Etymology
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a la mode (adv.)

also alamode, 1640s, from French à la mode (15c.), literally "in the (prevailing) fashion" (see a la + mode (n.2)). In 17c., sometimes nativized as all-a-mode. Cookery sense in reference to a dessert served with ice cream is 1903, American English; earlier it was used of a kind of beef stew or soup (1753).

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day care (n.)

also daycare, day-care, "care and supervision of young children during the day," especially on behalf of working parents, by 1943, American English, from day + care (n.). Early references are to care for children of women working national defense industry jobs. For an earlier word, see baby-farmer.

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Santa Claus (n.)

1773 (as St. A Claus, in "New York Gazette"), American English, in reference to the customs of the old Dutch colony of New York, from dialectal Dutch Sante Klaas, from Middle Dutch Sinter Niklaas "Saint Nicholas," bishop of Asia Minor who became a patron saint for children. Now a worldwide phenomenon (Japanese santakurosu). Father Christmas is attested from 1650s.

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third degree (n.)

"intense interrogation by police," 1900, probably a reference to Third Degree of master mason in Freemasonry (1772), the conferring of which included an interrogation ceremony. Third degree as a measure of severity of burns (most severe) is attested from 1866, from French (1832); in American English, as a definition of the seriousness of a particular type of crime (the least serious type) it is recorded from 1865.

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long shot (n.)

also long-shot, in the figurative sense of "something unlikely," 1867, from long (adj.) + shot (n.). The notion is of a shot at a target from a great distance, thus difficult to make. The phrase by a long shot "by a considerable amount," frequently negative, is attested by 1830, American English colloquial. The cinematic sense of the noun phrase is from 1922. As an adjective by 1975.

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hang out (v.)

c. 1400, intransitive (as of the tongue, from the mouth); transitive use by 1560s; see hang (v.) + out (adv.). Colloquial meaning "to be found" is recorded from 1811, "in allusion to the custom of hanging out a sign or 'shingle' to indicate one's shop and business" [Century Dictionary]. As a noun (often hangout) "residence, lodging" attested from 1893; earlier "a feast" (1852, American English).

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Marie Antoinette 

(1755-1793), queen consort of Louis XVI; as the name for a decorative style of France in that period, by 1887. She likely did not say "let them eat cake" (see cake (n.)). The city of Marietta, Ohio, U.S., founded in 1788, was named for her in honor of Louis XVI's financial support of the American Revolution.

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witch hazel (n.)

1540s, probably from Old English wice "Applied generally or vaguely to various trees having pliant branches" [OED], from wican "to bend" (from PIE root *weik- (2) "to bend, to wind") + hæsel, used for any bush of the pine family (see hazel (n.)). The North American bush, from which a soothing lotion is made, was so called from 1670s. This is the source of the verb witch in dowsing.

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stool pigeon (n.)

"police informer," 1859, American English; earlier "one who betrays the unwary (or is used to betray them)," 1821, originally a decoy bird (1812); said to be from decoys being fastened to stools to lure other pigeons. But perhaps related to stall "decoy bird" (c. 1500), especially "a pigeon used to entice a hawk into the net" (see stall (n.2)). Also see pigeon.

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care package (n.)

1945, originally CARE package, supplies sent out by "Cooperative for American Remittances to Europe," established 1945 by U.S. private charities to coordinate delivery of aid packages to displaced persons in Europe after World War II and obviously named for the sake of the acronym. The name was repackaged late 1940s to "Cooperative for Assistance and Relief Everywhere," to reflect its expanded mission.

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