter
of great importance in wing movements, as the elevating and propelling
power of the pinion depends to a great extent upon the rapidity with
which it is urged. Speed, however, may be produced in two ways--either
by a series of separate and opposite movements, such as is witnessed
in the action of a piston, or by a series of separate and opposite
movements acting upon an instrument so designed, that a movement
applied at one part increases in rapidity as the point of contact
is receded from, as happens in the wing. In the piston movement the
motion is uniform, or nearly so; all parts of the piston travelling at
very much the same speed. In the wing movements, on the contrary, the
motion is gradually accelerated towards the tip of the pinion, where
the pinion is most effective as an elevator, and decreased towards the
root, where it is least effective--an arrangement calculated to reduce
the number of muscular contractions, while it contributes to the actual
power of the wing. This hypothesis, it will be observed, guarantees
to the wing a very high speed, with comparatively few reversals and
comparatively few muscular contractions.

In the bat and bird the wings do not vibrate with the same rapidity as
in the insect, and this is accounted for by the circumstance, that in
them the muscles do not act exclusively at the root of the wing. In the
bat and bird the muscles run along the wing towards the tip for the
purpose of flexing or folding the wing prior to the up stroke, and for
opening out and expanding it prior to the down stroke.

As the wing must be folded or flexed and opened out or expanded every
time the wing rises and falls, and as the muscles producing flexion
and extension are long muscles with long tendons, which act at long
distances as long levers, and comparatively slowly, it follows that
the great short muscles (pectorals, etc.) situated at the root of the
wing must act slowly likewise, as the muscles of the thorax and wing
of necessity act together to produce one pulsation or vibration of the
wing. What the wing of the bat and bird loses in speed it gains in
power, the muscles of the bat and bird’s wing acting directly upon the
points to be moved, and under the most favourable conditions. In the
insect, on the contrary, the muscles act indirectly, and consequently
at a disadvantage. If the pectorals only moved, they would act as
short levers, and confer on the wing of the bat and bird the rapidity
peculiar to the wing of the insect.

The tones emitted by the bird’s wing would in this case be heightened.
The swan in flying produces a loud whistling sound, and the pheasant,
partridge, and grouse a sharp whirring noise like the stone of a
knife-grinder.

It is a mistake to suppose, as many do, that the tone or note produced
by the wing during its vibrations is a true indication of the number
of beats made by it in any given time. This will be at once understood
when I state, that a long wing will produce a higher note than a
shorter one driven at the same speed and having the same superficial
area, from the fact that the tip and body of the long wing will move
through a greater space in a given time than the tip and body of the
shorter wing. This is occasioned by all wings being jointed at their
roots, the sweep made by the different parts of the wing in a given
time being longer or shorter in proportion to the length of the pinion.
It ought, moreover, not to be overlooked, that in insects the notes
produced are not always referable to the action of the wings, these, in
many cases, being traceable to movements induced in the legs and other
parts of the body.

It is a curious circumstance, that if portions be removed from the
posterior margins of the wings of a buzzing insect, such as the wasp,
bee, blue-bottle fly, etc., the note produced by the vibration of
the pinions is raised in pitch. This is explained by the fact, that
an insect whose wings are curtailed requires to drive them at a much
higher speed in order to sustain itself in the air. That the velocity
at which the wing is urged is instrumental in causing the sound, is
proved by the fact, that in slow-flying insects and birds no note
is produced; whereas in those which urge the wing at a high speed,
a note is elicited which corresponds within certain limits to the
number of vibrations and the form of the wing. It is the posterior or
thin flexible margin of the wing which is more especially engaged in
producing the sound; and if this be removed, or if this portion of the
wing, as is the case in the bat and owl, be constructed of very soft
materials, the character of the note is altered. An artificial wing,
if properly constructed and impelled at a sufficiently high speed,
emits a drumming noise which closely resembles the note produced by the
vibration of short-winged, heavy-bodied birds, all which goes to prove
that sound is a concomitant of rapidly vibrating wings.

_The Wing area Variable and in Excess._--The travelling-surfaces of
insects, bats, and birds greatly exceed those of fishes and swimming
animals; the travelling-surfaces of swimming animals being greatly
in excess of those of animals which walk and run. The wing area of
insects, bats, and birds varies very considerably, flight being
possible within a comparatively wide range. Thus there are light-bodied
and large-winged insects and birds--as the butterfly (fig. 57) and
heron (fig. 60, p. 126); and others whose bodies are comparatively
heavy, while their wings are insignificantly small--as the sphinx moth
and Goliath beetle (fig. 58) among insects, and the grebe, quail, and
partridge (fig. 59, p. 126) among birds.

[Illustration:

  FIG. 57.--Shows a butterfly with comparatively very large wings.
  The nervures are seen to great advantage in this specimen; and the
  enormous expanse of the pinions readily explains the irregular
  flight of the insect on the principle of recoil. _a_ Anterior
  wing. _b_ Posterior wing. _e_ Anterior margin of wing. _f_ Ditto
  posterior margin. _g_ Ditto outer margin. Compare with beetle, fig.
  58.--_Original._]

[Illustration:

  FIG. 58.--Under-surface of large beetle (_Goliathus micans_), with
  deeply concave and comparatively small wings (compare with butterfly,
  fig. 57), shows that the nervures (_r_, _d_, _e_, _f_, _n_, _n_, _n_)
  of the wings of the beetle are arranged along the anterior margins
  and throughout the substance of the wings generally, very much as the
  bones of the arm, forearm, and hand, are in the wings of the bat, to
  which they bear a very marked resemblance, both in their shape and
  mode of action. The wings are folded upon themselves at the point _e_
  during repose. Compare letters of this figure with similar letters of
  fig. 17, p. 36.--_Original._]

The apparent inconsistencies in the dimensions of the body and wings
are readily explained by the greater muscular development of the
heavy-bodied short-winged insects and birds, and the increased power
and rapidity with which the wings in them are made to oscillate. In
large-winged animals the movements are slow; in small-winged ones
comparatively very rapid. This shows that flight may be attained by a
heavy, powerful animal with comparatively small wings, as well as by a
lighter one with enormously enlarged wings. While there is apparently
no fixed relation between the area of the wings and the animal to be
raised, there is, unless in the case of sailing birds,[70] an unvarying
relation between the weight of the animal, the area of its wings, and
the number of oscillations made by them in a given time. The problem
of flight thus resolves itself into one of weight, power, velocity,
and small surfaces; _versus_ buoyancy, debility, diminished speed,
and extensive surfaces,--weight in either case being a _sine quâ non_.
In order to utilize the air as a means of transit, the body in motion,
whether it moves in virtue of the life it possesses, or because of a
force superadded, must be heavier than the air. It must tread and rise
upon the air as a swimmer upon the water, or as a kite upon the wind.
It must act against gravity, and elevate and carry itself forward at
the expense of the air, and by virtue of the force which resides in it.
If it were rescued from the law of gravity on the one hand, and bereft
of independent movement on the other, it would float about uncontrolled
and uncontrollable, as happens in the ordinary gas-balloon.

  [70] In birds which skim, sail, or glide, the pinion is greatly
  elongated or ribbon-shaped, and the weight of the body is made to
  operate upon the inclined planes formed by the wings, in such a
  manner that the bird when it has once got fairly under weigh, is in
  a measure self-supporting. This is especially the case when it is
  proceeding against a slight breeze--the wind and the inclined planes
  resulting from the upward inclination of the wings reacting upon each
  other, with this very remarkable result, that the mass of the bird
  moves steadily forwards in a more or less horizontal direction.

[Illustration:

  FIG. 59.--The Red-legged Partridge (_Perdix rubra_) with wings fully
  extended as in rapid flight, shows deeply concave form of the wings,
  how the primary and secondary feathers overlap and support each other
  during extension, and how the anterior or thick margins of the wings
  are directed upwards and forwards, and the posterior or thin ones
  downwards and backwards. The wings in the partridge are wielded with
  immense velocity and power. This is necessary because of their small
  size as compared with the great dimensions and weight of the body.

  If a horizontal line be drawn across the feet (_a_, _e_) to represent
  the horizon, and another from the tip of the tail (_a_) to the root
  of the wing (_d_), the angle at which the wing strikes the air is
  given. The body and wings when taken together form a kite. The
  wings in the partridge are rounded and broad. Compare with heron,
  fig. 60.--_Original._]

[Illustration:

  FIG. 60.--The Grey Heron (_Ardea cinerea_) in full flight. In the
  heron the wings are deeply concave, and unusually large as compared
  with the size of the bird. The result is that the wings are moved
  very leisurely, with a slow, heavy, and almost solemn beat. The
  heron figured weighed under 3 lbs.; and the expanse of wing was
  considerably greater than that of a wild goose which weighed over
  9 lbs. Flight is consequently more a question of power and weight
  than of buoyancy and surface. _d_, _e_, _f_ Anterior thick strong
  margin of right wing. _c_, _a_, _b_ Posterior thin flexible margin,
  composed of primary (_b_), secondary (_a_), and tertiary (_c_)
  feathers. Compare with partridge, fig. 59.--_Original._]

That no fixed relation exists between the area of the wings and the
size and weight of the body, is evident on comparing the dimensions
of the wings and bodies of the several orders of insects, bats, and
birds. If such comparison be made, it will be found that the pinions in
some instances diminish while the bodies increase, and the converse.
No practical good can therefore accrue to aërostation from elaborate
measurements of the wings and trunks of any flying thing; neither
can any rule be laid down as to the extent of surface required for
sustaining a given weight in the air. The wing area is, as a rule,
considerably in excess of what is actually required for the purposes of
flight. This is proved in two ways. First, by the fact that bats can
carry their young without inconvenience, and birds elevate surprising
quantities of fish, game, carrion, etc. I had in my possession at one
time a tame barn-door owl which could lift a piece of meat a quarter of
its own weight, after fasting four-and-twenty hours; and an eagle, as
is well known, can carry a moderate-sized lamb with facility.

The excess of wing area is proved, secondly, by the fact that a large
proportion of the wings of most volant animals may be removed without
destroying the power of flight. I instituted a series of experiments
on the wings of the fly, dragon-fly, butterfly, sparrow, etc., with a
view to determining this point in 1867. The following are the results
obtained:--

_Blue-bottle Fly._--_Experiment 1._ Detached posterior or thin half of
each wing in its long axis. Flight perfect.

_Exp. 2._ Detached posterior _two-thirds_ of either wing in its long
axis. Flight still perfect. I confess I was not prepared for this
result.

_Exp. 3._ Detached one-third of anterior or thick margin of either
pinion obliquely. Flight imperfect.

_Exp. 4._ Detached one-half of anterior or thick margin of either
pinion obliquely. The power of flight completely destroyed. From
experiments 3 and 4 it would seem that the anterior margin of the wing,
which contains the principal nervures, and which is the most rigid
portion of the pinion, cannot be mutilated with impunity.

_Exp. 5._ Removed one-third from the extremity of either wing
transversely, _i.e._ in the direction of the short axis of the pinion.
Flight perfect.

_Exp. 6._ Removed _one-half_ from either wing transversely, as in
experiment 5. Flight very slightly (if at all) impaired.

_Exp. 7._ Divided either pinion in the direction of its long axis
into three equal parts, the anterior nervures being contained in the
anterior portion. Flight perfect.

_Exp. 8._ Notched two-thirds of either pinion obliquely from behind.
Flight perfect.

_Exp. 9._ Notched anterior third of either pinion transversely. The
power of flight destroyed. Here, as in experiment 4, the mutilation of
the anterior margin was followed by loss of function.

_Exp. 10._ Detached posterior two-thirds of right wing in its long
axis, the left wing being untouched. Flight perfect. I expected that
this experiment would result in loss of balancing-power; but this was
not the case.

_Exp. 11._ Detached half of right wing transversely, the left one being
normal. The insect flew irregularly, and came to the ground about a
yard from where I stood. I seized it and detached the corresponding
half of the left wing, after which it flew away, as in experiment 6.

_Dragon-Fly._--_Exp. 12._ In the dragon-fly either the first or second
pair of wings may be removed without destroying the power of flight.
The insect generally flies most steadily when the posterior pair of
wings are detached, as it can balance better; but in either case flight
is perfect, and in no degree laboured.

_Exp. 13._ Removed one-third from the posterior margin of the first and
second pairs of wings. Flight in no wise impaired.

If more than a third of each wing is cut away from the posterior or
thin margin, the insect can still fly, but with effort.

Experiment 13 shows that the posterior or thin flexible margins of the
wings may be dispensed with in flight. They are more especially engaged
in propelling. Compare with experiments 1 and 2.

_Exp. 14._ The extremities or tips of the first and second pair of
wings may be detached to the extent of one-third, without diminishing
the power of flight. Compare with experiments 5 and 6.

If the mutilation be carried further, flight is laboured, and in some
cases destroyed.

_Exp. 15._ When the front edges of the first and second pairs of wings
are notched or when they are removed, flight is completely destroyed.
Compare with experiments 3, 4, and 9.

This shows that a certain degree of stiffness is required for the
front edges of the wings, the front edges indirectly supporting the
back edges. It is, moreover, on the front edges of the wings that the
pressure falls in flight, and by these edges the major portions of the
wings are attached to the body. The principal movements of the wings
are communicated to these edges.

_Butterfly._--_Exp. 16._ Removed posterior halves of the first pair of
wings of white butterfly. Flight perfect.

_Exp. 17._ Removed posterior halves of first and second pairs of wings.
Flight not strong but still perfect. If additional portions of the
posterior wings were removed, the insect could still fly, but with
great effort, and came to the ground at no great distance.

_Exp. 18._ When the tips (outer sixth) of the first and second pairs
of wings were cut away, flight was in no wise impaired. When more was
detached the insect could not fly.

_Exp. 19._ Removed the posterior wings of the brown butterfly. Flight
unimpaired.

_Exp. 20._ Removed in addition a small portion (one-sixth) from the
tips of the anterior wings. Flight still perfect, as the insect flew
upwards of ten yards.

_Exp. 21._ Removed in addition a portion (one-eighth) of the posterior
margins of anterior wings. The insect flew imperfectly, and came to the
ground about a yard from the point where it commenced its flight.

_House Sparrow._--The sparrow is a heavy small-winged bird, requiring,
one would imagine, all its wing area. This, however, is not the case,
as the annexed experiments show.

_Exp. 22._ Detached the half of the secondary feathers of either pinion
in the direction of the long axis of the wing, the primaries being left
intact. Flight as perfect as before the mutilation took place. In this
experiment, one wing was operated upon before the other, in order to
test the balancing-power. The bird flew perfectly, either with one or
with both wings cut.

_Exp. 23._ Detached the half of the secondary feathers and a fourth
of the primary ones of either pinion in the long axis of the wing.
Flight in no wise impaired. The bird, in this instance, flew upwards
of 30 yards, and, having risen a considerable height, dropped into a
neighbouring tree.

_Exp. 24._ Detached nearly the half of the primary feathers in the long
axis of either pinion, the secondaries being left intact. When one wing
only was operated upon, flight was perfect; when both were tampered
with, it was still perfect, but slightly laboured.

_Exp. 25._ Detached rather more than a third of both primary and
secondary feathers of either pinion in the long axis of the wing.
In this case the bird flew with evident exertion, but was able,
notwithstanding, to attain a very considerable altitude.

From experiments 1, 2, 7, 8, 10, 13, 16, 22, 23, 24, and 25, it would
appear that great liberties may be taken with the posterior or thin
margin of the wing, and the dimensions of the wing in this direction
materially reduced, without destroying, or even vitiating in a marked
degree, the powers of flight. This is no doubt owing to the fact
indicated by Sir George Cayley, and fully explained by Mr. Wenham, that
in all wings, particularly long narrow ones, the elevating power is
transferred to the anterior or front margin. These experiments prove
that the upward bending of the posterior margins of the wings during
the down stroke is not necessary to flight.

_Exp. 26._ Removed alternate primary and secondary feathers from either
wing, beginning with the first primary. The bird flew upwards of fifty
yards with very slight effort, rose above an adjoining fence, and
wheeled over it a second time to settle on a tree in the vicinity. When
one wing only was operated upon, it flew irregularly and in a lopsided
manner.

_Exp. 27._ Removed alternate primary and secondary feathers from either
wing, beginning with the _second primary_. Flight, from all I could
determine, perfect. When one wing only was cut, flight was irregular or
lopsided, as in experiment 26.

From experiments 26 and 27, as well as experiments 7 and 8, it would
seem that the wing does not of necessity require to present an unbroken
or continuous surface to the air, such as is witnessed in the pinion
of the bat, and that the feathers, when present, may be separated
from each other without destroying the utility of the pinion. In the
raven and many other birds the extremities of the first four or five
primaries divaricate in a marked manner. A similar condition is met
with in the _Alucita hexadactyla_, where the delicate feathery-looking
processes composing the wing are widely removed from each other. The
wing, however, _ceteris paribus_, is strongest when the feathers are
not separated from each other, and when they _overlap_, as then they
are arranged so as mutually to support each other.

_Exp. 28._ Removed half of the primary feathers from either wing
transversely, _i.e._ in the direction of the short axis of the wing.
Flight very slightly, if at all, impaired when only one wing was
operated upon. When both were cut, the bird flew heavily, and came to
the ground at no very great distance. This mutilation was not followed
by the same result in experiments 6 and 11. On the whole, I am inclined
to believe that the area of the wing can be curtailed with least injury
in the direction of its long axis, by removing successive portions from
its posterior margin.

_Exp. 29._ The carpal or wrist-joint of either pinion rendered immobile
by lashing the wings to slender reeds, the elbow-joints being left
free. The bird, on leaving the hand, fluttered its wings vigorously,
but after a brief flight came heavily to the ground, thus showing that
a certain degree of twisting and folding, or flexing of the wings, is
necessary to the flight of the bird, and that, however the superficies
and shape of the pinions may be altered, the movements thereof must not
be interfered with. I tied up the wings of a pigeon in the same manner,
with a precisely similar result.

The birds operated upon were, I may observe, caught in a net, and the
experiments made within a few minutes from the time of capture.

Some of my readers will probably infer from the foregoing, that the
figure-of-8 curves formed along the anterior and posterior margins of
the pinions are not necessary to flight, since the tips and posterior
margins of the wings may be removed, without destroying it. To such
I reply, that the wings are flexible, elastic, and composed of a
congeries of curved surfaces, and that so long as a portion of them
remains, they form, or tend to form, figure-of-8 curves in every
direction.

Captain F. W. Hutton, in a recent paper “On the Flight of Birds”
(_Ibis_, April 1872), refers to some of the experiments detailed above,
and endeavours to frame a theory of flight, which differs in some
respects from my own. His remarks are singularly inappropriate, and
illustrate in a forcible manner the old adage, “A little knowledge is
a dangerous thing.” If Captain Hutton had taken the trouble to look
into my memoir “On the Physiology of Wings,” communicated to the Royal
Society of Edinburgh, on the 2d of August 1870,[71] fifteen months
before his own paper was written, there is reason to believe he would
have arrived at very different conclusions. Assuredly he would not have
ventured to make the rash statements he has made, the more especially
as he attempts to controvert my views, which are based upon anatomical
research and experiment, without making any dissections or experiments
of his own.

  [71] “On the Physiology of Wings, being an Analysis of the Movements
  by which Flight is produced in the Insect, Bat, and Bird.”--Trans.
  Roy. Soc. of Edinburgh, vol. xxvi.

_The Wing area decreases as the Size and Weight of the Volant Animal
increases._--While, as explained in the last section, no definite
relation exists between the weight of a flying animal and the size
of its flying surfaces, there being, as stated, heavy bodied and
small-winged insects, bats, and birds, and the converse; and while, as
I have shown by experiment, flight is possible within a wide range, the
wings being, as a rule, in excess of what are required for the purposes
of flight; still it appears, from the researches of M. de Lucy, that
there is a general law, to the effect that the larger the volant animal
the smaller by comparison are its flying surfaces. The existence
of such a law is very encouraging as far as artificial flight is
concerned, for it shows that the flying surfaces of a large, heavy,
powerful flying machine will be comparatively small, and consequently
comparatively compact and strong. This is a point of very considerable
importance, as the object desiderated in a flying machine is elevating
capacity.

M. de Lucy has tabulated his results, which I subjoin:[72]--

  [72] “On the Flight of Birds, of Bats, and of Insects, in reference
  to the subject of Aërial Locomotion,” by M. de Lucy, Paris.

    +------------------------------------------------------+
    |                       INSECTS.                       |
    +------------------------------+-----------------------+
    |                              |    Referred to the    |
    |                              |      kilogramme       |
    |            NAMES.            |= 2lbs. 8oz. 3dwt. 2gr.|
    |                              |        Avoird.        |
    |                              | = 2lbs. 3oz. 4·428dr. |
    +------------------------------+-----------------------+
    |                              |     sq. ft. in.       |
    |                              |    yds.               |
    |Gnat,                         |     11   8   92       |
    |Dragon-fly (small),           |      7   2   56       |
    |Coccinella (Lady-bird),       |      5  13   87       |
    |Dragon-fly (common),          |      5   2   89       |
    |Tipula, or Daddy-long-legs,   |      3   5   11       |
    |Bee,                          |      1   2   74-1/2   |
    |Meat-fly,                     |      1   3   54-1/2   |
    |Drone (blue),                 |      1   2   20       |
    |Cockchafer,                   |      1   2   50       |
    |Lucanus} Stag beetle (female),|      1   1   39-1/2   |
    | cervus} Stag-beetle (male),  |      0   8   33       |
    |Rhinoceros-beetle,            |      0   6  122-1/2   |
    +------------------------------+-----------------------+
    +------------------------------------------------------+
    |                        BIRDS.                        |
    +------------------------------+-----------------------+
    |                              |       Referred        |
    |            NAMES.            |        to the         |
    |                              |      kilogramme.      |
    +------------------------------+-----------------------+
    |                              |     sq.               |
    |                              |    yds. ft. in.       |
    | Swallow,                     |      1   1  104-1/2   |
    | Sparrow,                     |      0   5  142-1/2   |
    | Turtle-dove,                 |      0   4  100-1/2   |
    | Pigeon,                      |      0   2  113       |
    | Stork,                       |      0   2   20       |
    | Vulture,                     |      0   1  116       |
    | Crane of Australia,          |      0   0  139       |
    +------------------------------+-----------------------+

“It is easy, by aid of this table, to follow the order, always
decreasing, of the surfaces, in proportion as the winged animal
increases in size and weight. Thus, in comparing the insects with one
another, we find that the gnat, which weighs 460 times less than the
stag-beetle, has fourteen times more of surface. The lady-bird weighs
150 times less than the stag-beetle, and possesses five times more of
surface. It is the same with the birds. The sparrow weighs about ten
times less than the pigeon, and has twice as much surface. The pigeon
weighs about eight times less than the stork, and has twice as much
surface. The sparrow weighs 339 times less than the Australian crane,
and possesses seven times more surface. If now we compare the insects
and the birds, the gradation will become even much more striking. The
gnat, for example, weighs 97,000 times less than the pigeon, and has
forty times more surface; it weighs 3,000,000 times less than the crane
of Australia, and possesses 149 times more of surface than this latter,
the weight of which is about 9 kilogrammes 500 grammes (25 lbs. 5 oz.
9 dwt. troy, 20 lbs. 15 oz. 2-1/4 dr. avoirdupois).

“The Australian crane is the heaviest bird that I have weighed. It
is that which has the smallest amount of surface, for, referred to
the kilogramme, it does not give us a surface of more than 899 square
centimetres (139 square inches), that is to say about an eleventh part
of a square metre. But every one knows that these grallatorial animals
are excellent birds of flight. Of all travelling birds they undertake
the longest and most remote journeys. They are, in addition, the eagle
excepted, the birds which elevate themselves the highest, and the
flight of which is the longest maintained.”[73]

  [73] M. de Lucy, _op. cit._

Strictly in accordance with the foregoing, are my own measurements of
the gannet and heron. The following details of weight, measurement,
etc., of the gannet were supplied by an adult specimen which I
dissected during the winter of 1869. Entire weight, 7 lbs. (minus 3
ounces); length of body from tip of bill to tip of tail, three feet
four inches; head and neck, one foot three inches; tail, twelve inches;
trunk, thirteen inches; girth of trunk, eighteen inches; expanse of
wing from tip to tip across body, six feet; widest portion of wing
across primary feathers, six inches; across secondaries, seven inches;
across tertiaries, eight inches. Each wing, when carefully measured
and squared, gave an area of 19-1/2 square inches. The wings of the
gannet, therefore, furnish a supporting area of three feet three inches
square. As the bird weighs close upon 7 lbs., this gives something like
thirteen square inches of wing for every 36-1/3 ounces of body, _i.e._
one foot one square inch of wing for every 2 lbs. 4-1/3 oz. of body.

The heron, a specimen of which I dissected at the same time, gave a
very different result, as the subjoined particulars will show. Weight
of body, 3 lbs. 3 ounces; length of body from tip of bill to tip of
tail, three feet four inches; head and neck, two feet; tail, seven
inches; trunk, nine inches; girth of body, twelve inches; expanse of
wing from tip to tip across the body, five feet nine inches; widest
portion of wing across primary and tertiary feathers, eleven inches;
across secondary feathers, twelve inches.

Each wing, when carefully measured and squared, gave an area of
twenty-six square inches. The wings of the heron, consequently, furnish
a supporting area of four feet four inches square. As the bird only
weighs 3 lbs. 3 ounces, this gives something like twenty-six square
inches of wing for every 25-1/2 ounces of bird, or one foot 5-1/4
inches square for every 1 lb. 1 ounce of body.

In the gannet there is only one foot one square inch of wing for
every 2 lbs. 4-1/3 ounces of body. The gannet has, consequently, less
than half of the wing area of the heron. The gannet’s wings are,
however, long narrow wings (those of the heron are broad), which
extend transversely across the body; and these are found to be the
most powerful--the wings of the albatross--which measure fourteen feet
from tip to tip (and only one foot across), elevating 18 lbs. without
difficulty. If the wings of the gannet, which have a superficial
area of three feet three inches square, are capable of elevating
7 lbs., while the wings of the heron, which have a superficial area
of four feet four inches, can only elevate 3 lbs., it is evident
(seeing the wings of both are twisted levers, and formed upon a common
type) that the gannet’s wings must be vibrated with greater energy
than the heron’s wings; and this is actually the case. The heron’s
wings, as I have ascertained from observation, make 60 down and 60
up strokes every minute; whereas the wings of the gannet, when the
bird is flying in a straight line to or from its fishing-ground, make
close upon 150 up and 150 down strokes during the same period. The
wings of the divers, and other short-winged, heavy-bodied birds, are
urged at a much higher speed, so that comparatively small wings can
be made to elevate a comparatively heavy body, if the speed only be
increased sufficiently.[74] Flight, therefore, as already indicated,
is a question of power, speed, and small surfaces _versus_ weight.
Elaborate measurements of wing, area, and minute calculations of speed,
can consequently only determine the minimum of wing for elevating the
maximum of weight--flight being attainable within a comparatively wide
range.

  [74] The grebes among birds, and the beetles among insects, furnish
  examples where small wings, made to vibrate at high speeds, are
  capable of elevating great weights.

_Wings, their Form, etc.; all Wings Screws, structurally and
functionally._--Wings vary considerably as to their general contour;
some being falcated or scythe-like, some oblong, some rounded or
circular, some lanceolate, and some linear.[75]

  [75] “The wing is short, broad, convex, and rounded in grouse,
  partridges, and other rasores; long, broad, straight, and pointed
  in most pigeons. In the peregrine falcon it is acuminate, the
  second quill being longest, and the first little shorter; and in
  the swallows this is still more the case, the first quill being the
  longest, the rest rapidly diminishing in length.”--Macgillivray,
  Hist. Brit. Birds, vol. i. p. 82. “The hawks have been classed as
  noble or ignoble, according to the length and sharpness of their
  wings; and the falcons, or long-winged hawks, are distinguished from
  the short-winged ones by the second feather of the wing being either
  the longest or equal in length to the third, and by the nature of the
  stoop made in pursuit of their prey.”--Falconry in the British Isles,
  by F. H. Salvin and W. Brodrick. Lond. 1855, p. 28.

[Illustration:

  FIG. 61.--Right wing of the Kestrel, drawn from the specimen, while
  being held against the light. Shows how the primary (_b_), secondary
  (_a_), and tertiary (_c_) feathers overlap and buttress or support
  each other in every direction. Each set of feathers has its coverts
  and subcoverts, the wing being conical from within outwards, and from
  before backwards. _d_, _e_, _f_ Anterior or thick margin of wing.
  _b_, _a_, _c_ Posterior or thin margin. The wing of the kestrel is
  intermediate as regards form, it being neither rounded as in the
  partridge (fig. 96, p. 176), nor ribbon-shaped as in the albatross
  (fig. 62), nor pointed as in the swallow. The feathers of the
  kestrel’s wing are unusually symmetrical and strong. Compare with
  figs. 92, 94, and 96, pp. 174, 175, and 176.--_Original._]

All wings are constructed upon a common type. They are in every
instance carefully graduated, the wing tapering from the root towards
the tip, and from the anterior margin in the direction of the posterior
margin. They are of a generally triangular form, and twisted upon
themselves in the direction of their length, to form a helix or screw.
They are convex above and concave below, and more or less flexible
and elastic throughout, the elasticity being greatest at the tip and
along the posterior margin. They are also moveable in all their parts.
Figs. 61, 62, 63 (p. 138), 59 and 60 (p. 126), 96 and 97 (p. 176),
represent typical bird wings; figs. 17 (p. 36), 94 and 95 (p. 175),
typical bat wings; and figs. 57 and 58 (p. 125), 89 and 90 (p. 171), 91
(p. 172), 92 and 93 (p. 174), typical insect wings.

In all the wings which I have examined, whether in the insect, bat,
or bird, the wing is recovered, flexed, or drawn towards the body
by the action of elastic ligaments, these structures, by their mere
contraction, causing the wing, when fully extended and presenting its
maximum of surface, to resume its position of rest and plane of least
resistance. The principal effort required in flight is, therefore, made
during extension, and at the beginning of the down stroke. The elastic
ligaments are variously formed, and the amount of contraction which
they undergo is in all cases accurately adapted to the size and form
of the wing, and the rapidity with which it is worked; the contraction
being greatest in the short-winged and heavy-bodied insects and birds,
and least in the light-bodied and ample-winged ones, particularly such
as skim or glide. The mechanical action of the elastic ligaments, I
need scarcely remark, insures an additional period of repose to the
wing at each stroke; and this is a point of some importance, as showing
that the lengthened and laborious flights of insects and birds are not
without their stated intervals of rest.

[Illustration:

  FIG. 62.--Left wing of the albatross. _d_, _e_, _f_ Anterior or
  thick margin of pinion. _b_, _a_, _c_ Posterior or thin margin,
  composed of the primary (_b_), secondary (_a_), and tertiary (_c_)
  feathers. In this wing the first primary is the longest, the primary
  coverts and subcoverts being unusually long and strong. The secondary
  coverts and subcoverts occupy the body of the wing (_e_, _d_), and
  are so numerous as effectually to prevent any escape of air between
  them during the return or up stroke. This wing, which I have in my
  possession, measures over six feet in length.--_Original._]

All wings are furnished at their roots with some form of universal
joint which enables them to move not only in an upward, downward,
forward, or backward direction, but also at various intermediate
degrees of obliquity. All wings obtain their leverage by presenting
oblique surfaces to the air, the degree of obliquity gradually
increasing in a direction from behind forwards and downwards during
extension and the down stroke, and gradually decreasing in an opposite
direction during flexion and the up stroke.

[Illustration:

  FIG. 63.--The Lapwing, or Green Plover (_Vanellus cristatus_, Meyer),
  with one wing (_c b_, _d´ e´ f´_) fully extended, and forming a
  long lever; the other (_d e f_, _c b_) being in a flexed condition
  and forming a short lever. In the extended wing the anterior or
  thick margin (_d´ e´ f´_) is directed _upwards_ and _forwards_
  (_vide_ arrow), the posterior or thin margin (_c_, _b_) _downwards_
  and _backwards_. The reverse of this happens during flexion, the
  anterior or thick margin (_d_, _e_, _f_) being directed _downwards_
  and _forwards_ (_vide_ arrow), the posterior or thin margin (_c b_)
  bearing the rowing-feathers _upwards_ and _backwards_. The wings
  therefore twist in opposite directions during extension and flexion;
  and this is a point of the utmost importance in the action of all
  wings, as it enables the volant animal to rotate the wings on and
  off the air, and to present at one time (in extension) resisting,
  kite-like surfaces, and at another (in flexion) knife-like and
  comparatively non-resisting surfaces. It rarely happens in flight
  that the wing (_d e f_, _c b_) is so fully flexed as in the figure.
  As a consequence, the under surface of the wing is, as a rule,
  inclined upwards and forwards, even in flexion, so that it acts
  as a kite in extension and flexion, and during the up and down
  strokes.--_Original._]

In the insect the oblique surfaces are due to the conformation of the
shoulder-joint, this being furnished with a system of check-ligaments,
and with horny prominences or stops, set, as nearly as may be, at right
angles to each other. The check-ligaments and horny prominences are
so arranged that when the wing is made to vibrate, it is also made to
rotate in the direction of its length, in the manner explained.

In the bat and bird the oblique surfaces are produced by the spiral
configuration of the articular surfaces of the bones of the wing, and
by the rotation of the bones of the arm, forearm, and hand, upon their
long axes. The reaction of the air also assists in the production of
the oblique surfaces.

[Illustration:

  FIG. 64. FIG. 64 shows left wing (_a_, _b_) of wasp in the act of
  twisting upon itself, the tip of the wing describing a figure-of-8
  track (_a_, _c_, _b_). From nature.--_Original._]

[Illustration: FIG. 65.  FIG. 66.

  FIGS. 65 and 66 show right wing of blue-bottle fly rotating
  on its anterior margin, and twisting to form double or figure-of-8
  curves (_a b_, _c d_). From nature.--_Original._]

That the wing twists upon itself structurally, not only in the insect,
but also in the bat and bird, any one may readily satisfy himself by a
careful examination; and that it twists upon itself during its action
I have had the most convincing and repeated proofs (figs. 64, 65, and
66). The twisting in question is most marked in the posterior or thin
margin of the wing, the anterior and thicker margin performing more
the part of an axis. As a result of this arrangement, the anterior or
thick margin cuts into the air quietly, and as it were by stealth,
the posterior one producing on all occasions a violent commotion,
especially perceptible if a flame be exposed behind the vibrating
wing. Indeed, it is a matter for surprise that the spiral conformation
of the pinion, and its spiral mode of action, should have eluded
observation so long; and I shall be pardoned for dilating upon the
subject when I state my conviction that it forms the fundamental
and distinguishing feature in flight, and must be taken into account
by all who seek to solve this most involved and interesting problem
by artificial means. The importance of the twisted configuration
or screw-like form of the wing cannot be over-estimated. That this
shape is intimately associated with flight is apparent from the fact
that the rowing feathers of the wing of the bird are every one of
them distinctly spiral in their nature; in fact, one entire rowing
feather is equivalent--morphologically and physiologically--to one
entire insect wing. In the wing of the martin, where the bones of
the pinion are short and in some respects rudimentary, the primary
and secondary feathers are greatly developed, and banked up in such
a manner that the wing as a whole presents the same curves as those
displayed by the insect’s wing, or by the wing of the eagle where the
bones, muscles, and feathers have attained a maximum development. The
conformation of the wing is such that it presents a waved appearance
in every direction--the waves running longitudinally, transversely,
and obliquely. The greater portion of the pinion may consequently be
removed without materially affecting either its form or its functions.
This is proved by making sections in various directions, and by
finding, as has been already shown, that in some instances as much as
two-thirds of the wing may be lopped off without visibly impairing
the power of flight. The spiral nature of the pinion is most readily
recognised when the wing is seen from behind and from beneath, and when
it is foreshortened. It is also well marked in some of the long-winged
oceanic birds when viewed from before (figs. 82 and 83, p. 158), and
cannot escape detection under any circumstances, if sought for,--the
wing being essentially composed of a congeries of curves, remarkable
alike for their apparent simplicity and the subtlety of their detail.

_The Wing during its action reverses its Planes, and describes a
Figure-of-8 track in space._--The twisting or rotating of the wing
on its long axis is particularly observable during extension and
flexion in the bat and bird, and likewise in the insect, especially
the beetle, cockroach, and such as fold their wings during repose. In
these in extreme flexion the anterior or thick margin of the wing
is directed downwards, and the posterior or thin one upwards. In the
act of extension, the margins, in virtue of the wing rotating upon
its long axis, reverse their positions, the anterior or thick margins
describing a spiral course from below upwards, the posterior or thin
margin describing a similar but opposite course from above downwards.
These conditions, I need scarcely observe, are reversed during flexion.
The movements of the margins during flexion and extension may be
represented with a considerable degree of accuracy by a figure-of-8
laid horizontally.

[Illustration: FIG. 67.  FIG. 68.  FIG. 69.  FIG. 70

  FIGS. 67, 68, 69, and 70 show the area mapped out by the left wing of
  the wasp when the insect is fixed and the wing made to vibrate. These
  figures illustrate the various angles made by the wing as it hastens
  to and fro, how the wing reverses and reciprocates, and how it twists
  upon itself and describes a figure-of-8 track in space. Figs. 67 and
  69 represent the forward or down stroke; figs. 68 and 70 the backward
  or up stroke. The terms forward and back stroke are here employed
  with reference to the head of the insect.--_Original._]

In the bat and bird the wing, when it ascends and descends, describes
a nearly vertical figure-of-8. In the insect, the wing, from the
more oblique direction of the stroke, describes a nearly horizontal
figure-of-8. In either case the wing reciprocates, and, as a rule,
reverses its planes. The down and up strokes, as will be seen from this
account, cross each other, as shown more particularly at figs. 67, 68,
69, and 70.

In the wasp the wing commences the down or forward stroke at _a_ of
figs. 67 and 69, and makes an angle of something like 45° with the
horizon (_x x´_). At _b_ (figs. 67 and 69) the angle is slightly
diminished, partly because of a rotation of the wing along its anterior
margin (long axis of wing), partly from increased speed, and partly
from the posterior margin of the wing yielding to a greater or less
extent.

At _c_ the angle is still more diminished from the same causes.

At _d_ the wing is slowed slightly, preparatory to reversing, and the
angle made with the horizon (_x_) increased.

At _e_ the angle, for the same reason, is still more increased; while
at _f_ the wing is at right angles to the horizon. It is, in fact, in
the act of reversing.

At _g_ the wing is reversed, and the up or back stroke commenced.

The angle made at _g_ is, consequently, the same as that made at a
(45°), with this difference, that the anterior margin and outer portion
of the wing, instead of being directed _forwards_, with reference to
the head of the insect, are now directed _backwards_.

During the up or backward stroke all the phenomena are reversed, as
shown at _g h i j k l_ of figs. 68 and 70 (p. 141); the only difference
being that the angles made by the wing with the horizon are somewhat
less than during the down or forward stroke--a circumstance which
facilitates the forward travel of the body, while it enables the
wing during the back stroke still to afford a considerable amount of
support. This arrangement permits the wing to travel backwards while
the body is travelling forwards; the diminution of the angles made by
the wing in the back stroke giving very much the same result as if the
wing were striking in the direction of the travel of the body. The
slight upward inclination of the wing during the back stroke permits
the body to fall downwards and forwards to a slight extent at this
peculiar juncture, the fall of the body, as has been already explained,
contributing to the elevation of the wing.

The pinion acts as a helix or screw in a more or less horizontal
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.

_The Wing at all times thoroughly under control._--The wing is moveable
in all parts, and can be wielded intelligently even to its extremity;
a circumstance which enables the insect, bat, and bird to rise upon
the air and tread it as a master--to subjugate it in fact. The wing,
no doubt, abstracts an upward and onward recoil from the air, but in
doing this it exercises a selective and controlling power; it seizes
one current, evades another, and creates a third; it feels and paws
the air as a quadruped would feel and paw a treacherous yielding
surface. It is not difficult to comprehend why this should be so.
If the flying creature is living, endowed with volition, and capable
of directing its own course, it is surely more reasonable to suppose
that it transmits to its travelling surfaces the peculiar movements
necessary to progression, than that those movements should be the
result of impact from fortuitous currents which it has no means of
regulating. That the bird, _e.g._ requires to control the wing, and
that the wing requires to be in a condition to obey the behests of the
will of the bird, is pretty evident from the fact that most of our
domestic fowls can fly for considerable distances when they are young
and when their wings are flexible; whereas when they are old and the
wings stiff, they either do not fly at all or only for short distances,
and with great difficulty. This is particularly the case with tame
swans. This remark also holds true of the steamer or race-horse duck
(_Anas brachyptera_), the younger specimens of which only are volant.
In older birds the wings become too rigid and the bodies too heavy for
flight. Who that has watched a sea-mew struggling bravely with the
storm, could doubt for an instant that the wings and feathers of the
wings are under control? The whole bird is an embodiment of animation
and power. The intelligent active eye, the easy, graceful, oscillation
of the head and neck, the folding or partial folding of one or both
wings, nay more, the slight tremor or quiver of the individual feathers
of parts of the wings so rapid, that only an experienced eye can detect
it, all confirm the belief that the living wing has not only the power
of directing, controlling, and utilizing natural currents, but of
creating and utilizing artificial ones. But for this power, what would
enable the bat and bird to rise and fly in a calm, or steer their
course in a gale? It is erroneous to suppose that anything is left to
chance where living organisms are concerned, or that animals endowed
with volition and travelling surfaces should be denied the privilege
of controlling the movements of those surfaces quite independently of
the medium on which they are destined to operate. I will never forget
the gratification afforded me on one occasion at Carlow (Ireland) by
the flight of a pair of magnificent swans. The birds flew towards and
past me, my attention having been roused by a peculiarly loud whistling
noise made by their wings. They flew about fifteen yards from the
ground, and as their pinions were urged not much faster than those of
the heron,[78] I had abundant leisure for studying their movements.
The sight was very imposing, and as novel as it was grand. I had seen
nothing before, and certainly have seen nothing since that could convey
a more elevated conception of the prowess and guiding power which birds
may exert. What particularly struck me was the perfect command they
seemed to have over themselves and the medium they navigated. They had
their wings and bodies visibly under control, and the air was attacked
in a manner and with an energy which left little doubt in my mind that
it played quite a subordinate part in the great problem before me. The
necks of the birds were stretched out, and their bodies to a great
extent rigid. They advanced with a steady, stately motion, and swept
past with a vigour and force which greatly impressed, and to a certain
extent overawed, me. Their flight was what one could imagine that of a
flying machine constructed in accordance with natural laws would be.[79]

  [78] I have frequently timed the beats of the wings of the Common
  Heron (_Ardea cinerea_) in a heronry at Warren Point. In March 1869
  I was placed under unusually favourable circumstances for obtaining
  trustworthy results. I timed one bird high up over a lake in the
  vicinity of the heronry for fifty seconds, and found that in that
  period it made fifty down and fifty up strokes; _i.e._ one down
  and one up stroke per second. I timed another one in the heronry
  itself. It was snowing at the time (March 1869), but the birds,
  notwithstanding the inclemency of the weather and the early time
  of the year, were actively engaged in hatching, and required to be
  driven from their nests on the top of the larch trees by knocking
  against the trunks thereof with large sticks. One unusually anxious
  mother refused to leave the immediate neighbourhood of the tree
  containing her tender charge, and circled round and round it right
  overhead. I timed this bird for ten seconds, and found that she
  made ten down and ten up strokes; _i.e._ one down and one up stroke
  per second precisely as before. I have therefore no hesitation in
  affirming that the heron, in ordinary flight, makes exactly sixty
  down and sixty up strokes per minute. The heron, however, like all
  other birds when pursued or agitated, has the power of greatly
  augmenting the number of beats made by its wings.

  [79] The above observation was made at Carlow on the Barrow in
  October 1867, and the account of it is taken from my note-book.

_The Natural Wing, when elevated and depressed, must move
forwards._--It is a condition of natural wings, and of artificial wings
constructed on the principle of living wings, that when forcibly
elevated or depressed, even in a strictly vertical direction, they
inevitably dart forward. This is well shown in fig. 81.

[Illustration: FIG. 81.]

If, for example, the wing is suddenly depressed in _a vertical
direction_, as represented at _a b_, it at once darts downwards and
forwards in a curve to _c_, thus converting the vertical down stroke
into _a down oblique forward stroke_. If, again, the wing be suddenly
elevated in a strictly vertical direction, as at _c d_, the wing as
certainly darts upwards and forwards in a curve to _e_, thus converting
the vertical up stroke into an _upward oblique forward stroke_. The
same thing happens when the wing is depressed from _e_ to _f_, and
elevated from _g_ to _h_. In both cases the wing describes a waved
track, as shown at _e g_, _g i_, which clearly proves that the wing
strikes _downwards and forwards_ during the down stroke, and _upwards
and forwards_ during the up stroke. The wing, in fact, is always
advancing; its under surface attacking the air like a boy’s kite.
If, on the other hand, the wing be forcibly depressed, as indicated
by the heavy waved line _a c_, and left to itself, it will as surely
rise again and describe a waved track, as shown at _c e_. This it
does by rotating on its long axis, and in virtue of its flexibility
and elasticity, aided by the recoil obtained from the air. In other
words, it is not necessary to elevate the wing forcibly in the
direction _c d_ to obtain the upward and forward movement _c e_. One
single impulse communicated at _a_ causes the wing to travel to _e_,
and a second impulse communicated at _e_ causes it to travel to _i_.
It follows from this that a series of vigorous down impulses would,
_if a certain interval were allowed to elapse between them_, beget a
corresponding series of up impulses, in accordance with the law of
action and reaction; the wing and the air under these circumstances
being alternately active and passive. I say if a certain interval
were allowed to elapse between every two down strokes, but this is
practically impossible, as the wing is driven with such velocity
that there is positively no time to waste in waiting for the purely
mechanical ascent of the wing. That the ascent of the pinion is not,
and ought not to be entirely due to the reaction of the air, is proved
by the fact that in flying creatures (certainly in the bat and bird)
there are distinct elevator muscles and elastic ligaments delegated to
the performance of this function. The reaction of the air is therefore
only one of the forces employed in elevating the wing; the others, as
I shall show presently, are vital and vito-mechanical in their nature.
The falling downwards and forwards of the body when the wings are
ascending also contribute to this result.

[Illustration: FIG. 82.  FIG. 83.

  Figs. 82 and 83 show that when the wings are elevated (_e_, _f_,
  _g_ of fig. 82) the body falls (_s_ of fig. 82); and that when the
  wings are depressed (_h_, _i_, _j_ of fig. 83) the body is elevated
  (_r_ of fig. 83). Fig. 82 shows that the wings are elevated as short
  levers (_e_) until towards the termination of the up stroke, when
  they are gradually expanded (_f_, _g_) to prepare them for making
  the down stroke. Fig. 83 shows that the wings descend as long levers
  (_h_) until towards the termination of the down stroke, when they are
  gradually folded or flexed (_i_, _j_), to rob them of their momentum
  and prepare them for making the up stroke. Compare with figs. 74 and
  75, p. 145. By this means the air beneath the wings is vigorously
  seized during the down stroke, while that above it is avoided during
  the up stroke. The concavo-convex form of the wings and the forward
  travel of the body contribute to this result. The wings, it will be
  observed, act as a parachute both during the up and down strokes.
  Compare with fig. 55, p. 112. Fig. 83 shows, in addition, the
  compound rotation of the wing, how it rotates upon a as a centre,
  with a radius _m b n_, and upon _a c b_ as a centre, with a radius _k
  l_. Compare with fig. 80, p. 149.--_Original._]

_The Wing ascends when the Body descends, and_ vice versâ.--As the
body of the insect, bat, and bird falls forwards in a curve when the
wing ascends, and is elevated in a curve when the wing descends, it
follows that the trunk of the animal is urged along a waved line, as
represented at 1, 2, 3, 4, 5 of fig. 81, p. 157; the waved line _a c
e g i_ of the same figure giving the track made by the wing. I have
distinctly seen the alternate rise and fall of the body and wing when
watching the flight of the gull from the stern of a steam-boat.

The direction of the stroke in the insect, as has been already
explained, is much more horizontal than in the bat or bird (compare
figs. 82 and 83 with figs. 64, 65, and 66, p. 139). In either case,
however, the down stroke must be delivered in a more or less forward
direction. This is necessary for support and propulsion. A horizontal
to-and-fro movement will elevate, and an up-and-down vertical movement
propel, but an oblique forward motion is requisite for progressive
flight.

In all wings, whatever their position during the intervals of rest,
and whether in one piece or in many, this feature is to be observed
in flight. The wings are slewed downwards and forwards, _i.e._ they
are carried more or less in the direction of the head during their
descent, and reversed or carried in an opposite direction during their
ascent. In stating that the wings are carried away from the head
during the back stroke, I wish it to be understood that they do not
therefore necessarily travel backwards in space when the insect is
flying forwards. On the contrary, the wings, as a rule, move forward
in curves, both during the down and up strokes. The fact is, that the
wings at their roots are hinged and geared to the trunk so loosely,
that the body is free to oscillate in a forward or backward direction,
or in an up, down, or oblique direction. As a consequence of this
freedom of movement, and as a consequence likewise of the speed at
which the insect is travelling, the wings during the back stroke are
for the most part actually travelling forwards. This is accounted for
by the fact, that the body falls downwards and forwards in a curve
during the up or return stroke of the wings, and because the horizontal
speed attained by the body is as a rule so much greater than that
attained by the wings, that the latter are never allowed time to travel
backward, the lesser movement being as it were swallowed up by the
greater. For a similar reason, the passenger of a steam-ship may travel
rapidly in the direction of the stern of the vessel, and yet be carried
forward in space,--the ship sailing much quicker than he can walk.
While the wing is descending, it is rotating upon its root as a centre
(short axis). It is also, and this is a most important point, rotating
upon its anterior margin (long axis), in such a manner as to cause the
several parts of the wing to assume various angles of inclination with
the horizon.

Figs. 84 and 85 supply the necessary illustration.

[Illustration: FIG. 84.]

[Illustration: FIG. 85.]

In flexion, as a rule, the under surface of the wing (fig. 84 _a_) is
arranged in the same plane with the body, both being in a line with or
making a slight angle with the horizon (_x x_).[80] When the wing is
made to descend, it gradually, in virtue of its simultaneously rotating
upon its long and short axes, makes a certain angle with the horizon
as represented at _b_. The angle is increased at the termination of
the down stroke as shown at _c_, so that the wing, particularly its
posterior margin, during its descent (_A_), is screwed or crushed down
upon the air with its concave or biting surface directed forwards and
towards the earth. The same phenomena are indicated at _a b c_ of
fig. 85, but in this figure the wing is represented as travelling more
decidedly forwards during its descent, and this is characteristic of
the down stroke of the insect’s wing--the stroke in the insect being
delivered in a very oblique and more or less horizontal direction
(figs. 64, 65, and 66, p. 139; fig. 71, p. 144). The forward travel of
the wing during its descent has the effect of diminishing the angles
made by the under surface of the wing with the horizon. Compare _b c d_
of fig. 85 with the same letters of fig. 84. At fig. 88 (p. 166) the
angles for a similar reason are still further diminished. This figure
(88) gives a very accurate idea of the kite-like action of the wing
both during its descent and ascent.

  [80] It happens occasionally in insects that the posterior margin
  of the wing is on a higher level than the anterior one towards the
  termination of the up stroke. In such cases the posterior margin is
  suddenly rotated in a downward and forward direction at the beginning
  of the down stroke--the downward and forward rotation securing
  additional elevating power for the wing. The posterior margin of the
  wing in bats and birds, unless they are flying downwards, never rises
  above the anterior one, either during the up or down stroke.

[Illustration: FIG. 86.]

The downward screwing of the posterior margin of the wing during the
down stroke is well seen in the dragon-fly, represented at fig. 86,
p. 161.

Here the arrows _r s_ indicate the range of the wing. At the beginning
of the down stroke the upper or dorsal surface of the wing (_i d f_)
is inclined slightly upwards and forwards. As the wing descends the
posterior margin (_i f_) twists and rotates round the anterior margin
(_i d_), and greatly increases the angle of inclination as seen at
_i j_, _g h_. This rotation of the posterior margin (_i j_) round
the anterior margin (_g h_) has the effect of causing the different
portions of the under surface of the wing to assume various angles
of inclination with the horizon, the wing attacking the air like a
boy’s kite. The angles are greatest towards the root of the wing and
least towards the tip. They accommodate themselves to the speed at
which the different parts of the wing travel--a small angle with a
high speed giving the same amount of buoying power as a larger angle
with a diminished speed. The screwing of the under surface of the wing
(particularly the posterior margin) in a downward direction during the
down stroke is necessary to insure the necessary upward recoil; the
wing being made to swing downwards and forwards pendulum fashion, for
the purpose of elevating the body, which it does by acting upon the
air as a long lever, and after the manner of a kite. During the down
stroke the wing is active, the air passive. In other words, the wing is
depressed by a purely vital act.

The down stroke is readily explained, and its results upon the body
obvious. The real difficulty begins with the up or return stroke. If
the wing was simply to travel in an upward and backward direction from
_c_ to _a_ of fig. 84, p. 160, it is evident that it would experience
much resistance from the superimposed air, and thus the advantages
secured by the descent of the wing would be lost. What really happens
is this. The wing does not travel upwards and _backwards_ in the
direction _c b a_ of fig. 84 (the body, be it remembered, is advancing)
but upwards and _forwards_ in the direction _c d e f g_. This is
brought about in the following manner. The wing is at right angles
to the horizon (_x x´_) at _c_. It is therefore caught by the air at
the point (2) because of the more or less horizontal travel of the
body; the elastic ligaments and other structures combined with the
resistance experienced from the air rotating the posterior or thin
margin of the pinion in an upward direction, as shown at _d e f g_
and _d f g_ of figs. 84 and 85, p. 160. The wing by this partly vital
and partly mechanical arrangement is rotated off the wind in such a
manner as to keep its dorsal or non-biting surface directed upwards,
while its concave or biting surface is directed downwards. The wing,
in short, has its planes so arranged, and its angles so adjusted to
the speed at which it is travelling, that it darts up a gradient like
a true kite, as shown at _c d e f g_ of figs. 84 and 85, p. 160, or _g
h i_ of fig. 88, p. 166. The wing consequently elevates and propels
during its _ascent_ as well as during its _descent_. It is, in fact,
a kite during both the down and up strokes. The ascent of the wing is
greatly assisted by the _forward travel_, and _downward and forward
fall_ of the body. This view will be readily understood by supposing,
what is really the case, that the wing is more or less fixed by the air
in space at the point indicated by 2 of figs. 84 and 85, p. 160; the
body, the instant the wing is fixed, falling downwards and forwards
in a curve, which, of course, is equivalent to placing the wing
above, and, so to speak, behind the volant animal--in other words, to
elevating the wing preparatory to a second down stroke, as seen at _g_
of the figures referred to (figs. 84 and 85). The ascent and descent
of the wing is always very much greater than that of the body, from
the fact of the pinion acting as a long lever. The peculiarity of the
wing consists in its being a flexible lever which acts upon yielding
fulcra (the air), the body participating in, and to a certain extent
perpetuating, the movements originally produced by the pinion. The
part which the body performs in flight is indicated at fig. 87. At _a_
the body is depressed, the wing being elevated and ready to make the
down stroke at _b_. The wing descends in the direction _c d_, but the
moment it begins to descend the body moves _upwards and forwards_ (see
arrows) in a curved line to _e_. As the wing is attached to the body
the wing is made gradually to assume the position _f_. The body (_e_),
it will be observed, is now on a higher level than the wing (_f_); the
under surface of the latter being so adjusted that it strikes upwards
and forwards as a kite. It is thus that the wing sustains and propels
during the up stroke. The body (_e_) now falls _downwards and forwards_
in a curved line to _g_, and in doing this it elevates or assists in
elevating the wing to _j_. The pinion is a second time depressed in
the direction _k l_, which has the effect of forcing the body along a
waved track and in _an upward direction_ until it reaches the point
_m_. The ascent of the body and the descent of the wing take place
simultaneously (_m n_). The body and wing, are alternately above and
beneath a given line _x x´_.

[Illustration: FIG. 87.]

A careful study of figs. 84, 85, 86, and 87, pp. 160, 161, and 163,
shows the great importance of the twisted configuration and curves
peculiar to the natural wing. If the wing was not curved in every
direction it could not be rolled on and off the wind during the down
and up strokes, as seen more particularly at fig. 87, p. 163. This,
however, is a vital point in progressive flight. The wing (_b_) is
rolled on to the wind in the direction _b a_, its under concave or
biting surface being crushed hard down with the effect of elevating
the body to _e_. The body falls to _g_, and the wing (_f_) is rolled
off the wind in the direction _f j_, and elevated until it assumes the
position _j_. The elevation of the wing is effected partly by the fall
of the body, partly by the action of the elevator muscles and elastic
ligaments, and partly by the reaction of the air, operating on its
under or concave biting surface. The wing is therefore to a certain
extent resting during the up stroke.

The concavo-convex form of the wing is admirably adapted for the
purposes of flight. In fact, the power which the wing possesses of
always keeping its concave or under surface directed _downwards_ and
_forwards_ enables it to seize the air at every stage of both the up
and down strokes so as to supply a persistent buoyancy. The action
of the natural wing is accompanied by remarkably little slip--the
elasticity of the organ, the resiliency of the air, and the shortening
and elongating of the elastic ligaments and muscles all co-operating
and reciprocating in such a manner that the descent of the wing
elevates the body; the descent of the body, aided by the reaction
of the air and the shortening of the elastic ligaments and muscles,
elevating the wing. The wing during the up stroke _arches above the
body_ after the manner of a parachute, and prevents the body from
falling. The sympathy which exists between the parts of a flying
animal and the air on which it depends for support and progress is
consequently of the most intimate character.

The up stroke (_B_, _D_ of figs. 84 and 85, p. 160), as will be seen
from the foregoing account, is a compound movement due in some measure
to recoil or resistance on the part of the air; to the shortening of
the muscles, elastic ligaments, and other vital structures; to the
elasticity of the wing; and to the falling of the body in a downward
and forward direction. The wing may be regarded as rotating during the
down stroke upon 1 of figs. 84 and 85, p. 160, which may be taken to
represent the long and short axes of the wing; and during the up stroke
upon 2, which may be taken to represent the yielding fulcrum furnished
by the air. A second pulsation is indicated by the numbers 3 and 4 of
the same figures (84, 85).

_The Wing acts upon yielding Fulcra._--The chief peculiarity of the
wing, as has been stated, consists in its being a twisted flexible
lever specially constructed to act upon yielding fulcra (the air). The
points of contact of the wing with the air are represented at _a b c
d e f g h i j k l_ respectively of figs. 84 and 85, p. 160; and the
imaginary points of rotation of the wing upon its long and short axes
at 1, 2, 3, and 4 of the same figures. The assumed points of rotation
advance from 1 to 3 and from 2 to 4 (_vide_ arrows marked _r_ and _s_,
fig. 85); these constituting the steps or pulsations of the wing. The
actual points of rotation correspond to the little loops _a b c d f g h
i j l_ of fig. 85. The wing descends at _A_ and _C_, and ascends at _B_
and _D_.

_The Wing acts as a true Kite both during the Down and Up
Strokes._--If, as I have endeavoured to explain, the wing, even when
elevated and depressed in a strictly vertical direction, inevitably
and invariably darts forward, it follows as a consequence that the
wing, as already partly explained, flies forward as a true kite, both
during the down and up strokes, as shown at _c d e f g h i j k l m_ of
fig. 88; and that its under concave or biting surface, in virtue of the
forward travel communicated to it by the body in motion, is closely
applied to the air, both during its ascent and descent--a fact hitherto
overlooked, but one of considerable importance, as showing how the wing
furnishes a persistent buoyancy, alike when it rises and falls.

[Illustration: FIG. 88.]

In fig. 88 the greater impulse communicated during the down stroke
is indicated by the double dotted lines. The angle made by the wing
with the horizon (_a b_) is constantly varying, as a comparison of
_c_ with _d_, _d_ with _e_, _e_ with _f_, _f_ with _g_, _g_ with
_h_, and _h_ with _i_ will show; these letters having reference to
supposed transverse sections of the wing. This figure also shows that
the _convex_ or non-biting surface of the wing is always directed
upwards, so as to avoid unnecessary resistance on the part of the air
to the wing during its ascent; whereas the _concave_ or biting surface
is always directed downwards, so as to enable the wing to contend
successfully with gravity.

_Where the Kite formed by the Wing differs from the Boy’s Kite._--The
natural kite formed by the wing differs from the artificial kite
only in this, that the former is capable of being moved in all its
parts, and is more or less flexible and elastic, the latter being
comparatively rigid. The flexibility and elasticity of the kite formed
by the natural wing is rendered necessary by the fact that the wing
is articulated or hinged at its root; its different parts travelling
at various degrees of speed in proportion as they are removed from
the axis of rotation. Thus the tip of the wing travels through a much
greater space in a given time than a portion nearer the root. If the
wing was not flexible and elastic, it would be impossible to reverse it
at the end of the up and down strokes, so as to produce a continuous
vibration. The wing is also practically hinged along its anterior
margin, so that the posterior margin of the wing travels through a
greater space in a given time than a portion nearer the anterior
margin (fig. 80, p. 149). The compound rotation of the wing is greatly
facilitated by the wing being flexible and elastic. This causes the
pinion to twist upon its long axis during its vibration, as already
stated. The twisting is partly a vital, and partly a mechanical act;
that is, it is occasioned in part by the action of the muscles, in
part by the reaction of the air, and in part by the greater momentum
acquired by the tip and posterior margin of the wing, as compared
with the root and anterior margin; the speed acquired by the tip and
posterior margin causing them to reverse always subsequently to the
root and anterior margin, which has the effect of throwing the anterior
and posterior margins of the wing into figure-of-8 curves. It is in
this way that the posterior margin of the outer portion of the wing
is made to incline forwards at the end of the down stroke, when the
anterior margin is inclined backwards; the posterior margin of the
outer portion of the wing being made to incline backwards at the end
of the up stroke, when a corresponding portion of the anterior margin
is inclined forwards (figs. 69 and 70, _g_, _a_, p. 141; fig. 86, _j_,
_f_, p. 161).

_The Angles formed by the Wing during its Vibrations._--Not the least
interesting feature of the compound rotation of the wing--of the
varying degrees of speed attained by its different parts--and of the
twisting or plaiting of the posterior margin around the anterior,--is
the great variety of kite-like surfaces developed upon its dorsal
and ventral aspects. Thus the tip of the wing forms a kite which is
inclined upwards, forwards, and outwards, while the root forms a kite
which is inclined upwards, forwards, and inwards. The angles made by
the tip and outer portions of the wing with the horizon are less than
those made by the body or central part of the wing, and those made by
the body or central part less than those made by the root and inner
portions. The angle of inclination peculiar to any portion of the wing
increases as the speed peculiar to said portion decreases, and _vice
versâ_. The wing is consequently mechanically perfect; the angles made
by its several parts with the horizon being accurately adjusted to
the speed attained by its different portions during its travel to and
fro. From this it follows that the air set in motion by one part of the
wing is seized upon and utilized by another; the inner and anterior
portions of the wing supplying, as it were, currents for the outer and
posterior portions. This results from the wing always forcing the air
outwards and backwards. These statements admit of direct proof, and I
have frequently satisfied myself of their exactitude by experiments
made with natural and artificial wings.

In the bat and bird, the twisting of the wing upon its long axis is
more of a vital and less of a mechanical act than in the insect; the
muscles which regulate the vibration of the pinion in the former (bat
and bird), extending quite to the tip of the wing (fig. 95, p. 175;
figs. 82 and 83, p. 158).

_The Body and Wings move in opposite Curves._--I have stated that the
wing advances in a waved line, as shown at _a c e g i_ of fig. 81,
p. 157; and similar remarks are to be made of the body as indicated
at 1, 2, 3, 4, 5 of that figure. Thus, when the wing descends in the
curved line _a c_, it elevates the body in a corresponding but minor
curved line, as at 1, 2; when, on the other hand, the wing ascends in
the curved line _c e_, the body descends in a corresponding but smaller
curved line (2, 3), and so on _ad infinitum_. The undulations made by
the body are so trifling when compared with those made by the wing,
that they are apt to be overlooked. They are, however, deserving of
attention, as they exercise an important influence on the undulations
made by the wing; the body and wing swinging forward alternately, the
one rising when the other is falling, and _vice versâ_. Flight may be
regarded as the resultant of three forces:--the _muscular and elastic
force_, residing in the wing, which causes the pinion to act as a true
kite, both during the down and up strokes; the _weight of the body_,
which becomes a force the instant the trunk is lifted from the ground,
from its tendency to fall downwards and forwards; and _the recoil
obtained from the air_ by the rapid action of the wing. These three
forces may be said to be active and passive by turns.

When a bird rises from the ground it runs for a short distance,
or throws its body into the air by a sudden leap, the wings being
simultaneously elevated. When the body is fairly off the ground, the
wings are made to descend with great vigour, and by their action to
continue the upward impulse secured by the preliminary run or leap. The
body then falls in a curve downwards and forwards; the wings, partly
by the fall of the body, partly by the reaction of the air on their
under surface, and partly by the shortening of the elevator muscles
and elastic ligaments, being placed above and to some extent behind
the bird--in other words, elevated. The second down stroke is now
given, and the wings again elevated as explained, and so on in endless
succession; the body falling when the wings are being elevated, and
_vice versâ_, (fig. 81, p. 157). When a long-winged oceanic bird rises
from the sea, it uses the tips of its wings as levers for forcing the
body up; the points of the pinions suffering no injury from being
brought violently in contact with the water. A bird cannot be said to
be flying until the trunk is swinging forward in space and taking part
in the movement. The hawk, when fixed in the air over its quarry, is
simply supporting itself. To fly, in the proper acceptation of the
term, implies to support and propel. This constitutes the difference
between a bird and a balloon. The bird can elevate _and carry itself
forward_, the balloon can simply elevate itself, and must rise and fall
in a straight line in the absence of currents. When the gannet throws
itself from a cliff, the inertia of the trunk at once comes into play,
and relieves the bird from those herculean exertions required to raise
it from the water when it is once fairly settled thereon. A swallow
dropping from the eaves of a house, or a bat from a tower, afford
illustrations of the same principle. Many insects launch themselves
into space prior to flight. Some, however, do not. Thus the blow-fly
can rise from a level surface when its legs are removed. This is
accounted for by the greater amplitude and more horizontal play of the
insect’s wing as compared with that of the bat and bird, and likewise
by the remarkable reciprocating power which the insect wing possesses
when the body of the insect is not moving forwards (figs. 67, 68,
69, and 70 p. 141). When a beetle attempts to fly from the hand, it
extends its front legs and flexes the back ones, and tilts its head
and thorax upwards, so as exactly to resemble a horse in the act of
rising from the ground. This preliminary over, whirr go its wings with
immense velocity, and in an almost horizontal direction, the body being
inclined more or less vertically. The insect rises very slowly, and
often requires to make several attempts before it succeeds in launching
itself into the air. I could never detect any pressure communicated to
the hand when the insect was leaving it, from which I infer that it
does not leap into the air. The bees, I am disposed to believe, also
rise without anything in the form of a leap or spring. I have often
watched them leaving the petals of flowers, and they always appeared
to me to elevate themselves by the steady play of their wings, which
was the more necessary, as the surface from which they rose was in many
cases a yielding surface.


THE WINGS OF INSECTS, BATS, AND BIRDS.

_Elytra or Wing-cases, Membranous Wings--their shape and uses._--The
wings of insects consist either of one or two pairs. When two pairs
are present, they are divided into an anterior or upper pair, and
a posterior or under pair. In some instances the anterior pair are
greatly modified, and present a corneous condition. When so modified,
they cover the under wings when the insect is reposing, and have
from this circumstance been named elytra, from the Greek ἔλυτρον, a
sheath. The anterior wings are dense, rigid, and opaque in the beetles
(fig. 89, _r_); solid in one part and membranaceous in another in the
water-bugs (fig. 90, _r_); more or less membranous throughout in the
grasshoppers; and completely membranous in the dragon-flies (fig. 91,
_e e_, p. 172). The superior or upper wings are inclined at a certain
angle when extended, and are indirectly connected with flight in the
beetles, water-bugs, and grasshoppers. They are actively engaged in
this function in the dragon-flies and butterflies. The elytra or
anterior wings are frequently employed as _sustainers_ or _gliders_
in flight,[81] the posterior wings acting more particularly as
_elevators_ and _propellers_. In such cases the elytra are twisted upon
themselves after the manner of wings.

  [81] That the elytra take part in flight is proved by this, that when
  they are removed, flight is in many cases destroyed.

[Illustration: FIG. 89.  FIG. 90.

  FIG. 89.--The Centaur Beetle (_Augusoma centaurus_), seen
  from above. Shows elytra (_r_) and membranous wings (_e_) in the
  extended state. The nervures are arranged and jointed in such a
  manner that the membranous wings can be folded (_e_) transversely
  across the back beneath the elytra during repose. When so folded,
  the anterior or thick margins of the membranous wings are directed
  outwards and slightly downwards, the posterior or thin margins
  inwards and slightly upwards. During extension the positions of
  the margins are reversed by the wings twisting and rotating upon
  their long axes, the anterior margins, as in bats and birds, being
  directed upwards and forwards, and making a very decided angle with
  the horizon. The wings in the beetles are insignificantly small
  when compared with the area of the body. They are, moreover, finely
  twisted upon themselves, and possess great power as propellers and
  elevators.--_Original._

  FIG. 90.--The Water-Bug (_Genus belostoma_). In this insect
  the superior wings (elytra or wing covers _r_) are semi-membranous.
  They are geared to the membranous or under wings (_a_) by a hook, the
  two acting together in flight. When so geared the upper and under
  wings are delicately curved and twisted. They moreover taper from
  within outwards, and from before backwards.--_Original._]

[Illustration:

  FIG. 91.--The Dragon-fly (_Petalura gigantea_). In this insect the
  wings are finely curved and delicately transparent, the nervures
  being most strongly developed at the roots of the wings and along
  the anterior margins (_e e_, _f f_), and least so at the tips (_b
  b_), and along the posterior margins (_a a_). The anterior pair (_e
  e_) are analogous in every respect to the posterior (_f f_). Both
  make a certain angle with the horizon, the anterior pair (_e e_),
  which are principally used as elevators, making a smaller angle than
  the posterior pair (_f f_), which are used as drivers. The wings of
  the dragon-fly make the proper angles for flight even in repose, so
  that the insect can take to wing instantly. The insect flies with
  astonishing velocity.--_Original._]

The wings of insects present different degrees of opacity--those of the
moths and butterflies being non-transparent; those of the dragon-flies,
bees, and common flies presenting a delicate, filmy, gossamer-like
appearance. The wings in every case are composed of a duplicature of
the integument or investing membrane, and are strengthened in various
directions by a system of hollow, horny tubes, known to entomologists
as the neuræ or nervures. The nervures taper towards the extremity of
the wing, and are strongest towards its root and anterior margin, where
they supply the place of the arm in bats and birds. They are variously
arranged. In the beetles they pursue a somewhat longitudinal course,
and are jointed to admit of the wing being folded up transversely
beneath the elytra.[82] In the locusts the nervures diverge from a
common centre, after the manner of a fan, so that by their aid the
wing is crushed up or expanded as required; whilst in the dragon-fly,
where no folding is requisite, they form an exquisitely reticulated
structure. The nervures, it may be remarked, are strongest in the
beetles, where the body is heavy and the wing small. They decrease in
thickness as those conditions are reversed, and entirely disappear in
the minute chalcis and psilus.[83] The function of the nervures is
not ascertained; but as they contain spiral vessels which apparently
communicate with the tracheæ of the trunk, some have regarded them as
being connected with the respiratory system; whilst others have looked
upon them as the receptacles of a subtle fluid, which the insect can
introduce and withdraw at pleasure to obtain the requisite degree of
expansion and tension in the wing. Neither hypothesis is satisfactory,
as respiration and flight can be performed in their absence. They
appear to me, when present, rather to act as mechanical stays or
stretchers, in virtue of their rigidity and elasticity alone,--their
arrangement being such that they admit of the wing being folded in
various directions, if necessary, during flexion, and give it the
requisite degree of firmness during extension. They are, therefore,
in every respect analogous to the skeleton of the wing in the bat and
bird. In those wings which, during the period of repose, are folded up
beneath the elytra, the mere extension of the wing in the dead insect,
where no injection of fluid can occur, causes the nervures to fall into
position, and the membranous portions of the wing to unfurl or roll
out precisely as in the living insect, and as happens in the bat and
bird. This result is obtained by the spiral arrangement of the nervures
at the root of the wing; the anterior nervure occupying a higher
position than that further back, as in the leaves of a fan. The spiral
arrangement occurring at the root extends also to the margins, so
that wings which fold up or close, as well as those which do not, are
twisted upon themselves, and present a certain degree of convexity on
their superior or upper surface, and a corresponding concavity on their
inferior or under surface; their free edges supplying those fine curves
which act with such efficacy upon the air, in obtaining the maximum of
resistance and the minimum of displacement; or what is the same thing,
the maximum of support with the minimum of slip (figs. 92 and 93).

  [82] The wings of the May-fly are folded longitudinally and
  transversely, so that they are crumpled up into little squares.

  [83] Kirby and Spence, vol. ii. 5th ed., p. 352.

[Illustration: FIG. 92.

  FIG. 92.--Right wing of Beetle (_Goliathus micans_), dorsal
  surface. This wing somewhat resembles the kestrel’s (fig. 61, p. 136)
  in shape. It has an anterior thick margin, _d e f_, and a posterior
  thin one, _b a c_. Strong nervures run along the anterior margin
  (_d_) until they reach the joint (_e_), where the wing folds upon
  itself during repose. Here the nervures split up and divaricate and
  gradually become smaller and smaller until they reach the extremity
  of the wing (_f_) and the posterior or thin margin (_b_); other
  nervures radiate in graceful curves from the root of the wing. These
  also become finer as they reach the posterior or thin margin (_c a_).
  _r_, Root of the wing with its complex compound joint. The wing of
  the beetle bears a certain analogy to that of the bat, the nervures
  running along the anterior margin (_d_) of the wing, resembling the
  humerus and forearm of the bat (fig. 94, _d_, p. 175), the joint of
  the beetle’s wing (_e_) corresponding to the carpal or wrist-joint
  of the bat’s wing (fig. 94, _e_), the terminal or distal nervures of
  the beetle (_f b_) to the phalanges of the bat (fig. 94, _f b_). The
  parts marked _f b_ may in both instances be likened to the primary
  feathers of the bird, that marked _a_ to the secondary feathers,
  and _c_ to the tertiary feathers. In the wings of the beetle and
  bat no air can possibly escape through them during the return or up
  stroke.--_Original._]

[Illustration: FIG. 93.

  FIG. 93.--Right wing of the Beetle (_Goliathus micans_), as
  seen from behind and from beneath. When so viewed, the anterior or
  thick margin (_d f_) and the posterior or thin margin (_b x c_) are
  arranged in different planes, and form a true helix or screw. Compare
  with figs. 95 and 97.--_Original._]

The wings of insects can be made to oscillate within given areas
anteriorly, posteriorly, or centrally with regard to the plane of
the body; or in intermediate positions with regard to it and a
perpendicular line. The wing or wings of the one side can likewise be
made to move independently of those of the opposite side, so that the
centre of gravity, which, in insects, bats, and birds, is suspended,
is not disturbed in the endless evolutions involved in ascending,
descending, and wheeling. The centre of gravity varies in insects
according to the shape of the body, the length and shape of the limbs
and antennæ, and the position, shape, and size of the pinions. It
is corrected in some by curving the body, in others by bending or
straightening the limbs and antennæ, but principally in all by the
judicious play of the wings themselves.

The wing of the bat and bird, like that of the insect, is
concavo-convex, and more or less twisted upon itself (figs. 94, 95, 96,
and 97).

[Illustration: FIG. 94.

  FIG. 94.--Right wing of the Bat (_Phyllorhina gracilis_),
  dorsal surface. _d e f_, Anterior or thick margin of the wing,
  supported by the bones of the arm, forearm, and hand (first and
  second phalanges); _c a b_, posterior or thin margin, supported
  by the remaining phalanges, by the side of the body, and by the
  foot.--_Original._]

[Illustration: FIG. 95.

  FIG. 95.--Right wing of the Bat (_Phyllorhina gracilis_),
  as seen from behind and from beneath. When so regarded, the anterior
  or thick margin (_d f_) of the wing displays different curves from
  those seen on the posterior or thin margin (_b c_); the anterior and
  posterior margins being arranged in different planes, as in the blade
  of a screw propeller.--_Original._]

The twisting is in a great measure owing to the manner in which
the bones of the wing are twisted upon themselves, and the spiral
nature of their articular surfaces; the long axes of the joints
always intersecting each other at nearly right angles. As a result of
this disposition of the articular surfaces, the wing is shot out or
extended, and retracted or flexed in a variable plane, the bones of the
wing rotating in the direction of their length during either movement.
This secondary action, or the revolving of the component bones upon
their own axes, is of the greatest importance in the movements of the
wing, as it communicates to the hand and forearm, and consequently to
the membrane or feathers which they bear, the precise angles necessary
for flight. It, in fact, insures that the wing, and the curtain, sail,
or fringe of the wing shall be screwed into and down upon the air in
extension, and unscrewed or withdrawn from it during flexion. The wing
of the bat and bird may therefore be compared to a huge gimlet or
auger, the axis of the gimlet representing the bones of the wing; the
flanges or spiral thread of the gimlet the frenum or sail (figs. 95 and
97).

[Illustration: FIG. 96.

  FIG. 96.--Right wing of the Red-legged Partridge (_Perdix
  rubra_), dorsal aspect. Shows extreme example of short rounded wing;
  contrast with the wing of the albatross (fig. 62, p. 137), which
  furnishes an extreme example of the long ribbon-shaped wing; _d e
  f_, anterior margin; _b a c_, posterior ditto, consisting of primary
  (_b_), secondary (_a_), and tertiary (_c_) feathers, with their
  respective coverts and subcoverts; the whole overlapping and mutually
  supporting each other. This wing, like the kestrel’s (fig. 61, p.
  136), was drawn from a specimen held against the light, the object
  being to display the mutual relation of the feathers to each other,
  and how the feathers overlap.--_Original._]

[Illustration: FIG. 97.

  FIG. 97.--Right wing of Red-legged Partridge (_Perdix
  rubra_), seen from behind and from beneath, as in the beetle
  (fig. 93) and bat (fig. 95). The same lettering and explanation does
  for all three.--_Original._]


THE WINGS OF BATS.

_The Bones of the Wing of the Bat--the spiral configuration of their
articular surfaces._--The bones of the arm and hand are especially
deserving of attention. The humerus (fig. 17, _r_, p. 36) is short
and powerful, and twisted upon itself to the extent of something less
than a quarter of a turn. As a consequence, the long axis of the
shoulder-joint is nearly at right angles to that of the elbow-joint.
Similar remarks may be made regarding the radius (the principal bone
of the forearm) (_d_), and the second and third metacarpal bones with
their phalanges (_e f_), all of which are greatly elongated, and give
strength and rigidity to the anterior or thick margin of the wing. The
articular surfaces of the bones alluded to, as well as of the other
bones of the hand, are spirally disposed with reference to each other,
the long axes of the joints intersecting at nearly right angles. The
object of this arrangement is particularly evident when the wing of
the living bat, or of one recently dead, is extended and flexed as in
flight.

In the flexed state the wing is greatly reduced in size, its under
surface being nearly parallel with the plane of progression. When
the wing is fully extended its under surface makes a certain angle
with the horizon, the wing being then in a position to give the
down stroke, which is delivered _downwards_ and _forwards_, as in
the insect. When extension takes place the elbow-joint is depressed
and carried forwards, the wrist elevated and carried backwards, the
metacarpo-phalangeal joints lowered and inclined forwards, and the
distal phalangeal joints slightly raised and carried backwards. The
movement of the bat’s wing in extension is consequently a spiral one,
the spiral running alternately from below upwards and forwards, and
from above downwards and backwards (compare with fig. 79, p. 147). As
the bones of the arm, forearm, and hand rotate on their axes during
the extensile act, it follows that the posterior or thin margin of
the wing is rotated in a downward direction (the anterior or thick
one being rotated in an opposite direction) until the wing makes
an angle of something like 30° with the horizon, which, as I have
already endeavoured to show, is the greatest angle made by the wing in
flight. The action of the bat’s wing at the shoulder is particularly
free, partly because the shoulder-joint is universal in its nature,
and partly because the scapula participates in the movements of this
region. The freedom of action referred to enables the bat not only to
rotate and twist its wing as a whole, with a view to diminishing and
increasing the angle which its under surface makes with the horizon,
but to elevate and depress the wing, and move it in a forward and
backward direction. The rotatory or twisting movement of the wing
is an essential feature in flight, as it enables the bat (and this
holds true also of the insect and bird) to balance itself with the
utmost exactitude, and to change its position and centre of gravity
with marvellous dexterity. The movements of the shoulder-joint are
restrained within certain limits by a system of check-ligaments, and
by the coracoid and acromian processes of the scapula. The wing is
recovered or flexed by the action of elastic ligaments which extend
between the shoulder, elbow, and wrist. Certain elastic and fibrous
structures situated between the fingers and in the substance of the
wing generally take part in flexion. The bat flies with great ease and
for lengthened periods. Its flight is remarkable for its softness,
in which respect it surpasses the owl and the other nocturnal birds.
The action of the wing of the bat, and the movements of its component
bones, are essentially the same as in the bird.


THE WINGS OF BIRDS.

_The Bones of the Wing of the Bird--their Articular Surfaces,
Movements, etc._--The humerus, or arm-bone of the wing, is supported
by three of the trunk-bones, viz. the scapula or shoulder-blade, the
clavicle or collar-bone, also called the _furculum_,[84] and the
coracoid bone,--these three converging to form a _point d’appui_, or
centre of support for the head of the humerus, which is received in
_facettes_ or depressions situated on the scapula and coracoid. In
order that the wing may have an almost unlimited range of motion, and
be wielded after the manner of a flail, it is articulated to the trunk
by a somewhat lax universal joint, which permits vertical, horizontal,
and intermediate movements.[85] The long axis of the joint is directed
vertically; the joint itself somewhat backwards. It is otherwise with
the elbow-joint, which is turned forwards, and has its long axis
directed horizontally, from the fact that the humerus is twisted upon
itself to the extent of nearly a quarter of a turn. The elbow-joint is
decidedly spiral in its nature, its long axis intersecting that of the
shoulder-joint at nearly right angles. The humerus articulates at the
elbow with two bones, the radius and the ulna, the former of which is
pushed from the humerus, while the other is drawn towards it during
extension, the reverse occurring during flexion. Both bones, moreover,
while those movements are taking place, revolve to a greater or less
extent upon their own axes. The bones of the forearm articulate at the
wrist with the carpal bones, which being spirally arranged, and placed
obliquely between them and the metacarpal bones, transmit the motions
to the latter in a curved direction. The long axis of the wrist-joint
is, as nearly as may be, at right angles to that of the elbow-joint,
and more or less parallel with that of the shoulder. The metacarpal or
hand-bones, and the phalanges or finger-bones are more or less fused
together, the better to support the great primary feathers, on the
efficiency of which flight mainly depends. They are articulated to each
other by double hinge-joints, the long axes of which are nearly at
right angles to each other.

  [84] The furcula are usually united to the anterior part of the
  sternum by ligament; but in birds of powerful flight, where the
  wings are habitually extended for gliding and sailing, as in
  the frigate-bird, the union is osseous in its nature. “In the
  frigate-bird the furcula are likewise anchylosed with the coracoid
  bones.”--Comp. Anat. and Phys. of Vertebrates, by Prof. Owen,
  vol. ii. p. 66.

  [85] “The os humeri, or bone of the arm, is articulated by a small
  rounded surface to a corresponding cavity formed between the coracoid
  bone and the scapula, in such a manner as to allow great freedom of
  motion.”--Macgillivray’s Brit. Birds, vol. i. p. 33.

  “The arm is articulated to the trunk by a ball-and-socket joint,
  permitting all the freedom of motion necessary for flight.”--Cyc. of
  Anat. and Phys., vol. iii. p. 424.

As a result of this disposition of the articular surfaces, the wing is
shot out or extended and retracted or flexed in a variable plane, the
bones composing the wing, particularly those of the forearm, rotating
on their axes during either movement.

This secondary action, or the revolving of the component bones upon
their own axes, is of the greatest importance in the movements of the
wing, as it communicates to the hand and forearm, and consequently
to the primary and secondary feathers which they bear, the precise
angles necessary for flight; it in fact insures that the wing, and the
curtain or fringe of the wing which the primary and secondary feathers
form, shall be screwed into and down upon the air in extension, and
unscrewed or withdrawn from it during flexion. The wing of the bird may
therefore be compared to a huge gimlet or auger; the axis of the gimlet
representing the bones of the wing, the flanges or spiral thread of the
gimlet the primary and secondary feathers (fig. 63, p. 138, and fig.
97, p. 176).

_Traces of Design in the Wing of the Bird--the arrangement of the
Primary, Secondary, and Tertiary Feathers, etc._--There are few things
in nature more admirably constructed than the wing of the bird, and
perhaps none where design can be more readily traced. Its great
strength and extreme lightness, the manner in which it closes up or
folds during flexion, and opens out or expands during extension, as
well as the manner in which the feathers are strung together and
overlap each other in divers directions to produce at one time a solid
resisting surface, and at another an interrupted and comparatively
non-resisting one, present a degree of fitness to which the mind must
necessarily revert with pleasure. If the feathers of the wing only
are contemplated, they may be conveniently divided into three sets
of three each (on both sides of the wing)--an upper or dorsal set
(fig. 61, _d_, _e_, _f_, p. 136), a lower or ventral set (_c_, _a_,
_b_), and one which is intermediate. This division is intended to
refer the feathers to the bones of the arm, forearm, and hand, but is
more or less arbitrary in its nature. The lower set or tier consists
of the primary (_b_), secondary (_a_), and tertiary (_c_) feathers,
strung together by fibrous structures in such a way that they move in
an outward or inward direction, or turn upon their axes, at precisely
the same instant of time,--the middle and upper sets of feathers,
which overlap the primary, secondary, and tertiary ones, constituting
what are called the “coverts” and “sub-coverts.” The primary or rowing
feathers are the longest and strongest (_b_), the secondaries (_a_)
next, and the tertiaries third (_c_). The tertiaries, however, are
occasionally longer than the secondaries. The tertiary, secondary, and
primary feathers increase in strength from within outwards, _i.e._ from
the body towards the extremity of the wing, and so of the several sets
of wing-coverts. This arrangement is necessary, because the strain on
the feathers during flight increases in proportion to their distance
from the trunk.

[Illustration: FIG. 98.  FIG. 99.  FIG. 100.  FIG. 101.

  FIGS. 98, 99, 100, and 101 show the muscles and elastic ligaments,
  and the arrangement of the primary and secondary feathers on the
  ventral aspects of the wing of the crested crane. The wing is in the
  extended condition.

  _y_ (fig. 98), Great pectoral muscle which depresses the wing.

  _a b_, Voluntary muscular fibres terminating in elastic band _k_.
  This band splits up into two portions (_k_, _m_). A somewhat similar
  band is seen at _j_. These three bands are united to, and act in
  conjunction with, the great fibro-elastic web _c_, to flex the
  forearm on the arm. The fibro-elastic web is more or less under the
  influence of the voluntary muscles (_a_, _b_).

  _o_, _p_, _q_, Musculo-fibro-elastic ligament, which envelopes the
  roots of the primary and secondary feathers, and forms a symmetrical
  network of great strength and beauty, its component parts being
  arranged in such a manner as to envelope the root of each individual
  feather. The network in question supports the feathers, and limits
  their peculiar valvular action. It is enlarged at figs. 99 and
  101, and consists of three longitudinal bands, _r s_, _t u_, _v
  w_. Between these bands two oblique bands, _g_ and _h_, run; the
  oblique bands occurring between every two feathers. The marginal
  longitudinal band (_v_, _w_) splits up into two processes, one of
  which curves round the root of each feather (_x_) in a direction from
  right to left (_c_, _b_, _a_), the other in a direction from left to
  right (_d_, _e_, _f_). These processes are also seen at _m_, _n_ of
  fig. 100.--_Original._]

The manner in which the roots of the primary, secondary, and tertiary
feathers are geared to each other in order to rotate in one direction
in flexion, and in another and opposite direction in extension, is
shown at figs. 98, 99, 100, and 101, p. 181. In flexion the feathers
open up and permit the air to pass between them. In extension they flap
together and render the wing as air-tight as that of either the insect
or bat. The primary, secondary, and tertiary feathers have consequently
a valvular action.

_The Wing of the Bird not always opened up to the same extent in the
Up Stroke._--The elaborate arrangements and adaptations for increasing
the area of the wing, and making it impervious to air during the down
stroke, and for decreasing the area and opening up the wing during
the up stroke, although necessary to the flight of the heavy-bodied,
short-winged birds, as the grouse, partridge, and pheasant, are by no
means indispensable to the flight of the long-winged oceanic birds,
unless when in the act of rising from a level surface; neither do the
short-winged heavy birds require to fold and open up the wing during
the up stroke to the same extent in all cases, less folding and opening
up being required when the birds fly against a breeze, and when they
have got fairly under weigh. All the oceanic birds, even the albatross,
require to fold and flap their wings vigorously when they rise from
the surface of the water. When, however, they have acquired a certain
degree of momentum, and are travelling at a tolerable horizontal speed,
they can in a great measure dispense with the opening up of the wing
during the up stroke--nay, more, they can in many instances dispense
even with flapping. This is particularly the case with the albatross,
which (if a tolerably stiff breeze be blowing) can sail about for
an hour at a time without once flapping its wings. In this case the
wing is wielded in one piece like the insect wing, the bird simply
screwing and unscrewing the pinion on and off the wind, and exercising
a restraining influence--the breeze doing the principal part of the
work. In the bat the wing is jointed as in the bird, and folded during
the up stroke. As, however, the bat’s wing, as has been already
stated, is covered by a continuous and more or less elastic membrane,
it follows that it cannot be opened up to admit of the air passing
through it during the up stroke. Flight in the bat is therefore secured
by alternately diminishing and increasing the area of the wing during
the up and down strokes--the wing rotating upon its root and along its
anterior margin, and presenting a variety of kite-like surfaces, during
its ascent and descent, precisely as in the bird (fig. 80, p. 149, and
fig. 83, p. 158).

[Illustration:

  FIG. 102.--Shows the upward inclination of the body and the flexed
  condition of the wings (_a b_, _e f_; _a´ b´_, _e´ f´_) in the
  flight of the kingfisher. The body and wings when taken together
  form a kite. Compare with fig. 59, p. 126, where the wings are fully
  extended.]

_Flexion of the Wing necessary to the Flight of Birds._--Considerable
diversity of opinion exists as to whether birds do or do not flex their
wings in flight. The discrepancy is owing to the great difficulty
experienced in analysing animal movements, particularly when, as in
the case of the wings, they are consecutive and rapid. My own opinion
is, that the wings are flexed in flight, but that all wings are not
flexed to the same extent, and that what holds true of one wing does
not necessarily hold true of another. To see the flexing of the wing
properly, the observer should be either immediately above the bird or
directly beneath it. If the bird be contemplated from before, behind,
or from the side, the up and down strokes of the pinion distract the
attention and complicate the movement to such an extent as to render
the observation of little value. In watching rooks proceeding leisurely
against a slight breeze, I have over and over again satisfied myself
that the wings are flexed during the up stroke, the mere extension and
flexion, with very little of a down stroke, in such instances sufficing
for propulsion. I have also observed it in the pigeon in full flight,
and likewise in the starling, sparrow, and kingfisher (fig. 102,
p. 183).

It occurs principally at the wrist-joint, and gives to the wing the
peculiar quiver or tremor so apparent in rapid flight, and in young
birds at feeding-time. The object to be attained is manifest. By the
flexing of the wing in flight, the “_remiges_,” or rowing feathers,
are opened up or thrown out of position, and the air permitted
to escape--advantage being thus taken of the peculiar action of
the individual feathers and the higher degree of differentiation
perceptible in the wing of the bird as compared with that of the bat
and insect.

In order to corroborate the above opinion, I extended the wings of
several birds as in rapid flight, and fixed them in the outspread
position by lashing them to light unyielding reeds. In these
experiments the shoulder and elbow-joints were left quite free--the
wrist or carpal and the metacarpal joints only being bound. I took
care, moreover, to interfere as little as possible with the action of
the elastic ligament or alar membrane which, in ordinary circumstances,
recovers or flexes the wing, the reeds being attached for the most
part to the primary and secondary feathers. When the wings of a pigeon
were so tied up, the bird could not rise, although it made vigorous
efforts to do so. When dropped from the hand, it fell violently upon
the ground, notwithstanding the strenuous exertions which it made with
its pinions to save itself. When thrown into the air, it fluttered
energetically in its endeavours to reach the dove-cot, which was close
at hand; in every instance, however, it fell, more or less heavily, the
distance attained varying with the altitude to which it was projected.

Thinking that probably the novelty of the situation and the
strangeness of the appliances confused the bird, I allowed it to walk
about and to rest without removing the reeds. I repeated the experiment
at intervals, but with no better results. The same phenomena, I may
remark, were witnessed in the sparrow; so that I think there can be no
doubt that a certain degree of flexion in the wings is indispensable
to the flight of all birds--the amount varying according to the length
and form of the pinions, and being greatest in the short broad-winged
birds, as the partridge and kingfisher, less in those whose wings are
moderately long and narrow, as the gulls, and many of the oceanic
birds, and least in the heavy-bodied long and narrow-winged sailing or
gliding birds, the best example of which is the albatross. The degree
of flexion, moreover, varies according as the bird is rising, falling,
or progressing in a horizontal direction, it being greatest in the two
former, and least in the latter.

It is true that in insects, unless perhaps in those which fold or
close the wing during repose, no flexion of the pinion takes place in
flight; but this is no argument against this mode of diminishing the
wing-area during the up stroke where the joints exist; and it is more
than probable that when joints are present they are added to augment
the power of the wing during its active state, _i.e._ during flight,
quite as much as to assist in arranging the pinion on the back or
side of the body when the wing is passive and the animal is reposing.
The flexion of the wing is most obvious when the bird is exerting
itself, and may be detected in birds which skim or glide when they are
rising, or when they are vigorously flapping their wings to secure the
impetus necessary to the gliding movement. It is less marked at the
elbow-joint than at the wrist; and it may be stated generally that,
as flexion _decreases_, the twisting flail-like movement of the wing
at the shoulder _increases_, and _vice versâ_,--the great difference
between sailing birds and those which do not sail amounting to this,
that in the sailing birds the wing is worked from the shoulder by
being alternately rolled on and off the wind, as in insects; whereas,
in birds which do not glide, the spiral movement travels along the
arm as in bats, and manifests itself during flexion and extension in
the bending of the joints and in the rotation of the bones of the
wing on their axes. The spiral conformation of the pinions, to which
allusion has been so frequently made, is best seen in the heavy-bodied
birds, as the turkey, capercailzie, pheasant, and partridge; and here
also the concavo-convex form of the wing is most perceptible. In the
light-bodied, ample-winged birds, the amount of twisting is diminished,
and, as a result, the wing is more or less flattened, as in the
sea-gull (fig. 103).

[Illustration:

  FIG. 103.--Shows the twisted levers or screws formed by the wings of
  the gull. Compare with fig. 53, p. 107; with figs. 76, 77, and 78,
  p. 147, and with figs. 82 and 83, p. 158.---_Original._]

_Consideration of the Forces which propel the Wings of Insects._--In
the thorax of insects the muscles are arranged in two principal sets
in the form of a cross--_i.e._ there is a powerful vertical set which
runs from above downwards, and a powerful antero-posterior set which
runs from before backwards. There are likewise a few slender muscles
which proceed in a more or less oblique direction. The antero-posterior
and vertical sets of muscles are quite distinct, as are likewise the
oblique muscles. Portions, however, of the vertical and oblique muscles
terminate at the root of the wing in jelly-looking points which greatly
resemble rudimentary tendons, so that I am inclined to believe that
the vertical and oblique muscles exercise a direct influence on the
movements of the wing. The shortening of the antero-posterior set
of muscles (indirectly assisted by the oblique ones) elevates the
dorsum of the thorax by causing its anterior extremity to approach
its posterior extremity, and by causing the thorax to bulge out or
expand laterally. This change in the thorax necessitates the descent
of the wing. The shortening of the vertical set (aided by the oblique
ones) has a precisely opposite effect, and necessitates its ascent.
While the wing is ascending and descending the oblique muscles cause
it to rotate on its long axis, the bipartite division of the wing at
its root, the spiral configuration of the joint, and the arrangement
of the elastic and other structures which connect the pinion with
the body, together with the resistance it experiences from the air,
conferring on it the various angles which characterize the down and
up strokes. The wing may therefore be said to be depressed by the
shortening of the antero-posterior set of muscles, aided by the oblique
muscles, and elevated by the shortening of the vertical and oblique
muscles, aided by the elastic ligaments, and the reaction of the air.
If we adopt this view we have a perfect physiological explanation
of the phenomenon, as we have a complete circle or cycle of motion,
the antero-posterior set of muscles shortening when the vertical set
of muscles are elongating, and _vice versâ_. This, I may add, is in
conformity with all other muscular arrangements, where we have what are
usually denominated extensors and flexors, pronators and supinators,
abductors and adductors, etc., but which, as I have already explained
(pp. 24 to 34), are simply the two halves of a circle of muscle and of
motion, an arrangement for securing diametrically opposite movements in
the travelling surfaces of all animals.

Chabrier’s account, which I subjoin, virtually supports this
hypothesis:--

“It is generally through the intervention of the proper motions of
the dorsum, which are very considerable during flight, that the wings
or the elytra are moved equally and simultaneously. Thus, when it is
elevated, it carries with it the internal side of the base of the wings
with which it is articulated, from which ensues the depression of the
external side of the wing; and when it approaches the sternal portion
of the trunk, the contrary takes place. During the depression of the
wings, the dorsum is curved from before backwards, or in such a manner
that its anterior extremity is brought nearer to its posterior, that
its middle is elevated, and its lateral portions removed further from
each other. The reverse takes place in the elevation of the wings; the
anterior extremity of the dorsum being removed to a greater distance
from the posterior, its middle being depressed, and its sides brought
nearer to each other. Thus its bending in one direction produces a
diminution of its curve in the direction normally opposed to it; and
by the alternations of this motion, assisted by other means, the body
is alternately compressed and dilated, and the wings are raised and
depressed by turns.”[86]

  [86] Chabrier, as rendered by E. F. Bennett, F.L.S., etc.

In the _libellulæ_ or dragon-flies, the muscles are inserted into
the roots of the wings as in the bat and bird, the only difference
being that in the latter the muscles creep along the wings to their
extremities.

In all the wings which I have examined, whether in the insect, bat,
or bird, the wings are recovered, flexed, or drawn towards the body
by the action of elastic ligaments, these structures, by their mere
contraction, causing the wings, when fully extended and presenting
their maximum of surface, to resume their position of rest, and plane
of least resistance. The principal effort required in flight would
therefore seem to be made during extension and the down stroke. The
elastic ligaments are variously formed, and the amount of contraction
which they undergo is in all cases accurately adapted to the size and
form of the wings, and the rapidity with which they are worked--the
contraction being greatest in the short-winged and heavy-bodied insects
and birds, and least in the light-bodied and ample-winged ones,
particularly in such as skim or glide. The mechanical action of the
elastic ligaments, I need scarcely remark, insures a certain period
of repose to the wings at each stroke, and this is a point of some
importance, as showing that the lengthened and laborious flights of
insects and birds are not without their stated intervals of rest.

_Speed attained by Insects._--Many instances might be quoted of the
marvellous powers of flight possessed by insects as a class. The male
of the silkworm-moth (_Attacus Paphia_) is stated to travel more than
100 miles a day;[87] and an anonymous writer in Nicholson’s Journal[88]
calculates that the common house-fly (_Musca domestica_), in ordinary
flight, makes 600 strokes per second, and advances twenty-five feet,
but that the rate of speed, if the insect be alarmed, may be increased
six or seven fold, so that under certain circumstances it can outstrip
the fleetest racehorse. Every one when riding on a warm summer day
must have been struck with the cloud of flies which buzz about his
horse’s ears even when the animal is urged to its fastest paces; and
it is no uncommon thing to see a bee or a wasp endeavouring to get in
at the window of a railway car in full motion. If a small insect like
a fly can outstrip a racehorse, an insect as large as a horse would
travel very much faster than a cannon-ball. Leeuwenhoek relates a most
exciting chase which he once beheld in a menagerie about 100 feet long
between a swallow and a dragon-fly (_Mordella_). The insect flew with
incredible speed, and wheeled with such address, that the swallow,
notwithstanding its utmost efforts, completely failed to overtake and
capture it.[89]

  [87] Linn. Trans. vii. p. 40.

  [88] Vol. iii. p. 36.

  [89] “The hobby falcon, which abounds in Bulgaria during the summer
  months, hawks _large dragonflies_, which it seizes with the foot and
  devours whilst in the air. It also kills swifts, larks, turtle-doves,
  and bee-birds, although more rarely.”--Falconry in the British Isles,
  by Francis Henry Salvin and William Brodrick. Lond. 1855.

_Consideration of the Forces which propel the Wings of Bats and
Birds._--The muscular system of birds has been so frequently and
faithfully described, that I need not refer to it further than to say
that there are muscles which by their action are capable of elevating
and depressing the wings, and of causing them to move in a forward and
backward direction, and obliquely. They can also extend or straighten
and bend, or flex the wings, and cause them to rotate in the direction
of their length during the down and up strokes. The muscles principally
concerned in the elevation of the wings are the smaller pectoral
or breast muscles (_pectorales minor_); those chiefly engaged in
depressing the wings are the larger pectorals (_pectorales major_). The
pectoral muscles correspond to the fleshy mass found on the breast-bone
or sternum, which in flying birds is boat-shaped, and furnished with
a keel. These muscles are sometimes so powerful and heavy that they
outweigh all the other muscles of the body. The power of the bird is
thus concentrated for the purpose of moving the wings and conferring
steadiness upon the volant mass. In birds of strong flight the keel
is very large, in order to afford ample attachments for the muscles
delegated to move the wings. In birds which cannot fly, as the members
of the ostrich family, the breast-bone or sternum has no keel.[90]

  [90] One of the best descriptions of the bones and muscles of the
  bird is that given by Mr. Macgillivray in his very admirable,
  voluminous, and entertaining work, entitled History of British Birds.
  Lond. 1837.

The remarks made regarding the muscles of birds, apply with very slight
modifications to the muscles of bats. The muscles of bats and birds,
particularly those of the wings, are geared to, and act in concert
with, elastic ligaments or membranes, to be described presently.

_Lax condition of the Shoulder-Joint in Bats, Birds, etc._--The great
laxity of the shoulder-joint in bats and birds, readily admits of their
bodies falling downwards and forwards during the up stroke. This joint,
as has been already stated, admits of movement in every direction, so
that the body of the bat or bird is like a compass set upon gimbals,
_i.e._ it swings and oscillates, and is equally balanced, whatever
the position of the wings. The movements of the shoulder-joint in
the bird, bat, and insect are restrained within certain limits by a
system of check ligaments and prominences; but in each case the range
of motion is very great, the wings being permitted to swing forwards,
backwards, upwards, downwards, or at any degree of obliquity. They are
also permitted to rotate along their anterior margin, or to twist in
the direction of their length to the extent of nearly a quarter of a
turn. This great freedom of movement at the shoulder-joint enables the
insect, bat, and bird to rotate and balance upon two centres--the one
running in the direction of the length of the body, the other at right
angles or across the body, _i.e._ in the direction of the length of the
wings.

In the bird the head of the humerus is convex and somewhat oval (not
round), the long axis of the oval being directed from above downwards,
_i.e._ from the dorsal towards the ventral aspect of the bird. The
humerus can, therefore, _glide up and down_ in the _facettes_ occurring
on the articular ends of the coracoid and scapular bones with great
facility, much in the same way that the head of the radius glides upon
the distal end of the humerus. But the humerus has another motion; it
moves _like a hinge from before backwards, and_ vice versâ. The axis of
the latter movement is almost at right angles to that of the former.
As, however, the shoulder-joint is connected by long ligaments to the
body, and can be drawn away from it to the extent of one-eighth of
an inch or more, it follows that _a third and twisting movement can
be performed_, the twisting admitting of rotation to the extent of
something like a quarter of a turn. In raising and extending the wing
preparatory to the downward stroke two opposite movements are required,
viz. one from before backwards, and another from below upwards. As,
however, the axes of these movements are at nearly right angles to each
other, a spiral or twisting movement is necessary to run the one into
the other--to turn the corner, in fact.

From what has been stated it will be evident that the movements of the
wing, particularly at the root, are remarkably free, and very varied. A
directing and restraining, as well as a propelling force, is therefore
necessary.

The guiding force is to be found in the voluntary muscles which connect
the wing with the body in the insect, and which in the bat and bird, in
addition to connecting the wing with the body, extend along the pinion
even to its tip. It is also to be found in the musculo-elastic and
other ligaments, seen to advantage in the bird.

_The Wing flexed and partly elevated by the Action of Elastic
Ligaments--the Nature and Position of such Ligaments in the Pheasant,
Snipe, Crested Crane, Swan, etc._--When the wing is drawn away from
the body of the bird by the hand the posterior margin of the pinion
formed by the primary, secondary, and tertiary feathers rolls down
to make a variety of inclined surfaces with the horizon (_c b_, of
fig. 63, p. 138). When, however, the hand is withdrawn, even in the
dead bird, the wing instantly folds up; and in doing so reduces the
amount of inclination in the several surfaces referred to (_c b_, _d
e f_ of the same figure). The wing is folded by the action of certain
elastic ligaments, which are put upon the stretch in extension, and
which recover their original form and position in flexion (fig. 98,
_c_, p. 181). This simple experiment shows that the various inclined
surfaces requisite for flight are produced by the mere acts of
extension and flexion in the dead bird. It is not, however, to be
inferred from this circumstance that flight can be produced without
voluntary movements any more than ordinary walking. The muscles,
bones, ligaments, feathers, etc., are so adjusted with reference to
each other that if the wing is moved at all, it must move in the
proper direction--an arrangement which enables the bird to fly without
thinking, just as we can walk without thinking. There cannot, however,
be a doubt that the bird has the power of controlling its wings both
during the down and up strokes; for how otherwise could it steer and
direct its course with such precision in obtaining its food? how fix
its wings on a level with or above its body for skimming purposes? how
fly in a curve? how fly with, against, or across a breeze? how project
itself from a rock directly into space, or how elevate itself from a
level surface by the laboured action of its wings?

The wing of the bird is elevated to a certain extent in flight by the
reaction of the air upon its under surface; but it is also elevated by
muscular action--by the contraction of the elastic ligaments, and by
the body falling downwards and forwards in a curve.

That muscular action is necessary is proved by the fact that the pinion
is supplied with distinct elevator muscles.[91] It is further proved
by this, that the bird can, and always does, elevate its wings prior
to flight, quite independently of the air. When the bird is fairly
launched in space the elevator muscles are assisted by the tendency
which the body has to fall downwards and forwards: by the reaction of
the air; and by the contraction of the elastic ligaments. The air and
the elastic ligaments contribute to the elevation of the wing, but both
are obviously under control--they, in fact, form links in a chain of
motion which at once begins and terminates in the muscular system.

  [91] Mr. Macgillivray and C. J. L. Krarup, a Danish author, state
  that the wing is elevated by a vital force, viz. by the contraction
  of the _pectoralis minor_. This muscle, according to Krarup, acts
  with one-eighth the intensity of the _pectoralis major_ (the
  depressor of the wing). He bases his statement upon the fact that
  in the pigeon the pectoralis minor or elevator of the wing weighs
  one-eighth of an ounce, whereas the pectoralis major or depressor
  of the wing weighs seven-eighths of an ounce. It ought, however, to
  be borne in mind that the volume of a muscle does not necessarily
  determine the precise influence exerted by its action; for the
  tendon of the muscle may be made to act upon a long lever, and,
  under favourable conditions, for developing its powers, while that
  of another muscle may be made to act upon a short lever, and,
  consequently, under unfavourable conditions.--On the Flight of Birds,
  p. 30. Copenhagen, 1869.

That the elastic ligaments are subsidiary and to a certain extent under
the control of the muscular system in the same sense that the air is,
is evident from the fact that voluntary muscular fibres run into the
ligaments in question at various points (_a_, _b_ of fig. 98, p. 181).
The ligaments and muscular fibres act in conjunction, and fold or flex
the forearm on the arm. There are others which flex the hand upon the
forearm. Others draw the wing towards the body.

The elastic ligaments, while occupying a similar position in the wings
of all birds, are variously constructed and variously combined with
voluntary muscles in the several species.

_The Elastic Ligaments more highly differentiated in Wings which
vibrate rapidly._--The elastic ligaments of the swan are more
complicated and more liberally supplied with voluntary muscle than
those of the crane, and this is no doubt owing to the fact that the
wings of the swan are driven at a much higher speed than those of
the crane. In the snipe the wings are made to vibrate very much more
rapidly than in the swan, and, as a consequence, we find that the
fibro-elastic bands are not only greatly increased, but they are also
geared to a much greater number of voluntary muscles, all which seems
to prove that the musculo-elastic apparatus employed for recovering or
flexing the wing towards the end of the down stroke, becomes more and
more highly differentiated in proportion to the rapidity with which
the wing is moved.[92] The reason for this is obvious. If the wing is
to be worked at a higher speed, it must, as a consequence, be more
rapidly flexed and extended. The rapidity with which the wing of the
bird is extended and flexed is in some instances exceedingly great; so
great, in fact, that it escapes the eye of the ordinary observer. The
speed with which the wing darts in and out in flexion and extension
would be quite inexplicable, but for a knowledge of the fact that the
different portions of the pinion form angles with each other, these
angles being instantly increased or diminished by the slightest quiver
of the muscular and fibro-elastic systems. If we take into account the
fact that the wing of the bird is recovered or flexed by the combined
action of voluntary muscles and elastic ligaments; that it is elevated
to a considerable extent by voluntary muscular effort; and that it is
extended and depressed entirely by muscular exertion, we shall have
difficulty in avoiding the conclusion that the wing is thoroughly under
the control of the muscular system, not only in flexion and extension,
but also throughout the entire down and up strokes.

  [92] A careful account of the musculo-elastic structures occurring in
  the wing of the pigeon is given by Mr. Macgillivray in his History of
  British Birds, pp. 37, 38.

An arrangement in every respect analogous to that described in the bird
is found in the wing of the bat, the covering or web of the wing in
this instance forming the principal elastic ligament (fig. 17, p. 36).

_Power of the Wing--to what owing._--The shape and power of the
pinion depend upon one of three circumstances--to wit, the length
of the humerus,[93] the length of the cubitus or forearm, and the
length of the primary feathers. In the swallow the humerus, and in
the humming-bird the cubitus, is very short, the primaries being very
long; whereas in the albatross the humerus or arm-bone is long and the
primaries short. When one of these conditions is fulfilled, the pinion
is usually greatly elongated and scythe-like (fig. 62, p. 137)--an
arrangement which enables the bird to keep on the wing for immense
periods with comparatively little exertion, and to wheel, turn, and
glide about with exceeding ease and grace. When the wing is truncated
and rounded (fig. 96, p. 176), a form of pinion usually associated
with a heavy body, as in the grouse, quail, diver, and grebe, the
muscular exertion required, and the rapidity with which the wing moves
are very great; those birds, from a want of facility in turning, flying
either in a straight line or making large curves. They, moreover, rise
with difficulty, and alight clumsily and somewhat suddenly. Their
flight, however, is perfect while it lasts.

  [93] “The humerus varies extremely in length, being very short in
  the swallow, of moderate length in the gallinaceous birds, longer
  in the crows, very long in the gannets, and unusually elongated in
  the albatross. In the golden eagle it is also seen to be of great
  length.”--Macgillivray’s British Birds, vol. i. p. 30.

The goose, duck (fig. 107, p. 204), pigeon (fig. 106, p. 203) and crow,
are intermediate both as regards the form of the wing and the rapidity
with which it is moved.

The heron (fig. 60, p. 126) and humming-bird furnish extreme examples
in another direction,--the heron having a large wing with a leisurely
movement, the humming-bird a comparatively large wing with a greatly
accelerated one.

But I need not multiply examples; suffice it to say that flight may be
attained within certain limits by every size and form of wing, if the
number of its oscillations be increased in proportion to the weight to
be raised.

_Reasons why the effective Stroke should be delivered downwards and
forwards._--The wings of all birds, whatever their form, act by
alternately presenting oblique and comparatively non-oblique surfaces
to the air,--the mere extension of the pinion, as has been shown,
causing the primary, secondary, and tertiary feathers to roll down till
they make an angle of 30° or so with the horizon, in order to prepare
it for giving the effective stroke, which is delivered, with great
rapidity and energy, in a _downward_ and _forward_ direction. I repeat,
“downwards and forwards;” for a careful examination of the relations of
the wing in the dead bird, and a close observation of its action in the
living one, supplemented by a large number of experiments with natural
and artificial wings, have fully convinced me that the stroke is
invariably delivered in this direction.[94] If the wing did not strike
downwards and _forwards_, it would act at a manifest disadvantage:--

  [94] _Prevailing Opinions as to the Direction of the Down
  Stroke._--Mr. Macgillivray, in his History of British Birds,
  published in 1837, states (p. 34) that in flexion the wing is drawn
  upwards, forwards, and inwards, but that during extension, when the
  effective stroke is given, it is made to strike outwards, downwards,
  and _backwards_. The Duke of Argyll holds a similar opinion. In
  speaking of the hovering of birds, he asserts that “if a bird, by
  altering the axis of its own body, can direct its wing stroke in some
  degree _forwards_, it will have the effect of _stopping_ instead
  of promoting progression;” and that, “Except for the purpose of
  _arresting_ their flight, birds can never strike except _directly
  downwards_--that is, directly against the opposing force of
  gravity.”--Good Words, Feb. 1865, p. 132.

  Mr. Bishop, in the Cyc. of Anat. and Phys., vol. iii. p. 425, says,
  “In consequence of the planes of the wings being disposed either
  _perpendicularly_ or _obliquely backwards_ to the direction of
  their motion, a corresponding impulse is given to their centre of
  gravity.” Professor Owen, in like manner, avers that “a downward
  stroke would only tend to raise the bird in the air; to carry it
  forwards, the wings require to be moved in an oblique plane, so as to
  _strike backwards_ as well as downwards.”--Comp. Anat. and Phys. of
  Vertebrates, vol. ii. p. 115.

  The following is the account given by M. E. Liais:--“When a bird is
  about to depress its wing, this is a little inclined from before
  backwards. When the descending movement commences, the wing does not
  descend parallel to itself in a direction from before backwards;
  but the movement is accompanied by a rotation of several degrees
  round the anterior edge, so that the wing becomes more in front
  than behind, and the _descending movement is transferred more and
  more backwards_.... When the wing has completely descended, it
  is both _further back_ and lower than at the commencement of the
  movement.”--“On the Flight of Birds and Insects.” Annals of Nat.
  Hist. vol. xv. 3d series, p. 156.

_1st._ Because it would present the back or convex surface of the wing
to the air--a convex surface dispersing or dissipating the air, while a
concave surface gathers it together or focuses it.

_2d._ In order to strike backwards effectually, the concavity of the
wing would also require to be turned backwards; and this would involve
the depression of the anterior or thick margin of the pinion, and the
elevation of the posterior or thin one, during the down stroke, which
never happens.

_3d._ The strain to which the pinion is subjected in flight would, if
the wing struck _backwards_, fall, not on the anterior or strong margin
of the pinion formed by the bones and muscles, but on the posterior or
weak margin formed by the tips of the primary, secondary, and tertiary
feathers--which is not in accordance with the structure of the parts.

_4th._ The feathers of the wing, instead of being closed, as they
necessarily are, by a downward and _forward_ movement, would be
inevitably opened, and the integrity of the wing impaired by a downward
and _backward_ movement.

_5th._ The disposition of the articular surfaces of the wing
(particularly that of the shoulder-joint) is such as to facilitate the
downward and _forward_ movement, while it in a great measure prevents
the downward and _backward_ one.

_6th and lastly._ If the wing did in reality strike downwards and
_backwards_, a result the converse of that desired would most assuredly
be produced, as an oblique surface which smites the air in a downward
and _backward_ direction (if left to itself) tends to depress the body
bearing it. This is proved by the action upon the air of free inclined
planes, arranged in the form of a screw.

_The Wing acts as an Elevator, Propeller, and Sustainer, both during
extension and flexion._--The wing, as has been explained, is recovered
or drawn off the wind principally by the contraction of the elastic
ligaments extending between the joints, so that the pinion during
flexion enjoys a certain degree of repose. The time occupied in
recovering is not lost so long as the wing makes an angle with the
horizon and the bird is in motion, it being a matter of indifference
whether the wing acts on the air, or the air on the wing, so long as
the body bearing the latter is under weigh; and this is the chief
reason why the albatross, which is a very heavy bird,[95] can sail
about for such incredible periods without flapping the wings at
all. Captain Hutton thus graphically describes the sailing of this
magnificent bird:--“The flight of the albatross is truly majestic, as
with outstretched motionless wings he sails over the surface of the
sea--now rising high in air, now with a bold sweep, and wings inclined
at an angle with the horizon, descending until the tip of the lower one
all but touches the crest of the waves as he skims over them.”[96]

  [95] The average weight of the albatross, as given by Gould, is 17
  lbs.--Ibis, 2d series, vol. i. 1865, p. 295.

  [96] “On some of the Birds inhabiting the Southern Ocean,” by Capt.
  F. W. Hutton.--Ibis, 2d series, vol. i. 1865, p. 282.

_Birds of Flight divisible into four kinds:--_

_1st._ Such as have heavy bodies and short wings with a rapid movement
(fig. 59, p. 126).

_2d._ Such as have light bodies and large wings with a leisurely
movement (fig. 60, p. 126; fig. 103, p. 186).

_3d._ Such as have heavy bodies and long narrow wings with a decidedly
slow movement (fig. 105, p. 200).

_4th._ Such as are intermediate with regard to the size of body,
the dimensions of the wing, and the energy with which it is driven
(fig. 102, p. 183; fig. 106, p. 203; fig. 107, p. 204).

They may be subdivided into those which float, skim, or glide, and
those which fly in a straight line and irregularly.

The pheasant, partridge (fig. 59, p. 126), grouse, and quail, furnish
good examples of the heavy-bodied, short-winged birds. In these the
wing is rounded and deeply concave. It is, moreover, wielded with
immense velocity and power.

The heron (fig. 60, p. 126), sea-mew (fig. 103, p. 186), lapwing
(fig. 63, p. 138), and owl (fig. 104), supply examples of the second
class, where the wing, as compared with the body, is very ample, and
where consequently it is moved more leisurely and less energetically.

[Illustration:

  FIG. 104.--The Cape Barn-Owl (_Strix capensis_, Smith), as seen
  in full flight, hunting. The under surface of the wings and body
  are inclined slightly upwards, and act upon the air after the
  manner of a kite. (Compare with fig. 59, p. 126, and fig. 102,
  p. 183.)--_Original._]

The albatross (fig. 105, p. 200) and pelican afford instances of the
third class, embracing the heavy-bodied, long-winged birds.

The duck (fig. 107, p. 204), pigeon (fig. 106, p. 203), crow and
thrush, are intermediate, both as regards the size of the wing and
the rapidity with which it is made to oscillate. These constitute the
fourth class.

The albatross (fig. 105, p. 200), swallow, eagle, and hawk, provide
instances of sailing or gliding birds, where the wing is ample,
elongated, and more or less pointed, and where advantage is taken of
the weight of the body and the shape of the pinion to utilize the air
as a supporting medium. In these the pinion acts as a long lever,[97]
and is wielded with great precision and power, particularly at the
shoulder.

  [97] _Advantages possessed by long Pinions._--The long narrow wings
  are most effective as elevators and propellers, from the fact
  (pointed out by Mr. Wenham) that at high speeds, with very oblique
  incidences, the supporting effect becomes transferred to the _front
  edge_ of the pinion. It is in this way “that the effective propelling
  area of the two-bladed screw is tantamount to its entire circle
  of revolution.” A similar principle was announced by Sir George
  Cayley upwards of fifty years ago. “_In very acute angles with the
  current_, it appears that the centre of resistance in the sail does
  not coincide with the centre of its surface, _but is considerably
  in front of it_. As the obliquity of the current decreases, these
  centres approach, and coincide when the current becomes perpendicular
  to the plane; hence any heel of the machine backwards or forwards
  removes the centre of support behind or before the point of
  suspension.”--Nicholson’s Journal, vol. xxv. p. 83. When the speed
  attained by the bird is _greatly accelerated_, and _the stratum of
  air passed over in any given time enormously increased_, the support
  afforded by the air to the inclined planes formed by the wings _is
  likewise augmented_. This is proved by the rapid flight of skimming
  or sailing birds when the wings are moved at long intervals and
  very leisurely. The same principle supports the skater as he rushes
  impetuously over insecure ice, and the thin flat stone projected
  along the surface of still water. The velocity of the movement in
  either case prevents sinking by not giving the supporting particles
  time to separate.

_The Flight of the Albatross compared to the Movements of a Compass
set upon Gimbals._--A careful examination of the movements in
skimming birds has led me to conclude that by a judicious twisting or
screw-like action of the wings at the shoulder, in which the pinions
are alternately advanced towards and withdrawn from the head in a
manner analogous to what occurs at the loins in skating without lifting
the feet, birds of this order can not only maintain the motion which
they secure by a few energetic flappings, but, if necessary, actually
increase it, and that without either bending the wing or beating the
air.

The forward and backward screwing action of the pinion referred to, in
no way interferes, I may remark, with the rotation of the wing on its
long axis, the pinion being advanced and screwed down upon the wind,
and retracted and unscrewed alternately. As the movements described
enable the sailing bird to tilt its body from before backwards, or the
converse, and from side to side or laterally, it may be represented
as oscillating on one of two centres, as shown at fig. 105; the one
corresponding with the long axis of the body (fig. 105, _a b_), the
other with the long axis of the wings (_c d_). Between these two
extremes every variety of sailing and gliding motion which is possible
in the mariner’s compass when set upon gimbals may be performed; so
that a skimming or sailing bird may be said to possess perfect command
over itself and over the element in which it moves.

[Illustration: FIG. 105.]

Captain Hutton makes the following remarkable statement regarding the
albatross:--“I have sometimes watched narrowly one of these birds
sailing and wheeling about in all directions for more than an hour,
without seeing the slightest movement of the wings, and have never
witnessed anything to equal the ease and grace of this bird as he
sweeps past, often within a few yards, every part of his body perfectly
motionless except the head and eye, which turn slowly and seem to take
notice of everything.”[98]

  [98] “On some of the Birds inhabiting the Southern Ocean.”--Ibis, 2d
  series, vol. i. 1865.

    “Tranquil its spirit seem’d and floated slow;
    Even in its very motion there was rest.”[99]

  [99] Professor Wilson’s Sonnet, “A Cloud,” etc.

As an antithesis to the apparently lifeless wings of the albatross,
the ceaseless activity of those of the humming-bird may be adduced. In
those delicate and exquisitely beautiful birds, the wings, according to
Mr. Gould, move so rapidly when the bird is poised before an object,
that it is impossible for the eye to follow each stroke, and a hazy
circle of indistinctness on each side of the bird is all that is
perceptible. When the humming-bird flies in a horizontal direction,
it occasionally proceeds with such velocity as altogether to elude
observation.

_The regular and irregular in Flight._--The coot, diver, duck, and
goose fly with great regularity in nearly a straight line, and with
immense speed; they rarely if ever skim or glide, their wings being too
small for this purpose. The woodpecker, magpie, fieldfare and sparrow,
supply examples of what may be termed the “irregular” in flight. These,
as is well known, fly in curves of greater or less magnitude, by giving
a few vigorous strokes and then desisting, the effect of which is to
project them along a series of parabolic curves. The snipe and woodcock
are irregular in another respect, their flight being sudden, jerky, and
from side to side.

_Mode of ascending, descending, turning, etc._--All birds which do
not, like the swallow and humming-birds, drop from a height, raise
themselves at first by a vigorous leap, in which they incline their
bodies in an upward direction, the height thus attained enabling them
to extend and depress their wings without injury to the feathers. By
a few sweeping strokes delivered downwards and forwards, in which the
wings are made nearly to meet above and below the body, they lever
themselves upwards and forwards, and in a surprisingly short time
acquire that degree of momentum which greatly assists them in their
future career. In rising from the ground, as may readily be seen in
the crow, pigeon, and kingfisher (fig. 102, p. 183), the tail is
expanded and the neck stretched out, so that the body is converted
into an inclined plane, and acts mechanically as a kite. The centre of
gravity and the position of the body are changed at the will of the
bird by movements in the neck, feet, and tail, and by increasing or
decreasing the angles which the under surface of the wings makes with
the horizon. When a bird wishes to fly in a horizontal direction, it
causes the under surface of its wings to make a slight _forward_ angle
with the horizon. When it wishes to ascend, the angle is increased.
When it wishes to descend, it causes the under surface of the wings
to make a slight _backward_ angle with the horizon. When a bird flies
up, its wings strike downwards and _forwards_. When it flies down, its
wings strike downwards and _backwards_. When a sufficient altitude
has been attained, the length of the downward stroke is generally
curtailed, the mere extension and flexion of the wing, assisted by the
weight of the body, in such instances sufficing. This is especially
the case if the bird is advancing against a slight breeze, the effort
required under such circumstances being nominal in amount. That little
power is expended is proved by the endless gyrations of rooks and other
birds; these being continued for hours together. In birds which glide
or skim, it has appeared to me that the wing is recovered much more
quickly, and the down stroke delivered more slowly, than in ordinary
flight--in fact, that the rapidity with which the wing acts in an
upward and downward direction is, in some instances, reversed; and this
is what we should naturally expect when we recollect that in gliding,
the wings require to be, for the most part, in the expanded condition.
If this observation be correct, it follows that birds have the power of
modifying the duration of the up and down strokes at pleasure. Although
the wing of the bird usually strikes the air at an angle which varies
from 15° to 30°, the angle may be increased to such an extent as to
subvert the position of the bird. The tumbler pigeon, _e.g._ can, by
slewing its wings forwards and suddenly throwing back its head, turn
a somersault. When birds are fairly on the wing they have the air,
unless when that is greatly agitated by a storm, completely under
control. This arises from their greater specific gravity, and because
they are possessed of independent motion. If they want to turn, they
have simply to tilt their bodies laterally, as a railway carriage would
be tilted in taking a curve,[100] or to increase the number of beats
given by the one wing as compared with the other; or to keep the one
wing extended while the other is partially flexed. The neck, feet, and
tail may or may not contribute to this result. If the bird wishes to
rise, it tilts its entire body (the neck and tail participating) in
an upward direction (fig. 59, p. 126; fig. 102, p. 183); or it rises
principally by the action of the wings and by muscular efforts, as
happens in the lark. The bird can in this manner likewise retain its
position in the air, as may be observed in the hawk when hovering
above its prey. If the bird desires to descend, it may reverse the
direction of the inclined plane formed by the body and wings, and
plunge head foremost with extended pinions (fig. 106); or it may flex
the wings, and so accelerate its pace; or it may raise its wings and
drop parachute-fashion (fig. 55, p. 112; _g_, _g_ of fig. 82, p. 158);
or it may even fly in a downward direction--a few sudden strokes, a
more or less abrupt curve, and a certain degree of horizontal movement
being in either case necessary to break the fall previous to alighting
(fig. 107, below). Birds which fish on the wing, as the osprey and
gannet, precipitate themselves from incredible heights, and drop into
the water with the velocity of a meteorite--the momentum which they
acquire during their descent materially aiding them in their subaqueous
flight. They emerge from the water and are again upon the wing before
the eddies occasioned by their precipitous descent have well subsided,
in some cases rising apparently without effort, and in others running
along and beating the surface of the water for a brief period with
their pinions and feet.

  [100] “If the albatross desires to turn to the right he bends
  his head and tail slightly upwards, at the same time raising his
  left side and wing, and lowering the right in proportion to the
  sharpness of the curve he wishes to make, the wings being kept quite
  rigid the whole time. To such an extent does he do this, that in
  sweeping round, his wings are often pointed in a direction nearly
  perpendicular to the sea; and this position of the wings, more or
  less inclined to the horizon, is seen always and only when the bird
  is turning.”--“On some of the Birds inhabiting the Southern Ocean.”
  Ibis, 2d series, vol. i. 1865, p. 227.

[Illustration:

  FIG. 106.--The Pigeon (_Treron bicincta_, Jerdon), flying downwards
  and turning prior to alighting. The pigeon expands its tail both in
  ascending and descending.--_Original._]

[Illustration:

  FIG. 107.--The Red-headed Pochard (_Fuligula ferina_, Linn.)
  in the act of dropping upon the water; the head and body being
  inclined upwards and forwards, the feet expanded, and the wings
  delivering vigorous short strokes in a downward and forward
  direction.--_Original._]

_The Flight of Birds referable to Muscular Exertion and Weight._--The
various movements involved in ascending, descending, wheeling, gliding,
and progressing horizontally, are all the result of muscular power and
weight, properly directed and acting upon appropriate surfaces--that
apparent buoyancy in birds which we so highly esteem, arising not from
superior lightness, but from their possessing that degree of solidity
which enables them to subjugate the air,--weight and independent
motion, _i.e._ motion associated with animal life, or what is
equivalent thereto, being the two things indispensable in successful
aërial progression. The weight in insects and birds is in great measure
owing to their greatly developed muscular system, this being in that
delicate state of tonicity which enables them to act through its
instrumentality with marvellous dexterity and power, and to expend or
reserve their energies, which they can do with the utmost exactitude,
in their apparently interminable flights.

_Lifting-capacity of Birds._--The muscular power in birds is usually
greatly in excess, particularly in birds of prey, as, _e.g._ the
condors, eagles, hawks, and owls. The eagles are remarkable in this
respect--these having been known to carry off young deer, lambs,
rabbits, hares, and, it is averred, even young children. Many of
the fishing birds, as the pelicans and herons, can likewise carry
considerable loads of fish;[101] and even the smaller birds, as the
records of spring show, are capable of transporting comparatively large
twigs for building purposes. I myself have seen an owl, which weighed
a little over 10 ounces, lift 2-1/2 ounces, or a quarter of its own
weight, without effort, after having fasted twenty-four hours; and a
friend informs me that a short time ago a splendid osprey was shot at
Littlehampton, on the coast of Sussex, with a fish 5 lbs. weight in its
mouth.

  [101] The heron is in the habit, when pursued by the falcon, of
  disgorging the contents of his crop in order to reduce his weight.

There are many points in the history and economy of birds which crave
our sympathy while they elicit our admiration. Their indubitable
courage and miraculous powers of flight invest them with a superior
dignity, and secure for their order almost a duality of existence. The
swallow, tiny and inconsiderable as it may appear, can traverse 1000
miles at a single journey; and the albatross, despising compass and
landmark, trusts himself boldly for weeks together to the mercy or
fury of the mighty ocean. The huge condor of the Andes lifts himself
by his sovereign will to a height where no sound is heard, save the
airy tread of his vast pinions, and, from an unseen point, surveys in
solitary grandeur the wide range of plain and pasture-land;[102] while
the bald eagle, nothing daunted by the din and indescribable confusion
of the queen of waterfalls, the stupendous Niagara, sits composedly on
his giddy perch, until inclination or desire prompts him to plunge
into or soar above the drenching mists which, shapeless and ubiquitous,
perpetually rise from the hissing waters of the nether caldron.

  [102] The condor, on some occasions, attains an altitude of six miles.

[Illustration: FIG. 108.--Hawk and quarry.--_After The Graphic_.]




AËRONAUTICS.




[Illustration: THE VAUXHALL BALLOON OF MR. GREEN.]




AËRONAUTICS.


The subject of artificial flight, notwithstanding the large share of
attention bestowed upon it, has been particularly barren of results.
This is the more to be regretted, as the interest which has been
taken in it from early Greek and Roman times has been universal. The
unsatisfactory state of the question is to be traced to a variety of
causes, the most prominent of which are--

_1st_, The extreme difficulty of the problem.

_2d_, The incapacity or theoretical tendencies of those who have
devoted themselves to its elucidation.

_3d_, The great rapidity with which wings, especially insect wings,
are made to vibrate, and the difficulty experienced in analysing their
movements.

_4th_, The great weight of all flying things when compared with a
corresponding volume of air.

_5th_, The discovery of the balloon, which has retarded the science of
aërostation, by misleading men’s minds and causing them to look for a
solution of the problem by the aid of a machine lighter than the air,
and which has no analogue in nature.

Flight has been unusually unfortunate in its votaries. It has been
cultivated, on the one hand, by profound thinkers, especially
mathematicians, who have worked out innumerable theorems, but have
never submitted them to the test of experiment; and on the other, by
uneducated charlatans who, despising the abstractions of science,
have made the most ridiculous attempts at a practical solution of the
problem.

Flight, as the matter stands at present, may be divided into two
principal varieties which represent two great sects or schools--

_1st_, The Balloonists, or those who advocate the employment of a
machine specifically lighter than the air.

_2d_, Those who believe that weight is necessary to flight. The second
school may be subdivided into

(_a_) Those who advocate the employment of rigid inclined planes driven
forward in a straight line, or revolving planes (aërial screws); and

(_b_) Such as trust for elevation and propulsion to the vertical
flapping of wings.

_Balloon._--The balloon, as my readers are aware, is constructed on the
obvious principle that a machine lighter than the air must necessarily
rise through it. The Montgolfier brothers invented such a machine in
1782. Their balloon consisted of a paper globe or cylinder, the motor
power being super-heated air supplied by the burning of vine twigs
under it. The Montgolfier or fire balloon, as it was called, was
superseded by the hydrogen gas balloon of MM. Charles and Robert, this
being in turn supplanted by the ordinary gas balloon of Mr. Green.
Since the introduction of coal gas in the place of hydrogen gas, no
radical improvement has been effected, all attempts at guiding the
balloon having signally failed. This arises from the vast extent of
surface which it necessarily presents, rendering it a fair conquest
to every breeze that blows; and because the power which animates it
is a mere lifting power which, in the absence of wind, must act in
a vertical line. The balloon consequently rises through the air in
opposition to the law of gravity, very much as a dead bird falls in a
downward direction in accordance with it. Having no hold upon the air,
this cannot be employed as a fulcrum for regulating its movements, and
hence the cardinal difficulty of ballooning as an art.

Finding that no marked improvement has been made in the balloon since
its introduction in 1782, the more advanced thinkers have within
the last quarter of a century turned their attention in an opposite
direction, and have come to regard flying creatures, all of which are
much heavier than the air, as the true models for flying machines. An
old doctrine is more readily assailed than uprooted, and accordingly
we find the followers of the new faith met by the assertion that
insects and birds have large air cavities in their interior; that
those cavities contain heated air, and that this heated air in some
mysterious manner contributes to, if it does not actually produce,
flight. No argument could be more fallacious. Many admirable fliers,
such as the bats, have no air-cells; while many birds, the apteryx
for example, and several animals never intended to fly, such as the
orang-outang and a large number of fishes, are provided with them.
It may therefore be reasonably concluded that flight is in no way
connected with air-cells, and the best proof that can be adduced is to
be found in the fact that it can be performed to perfection in their
absence.

_The Inclined Plane._--The modern school of flying is in some respects
quite as irrational as the ballooning school.

The favourite idea with most is the wedging forward of a rigid
_inclined plane_ upon the air by means of a “_vis a tergo_.”

The inclined plane may be made to advance in a _horizontal line_,
or made _to rotate_ in the form of a screw. Both plans have their
adherents. The one recommends a large supporting area extending on
either side of the weight to be elevated; the surface of the supporting
area making a very slight angle with the horizon, and the whole being
wedged forward by the action of vertical screw propellers. This was the
plan suggested by Henson and Stringfellow.

Mr. Henson designed his aërostat in 1843. “The chief feature of the
invention was the very great expanse of its sustaining planes, which
were larger in proportion to the weight it had to carry than those of
many birds. The machine advanced _with its front edge a little raised_,
the effect of which was to present its under surface to the air over
which it passed, the resistance of which, acting upon it like a strong
wind on the sails of a windmill, prevented the descent of the machine
and its burden. The sustaining of the whole, therefore, depended upon
_the speed at which it travelled through the air, and the angle at
which its under surface impinged on the air in its front_.... The
machine, fully prepared for flight, was started from the top of an
inclined plane, in descending which it attained a velocity necessary to
sustain it in its further progress. That velocity would be gradually
destroyed by the resistance of the air to forward flight; it was,
therefore, the office of the steam-engine and the vanes it actuated
simply to repair the loss of velocity; it was made therefore only of
the power and weight necessary for that small effect” (fig. 109). The
editor of Newton’s Journal of Arts and Science speaks of it thus:--“The
apparatus consists of a car containing the goods, passengers, engines,
fuel, etc., to which a rectangular frame, made of wood or bamboo cane,
and covered with canvas or oiled silk, is attached. This frame extends
on either side of the car in a similar manner to the outstretched wings
of a bird; but with this difference, that _the frame is immovable_.
Behind the wings are two vertical fan wheels, furnished with oblique
vanes, which are intended to propel the apparatus through the air.
The rainbow-like circular wheels are the propellers, answering to the
wheels of a steam-boat, and acting upon the air after the manner of a
windmill. These wheels receive motion from bands and pulleys from a
steam or other engine contained in the car. To an axis at the stern of
the car a triangular frame is attached, resembling the tail of a bird,
which is also covered with canvas or oiled silk. This may be expanded
or contracted at pleasure, and is moved up and down for the purpose of
causing the machine to ascend or descend. Beneath the tail is a rudder
for directing the course of the machine to the right or to the left;
and to facilitate the steering a sail is stretched between two masts
which rise from the car. The amount of canvas or oiled silk necessary
for buoying up the machine is stated to be equal to one square foot for
each half pound of weight.”

[Illustration: FIG. 109.--Mr. Henson’s Flying Machine.]

Wenham[103] has advocated the employment of _superimposed planes_,
with a view to augmenting the support furnished while it diminishes
the horizontal space occupied by the planes. These planes Wenham
designates _Aëroplanes_. They are inclined at a very slight angle to
the horizon, and are wedged forward either by the weight to be elevated
or by the employment of vertical screws. Wenham’s plan was adopted
by Stringfellow in a model which he exhibited at the Aëronautical
Society’s Exhibition, held at the Crystal Palace in the summer of 1868.

  [103] “Aërial Locomotion,” by F. H. Wenham.--_World of Science_, June
  1867.

The subjoined woodcut (fig. 110), taken from a photograph of Mr.
Stringfellow’s model, gives a very good idea of the arrangement; _a b
c_ representing the superimposed planes, _d_ the tail, and _e f_ the
vertical screw propellers.

[Illustration: FIG. 110.--Mr. Stringfellow’s Flying Machine.]

The superimposed planes (_a b c_) in this machine contained a
sustaining area of twenty-eight square feet in addition to the tail
(_d_).

Its engine represented a third of a horse power, and the weight of
the whole (engine, boiler, water, fuel, superimposed planes, and
propellers) was under 12 lbs. Its sustaining area, if that of the tail
(_d_) be included, was something like thirty-six square feet, _i.e._
three square feet for every pound--the sustaining area of the gannet,
it will be remembered (p. 134), being less than one square foot of wing
for every two pounds of body.

The model was forced by its propellers along a wire at a great speed,
but, so far as I could determine from observation, failed to lift
itself notwithstanding its extreme lightness and the comparatively very
great power employed.[104]

  [104] Mr. Stringfellow stated that his machine occasionally left the
  wire, and was sustained by its superimposed planes alone.

The idea embodied by Henson, Wenham, and Stringfellow is plainly
that of a boy’s kite sailing upon the wind. The kite, however, is a
more perfect flying apparatus than that furnished by Henson, Wenham,
and Stringfellow, inasmuch as the inclined plane formed by its body
strikes the air at various angles--the angles varying according to the
length of string, strength of breeze, length and weight of tail, etc.
Henson’s, Wenham’s, and Stringfellow’s methods, although carefully
tried, have hitherto failed. The objections are numerous. In the first
place, the supporting planes (aëroplanes or otherwise) are not flexible
and elastic as wings are, but _rigid_. This is a point to which I wish
particularly to direct attention. Second, They strike the air _at a
given angle_. Here, again, there is a departure from nature. Third, A
machine so constructed must be precipitated from a height or driven
along the surface of the land or water at a high speed to supply it
with initial velocity. Fourth, It is unfitted for flying with the
wind unless its speed greatly exceeds that of the wind. Fifth, It is
unfitted for flying across the wind because of the surface exposed.
Sixth, The sustaining surfaces are comparatively very large. They are,
moreover, passive or dead surfaces, _i.e._ they have no power of moving
or accommodating themselves to altered circumstances. Natural wings,
on the contrary, present small flying surfaces, the great speed at
which wings are propelled converting the space through which they are
driven into what is practically a solid basis of support, as explained
at pp. 118, 119, 151, and 152 (_vide_ figs. 64, 65, 66, 82, and 83,
pp. 139 and 158). This arrangement enables natural wings to seize and
utilize the air, and renders them superior to adventitious currents.
Natural wings work up the air in which they move, but unless the flying
animal desires it, they are scarcely, if at all, influenced by winds
or currents which are not of their own forming. In this respect they
entirely differ from the balloon and all forms of fixed aëroplanes.
In nature, small wings driven at a high speed produce the same result
as large wings driven at a slow speed (compare fig. 58, p. 125, with
fig. 57, p. 124). In flight a certain space must be covered either by
large wings spread out as a solid (fig. 57, p. 124), or by small wings
vibrating rapidly (figs. 64, 65, and 66, p. 139).

[Illustration: FIG. 111.--Cayley’s Flying Apparatus.]

_The Aërial Screw._--Our countryman, Sir George Cayley, gave the first
practical illustration of the efficacy of the screw as applied to the
air in 1796. In that year he constructed a small machine, consisting
of two screws made of quill feathers (fig. 111). Sir George writes as
under:--

“As it may be an amusement to some of your readers to see a machine
rise in the air by mechanical means, I will conclude my present
communication by describing an instrument of this kind, which any one
can construct at the expense of ten minutes’ labour.

“_a_ and _b_ (fig. 111, p. 215) are two corks, into each of which
are inserted four wing feathers from any bird, so as to be slightly
inclined like the sails of a windmill, but in opposite directions in
each set. A round shaft is fixed in the cork _a_, which ends in a sharp
point. At the upper part of the cork _b_ is fixed a whalebone bow,
having a small pivot hole in its centre to receive the point of the
shaft. The bow is then to be strung equally on each side to the upper
portion of the shaft, and the little machine is completed. Wind up the
string by turning the flyers different ways, so that the spring of the
bow may unwind them with their anterior edges ascending; then place the
cork with the bow attached to it upon a table, and with a finger on the
upper cork press strong enough to prevent the string from unwinding,
and, taking it away suddenly, the instrument will rise to the ceiling.”

Cayley’s screws were peculiar, inasmuch as they were superimposed and
rotated in opposite directions. He estimated that if the area of the
screws was increased to 200 square feet, and moved by a man, they would
elevate him. Cayley’s interesting experiment is described at length,
and the apparatus figured in Nicholson’s Journal for 1809, p. 172.
In 1842 Mr. Phillips also succeeded in elevating a model by means of
revolving fans. Mr. Phillips’s model was made entirely of metal, and
when complete and charged weighed 2 lbs. It consisted of a boiler or
steam generator and four fans supported between eight arms. The fans
were inclined to the horizon at an angle of 20°, and through the arms
the steam rushed on the principle discovered by Hero of Alexandria. By
the escape of steam from the arms, the fans were made to revolve with
immense energy, so much so that the model rose to a great altitude, and
flew across two fields before it alighted. The motive power employed
in the present instance was obtained from the combustion of charcoal,
nitre, and gypsum, as used in the original fire annihilator; the
products of combustion mixing with water in the boiler, and forming
gas charged steam, which was delivered at a high pressure from the
extremities of the eight arms. This model is remarkable as being
probably the first which actuated by steam has flown to a considerable
distance.[105] The French have espoused the aërial screw with great
enthusiasm, and within the last ten years (1863) MM. Nadar,[106]
Pontin d’Amécourt, and de la Landelle have constructed clockwork
models (_orthopteres_), which not only raise themselves into the air,
but carry a certain amount of freight. These models are exceedingly
fragile, and because of the prodigious force required to propel them
usually break after a few trials. Fig. 112, p. 217, embodies M. de la
Landelle’s ideas.

  [105] Report on the First Exhibition of the Aëronautical Society of
  Great Britain, held at the Crystal Palace, London, in June 1868,
  p. 10.

  [106] Mons. Nadar, in a paper written in 1863, enters very fully into
  the subject of artificial flight, as performed by the aid of the
  screw. Liberal extracts are given from Nadar’s paper in Astra Castra,
  by Captain Hatton Turner. London, 1865, p. 340. To Turner’s handsome
  volume the reader is referred for much curious and interesting
  information on the subject of Aërostation.

[Illustration: FIG. 112.--Flying Machine designed by M. de la Landelle.]

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

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

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

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

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

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

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

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

[Illustration: FIG. 113.--Borelli’s Artificial Bird.]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[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.

  FIG. 117.--Represents a longitudinal section of bamboo cane ten feet
  long, and one inch wide.--_Original._]

[Illustration: FIG. 118.

  FIG. 118.--The appearance presented by the same cane when made to
  vibrate by the hand. The cane vibrates on either side of a given line
  (_x x_), and appears as if it were in two places at the same time,
  viz., _c_ and _f_, _g_ and _d_, _e_ and _h_. It is thus during its
  vibration thrown into figures-of-8 or opposite curves.--_Original._]

[Illustration: FIG. 119.

  FIG. 119.--The same cane when made to vibrate more rapidly. In this
  case the waves made by the cane are less in size, but more numerous.
  The cane is seen alternately on either side of the line _x x_, being
  now at _i_ now at _m_, now at _n_ now at _j_, now at _k_ now at
  _o_, now at _p_ now at _l_. The cane, when made to vibrate, has no
  dead points, a circumstance due to the fact that no two parts of it
  reverse or change their curves at precisely the same instant. This
  curious reciprocating motion enables the wing to seize and disengage
  itself from the air with astonishing rapidity.--_Original._]

[Illustration: FIG. 120.

  FIG. 120.--The same cane with a flexible elastic curtain or fringe
  added to it. The curtain consists of tapering whalebone rods covered
  with a thin layer of india-rubber. _a b_ anterior margin of wing, _c
  d_ posterior ditto.--_Original._]

[Illustration: FIG. 121.

  FIG. 121.--Gives the appearance presented by the artificial wing
  (fig. 120) when made to vibrate by the hand. It is thrown into
  longitudinal and transverse waves. The longitudinal waves are
  represented by the arrows _c d e_, and the transverse waves by
  the arrows _f g h_. A wing constructed on this principle gives a
  continuous elevating and propelling power. It develops figure-of-8
  curves during its action in longitudinal, transverse, and oblique
  directions. It literally floats upon the air. It has no dead
  points--is vibrated with amazingly little power, and has apparently
  no slip. It can fly in an upward, downward, or horizontal direction
  by merely altering its angle of inclination to the horizon. It
  is applied to the air by an irregular motion--the movement being
  most sudden and vigorous always at the beginning of the down
  stroke.--_Original._]

The wave wing is endowed with the very remarkable property that it
will fly in any direction, demonstrating more or less clearly that
flight is essentially a progressive movement, _i.e._ a horizontal
rather than a vertical movement. Thus, if the anterior or thick margin
of the wing be directed upwards, so that the under surface of the
wing makes a _forward_ angle with the horizon of 45°, the wing will,
when made to vibrate by the hand, fly with an undulating motion _in
an upward direction_, like a pigeon to its dovecot. If the under
surface of the wing makes no angle, or a very small _forward_ angle,
with the horizon, it will dart forward in a series of curves in a
_horizontal direction_, like a crow in rapid horizontal flight. If the
anterior or thick margin of the wing be directed downwards, so that
the under surface of the wing makes a _backward_ angle of 45° with the
horizon, the wing will describe a waved track, and _fly downwards_,
as a sparrow from a house-top or from a tree (p. 230). In all those
movements progression is a necessity. The movements are continuous
gliding _forward movements_. There is no halt or pause between the
strokes, and if the angle which the under surface of the wing makes
with the horizon be properly regulated, the amount of steady tractile
and buoying power developed is truly astonishing. This form of wing,
which may be regarded as the realization of the figure-of-8 theory of
flight, elevates and propels both during the down and up strokes, and
its working is accompanied with almost no slip. It seems literally
to float upon the air. No wing that is rigid in the anterior margin
can twist and untwist during its action, and produce the figure-of-8
curves generated by the living wing. To produce the curves in question,
the wing must be flexible, elastic, and capable of change of form in
all its parts. The curves made by the artificial wing, as has been
stated, are largest when the vibration is slow, and least when it is
quick. In like manner, the air is thrown into large waves by the slow
movement of a large wing, and into small waves by the rapid movement
of a smaller wing. The size of the _wing curves_ and _air waves_ bear
a fixed relation to each other, and both are dependent on the rapidity
with which the wing is made to vibrate. This is proved by the fact
that insects, in order to fly, require, as a rule, to drive their small
wings with immense velocity. It is further proved by the fact that the
small humming-bird, in order to keep itself stationary before a flower,
requires to oscillate its tiny wings with great rapidity, whereas the
large humming-bird (_Patagona gigas_), as was pointed out by Darwin,
can attain the same object by flapping its large wings with a very slow
and powerful movement. In the larger birds the movements are slowed in
proportion to the size, and more especially in proportion to the length
of the wing; the cranes and vultures moving the wings very leisurely,
and the large oceanic birds dispensing in a great measure with the
flapping of the wings, and trusting for progression and support to the
wings in the expanded position.

[Illustration: FIG. 122.

  FIG. 122.--Elastic spiral wing, which twists and untwists during
  its action, to form _a mobile helix or screw_. This wing is made
  to vibrate by steam by a direct piston action, and by a slight
  adjustment can be propelled vertically, horizontally, or at any
  degree of obliquity.

  _a_, _b_, Anterior margin of wing, to which the neuræ or ribs are
  affixed. _c_, _d_, Posterior margin of wing crossing anterior one.
  _x_, Ball-and-socket joint at root of wing; the wing being attached
  to the side of the cylinder by the socket. _t_, Cylinder. _r_,
  _r_, Piston, with cross heads (_w_, _w_) and piston head (_s_).
  _o_, _o_, Stuffing boxes. _e_, _f_, Driving chains. _m_, Superior
  elastic band, which assists in elevating the wing. _n_, Inferior
  elastic band, which antagonizes _m_. The alternate stretching of the
  superior and inferior elastic bands contributes to the continuous
  play of the wing, by preventing dead points at the end of the down
  and up strokes. The wing is free to move in a vertical and horizontal
  direction and at any degree of obliquity.--_Original._]

This leads me to conclude that very large wings may be driven with a
comparatively slow motion, a matter of great importance in artificial
flight secured by the flapping of wings.

_How to construct an artificial Wave Wing on the Insect type._--The
following appear to me to be essential features in the construction of
an artificial wing:--

The wing should be of a generally triangular shape.

It should taper from the root towards the tip, and from the anterior
margin in the direction of the posterior margin.

It should be convex above and concave below, and slightly twisted upon
itself.

It should be flexible and elastic throughout, and should twist and
untwist during its vibration, to produce figure-of-8 curves along its
margins and throughout its substance.

Such a wing is represented at fig. 122, p. 239.

If the wing is in more than one piece, joints and springs require to be
added to the body of the pinion.

In making a wing in one piece on the model of the insect wing, such
as that shown at fig. 122 (p. 239), I employ one or more tapering
elastic reeds, which arch from above downwards (_a b_) for the anterior
margin. To this I add tapering elastic reeds, which radiate towards the
tip of the wing, and which also arch from above downwards (_g_, _h_,
_i_). These latter are so arranged that they confer _a certain amount
of spirality_ upon the wing; the anterior (_a b_) and posterior (_c
d_) margins being arranged in different planes, so that they appear
to cross each other. I then add the covering of the wing, which may
consist of india-rubber, silk, tracing cloth, linen, or any similar
substance.

If the wing is large, I employ steel tubes, bent to the proper shape.
In some cases I secure additional strength by adding to the oblique
ribs or stays (_g h i_ of fig. 122) a series of very oblique stays, and
another series of cross stays, as shown at _m_ and _a_, _n_, _o_, _p_,
_q_ of fig. 123, p. 241.

This form of wing is made to oscillate upon two centres viz. the root
and anterior margin, to bring out the peculiar eccentric action of the
pinion.

If I wish to produce a very delicate light wing, I do so by selecting a
fine tapering elastic reed, as represented at _a b_ of fig. 124.

To this I add successive layers (_i_, _h_, _g_, _f_, _e_) of some
flexible material, such as parchment, buckram, tracing cloth, or even
paper. As the layers overlap each other, it follows that there are five
layers at the anterior margin (_a b_), and only one at the posterior
(_c d_). This form of wing is not twisted upon itself structurally, but
it twists and untwists, and becomes a true screw during its action.

[Illustration: FIG. 123.

  FIG. 123.--_Artificial Wing with Perpendicular (r s) and Horizontal
  (t u) Elastic Bands_ attached to ferrule (_w_).

  _a_, _b_, Strong elastic reed, which tapers towards the tip of the
  wing.

  _d_, _e_, _f_, _h_, _i_, _j_, _k_, Tapering curved reeds, which run
  obliquely from the anterior to the posterior margin of the wing, and
  which radiate towards the tip.

  _m_, Similar curved reeds, which run still more obliquely.

  _a_, _n_, _o_, _p_, _q_, Tapering curved reeds, which run from the
  anterior margin of the wing, and at right angles to it. These support
  the two sets of oblique reeds, and give additional strength to the
  anterior margin.

  _x_, Ball-and-socket joint, by which the root of the wing is attached
  to the cylinder, as in fig. 122, p. 239.--_Original._]

[Illustration: FIG. 124.

  FIG. 124.--Flexible elastic wing with tapering elastic reed (_a b_)
  running along anterior margin.

  _c_, _d_, Posterior margin of wing. _i_, Portion of wing composed of
  one layer of flexible material. _h_, Portion of wing composed of two
  layers. _g_, Portion of wing composed of three layers. _f_, Portion
  of wing composed of four layers. _e_, Portion of wing composed of
  five layers. _x_, Ball-and-socket joint at root of wing.--_Original._]

[Illustration: FIG. 125.

  FIG. 125.--Flexible _valvular wing_ with india-rubber springs
  attached to its root.

  _a_, _b_, Anterior margin of wing, tapering and elastic. _c_, _d_,
  Posterior margin of wing, elastic. _f_, _f_, _f_, Segments which open
  during the up stroke and close during the down, after the manner of
  valves. These are very narrow, and open and close instantly. _x_,
  Universal joint. _m_, Superior elastic band. _n_, Ditto inferior.
  _o_, Ditto anterior. _p_, _q_, Ditto oblique. _r_, Ring into which
  the elastic bands are fixed.--_Original._]

_How to construct a Wave Wing which shall evade the superimposed Air
during the Up Stroke._--To construct a wing which shall elude the air
during the up stroke, it is necessary to make it valvular, as shown at
fig. 125, p. 241.

This wing, as the figure indicates, is composed of _numerous narrow
segments_ (_f f f_), so arranged that the air, when the wing is made to
vibrate, opens or separates them at the beginning of the up stroke, and
closes or brings them together at the beginning of the down stroke.

The time and power required for opening and closing the segments is
comparatively trifling, owing to their extreme narrowness and extreme
lightness. The space, moreover, through which they pass in performing
their valvular action is exceedingly small. The wing under observation
is flexible and elastic throughout, and resembles in its general
features the other wings described.

I have also constructed a wing which is self-acting in another sense.
This consists of two parts--the one part being made of an elastic
reed, which tapers towards the extremity; the other of a flexible
sail. To the reed, which corresponds to the anterior margin of the
wing, delicate tapering reeds are fixed at right angles; the principal
and subordinate reeds being arranged on the same plane. The flexible
sail is attached to the under surface of the principal reed, and is
stiffer at its insertion than towards its free margin. When the wing is
made to ascend, the sail, because of the pressure exercised upon its
upper surface by the air, assumes a very oblique position, so that the
resistance experienced by it during the _up stroke_ is very slight.
When, however, the wing descends, the sail instantly flaps in an upward
direction, the subordinate reeds never permitting its posterior or free
margin to rise above its anterior or fixed margin. The under surface of
the wing consequently descends in such a manner as to present a nearly
flat surface to the earth. It experiences much resistance from the air
during the _down stroke_, the amount of buoyancy thus furnished being
very considerable. The above form of wing is more effective during the
down stroke than during the up one. It, however, elevates and propels
during both, the forward travel being greatest during the down stroke.

_Compound Wave Wing of the Author._--In order to render the movements
of the wing as simple as possible, I was induced to devise a form
of pinion, which for the sake of distinction I shall designate the
_Compound Wave Wing_. This wing consists of two wave wings united at
the roots, as represented at fig. 126. It is impelled by steam, its
centre being fixed to the head of the piston by a compound joint (_x_),
which enables it to move in a circle, and to rotate along its anterior
margin (_a b c d_; _A_, _A´_) in the direction of its length. The
circular motion is for steering purposes only. The wing rises and falls
with every stroke of the piston, and the movements of the piston are
quickened during the down stroke, and slowed during the up one.

[Illustration: FIG. 126.]

During the up stroke of the piston the wing is very decidedly convex
on its upper surface (_a b c d_; _A_, _A´_), its under surface
being deeply concave and inclined obliquely upwards and forwards.
It thus evades the air during the up stroke. During the down stroke
of the piston the wing is flattened out in every direction, and its
extremities twisted in such a manner as to form two screws, as shown
at _a´ b´ c´ d´_; _e´ f´ g´ h´_; _B_, _B´_ of figure. The active area
of the wing is by this means augmented, the wing seizing the air with
great avidity during the down stroke. The area of the wing may be still
further increased and diminished during the down and up strokes by
adding joints to the body of the wing. The degree of convexity given
to the upper surface of the wing can be increased or diminished at
pleasure by causing a cord (_i j_; _A_, _A´_) and elastic band (_k_) to
extend between two points, which may vary according to circumstances.
The wing is supplied with vertical springs, which assist in slowing and
reversing it towards the end of the down and up strokes, and these, in
conjunction with the elastic properties of the wing itself, contribute
powerfully to its continued play. The compound wave wing produces the
currents on which it rises. Thus during the up stroke it draws after
it a current, which being met by the wing during its descent, confers
additional elevating and propelling power. During the down stroke the
wing in like manner draws after it a current which forms an eddy,
and on this eddy the wing rises, as explained at p. 253, fig. 129.
The ascent of the wing is favoured by the superimposed air playing
on the upper surface of the posterior margin of the organ, in such a
manner as to cause the wing to assume a more and more oblique position
with reference to the horizon. This change in the plane of the wing
enables its upper surface to avoid the superincumbent air during the
up stroke, while it confers upon its under surface a combined kite
and parachute action. The compound wave wing leaps forward in a curve
both during the down and up strokes, so that the wing during its
vibration describes a waved track, as shown at _a_, _c_, _e_, _g_,
_i_ of fig. 81, p. 157. The compound wave wing possesses most of the
peculiarities of single wings when made to vibrate separately. It forms
a most admirable elevator and propeller, and has this advantage over
ordinary wings, that it can be worked without injury to itself, when
the machine which it is intended to elevate is resting on the ground.
Two or more compound wave wings may be arranged on the same plane, or
superimposed, and made to act in concert. They may also by a slight
modification be made to act horizontally instead of vertically. The
length of the stroke of the compound wave wing is determined in part,
though not entirely by the stroke of the piston--the extremities of the
wing, because of their elasticity, moving through a greater space than
the centre of the wing. By fixing the wing to the head of the piston
all gearing apparatus is avoided, and the number of joints and working
points reduced--a matter of no small importance when it is desirable to
conserve the motor power and keep down the weight.

_How to apply Artificial Wings to the Air._--Borelli, Durckheim, Marey,
and all the writers with whom I am acquainted, assert that the wing
should be made to vibrate _vertically_. I believe that if the wing be
in one piece it should be made to vibrate _obliquely and more or less
horizontally_. If, however, the wing be made to vibrate _vertically_,
it is necessary to supply it with a ball-and-socket joint, and with
springs at its root (_m n_ of fig. 125, p. 241), to enable it _to leap
forward in a curve_ when it descends, and in another and _opposite
curve_ when it ascends (_vide a_, _c_, _e_, _g_, _i_ of fig. 81, p.
157). This arrangement practically converts the vertical vibration
into _an oblique one_. If this plan be not adopted, the wing is apt to
foul at its tip. In applying the wing to the air it ought to have a
figure-of-8 movement communicated to it either directly or indirectly.
It is a peculiarity of the artificial wing properly constructed (as
it is of the natural wing), _that it twists and untwists and makes
figure-of-8 curves during its action_ (see _a b_, _c d_ of fig. 122,
p. 239), this enabling it to seize and let go the air with wonderful
rapidity, and in such a manner as to avoid dead points. If the wing
be in several pieces, it may be made to vibrate more vertically than
a wing in one piece, from the fact that the outer half of the pinion
moves forwards and backwards when the wing ascends and descends so
as alternately to become a short and a long lever; this arrangement
permitting the wing to avoid the resistance experienced from the air
during the up stroke, while it vigorously seizes the air during the
down stroke.

If the body of a flying animal be in a horizontal position, a wing
attached to it in such a manner that its under surface shall look
forwards, and make an upward angle of 45° with the horizon is in a
position to be applied either vertically (figs. 82 and 83, p. 158), or
horizontally (figs. 67, 68, 69, and 70, p. 141). Such, moreover, is the
conformation of the shoulder-joint in insects, bats, and birds, that
the wing can be applied vertically, horizontally, or at any degree of
obliquity without inconvenience.[118] It is in this way that an insect
which may begin its flight by causing its wings to make figure-of-8
horizontal loops (fig. 71, p. 144), may gradually change the direction
of the loops, and make them more and more oblique until they are
nearly vertical (fig. 73, p. 144). In the beginning of such flight the
insect is screwed _nearly vertically upwards_; in the middle of it,
it is screwed _upwards and forwards_; whereas, towards the end of it,
the insect advances in _a waved line_ almost horizontally (see _q´_,
_r´_, _s´_, _t´_ of fig. 72, p. 144). The muscles of the wing are so
arranged that they can propel it in a horizontal, vertical, or oblique
direction. It is a matter of the utmost importance that the direction
of the stroke and the nature of the angles made by the surface of the
wing during its vibration with the horizon be distinctly understood; as
it is on these that all flying creatures depend when they seek to elude
the upward resistance of the air, and secure a maximum of elevating and
propelling power with a minimum of slip.

  [118] The human wrist is so formed that if a wing be held in the
  hand at an upward angle of 45°, the hand can apply it to the air in
  a vertical or horizontal direction without difficulty. This arises
  from the power which the hand has of moving in an upward and downward
  direction, and from side to side with equal facility. The hand can
  also rotate on its long axis, so that it virtually represents all the
  movements of the wing at its root.

_As to the nature of the Forces required for propelling Artificial
Wings._--Borelli, Durckheim, and Marey affirm that it suffices if the
wing merely elevates and depresses itself by a rhythmical movement in a
perpendicular direction; while Chabrier is of opinion that a movement
of depression only is required. All those observers agree in believing
that the details of flight are due to the reaction of the air on the
surface of the wing. Repeated experiment has, however, convinced me
that the artificial wing must be thoroughly under control, both during
the down and up strokes--the details of flight being in a great measure
due to the movements communicated to the wing by an intelligent agent.
In order to reproduce flight by the aid of artificial wings, I find
it necessary to employ a power which varies in intensity at every
stage of the down and up strokes. The power which suits best is one
which is made to act very suddenly and forcibly at the beginning of
the down stroke, and which gradually abates in intensity until the end
of the down stroke, where it ceases to act in a downward direction.
The power is then made to act in an upward direction, and gradually
to decrease until the end of the up stroke. The force is thus applied
more or less continuously; its energy being increased and diminished
according to the position of the wing, and the amount of resistance
which it experiences from the air. The flexible and elastic nature of
the wave wing, assisted by certain springs to be presently explained,
insure a continuous vibration where neither halts nor dead points are
observable. I obtain the varying power required by a direct piston
action, and by working the steam expansively. The power employed is
materially assisted, particularly during the up stroke, by the reaction
of the air and the elastic structures about to be described. An
artificial wing, propelled and regulated by the forces recommended, is
in some respects as completely under control as the wing of the insect,
bat, or bird.

_Necessity for supplying the Root of Artificial Wings with Elastic
Structures in imitation of the Muscles and Elastic Ligaments of
Flying Animals._--Borelli, Durckheim, and Marey, who advocate the
perpendicular vibration of the wing, make no allowance, so far as I am
aware, for the wing _leaping forward in curves_ during _the down and
up strokes_. As a consequence, the wing is jointed in their models to
the frame by a simple joint which moves only in one direction, viz.,
from above downwards, and _vice versâ_. Observation and experiment
have fully satisfied me that an artificial wing, to be effective as
an elevator and propeller, ought to be able to move not only in an
upward and downward direction, but also in a _forward_, _backward_, and
_oblique direction_; nay, more, that it should be free to rotate along
its anterior margin _in the direction of its length_; in fact, that its
movements should be universal. Thus it should be able to rise or fall,
to advance or retire, to move at any degree of obliquity, and to rotate
along its anterior margin. To secure the several movements referred to
I furnish the root of the wing with a ball-and-socket joint, _i.e._, a
universal joint (see _x_ of fig. 122, p. 239). To regulate the several
movements when the wing is vibrating, and to confer on the wing the
various inclined surfaces requisite for flight, as well as to delegate
as little as possible to the air, I employ a cross system of elastic
bands. These bands vary in length, strength, and direction, and are
attached to the anterior margin of the wing (near its root), and to the
cylinder (or a rod extending from the cylinder) of the model (_vide m_,
_n_ of fig. 122, p. 239). The principal bands are four in number--a
superior, inferior, anterior, and posterior. The superior band (_m_)
extends between the upper part of the cylinder of the model, and the
upper surface of the anterior margin of the wing; the inferior band
(_n_) extending between the under part of the cylinder or the boiler
and the inferior surface of the anterior margin of the pinion. The
anterior and posterior bands are attached to the anterior and posterior
portions of the wing and to rods extending from the centre of the
anterior and posterior portions of the cylinder. Oblique bands are
added, and these are so arranged that they give to the wing during its
descent and ascent the precise angles made by the wing with the horizon
in natural flight. The superior bands are stronger than the inferior
ones, and are put upon the stretch during the down stroke. Thus they
help the wing over the dead point at the end of the down stroke,
and assist, in conjunction with the reaction obtained from the air,
in elevating it. The posterior bands are stronger than the anterior
ones to restrain within certain limits the great tendency which the
wing has to leap forward in curves towards the end of the down and up
strokes. The oblique bands, aided by the air, give the necessary degree
of rotation to the wing in the direction of its length. This effect
can, however, also be produced independently by the four principal
bands. From what has been stated it will be evident that the elastic
bands exercise a restraining influence, and that they act in unison
with the driving power and with the reaction supplied by the air.
They powerfully contribute to the continuous vibration of the wing,
the vibration being peculiar in this that it varies in rapidity at
every stage of the down and up strokes. I derive the motor power, as
has been stated, from a direct piston action, the piston being urged
either by steam worked expansively or by the hand, if it is merely a
question of illustration. In the hand models the “_muscular sense_” at
once informs the operator as to what is being done. Thus if one of the
wave wings supplied with a ball-and-socket joint, and a cross system of
elastic bands as explained, has a sudden vertical impulse communicated
to it at the beginning of the down stroke, the wing darts _downwards
and forwards in a curve_ (_vide a c_, of fig. 81, p. 157), and in doing
so _it elevates_ and carries the piston and cylinder _forwards_. The
force employed in depressing the wing is partly expended in stretching
the superior elastic band, the wing being slowed towards the end of
the down stroke. The instant the depressing force ceases to act, the
superior elastic band contracts and the air reacts; the two together,
coupled with the tendency which the model has to fall downwards and
forwards during the up stroke, elevating the wing. The wing when it
ascends describes an _upward and forward curve_ as shown at _c e_
of fig. 81, p. 157. The ascent of the wing stretches the inferior
elastic band in the same way that the descent of the wing stretched the
superior band. The superior and inferior elastic bands antagonize each
other and reciprocate with vivacity. While those changes are occurring
the wing is _twisting_ and _untwisting_ in the direction of its length
and developing figure-of-8 curves along its margins (p. 239, fig.
122, _a b_, _c d_), and throughout its substance similar to what are
observed under like circumstances in the natural wing (_vide_ fig. 86,
p. 161; fig. 103, p. 186). The angles, moreover, made by the under
surface of the wing with the horizon during the down and up strokes
are continually varying--the wing all the while acting as a kite,
which flies steadily _upwards and forwards_ (fig. 88, p. 166). As the
elastic bands, as has been partly explained, are antagonistic in their
action, the wing is constantly oscillating in some direction; there
being no dead point either at the end of the down or up strokes. As a
consequence, the curves made by the wing during the down and up strokes
respectively, run into each other to form a continuous waved track,
as represented at fig. 81, p. 157, and fig. 88, p. 166. A continuous
movement begets a continuous buoyancy; and it is quite remarkable
to what an extent, wings constructed and applied to the air on the
principles explained, elevate and propel--how little power is required,
and how little of that power is wasted in slip.

[Illustration: FIG. 127.

  FIG. 127.--Path described by artificial wave wing from right to left.
  _x_, _x´_, Horizon. _m_, _n_, _o_, Wave track traversed by wing
  from right to left. _p_, Angle made by the wing with the horizon
  at beginning of stroke. _q_, Ditto, made at middle of stroke. _b_,
  Ditto, towards end of stroke. _c_, Wing in the act of reversing;
  at this stage the wing makes an angle of 90° with the horizon, and
  its speed is less than at any other part of its course. _d_, Wing
  reversed, and in the act of darting up to _u_, to begin the stroke
  from left to right (_vide u_ of fig. 128).--_Original._]

[Illustration: FIG. 128.

  FIG. 128.--Path described by artificial wave wing from left to right.
  _x_, _x´_, Horizon. _u_, _v_, _w_, Wave track traversed by wing from
  left to right. _t_, Angle made by the wing with horizon at beginning
  of stroke. _y_, Ditto, at middle of stroke. _z_, Ditto, towards end
  of stroke. _r_, Wing in the act of reversing; at this stage the wing
  makes an angle of 90° with the horizon, and its speed is less that at
  any other part of its course. _s_, Wing reversed, and in the act of
  darting up to _m_, to begin the stroke from right to left (_vide m_
  of fig. 127).--_Original._]

If the piston, which in the experiment described has been working
_vertically_, be made to work _horizontally_, a series of essentially
similar results are obtained. When the piston is worked horizontally,
the anterior and posterior elastic bands require to be of nearly
the same strength, whereas the inferior elastic band requires to be
much stronger than the superior one, to counteract the very decided
tendency the wing has to fly upwards. The power also requires to be
somewhat differently applied. Thus the wing must have a violent impulse
communicated to it when it begins the stroke from right to left, and
also when it begins the stroke from left to right (the _heavy parts_
of the spiral line represented at fig. 71, p. 144, indicate the points
where the impulse is communicated). The wing is then left to itself,
the elastic bands and the reaction of the air doing the remainder of
the work. When the wing is forced by the piston from right to left,
it darts forward in double curve, as shown at fig. 127; the various
inclined surfaces made by the wing with the horizon changing at every
stage of the stroke.

At the beginning of the stroke from right to left, the angle made by
the under surface of the wing with the horizon (_x x´_) is something
like 45° (_p_), whereas at the middle of the stroke it is reduced
to 20° or 25° (_q_). At the end of the stroke the angle gradually
increases to 45° (_b_), then to 90° (c), after which the wing suddenly
turns a somersault (_d_), and reverses precisely as the natural wing
does at _e_, _f_, _g_ of figs. 67 and 69, p. 141. The artificial
wing reverses with amazing facility, and in the most natural manner
possible. The angles made by its under surface with the horizon depend
chiefly upon the speed with which the wing is urged at different stages
of the stroke; the angle always decreasing as the speed increases, and
_vice versâ_. As a consequence, the angle is greatest when the speed is
least.

When the wing reaches the point _b_ its speed is much less than it was
at _q_. The wing is, in fact, preparing to reverse. At _c_ the wing is
in the act of reversing (compare _c_ of figs. 84 and 85, p. 160), and,
as a consequence, its speed is at a minimum, and the angle which it
makes with the horizon at a maximum. At _d_ the wing is reversed, its
speed being increased, and the angle which it makes with the horizon
diminished. Between the letters _d_ and _u_ the wing darts suddenly
up like a kite, and at _u_ it is in a position to commence the stroke
from left to right, as indicated at _u_ of fig. 128, p. 250. The course
described and the angles made by the wing with the horizon during the
stroke from left to right are represented at fig. 128 (compare with
figs. 68 and 70, p. 141). The stroke from left to right is in every
respect the converse of the stroke from right to left, so that a
separate description is unnecessary.

_The Artificial Wave Wing can be driven at any speed--it can make its
own currents, or utilize existing ones._--The remarkable feature in
the artificial wave wing is its adaptability. It can be driven slowly,
or with astonishing rapidity. It has no dead points. It reverses
instantly, and in such a manner as to dissipate neither time nor
power. It alternately seizes and evades the air so as to extract the
maximum of support with the minimum of slip, and the minimum of force.
It supplies a degree of buoying and propelling power which is truly
remarkable. Its buoying area is nearly equal to half a circle. It can
act upon still air, and it can create and utilize its own currents.
I proved this in the following manner. I caused the wing to make a
horizontal sweep from right to left over a candle; the wing rose
steadily as a kite would, and after a brief interval, the flame of the
candle was persistently blown from right to left. I then waited until
the flame of the candle assumed its normal perpendicular position,
after which I caused the wing to make another and opposite sweep from
left to right. The wing again rose kite fashion, and the flame was a
second time affected, being blown in this case from left to right. I
now caused the wing to vibrate steadily and rapidly above the candle,
with this curious result, that the flame did not incline alternately
from right to left and from left to right. On the contrary, it was
blown steadily away from me, _i.e._ in the direction of the tip of the
wing, thus showing that the artificial currents made by the wing, met
and neutralized each other always at mid stroke. I also found that
under these circumstances the buoying power of the wing was remarkably
increased.

_Compound rotation of the Artificial Wave Wing: the different parts of
the Wing travel at different speeds._--The artificial wave wing, like
the natural wing, revolves upon two centres (_a b_, _c d_ of fig. 80,
p. 149; fig. 83, p. 158, and fig. 122, p. 239), and owes much of its
elevating and propelling, seizing, and disentangling power to its
different portions travelling at different rates of speed (see fig. 56,
p. 120), and to its storing up and giving off energy as it hastens to
and fro. Thus the tip of the wing moves through a very much greater
space in a given time than the root, and so also of the posterior
margin as compared with the anterior. This is readily understood by
bearing in mind that the root of the wing forms the centre or axis of
rotation for the tip, while the anterior margin is the centre or axis
of rotation for the posterior margin. The momentum, moreover, acquired
by the wing during the stroke from right to left _is expended in_
_reversing the wing_, and in preparing it for the stroke from left to
right, and _vice versâ_; a continuous to-and-fro movement devoid of
dead points being thus established. If the artificial wave wing be
taken in the hand and suddenly depressed _in a more or less vertical
direction_, it immediately springs up again, and carries the hand
with it. It, in fact, describes a curve whose convexity is directed
downwards, and in doing so, carries the hand upwards and forwards. If
a second down stroke be added, a second curve is formed; the curves
running into each other, and producing a progressive waved track
similar to what is represented at _a_, _c_, _e_, _g_, _i_, of fig. 81,
p. 157. This result is favoured if the operator runs forward so as not
to impede or limit the action of the wing.

[Illustration: FIG. 129.]

_How the Wave Wing creates currents, and rises upon them, and how the
Air assists in elevating the Wing._--In order to ascertain in what
way the air contributes to the elevation of the wing, I made a series
of experiments with natural and artificial wings. These experiments
led me to conclude that when the wing descends, as in the bat and
bird, it compresses and pushes before it, in a downward and forward
direction, a column of air represented by _a_, _b_, _c_ of fig. 129,
p. 253.[119] The air rushes in from all sides to replace the displaced
air, as shown at _d_, _e_, _f_, _g_, _h_, _i_, and so produces a circle
of motion indicated by the dotted line _s_, _t_, _v_, _w_. The wing
rises upon the outside of the circle referred to, as more particularly
seen at _d_, _e_, _v_, _w_. The arrows, it will be observed, are all
pointing upwards, and as these arrows indicate the direction of the
reflex or back current, it is not difficult to comprehend how the air
comes indirectly to assist in elevating the wing. A similar current is
produced to the right of the figure, as indicated by _l_, _m_, _o_,
_p_, _q_, _r_, but seeing the wing is always advancing, this need not
be taken into account.

  [119] The artificial currents produced by the wing during its descent
  may be readily seen by partially filling a chamber with steam, smoke,
  or some impalpable white powder, and causing the wing to descend in
  its midst. By a little practice, the eye will not fail to detect the
  currents represented at _d_, _e_, _f_, _g_, _h_, _i_, _l_, _m_, _o_,
  _p_, _q_, _r_ of fig. 129, p. 253.

If fig. 129 be made to assume a horizontal position, instead of the
oblique position which it at present occupies, the manner in which
_an artificial current_ is produced by one sweep of the wing from
right to left, and utilized by it in a subsequent sweep from left to
right, will be readily understood. The artificial wave wing makes a
horizontal sweep from right to left, _i.e._ it passes from the point
_a_ to the point _c_ of fig. 129. During its passage it has displaced
a column of air. To fill the void so created, the air rushes in from
all sides, viz. from _d_, _e_, _f_, _g_, _h_, _i_; _l_, _m_, _o_, _p_,
_q_, _r_. The currents marked _g_, _h_, _i_; _p_, _q_, _r_, represent
the reflex or _artificial currents_. These are the currents which,
after a brief interval, force the flame of the candle from right to
left. It is those same currents which the wing encounters, and which
contribute so powerfully to its elevation, when it sweeps from left
to right. The wing, when it rushes from left to right, produces a new
series of artificial currents, which are equally powerful in elevating
the wing when it passes a second time from right to left, and thus
the process of making and utilizing currents goes on so long as the
wing is made to oscillate. In waving the artificial wing to and fro, I
found the best results were obtained when the range of the wing and
the speed with which it was urged were so regulated as to produce a
perfect reciprocation. Thus, if the range of the wing be great, the
speed should also be high, otherwise the air set in motion by the right
stroke will not be utilized by the left stroke, and _vice versâ_. If,
on the other hand, the range of the wing be small, the speed should
also be low, as the short stroke will enable the wing to reciprocate
as perfectly as when the stroke is longer and the speed quicker. When
the speed attained is high, the angles made by the under surface
of the wing with the horizon are diminished; when it is low, the
angles are increased. From these remarks it will be evident that the
artificial wave wing reciprocates in the same way that the natural wing
reciprocates; the reciprocation being most perfect when the wing is
vibrating in a given spot, and least perfect when it is travelling at a
high horizontal speed.

_The Artificial Wing propelled at various degrees of speed during the
Down and Up Strokes._--The tendency which the artificial wave wing has
to rise again when suddenly and vigorously depressed, explains why the
_elevator_ muscles of the wing should be so small when compared with
the _depressor_ muscles--the latter being something like seven times
larger than the former. That the contraction of the elevator muscles is
necessary to the elevation of the wing, is abundantly proved by their
presence, and that there should be so great a difference between the
volume of the elevator and depressor muscles is not to be wondered at,
when we remember that the whole weight of the body is to be elevated by
the rapid descent of the wings--the descent of the wing being entirely
due to the vigorous contraction of the powerful pectoral muscles.
If, however, the wing was elevated with as great a force as it was
depressed, no advantage would be gained, as the wing, during its ascent
(it acts against gravity) would experience a much greater resistance
from the air than it did during its descent. The wing is consequently
elevated more slowly than it is depressed; the elevator muscles
exercising a controlling and restraining influence. By slowing the wing
during the up stroke, the air has an opportunity of reacting on its
under surface.

_The Artificial Wave Wing as a Propeller._--The wave wing makes an
admirable propeller if its tip be directed _vertically downwards_,
and the wing lashed from side to side with a sculling figure-of-8
motion, similar to that executed by the tail of the fish. Three wave
wings may be made to act in concert, and with a very good result; two
of them being made to vibrate figure-of-8 fashion in a more or less
horizontal direction with a view to elevating; the third being turned
in a downward direction, and made to act vertically for the purpose of
propelling.

[Illustration:

  FIG. 130.--Aërial wave screw, whose blades are slightly twisted (_a
  b_, _c d_; _e f_, _g h_), so that those portions nearest the root (_d
  h_) make a greater angle with the horizon than those parts nearer
  the tip (_b f_). The angle is thus adjusted to the speed attained
  by the different portions of the screw. The angle admits of further
  adjustment by means of the steel springs _z_, _s_, these exercising
  a restraining, and to a certain extent a regulating, influence which
  effectually prevents shock.

  It will be at once perceived from this figure that the portions of
  the screw marked _m_ and _n_ travel at a much lower speed than those
  portions marked _o_ and _p_, and these again more slowly than those
  marked _q_ and _r_ (compare with fig. 56, p. 120). As, however, the
  angle which a wing or a portion of a wing, as I have pointed out,
  varies to accommodate itself to the speed attained by the wing, or a
  portion thereof, it follows, that to make the wave screw mechanically
  perfect, the angles made by its several portions must be accurately
  adapted to the travel of its several parts as indicated above.

  _x_, Vertical tube for receiving driving shaft. _v_, _w_, Sockets
  in which the roots of the blades of the screw rotate, the degree of
  rotation being limited by the steel springs _z_, _s_. _a b_, _e f_,
  Tapering elastic reeds forming anterior or thick margins of blades of
  screw. _d c_, _h g_, Posterior or thin elastic margins of blades of
  screw. _m n_, _o p_, _q r_, Radii formed by the different portions of
  the blades of the screw when in operation. The arrows indicate the
  direction of travel.--_Original._]

_A New Form of Aërial Screw._--If two of the wave wings represented
at fig. 122, p. 239, be placed end to end, and united to a vertical
portion of tube to form a two-bladed screw, similar to that employed in
navigation, a most powerful elastic aërial screw is at once produced,
as seen at fig. 130.

This screw, which for the sake of uniformity I denominate _the aërial
wave screw_, possesses advantages for aërial purposes to which no
form of _rigid_ screw yet devised can lay claim. The way in which it
clings to the air during its revolution, and the degree of buoying
power it possesses, are quite astonishing. It is a self-adjusting,
self-regulating screw, and as its component parts are flexible and
elastic, it accommodates itself to the speed at which it is driven, and
gives a uniform buoyancy. The slip, I may add, is nominal in amount.
This screw is exceedingly light, and owes its efficacy to its shape and
the graduated nature of its blades; the anterior margin of each blade
being comparatively rigid, the posterior margin being comparatively
flexible and more or less elastic. The blades are kites in the same
sense that natural wings are kites. They are flown as such when the
screw revolves. I find that the aërial wave screw flies best and
elevates most when its blades are inclined at a certain upward angle
as indicated in the figure (130). The aërial wave screw may have the
number of its blades increased by placing the one above the other; and
two or more screws may be combined and made to revolve in opposite
directions so as to make them reciprocate; the one screw producing the
current on which the other rises, as happens in natural wings.

_The Aërial Wave Screw operates also upon Water._--The form of screw
just described is adapted in a marked manner for water, if the blades
be reduced in size and composed of some elastic substance, which will
resist the action of fluids, as gutta-percha, carefully tempered
finely graduated steel plates, etc. It bears the same relation to, and
produces the same results upon, water, as the tail and fin of the fish.
It throws its blades during its action into double figure-of-8 curves,
similar in all respects to those produced on the anterior and posterior
margins of the natural and artificial flying wing. As the speed
attained by the several portions of each blade varies, so the angle at
which each part of the blade strikes varies; the angles being always
greatest towards the root of the blade and least towards the tip. The
angles made by the different portions of the blades are diminished in
proportion as the speed, with which the screw is driven, is increased.
The screw in this manner is self-adjusting, and extracts a large
percentage of propelling power, with very little force and surprisingly
little slip.

A similar result is obtained if two finely graduated angular-shaped
gutta-percha or steel plates be placed end to end and applied to the
water (vertically or horizontally matters little), with a slight
sculling figure-of-8 motion, analogous to that performed by the tail
of the fish, porpoise, or whale. If the thick margin of the plates be
directed forwards, and the thin ones backwards, an unusually effective
propeller is produced. This form of propeller is likewise very
effective in air.




CONCLUDING REMARKS.


From the researches and experiments detailed in the present volume,
it will be evident that a remarkable analogy exists between walking,
swimming, and flying. It will further appear that the movements of
the tail of the fish, and of the wing of the insect, bat, and bird
can be readily imitated and reproduced. These facts ought to inspire
the pioneer in aërial navigation with confidence. The land and water
have already been successfully subjugated. The realms of the air alone
are unvanquished. These, however, are so vast and so important as a
highway for the nations, that science and civilisation equally demand
their occupation. The history of artificial progression indorses
the belief that the fields etherean will one day be traversed by a
machine designed by human ingenuity, and constructed by human skill.
In order to construct a successful flying machine, it is not necessary
to reproduce the filmy wing of the insect, the silken pinion of the
bat, or the complicated and highly differentiated wing of the bird,
where every feather may be said to have a peculiar function assigned
to it; neither is it necessary to reproduce the intricacy of that
machinery by which the pinion in the bat, insect, and bird is moved:
all that is required is to distinguish the properties, form, extent,
and manner of application of the several flying surfaces, a task
attempted, however imperfectly executed, in the foregoing pages.
When Vivian and Trevithick devised the locomotive, and Symington and
Bell the steamboat, they did not seek to reproduce a quadruped or a
fish; they simply aimed at producing motion adapted to the land and
water, in accordance with natural laws, and in the presence of living
models. Their success is to be measured by an involved labyrinth of
railway which extends to every part of the civilized world; and by
navies whose vessels are despatched without trepidation to navigate
the most boisterous seas at the most inclement seasons. The aëronaut
has a similar but more difficult task to perform. In attempting to
produce a flying-machine he is not necessarily attempting an impossible
thing. The countless swarms of flying creatures testify as to the
practicability of such an undertaking, and nature supplies him at once
with models and materials. If artificial flight were not attainable,
the insects, bats, and birds would furnish the only examples of animals
whose movements could not be reproduced. History, analogy, observation,
and experiment are all opposed to this view. The success of the
locomotive and steamboat is an earnest of the success of the flying
machine. If the difficulties to be surmounted in its construction are
manifold, the triumph and the reward will be correspondingly great. It
is impossible to over-estimate the boon which would accrue to mankind
from such a creation. Of the many mechanical problems before the
world at present, perhaps there is none greater than that of aërial
navigation. Past failures are not to be regarded as the harbingers
of future defeats, for it is only within the last few years that the
subject of artificial flight has been taken up in a true scientific
spirit. Within a comparatively brief period an enormous mass of
valuable data has been collected. As societies for the advancement of
aëronautics have been established in Britain, America, France, and
other countries, there is reason to believe that our knowledge of this
most difficult department of science will go on increasing until the
knotty problem is finally solved. If this day should ever come, it will
not be too much to affirm, that it will inaugurate a new era in the
history of mankind; and that great as the destiny of our race has been
hitherto, it will be quite out-lustred by the grandeur and magnitude of
coming events.


[Illustration]




INDEX.


  PAGE

  Aerial creatures not stronger than terrestrial ones, 13

  Aërial flight as distinguished from sub-aquatic flight, 92

  Aëronautics, 209

  Air cells in insects and birds not necessary to flight, 115

  Albatross, flight of, compared to compass set upon gimbals, 199

  Amphibia have larger travelling surfaces than land animals, but less
    than aërial ones, 8

  Artificial fins, flippers, and wings, how constructed, 14

  Artificial wings, Borelli, 219

  Do. Marey, 226

  Do. Chabrier, 233

  Do. Straus-Durckheim, 233

  Do. how to apply to the air, 245

  Do. nature of forces required to propel, 246

  Artificial _wave_ wing of Pettigrew, 236

  Do. how to construct on insect type, 240

  Do. how to construct to evade the superimposed air during the up
    stroke, 241

  Do. can create currents and rise upon them, 253

  Do. can be driven at any speed; can make new currents and utilize
    old ones, 251, 255

  Do. as a propeller and aërial screw, 256

  Do. compound rotation of: the different parts of the wing travel at
    different speeds, 252

  Do. necessity for supplying root of, with elastic structures, 247

  Artificial _compound wave_ wing of Pettigrew, 242

  Atmospheric pressure, effects of, on limbs, 24

  Axioms, fundamental, 17


  Balancing, how effected in flight, 118

  Balloon, 210

  Bats and birds, lax condition of shoulder-joint in, 190

  Birds, lifting capacity of, 205

  Body and wing reciprocate in flight, and each describes a waved
    track, 12

  Bones, 21

  Bones of the extremities twisted and spiral, 28, 29

  Bones of wing of bat--spiral configuration of their articular
    surfaces, 176

  Bones of wing of bird--their articular surfaces, movements,
    etc., 178

  Borelli’s artificial bird, 220


  Chabrier’s artificial wings, 233


  Elytra or wing cases and membranous wings, 170


  Feathers, primary, secondary, and tertiary, 180

  Fins, flippers, and wings form mobile helices or screws, 14

  Flight, weight necessary to, 3, 4, 110, 111, 112, 113

  Flight the poetry of motion, 6

  Flight the least fatiguing kind of motion, 13

  Flight under water, 90

  Flight of the flying-fish, 98

  Flight, horizontal, in part due to weight of flying mass, 110

  Flight--the regular and irregular, 201

  Flight--how to ascend, descend, and turn, 201

  Flight of birds referrible to muscular exertion and weight, 204

  Fluids, mechanical effects of, on animals immersed in them, 18

  Fluids, resistance of, 18

  Flying machine, Henson, 212

  Do.  Stringfellow, 213

  Do.  Cayley, 215

  Do.  Phillips, 216

  Do.  M. de la Landelle, 217

  Do.  Borelli, 219

  A flying machine possible, 2, 3

  Forces which propel the wings of insects, bats, and birds, 186, 189

  Fulcra, yielding, 8, 104, 165


  Gravity, the legs move by the force of, 18

  Gravity, centre of, 18


  History of the figure-of-8 theory of walking, swimming, and
    flying, 15


  Joints, 23


  Kite-like action of the wings, 98

  Kite--how kite formed by wing differs from boy’s kite, 166


  Laws of natural and artificial progression the same, 4, 17

  Legs, moved by the force of gravity, 18

  Lever--the wing one of the third order, 103

  Levers, the three orders of, 19

  Life linked to motion, 3

  Lifting capacity of birds, 205

  Ligaments, 24

  Ligaments, elastic, position and action of, in wing of pheasant,
    snipe, crested crane, swan, etc., 191

  Ligaments, elastic, more highly differentiated in wings which
    vibrate quickly, 193

  Locomotion, the active organs of, 24

  Locomotion, the passive organs of, 21

  Locomotion of the horse, 39

  Locomotion of the ostrich, 45

  Locomotion of man, 51


  Marey’s artificial wings, 233

  Membranous wings, 170

  Motion associated with the life and well-being of animals, 1

  Motion not confined to the animal kingdom, 2

  Motion, natural and artificial, 4

  Motion, of uniform, 17

  Motion uniformly varied, 17

  Muscles, their properties, mode of action, etc., 24

  Muscles arranged in longitudinal, transverse, and oblique spiral
    lines, 28

  Muscles, oblique spiral, necessary for spiral bones and joints, 31

  Muscles take precedence of bones in animal movements, 29

  Muscular cycles, 26

  Muscular waves, 26


  Pendulums, the extremities of animals act as, in walking,
    9, 18, 56, 57

  Plane, inclined, as applied to the air, 211

  Pettigrew’s method of constructing and applying artificial wings as
    contradistinguished from that of Borelli, Chabrier, Durckheim,
    Marey, etc., 235

  Pettigrew’s _wave_ wing, 236

  Pettigrew’s _compound wave_ wing, 242

  Progression on the land, 37

  Do. on or in the water, 64

  Do. in or through the air, 103


  Quadrupeds walk, fishes swim, and insects, bats, and birds fly, by
    figure-of-8 movements, 15, 16


  Screws--the wing of the bird and the extremity of the biped and
    quadruped screws, structurally and functionally, 12

  Screws--difference between those formed by the wings and those
    employed in navigation, 151

  Sculling action of the wing, 231

  Speed attained by insects, 188

  Speed of wing movements partly accounted for, 120

  Spine, spiral movements of, transferred to the extremities, 33

  Straus-Durckheim’s artificial wings, 233

  Swimming of the fish, whale, porpoise, etc., 66

  Swimming of the seal, sea-bear, and walrus, 74

  Swimming of man, 78

  Swimming of the turtle, triton, crocodile, etc., 89


  Terrestrial animals have smaller travelling surfaces than amphibia,
    amphibia than fishes, and fishes than insects, bats, and birds, 8

  The travelling surfaces of animals increase as the density of the
    media traversed decreases, 7, 8

  The travelling surfaces of animals variously modified and adapted
    to the media on or in which they move, 34


  Walking, swimming, and flying correlated, 5

  Walking of the quadruped, biped, etc., 9, 10, 11

  _Wave_ wing of Pettigrew, 236

  Do. how to construct on insect type, 240

  Do. how to construct to evade the superimposed air during the up
    stroke, 241

  Do. can be driven at any speed, 251, 255

  Do. can create currents and rise upon them, 253

  Do. can make new currents and utilize existing ones, 251, 255

  Do. as a propeller, 256

  Do. as an aërial screw, 256

  Do. forces required to apply to the air, 245, 246

  Do. necessity for supplying root of, with elastic structures, 247

  Wave wing, _compound_, 242

  Weight necessary to flight, 110

  Weight contributes to flight, 112

  Weight, momentum, and power to a certain extent synonymous in
    flight, 114

  Wing of the bird and the extremity of the biped and quadruped are
    screws, structurally and functionally, 12, 136

  Wing in flight describes figure-of-8 curves, 12

  Wing during its action reverses its planes and describes a
    figure-of-8 track in space, 140

  Wing when advancing with the body describes looped and waved
    tracks, 143

  Wing, margins of, thrown into opposite curves during extension and
    flexion, 146

  Wing, tip of, describes an ellipse, 147

  Wing and body reciprocate in flight, and each describes a wave
    track, 12

  Wing moves in opposite curves to body, 168

  Wing ascends when body descends, and _vice versâ_, 159

  Wing during its vibrations produces a cross pulsation, 148

  Wing vibrates unequally with reference to a given line, 150, 231

  Wing, compound rotation of, 149

  Wing a lever of the third order, 103

  Wing acts on yielding fulcra, 8, 104, 165

  Wings, their form, etc., all wings screws, structurally and
    functionally, 136

  Wing capable of change of form in all its parts, 147

  Wing-area variable and in excess, 124

  Wing-area decreases as the size and weight of the volant animal
    increases, 132

  Wing, natural, when elevated and depressed must move forwards, 156

  Wing, angles formed by, when in action, 167

  Wing acts as true kite both during down and up strokes, 165

  Wing, traces of design in, 180

  Wing of bird not always opened up to same extent in up stroke, 182

  Wing, flexion of, necessary to flight of birds, 183

  Wing flexed and partly elevated by action of elastic ligaments, 191

  Wing, power of, to what owing, 194

  Wing, effective stroke of, why delivered downwards and forwards, 195

  Wing acts as an elevator, propeller, and sustainer both during
    extension and flexion, 197

  Wings, points wherein the screws formed by, differ from those in
    ordinary use, 151

  Wings at all times thoroughly under control, 154

  Wings of insects, consideration of forces which propel, 186

  Wings of bats and birds, consideration of forces which propel, 189


[Illustration]


  PRINTED BY T. AND A. CONSTABLE, PRINTERS TO HER MAJESTY, AT THE
  EDINBURGH UNIVERSITY PRESS.





End of the Project Gutenberg EBook of Animal Locomotion, by J. Bell Pettigrew

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