Bigelow — Determination of the "Solar Constant." 277 



Art. XXIII. — The Determination of the "Solar Constant" 

 by Means of Computations Based on the Data of Balloon 

 Ascensions; by Frank H. Bigelow. 



It is well known that the value of the " solar constant " as 

 derived from pyrheliometer observations, extrapolated by the 

 Bouguer Formula I=I j? m , is found to be something less than 

 2*00 gr.cal/cm. 2 min. On the other hand, Abbot's ordinates 

 in the bolometer spectrum energy curve are best satisfied by an 

 initial effective temperature at the sun of about 6900°, corre- 

 sponding with which the solar radiation at the distance of the 

 earth is about 4*00 gr.cal./cm. 2 min. This wide discrepancy 

 has been the subject of research in connection with the writer's 

 development of non-adiabatic meteorology, and the results of 

 an extensive computation are here summarized, the method of 

 procedure being described in Bulletins No. 3, No. 4, Oficina 

 Meteorologica Argentina, 1912, 1914 ; this Journal, Dec. 

 1912, April 1913 ; Bigelow's Treatise on Meteorology, 1914. 



If T is the temperature, P pressure, p density, R gas- 

 coefficient on the level s , satisfying P == p R T , the corre- 

 sponding P x = jOj R t Tj on the ^-level are computed from the 

 observed temperatures (T, T ) by 



nk n 7i — l 



T — T 



where ti= jp 5 — ^ per (z x — s ) meters; 1000 for example. 



■*- 1 -*-o 



Thence, R is variable, Cj> = R | — - is variable, h = j~. The 

 working gravity equation becomes 



(2) -Cp,(T,-T t )=ff(z-z a ) = -?^-'- !(}■ -g\)-(Q ,-Q.) 



T a is the adiabatic temperature at z x ; T a — T = — 9°'87 per 

 1000-meters for example; p 1Q is the mean density in the 

 column (5^— s ) for same value of n; (q 1 g ) are the observed 

 velocities. 



(3) (Q 1 -Q )-(W-W a ) + (U 1 -U )=P 10 (u-^ ) + (U 1 -U ) 



(Qi — Qo) is tne free or non-adiabatic heat, (W 1 — W ) the 

 work, (U I — U ) the inner energy, (v 1 —v ) the change of 

 volume. Hence, 



« 



(5) 



Q - Qo 



U — TJ 



P — ] ° — "K" /* T n i 



?, i- W o 



1 v — v u ld x : 



J^c.T/1 



-<!?»• (*J J.=fl,T/-«.T.« 



