There was also a marked difference between the effects produced by discharges in opposite directions on the same saturated needle.

(1.) When the first half-oscillation tended to magnetize the needle in the same direction as it already was magnetized the first half-oscillation had no effect on the needle, it being already saturated. The second half-oscillation tended to demagnetize the needle, the third to magnetize it, and so on.

As an example of the effect of continued sparks in this direction we have the following:—

(2.) When first half-oscillation tended to demagnetize the needle the effect on the reduction of the deflection is much greater; for example:—

The deflection did not fall below 10 div., however many sparks were passed. The iron has then arrived at the steady state. The gradual demagnetization of iron by successive discharges is well illustrated by the above table. The cause of the effect was not at first clear, but further experiment showed that it was due to the very rapid damping of the oscillations. The first oscillation demagnetizes the surface-layers, and probably magnetizes a thin surface-shell to saturation in the opposite direction. The second half-oscillation wipes out some of this opposing magnetism, but to no appreciable depth, since the amplitude of the oscillation is by that time greatly reduced. The third half-oscillation tends to magnetize the iron again, and so on.

When another discharge is passed through the solenoid the first half-oscillation has first of all to demagnetize and magnetize the surface-layers in opposite direction to magnetism of needle. When it has penetrated through the thin surface-shell the magnetic force meets with a layer of iron of

low permeability, since the greater part is already magnetized nearly to saturation in the same direction by the action of the first half-oscillation of the first discharge. It therefore penetrates further, for we know the magnetic force penetrates deeper in a conductor like copper (μ = 1) than in a conductor like iron, where μ may be considerable. More iron is demagnetized and the deflection reduced. This continues as spark after spark is passed, till finally the discharge cannot penetrate any further. This corresponds to the steady state. It was found, by dissolving a needle acted on in this way by a succession of discharges, that the deflection rose steadily as the needle was eaten away, showing that the surface-layer was magnetized in an opposite direction to the central part.

In the experiment above detailed it was found that the discharge had penetrated to about one-quarter of the radius—i.e., a distance of 0.008in. When thin steel needles were experimented on they were often totally demagnetized and magnetized in the opposite direction by successive discharges: e.g., thin steel needle, 0.008in. diameter:—

Soft iron as well as steel needles exhibited the same effect.

The difference between the effect of the first and the second half-oscillation in demagnetizing iron is very marked. The experiments show clearly how rapidly the oscillations decay in amplitude. When we are dealing with capacities of about 1,000 electrostatic units and small inductance in the circuit it seems very probable that there is only one complete oscillation. The others are damped down to such an extent as to be inappreciable. The fact that the deflection due to the needle always falls, whatever the direction of the first oscillation, shows clearly that the discharge is oscillatory. If there was only a unidirectional discharge the needle should only be affected when the discharge is in one direction.

Simple experiments of this nature on ordinary steel needles

show that a leyden-jar discharge is oscillatory, and show also the rapid decay of the amplitude of the vibrations.

A method of deducing the ratio of the second half-oscillation to the first will be given later.

The subject of the decay of amplitude of the vibrations of a leyden-jar discharge is of considerable interest, especially in connection with the resistance of spark-gaps and the radiation of energy into space.

Let L = self-inductance of discharge circuit for rapid alternations;

C = capacity of condenser;

V_o = potential of jar;

R = resistance of connections and spark-gap to the discharge.

Then the current j at any instant is given by

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j = CV₀/(LC)^½ e ^—R/2L.t sin. t/(LC)^½

The exponential factor only includes the case of frictional dissipation of energy, and does not take into account radiation into space. In the experiments at present considered, where the condenser is a leyden-jar, the lines of force of which pass from one coating to the other, there can be a very small amount of dissipation of energy due to radiation (“Recent Researches,” J. J. Thomson, p. 482). We can obtain a fairly accurate estimate of the decay of amplitude of the vibrations from the experiments of eating away of needles by HNO₃, but a more useful estimate may be obtained from considerations of the loss of magnetism of a needle as determined by a magnetometer.

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Two small oppositely-wound solenoids, A and B, were placed in series connecting the coatings of an ordinary leyden-jar discharging through a spark-gap of 1/10in. Two steel needles similar in all respects and magnetized to saturation were taken and placed in the solenoids A and B, so that their north poles faced in the same direction.

Plate XLVIII., Fig 6.

When the leyden-jar was discharged through the spark-gap the first half-oscillation tended to magnetize the needle in A to a greater extent; but, as it was practically saturated, no; effect was produced. The second half-oscillation tended to demagnetize the needle, the third half-oscillation to magnetize it again, and so on.

On the needle in B, however, the first half-oscillation produced its full effect in demagnetizing, the second half tending to magnetize again, and so on.

On needle in A: First, third, fifth, seventh, & c., half-oscillations tend to magnetize needle in original direction; second, fourth, sixth, eighth, & c., tend to demagnetize needle.

On needle in B: Second, fourth, sixth, & c., tend to magnetize needle; first, third, fifth, & c., tend to demagnetize needle.

Now, the strength of field H in a solenoid of length large compared with its radius is given by

H = 4πnc

when n is number of turns per centimetre.

Now, suppose that the solenoids A and B are of the same number of turns per centimetre. Then the needle in B, since it is acted on by the first half-oscillation, will be demagnetized to a greater extent than the needle in A. The fall of the deflection in every case was readily determined by the small mirror magnetometer.

Let the number of turns per centimetre on solenoid B be reduced until there is exactly the same fall of deflection in each needle after one discharge. The maximum magnetizing force on needle in A = 4πnc, where c is maximum current of second half-oscillation; the maximum magnetizing force on needle in B = 4πn′c′, where n′ = number of turns per centimetre, and c′ = maximum current of first half-oscillation.

Now, since the effects on the needles are identical in the two cases, and the period is the same for both, the maximum magnetizing forces in the two solenoids must have been equal.

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∴ 4πnc = 4πn′c′.

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∴ c/c′ = n′/n′

or the maximum currents of the two half-oscillations are to one another inversely as the number of turns per centimetre on solenoids. There is, of course, an assumption here that the effect on the needles is ::^al to maximum magnetizing force when the period is constant. Experimentally it was found that the depth of penetration of magnetic force was ::^al to the maximum current ordinate when period was constant, and the assumption made is a very close approximation to the truth.

The connection between the depths of penetration when the periods varied was more complicated, and not expressed by any simple law.

In experimenting it was found advantageous to pass about twenty discharges instead of one, as the depth of penetration was greatly increased, and also the action of the first effective oscillation was in a great measure differentiated from the effect of the secondary ones.

Many experiments on the relation between the amplitudes

of the first and second half-oscillations were made under varying conditions. A few of these are incorporated in a “Note on the Resistance of Spark-gaps,” placed at the end of this paper.

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The general result obtained was that for a spark-gap of 1/10in., and inductance of about 4,000 C.G.S. units in circuit, the amplitude of the second half-oscillation was less than half that of the first.

As an example of a balance of the kind explained, when 2.15 turns per centimetre were on the one solenoid and 1.06 turns per centimetre on the other the effect on the needles was exactly equal.

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∴amplitude of second half-oscillation/amplitude of first half-oscillation} = 1.06/2.15 = 0.493,

or nearly one-half.

If this rate of decay holds for succeeding oscillations: the return oscillation has only one-quarter of maximum value of first oscillation.

Plate XLVIII., Fig. 7.

The curve, in Fig. 7 is a rough representation of the rapid decay of the oscillations. If the rate of decay continues for several oscillations the current will have a very small fraction of its original maximum value. It has been shown how a magnetized steel needle placed in a small solenoid may be used as a detector of an oscillatory discharge, and also as a means of determining the rate of decay of the oscillation.

A series of different experiments was then undertaken to show that iron possesses magnetic properties under the influence of all kinds of discharges.

The needle was placed in a solenoid connecting the extenial coatings of leyden-jars A and B, arranged as in Lodge's experiments on the “alternate path.”

Plate XLVIII., Fig. 8.

A and B are two leyden-jars connected in series through the solenoid D. When a spark occurs at C there is an impulsive rush of electricity through the solenoid D. The steel or soft-iron wire placed in the solenoid exhibited the same effect as when the discharge occurs in the ordinary way. The wire was always demagnetized, and the loss of magnetism was almost exactly the same as when the jars are connected in series in the ordinary way and discharged. There was the same rate of decay of amplitude also, and, as far as regards the effect on magnetized needles, the impulsive discharge is of the same nature as the ordinary discharge.

(2.) The needle was next placed in a small solenoid in series with one of the long wires reaching from the coatings of the