of tlie Atmospheric Absorption. 303 



be divided into ten parts, A, B, C, .... J, each having its 

 separate coefficient of transmission a, b, &c. — an arrangement 

 which may be taken to represent some sort of adumbration of 

 the complexity of nature's problem and the method of her 

 work. It is given here only in illustration of the kind and 

 degree of the errors induced by use of the usual formulas ; 

 and the demonstration already given in no way depends on 

 these numerical values, whose approximate exactness I do 

 not need to maintain, since they are offered merely as a 

 numerical illustration and in justification of the previous 

 assertion, that the absorption at any rate may be more than 

 double what we think it (as in this specific case) without our 

 having means of knowing of our error through our present 

 formula. 



It may, however, be incidentally observed that these values 

 do typify the facts, with a certain approximation to the real 

 values of nature, for they are obtained by approximate solution 

 of equations of the form 



ka +Bb + Cc +Vd +Ee &c.=M, 



Aa 2 + Bb 2 + Oc 2 + DtP + Ee 2 &c. = N, 

 Aa 3 + Bb 3 + Cc 3 + Bd" + Ee 3 &c. - 0, 



where M, N, 0, &c. do not differ widely from the results of 

 observation. The conclusion in this specific case therefore 

 seems Fairly typical of that in the general one. 



We have here supposed that the radiant energy from the 

 sun or star before it enters our atmosphere is divided into ten 

 equal parts, each of which in general suffers some different 

 partial absorption. While no ray may be absolutely absorbed 

 or wholly transmitted, a certain small part (represented in the 

 spectrum by known telluric lines) is so nearly absorbed, that 

 its coefficient in the first decimal place would be 0, and a 

 certain more considerable portion, corresponding in a general 

 sense to certain infra-red rays, has coefficients here undistin- 

 guishable from unity. Probably the greater part of the 

 spectral energy, however, is intermediate between these two 

 extreme types, and so our numerical values indicate. 



The first column is the original intensity before absorption 

 (we have in this particular example, for simplicity, supposed 

 A = B = C . . . . =J = 1, though this condition is not neces- 

 sary. It will be observed, however, that under it in the 

 second column Aa = a, Bb = b, &c, so that the coefficients of 

 transmission, the ratios of each geometric progression, are 

 the same in this particular column as the intensity after 

 absorption). 



