INTRODUCTION 
XI 
THE STANDARD CATALOGUE. 
Primarily the standard catalogue contained within this General Catalogue has 
been prepared for use in this investigation. It is designed to serve any other pur¬ 
pose where high precision is required. In the present investigation the standard 
catalogue and the systematic corrections were involved together, virtually as the 
solution by successive approximations of equations containing a large number of 
unknown quantities. The problem was to make the sums of squares of the devia¬ 
tions of the several component star-catalogues at various epochs from the standard 
a minimum. The effect should be, that when a catalogue of observation, by the 
application of systematic corrections to it, has been brought into close general con¬ 
formity to the standard, it represents the latter at that epoch, and for that epoch 
extends the latter to stars not already contained in the standard. To a certain 
extent, the catalogue of observation so treated represents systematically the ex¬ 
cellence and weight of all the observations concerned in the construction of the 
standard. To what extent this will actually be the case will depend chiefly upon 
two conditions: first, upon whether the standard catalogue has been made to 
represent, as consistently as possible, the sum total of observations having funda¬ 
mental value; secondly, upon whether the relation of the individual catalogue to 
this standard can be ascertained with the required accuracy. The latter condition 
is one whose importance is more liable to be overlooked. If the weight of determi¬ 
nation for the individual catalogue to be compared is feeble, or the number of pos¬ 
sible comparisons with the standard too few, then, no matter what the precision of 
the standard may.be, the resultant effects of casual error in the individual catalogue 
may be so mixed up with the true systematic error as to vitiate the result. One of 
the distinctive features of the present work is that it aims to minimize this difficulty 
by furnishing a standard catalogue containing a very unusually large number of 
stars to represent it. The best determined standards alone are suitable for ascer¬ 
taining the systematic corrections of the catalogues of superior weight — say those 
whose computed probable errors of position in either coordinate is not more than 
o"io or o'.'i2 at the epoch of comparison; while quite one-half of the stars in this 
General Catalogue are standards suitable for ascertaining the systematic errors 
of the general run of the larger catalogues of observation. It seems scarcely neces¬ 
sary to remark that there is no well-defined line of distinction between standard 
stars and others. What may be considered a suitable and sufficient standard for 
one purpose may not do at all for another. For instance, as standards in differential 
observations with meridian instruments at the present time one might safely decide 
that where the probable error for position in 1910 is given as ±.”08, or less, the 
star-place is sufficiently accurate for the most refined use. Such stars might be 
termed primary standards. But for the less exacting class of zone-observations, 
or for miscellaneous observations, it may be considered that a probable error of the 
standard for 1910 of "12, or even "15, could be tolerated; since it is rarely the 
case that the probable error of a single observation would not be at least twice that 
amount. 
