22 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 7I 



between means in which the second interval is about twice the length 

 of the first. These differences rarely show more than four distinct 

 sets of waves, the first having intervals of two to four days between 

 the maxima, the second intervals of five to seven, the third 9 to 13 

 and the fourth 20 to 30 days. The correlation factors are given in 

 table VIII in percentages. 



In figure 6 are plotted the correlations between successive days 

 for different sets of waves obtained for the first six months of 191 5. 

 Curve a^ shows the correlations for the differences between the 

 observed and three and one-half-days means, b^ the correlations for 

 the means of three and one-half minus seven days, c^ the correlations 

 for the means of 7 minus 14 days, and d-^^ the correlations for the 

 means of 14 minus 28 days. (These were the intervals used at the 

 beginning of the investigation instead of the means of the odd num- 

 bers three, five, seven, etc., now used.) It is seen that the shorter 

 residuals showed irregular sequences with a maximum at 26 days. 

 The curve b^ shows regular beats of six and one-half days with 

 maxima at 20 and 26 days, the curve c^ shows maxima at 14 and 27 

 days, and the curve d^ shows a maximum at 22 days. 



In a similar manner curves a,, b.^, Co, and c?2 show the correlations 

 for the second six months of 191 5 and curve d. for the first six 

 months of 191 6. Curve a^ shows a maximum correlation at 26 days 

 and secondary maxima such as might be caused by periods of 2.2 days 

 (one-twelfth of 26) and 3.3 days (one-eighth of 26). Curve b^ 

 shows maxima at 22 and 26 days and reg'ular beats of 6.6 days (one- 

 fourth of 26). Curve c, shows maxima at 14 and zy days. These 

 variations might reasonably be explained by periodicities connected 

 with an equatorial rotation of the sun whose synodic period is about 

 26.37 days, since all of them are approximate fractions of this period. 

 But when one comes to curve d^ derived from the correlations of the 

 means of 14 minus 28 days, a sharp maximum is found at 22 days 

 which no longer fits a rotation period of the sun. 



Turning now to the curves for the latter half of 191 5 shown in 

 figure 6, ao shows regular periods of 3.6 days (one-sixth of 22), 

 bo shows periods of 7.3 days (one-third of 22), and c^ periods of ii 

 days (one-half of 22) while d., shows a distinct maximum at 33 days. 

 In this case all the periods except 7.3 are also approximate fractions 

 of a 33-day period. Now, 33 days is the synodic period of rotation 

 of the sun in the latitude of about 50 degrees where the eruptions on 

 the sun which produce prominences are most common at the time of 

 a sun-spot maximum according to Lockyer (see Proceedings of the 

 Royal Society, Vol. 71, pp. 446-452). 



