  Linear perturbations of Friedmann-Robertson-Walker universes with any
curvature and cosmological constant are studied in a general gauge without
decomposition into harmonics. Desirable gauges are selected as those which
embody best Mach's principle: in these gauges local inertial frames can be
determined instantaneously via the perturbed Einstein field equations from the
distributions of energy and momentum in the universe. The inertial frames are
identified by their `accelerations and rotations' with respect to the
cosmological frames associated with the `Machian gauges'. In closed spherical
universes, integral gauge conditions are imposed to eliminate motions generated
by the conformal Killing vectors. The meaning of Traschen's integral constraint
vectors is thus elucidated. For all three types of FRW universes the Machian
gauges admit much less residual freedom than the synchronous or generalized
harmonic gauge. Mach's principle is best exhibited in the Machian gauges in
closed spherical universes. Independent of any Machian motivation the general
perturbation equations and discussion of gauges are useful for cosmological
perturbation theory.
