NO. 10 SOLAR RADIATION AND WEATHER STUDIES ABBOT 43 



D. Criterion for True and False Periodicities and Limit to the Number 

 OF Periodicities 



If it were the case that in long intervals of time only very small 

 changes in phase and amplitude took place in the forms of the peri- 

 odicity curves, it would be simple as well as obviously indicated to 

 pick out, evaluate, and remove periodicity after periodicity until no 

 more of them could be discerned in the residual temperature depar- 

 tures. In fact it would have been done by meteorologists long ago. 

 But as we have now shown, this simplicity does not obtain. Although, 

 for instance, the ii -month less 3 days periodicity may be traced at 

 Berlin during times of low sun-spot numbers for no years, with an 

 average amplitude of about o.°4 Centigrade, there are wide fluctua- 

 tions of phase and amplitude during that long interval. So the ques- 

 tion arises, if we are to admit that obscure causes produce reversals 

 of phase and wide fluctuations in amplitude, how shall we know if a 

 supposed periodicity is real or arbitrary? 



The quandary is much more serious for long periods than for short 

 ones. During ii|^ years there are, for instance, twelve 11 -month 

 periods and still more of 7, 8, and 9f months. If so many repetitions 

 yield, as we have seen that they do, definite smooth mean curves of 

 considerable amplitude representing the periodicity throughout these 

 abundant repetitions, and there follows an abrupt change to another 

 type which continues equally well verified through a second interval 

 of ii| years, the mere change of type, associated as Hale has shown 

 it to be with a reversal of the magnetic status of the sun, is not a valid 

 argument for the rejection of this otherwise excellent periodicity. 



When, however, the longer periods of 21 to 68 months are in ques- 

 tion, the number of repetitions of them in 11^ or even in 23 years 

 is not enough to eliminate irregular fluctuations, or to inspire much 

 confidence. For the mean curves are left very ragged. If no sup- 

 porting evidences were available, they would sometimes seem probably 

 accidental. 



But let us take as a specific example the 68-month curve at Berlin, 

 as shown in figure 18, I to V. The following observations may be 

 made : 



1. Each curve shows seven waves, indicating a periodicity of 9I 

 months. 



2. Removing, in imagination, the waves due to the 95-month peri- 

 odicity, each subfigure shows a smooth curve of 68 months' period, 

 roughly similar in form to a sine curve. 



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