240 The Evolution of Star-Clusters [CH. x 



As the system of stars expanded these stellar velocities must have decreased, 

 the tangential components in accordance with the law of conservation of 

 angular momentum and the radial components on account of the gravita- 

 tional attraction of the central mass. In the present state we may suppose 

 orbits of an average of perhaps 2000 parsecs diameter to be described in 

 about 160,000,000 years, this rate of description of orbits would give linear 

 velocities of the order of 25 kms. a second, which is of the order of magnitude 

 of observed velocities. 



Stars of different masses will describe orbits of different sizes. We have 

 already seen that according to the equipartition law (576), the most massive 

 stars will stay nearest to the centre of the universe ; they will therefore 

 describe the smallest orbits. As the period of an orbit is approximately 

 independent of its size*, it follows that the most massive stars will move 

 most slowly. If the law (576) were fully obeyed, the relation between mass 

 and velocity would be that already obtained in equation (577). 



248. A fourth property implied in the law (576) is that there is no star- 

 streaming at any point or region of the system. The system rotates as a 

 whole with a uniform angular velocity o>, so that any selected set of com- 

 parison stars would rotate as a whole with this same angular velocity, and 

 the only means of detecting the rotation of the system would be by some 

 method such as that of Charlier explained in 221. Relative to axes rotating 

 with this angular velocity, the stellar velocities will, if law (576) is obeyed, 

 be uniformly distributed over all directions in space, and the velocity diagrams 

 will be uniformly spherical. 



Thus the fact that star-streaming is observed is definite evidence that 

 law (576) is not fully obeyed. On general principles we might expect the 

 least massive stars to have advanced furthest towards equipartition. As we 

 believe that there is correlation between spectral type and mass, there ought 

 also to be correlation between spectral type and star-streaming, in the sense 

 of Jf-type stars shewing star-streaming least. Such correlation is observed, 

 with the 5-type stars forming an exception. 



249. A fifth property implied in the law (576), or indeed in any other 

 steady-state law, is that the average radial velocity of the stars of any type 

 measured from any point which is at rest relatively to the system as a whole 

 shall be nil. 



Campbell f has measured the radial velocities of 1060 stars and after 

 freeing them from the solar motion finds that 586 are receding from the sun 

 while only 474 are advancing towards it. Dividing the stars into first type 



* If the stars were arranged in a spherical cluster of uniform density, the period would be 

 entirely independent of the size of orbit. 

 t Stellar Motions, Chap. VI. 



