21 
18 — 21 ] Binary Stars 
the speed with which any star is advancing towards, or receding from, the earth. 
As a result of their motion around one another, the two components of a binary 
star will generally be advancing towards the earth or receding from it at 
different rates, and when both components are bright enough for their spectra 
to be visible the spectrum of a binary star shews two distinct sets of lines, 
which oscillate about their mean position in a period equal to the period of 
the star. There are only very few stars whose distance and period are such 
that they can be observed both visually and spectroscopically as binaries : in 
these rare cases the period can be determined from either visual or spectro 
scopic observations. There is a far larger number of stars whose spectra shew 
the special characteristics of binary stars, although their period is so short, and 
the two constituents consequently so close together, that their binary nature 
is not susceptible to direct visual observation. Such stars are called spectro 
scopic binaries. The periods of spectroscopic binaries range from 1\ hours 
(7 Ursae Minoris) to 153 years (e Hydrae). 
21. The periods of Binary Stars. The frequency with which the different 
classes of binary stars figure in star catalogues gives a very misleading idea as 
to the frequencies with which the stars themselves occur in space. It is a slow 
and difficult process to determine the orbits of long-period binaries with any 
accuracy, so that only few of these appear in star catalogues at all. Hertz- 
sprung* considers that out of 15,000 known double stars it is only possible 
to calculate reliable orbits for 80, while about 1000 more shew traces of 
orbital motion but with periods so long that it is not yet possible to calculate 
them with any accuracy. On the other hand the periods of short-period 
binaries, and especially of fairly bright spectroscopic binaries, are easily and 
rapidly determined, with the result that these figure to a very disproportionate 
extent in star catalogues. 
Hertzsprung has attempted to obtain information as to the true frequency 
with which the different types of orbit occur in space by studying the known 
binaries within a short distance of the sun. Twenty-one binaries are known 
to be within 10 parsecs of the sun. The actual periods of 13 of these are 
known, and Hertzsprung estimates periods for the remaining 8 from the 
observed angular motion or the observed distance between the components. 
The adopted values for the period are shewn in the following table. The 
second column contains the period in years where this is known with accuracy, 
and the third column contains Hertzsprung’s estimated value of log P, where 
P is the period in years. Of the 21 stars only two, ^ Draconis and £ Ursae 
Maj. are spectroscopic binaries, so that visual binaries outnumber spectroscopic 
binaries by ten to one. Hertzsprung notes that the distribution of log P is 
approximately Gaussian about a median value of log P — 2, with a mean 
deviation of ± 1. These 21 binaries probably constitute the best sample 
* Bulletin of the Astronomical Institute of the Netherlands, No. 25, 1922.