3 Reduction of the data

3.1 The reduction of star residuals

The fundamental equation of observation is

$$15X\cos\varphi_0\sin A + Y\cos A - Z + \delta h = 0,$$ (1)

where

$\varphi_0$ - the adopted value of the latitude at the site of the instrument;

A - the azimuth of the observation, measured eastwards from the north;

X - the observed clock correction;

Y - the correction of latitude;

Z - the correction of instrumental zenith distance;

$\delta h$ - a known term which is related to the position of the instrument and systematic errors in the observation.

As the Eqs. (1) are not strictly verified in the least square method of resolution, each of them gives a residual v which can be computed as:

$$v=15X\cos\varphi_0\sin A + Y\cos A - Z + \delta h.$$ (2)

There are 384 stars in 12 fundamental groups. The corrections of astronomical time, latitude, zenith distance and residuals are obtained by observing the stars of fundamental groups and by solving for each fundamental group the system of Eqs. (2). The residuals of the catalogue stars, observed at the same epoch are computed applying the corrections of astronomical time, latitude and zenith distance found from fundamental groups observations. Then, the mean values of the star residuals are computed by weighted means. The weight P's are computed from the formula:

$$P = \frac{0.1}{\sigma^2},$$ (3)

where $\sigma$ is the precision of a single star observation in the reference group of stars.

3.2 The reduction of position corrections of stars

Assumed that $V_{\rm e}$ and $V_{\rm w}$ are the residuals reduced to the mean instrumental system and considering the instrumental system errors at both eastern and western transits, we obtain the equation defining the position corrections (Lu et al. 1980):

$$\Delta\alpha=\frac{V_{\rm e}-V_{\rm w}}{30\cos\varphi_0\vert\sin A\vert}+\xi,$$ (4)

and

$$\Delta\delta=-\frac{V_{\rm e}+V_{\rm w}-2K}{2\cos q}+l\cos\delta,$$ (5)

where q is the parallactic angle of the star when it transits the almucantar of the astrolabe.

The term 2K can be computed from

$$K=\frac{1}{2}(V_{\rm e}+V_{\rm w})_{q=90^\circ}.$$ (6)

In fact only the stars with $\vert\cos q\vert<0.2$ (in this catalogue there are 736 such stars) are used to computed 2K. The weighted mean value of this term is:

$2K=0.018'' \pm0.003''.$