Etymology
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log-rolling (n.)

also logrolling, in the legislative vote-trading sense, "mutual aid given in carrying out several schemes or gaining individual ends," 1823, American English, from the notion of neighbors on the frontier joining forces for rolling logs into heaps after the trees have been felled to clear the land (as in phrase you roll my log and I'll roll yours); see log (n.1) + verbal noun from roll (v.). "Sometimes many neighbors were invited to assist, and a merrymaking followed. [Century Dictionary]. In lumbering, in reference to rolling logs into a stream where they bound together and floated down to the mills.

LOG-ROLLING. 1. In the lumber regions of Maine it is customary for men of different logging camps to appoint days for helping each other in rolling the logs to the river, after they are felled and trimmed — this rolling being about the hardest work incident to the business. Thus the men of three or four camps will unite, say on Monday, to roll for camp No. 1, — on Tuesday for camp No. 2, — on Wednesday for camp No. 3, — and so on, through the whole number of camps within convenient distance of each other. [Bartlett]

However the phrase is not attested in any literal sense, only the political sense, until 1848.

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day (n.)

Old English dæg "period during which the sun is above the horizon," also "lifetime, definite time of existence," from Proto-Germanic *dages- "day" (source also of Old Saxon, Middle Dutch, Dutch dag, Old Frisian di, dei, Old High German tag, German Tag, Old Norse dagr, Gothic dags), according to Watkins, from PIE root *agh- "a day."  He adds that the Germanic initial d- is "of obscure origin." But Boutkan says it is from PIE root *dhegh- "to burn" (see fever). Not considered to be related to Latin dies (which is from PIE root *dyeu- "to shine").

Meaning originally, in English, "the daylight hours;" it expanded to mean "the 24-hour period" in late Anglo-Saxon times. The day formerly began at sunset, hence Old English Wodnesniht was what we would call "Tuesday night." Names of the weekdays were not regularly capitalized in English until 17c.

From late 12c. as "a time period as distinguished from other time periods." Day-by-day "daily" is from late 14c.; all day "all the time" is from late 14c.  Day off "day away from work" is attested from 1883; day-tripper first recorded 1897. The days in nowadays, etc. is a relic of the Old English and Middle English use of the adverbial genitive.

All in a day's work "something unusual taken as routine" is by 1820. The nostalgic those were the days is attested by 1907. That'll be the day, expressing mild doubt following some boast or claim, is by 1941. To call it a day "stop working" is by 1919; earlier call it a half-day (1838). One of these days "at some day in the near future" is from late 15c. One of those days "a day of misfortune" is by 1936.

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merry (adj.)

Middle English mirie, from Old English myrge "pleasing, agreeable, pleasant, sweet, exciting feelings of enjoyment and gladness" (said of grass, trees, the world, music, song); also as an adverb, "pleasantly, melodiously," from Proto-Germanic *murgijaz, which probably originally meant "short-lasting," (compare Old High German murg "short," Gothic gamaurgjan "to shorten"), from PIE root *mregh-u- "short." The only exact cognate for meaning outside English was Middle Dutch mergelijc "joyful."

The connection to "pleasure" likely was via the notion of "making time fly, that which makes the time seem to pass quickly" (compare German Kurzweil "pastime," literally "a short time;" Old Norse skemta "to amuse, entertain, amuse oneself," from skamt, neuter of skammr "short"). There also was a verbal form in Old English, myrgan "be merry, rejoice." For vowel evolution, see bury (v.).

Not originally applied to humorous moods or speech or conduct, yet the word had a much wider senses in Middle English than modern: "pleasant-sounding" (of animal voices), "fine" (of weather), "handsome" (of dress), "pleasant-tasting" (of herbs). The evolution of the modern senses is probably via the meaning "pleased by a certain event or situation or state of things" (c. 1200). Of persons, "cheerful by disposition or nature; playfully cheerful, enlivened with gladness or good spirits," by mid-14c.

Merry-bout "an incident of sexual intercourse" was low slang from 1780. Merry-begot "illegitimate" (adj.), also "bastard" (n.) are in Grose (1785). Merrie England (now frequently satirical or ironic) is c. 1400, meri ingland, originally in a broader sense of "bountiful, prosperous." Merry Monday was a 16c. term for "the Monday before Shrove Tuesday" (Mardi Gras).

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