1898.] on Magneto-Optic Botation. 715 



A little consideration will show that the direction of the resultant 

 rectilinear motion will, in consequence of the unequal speeds of 

 propagation, turn round as the wave advances, and will do so in the 

 direction of motion of the particles in the more quickly travelling 

 wave, generating the screw surface shown in the model I have already 

 exhibited. 



We must now consider the forces. The jmrticles moving in the 

 circular paths have accelerations towards the centres of these paths, 

 and forces must be applied to them to produce these accelerations. 

 These forces are applied in the present theory by the action of the 

 medium, and it is the reactions of the partcles on the medium that 

 are properly called the centrifugal forces of the particles. The 

 requisite centreward forces then are supplied by the state of strain 

 into which the medium is thrown by the displacement of parts of it, 

 which form in the undisturbed position a series of straight arrays in 

 the direction of propagation, into these helical arrangements round 

 that direction. The greater these elastic forces the greater the 

 velocity of propagation of the wave. 



In an elastic medium these forces depend on the amount of the 

 relative displacements of the particles, and will be greater for dis- 

 placements in the right-hand helical arrangement than for displace- 

 ments in the opposite direction if the medium has a greater rigidity 

 for right-handed distortion than for left, and the right-handed wave of 

 distortion will be transmitted with greater speed, and vice versa. 

 This is the case of solutions of sugar and tartaric acid, quartz, &c., 

 for which a helical structure has been supposed to exist in the 

 medium. 



Taking this case, refer to Figs. A and B of our large diagram 

 (Fig. 10), and let the right-handed wave travel the faster. Let the 

 waves travel up, be reflected at the upper ends, as at the surface of a 

 denser medium, and then travel down again. The reflected waves 

 are those shown in Fige;. A', B' of the diagram. By the reflection the 

 helical arrangement will be unaltered. But the plane of polarisation, 

 as we have seen, turns round in space in the direction of the motion 

 of the particles in the more quickly moving wave ; it therefore turns 

 round in the direction of the hands of a watch as the wave moves in 

 the upward direction in the diagram, and in the opposite direction 

 when the wave is travelling back. Thus the rotation of the plane of 

 polarisation produced in the forward passage is undone in the backward. 



It is easy to see that the same thing will take place if the 

 reflection is at the surface of an optically rarer medium, so that the 

 direction of motion of the particles is the same in the reflected as in 

 the direct wave. The helical arrangements, however, are reversed by 

 the reflection, and hence the wave which travelled the more quickly 

 forward travels the more slowly back, and again the turning of the 

 plane of polarisation is annulled by the backward passage. Thus Lord 

 Kelvin's hypothesis of difference of structure completely explains the 

 phenomena. 



