| KING] ABSORPTION OF LIGHT IN GASEOUS MEDIA 135 
ape. l-e* 
Co). 
T 
C2) has | 
te e™ du i e 
{ (x) = zx —— =e* + x In (2) 
uw 
Zz 
where Ei (-x) represents Glaisher’s exponential integral. (vil) 
B (x) = Ei (2) — log x 
B (-x) = Ei (x) — log x 
and. 
x el Jade AR | 
DO) (ea) let (Cr) + i (x) —B (2x) | + € di B Cat 
y representing Euler’s constant. 
The intensity of sky-radiation for any direction of sun and sky can then 
be obtained from the approximate solution of the integral equation 
which expresses by means of the functions in (vil) the sky-intensities in 
terms of the attenuation coefficients for the various wave-lengths. 
The total sky-radiation on a horizontal plane can also be calculated 
by a process of integration, and a rough estimate made of the degree 
of polarization of different regions of the sky. 
5. Numerous observations on the attenuation of solar radiation 
by the earth’s atmosphere have been taken by the Smithsonian Astro- 
physical Observatory? in connection with the determination of the solar 
constant. At anystation the law of attenuation at height x above sea- 
level is of the form 
E (a3) = Se = Se 
where (vill) 
C= B/N + vy and fr Er 
p is the barometric pressure at the station, p, that at sea-level. $ is 
the value of the intensity of solar radiation outside the earth’s atmos- 
phere corresponding to wave-length À. 8 is expressed in terms of the 
optical properties of the atmosphere, n, is the refractive index at standard 

The function f(z) is of importance in absorption problems: the function is 
tabulated by the writer: King, ‘“‘Absorption Problems in Radioactivity,’ Phil. 
Mag., February, 1912. 
? The Annals of the Smithsonian Astrophysical Observatory, Vol. 11—. 
