1898.] on Magneto-Optic Botation. 719 



in the same direction. Now let a wave of transverse displacement 

 of the medium in the vertical direction pass along the medium in the 

 direction of the chain. The vibratory motion of each part of the 

 medium will turn the gyrostatic axis from the horizontal, and there- 

 by introduce horizontal reactions on the medium. Again, a wave of 

 horizontal vibratory motion will introduce vertical reactions in the 

 medium from the gyrostats. 



Now a wave of circular vibrations, like those we liave already 

 considered, passing through the medium in the direction of the chain, 

 could be resolved into two waves of rectilinear vibration, one in which 

 the vibration is horizontal, and another in which the vibration is 

 vertical, giving respectively vertical and horizontal reactions in the 

 medium. The magnetisaticm of the medium is regarded as due to the 

 distribution throughout it of a multitude of rotating molecules, so 

 small that the medium, notwithstanding their presence, seems of uni- 

 form quality. The molecules have, on the whole, an alignment of 

 their axes in the direction of magnetisation. These reactions on the 

 medium when worked out give terms in the equations of wave propa- 

 gation of the proper kind to represent magneto-optic rotation. 



It is worthy of mention that the addition of such terms to the equa- 

 tion was made by McCullagh, the well-known Irish mathematician, 

 who, however, was unable to account for them by any physical theory. 

 The necessary physical theory may be regarded as afforded by the 

 mechanism which thus forms an essential part of Lord Kelvin's mode 

 of accounting for magneto-optic effects. 



Lord Kelvin, in his Baltimore Lectures, has suggested for magneto- 

 optic rotation a form of gyrostatic molecule consisting, as shown in 

 the figure, of a spherical sheath enclosing two equal gyrostats. These 

 are connected with each other and with 

 the case by ball-and-socket joints at 

 the extremities of their axes, as shown 

 in Fig. 15. If the spherical case were 

 turned round any axis through the 

 centre no disalignment of the gyro- 

 stats contained in it would take place, 

 and it would act just like a simple 

 gyrostat. If, however, the case were 

 to undergo translation in any direction 

 except along the axis, the gyrostats 

 would lag behind, and the two-link 

 chain which they form would bend at 

 the centre. This bending would be Fig. 15. 



resisted by the quasi-rigidity of the 



chain produced by the rotation, and the gyrostats would react on the 

 sheath at the joints with forces as before at right angles to the plane 

 in which the change of direction of the axis takes place. 



The general result is, that if the centre of this molecule be carried 

 with uniform velocity in a circle in a plane at right angles to the line 



