Stellar velocity distribution 31 



and the latter 



+ <* 



(i4) N ijk = ffj d u ri v d w 7 ( u, r, w) ( u — u 0 y ( v— v 0 y ( w — tf 0 )*. 



Hereby the significations below are explained. 



28. Assume the velocities of the stars to be distributed according to the 

 generalized law of Maxwell and let U', V , W denote the three velocity components 

 of a star relative to the sun, then the number of stars with components of velocity 

 between the limits 



U' ± Va dU\ V ± Vs d V, W ± V« dW 

 is given through the formula 



The surface 



A' U' 2 + B' V' 2 + C W' 2 = const 

 is called the velocity ellipsoid and the coefficients have the following expression 



a'=-L, e=-L, 



°1 °2 °3 



where o/, a 2 ' and o 3 ' denote the dispersions in the directions of the three axes of 

 the ellipsoid. 



From the schemes page 13 we get the relation between the velocity components 

 in the different systems. These schemes give us now: 



V" = Tu V + Yl2 V + Yt3 W, 

 (16) V" = l tl U+^ s V+i n W, 



and 



(16*) T = Tl2 f" + Ï22 F" + y 32 TF", 



likewise 



u" = 8 U tr + Bll i" + s 13 w, 



(17) F" = e 21 £7' -f s 22 V s 23 W, 



w" = s 31 er + e 3 2 + •» w, 



and 



[/' = .„ U" + ■» r + s 31 TF", 

 (17*) V = 6 12 V" -f e 2g F" -)- s 32 TF", 



TF = 6 13 f" + e 23 F" + s 3a PF". 



