Darwin (1920) noted that when radiation can be neglected it should be
possible to eliminate the radiation degrees-of-freedom from the action of
classical electrodynamics and keep the discrete particle degrees-of-freedom
only. Darwin derived his well known Lagrangian by series expansion in v/c
keeping terms up to order (v/c)2. Since radiation is due to acceleration the
assumption of low speed should not be necessary. A Lagrangian is suggested that
neglects radiation without assuming low speed. It cures deficiencies of the
Darwin Lagrangian in the ultra-relativistic regime.Comment: 2.5 pages, no figure