INTRODUCTION 
XIII 
preserved. In other words, the systematic correction of a catalogue of observation 
compared with the corrected catalogue of 627 standard stars should result the same 
as it does from comparison with the additional standard stars, within admissible 
limits of casual error. 
MAGNITUDE-EQUATION. 
Another special point in relation to this standard catalogue, as well as to the 
catalogue in general, may appropriately be mentioned here, since it constitutes a 
departure from the practice that has heretofore prevailed. An attempt has been 
made to produce published right-ascensions that shall be free from the effect of 
magnitude-equation. The magnitude-equation is a well-established effect in conse¬ 
quence of which the observer at the telescope ordinarily registers the transit of a 
faint star later than he would that of a brighter star actually in the same place. 
The equations of the different observers are by no means the same, and there appear 
to be a very few whose magnitude-equations are very near zero. The general aver¬ 
age of all equations appears to be not far from ^007 per magnitude on the historic 
scale (log. light ratio .36), or ?oo8 on the Pogson scale (log. ratio, .4). Furthermore 
it appears that the equation for observations by chronographic registry is not 
very different from that for observations by eye-and-ear. (Ast. Jour., 536.) From 
this it would appear that determinations of proper-motion in right-ascension would 
not be very sensibly affected by the neglect of correction for this equation in the 
past and present; but that the right-ascensions of the fainter stars would generally 
come out too large relatively to those of the brighter stars, and in a different 
degree for different observers. For the purposes of a standard catalogue this is a 
matter of some importance, since stars of different magnitudes, in the case of many 
observers having equations different from the average, would give systematically 
different clock corrections. 
Since the published discussion of this effect ( A . /., 536) the investigation of the 
magnitude-equations and the corresponding corrections required to eliminate this 
effect from the individual catalogues of observation has been continued here more 
critically and upon an enlarged scale. The essential outcome has been substantial 
confirmation of the earlier results, as will be seen by consulting the tables of Aa„ in 
Appendix III. 
The magnitude-equation of the Catalogue of 627 Principal Standard Stars was 
found to be — ^0077 M( — 3.5), where M represents the magnitude of a given star on 
the Pogson scale (A. /., 536). This is equivalent to — ^0069 (M — 3.5) on the mag¬ 
nitude-scale of this Preliminary General Catalogue , the magnitudes for which, when 
brighter than 6^6, are taken from a manuscript catalogue of normal magnitudes 
prepared by Dr. S. C. Chandler, based upon a combination of substantially all useful 
material contained in the various uranometries and photometric determinations, 
adjusted to the historic scale. Accordingly the right-ascensions of the Catalogue 
of 627 Principal Standard Stars, in addition to other revisions for many of the stars, 
were corrected by — ^0069 (M — 3.5) (where M was adopted from the present work) 
and were then transferred to this Catalogue. For all stars not included in that 
