  Measurements of the asymmetry of the emission peaks in the core of the Ca II
H line for 105 giant stars are reported. The asymmetry is quantified with the
parameter V/R, defined as the ratio between the maximum number of counts in the
blueward peak and the redward peak of the emission profile. The Ca II H and K
emission lines probe the differential motion of certain chromospheric layers in
the stellar atmosphere. Data on V/R for the Ca II K line are drawn from
previous papers and compared to the analogous H line ratio, the H and K spectra
being from the same sets of observations. It is found that the H line V/R value
is +0.04 larger, on average, than the equivalent K line ratio, however, the
difference varies with B-V color. Red giants cooler than B-V = 1.2 are more
likely to have the H line V/R larger than the K line V/R, whereas the opposite
is true for giants hotter than B-V = 1.2. The differences between the Ca II H
and K line asymmetries could be caused by the layers of chromospheric material
from which these emission features arise moving with different velocities in an
expanding outflow.
