Stellar velocity distribution 



35 



As the stars in the different squares are varying in number, the weight of each 

 equation was put equal to the number of stars entered. Further by this combination 

 of the spectral classes, in the left member of (29) the quantity iV 002 was exchanged by: 



where n l , o i and n 2 , o 2 are referred to the two combined spectral classes. The 

 procedure mentioned signifies indeed a neglecting of the difference of the two means, 

 but as this is small for neighbouring spectral classes I have for practical reasons 

 used the above expression. For the two groups »magn <4.9» and »all stars» the 

 dispersions were computed about the observed means and the weights were considered 

 equal for all squares. 



TABLE XI. 



The axes of the velocity ellipsoids and their directions from observations 

 in the line of sight. 



Type 



Number 

 of stars 



Principal vertex 



Secondary vertex 



Third direction 



o. 





0 





8 





a 



3 





B and ,1 



510 



280°.l 



— 19°.5 



3.102 



12° 9 



— 8°.o 



2.728 



304°.2 



+ 68°.8 



1.727 



F and Gr 



445 



253°.7 



+ 0°.o 





343°.3 



— 37°.9 



3 670 



344°.i 



+ 53°.o 



3.023 



K and M 



571 



248°.9 



— 14°.l 



4.508 



338°.5 



- 2°.2 



4 266 



257°.2 



+ 76°.o 



4.003 



Magn. 























magn <L 4.9 



1069 s 



262°.3 



— 7°.2 



4.201 



358°4 



- 40°.5 



3.473 



344°.l 



+ 48°6 





magn >. 5.0 



462 



259°.9 



- 0°.2 



4.507 



349°.8 



— 6°5 



4.191 



348°.2 



+ 83°.8 



3.635 



all stars 



1526 3 



264°.l 



— 5°.2 



4.246 



357°.l 



— 29°.9 



3.766 



336°5 



+ 59°5 



3.056 



33. In table XI the results are tabulated. The column indicated by principal 

 vertex gives the magnitude and the direction of the largest axis and coincides 

 approximatively with the vertex found by Schwartzschild 1 from the proper motions 

 of stars (a = 273°, 8 = — 6°). The column secondary vertex contains the next axis, 

 which is directed against the pole of the Milky Way. The last column finally 

 gives the direction of the shortest axis and its length. It is remarkable that the 

 shortest axis as well as the longest coincides approximatively with the plane of the 

 Milky Way. 



34. To get a wiew of the positions of the velocity ellipsoids I have tried to 

 make a graphical demonstration. The figures 10 — 13 represent the sky and its 

 division into squares. The dotted line and the black star indicate the position of 

 the Milky Way (pole: a = 191°.2 S=+ 18°.o). The ellipsoids are assumed to be 

 drawn in the system of coordinates determined by the position of the axes, and 



1 K. Schwartzschild: Ueber die Eigenbewegungen der Fixsterne. 

 * Including 5 stars of spectral type Oe. 



