Etymology
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blue (adj.2)

"lewd, indecent" recorded from 1840 (in the form blueness, in an essay of Carlyle's); the sense connection with the color name (see blue (adj.1)) is unclear, and is opposite to that in blue laws (q.v.). John Mactaggart's "Scottish Gallovidian Encyclopedia" (1824), containing odd words he had learned while growing up in Galloway and elsewhere in Scotland, has an entry for Thread o'Blue, "any little smutty touch in song-singing, chatting, or piece of writing." Farmer ["Slang and Its Analogues Past and Present," 1890] offers the theory that this meaning derives from the blue dress uniforms issued to harlots in houses of correction (from c. 1600), but he writes that the earlier slang authority John Camden Hotten "suggests it as coming from the French Bibliothèque Bleu, a series of books of very questionable character," and adds, from Hotten, that, "Books or conversation of an entirely opposite nature are said to be Brown or Quakerish, i.e., serious, grave, decent."

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blue (v.)

"to make blue," c. 1600, from blue (adj.1).

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blue (n.)

"the color of the clear sky," c. 1300, from blue (adj.1). From late 15c. as "blue clothing." The blue is from 1640s as "the sky" (hence bolt from the blue "lightning," 1837); from 1821 as "the sea." In reference to a particular party which has chosen blue for its color, by 1835. "In most parts of England the Conservative party" [OED], but in 17c. it often was the Whig color (opposed to royal red).

Blue was by c. 1600 the distinctive color of the dress of servants, which may be the reason police uniforms are blue, a tradition Farmer dates to Elizabethan times. Blue as the color of police uniforms in U.S. is by 1853, when New York City professionalized its force. They previously had had no regular uniforms, only badges.

An outburst of indignation followed [the order to wear uniforms]. The men declared the order was a violation of their rights as free men ; that no respecting American would wear livery, and raised a fund of five hundred dollars to test in the courts the authority of the Commissioners to compel them to wear uniforms. But the order was enforced when the day came. [John Bach McMaster, "A History of the People of the United States,"  vol. viii, 1913] 
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blue (adj.1)

"of the color of the clear sky," c. 1300, bleu, blwe, etc., "sky-colored," also "livid, lead-colored," from Old French blo, bleu "pale, pallid, wan, light-colored; blond; discolored; blue, blue-gray," from Frankish *blao or some other Germanic source, from Proto-Germanic *blæwaz (source also of Old English blaw, Old Saxon and Old High German blao, Danish blaa, Swedish blå, Old Frisian blau, Middle Dutch bla, Dutch blauw, German blau "blue").

This is from PIE *bhle-was "light-colored, blue, blond, yellow," from root *bhel- (1) "to shine, flash, burn," also "shining white" and forming words for bright colors. The same PIE root yielded Latin flavus "yellow," Old Spanish blavo "yellowish-gray," Greek phalos "white," Welsh blawr "gray," showing the slipperiness of definition in Indo-European color-words. Many Indo-European languages seem to have had a word to describe the color of the sea, encompassing blue and green and gray; such as Irish glass (from PIE root *ghel- (2) "to shine,"); Old English hæwen "blue, gray," related to har (see hoar); Serbo-Croatian sinji "gray-blue, sea-green;" Lithuanian šyvas, Russian sivyj "gray."

The exact color to which the Gmc. term applies varies in the older dialects; M.H.G. bla is also 'yellow,' whereas the Scandinavian words may refer esp. to a deep, swarthy black, e.g. O.N. blamaðr, N.Icel. blamaður 'Negro' [Buck] 

The present spelling in English is since 16c., common from c. 1700. The sense "lead-colored, blackish-blue, darkened as if by bruising" is perhaps by way of the Old Norse cognate bla "livid, lead-colored." It is the meaning in black and blue, and blue in the face "livid with effort" (1864, earlier black and blue in the face, 1829).

The color of constancy since Chaucer at least, but apparently for no deeper reason than the rhyme in true blue (c. 1500). The figurative meaning "sad, sorrowful, afflicted with low spirits" is from c. 1400, perhaps from the "livid" sense and implying a bruised heart or feelings. Of women, "learned, pedantic," by 1788 (see bluestocking). In some phrases, such as blue murder, it appears to be merely intensive.

Few words enter more largely into the composition of slang, and colloquialisms bordering on slang, than does the word BLUE. Expressive alike of the utmost contempt, as of all that men hold dearest and love best, its manifold combinations, in ever varying shades of meaning, greet the philologist at every turn. [John S. Farmer, "Slang and Its Analogues Past and Present," 1890, p.252] 

Blue pencil as an editor's characteristic tool to mark corrections in copy is from 1885; also as a verb from 1885. The fabulous story of Blue-beard, who kept his murdered wives in a locked room, is in English from 1798. For blue ribbon see cordon bleu under cordon. Blue whale is attested from 1851, so called for its color. Blue cheese is from 1862. Blue water "the open ocean" is from 1822. Blue streak, of something resembling a bolt of lightning (for quickness, intensity, etc.) is from 1830, Kentucky slang. Delaware has been the Blue Hen State at least since 1830, supposedly from a nickname of its regiments in the Revolutionary War.

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blue-jeans (n.)

from 1843 as a type of fabric; see blue (adj.1) + jean. As short for blue-jeans trousers, from 1878.

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blue peter (n.)

a nautical term for a blue flag having a white square in the center, hoisted at the fore royal masthead as a signal to report on board as the vessel is about to go to sea, attested by c. 1800, from blue (adj.1), but the significance of peter is uncertain and disputed. Two common guesses are that it is an abbreviation of repeater or that it stands for French partir

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blue-chip (adj.)

1904 in reference to the high-value poker counter, also in the figurative sense of "valuable." The stock exchange sense, in reference to "shares considered a reliable investment," is recorded by 1929; especially of stocks that saw spectacular rises in value in the four years or so before the Wall Street crash of that year wiped out most of it. See blue (adj.1) + chip (n.1).

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blue laws 

severe Puritanical code said to have been enacted mid-17c. at the founding of New Haven and Connecticut colonies, 1781; of uncertain signification, perhaps from the notion of coldness, or from one of the figurative senses in blue (adj.1). Blue was the color adopted by 17c. Scottish Covenanters (in contradistinction to the royal red) and hence the color for a time acquired an association with strictness in morals or religion. Or perhaps connected to bluestocking in the sense of "puritanically plain or mean" (see bluestocking, which is a different application of the same term); the parliament of 1653 was derisively called the bluestocking parliament.

The assertion by some writers of the existence of the blue laws has no other basis than the adoption by the first authorities of the New Haven colony of the Scriptures as their code of law and government, and their strict application of Mosaic principles. [Century Dictionary]

Long, detailed lists of them often are given, but the original reference (in an anonymous history of Connecticut printed in London during the Revolution) says they were so-called by the neighboring colonies, "were never suffered to be printed," and then gives its own long list of them in quotations. The common explanation (dating to 1788) that they were written on blue paper is not now considered valid.

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blue moon (n.)

"a long time," 1821, often in phrases indicating something rarely occurring. Compare at the Greek calends (from an ancient Roman phrase alluding to the fact that the Greeks had nothing corresponding to the Roman calends), and the native in the reign of Queen Dick and Saint Geoffrey's Day "Never, there being no saint of that name," reported in Grose (1788). Nevermass "date which never comes" is from 1540s. Blue moon is suggested earliest in this couplet from 1528:

Yf they say the mone is blewe,
We must beleve that it is true.

Though this might refer to calendrical calculations by the Church. Thus the general "rareness" sense of the term is difficult to disentangle from the specific calendrical one (commonly misinterpreted as "second full moon in a calendar month," but actually a quarterly calculation). In either case, the sense of blue here is obscure. Literal blue moons do sometimes occur under extreme atmospheric conditions.

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blue-plate (adj.)

in reference to restaurant meals, 1918, from blue (adj.1) + plate (n.). The term arose in the trade, to refer to a complete dinner offered at a reasonable price and served on a single, large plate of a good grade of china.

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