62 Walter Gyllenberg 



TABLE XXI. 



The distribution of the apparent velocities (proper m >tion) of stars of magn<4.9. 



Axes directed towards the 



Mean 

 velocity 



Position 



a 



8 



Principal vertex 



Pole of the Milky Way... 

 Third direction 



0".1125 

 0".0724 

 0".0826 



284°l 

 180°.o 

 235°.o 



— 8°.0, 



+ 8°.2, 



-1- 78°.l . 



The velocity ellipsoid has, as shown from these results a distinct principal 

 direction in agreement with the radial velocity results, but is in contrast with this 

 flattened in the plane of the Milky Way. In table XXI the unit used is seconds 

 of arc per year. 



58. In the equation (52) we know the values of ^ , as well as the values of 

 N£ 00 , Nq 20 and 'Nl 02 (table XIII page 42). The velocity components £ 0 , Y] 0 , Ç 0 of 

 the sun, relative to the stars we may compute from the known solar velocity and 

 the apex direction. 



The axes of the apparent velocity ellipsoids are further very nearly coincident 

 with the axes of the galactic system of coordinates — G — and we may in an 

 approximative computation for the moments v,^ in the formulae (52) substitute 

 the squares of the three mean velocities in table XXI. 



From the three equations (52) we now get the values of q . The following- 

 results were obtained: 



Axis directed towards: corresponding value of q : 



Principal vertex -f- 0.466 



Pole of the Milky Way -f 0.690 



Third direction -f 0.403 



The values of q obtained are unexpectedly small, with the exception of the 

 result from the comparison between the mean velocities perpendicular to the plane 

 of the Milky Way. The mean velocity in this direction is, however, from the 

 proper motion solution, almost exclusively determined from stars surrounding the 

 plane of the Milky Way. Introducing into the formulae the corresponding mean value 

 of xr 1 , — 0.0135 — for these stars, the value of q will diminish from -f 0- 690 to -+- 0.493. 



59. It is however possible in another way to get an approximative value of q. 



The proper motions in a zone surrounding the galactic pole may be quite com- 

 parable with the radial motion in the galactic plane. The proper motion components in 

 the direction of the pole of the Milky Way of stars situated in the galactic plane are 

 on the other hand comparable with the radial velocities of stars in the polar zone. 



In this way I have derived the following results noted in the table below. The 

 first columns indicate the moments compared, and the value of d- 1 used in the formulae. 

 The last column gives the corresponding value of q . The next four tabulated 

 determinations were made from a comparison between the moments over the whole sky. 



