44 Sven Wicksell 



The values of q are chosen rather arbitrarily. The value q — 0.6205 is the 

 oue used by Oharlier. 



TABLE VI. 

 The roots of the cubic. 



9.' 



Sj 



S 2 



S 8 



1 .0000 



3.4057 



1.6036 



1.0412 



0.8422 



2.7906 



1.2778 



0.8517 



0.6205 



1.9462 



0.8234 



0.5626 



0.4500 



1.3270 



0 5177 



0.2663 



TABLE VII. 



The Axes and the Vertices of the Velocity-ellipsoid for different values of q' . 



i 







Sj 



*1 °2 













\ 



1.00 



1.8454 



274°.3 



— 12°.4 



1.2663 



339°.l 



<52°.5 



1.0204 



189°.9 



24°.l 



4° 



0.84 



1.6705 



274°.l 



— 15°.8 



1.1304 



338". 3 



57°.9 



0.9229 



192°.2 



27°.5 



1° 



0.62 



1 .3950 



273°.6 



—21 ".3 



0.9074 



342°.i 



43°.3 



0.7501 



202°.o 



39°.o 



16° 



0.45 



1.1520 



272°.9 



-28 u .7 



0.7195 



351° 



21° 



0.5160 



230°.6 



53°.5 



37° 



The pole of the Milky way is according to Kobold 

 a = 191 °.2 

 3 = 28°.o. 



The last column of table VII contains the distance of the smallest axis from this pole. 

 The distance will be a minimum for q somewhat smaller than 0.84, and it will then 

 not amount to even 1°. Further we see that when q decreases below 0.84 this 

 axis will lie more and more distant from the pole, being for q = 0.45 already 

 37° from it. 



Accordingly we see that for q between l.o and 0.7 the system of the axes of the 

 velocity ellipsoid can be regarded as a galactic system. 



As it has been found by Gyllenberg from the radial velocities that the 

 velocity ellipsoid has two axes in the plane of the Milky Way we already here 

 may conclude that q cannot well have a value beloiv 0.7. Compare, however, p. 66. 



The value q = 1 gives the ellipsoid of the apparent motions. We call it the 

 apparent ellipsoid. We find, that using as unity the second of arc we have: 

 The Apparent Ellipsoid 



Axes: o 1 = 0".0923 Vertex: a t = 274°3 8 1 = — 12° A 



o, = 0".0633 a 2 = 339°.i 8 2 = + 62°.6 



a 3 = 0".05l0 a s = 189°.9 S 3 = + 24°.i. 



