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"The way you write science fiction is: you sit down at your writing machine and you open your mind to the first thought that comes through."
- Frederik Pohl

Gravity Train  
  An underground railway system that utilizes gravity for acceleration.  

This same idea is a major plot 'device' in the 2012 version of the Total Recall movie.

They joined the line for the gravity train to Archimedes. The four of them boarded, the car was sealed, and Lilo's weight dropped away as the car fell down the inclined tunnel for almost four hundred kilometers. Somewhere under the Appenines the tunnel begain to slope up again, gradually slowing their speed to a crawl as the car nosed into the elevator which took them up to inhabited levels.
From The Ophiuchi Hotline, by John Varley.
Published by Quantum Science Fiction in 1977
Additional resources -

This idea was also used in Hugo Gernsback's 1911 novel Ralph 124c 41 + - see the entry for Sub-Atlantic Tube.

And what is the best shape or curve for this tunnel to follow? See the discussion in the article for gravity-assisted subway from Larry Niven's 1976 story A World Out of Time.

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Additional resources:
  More Ideas and Technology from The Ophiuchi Hotline
  More Ideas and Technology by John Varley
  Tech news articles related to The Ophiuchi Hotline
  Tech news articles related to works by John Varley

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