332 



by 11, the absolute index of the nioditied medium by n\ we iiave 



32 jr' I - — 1 1 

 _ \n ) _32jt'(n'— n)'_32jr'(n'-n)' 



' ~ ^NX* ~" 3A^ASi' ~" 3iVA' 



because for thin gases we may put n'z=\. 



We shall lake for granted that this expression for Ji remains 

 valid in those regions of the spectrum where the scattering particles 

 produce anomalous dispersion. It is precise!}' in those regions tliat 

 h will assume considerable values. 



Now suppose (here be a mixture consisting of JSf^^N iV,-, . . . 



scattering particles of the kinds 1,2, . . . i, . . . For each kind the 

 mixture of tlie remaining kinds forms the "unmodified medium", 

 whilst the "modified medium" is the same in all cases, viz. the 

 complete mixture. We are concerned, therefore, with a single quantity 

 n' and several values i\\),n(o), . . . n^i-^, ... of n, if ii'^i) denotes the 

 absolute refractive index of the mixture without the constituent i. 



The scattering-coellicient h of the complete mixture will be the 

 sum of the scattering-coeflticients peculiar to the separate constituents, 

 each in its proper medium: 



32 .t' («'— m(o)' 



3 X' A',- 



This expression may be simplified because the above-mentioned 

 law of BiOT and Ak.\go requires, that 



«'-1 =(«(.)- 1) + K-1) 



m representing the absolute refractive index which the gas z would 

 show if it were alone in the given space. We, therefoi'e, have 

 n' — »»(,-•)=: Hi — 1, and may write: 



32 ji' (tii—iy 



h=z2: hi — --- :e — — '- . 



3 1' Ni 



A beam of light, having travelled a long way through such a 

 mixture of gases, will emerge with a loss of intensity expressible 

 as a certain function of h which has the property of increasing 

 and decreasing with k. In regions of the spectrum sufficiently small 

 to permit of neglecting the change of ).'' in them, we see that now 



^^^^ (2) 



Ni 



is the variable quantity determining the loss of light. (Compare this 

 expression (2) with the corresponding one (1) which applies to 

 refractional scattering). 



