ABSORPTION OF LIGHT IN GASEOUS MEDIA. 
385 
In the notation of the preceding section we have to solve the above integral 
equation for 
u{X.) = J(X)/S/>c,(0). 
We have 
A = I and a = .(33) 
while 
0(X) = -h 
If we notice that 
where 
we find 
r Ei { -Ko (X-X')} dX'+ r Ei { -K„ (X'-X)} dX' 
0 j X 
—Ei{—ax)dx=f{ac)fa, .(34) 
f{x)* = e ^ + xEi{ — x) — x \ e "ii chi, 
J -r 
(35) 
^.(X) = i[2-/(K.X) -/{K.(H-X)}],./K„.(36) 
This expression is symmetrical with respect to the plane X = where it has its 
maximum value. The minimum value of the expression occurs at X = 0 and X = H. 
We write for brevity 
C = KoH, C = /foH, y = ttoJH, C = c + y .(37) 
We then find 
B= {l-f(iC)}c/C and b = i{l-/(G}}c/a .(38) 
We also have 
a = H-i r sec C, 
Jo 
or, introducing the notation 
we have 
Further, we find 
G (x) — (1—e ^)lx, 
ct = G (C sec f). . 
^ = H-i r0(X)dX, 
or 
(3 = 
"{1-/(K.X)} dX+ f[l-/{K.(H-X)}]cZX 
0 Jo 
e/C. 
(39) 
(40) 
(41) 
13 = C-' 
[ {l — f{u)} du 
c/C. 
* The function / (x), as defined above, occurs in a number of absorption problems. Its properties are 
described in a paper by the writer (King, L. V., ‘Phil. Mag.,' February, 1912, p, 245), where a short 
numerical table of the function is given, 
VOL. CCXII.—A. 3 D 
