331 



periments of Biot and Araüo (confirmed by modern observations), 

 tlie refracting power of tlie mixture equals the sum of tiie refracting 

 powers of the constituents: 



n — 1 = ^ (ui—l). 



The condition is implied that the gases do not act on each other. 

 We shall assume this law to be valid also in those spectral regions 

 where one of the constituents causes anomalous dispersion, although 

 no very accurate direct measurements concerning such cases are as 

 yet available. (The exceedingly narrow regions of true absorption 

 are not considered here). 



If the gaseous mass is very extensive and of unequal optical 

 density, with irregular gradients in all directions, it will make every 

 beam of light spread out like a bunch of feathers. According to 

 Ohnstein and Zernickk ') tiie rate of this kind of scattering is 

 determined by "the average square of the spreading per unit of 



o' 



length" — ; to any short path / corresponds an angle « depending on 



the average value of the irregular density gradients, and proportional 

 to 71 — J of the mixture. The weakening of the transmitted light 

 will therefore be a function of 



(n-\r = [2(ni-l)y ....... (1) 



that has the property of increasing and decreasing with this quantity. 

 A characteristic difference between scattering by irregular refraction, 

 and molecular scattering, is, that in the latter process a considerable 

 part of each beam passes straight, and a small part of it disperses 

 in all directions, whereas in refractional scattering every beam itself 

 widens like a plume. 



^ 2. Scattering of light by the molecules of a gaseous mixture. 



If a beam of light of intensity 7„ has travelled a distance z 

 through a medium containing A' scattering particles per cube cm., 

 its intensity has diminished to 1 = l^e~''-, where, according to 

 Rayleigh, h has the value 



32 jr' (»—!)' 

 ' ~ 3 A^"* 

 In this expression v is explicitly stated to represent the refractive 

 index of the medium as modified by the scattering particles against 

 the unmodified medium'). Denoting the absolute index of the latter 



') Ornstein and Zernicke, These Proceedings, Vol. 21, p. 115 (1917). 

 ■') Rayleigh, Phil. Mag. 47, 375, 1899. — Scientific Papers IV, 400. 



22 

 Proceedings Royal Acad. Amsterdam. Vol. XXVI. 



