If the velocity of light \Foreign{in vacuo} were a constant~$c'$ differing from the fundamental velocity~$c$, the foregoing calculation would give for Fresnel's convection-coefficient \[ 1 - \frac{c'^{2}}{c^{2}} · \frac{1}{\mu^{2}}. \] Thus Fizeau's experiment provides independent evidence that the fundamental \index{Fizeau's experiment}% velocity is at least approximately the same as the velocity of light. In the most recent repetitions of this experiment made by Zeeman\footnote {\Title{Amsterdam Proceedings}, vol.~\Vol{XVIII}, pp.~398 and 1240.} the agreement between theory and observation is such that $c'$~cannot differ from~$c$ by more than $1$~part in~$500$. \PageSep{22} \Section{7.}{Timelike and spacelike intervals} \index{Spacelike intervals}% \index{Timelike intervals}% We make a slight change of notation, the quantity hitherto denoted by~$ds^{2}$ being in all subsequent formulae replaced by $-ds^{2}$, so that \Eq{(4.6)}~becomes \[ ds^{2} = c^{2}\, dt^{2} - dx^{2} - dy^{2} - dz^{2}. \Tag{(7.1)} \] There is no particular advantage in this change of sign; it is made in order to conform to the customary notation. The formula may give either positive or negative values of~$ds^{2}$, so that the interval between real events may be a real or an imaginary number. We call real intervals timelike, and imaginary intervals spacelike. From \Eq{(7.1)} \begin{align*} \left(\frac{ds}{dt}\right)^{2} &= c^{2} - \left(\frac{dx}{dt}\right)^{2} - \left(\frac{dy}{dt}\right)^{2} - \left(\frac{dz}{dt}\right)^{2} \\ &= c^{2} - v^{2}, \Tag{(7.2)} \end{align*} where $v$~is the velocity of a point describing the track along which the interval lies. The interval is thus real or imaginary according as $v$~is less than or greater than~$c$. Assuming that a material particle cannot travel faster than light, the intervals along its track must be timelike. We ourselves are limited by material bodies and therefore can only have direct experience of timelike intervals. We are immediately aware of the passage of time without the use of our external senses; but we have to infer from our sense perceptions the existence of spacelike intervals outside us. From any event $x$,~$y$, $z$,~$t$, intervals radiate in all directions to other events; and the real and imaginary intervals are separated by the cone \[ 0 = c^{2}\, dt^{2} - dx^{2} - dy^{2} - dz^{2}, \] which is called the \emph{null-cone}. Since light travels with velocity~$c$, the track of \index{Null-cone}% any light-pulse proceeding from the event lies on the null-cone. When the $g$'s are not constants and the fundamental quadratic form is not reducible to~\Eq{(7.1)}, there is still a null-surface, given by $ds = 0$ in~\Eq{(2.1)}, which separates the timelike and spacelike intervals. There can be little doubt that in this case also the light-tracks lie on the null-surface, but the property is perhaps scarcely self-evident, and we shall have to justify it in more detail later.