A REPRESENTATION OF THE SUNSPOT CYCLE 295 



twenty-two years instead of eleven years and the physical justification 

 is the similarity in the polarity of the leading spots in alternate eleven- 

 year periods. 



(c) Quarterly values were obtained from the curve in order to 

 obtain a smaller unit and to approximate better such periods as 

 22.25 years, 17.33 years and other periods not an integral number of 

 years; the values were assigned + or — signs in accordance with 

 whether they were above or below the time axis. 



(d) A periodogram was computed and the component of maximum 

 amplitude appeared to be 22.75 years; this component was eliminated, 

 a new periodogram computed and so on; after many trials it was 

 finally decided that no solution could be found which would reduce 

 the residue satisfactorily with 22.75 years as the main component. 



(e) Inspection of the analysis indicated an improvement would be 

 obtained by a decrease in the period and accordingly a change was 

 made to 22.5 years and the computations repeated; a solution was 

 finally obtained which fit the 1749-1937 curve of sunspots fairly well 

 but, when extrapolated back to 1600 A.D., did not fit particularly 

 well the observed times of maxima and minima for the period 1610 

 to 1749; a still further reduction in the chief component was necessary. 



(/) The computations were repeated with 22.25 years as the chief 

 component; after the computation of the series was completed, it was 

 discovered that the components were either harmonics or nearly 

 integral harmonics of 312 years; many of these components had been 

 in use since the original periodogram. 



(g) A search was made for the 312-year period, since it should be 

 possible to check in the cases of two minima and two maxima, with 

 the following results : 



giving a weighted average of 312.5 years or an average of 312.0 years 

 using the two most reliable values. 



(h) Computations were again repeated using harmonic components 

 of 312 years. This gave a very good representation of the data from 

 1749 to date and also agreed with the times of maxima and minima 

 for the period 1610 to 1749. The resultant curve is shown in Figs. 

 2 and 3. 



The components of the reconstructed curve are shown in Fig. 4. 

 It is of interest to note that the 22.25-year component which is largely 



