It may be noted that even in non-Galilean coordinates the charge-and-current vector satisfies the strict law of conservation \index{Conservation!of electric charge}% \[ \frac{\dd\mf{J}^{\mu}}{\dd x_{\mu}} = 0. \] This may be contrasted with the material energy and momentum which, it will be remembered, do not in the general case satisfy \[ \frac{\dd\mf{T}_{\mu}^{\nu}}{\dd x_{\nu}} = 0, \] so that it becomes necessary to supplement them by the pseudo-energy-tensor~$\mf{t}_{\mu}^{\nu}$ (\SecRef{59}) in order to maintain the formal law. Both $T^{\mu\nu}$ and~$J^{\mu}$ have the property which in the relativity theory we recognise as the natural generalisation of conservation, viz.\ $T_{\nu}^{\mu\nu} = 0$, $J_{\mu}^{\nu} = 0$. If the charge is moving with velocity \[ \frac{dx}{dt},\ \frac{dy}{dt},\ \frac{dz}{dt}, \] \PageSep{174} we have \begin{align*} J^{\mu} &= \rho\, \frac{dx}{dt}, \rho\, \frac{dy}{dt}, \rho\, \frac{dz}{dt}, \rho \\ &= \rho\, \frac{ds}{dt}\left(\frac{dx}{ds}, \frac{dy}{ds}, \frac{dz}{ds}, \frac{dt}{ds}\right). \Tag{(73.81)} \end{align*} The bracket constitutes a contravariant vector; consequently $\rho\, ds/dt$~is an invariant. Now $ds/dt$~represents the FitzGerald contraction, so that a volume which would be measured as unity by an observer moving with the charge \index{Charge, electric, conservation of!invariance of}% \index{Electric charge!invariance of}% will be measured as~$ds/dt$ by an observer at rest in the coordinates chosen. The invariant $\rho\, ds/dt$ is the amount of charge in this volume, i.e.\ unit proper-volume. We write \[ \rho_{0} = \rho\, \frac{ds}{dt}, \] so that $\rho_{0}$~is the proper-density of the charge. If $A^{\mu}$~is the velocity-vector $dx_{\mu}/ds$ of the charge, then \Eq{(73.81)}~becomes \[ J^{\mu} = \rho_{0} A^{\mu}. \Tag{(73.82)} \] \emph{Charge, unlike mass, is not altered by motion relative to the observer.} This follows from the foregoing result that the amount of charge in an absolutely defined volume (unit proper-volume) is an invariant. The reason for this difference of behaviour of charge and mass will be understood by reference to~\Eq{(53.2)} where the FitzGerald factor $ds/dt$ occurs squared.