l6 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65 



atmospheric refraction, and the fall of temperature and barometer 

 with elevation. His assumption regarding the rate of fall of tem- 

 perature is not quite in accord with recent balloon work, and this 

 leads him to values of F(s) slightly too high, but this error would 

 not exceed 0.5 per cent. As is well known, the atmospheric refrac- 

 tion is uncertain very near the horizon, so that it cannot be expected 

 that the air-masses obtained with apparent zenith distances of 88°, 

 computed from hour angles of observation, should be perfectly 

 accurate. 



Strictly, we should determine the value, F(s), to correspond to 

 the apparent center of intensity of the sun's light emission at the 

 proper instant for every wave length, for on account of atmospheric 

 extinction and refraction this is not coincident with the center of 

 form of the sun. But we have found the correction to be always 

 less than 0.5 per cent, and have neglected it. 



A far more important consideration relates to the distribution in 

 the atmosphere of the materials which diminish the intensity of 

 sunlight, as the zenith distance increases. Bemporad's discussion 

 assumes that the atmosphere is of uniform optical quality from top 

 to bottom, so that equal masses of it transmit equal fractions of 

 incident light. The researches of Schuster, Natanson, King, Fowle, 

 and Kron show that on clear days at Mt. Wilson the atmospheric 

 extinction, for a large part of the spectrum, seems to be in almost 

 complete accord with the requirements of Rayleigh's theory of 

 scattering. Where this holds, Bemporad's assumption also holds 

 good. But it appears distinctly from Fowle's researches . that in 

 certain parts of the spectrum, notably in the yellow, red, and infra- 

 red, the atmospheric extinction is partly or mainly attributable to 

 water vapor, or substances which accompany it. These atmospheric 

 constituents, being mainly at low altitudes, require special considera- 

 tion. We give in the following paragraphs our solution of this 

 difficulty. 



By Crawford's tables (Lick Observatory Publications, Vol. VII) : 



If apparent zenith distance is 87 50', Ref r. = 13' 46" 



If apparent zenith distance is 87° 58', Refr. =- 14' 14" 



Hence assume Refr. = 14' 16" 



Whence sun's apparent zenith distance is 87 58' 30 



By Bemporad's air-mass tables : 



If apparent zenith distance is 87 58' 30", F(z) = 19-650 



But if 5 = 620, T=i6° F 1 (z)—F(z)= — 0.433 



Hence air-mass, F 1 (^), — i9- 2I o 



