14 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 94 



Unfortunately, accurate solar-constant determinations have not been 

 available long enough to fix the lengths of these periods very ac- 

 curately. In the discussion of weather periodicities below, evidence 

 is presented indicating corrections of plus i day, minus 3 days, and 

 plus I month, respectively, to the periodicities stated above as 8, 11, 

 and 45 months. 



6. Synthesis of Solar Variation 



Having resolved the curve of observation of solar variation into 

 12 periodicities of approximately determined lengths and amplitudes, 

 the next step was to synthesize these constituents and see how well 

 their summation represents the original curve of observation. This 

 operation is shown graphically in its details and completion in figure 7. 

 The average of residuals between the original curve A and the syn- 

 thetic curve B is only 0.0036 calories, or 0.19 percent. It appears that 

 the whole solar variation displayed by the observed monthly means is 

 comprised in these 12 periodicities. The small average deviation may 

 reasonably be ascribed to experimental error. 



7. Long-Range Predictions of Solar Variation 



The curves in figure 7 represent the third analysis and synthesis of 

 solar variation. A 3-year forecast of solar variation is given there. 

 This analysis is based on so much longer a period of observation than 

 the first and second analyses that several new long periodicities are 

 disclosed which add decidedly to the accuracy of the representation. 

 The first and second analyses were published each with a 2-year fore- 

 cast attached. (See Smithsonian Misc. Coll., vol. 85, no. i, 1931 ; 

 vol. 89, no. 5, 1933.) These predictions and the events are shown 

 in figure 8. The average of residuals for the first prediction is 0.0079 

 calorie, or 0.41 percent. The reader will observe that the first pre- 

 diction indicated an expectation of values all above normal, although 

 at the time the prediction was made the solar radiation had been almost 

 continuously below normal for many months. The event generally 

 confirmed this expectation. 



Unfortunately, a volcanic eruption in Chile interrupted the con- 

 tinuity of the solar-constant observations at Montezuma, so that this 

 series of 2-years' observations is at a disadvantage. It is probable 

 that part of the discrepancy, May to November, 1932, is caused by 

 the volcano. Only Montezuma values are used in preparing the figure. 

 The second prediction was made from data closing in September 

 1932, and again a prediction of solar variation for 2 years in advance 



