It should be understood that in this section we have been occupied with the transition between the old and new points of view. The quantity~$\mf{t}_{\mu}^{\nu}$ represents the potential energy of classical mechanics, but we do not ourselves recognise it as an energy of any kind. It is not a tensor-density and it can be made to vanish at any point by suitably choosing the coordinates; we do not associate it with any absolute feature of world-structure. In fact finite values of~$\mf{t}_{\mu}^{\nu}$ can be produced in an empty world containing no gravitating matter merely by choice of coordinates. The tensor-density~$\mf{T}_{\mu}^{\nu}$ comprises all the energy which we recognise; and we call it gravitational or material energy indiscriminately according as it is expressed in terms of~$g_{\mu\nu}$ or $\rho_{0}$, $u$, $v$,~$w$. This difference between the classical and the relativity view of energy recalls the remarks on the definition of physical quantities made in the Introduction. As soon as the principle of conservation of energy was grasped, the physicist practically made it his definition of energy, so that energy was that \emph{something} which obeyed the law of conservation. He followed the practice of the pure mathematician, defining energy by the properties he wished it to have, instead of describing how he had measured it. This procedure has turned out to be rather unlucky in the light of the new developments. It is true that a quantity~$\mf{S}_{\mu}^{\nu}$ can be found which obeys the definition, but it is not a tensor and is therefore not a direct measure of an intrinsic condition of the world. Rather than saddle ourselves with this quantity, which is not now of primary interest, we go back to the more primitive idea of \Foreign{vis viva}---generalised, it is true, by admitting heat or molecular \Foreign{vis viva} but not potential energy. We find that this is not in all cases formally conserved, but it obeys the law that its divergence vanishes; and from our new point of view this is a simpler and more significant property than strict conservation. Integrating over an isolated material body we may set \begin{align*} \iiint \mf{T}_{\mu}^{4}\, dx\, dy\, dz &= -Mu,\ -Mv,\ -Mw,\ M, \\ \iiint \mf{S}_{\mu}^{4}\, dx\, dy\, dz &= -M'u',\ -M'v',\ -M'w',\ M', \end{align*} \PageSep{137} where the latter expression includes the potential energy and momentum of the body. Changes of~$M'u'$, etc.\ can only occur by transfer from regions outside the body by action passing through the boundary; whereas changes of~$Mu$, \index{Action, material or gravitational}% etc.\ can be produced by the mutual attractions of the particles of the body. It is clear that the kinematical velocity, or direction of the world-line of the body, corresponds to $u : v : w : 1$; the direction of $u' : v': w' : 1$ can be varied at will by choosing different coordinate-systems.