Introduction vii 
tances from the solar system are wholly unknown, and are likely to remain so until by some new 
method the present errors of observation can be greatly reduced. In addition to all this it must be 
remembered that the apparent distribution of the stars in right ascension is influenced by conditions 
which have nothing to do with the real number of these objects, or with the actual number of stars 
catalogued in the given area. The season of the year when a particular part of the sky can be 
examined, particularly in the first half of the night, the length of the nights, the probable proportion 
of clear nights, and to some extent the mean temperature in the colder season, all have an influence 
on discoveries as well as measures. Practically nothing has been done in the way of finding close 
pairs in the stars below the ninth magnitude except at the Lick Observatory, and there it has been 
almost wholly confined to stars north of the equator. Only large apertures, in exceptionally favored 
localities, can successfully carry on such work. All the stars of this class are of comparatively recent 
discovery, and nothing is known as to what rank they will take in the physical class of double stars. 
At present all that is needed for all the double stars, old and new, and of all orders of brightness, is 
careful and systematic measurement. When this has been carried far enough to furnish the necessary 
facts, theories and speculations will be in order, and doubtless this part of the subject will be properly 
attended to by the astronomers of future centuries when it shall be warranted by the necessary 
preliminary work of their predecessors. 
ORBITS OF BINARY STARS 
In the indexes to the several classes of double stars will be found a list of 88 systems for 
which orbits have been found. Of this number only 34, marked (*), can be regarded as of any value. 
These may be considered as giving the periods and other elements with substantial correctness; but at 
the best they are only provisional, and will be supplanted at no very distant time by investigations based 
upon a continuation of careful and accurate measures of these systems. The observations of another 
half-century should determine the elements of all these orbits with very little error. As to the remaining 
54 systems, the periods and all the elements of the orbits are wholly uncertain and worthless. They 
cannot be regarded as even approximations, since there is nothing in the given data to warrant a guess 
as to what will be the future relative motion of the components. In fact, in some instances it is not 
certain that they are physical systems at all. For anything that appears the change may be due to 
proper motion. Generally speaking, the arc described by the companion must be at least 270 
to give results entitled to any confidence, but frequently this is insufficient, and in such cases nearly 
a complete revolution must be made before the apparent ellipse can be certainly known. When the 
described arc is short, the agreement of the observed and computed places does not even tend to 
prove that the deduced orbit is approximately correct, or anything like the real orbit. In such 
cases a great variety of ellipses, entirely dissimilar in all respects, will represent the observed 
positions equally well, and with errors of observation less than those which are probable in the 
measures by the best observers with the most complete and powerful equatorials. It did not seem 
worth while taking space to give the elements of these orbits, other than the periods. The place of 
publication is always cited, and the details of the results can be readily referred to. 
BINARY SYSTEMS 
The list of binaries does not include those for which orbits have been computed. It is evident 
that it is not easy to draw a sharp line between binary stars, and those which are probably binary. 
It is a matter of judgment, based upon the best observations, in reference to which opinions might 
well differ. The list of probable binaries might be very considerably extended by including many 
stars which are presumably physically related from the observed relative motion, and the closeness 
of the components. This is not a safe conclusion, whatever the probabilities may be in its favor. 
Stars which are widely separated now by reason of the proper motion of one of the components, 
at one time formed very close pairs, and the rapid angular change then might readily have been 
mistaken for orbital motion. 
