PROFESSOR A. SCHUSTER ON THE PERIODICITIES OF SUNSPOTS. 
81 
together with their first sub-periods. The intensities of' the periodogram depend to 
a great extent on the particular part of the 11 years’ cycle which is being 
investigated, the variations being greater when the intensities are great. The data 
are not sufficient to deal with a considerable number of cycles, and the correct average 
cannot be formed. I therefore give the values for each of the three groups 1886-90, 
1891-95, and 1896-1900, the middle one of which coincides with a period of great 
activity. The numbers are collected in Table VII. There is a great variability in the 
numbers, but if a mean value is obtained for each period, and then, as in the last 
column of the table, an average of three successive periods is formed, a good agreement 
is obtained. 
It will be noticed that somewhere between 15 and 24 days a considerable rise in 
the intensity of the periodogram takes place. This was to be expected. In the first 
place there must be a depression in the value of the intensities for short intervals of 
time due to the length of life of a spot. It has already been pointed out that if all 
spots lasted exactly the same time, the intensity of the periodogram would be zero for 
periodic times equal to this duration. The depression in the actual case will spread 
over a considerable range of periods, and will not allow the full value of the intensity 
to show itself until times which are at least twice as long as the average life of a spot. 
Such of the larger spots as come into view at one edge and traverse the whole disc 
would furnish a contribution to the periodogram in which the periods corresponding 
to half the synodic revolution are absent, provided the area covered by the spot is 
constant. We might therefore have expected a specially low value in the intensities 
corresponding to periods between 13 5 and 14 days. This is not shown by the tables, 
a fact probably accounted for by the great variability of the area of a large spot as 
it traverses the disc. 
The periodic re-appearance of spots during successive rotations of the sun should 
increase the intensity for periods approximating to the average rotation period. 
A definite periodicity must not, however, be expected, quite apart from the fact that 
the rotation period itself is indefinite. The re-appearance of a phenomenon at regular 
intervals of time only constitutes an approximately homogeneous periodic phenomenon 
when the re-appearances are sufficiently numerous. With a life of three or four 
rotations only, there can be little distinction between periodicities ranging from 25 to 
29 days. 
The comparatively large value of the periodogram (2400) for a period of 13 ‘2 5 days 
deserves some notice. Both in the interval 1890—95 and 1895—1900 there is a very 
decided rise of intensity corresponding to that period. But if the periodicity were 
real, the phases should be in regular progression. This is not the case, though we 
may obtain a better agreement by slightly altering the periodic time to 13’296 days, 
treating the whole interval of fifteen years, the intensity is found to be 3080. If 
there were a real period, the increase should be much larger than this, and for the 
present we must therefore treat this period as accidental. 
VOL. CCVI.—A. M 
