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and birds on the oneippers, files to show thing of the flight,

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 :1 in June of the same year (1867) I read a memoir “ On the Mechanism of Flight” to the Linnean Society of London ;2 and in August of 1870 I communicated a memoir “ On the Physiology of Wings” to the Royal Society of Edinburgh.3 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 screwpropeller.

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.

1 « On the various modes of Flight in relation to Aëronautics.”—Proceedings of the Royal Institution of Great Britain, March 22, 1867.

26 On the Mechanical Appliances by which Flight is attained in the Animal Kingdom.”—Transactions of the Linnean Society, vol. xxvi.

3 « On the Physiology of Wings.”—Transactions of the Royal Society of Edinburgh, vol. xxvi.

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'Etranger) 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'Etranger), 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

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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

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