XXII 
PRELIMINARY GENERAL CATALOGUE OF STARS FOR 1900 
RIGHT-ASCENSIONS AND DECLINATIONS. 
The fourth column on the left-hand page contains the right-ascension for 1900 
(reduced to that epoch with proper-motion, so that both equinox and epoch are 
1900); and the second column on the right-hand page contains the corresponding 
declination. The most important general points relating to the computation of 
these quantities have been set forth in preceding paragraphs of this Introduction. 
The list of star-catalogues employed has been given, as well as a sketch of the 
means employed to secure the greatest possible immunity from the effects of sys¬ 
tematic error. (See also Ast. Jour., Vol. XXIII; also Catalogue of 627 Principal 
Standard Stars.) A few words about the methods employed in the computation of 
the individual positions and motions may be useful. For each star, from a prelimi¬ 
nary estimate of position and annual variation for 1875, an ephemeris covering the 
required dates of observation for that star from 1755 down to the present was 
formed and carefully checked. In expanding these ephemerides the third term of 
precession was taken into account. For stars of greater declination than 82°, 
standard dates, at suitable intervals, were derived through use of the trigonometrical 
formulas, as given by Newcomb; and other intermediate dates were interpolated 
from these. 
Then conditional equations were formed by means of the corrections to the 
ephemeris given by each star-catalogue containing a position of that star. These 
conditional equations involved unknowns for correction of the before-mentioned 
assumed positions and annual variations for 1875. The unit of the coefficient of 
proper-motion was taken as twenty-five years, in order to render the coefficients of 
the normal equations fairly homogeneous. In forming the absolute terms of the 
conditional equations, systematic corrections of the catalogues of observation were 
employed. In the early stages of the work these corrections sometimes differed 
slightly from those given in Appendix III, but the residual effect upon the posi¬ 
tions and motions is negligible. The conditional equations were also carefully 
weighted in conformity with the tables of weights contained in Appendix III. The 
normal equations were solved in the usual manner, and the resulting corrections 
were applied to the quantities assumed as the basis for correction. 
All the operations were duplicated, or adequately checked. 
The catalogue positions in right-ascension for 1900 are supposed to be cleared 
from the effect of magnitude-equation, as already stated in this Introduction. 
For several binary stars, where orbits of a fair degree of accuracy have been 
computed, and where meridian-observations exist in sufficient weight to make the 
attempt worth while, computations have been made to obtain an approximation to 
the relative masses of the two components. The respective radii of the two com¬ 
ponents in their orbits around the center of gravity lie on diametrically opposite 
sides of that common center; and the ratio of these respective radii to each other 
and to their sum remains constant in all parts of the orbit. Therefore, to obtain 
this ratio it is simply necessary to take advantage of the fact that the form of the 
orbit of the principal star around the center of gravity is the same as that of the 
