264 
CAPTAIN W. DE W. ABNEY ON THE TRANSMISSION 
metry during this century. But it is, in my opinion, a fallacy to think so ; and I 
believe, as I have elsewhere tried to show, that the error might be enormous—that 
the actual absorption might be twice what it is customarily taken, or 40 per cent, 
instead of 20 per cent., without the errors being detected by such observations as are 
now made.” 
It will be found from my observations, and also from those of Professor Langley 
himself, that the error made by astronomers in not taking into account the different 
coefficients of absorption of the different rays is negligible. 
I will first of all take a value which was derived for atmospheric absorption in which 
k was '001183. (Be it remembered, this is not one I adopt, but it was a value 
obtained by certain combinations.) The areas obtained for the curves of illumination 
of 0, 1, 2, 3, 4 atmospheres, and which would have been the values observed by any 
integration method, were as follows :— 
740, 657, 572, 505, 441. 
Now, as the least atmosphere through which an observer can observe at sea-level 
is 1, we may take 1 and 4 atmospheres as lying on the true curve and calculate the 
others from them, using the formula I' = Ie~ fLX , where g is the coefficient of absorp¬ 
tion and x the thickness in atmospheres. We find 
log 657 = — g + log I 
and log 441 = — 4 g log I; 
from which g = T324. 
The calculated values for 0, 2, and 3 atmospheres are then 749, 573, and 503 
respectively, values which might be said to be identical with the above. 
It may be thought that it is owing to a happy accident that these numbers are so 
close. If we take the value of the coefficient k = '0015, we find that the values of the 
areas for 0, 1, 2, 3, and 4 atmospheres are— 
730, 625, 534, 459, and 396 
respectively. Using the logarithmic formula, we find that the value of g is T529 
and the values of light passing through the above thicknesses are— 
730, 627, 538, 461, and 396 
respectively. In this case, if a be the coefficient of transmission, 
and 
of = e - ^, 
a = '858. 
Once more we may take the coefficient of scattering as k 
areas of the curves for 0, 1, 2, 3, and 4 atmospheres are— 
930, 755, 623, 513, and 
The values derived from the formula are as follows— 
755, 620, 
'0019, and we find that 
418. 
917, 
508, 
and 
418. 
