A Representation of the Sunspot Cycle * 



By C. N. ANDERSON 



ALTHOUGH sunspots had been observed occasionally back to 

 ancient times, their study may be said to date from their redis- 

 covery by Galileo in the spring of 1610 with the then newly invented 

 telescope. Since then much has been written about their nature, their 

 periodicities and possible influence on human affairs. 



The purpose of the study reported on in this paper was to analyze 

 the components of the sunspot data and thereby to reconstruct a 

 curve which would not only represent the variation in sunspot numbers 

 from 1749 to date but would also be consistent with times of maxima 

 and minima from 1610 to 1749. A number of attempts along this 

 line have been made in the past,^' *• ^- ^- ^' " all of which have neg- 

 lected the data previous to 1749 and all have used a slightly different 

 method of analysis. It is believed that the agreement in the present 

 study is somewhat better than in those of the past; nevertheless, no 

 claim is made for any great accuracy in predicting future sunspot 

 activity. Harmonic analysis based on a fraction of a period is always 

 a source of danger and, furthermore, we have no assurance that all 

 the components of the sunspot curve are periodic functions.^ In fact, 

 some papers have appeared in which each cycle was treated as a more 

 or less independent outburst.^- ^'^•^^' ^^ Nevertheless, because of the 

 long base line over which agreement is obtained in this present study, 

 it is hoped that the results may not be too much in error for at least 

 a few cycles. 



The data used are the series of relative sunspot numbers begun by 

 Rudolph Wolf,^ Professor of Astronomy at Zurich and continued by 

 his successors Wolfer and Brunner. Wolf began his systematic 

 observations of sunspot numbers in 1849. He endeavored to make 

 some allowance for the area of the spots and to avoid having a small 

 spot of short duration count as much as a large group. With this in 

 mind, he applied the following formula to his observation: 



Relative sunspot number = k^lOg +/), 



where g and / are the group and total spot numbers respectively, 



* Presented before the Astronomy Section of A.A.A.S. at Richmond, Va., De- 

 cember 28, 1938. 



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