Part 2

The above method of determining the geographical meridian has the serious objection that it is necessary to know the error of the chronometer with very considerable accuracy, a matter of some difficulty when observing at any distance from a fixed observatory. If, however, a theodolite, fitted with a telescope which can rotate about a horizontal axis and having an altitude circle, is employed, so that when observing a transit the altitude of the sun or star can be read off, then the time need only be known to within a minute or so. Hence in more recent patterns of magnetometer it is usual to do away with the transit mirror method of observing and either to use a separate theodolite to observe the azimuth of some distant object, which will then act as a fixed mark when making the declination observations, or to attach to the magnetometer an altitude telescope and circle for use when determining the geographical meridian.

The chief uncertainty in declination observations, at any rate at a fixed observatory, lies in the variable torsion of the silk suspension, as it is found that, although the fibre may be entirely freed from torsion before beginning the declination observations, yet at the conclusion of these observations a considerable amount of torsion may have appeared. Soaking the fibre with glycerine, so that the moisture it absorbs does not change so much with the hygrometric state of the air, is of some advantage, but does not entirely remove the difficulty. For this reason some observers use a thin strip of phosphor bronze to suspend the magnet, considering that the absence of a variable torsion more than compensates for the increased difficulty in handling the more fragile metallic suspension.

_Measurement of the Horizontal Component of the Earth's Field._--The method of measuring the horizontal component which is almost exclusively used, both in fixed observatories and in the field, consists in observing the period of a freely suspended magnet, and then obtaining the angle through which an auxiliary suspended magnet is deflected by the magnet used in the first part of the experiment. By the vibration experiment we obtain the value of the product of the magnetic moment (M) of the magnet into the horizontal component (H), while by the deflexion experiment we can deduce the value of the ratio of M to H, and hence the two combined give both M and H.

In the case of the Kew pattern unifilar the same magnet that is used for the declination is usually employed for determining H, and for the purposes of the vibration experiment it is mounted as for the observation of the magnetic meridian. The time of vibration is obtained by means of a chronometer, using the eye-and-ear method. The temperature of the magnet must also be observed, for which purpose a thermometer C (fig. 1) is attached to the box A.

When making the deflection experiment the magnetometer is arranged as shown in fig. 2. The auxiliary magnet has a plane mirror attached, the plane of which is at right angles to the axis of the magnet. An image of the ivory scale B is observed after reflection in the magnet mirror by the telescope A. The magnet K used in the vibration experiment is supported on a carriage L which can slide along the graduated bar D. The axis of the magnet is horizontal and at the same level as the mirror magnet, while when the central division of the scale B appears to coincide with the vertical cross-wire of the telescope the axes of the two magnets are at right angles. During the experiment the mirror magnet is protected from draughts by two wooden doors which slide in grooves. What is known as the method of sines is used, for since the axes of the two magnets are always at right angles when the mirror magnet is in its zero position, the ratio M/H is proportional to the sine of the angle between the magnetic axis of the mirror magnet and the magnetic meridian. When conducting a deflexion experiment the deflecting magnet K is placed with its centre at 30 cm. from the mirror magnet and to the east of the latter, and the whole instrument is turned till the centre division of the scale B coincides with the cross-wire of the telescope, when the readings of the verniers on the azimuth circle are noted. The magnet K is then reversed in the support, and a new setting taken. The difference between the two sets of readings gives twice the angle which the magnetic axis of the mirror magnet makes with the magnetic meridian. In order to eliminate any error due to the zero of the scale D not being exactly below the mirror magnet, the support L is then removed to the west side of the instrument, and the settings are repeated. Further, to allow of a correction being applied for the finite length of the magnets the whole series of settings is repeated with the centre of the deflecting magnet at 40 cm. from the mirror magnet.

Omitting correction terms depending on the temperature and on the inductive effect of the earth's magnetism on the moment of the deflecting magnet, if [theta] is the angle which the axis of the deflected magnet makes with the meridian when the centre of the deflecting magnet is at a distance r, then

r³H P Q --- sin [theta] = 1 + --- + --- + &c., 2M r r²

in which P and Q are constants depending on the dimensions and magnetic states of the two magnets. The value of the constants P and Q can be obtained by making deflexion experiments at three distances. It is, however, possible by suitably choosing the proportions of the two magnets to cause either P or Q to be very small. Thus it is usual, if the magnets are of similar shape, to make the deflected magnet 0.467 of the length of the deflecting magnet, in which case Q is negligible, and thus by means of deflexion experiments at two distances the value of P can be obtained. (See C. Börgen, _Terrestrial Magnetism_, 1896, i. p. 176, and C. Chree, _Phil. Mag._, 1904 [6], 7, p. 113.)

In the case of the vibration experiment correction terms have to be introduced to allow for the temperature of the magnet, for the inductive effect of the earth's field, which slightly increases the magnetic moment of the magnet, and for the torsion of the suspension fibre, as well as the rate of the chronometer. If the temperature of the magnet were always exactly the same in both the vibration and deflexion experiment, then no correction on account of the effect of temperature in the magnetic moment would be necessary in either experiment. The fact that the moment of inertia of the magnet varies with the temperature must, however, be taken into account. In the deflexion experiment, in addition to the induction correction, and that for the effect of temperature on the magnetic moment, a correction has to be applied for the effect of temperature on the length of the bar which supports the deflexion magnet.

See also Stewart and Gee, _Practical Physics_, vol. 2, containing a description of the Kew pattern unifilar magnetometer and detailed instructions for performing the experiments; C. Chree, _Phil. Mag._, 1901 (6), 2, p. 613, and _Proc. Roy. Soc._, 1899, 65, p. 375, containing a discussion of the errors to which the Kew unifilar instrument is subject; E. Mascart, _Traité de magnétisme terrestre_, containing a description of the instruments used in the French magnetic survey, which are interesting on account of their small size and consequent easy portability; H. E. D. Fraser, _Terrestrial Magnetism_, 1901, 6, p. 65, containing a description of a modified Kew pattern unifilar as used in the Indian survey; H. Wild, _Mém. Acad. imp. sc. St Pétersbourg_, 1896 (viii.), vol. 3, No. 7, containing a description of a most elaborate unifilar magnetometer with which it is claimed results can be obtained of a very high order of accuracy; K. Haufsmann, _Zeits. für Instrumentenkunde_, 1906, 26, p. 2, containing a description of a magnetometer for field use, designed by M. Eschenhagen, which has many advantages.

_Measurements of the Magnetic Elements at Sea._--Owing to the fact that the proportion of the earth's surface covered by sea is so much greater than the dry land, the determination of the magnetic elements on board ship is a matter of very considerable importance. The movements of a ship entirely preclude the employment of any instrument in which a magnet suspended by a fibre has any part, so that the unifilar is unsuited for such observations. In order to obtain the declination a pivoted magnet is used to obtain the magnetic meridian, the geographical meridian being obtained by observations on the sun or stars. A carefully made ship's compass is usually employed, though in some cases the compass card, with its attached magnets, is made reversible, so that the inclination to the zero of the card of the magnetic axis of the system of magnets attached to the card can be eliminated by reversal. In the absence of such a reversible card the index correction must be determined by comparison with a unifilar magnetometer, simultaneous observations being made on shore, and these observations repeated as often as occasion permits. To determine the dip a Fox's dip circle[1] is used. This consists of an ordinary dip circle (see INCLINOMETER) in which the ends of the axle of the needle are pointed and rest in jewelled holes, so that the movements of the ship do not displace the needle. The instrument is, of course, supported on a gimballed table, while the ship during the observations is kept on a fixed course. To obtain the _strength_ of the field the method usually adopted is that known as Lloyd's method.[2] To carry out a determination of the total force by this method the Fox dip circle has been slightly modified by E. W. Creak, and has been found to give satisfactory results on board ship. The circle is provided with two needles in addition to those used for determining the dip, one (a) an ordinary dip needle, and the other (b) a needle which has been loaded at one end by means of a small peg which fits into one of two symmetrically placed holes in the needle. The magnetism of these two needles is never reversed, and they are as much as possible protected from shock and from approach to other magnets, so that their magnetic state may remain as constant as possible. Attached to the cross-arm which carries the microscopes used to observe the ends of the dipping needle is a clamp, which will hold the needle _b_ in such a way that its plane is parallel to the vertical circle and its axis is at right angles to the line joining the two microscopes. Hence, when the microscopes are adjusted so as to coincide with the points of the dipping needle _a_, the axes of the two needles must be at right angles. The needle _a_ being suspended between the jewels, and the needle _b_ being held in the clamp, the cross-arm carrying the reading microscopes and the needle _b_ is rotated till the ends of the needle a coincide with the cross-wires of the microscopes. The verniers having been read, the cross-arm is rotated so as to deflect the needle _a_ in the opposite direction, and a new setting is taken. Half the difference between the two readings gives the angle through which the needle a has been deflected under the action of the needle _b_. This angle depends on the ratio of the magnetic moment of the needle _b_ to the total force of the earth's field. It also involves, of course, the distance between the needles and the distribution of the magnetism of the needles; but this factor is determined by comparing the value given by the instrument, at a shore station, with that given by an ordinary magnetometer. Hence the above observation gives us a means of obtaining the _ratio_ of the magnetic moment of the needle _b_ to the value of the earth's total force. The needle _b_ is then substituted for _a_, there being now no needle in the clamp attached to the microscope arm, and the difference between the reading now obtained and the dip, together with the weight added to the needle, gives the product of the moment of the needle _b_ into the earth's total force. Hence, from the two observations the value of the earth's total force can be deduced. In an actual observation the deflecting needle would be reversed, as well as the deflected one, while different weights would be used to deflect the needle _b_.

For a description of the method of using the Fox circle for observations at sea consult the _Admiralty Manual of Scientific Inquiry_, p. 116, while a description of the most recent form of the circle, known as the Lloyd-Creak pattern, will be found in _Terrestrial Magnetism_, 1901, 6, p. 119. An attachment to the ordinary ship's compass, by means of which satisfactory measurements of the horizontal component have been made on board ship, is described by L. A. Bauer in _Terrestrial Magnetism_, 1906, 11, p. 78. The principle of the method consists in deflecting the compass needle by means of a horizontal magnet supported vertically over the compass card, the axis of the deflecting magnet being always perpendicular to the axis of the magnet attached to the card. The method is not strictly an absolute one, since it presupposes a knowledge of the magnetic moment of the deflecting magnet. In practice it is found that a magnet can be prepared which, when suitably protected from shock, &c., retains its magnetic moment sufficiently constant to enable observations of H to be made comparable in accuracy with that of the other elements obtained by the instruments ordinarily employed at sea. (W. Wn.)

FOOTNOTES:

[1] _Annals of Electricity_, 1839, 3, p. 288.

[2] Humphrey Lloyd, _Proc. Roy. Irish Acad._, 1848, 4, p. 57.

MAGNETO-OPTICS. The first relation between magnetism and light was discovered by Faraday,[1] who proved that the plane of polarization of a ray of light was rotated when the ray travelled through certain substances parallel to the lines of magnetic force. This power of rotating the plane of polarization in a magnetic field has been shown to be possessed by all refracting substances, whether they are in the solid, liquid or gaseous state. The rotation by gases was established independently by H. Becquerel,[2] and Kundt and Röntgen,[3] while Kundt[4] found that films of the magnetic metals, iron, cobalt, nickel, thin enough to be transparent, produced enormous rotations, these being in iron and cobalt magnetized to saturation at the rate of 200,000° per cm. of thickness, and in nickel about 89,000°. The direction of rotation is not the same in all bodies. If we call the rotation positive when it is related to the direction of the magnetic force, like rotation and translation in a right-handed screw, or, what is equivalent, when it is in the direction of the electric currents which would produce a magnetic field in the same direction as that which produces the rotation, then most substances produce positive rotation. Among those that produce negative rotation are ferrous and ferric salts, ferricyanide of potassium, the salts of lanthanum, cerium and didymium, and chloride of titanium.[5]

The magnetic metals iron, nickel, cobalt, the salts of nickel and cobalt, and oxygen (the most magnetic gas) produce positive rotation.

For slightly magnetizable substances the amount of rotation in a space PQ is proportional to the difference between the magnetic potential at P and Q; or if [theta] is the rotation in PQ, [Omega]_P, [Omega]_Q, the magnetic potential at P and Q, then [theta] = R([Omega]_P - [Omega]_Q), where R is a constant, called Verdet's constant, which depends upon the refracting substance, the wave length of the light, and the temperature. The following are the values of R (when the rotation is expressed in circular measure) for the D line and a temperature of 18° C.:--

Substance. R × 10^5. Observer.

Carbon bisulphide / 1.222 Lord Rayleigh[6] and Köpsel.[7] \ 1.225 Rodger and Watson.[8] Water / .377 Arons.[9] \ .3808 Rodger and Watson.[8] Alcohol .330 Du Bois.[10] Ether .315 Du Bois.[10] Oxygen (at 1 atmosphere) .000179 Kundt and Röntgen (_loc. cit._) Faraday's heavy glass 1.738

The variation of Verdet's constant with temperature has been determined for carbon bisulphide and water by Rodger and Watson (_loc. cit._). They find if R_t, R0 are the values of Verdet's constant at t°C and 0°C. respectively, then for carbon bisulphide R_t = R0 (1 - .0016961), and for water R_t = R0 (1 - .0000305t - .00000305t²).

For the magnetic metals Kundt found that the rotation did not increase so rapidly as the magnetic force, but that as this force was increased the rotation reached a maximum value. This suggests that the rotation is proportional to the intensity of magnetization, and not to the magnetic force.

The amount of rotation in a given field depends greatly upon the wave length of the light; the shorter the wave length the greater the rotation, the rotation varying a little more rapidly than the inverse square of the wave length. Verdet[11] has compared in the cases of carbon bisulphide and creosote the rotation given by the formula

c² / di \ [theta] = mc[gamma] --------- ( c - [lamda] --------- ) [lambda]² \ d[lambda]/

with those actually observed; in this formula [theta] is the angular rotation of the plane of polarization, m a constant depending on the medium, [lambda] the wave length of the light in air, and i its index of refraction in the medium. Verdet found that, though the agreement is fair, the differences are greater than can be explained by errors of experiment.

Verdet[12] has shown that the rotation of a salt solution is the sum of the rotations due to the salt and the solvent; thus, by mixing a salt which produces negative rotation with water which produces positive rotation, it is possible to get a solution which does not exhibit any rotation. Such solutions are not in general magnetically neutral. By mixing diamagnetic and paramagnetic substances we can get magnetically neutral solutions, which, however, produce a finite rotation of the plane of polarization. The relation of the magnetic rotation to chemical constitution has been studied in great detail by Perkin,[13] Wachsmuth,[14] Jahn[15] and Schönrock.[16]

The rotation of the plane of polarization may conveniently be regarded as denoting that the velocity of propagation of circular-polarized light travelling along the lines of magnetic force depends upon the direction of rotation of the ray, the velocity when the rotation is related to the direction of the magnetic force, like rotation and translation on a right-handed screw being different from that for a left-handed rotation. A plane-polarized ray may be regarded as compounded of two oppositely circularly-polarized rays, and as these travel along the lines of magnetic force with different velocities, the one will gain or lose in phase on the other, so that when they are again compounded they will correspond to a plane-polarized ray, but in consequence of the change of phase the plane of polarization will not coincide with its original position.

_Reflection from a Magnet._--Kerr[17] in 1877 found that when plane-polarized light is incident on the pole of an electromagnet, polished so as to act like a mirror, the plane of polarization of the reflected light is rotated by the magnet. Further experiments on this phenomenon have been made by Righi,[18] Kundt,[19] Du Bois,[20] Sissingh,[21] Hall,[22] Hurion,[23] Kaz[24] and Zeeman.[25] The simplest case is when the incident plane-polarized light falls normally on the pole of an electromagnet. When the magnet is not excited the reflected ray is plane-polarized; when the magnet is excited the plane of polarization is rotated through a small angle, the direction of rotation being opposite to that of the currents exciting the pole. Righi found that the reflected light was slightly elliptically polarized, the axes of the ellipse being of very unequal magnitude. A piece of gold-leaf placed over the pole entirely stops the rotation, showing that it is not produced in the air near the pole. Rotation takes place from magnetized nickel and cobalt as well as from iron, and is in the same direction (Hall). Righi has shown that the rotation at reflection is greater for long waves than for short, whereas, as we have seen, the Faraday rotation is greater for short waves than for long. The rotation for different coloured light from iron, nickel, cobalt and magnetite has been measured by Du Bois; in magnetite the direction of rotation is opposite to that of the other metals. When the light is incident obliquely and not normally on the polished pole of an electromagnet, it is elliptically polarized after reflection, even when the plane of polarization is parallel or at right angles to the plane of incidence. According to Righi, the amount of rotation when the plane of polarization of the incident light is perpendicular to the plane of incidence reaches a maximum when the angle of incidence is between 44° and 68°, while when the light is polarized in the plane of incidence the rotation steadily decreases as the angle of incidence is increased. The rotation when the light is polarized in the plane of incidence is always less than when it is polarized at right angles to that plane, except when the incidence is normal, when the two rotations are of course equal.

_Reflection from Tangentially Magnetized Iron._--In this case Kerr[26] found: (1) When the plane of incidence is perpendicular to the lines of magnetic force, no rotation of the reflected light is produced by magnetization; (2) no rotation is produced when the light is incident normally; (3) when the incidence is oblique, the lines of magnetic force being in the plane of incidence, the reflected light is elliptically polarized after reflection, and the axes of the ellipse are not in and at right angles to the plane of incidence. When the light is polarized in the plane of incidence, the rotation is at all angles of incidence in the opposite direction to that of the currents which would produce a magnetic field of the same sign as the magnet. When the light is polarized at right angles to the plane of incidence, the rotation is in the same direction as these currents when the angle of incidence is between 0° and 75° according to Kerr, between 0° and 80° according to Kundt, and between 0° and 78° 54´ according to Righi. When the incidence is more oblique than this, the rotation of the plane of polarization is in the opposite direction to the electric currents which would produce a magnetic field of the same sign.