  We examined the sizes of the absorption clouds in a z=1.3911 damped Ly-alpha
absorber (DLA) in the double image lensed quasar Q0957+561 A,B (separation 135
pc at the absorber redshift). Using HIRES/Keck spectra, we studied the MgII
2796,2803 doublet, FeII multiplet, and MgI 2853 transition in absorption. We
defined six "clouds" in the system of sightline A and seven clouds in the
system of sightline B. An examination of the N(v) profiles, using the apparent
optical depth method, reveals no clear physical connection between the clouds
in A and those in B. The observed column density ratios of all clouds is
log[N(MgI)/N(FeII)] ~ -2 across the full velocity range in both systems and
also spatially (in both sightlines). This is a remarkable uniformity not seen
in Lyman limit systems. The uniformity of the cloud properties suggests that
the multiple clouds are not part of a "halo". Based upon photoionization
modeling, we constrain the ionization parameters in the range -6.2 < log(U) <
-5.1, where the range brackets known abundance ratio and dust depletion
patterns. The inferred cloud properties are densities of 2 < n_H < 20 cm^-3,
and line of sight sizes of 1 < D < 25 pc. The masses of the clouds in system A
are 10 < M/M_sun < 1000 and in system B are 1 < M/M_sun < 60 for spherical
clouds. For planar clouds, the upper limits are 400 M_sun and 160 M_sun for A
and B, respectively. We favor a model of the absorber in which the DLA region
itself is a single cloud in thiscomplex, which could be a parcel of gas in a
galactic ISM. A spherical cloud of ~10 pc would be limited to one of the
sightlines (A) and imply a covering factor less than 0.1 for the DLA complex.
We infer that the DLA cloud properties are consistent with those of lower
density, cold clouds in the Galactic interstellar medium.
