Etymology
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mid-air (n.)

also midair, "the part of the air between the clouds and the air near the ground," from mid (adj.) + air (n.1).

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mid (adj.)

"middle; being the middle part or midst; being between, intermediate," Old English mid, midd from Proto-Germanic *medja- (source also of Old Norse miðr, Old Saxon middi, Old Frisian midde, Middle Dutch mydde, Old High German mitti, German mitte, Gothic midjis "mid, middle"), from PIE root *medhyo- "middle."

By late Middle English probably felt as a prefix only, and now surviving in English only as a prefix (mid-air, midstream, etc.). Prefixed to months, seasons, etc. from late Old English. As a preposition, "in the middle of, amid" (c. 1400) it is from in midde or a shortened form of amid (compare midshipman) and sometimes is written 'mid.

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mid (prep.)

"with," a preposition formerly in common use but now entirely superseded by with (except in the compound midwife) from Old English mid "with, in conjunction with, in company with, together with, among, at the same time as," and in part from cognate Old Norse mið, from Proto-Germanic *medthi- (source also of Old Saxon mid, Old Frisian mith "together with, with the help of," Dutch met, Old High German and German mit, Danish med, Gothic miþ "with"), from PIE *meti-, suffixed form of root *me- "in the middle" (compare meta-).

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air (n.3)
"melody, tune, connected rhythmic succession of distinct musical sounds," 1580s, nativized from Italian aria (see aria), perhaps via French.
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air (n.1)

c. 1300, "invisible gases that surround the earth," from Old French air "atmosphere, breeze, weather" (12c.), from Latin aer "air, lower atmosphere, sky," from Greek aēr (genitive aeros) "mist, haze, clouds," later "atmosphere" (perhaps related to aenai "to blow, breathe"), which is of unknown origin. It is possibly from a PIE *awer- and thus related to aeirein "to raise" and arteria "windpipe, artery" (see aorta) on notion of "lifting, suspended, that which rises," but this has phonetic difficulties.

In Homer mostly "thick air, mist;" later "air" as one of the four elements. Words for "air" in Indo-European languages tend to be associated with wind, brightness, sky. In English, air replaced native lyft, luft (see loft (n.)). In old chemistry, air (with a qualifying adjective) was used of any gas.

To be in the air "in general awareness" is from 1875; up in the air "uncertain, doubtful" is from 1752. To build castles in the air "entertain visionary schemes that have no practical foundation" is from 1590s (in 17c. English had airmonger "one preoccupied with visionary projects"). Broadcasting sense (as in on the air, airplay) first recorded 1927. To give (someone) the air "dismiss" is from 1900. Air pollution is attested by 1870. Air guitar is by 1983. Air traffic controller is from 1956.

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air (n.2)
1590s, "manner, appearance" (as in an air of mystery); 1650s, "assumed manner, affected appearance" (especially in phrase put on airs, 1781), from French air "look, appearance, mien, bearing, tone" (Old French aire "reality, essence, nature, descent, extraction" (12c.); compare debonair), which is perhaps from Latin ager "place, field, productive land" (from PIE root *agro- "field") on notion of "place of origin."

But some French sources connect this Old French word with the source of air (n.1), and it also is possible these senses in English developed from or were influenced by air (n.1); compare sense development of atmosphere and Latin spiritus "breath, breeze," also "high spirit, pride," and the extended senses of anima.
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air (v.)
1520s, "expose to open air," 1520s, from air (n.1). Figurative sense of "expose ostentatiously, make public" is from 1610s of objects, 1862 of opinions, grievances, etc. Meaning "to broadcast" (originally on radio) is from 1933. Related: Aired; airing.
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mid-Atlantic (n.)

by 1804, "the middle of the Atlantic Ocean," from mid (adj.) + Atlantic. In U.S. history, Mid-Atlantic states in reference to the middle states on the Atlantic coast is by 1842.

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mid-course 

"in the middle of one's course," 1560s, from mid (adj.) + course (n.).

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mid-afternoon (n.)

"the middle of the afternoon," c. 1400, from mid (adj.) + afternoon. Earlier in the same sense was mid-overnoon (late 13c.).

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