PROFESSOR A. SCHUSTER ON THE PERIODICITIES OF SUNSPOTS. 83 
Appearing without much change in intensity throughout the time that sunspots have 
been observed, it has been more regular in its activity than the period of 11 years 
which hitherto has been the only one recognised, 
To determine more exactly the periodic time, we may compare the phases as found 
from the two half intervals of Wolf’s series, starting with the assumed period of 
475 years. We thus find that there has been an acceleration of phase of 96° 43' in 
the two portions which are separated by 16 complete periods. This change of phase 
is corrected by taking the periodic time to be 4-83 years. If we turn to the more 
accurate data derived from the measurements of areas, we find the maximum to lie at 
478, hut the change in intensity with increasing or diminishing periodic time 
suggests a somewhat longer period. A rough graphical interpolation seemed to give 
4-81 years as the most probable length. Desiring to fix the time as accurately as 
possible, I arranged the records so as to give the intensity for this period and 
obtained 131,500, which is decidedly less than when a period of 478 years is 
assumed. This leaves us then with a certain amount of doubt as to the correct 
period, but the difference in the two values found would in 14 periods accumulate 
only to the extent of displacing the maximum by six months. 
The phase as derived from the measurements of areas gives September 9, 1836, as 
one of the maxima, assuming the period to be 4-81 years, and September 21, 1836, if 
the period is 478 years. Wolf’s numbers with a period of 4 - 83 years give February, 
1836, as the corresponding date of maximum phase. Table IX. contains the dates of 
the maxima of the periods according to the two suppositions. The civil dates are 
only approximate and are derived from the fraction of the year. In comparing these 
dates in the future with the maxima as they occur, it will have to be noted that the 
phases given are those of the simple period, and that the higher harmonics have the 
effect of slightly postponing the maxima of the fundamental period. 
Table IX. 
4-81. 
4-78. 
4-81. 
4-78. 
1831 - 9 (November 17) 
1836 • 7 (September 9) 
1841 • 5 (July 1) 
1846-3 (April 23) 
1851-1 (February 13) 
1855-9 (December 5) 
1860-7 (September 27) 
1865-6 (July 19) 
1870-4 (May 11) 
1831-9 (December 10) 
1836 - 7 (September 21) 
1841-5 (July 1) 
1846-3 (April 13) 
185U1 (January 2) 
1855*8 (November 4) 
1860-6 (August 15) 
1865-4 (May 27) 
1870 "2 (March 4) 
1875-2 (March 3) 
1880-0 (December 23, 
1879) 
1884-8 (October 15) 
1889-6 (August 7) 
1894-4 (May 29) 
1899-2 (March 21) 
1904-0 (January 11) 
1875-0 (December 17, 
1874) 
1879 - 7 (September 28) 
1884-5 (July 10) 
1889-3 (April 22) 
1894-1 (January 30) 
1898-9 (November 11) 
1903 - 6 (August 22) 
The average amplitude of the period has been 98; that of the 11-year period 
beinor 586. 
o 
Perhaps the severest test we can apply to prove the reality of the period is to 
m 2 
