  Thirteen spectroscopic orbits of late-type stars are determined from the
high-resolution spectra taken with the CHIRON echelle spectrometer at the 1.5-m
CTIO telescope. Most (HIP 14194B, 40523A, 41171A, 51578A, 57572B, 59426A,
62852B, 66438A, 87813B, and 101472A) are inner subsystems in hierarchical
multiple stars with three or four components. The periods range from 2.2 to
1131 days. Masses of the components, orbital inclinations, and projected
rotation velocities are estimated, the presence or absence of the lithium line
is noted. In addition to those systems, HIP 57021 is a simple 54-day twin
binary, and HIP 111598 is a compact triple-lined system with periods of 5.9 and
271 days. This object is likely old, but, nevertheless, the secondary component
in the inner pair does not rotate synchronously with the orbit. The
period-eccentricity diagram of 528 known inner low-mass spectroscopic
subsystems (including 36 from this paper series) is given. The distribution of
the inner periods is smooth, without any details around the tidal
circularization period of ~10 d.
