Etymology
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cocktail (n.)

"strong, stimulating, cold American drink," first attested 1806; H.L. Mencken lists seven versions of its origin, perhaps the most durable traces it to French coquetier "egg-cup" (15c.; in English cocktay). In New Orleans, c. 1795, Antoine Amédée Peychaud, an apothecary (and inventor of Peychaud bitters) held Masonic social gatherings at his pharmacy, where he mixed brandy toddies with his own bitters and served them in an egg-cup. On this theory, the drink took the name of the cup.

Ayto ("Diner's Dictionary") derives it from cocktail "horse with a docked tail" (one cut short, which makes it stand up somewhat like a cock's comb) because such a method of dressing the tail was given to ordinary horses, the word came to be extended to "horse of mixed pedigree" (not a thoroughbred) by 1800, and this, it is surmised, was extended to the drink on the notion of "adulteration, mixture."

Used from 1920s of any mix of substances (fruit, Molotov). Cocktail party attested by 1907.

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rum (n.)

"liquor distilled from the juice of sugar cane or molasses," 1650s, apparently a shortening of rumbullion (1651), rombostion (1652), words all of uncertain origin, but suspicion falls on rum (adj.) "excellent, fine, good, valuable;" the phrase rum bouse "good liquor" is attested from 1560s and through 17c. The English word was borrowed into Dutch, German, Swedish, Danish, Spanish, Portuguese, Italian, French, and Russian.

In the Library of Trinity College, Dublin, is a manuscript entitled "A briefe description of the Island of Barbados." It is undated but from internal evidence it must have been written about the year 1651. In describing the various drinks in vogue in Barbados, the writer says : "The chief fudling they make in the Island is Rumbullion alias Kill-Divill, and this is made of sugar canes distilled, a hot, hellish, and terrible liquor. ["The Etymology of the Word Rum,"  in Timehri, 1885]

Rum was used from c.1800 in North America as a general (hostile) name for intoxicating liquors, hence rum-runner and much other Prohibition-era slang.

Rum I take to be the name which unwashed moralists apply alike to the product distilled from molasses and the noblest juices of the vineyard. Burgundy in "all its sunset glow" is rum. Champagne, soul of "the foaming grape of Eastern France," is rum. ... Sir, I repudiate the loathsome vulgarism as an insult to the first miracle wrought by the Founder of our religion! [Oliver Wendell Holmes, "The Autocrat of the Breakfast-Table," 1871]
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rum (adj.)

"excellent, fine, good, valuable," canting slang, 1560s, also rome, "fine," said to be from Romany rom "male, husband" (see Romany). A very common 16c. cant word (opposed to queer), as in rum kicks "Breeches of gold or silver brocade, or richly laced with gold or silver" [Grose, "Dictionary of the Vulgar Tongue," 1785].

By 1774 it also had come to mean rather the opposite: "odd, strange, bad, queer, spurious," perhaps because it had been so often used approvingly by rogues in reference to one another. Or perhaps this is a different word. This was the main sense after c. 1800.

Rom (or rum) and quier (or queer) enter largely into combination, thus--rom = gallant, fine, clever, excellent, strong; rom-bouse = wine or strong drink; rum-bite = a clever trick or fraud; rum-blowen = a handsome mistress; rum-bung = a full purse; rum-diver = a clever pickpocket; rum-padder = a well-mounted highwayman, etc.: also queere = base, roguish; queer-bung = an empty purse; queer-cole = bad money; queer-diver = a bungling pickpocket; queer-ken = a prison; queer-mort = a foundered whore, and so forth. [John S. Farmer, "Musa Pedestris," 1896]
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rum-runner (n.)

"smuggler or transporter of illicit liquor," 1919, from rum (n.) + runner.

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mojito (n.)

type of rum-based Cuban cocktail, by 1946, from Cuban Spanish, a diminutive of mojo, a word for certain sauces and marinades; Ayto ("Diner's Dictionary") considers it  to be "probably a reapplication of the Spanish adjective mojo 'wet,'" from mojar "to moisten, make wet," from Vulgar Latin *molliare"to soften by soaking," from Latin mollire "to soften" (see emollient). 

MOJITO
I don't know who originated this one, but every bar in the West Indies serves it, practically every rum recipe booklet gives the formula for it, so my little collection of rum drinks would hardly be complete without it. Such popularity must be deserved, and it is. It's a swell drink! ["Trader Vic's Book of Food and Drink," 1946]
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dropper (n.)

1700, "a distiller" (in colloquial rum-dropper), agent noun from drop (v.). Meaning "small tube from which liquid may be made to fall in drops" is by 1889.

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rattlesnake (n.)

venomous serpent of the Americas noted for the rattle at the end of its tail, 1620s, from rattle + snake (n.).

RATTLE-SNAKE COCKTAIL.*
*So called because it will either cure Rattlesnake bite, or kill Rattlesnakes, or make you see them.
[Harry Craddock, "The Savoy Cocktail Book," 1930]
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Bacardi 

1921, name for a brand of West Indian rum produced by Compania Ron Bacardi, originally of Cuba.

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old-fashioned (adj.)

1650s, "in an outdated style, formed in a fashion that has become obsolete," from old + past participle of fashion (v.). Meaning "partaking of the old ways, suited to the tastes of former times" is from 1680s. Related: Old-fashionedness. New-fashioned is recorded from 1610s.

As a type of cocktail, Old Fashioned is attested by 1901, American English, short for a fuller name.

Old Fashioned Tom Gin Cocktail Mix same as Holland Gin Old Fashioned Cocktail using Old Tom gin in place of Holland [George J. Kappeler, "Modern American Drinks," Akron, Ohio, 1900]

(Old Tom (1821) was a name for a strong variety of English gin.)

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Moscow 

Russian capital, named for the Moskva River, the name of which is of unknown origin. Moscow mule vodka cocktail is attested from 1950.

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