■The Motion and Distribution of the Sun-spots 63 

 The observed dispersion of the motions evidently arises from two sources: 



1. Actual proper motions of the spots ; 



2. Errors in the measurements of the photographs. 



If we call the dispersions arising from these two sources, and respectively, 

 and the observed dispersion a, we may put 



(34) rs2 = aj2^a/. 



Of course, it may now be expected that will diminish, while, on the other hand, 

 O2 must undoubtedly increase with increasing spot-area. A closer examination now 

 shows that a diminishes in no small degree as the spot-area increases. Hence we 



Fig. 7. The Dispersion in Longitude and Latitude as Function of the Spot-area. 



may conclude that the part of the dispersion arising from the errors of observation 

 is rather inconsiderable, when compared with that part of the dispersion which is 

 caused by the actual motions of the spots. 



I had thought to examine the relation between 0^ and in some way or other. 

 This proves, however, to be rather a difficult task. A method that might possibly be 

 practicable is the following. Suppose the motions of the spots to be determined not 

 as we have done, from the co-ordinates on two consecutive days, but from greater 

 intervals. In this way one might possibly assume to be reduced to a small 

 quantity, and the observed dispersion might be considered as arising only from the 

 proper motions of the spots. But the dispersion obtained in this way is evidently 

 not quite of the same size as . If this were the case, a., might be obtained directly 



