Therefore
| m = | HP | = | d1²HE | tan θ, |
| (1 / d1²) − (d1 / d2³) | 1 − (d1 / d2)³ |
and
| I = | ld1² HE | tan θ. |
| v {1 − (d1 / d2)³ } |
(47)
This last method of arrangement is called by Ewing the “one-pole” method, because the magnetometer deflection is mainly caused by the upper pole of the rod (Magnetic Induction, p. 40). For experiments with long thin rods or wires it has an advantage over the other arrangements in that the position of the poles need not be known with great accuracy, a small upward or downward displacement having little effect upon the magnetometer deflection. On the other hand, a vertically placed rod is subject to the inconvenience that it is influenced by the earth’s magnetic field, which is not the case when the rod is horizontal and at right angles to the magnetic meridian. This extraneous influence may, however, be eliminated by surrounding the rod with a coil of wire carrying a current such as will produce in the interior a magnetic field equal and opposite to the vertical component of the earth’s field.
If the cardboard scale upon which the beam of light is reflected by the magnetometer mirror is a flat one, the deflections as indicated by the movement of the spot of light are related to the actual deflections of the needle in the ratio of tan 2θ to θ. Since θ is always small, sufficiently accurate results may generally be obtained if we assume that tan 2θ = 2 tan θ. If the distance of the mirror from the scale is equal to n scale divisions, and if a deflection θ of the needle causes the reflected spot of light to move over s scale divisions, we shall have
s / n = tan 2θ exactly,
s / 2n = tan θ approximately.
We may therefore generally substitute s/2n for tan θ in the various expressions which have been given for I.