In empty space \Eq{(57.7)}~becomes \[ \Wave h_{\mu\nu} = 0, \] showing that the deviations of the gravitational potentials are propagated as waves with unit velocity, i.e.\ the velocity of light (\SecRef{30}). But it must be \index{Waves!gravitational}% remembered that this representation of the propagation, though always permissible, \index{Propagation!of gravitational waves}% is not unique. In replacing \Eq{(57.2)} by \Eq{(57.31)} and \Eq{(57.32)}, we introduce a restriction which amounts to choosing a special coordinate-system. Other solutions of~\Eq{(57.2)} are possible, corresponding to other coordinate-systems. All the coordinate-systems differ from Galilean coordinates by small quantities of the first order. The potentials~$g_{\mu\nu}$ pertain not only to the gravitational influence which has objective reality, but also to the coordinate-system which we select arbitrarily. We can ``propagate'' coordinate-changes with the \emph{speed of thought}, and these may be mixed up at will with the more dilatory propagation discussed above. There does not seem to be any way of distinguishing a physical and a conventional part in the changes of the~$g_{\mu\nu}$. The statement that in the relativity theory gravitational waves are propagated with the speed of light has, I believe, been based entirely on the \PageSep{131} foregoing investigation; but it will be seen that it is only true in a very conventional sense. If coordinates are chosen so as to satisfy a certain condition which has no very clear geometrical importance, the speed is that of light; if the coordinates are slightly different the speed is altogether different from that of light. The result stands or falls by the choice of coordinates and, so far as can be judged, the coordinates here used were purposely introduced in order to obtain the simplification which results from representing the propagation as occurring with the speed of light. The argument thus follows a vicious circle.