solenoid is to reduce the amplitude of the second half-oscillation considerably, for when the iron is removed and discharges passed the deflection falls from 200 to 150, and when the iron is in the solenoid from 200 to 162.

We must now consider to what this effect is due. If the iron increased the inductance of the circuit the effect would be to increase the amplitude of the second half-oscillation rather than decrease it. The iron cannot sensibly alter the inductance of the circuit, for we observe that the effect of the first half-oscillation is diminished very slightly—in this particular case from 200 to 100 to 200 to 103.

The result must therefore be due to an absorption of energy by the iron core, and a consequent increase of actual resistance in the circuit. The absorption of energy represents an addition of real resistance to the circuit, and increases the rate of dissipation of energy in the circuit.

The energy absorbed by the conductor may then be readily compared with the energy absorbed when a resistance of very small inductance is placed in the circuit—e.g., a carbon pencil, or a tube containing an electrolyte.

The final deflection when the cylinder was in the solenoid was carefully observed. The cylinder was removed, and a short length of carbon rod of high resistance introduced into the circuit until the added resistance caused the final deflection to be the same as when the metal cylinder was in the solenoid.

Since the damping is identical in the two cases, the added resistance must absorb the same amount of energy as the metal core. The absorption of energy in the metal core therefore increases the impedance of the circuit, and this increase of impedance may be expressed in ohms.

The resistance of the carbon rod or electrolyte was determined for steady currents, and, since the conductivity is small, it will be found, by substitution in the equations given by Lord Rayleigh, that its resistance is practically the same for steady currents as for a frequency of 2,000,000 per second, which is very approximately the frequency of the discharge.

Proceeding in this way, the absorption of energy by various conductors was compared.

Table of Absorption of Energy by Various Conductors. (The absorption of energy is proportional to the increase of impedance of the circuit.)

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Professor J. J. Thomson (“Recent Researches,” pp. 321, 322) shows that the increase of impedance of the primary circuit due to absorption of energy by an iron cylinder of length l and radius a

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= 4π²lN² (pμσ/2π)^½a

where p = 2πn; n being the number of oscillations per second;

N = number of turns per centimetre cf solenoid;

μ = permeability of iron;

σ = specific resistance of iron.

Now, we have shown that a soft-iron cylinder increases the impedance of the circuit by 3.9 ohms.

From this equation we can deduce a rough approximation of the value of μ for iron in fields of high frequency.

The number of oscillations per second was 2,000,000, calculated from data of discharge circuit.

σ is approximate for soft iron, 10⁴;

l = 14cm.;

a = 0.95cm.;

N = 2, nearly.

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∴ 3.9×10⁹ = 4π²× 14.(2)² (2π.2.10⁶.10⁴μ/2π)^½

An approximate solution of this is μ = 172, which shows that iron has considerable permeability even under the influence of these very transient fields.

It is interesting to observe that it is not necessarily the best conductors that absorb the most energy in these fields: in fact, the very reverse is the case. A copper cylinder does not absorb more than one-fortieth of the energy that an