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.