Sun-spot Frequencies Contrasted. 155 



The central period 1794—1826 comprises that period of 

 33 consecutive years which gives a minimum mean sun-spot 

 frequency. That mean is only a third of the mean appro- 

 priate to the combined periods 1761-93 and 1827-59! 



As a rule, three successive years of conspicuously high 

 f requeue}- occur at each sun-spot maximum, and three of 

 conspicuously low frequency at each minimum. TVolfer's 

 table includes 13 groups of these 3 extreme years of sun-spot 

 maximum, and 13 of sun-spot minimum. The respective 

 means from these 39 years of maximum and 39 years of 

 minimum form the fifth and sixth rows of Tables I. and II. 

 The Inst two lines in these Tables refer to shorter groups of 

 33 years of sun-spot maximum and 33 of minimum which 

 correspond more closely to the auroral data presently to be 

 described. 



§ 6. Probably the simplest way of investigating the 

 relationship between sun-spot frequency and the magnitude 

 of any element is to form two mean values for the element, 

 the one corresponding to years of many, the other to years of 

 few sun-spots, and then to assume that the difference between 

 these means depends on the corresponding difference in sun- 

 spot frequency. In applying this method to data from the 

 whole period covered by Wolfer's table, one would emplov 

 the sun-spot frequencies given in the 5th and 6th rows of 

 Table I. Doing so. we should get differences of sun-spot 

 frequency varying from 81*76-13'63, or 68'13, in January, 

 to 78* 7 7 in August. The existence of so large a difference 

 between the sun-spot data for January and August is im- 

 material, provided there is a direct connexion, which possesses 

 no lag, between sun-spot frequency and the element concerned. 

 If, however, the connexion is of a less simple character, for 

 instance if the element depends on the sun-spot frequency 

 for some months previously, the application of the above 

 method would lead to an overestimate of the influence of 

 sun-spot frequency in January and an underestimate in 

 August. If we use more exact methods, e. g. the method of 

 least squares, — still assuming purely synchronous variation — 

 the above source of uncertainty is less easily recognized, but 

 it exists all the same. Considered absolutely, the difference 

 between the mean monthly values in Table I. is greater for 

 the 39 or the 33 years of S max. than for the corresponding- 

 group of S min. years ; but relatively considered — 

 cf. Table II. — the variability from month to month is greater 

 for the S min. group. Thus in the 39 years of S min. the 

 means for March and September differ by 39 per cent, of the 

 mean from the 12 months. Moreover in the S min. groups 



