constructing a catalogue of fixed stars. 409 
Let us next suppose that, from some accidental cause, the 
inferior passage of the pole star had been omitted ; then, if 
the declination of this star be supposed to be known from 
previous observation, the polar point may be deduced from this 
supposition ; but the pole star, in this case, would have no 
superiority over any other star, whose polar distance should 
previously have been determined. If we employ two stars 
equally well known, it is evident that greater accuracy will 
be obtained ; and it is easy to conceive that by taking a greater 
number of stars, for instance the whole twelve, we may 
obtain greater accuracy than even by a double observation 
of the pole star, because the error of observation, and that 
arising from false assumption of polar distance, will necessarily 
be much diminished by the natural tendency which the positive 
and negative errors will have to counteract each other. 
These considerations, aided by daily trial and experience, 
induced me very soon after the mural circle was erected, to 
abandon every method which assumed one particular point 
of departure, and I directed all my efforts to the determina- 
tion of the difference of declination which existed between 
every star and all the rest ; constructing by this means a 
catalogue, which, with respect to the pole or the zenith, 
might be subject to a common error; reserving to myself the 
power of investigating this common error by a process 
which will afterwards be explained. In the practical execution 
of this method, the observation of each star is employed for 
a double purpose ; it first serves, in combination with all 
the others, to find the common index error ; this common 
error again applied to the individual observation, gives a 
