Animal Locomotion; or, walking, swimming, and flying. James Bell Pettigrew
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.
Fig. 1.
“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.
Fig. 2.
“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.
Fig. 3.
“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.
Fig. 4. Skeleton of the Deer (after Pander and D’Alton). The bones in the extremities of this the fleetest of quadrupeds are inclined very obliquely towards each other, and towards the scapular and iliac bones. This arrangement increases the leverage of the muscular system and confers great rapidity on the moving parts. It augments elasticity, diminishes shock, and indirectly begets continuity of movement, a. Angle formed by the femur with the ilium, b. Angle formed by the tibia and fibula with the femur, c. Angle formed by the cannon bone with the tibia and fibula, d. Angle formed by the phalanges with the cannon bone. e. Angle formed by the humerus with the scapula. f. Angle formed by the radius and ulna with the humerus.
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