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." 1 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 1 Cyc. of Anat. and Phy., Art. "Motion," by John Bishop, Esq. : 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. Р B 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. 1⁄2 AF = W. BF + BF. BF; in the first order, where AF and BF represent the weights of these portions of the lever respectively. Similarly, in the second order P. AFW.BF + AF. AF 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."1 The levers and fulcra are well seen in the extremities of the deer, the skeleton of which is selected for its extreme elegance. a 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. 1 Bishop, op. cit. While the bones of animals form levers and fulera for portions of the muscular system, it must never be forgotten that the earth, water, or air form fulera 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. The bones of vertebrated animals, especially those which are entirely terrestrial, are much more elastic, hard, and calculated by their chemical elements to bear the shocks and strains incident to terrestrial progression, than those of the aquatic vertebrata; the bones of the latter being more fibrous and spongy in their texture, the skeleton is more soft and yielding. The bones of the higher orders of animals are constructed according to the most approved mechanical principles. Thus they are convex externally, concave within, and strengthened by ridges running across their discs, as in the scapular and iliac bones; an arrangement which affords large surfaces for the attachment of the powerful muscles of locomotion. The bones of birds in many cases are not filled with marrow but with air, a circumstance which insures that they shall be very strong and very light. In the thigh bones of most animals an angle is formed by the head and neck of the bone with the axis of the body, which prevents the weight of the superstructure coming vertically upon the shaft, converts the bone into an elastic arch, and renders it capable of supporting the weight of the body in standing, leaping, and in falling from considerable altitudes. Joints. Where the limbs are designed to move to and fro simply in one plane, the ginglymoid or hinge-joint is applied; and where more extensive motions of the limbs are requisite, the enarthrodial, or ball-and-socket joint, is introduced. These two kinds of joints predominate in the locomotive organs of the animal kingdom. The enarthrodial joint has by far the most extensive power of motion, and is therefore selected for uniting the limbs to the trunk. It permits of the several motions of the limbs termed pronation, supination, flexion, extension, abduction, adduction, and revolution upon the axis of the limb or bone about a conical area, whose apex is the axis of the head of the bone, and base circumscribed by the distal extremity of the limb."1 The ginglymoid or hinge-joints are for the most part spiral in their nature. They admit in certain cases of a limited degree of lateral rocking. Much attention has been paid to the subject of joints (particularly human ones) by the brothers Weber, Professor Meyer of Zürich, and likewise by Langer, Henke, Meissner, and Goodsir. Langer, Henke, and Meissner succeeded in demonstrating the "screw configuration" of the articular surfaces of the elbow, ankle, and calcaneo-astragaloid joints, and Goodsir showed that the articular surface of the knee-joint consist of " a double conical screw combination." The last-named observer also expressed his belief "that articular combinations with opposite windings on opposite sides of the body, similar to those in the knee-joint, exist in the ankle and tarsal, and in the elbow and carpal joints; and that the hip and shoulder joints consist of single threaded couples, but also with opposite windings on opposite sides of the body." I have succeeded in demonstrating a similar spiral configuration in the several bones and joints of the wing of the bat and bird, and in the extremities of most quadrupeds. The bones of animals, particularly the extremities, are, as a rule, twisted levers, and act after the manner of screws. This arrangement enables the higher 1 Bishop, op. cit. |