  This paper provides long-period and revised orbits for barium and S stars
adding to previously published ones. The sample of barium stars with strong
anomalies comprise all such stars present in the Lu et al. catalogue. We find
orbital motion for all barium and extrinsic S stars monitored. We obtain the
longest period known so far for a spectroscopic binary involving an S star,
namely 57 Peg with a period of the order of 100 - 500 yr. We present the mass
distribution for the barium stars, which ranges from 1 to 3 Msun, with a tail
extending up to 5 Msun in the case of mild barium stars. This high-mass tail
comprises mostly high-metallicity objects ([Fe/H] >= -0.1). Mass functions are
compatible with WD companions and we derive their mass distribution which
ranges from 0.5 to 1 Msun. Using the initial - final mass relationship
established for field WDs, we derived the distribution of the mass ratio q' =
MAGB,ini / MBa (where MAGB, ini is the WD progenitor initial mass, i.e., the
mass of the system former primary component) which is a proxy for the initial
mass ratio. It appears that the distribution of q' is highly non uniform, and
significantly different for mild and strong barium stars, the latter being
characterized by values mostly in excess of 1.4, whereas mild barium stars
occupy the range 1 - 1.4. We investigate as well the correlation between
abundances, orbital periods, metallicities, and masses (barium star and WD
companion). The 105 orbits of post-mass-transfer systems presented in this
paper pave the way for a comparison with binary-evolution models.
