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MAGNETOMETER
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MAGNETOMETER , a name, in its most See also:general sense, for any See also:instrument used to measure the strength of any magnetic See also: 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 See also:Kew See also:Observatory See also:pattern unifilar magnetometer is shown in See also:figs. 1 and 2. The magnet consists of a hollow See also:steel See also:cylinder fitted with a scale and lens as described above, and is suspended by a See also:long See also:thread of unspun See also:silk, which is attached at the upper end to the torsion See also:head H. The magnet is protected front See also:draughts by the See also: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 See also:brass plummet having the same See also:weight as the magnet is first suspended in its See also:place, and the torsion of the fibre is taken out. The magnet having been attached, the instrument is rotated about its See also:vertical axis till the centre division of the scale appears to coincide with the vertical See also:cross-See also: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 See also:original position. The mean of all the readings of the verniers gives the See also:reading on the azimuth circle corresponding to the magnetic meridian. To obtain the geographical meridian the box A is removed, and an See also: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 See also:period of a freely suspended magnet, and then obtaining the angle through which an See also:auxiliary suspended magnet is deflected by the magnet used in the first See also: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 See also:time of vibra- tion is obtained by means of a chronometer, using the See also:eye-and-See also: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 See also:plane mirror attached, the plane of which is at right angles to the axis of the magnet. An image of the See also: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 See also:carriage L which can slide along the graduated See also: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 See also: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 See also:error due to the zero of the scale D not being exactly below the mirror magnet, the support L is then removed to the See also:west See also: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 See also: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 See also: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 See also: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 See also: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 See also:latitude and See also: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 See also:matter of some difficulty when observing at any distance from a fixed observatory. If, however, a See also:theodolite, fitted with a telescope which can rotate about a horizontal axis and having an See also: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 See also:minute or so. Hence in more See also: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 See also: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 See also: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 See also:change so much with the hygrometric See also:state of the See also:air, is of some See also:advantage, but does not entirely remove the difficulty. For this reason some observers use a thin See also:strip of phosphor See also: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 See also: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 See also: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 See also: See also: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 See also:French magnetic survey, which are interesting on account of their small See also:size and consequent easy portability; H. E. D. See also:Fraser, Terrestrial Magnetism, 1901, 6, p. 65, containing a description of a modified Kew pattern unifilar as used in the See also:Indian survey; H. See also:Wild, Mem. Acad. See also: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 See also:Sea.—Owing to the fact that the proportion of the earth's surface covered by sea is so much greater than the dry See also:land, the determinaton of the magnetic elements on See also:board See also: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 See also: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 See also:system of magnets attached to the card can be eliminated by reversal. In the absence of such a reversible card the See also:index correction must be determined by comparison with a unifilar magnetometer, simultaneous observations being made on See also:shore, and these observations repeated as often as occasion permits. To determine the dip a See also:Fox's dip circle' is used. This consists of an See also:ordinary dip circle (see INCLINOMETER) in which the ends of the See also:axle of the See also:needle are pointed and See also: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 See also:Lloyd's method.2 To carry out a determination of the See also: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-See also: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 See also:shock and from approach to other magnets, so that their magnetic state may re-See also:main as See also:constant as possible. Attached to the cross-See also:arm which carries the microscopes used to observe the ends of the dipping needle is a clamp, which will hold the needle See also: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. See also:Half the difference between the two readings gives ' See also:Annals of See also:Electricity, 1839, 3, p. 288. 2 See also:Humphrey Lloyd, Proc. Roy. Irish Acad., 1848, 4, p. 57.the angle through which the needle a has been deflected under the See also: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 See also:distribution of the magnetism of the needles; but this See also: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 See also: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 See also:Admiralty See also:Manual of Scientific Inquiry, p. 116, while a description of the most recent See also:form of the circle, known as the Lloyd-Creak pattern, will be found in Terrestrial Magnetism, 1901, 6, p. 119. An See also: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. See also: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 See also: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-See also:OPTICS. The first relation between magnetism and See also:light was discovered by See also:Faraday,' who proved that the plane of polarization of a See also:ray of light was rotated when the ray travelled through certain substances parallel to the lines of magnetic force. This See also: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. See also:Becquerel,2 and See also:Kundt and RSntgen,3 while Kundt' found that films of the magnetic metals, See also:iron, See also:cobalt, See also: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 See also:call the rotation See also:positive when it is related to the direction of the magnetic force, like rotation and See also:translation in a right-handed See also:screw, or, what is See also: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 See also:potassium, the salts of lanthanum, See also:cerium and See also:didymium, and chloride of See also:titanium.' The magnetic metals iron, nickel, cobalt, the salts of nickel and cobalt, and See also:oxygen (the most magnetic See also: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 See also: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 See also:Lord See also:Rayleigh' and Kopsel.' 1.225 Rodger and See also:Watson.' 3 377 Arons.5 •3808 Rodger and Watson.' .330 Du Bois.'" .315 Du Bois.'" .000179 Kundt and See also:Rontgen (loc.cit. ) 1.738 Substance. See also:Carbon bisulphide See also:Water See also:Alcohol See also:Ether Oxygen (at I See also: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 See also:creosote the rotation given by the See also: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 See also:medium, a the wave length of the light in air, and i its index of See also:refraction in the medium. Verdet found that, though the agreement is See also:fair, the See also:differences are greater than can be explained by errors of experiment.
Verdet 12 has shown that the rotation of a See also:salt See also: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 See also:great detail by See also:Perkin,3 See also:Wachsmuth,4 See also:Jahn' and Schonrock.6
The rotation of the plane of polarization may conveniently be regarded as denoting that the velocity of See also: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 See also: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 See also: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 See also: A piece of See also:gold-See also: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 See also: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 See also: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 See also:Airy,27 C. See also:Neumann,28 See also:Maxwell,29 See also:Fitzgerald,30 See also:Rowland,34 H. A. Lorentz,32 Voight,33 See also:Ketteler,34 See also:van Loghem,35 Potier,36 See also:Basset,37 Goldhammer,33 Drude,39 J. J. See also:Thomson,40 and Leatham;41 for a See also:critical discussion of many of these theories we refer the reader to Larmor's 42 See also:British Association See also:Report. Most of these theories have proceeded on the See also:plan of adding to the expression for the electromotive force terms indicating a force similar in See also: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 See also:term of this See also:kind gives rotation of the plane of polarization by trans-See also: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 See also:ion in a magnetic field will be acted upon by a See also:mechanical force which is at right angles to its direction of See also:motion, and also to the magnetic force, and is equal per unit See also:charge to the product of these two vectors and the sine of the angle between them. For the See also:sake of brevity we will take the See also: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 See also:mass m and charge e per unit See also:volume, the equations representing the field are (see ELECTRIC WAVES) : Ko--+4rrne d~ = d~; dXo d9 dz See also:fit' K da -+4rrne dt = — d dYo da dz = dt z di? mdt +R'dt+at= (Xo+3-See also:net)e+Hedt 2 mdt +RI dt+See also:art= (Yo+43 ne,t)e—Hedt; where H is the See also: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 See also: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 See also: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 See also: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 See also: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 See also: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 See also:hand. This has been verified for See also:sodium vapour by Macaluso and Corbino.93 If plane-polarized light falls normally on a plane See also: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 See also: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 See also: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 See also:body, but without success. In 1885 Fievez,44 a Belgian physicist, noticed that the spectrum of a sodium See also:flame was changed slightly in See also:appearance by a magnetic field; but his observation does not seem to have attracted much See also:attention, and was probably ascribed to secondary effects. In 1896 Zeeman 45 saw a distinct broadening of the lines of See also: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 (See also:pit+R)+B See also: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 See also: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 See also: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 See also: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 See also:elm is of the order Io7. This result is of great See also:interest, as this is the order of the value of e/m in the negatively electrified particles which constitute the See also:Cathode Rays (see See also: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 See also:electrical See also:fields, and are in fact an ordinary constituent of the See also:molecule. Similar particles are found near an incandescent wire, and also near a See also:metal See also:plate illuminated by ultra-See also: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 See also:numbers larger than this, the maximum being about twice this value. remarkable and interesting results, of which those observed with the See also:blue-See also: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 See also: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= —See also: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 See also:simple cases are much less numerous than the more complex. Thus See also:Preston 97 and See also: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 See also: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 See also: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 See also:echelon spectroscope.
There are some interesting phenomena connected with the Zeeman effect which are more easily observed than the effect itself. Thus See also:Cotton 51 found that if we have two See also: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 See also:longitudinal field between two crossed Nicols, and a ray of See also: 67, p. 345) detected the See also: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. See also:Jean Becquerel has made some very interesting experiments on the effect of a magnetic field on the See also:fine absorption bands produced by xenotime, a phosphate of See also:yttrium and See also: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 See also: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. See also:Leiden, 1893. 26 Phil. Mag. [5] 5, p. 161. 27 Phil. Mag. [3] 28, p. 469. 28 See also:Die magn. Drehung d. Polarisationsebene See also:des Lichts, See also:Halle, 1863. 29 Electricity and Magnetism, See also:chap. xxi. 30 Phil. Trans. 188o (2), p. 691. 31 Phil. Mag. (5) 11, p. 254, 1881. 32 See also: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; See also: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 See also: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. Additional information and CommentsThere are no comments yet for this article.
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