  A relativistic analysis based on the paths, in a non-rotating frame comoving
with the centroid of the Earth, of clocks carried by aircraft circumnavigating
the Earth in different directions, as in the Hafele-Keating experiment,
predicts time differences between airborne and Earth-bound clocks at variance
with the results of the experiment. The latter imply new relativistic velocity
transformations differing from the conventional ones. These transformations
demonstrate in turn the invariance of length intervals on the surface of the
rotating Earth and so resolve the Ehrenfest paradox for this case.
