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"It was [H.G. Wells'] adolescent fiction, his imaginative stories, that live forever - and yet are not acknowledged in literature classes as being great literature. So to hell with the academics!"
- Greg Bear

Artificial Gravity  
  Procuring gravitational forces without a suitably large mass.  

This appears to be the first mention of the phrase "artificial gravity" in science fiction, but not the first use of the phrase (see discussion below). As far as I know, this is a reference to gravitational force despite the mention of magnetic force in the control room.

It was near midnight when Snap and I closed and sealed the helio-room and started for the chart-room, where we were to meet with Captain Carter and the other officers. The passengers had nearly all retired. A game was in progress in the smoking room, but the deck was almost deserted.

Snap and I were passing along one of the interior corridors. The stateroom doors, with the illumined names of the passengers, were all closed. The metal grid of the floor echoed our footsteps. Snap was in advance of me. His body suddenly rose in the air. He went like a balloon to the ceiling, struck it gently, and all in a heap came floating down and landed on the floor!

"What in the infernal!--"

He was laughing as he picked himself up. But it was a brief laugh. We knew what had happened: the artificial gravity-controls in the base of the ship, which by magnetic force gave us normality aboard, were being tampered with! For just this instant, this particular small section of this corridor had been cut off. The slight bulk of the Planetara, floating in space, had no appreciable gravity pull on Snap's body, and the impulse of his step as he came to the unmagnetized area of the corridor had thrown him to the ceiling. The area was normal now. Snap and I tested it gingerly.

He gripped me. "That never went wrong by accident, Gregg! Someone down there--"

* * * * *

We rushed to the nearest descending ladder. In the deserted lower room the bank of dials stood neglected. A score of dials and switches were here, governing the magnetism of different areas of the ship. There should have been a night operator, but he was gone.

Technovelgy from Brigands of the Moon, by Ray Cummings.
Published by Astounding Stories of Super Science in 1930
Additional resources -

The phrase "artificial gravity" was used in engineering at least a century earlier; this from The Circle of the Mechanical Arts (1813):

One method was, by applying a loadstone so as to affect the balance in the manner that gravity affects the pendulum, and this appears to be an ingenious notion: for, by the applications of this, as a kind of artificial gravity, a pendulum might be made to vibrate, either in the plane of the horizon, or in any degree inclined, as well as perpendicular to it.

This basic problem of space travel was recognized as early as the 17th century; see the entry for weightlessness in space from The Man in the Moone (1638), by Francis Godwin.

Compare this scheme for providing a way for people to stay on the floor and off the ceiling in a space station or space craft with the method used in the city of space in Jack Williamson's The Prince of Space (1931).

See also the entry for paragravity from Collision Orbit (1941) by Jack Williamson. Robert Heinlein called it "pseudogravity", as in the story Common Sense (1941).

The references to "magnetic force" probably reflected a belief that, just as it is possible to produce electricity with magnetism, and magnetism with electricity, so it would one day be possible to relate a third force, gravitation, with the better-controlled forces of electricity and magnetism. A hope not borne out by scientific efforts thus far. See also Electronized Gravity Plate from Blood of the Moon (1936) by Ray Cummings.

Physicist Patrick Blackett formulated a theory of planetary magnetism and gravity in the late 1940's that greatly influenced the thinking of sf writer James Blish; see the discussion in the article on the spindizzy from Blish's 1950's novel City in Flight.

Also, I believe Olaf Stapledon mentions the idea of artificial gravity in this same year, but in a later month of publication; see artificial gravity system from Last and First Men (1930) by Olaf Stapledon.

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Additional resources:
  More Ideas and Technology from Brigands of the Moon
  More Ideas and Technology by Ray Cummings
  Tech news articles related to Brigands of the Moon
  Tech news articles related to works by Ray Cummings

Artificial Gravity-related news articles:
  - Artificial Gravity? Why Not?

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Denmark Joins The 'Zero Debris Charter' To Clean Up Space
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Project Hyperion - Generation Ship Designers Needed!

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