Prof. Thomson, On the theory of the rotation, etc. 313 
On the theory of the rotation of the plane of polarization by 
solutions. By Prof. J. J. Thomson, M.A., F.R.S. 
\Read 20 May 1907.] 
The rotation of the plane of polarization by solutions of such 
substances as sugar or tartaric acid has been the subject of many 
investigations largely owing to the fact that by the theory of 
the unsymmetric carbon atom developed by Van ’t Hoff and 
Le Bel, the measurement of the rotation of the plane of polari- 
zation by a substance affords a valuable means of determining 
the chemical structure of the atom of the substance. Very little 
work seems, however, to have been done in connection with the 
theory of this effect. In this paper I propose to discuss under 
what conditions a collection of atoms would possess the power of 
rotation if each atom consisted of a number of electrified parts 
rigidly connected together. 
First, let us consider what terms in the mathematical equations 
which express the propagation of waves of light represent this 
effect. If X, F, Z are the components of the electric force, a, /3, y 
those of the magnetic force, u, v, w the components of the current, 
then, 
dZ dY da. 
dy dz ^ dt ’ 
dX dZ d/3 
dz dx ^ dt ’ 
d Y dX dy 
dx dy ^ dt ’ 
dy 
dy 
da 
dz 
d(3 
dz 
= 47 rUy 
dy 
dx 
= 4>7TV, 
— -j — = 47 TU), 
d(3 da 
dx dy 
where p is the magnetic permeability of the medium. 
If no matter is present, the current is merely the polarization 
, , , K dX K dY K dZ , 
current whose components are -r- — , ^ , — where 
47t dt 47 r dt 47 r dt 
K is the specific inductive capacity of the medium. When, how- 
21 
VOL. XIV. PT. III. 
