Heliocentric radial velocities are obtained from optical or radio measurements vopt or vrad, 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 svopt. 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 vopt and vrad 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 vopt and vrad 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 v3k. It is
calculated from the heliocentric velocity v using the total solar
motion of 
towards the direction defined by the 1950-
equatorial coordinates al3k=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:
