6 



C. V. L, Charlier 



(25) 



and 



(26) 



It may be observed that the expressions for the skewness and for the excess 

 are independent of the parameter 



4. The observed proper motions. These are taken from the »PreHminary Ge- 

 neral Catalogue of Stars» (P. G. C.) by Boss. This catalogue aims to include all the 

 stars down to the sixth magnitude from the North to the South pole (compare Astr. 

 Journal N:o 612, 1910). Moreover it contains some 2000 stars, mostly contained 

 between the magnitudes 6™ to T^^ö, »for which the propermotion can be determined 

 with mere than customary accuracy for the generality of stars within those limits 

 of magnitude». I first determined the characteristics for each square taking into 

 consideration all the stars in P.G.C. Afterwards I found that, for a proper dis- 

 cussion of the results, it was necessary to exclude all stars fainter than the sixth 

 magnitude, because it is an essential demand to the material used, that all stars 

 between given magnitudes are considered in the investigation. 



From this reason I have calculated the moments and the characteristics in four 

 different ways; 



1) Taking together, for each square, all stars brighter than 4"*; 



2) Taking together, for each square, the stars of the fourth magnitude, 



3) In like manner with the stars of the fifth magnitude, 



4) finally, taking together all stars brighter than the sixth magnitude. 



The method for computing the moments and the characteristics is that given 

 in Meddelanden Serie II N:o 4 and in my pamphlet »Grunddragen af den mate- 

 matiska statistiken». In 1) only the characteristics of the first order — the means — 

 and ^/q) are computed. Here there are indeed only 424 observations in all, and 

 even the determination of the means is very uncertain, the mean error of the means 

 amounting to some 0,5 class-breadths (a class-breadth = 0,"o5o). Nevertheless, the 

 general character of the proper motions — caused by the motion of the sun — is 

 well developed in the obtained values of x^^ and y^. 



In 2), embracing the stars of the fourth magnitude, the characteristics of the 

 two first orders were computed, h. e. besides the mean motions in a and S also the 

 dispersions and the coefficient of correlation. There are in all 922 stars of the 

 4:th magnitude, h. e. upon an average 19,2 stars on each square. The mean error 

 in the mean for each square here amounts to about a third of a classbreadth (more 

 accurats values are given beneath) or 0."oi7. 



In 3), embracing the stars of the 5:th magnitude, there are in all 2695 stars, or 

 upon an average 56.15 stars on each square. The mean error in the means here 

 amounts to about a sixth part of the class-breadth (= 0."oo82). 



