66 



Sven Wicksell 



the »angular» velocity of the sun & 1 S with the linear velocity found from the radial 

 motions, we put 



(84*) (S% = 



Accordingly we correct for the variation of & l with galactic latitude by multiplying 

 our values found for %-\ hy the factor m . 



The values thus corrected will be the true values of ■&* £M in as much as they 

 before were faulty on account of the variation. 



Now we may at once ascertain the effect of the variation on the vertices. If 

 the vertices coincide with the galactic system of coordinates, which is nearly the 

 case, the moments Nf 10 iV ( j' 01 and N < $ 11 are all zero. The factoreal correction 

 cannot change them and accordingly the vertices will not be displaced. The same 

 may be shown to be the case if the two axes of the ellipsoid lie in the plane of 

 the Milky Way without necessarily coinciding with our specially chosen galactic 

 system of coordinates. Shortly we may state that if one axis points toward or in 

 the vicinity of the pole of the Milky Way the vertices will he unaffected or nearly 

 unaffected by the variation of $ 1 with galactic latitude. 



It will be of interest to see how the vertices are affected when not forming a 

 galactic system, as is the case for low values of q . The principal vertex, as is seen 

 from table VII and fig. 1, will never move out of the Milky Way, since when q de- 

 creases it moves nearly along that plane. It will therefore be very little changed 

 by a correction for a varying & v Now we have found the shortest axis most near 

 the galactic pole. For such values of q as make its polar distance sensible the 

 correction for a d- 1 growing with galactic latitude will increase that distance, so that 

 the effect will be a rotation of the ellipsoid about the principal axis in a retrograde 

 direction. A variation in è x , great enough to exchange the ratio of the two smaller 

 axes, will produce the effect that the medium axis comes up in the vicinity of 

 the pole. Indeed, it seems, as I have found by a rough computation, as if even 

 for q =0.6 a variation of great enough to make the ratio of the axes the same 

 as found from the radial velocities, would make the medium axis point very near 

 to the galactic pole, a fact that I consider to be of great interest. 



The facts above stated are found by reasoning in the following way. Taking 

 a galactic system of coordinates having its X-axis directed toward the principal 

 vertex the polar distance <p of the transgalactic axis is given by the formula 



tg 2'f = N , (uncorrected JV 020 > N 002 ) 



iV 020 1V 002 



and as the correction for a ti 1 growing with galactic latitude evidently decreases 

 and finally even changes the sign of the difference N 020 — N 002 the above statements 

 are easily verified. 



