August lo, 1893] 



NATURE 



347 



particle will be the same all along the wave, but if they 

 travel with unequal speeds the direction of this motion 

 will turn round as the wave advances in the direction of 

 the motion of the particles in the more quickly traveling 

 wave, generating if the speeds are constant, the surface 

 of a screw. 



To constrain the particles to maintain the circular 

 motions forces must be applied towards the centre of 

 the orbit in each case. The reactions of the particles 

 against these motions are what are properly called the 

 centrifugal forces of the particles. But the different 

 particles are connected by the elastic medium and the 

 required centreward forces are supplied by its rigidity. 

 Thus for given displacements produced by the beam 

 entering the medium the forces due to the medium will 

 be different if the rigidity is less for, say, a left-handed 

 helical distortion than for a right-handed one, and the 

 latter distortion will be propagated with the greater speed. 



Now let the wave be reflected after passage, and let 

 the direction of motion of each vibrating particle be 

 reversed in the act of reflection. The direction of the 

 helical arrangement will remain unchanged in each case. 

 The wave which travelled the faster when direct will 

 again do so, but the direction of motion being reversed 

 the direction of motion in the plane polarised beam 

 will turn round in the opposite direction as the wave 

 moves forward, thus undoing the previous turning. 



The same thing it is easy to see will take place if the 

 reflection takes place without reversal of motion as at 

 the surface of a rarer medium. In this case the helical 

 arrangement which was left-handed becomes right-handed, 

 and vice versa after reflection. The arrangement which 

 lagged behind before now that is reversed travels the 

 faster and the line of resultant vibration again turns 

 round, but in the direction of the circular motion in that 

 circularly polarised wave which now moves the faster, 

 that is in the opposite direction to that in which it 

 moved before. Diagrams (3) and (4) of the figure show 

 the configurations of parts of (1} and (2) after having 

 been thus reflected. 



Now consider the other case. It is observed, we shall 

 suppose, that the right-handed circular ray travels faster 

 than the other, and that whether direct or reversed. 

 As before, the elastic action of the medium on the moving 

 particles can depend only on the displacements of the 

 particles in the helical displacement, and in the absence 

 of any structural peculiarity to produce a difference 

 must react in the same degree on the particles in both 

 circular waves. Thus the centrifugal force reactions 

 being the same for both waves, and the velocity of trans- 

 mission being different, the luminiferous motions must be 

 unequal, and such that compounded with a motion 

 existing in the medium two motions are produced which 

 exert equal centrifugal force reactions, balancing the 

 equal elastic forces applied in consequence of the equal 

 helical displacements. 



According to this theory, which is due to Lord Kelvin, 

 there exists in the medium a motion capable of being 

 compounded with the luminiferous motion of either 

 circularly polarised beam which is therefore a component 

 only of the whole rotational motion. In the passage in 

 which this dynamical explanation is put forward Lord 

 Kelvin goes on to say, 



" I think it is not only impossible to conceive any 

 other than this dynamical explanation of the fact that 

 circularly polarised light transmitted through magnetised 

 glass parallel to the lines of magnetising force, with the 

 same quality, right-handed always, or left-handed always, 

 is propagated at different rates according as its course 

 is in the direction or is contrary to the direction in 

 which a north magnetic pole is drawn ; but I believe it 

 can be demonstrated that no other explanation of that 

 fact is possible. Hence it appears that Faraday's 

 optical discovery affords a demonstration of the reality 



NO. I24I, VOL, 48] 



of Ampere's explanation of the ultimate nature of 

 magnetism." 



A number of interesting conclusions seem to follow 

 from this theory. In the first place the turning effect is 

 not found to any sensible extent unless there is matter of 

 some kind, magnetic or diamagnetic, present in the field. 

 Hence the theory does not point to rotation of the parts 

 of the ether but only to rotational motion of other 

 matter imbedded in it and reacting on the ether in 

 consequence of that motion. 



Further, the explanation seems to decide against that 

 view of diamagnetism which regards it as a differential 

 effect due to the greater magnetisation of the surrounding 

 medium. The rotation of the plane of polarisation is 

 found in both paramagnetic and diamagnetic substances, 

 but for the same direction of magnetic field is opposite 

 in the two cases. This points to opposite rotations of 

 the matter in the field according as it is paramagnetised 

 or diamagnetised. 



In all ordinary transparent substances which have 

 been experimented on the effect has been found to be 

 small. This of course was what was to be expected 

 from the small amount of magnetisation (or diamag- 

 netisation) produced in such substances even by very 

 powerful fields. As a rule the substances are diamagnetic 

 and give rotation of the plane of polarisation varying 

 directly as the intensity of the magnetic field in which 

 the substance is placed, and directly as the thickness of 

 the medium through which the light is passed. It has 

 been found however by Kundt that the turning produced 

 by passing the light through a thin film of iron or cobalt is 

 very great, a result which forcibly recalls the idea suggested 

 by Lord Kelvin in the paper quoted above, that the 

 moment of momentum of the matter in unit of volume of 

 the magnetised substance might be the proper dynamical 

 measure of the intensity of magnetisation. 



Another result found both for magneto-optic rotation 

 and for the turning produced by substances of helical 

 structure is that the effect is greatest for the more 

 refrangible rays of the spectrum, in fact is nearly 

 inversely proportional to the square of the wave length 

 of the light. This is of great importance in connection 

 with the remarkable theory of the production of magneto- 

 optic rotation in a medium having imbedded a large 

 number of very small gyrostats which has been given by 

 Lord Kelvin. In a continuation of the present article I 

 shall endeavour to give a short account of the behaviour 

 of such a medium when subjected to the disturbance due 

 to the passage through it of a beam of plane polarised 

 light. In connection with this theory the fact observed 

 by H. Becquerel, Kundt and others that magneto-optic 

 rotation is produced also in gases is of great interest. 



Absolute measurements made by Lord Rayleigh give 

 for bisulphide of carbon "042 of a minute of angle for 

 the turning of the plane of polarisation of sodium light 

 in passing through a stratum i centimetre thick in a 

 field of I C.G.S. unit of intensity the temperature being 

 18° C. A knowledge of this quantity (which is called 

 Verdet's constant for bisulphide of carbon) enables the 

 turning in other substances produced by a given field 

 to be inferred by experiments of comparison. Further 

 the intensities of magnetic fields can be inferred from 

 observed amounts of turning produced by the passage of 

 light through a column of measured length of any 

 substance for which the constant has been determined. 



In a succeeding article an attempt will be made to 

 discuss with as little as possible of the aid of technical 

 mathematics the propagation of plane polarised light in 

 a gyrostatically loaded transparent medium, the " Hall 

 effect" which, existing in a transparent dielectric, would 

 there produce magneto-optic rotation, and to indicate 

 shortly some of the bearings of magneto-optic phen- 

 omena generally on the electromagnetic theory of light. 



Andrew Gray. 



