  When the electrons stored in the ring of the European Synchrotron Radiation
Facility (ESRF, Grenoble) scatter on a laser beam (Compton scattering in
flight) the lower energy of the scattered electron spectra, the Compton Edge
(CE), is given by the two body photon-electron relativistic kinematics and
depends on the velocity of light. A precision measurement of the position of
this CE as a function of the daily variations of the direction of the electron
beam in an absolute reference frame provides a one-way test of Relativistic
Kinematics and the isotropy of the velocity of light. The results of GRAAL-ESRF
measurements improve the previously existing one-way limits, thus showing the
efficiency of this method and the interest of further studies in this
direction.
