number as the minimum necessary to produce the state of apparent immobility of the electrically tetanized muscle.

If voluntary contraction, studied with the aid of the myograph, furnishes no trace of vibrations, we must not be surprised, since the essential character of that act consists in the coalescence of shocks. But the existence of the sound which. accompanies the contraction of the muscle sufficiently proves the complexity of this phenomenon. Let us add another proof in favour of this theory. When a muscle receives excitations. of equal intensity, the contraction which results from them is all the stronger in proportion to their frequency. Now, in contracting the muscles of the jaws with more or less force, we have been able to convince ourselves that the acuteness of the muscular sound increased with the energy of the effort. We may thus obtain variations of a fifth in the tone of the muscular sound.

We shall also see hereafter how the electric state of the muscles in contraction proves still more the complexity of this phenomenon.

The conclusion at which we have arrived is, that during voluntary contraction, the motor nerves are the seat of successive acts, each of which produces an excitation of the muscle. The latter, in its turn, causes a series of acts, each of which gives birth to a muscular wave producing a shock. It is in the elasticity of the muscle that we must seek for the cause of the coalescence of these multiplied shocks; they are extinguished just as the jerks of the piston of a fire-enginedisappear in the elasticity of its reservoir of air.

Of work done by the muscles. After having seen how mechanical force is produced, let us try to measure it—that is to say, to compare it with the kilogrammetre, the unit of measure of work. If we suspend a weight to the tendon of a muscle which we cause to contract, we easily obtain the measure of work by multiplying this weight by the height to which the muscle raises it.

In animated motors, the measure of work is less easy to obtain. Sometimes, indeed, the strength of an animal is utilized in the lifting of a weight, but the greater part of the acts in which the strength of animals is employed can only

be estimated by enlarging the definition of mechanical work. Thus, a horse which tows a boat, a man who planes a board, a bird which strikes the air with its wing, does mechanical work, and yet they do not lift weights. In order to reduce cases of this kind to a general definition, we must admit as the expression of work, the effort multiplied by the space traversed. This effort, besides, may always be compared with the weight, the lifting of which would necessitate an equal effort, so that we say of a traction or an impulse, that it corresponds with 10 or 20 kilogrammes. When a workman planes or turns a piece of metal, if the tool which he drives into it penetrates only on condition of receiving an impulse of one kilogramme, the workman, in order to have effected a kilogrammetre of work, ought to have detached from the mass a shaving of a metre in length. A horse which tows a boat with 20 kilogramme force, will have employed a force of 20,000 kilogrammetres when he has gone 1,000 metres.

But still that is not yet sufficient to be applied to all the forms of mechanical labour. If, for example, force be employed to displace a mass, the effort necessary for the move-, ment will vary with the speed which is given to that mass. Let us imagine a block of stone suspended freely at the end of a very long rope; the lightest pressure applied to this block for a few instants will produce movement in it, while the strongest blow of the fist will scarcely cause any sensible displacement, because the force requisite to displace masses increases according to the square of the speed which is communicated to them.*

A force of very short duration applied to a mass, produces only a shock incapable of displacing it. But this same shock, if it be exerted by means of an elastic medium, is transformed into an act of longer duration, and without having added anything to the quantity of motion, becomes capable of producing work.

This elasticity intervenes in the animal economy to permit the utilization of the very brief act which constitutes the formation of the muscular wave. The formation of the wave, * This action is expressed by m_v2

2

which lasts only for some hundredths of a second, represents the time of application of each element of the force of the muscle. At each new wave, there would be produced a true shock if the elasticity of the fibre did not extinguish this abruptness, and transform these jerky little contractions into a gradual increase of tension which constitutes the prolonged effort of the muscle.

A motor only works on the double condition of developing an effort, and accomplishing a motion. Thus a muscle which contracts, performs no external work, except while it is contracting; as soon as it has reached the limit of its contraction, it ceases to work, whatever may be the effort which it develops. When we sustain a weight after having lifted it, the act of sustainment does not constitute work.

But, in these conditions, to maintain the elastic force of the muscle, the same acts are produced in its interior as during the work; the muscular waves succeed each other at short intervals, and heat is disengaged by chemical action. Now, this heat, which cannot transform itself into action, ought to remain in the muscle, and heat it strongly. This is precisely what we observe, so that in the malady called tetanus, which consists of a permanent tension of the muscles, it is ascertained that heat is produced with an exaggerated intensity, the temperature of the entire body rising several degrees.

CHAPTER VI.

OF ELECTRICITY IN ANIMALS.

Electricity is produced in almost all organised tissues-Electric currents of the muscles and the nerves-Discharges of electric fishes; old theories; demonstration of the electric nature of this phenomenonAnalogies between the discharge of electrical apparatus and the shock of a muscle-Electric tetanus-Rapidity of the nervous agent in the electrical nerves of the torpedo; duration of its discharge.

Most of the animal or vegetable tissues are the seat of chemical actions, whence result an incessant disengagement of electricity. In this way, the nerves and muscles of an

animal furnish manifestations of dynamic electricity. Matteucci has discovered the manner in which the muscular current is usually produced. Du Bois Reymond has added much to our knowledge of this current, of its intensity, and of its direction in every part of a muscle. Treatises on physiology give copious details of experiments relative to nervous and muscular electric currents. This study has been the more eagerly pursued because the proximate cause of the function of the nerves and muscles was expected to be found in these electric phenomena.

The most interesting fact connected with muscular electricity, with respect to the transformation of force, appears to be the disappearance of the electrical state of a muscle at the moment when it contracts, or when it is tetanized. It appears then that the chemical actions of which the muscles are the seat, are entirely employed in the production of heat and

motion.

To observe these phenomena, we must make use of a very sensitive galvanometer. Suppose a muscle connected with one of these instruments; it gives its currents, and deflects the magnetic needle a certain number of degrees. When this deviation has been effected, and the needle has become stationary in its new position, it is only necessary to produce tetanus in the muscle, and immediately the needle retrogrades towards zero. This is what Du Bois Reymond calls the negative variation of the muscular current. The same phenomenon is observed in the voluntary contraction of the muscles.

The interpretation of the negative variation is very important. Du Bois Reymond having remarked, that for a single muscular shock no deflection of the needle from zero is obtained, concluded that this is on account of the short duration of the electrical disturbance accompanying a shock. In tetanus, on the contrary, a series of modifications in the electrical condition of the muscle correspond to the series of shocks produced their accumulated influence deflects the magnetic needle.

This phenomenon is familiar to physicists. It is known that the needle of a galvanometer subjected to a frequentlyinterrupted current, takes a fixed position intermediate be

tween zero and the extreme point which it would have occupied if the current had been continuous.

In the muscles in which the shock is protracted, as in the tortoise, a very prolonged change in the electrical state is produced; and therefore these muscles can by each of their shocks cause a deflection of the magnetic needle. It is the same with the movements of the heart; each of these appears to be only a shock of the cardiac muscle, and yet it deflects the magnetic needle in the same manner as tetanus of an ordinary muscle. This fact, that a negative variation is equally seen in a muscle which is contracted voluntarily, is of the greatest importance. It confirms the theory which assimilates contraction with tetanus, that is to say, with a discontinuous or vibratory action.

One point which has been long under discussion relative to the manifestations of muscular electricity, is whether the negative variation is caused by a change of direction in the muscular current, or by a transitory suppression of this current. The latter hypothesis has been rendered extremely probable by the numerous experiments in which the needle of the galvanometer has never been seen to retrograde beyond the zero point. Thus the phenomenon of negative variation seems to prove the principle which we laid down at the commencement of this article, that force is manifested in the muscles in a different manner during activity and repose, and that the manifestation under the form of mechanical work is substituted for that under the form of electricity.

Electric fishes.-Animal electricity appears in a much more striking form in the discharges produced by certain fishes. In this case the special organs have for their object the production of electricity; nevertheless, by their structure, their chemical composition, and their dependence on the nervous system, these organs remind us of the conditions of the mus. cular apparatus.

The number of species provided with electrical organs which was formerly restricted to five,* has been remarkably

* The five species formerly known were the Raya torpedo, the Gymnotus electricus, the Silurus electricus, the Tetraodon electricus, and the Trichiurus electricus.