XXVI 
PRELIMINARY GENERAL CATALOGUE OF STARS FOR 1900 
in the columns following these, and not separated by a rule, are found the secular 
variations of the annual variations. These are different from the geometrical 
secular variations of the precession, and again different from the variation of the 
precession as affected by proper-motion. For the sake of clearness, let us begin 
with the secular variation of the proper-motion, A/x (tenth column , left-hand page) 
and A/x' (eighth column, right-hand page). We have: 
A/x = [7.98762] /x cos a tg ST [6.81153] /x' sin a sec 2 S T [6.9866]/x/x'tg S ^ 
A/x' = [9.16371 w]/xsin aT [8.7367^/x 2 sin S 
The numbers in brackets are logarithms, computed after Newcomb’s constants of 
precession. To denote equations (A) when terms in (/x/x') and /x 2 are omitted, 
put A'/x and A'/x' respectively. Let p and p' denote the precessions. Then we 
shall have: 
Geometrical sec. var. 
A p. 
At 
True sec. var. of precession = ^ + A'xx. 
A t 
Sec. var. of annual variation = ™ + A'/x T A/x. 
At 
Accenting p and /x, we have the equations for declination. Usually we shall have 
A p 
with sufficient accuracy for the secular variation of the annual variation —f T 2 A'/x, 
since the omitted terms in A'/x and A'/x' are usually insensible. In the computa¬ 
tions of annual variations for the Catalogue no assumption was made as to the 
precession; but in computing the secular variation such an assumption becomes 
necessary. Therefore Newcomb’s constants were adopted and formulas (A) and 
A p , A p f 
(B) were employed. In the practical computation of — and manuscript 
tables were formed for declinations less than 6o°, and the terms of (A) were con¬ 
veniently tabulated in part. 
For stars of numerically greater declination than 82° or 83°, use of the trigono¬ 
metrical formulas was made to form standard epochs either twenty-five years or 
five years apart, according to need. From these dates interpolation was effected 
by means of the computed annual and secular variations, with third terms roughly 
derived from differencing the latter. For these stars in the Catalogue the third 
term is not given, and one decimal place is dropped in printing the annual and 
secular variations. At the same time, as a matter of convenience for those wishing 
to compare results of observation with this Catalogue, positions, motions, and secu¬ 
lar variations have been computed for certain standard dates up to 1925, as given in 
Appendix I. For the purposes of interpolation, sufficiently accurate values of the 
third term can be derived from the differences of successive secular variations. 
The trigonometrical formulas and constants of Newcomb were employed. (See 
The Precessional Constant, pp. 73 to 76.) 
