pressure to which the experimental shoe is subjected (fig. 19), and the other, ten vibrations per second furnished by a chrono graphic tuning-fork of large size.

FIG. 26.-A large tuning-fork whose vibrations are reduced by masses of lead to 10 per second, acts on the registering lever drum, by an experimental drum attached to one of its branches. This also receives at the same time, by a tube with two branches, the influence both of the impact and rising of the foot of the person who walks.

Fig. 20 shows how these instruments are arranged. It is seen that the drum will be affected by the double influence

of the changes in the pressure of the foot on the ground, and of the vibrations of the tuning-fork; and this produces in a single tracing the interference of two movements, giving at the same time the notion of the space traversed, and that of the time employed in passing over it.

In order to analyse this tracing, let us consider only, in the first place, the sinuous curve which obeys at the same time the tuning-fork, and the experimental shoe on the right foot; and in this curve let us only examine the elevated part-that which corresponds with the pressure of the foot upon the ground. We see that, during the duration of this pressure, the style has passed through a space on the cylinder measuring about 2 centimetres; therefore, as the displacement of the style is fifty times less than that of the person walking, he will have advanced about one metre during the pressure of one foot. But while he traversed this metre, he did not advance with an uniform velocity; in fact, during the first half of this distance, the tuning-fork made about four vibrations, whilst in the second, it has scarcely made two and a half. Thus the foot which presses the ground with a force increasing from the commencement to the end of its impact, gives the body an impulse whose velocity equally increases.

During the rise of the foot, the line traced by the tuningfork indicates also that the body of the person walking progresses with an accelerated motion. That is easily understood if we remember that, in walking, the rise of one foot corresponds exactly with the tread of the other. It is, therefore, the impact of the left foot on the ground which gives the body of the walking person an accelerated motion, which is observed during the rise of the right foot.

This method appears to us applicable to all cases in which it is necessary to measure the relative durations of different phases of movement.

The inequality in the speed of the man who walks brings with it an important consequence. When a man drags a load, the effort which he makes cannot be constant; at each foot-fall a redoubled energy is produced in the traction that is developed, and as this increase of effort has but a very short duration, a series of shocks, as we may call them, occurs at

each instant. But we know that these shocks are very unfavourable to the full utilization of mechanical force; we have explained (page 49) the inconvenience which would arise. from them in the work of living motive agents, and the manner in which these shocks are lessened by the elasticity of muscular fibre.

Under the conditions in which a man dragging a load is placed, if he is attached by a rigid strap to the mass which he has to draw, the shocks of which we have spoken will be produced, and he will feel their reaction on his shoulders. In order to avoid these painful jerks, and to utilize more fully the effort which he makes, we have placed between the carriage and the traction strap an intermediate elastic portion, the effect of which has answered our expectations.

We are endeavouring to construct analogous contrivances, which may be adapted to the traces of ordinary carriages, so as to lessen the violence of the pressure on the collar, and to utilize more fully the strength of the horse.

CHAPTER III.

THE DIFFERENT MODES OF PROGRESSION USED BY MAN. Description of the apparatus for the purpose of studying the various modes of progression used by man-Portable registering apparatus-Experimental apparatus for vertical reactions-Walking-Running-Gallop --Leaping on two feet and hopping on one-Notation of these various methods-Definition of a pace in any of these kinds of locomotion -Synthetic reproduction of the various modes of progression.

THE principal modes of progression employed by animals, are walking, which we have already described at some length as far as it relates to man, running at different rates of speed, the gallop, and leaping on one or two feet.

The act of walking varies according to the nature or the slope of the ground; we shall have to treat of these different influences.

In this new study it is no longer possible to employ the

apparatus which we have used in our previous researches. The circular and horizontal track on which the experimenter was obliged to walk must be exchanged for surfaces of every kind and of every slope.

If the new instruments to which we must have recourse leave the experimenter more liberty in his movements, they are, on the other hand, relatively less complete as to the indications which they furnish; therefore, we can only require from them two kinds of indications; those of the pressures of the feet on the ground, and those of the vertical re-actions which are communicated to the body by these pressures.

Fig. 27 shows a runner furnished with apparatus of the new construction. He wears the experimental shoes which we have already described, and holds in his hand a portable registering instrument, on which are traced the curves produced by the pressure of his feet. As the cylinder of this instrument turns uniformly, the curves will be registered in proportion to the time, and not to the space traversed during each of the acts by which this curve is traced.

In order to facilitate the experiment, and to allow the apparatus to assume a uniform motion before it traces on the paper, we have recourse to a special expedient. The points of the tracing levers do not touch the cylinder; but in order to bring them in contact with the paper, an india-rubber ball must be compressed. As soon as this compression ceases, the points retreat from the cylinder, and the tracing is no longer produced. In fig. 27 the runner holds this ball in his left hand, and compresses it with his thumb.

In addition to this, the runner, in order to obtain the tracings of the vertical re-actions, carries on his head an instrument whose arrangement is represented in fig. 28.

It is an experimental lever-drum fixed on a piece of wood, which is fastened with moulding wax on the head of the experimenter, as seen in fig. 27. The drum is provided with a piece of lead placed at the extremity of its lever; this mass acts by its inertia.

While the body oscillates vertically, the mass of lead resists these movements, and causes the membrane of the drum to sink when the body rises, and to rise when the body descends.