Hackett — The Ionic Theories of Magneto-optic Rotation. 7 



consider that the period is the same as the corresponding light vibra- 

 tion. This is not the case. Assuming that some mode of motion of 

 the ion persists, a close examination shows that it is only the 

 disturbance introduced into the path of the ion by the external 

 magnetic field which produces magneto-optic rotation, and that the 

 influence of this disturbance may be represented by the ion describing 



eir 



an orbit with angular velocity — in a plane normal to ZT in the 



customary notation. 



The average magnetic field for a time t, during which the ion 

 describes any path, is equal to the magnetic field due to a current of 



strength ^ in the path, whether this path be closed or not., provided 



the ion is not moving with a speed approaching that of light. If an 

 ion of charge e describe an orbit in the periodic time T, the magnetic 

 field of the ion can be replaced by the field due to a current of strength 



^ in the same orbit, or by a magnetic shell of the same area and 



strength, which can be resolved into three component magnetic shells 

 or current circuits, q^, q,,, q., in the rectangular planes, each circuit 



having a current strength — where q^^ qy, q. are the projected paths 



of the ion on these planes. The distortion of the path by the external 

 magnetic field, as Larmor showed, can be represented by a rotation of 



eH 



the axes round the magnetic force with an angular velocity — , while 



the ion describes its original path with reference to the moving 

 axes. It simplifies matters to take the axis of s along the 

 du'ection of the external field, and, if this be done, it is seen that the 

 magnetic field of the ion is now equivalent to a rotation of the system 

 9.xy 9.Z ^ith the axes, with an increased current in the circuit q,. 

 The rotation of the axes has a period very great in comparison with 

 the natural periods of the ions, so that the actual path of an ion is but 

 slightly altered during the period T] the average magnetic force 

 during this time will then be given by the same system as before, 



the components 5^, q,j, q., each with current strength ^ in the 



instantaneous position of the rectangular planes. This is only a 

 first approximation, and the influence of the change in the path has 

 yet to be allowed for. The actual projections of the path during the 



