  Though sufficient for local conservation of charge, Maxwells displacement
current is not necessary. An alternative to the Ampere-Maxwell equation is
exhibited and the alternatives electric and magnetic fields and scalar and
vector potentials are expressed in terms of the charge and current densities.
The magnetic field is shown to satisfy the Biot_Savart Law. The electric field
is shown to be the sum of the gradient of a scalar potential and the time
derivative of a vector potential which is different from but just as tractable
as the simplest vector potential that yields the Biot_Savart Law The
alternative describes a theory in which action is instantaneous and so may
provide a good approximation to Maxwells equations where and when the finite
speed of light can be neglected. The result recalls the Darwin approximation
which arose from the study classical charged point particles to order (v/c)2 in
the Lagrangian. Unlike Darwin, this approach does not depend on the
constitution of the electric current. Instead, this approach grows from a
straightforward revision of the Ampere Equation that enforces the local
conservation of charge.
