INTRODUCTION 
XXXI 
second of these columns, under the caption, “ ioo ft,” gives the probable error of the 
centennial motion. The third column, under a io, gives the computed probable 
error of the catalogue right-ascension at 1910. Corresponding quantities are given 
on the right-hand page for the declinations. 
Seconds of arc are given in relation to right-ascension, so as to have the unit of 
p.e. the same as that for declination and also the same in right-ascension for all 
declinations. To convert these into time on the respective parallels, multiply by 
sec 8. 
In possession of these quantities, it is possible to produce an estimate of the 
probable error of right-ascension or declination for any given epoch. In fact, the 
columns under a 10 and 8 10 are not needed for this purpose. They are given for 
the convenience of the reader because of their obvious usefulness at the present 
time. The date 1910 is therefore given in preference to 1900. As an example of 
the method of computing the probable error for any given date, let us suppose the 
probable error of the right-ascension of Br 3208, the first star of the Catalogue, to be 
required for 1900. If E be the mean epoch for a given star, T the required date, 
T — E 
put r = ; then if e E be the probable error of the right-ascension at the mean 
epoch and the probable error of centennial /a, while e T represents the probable 
error for the required date, we shall have: 
€ r = A/ e E + (re^) 2 ' 
In the case of Br 3208, this becomes: 
±'094= e r = VO'05) 2 + ("296 x - 2 7 ) 2 
If we choose ± '.'30 as the p.e. of the unit of weight, as has been the case with all the 
computations for this Catalogue, we shall have as the weights of catalogue-right- 
ascension at the respective epochs: 
T 
Weight. 
1870.4 
1900 
1910 
36.0 
IO.I 
6.2 
Thus it is seen that the weight of the predicted right-ascension is rapidly falling, 
until in 1910 it has only one-sixth the value it had in 1870. By 1920 this weight will 
have fallen still farther to 4.4. Thus we are able to obtain a very precise idea of the 
manner in which the precision of the determination for a given star is varying 
information that is specially important in the case of a star used as standard in 
meridian-observations, or for any other purpose requiring high precision. 
The applicability of these probable errors has been repeatedly tested in the course 
of computations for this Catalogue, and they are believed to be relatively accurate, 
and quite certainly not too small in the mean. In order to secure the general 
reliability of these probable errors in the case of each individual star, they are not 
