Maxwell?s equations are covariant under the Lorentz transformation, whereas Hertz?s equations are invariant under the Galilean transformation. At first order in v/c, both are (rival) candidates to describe electromagnetic physics. Hertz?s equations entail a law of force on charge or current inherent in the field theoretical formalism. Maxwell?s equations do not; hence they require postulational supplementation by a force law due to Lorentz. The Hertzian force law is similar to the Lorentz law, with an extra term unobservable in closed circuits. Both formalisms, considered at first order, describe radiation. But we show that only Hertz?s theory correctly describes the weak radiation (few photon) limit.