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 7.

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 0.01 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),

V
R'

T = KR.

The whole quantity discharged is QCT VK, and if is the resistance of the body of the victim, the work done by the discharge in the body is

(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.

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.

The resistance of the discharging circuit of the tenth of a microfarad was 3600, so that r' = 3.6 × 107.

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 0.4 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.

been an apparatus by which his hands were well wetted with salt water, so that the resistance of his body would be between 1000 and 2000 Ohms.

The capacity of his battery of 49 jars was 321000 glob. inc., which comes to rather less than half a microfarad.

The discharges of this through 2000 Ohms would have a timemodulus of about one-thousandth of a second.

The following table gives the different results obtained by Cavendish and by myself, with the time-modulus of the discharges compared. The quantity p is such that the ratio of the initial strength of the two discharges is inversely as the p power of the ratio of the time-moduli when the shocks are equal in intensity, or

The number of jars among which a quantity of electricity must be divided in order to give a shock of a given intensity through a given

1

resistance, varies as the

power of the quantity of electricity.

1-p

Experiments on the prepared nerve and muscle of a frog.

0.00001

0.014

0.640

This value of p does not differ much from 0-652, the only result which Cavendish has deduced in a numerical form from his experiments.

The most unaccountable of all the results arrived at by Cavendish is one which seems to have perplexed him so much that he has left the account of the experiments among which it occurs in a very imperfect state. He found (Arts. 639, 644) that the shock of a Leyden jar taken through a long thin copper wire produced a more intense sensation than when it was taken from the jar directly.

As in some of the experiments the wire was wound on a reel, and therefore the self-induction of the current might produce an oscillatory discharge, the physiological effects of which might be different from

those of the simple discharge; I charged two Leyden jars to the same potential, using Thomson's Portable Electrometer as a gauge electrometer, and took the discharge of one through the secondary wire of an induction-coil, the resistance of which was about 1000 Ohms, and that of the other through an ordinary resistance-coil of 1000 Ohms.

In every trial I found that the sensation was more intense when taken through the ordinary resistance-coil than when taken through the induction-coil, and it is manifest that in the latter case the current begins and ends much less abruptly, so that the result is quite in accordance with the modern theory, that the sensation depends on the rapidity with which the strength of the current changes. I am, therefore, quite unable to account for the opposite result obtained by Cavendish. At the same time it is quite impossible that Cavendish could be mistaken in this comparison of the intensity of his sensations, for he had more practice than any other observer in comparing them, and he repeated this experiment many times.

The only apparent objection to the experiment is that the resistance of the copper wires was only 430 in one case and only 1000 in the other, whereas the resistance of a man's body, from one hand to the other, varies from about 1000 when the hands are thoroughly wet, to about 12000 when they are dry, so that the resistance of the copper was small compared with the possible variations of the resistance of Cavendish's body.

The resistances of the tubes filled with solutions of salt, &c., were very much greater, being from 20000 to 900000.

NOTE 32, ARTS. 398, 576, 687.

Comparison of the Resistance of Iron Wire and Salt Water.

Cavendish never published the method by which he made this comparison, but the result given in Art. 398 seems to have been accepted by men of science on Cavendish's bare word, without any question as to how it was obtained.

It appears from Art. 576 that Cavendish made his body and the iron wire the branches of a divided circuit, and then tried how many inches of salt water must be put in the place of the iron wire, so that the shock might appear of the same strength.

By Matthiessen's experiments on the resistance of metals, the resistance of an iron wire of the dimensions given by Cavendish would be about 196 Ohms. As this is much less than that of a man's body from hand to hand, it would have made hardly any difference to the shock whether Cavendish took it through his body alone, or through his body and the iron wire in series.