2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 128 



reasonable. That is to say, our estimates of atmospheric transmission 

 are sound. 



Since the total range of variation found in lO-day mean values of 

 the measures of the solar constant only rarely exceeds 2 percent, 

 and usually is less than i percent, scientists, well knowing the seri- 

 ousness of the obstacle to accuracy presented by variable atmospheric 

 transmission, very reasonably fear that we cannot certainly determine 

 variations of the sun. It is therefore well to present at the outset the 

 evidence on the accuracy of our solar-constant measures. 



As stated in volume 6, page 163, of the Annals of the Astrophysi- 

 cal Observatory, a comparison has been made between very large 

 numbers of pairs of daily solar-constant measurements, made thou- 

 sands of miles apart, in opposite hemispheres, over a period of many 

 years. It yields, from their differences, the result that the probable 

 error of a well-observed solar-constant value, the mean of the results 



at two stations on a single day, is ' _1 percent, or ^ percent. 



V2 

 In the work I am about to present on periods in solar variation, 

 20 out of 31 of the periodic tabulations (excluding ii tables on a 

 monthly basis, made upon periods of variation exceeding 20 months) 

 comprise tables of lO-day means of the measurements at two or 

 more stations.^ These tables each contain from 10 to 100 repetitions 

 of such lo-day means. Going back to daily observations, published 

 in volumes 6 and 7 of the Annals, it will be found that most of the 

 lo-day means are means of the average results of two or more sta- 

 tions over at least 4 days, sometimes even 10 days, and of one station 

 during the remainder of the decade. Using the well-known rule that 

 the probable error of the general mean is the probable error of the 

 individual observation divided by the square root of the number of 

 observations, we see that for two-thirds of the tabulations, and exces- 

 sively so for the periods under 10 months, for which the number of 

 columns of repetition is above 40, the probable error of the individual 

 values in the final column of means is of the order of 1/60 of i per- 

 cent or less. Hence readers should not be skeptical, when smoothly 

 running curves of periodic variation are presented that have a range 

 as small as 0.04 percent. From that minimum, the ranges to be pre- 

 sented in this paper rise to values for some periodic variations of 

 0.15 to 0.20 percent. In fact, all the periods, some 23 in number, 

 used in my weather papers on precipitation and temperature at vari- 

 ous cities, have ranges in solar variation exceeding 0.05 percent. As 



1 1 shall deal with monthly data below. 



