Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/445

 830.] FORMULA FOR THE ROTATION. 413

constant determined by observation of the medium, y the intensity of the magnetic force resolved in the direction of the ray, c the length of the ray within the medium, A. the wave-length of the light in air, and i its index of refraction in the medium.

830.] The only test to which this theory has hitherto been sub jected, is that of comparing the values of 6 for different kinds of light passing through the same medium and acted on by the same magnetic force.

This has been done for a considerable number of media by M. Verdet *, who has arrived at the following results :

(1) The magnetic rotations of the planes of polarization of the rays of different colours follow approximately the law of the inverse square of the wave-length.

(2) The exact law of the phenomena is always such that the pro duct of the rotation by the square of the wave-length increases from the least refrangible to the most refrangible end of the spectrum.

(3) The substances for which this increase is most sensible are also those which have the greatest dispersive power.

He also found that in the solution of tartaric acid, which of itself produces a rotation of the plane of polarization, the magnetic rotation is by no means proportional to the natural rotation.

In an addition to the same memoir f Verdet has given the results of very careful experiments on bisulphide of carbon and on creosote, two substances in which the departure from the law of the inverse square of the wave-length was very apparent. He has also com pared these results with the numbers given by three different for- mula3&amp;gt; ; 2, fli ^

(I) e, (ii) e =

A&quot; x l*A.

(Ill) e = mcy ( -X^).

The first of these formulae, (I), is that which we have already ob tained in Art. 829, equation (26). The second, (II), is that which results from substituting in the equations of motion, Art. 826, equa-

d z n r/ 3 &quot;

tions (10), (11), terms of the form -^ and ~-, instead of

��dz*dt

��* Recherches sur les propri^t^s optiques developpdes dans les corps transparents par Faction du magn^tisme, 4 rae partie. Comptes Rendu*, t. Ivi. p. 630 (6 April, 1863). t Comptes Bendus. Ivii. p. 670 (19 Oct., 1863).

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