cos 2 6 



the Weights of Atoms. 291 



stratum subtending a small solid angle 12 viewed at an angular 

 distance ft from the zenith by an eye at distance r. The 

 volume of this portion of the stratum is ft sec ft r 2 cubic 

 centimetres : and therefore, if X denotes summation for all 

 the particles in a cubic centimetre, small enough for applica- 

 tion of Rayleigh's theory, and q the quantity of light shed by 

 them from the portion O sec ft r* 2 of the stratum, and incident 

 on a square centimetre at E, perpendicular to ET, we have 



g= g 2 ^ 1 /)""^ ]* sec/3 <^ Q*>s 2 fl+/o a ) • • (13). 



Summing this expression for the contributions by all the 

 luminous elements of the sun and taking 



\i=Q 



to denote this summation, we have instead of the factor 



-5T 2 cos 2 d -f p 2 , 



and we have \(o 2 = \p 2 = ±S (14), 



where S denotes the total quantity of light from the sun 

 falling perpendicularly on unit of area in the particular place 

 of the atmosphere considered. Hence the summation of (13) 

 for all the sunlight incident on the portion Q sec ft r 2 of the 

 stratum, gives 



Q-^[ :Z( " D D ~ 7)) ] 2 Q s ec ft(i cos 2 e + i)S . (15). 



§ 66. To define the point of the sky of which the illumina- 

 tion is thus expressed, let f be the zenith distance of the sun, 

 and yfr the azimuth, reckoned from the sun, of the place of 

 the sky seen along the line ET. This place and the sun and 

 the zenith are at the angles of a spherical triangle SZT, of 

 which ST is equal to 6. Hence we have 



cos 6 = cos £ cos fi+ sin f sin ]3 cosy . . . (16). 



Let now, as an example, the sun be vertical : we have f = 0, 

 6 = ft, and (15) becomes 



Q=£ 2 [ ^"-^ Jft-itco^ + ^ec^ . . (17). 



