  We present CO (J = 1 - 0) and CO (J = 2 - 1) spectra for 19 bright, late-type
galaxies (spirals) in the central region of the galaxy cluster Abell 1367 (z =
0.02) from observations made with the IRAM 30 - m telescope. All 19 spirals
were observed at the position of their optical center and for a subset, at
multiple positions. For each spiral the integrated CO (J = 1 - 0) intensity
from the central pointing, in few cases supplemented with intensities from
offset pointings, was used to estimate its molecular hydrogen mass and H_2
deficiency. Accepting the considerable uncertainties involved in determining
H_2 deficiencies, spirals previously identified by us to have redder colours
and higher HI deficiencies as a result of environmental influence, were found
to be more H_2 deficient compared to members of the sample in less advanced
evolutionary states. For eight of the observed spirals multiple pointing
observations were made to investigate the distribution of their molecular gas.
For these spirals we fitted Gaussians to the CO intensities projected in a line
across the galaxy. In two cases, CGCG 097-079 and CGCG 097-102(N), the offset
between the CO and optical intensity maxima was significantly larger than the
pointing uncertainty and the FWHMs of the fits were significantly greater than
those of the other spirals, irrespective of optical size. Both signatures are
indicators of an abnormal molecular gas distribution. In the case of CGCG
097-079, which is considered an archetype for ram pressure stripping, our
observations indicate the CO intensity maximum lies ~ 15.6 +/- 8.5 arcsec (6
kpc) NW of the optical centre at the same projected position as the HI
intensity maximum.
