Absorption of Light by the Earth's Atinosphere. 
5 
It was at first hoped that these observations would yield both the 
coefficient of absorption ( = y) and the height of the atmosphere ( ■= d), 
but a variety of solutions confirmed me in the view that a far more 
refined series of observations would require to be made before any value 
of the height of the atmosphere worthy of credence would emerge from 
the equations. 
In the present solution, therefore, the coefficient of absorption is 
expressed as a function of the height of the atmosphere. 
We may, however, indicate an approximate solution in which the 
height of the atmosphere is also determined. 
A first solution yields as a value of the coefficient of atmospheric 
absorption — 
As the magnitudes given above are those which are obtained from a 
comparison with zenith magnitudes, it is necessary to add to these 
differences the coefficient of absorption in order to obtain the absolute 
decrease in brightness due to the amount of atmosphere passed through. 
We may term these new quantities absolute values : they represent 
the difference between the observed brightness of a star at certain 
zenith distance and the real brightness of the star if there were no 
atmosphere. 
The foregoing table of decrease in magnitude becomes therefore by the 
addition of the coefficient of absorption — 
0-20 m. 
Zenith distance 79° 
Decrease in brightness 0*84 m. 
81 
83 
85 
87 
89 
0- 95 
1- 15 
1- 48 
2- 02 
2-90 
And the resulting equations of condition are — 
(0-95)^ + 0-296 
(1-15)- + 0-281 
(1-48)- + 0-257 
(2-02)- + 0-210 
(2-90)- + 0-099 
