326 
The Ages of the Stars [ch. xii 
components of the binary may momentarily be considered as separate systems, 
and the interaction between the passing star and the near component will be 
approximately the same as though the other component were non-existent. 
It follows that the time necessary to change completely the orbit of a 
visual binary is about the same as that necessary to set up an approxi 
mation to equipartition in the motions of translation of the stars. Thus the 
observed law of distribution of eccentricities in visual binaries suggests that 
their age, as binary systems, is about equal to that we have estimated for 
the stars in general, namely an age of millions of millions of years. 
For spectroscopic binaries formula (2921) shews that the effect of the 
encounters which occur within a specified time must be reduced at least by 
a factor of the order of r 2 /R 2 , where r is the linear dimension of the binary 
orbit, of the order of 10 u or 10 12 cms., and R is the distance of effective 
encounters, of the order of 10 18 or 10 14 cms. The factor r 2 /R 2 is roughly of 
the order of 10~ 4 , and we see that, within the ages we have found it necessary 
to allot to the stars, the effect of encounters on the periods and eccentricities 
of binary systems must be almost negligible. Thus the eccentricities and 
periods of spectroscopic binaries can be increased for a short time after their 
birth by tidal friction; subsequent diminution of mass will increase their 
periods, but not their eccentricities, while encounters with other stars produce 
effects which are so small as to be almost negligible. 
These conclusions are entirely in accord with the results of observation 
as shewn in Tables XIX—XXIII of the last chapter. Tables XX and XXIII 
shew that the spectroscopic binaries, regardless of their periods and spectral 
class, and so presumably of their ages, reach a limiting average eccentricity 
of 02 or 0*3; this must be the average eccentricity attained when tidal 
friction ceases to have any appreciable further action. The periods of spectro 
scopic binaries increase with advancing spectral type to just about the extent 
that might be expected as a result of decrease of mass. 
On the other hand, visual binaries shew a partial approach to the final 
steady-state law in their distribution of eccentricities and, in so far as it is 
possible to form a judgment, in their periods also. This can be attributed to 
the effect of encounters with other stars, and enables us to assign to them an 
age of the order of millions of millions of years. 
Mass-ratio in Binary Systems. 
294. Another quantity associated with a binary system has been reserved 
for separate discussion, namely the ratio of the masses of the two components. 
Aitken * has tabulated the mass-ratio of 67 binary systems, taken from the 
Lick “Third Catalogue of Spectroscopic Binary Starsf,” with results shewn 
in the following table : 
Lick Obs. Bull. No. 365 (1925), p. 46. 
f Ibid. No. 141 (1924).