of the feet and limbs upon the trunk, generate a forward wave movement, accompanied by a certain amount of vertical undulation. The diagonal movements of the trunk and extremities are accompanied by a certain degree of lateral curvature; the right leg and left arm, when they advance to make a step, each describing a curve, the convexity of which is directed to the right and left respectively. Similar curves are described by the left leg and right arm in making the second or complementary step. When the curves formed by the right and left legs or the right and left arms are joined, they form waved tracks symmetrically arranged on either side of a given line. The curves formed by the legs and

FIG. 27 shows the simultaneous positions of both legs during a step, divided into four groups. The first group (4), 4 to 7, gives the different positions which the legs simultaneously assume while both are on the ground; the second group (B), 8 to 11, shows the various positions of both legs at the time when the posterior leg is elevated from the ground, but behind the supported one; the third group (C), 12 to 14, shows the positions which the legs assume when the swinging leg overtakes the standing one; and the fourth group (D), 1 to 3, the positions during the time when the swinging leg is propelled in advance of the resting one. The letters a, b, and c indicate the angles formed by the bones of the right leg when engaged in making a step. The letters m, n, and o, the positions assumed by the right foot when the trunk is rolling over it. g Shows the rotating forward of the trunk upon the left foot (f) as an axis. h Shows the rotating forward of the left leg and foot upon the trunk (a) as an axis. Compare with fig. 4, p. 21; with fig. 24, p. 47; and with fig. 26, p. 55.-After Weber.

arms intersect at every step, as shown at fig. 19, p. 39. Similar curves are formed by the quadruped when walking

(fig. 18, p. 37), the fish when swimming (fig. 32, p. 68), and the bird when flying (figs. 73 and 81, pp. 144 and 157).

The alternate rotation of the trunk upon the limb and the limb upon the trunk is well seen in fig. 27, p. 59.

At

At 1 of fig. 27 the trunk (g) is observed rotating on the left foot (f). At D of fig. the left leg (h) is seen rotating on the trunk (a, i): these, as explained, are complementary movements. At A of fig. the right foot (c) is firmly placed on the ground, the left foot (f) being in the act of leaving it. The right side of the trunk is on a lower level than the left, which is being elevated, and in the act of rolling over the foot. B of fig. the right foot (m) is still upon the ground, but the left foot having left it is in the act of swinging forward. At C of fig. the heel of the right foot (n) is raised from the ground, and the left foot is in the act of passing the right. The right side of the trunk is now being elevated. At D of fig. the heel of the right foot (0) is elevated as far as it can be, the toes of the left foot being depressed and ready to touch the ground. The right side of the trunk has now reached its highest level, and is in the act of rolling over the right foot. The left side of the trunk, on the contrary, is subsiding, and the left leg is swinging before the right one, preparatory to being deposited on the ground.

From the foregoing it will be evident that the trunk and limbs have pendulum movements which are natural and peculiar to them, the extent of which depends upon the length of the parts. A tall man and a short man can consequently never walk in step if both walk naturally and according to inclination.1

In traversing a given distance in a given time, a tall man

1 "The number of steps which a person can take in a given time in walking depends, first, on the length of the leg, which, governed by the laws of the pendulum, swings from behind forwards; secondly, on the earlier or later interruption which the leg experiences in its arc of oscillation by being placed on the ground. The weight of the swinging leg and the velocity of the trunk serve to give the impulse by which the foot attains a position vertical to the head of the thigh-bone; but as the latter, according to the laws of the pendulum, requires in the quickest walking a given time to attain that position, or half its entire curve of oscillation, it follows that every person has a certain measure for his steps, and a certain number of steps in a given time, which, in his natural gait in walking, he cannot exceed."

will take fewer steps than a short man, in the same way that a large wheel will make fewer revolutions in travelling over a given space than a smaller one. The relation is a purely mechanical one. The nave of the large wheel corresponds to the ilio-femoral articulation (hip-joint) of the tall man, the spokes to his legs, and portions of the rim to his feet. The nave, spokes, and rim of the small wheel have the same relation to the ilio-femoral articulation (hip-joint), legs and feet of the small man. When a tall and short man walk together, if they keep step, and traverse the same distance in the same time, either the tall man must shorten and slow his steps, or the short man must lengthen and quicken his.

The slouching walk of the shepherd is more natural than that of the trained soldier. It can be kept up longer, and admits of greater speed. In the natural walk, as seen in rustics, the complementary movements are all evoked. In the artificial walk of the trained army man, the complementary movements are to a great extent suppressed. Art is consequently not an improvement on nature in the matter of walking. In walking, the centre of gravity is being constantly changed, a circumstance due to the different attitudes assumed by the different portions of the trunk and limbs at different periods of time. All parts of the trunk and limbs of a biped, and the same may be said of a quadruped, move when a change of locality is effected. The trunk of the biped and quadruped when walking are therefore in a similar condition to that of the body of the fish when swimming.

In running, all the movements described are exaggerated. Thus the steps are more rapid and the strides greater. In walking, a well-proportioned six-feet man can nearly cover his own height in two steps. In running, he can cover without difficulty a third more.

In fig. 28 (p. 62), an athlete is represented as bending forward prior to running.

The left leg and trunk, it will be observed, are advanced beyond the vertical line (x), and the arms are tucked up like the rudimentary wings of the ostrich, to correct undue oscillation at the shoulders, occasioned by the violent oscillation produced at the pelvis in the act of running.

In order to enable the right leg to swing forward, it is evident that it must be flexed, and that the left leg must be extended, and the trunk raised. The raising of the trunk causes it to assume a more vertical position, and this prevents the swinging leg from going too far forwards; the swinging

FIG. 28.-Preparing to run, from a design by Flaxman. Adapted. In the original of this figure the right arm is depending and placed on the right thigh.

leg tending to oscillate in a slightly backward direction as the trunk is elevated. The body is more inclined forwards in running than in walking, and there is a period when both legs are off the ground, no such period occurring in walking. "In quick walking, the propelling leg acts more obliquely on the trunk, which is more inclined, and forced forwards more rapidly than in slow walking. The time when both legs are on the ground diminishes as the velocity increases, and it vanishes altogether when the velocity is at a maximum. In quick running the length of step rapidly increases, whilst the duration slowly diminishes; but in slow running the length diminishes rapidly, whilst the time remains nearly the same. The time of a step in quick running, compared to that in quick walking, is nearly as two to three, whilst the length of the steps are as two to one; consequently a person can run in

a given time three times as fast as he can walk. In running, the object is to acquire a greater velocity in progression than can be attained in walking. In order to accomplish this, instead of the body being supported on each leg alternately, the action is divided into two periods, during one of which the body is supported on one leg, and during the other it is not supported at all.

The velocity in running is usually at the rate of about ten miles an hour, but there are many persons who, for a limited period, can exceed this velocity." i

1 Cyc. of Anat. and Phy., article "Motion."