170 S. P. Langley—Atmospheric Absorption. 
A+B= 49) ic vo 
while if we observe by the ordinary method, peer makes no 
discrimination, we shall] have the erroneous equa 
(Aa+ BO)’ 
a’ + BO? 
which is algebraically less a the first, or correct value, for 
the expression 
A+B=— 
(Aa)? (Bd)? — (Aa+BB)" 
Se > Aw us 
readily reduces to the known form 
a’ +b? > 2ab. 
Moreover since a’?+0’—2ab= ie b)*, the error increases with the 
difference between the coefficven 
Now, in the general case, if we suppose the original radiation 
L to be composed before absorption, of any number of parts 
A,, A, A, +... having respectively the coefficients of 
absorption a,,4,, a, +... the true value of L is at by 
a series of fractions which may be written in the for 
f= send OFA 
whereas the value of the geri energy by the suntan 
formula would be 
= (Aa)? 
= 2 Ao 
so that, all the quantities being positive, by a known i 
this 
i and for the same values of A,, 
inequality is Spe she Lees the difference in the values of | 
the uaoresa meee 
the radiations of which the light (or heat) of the star or sun is 
composed, and also that the amount by which the true values 
are “hate a with the difference between the coefficients. 
tated above that the usual hypothesis makes t 
sbéfiicient of eg sth gis a constant. It will be seen from the 
above table, however, that it varies from one stratum to the 
next; that it is least ‘when obtained by observations near the 
zenith ; and that it increases progressively as we approach A the 
horizon. For since a and 5 are each less than unity, each 
the sums Aa+Bi, etc., in the above table is less than the pre 
ceding. It is also evident that their rate of diminution - 
eat ek 
‘ eas 
¢ 
x 
