of the Atmospheric Absorption, 305 



A + B + C+ (Aa + B6 + C C +-)* _(5.9)' 



We give the most favourable case for the observer, where 

 (what is rarely or never actually possible) he begins his 

 observations with the sun or star in the zenith, in a sky so 

 changelessly serene that he may continue them up to a point 

 where secant ?=4 (corresponding to column V.), and where 

 the altitude is less than 15°. And we here suppose ourselves 

 to have a prior knowledge both of the actual amount of the 

 light or heat before absorption and of its composition, while 

 he is assumed to attempt to deduce the prior amount by the 

 usual formula, and from the usual observations made in the 

 gross by the 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 observers conversant with this matter will readily admit, 

 and yet the actual value is all the while 



1 — zr-^ — 77, 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 observa- 

 tion will be accordant in giving the wholly wrong absorption 

 of from 19 to 22^ per cent., and that the actual minute syste- 

 matic discrepancies pointed out by our theory, and which are 

 significant 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 observations that, if there be an error in his formula, 

 it is practically negligible, yet this evidence, according to 

 our demonstration, is fallacious, and the actual error, as ap- 

 pears from the numerical illustration, may icell exceed double 

 the amount in question, for the above values might evidently 

 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 at its minimum 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 considerable colour is present) remain 



