89 
PROFESSOR A. SCHUSTER ON THE PERIODICITIES OF SUNSPOTS. 
The highest point of the complete curve is reached at a time 1903 * 76 = 1 : rx 11*12, 
but there is naturally a good deal of uncertainty as to the dates of the maxima, 
within the limits of a year. The positions of the maxima and minima of the harmonic 
components as given in Table XII. are marked in fig. 5 by an upward arrow denoting a 
maximum and a downward arrow a minimum. The order of the harmonic is indicated 
by the figures attached to the arrows. A retardation of 18 months in the principal 
maximum may occur owing to the temporary disappearance of the first harmonic, and 
does not therefore necessarily indicate an irregularity in the main periodicity. 
The discussion of the HT25 years period has been entirely based on the results 
of the last 75 years of last century. Between 1749 and about 1826 the periodogram 
only gives a faint indication of the period. This remnant I ascribed at first without 
further investigation to the fact, that the 11 years’ period had come into life towards 
the beginning of the century, and therefore had to some extent affected the interval 
1750-1826 to which curve B of fig. 2 applies. This was an error which for some 
time kept me off the right track. 
The question of the permanence of the periodicities is one of vital importance, and I 
have endeavoured throughout to keep my mind free from all preconceived notions. 
Every one thus looking with unprejudiced eyes at the main facts must feel himself 
drawn in opposite directions. On the one hand there is the evidence of the periodo¬ 
gram which indicates almost decisively a new departure at the beginning of the 
nineteenth century ; on the other hand we have the remarkable fact that Wolfer, 
making use of all the data since 1610, deduced 11*124 years as the most probable 
period a result identical with mine. Similarly Newcomb, # after a most careful 
examination of the same records, arrives at a period of 11*13 years. It needs to be 
explained why the years in which, according to our results, the periodicity was 
apparently absent do not affect the mean duration of the period, so that the same 
value is obtained whether the time during which the periodicity is ex hypotliesi 
absent is included in the calculations or not. My first impression was that the 
coincidence was partly a matter of accident and partly due to the fact that both 
observers attached weights to the times of the observed maxima according to their 
trustworthiness. The weights thus attached to the records of the last 70 years 
natuially much exceeded those with which previous records were credited. Hence 
the whole result might very well be found to depend on the later periods only. 
When first writing out the account of my work, this was the view I took, and it was 
only very gradually that I abandoned it. I am convinced now that it is untenable. 
To put the reader into possession of all the facts, and to get at a clear view of the 
subject, it seems advisable to state in detail the arguments which seemed to point to 
the conclusion that the 11 years’ period was only of recent origin. In Table XIII. the 
fiist column contains the times of sunspot maxima as copied from Wolfer’s tables. 
The third column contains the intervals between two successive maxima. The fourth 
* ‘ Astrophysical Journal,’ vol. 13, p. 1 (1901). 
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VOL. CCVI.—A. 
