For the observer~$S$ using our original system of Galilean coordinates, the quantities $k_{\mu}$, $F_{\mu\nu}$ and~$J^{\mu}$ represent the electromagnetic potential, force, and current, according to definition. For another observer~$S'$ with different velocity, we have corresponding quantities $\kappa_{\mu}'$, $F_{\mu\nu}'$, $J'^{\mu}$, obtained by the transformation-laws; but we have not yet shown that these are the quantities which $S'$~will measure when he makes experimental determinations of potential, force, and current relative to his moving apparatus. Now if $S'$~recognises certain measured quantities as potential, force, and current it must be because they play the same part in the world relative to him, as $\kappa_{\mu}$, $F_{\mu\nu}$ and~$J^{\mu}$ play in the world relative to~$S$. To play the same part means to have the same properties, or fulfil the same relations or equations. But $\kappa_{\mu}'$, $F_{\mu\nu}'$ and~$J'^{\mu}$ fulfil the same equations in~$S'$'s coordinates as $\kappa_{\mu}$, $F_{\mu\nu}$ and~$J^{\mu}$ do in $S$'s~coordinates, \emph{because the fundamental equations \Eq{(73.73)}, \Eq{(73.74)} and \Eq{(73.77)} are tensor equations holding in all systems of coordinates}. The fact that Maxwell's equations are tensor equations, enables us to make the identification of $\kappa_{\mu}$, $F_{\mu\nu}$, $J^{\mu}$ with the experimental potential, force, and current in all systems of Galilean coordinates and not merely in the system initially chosen. In one sense our proof is not yet complete. There are other equations obeyed by the electromagnetic variables which have not yet been discussed. In particular there is the equation which prescribes the motion of a particle carrying a charge in the electromagnetic field. We shall show in \SecRef{76} that this also is of the tensor form, so that the accented variables continue to play the same part in $S'$'s~experience which the unaccented variables play in~$S$'s \PageSep{175} experience. But even as it stands our proof is sufficient to show that \emph{if} there exists for~$S'$ a potential, force, and current precisely analogous to the potential, \index{Potential!electromagnetic}% force, and current of~$S$, these must be expressed by $\kappa_{\mu}'$, $F_{\mu\nu}$, $J'^{\mu}$, because other quantities would not satisfy the equations already obtained. The proviso must clearly be fulfilled unless the special principle of relativity is violated.