243-247] Stellar Motions in the Galactic Universe 239 



denote typical velocities of stars of two types of masses M, M', then the law 

 of equipartition requires that 



M^ = M'^ (577), 



where the bars over c 2 and c' 2 denote that the means of these quantities are to 

 be taken over a number of stars of the appropriate types ; the stars included in 

 these means may be selected in any way provided that this does not, directly 

 or indirectly, imply a selection according to velocity. Clearly the law (577) 

 requires that, statistically, the most massive stars shall move with the smallest 

 velocities. 



It appears to be generally accepted that the stars of greatest mass do, on 

 the whole, move with the lowest velocities*; Halmf has gone so far as to 

 claim that the correlation between mass and velocity is actually that required 

 by the equipartition law (577). Whether we accept this result or not, it is an 

 undoubted fact that there is a very marked correlation between a star's 

 velocity and its spectral type, the 5-type stars moving the most slowly, and 

 so onj, while there is little doubt that B- type stars are on the whole the 

 most massive. 



246. A second property implied in the law (576) is one of correlation 

 between mass and distance from the centre of the system ; the most massive 

 stars tend to remain in the more intense parts of the gravitational field 

 while the lighter stars spread to greater distances, just as is the case with 

 molecules of different masses in planetary atmospheres. Remembering that 

 there is also a correlation between mass and spectral type, it appears that 

 there ought to be correlation between spectral type and distance from the 

 centre of the universe, the .Af-stars being statistically the most remote. Cor- 

 relation of this kind has been found, but the .5-stars, and apparently also 

 the A -stars down at least to about A 4, appear to form an exception . 



247. A third property implied in law (576) is that stars of similar type 

 shall have the same average linear velocity relatively to the system as a whole, 

 no matter what part of the system they are selected from. This is probably 

 approximately true in our system ; there appears to be no correlation between 

 a star's distance and its velocity ||. 



In 221 we imagined our system initially to have been a nebula of about 

 30 parsecs radius rotating in a period of about 160,000 years. The velocity 

 of a point on the equator would be approximately 1200 kms. a sec., and the 

 velocity of the ejected stars must at first have been comparable with this. 



* See, for instance, Eddington's Stellar Movements, Chap. VIII, or Charlier, The Observatory, 

 40 (1917), p. 391. 



f Monthly Notices R.A.S. 71 (1911), p. 634. 



Eddington, Stellar Movements, p. 154 ; Campbell, Stellar Motions, Chap. VI. 



Eddington, Stellar Movements, p. 167. 



|| Eddington, Stellar Movements, p. 161; Kapteyn, Amsterdam. Akad. Proc. 1911, pp. 528, 911. 



