PROFESSOR A. SCHUSTER ON THE PERIODICITIES OF SUNSPOTS. 
91 
as those of 1727, 1738, 1750, and 1761 are at a distance of nearly 11 years, the 
differences between the calculated and observed times are always small. The two 
maxima of 1649 and 1660 fit in well in a similar manner with the computed times. 
These facts are difficult to explain unless we believe in the permanency of the period. 
Having thus once more become a partial convert to that belief, I turned again to the 
periodogram of 1750 to 1826 (curve B, fig. 2). The small peak showing at 11^ years 
I had, as explained, ascribed to the years 1800-1826, during which, as I then 
thought, the 11-year period had come into existence. In order to clear up the 
matter, I investigated separately the five cycles between 1749 and 1794. The 
II years’ oscillation now came out with an amplitude of 256, rather larger than I 
expected (the present amplitude being 586), and the phase was such as to give a 
maximum in 1747'5. A period of exactly 11^ years would bring us after thirteen 
cycles to about 1903T, agreeing to about two years with the actual date of the 
maximum of the 11-year period, as given in Table XII. 
[Not much value can be attached to the phase calculated from five periods only at 
a time, when we know that other and stronger influences were at work. The 
conclusion to be drawn is that even when the periodicity in question was weak, its 
phase was not inconsistent with that calculated from other intervals of time.— 
February 18, 1906.] 
The result reached at this point was that the 11 years’ period though 
diminishing occasionally in intensity was yet permanent throughout the range of 
available sunspot records, and that whenever the time of successive maxima was 
nearly equal to 11 years they fitted in well with each other as regards phase. 
14. Let us follow up the suggestion furnished by the last remark. Notice that 
during the three centuries to which Table XIII. applies there were three cases 
in which the interval between two successive sunspot maxima was nearly 13’5 years. 
Table XIV. shows that the intervals between each of these three single periods is 
nearly a multiple of the same duration, so that all figures fit in with a general 
periodicity of about 13'6 years. 
Table XIV. 
Sunspot maxima. 
Length of period. 
Intervals between periods. 
1626 1 
1639-5/ 
13-5 
— 
— 
1816-4- 1639-5 = 176-9 = 13 x 13-61. 
1816-41 
1829-9/ 
13-5 
__ 
— 
1870-6 - 1829-9 = 40-7 = 3 x 13-57. 
1870-61 
1883-9/ 
13-3 
— 
— 
1883-9- 1626 = 257-9 = 19 x 13-57. 
n 2 
