134 BACASTOW AND KEELING 



APPENDIX F: DERIVATION OF ANNUAL SUNSPOT NUMBERS 

 FOR THE YEARS 1500 to 1699 



Sunspot numbers from the Zurich Observatory, as calculated by Wolf and his 

 successors, are given by Abetti 46 for the period 1749 to 1961. Schove 47 gives 

 comparable numbers for 1700 to 1749 and has extended the record back to 649 

 by estimating the years of sunspot maximums and the intensity of the 

 maximums from records of sunspots seen with the naked eye and displays of 

 northern lights. To obtain annual numbers before 1700, we have calculated an 

 average normalized sunspot cycle from the data after 1749. Then, by adjusting 

 this curve to the years and intensities of maximum activity from 1500 to 1699, 

 we have filled in sunspot numbers for the intervening years. 



Twenty sunspot maximums occurred between 1750 and 1960. The number 

 of years between maximums varied from 7 to 16. To obtain a valid average 

 cycle, we projected the record forward and backward from each maximum and 

 found the average number of sunspots for equidistant years. If the number of 

 intervening years was even, we split the record into equal numbers of years 

 forward and backward, and, if odd, we included one more year forward. Beyond 

 6 years in either direction, too few instances occurred to give a statistically good 

 average. 



The number of sunspots for each year of the average cycle, expressed as a 

 percentage of the average maximum, is as follows: 



To estimate the annual record before 1700, we multiplied the percent values 

 of the average cycle by the appropriate maximum, and used this value to project 

 each cycle forward and backward in the same manner as in constructing the 

 average cycle. On three occasions, 1512, 1565, and 1667, the average cycle was 

 too short to give a value; we obtained values of 6, 12, and 3 sunspots, 

 respectively, by interpolation. The reconstructed record is plotted in Fig. 9. 



