In a recent note, the author presented a derivation of Faraday's law of electromagnetic induction for a closed filamentary circuit C(t) which is moving at relativistic velocities and also changing its shape as it moves via the magnetic vector potential. Recently, Kholmetskii et al, while correcting an error in an equation, showed that it can be recast in a different method. In this article, the author generalizes a recent derivation of Faraday's law via the magnetic vector potential by Kholmetskii et al (2008 "European Journal of Physics" 29 L1-L4) and presents a new proof of the Hertz-Helmholtz identity. (Contains 4 footnotes.)