When an observer uses non-Galilean coordinates, he will as usual treat them as though they were Galilean and attribute all discrepancies to the effects of the field of force which is introduced. $\kappa_{\mu}$, $F_{\mu\nu}$ and~$J^{\mu}$ will be identified with the potential, force, and current, just as though the coordinates were Galilean. These quantities will no longer accurately obey Maxwell's original form of the equations, but will conform to our generalised tensor equations \Eq{(73.73)} and~\Eq{(73.74)}. The replacement of~\Eq{(73.72)} by the more general form~\Eq{(73.74)} extends the classical equations to the case in which a gravitational field of force is acting in addition to the electromagnetic field. \Section{74.}{Electromagnetic waves} \index{Electromagnetic action!waves, propagation of}% \index{Light!propagation of}% \index{Waves!electromagnetic}% \Subsection[(a)]{Propagation of electromagnetic potential.} \index{Propagation!of electromagnetic waves}% It is well known that the electromagnetic potentials $F$, $G$, $H$, $\Phi$ are not determinate. They are concerned in actual phenomena only through their curl---the electromagnetic force. The curl is unaltered, if we replace \[ -F,\ -G,\ -H,\ \Phi\quad\text{by}\quad -F + \frac{\dd V}{\dd x},\ -G + \frac{\dd V}{\dd \smash[b]{y}},\ -H + \frac{\dd V}{\dd z},\ \Phi + \frac{\dd V}{\dd t}, \] where $V$~is an arbitrary function of the coordinates. The latter expression gives the same field of electromagnetic force and may thus equally well be adopted for the electromagnetic potentials. It is usual to avoid this arbitrariness by selecting from the possible values the set which satisfies \[ \frac{\dd F}{\dd x} + \frac{\dd G}{\dd y} + \frac{\dd H}{\dd z} + \frac{\dd\Phi}{\dd t} = 0. \] Similarly in general coordinates we remove the arbitrariness of~$\kappa_{\mu}$ by imposing the condition \[ (\kappa^{\mu})_{\mu} = 0. \Tag{(74.1)} \] When the boundary-condition at infinity is added, the value of~$\kappa_{\mu}$ becomes completely determinate. By \Eq{(73.74)} and~\Eq{(73.3)} \begin{align*} J = (F_{\mu}^{\alpha})_{\alpha} &= (g^{\alpha\beta} F_{\mu\beta})_{\alpha} = g^{\alpha\beta} (F_{\mu\beta})_{\alpha} \\ &= g^{\alpha\beta} (\kappa_{\mu\beta\alpha} - \kappa_{\beta\mu\alpha}) \Tag{(74.2)}\displaybreak[0] \\ &= g^{\alpha\beta} (\kappa_{\mu\beta\alpha} - \kappa_{\beta\alpha\mu} + B_{\beta\alpha\mu}^{\epsilon} \kappa_{\epsilon}) \quad\text{by~\Eq{(34.3)}}\displaybreak[0] \\ &= g^{\alpha\beta} (\kappa_{\mu})_{\beta\alpha} - (\kappa_{\alpha}^{\alpha})_{\mu} + G_{\mu}^{\epsilon} \kappa_{\epsilon}. \end{align*}