A CATALOGUE OF STANDARD STARS. 543 
The effect of these corrections was in no case over 0".01, when substituted in the 
right-ascension equations; so that the former values of y, y” were retained. 
This process is equivalent simply to this: the computed declinations derived from 
our final theory are virtually employed to reduce the observed right-ascensions to 
1855.0, and the resulting right-ascensions treated by the method of least squares give 
the final values of right-ascension and proper motion. 
It remains to explain the details of the application of the method of least squares. 
For the four stars treated rigorously we have 
1 
7) 7j 
I. =, — = Ee CSS v=z. 
The assumed weights are denoted by c for right-ascension, by o for declination. 
` These were assigned in a somewhat arbitrary manner; bearing in mind the magnifying 
power of the various instruments employed, and in one or two instances the less than 
usual care bestowed on observation and reduction. It is possible that the weight 
which has been assigned is in some cases too large or too small; thus Bradley's 
observations have received a weight which, though small in itself, is yet rather larger 
than the probable error as given in the Fundamenta would seem to warrant. This, 
however, if an error, is but a venial one, as the Fundamenta are justly considered as 
entitled to a very large proportional weight. 
In all cases where many observations have been made at the same observatory and 
with the same instrument, less than the proportional weight has been given. The : 
maximum weight has been put at 3, while the minimum for a single observation has 
been i. : 
We shall now make in AR. 
a= yu 15 cos ô cos E, 
t — 1855 
a —————— 
= 30. 
i 50 [if ¢ be counted from 1855], 
e — v a sin $ 
g— t185 et 
put DO 
[if be counted from 1855], 
n= yu 4 a! cos & [taking 4a’ in the sense e — o]. 
And in declination 
a — — yu! 15 cos d sin $, 
