and their Magneto-optic Properties. 281 



provided that the mean time of revolution is comparable 

 with r, and, of course, that the axes of rotation are hap- 

 hazardly distributed. 



Without entering upon the details of my calculations, 

 which in vector language have assumed a very simple form, 

 I shall quote here the final result only. Let, for the sake of 

 simplicity, the absolute value of the angular velocity, cd, be 

 the same for all atoms or molecules, but let all directions of 

 axes of rotation be equally represented. Then the amount 

 of polarization P, ranging from to J , is nil for rays parallel 

 to the ray n of the exciting (unpolarized) light, and, for any 

 ray perpendicular to n, for the fundamental line of the 

 spectrum, 



g- i+ffia* '''"'"'- • • • (^ 



where t has the same meaning as throughout the paper, and 

 u is the angle through which the atoms are turned during 

 the time t. [In reality, the angles a. will not be equal but 

 distributed round their average a, say, according to the 

 error-law. But, for the present, we shall content ourselves 

 with the above formula, keeping in mind that (or is not 

 precisely the average wt] . For © = we have P = 1, i. e. full 

 polarization. When co (or, better, cor) increases, P decreases, 

 tending to nothing. If, as in one of Wood's more recent 

 experiments with iodine vapour, P = '064, then, if the whole 

 of the missing 93*6 per cent, can be thrown upon molecular 

 rotation, formula (28) would require that 



a>T = 4-072 radians (29) 



This is a huge angle (warning us not to neglect a 4 in 

 the above formula). If t) is of the electronic order, or t 

 equal to about 5900 T, as in our example of section 6, 

 then ft>T=0° 2' 23". That is to say, during one period of 

 luminous oscillation, of the fundamental period, the atoms 

 would turn round through less than 2 -J angular minutes, so 

 that their revolutions would still be very slow in comparison 

 with the fluorescent oscillations, although comparable with 

 the quickness of their extinction. Owing to the small value 

 of &)T, the equations leading to (28) have been considerably 

 simplified. Further details concerning this subject will be 

 given in a later publication. Here but one more remark. 

 If the ratio q/m has the electronic value, then, by (27) 

 and (29), 



co = 3*81 . 10 u radians per second. 

 This seems a prodigious angular velocity. Now. it is very 



Phil. Mag. S. 6. Vol. 32. No. 189. Sept. 1916. U 



