82 
PROFESSOR A. SCHUSTER ON THE PERIODICITIES OF SUNSPOTS. 
The literature connected with the relation between solar terrestrial phenomena is 
full of supposed periodicities approximately coinciding with that of a solar rotation. 
Most of these periods are in the neighbourhood of 26 days, a time agreeing neither 
with the sidereal nor the synodic rotation, but it seemed worth while to investigate 
whether any definite periodicity in the sunspot areas can be discovered which takes 
place in a period near to that of 26 or 27 days. I have for this purpose worked out 
the Fourier coefficients of these two periods separately for each of the 15 years, 
1885-1900. The deduced values of the periodogram and the phases are given in 
Table VIII. By a graphical method, explained in my discussion of the Magnetic 
Declination, w the periodicities of specially large intensity lying near the two selected 
times may be determined. Applying this method, I have not been able to discover 
any variation which suggests a true periodicity. The mean value of the periodogram 
for the periods of 26 and 27 days, as determined from individual years, agrees well 
with the general average shown by the last column of Table VII., which wms based on 
a time range of 5 years. 
10. A planetary influence on sunspots has often been suspected, and I have there¬ 
fore specially considered the rotation periods of Jupiter, Mercury, and Venus! 
Table I. shows, as already pointed out, that the rotation period of Jupiter (11 -86 
years) gives no increased intensity to the periodogram. As regards the planets 
Venus and Mercury, Professor Turner kindly sent me a list of the dates of their 
upper conjunction with the earth since 1833. Tables were formed in wdiich, iii the 
case of Venus, the values of the sunspot areas during 21 successive rotations were 
arranged in order, the first column always giving the sunspot area for the rotation 
during which upper conjunction took place. The synodic revolution of Venus being 
approximately 21A rotations, the tables so arranged could be used to determine the 
Fourier coefficients for the rotation period. In the case of Mercury the same process 
was followed, except that there were only four columns corresponding to the four 
complete solar rotations which take place within one synodic orbital revolution of the 
planet. Table VI. shows a small rise in the periodogram corresponding to the rotation 
period of P5986 years, which is that of Venus. The number given is the mean value 
of four, obtained by splitting the 68 available years into four periods of 17 years. 
It is found that the phases for the four separate intervals do not agree, so that, if 
we combine the whole series of years, it is found that the periodogram intensity is 
smaller than the average. The synodic revolution of Mercury (115*88 days) similarly 
gives an exceptionally small value for the intensity of the periodogram. The semi¬ 
periods also show no effect. 
11. We may now turn to the special consideration of the periodicities which have 
been found. The most persistent of the periods indicated by the periodogram is one 
having a period of about 4*8 years. It appears separately in the two series of 
Wolf’s numbers and is confirmed by the records based on the measurement of areas. 
* ‘ Cambridge Phil. Soc. Trans.,’ vol. 18, p. 107 (1899). 
