Stellar velocity distribution 



4i 



and 



(36*) H = ß 21 ?7+ß 22 F+ß 23 Tr, 



Z = ß 31 ^+ß 32 ^+ß 3 3 ^ 



The moments in the galactic system are now easily found through the trans- 

 formation of the coordinates. 

 In general we get: 



(37) M [in Vi W) = M [(ß u 3+ß 21 H+ß 31 Z)* (ß 12 S+ß 22 H+ß 32 Z)i (ß 13 3 +ß M H+ß M Z)*] . 

 and 



(37*) Jf (3TI'7/')=1/ [(ß n CT-f- ß 18 F+ ß 13 TT )<(ß LM CT-|- ß 22 ß 23 JF}>'(ß 31 £7+ ß 32 F+ ß 33 W)*]. 



Regarding the first of these expressions for i=j = Q and Jc = 2, and developing 

 the right member, we now get the following relation: 



(38) ^O0 2 = ß\3^0 + ß 2 a 3^0 + ßl3^2+2ß 23 ß 3a ^ 11 + 2ß 13 ß g8 ^ 01 + 



+2ß 13 ß 23 ^ 10 . 



Here are 



N tit = M{V t V i W k ) t 



and 



N£=M{EWZ h ). 



The left member of (38) is the observed quantity in the square and the right 

 member contains the unknown moments in the galactic system. The number of 

 these may however be reduced. Assuming the velocity distribution uncorrected in 

 this system, the last three unknown quantities may be put equal to zero. In the 

 same manner we may solve the equation when the frequency surface is assumed to 

 be represented by an ellipsoid of revolution. Then we have to put 



ll 0 2 0 I, 0 0 2 ' 



Here however the restriction remains that the frequency function is regarded as 

 uncorrected in the S-H plane as well as the S-Z plane. 



From equation (38) the dispersions in the three galactic main directions were 

 now computed. In the table XIII the results are given for each separate spectral- 

 class. The dispersions are indicated by 



Lunds Universitets Årsskrift. N. F. Afd. 2. Bd 11. 



(i 



