  We propose a method of determining masses in brane scenarios which is
independent of coordinate transformations. We apply our method to the scenario
of Randall and Sundrum (RS) with two branes, which provides a solution to the
hierarchy problem. The core of our proposal is the use of covariant equations
and expressing all coordinate quantities in terms of invariant distances. In
the RS model we find that massive brane fields propagate proper distances
inversely proportional to masses that are not exponentially suppressed. The
hierarchy between the gravitational and weak interactions is nevertheless
preserved on the visible brane due to suppression of gravitational interactions
on that brane. The towers of Kaluza-Klein states for bulk fields are observed
to have different spacings on different branes when all masses are measured in
units of the fundamental scale. Ratios of masses on each brane are the same in
our covariant and the standard interpretations. Since masses of brane fields
are not exponentiated, the fundamental scale of higher-dimensional gravity must
be of the order of the weak scale.
