INTRODUCTION 
XXV 
MEAN EPOCHS. 
The fifth column on the left-hand pages and the third on the right-hand pages of 
the Catalogue contain respectively the mean epochs in right-ascension and declina¬ 
tion. These are the means by weight (App. Ill) of the epochs of observation con¬ 
tained in the individual catalogues of observation relating to the star in question. 
The mean epoch has this useful property that, if we reduce the separately observed 
right-ascensions and declinations from their respective mean epochs to that given 
in this Catalogue, and combine the resulting positions by weights identical with those 
employed in forming the mean epoch in this Catalogue, the resulting coordinates 
will be independent of the proper-motion employed. For any date before or after 
this, the probable error of the computed position (employing the elements of this 
Catalogue) will be compounded of the probable error at the mean epoch and the 
probable error of the motion during the time elapsed. The statement of the mean 
epoch also serves to indicate, in connection with the probable errors, the general 
distribution of the observation available in the case of each star. Thus, if the prob¬ 
able error of the proper-motion is relatively large in comparison with the p.e. at 
epoch, then a very early mean epoch would indicate that the star has been neglected 
in recent times; and under the like conditions, if the mean epoch is relatively late, 
that the star was neglected in earlier times. If the mean epoch is so early as i860, 
for instance, we have already in 1910, as a component of the probable error of 
position for that date, one-half of the probable error of centennial variation. For 
illustration, take No. 44 in declination. The mean epoch is 1860.0; the probable 
error of declination at mean epoch is ± '.'19; the probable error of centennial proper- 
motion (100 /a') is ±"64; therefore that part of the probable error of declination 
for 1910, due to probable error of centennial proper-motion, is 0.5 x '.'64= ±"32. 
And this is very much more important than the probable error of declination, ± .19, 
that attaches to the position at mean epoch i860. The probable error of the 
declination for 1910 is evidently: -^(.19) 2 + G32) 2 = ±"37; so that the weight for 
the catalogue-declination reduced to 1910 is only about equal to that of a single 
good meridian-observation. 
ANNUAL AND SECULAR VARIATION AND THIRD TERM OF PRECESSION. 
The sixth, seventh, and eighth columns on the left-hand page and the fourth, 
fifth, and sixth columns on the right-hand page contain the elements necessary for 
reducing the catalogue-positions from 1900 to any required epoch. Under “3d t.” 
(third term) the element of geometrical precession that depends on the third power 
of the time is given. It is usually quite closely equal to or 
O Gl O Gl 
In a few cases the proper-motion has been taken into account in computing this 
term. If we denote the fraction of a century from 1900 by r (minus, reckoning 
back), then the effect of the third term upon the deduced position is: r 3 x (3d t.). 
In the sixth column is given the annual variation in right-ascension, and in the 
fourth , on the right-hand page, the annual variation in declination. Respectively 
