56 



Sven Wicksell 





1.0000 



0.8422 



0.6205 



^1 



-|- 0.3329 



— 0.0570 



— 0.6440 







+ 0.2791 



— 0.6591 



Z x 



-f- 0.8524 



+ 0.3704 



— 0.3116 



Obviously, for the above values of q, the characteristics are too great to allow the 

 use of the formula (26). But one thing we may conclude, namely that for values 

 of q about 0.75 the mode will not lie far out of the X-axis. As by q = 0 75 our 

 galactic system of coordinates is nearly coincident with the vertex system we may 

 say: for q' = 0.75 the mode will practically lie on the axis toward the principal 

 vertex. Evidently this is required by the two stream-hypothesis. 



As one more in a way suggestive fact I will remark that for q somewhere 

 near 0.75 the total excess E of the small velocity components as given in formula 

 (32**) will disappear. 



24. We have just pointed out that for q about 0.75 the mode vector is di- 

 rected as required by the two-stream hypothesis. We will here look a little further 

 into the question what our figures have to say about this hypothesis. The two- 

 stream hypothesis requires that the frequency function of stellar motion shall be 

 the addition of two normal » components*. 



We denote by 



Mj and n 2 the relative number of stars in the two drifts, 



otj and a 2 the dispersions of the velocities in the two drifts, 



»Hj and flic, the stream velocities relative to the mean velocity of both the drifts. 



According to Charlier* we then have for the characteristics of the resultant 

 velocity distribution referred to the vertex system (Compare also our equations 

 (68), (68*), (68**) and (68***)): 



n i + n i = 1 

 n 1 m l -f- n 2 m. 2 = 0 



^200 = n i ry i 2 + n -i «>' + n i n i K — ™l>) 2 

 ^020 = n i a i 2 + n 2 a s 2 

 ^002 = n i a i 2 + rc 2 a., 2 



#H0 = 0 ^ioi = 0 N on = 0. 



-B 300 = — '/2 n l n 2 (a t 2 — a 2 2 ) (m 1 — m 2 ) + Ve n l n 2 (n, — n 2 ) (m 1 — w 2 ) s 

 B 120 = — l /i »! n 2 (a/ 2 — a 2 2 ) (m t — m 2 ) 

 #io2 = — V» »i n 2 (a t 2 — a 2 a ) {m t — m 2 ) 



B a ,„ = 0 B an * — 0 J? no , - - 0 J?„ Qil = 0 B n , a = 0 B nn0 = 0. 



• Charlier 1. c. pp. 94 and 95. 



