I56 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65 



MEASUREMENTS OF THE TOTAL RADIATION 



The general basis of the Angstrom-Kimball method of calculation has 

 already been described. It is here convenient to make use of the spectrum of 

 constant energy introduced by Langley, where the abscissa represents the 

 energy included between an extreme (ultra-violet) wave length and the wave 

 length corresponding to the abscissa ; the energy-density plotted as ordinate 

 would then be constant. A table giving wave lengths and corresponding 

 abscissae is given by Kimball. 1 



Referred to such a spectrum, the atmospheric transmission yx for any wave- 

 length is well represented by the empirical formula 



y x ^pm8xnm<p(5) (i) 



where x is the abscissa, m the air mass, and 8 a quantity dependent upon the 

 scattering power of the atmosphere. Angstrom made the natural assumption 

 0(8) =6. Kimball 2 finds that 0(8) = V 8 better fits the observations at 

 Washington and Mount Wilson. In the latter case we have, 



/> = 0.93, w = o.i8 

 Making these substitutions in (1) and integrating, 



Qw=Qo o.93» !5 A'0-i8mV5^ A - 



0-93 



m8 



Qm — Q01 + 0.18m V8 



Kimball then adds an empirical correction for the absorption due to water 

 vapor, based upon bolometric measurements at Washington and at Mount 

 Wilson, and finally obtains 



Qi 



- [0 . 061—0 . 008S+0 . oi2Eom ] 



Qo= -. ^ (2) 



0.93 '"5 



i -|- 0.1 8m V 8 



where £0 represents the depth in millimeters to which the earth's surface 

 would be covered by water if all the aqueous vapor were precipitated. We 

 have adopted this expression, but instead of attempting to determine E from 

 humidity measurements at the earth's surface we have eliminated it between 

 two equations such as (2) involving different air masses. 



Kimball eliminates 8 between two such equations. We have, however, 

 followed the original method of K. Angstrom and have determined 8 for each 

 day from our measurements with the green glass. The energy maximum of 

 the light transmitted by it lies at 0.526 u. (see fig. 1), to which corresponds the 

 abscissa 0.27 in the constant energy spectrum. Hence for the transmitted 

 green light 



I m =I o . 93"'5 . 270-ismv'5 



from which 8 can be computed. The values of 8 thus obtained are given in 

 table 19. 



1 Bulletin of the Mount Weather Observatory, 1, Parts 2 and 4. 



2 Ibid. 



