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 example1) which begin their career by swimming, come ultimately to walk, leap, and even fly.2

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

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

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.

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.:—

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

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.

“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.

“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.

“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. 1/2AF and in the third order P.AF= W.BF+BF. 1/2BF.

“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.

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

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 26lbs. The pressure on the knee-joint is estimated by Dr. Arnott at 60 lbs.”13

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.