NO. 10 SOLAR RADIATION AND WEATHER STUDIES ABBOT 49 



whether there are not other periodicities not integrally related to 23 

 years. The answers to these questions will be found in sections 14-C 

 and 14-D. 



C. RESIDUALS AFTER REMOVAL OF EVALUATED PERIODICITIES 



Having evaluated and removed, in Berlin temperature departures, 

 after the manner discussed in caption 14-B, periodicities of 7, 8, 9f , 

 II, 12, 13.6, 21, 25, 34, 46, 55, and 68 months, mean values for 

 each 6 months were computed from the residuals. From these 6-month 

 mean values, periodicities of 92 and 138 months were sought. These 

 computations were segregated into groups covering 23-year intervals. 

 In both instances, groups I, III, and V showed considerable and 

 nearly similar ranges of the periodicity, while groups II and IV 

 showed slight ranges in opposite phase. These results are indicated 

 in figure 20. The respective ranges are as follows : 



Ranges of Mean J'ahics, Berlin 



92-month period 138-month period 



In mean of I, III, and V \°.2 C. o'.y C. 



In mean of II and IV 0.4 C. 0.3 C. 



After removing all of the periodicities, including the two last men- 

 tioned, the residuals remaining were compared with the original 

 5-month smoothed temperature departures of Berlin as shown in 

 figure 21. 



It is apparent that the range of the residuals shown in curve B of 

 the figure is very much less than the range of the original data shown 

 in curve A. The average amplitudes are in fact o.°6o and o.°9oC. 

 Careful scrutiny has not suggested to us any other periodicities exist- 

 ing in the residuals except perhaps the Bruckner period of 34-| years. 

 This seems to show an average amplitude of o.°6 Centigrade in the 

 residuals. For reasons explained at much length above, but by no 

 means exhaustive of all the evidence in our hands, I believe that all 

 of the many periodicities named above have real veridity, and that 

 the processes described in their evaluation and removal are defensible. 

 Further evidence, however, will follow. 



Nevertheless, I am sure that statisticians, if they take a snap judg- 

 ment, will make the obvious remark that complex curves may be repre- 

 sented with much accuracy by a Fourier analysis of 14 terms, though 

 these terms have no physical significance whatever. For an example. 

 Dr. D. C. Miller has represented almost perfectly the profile of a 

 girl's face by Fourier analysis in 30 terms. But I think great diffi- 



