[RING] ABSORPTION OF LIGHT IN GASEOUS MEDIA 133 

Fig. 1 
The mathematical expression of this result gives rise to an integral 
equation which may be written 
(iv) 
—fT K dr’ 
Pr, 7,2,0,0)— 140) Ex, y, 2) MGR GES 2010 00e dy 
FT UE 
5 y 
/ 
I (x’ y’ 2’ 0,9) dv dw denotes the intensity of the scattered radiation 
near an element of volume dv contained in a small solid angle dw 
making an angle 9 with some fixed direction. / (®) is defined in equa- 
tion (1) and E (x’ y’ 2’) is the intensity of the external illumination at 
(x’ y’z’). The accented letters under the integral refer to the correspond- 
ing quantities for an element of volume dv’ at (2’ y’ 2’). The intensity 
at any point contained in a small solid angle @ in any direction is given 
by 
=} K dr 
QUIL = w f i (US oc (v) 
the integrals being taken so as to include scattered radiation from that 
portion of the gas contained in the small solid angle o. 
A differential equation for E completes analytical expression of the 
problem. 
The importance of the factor of self-llumination is recognized both 
by Kelvin and Rayleigh, although no attempt seems to have been made 
to estimate its effect. Schuster! in a paper on “ Radiation in a Foggy 

‘Schuster, Astrophysical Journal, xxi, p. 1, January, 1905. 
