44 smithsonian miscellaneous collections vol. jl 



Studies of Periods in Solar Radiation by Means of the 

 " Phasogram " 



Owing to the difficulty of obtaining accurate means of the sub- 

 multiples of such periods as 29, 34, etc., the necessary calculations 

 were made to determine whether by means of a "phasogram" 

 periodic changes could be found in the measures of solar radiations 

 from the observations in Chile. Taking periods between 26 and 40 

 days the data for each day of the chosen period were placed in 

 columns with the corresponding days under each other. Thus in 

 a period of 26 days the ist, 27th, 53d, etc. days were in the same 

 column, while the 2d, 28th, 54th, etc., were in the succeeding. column. 

 After arranging in this manner the means of fives were obtained 

 for each day of the period ; for example, in the first column the means 

 of the periods from i to 5, then from 2 to 6, 3 to 7, and so forth. The 

 same was done for the second column and so on successively. When 

 observations were missing the sum of those actually observed was 

 taken and divided by the number present. 



In this way overlapping means of 5 were made for all the periods 

 mentioned, using the same epoch for each, namely, January i, 1919. 

 Then the harmonic terms were computed for each successive period, 

 and for each submultiple when the period could be divided by a whole 

 number, as 2, 3, 4, 5, 7, 8, 9. The results were plotted in " phaso- 

 grams '' like that represented in figure 10. Lines were then drawn 

 through these plots according to the rules given in describing this 

 figure. From the slope of these lines the lengths of the periods 

 indicated were computed. This method permits of no personal 

 bias because it is impossible to know beforehand what the result 

 will be. 



Hence it seems to me very strong evidence of the reality of the 

 periods when so many of the plots gave almost identical results. 



Take for example the period of 18 days, it is shown by the plot 

 of one-half of 26 days, of 30 days, of 32 days, of 34 days, of 36 days 

 and of 40 days, and also by the plot of one-third of 36 days. Periods 

 of about 1 1.3, 13.3 and 15.3 days were almost equally defined by 

 mutually independent trial periods. Furthermore in the same period, 

 as for example that of 36 da3^s, the fractions of the periods such as 

 the half, the third, etc., depended on entirely independent observa- 

 tions, yet they rarely failed to fall along the same lines as those 

 indicated by the first part of the period. 



Finally the plots indicate clearly that the periods continued 

 in nearly the same phase throughout the year covered by the 

 observations. 



