an Atmosphere containing Small Particles in Suspension. 379 

 them. If this be represented by 



cos ^ (fa- a- 8), (7) 



A- 



8 is the retardation due to the particles, and we have 



8 = wT^(D / -D)/2D (8) 



If fju be the refractive index of the medium as modified by 

 the particles, that of the original medium being taken as 

 unity, b s =({i — l)dw, and 



At -l = nT(D , -D)/2D (9) 



If /j! denote the refractive index of the material composing 

 the particles regarded as continuous, D' /D = fi' 2 , and 



/.-l=i«T0i»-l), (10) 



reducing to 



ft-I = «T(/*'-l) (11) 



in the case where yJ — 1 can be regarded as small. 



It is only in the latter case that the formulas of the elastic- 

 solid theory are applicable to light. In the electric theory, 

 to be preferred on every ground except that of easy intelli- 

 gibility, the results are more complicated in that when (//— 1) 

 is not small, the scattered ray depends upon the shape and 

 not merely upon the volume of the small obstacle. In 

 the case of spheres we are to replace (D / — D)/D by 

 3(K / -K)/(K' + 2K), where K, K' are the dielectric constants 

 proper to the medium and to the obstacle respectively*; so 

 that instead of (10) 



1 3tiT fS*-l 



^ 1= TAl ^ 



On the same suppositions (5) is replaced by 

 On either theory 



( u '2_\ \2 T2 



3nX 4 ' { J 



a formula giving the coefficient of transmission in terms of 

 the refraction, and of the number of particles per unit volume. 

 We have seen that when we attempt to find directly from 

 (1) the effect of the particles upon the transmitted primary 

 wave, we succeed only so far as regards the retardation. In 



* Phil. Mag-, xii. p. 98 (1881). For the corresponding theory in the 

 case of an ellipsoidal obstacle, see Phil. Mag. vol. xliv. p. 18 (1897). 



