Relative radial velocities of both the programme and the standard stars were calculated from cross-correlating (using the cross-correlation programme available in the FIGARO package) each programme star with a set of appropriate model spectra. The stellar atmosphere models were produced using the MARCS code (Gustafsson et al. 1975), and the synthetic spectra generated using the SSG code (Bell & Gustafsson 1978).
The models had a range in 
between
3700 K and 4500 K, and log g between 0 and 0.7, following roughly the
corresponding ranges in the model atmospheres for carbon stars of Querci
et al. (1974). We also assumed metal abundance of 
,
carbon abundances [C/A] in the range
between 0.0 and 2.0, and 
in the range between 3 and 30.
The radial velocity corresponding to the highest
cross-correlation peak
(from a series of peaks obtained from cross-correlating the programme star
with the set of model spectra) was adopted in each case. The corresponding
model can be considered as being closest to the particular stellar spectrum.
Zero-point of the velocity system:
The absolute zero-point of the velocity system was
determined from the velocities of the standard stars.
During the first observing run, the zero-point was determined with an
accuracy of 
km/s (which becomes 
km/s, if we exclude one
discrepant point).
In the second observing run, a larger number of observations of standards
was secured, and the zero-point was determined with an accuracy of
km/s.
This very good agreement between the standard (carbon) stars
confirms in an indirect way the suitability of the models used.
However, two stars (HD 75021 and HD 223392)
showed a systematically different
velocities from the bibliographic values
(of 
km/s in both cases). They are suspected variables, and they
were excluded from the zero-point determination.
Finally, it should be noted that the velocities of the five programme
stars that were observed in both observing runs (Table 1) showed a mean
difference
of 
km/s, which is well within the combined zero-point
error from the two observing runs.
The final heliocentric radial velocities of the programme stars are given in Table 1. All of the programme stars given in Tables 1a and b yielded cross-correlation peaks (ccp) higher than 30%. Whenever two consecutive observations were available, the two spectra were co-added before deriving the final velocity appearing in Table 1.
Random errors in the velocity measurements:
1. From repeated observations:
To estimate the random errors in the velocities,
we compared the velocities derived from the individual observations of the
same star for the cases for which all repeated spectra yielded
ccp higher than 30%.
For the first observing run, there were 30 such cases, yielding a
rms of the velocity difference
of 4.7 km/s for the whole sample, or 3.4 km/s, if we remove two discrepant
stars from the sample (with velocity differences between the two measurements
of 13.0, and 14.5 km/s respectively).
For the second observing run, there were 25 such cases yielding a
rms of the velocity difference of 1.7 km/s. It should be noted that
for the majority of the repeats in the second observing run both
measurements gave ccp higher than 60%, while in the
first observing run, most ccp were less than 60%, hence
the higher absolute velocity difference in the latter case. The
final velocities of Table 1
come from the co-addition of the repeated observations, therefore they should
be more accurate than the individual measurements.
All these repeats were generally done consecutively.
There is one case where a programme star was observed on two different nights
of the same observing run
(star MH 1185). The velocity difference between the two velocities was 0.4 km/s.
As mentioned in the discussion of the zero-point above, there were also
five programme stars that were observed in both observing runs (see Table 1a).
The rms of the velocity difference for the five stars was 6.1 km/s, or
2.4 km/s excluding one
discrepant point (MH 1153). It should be noted that this particular
star was observed twice
in each of the observing runs. In the first run the velocity difference
between the two measurements was 3 km/s, and in the second run, 2 km/s.
Therefore, it is unlikely that the 10 km/s difference between the
two runs is just due to random errors.
It is possible that the star (MH 1153) is a binary (see below).
2. From simulation: Finally, we conducted the following experiment: we artificially added different amounts of noise to a high signal-to noise spectrum of a standard star, and cross-correlated the resulting spectrum with the series of models, as was done for the real data. This was repeated several times in each case. We found that, the rms of the velocity difference was 3.6 km/s (with a maximum of 6.7 km/s) for a ccp of 30%. This rms decreased to 1.1 km/s (max of 2.7 km/s) for a ccp of 55%, and to 0.3 km/s (max of 0.6 km/s) for a ccp of 70%.
Using all of the above, we estimate that the individual random errors in the velocities of Table 1 range from about 5 km/s for the lowest ccp (i.e. <0.40) to 1 km/s for the best observed stars. Most of the stars have velocity determinations of intermediate accuracy, i.e. of 2-4 km/s.
The effect of the choice of models on the derived velocities:
The choice of models used as cross-correlation templates may have an
influence
on the derived radial velocities. We examined the cases for which more than
one exposure was available, and for which all individual spectra gave
acceptable ccp (this exercise could only be performed
for the red spectra). It was found that for more than half the cases, the
models that gave the highest ccp were identical for the
different exposures of the same star. In the rest of the cases, the models
picked were similar, and most importantly the effect on the radial velocities
was well within the error margins previously mentioned (i.e. <6 km/s).
In 70% of the stars, the overall range
of velocities yielded by the full range of models used was less than 6 km/s.
The maximum range observed was 
km/s (just for one star).
However in this latter case the large range was
caused by models that gave low ccp (well below 30%).
From the above analysis it becomes clear that the use of models is
necessary for the proper derivation of the velocity shifts, as
the correct matching of the template to the programme star can be crucial.
Therefore, just the use of a selection of a few galactic carbon stars
as templates for the cross-correlation, which is the usual practice, may
not be good enough.
Comparison between the Red and Blue spectra: The above analysis was based on the velocities derived from the red spectra. Generally, the "red'' spectra (8335-8879 Å) had much higher signal-to-noise ratios than the "blue'' spectra (4656-5785 Å), mostly due to the fact that carbon stars are much brighter in the red. This, coupled with the smaller pixel size (by a factor of 3 in km/s) of the red spectra and with the fact that in the red spectra there is a forest of strong but unsaturated lines, led to much more accurate velocities from the red spectra.
It is important, however, to compare the radial velocities derived
from the two different
wavelength regions. The results for the first run are discussed here.
There is a small
zero-point difference between the blue and red spectra velocities
amounting to 
km/s, corresponding to less than 0.10 of
the combined pixel size.
The rms of the velocity difference between the red and blue spectra of the
standard stars
is 8.7 km/s,
corresponding to 0.13 of the combined pixel size
(the maximum difference being 17.4 km/s, corresponding to 0.26 of the combined
pixel size). For the programme stars, the rms of the velocity difference
between the two sets of velocities, for ccp higher than
30%, was 20.5 km/s corresponding to 0.31 of the combined pixel size, which
is expected given the lower signal-to-noise of the blue spectra.
This comparison between the velocities yielded by the red and blue spectra
provides a check against gross errors caused by mis-identification of
the ccp. No such instances were noted. In Table 1,
we have adopted the velocities derived from the "red'' spectra.