gives the length of the rod at rest on the embankment. Of course, the positions of the extremities of the rods at the instant the observers pass
must be computed according to the simultaneity determinations of the respective observers. If the rods are 186,000 miles in length,
= one centimetre, and the two hyperbolas will be geometrically alike. We may also infer that the space-time distances from
to any of the points on the second hyperbola are all equal to one another. In fact, we may repeat for the second hyperbola, or space hyperbola, the same arguments we made when discussing the time one.
We are now in a position to understand how the FitzGerald contraction arises. Consider, for instance, a rod,
, lying on the embankment. The world-lines of its two extremities will be