Stellar velocity distributioi 



lit 



As is easily seen, the form (6) involves that all squares have the same weight. 

 Dividing the stars into spectral classes, the number of stars in the different squares 

 is very varying, partly due to the small total number, but also to the real distribution . 

 in relation to the Milky Way. 



For the solution of the two groups denoted by »magn. < 4.9 ; stars over the 

 whole sky» and »all stars over the whole sky» the formulfe (5) were used. 



When the other groups were treated, account was taken of the weight in each 

 square. Assuming these weights proportional to the numbers of stars, the normal 

 equations now take the form : 



I" T» Tis] U 0 " + [« Tis T 23 ] V o" + [* ha T S3 ] W o" + [* T i3 ] K ~ [ n Tia * 0 ] = °. 



/ 7 j i n T 23 Tis] ^o" + \ n Ï23 T 28 ] V o" + [n T 23 T 33 ] W o" + l n Tss] K ~ i n T 23 3 o\ = °> 



\ n T 38 T 13 ] U Q " + [n T 33 T 28 ] F 0 " + [ti t 33 T 33 ] PT 0 " + [« y S3 ] Z — [» Y 33 i 0 ] = 0, 



[»T U ] ^o" + L»T 23 ] V + [^T 33 J ^o"+ J*" Z- [n#J=0. 



Here w denotes the number of stars in each square and N the total number 

 of stars. The equation (7) is however nothing but the solution obtained by treating 

 the stars separately. Yet there remains the approximation that all stars in a square 

 are assumed to have the same coordinates as the centre of the square. 



15. In tables IV a and IV b the results from these computations are tabulated. 



The second column gives the number of stars in each solution. The three 

 following columns give the three components of the sun's relative velocity in the 

 if 2 - system. S denotes this velocity and the column K gives the value of this con- 

 stant for each spectral type. 



A new solution was made for each group, assuming the constant K to be zero. 

 These solutions are noted in the last column. 



Table IV b contains the results obtained when dividing the stars into magnitudes. 

 In two cases I have made one solution for stars surrounding the pole of the Milky 

 Way and another for stars in the plane of the Milky Way as remarked in the 

 first column. 



For this purpose I divided the sky into two equal parts, the one containing 

 24 squares situated approximatively in a zone with galactic latitudes within + 30°, 

 the other part containing the rest of the squares surrounding the pole of the 

 Milky Way. The squares were distributed as follows: 



Squares within galactic latitude ± 30°: 

 A v A„ B v B v B 3 , B s , B 9 , B 10 , C a , C v G w C 1V Z) 4 , Z> 5 , D 9 , D w E v E v E 5 , E 6 , 

 E v E s , F v F,. 



Squares surrounding the pole of the Milky Way: 

 B,, B h , B,, B v C v <7 2 , C 6 , C,, C v G s , G' !P C 1V D v D 2 , D,, D,, D v D s , D lt , D 12 , 

 E v E v Eq, E w . 



This division was made to get an idea of the influence of stars in different 

 galactic zones on the apex solution. The results from the two zones seem however 



