an Atmosphere containing Small Particles in Suspension. 381 



particles in the layer dx from unity to (l—^k 4 c 6 7rndx), and 

 the coefficient of s'm k (at + x) from to \kc ?Jr nndx. Thus, if 

 E be the energy of the primary wave, 



dE/E=-%k 4 c 6 7rndx; 



so that if, as in (4), E =E e~ hx , 



h = l7rnk 4 c 6 (19) 



The same result may be obtained indirectly from the first 

 term of (15). For the whole energy emitted from one sphere 

 may be reckoned as 



|£j_W(l+|/.)ty=-^p > . ■ • (20) 



unity representing the energy of the primary wave per unit 

 area of wave-front. From (20) we deduce the same value of 

 h as in (19). 



The first term of (18) gives the refractivity of the medium. 

 If 8 be the retardation due to the spheres of the stratum dx, 



sin k8=^kc d irndXj 



or h = ±Trnc z dx (21) 



Thus, if fi be the refractive index as modified by the spheres, 

 that of the original medium being unity, 



^-l=j7rnc 3 = ip, (22) 



where p denotes the (small) ratio of the volume occupied by 

 the spheres to the whole volume, This result agrees with 

 equations formerly obtained for the refractivity of a medium 

 containing spherical obstacles disposed in cubic order*. 



Let us now inquire what degree of transparency of air is 

 admitted by its molecular constitution, i. e., in the absence 

 of all foreign matter. We may take A=6xl0~ 5 centim., 

 fi — 1 = *0003; whence from (14) we obtain as the distance x, 

 equal to 1/h, which light must travel in order to undergo 

 attenuation in the ratio e : 1 , 



<z>=4-!xl0- 13 xn (23) 



The completion of the calculation requires the value of n. 

 Unfortunately this number — according to Avogadro's law 

 the same for all gases — can hardly be regarded as known. 

 Maxwell f estimates the number of molecules under standard 



* Phil. Mag. vol. xxxiv. p. 499 (1892). Suppose m = oo , o- = oo . 

 t " Molecules," Nature, viii. p. 440 (1873). 



Phil. Mag. S. 5. Vol. 47. No. 287. April 1899. 2 D 



