This system has some advantages. For example, to obtain the motion of a light-pulse we set $ds = 0$ in~\Eq{(43.3)}. This gives \[ \left(\frac{dx}{dt}\right)^{2} + \left(\frac{dy}{dt}\right)^{2} + \left(\frac{dz}{dt}\right)^{2} = \frac{(1 - m/2r_{1})^{2}}{(1 + m/2r_{1})^{6}}. \] At a distance~$r_{1}$ from the origin the velocity of light is accordingly \index{Velocity of light!in sun's gravitational field}% \[ \frac{(1 - m/2r_{1})}{(1 + m/2r_{1})^{3}} \Tag{(43.4)} \] in all directions. For the original coordinates of~\Eq{(38.8)} the velocity of light is not the same for the radial and transverse directions. Again in the isotropic system the coordinate length ($\Chg{\surd(x^{2} + y^{2} + z^{2})}{\sqrt{x^{2} + y^{2} + z^{2}}}$) of a small rod which is rigid ($ds = \text{constant}$) does not alter when the orientation of the rod is altered. This system of coordinates is naturally arrived at when we partition space by rigid scales or by light-triangulations in a small region, e.g.\ in terrestrial measurements. Since the ultimate measurements involved \PageSep{94} in any observation are carried out in a terrestrial laboratory we ought, strictly speaking, always to employ the isotropic system which conforms to assumptions made in those measurements\footnotemark.\footnotetext {But the terrestrial laboratory is falling freely towards the sun, and is therefore accelerated relatively to the coordinates $(x, y, z, t)$.} But on the earth the quantity~$m/r$ is negligibly small, so that the two systems coalesce with one another and with Euclidean coordinates. Non-Euclidean geometry is only required in the theoretical part of the investigation---the laws of planetary motion and propagation of light through regions where $m/r$~is not negligible; as soon as the light-waves have been safely steered into the terrestrial observatory, the need for non-Euclidean geometry is at an end, and the difference between the isotropic and non-isotropic systems practically disappears. In either system the forward velocity of light along any line is equal to the backward velocity. Consequently the coordinate~$t$ conforms to the convention (\SecRef{11}) that simultaneity may be determined by means of light-signals. If we have a clock at~$A$ and send a light-signal at time~$t_{A}$ which reaches~$B$ and is immediately reflected so as to return to~$A$ at time~$t_{A}'$, the time of arrival at~$B$ will be $\frac{1}{2}(t_{A} + t_{A}')$ just as in the special relativity theory. But the alternative convention, that simultaneity can be determined by slow transport of chronometers, breaks down when there is a gravitational field. This is evident from \SecRef{42}, since the time-rate of a clock will depend on its position in the field. In any case slow transport of a clock is unrealisable because of the acceleration which all objects must submit to.