  In his analysis of the Classical Theory of Radiating Electrons, Dirac (1938)
draws attention to the characteristic instability of solutions to the third
order equation of motion. He remarks that changing the sign of the self-force
eliminates the runaway solutions and gives `reasonable behaviour'. Dirac
rejects such a change and proceeds with an ad hoc modification to the solutions
of the initial value problem that is not consistent with the principle of
causality. We argue that his reasons for rejecting the change of sign are
invalid on both physical and mathematical grounds.
  The conceptual shift is to treat the physical particle as a composite of the
source particle and the energy-momentum that is reversibly generated in its
self-field by its motion. The reversibly generated energy in the self-field is
interpreted as kinetic energy, and the changes that follow result in Dirac's
change of sign. Several exact solutions to the new equation of motion and its
linearisation are given. For a particle in orbital motion the self-force
enables the applied force to generate radiation and kinetic energy in the
self-field that results in an outward spiral motion. The theory is consistent
with all well-established principles of physics, including the principle of
causality.
