PROFESSOR A. SCHUSTER ON THE PERIODICITIES OF SUNSPOTS. 
79 
When we come to periods which are near to that of the solar rotation, periodicities 
appear, owing to the fact that some of the spots persist during more than one rotation. 
This effect will, however, disappear when the period is well above that of the solar 
rotation. When the periods come near to 1'5 years, the sub-periods of well-ascertained 
periodicities make their presence felt. Hence the limits chosen for calculating the 
natural intensity of the periodogram must be confined to about 35 days on the one 
hand and 1'5 years on the other. The average intensity of these periods may be 
determined from Table VI., and is found to be 15,000. The probability of an intensity 
greater than h times the average value is e ~ h , and we may perhaps begin to suspect a 
real periodicity when this value is 1 in 200. This gives 5‘3 as the value of h and 
80,000 as the smallest value of the intensity which invites further discussion. When 
h has the value 8, the probability of an intensity greater than h times the expectancy 
is 1 in 3,000 and we may begin to be more confident that there is some definite cause 
at work to bring up the periodogram to that value. The intensity in that case is 
120,000. When h is 16, the chances of being misled by accident is only one in a million. 
8. Periodic times between 5'18 years and about 2 years were investigated by 
taking as basis the mean sunspot areas for each assumed synodic rotation, as given in 
publication (6). For this purpose four successive numbers, as given in the tables 
published by the Solar Physics Committee, were added together, and rows were 
formed containing a number of successive entries. The longest period chosen was 
that containing seventeen times four, or 68, synodic rotations, each assumed to be 
of duration 27’275 days, giving a period of 5*18 years. The process was repeated 
by forming tables containing columns varying in number between 10 and 17, and 
intermediate periods were treated by the well-known process of shifting successive 
rows to the right or left. The semi-periods were treated in the usual manner. 
Table V. gives the result, which is graphically represented in fig. 3, curve A. The 
periodogram curves, as deduced from Wolf’s sunspot number in the manners explained 
above, are shown in curves B and C, the former referring to the second, and the 
latter to the first half of the total range of 150 years. 
The main features of curve A are formed by the elevations at 2 - 69, 378, 4'38 and 478 
years. The first two of these elevations are in all probability only due to sub¬ 
periods, being the second and third harmonic of the 11725 variation which we should 
expect to find at 278 and 371. The divergence between the observed and calculated 
periods is probably not more than may be accounted for by superposed irregularities. 
The rise at 4'38 does not occur on curve C and only to a slight extent on curve B, 
but the intensity as determined from the areas is sufficient to make the reality of the 
period probable. There is also a slight rise of doubtful reality at a period corres¬ 
ponding to 4 - 08. 
9. With regard to periods which are shorter than 1'89 years, the labour of a 
complete investigation which would have to secure that no existing periodicity could 
escape notice would be very great. I have, therefore, for the present considered only 
