Stellar velocity distribution 53 

 49. The formula (50) may, however, be obtained in a direct way. Observing that 



X" = *i n x-\- 7,,?/ 4- y 13 



Y" = Ï21 X + Ï22 V + Ï23 *i 

 ^" = Ysi ^ + ?32 .'/ + Ï88 *. 



we get by summing up: 



2 X" = N », U 0 " = [ Tu 2b] + [ Vl2 2>] + [ Tl , Ä] », , 

 2 Y" = N^ V 0 " = [ Tll 2fc] + [t 32 2>] + [t 2S S»] » lt 

 v Z » = W » = [ 7m v„] + [ Ï32 v//] + [ Ï38 2fc] . 



Observing that 



these formulae are found to be quite identical with (50). 



50. In the following all stars fainter than 5.0 were rejected. Such a limitation 

 was made to get results comparable with the proper motion results. 



In table XVI the mean displacements for each spectral group in proper motions 

 and radial velocities are tabulated. The table XVII gives the same values for stars 

 brighter than 4.9. 



From the equation (49*) the motion of the invariable plane was obtained and 

 expressed through 



tà x = — 0.00287, 

 (ù y = — 0.00165, 

 M z = 4- 0.00234, 



wich gives 



to = 4- 0.00406, 



a 0 = 209°.3, 

 3 0 = + 300.2. 



Thus the invariable plane has a direct motion to the amount of 0.00406 seconds 

 of arc per year, which value agrees very well with that found by Charlier. The 

 axis of rotation is directed towards a point about 15 degrees from the pole of the 

 Milky Way. For the same motion Charlier has found: . 



to = 4- 0.003528, 



a o = 186°.7, 

 8 n = 4- 15°i. 



51. From the equations (49) and (50) the components of the sun's relative 

 velocity were now computed. Considering these velocities to be known from table 

 IV we may easily find the corresponding value of x> r 



