Stellar velocity distribution 



33 



Substituting the relation (22) in (24) we get 



A"B"C"— A"D" 2 —B"E'" 



H 



G"F"*-\- 2B"E"F" 



AB - F 2 

 Here 



AB - F 2 = (B" C" - D" 2 )- !r 2 + (C'A" — E" 2 )y 23 2 



+ [A" B" - K' 2 ) y 33 2 + 2 (D"E" - C"F") Tl8 Ï23 



+ 2 (F" F" - A" B") y 23 y 33 + 2 (F"D" - y 33 Y 13 • 



In the expression for if, the numerator does not contain the direction cosines 

 of the squares and is therefore a constant. 

 Observing that 



1 



(27) 



and 

 (27*) 



#00 2 



where o denotes the dispersion in the frequency distribution of the observed radial 

 velocities, and putting 



(28) 



A"B"C"~ A"D"' 



B'E' 



C"F" 2 + 2D"E"F' 



A", F", E" = const. 

 F", B", B" 

 E", B", G" 



the equation to be solved takes the form : 



(29) Û 2V 002 = (B"C" - Z)" 2 ) Yl3 8 + (C'A" - E" 2 ) y 23 ° 



+ (A"B" - F"*) y 33 2 + 2 (D"JS" - C"F") Yl3 Y 23 



+ 2 (^"J"' - ^"//') y 23 Y 33 + 2 (F"D" - B"E") Ï33 Yl3 ■ 



30. Integrating however the expression (18) over the other axes one by one, 

 the moments of the second order expressed in the constants of the ellipsoid are 

 easily found. The following six relations are thus obtained: 



(30) 



From these relations it is possible to express the coefficients of the ellipsoid in 

 the moments N ijk . We get for these coefficients: 



Lnnds Universitets Årsskrift. N. F. Afd. 2. Bd 11. 5 



^ #200 



BO- 



D 2 , 



A JV 020 = 



CA — 



E 2 , 



A #002 = 



AB — 



F\ 



* #oii = 



EF — 



AD, 



A #101 = 



FD — 



BE, 



A #110 = 



DE - 



CF. 



