122 



DR L. BECKER ON THE SOLAR SPECTRUM. 



For small Z (10) gives 



Supposing n=\, (7) gives for large Z, if j^= 1 corresponds to the zenith 



l!Vsm 2 Zj J $ + 2!Vsin 2 ZJ 



(12a). 



f*~ sinZ 1 

 and for smaller Z 



272^1,31^^(2) l/3 aj 8\ ^1^(3) 



n/2 



+ 



JA 



+ 



^^b-Hw-iV^iw-^)^ 



(13), 



(13a), 



which may he used up to Z = 85°. 



If Bessel's constants be introduced, f refers to a barometric pressure of 29 '6 inches 

 and about 50° Fahrenheit. In the case of w = any change of pressure and tempera- 

 ture is easily taken into account by employing Bessel's tables of refraction. From these 

 a table was computed which gave f x and its corrections for any barometer and thermo- 

 meter readings. The interval of the argument " Apparent Zenith-Distance" was taken at 

 0°"1 between Z = 90° and Z = 83°. 



The ^ functions in (13) were interpolated from Bessel's tables in the Fundamenta 

 Astronomies. The following is an abstract of our tables : — 



Apparent Zenith- 

 Distance. 



Absorption proportional to the Density. 



Absorption proportional to the Square 

 of the Density. 



A 



Fj in Miles. 



ft 



F 2 in Miles. 



0° 

 20 

 40 

 60 

 80 



83 

 84 

 85 

 86 

 87 

 88 

 89 

 90 



1-0 

 1-1 

 1-3 

 2-0 



5-6 



7-7 

 8-8 

 10-2 

 12-1 

 14-8 

 18-9 

 25-4 

 36-4 



11 

 1-2 

 1-4 

 2-2 

 6-2 



8-5 

 9-8 

 113 

 134 

 16-4 

 21-0 

 28-2 

 40-4 



10 



11 



1-3 

 2-0 



5-7 



7-9 

 91 

 10-7 

 131 

 165 

 22-0 

 32-1 

 537 



0-12 

 0-13 

 0-15 

 0-23 

 0-66 



0-9 

 1-0 

 1-2 

 1-5 

 1-9 

 2-5 

 3-7 

 6-2 



F gives the length in miles of a column of oxygen under a pressure of 29 6 inches at 

 50° Fahrenheit, which would produce the same effect as the oxygen of our atmosphere. 

 To assign to every line the corresponding value of f, the zenith distance was 



