EOTATION OF THE GALAXY EDDIN-GTON 251 



those who dabble in the long time scale of billions of years now 

 fashionable (and I have to confess myself one of them) we must 

 simply ignore them. Whatever the study of individual stars may 

 bring forth in its favor, the evidence of galaxies and of systems of 

 galaxies is dead against so leisurely a rate of progress. The problem 

 of the galaxies is unapproachable except from the standpoint that 

 the material universe is a much more evanescent affair. 



The term " steady state " is used with two distinct meanings, and 

 we must further define which meaning concerns us here. Starting 

 with an entirely irregular distribution of stars and stellar velocities, 

 there are two stages in the approach toward ultimate equilibrium. 

 The first stage is accomplished when the orbits described under the 

 general attraction of the whole mass have become so distributed as 

 to preserve the shape and density unaltered ; the " density of popula- 

 tion " at any point then remains steady although the individuals are 

 moving to and fro. This is called dynamical equilibrium. But these 

 orbits are from time to time perturbed by chance approaches of the 

 stars to one another, and the distribution slowly changes until a 

 special form of dynamical equilibrium is reached with the additional 

 property that these haphazard perturbations produce no change on 

 balance. This is called statistical equilibrium. We shall see pres- 

 ently that the steady state of the stellar system is that of dynamical 

 equilibrium, and not the ultimate statistical equilibrium which 

 belongs to a far distant future. 



The rate of approach to equilibrium, whether dynamical or statis- 

 tical, may be measured by a " time of relaxation " — a time in which 

 deviations from the equilibrium distribution decay to about half their 

 original magnitude. For statistical equilibrium the time of relaxa- 

 tion is estimated by Jeans and Charlier at 10^* to 10^" years. This 

 is so great compared with even the most extreme time scale that we 

 may put statistical equilibrium outside our thoughts. But the time 

 of relaxation toward dynamical equilibrium is of the order 1,000 

 million years. Remembering that in our part of the system individ- 

 ual stars go right round their orbits in 250 million years, any irreg- 

 ularity will in general be dissipated all over the system in something 

 like that period. We, therefore, expect to find dynamical e(iuilibrium 

 fairly complete. 



In a series of three papers in 1913-1915 I discussed the conditions 

 for a steady state (dynamical equilibrium) of a system of moving 

 stars, including the case of a flattened system like our galaxy, both 

 with and without rotation. Re-reading these papers I do not find 

 anything to modify in the mathematical investigations, except that 

 later writers have found short cuts to some of the results; nor do 

 Ihey seem to need much extension or adaptation to cope with the prob- 



