Etymology
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hair (n.)

Old English hær "hair, a hair," from Proto-Germanic *hēran (source also of Old Saxon, Old Norse, Old High German har, Old Frisian her, Dutch and German haar "hair"), perhaps from PIE *ghers- "to stand out, to bristle, rise to a point" (source also of Lithuanian šerys "bristle;" see horror).

Spelling influenced by Old Norse har and Old English haire "haircloth," from Old French haire, from Frankish *harja or some other Germanic source (see above). Hair-dye is from 1803. To let one's hair down "become familiar" is first recorded 1850. Homeopathic phrase hair of the dog (that bit you), remedy from the same thing that caused the malady, especially a drink on the morning after a debauch, 1540s in English, is in Pliny.

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hair-trigger (n.)

1795; Figurative use by 1841. Hair perhaps in reference to the slight pressure required to activate it.

The difference between a hair-trigger and a common trigger is this—the hair-trigger, when set, lets off the cock by the slightest touch, whereas the common trigger requires a considerable degree of force, and consequently is longer in its operation. [Charles James, "Military Dictionary," London, 1802]
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fund-raiser (n.)
also fundraiser, 1957, from fund (n.) + raise (v.).
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hell-raiser (n.)
1906 (to raise hell "create a ruckus" is from 1847, American English), from hell + agent noun from raise (v.). Related: Hell-raising. Probably not from the U.S. political cry "Kansas should raise less corn and more hell" (1900).
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long-hair (n.)

also longhair, 1893, "cat with long hair," from long (adj.) + hair (n.). As "intellectual," especially in musical tastes, "devotee of classical music," 1920 (late 19c. long hair was noted as a characteristic of classical musicians, perhaps inspired by the famous locks of Liszt). Sense of "hippie" attested from 1969. The adjective long-haired is attested from mid-15c.

Forty years ago, a music teacher who was not born abroad and who did not wear long hair was regarded with suspicion. He was spurious—not the real thing. On the face of it he could not be a good musician. [W. Francis Gates, in "The Music Student," vol. i, no. 3, October 1915]
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cross-hair (n.)

also crosshair, cross-hairs, "very fine line (originally spider's silk) stretched across the focal plane of a telescope or microscope, forming a cross with another," 1755 of a telescope, 1780 in gunnery, from cross- + hair (n.). Also often in early 19c. spider-line, spider's-line (1819).

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hair-splitting (n.)
"making over-nice distinctions," by 1739, from hair + verbal noun from split (v.). To split hairs "make over-fine distinctions" is first recorded 1650s, as to cut the hair. Hair also being 18c. slang for "female pudendum," hair-splitter was noted in 1811 as slang for "penis."
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hair-shirt (n.)
garment of ascetics and penitents, 1680s, from hair + shirt. Figurative use by 1884. Earlier, such a garment was called simply a hair (c. 1200); and compare haircloth.
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hair-raising (adj.)
"exciting," 1837, from hair + raise (v.). In 19c. works, sometimes as jocular mock-classical tricopherous.
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