results as yet incomplete, but which tend to assimilate the electrical with the muscular action. These results are as follow :

I. The rapidity of the nervous agent in the electrical nerves of the torpedo seems evidently to be the same as that of the nervous agent producing motion in the frog.

2. The phenomenon called by Helmholtz lost time exists also in the electric apparatus of the torpedo, and lasts about the same time as in the muscle.

3. The discharge of the torpedo is not instantaneous, like that of certain kind of tension electrical apparatus, but it is prolonged about fourteen hundredths of a second; which is, in a remarkable degree equal to the duration of a shock in a frog's muscle.

We cannot enter here into the details of the experiments which have furnished these results, but we will endeavour, in a few lines, to explain the method which we employed.

Registering apparatus measure the slightest intervals of time; this we have seen in speaking of the estimated rapidity of the nervous agent. But, in order to employ the graphic method, we must have motion to give the required signal.

Thus, in the experiment of Helmholtz, the muscular shock itself announced that the order of movement which the nerve had to convey had arrived at its destination.

In order to obtain the signal of the electric discharge, we have employed it to excite the muscle of a frog, the shock of which was inscribed on the registering cylinder.

The trace furnished by the frog-signal is somewhat delayed, it is true, after the excitation has been produced; but this delay is a known quantity, and it can easily be taken into account.

The following is the method adopted to measure with the ordinary myograph the duration of the different acts which precede the discharge of the torpedo.

In a preliminary experiment (fig. 12) the nerve of the frog was directly excited, and a note was taken of the time (e g) which elapsed between the instant (e) of the excitation, and the signal (g) given by the frog.

In a second experiment the torpedo was excited, still at the

instant (e), and the electricity of its discharges was collected by means of conducting wires which sent it to the nerve of the frog signal. This would give its shock at the point (t).

The difference (9 t) would express the time consumed by the torpedo between the excitation of its nerve and the discharge. By varying the experiment, as we have done for the motive nerves (page 43), we obtain the measure of the rapidity of the electric nervous agent, and that of the lost time in the torpedo apparatus.*

Finally, in order to measure the duration of the electrical action, we had recourse to a method which consists in collecting this discharge during a very short time (1-100th of a second) to send it to the frog signal, and varying gradually the instant at which the electricity of the torpedo was collected. It was thus ascertained that starting from the point (t) one might, during 14-100ths of a second, obtain a series of signals from the frog-t', t', t'", t'""', but that beyond that time the frog gave no signals, thus proving that the discharge had terminated.

We have not been able to follow out farther the comparison of the electric with the muscular action; but, according to the results already furnished by experiment, we can foresee

*

Deprived of appropriate apparatus, we have been obliged to construct for ourselves a kind of registering instrument which should measure short intervals of time with sufficient precision. We refer the reader, for the real arrangement of the experiments, to the "Journal de l'anatomie et de la physiologie," loc. cit. Fig. 12 represents tracings which one would obtain with the registering instruments already known.

that new analogies will still show themselves between these two manifestations of force in living beings, mechanical work and electricity.

CHAPTER VII.

ANIMAL MECHANISM.

Of the forms under which mechanical work presents itself— Every machine must be constructed with a view to the kind of work which it has to perform-Correspondence of the form of muscle with the work which it accomplishes-Theory of Borelli-Specific force of muscles -Of machines; they only change the form of work, but do not increase its quality-Necessity of alternate movements in living motive powers-Dynamical energy of animated motors.

If we have lingered long over the origin of heat, of mechanical work, and of electricity in the animal kingdom, it was in order to establish clearly that these forces are the same as those which are seen in the inorganic world. Certain evident differences must have struck the earlier observers, but the progress of science has shown, more and more clearly, this identity, which is now disbelieved only by those whose minds are still under the influence of obsolete theories.

Mechanical force, to which our attention must now be exclusively directed, has hitherto been studied only in its origin; we must follow it through all its applications to work of different kinds which it executes in animal mechanism.

In all the machines employed in the arts we must have organs which serve as media between the forces which we employ and the resistance which are required to be overcome. This word organ is precisely that which anatomists use to designate the portions which compose the animal machine. The laws of mechanics are applicable as well to animated motors as to other machines; this truth, however, has to be demonstrated, but, like many others, it was for a long time unrecognized.

Of the forms of mechanical work.-When we have at our disposal a certain quantity of force, it is necessary, in order to utilize it, to collect it under conditions which vary according to the nature of the effects which we desire to produce.

We have seen that the measure of work actually employed is the product of the resistance multiplied by the space through which it has to pass. Such a measure, being the product of two factors, may remain constant if the two factors vary inversely. So that a considerable weight, raised to a slight height, will give the same result of work as a light weight raised to a greater height.

These will be two different forms of the same quantity of work; but, in this case, the form is of extreme importance. In order that the work applied should be available, it is necessary that its form should be the same as that of the resisting force—that is, of the work required to be done.

If we have as a moving power a piston of a steam engine of large diameter and short length, capable of lifting 100 kilogrammes to the height of a centimetre, and that it is necessary with this generator of force to lift one kilogramme to the height of a metre, which equally represents a kilogrammetre of work, the motive force in this machine cannot be utilized directly; for at the end of the stroke of the piston the weight of a kilogramme will only have been lifted one centimetre, and of the force at our disposal will remain unemployed. Every machine, therefore, must be constructed with a view to the special form under which the resistance to be overcome presents itself.

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It is true that by means of certain contrivances, levers or wheel-work properly combined, it is possible to cause a certain quantity of work to pass from one form to another, and to apply it to the resistance to be overcome. But this will be the object of ulterior study. We have only to consider at this moment the case in which the force is directly applied to the obstacle which it has to surmount, which is a very frequent condition in animated motive powers.

Let us return, then, to the hypothesis in which the moving force of the piston of an engine must be applied directly to overcome resistance. Under these conditions the constructor

will be careful to give to the surface of the piston such an area, that the pressure on this surface may be precisely equal to the resistance which it has to overcome; then he will give to the cylinder such a length that it will allow the piston to travel just as far as the resistance ought to move. It is only

under these conditions that the machine will do the desired work, and utilize all its moving power. On the contrary, in the case in which work answering to a kilogrammetre must be done by lifting 100 kilogrammes to the height of a centimetre, the cylinder must be made so large that the pressure of steam on the surface of the piston will develop an effort of 100 kilogrammes, and such a length only must be given to the cylinder, that the movement of the piston may be merely a centimetre.

One cannot substitute one of these forms of cylinder for the other, for in one case the force would be insufficient, and in the other, the range would be too restricted.

The only thing which is equal in both is the amount of work that the two machines can do, that is to say, the pro-duct of the force employed multiplied by the space passed through; this is again the product of the surface of a section of the cylinder multiplied by its length, or, in other terms, it is the volume of steam contained in each machine, this vapour being supposed to be at an equal tension.

This proportion of the volume of the matter which works to the work performed, is found in every case in which a moving force is employed.

Two masses of lead falling from the same height will do work proportionate to their volume, or, which is the same thing, to their weight. Two threads of india-rubber of the same length, both of which have been stretched to the same degree, will do work proportionate to their transverse sections, and, consequently, to their respective weights. Lastly, two threads of the same diameter, but of unequal lengths, after having been subjected to the same elongation in proportion to their original lengths, will, as they contract, do work proportionate to their respective lengths, that is to say, to their weight.

This leads to the consideration of muscle, which conforms