control depends on the temperature ; whereas in all former theories
the control is supposed to be independent of temperature.
The calculation of K applies to two-atom molecules, but it is clear that a similar result will hold for a more complicated molecule, pro- vided that the energy of those co-ordinates, which are affected by an electrical field, can be affected by the communication of heat.
I have next considered the optical effects. The free atoms are first considered, and the method used is due to Lord Rayleigh, viz., calcu- lating the effect of the waves on the particles, and then the modifica- tion of the waves, which these disturbed particles produce.
The motion of a free atom under the influence of plane waves can be completely determined, and the results are as follows : Each atom moves in a complicated manner, but as a first approximation the motion may be regarded as made up of a linear motion and a periodic motion. For any individual atom this periodic motion is not parallel to the plane of the waves, nor is it strictly of the same period as the incident waves ; but on integration for the whole set, the component normal to the plane of the waves vanishes, and only the component in the plane of the waves remains. The free atoms accelerate the velocity of propagation by a term proportional to the square of the wave-length, and hence the refractive index is diminished by the same term. This is identical with the term introduced by Ketteler in Cauchy's formula to explain the observed facts in cases of abnormal not anomalous dispersion. The atoms scatter the light, and conse- quently the intensity of the transmitted light is diminished, but the effect is independent of the wave-length.
With respect to the molecules, it is found that a new distribution law obtains, the change being of such a nature that there is a periodic orientation of the axes of the molecules and a periodic surging of the centres of inertia of the molecules in the plane of the waves. Both effects contribute to the refractive index, but the former is of far greater importance than the second. The final result, which involves a function of considerable complexity, is shown to be capable of explaining ordinary or anomalous dispersion.
The formulae for K and /A, which agree in giving K = /o^ 2 , are con- sidered in their bearing on the supposed additive law. They would not give a strictly additive law, but the divergence would not be great if the properties of the constituents were not widely different. They aoree with an additive law as well as experiment warrants.
The coefficient of rotation of the plane of polarisation in a magnetic field is obtained, and is found to vanish if the masses of the positive and negative atoms are equal. Combined with the formula for refractive index an estimate of w for oxygen is obtained, w being called the angular velocity of rotation of mean square, from analogy with the ordinary velocity of mean square.
