Historical Remarks

The T.E. scalar and the T.M. scalar whose derivatives yield the respective vector potentials Eqs.(10) and (12) can be related to Righi's magnetic ``super potential'' vector $\vec{\Pi}^m$ and Hertz's electric ``super potential'' vector $\vec{\Pi}^e$[#!Phillips!#]. Indeed, if $\psi_{T.E.}$ is the T.E. scalar and $\psi_{T.M.}$ is the T.M. scalar, then these scalars are simply the $z$-components of the corresponding super potential vectors

$$\vec{\Pi}^m \equiv (\Pi^m_x , \Pi^m_y,\Pi^m_z)=(0,0,\psi_{T.E.})~~~\textrm{\lq\lq Righi''}$$ (23)

$$\vec{\Pi}^e \equiv (\Pi^e_x, \Pi^e_y,\Pi^e_z)=(0,0,\psi_{T.M.})~~~~~\textrm{\lq\lq Hertz''}$$ (24)

In fact, subsequent to Hertz's 1900 and Righi's 1901 introduction of their super potential vectors, Whittaker in 1903 showed that the Maxwell field can be derived precisely from our two gauge invariant scalars $\psi^{TE}$ and $\psi^{TM}$[#!Phillips!#].