386 
ME. LOUIS VESSOT KING ON THE SCATTEEING AND 
It can easily be shown by integrating by parts that 
["/(«)£«« = i(l-e-“)+iC/(C), . 
Jo 
so that 
/3={l-i/(C)-iG(C)}c/C. . 
Finally we obtain for eg, e, ej the expressions 
1 
'^~y/C + /(iC)c/C 
_ G(Csec^) 
' “y/C!+i{/(C)+G(C)}e/0’ 
g-C sec f 
'‘ = r/C+i{l + /(0)}c/C- 
The approximate solution of (32) may now be written 
J(X) 
Mo(^)S 
_ g-Ko(lI-X) sec f 
(42) 
(48) 
(44) 
(45) 
where ?!> (X) is defined by (36) and the values ej, e, €2 are given by (44) and are 
employed in (4S'! according as we wish to make use of the extreme or mean solutions. 
From ( 20 ) the radiation scattered to a point on the earth’s surface, contained in a 
small solid angle w in a direction ^ with the vertical, is given by 
wT = 0, f" J (X) dK 
Jo 
Since R = X sec </) this equation becomes 
T {<p, i) = sec 0 r J (X) dX,.(46) 
Jo 
where the dependence of the sky radiation per unit solid angle on the direction (p and 
on the zenith distance of the sun i is denoted by T (0, ^). 
If we denote by mR ( 0 , the radiation to a point at X = H contained in a small 
solid angle w pointing earthwards in a direction 0 with the vertical, we have 
R ( 0 , 0 = sec 0 pe-Ko(ii-x)sec^ J (X) dX.(47) 
Jo 
Substituting for J (X) from (45) we obtain from (46) 
-KoII sec f 
H 
-KoX (sec <?>—sec f) 
<ix+(:■)}%- 
K.I„»*^(X)(iX 
T ( 0 , 0 = Mo (0) S sec 0 
