86 PROFESSOR A. SCHUSTER ON THE PERIODICITIES OF SUNSPOTS. 
with a sum of four rotations, the first of which coincides most nearly with the date 
189777 + 4-38 n. 
Table XI. 
1 . 
2. 
I 
3. 
4. 
5. 
6. 
7. 
8. 
39,998 
39,523 
33,196 
34,432 
39,648 
37,201 
32,956 
34,324 ' 
1,27G 
1,688 
764 
2,179 
662 
598 
128 
276 ■ 
228 
150 
219 
811 
579 
3,017 
1,386 
• 
— 
9. 
10. 
11. 
12. 
13. 
14. 
15. 
— 
37,989 
41,414 
45,278 
49,487 
42,504 
43,543 
38,944 
— 
445 
209 
171 
23 
278 
71 
313 
The records which have been published since this investigation was first begun 
enable us to add more than one complete column to those which I have used, and 
these have been entered in the table. 
13. The principal period which gives the present sunspot curve its characteristic 
shape deserves treatment in detail. Fig. 4 shows the average variation of the six 
sunspot cycles included between 1833-1899. The curve gives the rise and fall of the 
annual value of the mean daily area, while the crosses indicate the position of the 
points through which the curve would pass if deduced from Wolf’s sunspot numbers, 
the close proximity of the crosses to the curve shows that, at any rate as far as the 
long-period variations are concerned, Wolf’s numbers are proportional to the sunspot 
areas, and that the factor 1 have used is sufficiently accurate. The figure also 
illustrates the fact that Wolf’s numbers underrate somewhat the activity near the 
times of a maximum, as has already been pointed out in § 1. But this deficiency is 
apparent throughout the rising branch of the curve. This points to a systematic 
difference in the sunspot statistics before and after the maximum. I have carefully 
examined the sunspot records as far back as the Greenwich records allow me to do 
so, and there seems indeed to have been a tendency during the 20 available years 
towards larger average areas (and also average duration) of spots during the rise as 
compared with the fall in the sunspot cycle. This would explain the deviations of 
Wolf’s numbers from the curve marking the areas. 
