  We evaluated the emission of a low-mass particle in the system (atomic)
transition for the case when the particle Lorentz factor is $10^{18}$ and found
that the angular distribution of emission in the laboratory inertial system is
strongly affected by the directional variation of the maximum attainable speed
of the particle. We show that for a photon mass consistent with the
experimental limit, $m_{ph} \leq 10^{-18}$ eV, due to the experimentally known
absence of a significant anisotropy of the photon emission by an atom, the
anisotropy of the one-way speed of light, $\Delta c_1/c$, is $10^{-37}$ or
less. This is many orders of magnitude smaller than previously reported and the
limit becomes even stronger for the lower mass of the photon.
