The Astronomical Survey of the Universe [ch. i 
found the star-density at a distance r from the centre to be proportional to 
(r 2 + a 2 ) “ * where the constant a which determines the scale of the cluster is 
very approximately the same for all clusters. This law gives a density which 
falls off as r -5 at great distances from the centre ; I have, however, found * 
that the observed distribution in the outer regions of the clusters is better 
represented by a density falling off as r~ 
The central dense portions of all the clusters is about 5 parsecs in diameter, 
the star-density remaining appreciable to a distance of 15 or 20 parsecs from 
the centre. The star-density in the central regions is very high. Within 10 
parsecs of the centre of the cluster M 3 there are at least 150,000 stars which 
are at least four times as bright photographically as the sun. Thus the density 
of distribution of these bright stars alone is several hundreds of times as 
great as the density of stars of all kinds in the neighbourhood of the sun. 
The distances of the globular clusters are so great that only stars of high 
luminosity are accessible to observation. It seems probable that, as in the 
galactic system, very bright stars must be accompanied by far greater numbers 
of fainter stars; if so, when stars of all degrees of luminosity are taken into 
account, the star-density in the globular clusters must be very great indeed 
in comparison with that in the galactic system. 
Finally it may be added that only about 100 of these globular clusters 
are known to exist, practically all of which were known to the Herschels. As 
they appear to be all of similar dimensions and to lie within a definitely limited 
region of space it is unlikely that many more, if any, remain to be discovered, 
at any rate in those parts of space which are near to the sun. 
It is not altogether clear to what extent the globular clusters and the 
moving clusters form distinct formations. In some respects the group of 
objects known as open clusters seem to form a connecting link between themj*. 
Boss has remarked that if the Taurus cluster were to continue its present 
motion undisturbed for another 65 million years, it would then appear to us 
as an ordinary globular cluster 20' in diameter. On the other hand, it must 
be remarked that the moving clusters move with ordinary stellar velocities, 
whereas the globular clusters have far higher than stellar velocities, and 
that the groups which are clearly established as moving clusters contain 
few stars, whereas the globular clusters contain hundreds of thousands. We 
shall return to the problem of the clusters in a later chapter. 
Nebulae. 
28 . Astronomical objects in general may be divided into two broad classes 
according as the telescope shews them as points of light or as areas of finite- 
size. The quite small planets are so near as to shew finite discs in the 
telescope, whereas the far larger stars are so remote as to appear as mere 
* Monthly Notices of the R.A.S. lxxvi. (1916), p. 567. 
I Sigfrid Raab, “A Research on Open Clusters,” Lund Meddelanden, n. No. 28 (1922).