NO. 10 SOLAR RADIATION AND WEATHER STUDIES ABBOT 



31 



were limited to times of low Wolf numbers. Smoothed departures 

 from normal temperatures at Berlin were arranged in periodicity tables 

 each of which fell entirely within a period of 23 years, and the be- 

 ginnings and ends of such 23-year periods fell always at an integral 

 multiple of 23 years counting from January 1819. Periodicities of 

 7, 8, 9f, II, 12, 13.6, 21, 25, 34, and 46 months were investigated in 

 this manner. Owing to the moderating influence of the 5-month 

 smoothing, already referred to, the 7-month periodicity was indecisive 

 and is omitted here. Of the 12-month periodicity I shall treat sepa- 

 rately. Figure 14 shows the results of all others. In the figure the 

 8-month curves are corrected in phase to the more exact period 8 

 months plus i day, and the 11 -month curves are corrected in phase 

 to the more exact period ii months minus 3 days. The scales of 

 abscissae and ordinates are altered in the 21-, 25-, 34-, and 46-month 

 plots for greater convenience. 



In table 6 the Roman numerals I to V refer to 23-year intervals 

 ending respectively at one. two, three, four, and five times 23 years 

 after January i, 1819. 



Table 6. — Comparison of Phases and Amplitudes. Berlin Temperature 

 Periodicities 



Xotcs. — As all the tables were prepared from the same original smoothed departures, the 

 influence of the unremoved shorter periodicities is very pronounced in causing irregularities 

 in the curves representing longer periodicities. This must obviously occur because only a few 

 repetitions (in the 46-month tables sometimes only two, sometimes three) were available for 

 the longer periodicities. Sometimes the longer periodicities display periodic submultiples 

 conspicuously. For instance in 46-I there is obviously a periodicity of 9.2 months superposed, 

 while in 46-II there is obviously a periodicity of 11.5 months superposed. These two unusual 

 periodicities correspond, respectively, to 1/30 and 1/24 of 23 years. 



Referring to the table, let us now tentatively suppose that the 

 smoothed temperature departures of Berlin were plotted in 23-year 

 cycles for the 115 years, 1819 to 1923. Considering figure 14 and 

 table 6, it would almost certainly be found that many features of simi- 

 larity would appear in the successive plots. For so many periodic 



