APPENDIX III. 
SYSTEMATIC CORRECTIONS AND WEIGHTS. 
The principal points concerning the formation of the systematic corrections and weights con¬ 
tained in this Appendix have been explained in the articles upon these subjects contained in Volume 
XXIII of the Astronomical Journal (Nos. 534, 536, 540, 541, 545, 549, and 550). There has been 
frequent occasion to allude to these quantities in the Introduction to the present volume. The 
Systematic Corrections herein contained are the result of an extension and thorough revision of the 
tables contained in Nos. 549 and 550 of the Astronomical Journal. 
The tables which follow give : 
Aa*. Systematic corrections in right-ascension that vary with the argument, a, are given in the 
first table. Bracketed with Aa a is sometimes given A'a a , the coefficient of a term of correc¬ 
tion, Aa a tg 8 . The distinction between these quantities is that Aa a is a correction com¬ 
posed of a constant in combination with a term periodic with right-ascension. At any particu¬ 
lar value of a it is constant for all declinations. This may be termed the equinox-correction. 
But in some cases there is associated with this a term which might be called the A'a a term. 
It is not only periodic in a, but at the same time varies with the declination — more commonly 
as tg 8 . Among other causes the term in A'a a may be attributed to an annual periodic error 
in determining the polar point of the instrument, so that, in reducing transits there is an out¬ 
standing error in them of the form, n tg 8 , with n having an annual period. In some cases 
there may be a sensible error of annual period in determination of collimation. This would 
produce an error in the transits of the approximate form, A'a a (tg — — tg — in which p 
\ 2 2) 
is 
the polar distance of a given star, and P is the mean polar distance of the clock stars 
employed. 
Aa£. Systematic corrections in right-ascension that vary with the declination alone are given 
in the table next following that for Aa a . They may be due to irregularities of pivots, personal 
errors of the observers, errors of illumination, and a variety of causes. For convenience of in¬ 
terpolation, A«5 cos 8 is given in the tables for declinations higher than 8o°. Between +8o° 
and — 8o° Aa$ is given, as it is to be applied to observed right-ascension without multiplica¬ 
tion by cos 8. 
Aa M . At the foot of the pages giving Aa§ are given the systematic corrections for Magnitude- 
equations, Aa M , of the several catalogues. The values of Aa M are probably more reliable for 
stars brighter than 7^0 than they are for fainter stars; but they should still be good approxi¬ 
mations in most cases down to 8“o, or fainter. Values of Aa M marked * are not the result of 
observation, but are mean values computed from — ^0069 (M — 3.5). 
The total correction to be applied to the right-ascension found in the original catalogues of 
observation is : Aa = Aa a + Aas + Aa M , where Aa a may be taken as Aa a + A a a tg 8 , when¬ 
ever the latter term becomes sensible. 
Corrections to the right-ascensions of the Zones of the Astronomische Gesellschaft follow in the 
next table. These corrections were derived with very great care and are based upon more than 
2,900 quasi-standards. In determination of Aa M beyond seventh magnitude, much assistance was 
derived from the comparisons of the A. G. zones with each other and with Pulk 75, instituted by 
Dr. Auwers. (Ast. Nach., Vol. 161, Nos. 3842-3-4.) 
279 
