Must we then conclude that the speed of propagation of gravitation is necessarily a conventional conception without absolute meaning? I think not. The speed of gravitation is quite definite; only the problem of determining it does not seem to have yet been tackled correctly. To obtain a speed independent of the coordinate-system chosen, we must consider the propagation not of a world-tensor but of a world-invariant. The simplest world-invariant for this purpose is $B_{\mu\nu\sigma}^{\epsilon} B_{\epsilon}^{\mu\nu\sigma}$, since $G$~and $G_{\mu\nu}G^{\mu\nu}$ vanish in empty space. It is scarcely possible to treat of the propagation of an isolated pulse of gravitational influence, because there seems to be no way of starting a sudden pulse without calling in supernatural agencies which violate the equations of mechanics. We may consider the regular train of waves caused by the earth in its motion round the sun. At a distant point in the ecliptic $B_{\mu\nu\sigma}^{\epsilon} B_{\epsilon}^{\mu\nu\sigma}$ will vary with an annual periodicity; if it has a maximum or minimum value at the instant when the earth is \emph{seen} to transit the sun, the inference is that the wave of disturbance has travelled to us at the same speed as the light. (It may perhaps be objected that there is no proof that the disturbance has been propagated from the earth; it might be a stationary wave permanently located round the sun which is as much the cause as the effect of the earth's annual motion. I do not think the objection is valid, but it requires examination.) There does not seem to be any grave difficulty in treating this problem; and it deserves investigation. \Section{58.}{Lagrangian form of the gravitational equations} The Lagrangian function~$\mf{L}$ is defined by \index{Lagrangian function}% \[ \mf{L} = g^{\mu\nu} \sqrt{-g} \bigl(\{\mu\alpha, \beta\}\{\nu\beta, \alpha\} - \{\mu\nu, \alpha\} \{\alpha\beta, \beta\}\bigr), \Tag{(58.1)} \] which forms part of the expression for~$\mf{G}$ ($= g^{\mu\nu} G_{\mu\nu} \sqrt{-g}$). For any small variation of~$\mf{L}$ \begin{multline*} \delta\mf{L} = \{\mu\alpha, \beta\}\, \delta\bigl(g^{\mu\nu} \sqrt{-g}\, \{\nu\beta, \alpha\}\bigr) + \{\nu\beta, \alpha\}\, \delta\bigl(g^{\mu\nu} \sqrt{-g}\, \{\mu\alpha, \beta\}\bigr) \\ - \{\mu\nu, \alpha\}\, \delta\bigl(g^{\mu\nu} \sqrt{-g}\, \{\alpha\beta, \beta\}\bigr) - \{\alpha\beta, \beta\}\, \delta\bigl(g^{\mu\nu} \sqrt{-g}\, \{\mu\nu, \alpha\}\bigr) \\ - \bigl(\{\mu\alpha, \beta\}\, \{\nu\beta, \alpha\} - \{\mu\nu, \alpha\}\{\alpha\beta, \beta\}\bigr) \delta\bigl(g^{\mu\nu} \sqrt{-g}\bigr). \Tag{(58.2)} \end{multline*} %\PageSep{132}