NO. 2 



THE SUNSPOT PERIOD CLAYTON 



II 



the period shown would have been exactly the 12-months' period 

 which exists in nature. The ordinary process of harmonic analysis 

 gives the elements of a fixed period which is assumed in advance, but 

 the process described above gives any period which may exist in the 

 data near the length of the assumed period. The true length of the 

 period is determined by the average length of the interval between the 

 maxima and minima shown by the analysis. 



In the case of cosine analysis of random data the maxima and 

 minima occur at irregular intervals and the average amplitude approxi- 



11 1 1 1 1 1 1 M 111 1 11 1 mi 1 1 1 iiiiiii 11 ii|ii i ■ ■■■■ ■ 1 1 1 1 11 "nil 



1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 n 1 1 1 1 1 1 n h 1 1 1 1 1 1 1 1 1 1 1 1 n. 

 Fig. 8. — Some random data, smoothed harmonically. 



+ 10 



1 11 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ' 



1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 11 1 1 



Fig. 9. — A sequence of 5 cosine curves. 



mates zero. A plot of a series of random numbers smoothed har- 

 monically is given in figure 8. These were treated by the same method 

 as were the monthly temperatures at New York (see fig. 2) and the 

 yearly pressures at Stykkisholm (see fig. 4). The curve in figure 8 

 shows large oscillations but no evidence of periodicity. 



When evidence of periodicity is found it can usually be separated 

 from random oscillations by obtaining means of three, five, or more 

 successive periods. 



In case the amplitudes of the periodic terms are relatively small, it 

 is desirable, in order to bring out the periodic term clearly, to repeat 

 the cosine series several times consecutively. When plotted, these 

 successive series have the form of waves, as shown in figure 9. 



Observed data are multiplied by such a series of 3, 5, or 10 waves, 

 mean values are obtained, and the process is repeated by dropping one 



