  A new approximation scheme, designed to solve the covariant Maxwell equations
inside a rotating hollow slender conducting cavity (modelling a ring-laser), is
constructed. It is shown that for well-defined conditions there exist TE and TM
modes with respect to the longitudinal axis of the cavity. A twisted mode
spectrum is found to depend on the integrated Frenet torsion of the cavity and
this in turn may affect the Sagnac beat frequency induced by a non-zero
rotation of the cavity. The analysis is motivated by attempts to use
ring-lasers to measure terrestrial gravito-magnetism or the Lense-Thirring
effect produced by the rotation of the Earth.
