  We report on residual gas damping of the motion of a macroscopic test mass
enclosed in a nearby housing in the molecular flow regime. The damping
coefficient, and thus the associated thermal force noise, is found to increase
significantly when the distance between test mass and surrounding walls is
smaller than the test mass itself. The effect has been investigated with two
torsion pendulums of different geometry and has been modelled in a numerical
simulation whose predictions are in good agreement with the measurements.
Relevant to a wide variety of small-force experiments, the residual-gas force
noise power for the test masses in the LISA gravitational wave observatory is
roughly a factor 15 larger than in an infinite gas volume, though still
compatible with the target acceleration noise of 3 fm s^-2 Hz^-1/2 at the
foreseen pressure below 10^-6 Pa.
