238 ABBOT— SOLAR CONSTANT OF RADIATION. [April 21, 



Having perfected the standard and secondary pyrheliometers 

 to a satisfactory degree of accuracy and durability, the first branch 

 of solar-constant work is accomplished by reading with the silver- 

 disk i)yrhcliometer at the earth's surface, and reducing its indi- 

 cations to calories per square centimeter per minute. We now turn 

 to the discussion of the second branch of the work, namely the 

 estimation of the transmission of the atmosphere for radiation. 



Lambert and ]5ouguer showed almost simultaneously, about 1760, 

 that the transmission of light through a homogeneous medium may 

 be expressed by an exponential formula, such as : 



E = E^a»\ 



Here E is the intensity transmitted, £(, the original intensity, a 

 the fraction transmitted by unit thickness, and m the actual thick- 

 ness of the transparent medium. 



Pouillet applied Bouguer's formula to the atmosphere. As the 

 atmosphere is not homogeneous, but decreases in turbidity and 

 density from the earth's surface upward, this would seem at first 

 sight unjustified. But if we consider unit thickness to be the thick- 

 ness of the atmosphere traversed by a vertical beam, then as the ray 

 departs from the vertical, it still shines through every layer which 

 it did at first, and the path in every layer increases nearly as the 

 secant of the zenith distance of the ray. Under these circumstances 

 it can be shown that (subject to certain limitations to be mentioned) 

 the exponential formula given above should hold, if we consider E 

 to be the intensity at the earth's surface, E^ the intensity outside the 

 atmosphere, a the transmission coefficient for a vertical beam, and ni 

 the secant of the sun's zenith distance. ° 



Owing to atmospheric refraction, the fractional increase in path 

 of the ray, as the zenith distance waxes, tends to be greater for the 

 outer layers of the atmosphere than for its inner ones. On the 

 other hand, the curvature of the earth's surface produces an oppo- 

 site tendency. But for zenith distances less than 70° these effects 

 may be neglected, and they are hardly worth considering at 75° 



"See Annals Smithson. Astrophys. Obscr., Vol. ![., p. 14, 1908. 



