12 



SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 98 



unit of time and adding another. In this way, whenever there is a 

 period in the observed data near the period of the cosine waves, it is 

 separated from chance variations and from periods of other length so 

 as to stand out prominently in a plot of the results of the computa- 

 tions. The numerical work is like that shown in column 7 of table 1 

 repeated several times consecutively, or else the values are treated as 

 shown in table 3. In this table column I contains the numbers which, 

 when plotted, form a curve like that in figure 9. These numbers are 

 then correlated with numbers representing sunspots, solar radiation, 

 atmospheric pressure, or other physical quantity. If the correlation 

 is sufficiently high, a period of the approximate length of the cosine 



I I I I I II I I I I I I I I I I II I II I |l I I I I III I I I I I I I I I I II 1 I I I I I I I II I II I I J II I I I I I I I I l| I I! I I II I 



SOLAR RADIATION 



II II llll I I llllllll 111 I II I II I I I I Ml I I I 1 I I I I I I I I I I I I II I I 1 II I I II IIJI ill II I I II I I I I 



Fig. 10. — Eleven-month period in solar radiation and sunspots. 



waves in column 1 is indicated. Then, if successive values of a 

 (commonly called the regression coefficient) are computed, the num- 

 bers when plotted give curves like that shown in figures 10 and 11. In 

 other words, whether the data are treated by the harmonic formulas or 

 by the correlation formulas, the same results are obtained. Since the 

 correlation formulas are in general use, it will perhaps be easier for 

 most readers to understand the problem as one of correlation. Physi- 

 cists to whom I presented the method understood it better in that way. 

 The monthly mean values of solar radiation obtained by the Astro- 

 physical Observatory of the Smithsonian Institution were treated in 

 this manner, and the results are plotted in three curves a, b, and c in 

 figure 10. 



