Etymology
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air-rifle (n.)
rifle that uses compressed air power to fire the projectile, 1851, from air (n.1) + rifle (n.).
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air-space (n.)

also airspace, by 1821 in reference to stove and furnace construction, from air (n.1) + space (n.). From 1852 in reference to the cubic contents of a room (with reference to the persons in it) in sanitary regulations for boarding rooms, hospitals, etc. In firearms, "a vacant space between the powder charge and the projectile" (1847). By 1910 as "portion of the atmosphere controlled by a country above its territory."

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air-lock (n.)

by 1851, "air-tight chamber in which operations are carried on under water," to regulate pressure for the safety of workers, from air (n.1) + lock (n.1) in the canal sense.

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hot air (n.)
"unsubstantiated statements, boastful talk," 1900, from hot (adj.) + air (n.1). The adjectival phrase hot-air (of balloons, etc.) is from 1813.
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air-hole (n.)

"an opening to admit or discharge air," 1766, from air (n.1) + hole (n.).

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open-air (adj.)

"outdoor, in the open air," 1520s, from open (adj.) + air (n.1).

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air force (n.)
1917, from air (n.1) + force (n.); first attested with creation of the Royal Air Force. There was no United States Air Force until after World War II. The Air Corps was an arm of the U.S. Army. In 1942, the War Department reorganized it and renamed it Army Air Forces. The National Security Act of 1947 created the Department of the Air Force, headed by a Secretary of the Air Force, and the U.S.A.F.
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air-conditioner (n.)
from air (n.1) + conditioner. Along with air-conditioning first attested 1909, originally an industrial process in textile manufacturing. The word conditioning was applied to the determination of the moisture content of textiles, control of which was essential to spin fine cotton yarns. The original purpose of air-conditioning was to purify air and regulate moisture. In 1906 Stuart W. Cramer of Charlotte, N.C., and Willis H. Carrier of Buffalo, N.Y., independently devised methods of using a fine spray of water to cool air. Self-contained air-conditioning units, complete with refrigeration equipment, were widely used to cool air in U.S. stores, restaurants, etc. from the 1930s. An earlier name for such a device (using ice and fans) was air cooler (1875).
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