How do cable cars clang up and down steep San Francisco hills?

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The motive force for cable cars is provided by a moving cable generated from a power station.  The system was conceived in 1867 by the American mechanic Andrew S. Hallidie.  By 1873 the first cable railroad, built by the Clay Street Hill Railroad Company, was in operation in San Francisco.  This remarkable system, which aroused considerable excitement at the time, is basically the same today and continues to draw admiration from visitors to the city.  Many cities followed San Francisco’s lead in the 1870’s but abandoned the system for practical electrical power in the twentieth century.
The first cable car line was in San Francisco extended 2,800 feet over a 307-foot incline.  A grip device on the car (“Hallidie’s grip”) clamps onto a continuously moving subsurface cable between the rails, which draws the car along.  An operator stops the car by releasing the grip and applying the brakes.
On exceptionally steep inclines a funicular system employing two cars connected by cables is more efficient.  As one car ascends, the other descends and provides a counterbalance.  This works best on a single track, except, of course, in the middle, where a double track allows the cars to pass each other.

The motive force for cable cars is provided by a…