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.