  Galilean Electromagnetism was discovered thirty years ago by Levy-Leblond &
Le Bellac. However, these authors only explored the consequences for the fields
and not for the potentials. Following De Montigny & al., we show that the
Coulomb gauge condition is the magnetic limit of the Lorenz gauge condition
whereas the Lorenz gauge condition applies in the electric limit of
L\'{e}vy-Leblond & Le Bellac. Contrary to De Montigny & al. who used Galilean
tensor calculus, we use orders of magnitude based on physical motivations in
our derivation.
