38 



Walter Gyllenberg 



with its origin coincident with the centre of the sphere. The numbers indicate the 

 lengths of the axes. The figure 13 contains besides the denominations of the squares. 



35. In order to get an idea of to what degree the ellipsoidal hypothesis satis- 

 fies the observed data I have recalculated from the elements of the ellipsoid the 

 dispersion in the velocity distribution for each square, and compared it with the 

 observed value. These recalculations were easily performed with the aid of the formula 

 (29) page 33. 



TABLE XII. 



Comparison between observed and recomputed 

 dispersion in the line of sight. 







Magn 



^4.9. 



fe £ 



AÎ1 stars. 



Square 



s » 



Dispersion 



s ts 



Dispersion 







computed 



observed 





computed 



observed 





26 



3.175 



3.328 



46 



3.337 



3 513 





39 



3.024 



4.099 



67 



3.244 



3.!>79 



B. + E t 



67 



2.961 



2.763 



89 



3.260 



3.426 



B, +£, 



57 



3.535 



2.791 



82 



3.642 



3.408 



B s + A 



51 





3.955 



69 





4.179 



B, + A 



36 



3.730 





63 



3.869 



3.383 



B, + Ao 



41 



3.507 



3.564 



65 



3.747 



3.821 



B, + A 



33 



3.496 



2.227 



59 



3.729 



3.027 



B, +E 2 



42 



3.597 



3,419 



62 



3.769 



3.501 



B, +E B 



48 



3.458 



3.164 



78 



3.653 



3132 



B, + A 



70 



3.006 



2.709 



104 



3.343 



3.191 



B 10 + A 



60 



2.675 



2.590 



86 



3.110 



2.941 



<-\ + A 



35 



3.209 



3.046 



38 



3.565 



3.216 



c 2 + A 



40 



3.793 



3.976 



51 



3.929 



3.770 



c s + A 



68 



4.162 



3.879 



87 



4.196 



3.705 



c 4 +Ao 



43 



4.082 



4.462 



63 



4.178 



4.441 



c, +D n 



38 



3.671 



3.643 



52 



3.937 



3.918 



C e + A. 



32 



3.344 



3.621 



39 



3.733 



3.956 



c, +A 



27 



3.474 



3.135 



47 



3.790 



3.932 



c s + A 



37 



3.872 



4.826 



54 



4.026 



4.783 



c» +A 



46 



4.076 



4.018 



60 



4.158 



4.339 



Cio + A 



61 



3.849 



3.654 



75 



4.016 





<?u + A 



38 



3.315 



3.210 



53 



3.676 



3.861 



o M + A 



34 



2.954 



3.375 



42 



3.439 





The table XII gives this comparison for the groups »magn <4.9» and 

 »all stars». It is however very difficult from this table to draw any positive con- 

 clusions to the favour of the ellipsoidal hypothesis. A graphical comparison will 

 meet with obstacle. I have however in the fig. 14 and fig. 15 for the _Z?-squares 

 and the C-squares compared the observed and the recomputed values of the disper- 

 sion for the group »magn <4.9». The former are represented by small circles 

 and the latter by the full drawn line. The agreement seems very good in spite of 

 the small number of stars used. The shortest axis, situated in the square B w is 

 very well marked out by the observations. It is however to be observed that these 

 curves are only sections through the surface in question. 



