NO. 3 SIXTY-YEAR WEATHER FORECASTS — ABBOT 21 



Turning now to the times when Wolf numbers were < 20, the 

 curves ai^ and a^- on the right of figure 1 1 represent the mean results 

 of only four intervals before, and four after 1900. I feel sure that no 

 one, glancing at these two curves, would think that they really indi- 

 cate a period of 45^ months in Peoria precipitation ! But on removing 



" ' months from 02^, the curve F results. It indicates a period of — -^^ 



months remaining. Removing this, we get curve G. (At several 

 places in figure ill trace its course by guide lines.) Curve G is not 

 smooth, but no subordinate periods are plainly seen. Indeed, from 

 only four repetitions one could not expect a smooth curve, consider- 

 ing interferences from 21 other periods. Removing months from 



curve a2^, we have the dotted curve H, and from this months is 



5 

 removed, yielding curve I. This also is made irregular by lack of suf- 

 ficient repetitions of the 45^-month curve in the original data. Curve G 

 is now shifted 20 months to the right and combined with curve I, yield- 

 ing the dotted curve J. A heavy smooth curve is drawn to better 

 represent the 452-month period in Peoria precipitation, for all times 

 when Wolf numbers < 20, from 1856 to 1939. If the heavy smooth 

 curve representing times when Wolf numbers < 20 is now displaced 

 to the left 17 months, and superposed, as shown dotted at K over the 

 heavy smooth curve representing Wolf numbers > 20, the differences 

 found are small. However the curve for Wolf numbers < 20 has the 

 amplitude of 25 percent of normal precipitation at Peoria, while the 

 other has a range of only 22 percent. 



From these reductions, shown graphically in figure 11, we find 

 periods of ^, V12, Vis, and %o of 22| years. Many other examples 

 might be given of overriding periods, which are aliquot submultiples 

 of the periods of greater length, with which they are associated. But 

 surely these three samples, which disclose periods of ^, ^, ^, Vq, 



tabulations are always made with departures from the mean of the long column 

 representing a long period, half of the departures are above, and half below the 

 mean. Hence, in making the tabulation for the subordinate period, though half 

 of the values employed in the tabulation are larger than truly representative 

 of the subordinate period, the other half are equally smaller than they should 

 be. These excess and deficient parts nearly cancel, leaving the subordinate 

 period approximately correct. When it is removed from the longer one, this 

 longer curve also is approximately correct. As a check, however, I once drew a 

 smooth curve touching all the low points of the longer curve and computed the 

 subordinate period from differences between this smooth curve and the original. 

 Comparing, there was no considerable difference from the characteristics of the 

 subordinate curve when obtained in the usual way. 



