80 PROFESSOR A. SCHUSTER ON THE PERIODICITIES OF SUNSPOTS. 
some of the special periodicities, the existence of which has been suspected, leaving a 
more detailed investigation for future treatment. In order to find the average values 
of the periodogram within this region, the mean sunspot areas (publication b) were 
grouped so that the times of the period were 16, 18, 20,. 30 solar rotations. 
Each group was divided into four parts, corresponding to a division of the w T hole 
material, extending from 1832 to 1900, into approximately equal intervals of time, 
12000 
each such interval being therefore about 16f years. The mean intensity of the four 
groups for each period gives us a better estimate of the mean intensity of the periodo¬ 
gram than the values obtained from the group as a whole. If a periodicity were 
suspected, then of course the combined intensity of the whole time interval would 
have to be calculated. For the special investigation of a possible periodicity 
corresponding to the synodic revolution of Mercury, two tables were formed in which 
each row consisted of the numbers belonging to 4 and 5 rotations respectively, and 
each such table was subdivided into six groups. The calculations were completed by 
obtaining in each case the coefficients of the semi-periods. The results are given in 
Table VI. 
For periods of still shorter duration the Greenwich results (c) had to be used. The 
available time interval, extending from 1886 to 1900, was divided into three sets of 
five years each, and periodic times of 24, 25 . 30 days were investigated, 
