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MAGNETOMETER

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Originally appearing in Volume V17, Page 391 of the 1911 Encyclopedia Britannica.
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MAGNETOMETER, a name, in its most general sense, for any instrument used to measure the strength of any magnetic field; it is, however, often used in the restricted sense of an instrument for measuring a particular magnetic field, namely, that due to the earth's magnetism, and in this article the instruments used for measuring the value of the earth's magnetic field will alone be considered. The elements which are actually measured when determining the value of the earth's field are usually the declination, the dip and the horizontal component (see MAGNETISM, TERRESTRIAL). For the instruments and methods used in measuring the dip see INCLINOMETER. It remains to consider the measurement of the declination and the horizontal component, these two elements being generally measured with the same instrument, which is called a unifilar magnetometer. Measurement of Declination.—The measurement of the declination involves two separate observations, namely, the determination of (a) the magnetic meridian and (b) the geographical meridian, the angle between the two being the declination. In order to determine the magnetic meridian the orientation of the magnetic axis of a freely suspended magnet is observed; while, in the absence of a distant mark of which the azimuth is known, the geographical meridian is obtained from observations of the transit of the sun or a star. The geometrical axis of the magnet is sometimes defined by means of a mirror rigidly attached to the magnet and having the normal to the mirror as nearly as may be parallel to the magnetic axis. This arrangement is not very convenient, as it is difficult to protect the mirror from accidental displacement, so that the angle between the geometrical and magnetic axes may vary. For this reason the end of the magnet is sometimes polished and acts as the mirror, in which case no displacement of the reflecting surface with reference to the magnet is possible. A different arrangement, used in the instrument described below, consists in having the magnet hollow, with a small scale engraved on glass firmly attached at one end, while to the other end is attached a lens, so chosen that the scale is at its principal focus. In this case the geometrical axis is the line joining the central division of the scale to the optical centre of the lens. The position of the magnet is observed by means of a small telescope, and since the scale is at the principal focus of the lens, the scale will be in focus when the telescope is adjusted to observe a distant object. Thus no alteration in the focus of the telescope is necessary whether we are observing the magnet, a distant fixed mark, or the sun. The Kew Observatory pattern unifilar magnetometer is shown in figs. 1 and 2. The magnet consists of a hollow steel cylinder fitted with a scale and lens as described above, and is suspended by a long thread of unspun silk, which is attached at the upper end to the torsion head H. The magnet is protected front draughts by the box A, which is closed at the sides by two shutters when an observation is being taken. The telescope B serves to observe the scale attached to the magnet when determining the magnetic meridian, and to observe the sun or star when determining the geographical meridian. When making a determination of declination a brass plummet having the same weight as the magnet is first suspended in its place, and the torsion of the fibre is taken out. The magnet having been attached, the instrument is rotated about its vertical axis till the centre division of the scale appears to coincide with the vertical cross-wire of the telescope. The two verniers on the azimuth circle having been read, the magnet is then inverted, i.e. turned through 18o° about its axis, and the setting is repeated. A second setting with the magnet inverted is generally made, and then another setting with the magnet in its original position. The mean of all the readings of the verniers gives the reading on the azimuth circle corresponding to the magnetic meridian. To obtain the geographical meridian the box A is removed, and an image of the sun or a star is reflected into the telescope B by means of a small transit mirror N. This mirror can rotate about a horizontal axis which is at rightalmost 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 vibra- tion 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. I) 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 ex- periment 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 posi- tion, the ratio M/H is propor- tional to the sine of the angle between the magnetic axis of the mirror magnet and the magnetic meridian. When conducting a deflexion experiment the de- flecting 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 B 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 2aM sin B= I + P+ ya+ &c., 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 pro-portions 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. Borgen, Terrestrial Magnetism, 1896, i. p. 176, and C. Chree, Phil. Mag., 1904 16], 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. angles to the line of collimation of the telescope, and is parallel to the surface of the mirror. The time of transit of the sun or star across the vertical wire of the telescope having been observed by means of a chronometer of which the error is known, it is possible to calculate the azimuth of the sun or star, if the latitude and longitude of the place of observation are given. Hence if the readings of the verniers on the azimuth circle are made when the transit is observed we can deduce the reading corresponding to the geographical meridian. 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 ose 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 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, Traite de magnetisme 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, Mem. Acad. imp. sc. St Petersbourg, 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. fiir 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 determinaton 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' 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 deter-mining 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 re-main 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 bin 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 ' Annals of Electricity, 1839, 3, p. 288. 2 Humphrey Lloyd, Proc. Roy. Irish Acad., 1848, 4, p. 57.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 know-ledge 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.) MAGNETO-OPTICS. The first relation between magnetism and light was discovered by Faraday,' 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 RSntgen,3 while Kundt' 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.' 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 0 is the rotation in PQ, SOP, StQ, the magnetic potential at P and Q, then U=R(Sl5-t2Q), 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.: R X i o 5. Observer. 1.222 Lord Rayleigh' and Kopsel.' 1.225 Rodger and Watson.' 3 377 Arons.5 •3808 Rodger and Watson.' .330 Du Bois.'" .315 Du Bois.'" .000179 Kundt and Rontgen (loc.cit. ) 1.738 Substance. Carbon bisulphide Water Alcohol Ether Oxygen (at I atmosphere) Faraday's heavy glass 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,, Ro are the values of Verdet's constant at t°C. and o°C. respectively, then for carbon bisulphide R;=Ro (1 —.0016961), and for water R,=Ro (I-•00003o5t—•000003o5t2). 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" has compared in the cases of carbon bisulphide and creosote the rotation given by the formula B=mc-y (c—add) with those actually observed; in this formula B is the angular rotation of the plane of polarization, m a constant depending on the medium, a 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 consitution has been studied in great detail by Perkin,3 Wachsmuth,4 Jahn' and Schonrock.6 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.—Kerr17 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,43 Kundt,19 Du Bois,Y° Sissingh,21 Hall,22 Hurion,23 Kaz24 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 440 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: (r) 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 o° and 75° according to Kerr, between o° and 80° according to Kundt, and between o° 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. The theory of the phenomena just described has been dealt with by Airy,27 C. Neumann,28 Maxwell,29 Fitzgerald,30 Rowland,34 H. A. Lorentz,32 Voight,33 Ketteler,34 van Loghem,35 Potier,36 Basset,37 Goldhammer,33 Drude,39 J. J. Thomson,40 and Leatham;41 for a critical discussion of many of these theories we refer the reader to Larmor's 42 British Association Report. Most of these theories have proceeded on the plan of adding to the expression for the electromotive force terms indicating a force similar in character to that discovered by Hall (see MAGNETISM) in metallic conductors carrying a current in a magnetic field, i.e. an electromotive force at right angles to the plane containing the magnetic force and the electric current, and proportional to the sine of the angle between these vectors. The introduction of a term of this kind gives rotation of the plane of polarization by trans-mission through all refracting substance, and by reflection from magnetized metals, and shows a fair agreement between the theoretical and experimental results. The simplest way of treating the questions seems, however, to be to go to the equations which represent the propagation of a wave travelling through a medium containing ions. A moving ion in a magnetic field will be acted upon by a mechanical force which is at right angles to its direction of motion, and also to the magnetic force, and is equal per unit charge to the product of these two vectors and the sine of the angle between them. For the sake of brevity we will take the special case of a wave travelling parallel to the magnetic force in the direction of the axis of z. Then supposing that all the ions are of the same kind, and that there are n of these each with mass m and charge e per unit volume, the equations representing the field are (see ELECTRIC WAVES) : Ko--+4rrne d~ = d~; dXo d9 dz fit' K da -+4rrne dt = — d dYo da dz = dt z di? mdt +R'dt+at= (Xo+3-net)e+Hedt 2 mdt +RI dt+art= (Yo+43 ne,t)e—Hedt; where H is the external magnetic field, X,, Yo the components of the part of the electric force in the wave not due to the charges on the atoms, a and ,B the components of the magnetic force, f and 7, the co-ordinates of an ion, R1 the coefficient of resistance to the motion of the ions, and a the force at unit distance tending to bring the ion back to its position of equilibrium, Ko the specific inductive capacity of a vacuum. If the variables are proportional to EI(pz-4z) we find by substitution that q is given by the equation q2—Kop2—P2anHeap2 ±P2nH2e2p2' where Per (a — aane2) +RiLp —mpg, or, by neglecting R, P=m(s2—p2), where s is the period of the free ions. If, ql, q are the roots of this equation, then corresponding to qi we have Xo =1Yo and to q2 Xo = —No. We thus get two oppositely circular :polarized rays travelling with the velocities p/qi and p/q2 respectively. Hence if v1, v2 are these velocities, and v the velocity when there is no magnetic field, we obtain, if we neglect terms in H2, I I 4,rne3H p 2,12 — v2 c m2 (s2 — p2)2 I I 4,rne'l-1'p v22 =v2 —m2(s2 —p2)2 The rotation r of the plane of polarization per unit length I I 2,rne3Hp2v _1P (vi v2) m2(s2_p2)2 Since I/v2=Ko+4,rne2/m(s2—p2), we have if µ is the refractive index for light of frequency p, and vo the velocity of light in vacuo. µ2—I =4,rne2v2o/m(s2-p2) . . (I) So that we may put r = (,o2 — I )2p2H /slrfznevoa (2 ) Becquerel (Comptes rendus, 125, p. 683) gives for r the expression e H dµ 1mvodX' where X is the wave length. This is equivalent to (2) if is given by (I). He has shown that this expression is in good agreement with experiment. The sign of r depends on the sign of e, hence the rotation due to negative ions would be opposite to that for positive. For the great majority of substances the direction of rotation is that corresponding to the negation ion. We see from the equations that the rotation is very large for such a value of p as makes P=o: this value corresponds. to a free period of the ions, so that the rotation ought to be very large in the neighbourhood of an absorption hand. This has been verified for sodium vapour by Macaluso and Corbino.93 If plane-polarized light falls normally on a plane face of the medium containing the ions, then if the electric force in the incident wave is parallel to x and is equal to the real part of Ael(P'-° ) if the reflected beam in which the electric force is parallel to x is represented by Bol(Pi+qz) and the reflected beam in which the electric force is parallel to the axis of y by CEi(pt+q.), then the conditions that the magnetic force parallel to the surface is continuous, and that the electric forces parallel to the surface in the air are continuous with Yo, Xo in the medium, give A B 1C (q+ql) (q+q2) (q2—gig2) q(q2—qi) or approximately, since qi and q2 are nearly equal, 1C _ q (q2 — (µ2 — I) PH. B q2 — qo2 4rrµneV o2 Thus in transparent bodies for which µ is real, C and B differ in phase by ,r/2, and the reflected light is elliptically polarized, the major axis of the ellipse being in the plane of polarization of the incident light, so that in this case there is no rotation, but only elliptic polarization; when there is strong absorption so that µ contains an imaginary term, C/B will contain a real part so that the reflected light will be elliptically polarized, but the major axis is no longer in the plane of polarization of the incident light; we should thus have a rotation of the plane of polarization superposed on the elliptic polarization. Zeeman's Effect.—Faraday, after discovering the effect of a magnetic field on the plane of polarization of light, made numerous experiments to see if such a field influenced the nature of the light emitted by a luminous body, but without success. In 1885 Fievez,44 a Belgian physicist, noticed that the spectrum of a sodium flame was changed slightly in appearance by a magnetic field; but his observation does not seem to have attracted much attention, and was probably ascribed to secondary effects. In 1896 Zeeman 45 saw a distinct broadening of the lines of lithium and sodium when the flames containing salts of these metals were between the poles of a powerful electromagnet; following up this observation, he obtained some exceedingly The solution of these equations is x = Acos (pit+R)+B cos (pet+Nqi) y = A sin (pot+9) —B sin (pet+$1) z = C cos (pt+y) a — mpi2= —Hepi a — mp22 = Hep2 p2 = a'm' or approximately pi =p+%me, p2=p—2 me, Thus the motion of the ion on the xy plane may be regarded as made up of two circular motions in opposite directions described with frequencies pi and p2 respectively, while the motion along z has the period p, which is the frequency for all the vibrations when H =o. Now suppose that the cadmium line is due to the motion of such an ion; then if the magnetic force is along the direction of propagation, the vibration in this direction has its period unaltered, but since the direction of vibration is perpendicular to the wave front, it does not give rise to light. Thus we are left with the two circular motions in the wave front with frequencies pi and p2 giving the circularly polarized constituents of the doublet. Now suppose the magnetic force is at right angles to the direction of propagation of the light; then the vibration parallel to the magnetic force being in the wave front produces luminous effects and gives rise to a plane-polarized ray of undisturbed period (the middle line of the triplet), the plane of polarization being at right angles to the magnetic force. The components in the wave-front of the circular orbits at right angles to the magnetic force will be rectilinear motions of frequency pi and p2 at right angles to the magnetic force—so that they will produce plane-polarized light, the plane of polarization being parallel to the magnetic force; these are the outer lines of the triplet. If Zeeman's observations are interpreted from this point of view, the directions of rotation of the circularly-polarized light in the doublet observed along the lines of magnetic force show that the ions which produce the luminous vibrations are negatively electrified, while the measurement of the charge of frequency due to the magnetic field shows that elm is of the order Io7. This result is of great interest, as this is the order of the value of e/m in the negatively electrified particles which constitute the Cathode Rays (see CONDUCTION, ELECTRIC III. Through Gases). Thus we infer that the " cathode particles " are found in bodies, even where not subject to the action of intense electrical fields, and are in fact an ordinary constituent of the molecule. Similar particles are found near an incandescent wire, and also near a metal plate illuminated by ultra-violet light. The value of e/m deduced from the Zeeman effect ranges from to7 to 3.4 X Io7, the value of e/m for the particle in the cathode rays is 1.7.X Io7. The majority of the determinations of e/m from the Zeeman .effect give numbers larger than this, the maximum being about twice this value. remarkable and interesting results, of which those observed with the blue-green cadmium line may be taken as typical. He found that in a strong magnetic field, when the lines of force are parallel to the direction of propagation of the light, the line is split up into a doublet, the constituents of which are on opposite sides of the undisturbed position of the line, and that the light in the constituents of this doublet is circularly polarized, the rotation in the two lines being in opposite directions. When the magnetic force is at right angles to the direction of propagation of the light, the line is resolved into a triplet, of which the middle line occupies the same position as the undisturbed line; all the constituents of this triplet are plane-polarized, the plane of polarization of the middle line being at right angles to the magnetic force, while the outside lines are polarized on a plane parallel to the lines of magnetic force. A great deal of light is thrown on this phenomenon by the following considerations due to H. A. Lorentz.96 Let us consider an ion attracted to a centre of force by a force proportional to the distance, and acted on by a magnetic force parallel to the axis of z: then if m is the mass of the particle and e its charge, the equations of motion are z m diz+ax= —Heat z and +ay=Hedt ; d2z matt +az =O. where A more extended study of the behaviour of the spectroscopic lines has afforded examples in which the effects produced by a magnet are more complicated than those we have described, indeed the simple cases are much less numerous than the more complex. Thus Preston 97 and Cornu 48 have shown that under the action of a transverse magnetic field one of the D lines splits up into four, and the other into six lines; Preston has given many other examples of these quartets and sextets, and has shown that the change in the frequency, which, according to the simple theory indicated, should be the same for all lines, actually varies considerably from one line to another, many lines showing no appreciable displacement. The splitting up of a single line into a quartet or sextet indicates, from the point of view of the ion theory, that the line must have its origin in a system consisting of more than one ion. A single ion having only three degrees of freedom can only have three periods. When there is no magnetic force acting on the ion these periods are equal, but though under the action of a magnetic force they are separated, their number cannot be increased. When there-fore we get four or more lines, the inference is that the system giving the lines must have at least four degrees of freedom, and therefore must consist of more than one ion. The theory of a system of ions mutually influencing each other shows, as we should expect, that the effects are more complex than in the case of a single ion, and that the change in the frequency is not necessarily the same for all systems (see J. J. Thomson, Proc. Camb. Phil. Soc. 13, p. 39). Preston 49 and Runge and Paschen have proved that, in some cases at any rate, the change in the frequency of the different lines is of such a character that they can be grouped into series such that each line in the series has the same change in frequency for the same magnetic force, and, moreover, that homologous lines in the spectra of different metals belonging to the same group have the same change in frequency. A very remarkable case of the Zeeman effect has been discovered by H. Becquerel and Deslandres (Comptes rendus, 127, p. 18). They found lines in iron when the most deflected components are those polarized in the plane at right angles to the magnetic force. On the simple theory the light polarized in this way is not affected. Thus the behaviour of the spectrum in the magnetic field promises to throw great light on the nature of radiation, and perhaps on the constitution of the elements. The study of these effects has been greatly facilitated by the invention by Michelson 5° of the echelon spectroscope. There are some interesting phenomena connected with the Zeeman effect which are more easily observed than the effect itself. Thus Cotton 51 found that if we have two Bunsen flames, A and B, coloured by the same salt, the absorption of the light of one by the other is diminished if either is placed between the poles of a magnet: this is at once explained by the Zeeman effect, for the times of vibration of the molecules of the flame in the magnetic field are not the same as those of the other flame, and thus the absorption is diminished. Similar considerations explain the phenomenon observed by Egoroff and Georgiewsky,52 that the light emitted from a flame in a transverse field is partially polarized in a plane parallel to the magnetic force; and also Righi's 53 observation that if a sodium flame is placed in a longitudinal field between two crossed Nicols, and a ray of white light sent through one of the Nicols, then through the flame, and then through the second Nicol, the amount of light passing through the second Nicol is greater when the field is on than when it is off. Voight and Wiechert (Wied. Ann. 67, p. 345) detected the double refraction produced when light travels through a substance exposed to a magnetic field at right angles to the path of the light; this result had been predicted by Voight from theoretical considerations. Jean Becquerel has made some very interesting experiments on the effect of a magnetic field on the fine absorption bands produced by xenotime, a phosphate of yttrium and erbium, and tysonite, a fluoride of cerium, lanthanum and didymium, and has obtained effects which he ascribes to the presence of positive electrons. A very complete account of magneto- and electro-optics is contained in Voight's Magneto-and Elektro-optik. 1 Experimental Researches, Series 19. 2 Comptes rendus, 88, p. 709. Wied. Ann. 6, p. 332; 8, p. 278; 10, p. 257. 4 Wied. Ann. 23, p. 228; 27, p. 191. 5 Wied. Ann. 31, p. 941. 6 Phil. Trans., A. 1885, Pt. I I, p. 343. 7 Wied. Ann. 26, p. 456. 8 Phil. Trans., A. 1895, Pt. 17, p. 621. 9 Wied. Ann. 24, p. 161. 1° Wied. Ann. 31, p. 970. 11 Comptes rendus, 57, p. 670. 12 Comptes rendus, 43, p. 529; 44, p. 1209. 13 Journ. Chem. Soc. 1884., p. 421; 1886, p. 177; 1887, pp. 362 and 808; 1888, p. 561; 1889, pp. 68o and 750; 1891, p. 981; 1892, p. 800; 1893, pp. 75, 99 and 488. 14 Wied. Ann. 44, p. 377. 15 Wied. Ann. 43, p. 280. 16 Zeitschrift f. physikal. Chem. II, p. 753. 17 Phil. Mag. [5] 3, p. 321. 18 Ann. de chim. et de phys. [6] 4, p. 433; 9, p. 65; 10, p. 200. 19 Wied. Ann. 23, p. 228; 27, p. 191. 20 Wied. Ann. 39, p. 25. 21 Wied. Ann. 42, p. 115. 22 Phil. Mag. (51 12, p. 171. 23 Journ. de Phys. 1884, p. 36o. 24 Beiblatter 2u Wied. Ann. 1885, p. 275. 25 Messungen fiber d. Kerr'sche Erscheinung. Inaugural Dissert. Leiden, 1893. 26 Phil. Mag. [5] 5, p. 161. 27 Phil. Mag. [3] 28, p. 469. 28 Die magn. Drehung d. Polarisationsebene des Lichts, Halle, 1863. 29 Electricity and Magnetism, chap. xxi. 30 Phil. Trans. 188o (2), p. 691. 31 Phil. Mag. (5) 11, p. 254, 1881. 32 Arch. Merl. 19, p. 123. 33 Wied. Ann. 23, p. 493; 67, P. 345. 34 Wied. Ann. 24, p. 119. 36 Wied. Bei blotter, 8, p. 869. 36 Comptes rendus, 1o8, p. 510. 27 Phil. Trans. 182, A. p. 371, 1892; Physical Optics, p. 393. 38 Wied. Ann. 46, p. 71; 47, p. 345; 48, p. 740; 50, p. 722. 39 Wied. Ann. 46, p. 353; 48, p. 122; 49, p. 690. 40 Recent Researches, p. 489 et seq. 41 Phil. Trans., A. 1897, p. 89. 42 Brit. Assoc. Report, 1893. 43 Comptes rendus, 127, p. 548. 44 Bull. de l'Acad. des Sciences Belg. (3) 9, pp. 327, 381, 1885; 12 p. 30, 1886. 45 Communications from the Physical Laboratory, Leiden, No. 33, 1896; Phil. Mag. 43, p. z26; 44, pp. 55 and 255; and 45, p. 197. 46 Arch. Merl. 25, p. 190. 47 Phil. Meg. 45, p. 325; 47, p. 165. 48 Comptes rendus, 126, p. 181. 49 Phil. Mag. 46, p. 187. 50 Phil. Mag. 45, p. 348. 51 Comptes rendus, 125, p. 865. 52 Comptes rendus, pp. 748 and 949, t897• 63 Comptes rendus, 127, p. 216; 128, p. 45. (J. J. T.)
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