Page:Relativity (1931).djvu/64

Let us now consider a seconds-clock which is permanently situated at the origin $(x'=0)$ of $K'$. $t'=0$ and $t'=1$ are two successive ticks of this clock. The first and fourth equations of the Lorentz transformation give for these two ticks:

$t=0$

and

$t={\frac {1}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}$

As judged from $K$, the clock is moving with the velocity $v$; as judged from this reference-body, the time which elapses between two strokes of the clock is not one second, but ${\frac {1}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}$ seconds, i.e. a somewhat larger time. As a consequence of its motion the clock goes more slowly than when at rest. Here also the velocity $c$ plays the part of an unattainable limiting velocity.