and the Rotatory Dispersion Formula. 415 



much greater than that employed for the visual observations, 

 and the dark bands were found to be symmetrical with respect 

 to the D lines, that is the rotation was the same at points 

 in the spectrum at equal distances (measured in wave-lengths) 

 to the right and left of the D lines. This was not the case 

 with less dense vapours, the rotation being greater in the 

 vicinity of D 2 than in the vicinity of Dj. The rotation con- 

 stant of D 2 was found to be about double that of D x ; but 

 since the direction of rotation is the same on opposite sides 

 of the absorption-bands, the effects of the two bands are addi- 

 tive, and lack of symmetry will be less noticeable with very 

 dense vapours, where the measurements are made in a region 

 not very close to the lines. 



Verification of the Rotatory Dispersion Formula. 



Drude, in his Lehrbuch der Optik, has given two formulae 

 for the magnetic rotatory dispersion, the first of which, 

 developed from the hypothesis of molecular currents, calls 

 for an anomalous effect on crossing the band, and obviously 

 does not apply to sodium vapour. The second, developed from 

 the Hall-Effect Hypothesis, predicts rotations of similar sign 

 and equal magnitude for wave-lengths symmetrically situated 

 in the spectrum, with respect to the centre of the absorption- 

 band. The formula deduced for the rotation is 



_ 1 U b\ 2 \ 



~nW + (V-Xlf) 



In the case of sodium vapour n differs so little from unity 

 that it can be left out of account. Investigations of the 

 refractivity of the vapour by the writer, have shown that with 

 very dense vapour (comparatively speaking) the value of n 

 may be as great as 1*3 in the immediate vicinity of D 2 , but 

 calculations showed that in all of the cases dealt with in the 

 study of the magnetic rotation, n was practically equal to 

 unity. When working very near the D lines the vapour was- 

 extremely rare, while observations made with denser vapours 

 covered regions not very near the absorption-lines. Since, 

 moreover, the rotation is zero for very short waves, the first 

 term in the formula drops out, i. e., a = 0. Precisely the 

 same thing was done in the case of the ordinary dispersion 

 formula, since the refractive index was found to be unity for 

 very short waves *. The similarity in the sign of the rotation 

 on opposite sides of the bands results from the fact that the 



* See previous paper on the "Dispersioi of Sodium Vapour," this 

 Journal, vol. viii. p. 293 (1904). 



