370 Scientific Proceedings, Royal Dublin Society. 
Another was obtained from theoretical considerations as 
follows :—When a ray of light is transmitted through a layer of 
an absorbing medium a certain fraction of it is absorbed, and it is 
assumed that this fraction is independent of the intensity of the 
incident beam. 
If Q, denotes the intensity of the incident beam, then Q,a 
will be the intensity after transmission through a layer of unit 
thickness, where a is the coefficient of transmission. 
Similarly, (Q.a)a = Q.a? will be the intensity after transmis- 
sion through two layers of unit thickness. 
.. for a layer of thickness J, 
Q = Qa = Qe, (1) 
since @ is a proper fraction ; also u = — loga = log @ . 
Now let SRkZ (fig. 2) be the plane through the Sun S, the 
place of observation R, and the 
centre of the Earth. Then, if RR’ 
be the surface of the Earth, QQ’, 
approximately a circle parallel to 
ER’, will be the limiting height 
of atmosphere. 
Also let 
SET =a = altitude of the Sun. 
Then we have 
RQ = KN cosec a approximately. 
But the beam of light reaching 
fi from the Sun passes through a Bee 
layer of thickness RQ; hence we may write in (1), 
‘= h cosec a, 
thus Q = Qoe7 ht cosec a, 
Let 
J 1 
yu = h log @ = Ih, 
where / is a constant which is always positive and depends only on 
our atmosphere. 
Then 
Q o— Qoe™ eoseea (2) 
