14ê 



,.=^l/!;zii „5) 



4 K 2 mun^ 



This is the maximum value of the index of absorption which is 

 found at tiie middle of the line (n = 0). 



Whether the supposition that the eoefticient of i in (22) is much 

 smaller than unily be right, may be decided by calculating /<„. For 

 it is evident that this supposition is equivalent to the inequality 



KK « 1 ; 



it requires therefore that the absorption over a distance of one 

 wave-length is small. 



If this is not the case we may not use (24). However, by combining 



(22) and (4), we then find 



h=z- e 2"- , 

 H 



where ft may differ considerably from 1, and h^ still has the value 



determined by (25). (This will however no longer be the index of 



absorption for v = 0.) 



Formula (25) may be so transformed that it becomes fit for 



numerical calculation. If we express u in the absolute temperature 



T and the molecular weight M of the gas, N in Tand the pressure 



p (in mm. of mercury), »„ in the wave-length ).„ (in A.U.), substituting 



also the values for e and in, we find 



/<„ = 5,7.10^pA„[/^ (26) 



We shall now make some applications of these )'esults. 



§ 9. Wood's remarkable experiments ') on the scattering of the 

 rays of the ulti-aviolet mercury line ^2536 by mercury vapour have 

 shown that e\'en at ordinary temperatures this scattering is very 

 considerable. The intensity of the beam decreases to half its original 

 value over a distance of 5 mm. 



The vapour pressure at this temperature is about p =: 0,001 and 

 putting il/=i:200 and 7"= 290 I find from (26) a value a little 

 above 400 for /<„. This is much too high compared with Wood's 

 result. It must however be borne in mind that the beam for which 

 he measured the extinction contained a small interval of frequencies, 

 so that we are concerned, not only with the value of /t„, but also 

 with those of h which correspond to small positive and negative 

 values of v and may be considerably smaller than h^. However, 



1) R. W. Wood, Selective reflexion, scattering aud absorption by resonating gas- 

 molecules, Phil. Mag. (6) 23 a912), p. 689. 



