300 Mr. S. P. Langley on the Amount 



sistent with the conditions, which shall make the difference 



M N 

 between ^ and j? as small as we please, for in the equations 



Aa + Bb +Cc + T>d +&c. Aa 2 + Bfr 2 + Cc 2 + D^ + &c. 

 Aa a + B/, 2 + Oc 2 + Vd 2 + &c. Aa s + Bb* + C6 S + Dd 3 + &c. ~ 



we can always assign positive and real values to A, a, &c, 

 such that R may be as small as we desire. 



But R represents here the apparent error of observation, as 

 inferred from a comparison between "high and low stars." 

 Hence it follows that however close the agreement may be 

 between observations on absorption, made at quite different alti- 

 tudes of the heavenly body, ive have no right to infer that the 

 error of the final result is not indefinitely great. 



If, while the truth of the above proposition is admitted in 

 the abstract, it be still urged that we do not as a matter of 

 fact have reason to suppose that so indefinitely large a part of 

 the solar rays are quite extinguished ere they reach us, I 

 would point out that it is not in reality necessary to suppose 

 the present extreme case (i. e. that of a large part of the 

 original radiation being wholly absorbed), which has been 

 taken here only to make the nature of the argument more 

 evident. 



For if we agree (as we certainly may) that a notable por- 

 tion of the coefficients are near zero, and another notable por- 

 tion still but small fractions of unity, what we have just shown 

 for an extreme case will also follow for the usual one, for it 

 follows from the previous demonstration that the greater the 

 discrepancy between the coefficients the more shall we under- 

 rate the true absorption, and the greater will be our error. 

 To see what the conditions actually are, in inferring it from 

 the ordinary formula, Ave must now consider more narrowly 

 how this telluric absorption takes place. I have already 

 spoken of the general or non-selective absorption, whose ex- 

 treme type is the scattering of light by large dust-particles in 

 a sunbeam, "and now proceed to consider the other typical 

 extreme, which is that of purely selective absorption. 



I have here some photographs*, which I owe to the kind- 

 ness of Professor Rowland of Baltimore, in which we have a 

 portion of the spectrum near D, photographed when the sun 

 was on the meridian, and a second photograph of the same 

 limited portion, at about half-past three in the afternoon, 

 when the air-mass traversed was only about one half greater. 

 Notice nevertheless the immense difference caused by the 



* Not given here. 



