NO. 2 THE SUNSPOT PERIOD CLAYTON I 5 



cosine series of harmonic waves. Plate i shows a photograph of 

 these instruments arranged for use. 



Analysis by this method brings out the hidden periods both in 

 length and amplitude and discloses any changes which take place in 

 phase or amplitude. 



ANALYSIS OF THE SUNSPOT NUMBERS 



The sunspot period is one of those periods in nature which vary 

 in length and in intensity. The question arises whether these varia- 

 tions are capable of being analyzed into a number of regular periods 

 which can be extended into the future, as are the tidal fluctuations, or 

 whether the sunspots are due to irregular explosions in the sun which 

 cannot be resolved into regular periods. 



To test this question, the sunspot numbers published at Zurich were 

 subjected to an analysis by the method outlined in the preceding pages. 

 The method was applied to the sunspot data in order to see whether 

 they could be analyzed into regular periods of different lengths which 

 could be used to predict the times and intensity of maxima and 

 minima of sunspots. The results are very encouraging. 



The first analysis indicated a fundamental sunspot period of 11.35 

 years which was modified by other periods, several of which tend to 

 coincide with the fundamental period every 68 years. 



In obtaining these periods, all the sunspot data from 1749 to 1936 

 were used. The data preceding 1793 were, however, meager and are 

 given little weight by the directors of the Zurich Observatory, who 

 are responsible for the collection. Beginning the analysis with the 

 more trustworthy data in 1793, the fundamental sunspot period 

 becomes 11. 17 years. 



The length and amplitude of the secondary periods in sunspots 

 were determined in two ways, first, directly from the observed annual 

 means ; and, second, from the residuals after determining the average, 

 or normal value, for each year of the 11.17-year fundamental period 

 and subtracting these normals from the observed data, thus approxi- 

 mately or entirely eliminating the influence of that period. 



These secondary periods have an amplitude much less than the 

 fundamental period, but the amplitude increases as the length of the 

 period approaches that of the fundamental period. The periods of 

 9.93 and 1 1.9 have amplitudes nearly half that of the fundamental 

 period. 



