A Note on Hertz's “Derivation” of Maxwell's Equations

In a recent article, Zatzkis has drawn attention to Hertz's “derivation” of Maxwell's equations from an earlier action-at-a-distance theory. Hertz's procedure leads to an infinite series for the potentials which satisfies Maxwell's equations. It is demonstrated that for a current distribution which is an analytic function of the time this series is the Lagrange expansion of the half-retarded, half-advanced solution of Maxwell's equations; for general source functions the series has no physical meaning. Thus Hertz's procedure does not yield the full Maxwell theory and, in particular, can not account for radiation. It is then shown that, contrary to Zatzkis's contention, in the illustrative example treated by Hertz the original solution is mathematically correct; however, it is physically inadequate.