If it is assumed that Schwarzschild's result \[ a < \Chg{\surd(8/9\alpha)}{\sqrt{8/9\alpha}} \] is correct as regards order of magnitude, the radius of the greatest possible mass of water would be $370$~million kilometres. The radius of the star Betelgeuse is something like half of this; but its density is much too small to lead to any interesting applications of the foregoing result. Admitting Einstein's modification of the law of gravitation, with $\lambda$~depending on the total amount of matter in the world, the size of the greatest sphere is easily determined. By~\Eq{(69.4)} $R^{2} = 1/4\pi\rho_{0}$, from which $R$~(for water) is very nearly $300$~million kilometres. \PageSep{171} \Chapter{VI}{Electricity} \Section{73.}{The electromagnetic equations} \index{Electromagnetic action!force}% \index{Electromagnetic action!potential}% \index{F@$F_{\mu\nu}$ (electromagnetic force)}% In the classical theory the electromagnetic field is described by a scalar potential~$\Phi$ and a vector potential $(F, G, H)$. The electric force $(X, Y, Z)$ \index{Force!electromagnetic}% \index{Potential!electromagnetic}% and the magnetic force $(\alpha, \beta, \gamma)$ are derived from these according to the equations \[ \left. \begin{aligned} X &= -\frac{\dd\Phi}{\dd x} - \frac{\dd F}{\dd t}\Add{,} \\ \alpha &= \Neg\frac{\dd H}{\dd y} - \frac{\dd G}{\dd z}. \end{aligned} \right\} \Tag{(73.1)} \] The classical theory does not consider any possible interaction between the gravitational and electromagnetic fields. Accordingly these definitions, together with Maxwell's equations, are intended to refer to the case in which no field of force is acting, i.e.\ to Galilean coordinates. We take a special system of Galilean coordinates and set \[ \kappa^{\mu} = (F, G, H, \Phi) \Tag{(73.21)} \] for that system. Having decided to make $\kappa^{\mu}$ a contravariant vector we can find its components in any other system of coordinates, Galilean or otherwise, by the usual transformation law; but, of course, we cannot tell without investigation what would be the physical interpretation of those components. In particular we must not assume without proof that the components of~$\kappa^{\mu}$ in another Galilean system would agree with the new $F$, $G$, $H$,~$\Phi$ determined experimentally for that system. At the present stage, we have defined~$\kappa^{\mu}$ in all systems of coordinates, but the equation~\Eq{(73.21)} connecting it with experimental quantities is only known to hold for one particular Galilean system. Lowering the suffix with Galilean~$g_{\mu\nu}$, we have \[ \kappa_{\mu} = (-F, -G, -H, \Phi). \Tag{(73.22)} \] Let the tensor \[ F_{\mu\nu} \equiv \kappa_{\mu\nu} - \kappa_{\nu\mu} = \frac{\dd\kappa_{\mu}}{\dd x_{\nu}} - \frac{\dd\kappa_{\nu}}{\dd x_{\mu}} \Tag{(73.3)} \] as in~\Eq{(32.2)}.