XXVIII 
PRELIMINARY GENERAL CATALOGUE OF STARS FOR 1900 
PROPER-MOTIONS. 
The ninth and tenth columns on the left-hand pages give the proper-motion, /x, 
in right-ascension, and its centennial, or secular, variation, 100 A/x, in units of the 
fourth decimal; correspondingly, the seventh and eighth columns on the right-hand 
page give the proper-motion, /x', in declination, and its secular variation, 100 A/x', 
in units of the third decimal place. 
The proper-motions are derived by subtracting from the annual variations the 
precessions computed from Newcomb’s constants for 1900. They are: 
Precession in R.A. = p = + 3^07234 + T33646 sin a tan 8 
Precession in decl. =p'= + 20'.0468 cos a 
In the practical computation, Becker’s tables (Vol. II, Strassburg Observations) or 
Downing’s tables for 1910 were employed. It did not seem necessary to print the 
computed precessions; they can readily be recovered for any star by subtracting the 
proper-motion from the annual variation. 100 A/x and 100 A/x' were computed by 
means of formulas (A) under “Annual and Secular Variation, etc.” in the fore¬ 
going. 
As already stated in the earlier part of this introduction, the ascertainment of 
proper-motions of the stars constituted the chief motive for the labors that led to 
the production of this Catalogue. In pursuance of this object, the next step would 
naturally be to find out what corrections of the adopted precession and of the 
adopted motion of the equinox are most consistent with the results for annual varia¬ 
tions in this Catalogue. A tentative investigation indicates that the proper-motions 
in right-ascension and declination as printed in this Catalogue require corrections of 
+ •00021 — foooi5 sin a tan 8 for /x and — '.0023 cos a for /x' 
This implies a correction of Newcomb’s luni-solar precession for 1875 of +'0058 
(annual); of his planetary precession (annual) at the same epoch, of + "0006; and a 
further correction to the right-ascensions of Newcomb’s system, Ni, which is the 
basis of this Catalogue, of +'.0079 (T— 1850), T being expressed in years. The 
deduced correction for Newcomb’s m is: +"0058 cos w—"0006 = +"0047; and of 
Newcomb’s n is: + '0058 sin w = + "0023, in which (o is the obliquity of the ecliptic 
for 1875. I n the normal equations derived from the discussion of solar-motion 
recently undertaken by the writer, an unknown quantity A& was introduced to 
represent the constant effect upon all the proper-motions in right-ascension of 
required corrections: 
A £ a — A 'm + A\ = A&= + '.'37 ± '.'08 (Centennial) 
as derived from the equations. In other words, the mean of all the 5413 values of 
/x cos 8 came out — '.'37, about 600 of the larger proper-motions having been 
symmetrically excluded. A £ a represents a correction to Newcomb’s motion of 
the equinox, Ni; A 'm represents that part of the correction to m that arises from 
correction of the luni-solar precession; and A\ represents a correction to New¬ 
comb’s annual planetary precession. In these same equations an unknown A n 
was introduced to represent the effect of an unknown correction to Newcomb’s n. 
