NO. 10 SOLAR-CONSTANT VALUES — ABBOT 7 



from the data, I proceeded in the following manner in the present 

 analysis. Having computed the average characteristics of the periodic- 

 ities of 8^, 9|, 11:1, and ii| months, I added their effects together for 

 all months from 1923 to 1945, and subtracted the sums from the 

 original data. I then used these revised residual data to compute for 

 16 months, 21 months, and 25 j months. But as neither 21 nor 25^ 

 months proved satisfactory, I rejected them in favor of 22^ months. 

 Then I removed the joint effects of 16- and 22^-month periodicities, to 

 give a second type of residual data. From these residual data I com- 

 puted for 30J months, removed its effects, and in each succeeding case 

 used residual data from which the effects of all lesser periods had been 

 removed. Arriving at 45^ months, I found its range too small to be 

 considered, and rejected it. 



Arrived at 91 months, after computing this periodicity a very 

 definite and persistent periodicity of about 6 months was for the first 

 time disclosed as a sort of nuisance rider on the 91 -month periodic- 

 ity. I thought to remove it by computing such a period from the data 

 as they stood before computing for 91 months. The effects of all 

 periods up to and including 68 months had been removed. The 

 result of this computation showed that a period of 6-1/16 months did 

 in fact persist from 1923 to 1945, but its effect could not be fully re- 

 moved. It had larger residual amplitudes in the latter part of the 

 computed curve for 91 months. In other words the 6-1/16-month peri- 

 odicity is of variable amplitude, and is really a subordinate feature of 

 the 91 -month periodicity. I had to content myself, unwillingly, with 

 removing it in part as just stated and leaving it in, in part, as a feature 

 of the 9 1 -month periodicity. The part left in still appears as a nuisance 

 rider in the 91 -month periodicity, and makes that periodicity a very 

 irregular thing. Instead of being represented by a fairly smoothly 

 flowing curve like all the others, this periodicity has a succession of 

 ups and downs. But I saw no way to avoid it. The period of 273 

 months is very smooth after the removal of 6-1/16- and 91-month 

 effects. 



All the periodic terms were tabulated and summed up after the 

 manner of table 32, volume 6 of the Annals. The summation of them 

 having been added in each month to a constant term 1.9462, there re- 

 sulted a curve which could be compared with the original data, and 

 which could be continued by way of prophecy backward from the 

 middle of 1923 to August 1920, and forward from January 1946 to 

 December 1951, as shown in figure 2. I give in table 3 the prophecy, 

 1946 to 1951, to show the forms and magnitudes of the several 

 periodicities. 



