According to the new point of view Einstein's law of gravitation does not impose any limitation on the basal structure of the world. $G_{\mu\nu}$~may vanish or it may not. If it vanishes we say that space is empty; if it does not vanish we say that momentum or energy is present; and our practical test whether space is occupied or not---whether momentum and energy exist there---is the test whether $G_{\mu\nu}$~exists or not\footnotemark.\footnotetext {We are dealing at present with mechanics only, so that we can scarcely discuss the part played by electromagnetic fields (light) in conveying to us the impression that space is occupied by something. But it may be noticed that the \emph{crucial} test is mechanical. A real image has the optical properties but not the mechanical properties of a solid body.} Moreover it is not an accident that it should be this particular tensor which is capable of being recognised by us. It is because its divergence vanishes---because it satisfies the law of conservation---that it fulfils the primary condition for being recognised as substantial. If we are to surround ourselves with a perceptual world at all, we must recognise as substance that which has some element of permanence. We may not be able to explain how the mind recognises as substantial the world-tensor $G_{\mu}^{\nu} - \frac{1}{2}g_{\mu}^{\nu} G$, but we can see that it could not well recognise anything simpler. There are no doubt \PageSep{121} minds which have not this predisposition to regard as substantial the things which are permanent; but we shut them up in lunatic asylums. The invariant \begin{align*} T &= g_{\mu\nu} T^{\mu\nu} \\ &= g_{\mu\nu} · \rho_{0}\, \frac{dx_{\mu}}{ds}\, \frac{dx_{\nu}}{ds} \\ &= \rho_{0}, \end{align*} since \[ g_{\mu\nu}\, dx_{\mu}\, dx_{\nu} = ds^{2}. \] Thus \[ G = 8\pi T = 8\pi \rho_{0}. \Tag{(54.6)} \] Einstein and de~Sitter obtain a naturally curved world by taking instead of~\Eq{(54.3)} \[ G_{\mu}^{\nu} - \tfrac{1}{2}g_{\mu}^{\nu}(G - 2\lambda) = -8\pi T_{\mu}^{\nu}, \Tag{(54.71)} \] where $\lambda$~is a constant. Since the divergence of~$g_{\mu}^{\nu}$ or of~$g^{\mu\nu}$ vanishes, the divergence of this more general form will also vanish, and the laws of conservation of mass and momentum are still satisfied identically. Contracting \Eq{(54.71)}, we have \[ G - 4\lambda = 8\pi T = 8\pi \rho_{0}. \Tag{(54.72)} \] For empty space $G = 4\lambda$, and $T_{\mu}^{\nu} = 0$; and thus the equation reduces to \[ G_{\mu}^{\nu} = \lambda g_{\mu}^{\nu}, \] or \[ G_{\mu\nu} = \lambda g_{\mu\nu}, \] as in~\Eq{(37.4)}.