The weight of the body plays an important part in walking and swimming, as well as in flying. A biped which advances by steps and not by leaps may be said to roll over its extremities,[3] the foot of the extremity which happens to be upon the ground for the time forming the centre of a circle, the radius of which is described by the trunk in forward motion. In like manner the foot which is off the ground and swinging forward pendulum fashion in space, may be said to roll or rotate upon the trunk, the head of the femur forming the centre of a circle the radius of which is described by the advancing foot. A double rolling movement is thus established, the body rolling on the extremity the one instant, the extremity rolling on the trunk the next. During these movements the body rises and falls. The double rolling movement is necessary not only to the progression of bipeds, but also to that of quadrupeds. As the body cannot advance without the extremities, so the extremities cannot advance without the body. The double rolling movement is necessary to continuity of motion. If there was only one movement there would be dead points or halts in walking and running, similar to what occur in leaping. The continuity of movement necessary to progression in some bipeds (man for instance) is further secured by a pendulum movement in the arms as well as in the legs, the right arm swinging before the body when the right leg swings behind it, and the converse. The right leg and left arm advance simultaneously, and alternate with the left leg and right arm, which likewise advance together. This gives rise to a double twisting of the body at the shoulders and loins. The legs and arms when advancing move in curves, the convexities of the curves made by the right leg and left arm, which advance together when a step is being made, being directed outwards, and forming, when placed together, a more or less symmetrical ellipse. If the curves formed by the legs and arms respectively be united, they form waved lines which intersect at every step. This arises from the fact that the curves formed by the right and left legs are found alternately on either side of a given line, the same holding true of the right and left arms. Walking is consequently to be regarded as the result of a twisting diagonal movement in the trunk and in the extremities. Without this movement, the momentum acquired by the different portions of the moving mass could not be utilized. As the momentum acquired by animals in walking, swimming, and flying forms an important factor in those movements, it is necessary that we should have a just conception of the value to be attached to weight when in motion. In the horse when walking, the stride is something like five feet, in trotting ten feet, but in galloping eighteen or more feet. The stride is in fact determined by the speed acquired by the mass of the body of the horse; the momentum at which the mass is moving carrying the limbs forward.[4]