Stellar velocity distribution 45 



where n is equal to the Dumber of stars in a certain square. Putting now for n 

 a mean number so that 



n = N : 24 



and writing for a and s (a) the values from table X, then the formula takes the form 

 e (<,■) 



and consequently 



A new approximation by putting 2^ = t in the different cases will give the final 

 expression : 



£ (o)l/24 



In this way the mean errors in table XIII were computed. Especially for the class 

 B stars they will be erroneous, but the values on the whole give a view of the 

 magnitude of the mean errors for each spectral group. 



Concerning the mean error in the determination of the velocity ellipsoids, I 

 have for the group »stars of magn. < 4,9» derived the mean errors in the lengths 

 of the axes. These were found to be equal for the three axes and amounting to 

 0,160 Sin. From this value I have with the aid of the short method, used by Mr. 

 Wicksell, computed the mean error in the galactic coordinates of the vertices. The 

 following values were obtained : 



E axis II axis 



Mean error in gal. latitude ± 4°. 3, + 4°.3, 

 » » » » longitude ±3°. 4, + 17°.2. 



For the position of the axis directed towards the pole of the Milky Way, the mean 

 error in the direction E — Z is equal to + 3°. 4, and in the direction H — Z the mean 

 error amounts to + 17°. 2. 



= 2 a e (a) |/ 2 4 

 2o £ (a) 1/24 



Vp 



The moments of higher order. 



43. In the following table XIV the values of the skewness — S — and the 

 excess — E — are tabulated. Owing to the small number of stars I have combi- 

 ned the spectral classes in groups; the stars of classes B and A were however se- 

 parated on account of the peculiar velocity distribution of the former class. 



For each computation the stars from six representative squares were used. 

 Further the stars were limited to magn < 4.9. 



Unfortunately the number of stars in the different spectral groups are small. 

 In several cases the mean errors are too large to give a real meaning of the charac- 

 teristic. The throughout negative skewness in the direction of the principal vertex is 



