  To date, classical mass renormalization has been invoked in all tube-based
self-force calculations, thus following the method introduced in Dirac's 1938
calculation of the electromagnetic self-force for the classical radiating
electron. In this paper a new tube method is described that does not rely on a
mass renormalization procedure. As a result, exact self-force calculations
become possible for classical radiating systems of finite size. A new
derivation of the Lorentz-Dirac equation is given and the relationship between
the new tube method and the classical mass renormalization procedure is
explained. It is expected that a similar tube method could be used to obtain
rigorous results in the gravitational self-force problem.
