Page:Popular Science Monthly Volume 6.djvu/464

448 duration of each step and the velocity of the foot at each instant while it is swinging in the air. The spaces gone over by the tracer, as before stated, are $1⁄100$th of the real distances traversed by the foot; that is, one centimetre on the paper equals one metre gone over by the foot.) Hence, every thing relative to the transport of the foot in walking is expressed in this figure.

1. Velocity of the Gait.—This is expressed by the general inclination of the curve, or by the relation existing between the lengths parallel to OX and to OY. As the different traces contained in the figure correspond to the same distance (three metres and a half; marked on the left-hand vertical line of the figure) gone over in variable times, it follows that the relation of these times to this distance will give the velocities of the different gaits. If we count on the chronograph-trace the time included between the beginning of each curve, and its termination in the line A, B, C, we shall have the measure of this time. (For example, the time occupied in going over $3 1⁄4$ metres with the gait B is given by counting the bends of the tuning-fork trace contained between 2 and the perpendicular line let fall from B on to the chronograph-trace.) Thus, for the slow walk from 1 to A, we count thirteen seconds; the more rapid walk from 2 to B occupied six and a half seconds; while with the rapid gait the distance from 5 to C was traversed in two seconds.

2. Alternate Periods of Rest and of Motion of the Foot.—It is evident that, whenever the traces show an horizontal line (that is, a line parallel to OY), those portions of the traces correspond to the traces made while the foot touched the ground and was immovable, since the spaces then gone over are nothing. The traces show that the duration of the periods of repose decreases as the gait is accelerated. The time during which the foot is in motion is shown by the oblique lines whose projection on the trace of the chronograph increases, relatively to the periods of repose, as the gait is more rapid. This proves that the length of the step increases with the velocity of the gait.

We can also, from the traces, estimate with precision the relation of the velocity of gait to the length of step, the relative variations of the duration of the periods of repose and of motion of the foot, etc.; but we will not here dwell on these details; the essential point under consideration is the following:

3. The Nature of the Movement of Translation of the Foot.—The trace of this movement is shown in a line which is nearly straight in all of its parts; the motion of the foot is therefore uniform during nearly the whole of its translation; the inflections of the line at its beginning and at its end show that, in rapid gaits especially, the motion of the foot begins and ends in short periods of variable velocities. From the above we are now able to judge how far the oscillation of the leg is analogous to that of a pendulum.