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.