506 ON PHYSICAL LINES OF FORCE. 



is, that the particles describe their circles in opposite directions. Since, therefore, 

 the configuration is the same in the two cases, the forces acting between par- 

 ticles must be the same in both, and the motions due to these forces must be 

 equal in velocity if the medium was originally at rest ; but if the medium be 

 in a state of rotation, either as a whole or in molecular vortices, the circular 

 vibrations of light may differ in velocity according as their direction is similar 

 or contrary to that of the vortices. 



We have now to investigate whether the hypothesis developed in this 

 paper that magnetic force is due to the centrifugal force of small vortices, and 

 that these vortices consist of the same matter the vibrations of which constitute 

 light leads to any conclusions as to the effect of magnetism on polarized light. 

 We suppose transverse vibrations to be transmitted through a magnetized 

 medium. How will the propagation of these vibrations be affected by the 

 circumstance that portions of that medium are in a state of rotation ? 



In the following investigation, I have found that the only effect which the 

 rotation of the vortices will have on the light will be to make the plane of 

 polarization rotate in the same direction as the vortices, through an angle 

 proportional 



(A) to the thickness of the substance, 



(B) to the resolved part of the magnetic force parallel to the ray, 



(C) to the index of refraction of the ray, 



(D) inversely to the square of the wave-length in air, 



(E) to the mean radius of the vortices, 



(F) to the capacity for magnetic induction. 



A and B have been fully investigated by M. Verdet*, who has shewn that 

 the rotation is strictly proportional to the thickness and to the magnetizing 

 force, and that, when the ray is inclined to the magnetizing force, the rotation 

 is as the cosine of that inclination. D has been supposed to give the true 

 relation between the rotation of different rays ; but it is probable that C must 

 be taken into account in an accurate statement of the phenomena. The rotation 

 varies, not exactly inversely as the square of the wave length, but a little faster; 

 so that for the highly refrangible rays the rotation is greater than that given 

 by this law, but more nearly as the index of refraction divided by the square 

 of the wave-length. 



* Annales de Chimie et de Physique, s6r. 3, Vol. ILL p. 370; Vol. XLIII. p. 37. 



