The Motion and Distribution of the Sun-spots 



23 



uQore. In a normal distribution the probability of such a deviation is approximatel}^ 

 0.00001. There is moreover another thing. Several of these great motions may be 

 thus explained, that in a spot-group, consisting of a long line of spots, part of 

 these spots disappear, which may evidently cause a displacement of the centre of 

 gravity of the spot. 



As the co-ordinates of the group are co-ordinates of the centre of gravity, it 

 is evident that great proper motions, caused in this way, are only apparent, which 

 fact justifies the exclusion of such great motions. Since it is here a question of 

 giving the essential features of the state of the motions of the spots, it seems the 

 more necessary to exclude these motions from the investigation as they would 

 have a very considerable influence especially on the higher characteristics, skewness 

 and excess. 



Tables VIII and IX show the distribution of the cards (or observations) accor- 

 ding to years and latitudes before and after the exclusion. 



In table X, showing the distribution of the motions in longitude, I have given an 

 extract from the tables of correlation, without taking into account the corresponding 

 motions in latitude. 



B. Characteristics of the Motions in Longitude. 



Summary of the Method employed. Before }iroceeding to a computation 

 of the characteristics of the motions of the spots, I will give a summary of the 

 method employed in this calculation. This method has been developed by Prof. 

 Charliek ^ in several papers. 



For short, we put in the following 



= AX cos ß 



and 



= the mean of oc . 



Suppose F{x) to be the frequency-function of x. As this function (see table X) 

 is of type A according to the nomenclature of Charliek, F{x) may be represented 

 by the series 



F{x) = A, 'f(,r) + A3 'f\x) + A, f'\r) + . . . . 

 where fp(r) represents the function of normal distribution 



(1) 



' For example see Chaemkr: Researches into the Tlieory of Probability. Lund 1906. 



