This paper supplements a former one with corrections and additional matter. A few changes are made in the Fritz epochs of “probable maxima” of sun spots, dating from 300 A.D., and it is shown that the frequency distribution of the 11-year sun-spot intervals derived from the ancient epochs has about the same mean, skewness, and dispersion as that of the Wolfer intervals from 1610. For the whole period of 1,600 years the most frequent interval or mode is computed to be 10.94 years while the normal length of the period computed by a least-square method is 11.067 years. The mean deviation from 11.0 years is ± 1.69 years.
By appropriate statistical processes and criteria, the sequence of the 11-year intervals is shown to be systematic rather than fortuitous. While the most frequent interval between peaks or hollows in a random sequence is the two-interval, there is a marked tendency for maxima or minima in the solar curve to recur about every third interval. In other words the most frequent interval of recurrence is about 36 years.
The epochs of maximum and minimum length of the 11-year period, derived from the curve of 11-year intervals, yield by the least-square computation a normal length of 37.5 years for the long period, with an amplitude of 2.4 years. On eliminating the 37-year period by an appropriate smoothing of the 11-year intervals, a still longer period is disclosed with a normal length of about 83 years and an amplitude of 1.5 years. Further smoothing discloses a 300-year period with an amplitude of 0.5 year. The 300-year period undergoes a long secular variation in length, roughly estimated at 1,400 years.
Both the 37-year and the 83-year periods undergo a 300-year variation in length, comparable with that of the 11-year period, the maximum lengths being about twice the minimum lengths.
These three periods exist also in the relative numbers and the ratios, a : b, that is, time of increase to time of decrease of sun spots from minimum to minimum, the numbers varying inversely and the ratios directly with the length of the 11-year period.
These periods are apparent not only in auroral data but in various other terrestrial data—frequency of severe winters, frequency of Chinese earthquakes, flood and low stages of the Nile, tree growth in Arizona and California, and wheat prices in England.
The epochs of maxima of the three periods lag some-what behind the epochs of maximum solar activity, and the amount of the lag is proportional to the length of the period. The lags of the 37-year and 83-year epochs exhibit a 300-year period, also a long secular variation—the lag after 1,000 A.D. being about two thirds that previously.