310 The Evolution of Binary Systems [ch. xi
and M' in terms of the sun’s mass, the critical period P 0 given by formula
(277-3) takes the form
P, = 0-21 years (277 4),
(M + M)*
and in terms of this critical period the law of distribution (276'3) becomes
2^0-79 (P/PoP^p (277-5).
When each constituent is of mass equal to the sun, the critical period is
found to be about 55 days. For more massive stars it is longer in proportion
to the mass.
278. Known binary stars fall into the almost distinct classes of spectro
scopic and visual binaries. The majority of spectroscopic binaries have periods
of less than the critical period, while the visual binaries, without exception,
have periods greater than the critical period.
The known binaries cannot, however, be assumed to form a fair sample of
binaries as a whole. They represent the fruits of two distinct methods of
search, and the apparent division between the visual and spectroscopic
binaries may merely represent a no-man’s-land in which neither method of
search is effective, rather than a region in which no binaries exist.
The best way of obtaining a fair sample of binaries as a whole is by fixing
our attention on regions of space so near to the sun that few binaries are
likely to have remained undiscovered.
We have seen that six binaries are known to exist within four parsecs
of the sun; four of their periods are known with tolerable accuracy and are
approximately 39, 50, 55 and 80 years, while the other two have much longer
periods. Every one of these six is a visual binary, and it is reasonably certain
that there is not a spectroscopic binary within four parsecs of the sun.
Table III (p. 22) contains Hertzsprung’s list of 21 binaries of known
periods lying within ten parsecs of the sun. Here we found two spectro
scopic binaries with periods of 9 and 22 months, the remainder being visual
binaries with periods ranging from about 25 to 10.000 years. Even the spectro
scopic binaries had periods well above the critical period.
Now if the binaries in the sky had reached a final steady state, or even
approximated to such a state, there ought to be about as many binaries whose
periods are being lengthened by encounters, and so are now less than the
critical period, as there are binaries whose periods were being shortened by
encounters, and so are over the critical period. Actual observation shews an
enormous predominance of binaries of long periods. Every binary within four
parsecs of the sun, and probably every binary within ten parsecs of the sun, has
a period greater than the critical period of about 55 days, so that, speaking
statistically, every binary within these regions is at present having its period
reduced by encounters with other systems. Since the periods are decreasing
