  A general analysis of thermal noise in torsion pendulums is presented. The
specific case where the torsion angle is kept fixed by electronic feedback is
analyzed. This analysis is applied to a recent experiment that employed a
torsion pendulum to measure the Casimir force. The ultimate limit to the
distance at which the Casimir force can be measured to high accuracy is
discussed, and in particular the prospects for measuring the thermal correction
are elaborated upon.
