posed on the existing permanent magnetisation, and therefore increases the moment M. The correction due to this is, however, only small in observations on terrestrial magnetism; nevertheless, it is always better to place the auxiliary magnet in a nearly east and west position. The transverse magnetisation then produced has scarcely any effect. For instance, the auxiliary magnet may be suspended in this position to a bifilar or torsion arrangement, the directive torque of which is known (note 3, p. 297). The latter is multiplied with the tangent of half the deflection produced by reversing the magnet to the west and east direction. The product gives then directly the value M H.

§ 191. Observations of Deflection.-After the auxiliary magnet has been taken away, the magnetometer M is put in its place. Its magnetic system then sets itself in the direction of the field, which we have called the magnetic meridian, and which is marked NS in fig. 61. In order now to produce a deflection of the magnetic system, the auxiliary magnet is placed in one of two different positions, its own direction in both cases being either west-easterly or east-westerly.

1. First Principal Position.-Auxiliary magnet at distance. D, in W or O at right angles to the meridian. The component , induced by it at M is also at right angles to the meridian, and amounts to [equation (5), § 22]

1

in which L is the geometrical (or 'virtual,' § 210) length of the auxiliary magnet.

2. Second Principal Position.—Auxiliary magnet at N or S at distance D, at right angles to the meridian, as well as the component, due to it, which in this case has the following value [equation (6), § 22]1:

The deflections a, or a, due to the second component are obviously given by the following equations:

From equations (3,) or (3) and (4), neglecting the factors in the brackets, we get, as a first approximation,

After having expressed MH and M/H as functions of determinate quantities, not only the intensity 5, but also incidentally the moment of the auxiliary magnet, may be calculated. If the latter is already known, is obviously obtained from equation (5) without further determinations.

These simplified equations, however, only hold for distances which are very great in comparison with the length of the deflecting magnet (§ 22); but as the deflections obtained at such distances are usually too small, the magnet must be brought nearer the magnetometer, so that several members of the series in equation (3) or (3) have to be brought into account. The length of the magnet is, however, usually eliminated by observing at two successive distances (Kohlrausch, loc. cit., p. 231).

Gauss's method is used mostly for determining the absolute value of the earth's horizontal intensity. It may, however, in principle be applied to measuring the horizontal components of

An elementary deduction of equations (3,) and (3) is found, for instance, in F. Kohlrausch, loc. cit. pp. 389, 390.

uniform fields due to any agent, provided their intensity does not exceed 1 C.G.S. If the field is stronger, it is scarcely possible to produce sufficient deflection by means of magnets of the usual size.

B. Electrodynamic Methods

§ 192. Measurement of a Dynamical Force. It was mentioned in § 1 that the magnetic field can be completely defined by the two chief forms in which it manifests itself the electrodynamic and the inductive; and for the practical methods of

F

W

о

S

FIG. 62

Роз

measurement based on this, reference was made to the present chapter.

As regards electrodynamic methods, we will mention the following simple arrangement, due to Lord Kelvin.? In the field F a metal wire hangs between two pole-pieces, supposed horizontal and at right angles to the plane of fig. 62. By means of two mercury cups C, C a current of known strength I (in decamperes) is passed. If then the intensity of the field is, its effective height L, and its direction is such that a force, &, expressed

in dynes, is exerted, say, towards the left on the wire, this, from electro-dynamical principles, is given by the equation

This force is held in equilibrium by the tension of the threads t, and t, which are fastened to the string pendulums PP or P2 P. It needs no explanation how that force can be

1 By electrodynamic action all forces are understood which are exerted on conductors conveying currents in the magnetic field, no matter whether the field is due to other conductors, or depends on other sources, such as rigid magnets.

2 A. Gray, Absolute Measurements in Electricity and Magnetism, vol. 2, p. 701, London, 1893.

MEASUREMENT OF A TORQUE

297

determined in absolute measure from the readings on the scales S1 and S2, as well as from the weights P, and P.

1

The wire conveying the current may also be stretched. By the action of the electrodynamic forces it will then sag laterally, like a tight string. The elongation, which may be measured by a microscope, or by mirror reading, is, as a first approximation, proportional to the force, and therefore, with a constant current, proportional also to the intensity of the field. This principle has been applied in Ewing's magnetic curve-tracer (§ 214). The method described is suitable for fields of the order of 100 C.G.S. units and upwards.

§ 193. Measurement of a Torque. The simple method which has been described is obviously not very accurate. More trustworthy results are obtained when the conductor is bent into a loop of one or more turns; and the couple exerted in general on such a loop-that is to say, on a coil in the field-is determined by one of the known methods, such as weighing, torsion, or bifilar suspension.

Stenger has described a special apparatus based on this last principle,' which may be regarded as an inversion of the wellknown 'syphon recorder' of Lord Kelvin, and of the bifilar galvanometer of F. Kohlrausch.2 A small coil is suspended by two wires, which at the same time convey the current I, which is separately measured. Let the plane of the coil be parallel to the field; let the total area of the windings be S, the directive torque 3 of the bifilar D, and the deflection observed be a. The field-intensity to be measured is then given by the equation

Stenger thus succeeded in determining in absolute measure fields of the order of 100 C.G.S. to within 0.1 per cent. with certainty and convenience. The sensitiveness of such methods may be lowered at will by diminishing the current through the

Stenger, Wied. Ann. vol. 33, p. 312, 1888. Compare also Himstedt, Wied. Ann. vol. 11, p. 829, 1880.

2 F. Kohlrausch, Wied. Ann. vol. 17, p. 752, 1882.

* In a suspended system directed by any appliance we suppose the directive torque referred to unit deflection expressed in circular measure (57·296°).

coil, and they may thus also be used for measuring the most intense fields.

Torsion, applied as directive torque, has been used in measurements of fields, which A. du Bois-Reymond' has published. The arrangement in this case may be regarded as an inversion of the Deprez-d'Arsonval galvanometer. On a similar principle Edser and Stansfield have recently constructed a convenient portable instrument for measuring a field. A plate of mica supports a coil of thin copper wire, which is stretched by two German silver wires conveying the current. One of the wires is fastened to a torsion head, which at the same time is ingeniously made to serve as commutator. A Hellesen dry cell furnishes a nearly constant current of, at most, two centiamperes, since the coil itself has a resistance of 50 ohms. By inserting independent resistances the sensitiveness can be diminished, if necessary. The instrument, it is stated, measures fields of any direction from 1 C.G.S. upwards, with an accuracy of about two per cent. It is especially suitable for measuring leakage in and about dynamo machines, as Edser and Stansfield show (loc. cit.) by some examples.

E

R

§ 194. Measurement of a Hydrostatic Pressure. The method of measuring force just mentioned may, lastly, be so modified that, instead of a solid wire conductor, a liquid one-mercury-is used. This is contained in a flat insulating cavity perpendicular to the direction of the field, which is again assumed to be horizontal, and at right angles to the plane of the figure. The width of the cavity d does not exceed a fraction of a millimetre. Let the current traverse the mercury in a vertical direction, for which purpose two platinum electrodes, E, and E, (fig. 63), are in contact with it. By electrodynamic action a lateral thrust is exerted on the mercury, driving it out, so that a difference of level results between the tubes R, and R2, which represents a pressure P

E2

FIG. 63

A. du Bois-Reymond, Elektrotech. Zeitschrift, vol. 12, p. 305, 1891. 2 Deprez and d'Arsonval, Compt. Rend. vol. 94, p. 1347, 1882. 3 Edser and Stansfield, Phil. Mag. [5], vol. 34, p. 186, 1892.