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\begin{document}
\title{AC 2000.2:  The Astrographic Catalogue on \\
 The Hipparcos System}
\author{Sean E. Urban, Thomas E. Corbin and Gary L. Wycoff \\
United States Naval Observatory, Washington, DC
\vspace*{0.3 in}
\and
Erik H{\o}g, Claus Fabricius, and Valeri Makarov \\
Copenhagen University Observatory, Denmark}
\date{August 22, 2001}
\maketitle

\begin{center}
\Large
\vspace*{1.0 in}
Catalogue of Positions Derived from the Astrographic Catalogue
Measures.  Positions are on the Hipparcos System (HCRS, J2000.0) at the
Mean Epochs of Observation.
\end{center}

\normalsize
\newpage
\tableofcontents
\newpage
\listoftables
\newpage

\section{Introduction}
The AC~2000.2 is a revised version of the 1997 release of the
AC~2000 (Urban et al. 1998).  It was decided that the availability of
an improved reference catalogue
and the inclusion of the Tycho-2 photometry would be sufficient to 
warrant a complete re-reduction of the data and a new
distribution of the catalogue.

The AC~2000.2 is a
catalogue of positions and magnitudes of 4,621,751 stars covering
the entire sky around the epoch of 1900.  The data
are derived from the images measured and published as part of the Astrographic
Catalogue (AC).  The positions are on the Hipparcos reference frame
(ESA 1997), having originally been
reduced plate-by-plate using an updated version of the Astrographic Catalog
Reference Stars.
Each of the 22~zones of the AC has been reduced independently,
since telescopes, observing techniques and measurement methods varied.
This document describes the history behind the Astrographic Catalogue,
the reference catalogue used to transform the measurements to equatorial
coordinates, the methodology employed in this transformation,
the resulting catalogue and information about each participating observatory.

\section{The Carte du Ciel}

The Carte du Ciel was an international effort begun more than a century ago to
determine positions better than 0.5~arcsec for all stars 11th magnitude 
and brighter using photographic plates and, using another set of plates, to
publish charts representing the relative positions of all stars of 14th
magnitude and brighter.  The charts -- generally called CdC --
proved to be very expensive to photograph
and reproduce, so many institutions did not complete this part of the work.
However, the astrographic program
designed to measure all stars to 11th magnitude was completed.  Actually,
the original goal of 11th magnitude was generally surpassed.  In fact, some
observatories routinely measured stars as faint as 13th magnitude.
These plate measures, as well as the formulae used to transform them to 
equatorial
coordinates, have been published in what is known as the Astrographic Catalogue
(AC). 

In total, 20 observatories from around the world participated in 
exposing and measuring the AC plates.
Each was assigned a specific zone, between
two parallels of declination, to photograph.  In order to compensate for    
any plate defects, each area of the sky was to be photographed twice, using
a two-fold, corner-to-center overlap pattern.  This pattern was continued 
even at the zone boundaries; each observatory's plates would overlap with
those of the observatories responsible for the adjacent zones.
The participating observatories agreed to standardize the type of telescope,
so each plate photographed had a similar scale of approximately 60 arcsec/mm.
The measurable areas of the plates were 2 $\times$ 2 degrees, so the 
overlap pattern consisted of plates that were centered on every
degree band in declination, but offset in right ascension by two degrees.
The first plates in the even degree bands were centered at right ascension
0 hours 0 minutes; the first plates in the odd degree bands were centered
with right ascension several minutes higher (corresponding to approximately
one degree).

In addition to the overlap pattern and type of telescope, the 
observatories also agreed to expose a grid, 
called a {\em r\'{e}seau}, on each plate.  It was originally  used to monitor
emulsion shifts.
After the shifts were demonstrated to be quite small, the practice of exposing
a r\'{e}seau on each plate was continued because it aided in the measuring
of the star positions by letting the measurer refer each image position to
the grid lines.  Each r\'{e}seau unit was approximately 5 mm.
The r\'{e}seau orientation defined the plate's $x,y$ coordinate system.

All participating observatories (with the exception of Vatican) used one of
two measuring methods, {\em short-screw} or {\em eyepiece scale}.
In both methods, a set of spider wires was centered over an image, then
the distance traveled by the slides carrying the spider wires was read.
With the short-screw method, this distance was read off of the screws
used to move the slides.  Whereas for the eyepiece scale method,
this distance was inferred by a
scale in the focal plane of the microscope.  In general, the eyepiece
scale method was faster, but less precise. 

Although telescope type, plate size, and use of a r\'{e}seau were standardized,
many other factors, such as reference catalogue used,
reduction technique and printing formats were left up to the individual 
institutions. 

\section{Published Data}

Most observatories published their results in several volumes, each of
which consists
of measures from plates centered on the same degree of declination.
Generally, each line in the printed volumes contains data for one star,
including the measured
$x,y$ value, a measure of brightness (magnitude or diameter), the plate
number and a running number on the plate.  
Other data concerning epoch of exposure, hour angle at mid-exposure,
air temperature, barometric pressure, r\'{e}seau used, observer,
measurer and measuring machine are usually provided by plate
in separate tables.  Additionally, provisional
plate constants used to transform the $x,y$ measures to standard coordinates
are typically supplied.

The published data have been transferred to machine-readable
form via double-entry (that is, typing each record twice to remove most 
keying mistakes) including errata found in the published volumes.
An additional literature search has been conducted on all
zones to increase the probability that all published errata not found with the
original volumes have been corrected.  Each page of each volume was searched 
for pertinent notes.  If important notes were found, they were entered and
the measures to which they refer were flagged.  A summary of the data entry 
information can be found in Table~\ref{tab:keypunch}.

\section{Compiling a New Reference Star Catalogue}
  The reference catalogue used throughout the individual plate reductions
of the 1997 version of AC~2000 (hereafter referred to as AC~2000.1) was the 
Astrographic Catalog Reference Stars (ACRS; Corbin \& Urban 1988,
Corbin \& Urban 1990, Corbin \& Urban 1991).
This was compiled on the system of the FK5 as realized by the
International Reference Stars (IRS, Corbin 1991), and utilized the
best data and reduction techniques available in the early 1990s.

Since its compilation, the FK5 has been superseded by
the Hipparcos Catalogue.  It was recognized that with the increased 
number of stars in the Hipparcos Catalogue over the FK5/IRS
($\approx$ 118,000 vs. $\approx$ 40,000), the conversion of
the catalogues making up the ACRS to the
system of Hipparcos could be done more rigorously than the earlier 
conversions to the FK5 system.  Since the systematic errors could be
determined and removed more thoroughly, the final combined catalogue would
be better.  Additionally, the FK5/IRS data become
very sparse fainter than magnitude 9.0, whereas Hipparcos contains
over 35,000 stars listed as V=9.0 or fainter.  This magnitude extension
allows the removal of systematic errors in the fainter stars -- something
that was problematic for the original ACRS.

In addition to Hipparcos, several new catalogues unavailable at the time
of compiling the original ACRS have been released.
The most notable are the Tycho-1 Catalogue (ESA 1997),
the Twin Astrograph Catalogue
(TAC, Zacharias \& Zacharias 1999), FOKAT (Polozhentsev et al. 1989),
and a recompiled Second Cape Photographic Catalogue
(CPC2, Zacharias et al. 1999).

Due to these improvements
in astrometry, it was decided to compile a new
reference catalogue.  In this document, this new catalogue will be
referred to as ACRS\_1999.  The ACRS\_1999 is not being released as
a separate catalogue because the data used in computing
the astrometry were subsequently used in computing the proper motions of 
the Tycho-2 Catalogue (H{\o}g et al. 2000).  The ACRS\_1999
can be thought of as a specialized subset of the data going into Tycho-2,
which completely supersedes it.

\subsection{Conversion of input catalogues to HCRS}
The Hipparcos Catalogue (ESA 1997) plays a special part in the ACRS\_1999.
It is recognized as the optical realization of the International Celestial
Reference Frame, ICRF (IAU 1999).  The frame defined by the Hipparcos 
data is termed Hipparcos Celestial Reference Frame, HCRF (IAU 2001); the 
HCRF contains all Hipparcos stars with the exception of those believed 
to be multiple.  These data -- taken from the Hipparcos Catalogue -- were
used to convert all input catalogues
to the HCRF by the method described below.

In total, 145 different observational catalogues (termed {\em input catalogues}
in this document) were included specifically
to strengthen the positions of the ACRS\_1999 stars when brought to the 
epochs fo the AC plates.  A list of 
these catalogues is found in Table~\ref{tab:acrs}.
Each of the catalogues was converted to a standard format.  Next,
zero point corrections and elliptical
aberration terms were applied, when necessary, to convert
the positions to roughly coincide with the FK5 J2000.0 system.  Following this,
the Hipparcos stars contained in each catalogue were identified.
Differences in right ascension and declination were computed for these
stars following the application of the Hipparcos proper motions to bring the 
Hipparcos positions to the epochs of the input catalogue positions.

To remove the systematic differences between these input
catalogs and Hipparcos, ``local'' mean differences between each
catalogue and Hipparcos were made, and corrections to the input catalog
positions based on those differences were applied.  To compute
these differences, for each star in
the catalogue, nearby stars in common with Hipparcos were 
identified.  In order to compute local systematic errors and not
follow the random errors, a minimum number of stars in common to 
the input catalogue and Hipparcos had to be enforced.
This minimum number was based on each input catalogue's random errors.
For catalogues with large random errors, more Hipparcos stars were needed.
The range in required Hipparcos stars was from 3 for the most accurate
catalogues to 30 for the least accurate.

Additionally, since determining local systematics was the goal,
only those stars in common with Hipparcos and close on the celestial sphere
were used.
For astrographs, typically the Hipparcos stars within
two degrees of the star to be corrected were utilized.  For transit circles,
typically the Hipparcos
stars within 30~minutes of time in right ascension and 5~degrees in
declination were used.  If the minimum number of stars discussed in the
previous paragraph could not be met, the area could be expanded.  How
far this expansion was carried out was dependent on how quickly, spatially
speaking, the systematic deviations from Hipparcos were changing.  
Catalogues whose density of Hipparcos stars was too low to adequately 
perform a local reduction were dropped from the input catalogue list.

Once nearby catalogue entries of Hipparcos stars were found for each
input catalogue star, their
positional differences with the Hipparcos data -- that is, their residuals --
were used to 
compute the local reduction to the Hipparcos system.  Weights were assigned
to each residual based on the distance to the
star being corrected.
To more heavily favor nearby Hipparcos stars, an elliptical, parabolic 
weighting method was used, as seen in the following equation.
\begin{equation}
w_i = 1 - \left[ \left( \frac{ {\rm D}_{\alpha_i}}
                          { {\rm maxD}_\alpha} \right) ^2 + 
                 \left( \frac{ {\rm D}_{\delta_i}}
                          { {\rm maxD}_\delta} \right) ^2 \right]
\end{equation}
The value of $w_i$ is the weight of the $i^{th}$ residual, ${\rm D}_{\alpha_i}$
and ${\rm D}_{\delta_i}$ are the distances in right ascension and declination
between the catalogue star whose correction is being computed and the 
$i^{th}$ Hipparcos star, and $ {\rm maxD}_\alpha$ and ${\rm maxD}_\delta$
are the maximum distances whose weight is non-zero in right ascension
and declination.
Once weights to each nearby Hipparcos residual are computed, the weighted
mean residual vector can be computed in the standard way.  That is, for
right ascension,
\begin{equation}
\Delta_{(\alpha)} = \frac{\Sigma w_i \Delta_{i_{(\alpha)}}}
{\Sigma w_i}
\end{equation}
where $\Delta_{(\alpha)}$ is the weighted mean vector in the right ascension
direction,
$\Delta_{i_{(\alpha)}}$ is the
residual of the $i^{th}$ Hipparcos star.  Similar formulation is used for
the declination vector.  A summation is used to get the mean residual 
vector, which is the
systematic difference between the Hipparcos Catalogue and the input 
catalogue at that specific location.  Hence, subtracting this vector
from a star position will put it close to the HCRF.

The above technique describes correcting a catalogue for systematic
differences with Hipparcos based on right ascension and declination.
However, it is well known that other systematic deviations exist, 
most notably those based on magnitude and color.  These, in turn,
may have a positional dependency associated with them; so, corrections
based on right ascension, declination, magnitude, color and all 
combinations of the four were computed and applied.
This was done similarly to the technique just describe, however
the definition of ``local'' was expanded to include those stars
nearby not only in right ascension or declination, but also similar
in magnitude or color.  In order for a magnitude-dependent correction to
be computed, typically only Hipparcos data from stars that were
within 0.1 magnitudes of the input catalogue star were used.
The same 0.1 magnitude difference in B-V was usually utilized in 
performing color corrections.

\subsection{Computing catalogue weights}

Once a catalogue was believed to be on the HCRS, individual star differences
from Hipparcos were computed.  (Note that the conversion to
the HCRS utilized weighted mean differences using several stars,
not individual differences.)  These were used to compute the catalog
standard error and weight utilizing the well-known formulae
\begin{equation}
\sigma_{\alpha,\delta} = \sqrt {\frac{ \Sigma(x_i)^2 - \frac{(\Sigma x_i)^2}{N}}{N}} 
\end{equation}
and
\begin{equation}
W_{\alpha,\delta} = \frac{1}{\sigma_{\alpha,\delta}^2}
\end{equation}
where $\sigma_{\alpha,\delta}$ is the standard error per catalogue entry in 
right ascension and declination, $x_i$ are the individual differences
between the stars in common between the input catalogue and Hipparcos in
right ascension and declination, and $N$ is the total number of stars
in common between the two.  The value $W_{\alpha,\delta}$ is simply the
computed weight of the catalogue in right ascension and declination.
For some input catalogues, the number of observations per catalog
entry given.  In these cases, an error (hence weight) per observation
could be computed.  These catalogues have a ``Yes'' under the 
$\sigma/\sqrt{N}$ column of Table~\ref{tab:acrs}.  For many catalogues, however,
only a standard error (hence weight) per catalogue entry could be computed.
These catalogues have a ``No'' under the 
$\sigma/\sqrt{N}$ column of Table~\ref{tab:acrs}.

This procedure was used for most catalogs; a few, however, had error estimates
available for each star that closely coincided with the newly computed
estimates.    In these cases, the additional information in the form 
of published error estimates (hence weights) was used. 

\subsection{Computation of ACRS\_1999 positions and motions}

The reduced positions were grouped together by indivisual star.  Mean positions,
proper motions, and error estimates were computed following the method
outlined by Corbin (1977), briefly described here.

\subsubsection{ACRS\_1999 mean positions}
Computations are made using position unit vectors, defined by
\begin{equation}
x_i  = \cos \delta_i \times \cos \alpha_i
\end{equation}
\begin{equation}
y_i  = \cos \delta_i \times \sin \alpha_i
\end{equation}
\begin{equation}
z_i  = \sin \delta_i
\end{equation}
Weighted mean $(x,y,z)$ values, denoted as $(\bar{x},\bar{y},\bar{z})$
and their associated epochs can be easily computed using the computed weights.
Note that the weights $w_x, w_y,$ and $w_z$ are equal to $w_\alpha, w_\alpha,$
and $w_\delta$, respectively.  From $(\bar{x},\bar{y},\bar{z})$, a 
conversion back to mean right ascension and declination, $(\bar{\alpha},
\bar{\delta})$, is made using the
formulae
\begin{equation}
\bar{\alpha} = \arctan{ \left( \frac{\bar{y}} {\bar{x}} \right) }
\end{equation}
and
\begin{equation}
\bar{\delta} = \arctan{ \left( \frac{\bar{z}} {\sqrt{ 1 - \bar{z}^2}} \right) }
\end{equation}

\subsubsection{ACRS\_1999 proper motions}
To compute proper motions, first
the time derivatives of $(x,y,z)$, denoted $(\dot{x},\dot{y},\dot{z})$,
are computed using
\begin{equation}
\dot{x} = \frac{\Sigma x_i \cdot w_i \cdot \tau_i}{\Sigma \tau_i^2 \cdot w_i}
\end{equation}
with similar equations for $\dot{y}$ and $\dot{z}$.  The variable $\tau_i$
is the epoch difference between the $i^{th}$ catalogue position and the
weighted mean epoch.
Finally, proper motions in right ascension and declination, $\mu_\alpha,
\mu_\delta$, are computed using
\begin{equation}
\mu_\alpha = \frac { \dot{y} \bar{x} - \dot{x} \bar{y} }
{\bar{x}^2 + \bar{y}^2}
\end{equation}
and 
\begin{equation}
\mu_\delta = \frac {\dot{z}}{\sqrt{ (1-\bar{z}^2)} }
\end{equation}

\subsubsection{ACRS\_1999 error estimates}
The U.S. Naval Observatory typically computes standard error estimates based on
the residuals of catalogue positions making up the mean position and
proper motion.  This has been termed the {\em scatter method}, because it
is based on the scatter of the data around the computed value.
The formulae used are detailed in Corbin (1977).  For standard errors of the 
mean right ascension and declination, $\sigma_{\bar{\alpha}},
\sigma_{\bar{\delta}}$, we have
\begin{equation}
\sigma_{\bar {\alpha}} = \left[ \frac{ \Sigma (\Delta y_i \bar{x} - 
\Delta x_i \bar{y})^2 w_i}
{(1-\bar{z}^2)(n-2)\Sigma w_i} \right] ^{\frac {1}{2}}
\end{equation}
\begin{equation}
\sigma_{\bar {\delta}} = \left[ \frac{ \Sigma (\Delta z_i w_i)}
{(1-\bar{z}^2)(n-2)\Sigma w_i} \right] ^{\frac {1}{2}}
\end{equation}
where the values of $\Delta x_i, \Delta y_i, \Delta z_i$ are the
residuals of the $i^{th}$ catalogue position from the 
computed $(x,y,z)$ values at $i^{th}$ catalogue epoch.  For the computation
of the standard errors of $\mu_\alpha$ and $\mu_\delta$ we have
\begin{equation}
\sigma_{\mu_\alpha} = \left[ \frac{ \Sigma (\Delta y_i \bar{x} - 
\Delta x_i \bar{y})^2 w_i}
{(1-\bar{z}^2)(n-2)\Sigma w_i \cdot \tau_i^2} \right] ^{\frac {1}{2}}
\end{equation}
\begin{equation}
\sigma_{\mu_\delta} = \left[ \frac{ \Sigma (\Delta z_i w_i)}
{(1-\bar{z}^2)(n-2)\Sigma w_i \cdot \tau_i^2} \right] ^{\frac {1}{2}}
\end{equation}
where $n$ is the number of catalogue positions used to compute $\bar{\alpha},
\bar{\delta},\mu_\alpha,$ and $\mu_\delta$.  Even a cursory look at the 
above formulae will show that computation of the standard errors using this
method cannot be made if there are only two catalogue positions
used.  In this case, the formulae
\begin{equation}
\sigma_{\bar \alpha} = \left[ \frac{1}{\Sigma w_i^2}
\sum w_i^2 \cdot  \sigma_{\alpha_i}^2
\right]^{\frac{1}{2}}
\end{equation}
and
\begin{equation}
\sigma_{\mu_\alpha} = \left[ \left( \frac{1}{\Sigma \tau_i^2} \right)^2
\frac{1}{\Sigma w_i^2} \sum w_i^2 \cdot \sigma_{\alpha_i}^2 \cdot \tau_i^2
\right]^{\frac{1}{2}}
\end{equation}
were used.  Similar formulae were used to compute position and proper
motion errors in declination.

\subsubsection{Refining the catalog}
Since the purpose of compiling the ACRS\_1999 was to provide a source
of reference stars used to reduce the AC data on to the system defined
by Hipparcos, it was decided to utilize the astrometry from the 
Hipparcos Catalogue for the $\approx 30\%$ of the stars in common.
Hence the Hipparcos data were substituted for the compiled data.
Hipparcos stars flagged with a G, V, or X in the Double and Multiple
Flag field (H59) were removed from the ACRS\_1999, as their astrometry
is suspect.  Additionally, stars marked in that same field with an
O (orbit stars) were removed if the semi-major axis exceeded 100 mas. 
All stars marked as orbit stars in the Washington Double Star Catalog
(WDS; Worley and Douglass 1996) were removed.  Since measurements of
blended images on the AC plates are often suspect, when an ACRS\_1999
stars was found within 5 arcsec of another ACRS\_1999 star, both were removed.
Finally, all ACRS\_1999 stars whose positional errors in either coordinate
at epoch 1900 were computed to be at 450 mas or higher were removed. 

\subsubsection{ACRS\_1999 characteristics}
The ACRS\_1999 contains 391,838 stars distributed over the entire sky,
resulting in an average density of just under 10 stars per square degree.
The magnitude distribution, using the Tycho-1 visual magnitude, can
be seen in Fig~\ref{fig:magdist}.

The astrometric errors are magnitude dependent.  Figures~\ref{fig:poserr}
and~\ref{fig:muerr} -- indicating positional errors at the ACRS mean epoch
and proper motion at the same epoch, respectively --
show this dependency.  The wide range in positional errors, from near
1~mas for the brighter stars to over 30~mas for stars between magnitude
10 and 11, is due to the Hipparcos star distribution in the ACRS\_1999.
Positional errors
in the Hipparcos Catalogue are generally 1 to 3 mas; for the best non-Hipparcos
catalog, Tycho-1, the errors run from 10 to 50 mas.  This is reflected in 
Fig.~\ref{fig:poserr}.  For stars brighter
than 8th magnitude, the primary source of astrometry is Hipparcos.  Between
8 and 11, the ratio of Hipparcos to non-Hipparcos stars drops, and hence the 
errors increase.  Beyond about magnitude 11, this ratio begins to 
increase, so the positional errors once again drop.

This same trend is reflected in the proper motion errors, seen in
Fig.~\ref{fig:muerr}.  The span in errors is less, however, since the Hipparcos
values are generally between 1 and 3 mas/year whereas without Hipparcos,
values of 2 to 5 mas/year are normal.  No downturn of errors in the 
faintest stars is seen; this is where the Hipparcos proper motion errors
are their highest.

%%
%% *** Insert figures 1,2,3 near here
%% 
\begin{figure}[p]
\centerline{\psfig{file=magdist.ps,height=3.5in}}
\caption[magdist.ps]{Magnitude distribution of the 371,838 ACRS\_1999
stars is shown.  Magnitude is from the Tycho-1 V ($V_T$).
The bar centered at magnitude 5.25 contains all stars
brighter than 5.50.  The one at 12.25 contains all stars at 12.00 and
fainter. \label{fig:magdist}}
\end{figure}

\begin{figure}[p]
\centerline{\psfig{file=poserr.ps,height=3.5in}}
\caption[poserr.ps]
{Positional errors of the ACRS\_1999 stars by
magnitude.  The positional error is for the mean epoch of observation.
Plotted are the averages of all stars taken within each magnitude range.
\label{fig:poserr}}
\end{figure}

\begin{figure}[ht]
\centerline{\psfig{file=muerr.ps,height=3.5in}}
\caption[muerr.ps]
{Proper motion errors of the ACRS\_1999 stars by
magnitude. Plotted are the averages of all stars taken
within each magnitude range.
\label{fig:muerr}}
\end{figure}

Having the ACRS\_1999, with a density providing an adequate number of reference
stars on each AC plate (35 on average) and being on the Hipparcos system,
allows one to continue the plate reduction process.
  
\section{Preparing the Data for the Plate Reduction Software}

It was necessary to prepare the data for the plate    
adjustment software.  The preparation process consisted of three
discrete tasks: matching the images with reference stars; 
matching images with those of the same star on another plate; and
converting the data to a standard format.  The last two steps
were performed during the AC~2000.1 work.  However,
since they are an integral part of the reduction process, the descriptions
are repeated here. 

\subsection{Matching images with the reference stars}
              
Equatorial coordinates for all AC images were computed from the rectangular
coordinates via the published plate constants.  The ACRS\_1999 data were then
brought to the average epoch of each zone and transformed to the AC equinox,
B1900.0.  A positional match was then made between the AC and ACRS\_1999.
Checks were
made to ensure that {\em illegitimate} matches had not taken place.  An example
of an illegitimate match is an ACRS\_1999 star that matches with two separate
AC images that are on the same plate.  Also at this stage, all plates were
checked to ensure that each contains an adequate number of
identified reference stars.  
Fewer than expected matched reference stars on a plate may indicate problems
with the published constants or plate centers.  These plates were investigated,
and the problems were corrected.

\subsection{Matching images with those on other plates}

The same equatorial coordinates computed in the previous step
were used to identify images of the same
stars that lie on different plates.  Images within 2.0 arcsec
of each other were generally
identified as the same star at this stage.
Illegitimate matches were investigated and treated appropriately.
Each image was then assigned an {\em internal star number} that is unique
for each star in the zone, regardless of the number of plates on which it
appears.  The data were verified to ensure that all images marked with
an ACRS\_1999 number have the same
internal star number, and vice versa.  No two images on one plate were allowed
to have the same internal star number.

\subsection{Converting data to a standard format}
The data were combined in one, standard format file.  This file contained
all pertinent information about each plate and image.  Plate information
such as plate centers, sidereal time of exposure, meteorological data,
measuring machine and measurer, r\'{e}seau used,
emulsion type, and epoch of exposure were
included, if they were published.
Data pertaining to each star, that is the $x,y$ values, image diameter
or magnitude,
internal star number, and ACRS\_1999 identifier, were included.
A conversion from the published $x,y$ units to units of millimeters, along
with a translation of the coordinates to ensure that the origin is in
the approximate plate center, was performed when necessary.
The persons responsible for the zone preparations can be found in
Table~\ref{tab:people}.

\subsubsection{Conversion of the AC Magnitudes}
The Astrographic Catalogue as originally published contains
magnitude measures -- usually in the form of image diameters and 
formula to convert them to stellar magnitudes.  However these are
non-uniform between zones, in part
because of different techniques used by participating observatories.  Many of 
the published magnitude measures are unreliable, especially for the
faintest and 
brightest stars.  Thus, it is desirable to transform them to 
a well-known -- or often used -- system, preferably to the 
same system as the reference catalogue, thus facilitating the removal
of systematic errors that are a function of magnitude.
The plates used were most sensitive in the blue spectral region,
so a logical choice of systems was the Tycho-2 blue (${\rm B_T}$).  Tycho-2
contains about 2.5~million stars covering much of the AC magnitude range.
The Tycho-2 photometry was made available for
this in advance of publication.

Each zone was treated independently.  Only stars identified in Tycho-2 as being
single and with negligible variability were used for the calibration.
Differences between AC and
Tycho-2 ${\rm B_T}$ magnitudes as a function of AC magnitude were computed.  Polynomial
expressions describing the results were computed via least-squares fitting.
Some extrapolation of these polynomials was required because for most
zones the magnitude limit is fainter in the AC than in Tycho-2.
(Usually an extrapolation
of less than 0.5 magnitude was used. Beyond that the corrections were held 
constant).   For stars not used to 
compute the calibration -- primarily non-Tycho-2 stars -- the magnitudes found
in the AC~2000.2 are based on the published diameters and the 
derived polynomial expressions.  For stars in common with Tycho-2, the 
Tycho-2 ${\rm B_T}$ magnitudes are given.

\section{Preliminary Reductions and Investigation of Plate Models}

The core of the plate reduction software was the same as that used in the
reductions of the Cape Photographic Catalogue 2 data
(Zacharias et al. 1992).  For all zones,
an eight-constant plate model, consisting of four
orthogonal terms ($a,b,c,$ and $d$), two non-orthogonal terms ($e$ and $f$) and
two tilt terms ($p$ and $q$) was initially used, as shown in
Eqs.~\ref{eq:xmodel1} and~\ref{eq:ymodel1} .
\begin{equation}
\xi = ax + by + c + ex + fy + px^2 + qxy
\label{eq:xmodel1}
\end{equation}
\begin{equation}
\eta = ay - bx + d - ey + fx + pxy + qy^2
\label{eq:ymodel1}
\end{equation}
At this step, no corrections to the published
$x,y$ values were applied. Investigations of radial distortions,
tangential distortions,  magnitude equation, coma, periodic measuring errors
and r\'{e}seau-dependent systematic errors were investigated for each zone
following the procedures outlined previously (Urban \& Corbin 1996;
Urban et al. 1996).  Since an uncompensated systematic error may 
cause a star to be an outlier, only reference stars with residuals
over five times the standard deviation of unit weight of the solution
were removed while various plate models were investigated.

\subsection{Corrections to the $x,y$ values}

Results of investigations of systematic errors may lead to applying a
correction to the published star measures prior to final plate constant
determinations.  These are typically done on a zone-by-zone basis.
 
To investigate if radial distortion exists in the data, the reference star
radial residuals were plotted against distance from the plate center.
If a radial distortion was present, the corrections were described by a 
non-zero function.  Additionally, the radial residuals were examined for 
magnitude, measurer and measuring machine dependence.
A similar investigation was conducted looking for
the existence of a tangential distortion, however none was found in any of 
the zones.

The presence of a magnitude equation, which is a systematic offset of
stars based solely on
their brightness, was investigated by plotting the reference stars' residuals
with respect to the Tycho-2 ${\rm B_T}$ magnitude.  This was performed
separately for both the $x$ and $y$ coordinates.  The existence of a
magnitude equation that is dependent on the $x,y$
measures was also investigated.  Additionally, magnitude equation varying 
with measurer and plate epoch was considered.  Note that a magnitude
equation outside the range of the reference stars is extremely difficult
to find (Eichhorn 1974).  It is possible to compensate for a magnitude equation 
in the magnitude range of the reference stars, but it is unwise   
to extrapolate those corrections to field stars that may be two or three
magnitudes fainter.

The presence of coma, a change in scale based on magnitude, is uncovered
in two ways.  First, investigating the $x,y$-dependent magnitude equation will
reveal coma if it exists within the range of the reference stars. 
Second, using fainter stars, a plot of the difference between the mean
position (computed from overlapping plates) and an individual image position
vs. plate coordinates of the individual position will, using data from hundreds
of stars and different magnitude ranges, reveal the presence of coma.  If 
coma was found, it was examined for variations with respect to plate epoch.

Errors caused by the measuring mechanism were investigated 
by analyzing the residuals of reference stars as a function of
location on the $x$ and $y$ measuring apparatus (usually a screw or an eyepiece
scale, see Section 2).  The presence of an error with a period 
corresponding to the length of the measuring screw or eyepiece scale is quite
likely caused by the machining of that part, but may also be a function of the
measurer.  In either event, these errors can be corrected.

Additionally, the presence of a remaining field distortion pattern
can be examined by using plots similar to those produced while investigating
coma.  These patterns were investigated for dependence on magnitude, r\'{e}seau,
measuring machine and measurer. 

Using the information from these investigations, a plate model was     
developed for each of the AC zones.
Equations~(\ref{eq:xprime})
and~(\ref{eq:yprime}) show the corrected $x,y$ values used in the final plate
adjustments.
\begin{equation}
x^\prime = x+\rm RD + \rm TD + \rm ME_{ \mit x} + \rm MC_{ \mit x}
      + \rm S_{ \mit x} \mit mx + \rm MA_{ \mit x} + \rm FDP_{ \mit x}
\label{eq:xprime} 
\end{equation}
\begin{equation}
y^\prime = y+\rm RD + \rm TD + \rm ME_{ \mit y} + \rm MC_{ \mit y}
      + \rm S_{ \mit y} \mit my + \rm MA_{ \mit y} + \rm FDP_{ \mit y}
\label{eq:yprime}
\end{equation}
In Eqs.~(\ref{eq:xprime}) and~(\ref{eq:yprime}),
RD is the correction applied to compensate for radial
distortion; TD is the correction to compensate for tangential distortion;
ME and MC are corrections to compensate for magnitude equation and 
$x,y$-dependent magnitude equation; S is the correction for coma; MA corrects for
measuring apparatus errors, and FDP compensates for any remaining field distortion
pattern.  The variable $m$ is the computed magnitude.  By substituting 
$x^\prime, y^\prime$ for $x,y$ in Eqs.~\ref{eq:xmodel1} and~\ref{eq:ymodel1},
the 8 constants for each plate were computed.
The significant systematic errors found and corrected in each zone are listed in 
Table~\ref{tab:const}.

\section{Investigation of Discordant Data}
Once a suitable plate model was determined, the computed positions were
used to investigate problems such as mismatched images, blended images
of multiple stars and typographical errors.  Much of this work was
performed during the AC~2000.1 reductions; the description is 
repeated here for completeness.

\subsection{Incorrectly matched images from overlapping plates}

Images may be incorrectly matched in a variety of ways.  Images are originally
matched in the way described in the subsection ``Matching images with those on other
plates.''  Positions computed from the provisional plate constants can 
change significantly due to the new reductions. So, images earlier believed to
be from two stars because their positions were dissimilar may now
be recognized as coming only from one if their new positions are closer.
To investigate this possibility, images closer together than a certain
distance were investigated.  The distance chosen depended on the
range in plate epochs (since proper motion will then be a factor) as well as
accuracy of the $x,y$ measures.
Images that fall outside the expected precision may be a result of 
a double star, poor measurements of the same
star or good measurements of a star that has moved due to proper motion.
Deciding which was the case was often difficult because no 
comparable catalogue with the epoch of the AC plates exists with which
to check the stars in question.  The Preliminary Version of the Third 
Catalogue of Nearby Stars (Gliese \& Jahreiss 1991) aided in
detecting high proper motion stars, but this catalogue, as its name states,
contains only nearby stars.  The  Luyten's Two-Tenths Catalogue and its
supplement (Luyten 1979, 1980; Luyten \& Hughes 1980) has also been used in
aiding in the identification of high proper motion stars, as was the
Hipparcos Catalogue.
The Washington Double Star
catalogue (WDS; Worley \& Douglass 1996), the internationally recognized source
of visual double star data, was also used but is limited because of its
incompleteness over the AC magnitude range and its occasional use of AC data.
However, certain criteria were followed in deciding if two images were from
the same or different stars.  These criteria were zone   
specific, but for most zones images were identified as coming from the same 
star if an image was within 3.5~arcsec of a mean position and there was no
indication of duplicity.
Images from different stars, but incorrectly identified as coming from 
the same star, will result in a high standard deviation in right ascension
or declination, $\sigma_{\alpha}$ or $\sigma_{\delta}$.  Stars with the largest
$\sigma_{\alpha}$ and $\sigma_{\delta}$ were investigated for this possibility.

\subsection{Duplicate entries}
Virtually every zone has mistakenly printed some of its measures more than
once.  These were easily found since the data in question was either exactly
the same as another record (in cases of true duplication) or the resulting
star positions of two records were ridiculously close for the telescope scale
and typical seeing.  In general, images closer than 1.0~arcsec that appear 
on the same plate were suspected of being duplicate entries.  In cases of this
type, generally only one of the measures was kept.

\subsection{Blended images}

Images of double stars that are blended on one plate but discrete on another
require special treatment.  Two possible problems exist under these 
circumstances.  First, if the blend is identified as one of the separate
images, then the computed separation of the double star will be smaller than
it is in actuality (since the blend will fall near the photocenter).
Second, if the blend is not identified with either
discrete image, then three sets of coordinates will be computed where only
two stars exist.

Under the first scenario (a blend is matched with a discrete image),
the data will consist
of a multiple star system with at least one star having a large 
standard deviation of position, $\sigma_{\alpha}$ or $\sigma_{\delta}$.
To investigate this possibility, the area around each star was searched for
the presence of another star. If a nearby star was
found, then the data were examined for a blend if $\sigma_{\alpha}$ or
$\sigma_{\delta}$ of either star exceeded a certain amount (usually 
1.0~or 0.9~arcsec).  Additionally, any two 
stars closer than about 3.0 arcsec, or any triple or quadruple systems,
were examined.

Under the second scenario, (a blend is not identified with either of the 
discrete images), then a star system
will appear to have one more member than it really has.  To minimize this
occurrence, an area with a radius of about 10~arcsec
around each star was searched for the presence of two other stars.
Additionally, an area with a radius of about 15.0~arcsec was searched for three 
other stars.  If multiples were found, they were examined to ensure that
images were identified correctly.  In the situation described above, blends
are discarded.

\subsection{Large proper motion candidates}

Due to the span of plate epochs, images from large proper
motion stars may be displaced from one another by several arcsec and hence
not be matched as coming from the same star.  To minimize this occurrence,
a search in the Luyten's Two-Tenths Catalogue and its supplement
was made to identify high proper 
motion stars.  An additional search for large proper stars in the Third
Catalogue of Nearby Stars was also made.  Stars in 
the final catalogue having large standard deviations of position are known 
high proper motion stars.

\subsection{Typographical errors}
A bright star may only appear to have one image if one of its records
contains a typographical error.  To find and correct this, all bright,
single image
stars were investigated. (The exact magnitude limit depends on the zone. 
Typically all stars down to 11.5 are investigated.)

The process involved generating positions for these images if one
altered one of the digits of the printed $x$ or $y$ value, then performing 
a search within 2~arcsecs around these pseudo-positions.  If another image was
found at one of the locations, a typographical error may be present.
For zones with $x,y$ values published in millimeters, investigations 
down to the tenths position were made (0.1 mm $\approx$ 6~arcsec).
For those zones with  $x,y$ values published in  r\'{e}seau units,
investigations down to the hudreths position were made
(0.01 r\'{e}seau unit $\approx$ 3~arcsec).  The
Twin Astrograph Catalogue (TAC; Zacharias et al. 1996),
was used to determine which of the two records, if either, should be changed
for all zones north of, and including, Tacubaya.  For the more southerly zones
which are not covered by TAC, the Tycho Input Catalogue (Halbwachs et al. 1994)
has been used.
If a corresponding star was not found in the TAC or TIC, then a search in the 
the Digitized Sky Survey using the Skyview interface was made to determine 
which, if either, contains a typographical error. 

To minimize the possibility of a printing error in the magnitude data, 
a standard deviation of the magnitude, $\sigma_{ \rm mag}$, was generated
from the computed magnitudes for every star appearing on more than one plate.
The stars with the 
largest $\sigma_{ \rm mag}$ were investigated.  Additionally, range checks were
made on the original data as well as the final computed magnitudes to ensure
that all values were reasonable.

\subsection{Investigation of other potential problems}

To investigate the possibility of a few plates being adjusted incorrectly
due to such oddities as several poor reference stars on a plate or
incorrectly removing accurate reference stars for poorer ones, 
the positions of the 500 stars with the largest $\sigma_\alpha$ and
$\sigma_\delta$ were plotted for each zone.
Additionally, the percentage of stars on each plate whose $\sigma_\alpha$
and $\sigma_\delta$ are in the highest 1\% of that zone were computed.  Plates
that have more of these than expected were investigated.

Positions of all stars were plotted to ensure that the data contain no missing
areas, such as a block of data having not been typed or accidentally 
discarded.  Positions of stars having only one image, and positions of stars
having multiple images, were plotted separately to investigate the 
possibility of missing plates.

To avoid the presence of non-stellar objects in the final catalogue, a search
in the New General Catalogue of Nebulae
and Clusters of Stars (NGC), the Index Catalogue (IC), and the Second Index
Catalogue (Sinnot 1988) was made.  The Digitized Sky Survey, using the 
Skyview interface, was used to graphically show potential NGC and IC objects
present in the data.  Those records found to be non-stellar NGC or IC objects
have been discarded.

\section{Final Plate Model and Weights}

It was necessary to ensure that the plate models developed in each
zone and the corrections applied to the data were still valid because
they were originally developed on the data that included erroneous
identifications
and typographical errors.  Once any needed revisions were made, plate weights
were computed.  For most of the AC zones, a plate's weight is
the inverse of the variance of the positions of the stars which it contains,
after removing the stars with the highest 1\% $\sigma_{\alpha}$ and
$\sigma_{\delta}$.  The removal of these stars prior to computing the plate
weights reduced the possibility that a few, high proper motion stars  
adversely affected the weighting of an entire plate.

No grating was used in the AC program, so bright stars are over-exposed on the
plates and should not be used in the final adjustment nor be included in the 
final catalog.  All stars with mean computed magnitudes brighter than
4.0 have been removed prior to final plate adjustments.
Also removed from determining the final plate parameters were reference stars
with residuals larger than 3.0 times the standard deviation of unit weight
of a plate solution.  Once removed, the plate adjustment is performed again.
These stars are included in the
final catalog, but are treated as field stars.  

\section{Linking of Individual Zones}

 The Astrographic Catalogue was observed in discrete zones in the sky, and
the reductions, by necessity, were made on individual zones.  However it 
was desirable to link these together to make one, cohesive catalog.
To do this, stars in common to adjacent zones were identified.  Blended
images, high proper motion stars, and typographical errors were investigated
as described above.  Each star was assigned a new internal star number.
All images were combined to yield weighted mean right ascensions and 
declinations on the system defined by Hipparcos (HCRS) at the weighted
mean epochs of observation.

\subsection{AC~2000.2 plots}

Figures~\ref{fig:errra1} through~\ref{fig:epoch1} clearly demonstrate 
the zonal dependence 
of the AC 2000.2.  Figures~\ref{fig:errra1} and~\ref{fig:errdec1} 
show the average positional error for a single image with respect 
to location on the sky.  Of course individual errors will vary, and 
many of the stars have more than one image.  Figure~\ref{fig:epoch1}
provides information on the mean epochs of observation as function of 
location of the sky.  The combination of the positional errors and
epochs being a function of declination has consequences for any         
proper motions derived using the AC~2000.2 data.  That is, the proper 
motion accuracies will also contain this dependence.
This was true for the now superseded ACT Reference and Tycho Reference Catalogues,
both of which utilized earlier reductions of the Astrographic Catalogue
data.  It is also true for the Tycho-2 Catalogue, but 
some of this zonal dependence was eliminated by the inclusion of additional
astrometric catalogues.  Figure~\ref{fig:zones1} shows, on the same
scale as Figs.~\ref{fig:errra1} through~\ref{fig:epoch1}, the 
observatories responsible for photographing and measuring each area of the sky.

The average density of the AC~2000.2 is 112 stars per square degree;
however, the sky is hardly uniform.  The mean density as a function
of sky position is shown in Fig.~\ref{fig:dens1}.  The galactic plane
is clearly visible, where some areas exceed 500 stars per square degree.
On the other extreme, for large areas surrounding the galactic poles,
the density drops by more than half of the average.

As a courtesy to the reader, 
Figs.~\ref{fig:errra1} through~\ref{fig:dens1} are provided on this CD-ROM
in a larger format.  They can be found on this directory in the files
errra1.ps, errdc1.ps, epoch1.ps, zones1.ps and dens1.ps; each is in postscript
format.

\begin{figure}[ht]
\centerline{\psfig{file=errra1.ps,height=3.85in}}
\caption[errra1.ps]
{Average error in right ascension of a single image as a function
of sky coordinates.  Each bin is approximately 9 square degrees.
\label{fig:errra1}}
\end{figure}

\begin{figure}[pt]
\centerline{\psfig{file=errdec1.ps,height=3.85in}}
\caption[errdec1.ps]
{Average error in declination of a single image as a function
of sky coordinates.  Each bin is approximately 9 square degrees.
\label{fig:errdec1}}
\end{figure}

\begin{figure}[p]
\centerline{\psfig{file=epoch1.ps,height=3.85in}}
\caption[epoch1.ps]
{Mean epochs of observation as a function
of sky coordinates.  Each bin is approximately 9 square degrees.
\label{fig:epoch1}}
\end{figure}

\begin{figure}[tp]
\centerline{\psfig{file=zones1.ps,height=3.85in}}
\caption[zones1.ps]
{Identification of observatories as a function
of sky coordinates.
\label{fig:zones1}}
\end{figure}

\begin{figure}[p]
\centerline{\psfig{file=dens1.ps,height=3.85in}}
\caption[dens1.ps]
{Number of stars per square degree as a function
of sky coordinates.  Each bin is approximately 9 square degrees.
\label{fig:dens1}}
\end{figure}

\section{Cross-Referencing Information}

The numbering between the AC~2000.1 and AC~2000.2 has been
maintained.  It should be noted, however, that there is not a
strict one-to-one correspondence
between the two versions; the main reason is that some images now known
to be from high proper motions stars were not identified as such in AC~2000.1.
Note that AC~2000.1 contains 4,621,836 whereas AC~2000.2 contains
4,621,751 stars.  However, the numbering between the two remains consistent.
In other words, the star numbered ``1'' in both versions refers to the same
star.

In order to aid users and to facilitate other work utilizing the 
Astrographic Catalogue, most stars from the Hipparcos and Tycho-2
Catalogues have been identified.  This cross-reference is not intended to be
100\% complete; however, the vast majority of stars from these catalogues
are identified.

\newpage
\section{Description of AC~2000.2}

\subsubsection{Right ascension}

The mean right ascension for each star as computed from its weighted images,
in units of hours, minutes and seconds of time, referred to the Hipparcos
system (HCRS, J2000.0) at the weighted mean epoch of observation.

\subsubsection{Declination}

The mean declination for each star as computed from its weighted images,
in units of degrees, minutes and seconds of arc, referred to the Hipparcos
system (HCRS, J2000.0) at the weighted mean epoch of observation.

\subsubsection{B-Magnitude}
The magnitude is either taken directly from the Tycho-2 Catalogue
or is an average of the computed magnitude based on the measured image
diameters from the AC plates.  To determine which is the case,
one will need to check the 
{\em V-Magnitude} field.  All stars with the {\em V-magnitude} field non-blank
contain Tycho-2 photometry in both the {\em B-Magnitude} and 
{\em V-magnitude} fields.  Stars with the {\em V-magnitude} field blank
contain magnitudes based on the measured image diameters on the 
AC plates, which should roughly correspond to the Tycho-2 ${\rm B_T}$ system.
See the section ``Conversion of the AC Magnitudes'' for details.

\subsubsection{Epoch}
The mean epoch for each star as computed by its weighted images, in years.

\subsubsection{Number of images used}
The number of individual images used to compute position, magnitude (if
from image diameters), epoch and
standard deviation of position.

\subsubsection{Standard deviation of weighted mean}
The standard deviations of weighted means, $\sigma_{\overline{\alpha}} $ and 
$\sigma_{\overline{\delta}} $ are computed for every star with more than one 
image.  The formula used is:
\begin{equation}
\sigma^2_{\overline{x}} = \frac{\overline{x^2} - \overline{x}^2}
{N^\prime - 1}
\end{equation}
where
\begin{equation}
x = \alpha_i, \delta_i
\end{equation}
and 
\begin{equation}
N^\prime \equiv N \left[ \frac{\langle w \rangle^2}{\langle w^2 \rangle} \right] 
\end{equation}
where $w$ is the weight of an individual observation (generally the same
for all stars on a plate).

\subsubsection{AC 2000 number}
This number is used in the reduction process to
identify all images of the same star that may appear on different
plates.  This is generated at the U.S. Naval Observatory and
added to the original $x,y$ data.  When the $x,y$ data are
released, these numbers can be used to link the data to the final catalog.

\subsubsection{Hipparcos number}
If a star has been identified as being in the Hipparcos Catalogue
then the Hipparcos number is provided.  This cross-referencing 
information is not 100\% complete.

\subsubsection{Tycho-2 number}
If a star has been identified as being in the Tycho-2 Catalogue,
then the Tycho-2 identifier is provided.  Zeros have been inserted
in blank fields. This cross-referencing  information is not 100\% complete.

\subsubsection{V-Magnitude}
The magnitude listed here is taken directly from the Tycho-2 Catalogue,
otherwise it is blank.  There are 20 cases where the Tycho-2 ${\rm B_T}$
is given in the B-Magnitude column, but their is no corresponding 
Tycho-2 ${\rm V_T}$ magnitude.  For these stars, the V-Magnitude is 
set to .000 and a `3' is set in the Magnitude Flag field.

\subsubsection{Magnitude Flag}
This flag will give users caution regarding the photometry.  A `1' is 
given if the star has a B magnitude fainter than 13.5 or a V magnitude from
Tycho-2 ${\rm V_T}$ fainter than 12.5.
 A `2' is given if the star was identified 
as a Tycho-2 star but the AC magnitude computed from the published diameters 
is given.  This is done when the Tycho-2 ${\rm B_T}$ magnitude is either not 
given or is listed as fainter than 14.00.  No Tycho-2 ${\rm V_T}$
magnitudes are given
for these stars.  In cases where both `1' and `2' are set, only 
`2' is given.  A `3' is given if the star was identified as a
Tycho-2 star, but there is no Tycho-2 ${\rm V_T}$ magnitude.  In these
cases, the Tycho-2 ${\rm V_T}$ magnitude is set to .000.  There are 20
such instances.  Only 1 star (AC~408635, Tycho-2~107200084801) should
have a '3' flag in combination with another.  For this star, the Tycho-2
${\rm B_T}$ is 13.51 and no Tycho-2 ${\rm V_T}$ magnitude exists; the
flag is set to `3'.

\subsubsection{Verification Flag}
A `1' in this field indicates the star has a single image and is not
found in Hipparcos, Tycho-2, ACRS\_1999 or the Hubble Guide Star Catalogue 1.2.
These ``stars'' may not exist but instead may be the result of typographical
errors, plate defects or other such blunders.

\newpage

\section{Participating Observatories}

Work from the observatories that participated in the
photographing and measuring of the Astrographic Catalogue data are summarized
below.  Some important characteristics of each zone can be found in
Table~\ref{tab:obschar1} and in Appendix~A.  The telescope characteristics
agreed upon were a normal astrograph with an aperture of roughly 33~cm and
a this instrument having a focal length of 3.43~m.  This created a scale
close to 60~arcsec/mm on the plates.  All observatories, with the exception of 
Nizamiah, used this type of instrument.

\subsection{The Royal Observatory at Greenwich}

The Royal Observatory at Greenwich was an original participating institution
in the Astrographic Catalogue project, sending representatives to the
International Congress on Astronomical Photography held in Paris in 1887.  This
meeting outlined the plans for the Carte du Ciel project.  Funding was provided
shortly following this meeting.  A telescope built by Sir Howard Grubb
following the design agreed upon in Paris was delivered in May 1890.        
Greenwich centered its plates between +65 and +90 degrees, with five plates 
taken on the pole in different orientations. 
In total, 1153~plates were exposed and measured in this zone.  Three exposures
were made on each plate lasting six minutes, three minutes and 20~seconds.
The telescope was moved 20~arcsec between the exposures, so the six and
three minute exposures are offset from each other in declination, the six 
minute and 20~second exposure are offset in right ascension.
The plate epochs span from 1892 to 1905.

After initially measuring some plates using micrometer screws, Professor H.H.
Turner realized that a different measuring technique was required if the job
were to be completed in a timely fashion.  At his request, an eyepiece scale
type
measuring machine was built and greatly reduced the time to measure a plate.
Many other observatories adopted this measuring procedure.
Systematic measuring of the plates
began in October~1894.  A duplex micrometer, which is a measuring machine capable 
of measuring two plate simultaneously, was put into use in February~1895. 
This aided the identification of images of the same star but on different
plates since it was possible to arrange the plates in the machine so that 
the same field of sky was coincident under the measuring apparatus. (Remember
that each plate overlapped surrounding plates so that each area of sky appears
on at least two plates.)  All plates were measured in two orientations, with
the plates being rotated 180~degrees between measurements.  In all degree bands
except the +65, +66, and +67~degree bands, the same measurer was used for 
both orientations.  Both the six minute and three minute exposures were 
measured for all stars that appeared on the 20~second exposure.
Details can be found in the introductions to the published volumes
(Christy \& Dyson 1904-1932).

\subsection{The Vatican Observatory}

The Vatican Observatory, located in Vatican City, was founded
in 1888 while the Carte du Ciel program was in its infancy.
Vatican staff members realized that
participation in this program would immediately give their
young observatory international recognition.
Pope Leo XIII commissioned Father Francesco Denza and Father Giuseppe Lais
to attend the Astrographic Congress and enroll the Vatican as one of the 
participating institutions.

After being accepted as a participant, the Vatican commissioned
the Henry brothers of France to build the telescope and P. Gautier to build
a machine to measure the stars on the plates.
Father Denza describes the finished telescope:
``The instrument consists of two parallel telescopes:  The photographic
telescope
with an aperture of 33 cm and a focal length of 3.43 m; and the finding 
telescope or collimator with 20 cm aperture and a focal length of 3.6 m.  Both
are housed in a metal tube with a rectangular cross section of 37 by 68 cm.
Both objectives are fixed on the same block of bronze at one end of the 
tube and at the other end is the photographic plate holder and the eyepiece 
of the collimator.  A thin metallic diaphragm separates the two telescopes.
...The photographic objective is a doublet of flint and crown and it is
both achromatic and aplanic for the most intense chemical rays of the 
spectrum.''  (Denza 1891).

The telescope was installed in the Leonine Tower in 1891.  This tower,
located on the highest point of Vatican Hill,
was originally constructed in 840 AD under Pope Leo IV as a 
defense against the Saracen invasions.  It is about 20 meters above 
ground (about 100 meters above sea level) with walls about 4.5 meters in
thickness.  

The Vatican was assigned the strip of sky between +55 and +64 degrees on 
which to center the plates.  In order to achieve the two-fold sky coverage
1040 plates would be needed.  (Actually, 1046
plates were exposed and measured.)  The job of photographing and developing
the plates was 
carried out primarily by one person, Father Lais, who worked on this for
over 25 years until the time of his death in 1921.  Lais's aid, Carlo
Diadori, completed the photographing in 1922.                   
For the first several years
that Father Lais was working at the telescope, no plates were being measured.

Father Johann Hagen,
appointed director of the Observatory
in 1906, was committed to seeing the project completed.  He soon
realized that the machine built by Gautier to measure the
stars was too slow.  After investigating different measuring 
techniques employed by other institutions, he decided on the use of an eyepiece
grid.  In the method used by Vatican, a 10 $\times$ 10 mm area of a plate,
corresponding to 2 $\times$ 2 r\'{e}seau intervals, was magnified in a 
microscope along with a grid which is segmented into 0.05 mm steps.
The edge of the grid was aligned with the edge of the
2 $\times$ 2 r\'{e}seau interval
area.  The location of a star within the magnified area was read from its 
apparent position on the grid.  This method was indeed 
efficient, allowing the Vatican to be one of the first observatories to complete
its assigned zone despite utilizing minimal manpower.
However, the accuracy was not as high as can be obtained with the
measuring techniques used at other participating institutions.
Vatican was the only observatory in the Astrographic
Catalogue program to use the eyepiece grid technique.
Also during his trips to other observatories,
Father Hagen saw extensive use
of women in measuring the plates, freeing the full-time, male
astronomers from this time-consuming, repetitive task.
He brought in three nuns from the Instituto di
Maria Bambina to measure the plates.  These nuns worked from 1910 to 1921 and
measured the vast majority of the Vatican data.  The Oxford University 
Observatory agreed to compute the plate constants used to convert the
rectangular measures to equatorial coordinates.

For additional information concerning the history of the Vatican Observatory
and its personnel, see the book \underline {In the 
Service of Nine Popes} (Maffeo 1991).  Additional details regarding the 
Vatican's participation in the Astrographic Catalogue project 
can be found in the introductions to the data (Vatican 1914-1928), written
in Italian.

\subsection{The Catania Observatory}

The Catania University Observatory, located in Catania, Sicily, centered
its plates between +47 and +54 degrees.
In total, 1010 plates were exposed and measured in this zone.
The epochs span from 1894 to 1932, but over 95\% were exposed prior to 1906.
All the plates were measured using the short-screw method.  Additional 
details can be found in the introductions to the published data
(Catania 1907-1963).

\subsection{The Helsingfors Observatory}

The Helsingfors Observatory, located in Helsinki, Finland, centered its plates
between +40 and +46 degrees.
In total, 1008 plates were exposed and measured in this zone.
The epochs span from 1892 to 1909, but over 94\% were exposed prior to 1897.
All the plates were measured using the short-screw method.
One screw was used; the plates
were rotated 90 degrees to measure both $x$ and $y$ coordinates.  The plates
measured early in the work had images from both the longest and middle exposures
measured in one orientation.  Later (after 1896), only the images from the 
longest exposure were measured, but the plates were rotated 180 degrees between
measurements so these images were measured twice (this also helped remove any
bias a measurer may have).  
Various aspects of the work are detailed in the introduction to Volume~1
(Helsingfors 1903-1937).

\subsection{The Potsdam Observatory}

In 1887, at the meeting of the International Congress which established the
Astrographic Catalogue, the zone with plate centers from +39 to +32 degrees was
assigned to the Potsdam Observatory, Germany.  Potsdam
began photographing the plates by~1893 and 1226~plates were
exposed by the end of 1900.  Each plate had two exposures of 5~minutes duration.
Unfortunately, the measurements of the plates lagged
behind the exposures. By the start of World War I only 406 plates were
measured.  Following the war, Potsdam announced it could no longer continue
with the project, and a re-photographing of its zone was made by Oxford,
Uccle, and Hyderabad.  The remaining plates were never measured.
An allied bomb during World War II destroyed virtually the entire set of 
plates (Dick 1988, 1990).

In total, 406 plates were measured and published as the Potsdam zone.
These plate are scattered throughout the zone, so many are not overlapped
by others.  All were measured using one of two short-screw 
type measuring machines.  The plates were measured in one direction only;
the plates were not rotated.
Various aspects of the work are detailed in the introductions
of the printed volumes (Potsdam 1889-1915).

\subsection{The Nizamiah Observatory, Hyderabad}

In 1887, at the meeting of the International Congress which established the
Astrographic Catalogue, the
zone from --17 to --23 degrees was assigned to the Observatory of Santiago, Chile.
By 1900, the work was still not progressing, so a proposal to establish an
observatory in Montevideo, Uraguay was made.  This, too, did not progress so 
Santiago asked to re-undertake the project.  At the same time, the 
Nizamiah Observatory, located in Hyderabad, India, offered to work on this 
zone as well.  So, in 1909 there were two observatories offering to work on
the --17 to --23 zone.  A resolution passed by the Congress in 1909 assigned the
--17 to --20 zone to Hyderabad.  After completing the photographing and 
measuring of these four bands in 1920, the International Astronomical Union
recommended that Hyderabad continue photographing down to --23~degrees
declination.
This work was completed in 1928.  This zone between --17 and --23 degrees is
known as the Hyderabad South zone.  Hyderabad also observed a section of 
the sky in the Northern hemisphere that Potsdam was originally assigned.  This
zone, between +36 and +39 degrees, is known as the Hyderabad North zone.

In total, 1260 plates were exposed and measured in the Hyderabad South zone.
The epochs span from 1914 to 1928, with only a handful taken after 1923.
For the Hyderabad North zone, 592 plates were exposed and measured.
The epochs span from 1928 to 1937, with just a very few taken after 1934.
The telescope used was not one of the Henrys' design, as all the other AC
participation observatories used.  Instead of a 33~cm, the Hyderabad 
instrument, built by Cooke and Sons of York, had an aperture of only 20~cm.
Its objective was described as a
``patent photo-visual lens''.  The smaller aperture meant longer exposures
were required to achieve the desired magnitude limit set for the AC.  
The telescope's focal length was 133~inches.
All the plates were measured using one of four eyepiece scale 
type measuring machines, all built by Cooke and Sons.
Various aspects of the work are detailed in the introductions
of the printed volumes (Edinburgh 1918-1930, London 1934-1946).

\subsection{The Uccle Observatory}

The Royal Observatory of Belgium, located in Uccle, was assigned the zone
with plate centers running from +34 to +35 degrees.  Although Uccle
was not an original participating observatory in the AC project, it became
one because the Potsdam Observatory, originally assigned to cover 
this area, was unable to fulfill its commitment.  The      
telescope used was of similar design as the Henry brothers, but built by
Gautier.  In total, 320 plates 
were exposed between 1939 and 1950.  The epochs of the plates are spread fairly
uniformly, except for a lack of plates exposed between mid-1943 and mid-1945.
The measurements took place at the Paris Observatory with the use of three
short-screw measuring machines.
The r\'{e}seau used was one from the Toulouse Observatory.
An introduction can be found in Volume~1 of the printed catalog
(Paris 1960,1962).

\subsection{The Oxford Observatory}

The University Observatory at Oxford was originally assigned the zone +25 to
+31 degrees on which to center the plates.  This is known as the Oxford~I
zone.  An additional
zone with plates centered on +32 and +33 degrees declination was photographed
at Oxford after Potsdam announced they would not be able to complete their
assigned area (+32 to +39).  This two degree band is referred to as the
Oxford~II zone.

The telescope used was the same
design as the Henry brothers' instrument located in Paris.  The Oxford 
lens was made by Sir Howard Grubb and attached to an existing Grubb $12
\frac{1}{4}$ inch, which was utilized as a guiding instrument.  All plates
of the Oxford~1 zone
were taken between mid-1892 and 1910, with over 80\% exposed by the 
end of 1903.  These plates were measured mostly by boys from the New College
Choir School, and Mr. T. J. Moore, a gardener who was interested in astronomy.
The measuring apparatus was designed with an eyepiece scale, similar
to that employed
by the Greenwich Observatory in their AC work, with the exception that only one
plate was measured at a time whereas Greenwich measured two.

Mr. F.A. Bellamy of University Observatory at Oxford supervised much of the
work in photographing the 320 plates required to complete the Oxford~2
zone.  He employed the same techniques used in the Oxford~1 zone
and used the same Grubb refractor operated 30 years earlier.  
Mr. Bellamy would have photographed the entire zone himself, however he died 
with 32 fields left unobserved.  These 32 fields were exposed at the 
Royal Observatory at Greenwich by Mr. H.G.S. Barrett with the telescope used
for the Greenwich Zone (+65 to +90).  These last 32 plates were the only
plates in the Astrographic Catalogue that did not have a
r\'{e}seau exposed on them, however they were measured with one clamped on
the glass.
All plates of the Oxford~2 zone were exposed between 1930 
and 1936. (Actually there are two plates that appear to have typographical
errors in their epochs.  One is dated in 1918; the other in 1930, but 8 months
prior to any other plate.)   Mr. Barrett also supervised the 
measurement and reduction of these plates at Oxford, using the
eyepiece scale technique.
However World War~II intervened preventing
the determination of the plate constants for 92 of the fields.  After the
war, the constants for these remaining plates were determined under Dr. H.
Kox at the Hamburg Observatory at Bergedorf.
A detailed introduction covering the participation of the
University Observatory at Oxford in the Astrographic Catalogue project
can be found in Volume~1 of the Oxford~I zone catalogue (Turner 1906-1911),
as well as in the book \underline {The Great Star Map} also by Turner.  An 
introduction to the 
Oxford~II zones can be found in Volume~1 of the Oxford~II zone catalog
(Paris 1953-1954).

\subsection{The Paris Observatory}

The Paris Observatory agreed to photograph the zone with plate centers 
between declinations
+18 and +24 degrees.  The telescope used was the original Henry brothers'
instrument, after which all other AC telescopes were supposed to be patterned.
In total, 1261 plates were photographed and measured.  The measuring technique
employed at Paris was the short-screw method, which was the
most accurate utilized with the AC plates.
The epoch range of the plates are
from October 1891 through November 1927, however only 7 plates were exposed
after 1907 and all but 100 were exposed prior to 1900.
An introduction to the Paris Observatory's participation in the Astrographic
Catalogue can be found in the introductions to the individual volumes
(Paris 1902-1932).

\subsection{The Bordeaux Observatory}

The Bordeaux University Observatory, located in Floirac, France,
was assigned the zone between +11 and +17 degrees
declination on which to center its plates.  The telescope used was a similar
design to the Paris instrument and was built by the Henry brothers.
In total, 1260 plates were exposed between 1893 and 1925, all but five being
taken before 1913.  The plates were measured at Bordeaux using the 
short-screw method.
An introduction to the Bordeaux Observatory's participation in the
Astrographic Catalogue project can be found in Volume~1 of the published data
(Paris~1905-1934).

\subsection{The Toulouse Observatory}

The Toulouse University Observatory (France)
agreed to participate in the Astrographic
Catalogue project by taking plates centered between +5 and +11 degrees 
declination.  In total, 1260 were exposed and measured.  The epochs vary
from 1893 to 1935, and were taken in three fairly distinct groupings.  Most
were exposed before the end of 1910.  Another set is taken between 1918 and
1922.  The last few plates are scattered between 1930 and 1935.  All the 
plates were measured using a short-screw type measuring machine;
however, not all plates were measured at Toulouse.  Ninety plates were measured
at the Bordeaux University Observatory and 36 were measured at the Paris
Observatory.
Various aspects of the work are detailed in the introductions
of the printed volumes (Paris 1903-1948).

\subsection{The Algiers Observatory}

The Algiers Observatory was assigned the zone between --2 and +4 degrees on
which to center its plates.  All 1260 plates were exposed 
between 1891 and 1911.  The plates were measured using the 
short-screw method.  
Details about the Algiers Observatory's participation in the
Astrographic Catalogue project can be found in the introduction to the
catalogues (Tr\'{e}pied 1903,Paris 1903-1924).

\subsection{The San Fernando Observatory}

The Naval Observatory of San Fernando (Spain) was assigned the area between
--3 and --9 degrees declination on which to center its plates.  The telescope
used was built by Gautier, with the objective made by the Henry brothers.
All of the 1260 plates were exposed between 1891 and 1917.  Over 1000 were 
taken before 1899, then only a few per year until 1917.  The plates were
measured using a short screw micrometer.  
An introduction to San Fernando's participation in the Astrographic Catalogue
project can be found in Volume~1 of the published data (San Fernando 1921-1929).

\subsection{The Tacubaya Observatory}

At the meeting of the International Congress which established the
Astrographic Catalogue, the
zone from --10 to --16 degrees was assigned to the National Astronomical 
Observatory of Tacubaya, located near Mexico City, Mexico.   
In total, 1260 plates were exposed and measured in the Tacubaya zone.
(Actually, one of the plates had an incorrect and unknown plate center and
has been discarded from the reductions, leaving a total of 1259 plates).
All but five plates were exposed between 1900 and 1912.  The five later 
plates were exposed between 1926 and 1938.
All the plates were measured using the eyepiece scale method.
An introduction to the history
of the work can be found in Volume~1 part~1 of the --15 degree zone
(Tacubaya, 1913-1962).

\subsection{The Cordoba Observatory}

At the 1887 Paris meeting, the
zone from --24 to --31 degrees was assigned to the La Plata Astronomical   
Observatory.  In~1900, the zone was re-assigned to Cordoba.  The telescope
was installed at the end of~1901.  In~1908, Dr. Thome, the Director of Cordoba,
died and Dr. Perrine was named new director.  After some investigations,
Perrine decided  to re-observe all areas.  He discovered that the telescope
was out of focus and many of the plates were impaired, and that the plates
were centered on apparent place coordinates, not at those defined at
equinox 1900.  Plates of this series were exposed starting in~1909 and 
finished by the end of~1913.  These plates were measured between~1909 and
1920.  In total, 1360~plates were exposed as part of the Astrographic 
Catalog.

The telescope used was one of the Henrys' design and build, following the 
standard with a 33~cm
aperture and 3.47~m focal length.  In the introduction written by 
Perrine, he states that the guiding is difficult because the guide scope has
only a 19~cm aperture, as opposed to the more conventional 25~cm in use
by most of the participating observatories.  The mount was built by Gautier.
Some plates showed a ``triangular distortion'' that was traced to a warp in the
ring which held the lens in place.  This ring was replaced in~1911.  The 
lens, from August~9,~1910 until the end of the program, was stopped down to 
11~ inches.  This, according to Perrine, greatly improved the image quality.

Virtually all plates were taken and developed by R. Winter or F.P. \linebreak Symonds.
Four exposures on each plate were made; two long exposures of the same
duration (both of 5~or 6~minutes) one medium exposure (of~60 to 90~seconds)
and one short exposure (of~5 to 8~seconds).  The telescope was moved in 
declination between exposures.  In order to expedite the work, two measuring
machines of the short-screw type were retro-fitted with eyepiece 
scales.  As a result, 140~plates were measured using the short-screw
method, the remaining 1220~plates were measured using the eyepiece
scale method.  In total, five different 
measuring machines were used, allowing each measurer to have his or her 
own machine.  
The r\'{e}seaux used were supplied by Gautier and Prin; four were used
throughout the work.
Investigations of two of the r\'{e}seaux were made in 
Paris and the deviations were found to be negligible; no corrections
for the r\'{e}seaux were applied to the measures.
Only stars within one degree in right ascension and declination of the plate
center were measured.  All stars having three images were measured
unless images ran together, which was the case of 
the brightest stars.  Four measures were made on each star; a measure was made
on both of the long exposures in both orientations of the plate.
(Following an initial measurement of all stars, the plate was reversed 180
degrees and all stars re-measured.)
In general, measures in the direct and reverse
orientations of the plate were made on the same day by the same measurer.
In total, 37~man-years went into measuring the plates.
Various aspects of the work are detailed in the introduction of 
Volume~26 of the Observatory Results (Cordoba 1925-1934).

\subsection{The Perth Observatory}

At the International Congress which established
the Astrographic Catalogue, the Observatory
of Rio de Janeiro was assigned to photograph the area between --32 and --40
degrees declination.  In 1900, the work at Rio had not progressed and so the
Perth Observatory undertook the task.  The telescope used was from Sir 
Howard Grubb, and was of similar design to other telescopes used for the
AC work.  
Although observing was progressing, no resources were available to measure the
plates.  At this time, the Perth Observatory was primarily a meteorological
station, and the meteorological work took precedence.  This changed 
in 1908 when the Australian Federal Government established the 
Australian Weather Bureau.  About this time, four women were hired as plate  
measurers.  Professor Dyson of the Edinburgh Observatory
offered assistance in the measuring.  Perth accepted this offer and started
sending those plates of the --40~degree zone.
By 1915, the Edinburgh 
Observatory completed its commitment by measuring all of the plates centered
on the --40, --39 and --38 degree
band.  This area is known as the Perth-Edinburgh AC zone.
Observing continued at Perth until 1919, at which time all areas had been
photographed.  Personnel at Perth measured all plates between --37 and --32
degrees; this is known as the Perth zone.
In total, 432~and 944~plates make up the Perth-Edinburgh and Perth zones,
respectively.

All plates had three exposures taken, one of 4~minutes, 2~minutes and
13~seconds, or that of 6~minutes, 3~minutes or 20~seconds.  The change in
exposure times took place following a 1909 meeting of key personnel from
different observatories participating in the AC.  At that meeting, many
people expressed concern about the uniformity of limiting magnitudes on
different plates.  Many of the Perth plates were re-examined and found
to be unsatisfactory.  The areas affected were re-observed and a method 
of ensuring more uniformity was developed.

In general, no guiding of the instrument other than the sidereal drive
was made, as it was found unnecessary.  All plates were the brand
Ilford ``special rapid''.  All were measured using an eyepiece scale machine,
similar to the Oxford Observatory's.  For all but 5~plates, the measurements
done at Perth were made in two orientations of the plate by the same
person; the plate being rotated 180 degrees between measurements.  In total,
10~measurers were used at Perth.
For the plates measured at Edinburgh, images were measured in two orientations
of the plate, with the plate
being rotated 180 degrees between measurements.  For the direct orientation,
the second exposure (either 2~or 3~minutes) was measured; the longest 
exposure was measured with the plate in reverse orientation.  Quite often
more than one measurer was used on each plate. 
Various aspects of the work can be found in the introduction to Volume~23
of the Perth-Edinburgh data (Perth 1922, Paris 1949-1952) and in Volumes
1~and~17 of the Perth data (Perth 1911-1921).

\subsection{The Royal Observatory at the Cape of Good Hope}

The Royal Observatory at the Cape of Good Hope, South Africa, took the zone
between --41 and --51 on which to center its plates.  In all, 1512 plates 
were exposed and measured.  The epochs range from 1897 to 1912, with 97\%
of them being exposed prior to 1906.  The telescope used was built by 
Sir Howard Grubb.  Two machines were
used to measure the plates, both were designed by David Gill and built by
Repsold of Hamburg (Gill 1898).
Both machines employed the short-screw measuring method and
were of similar design.
An introduction to the participation of the Royal Observatory at the 
Cape of Good Hope in the Astrographic Catalogue
project can be found in Volume~1 of the published data (London 1913-1926) .

\subsection{The Sydney Observatory}

H.C. Russell, the Government
Astronomer at Sydney, was in attendance at the 1887
meeting of the International Congress.  He committed the Sydney Observatory
to photograph the sky between declinations --52 and --64 degrees.
The lens used for the project was built by Howard
Grubb of Dublin, and it followed the general design established by the 
International Congress.  The lens was
delivered in December of 1890.  Most of the telescope was built in Sydney. 
The observing program began in earnest 
in 1892.  The telescope was moved twice in the course of the AC work; first 
from inside Sydney to Redhill (located about 12 miles from Sydney) in 1899,
and then back to its original location in 1931.  The observing was left  
unchanged until 1912, when W.E. Cooke took over the project.  He was unsatisfied
with the quality of many plates and eventually rejected and rephotographed many
of the areas.  Until this time, plates were being sent to Melbourne for 
measurement, but under Cooke the Sydney Observatory began to measure their own
photographs.  Prior to Cooke's arrival, plates were positioned so the center
of the plate was in the sharpest focus (The astrograph used in photographing
the plates did not have a flat field of focus, so some areas of the plate
are in focus while others are not.  This is true for all the telescopes used
in the Astrographic Catalogue work).  Cooke altered this and made the ring
about 50~arcmin from the center the place with the sharpest focus.  In 1926,
Cooke retired and James Nagle took over.  He altered the place of best focus
in a ring about 40~arcmin from plate center.  Nagle died in 1941, and 
H.W. Woods took over.  Some plates were found unsatisfactory or missing.  The
remaining areas were photographed between 1944 and 1948.
In total, 1400~plates were taken as part of the Astrographic Catalogue.
All plates exposed between 1890 and 1930 were taken by James Short.

Plate measuring did not start for about six years after the first plates 
were taken.  Evidently there was a suggestion about having all plates from 
all participating observatories sent to Paris for 
measurement.  This plan was not ever put in place, but the Australians liked 
this idea so they decided that Melbourne would be used to measure both the
Sydney and Melbourne plates.  As mentioned above, this changed with Cooke's
arrival and Sydney started measuring their own plates.  There were four
short-screw measuring machines used in Melbourne, and two eyepiece
scale machines used at Sydney.
From this point on, all stars were measured twice with the plates being
rotated 180 degrees between measurements.
Various aspects of the work are detailed in the introduction of 
Volume~53 of the data (Sydney 1925-1971).

\subsection{The Melbourne Observatory}

In 1887, following the meeting which established
the Astrographic Catalogue, the British government agreed to have the 
Melbourne Observatory participate in the project.  Melbourne was assigned
the zone from --65 to --90 degrees.  The telescope used was built by Howard
Grubb of Dublin, and it followed the general design established by the 
International Congress.  The telescope was
delivered in December of 1890.  The observing program started about one year
later in January~1892 and continued until 1927 (Actually, one plate was 
exposed in 1940).  Over 80\% of the plates were exposed prior to 1898.
In total, 1149~plates were taken as part of the Astrographic Catalogue.
All plates had three exposures of 5~minutes,
2.5~minutes and 20~seconds duration, with the exception of the plates taken
prior to February~26,~1892, whose exposures were slightly longer.  The
r\'{e}seau was exposed on the plates shortly after the plates were removed
from the telescope.
In total, six different r\'{e}seaux were used during the
program; three were supplied by Gautier and three were made at Melbourne.

Plate measuring did not commence in earnest until November 1898, when six
women were hired at Melbourne.  Two measurers were used for each plate, one
taking the northern half and one the southern.  The plates were rotated 
180 degrees and each half was remeasured by the same person.
All reference stars on each plate were measured
by both measurers.
Four measuring machines were used throughout most of the work; all used
short-screws for the star measurements.
The Melbourne staff tried using
an eyepiece scale measuring machine for the plates but found the measuring
error too high.

Periodic and progressive screw errors were investigated.
These were not applied, as they were found to be negligible by the Melbourne
astronomers.  (Investiations of the screw errors performed at the
U.S. Naval Observatory as part of the AC~2000 work show this not to be
true.)  Investigations into errors of the r\'{e}seaux were made and these
corrections were applied to the data prior to publishing.
Various aspects of the work are detailed in the introduction of 
Volume~1 of the data (Melbourne 1926-1929; Paris 1955-1958; Sydney 1963).

\newpage
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\bibitem{Paris2}
Paris, 1953-1954, Astrographic Catalogue 1900.0, Potsdam-Oxford Section, Vol 1-2
\bibitem{Par8}
Paris, 1955-1958, Melbourne Astrographic Catalogue 1900.0, Vol 4 through 7
\bibitem{Paris1}
Paris, 1960 and 1962, Catalogue Photographique du Ciel, Zone Uccle-Paris,
Vol 1 and 2
\bibitem{Per1}
Perth, 1911-1921, Astrographic Catalogue 1900.0, Perth Section, Vol 1
through~24
\bibitem{Per2}
Perth, 1922 , Astrographic Catalogue 1900.0, Perth Section, Vol 33
\bibitem{Polo1}
Polozhentsev, D., Potter, K., Sal'Es, R., Selaiia, K., \& Bystrov, N.,
1989, Astronomicheskii Zhurnal 66 425
\bibitem{Pot1}
Potsdam, 1889-1915, Publicationen des Astrophysikalishen Observatoriums zu
Potsdam, Photographische Himmelskarte Catalog, Vol 1 through 7
\bibitem{SF1}
San Fernando, 1921-1929, Cat\'{a}logo Astrogr\'{a}fico para 1900.0,
secci\'{o}n del Observatorio de Marina de San Fernando, Vol 1 through 8
\bibitem{Sin1}
Sinnot, R.W., 1988,  NGC 2000.0, The Complete New General Catalogue and Index
Catalogue of Nebulae and Star Clusters by J. L. E. Dreyer, ed. R. W. Sinnott,
Sky Publishing Corporation and Cambridge University Press 
\bibitem{Syd1}
Sydney, 1925-1971, Astrographic Catalogue 1900.0, Sydney Section, Vol~1
through~53
\bibitem{Syd2}
Sydney, 1963, Melbourne Astrographic Catalogue 1900.0, Vol 8
\bibitem{Tacu1}
Tacubaya, 1913-1962, Catalogo Astrofotografico 1900, Vol. 1 through~7
\bibitem{Trepied}
Tr\'{e}pied, C. 1903, Observatoire D'Alger Catalogue Photographique du Ciel,
Introduction
\bibitem{Turner1}
Turner, H.H., 1906-1911, Astrographic Catalogue 1900.0, Oxford Section, vol 1
through 7
\bibitem{Turner2}
Turner, H.H., 1912, The Great Star Map, John Murray
\bibitem{Urban1}
Urban, S.E. and Corbin T.E., 1996, A\&A {\bf 305} 989
\bibitem{Urban2}
Urban, S.E., Martin, J.C., Jackson E.S. and Corbin, T.E., 1996,
A\&AS {\bf 118} 163
\bibitem{Urban3}
Urban, S.E., Corbin, T.E., Wycoff, G.W., Martin, J.C.,
Jackson, E.S, Zacharias, M.I., and Hall, D.M., 1998,
AJ 115 1212
\bibitem{Vatican}
Vatican, 1914-1928, Catalogo Astrografico 1900.0, Sezione Vaticana, Vol 1-10
\bibitem{Worley}
Worley, C.E. and Douglass, G.G., 1996, The Washington Double Star Catalog
\bibitem{Zach1}
Zacharias, N., de Vegt, C. Nicholson, W. and Penston, M.J., 1992,
\newline A\&A {\bf 254} 397
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Zacharias, N., Zacharias, M.I., Douglass G.G., and Wycoff, G.L., 1996,
AJ {\bf 112} (5), 2336
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Zacharias, N. \& Zacharias M., 1999, AJ 118 2503
\bibitem{Zach4}
Zacharias, N., Zacharias M., \& de Vegt, C., 1999, AJ 117 2895
\end{thebibliography}


\newpage
\appendix
\section{Notes on Participating Observatories Data Characteristics}
\begin{itemize}
\item{Greenwich notes:}
\begin{itemize}
\item{Five plates are centered on the pole.}
\item{A duplex micrometer was used; two plates were measured simultaneously.
 Formats of the  published volumes reflect this.}
\end{itemize}

\item{Vatican notes:}
\begin{itemize}
\item{One plate has a published epoch of 1891.}
\item{A measuring grid was used instead of eyepiece scale or screw.}
\item{Most plates were measured by one of three women.  Measurer ``E'', who measured
   about 50\% of the plates, was significantly worse than the other two.}
\item{Plate weights, computed at USNO, are based on measurer.}
\end{itemize}

\item{Catania notes:}
\begin{itemize}
\item{Over 95\% of the plates were exposed prior to 1906.}
\item{Errata are found throughout volumes, mostly at the end of each plate's
$x,y$ data.}
\item{Measures of large images (bright stars) are often listed many times
   (with slightly different values).}
\item{Multiple stars were often measured both as center of light AND individual
   images.}
\item{One plate has been taken with the same plate center as another, but only
   faint stars measured on the second.  Hence only reference stars near the
   edges were available on that plate.}
\item{Many typographical errors in the printed volumes were found by USNO.  These
   have been corrected.}
\end{itemize}

\item{Helsinki notes:}
\begin{itemize}
\item{Over 95\% of the plates were exposed before 1897.}
\item{Helsinki was under Russian rule during the period of exposure and
measurement of the plates.}
\end{itemize}

\item{Potsdam notes:}
\begin{itemize}
\item{The number of plates exposed was 1226, of which only 406~ were
measured and published.  No funds after World War~I were available to continue
the work.}  
\item{All but 34~plates were destroyed during World War~II.}
\item{In cases where stars were measured and published twice, USNO used the 
mean of the measures in the reductions.}
\item{Personal equation tables (describing observer dependent magnitude equation)
are published.  USNO developed its own corrections by observer that supersedes
the Potsdam tables.}
\item{Generally, only stars brighter than 11.0 were measured}
\item{Plate weights, computed at USNO, are based on measurer.}
\end{itemize}

\item{Hyderabad North notes:}
\begin{itemize}
\item{Nizamiah Observatory had the only instrument not of standard design.
  Objective diameter was 20~cm (not 33~cm) so longer exposures were required
  to achieve the desired limiting magnitude.  The plate scale was approximately
  61~arcsec/mm.}
\item{This zone was photographed in response to the
Potsdam region not being completed.}
\item{India was under British rule during the period of exposure
and measurement of the plates.}
\end{itemize}

\item{Uccle notes:}
\begin{itemize}
\item{This zone was photographed in response to the
Potsdam region not being completed.}
\item{One plate was broken prior to diameter measurements.}
\item{Measurements were made at Paris.}
\item{Hour angles of exposures are not given.}
\end{itemize}

\item{Oxford~II notes:}
\begin{itemize}
\item{This zone was photographed in response to the
Potsdam region not being completed.}
\item{Thirty two plates in this zone were exposed and measured at Greenwich.  These
   are the only plates of the AC without a reseau printed on them.}
\item{One plate has a published epoch of 1918, 12 years prior to the 
supposed start of this region.}
\item{Kox (Hamburg Observatory) determined plate constants for 92 of the plates.
   All others were computed at Oxford.}
\end{itemize}

\item{Oxford~I notes:}
\begin{itemize}
\item{Some reseaux had rulings of 5.04 mm (5.00~mm was standard). 
   Introductions indicate which ones, but the introduction appears to be wrong
   for 3~plates.}
\end{itemize}

\item{Paris notes:}
\begin{itemize}
\item{Only 7~plates were exposed after 1907.}
\item{Corrections indicated in the ARI version (1991) of the keypunched data
 have been applied.}
\item{Additional typographic errors found in Bull. of CDS 12 (p32-40) by Dunham
   and Herget were applied, where needed.}
\item{One plate was printed with the $x,y$ measures of two plates (see end of
 Volume~2).}
\item{Nine plates were measured using {\em Baillaud method}, not utilizing the
   reseau.  Since the field distortion pattern applied during 
   USNO's redudction is believed to arise from the reseaux, these
   corrections were not applied to these nine plates.}
\item{Notes indicate that several stars were  not measured to their full
 precision (0.1 microns).  Images were not kept if the $x,y$ values were not
 given to 1.0 micron or better.}
\end{itemize}   

\item{Bordeaux notes:}
\begin{itemize}
\item{Both Toulouse and Bordeaux have plates centered on +11 degrees.}
\item{Only five plates were taken after 1913.}
\item{Corrections indicated in the ARI version (1991) of the keypunched data
  have been applied.}
\item{Many more typographical errors were found by USNO in this zone than
  most other zones.}
\end{itemize}

\item{Toulouse notes:}
\begin{itemize}
\item{Both Toulouse and Bordeaux have plates centered on +11 degrees.}
\item{Ninety plates were measured at Bordeaux and 36~plates were measured at
  Paris.}
\item{Corrections indicated in the ARI version (1991) of the keypunched data
  have been applied.}
\item{Notes indicate that several stars were not measured to their full
   precision (0.1 microns).  Images were not kept if the $x,y$ values were not
   given to 1.0 micron or better.}
\item{The odd zones(+5,7,9 and 11) are split.  The
   plates of the first part (usually 0 to about 6h)
   do not have reseaux corrections applied, but information
   was given as to which
   measuring machine (1 or 2) and which reseau was used.  After the split,
   there is no information regarding micrometer or reseaux. 
   For the even zones, there is information regarding where the plates were
   measured and often what types of plate emulsions were used.  However, there
   are no data regarding which reseau was used.}
\end{itemize}

\item{Algiers notes:}
\begin{itemize}
\item{Algeria was under French rule during the AC data acquisition.}
\end{itemize}

\item{San Fernando notes:}
\begin{itemize}
\item{Y-coordinate increases to South}
\item{80\% of the plates were taken before mid-1898.}
\item{One plate was exposed with Saturn and 3 of its satellites.}
\item{Four records have footnotes saying ``body moved during exposure of the
   plate''.}
\end{itemize}

\item{Tacubaya notes:}
\begin{itemize}
\item{All but five plates were taken before 1913.}
\item{One of the plates was not used by USNO because it has an unknown plate
   center.}
\item{Many typographical errors in the printed volumes were found by USNO.
  These have been corrected.}
\item{The type is very poor in some of the volumes.}
\end{itemize}

\item{Hyderabad South notes:}
\begin{itemize}
\item{The Nizamiah Observatory had the only instrument not of standard design.
  The objective's diameter was 20~cm (not 33~cm) so longer exposures were
  required to achieve the desired limiting magnitude.  The plate scale
  is approximately 61~arcsec/mm.} 
\item{India was under British rule during the program.}
\item{Five reseaux were used, some with non-standard rulings.}
   Rulings of~5.00, 5.04~and 4.985~mm used.
\item{Y increases to South.}
\end{itemize}

\item{Cordoba notes:}
\begin{itemize}
\item{1220 plates were measured using an eyepiece scale, 140~were measured with
  a short-screw.}
\item{Errata were found in Information Bulletin of CDS 22 79-86 (1982).}
\item{Lens was stopped down to 28~cm in August 1910 to give better images.}
\item{Reseaux with rulings of 5.00~mm were used for all plates except those
   numbered 2001~through~2290. These have 5.05~mm between rulings.  Note that
   this is slightly different than what is given on page~xviii of Volume~26.}
\item{Many typographical errors in the printed volumes were found at USNO.
   These have been corrected.}
\end{itemize}

\item{Perth notes:}
\begin{itemize}
\item{This zone covers only those plates that were both photographed {\em AND}
measured at Perth (see Perth-Edinburgh notes).}
\item{A change of scale for plate~2063 through 2209 is present.  This was
  the result of someone altering the telescope focus.}
\item{A Scale value, usually given as a letter, is used as an estimate of
 magnitude for all but the brightest stars.}
\item{Very few typographical errors were found at USNO.}
\end{itemize}

\item{Perth-Edinburgh notes:}
\begin{itemize}
\item{This zone covers plates taken at Perth, but measured at Edinburgh,
 Scotland.}
\item{Very few typographical errors were found at USNO.}
\item{Y increases to South.}
\end{itemize}

\item{Cape notes:}
\begin{itemize}
\item{Images measured with micrometer one have significantly lower mean
   errors than those measured with micrometer two.}
\item{Actual diameters were measured for many stars, but the faintest stars
   were given a ``density'' measurement, dependent on how dark each image
   appears. }
\item{South Africa was under British control during the AC work.}
\end{itemize}

\item{Sydney notes:}
\begin{itemize}
\item{The telescope was relocated twice during the AC work.}
\item{The plate location of sharpest focus altered during the work, depending
   on observatory director (see Section~12).}
\item{Plates measured prior to 1912 were sent to Melbourne for measurement,
   using screw method. Later, the plates were measured at Sydney with
   an eyepiece scale.}
\item{The plates were exposed in three discrete epoch spans, 1892 to 1901,
   1918 to 1929, and 1944 to 1948.}
\item{Many typographical errors in the printed volumes were found at USNO.
   These have been corrected.}
\item{Authors suspect a magnitude equation by measurer, but no identification
   of the measurers of individual plates is given.}
\item{Scale value as estimate of magnitude is given for the majority of images.}
\item{X increases to the West}
\end{itemize}

\item{Melbourne notes:}
\begin{itemize}
\item{Over 80\% of the plates were taken before 1898.}
\item{One plate has an epoch of 1940.}
\item{Additional Melbourne errata were found in Sydney Volume 53, pg 64.}
\end{itemize}
\end{itemize}

\newpage
\begin{table}    
\caption{Byte-by-byte description of AC~2000.2 using format
requested by the CDS.}
\begin{flushleft}
\begin{tabular}{lllll}
\hline\noalign{\smallskip}
   Bytes & Format & Units &    Label &  Explanations        \\
\noalign{\smallskip}
\hline\noalign{\smallskip}
   1- 2& I2   &  h     & RAh           &   Right Ascension (hours)   \\
   4- 5& I2   &  min   & RAm           &   Right Ascension (minutes) \\
   7-12& F6.3 &  s     & RAs           &   Right Ascension (seconds) \\
     14& A1   &  ---   & DE-           &   Declination (sign)  \\
  15-16& I2   &  deg   & DEd           &   Declination (degrees)\\
  18-19& I2   &  arcmin& DEm           &   Declination (minutes) \\
  21-25& F5.2 &  arcsec& DEs           &   Declination (seconds) \\
  27-31& F5.2 &  mag   & B(mag)        &   Magnitude - Tycho-2 ${\rm B_T}$ if col 86-91 are \\ 
       &      &        &               &   non-blank; else from image diameters \\
  33-40& F8.3 &  yr    & Ep            &   Mean epoch of position \\
  42-43& I2   &  ---   & Num           &   Number of images used \\
  44-49& F6.3 &  arcsec& e\_RAs        &   ?Standard deviation of mean, RA \\
  50-55& F6.3 &  arcsec& e\_DEs        &   ?Standard deviation of mean, Dec \\
  57-64& I8   &  ---   & AC2000        &   AC 2000 Number \\
  66-71& I6   &  ---   & HIPP          &   ?Hipparcos Number\\
  73-84& A12  &  ---   & TYCHO-2       &   ?Tycho-2 ID\\
  86-91& F6.3 &  mag   & V(mag)        &   ?Magnitude - Tycho-2 ${\rm V_T}$ else blank\\
  92-92& I1   &  ---   & MGFL          &   ?Magnitude flag \\
  93-93& I1   &  ---   & VER           &   ?Verification Flag \\
\noalign{\smallskip}
\hline
\label{tab:format}
\end{tabular}
\end{flushleft}
\end{table}

\begin{table}[h!]
\caption{Characteristics of each observatory's plates}
\begin{flushleft}
\begin{tabular}{llclrc}
\hline\noalign{\smallskip}
Zone        & Country   & declination& mearuring & num of  &    epoch \\
            & or region & of centers & technique & plates  &          \\
\noalign{\smallskip}
\hline\noalign{\smallskip}
Greenwich   & England   &  +90  +65 & scale &  1153 & 1892  1905 \\
Vatican     & Italy     &  +64  +55 & grid  &  1046 & 1895  1922 \\
Catania     & Sicily    &  +54  +47 & screw &  1010 & 1894  1932 \\
Helsinki    & Finland   &  +46  +40 & screw &  1008 & 1892  1910 \\
Potsdam     & Germany   &  +39  +32 & screw &  406  & 1893  1900 \\
Hyderabad N & India     &  +39  +36 & scale &  592  & 1928  1938 \\
Uccle       & Belgium   &  +35  +34 & screw &  320  & 1939  1950 \\
Oxford II   & England   &  +33  +32 & scale &  320  & 1930  1936 \\
Oxford~I    & England   &  +31  +25 & scale & 1188  & 1892  1910 \\
Paris       & France    &  +24  +18 & screw & 1261  & 1891  1927 \\
Bordeaux    & France    &  +17  +11 & screw & 1260  & 1893  1925 \\
Toulouse    & France    &  +11  +5  & screw & 1260  & 1893  1936 \\
Algiers     & Algeria   &  +4  --2  & screw & 1260  & 1891  1912 \\
San Fernando& Spain     &  --3 --9  & screw & 1260  & 1891  1918 \\
Tacubaya    & Mexico    & --10 --16 & scale & 1259  & 1900  1938 \\
Hyderabad S & India     & --17 --23 & scale & 1260  & 1914  1929 \\
Cordoba     & Argentina & --24 --31 & both  & 1360  & 1909  1913 \\
Perth       & Australia & --32 --37 & scale &  944  & 1902  1919 \\
Perth-Edinb.& Australia & --38 --40 & scale &  432  & 1903  1914 \\
Cape        & S. Africa & --41 --51 & screw & 1512  & 1897  1912 \\
Sydney      & Australia & --52 --64 & both  & 1400  & 1892  1948 \\
Melbourne   & Australia & --65 --90 & screw & 1149  & 1892  1928 \\
\noalign{\smallskip}
\hline
\label{tab:obschar1}
\end{tabular}
\end{flushleft}
\end{table}

\begin{table}[h!]
\caption{Numbers of images in each zone and institutions aiding in keypunching
the data, by zone}
\begin{flushleft}
\begin{tabular}{lccl}
\hline\noalign{\smallskip}
Zone        &  stars  &  images & keyed and verified \\
            &(thousand)&(thousand)&                  \\
\noalign{\smallskip}
\hline\noalign{\smallskip}
Greenwich   & 179 & 322 & USNO         \\
Vatican     & 256 & 480 & CIDA, Venezuela (verified USNO)  \\
Catania     & 163 & 320 & USNO          \\
Helsinki    & 159 & 284 & USNO          \\
Potsdam     & 108 & 143 & CIDA, Venezuela (verified USNO)   \\
Hyderabad N & 149 & 242 & USNO          \\
Uccle       & 117 & 159 & USNO          \\
Oxford II   & 118 & 161 & USNO          \\
Oxford~I    & 277 & 471 & Strasbourg    \\
Paris       & 254 & 436 & Strasbourg    \\
Bordeaux    & 224 & 355 & Strasbourg    \\
Toulouse    & 270 & 433 & Strasbourg    \\
Algiers     & 200 & 330 & Strasbourg    \\
San Fernando& 226 & 346 & USNO          \\
Tacubaya    & 312 & 518 & USNO          \\
Hyderabad S & 293 & 521 & USNO          \\
Cordoba     & 309 & 467 & Sternberg, Russia \\
Perth       & 228 & 402 & USNO          \\
Perth-Edinb.& 139 & 202 & USNO          \\
Cape        & 545 & 901 & USNO          \\
Sydney      & 431 & 743 & USNO          \\
Melbourne   & 218 & 392 & Univ of Fla., USNO  \\
\noalign{\smallskip}
\hline
\label{tab:keypunch}
\end{tabular}
\end{flushleft}
\end{table}

\begin{table}[h!]
\caption{Personnel involved in USNO plate reductions}
\begin{flushleft}
\begin{tabular}{lll}
\hline\noalign{\smallskip}
Zone        &    prepared&  reduced \\
\noalign{\smallskip}
\hline\noalign{\smallskip}
Greenwich    &  Gary Wycoff, John Martin               & Sean Urban \\
Vatican     &  John Martin                            & Sean Urban  \\
Catania     &  John Martin, Gary Wycoff               & Sean Urban  \\
Helsinki    &  Harry Crull, Edward Jackson, David Hall & Sean Urban  \\
Potsdam     &  Marion Zacharias                       & Marion Zacharias  \\
Hyderabad N &  Edward Jackson                         & Sean Urban  \\
Uccle       &  Edward Jackson                         & Sean Urban  \\
Oxford II   &  John Martin                            & Sean Urban  \\
Oxford~I    &  John Martin                            & Sean Urban  \\
Paris       &  Edward Jackson                         & Sean Urban  \\
Bordeaux    &  Edward Jackson                         & Sean Urban  \\
Toulouse    &  David Hall                             & Sean Urban  \\
Algiers     &  Edward Jackson                         & Sean Urban  \\
San Fernando&  Gary Wycoff                            & Sean Urban  \\
Tacubaya    &  John Martin, Gary Wycoff               & Sean Urban  \\
Hyderabad S &  Edward Jackson, Sean Urban             & Sean Urban \\
Cordoba     &  Gary Wycoff                            & Sean Urban  \\
Perth       &  David Hall, Gary Wycoff, John Martin   & Marion Zacharias  \\
Perth-Edinb.&  David Hall, Gary Wycoff                & Sean Urban  \\
Cape        &  Sean Urban                             & Sean Urban  \\
Sydney      &  David Hall, Gary Wycoff                & Sean Urban  \\
Melbourne   &  Gary Wycoff                            & Sean Urban  \\
\noalign{\smallskip}
\hline
\label{tab:people}
\end{tabular}
\end{flushleft}
\end{table}

\begin{table}
\caption[Corrections applied to x,y data prior to final least squares
adjustment.  Also includes single image precisions by zone.]{Corrections applied
to x,y data prior to final least squares adjustment.  Also includes single
image precisions by zone.

\vspace*{.10in}
In the table, a ``Y'' indicates a correction was applied,
an ``n'' indicates it was not.
Values in parentheses indicates an additional dependence on those
characteristics.

\vspace*{.10in}
mg=magnitude, mr=measurer, mp=microscope, rs=reseau, ep=epoch, \\
x=x-coordinate, and y=y-coordinate.

\vspace*{.10in}
Note that Ox~II/Grn ``zone'' refers
to the 32~plates observed at Greenwich for the Oxford~II zone.}
\begin{flushleft}
\begin{tabular}{llllllll}
\hline\noalign{\smallskip}
 Zone       & radial dist& Mag Eq.      & Coma  & Screw & FDP      &$\overline{\sigma}$ ra  &  $\overline{\sigma}$ dec \\
\noalign{\smallskip}
\hline\noalign{\smallskip}
Greenwich   &  Y(mg)     & Y            & n     & n     & n        & .29 & .30 \\
Vatican     &  Y(mg)     & Y            & n     & Y(mr) & Y(mp)    & .42 & .44 \\
Catania     &  Y(mg)     & Y(x,y)       & n     & n     & Y(mg)    & .33 & .30 \\
Helsinki    &  Y(mg)     & Y(x,y)       & Y     & Y(mr) & Y        & .23 & .22 \\
Potsdam     &  n         & Y(mr)        & Y     & n     & Y        & .26 & .25 \\
Hyder. N    &  Y         & Y(x,y)       & Y     & n     & Y(mg)    & .33 & .30 \\
Uccle       &  Y(mg,x,y) & Y            & Y     & Y     & Y(mg)    & .33 & .38 \\
Oxford~II   &  n         & Y(x,y)       & n     & n     & Y        & .33 & .32 \\
Ox~II/Grn   &  Y         & Y            & n     & n     & n        &     &     \\
Oxford~I    &  n         & Y(x)         & n     & n     & Y        & .32 & .31 \\
Paris       &  Y(mg)     & Y            & Y     & Y(mp) & Y(rs)    & .21 & .21 \\
Bordeaux    &  n         & Y(ep)        & n     & Y     & Y(rs)    & .22 & .21 \\
Toulouse    &  Y(mg,mp)  & Y(y)         & n     & Y(mp) & Y(rs)    & .29 & .28 \\
Algiers     &  Y(mg)     & Y(y)         & n     & n     & n        & .19 & .18 \\
San Fer.    &  Y(mg)     & Y            & Y     & n     & Y(mg)    & .32 & .33 \\
Tacubaya    &  n         & Y(x)         & n     & n     & Y(mg)    & .25 & .24 \\
Hyder. S    &  Y(mg)     & Y(x,y)       & Y     & n     & Y(mg,rs) & .31 & .32 \\
Cordoba     &  Y(mg)     & Y(x,y)       & n     & Y(mp) & Y(mg)    & .32 & .29 \\
Perth       &  Y         & Y            & Y     & n     & Y        & .29 & .28 \\
Per-Edin.   &  Y(mg)     & Y(x,y)       & Y     & Y     & Y(mg)    & .29 & .28 \\
Cape        &  n         & Y(x,y)       & Y(ep) & Y(mp) & Y(mg,rs) & .28 & .26 \\
Sydney      &  Y(mg)     & Y(mp,rs,x,y) & n     & Y(mp) & Y(mg,rs) & .44 & .40 \\
Melbourne   &  Y         & Y            & n     & Y(mp) & Y(mg)    & .34 & .32 \\
\noalign{\smallskip}
\hline
\label{tab:const}
\end{tabular}
\end{flushleft}
\end{table}


\begin{table}
\caption[Catalogues used in the ACRS\_1999 (units of mas)]
{Catalogues used in the ACRS\_1999 (units of mas)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~}
\begin{flushleft}
\begin{tabular}{llrrl}
\hline\noalign{\smallskip}
Name & type & $\sigma_{\alpha}$ & $\sigma_{\delta}$ & $\sigma / \sqrt{N}$   \\ 
\noalign{\smallskip}
\hline\noalign{\smallskip}
1ST CAPE FUND 1900  & Transit Circle  &  589 &  564 & Yes \\
2ND CAPE FUND 1900  & Transit Circle  &  529 &  462 & Yes \\
2ND MELBRN GC 1880  & Transit Circle  & 1380 &  859 & Yes \\
3RD MELB GC 1890    & Transit Circle  & 1507 & 1117 & Yes \\
ABBADIA 00 --3/--9  & Transit Circle  &  975 &  849 & Yes \\
ABBADIA 00 +16/+24  & Transit Circle  &  988 &  810 & Yes \\
ABBADIA 00 --2/+4   & Transit Circle  &  951 &  929 & Yes \\
AGK2  (BERGEDORF)   &  Astrograph &  205 &  198 & No\\
AGK2  (BONN)        &  Astrograph &  261 &  259 & No\\
AGK2a               & Transit Circle  &  165 &  217 & No\\
AGK3                &  Astrograph &  204 &  191 & No\\
AGK3R               & Transit Circle  &   75 &  107 & No\\
ALBANY --2/+1 1900  & Transit Circle  &  840 &  844 & Yes \\
ALBANY --20/--40  00& Transit Circle  &  836 & 1156 & Yes \\
ALBANY 10           & Transit Circle  &  294 &  282 & No\\
ALGER AG   1900     & Transit Circle  & 1156 &  958 & Yes \\
BERGEDORF  I - 25   & Transit Circle  &  432 &  540 & Yes \\
BERLIN 10  79/90    & Transit Circle  &  504 &  617 & Yes \\
BERLIN 1920         & Transit Circle  &  559 &  660 & Yes \\
BONN 00  +40/+50    & Transit Circle  &  506 &  461 & Yes \\
BONN 20             & Transit Circle  &  533 &  504 & Yes \\
BORD 00-II RE-OBN   & Transit Circle  &  397 &  377 & Yes \\
BORDEAUX II  1900   & Transit Circle  & 1038 &  734 & Yes \\
BUCHAREST --11/+11  & Transit Circle  &  381 &  493 & Yes \\
CAMC Series         & Transit Circle  &  176 &  237 & Yes \\
CAPE  I - 50        & Transit Circle  &  368 &  373 & Yes \\
CAPE  II - 25       & Transit Circle  &  468 &  453 & Yes \\
CAPE  III - 25      & Transit Circle  &  474 &  420 & Yes \\
CAPE --40/--52  1900& Transit Circle  &  743 &  671 & Yes \\
\noalign{\smallskip}                     
\hline   
\label{tab:acrs}                
\end{tabular}                            
\end{flushleft}                          
\end{table}     

\addtocounter{table}{-1}
\begin{table}
\caption[Catalogues used in the ACRS\_1999 (units of mas), continued]
{Catalogues used in the ACRS\_1999 (units of mas), continued~~~~~~~~~~~~~~~~~~~~~~~}
\begin{flushleft}
\begin{tabular}{llrrl}
\hline\noalign{\smallskip}
Name & type & $\sigma_{\alpha}$ & $\sigma_{\delta}$ & $\sigma / \sqrt{N}$   \\ 
\noalign{\smallskip}
\hline\noalign{\smallskip}

CAPE 17 --30/--35   &  Astrograph &  391 &  407 & No\\
CAPE 18 --35/--40   &  Astrograph &  319 &  350 & No\\
CAPE 19 --52/--56   &  Astrograph &  298 &  319 & No\\
CAPE 20 --56/--60   &  Astrograph &  210 &  193 & No\\
CAPE 20 --60/--64   &  Astrograph &  196 &  200 & No\\
CAPE 21 --64/--68   &  Astrograph &  182 &  187 & No\\
CAPE 21 --68/--72   &  Astrograph &  190 &  195 & No\\
CAPE 21 --72/--76   &  Astrograph &  211 &  211 & No\\
CAPE 21 --76/--80   &  Astrograph &  186 &  202 & No\\
CAPE 22 --80/--89   &  Astrograph &  176 &  227 & No\\
CAPE G. C. (1900)   & Transit Circle  &  674 &  600 & Yes \\
CAPE I - 25         & Transit Circle  &  469 &  459 & Yes \\
CAPE II - 50        & Transit Circle  &  467 &  588 & Yes \\
CAPE ST 50 --30/--35& Transit Circle  &  742 &  668 & Yes \\
CAPE ST 50 --35/--40& Transit Circle  &  534 &  510 & Yes \\
CAPE ST 50 --52/--56& Transit Circle  &  722 &  608 & Yes \\
CAPE ST 50 --56/--60& Transit Circle  &  330 &  344 & Yes \\
CAPE ST 50 --60/--64& Transit Circle  &  302 &  336 & Yes \\
CAPE ST 50 --64/--68& Transit Circle  &  374 &  398 & Yes \\
CAPE ST 50 --68/--72& Transit Circle  &  376 &  380 & Yes \\
CAPE ST 50 --72/--76& Transit Circle  &  372 &  416 & Yes \\
CAPE ST 50 --76/--82& Transit Circle  &  328 &  370 & Yes \\
CAPE ST 50 --82/--90& Transit Circle  &  226 &  326 & Yes \\
CORDOBA 6429 ST 00  & Transit Circle  &  722 &  715 & Yes \\
CORDOBA D  1950     & Transit Circle  &  589 &  628 & Yes \\
CORDOBA E  1950     & Transit Circle  &  618 &  952 & Yes \\
CPC2                &  Astrograph     & Ind. & Ind. & NA  \\
FAYET +5 TO +15     & Transit Circle  &  559 &  607 & Yes \\
FAYET --5 TO +5     & Transit Circle  &  165 &  240 & No\\
FOKAT               &  Astrograph &  220 &  238 & Yes \\
\noalign{\smallskip}                     
\hline                                   
\end{tabular}                            
\end{flushleft}                          
\end{table}     

\addtocounter{table}{-1}
\begin{table}
\caption[Catalogues used in the ACRS\_1999 (units of mas), continued]
{Catalogues used in the ACRS\_1999 (units of mas), continued~~~~~~~~~~~~~~~~~~~~~~~}
\begin{flushleft}
\begin{tabular}{llrrl}
\hline\noalign{\smallskip}
Name & type & $\sigma_{\alpha}$ & $\sigma_{\delta}$ & $\sigma / \sqrt{N}$   \\ 
\noalign{\smallskip}
\hline\noalign{\smallskip}
GREENWICH 1910      & Transit Circle  &  426 &  324 & No\\
GREENWICH 9Y2       & Transit Circle  &  950 &  854 & Yes \\
GREENWICH I-50      & Transit Circle  &  504 &  487 & Yes \\
GREENWICH II-25     & Transit Circle  &  450 &  466 & Yes \\
HEIDELBERG ZOD 50   & Transit Circle  &  375 &  453 & Yes \\
HIPPARCOS           & Satellite       & Ind. & Ind. & NA  \\
KONIGSBERG 25       & Transit Circle  &  183 &  199 & Yes \\
KONIGSBERG 25-II    & Transit Circle  &  482 &  426 & Yes \\
KUSTNER - BONN 00   & Transit Circle  &  368 &  332 & No\\
LA PLATA 3710 S 50  & Transit Circle  &  712 &  658 & Yes \\
LA PLATA A  1925    & Transit Circle  &  808 &  790 & Yes \\
LA PLATA B  1925    & Transit Circle  &  811 &  679 & Yes \\
LA PLATA C  1925    & Transit Circle  &  801 &  698 & Yes \\
LA PLATA D  1925    & Transit Circle  & 1000 &  867 & Yes \\
LA PLATA E 1925     & Transit Circle  &  911 &  857 & Yes \\
LA PLATA EROS 1930  & Transit Circle  &  500 &  387 & No\\
LA PLATA F  1935    & Transit Circle  &  485 &  518 & Yes \\
LA PLATA GC  1950   & Transit Circle  &  564 &  585 & Yes \\
LEIDEN 25  XV/1     & Transit Circle  &  460 &  576 & Yes \\
LEIDEN 25  XV/2     & Transit Circle  &  458 &  664 & Yes \\
LEIDEN 25  XV/4     & Transit Circle  & 2308 & 2069 & Yes \\
LICK 17 HARVD AG    & Transit Circle  &  246 &  345 & No\\
LICK 28  20/30      & Transit Circle  &  222 &  202 & No\\
LICK ZODIACAL 1900  & Transit Circle  &  424 &  335 & Yes \\
LUND 50 FAINT AG    & Transit Circle  &  710 &  749 & Yes \\
LUND AG 25 35/40    & Transit Circle  &  661 &  696 & Yes \\
MADISON 1910        & Transit Circle  &  444 &  468 & Yes \\
MUNICH A  1900      & Transit Circle  &  681 &  749 & Yes \\
MUNICH B  1900      & Transit Circle  &  730 &  680 & Yes \\
NICOLAEV --5/--20 50& Transit Circle  &  306 &  367 & Yes \\
NICE                & Transit Circle  &  111 &  148 & No\\
PARIS 1900          & Transit Circle  & 1299 &  848 & Yes \\
\noalign{\smallskip}                     
\hline                                   
\end{tabular}                            
\end{flushleft}                          
\end{table}     

\addtocounter{table}{-1}
\begin{table}
\caption[Catalogues used in the ACRS\_1999 (units of mas), continued]
{Catalogues used in the ACRS\_1999 (units of mas), continued~~~~~~~~~~~~~~~~~~~~~~~}
\begin{flushleft}
\begin{tabular}{llrrl}
\hline\noalign{\smallskip}
Name & type & $\sigma_{\alpha}$ & $\sigma_{\delta}$ & $\sigma / \sqrt{N}$   \\ 
\noalign{\smallskip}
\hline\noalign{\smallskip}
PARIS ASTR +17/+25  &  Astrograph &  290 &  323 & No\\
PERTH 83            & Transit Circle  &  211 &  405 & Yes \\
PERTH VOL 2  1900   & Transit Circle  &  717 &  713 & Yes \\
PERTH VOL 3  1900   & Transit Circle  &  899 &  974 & Yes \\
PERTH VOL 4  1900   & Transit Circle  &  844 &  803 & Yes \\
PERTH VOL 5  1900   & Transit Circle  &  909 &  798 & Yes \\
PERTH VOL 6  1900   & Transit Circle  &  763 &  779 & Yes \\
PFKSZ 50            & Transit Circle  &   59 &   62 & No\\
PULKOVA   1900      & Transit Circle  & 1272 &  914 & Yes \\
PULKOVO 10  39/44   & Transit Circle  &  300 &  288 & No\\
SAN LUIS 1910       & Transit Circle  &  716 &  661 & Yes \\
SCHWACHER STERNE    & Transit Circle  &  108 &  148 & No\\
SRS                 & Transit Circle  &  268 &  367 & Yes \\
STRASBOURG AG 1900  & Transit Circle  & 1005 &  908 & Yes \\
SYDNEY 1499 IMD 25  & Transit Circle  &  782 &  771 & Yes \\
SYDNEY   --51/--63.5&  Astrograph &   84 &   80 & No\\
SYDNEY  --48 TO --54&  Astrograph &  156 &  144 & No\\
TOULOUSE 00 III-B   & Transit Circle  &  462 &  380 & No\\
TOULOUSE III        & Transit Circle  &  684 &  572 & Yes \\
TOKYO PMC 86-89     & Transit Circle  &  463 &  543 & Yes \\
TYCHO-1             & Satellite       & Ind. & Ind. & NA  \\
USNO TAC            &  Astrograph     & Ind. & Ind. & NA  \\
W1J00               & Transit Circle  &  204 &  236 & Yes \\
W2J00               & Transit Circle  &  274 &  319 & Yes \\
WASH 25 ZOD  6-IN   & Transit Circle  &  349 &  405 & Yes \\
WASH 33 --10/--20 33& Transit Circle  &  564 &  438 & Yes \\
WASHINGTON 00 9-IN  & Transit Circle  &  590 &  535 & Yes \\
WASHINGTON 20       & Transit Circle  &  642 &  540 & Yes \\
WASHINGTON 250      & Transit Circle  &  262 &  381 & Yes \\
WASHINGTON 350      & Transit Circle  &  290 &  383 & Yes \\
WASHINGTON 40 9-IN  & Transit Circle  &  370 &  447 & Yes \\
WASHINGTON AG 1900  & Transit Circle  & 1217 &  976 & Yes \\
WIEN AG  1900       & Transit Circle  &  806 &  807 & Yes \\
\noalign{\smallskip}                     
\hline                                   
\end{tabular}                            
\end{flushleft}                          
\end{table}     

\addtocounter{table}{-1}
\begin{table}
\caption[Catalogues used in the ACRS\_1999 (units of mas), continued]
{Catalogues used in the ACRS\_1999 (units of mas), continued~~~~~~~~~~~~~~~~~~~~~~~}
\begin{flushleft}
\begin{tabular}{llrrl}
\hline\noalign{\smallskip}
Name & type & $\sigma_{\alpha}$ & $\sigma_{\delta}$ & $\sigma / \sqrt{N}$   \\ 
\noalign{\smallskip}
\hline\noalign{\smallskip}
YALE v11  --10/--14 &  Astrograph &  360 &  358 & No\\
YALE v12/1 --14/--18&  Astrograph &  316 &  264 & No\\
YALE v12/2 --18/--20&  Astrograph &  278 &  254 & No\\
YALE v13/1 --20/--22&  Astrograph &  285 &  251 & No\\
YALE v13/2 --27/--30&  Astrograph &  336 &  350 & No\\
YALE v14  --22/--27 &  Astrograph &  305 &  277 & No\\
YALE v16   --6/--10 &  Astrograph &  242 &  236 & No\\
YALE v17   --2 / --6&  Astrograph &  247 &  233 & No\\
YALE v18  +15 / +20 &  Astrograph &  204 &  213 & No\\
YALE v19,22/2 +9/15 &  Astrograph &  205 &  190 & No\\
YALE v20   +1 / +5  &  Astrograph &  202 &  190 & No\\
YALE v21   +1 / --2 &  Astrograph &  226 &  230 & No\\
YALE v22/1 +5 / +9  &  Astrograph &  198 &  207 & No\\
YALE v24,25 +20/+30 &  Astrograph &  187 &  153 & No\\
YALE v26/1  +85/+90 &  Astrograph &  158 &  173 & No\\
YALE v26/2,27 50/60 &  Astrograph &  118 &  135 & No\\
YALE v28  --30/--35 &  Astrograph &  291 &  323 & No\\
YALE v29  --35/--40 &  Astrograph &  278 &  288 & No\\
YALE v30  --40/--50 &  Astrograph &  201 &  197 & No\\
YALE v31  --70/--90 &  Astrograph &  193 &  219 & No\\
YALE v32  --60/--70 &  Astrograph &  299 &  306 & No\\
\noalign{\smallskip}                     
\hline                                   
\end{tabular}                            
\end{flushleft}                          
\end{table}                              

\end{document}
