WOOD. — ANOMALOUS DISPEIISION OF SODIUM VAPOll. 393 



whicli is precisely what we require to explain the discrepancies between 

 the observed and the calculated values. 



Unfortunately sufTicient time did not remain for the repetition of the 

 experiment with a tube permanently in connection with the pump, but 

 the omission is not serious, for I feel certain that the explanation given 

 above is the correct one. 



An inspection of the formula shows us that, according as we are on 

 the red or blue side of the absorption band, the refractive index is given 

 by adding to or subtracting from unity the value of the constant )n = 



O.OOOOoo multiplied by the fraction -^ — ^ . In the case of all other 



substances showing anomalous dispersion, aniline dyes for example, to 

 the dispersion of which a formula has been ap{)lied, the value of this 

 fraction never exceeds 3 or 4, owing to tlie impossibility of applying it to 

 wave-lengths very close to the centre of the band. For example, in the 

 case of the dispersion of nitroso-dimethyl-aniliiie, with its strong absorp- 

 tion band at A =: 43, we cannot obtain accurate data nearer than A = 50. 



A^ 

 In this case — ; , = 3.9. 



A'^ — A,,;- 



In the case of sodium vapor the value of the fraction may be several 

 hundred or even thousand. In the case of A = 5882 the fraction is 307, 

 and yet the observed and calculated values agree closely. For A = 

 58884 the fraction is 1040; and for A = 5889.6 we have a value as 

 high as 3944. The product of these very large numbers and the small 

 fraction 0.000055 give, however, values of the index which are in close 

 agreement with the observed values. 



Discrepancies occur in the immediate vicinity of the D lines which 

 can be explained in the following way. To get values in any way con- 

 sistent with the observed values it was necessary to assign to A,„ the 

 value of the D., line, the mean value 5893 being too far removed from 

 the wave-lengths in question to give the requisite steepness to the curve. 

 The calculated values, therefore, apply to a medium with a single band 

 at D.2 and with a constant m = 0.00055. This gives us a pretty good 

 approximation to the ol)served curve, but the latter is due to the com- 

 bined effects of the bands Di and D.,, the presence of the Di band tending 

 to make the observed curve flatter than the calculated. A more correct 

 approximation could be obtained by assigning to A ,„ a value intermedi- 

 ate between Do and 5893. The proper method of procedure would, 

 of course, be to make use of two members in the dispersion formula, one 

 for I); and the other for Dj thus : 



