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.

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. } 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 AF order P. AF W. BF + AF. and in the third order " 2 BF P. AFW. BF + BF.

2

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." The levers and fulcra are well seen in the extremities of the deer, the skeleton of which is selected for its extreme elegance.

a

11. 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 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 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, Meissuer, 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.

animals to apply their travelling surfaces to the media on which they are destined to operate at any degree of obliquity so as to obtain a maximum of support or propulsion with a minimum of slip. If the travelling surfaces of animals did not form screws structurally aud functionally, they could neither seize nor let go the fulcra on which they act with the requisite rapidity to secure speed, particularly in water and air. "Ligaments. The office of the ligaments with respect to locomotion, is to restrict the degree of flexion, extension, and other motions of the limbs within definite limits.

Effect of Atmospheric pressure on Limbs.-The influence of atmospheric pressure in supporting the limbs was first noticed by Dr. Arnott, though it has been erroneously ascribed by Professor Müller to Weber. Subsequent experiments made. by Dr. Todd, Mr. Wormald, and others, have fully established the mechanical influence of the air in keeping the mechanism of the joints together. The amount of atmospheric pressure on any joint depends upon the area or surface presented to its influence, and the height of the barometer. According to Weber, the atmospheric pressure on the hip-joint of a man is about 26 lbs. The pressure on the knee-joint is estimated by Dr. Arnott at 60 lbs."1

Active organs of Locomotion. Muscles, their Properties, Arrangement, Mode of Action, etc.-If time and space had permitted, I would have considered it my duty to describe, more or less fully, the muscular arrangements of all the animals whose movements I propose to analyse. This is the more desirable, as the movements exhibited by animals of the higher types are directly referable to changes occurring in their muscular system. As, however, I could not hope to overtake this task within the limits prescribed for the present work, I shall content myself by merely stating the properties of muscles; the manner in which muscles act; and the manner in which they are grouped, with a view to moving the osseous levers which constitute the bony framework or skeleton of the animals to be considered. Hitherto, and by common consent, it has been believed that whereas a flexor muscle is situated on one aspect of a limb, and its correspond1 Bishop, op. cit.