The formal expression of the conservation of the material energy and \index{Conservation, formal law of}% momentum is contained in the equations \[ \frac{\dd\mf{T}_{\mu}^{\nu}}{\dd x_{\nu}} = 0, \Tag{(59.1)} \] or, if we name the coordinates $x$, $y$, $z$, $t$, \[ \frac{\dd}{\dd x}\mf{T}_{\mu}^{1} + \frac{\dd}{\dd y}\mf{T}_{\mu}^{2} + \frac{\dd}{\dd z}\mf{T}_{\mu}^{3} + \frac{\dd}{\dd t}\mf{T}_{\mu}^{4} = 0. \] Multiply by $dx\, dy\, dz$ and integrate through a given three-dimensional region. The last term is \[ \frac{\dd}{\dd t} \iiint \mf{T}_{\mu}^{4}\, dx\, dy\, dz. \] The other three terms yield surface-integrals over the boundary of the region. Thus the law~\Eq{(59.1)} states that the rate of change of $\iiint \mf{T}_{\mu}^{4}\, dx\, dy\, dz$ is equal to certain terms which describe something going on at the boundary of the region. In other words, changes of this integral cannot be created in the interior of the region, but are always traceable to transmission across the boundary. This is clearly what is meant by conservation of the integral. This equation~\Eq{(59.1)} applies only in the special case when the coordinates are such that there is no field of force. We have generalised it by substituting the corresponding tensor equation $T_{\mu\nu}^{\nu} = 0$; but this is no longer a formal expression of the conservation of anything. It is of interest to compare the traditional method of generalising~\Eq{(59.1)} in which formal conservation is adhered to. \PageSep{135} In classical mechanics the law of conservation is restored by recognising \index{Energy, potential}% \index{Potential energy}% another form of energy---potential energy---which is not included in~$\mf{T}_{\mu}^{\nu}$. This is supposed to be stored up in the gravitational field; and similarly the momentum and stress components may have their invisible complements in the gravitational field. We have therefore to add to~$\mf{T}_{\mu}^{\nu}$ a complementary expression~$\mf{t}_{\mu}^{\nu}$ denoting potential energy, momentum and stress; and conservation is only asserted for the sum. If \[ \mf{S}_{\mu}^{\nu} = \mf{T}_{\mu}^{\nu} + \mf{t}_{\mu}^{\nu}, \Tag{(59.2)} \] then \Eq{(59.1)}~is generalised in the form \[ \frac{\dd\mf{S}_{\mu}^{\nu}}{\dd x_{\nu}} = 0. \Tag{(59.3)} \]