172 ee of Langley—Atmospheric Absorption. 
those who — employ it, who might now with propriety be 
asked to show that the continued use of methods and formule, 
certainly in some degree inaccurate, does not lead to an error at 
least as great as the total absorption in question. This has 
never been done. ere is a common assumption that if there 
were any considerable error, its results would become apparent 
in such numerous observations as have been made all over the 
world in stellar photometry and solar actinometry during this 
century, since in these observations of stellar magnitudes, for in- 
stance, two stars whose relative magnitudes are positively known, 
give results closely agreeing with the ordinary formula when 
one is near the zenith and the other near the horizon. At firs 
this looks almost like evidence that there can be no great wail 
in the determination of absolute magnitudes by the ordinary 
formula, and yet this apparent proof is Seagnietrably a fallacy 
It is certainly a specious one, but it is absolutely demonstrable 
that the error might be enormous—that the actual absorption 
sche be, for instance, 50 per cent instead of 20, without this 
gross discrepancy being detected by our present modes of obser- 
vation. As the present methods are known to give, as 1 have 
just said, values in substantial agreement (within three or four 
per cent) from independent observations made at very different 
_ altitudes of the sun or star, the proof of nen last statement 
may well be demanded, and I er on to give 
error but maintain that it is covieile is that since we do 
know that O:N=N:M very nearly, therefore N N:M=M:% 
very nearly, or in other words that if observation proves that 
oo within three or four per cent, we are entitled to assume 
2 
that there is only a like small error in writing X= 
We can make the fallacy of the preceding gen most 
obvious by first considering a particular case. Let the original 
energy be divided into any number of parts A, B, OC, etc., eacd 
with its own coefficient a, 0, c, etc., so that 
Aa +Bb +Ce + Dd +++4+KkA +Li ete.=M 
Aa@’+ Be? +Ce?+Dda’?++4+KF+L7 ete. =N 
Aad’ + Bb +Ce*°+De?+ + +KA°+LI° ete. =O 
etc., ete., etc. 
~ 
