  It is shown that the Galilean limit (V << c, or L/T <<c)) of the Maxwell
equations admits three different limits: the magneto-quasi-static,
electro-quasi-static, and electromagnetic-quasi-static limits, in addition to
the two obvious static limits. The first two quasi-static limits have been
previously identified as Galilean Electromagnetics, while the latter is also
known as the Darwin approximation. Using a perturbation expansion, a
generalization of Rappetti and Rousseaux [Applied Numerical Mathematics, 79,
92] orders the vacuum Maxwell equations and obtains all three limits. To order
the equations, the dimensionless version of the Maxwell equations are derived
using a modification of Jackson's review of EM unit systems [Jackson, Classical
Electrodynamics, Wiley, 1999, 3rd ed.] The perturbation expansion is repeated
for the potential form of the Maxwell equations to emphasize the importance of
gauge conditions. The integral solutions of the potentials are derived for the
three limits, and the generalized Coulomb and Biot-Savart equations are derived
from these solutions. It is shown that although the forms are the same as the
static equations, the quasi-static forms of the Maxwell equations are
recovered. The induction term is recovered when the time derivative of the
vector potential is kept. The displacement current is recovered when the Lorenz
gauge is used. The equivalence of this approach and Jackson's derivation [Amer.
J. of Phys., 70, 917 (2002)] of the Darwin approximation is shown. The regions
of applicability of the quasi-static forms of the Maxwell equations are
discussed in terms of macroscopic media.
