CHAPTER XII 
THE AGES OF THE STARS 
284. The discussion of the last chapter shewed that the orbits of binary 
stars, both spectroscopic and visual, are still far from conforming to the 
statistical laws which must finally prevail after the stars have interacted with 
one another for an unlimited length of time. The same is true of the components 
of the velocities of the stars in space. After a sufficiently long time of interaction 
between stars, these ought to conform to the well-known Maxwell law of distri 
bution of velocities. The investigation of Seares already given has shewn that 
the resultant velocities conform well enough, at least to the extent of obeying 
the law of equipartition of energy, but the distribution of their directions is 
far from conforming to this law. After a sufficiently long time of interaction, 
stellar velocities must be distributed in all directions equally, their motion 
not favouring any one special direction. As Kapteyn shewed in 1904, the 
actual velocities of the stars shew a very marked favouritism for a definite 
direction in space, so that the law of distribution appropriate to the final state 
is far from being obeyed. 
If the statistical laws which specify the final steady state had proved 
to be exactly obeyed, we could have concluded that the stars had been 
interacting with one another for a very long time, but we could not have 
estimated the length of this time except possibly in terms of a lower limit. As 
we find that these laws are only partially obeyed, we conclude that the stars 
have not been interacting with one another for an indefinitely long time, and 
the extent to which the laws are obeyed makes it possible to form estimates, 
although necessarily vague ones, of the actual ages of different types of stars. 
We shall find (§ 291 below) that a star’s motion is determined mainly by 
the gravitational forces from distant stars, and only to a very minor degree 
by the forces from near stars, so that to a first approximation each star 
describes an orbit under the gravitational field of the universe as a whole. 
Although the amount and direction of the star’s velocity continually change, 
the description of this orbit does nothing towards bringing about the final 
statistical steady state. For the stars in any region have velocities whose 
amounts are determined by their equations of energy, and whose directions 
are determined by their orbits as a whole, and there is no reason why these 
should conform to the final steady state law. 
The tendency to obey this law is produced by the smaller forces which arise 
out of the interactions with the nearer stars, and we can estimate the ages 
of the stars by calculating the length of time necessary for these forces to 
produce the observed approximation to the steady state laws.