S. P. Langley—Atmospheric Absorption. 169 
Let A have a special coefficient of transmission (a), and B 
another, special to itself (6). Then, if we assume (still for con- 
siderations of convenience only) that each of these portions, is, 
separately considered, homogeneous, we may write down the 
results in the form of two geometrical progressions, thus: 
TABLE 1}. 
it Gee Radiation 
Rod one Ratio. stoorpecn be By two strata. | By three strata. avcin eta: 
one stratum. 
A a Aa Aad? Aa Aat 
B b Bb Bo? BB? j Bot 
A+B Aa+Bb Aa? + Bb? Aa + BB? Aa*+ Bot 
=(M) =(N) =(0) =(P) 
Then will 
Aa+Bb _ Aa?+Bo? Aa’ + Bd® Aa‘ + Bo* 
Se Aa+Be ~ Ag+Be SS Ad +B ety 
Aad’ + Be? Aa’ + Bd*\s —/Aat+ Bd*\4 
——_— a = ST Oo ies 
Aa+Bb “ ras <( Aaees ) oe 
The fractions here are the coefficients of transmission, as 
deduced from observations at different zenith distances. They 
evidently differ, and (as will be shown) each is larger than the 
preceding, : 
In the above table Aa+Bod is the sum of the two kinds of 
and 
; 1 
Value after m absorptions ie 
Value after m absorptions 
isa constant. It is in fact not a.constant, as we shall prove 
later; but we shall first show that, if we proceed upon the 
ordinary assumption, the value obtained for the original light 
of the star before absorption will in this case be too small. 
For, if we observe by a method which discriminates between 
the two radiations, we shall have, if we separately deduce the 
la lights from our observation of what remains after one 
and again after two absorptions, the true sum 
