168 S. P. Langley— Atmospheric Absorption. 
This neglect to make what seems so pertinent an applicatiom 
of Melloni’s observation, even after it had been explained and 
extended (by Biot) will seem more explicable, when it 1s re- 
membered that no direct means of measuring the absorption in 
even approximately homogeneous rays till very recently ex- 
isted, and that a departure from the old formula, which ignores. 
the difficulties, involves their recognition, and the devisal of 
new processes to meet them. Even if we, by the employment 
of such new processes, succeed in measuring the absorption in 
approximately homogeneous rays, the approximation is chiefly to- 
homogeneity in wave-length, and not to uniformity of physical 
properties in consecutive wave-lengths, so that we are unable to 
represent the absorption as any continuous function of the lat- 
ter. In other words, we may measure on separate narrow por- 
tions (4A,, 4d,, etc.) of the spectrum and determine for each its 
apparent coefficient of transmission, (p,, p,, etc.) which is in each 
case some function of the wave-length, but we are not at liberty 
to write that the original energy of the heavenly body 
An 
A, = Jona 
since our gd is really discontinuous, a remark the import of 
which will become more apparent in the sequel. For the pres- 
ent at least, we are at liberty only to divide the spectrum intoa 
finite number of parts and to sum the results. 
ave already stated elsewhere* that in neglecting the fact 
that the absorption is really selective, we not only commit a 
error, but an error that always lies in one way, so that any 
determination of the absorption we make by the ordinary and 
erroneous formula never errs by being too great, but is, so far 
as it depends on this formula, always, and invariably, too small. 
The demonstration may be put in an extremely simple form, 
but I am not aware that it has been elsewhere given, though It 
was indicated in the proceedings just cited. 
Let us first suppose the radiation of the heavenly body to be 
really composed before absorption of two portions, A and B. 
1876). See also the excellent little treatise “ Actinometrie” by M. Radau, The 
use of two coefficients is proposed in this, as it has been before, but does not seem 
to have been followed by others, who like M. Violle, have subsequently (Annales de 
Chimie et de Physique, 1879) employed but a single coefficient of transmission. 
Still more lately, however, the importance of the consideration on w e writer 
here insists has been remarked on by Messrs. Lecher and P and perhaps by 
ers loyment of the method of Forbes. especia modified and 
h a 
extended by Crova, appears to be the best means at the command of the observer 
p 
with the actinometer or photometer. This method, however, is unfortunately Vety 
limited in its practical application, owing to the insufficiency of data thus obtalt- 
able, and it still gives a necessarily too small result, though a larger one than 
Pouillet’s. 
* Comptes Rendus de |’Acad. des Sc., xcii, 701, March 21, 1881. 
