Heliocentric radial velocities are obtained from
optical or radio measurements *v*opt
or *v*rad, respectively. The original optical compilation was made for
the preparation of the
RC3 catalog (Fouqué et al. 1992). Velocities are corrected for systematic
errors from the intercomparison reference by reference. The weight
is deduced for each reference from this comparison. This allows the
calculation of the actual uncertainty *sv*opt.
Radio velocities
come essentially from 21-cm line measurements (plus some additional CO
measurements). The agreement between different authors is generally
excellent and there is no need of systematic correction. Mean error *svrad*
is given as a function of the velocity resolution (Bottinelli et al. 1990).

From both *v*opt and *v*rad we calculate a weighted mean heliocentric velocity
*v*, the weights being the inverse squares of *svopt* and *svrad* respectively.
The final weight leads to the actual uncertainty *sv*. When the discrepancy
between *v*opt and *v*rad is larger than , we do
not calculate
the mean heliocentric velocity *v* but adopt instead
the velocity having higher weight. Radial velocity *v* is available
for 39667 galaxies.

From this mean heliocentric velocity *v* we obtain four velocities defined
with different reference frames.
The velocity corrected to the galactic center *vgsr* is obtained by a
correction of the motion of the Sun with respect to the local standard
of rest (LSR) and a correction of the LSR motion with respect to the
galactic center. The resulting correction is:

The velocity corrected to the centroid of the Local Group *vlg* has been
adopted following Yahil et al. (1977):

This correction replaces the classical IAU correction .

The velocity corrected for infall of the Local Group towards Virgo
is noted *vvir*. It is calculated as:

where is the infall velocity of the Local Group according
to Sandage & Tammann (1990)
and where is the angular distance between
the observed direction *sgl*, *sgb* in supergalactic coordinates and
the direction of the center of the Virgo cluster (,
).

Finally, the radial velocity is also expressed in the reference frame
of the Cosmic Background Radiation. This velocity is noted *v*3*k*. It is
calculated from the heliocentric velocity *v* using the total solar
motion of towards the direction defined by the 1950-
equatorial coordinates *al*3*k*=11.25 *h* (Lubin &
Villela 1986). In 1997 this calculation should be replaced by the new
determination from COBE (Bennett et al. 1996). However, according to
the rule defined at the end of the present paper (see the section
"acknowledgements"), the old definition will be used until the end of
1996:

with given by:

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