tarnishes in the slightest degree. This glass at ordinary temperatures is sensibly a perfect insulator.

The conductivity of glass when heated makes it very difficult to determine its capacity as a dielectric. It appears from the experiments of Hopkinson on glasses of known composition, that the glasses made with soda and lime conduct more, and are also more subject to electric polarization" and "residual charge" than those made with potash and lead.

Both the conductivity and the susceptibility to residual charge increase as the temperature rises, and this makes it very doubtful whether the apparent increase of dielectric capacity, which was observed by Cavendish and also by recent experimenters, is a real increase of the specific inductive capacity, or merely an effect of increased conductivity.

The experiments of Messrs Ayrton and Perry* on wax at different temperatures would seem to indicate a real increase of dielectric capacity, as well as of conductivity, as the temperature rises up to the melting point. During the process of melting the capacity decreases and at higher temperatures begins to increase again, but the conductivity continues to increase as the temperature rises.

NOTE 28, Art. 383.

Capacity of a Cylindrical Condenser.

The rule by which Cavendish computed the charge of a condenser consisting of two cylindrical surfaces having the same axis is given at Art. 313.

Phil. Mag. August, 1878.

CYLINDRICAL CONDENSERS.

433

If R is the external and r the internal radius, and the length of the cylinders, then Cavendish's expression for the "computed charge"

1 R+ r

is

2 R -r

1.

The true expression for the capacity is

1

2 log R-logr

when the logarithms are Naperian.

We may express log R-logr in the form of the series

and we thus find as an approximate value of the capacity

The first term agrees with Cavendish's rule, for the "capacity" is half the "inches of electricity," but the other terms show that Cavendish's rule gives too large a value for the computed charge.

The following table gives the charge as computed by Cavendish compared with that given by the correct formula.

The fishes which are known to possess the power of giving electric shocks belong to two genera of Teleostean Fishes and one of Elasmobranch Fishes, and the position and relations of the electric organs are different in each.

In every instance, however, the electric organ may be roughly described as being divided in the first place into parallel prisms or columns by septa, which we may call (with reference to the organ, not the fish) longitudinal septa, and in the second place each column is divided transversely by diaphragms, the structure of which is different in the different families, but in every case the terminations of the nerves

lie on that surface of each diaphragm which during the discharge becomes its negative surface.

In the large family of the Torpedos the electric organs are formed of a large number of short columns, the columns running from the belly to the back of the fish. The nerves terminate on the ventral surface of each diaphragm, and the electric discharge is from belly to back through the organ, or in other words, the back of the fish becomes positive with respect to the belly.

There seems to be but one species of Gymnotus. It is a long eellike fish. Its electric organs consist of a smaller number of very long columns running from the tail to the head of the fish. The nerves terminate on the posterior surface of the diaphragms, and the electric discharge is from tail to head through the organ, or the head of the fish becomes positive with respect to the tail.

There are three species of Malapterurus which are known to be electrical. In these the electric organs run longitudinally. Bilharz, observing that the nerves appear to terminate in an expansion like the head of a nail on the posterior surface of the diaphragms, concluded that the electric discharge must be from tail to head through the organ, as in the Gymnotus. Ranzi* however, and afterwards, independently of him, Du Bois Reymond+ found that the discharge is really from head to tail through the organ, so that the tail becomes positive with respect to the head, and Schultze, who had been led to believe, from a comparison of his own observations on the organs of pseudo-electric fishes with the drawings of Bilharz, that the nerves might pass through the diaphragms. and terminate on their anterior surfaces, found, on examining the preparations sent him by Du Bois Reymond, that this was really the case in Malapterurus, so that we may now assert that in every known case the terminations of the nerves are on that side of each diaphragm which during discharge becomes negative.

The origin of the nerves which supply the electric organs is different in the three families.

In the Torpedos the electric nerves are derived from the posterior division of the brain. Irritation of this lobe produces an electric discharge of the organ, but no muscular contraction. Irritation of other parts of the brain produces muscular contractions, but not electric discharges, unless the disturbance produced affects the electric nerves.

In the Gymnotus the electric nerves arise from the whole length of the spinal cord, and in Malapterurus the electric organs are supplied by the 2nd and 3rd pair of spinal nerves.

The electric nerves are so called because they govern the discharges of the electric organ. No essential difference has been observed between

Nuovo Cimento, Tomo II, Dicembre 1856, p. 447, quoted by Du Bois Reymond "Zur Geschichte der Entdeckungen am Zitterwelse," Archiv fur Anatomie Physiologie, &c. Leipzig, 1859, p. 210.

+ Monatsbericht d. k. Akad. Berlin, 1858.

the electric phenomena in these nerves and those in other nerves. They must be classed, with respect to origin as well as function, among the motor nerves. The only difference is that their function is to govern the electric discharge of a peculiar organ, instead of the contraction of a muscle.

The experiments of Dr Davy* and those of Matteucci shewed that the discharge of the Torpedo produces all the known phenomena of an electric discharge. Faraday did the same for the Gymnotus, and Du Bois Reymond§ for the Malapterurus.

M. Marey has recently investigated some of the electrical phenomena of the discharge of the Torpedo. He employed three methods of indicating the discharge, the prepared leg of a frog, which is extremely sensitive to the feeblest current, but has the disadvantage that the time required for the contraction of the muscles, and still more the time required for their relaxation, is many times the period of the recurrence of the electric discharges of the Torpedo, so that the rapidly changing phases of the discharge cannot be distinguished by this method.

The second indicator used by Marey was the electromagnetic signal of M. Deprez, which can register 500 electric currents in a second by the motion of a tracing point over the smoked surface of a revolving cylinder. The action of this instrument was sufficiently prompt to register the number of the separate currents of which the "continued discharge" of the Torpedo consists. It was not, however, sufficiently sensitive to trace the curve of the intensity of the current when the strength of the current was less than that required to work the tracing point, and the trace therefore represents only the phases of greatest strength of current in each separate discharge.

M. Marey calls each separate discharge of the Torpedo an electric flux.

The whole discharge consists of a rapid succession of these fluxes, at the rate of from 60 to 140 per second, gradually decreasing in intensity, but remaining sensible sometimes for a second or a second and a half. In one of the tracings 120 fluxes may be counted quite distinctly, with a somewhat irregular continuation of feebler fluxes.

The electromagnetic signal, however, depending on the attraction of a soft iron armature, is acted on by a force varying nearly as the square of the strength of the current. It is therefore unable to respond to feeble currents, and it does not indicate the direction of the currents, even when improved in certain particulars by M. Marey.

The third indicator used by M. Marey was the capillary electrometer of M. Lippmann. In this instrument a capillary glass tube is filled in one part with mercury and in the other with dilute sulphuric acid. The pressure of the mercury is so adjusted that the division between the

Phil. Trans., 1834.

London Medical Gazette, 1838.

+ Comptes Rendus, 1836.
§ Berlin Monatsb., 1858.

Travaux du Laboratoire de M. Marey, III. (1877).

two liquids appears in the middle of the field of a microscope. The electrodes of the instrument are connected with the two liquids respectively, and when a small electromotive force acts from one electrode to the other, the surface of separation of the two liquids is seen to move in the same direction as the electromotive force, that is to say, the mercury advances if the electromotive force is from the mercury to the acid, and retreats if it is in the opposite direction.

This instrument, therefore, is admirably suited for the investigation of small electromotive forces, and the mass of the moving parts is so small that it responds most promptly to every variation of the electromotive force. Its only defect is that its range is limited to the electromotive force required to decompose the acid, and the electromotive force of the Torpedo, as we know, is of far greater intensity than this. M. Marey therefore used a shunt, so as to diminish the force acting on the electrometer to such a degree as to be within the working limits of the instrument.

He thus ascertained that the back of the fish is positive with respect to the belly, not only on the whole, but during every phase of each flux, and that it does not sink to zero between the fluxes.

The modern researches on the electric fishes would seem to point to the conclusion that the electric organ is not like a battery of Leyden jars in which electricity is stored up ready to be discharged at the will of the animal, but rather like a Voltaic battery, the metals of which are lifted out of the cells containing the electrolyte, but are ready to be dipped into them.

There seems to be no electric displacement in the organ till the electric nerve acts on it. The energy of the electric discharge which then takes place is not supplied to the organ by the nerve; the nerve only sets up an action which is carried on by the expenditure of energy previously supplied to the organ by the materials which nourish it.

During the discharge certain chemical changes take place in the organ. These changes involve a loss of intrinsic energy, and the chemical products found in the organ after repeated electric discharges are similar to the products found in muscles after they have performed mechanical work.

The organ, by repeated discharges, becomes incapable of responding to stimulation, and can only recover its power by the gradual process by which it is nourished.

Faraday proposed to try whether sending an artificial current through the Gymnotus would exhaust the organ, if sent in the direction of the natural discharge, or would restore it more rapidly to vigour if sent in the opposite direction. The only experiments on the effect of electricity on electric fishes seem to be those of Dr Davy, who found that an artificial current did not excite the electric organs of the Torpedo, though it had an effect on the muscles, but less than on those of other fishes, and of Du Bois Reymond, who found that Malap