280 
PRELIMINARY GENERAL CATALOGUE OF STARS FOR I90O 
DECLINATIONS. 
A8 a . Corrections in declinations that vary with the right-ascension alone as an argument are 
given next after the tables for A. G. zones—right-ascension. Corrections of this form maybe 
attributed to annual effects of temperature, etc., upon the instrument and its environment, 
neglected variation of latitude, and effect of faulty astronomical constants adopted in reduction 
from apparent place to epoch of catalogue, especially in earlier times. 
A8{. Systematic corrections in declination, with the argument declination, are found in the next 
table. In the case of Br 1755 the arguments 5 0 apart do not suffice. A special table of correc¬ 
tions, A85, for Br 1755 appears under Remark (11) at the end of these tables. A85 is easily 
accounted for through the effects of insufficiently corrected errors of graduation, flexure, 
refraction, etc. In some cases these curves have been analyzed and attributed to their probable 
sources (see, especially, Ast. Jour., Vol. XXIII, pp. 120-122, 126, 157-162, 210, etc.). 
Then follow corrections in declination of the Zone-Catalogues of the Astronomische Gcsellschajt. 
The full systematic correction in declination is: A8 = AS a + A8^. 
Next follow tables of weights that have been employed in the computations for this Catalogue. 
These were prepared from the probable errors of the residuals found in solution from the standard 
stars. For the catalogues of highest precision, only the principal standard stars were employed. 
In computing and successively revising the weights, particular attention was devoted to the pro¬ 
gressive relation of the weights to number of observations. It has been assumed that there is a 
probable error ( e 0 ) that is not affected by the number of observations but is inherent in the 
instrument, observer, or environment; or what is much the same thing, this part of probable error 
may be considered to be due in part to the practical impossibility of determining all the minor 
peculiarities of curves of systematic correction. This amounts to the assumption that when a 
certain number of observations is reached in a series of observations, the probable error is no longer 
sensibly diminished by increase in the number of observations. Usually, the weaker the catalogue, 
the smaller this maximum number of observations will be. Combined with this is the ordinary 
probable error of observation ( e t ) which diminishes proportionally with n being the number 
of observations. Obviously the probable error ( e c ) of the catalogue-place will be: 
= \j (e 0 ) 2 + — 
v n 
In the solution of such equations for determining q, and e\, it was customary to substitute — 
r 
for eo, in which r represents a trial ratio for such as 1, .4, 5, 6.8. Then by 
e o 
means of auxiliary tables that value of r is found which best harmonizes with the probable errors 
found for the residuals arranged in groups according to the number of observations. The adopted 
probable error of the unit of weight is ±"30, repeatedly verified as the computation progressed. 
For convenience in the formation of normal equations for determination of Aa 0 and A/^, etc., 
only the denominations of weight represented in the left-hand columns of these tables were used. 
This permits the formation of auxiliary tables in compact forms that greatly expedite the formation 
of the normal equations. 
When the zenith-distance of a star observed at a given observatory is more than 72 0 , it has been 
customary in the computations for this Catalogue to multiply the weights for right-ascensions, as 
given in the tables, by certain factors presently to be given. In like manner factors are adopted 
for reducing the weights in declination, beginning with 65° of zenith distance. The adopted 
factors are: 
