142 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1944 
therein, and the effects of these long-term solar variations on weather. 
Figure 2 gives the monthly mean solar-constant values from 1920 to 
1939. The curve shows fluctuations which appear to be wholly irregu- 
lar. If one asks, are these fluctuations really true changes in solar 
radiation, their very magnitudes give a strong presumption that they 
areso. For inthe comparison of daily values given above it was shown 
that the probable error of the result of a single day of observation 
from one station is but 14 of 1 percent. A monthly mean includes from 
30 to 80 such values. Hence, recalling that the probable error of a 
mean is the probable error of the individual value divided by the 
square root of the number of values entering into the mean, we see 
that the probable error of a monthly mean value is from a thirtieth 
to a fiftieth of 1 percent. Yet the fluctuations in figure 2 range up to 
more than 1 percent. Hence probably many of them are veridical. 
PERIODICITIES IN SOLAR VARIATION 
Although seemingly irregular, the march of solar variation shown 
in curve A, figure 2, like the characteristic voice of the violin or of 
the trumpet, comprises a long wave with many simultaneously active 
shorter waves related to it by simple ratios. However in the solar 
variation the simple relationships appear to be only approximate, 
not quite exact, to the master cycle of 2234 years, or 273 months. 
Nevertheless it is very interesting that this master period, so nearly 
a least common multiple of 13 shorter ones, is approximately double 
the well-known sunspot cycle of 1114 years, and thus equal to Hale’s 
period of magnetic changes in sunspots. Strangely enough, though, 
the sunspot cycle does not appear among the 13 submultiples of the 
solar-constant master period, for no evidence of this 1114-year period 
can be found in the variation of the solar constant.”* 
Here are the observed periods, and their approximate relationship 
to 273 months: 
1 % 1h % Ys Va % 
273 91 68 54 4514 39% 34 
% 7 Waa th Ya ths Veq 
30% 251% 21 11.87 11.29 9.79 8.12 
Curve B of figure 2 is made up by adding together the separate 
influences of these 14 periodicities as they were determined from 
curve A by numerical analysis. The fit of the observed curve by 
the synthetic one is so good that in figure 14 of the Annals, pub- 
lished several years ago, the curve B was carried on as a prophecy 
of solar variation to the end of 1945. Four years of observation 
have become available from Montezuma station, though only in a 
provisional, not the final, reduction. Figure 14 shows a comparison 
between the prophesied and actually observed solar variation. Not 
2a See, however, L. B. Aldrich, Smithsonian Misc. Coll., vol. 104, No. 12, July 2, 1945. 
