NO. 4 SOLAR RADIATION ABBOT, FOWLE, AND ALDRICH 1 5 



The two days, September 20 and September 21, are in almost 

 complete agreement in every feature observed, except that the 

 atmospheric humidity of September 21 slightly exceeded that of 

 September 20, and this of course led to a slight difference in pyr- 

 heliometry. We give below our reduction of the spectro-bolometric 

 work of September 20, and the circumstances of the observations 

 will be found so completely set forth that if any readers should desire, 

 they can re-reduce the day's work for themselves. 



It is the principal aim of the investigation to determine if there 

 was on these two days a systematic change of atmospheric trans- 

 parency sufficient to vitiate solar constant values obtained by our 

 usual method. Referring to our Annals, Vol. II, page 14, it may be 

 shown that for solar zenith distances less than 70 ° the intensities of 

 homogeneous rays observed at different zenith distances should be 

 expressible by the relation : 



log e = secant z log a + log e 

 where e is the observed intensity of a homogeneous ray ; e its 

 intensity outside the atmosphere ; z the zenith distance of the sun ; 



a a constant representing the fraction — in which e x is the intensity 



which would correspond to £ = 0. The above equation being the 

 equation of a straight line, the test of the uniformity of transparency 

 depends on the closeness with which the logarithmic plots for indi- 

 vidual wave lengths approximate straight lines. 



For zenith distances much greater than 70 ° the function secant z 

 must be replaced by another, F(z), representing the ratio of the 

 effective length of path of the beam in the atmosphere to that which 

 corresponds to £ = 0. This quantity, F(z), has been determined by 

 Bemporad, 1 taking into account the curvature of the earth, the 



1 Mitteilungen der Grossh. Sternwarte zu Heidelberg IV, 1904. The follow- 

 ing illustrates a computation of air-mass F(s). 



Example of Air-Mass Computation 

 For mean 120° meridian time : 



1914, Sept. 20, 5 h 51 111 o s (i. e., i m 50 s after start of first holograph). 



