Molecular line observations are reported of two regions containing sma
ll cometary globules at the edge of the Rosette Nebula. Observations o
f the CO, (CO)-C-13 and (CO)-O-18 J = 2 - 1, and CO J = 4 - 3 molecula
r lines towards Globule 1, the most prominent of the group, show it ha
s a well-developed head-tail structure, with a head diameter similar t
o 0.4 pc, and a tail extending similar to 1.3 pc behind it. The major
axis of the system points about 45 degrees away from the direction to
the centre of the Rosette Nebula (which contains the [presumed] illumi
nating stars), and 20 degrees out of the plane of the sky, along a pro
jected line towards the luminous (924 L-.) infrared source IRAS 063140427. The CO lines have a complex velocity structure; with a pronounce
d broadening at the front of the head (as viewed from IRAS 06314+0427)
; a velocity gradient similar to 1.4 km s(-1) along the tail, and mate
rial at the front of the head is blue-shifted by similar to 0.5 km s(-
1) compared to surrounding gas. The CO J = 2 - 1 line intensity peaks
towards the front of the head, and along the edges of the tail. The (C
O)-C-13 J = 2 - 1 antenna temperatures in the head are very similar to
those of CO, suggesting very high opacities or column densities, or t
hat there is significant CO self-absorption. There is a narrow rim of
CO J = 4 - 3 emission around the front of the head over a limited velo
city range, which correlates with the position of a faint optical rim,
and a narrow ridge of 2 mu m H-2 emission. These data give strong sup
port to the Radiation Driven Implosion (RDI) model of Lefloch and Laza
reff (1994 - hereafter LL94), which was developed to explain the physi
cal structure of cometary globules. Using an RDI simulation, a remarka
bly good fit to the data has been obtained, allowing the CO, (CO)-C-13
and (CO)-O-18 spatial structures and velocity field to be modelled. T
his simulation suggests that Globule 1 is similar to 400,000 years old
, and has a mass similar to 50 M-. Additional observations towards the
region close to IRAS 06314+0127 show that it is associated with an in
tense molecular concentration lying at the northern end of a similar t
o 5 pc long molecular ridge, with a mass similar to 330 M-., and lies
close to the centre of a shell-like condensation.