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348-350] The Origin of the Galactic System 
about 5 degrees. We see that the complete disintegration of the cluster takes 
about 10 12 years, and results from gradual scattering rather than from single 
violent encounters. 
This calculation has supposed the stars all to be of solar mass. The 
formulae of § 287 shew that the time needed to produce a specified deflection 
in the path of a star of mass m' is proportional to (m + m') 4 , where m is the 
mass of the average star. Thus for a cluster of stars of five times the mass of 
the sun, the times of disintegration just calculated must be increased 81 times, 
so that complete disintegration takes 10 14 years rather than 10 12 years. 
The foregoing rates of disintegration are the speediest possible, for they 
have been calculated for the maximum possible density of stars, namely that 
prevailing at the centre of the galactic system. A cluster can prolong its life 
almost indefinitely if it travels mainly in the outlying regions of the galaxy, 
where disturbing stars are sparsely scattered. Nevertheless, the foregoing 
figures give some indication of the ages of the star-clusters. 
Stars of mass equal to that of the sun would be knocked out of moving 
clusters after a few million million years, so that, with the ages we have 
already calculated for the stars, only stars considerably more massive than 
the sun ought, as a general rule, to be left in the moving clusters. 
In view of this result, it is significant that most recognised clusters consist 
mainly of stars of types B and A, which, as we have seen, are considerably 
more massive than the sun. The stars of a cluster do not range over all 
spectral types ; there is generally a clearly defined limit * both in spectral 
type and absolute magnitude, and this limit fixes the age of the cluster. It 
is impossible to give very precise figures, but a limit corresponding to a mass 
double that of the sun would fix the age of the cluster at about five million 
million years. 
The Origin of the Galactic System. 
350. Within a few million million years the clusters we now observe in the 
sky will become inextricably mixed with the general mass of stars in the sky, 
and a few million million years ago a large number of stars which now appear 
to be moving at random must have been recognisable as members of clusters. 
It is interesting to consider whether our whole galactic system may have been 
formed simply out of a collection of moving clusters and the débris of 
disintegrated clusters. We can imagine a great number of such clusters 
thrown together, passing through one another in their motion and gradually 
becoming inextricably mingled. Occasionally a cluster would break free from 
the main mass and form an approximately spherical structure under its own 
gravitation; such clusters would constitute the “globular clusters” described 
in § 27. 
* See, for instance, Curtis, Publ. Astron. Soc. Pac. 27, p. 248, Rasmuson, Lund Medde- 
landen, Series II, No. 26 (1921), and Trumpler, Lick Obs. Bulletins, 333 (1921) and 361 (1925). 
J