Hackett — The Ionic Theories of Magneto-optic Rotation. 3 



two possible points of view, and thus arrived at two distinct expressions 

 for the rotation. The hypothesis which assigns the effect entirely to 

 rotating ions will be examined first. 



Tlie ITypothe&is of Rotating Ions. 



The effect of a magnetic field on any substance may be expressed 

 by saying that the magnetic field induces molecular currents in the 

 case of diamagnetism, or changes the orientation of molecular currents 

 already existing in the case of paramagnetism. In terms of the ionic 

 theory, the molecular currents are due to ions describing closed circuits. 

 These circuits can all be taken, as will be shown later, to be in planes 

 perpendicular to the magnetic field. The current due to an ion of 

 charge e describing a circuit of area q in time t is «/t, and the circuit 

 acts as a magnet of moment qejT. The intensity of magnetisation is 

 nqejTy where n is the total number of such circuits per unit volume. 

 The sign of the moment of the circuit depends on the sign of the charge 

 and the direction of rotation. This can be expressed by making the 

 proper conventions connecting the signs of e and t. The flux of 

 magnetic force h per unit area due to all such circuits is given by 

 the equation 



T 



Each circuit may be regarded as indeformable, and vibrates under the 

 action of light with the same velocity as the ion would possess if its 

 motion were due i^olely to the action of light. This motion of the 

 magnetic field due to the ions causes an additional term to be added 

 to the rate of change in the magnetic induction in the equations of the 

 electro-magnetic field. By solving these equations, Drude gets the 

 rotation for the simple case of plane-polarised light travelling in the 

 direction of the magnetic field. His expression for the rotation is 

 expressed below in electromagnetic units, and in a more convenient 

 notation for the purposes of the present paper. The manner in which 

 the transformation is effected is given in detail in a note at the end of 

 the paper. When the necessary changes have been made, it is found 

 the magnetic rotation can be expressed in the form ' 



8 = ^ cvnz, (1) 

 A 2 



