CHAPTER IV 



The Dispersion of the Motions for different Spot-sizes. 



We shall now more closely investigate the dispersion of the motions for diffe- 

 rent spot-sizes. Already in discussing the positive excess of the longitude as well 

 as of the latitude motions, we pointed out the evident connection existing between 

 the dispersion and spot-area. Since the dispersion might be considered as a measure 

 of the stability of the spots during the motion, my first idea was to suppo.se a 

 smaller dispersion for the greater spots. This also proved to be the case. Then 

 we did not take the following matter into consideration. Since the co ordinates of 

 the great spots are determined with considerably greater uncertainty than the co- 

 ordinates of the small ones, this circumstance should evidently contribute to a greater 

 dispersion of the motions of the larger spots than of the smaller. 



Now we shall first compute the dispersion of the motions for different spot- 

 sizes. In treating the question of the positive excess of the latitude motions, the 

 distribution of the motions for different spot-sizes was also investigated. Tlie result 

 of these computations for the different hemispheres during both periods are brought 

 together in table XXIX. In this table the dispersions of the longitude motions are 

 also given. Since the mean values of the motions in longitude vary with the lati- 

 tude, it may at first sight seem appropriate to combine different latitudes in com- 

 puting these dispersions. The dispersions a^. given in table XXIX are, however, 

 obtained in displacing the distributions in such a way that the means coincide. 

 These dispersions have thus been computed from the values of table XVI, by 

 means of the well known formula 



wliere the terms in the right membrmn depending on the differences between the 

 means are omitted. 



Looking somewhat more closely at the table, we find a pervading diminishing 

 of the dispersion with increasing spot-area, during the two periods the investigation 

 embraces. Combining the entire material, we obtain the values of the four last 



