92 
PROFESSOR A. SCHUSTER ON THE PERIODICITIES OF SUNSPOTS. 
It should be noted that the first of the intervals of 13'5 years occurred previous 
to 1649, and is not brought into the calculation of the periodogram, which shows 
a decided maximum (fig. 1) for a period of 13‘5 years. This period has evidently 
been one of the characteristic ones during the time to which curve B (fig. 2) applies. 
The fact that the maxima 1870 - 6 to 1883’9 are connected with it shows that it has 
still been active till quite lately. If it does not appear in curve A (fig. 2), this is 
accounted for by the fact that the first diffraction band of the 11 years’ period overlaps 
and neutralises it. When the large period is eliminated, a rise at about 13 years 
becomes apparent. The process of elimination is, however, difficult, and errors may 
easily he introduced by means of it. There is evidence of two overlapping periods 
here, the broadness of the rise in curve B (fig. 2) being one of the indications of the 
duplicity. I refrain for the present, therefore, from discussing the period further. 
15. Having found the average action of the 11-| years’ period, we may eliminate 
it from the general sunspot curve. The result is shown in fig. 6, in which the annual 
values of sunspot areas since 1833 (publication b) has been used. The process of 
elimination brings out a period of about 8‘5 years in a striking manner. The maxima 
occurred in the years 1836, 1845, 1853, 1862, and 1870. The periodogram for the 
combined interval 1749 to 1900 shows a maximum at the period of 8’25 years. 
Taking the phase as obtained by means of the 8'25 years’ oscillation from the interval 
1749 to 1826 alone, and forecasting the maxima for the subsequent interval, we obtain 
1836T, 1844'5, 18527, 1861‘0, and 1869‘2, in almost exact agreement with the above. 
In fig. 6 short lines are drawn indicating the maxima of the curve, while arrows mark 
the positions of the maxima calculated, as first explained, from the observations which 
are not included in the time scale of the figure. 
The phases of the 8‘25 years’ period, as calculated from the two intervals separated 
by nine periods, are given in Table IV., and are there found to differ by 26°. When 
minutes of arc are taken into account, this angle is more accurately found to be 25° 16'. 
To bring the phases into coincidence, the period would have to be slightly lengthened, 
so as to be equal to 8'31 years. If we start from the 8‘5 years’ oscillation, we find 
similarly a diminution of phase equal to 34° 5', and the period calculated so as to 
destroy this difference would be 8'41 years. We may adopt the mean of these results 
and take 8‘36 as the most probable period. To get the phase we may use the method 
