An interesting fact about catenary is that the supports
which hold the wire
are arranged to vary in distance every other post. So one long, one short, one long. Granted, the difference in these distances is mere inches
but it is meant to encourage smooth, more even contact with the pantograph
of passing trains. This also ensures more dispersed wear on the contact portion of the pantograph itself - as the wire is constantly moving laterally
the chance of making a trough
in the metal is greatly reduced.
The tension is also kept up by way of large counterweights, usually hung from one of the supports, to ensure the wire won't droop (pantograph height is a precise thing). When this is done, the catenary is divided into sections. One wire will join the existing wire from an addition support, and the two will run parallel. After passing another support or two, the first wire will then run off to one side to either terminate or attach to the counterweight, while the second is now the power supply wire. This ensures uninterupted power for the train (otherwise you'd have that subway syndrome where the lights go off in the car as it passes over a switch where there's no third rail). This sometimes is how section breaks are isolated, in addition to being a convenient way to keep the wires up!
Edit: I've now discovered, in the UK at least, that the side-to-side movement of the wire is 50cm