392 
mi. LOUIS VESSOT KING ON THE SCATTERING AND 
(7l) may be written 
T;(<», 0 ^ cos''‘a + Q (0, fl/P(0, V 
i+Q(o,fl/P(0,f). > 
From this formula we see that sky polarization is most complete for 6 = j-tt, i.e., 
over a great circle an angular distance ^ir from the sun polarization would be 
complete in light from this direction if Q (O, were zero, i.e., if the effects of self¬ 
illumination were negligible. 
For the sake of comparison with observation the ratio Tj ( 0 , ^)/T 2 ( 0 , t) is calculated 
for zenith sky, = O), in the form 
T:(o,f) ^ i+Q(o,n/P(o,^) 
12 ( 0 ,^) cos" f+Q( 0 , ^)/P( 0 , f) 
Part III. 
§ 7. xinalysis of Ohservations on the Attenuation of Solar Radiation hy the Earth’s 
Atmosphei'e. 
The intensity of solar radiation transmitted to a station at a height x above sea- 
level is given by equation (23) in the form 
E(X) = 
where 
X = [ — dx, and H = I — dx 
Jo Pq a Po 
represents the height of the “ homogeneous atmosphere.” 
Thus 
CD 
p dx 
P_ 
,%dx 
Jo 
where and are the pressures of the atmosphere at the station and at the sea-level 
respectively. We thus have, writing C^, = Qpjp^, the expression 
E(x) = .(74) 
If the heights of the barometer at the station and at sea-level are known at the 
time of observation, the comparison of absorption coefficients is independent of the 
law of variation of atmospheric pressure-gradient with height. 
H-X 
H —X = — dx, so that 
Jx po H 
I 
