Again it follows from~\Eq{(5.2)} that when \[ \left(\frac{dx'}{dt'}\right)^{2} + \left(\frac{dy'}{dt'}\right)^{2} + \left(\frac{dz'}{dt'}\right)^{2} = c^{2}, \] $ds = 0$, and hence \[ \left(\frac{dx}{dt}\right)^{2} + \left(\frac{dy}{dt}\right)^{2} + \left(\frac{dz}{dt}\right)^{2} = c^{2}. \] Thus when the resultant velocity relative to~$S'$ is~$c$, the velocity relative to~$S$ is also~$c$, whatever the direction. We see that the velocity~$c$ has a unique and very remarkable property. According to the older views of absolute time this result appears incredible. Moreover we have not yet shown that the formulae have practical significance, since $c$~might be imaginary. But experiment has revealed a real velocity with this remarkable property, viz.\ $299,860$~km.\ per~sec. We shall call this the \emph{fundamental velocity}. \index{Fundamental velocity}% \index{Velocity, fundamental}% By good fortune there is an entity---light---which travels with the fundamental \index{Light!velocity of}% velocity. It would be a mistake to suppose that the existence of such an entity is responsible for the prominence accorded to the fundamental velocity~$c$ in our scheme; but it is helpful in rendering it more directly accessible to experiment. The Michelson-Morley experiment detected no difference in the \index{Michelson-Morley experiment}% velocity of light in two directions at right angles. Six months later the earth's \index{Velocity of light}% orbital motion had altered the observer's velocity by $60$~km.\ per~sec., corresponding to the change from~$S'$ to~$S$, and there was still no difference. Hence the velocity of light has the distinctive property of the fundamental velocity. Strictly speaking the Michelson-Morley experiment did not prove directly that the velocity of light was constant in all directions, but that the average to-and-fro velocity was constant in all directions. The experiment compared the times of a journey ``there-and-back.'' If $v(\theta)$~is the velocity of light in the direction~$\theta$, the experimental result is \[ \left. \begin{alignedat}{2} \frac{1}{v(\theta)} + \frac{1}{v(\theta + \pi)} &= \text{const.} &&= C \\ \frac{1}{v'(\theta)} + \frac{1}{v'(\theta + \pi)} &= \text{const.} &&= C' \end{alignedat} \right\} \Tag{(6.3)} \] for all values of~$\theta$. The constancy has been established to about $1$~part in~$10^{10}$. It is exceedingly unlikely that the first equation could hold unless \[ v(\theta) = v(\theta + \pi) = \text{const.}; \] and it is fairly obvious that the existence of the second equation excludes the possibility altogether. However, on account of the great importance of the identification of the fundamental velocity with the velocity of light, we give a formal proof.