Story, first published: Stellar #1 (1974)
The "cylinder" is an engine using time as a source of energy which falls from an alien ship near a think tank. Graduates of the think tank are summoned back to find out how to turn off the time machine. One of the volunteers turns the control clockwise and disappears back into time; the other volunteer, the narrator, turns the control in the opposite direction and vanishes into the future. By then the device has been duplicated and used to send ships to the stars.
Ewald, Robert J.: When the Fires Burn High and the Wind is from the North, p.114-115