ABSOEPTION OF LIGHT IN GASEOUS MEDIA. 
307 
8. On the Inteyisity of Sky Radiation as Calcuhited from the Mean Coefficients of 
Attenuation at Mount Wilson and Washington. 
It will 1)6 noticed from ((54) that the intensity from zenith sky for diderent Avave- 
leno’ths can l:)e expressed in terms of the zenith distance of the sun and the coethcients 
of attennation 0, v, and y which are determined for a given station hy an ajialysis of 
atmospheric transmission observations according to the method of the pi'eceding 
section. In order to simplify the calcidations from (64) the various fnnctions of 
C and ^ which occur in this formula are tal)ulated in Tables III., IV., and V. 
The intensity from zenith sky is then worked out for the two stations Mount 
Wilson and Washington from the mean coefficients of attenuation at these two places. 
In the first case the numerical values corresponding to the extreme and mean solutions 
of the integral equation are carried throughout all tlie calculations and in this Avay 
give the limit of errors due to an approximate solution. In the second case, which is 
taken as typical of a sea-level station, numerical values corresponding to the mean 
solution of the integral equation are alone gffien, the reason being that the absorption 
at sea-level is an extremely variable quantity which would give rise to fluctuations 
in sky radiation probably exceeding the difference of the extreme solutions. 
Zenith intensities of sky radiation for different Avave-lengths and for various zenith 
distances of the sun are given in Table VI. for Mount Wilson and in Table VIII. for 
Washington. The unit of intensities is arbitrary and is thaf employed in Table I. for 
the normal solar spectrum outside the earth’s atmosphere. The results are shoAvn 
graphically in Diagrams II. to VII. for Mount Wilson and in Diagram XII. 
for Washington. From these curves it is possible to obtain by double interpolation 
the intensity from zenith sky corresponding to any wave-length and zenith 
distance of the sun. In this way a comparison Avas made of the quality of sky 
radiation obtained by calculation Avith that obtained experimentally at Mount 
Wilson.* The results are given numerically in Table X. and are compared 
graphically in Diagram XIII. 
By integrating the curves for the zenith intensity and making use of the 
approximate formula ( 66 ) we are al)le to obtain a rough ap})roximation to the total 
Intensity of sky radiation from any direction. (3n comparing ( 66 ) Avith (65), for wliich 
0 = |- 7 r, it must be noted that the first of these fornmlm can only be used for zenith 
distances whicli are not too great. It will also be noticed that T (|- 7 r, f) does not 
vary as rapidly Avith the Avave-length as T (O, f). The nature of the scattered 
radiation from a portion of the sky near the horizon is goAmrned principally 
by the term i.e., it is of nearly the same quality as the direct sunlight 
except for the contribution to tfie intensity due to tlie second term in T (|- 7 r, 
which represents the effect of self-illumination. This feature is not shoAvn by 
* ‘ Anuals,’ vol. II., Table 32, j). 155. 
