154 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65 



GENERAL DISCUSSION OF THE EMPIRICAL METHODS FOR COMPUTING THE SOLAR 



CONSTANT 



Empirical methods for determining the solar constant from pyrheliometric 

 measurements alone have been proposed by K. Angstrom x and by Fowle. 2 

 Both these methods are based upon results obtained from spectrobolometric 

 observations. Angstrom's method assumes that from Abbot and Fowle's 

 observations we know both the distribution of energy in the sun's spectrum 

 and the general transmission of the atmosphere for all wave lengths in terms 

 of its value for any given wave length. It assumes further that the absorption 

 caused by the water vapor is a known function of the water-vapor pressure at 

 the earth's surface ; for this, Angstrom proposed an empirical formula based 

 upon his spectrobolometric curves. The influence of diffusion and absorption 

 can then be calculated if the transmission for some chosen wave length is 

 known from pyrheliometric observations on a limited part of the spectrum. 



Fowle's method is much briefer. He plots the logarithms of the observa- 

 tions against the air masses and extrapolates to air-mass zero by means of 

 the straight line that best fits the points. To the " apparent solar constant " 

 thus obtained he applies an empirical correction depending upon the locality, 

 and derived from local spectrobolometric observations. 



Since these methods are founded upon the spectrobolometric method, one 

 may ask, what is the justification for using them instead of the latter? Can 

 they be expected to give something more than the method upon which they 

 are founded? To the first question one may reply that the justification lies in 

 their simplicity, which makes it possible to apply them under a wide range of 

 conditions where the more cumbersome bolometric method could never be used. 

 A spectrobolometric investigation, like that of Abbot on Mount Whitney in 

 iqio, will probably always be a rare event. But especially in regard to the 

 question of solar variability it is desirable that the number of simultaneous 

 observations be large and extended to as high altitudes as possible. 



The second question, whether the abridged methods can ever deserve the 

 same confidence, or even in rare cases give greater accuracy than the spectro- 

 bolometric observations, is one that must be answered rather through experi- 

 mental results than through general considerations. Here, however, two 

 points may be noted. 



The first is, that the spectrobolometric method, which under ideal conditions 

 is naturally superior to any abridged method, is in all practical cases a method 

 involving a large number of precautions, some of which are very difficult to 

 take. The abridged methods, founded as they are upon mean values, may 

 possibly under special conditions avoid accidental errors to which single 

 spectrobolometric series are subjected. 



Secondly, it may be noted, that even in the analytical method of bolometry, 

 there arises some uncertainty in regard to the ordinates of the bolometric 

 curve, corrected for absorption, at the points where absorption bands are 

 situated. This causes an uncertainty in the water-vapor correction in this 

 method as well as in the abridged methods founded upon it. 



x Nova Acta Reg. Soc, Sc. Upsal., Ser. IV, 1, No. 7. 



2 Annals of the Astrophysical Observatory, Smithsonian Inst., 2, 114. 



