274-276]
Disturbances from Passing Stars
307
the 68 binaries do not form anything like a fair sample as regards distribu
tion of periods, since special reasons make binaries both of long and of short
periods difficult of detection, but the correlation between eccentricity and
period, which is very marked in the spectroscopic binaries, is almost entirely
absent in the visual binaries (see Table XXII on p. 291).
The observed agreement up to about e = 0‘6, and deficiency for higher
values of e, is naturally explained by the supposition that visual binaries as a
class start with low values of e; that encounters with other stars tend to
adjust these to the law 2 ede; and that there has not yet been time for
complete adjustment, but only for adjustment as far as to about e = 06.
We can perhaps best survey the whole situation by thinking in terms of
average eccentricities. In the final steady-state law 2 ede, the average value
of e is 0 - 667. If any class of binaries starts life with nearly circular orbits
(e = 0), the effect of encounters with other stars must be to increase the
average value of e progressively until it approximates asymptotically to 0667,
so that the average value of e observed in any class gives a rough measure of
the age of the class as binaries. The tables at the beginning of the present
chapter now become full of meaning. Table XXIII suggests that spectro
scopic binaries of types 0, B and A are not substantially younger than those
of the so-called later types, F, G, K, M, while Table XX suggests that spectro
scopic binaries of short period are younger than those of long period, and
Table XXII suggests that spectroscopic binaries as a class are younger than
visual binaries, but these conclusions would need some modification if the
process of adjustment were quicker in some classes of stars than in others, a
possibility to which we shall return later.
Distribution of Periods.
276. The law of distribution of periods in the theoretical steady state is
given by (cf. formula (273‘8))
HM M' /27r 7 \j
De (M+M')A P ) dp (276-1),
where D is a constant which depends on how many stars are under discussion.
Formula (272‘3) provides a means of determining the constant H from
the observed velocities of the stars in space. From a very thorough study of
the question, Seares* has concluded that stars of different masses all give
approximately the same value for H, thus shewing that the translational
motions of the stars very nearly conform to the steady-state law.
In the following table, taken from his paperf, the second column gives the
values of the mean masses of stars of different spectral types, the mass of the
sun being taken as unity, while the second column gives the mean values of
C‘\ the square of the velocity in space, the unit being one kilometre a second.
Astrophys. Journ. lv. (1922), p. 165.
■f l.c. p. 190.