86 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1919. 
cordingly, it would seem that a pyranometer measurement of the 
brightness of a limited area of the sky near the sun would furnish 
an index of the state of the transparency of the atmosphere at the 
moment of observation, and this combined with the usual observa- 
tions of the solar intensity at the earth's surface by the pyrheliome- 
ter, and combined further with the determination of the quantity of 
the aqueous vapor between the observer and sun (which is indicated 
by the state of the great infra-red absorption bands, p and <p) might 
give the means of estimating the solar radiation outside the atmos- 
phere from observations made at a single instant of time. 
With the various data mentioned above as a basis, the writer en- 
deavored to find some method of determining the solar constant of 
radiation without the necessity of treating the several wave lengths 
of radiation separately, but after almost a week spent in working 
over the data, trying to combine them along these lines, the effort had 
to be abandoned. Mr. Moore had, however, suggested that if we 
knew the coefficient of atmospheric transmission for all of the indi- 
vidual wave lengths on a given day and had observed with the 
spectrobolometer and pyrheliometer at air mass 2 or at air mass 3, 
we could determine the solar constant from these data at once. All 
simple means having failed to give a satisfactory method, Mr. 
Moore's suggestion was acted upon, and it was found possible, by 
noting the value of the function p/psc and the intensity of the sky 
light in the neighborhood of the sun, to determine at once the trans- 
mission coefficients for all wave lengths. This we do by means of 
plots in which the data for the 60 days mentioned are employed. 
These data were used in the following manner : 
Taking the value obtained at air mass 2 by the pyranometer for the 
limited area of sky around the sun, dividing it by the value of p/psc 
at the corresponding time, we obtain a function which we may call 
" F." Plotting values of " F " as abscissae against values of the trans- 
mission coefficients for each measured wave length as ordinates, we 
obtain about 40 plots. These for the infra-red region of the spectrum 
are nearly straight lines but they become more and more convex 
toward the axes of coordinates for the rays of shorter wave lengths. 
In the 60 days which were available for the investigations the func- 
tion " F " ranged through values running from 100 to 900 of a cer- 
tain scale, while the function " a " — that is, the transmission coeffi- 
cient — ranged only through a very few per cent and for a large por- 
tion of the spectrum, including the infra-red region, hardlj^ through 
more than 1 or 2 per cent. Accordingly great error is allowable in the 
function " F " without greatly affecting the accuracy of the inference 
as to the value of the function " a." In short, by means of the func- 
tion " F " we are able to determine the function " a " for all wave 
lengths with highly satisfactory accuracy from observations at a 
