ON OPTICAL THEORIES. 257 
and the equations of motion, 
PE dn, PEL aE 
P aa + CY ai 072 + righ etc. . : . (23) 
From this it follows that the rotation per unit length is 
= a 9 
0 = mcy (i r =) (24) 
where 7 is the index of refraction, and this formula agrees well with 
experiment. 
It should be noticed that in obtaining this formula Maxwell deals 
with the displacements of an ordinary medium ; the forces assumed are 
those arising from the elastic reactions of this medium, the vortex motion 
in which is connected with the magnetic force. The displacements are 
not treated as identical with the electric displacements, nor is any indi- 
cation given of the connection between the two. 
§ 3. Fitzgerald, in the paper already mentioned, applies the theory to 
the case of reflexion from a magnetic medium.. He finds that when 
plane polarised light is reflected directly from such a medium, the 
reflected light is slightly elliptically polarised. This is not in accordance 
with Kerr’s experimental result, but Fitzgerald treats the iron as a trans- 
parent, or nearly transparent, substance with a real refractive index. 
§ 4. It was shown by H. H. Hall that when a current passes across 
a conductor in a magnetic field an electromotive force is produced whose 
strength is proportional to the product of the current and the strength of 
the field, and whose direction is at right angles to the plane containing 
the current and the field. 
By introducing into the equations for the electromotive force terms 
expressing this, so that they become 
pa PSH yg — Bl) f aigiht eae 
etc., Prof. Rowland ! has calculated the magnetic rotation of the vectors 
FP, G, H, and, on the assumption that a similar effect will be produced 
in a dielectric, arrives at the same formula as that given by Maxwell. 
§ 5. The main difficulty of the theory, and the one which stands most in 
the way of its general acceptance, is the difficulty of forming a clear phy- 
sical idea of what electric displacement is, and various analogies have been 
suggested with a view to rendering the difficulty less serious. One of these, 
due to Helmholtz,” is developed ina paper on the molecular vortex theory 
of electro-magnetic action.? It is shown there that, if the components of 
the magnetic force be identified with the molecular rotations in a con- 
tinuous medium in which the displacements are £, y, ¢, then the compo- 
nents of the electro-kinetic momentum are equal to }yé, etc.; and the 
equations of the electrical field in a conductor would imply that the 
medium in the conductor has the properties of a viscous fluid, while in a 
dielectric, so far as the motion to which the undulatory effects are due is 
1 Rowland, Phil. Mag. April, 1881. 
? Helmholtz, Crelle Journal, t. xxii. 
$ Glazebrook, Phil. Mag. June, 1881. 
1885. 8 
