CONSTITUTION AND TEMPERATURE ON MAGNETIC SUSCEPTIBILITY. 
141 
the value of a c for the crystalline forms of these substances. The value deduced* (see 
footnote) on these assumptions must be at least of the order 10 2 and may be larger. Now 
reverting to equation (8), we see that the experimental value of By/x, approximately 
5 per cent., will be in accordance with the above theory of the effect of crystallization 
if the change of self-induction of an electron orbit of a substance in the liquid state, 
due to the presence of neighbouring molecules, be such that 
AH*/H* = 5xl0- 4 .t 
The value of this ratio will be still smaller if a c possesses a greater value than 10 2 . In 
the crystalline state, the modification of the electron orbit will be determined by 
a c AH./H, and since a c is large, this term accounts for the variation, 0y, found in the 
experimental investigation of Part I. In the case of liquids, where a t = l/3, this term 
produces no appreciable effect on the value of x, as equation (7) shows. 
(2) The Mean Molecular Field of a Diamagnetic Crystalline Substance. 
The large value of the electric polarisation constant a c is compatible with the 
considerable rigidity possessed by crystalline structures. The term a c . AH./H* will 
therefore be important in the crystalline state. For a super-cooled liquid we 
may write Ne 2 A 
* An extension of the theory of magnetic rotation has just been published by G. H. Livens (‘ Phil. 
Mag.,’ vol. 26, p. 362, 1913), in which the influence of the electric polarisation due to neighbouring 
molecules is taken into consideration. Livens shows that the rate of rotation of the plane of polarisation 
by a solution may be written 
± /h ?_ ^ V 
/xe m 2 (% 2 - n 2 ) 2 / \ m(n 0 2 -n 2 )) ’ 
where n is the frequency of the light wave, n 0 the restoring coefficient due to displacement of an electron, 
a the constant of electric polarisation, and e, H, y, and c have their usual interpretation. The 2 extends 
to all the electrons in unit volume. 
If a — 0 we get the result of Drude’s theory, where the mutual influences of the molecules are 
neglected; w is of the order 10 -2 for the liquid state, and if w is reduced to 1 per cent, of this value 
when crystallization sets in, the value of 
m (uq 2 - n 2 ) 
must be at least of the order 10. Now e == 10 -10 E.S.U., m = 10 -27 , and n 2 = n 0 2 = 10 30 . As there are 
about 10 22 electrons per cubic centimetre, a c must be of the order 10 2 at least. 
We have assumed that the medium is isotropic, but as the crystals are differently orientated this 
assumption will not change the order of a c . 
t This ratio corresponds to a small alteration of the area of an electron orbit to the maximum extent of 
1 in 2,000, a magnitude which is quite permissible. 
% This equation is in accordance with the observations of M. Chaudier, who has shown that, if a 
substance super-cools or assumes a gelatinous form, the magnetic rotation is the same as for the normal 
liquid state (i.e., a = 4 for the gelatinous state). 
