Hence if $(P, Q, R)$ is the total mechanical force per unit volume \[ \left. \begin{alignedat}{3} P &= \rho X &&+ \gamma \sigma_{y} &&- \beta \sigma_{z}\Add{,} \\ Q &= \rho Y &&+ \alpha \sigma_{z} &&- \gamma\sigma_{x}\Add{,} \\ R &= \rho Z &&+ \beta \sigma_{x} &&- \alpha\sigma_{y}. \end{alignedat} \right\} \Tag{(76.1)} \] The rate at which the mechanical force does work is \[ S = \sigma_{x} X + \sigma_{y} Y + \sigma_{z} Z. \] The magnetic part of the force does no work since it acts at right angles to the current of charged particles. \PageSep{181} By \Eq{(73.41)} and~\Eq{(73.5)} we find that these expressions are equivalent to \index{ham@$h_{\mu}$ (ponderomotive force)}% \[ (P, Q, R, -S) = F_{\mu\nu} J^{\nu}. \] We denote the vector~$F_{\mu\nu} J^{\nu}$ by~$h_{\mu}$. Raising the suffix with Galilean~$g_{\mu\nu}$ we have \[ (P, Q, R, S) = -h^{\mu} = -{F^{\mu}}_{\nu} J^{\nu}. \Tag{(76.2)} \] The mechanical force will change the momentum and energy of the material system; consequently the material energy-tensor taken alone will \index{M@$M_{\mu\nu}$ (material energy-tensor)}% no longer be conserved. In order to preserve the law of conservation of momentum and energy, we must recognise that the electric field contains an electromagnetic momentum and energy whose changes are equal and opposite \index{E@$E_{\mu\nu}$ (electromagnetic energy-tensor)}% to those of the material system\footnotemark.\footnotetext {Notwithstanding the warning conveyed by the fate of potential energy (\SecRef{59}) we are again running into danger by generalising energy so as to conform to an assigned law. I am not sure that the danger is negligible. But we are on stronger ground now, because we know that there is a world-tensor which satisfies the assigned law $T_{\nu}^{\mu\nu} = 0$; whereas the potential energy was introduced to satisfy $\dd\mf{S}_{\mu}^{\nu}/\dd x_{\nu} = 0$, and it was only a speculative possibility (now found to be untenable) that there existed a tensor with that property.} The whole energy-tensor will then consist of two parts, $M_{\mu}^{\nu}$~due to the matter and $E_{\mu}^{\nu}$~due to the electromagnetic field. {\Loosen We keep the notation~$T_{\mu}^{\nu}$ for the whole energy-tensor---the thing which is always conserved, and is therefore to be identified with $G_{\mu}^{\nu} - \frac{1}{2}g_{\mu}^{\nu}G$. Thus} \[ T_{\mu}^{\nu} = M_{\mu}^{\nu} + E_{\mu}^{\nu}. \Tag{(76.3)} \]