ABSOEPTION OF LIGHT IN GASEOUS MEDIA. 
381 
from a molecule can to a first approximation be taken equal in all directions, i.e., the 
equation can be reduced to one with a single variable by writing 
// ( 0 ) = fx = jut.. 
Equation (16) may now be written, since dv' = dJ dr', 
I (a;) = ME(a;) + M| I {x') dd dr' .(I7) 
Remembering that jn/jH^) = = aja^ — K/K,, = yo/p^, we now employ the transforma¬ 
tions 
R=r^d7’, X=r^c7a:, H=r^cZx, J(X)=^I(a;), . . (18) 
Jo Po Jo Po •'0 Po p 
and ( 17 ) now takes the form 
J{X) = g,E(X) + /i, [j(X')e-^'’'^'c/a)'rZR',.(19) 
while ( 15 ) transforms into 
T« = 0, r J (X) e-^'-VZR.(20) 
Jo 
The integral on the right-hand side of (19) must now be taken throughout a 
homogeneous atmosphere of density included between the planes X = 0 and X = H. 
Expressing the integral in 
(18) in cylindrical co-ordinates \h') (fig. 2), we have 
dY' 
dx' di'd^h' 
r-t(X'-X)^ ’ 
where xlr' is the azimuth of the element of volume dY' referred to some fixed direction 
of reference. The integral then becomes 
J (XO dX' r" dxh' [ 
Jo Jo 
+ (X'-X)--^] 
i'de 
r+{X'-xY 
The last integral when integrated with respect to i' gives 
f 
,-K„[r'“+(x'-xp] 
,v. 
£Ai' 
^'2^{X'-Xy ^ (X'-X)} when 
and = ——Ko (X—X')} when 
X<X'<H 
0<X'<X, 
