118 DR L. BECKER ON THE SOLAR SPECTRUM. 



The intensity of the lines adopted for medium sun is the mean of the estimations 

 made near the meridian ; yet if the mean fell between two classes of the intensity scale, 

 the low sun observations were consulted. As to the fainter lines the mean of the 

 intensity had often to be corrected in accordance with the definition of our classes of 

 inteusity. Thus a faint line which had only once been seen was considered equal 1, 

 except when it stood near a dark line, or was a component of a close double line. 

 Further, if a line of intensity " 3 " at high sun had frequently been overlooked in low 

 sun, we assumed it to be of intensity "2." Moreover, a line of intensity " 2 " was 

 entered as " 3 " when never missed either in high or low altitudes of the sun. 



Before the intensity of the telluric lines can be treated of, it is necessary to show how 

 the absorption at different altitudes may be expressed in units of that in the zenith. 



6. Absorption at Different Altitudes. 



This problem has been solved in its simplest form by Laplace. Supposing the 

 absorption to increase with the first power of the density, he finds the absorption in our 

 atmosphere, for any zenith-distance, proportional to the refraction divided by the sine of 

 the zenith-distance. Yet M. Janssen * has shown that, for certain bands in the absorp- 

 tion spectrum of oxygen, the same absorption is produced in columns of oxygen of 

 different lengths, if these are inversely proportional to the squares of the densities. 



This discovery induces us to develope the problem generally ; the more so, as one of 

 these remarkable oxygen bands falls within the region of our work. 



Let 5 be the uniform density of a layer of atmosphere bounded by spheres of the 

 radii r and r + dr ; and let v' be the angle between the curve of light and the radius r. 

 Suppose the absorption to be proportional to the (n + 1 )th power of the density ; then we 

 have 



dF = —, P ^ (1); 



where F denotes the length of a column of atmosphere of the density 1, which produces 

 the same absorption. 



Assuming Bessel's hypothesis t respecting the decrease of density, we have 



P = Po e ~ l3s anu * = 1 -^ .... (2). 



in which p designates the density at the surface of the earth, /3 a constant (= 745747), 

 and a the radius of the earth. 



Now suppose that /x and {x are respectively the indices of refraction in the layer of air 



* Vierteljahmschrift der Astronomischen Gesellschaft, 25 Jahrgang, Erstes Heft, Leipzig, 1890. 

 t Bessel, Fundamenta astronomies Regiomonti, 1818, Sectio iv. 



