A SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 69 



As a result of these determinations of correlation coefficients, peri- 

 odicities of solar variation would be exposed if they exist. For ex- 

 ample, if the sun throughout an observing season was warmer on 

 one hemisphere than the other, we should expect that high values of 

 the " solar constant " would tend to be succeeded by high values 

 after about 27 days, and low values would similarly tend to be suc- 

 ceeded by low values about 27 days later, whereas high values would 

 follow low values after about 13^ days. These tendencies would 

 express themselves in the coefficients of correlation. Positive cor- 

 relation coefficients would continue for about one week, negative ones 

 would succeed these for about two weeks more, and positive ones 

 would follow these for the fourth and fifth week. 



The results of the computations are shown graphically in the ac- 

 companying figure. On the left are plotted the " solar constant " 

 values as obtained on Mount Wilson, and published as far as 1912 in 

 volume 3 of the Annals of the Astrophysical Observatory. The ob- 

 servations of consecutive days have been connected in the plot. For 

 the use of readers who may be interested, I give in Table 1 prelimin- 

 ary values of the " solar constant " for the years 1913-1916. It is 

 possible that in the final publication of them in Vol. 4 of our Annals, 

 some changes may be made as a result of checking, but in the main 

 they will not be altered. 



On the right of the illustration are given curves of correlation 

 coefficients for each of the observing seasons 1908 to 1916, except 

 1912 when Mt. Kamai volcano was in eruption, and the " solar con- 

 stant " values were less trustworthy. The curve for 1913 is taken 

 from Clayton's paper. The others have been computed here. Two 

 curves are given for 1915, of which the full curve represents the 

 results of the whole year, and the dotted curve an independent com- 

 putation from the results prior to September 12, which were first 

 available. In Table 2 the correlation coefficients are printed. The 

 probable error of individual values of these coefficients is about .08. 

 For those unfamiliar with the correlation method it may be remarked 

 that + 1. 00 or — 1. 00 are the outside limits of correlation coefficients, 

 which both stand for perfect dependence between two variables. A 

 value 0.00 indicates a complete absence of dependence. 



(1) The first noticeable feature of the curves is their dissimilarity. 

 No well marked periodicity of the solar variation persists through all 

 of the eight years of the investigation. Each season is a law unto 

 itself. 



