Ahsorption of Light by the Earth's Atmosphere. 
and let — 
L = amount of light of a star seen in the zenith direction sa, 
if there were no atmosphere, 
= m^ in magnitudes, 
Ijq = amount of light of the same star seen in the direction sa, 
= m, the apparent magnitude of the star, 
Jjq^ ^ amount of hght of the same star seen in the direction s/3, 
= mj. 
Therefore, if K is the light ratio — 
1 
or- 
putting- 
log ^-^ = {m,-m^) log K 
Vog K/ 
- = t 
1 
now- 
let— 
logK ^ 
- m^ -- ty 
t = ^ 
as 
asl3 = 0, 
OS = 1, 
sa ^ d, 
then it can be easily shown from a simple consideration of the figure 
that — 
t'd + 2tGosd-d-2 = 0, 
or — 
^ _ - cos 0 + \/ (d + iy-sin^ 6 
d 
and — 
m^-m^ = ^ { \/((i + l)^-sin2(^-cos0}- 
a 
