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:

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.