NO. 10 SOLAR RADIATION AND WEATHER STUDIES ABBOT 33 



features would recur in successive 23-year intervals in nearly the 

 same phases that the successive complex curves formed by their 

 summation must themselves show features of some similarity, though 

 a little altered in phase and amplitude from one 23-year interval to 

 another. It is clear that, of the various intervals, V would be most 

 similar to I, because its phase is found similar to I for all periodicities 

 given except 13.6. Interval III is next most similar to I, but IV, and 

 next to that II, would be most dissimilar to I. On the other hand, 

 II and IV would be found to present many features of similarity each 

 to each. We shall recur to this when we consider the possible applica- 

 tion of periodicities to long-range forecasting. Here I content myself 

 with hinting that three most similar intervals, I, III, and V, and two 

 opposed similar intervals, II and IV, have separations of 46 years. 



The 12-month periodicity is particularly instructive. Meteorologists 

 have long known that a very long interval of years does not suffice 

 to yield monthly means of temperatures which will be closely followed 

 in the mean during a succeeding equally long interval of years. Hence 

 it was expected that a 12-month periodicity would be found in the de- 

 partures from normal temperatures at Berlin. But it would be natural 

 to suppose that its cause is purely terrestrial and that it would show 

 no relation to solar periodicities. The contrary is certainly the case. 

 Figure 15 shows clearly that the 23-year interval is of decisive in- 

 fluence in changing the phase and amplitude of the 12-month peri- 

 odicity. This is true not only at Berlin but at all other stations which 

 we have investigated, including Helsingfors, Copenhagen, Greenwich, 

 Cape Town, Adelaide, and others. 



In preparing figure 15, the 12-month data were not restricted to 

 times of low sun spots as were the data for figure 14. For it was 

 not to be presumed at first that this 12-month periodicity was due 

 to changes originating in the sun, but rather on the earth. These more 

 numerous data gave two tables of about a dozen lines each for each 

 23 years. In this way abundant evidence proves the critical importance 

 of January 181 9 and multiples of 23 years thereafter as determining 

 points in the pairing of the curves, such as has already been referred 

 to. Another interesting reference to these curves in figure 15 will be 

 found below under caption 14-B. 



From the studies rehearsed above under the various captions of 

 1 4- A, we conclude : 



1. Certain periodicities found in solar variation are found persisting 

 throughout more than a century in Berlin temperature departures. 



2. Small corrections to the supposed lengths of two of these solar 

 periods are indicated by these long ranges of data. 



