x 
178 S. P. Langley—Atmospheric Absorption. 
(the true value) while the ordinary and erroneous method, 
which does not discriminate, gives 
Sano y  L(ASL Bb HOOF. ot ot 
"Aa? +Bo7+Cei+ .... 
ive the most favorable case for the observer, where 
(what is rarely or never actually possible), he begins his obser- 
vation with the sun or star in the zenith, in a sky so change- 
lessly serene that he may continue them up to a point where 
— = 17.5 nearly. 
a 
photometer or actinometer. 
The successive values of the absorption thus found by 
comparing a zenith observation with three successively lower 
altitudes, are 21 per cent, 19 per cent, 18 per cent. All agree 
much within the probable error of actual observation, as ob- 
servers conversant with this matter will readily admit, and yet 
the true value is all the while 
5.9 
iG oP or 41 per cent. 
It will have been noticed in fact, that the determinations of 
this absorption-coefficient by various observers already cited, 
differ among themselves as much as these values do from 
each other, and if these conditions represent those of nature, 
the result must be in practice, that years of observation will be 
accordant in giving the wholly wrong absorption of from 19 
‘to 224 per cent, and that the actual minute systematic dis- 
crepancies pointed out by our theory, and which are signifi- 
ant of some error in the formula, would probably remain 
long undetected. While the observer, then, we admit, has 
strong apparent evidence from the close agreement of his obser- 
vations, that if there be an error in his formula, it is practl- 
cally negligible, yet this evidence according to our demonstra- 
tion is fallacious, and the actual error, as appears from the 
numerical illustration, may well exceed double the amount im 
question, for the above values might be increased without 
imposing any conditions but such as it may be reasonably 
assumed are those of nature. 
The writer believes the actual mean absorption of sun and 
star-light to be not improbably over 40 per cent, at the sea 
level ; but were the stars alone in question, the fact would have 
but little importance, since their relative magnitudes (unless 
