NO. 2 



THE SUNSPOT PERIOI 



-CLAYTOX 



for each month. These are nearly identical with the computed values 

 in table i when A = o. The small differences that exist are accounted 

 for by the fact that the cosine factors were only taken to two or three 

 decimals instead of to four or more. The successive values are thus 

 equivalent to those of moving means except that the smoothing is 

 done by harmonic terms instead of numerically. 



Table i. — Example computation by harmonic 



Cycle of 360° 

 divided into Sine 

 12 parts values 



(1) 



30° 



6o° 



90° 



120° 



150° 



180 



210° —0.50 



240 —0.866 



270 — 1.00 



300 —0.866 



330° —0.50 



(2) 



0.00 



0.50 



0.866 



1. 00 



0.866 



0.50 



0.00 



Sum . 



0.00 



Cosine 

 values 



(3) 



1. 00 



0.866 

 0.50 

 0.00 

 —0.50 

 -0.866 

 — 1. 00 

 -0.866 

 —0.50 

 —0.00 

 0.50 

 0.866 



0.00 



Normal monthly tempera- 

 tures. New York a 



CO (S) 

 ° F. 



January 30.6 



February 30.5 



March 38.0 



April 48.5 



May 59.4 



June 68.5 



July 735 



August 72.1 



September 66.4 



October 55.8 



November 44.1 



December 34.3 



—22.4 —130.3 



For A = . 

 For A = 5i.8 



Monthly values computed from 6 and a 



Jan. Feb. Mar. Apr. May 



—21.7 —20.7 — I4.I —3.8 7.6 



30.1 311 37-7 48.0 59-4 



July 

 21.7 

 73-5 



For A — 



For A = 51.8 



a Mean of 51 years, 1873-1923. 



a = £V(22.4) 2 + (130. 3) 2 = 22.04; tan 



Aug. 

 20.~ 



72.5 



130.3 



Sept. 

 14. 1 

 65-9 



5.81; 6 = 260° 



Oct. Nov. 



3-8 -7-6 



55-6 44-2 



June 

 17.O 



68.8 



Dec. 

 — 17.0 

 34-8 



6 = epoch; a = amplitude; A = 51.8 = Mean for year. 



The same results are obtained by the correlation formulas as is 

 shown by the computations in table 3. 



A cosine curve has the form exhibited in figure 1. Observed data 

 are multiplied by a cosine series representing such a curve and the 

 process repeated step by step, adding one unit of time and dropping 

 one. If the length of the cosine series is near the length of any period 

 which may exist in the observed data, that period will stand out 

 prominently. The process eliminates periods of much smaller and 



