  We study the Abraham model for $N$ charges interacting with the Maxwell
field. On the scale of the charge diameter, $R_{\phi}$, the charges are a
distance $\eps^{-1}R_{\phi}$ apart and have a velocity $\sqrt{\eps} c$ with
$\eps$ a small dimensionless parameter. We follow the motion of the charges
over times of the order $\eps^{-3/2}R_{\phi}/c$ and prove that on this time
scale their motion is well approximated by the Darwin Lagrangian. The mass is
renormalized. The interaction is dominated by the instantaneous Coulomb forces,
which are of the order $\eps^{2}$. The magnetic fields and first order
retardation generate the Darwin correction of the order $\eps^{3}$. Radiation
damping would be of the order $\eps^{7/2}$.
