terurus was very slightly affected by induction currents passing through the water of his tub, though they were strong enough to stun and even to kill other fishes. When the induction currents were made very strong, the fish swam about till he had placed his body transverse to the lines of discharge, but did not appear to be much annoyed by them*.

The most valuable experiments hitherto made are probably those of Dr Carl Sachs, who went out to Venezuela in 1876 for the express purpose of studying the Gymnotus in its native rivers, with all the resources of Du Bois Reymond's methods. Dr Sachs lost his life in an Alpine accident in 1878, and as he did not himself publish his researches, it is to be feared that their results are lost to science.

NOTE 30, ART. 560.

Excess of redundant fluid on positive side above deficient fluid on negative side of a coated plate.

When two equal disks have the same axis, the first being at potential V and the other connected to the earth, the algebraic sum of the charges of the two disks is just half the charge of the two disks together if they were both raised to potential V.

If the two disks are very near each other, the charge of the two together is very little greater than that of one by itself at the same potential.

Hence the excess of the redundant fluid above the deficient, when one of the disks is raised to potential V and the other connected with the earth, is very little greater than aV, where a is the radius. (See Note 4.)

NOTE 31, ART. 573.

Intensity of the Sensation produced by an Electric Discharge.

Cavendish tried this and several other experiments (Arts. 406, 573, 597, 610, 613) to determine in what way the intensity of the sensation of an electric shock is affected by the two quantities on which the physical properties of the discharge depend, namely the quantity of redundant fluid discharged, and the degree of electrification before it is discharged, the resistance of the discharging circuit being supposed constant.

He seems to have expected (Art. 597) that the strength of the shock would be "as the quantity of electricity into its velocity," or in modern language, as the product of the quantity into the mean strength of the current of discharge. Since the electromotive force acting on the body of the operator is measured by the product of the strength of the current into the resistance of the body, which we may

* A somewhat extensive account of the subject is given in a dissertation, De' Pesci elettrici e pseudoelettrici, per Stefano St. Sihleanu (di Bucuresti, Romania), Napoli, 1876.

suppose constant, Cavendish's hypothesis would make the intensity of the shock proportional to the work done by the discharge within the body.

According to this hypothesis, if a jar charged to a given degree produces a shock of a certain intensity, then a charge equal to n times the charge of this jar, communicated to n2 similar jars, and discharged through the same resistance, would give a shock of equal intensity.

By the experiment recorded in Arts. 406 and 573, in which n = 2, it appeared that the shock given by four jars charged with the electricity of two jars, was rather greater than that of a single jar.

In the experiment in Art. 610 Cavendish compared the shock of jar 1 electrified to 2, with that of B +24 electrified to the same degree and communicated to the whole battery. Here the capacity of B+ 24 was equal to 6 times jar 1, and that of the whole battery was 154 times jar 1, so that 6 times the quantity of electricity communicated to 154 jars gave a shock of about the same strength, though as Cavendish remarks, as there is a good deal of difference between the sensations of the two, it is not easy comparing them."

Here 154 is the 27 power of 6, so that the shock seems to depend rather more on the quantity of electricity than on the degree of electrification. This is the only experiment which Cavendish has worked out to a numerical result.

By the other experiments recorded in Art. 610, 34 communicated to 7 rows, gives a shock equal to 22 communicated to one row. This would make the number of jars as the 4.3 power of the charges. By Art. 613 the number of jars would be as the 3-3 power of the charge.

Cavendish had not the means of producing a steady current of electricity, such as we now obtain by means of a Voltaic battery, so that he could not discover the most important of the facts now known about the physiological action of the current, namely, that the effects of the current, whether in producing sensations, or in causing the contraction of muscles, depend far more on the rapidity of the changes in the strength of the current than on its absolute strength. It is true that a steady current, if of sufficient strength, produces effects of both kinds, but a current so weak that its effect, when steady, is imperceptible, produces strong effects, both of sensation and contraction, at the moments when the circuit is closed and broken.

But although this may be considered as established, I am not aware of any researches having been made, from the results of which it would be possible to determine, from the knowledge of the physical character of two electric discharges, which would produce the greater physiological effect.

The kind of discharges most convenient for experiments of this kind is that in which the current is a simple exponential function of the time, and of the form

x - Ce

COMPARISON OF ELECTRIC SHOCKS.

439

where x is the strength of the current at the time t, C its strength at the beginning of the discharge, and a small time, which we may call the time-modulus.

In this case the whole physical nature of the discharge is determined by the values of the two constants C and T. The intensity of the sensation produced by the discharge through our nerves is, therefore, some function of these two constants, and if we had any method of ascertaining the numerical ratio of the intensities of two sensations, we might determine the form of this function by experiments. We can hardly, however, expect much accuracy in the comparison of sensations, except in the case in which the two sensations are of the same kind, and we have to judge which is the more intense.

According to Johannes Müller, the sensation arising from a single nerve can vary only in one way, so that, of two sensations arising from the same nerve, if one remains constant, while the other is made to increase from a decidedly less to a decidedly greater value, it must, at some intermediate value, be equal in all respects to the first.

In the ordinary mode of taking shocks by passing them through the body from one hand to the other, the sensations arise from disturbances in different nerves, and these being affected in a different ratio by discharges of different kinds, it becomes difficult to determine whether, on the whole, the sensation of one discharge or the other is the more intense.

I find that when the hands are immersed in salt water the quality of the sensation depends on the value of T.

When is very small, say 0·00001 second, and C is large enough to produce a shock of easily remembered intensity in the wrists and elbows, there is very little skin sensation, whereas when is comparatively large, say 001 second, but still far too small for the duration of discharge to be directly perceived, the skin sensation becomes much more intense, especially in any place where the skin may have been scratched, so that it becomes almost impossible so to concentrate attention on the sensation of the internal nerves as to determine whether this part of the sensation is more or less intense than in the discharge in which T is small.

There are two convenient methods of producing discharges of this type.

(1) If a condenser of capacity K is charged to the potential V, and discharged through a circuit of total resistance R (including the body of the victim),

The whole quantity discharged is Q Cr resistance of the body of the victim, the work

in the body is

VK, and if is the done by the discharge

(2) If the current through the primary circuit of an induction coil is y, the coefficient of mutual induction of the primary and secondary coils M, that of the secondary circuit on itself L, and the resistance of the secondary circuit R, then for the discharge through the secondary circuit when the primary circuit is broken,

I first tried the comparison of shocks by means of an induction coil, in which M was about 0.78 and L about 52 earth quadrants, and in which the resistance of the secondary coil was 2710 Ohms. By adding some German silver wire to the primary coil, its resistance was made up to nearly 1 Ohm, and the primary thus lengthened, another wire of the same resistance, and a variable resistance Q were made into a circuit. One electrode of the battery was connected to the junction of the two equal resistances, and the other was connected alternately to the two ends of the resistance Q, so that the current through the primary was varied in the ratio of the primary P to P+Q, while the resistance of the batterycircuit remained always the same. When the smaller primary current, y, was interrupted, I took the secondary discharge through my body directly, but when the larger current, y, was interrupted, I made the secondary discharge pass through a capillary tube filled with salt solution as well as my body.

The resistance between my hands when both were immersed in saltwater was 1245 Ohms, making with the secondary coil a resistance of 3955 in the secondary circuit, so that the time-modulus of the discharge was T = 1.3 x 10-3 seconds.

T=

The resistance of the first capillary tube was 370000, so that when it was introduced T = 1.4 × 10

By a rough estimate of the comparative intensity of the shocks I supposed them to be of equal intensity when y' 8.4y, and therefore if we suppose that two shocks remain of equal intensity when C varies as T", p = 0·468.

By another experiment in which a tube was used whose resistance was 450000, p=0·534.

When the shocks at breaking contact were nearly equal, that at making contact was very much more intense with the small primary current and small secondary resistance than with the large primary current and large secondary resistance.

I then compared the discharges from two condensers of 1 and 0.1 microfarads capacity respectively, charging them with a battery of 25 Leclanché cells, the electromotive force of which was about 36 Ohms.

The resistance of the discharging circuit for the microfarad was 11200 Ohms, including my body, so that

T = 1·12 × 10-2 seconds.

COMPARISON OF ELECTRIC SHOCKS.

441

The resistance of the discharging circuit of the tenth of a microfarad was 3600, so that r' = 3.6 × 10−1.

The values of C were inversely as the resistances, so that if the two shocks were, as I estimated them, nearly equal, the value of p would be 0.670.

This experiment was much more satisfactory and more easily managed than that with the induction-coil, and I thought it desirable to apply the same method to the comparison of the contractions of a muscle when its nerve was acted on by the discharge. I therefore availed myself of the kindness of Mr Dew-Smith, who prepared for me the sciatic nerve and gastrocnemius muscle of a frog, and attached the preparation to his myograph. The discharge was conducted through about 04 cm. of the nerve by means of Du Bois Reymond's unpolarizable electrodes, the resistance of the electrodes and nerve being 35000 Ohms. When the electrodes were in contact their resistance was 23000, leaving about 12000 as the resistance of the nerve itself.

I used two condensers, one 01 microfarad, and the other an aircondenser of 270 centimetres capacity in electrostatic measure, or about 3 x 10-* microfarads.

The first was charged by one cell and the second by 25. The resistances were arranged so that the contractions produced in the muscle were much less than a third of a maximum contraction. The discharges were made alternately every 15 seconds, and when the resistances were 35000 and 140000 respectively, the alternate contractions as recorded on the myograph were as follows:

Here the time-modulus was 1.05 x 10-5 seconds for the small condenser and 14 x 10-2 for the large one, and the values of C were as 1 to 100, so that p = 640.

If we suppose that Cavendish took the shocks through pieces of metal held in his hands, the resistance of the circuit would depend on the state of his skin. He occasionally used a piece of apparatus, which he nowhere describes, but which he names in three places* a shock-melter.

From Art. 585 it would appear that it was filled with salt water, even when fresh water was the subject of the experiment, and from Art. 637 Cavendish seems to have considered it his last resource as a method of receiving shocks. I therefore think that it must have

*Arts. 585, 622, 637. See facsimile at p. 326.