396 Mr. G-. W. Walker. The Application of the Kinetic 



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 refrac- 

 tive 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. 



