ABSORPTION OF LIGHT IN GASEOUS MEDIA. 
391 
We notice that E.(0, C) is only approximately equal to T (0, when C is small, i.e., 
that the usual assumption that as much radiation is scattered in the direction of 
incidence as in the opposite direction only holds approximately when the coefficient of 
attenuation is small. 
§ 6. JVote 071 the Polarizatio7i of Sky Radiatio7i. 
It is well known that sky radiation is partly polarized in a vertical plane passing 
through the position of the sun (the principal plane): in so far as the radiation to be 
scattered is direct solar radiation, the polarization ought to be complete. That 
portion of the sky radiation due to self-illumination is largely unpolarized and may to 
a large extent account for this deficiency from complete polarization: this point is 
mentioned by Rayleigh in his 1871 paper and the analysis of the present paper 
enables the magnitude of this factor to be roughly estimated. The complete solution 
of the problem from this aspect would require us to split up the incident radiation 
into two components, one of which is polarized in the principal plane, the other at 
right angles to it: the effect of self-illumination would lead to two simultaneous 
integral equations in three variables, the solution of which would be much too 
complicated to be useful. 
If, however, we refer to equations (59) and (60) it will be noticed that the 
expression for the intensity of sky radiation may be written in the form 
T( 0 , 0 = Mu(d) S {P( 0 , ^)-tQ ( 0 , ^)}/K(,.(70) 
where P ( 9 !), ^) stands for the first term in the brackets of (59) or (60) and 
Q(0,O=i^( e )d>(C,0) 
represents the effect of self-illumination. 
In default of a rigorous solution it is not.unreasonable to suppose that the portion 
of the scattered radiation due to self-illumination is independent of the angle of 
polarization of the incident radiation. As far as the primary scattered radiation alone 
is concerned, the intensities polarized in the principal plane and in a plane at right 
angles to it are in the proportion 1 to cos^O. Thus from (70) the ratio of the sky 
intensities polarized in the principal plane and in the plane at right angles to it are 
given by the ratio 
T] {<p, f) _ P (0) f) + Q (0> C) 
cos^6P(0,0+Q(0,0 
If we make use of the approximations of equation ( 66 ), 
P (■?. f) = sec </. P ( 0 , f) Mo (9 )/mo (9. Q (i), 0 = sea<j,Q ( 0 ; 1) mo (9)/a<» {0 
(71) 
