Hackett — The Ionic Theories of Magneto-optic Rotation. 9 



cuiTents invoked to explain diamagnetism, and, since the sum of tlie 

 normal components h^,, of each kind of ion is null, with 



or without the external field, it is obvious, in calculating the suscepti- 

 bility, we may also ignore them. This result also follows, if we make 

 the assumption that the molecule is non-magnetic, and that all the 

 ions describing circuits are alike [_i.e., electrons], and consequently 

 under the influence of an external field the rotating axes for each 

 cii'cuit have the same angular velocity. In this case the total sum of 

 the^ components along the three axes 'Zqx, 2$'^, vanish when the 

 axes are fixed, and when they are rotating, since each molecule is 

 non-magnetic, and consequently the susceptibility depends on the 

 circuits qJ. In the expressions for magnetic rotation and magnetic 

 susceptibility, then we may ignore completely the normal components 

 of the magnetic field of the ion h^, h,,, h,, and regard the circuit qJ 



with a current - as the only circuit present. 



The ion then may be considered as simply describing, in a periodic 



277 ... . 



time T = the circuit q^^ which is the projection of its actual path 



2ni 



on a plane normal to the magnetic field. We have then for the 

 magnetic susceptibility, if /is the magnetic moment per unit volume 

 and q the area of the ionic circuit, 



AM = 4.2/ = 4.2 = "-^> 



k=2'^=X'!^. (6) 



A different mode of treatment of the question given by Langevin 

 for the magnetic susceptibility of diamagnetic substances leads to a 

 similar expression for 1c. The above course of reasoning shows that 

 the same simplified circuit, which occurs in the expression for is 

 the only efficient cause in producing the rotation which may be due to 

 motion of the ions in orbits. Therefore we cannot take the period in 



the expression as the natural period ; but we must take the modified 



period of the simplified circuit, and substitute 



2m 



