Part 3

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.

“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}.(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._

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.