stellar dusters 



15 



The determination of e from the ^--coorchuate of the centre is, in this case, 

 not possible, not only because of the large mean error in this coordinate, but also 

 because the mean value of z is highly dependent on the .^-coordinates of those 

 clusters which are situated farthest from the galactic plane. If such clusters are 

 excluded we find that the ^-coordinate of the remaining clusters changes the sign 

 and becomes negative agreeing with the centre of the J?-stars. The figures 1 and 

 2 on plate III show very clearly this infiuence of clusters far from the galactic 

 plane upon the ^-coordinate of the system of clusters. 



We may even use the extension of the system of clusters from the centre for 

 determining the scale. May be that we have no certainty for assuming that the 

 Helium stars and the clusters are spread equally far in the plane of the iMilky Way 

 — in fact the spread of clusters, in that plane, seems to be twice as great as that 

 of the 5-stars — but there is more reason for assuming the spread in the direction 

 perpendicular to the galactic plane to be approximately the same for both objects. 



The spread is measured i)y the coefficient of dispersion, a, which has, for the 

 clusters, in the plane of the galaxy the value 10.9 s, whereas perpendicular to it 

 we have for the dispersion, a~, the value 



a„ : £ = 1.448 ± 0.087. 



It may be observed that the mean error in nz is rather small, as compound 

 with the mean error in the coordinates of the centre. 



For the dispersion in the ,s-coordinates of the B-stars I found the value 13.09 

 sir. Equating these dispersions we get for the scale the value 



(15) e = 9.04 sir. 



Thus the two methods of computing tlie scale lead to values of the same 

 order of magnitude. Taking into consideration the mean errors we may confine us 

 to the value (15) which is by far the best determined. 



Using this value of s we multiply the spherical coordinates by 9.04 and thus 

 obtain the rectangular coordinates of the clusters expressed in siriometers. On the 

 plates II and III we have the system of the clusters projected on the XF, XZ 

 and the YZ-planes. Comparing with the plates II, III and IV of Meddel. 14 we 

 find that the clusters are somewhat wider spread than the l?-stars. We have, in- 

 deed, clusters rather numerous up to 200 sir., whereas almost all lî-stars lie within 

 a distance of 100 sir. It is a striking spread in the ^-coordinates of the clusters 

 in the direction of the Y-axis, wliich is also conspicuous in the apparent distri- 

 bution shown on plate 1. These scattered clusters he in the squares (r(?5 and GC^, 

 i. e. in the constellations Auriga and Gemini. It seems probable that the distance 

 of the smaller clusters in this direction has been exagerrated. 



9. The computation of the relative distances of the clusters has here been 

 based on their apparent diameter. This quantity is as far ambiguous as their is 

 generally no distinct limit where we can declare a cluster to be separated from the 



