306 The Evolution of Binary Systems [ch. xi
law, and from the outstanding irregularities we may hope to read something
of the course of events which has led to the present state of things.
Distribution of Eccentricities.
275. In the final steady-state law, the eccentricities are distributed
according to the law 2 ede, so that all values of e 2 are equally probable.
Observation shews that actually small values of e 2 predominate to an enormous
extent.
Taking spectroscopic binaries first, we may compare the eccentricity of
orbits of the 119 spectroscopic binaries given in Table XX (p. 290) with those
required by the steady-state law. The second column of the following table
gives the observed eccentricities, while the third column shews the distribu
tion to be expected if the steady-state law 2 ede were in operation:
e
from
o
©
to
0-2
Observed
78
Theoretical
5
e
»
0-2
to
0-4
18
14
e
0-4
to
06 ....
16
24
e
»
0-6
to
0-8
6
38
e
>>
0-8
to
1-0 ....
1
43
119
119
The theoretical law is nothing like obeyed, so that clearly spectroscopic
binaries have not existed long enough for even an approximation to a final
steady state to have become established. The predominance of low values of e
suggests that spectroscopic binaries as a class started with low values of e,
which interaction with other stars has nothing like raised to the steady-state
values.
The eccentricities of the 68 visual binaries tabulated on p. 291 may be
treated in a similar way and give the results shewn in the following table :
e = O'O
to
02 ....
Observed
7
Theoretical
6
e — 0*2
to
0-4 ....
18
18
e = 04
to
0-6 ....
28
30
e = 0’6
to
0-8 ....
11
42
e — 08
to
1-0 ....
4
54
68
The agreement between the observed and theoretical number of stars is
seen to be good up to e = 0’6 but fails entirely beyond. The 68 binaries in
question seem likely to provide a fair sample of all visual binaries as regards
distribution of eccentricities, since there is no reason which makes binaries
of abnormally high or low eccentricity specially liable to discovery. Of course
