Rotation of Sodium Vapour at the D Lines. 151 



was simplified by writing it in the form 

 , AX 2 BA 2 



O =-7^> ^ o no + 



a change which is probably allowable in the case of sodium 

 vapour, since n is very small in the case of the very rare 



vapours used, which enables us to drop the term - • The 



rotation is, moreover, zero except in the immediate vicinity 

 of the D lines, on which account we may neglect the term 



r-j , which would represent a rotatory power due to absorbing 



electron systems other than those causing the D lines. 



That the sign of the rotation is the same on opposite sides 

 of the absorption-bands is clear from the occurrence of the 

 term (A, 2 — A 2 D ) 2 in the denominator, which is always positive, 

 regardless of whether \ is larger or smaller than \jy. 



This formula is practically identical with the Becquerel 

 formula, and may be derived from it by differentiating n 

 with respect to A, in the dispersion formula, and substituting 

 the value so found in the Becquerel equation. For sodium 

 vapour, 



A • B 



A" - Af^ A' ~A^ 2 

 dn w AX , BA \ 



^A n\[X 2 -\lY ' (X 2 -X1) 2 /' 



or 



* r dn _C/ A\ 2 _5^__ \ 



A ^~nV(A 2 -X^) 2 + (X 2 -X^/" 



Becquerel's fundamental hypothesis of the revolving con- 

 formation of electrons does not appear to be very different 

 from the hypothesis of the Hall effect, for if we consider the 

 normal conformation to be a to-and-fro linear excursion, the 

 Hall-effect force, acting perpendicular to the field and to 

 the line of the electron's motion, will cause the electron to 

 describe an aster-shaped orbit, which may be regarded as the 

 normal conformation set in rotation. 



We will now see how nearly the magnetic rotation of 

 sodium vapour is represented by the Drude formula, lne 

 constants A and B can be determined from two values or o 

 for the two corresponding values of X- I have taken, for 

 convenience, the same values of h above and below the D lines. 



For example, in the case where the rotation is 720° mid- 

 way (nearly) between the D lines, we have rotations of 180 

 at wave-lengths 5885'83 and 5899'64. 



