XIV 
PRELIMINARY GENERAL CATALOGUE OF STARS FOR 1900 
list, the corrections Aa H for magnitude-equation were applied to the individual 
catalogues of observations and treated like any other form of systematic correction. 
The resulting right-ascensions as printed in the Catalogue are supposed to be free 
from this effect. 
The magnitude, 3.“5, was chosen as the zero of reference, so that the mean 
equinox of the right-ascensions would not be sensibly disturbed. 
Since the basis of these determinations was laid (A. /., 536), it has been possible 
to apply several further independent tests of considerable value in estimating the 
freedom of this catalogue from errors dependent on magnitude of the star. Tucker’s 
determination of his magnitude-equation for the right-ascensions of the Piazzi- 
stars affords one such test; Oertel’s determination of right-ascensions with the 
Repsold micrometer at Munich (Miin 00) presents another; and Kiistner’s right- 
ascensions at Bonn (Bonn 00 in Manuscript) offer still another. Arranging the 
comparisons in the order of magnitude there was obtained for the respective cata¬ 
logues, in the sense P.G.C.- Miin 00, etc.: 
Munich 1900 . 
Lick 1900 . 
Bonn 1900 . 
M 
No. of Stars. 
Obsd. Ao m 
M 
No. of Stars. 
Obsd. Aa u 
M 
No. of Stars. 
Obsd. Aa u 
S 
8 
8 
o -5 
6 
+ .009 
2.2 
21 
.OOO 
2.0 
*9 
.OOO 
3-3 
IOI 
.OOO 
4-5 
103 
- .003 
3-o 
35 
— .OOI 
4-3 
XO4 
— .002 
5-2 
224 
+ -003 
4.0 
73 
— .OOI 
5-i 
191 
— .002 
6.0 
260 
+ .OOI 
5-o 
47 
+ .OOI 
6.1 
3 11 
+ .002 
6.8 
64 
— .002 
5-9 
26 
— .OOI 
6.9 
89 
.000 
The observed quantities under Aa M in all these series appear to be quite insig¬ 
nificant. More testimony of the same kind has been derived from the recent right- 
ascensions of Albany and the Cape, where the respective observers applied their 
respective magnitude-equations in the reductions. 
Several courses are open to observers who may wish to use this standard cata¬ 
logue in observation of right-ascension. (1) Observers can use a self-registering 
micrometer. (2) They can determine their own magnitude-equations during the 
progress of their observations and free their transits from the effect of the equation. 
(3) They can assume their equations to be — ^0069 (M — 3.5), the mean of all observ¬ 
ers. In these cases the right-ascensions of the present Catalogue are ready for 
use as standards. If no attention is given to the magnitude-equation, instead of 
correcting the transits for mean equation, we can evidently correct the present 
Catalogue by + ^0069 (M —3.5) in order to make it systematically conform, in an 
approximate way, with standard catalogues heretofore in use that are uncorrected 
for magnitude-equation. 
SELECTION AND IMPROVEMENT OF STANDARDS. 
The Catalogue gives for each star, both in right-ascension and declination, the 
weighted mean epoch of observation from combinations of all catalogues; the prob¬ 
able error of the coordinate at this mean epoch; the probable error of the centennial 
motion; and, finally, as a matter of convenience and check, the probable error of 
