[ 69 ] 
II. On the Periodicities of Sunspots* 
By Arthur Schuster, F.R.S. 
Received January 7,—Read February 8, 1906. 
1. I he material used in this investigation consists of:— 
(a) The series of sunspot numbers collected by Dr. A. Wolf and Dr. A. Wolfer, 
and published by the latter in his “ Astronomische Mitteilungen.”t This 
series contains lor each month of the years 1749 to 1901 the sunspot 
frequency as expressed in Wolf’s “ Relativzahlen.” 
(h) I he mean daily areas during each synodic revolution of the sun from January, 
1832, to the end of 1900, which have been collected and are issued as a 
separate publication by the Solar Physics Committee. The publications of 
the Greenwich Observatory allow us to continue this series to the end of 1902. 
(c) The Greenwich observations extending from 1883 to 1902, and giving for each 
day of the year complete statistics of the position and areas of spots. I have 
used the numbers representing the sums of the daily areas of the whole spots 
(including umbra and penumbra), the areas being corrected for fore shortening. 
The unit of area throughout this investigation is the millionth of the sun’s 
hemisphere. 
The three series will be referred to as (a), (h) and (c) respectively. 
2. The series (a) being expressed in different units, the results obtained from it 
cannot be brought into very accurate comparison witli the calculations based on the 
two other series. Identical units were not necessary for my purpose, but nevertheless 
it was advisable to investigate in how far a constant ratio existed between the sun¬ 
spot frequency as expressed in Wolf and Wolfer’s series and the same frequency 
as more accurately determined by means of the measured areas. In Wolf’s sunspot 
numbers, each group of spots is weighted by a number which depends on the average 
number of spots in the groups visible at the time. If / is the total number of 
separate spots and g the number of groups, Wolf’s “ Relativzahl ” r is 
r = k (f + lOg) = Kg (10 + n), 
* Preliminary notice published in ‘ Ptoy. Soc. Proc.,’ A, vol. 77, p. 141. 
t ‘ Vierteljahrsehrift der Naturforschenden Gesellschaft in Zurich,’ vol. 47 (1902). 
VOL. CCVI.—A 403. 
6 . 6.06 
