On the addition of a carbon resistance of 8.5 ohms to the discharge circuit, the fall of the deflection was—(1) From 200 to 103; (2) from 200 to 176½.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

Since the fall of deflection is the same in the two cases, resistance of iron wire = 8.5 ohms + resistance of the copper, wire for that particular period. Now, from Lord Rayleigh's equations, the resistance of copper wire in rapidly alternating fields is given by R′ = √½p l R, where l = length of wire, and R is resistance of wire for steady currents. From knowledge of the period this may readily be calculated. The resistance of the iron wire is therefore known.

In order to determine the period very accurately, a plate condenser was used with ebonite as the dielectric. The S.I.G. of ebonite had been determined previously and found to be 2.2. The capacity of the condenser was found from calculation of the size of the plates to be 460 electrostatic units.

From knowledge of the data of the discharge circuit the self-inductance can be calculated. (See Lodge's “Experiments on Discharge of Leyden-jars,” Proc. Roy. Soc., June 4, 1891, p. 33.)

The self-inductance L = 4278;

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

frequency n = 2π √LC

= 3.5 × 10⁶;

and p = 2μn = 2.1 × 10⁷.

The effect of the increase of diameter of wires on the self-inductance of the circuits is small, so that in all cases the number of oscillations per second will be taken as 3,500,000. When the resistances of iron wires of different sections were being determined a copper wire of as near as possible the diameter of the iron wire under consideration was placed in the circuit. In the case of an iron wire 0.22in. in diameter, a lead pipe took the place of the copper conductor.

After the calculated resistance of the copper wires for a frequency of 3,500,000 had been added to the carbon resistance placed in the circuit, the following is the table of resistances observed:—

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

It will be observed that for the soft-iron wire 0.222in. in diameter the resistance of the wire is 125 times its resistance for steady currents.

The wire 0.145in. in diameter is seventy times its ordinary resistance, and wire 0.039in, about eight times.

The general result of this investigation supports the theory of increase of resistance of conductors as the rapidity of the oscillations is increased.

The experiments here recorded receive additional confirmation from later investigations on the circular magnetization of iron.

It will be observed that the wire 0.011in. in diameter does not double its ordinary resistance for a frequency of 3,500,000, and the resistances increase more rapidly for increase of diameter than ordinary theory would lead-us to expect.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

Lord Rayleigh has shown that the resistance of a wire of permeability μ for rapidly-alternating fields is √½ μPlR, where R = resistance for steady currents.

Now, for wire of diameter 0.222in;

and substituting p = 2.1 × 10⁷,

l = 377,

R = 0.032 ohm,

we get an equation for μ and it will be found that in this case μ = 121; and, if we thus determine μ for the different soft-iron wires, we get the following table:—

It will be observed that the apparent permeability of the wire increases proportionately to the radius. Where the radius of wire is increased twenty times, permeability is increased twenty times, and so on.

I am not aware that anything definite on this subject has been hitherto done; but the following approximate calculation possibly gives the true explanation:—

Consider a condenser charged with a quantity Q0 of electricity.

The maximum current of discharge J = pQ0, assuming no decrease in amplitude.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

Now, if this current be confined to a surface-skin of the conductor, the magnetic force, at a distance r from the centre, is given by H = 2J/r.

Now, this value of H at any point only depends on the current flowing external to that point; and, since the current is mainly confined to the surface, we may take r = radius of wire.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

H = 2pQ₀/r = 2/r PCV₀, where V₀ is potential between knobs,

and C is capacity of condenser.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

As the spark-gap was 1/10in. in length, the difference of potential was as near as possible 10,000 volts. Substituting these values, it will be found that H = 18.8/r nearly.

For the first wire r = 0.011in. = 0.027cm.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

∴ H = 18.8/0.013 = 1,400 approximately;

and, taking B = 12,000, we get a value of

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

μ = B/H = 9 approximately.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

The observed value is about 6; but the discrepancy between the two results is to be expected, and is due to the fact that the resistance of the iron is measured after a succession of discharges in the same direction, when, on account of the greater amplitude of the first half-oscillation, the inner part of the wire is practically saturated, and does not offer any considerable permeability when once the current has penetrated through the external skin, magnetized in the opposite direction by the second half-oscillation. The equations H = 2J/r and μ = B/H = Br/2J show that we should expect the permeability of the iron to vary as the radius of the wire, within, of course, the maximum limit of permeability of iron—i.e., about 3,000. The table given previously shows how closely the law is fulfilled in practice.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

Now, J = pQ₀ = 1/√LC CV₀, and V₀ varies as the spark length d.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

∴ J ∝ √C/√L . d,

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

and μ= Br/2J, and when the iron is saturated B may be takenas constant.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

∴ μ ∝ r√L/d√C.

Therefore increase of radius increases the permeability of iron in these fields, and the shorter the spark-gap the higher the permeability, and therefore the resistance.