Mapped in CO at a resolution of 
by Lebrun (1986)
and Grenier et al. (1989), the Cepheus Flare region contains a
massive molecular complex at an estimated distance of 
.
The complex lies high above the Galactic plane, at a displacement 
. A recent re-evaluation of the 
conversion factor in nearby clouds (Digel et al. 1996) brings
its total 
mass down to 
solar masses, equivalent to Orion B and slightly less than
Orion A (
). It is comparable in size to the Orion
and Taurus complexes, but it contains no massive star or HII region and
exhibits surprisingly little star formation. Extinction through the cloud
does not exceed 2 mag (Lebrun 1986). It is therefore
apparently a rather massive, but cold and diffuse, molecular object,
intermediate between the dense, active star-forming clouds near the Galactic
plane and the translucent, light ones at high latitude.
Because of its large angular size, the complex had been first surveyed in CO
at a resolution so low that only limited information as to its internal
structure could be obtained. To study this structure better, though on a
limited scale, we chose the brightest cloud of the complex, located near the
eastern border at 
and 
, to be
fully mapped in the CO(
) line at an angular resolution of
8.7', i.e. approximately 0.8 pc at 300 pc. This elongated cloud, which we
will refer to as the ``eastern cloud", spans a region of 10 by 20 pc. The
IRAS source 22343+7501, embedded in the southern tip of the cloud, has
been associated with a 1 or 2 pc-long bipolar outflow, observed in CO and
by Sato & Fukui (1989). No other infrared
source has been found in the cloud except IRAS 22376+7455 a little beyond
the southern edge. With no massive star, the cloud is almost free of
internal source of radiative heating.
To determine the gas characteristics, a multi-transition CO analysis has
been undertaken and observations have been carried out at the same
resolution in the 
and 
transitions of CO
and 
. The weakness of the emission and the extent
of the cloud prevented us from mapping it at all frequencies; instead, a set
of positions has been selected as representative of the entire cloud,
spanning both the brightness-temperature range and velocity structure.
The eastern cloud has also been chosen because it exhibited unusually wide CO lines in the low-resolution survey (Grenier et al. 1989). The higher resolution data show that the broad lines result from the superposition of two or three lines of normal width which drift in velocity across the cloud according to a peculiar, highly organized velocity field. The hydrodynamical study of this field, indicative of a slow, large-scale flow that stirs the cloud and spreads the line velocities between -8 and +2 km/s, will be presented in a following paper (Paper III). For the present purpose, the composite lines have been fitted by two or three gaussian profiles, which have then been treated as independent components of the cloud emission.
Surveys at comparable resolution of the Cepheus Flare region exist at
various wavelengths, from radio to 
rays, to map its gas and dust
content; the different tracers of molecular gas may therefore be compared in
a single cloud. This will be done in Paper II, using column-densities
derived from the present multi-transition study.
The following sections will describe the observations, determinations of the
transition and isotopic line ratios and their variations over the cloud, and
the derivation of the excitation conditions of the CO and
molecules under LTE and LVG assumptions.