l6 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 98 



The length and amplitudes of the periods found were as follows : 



Table 4. — Sunspot periods by harmonic analysis 



Length Amplitude 

 5.56 years 4 spots 



8.12 " 6 " 



8.94 " 10 



9-93 " 13 " 



XX.I7 " 35 " 



n.90 " 15 

 14.89 " 9 " 



19.86 " 4 " 



It is believed that this method of analysis gives the lengths and 

 amplitudes of these periods with more accuracy than has been attained 

 heretofore, but it is of interest to compare the results with the periods 

 derived by other methods of analysis by various research workers. 

 This comparison is given in table 5. 



Table 5. — Length of sunspot periods in years found by various research workers 



A. Schuster (1906) 4.8 8.4 11.13 13.5 



K. Stumpff (1928) 5.6 7.3 ... 8.8 10.0 11.13 12.9 14.3 20.5 



A. E. Douglass (1936) 8.510.011.4 13.5 14.3 ... 



D. Alter (1928) 7.6 8.1 8.7 10.0 11.37 ... 14.0 21.0 



H. H. Clayton (1938) 5.6 .. . 8.1 8.9 9.9 11.17 H-9 14-9 19-9 



The analysis of Schuster and Stumpff was made by means of the 

 Schuster periodogram, the analysis by Alter * was derived from the 

 correlation periodogram, and the analysis by Douglass 2 was made with 

 an ingenious instrument which he calls a cyclogram. 



It is interesting to note how well these periods by different workers 

 agree with each other, especially the periods between 8.1 and 14.9 

 years. The most marked discrepancy is in the periods of about 12 to 

 13.5 years, but here there are probably two periods, one of 11.9 years 

 and another of about 13 years. It is also of interest to note that most 

 of them are near submultiples of a period of about 89.36 years, a 

 period which is shown in tables 6 and 7 and in figure 12 to give very 

 closely the sunspot maxima and minima for more than 300 years. It 

 seems clear that if there are a number of periods combining to make 



1 Alter, D., A new analysis of sunspot numbers. Monthly Weather Rev., 

 vol. 56, p. 399, Oct. 1928. 



2 Douglass, A. E., A study of cycles, p. 129. Carnegie Inst, of Washington, 

 1936. 



