Tlie Motion and Distribution of the Sun-spots 



7 



The simplest assumption is 



^ = \.r 



where is a constant that may be determined from 37 equations of condition. 

 Next I supposed 



A = Zc^ + ]c_^ . r 



which assumption gave a somewhat better result than the preceding one. It seemed, 

 however, as if the relation between the relative number r and the spot area A were 

 dependent on A. Therefore I introduced lastly 

 ^ = k. 



where the constants h and n were determined. The results of the numerical com- 

 putations in these three cases were as follows: 



Aj = 15.98 . r, 



A,, = _ 65 + 17.23 . r, 



A3 = 7.466 . ri-'"-'. 



In order to get an idea of the accuracy of these three formulfe, I calculated 

 the mean deviations {)■ between the computed and observed values of A and found 

 = 64.3, 

 â-,, = 54.4, 

 = 48.5. 



k computation of the percentage of mean deviations in the three cases gave the values 

 0.27, 0,24 and 0.15. Hence it follows that of the formulée given above the third 

 gives the best result. In Table III, I have given the relative number r and the 

 spot area A in milhonths of the sun's visible disk from 1874 — 1910, and figure 1 

 gives a grapliical representation of the connection between the observed values 

 of A, and the values computed from the relative numbers with the help of the formula 

 A = 7.466 . ri'>«-'. 



The figure gives an unexpectedly close agreement between the observed and computed 

 values, which is the more surprising since these relative numbers are rather 

 arbitrarily chosen. 



After this digression we return to our historical summary. 



By a very diligent collection of old sun-spot observations ever since 1610, Wolf 

 succeeded in fixing the period indicated by Schwabe at about 10 years. In the 

 first discussion of this extensive material Wolf got a period of 



11.111 ± 0.038 years ^ 



In this research Wolf had not introduced his relative numbers for the old observa- 

 tions. This was done in the year 1858. For his own observations these numbers 



' R. Wolf: Neue Untersuchungen über die Periode der Sonnenflecken und ilire Bedeutung. 

 Bern 1852. 



