292 



Lord Kelvin on 



This shows least luminosity of the sky around the sun at the 

 zenith, increasing to x> at the horizon (easily interpreted). 

 The law of increase is illustrated in the following table of 

 values of \ (cos /3 + sec/3) for every 10° of /3 from 0° to 90°. 



<8. 



^ (cos /3-f sec/3). 



0. 



§ (cos/3 + secj8). 



0= 



1000 



50° 



1-099 



10° 



1000 



60° 



1-250 



20^ 



1002 



70° 



1-633 



30o 



1-010 



80° 



2-966 



40° 



1036 



90° 



CC 



§ 67. Instead now of considering illumination on a plane 

 perpendicular to the line of vision, consider the illumination 

 by light from our one-centimetre-thick great* horizontal 

 plane stratum of air, incident on a square centimetre of hori- 

 zontal plane. The quantity of this light per unit of time 

 coining from a portion of sky subtending a small solid angle 

 12 at zenith distance /3 is Q cos fi. Taking 12 ■ = sin fid/3dyjr and 

 integrating, we find for the light shed bv the one-centi- 

 metre-thick horizontal stratum on a horizontal square 

 centimetre of the ground, 



f *+£ 



://3sin/3.Q 



cos/3 4tt> rT(jy—D) 



n 



3\ 



a 



[ T iE - B] 



S .(18). 



Xow each molecule and particle of dust sheds as much light 

 upwards as downwards. Hence (18) doubled expresses the 

 quantity of light lost by direct rays from a vertical sun in 

 crossing the one-centimetre-tbick horizontal stratum. It- 

 agrees with the expression for k in (1) of § 55, as it ought 

 to do. 



§ 68. The expression (15) is independent of the distance of 

 the stratum above the level of the observer's eye. Hence if 

 H denote the height above this level, of the upper boundary 

 of an ideal homogeneous atmosphere consisting of all the 

 ultimate molecules and all the dust of the real atmosphere 

 scattered uniformly through it, and if s denote the whole light 

 on unit area of a plane at E perpendicular to E T, from all 

 the molecules and dust in the solid angle fl of the real atmo- 



* We are neglecting the curvature of the earth, and supposing the 

 density and composition of the air to be the same throughout the plane 

 horizontal stratum to distances from the zenith very great in comparison 

 with its height above the ground. 



