Regular Reflexion of Light by Gas Molecules. 99 



50. As hitherto, let the wave-fronts oil the primary dis- 

 turbance be parallel to the plane of yz, with the electric 

 vector parallel to the ^r-axis ; and let the resonant gas- 

 molecules be contained in a rectangular vessel with trans- 

 parent sides parallel to the three co-ordinate planes. Then, 

 if the molecules are of type I., each of them will be vibrating 

 ■symmetrically with respect to an axis parallel to the axis of z, 

 and the following deductions can be immediately made. The 

 secondary diffuse radiation proceeding in any assigned direc- 

 tion will be fully polarized, and in a direction making an 

 angle 6 with the axis of z, the intensity of the secondary 

 diffuse radiation will be proportional to sin 2 #. 



51. Alternatively, suppose the molecules to be of type II., 

 ■each having fixed within it a definite axis, with respect to 

 which any induced vibration will be symmetrical. Consider 

 a molecule whose axis is inclined 6 to the s-axis, while the 

 plane parallel to the r-axis through the axis of the molecule 

 makes an angle with the plane of xz. Then the vibration 

 of the molecule can be resolved into three rectangular com- 

 ponents having amplitudes proportional to 



sin 6 cos <f>, sin 6 sin <£, cos 6. 



For diffuse secondary radiation emitted in the direction of 

 the axis of .i 1 , the polarized components have intensities in 

 the proportion 



av cos 2 6 : av sin 2 6 sin 2 <£ = 2 : 1 ; 



average values being denoted by the prefix av, and the 

 stronger component being that for which the electric, vector 

 is parallel to the axis of: z. The same evidently holds good 

 for the diffuse secondary radiation emitted in any direction 

 parallel to the plane of xy. For a direction parallel to the 

 axis of z, the ratio is one of equality, the radiation being 

 unpolarized. Under the conditions contemplated in this 

 paragraph, it is easily seen that the total intensity of diffuse 

 secondary radiation emitted parallel to the axis of y bears to 

 that emitted parallel to the axis of z the ratio 3 : 2. 



52. From his experimental study of the absorption of 

 radiation (\2536) in mercury-vapour at low pressure, with 

 some considerations of a general nature, Wood has drawn 

 the conclusion that, at any given instant, only a small pro- 

 portion of the mercury molecules are acting as resonators. 

 This seems to be borne out by a somewhat more detailed 

 examination of the question. In Wood's experiments the 

 radiation from a quartz mercury arc, restricted to X2536, 



H2 



