ON THE EFFECTIVE TEMPERATURE OF THE SUN. 
381 
The Atmospheric Absorption. 
Until Langley* published his “Researches on Solar Heat,’’ the unaninrity with 
which nearly all observers agreed in giving a value of about 21 per cent, to the 
absorption of light and heat from a radiating body in the zenith, was so striking that 
there seemed little doubt as to the practical accuracy of this figure. Yet, in every 
case, since under most favourable conditions the experiments must have been done with 
a thickness of at least one atmosphere, an assumption had to be made as to the effect 
which would have been produced without this thickness, and Professor Langley 
showed conclusively that this assumption was not justified by the conditions of the 
problem. 
The formula which had been most generally accepted as expressing the amount of 
radiation received from a body at different altitudes is 
q — ah^ 
where 
q = the observed intensity of radiation, 
a = the intensity of radiation on unit surface outside the limits of the atmos¬ 
phere, 
h = & “ constant,” which is the fraction showing the amount of absorption for a 
body in the zenith ; i.e., the “absorption co-efficient,” 
and 
e = the thickness of the atmosphere, the value being taken as unity for a 
body in the zenith, e is approximately equal to sec. ZD. up to a zenith- 
distance of 60° or 65°. 
In the case of the sun, ct is the solar constant. One of the mistakes made by the 
older experimenters was that of assuming the cpiantity h to be really a constant, 
which it is not. It is, in fact, a function of two variables, viz., the wave-length of 
the radiation, and e, the thickness of atmosphere traversed by the radiation. 
(Langley, in commenting on this fact, seems to have overlooked Rosetti’s work, in 
which the increase of b with e is clearly and quantitatively stated.) 
From the results of his work, Langley obtains 41 per cent, as a probable approxi¬ 
mation to the absorption of total radiation for a body in the zenith. His argument 
may be briefly summarized thus ; 
The number of wave-lengths in a composite radiation is infinite. Each wave¬ 
length may have its own individual coefficient of absorption. The coefficients of 
absorption will be infinite in number and will vary in value between 0 and unity. 
As “ some sort of adumbration of the complexity of nature’s problem and the 
* Laxglky, ‘ Professional Papers of the Signal Service,’ Washington, 1884, and ‘ Phil. Mag.,’ 1884, 
vol. 18, p.'289. 
