"evening before the first day of the new year," c. 1300; "þer þay dronken & dalten ... on nwe gerez euen." The Julian calendar began on January 1, but the Christian Church frowned on pagan celebrations of this event and chose the Feast of the Annunciation (March 25) as its New Year's Day. The civic year in England continued to begin January 1 until late 12c., and even though legal documents then shifted to March 25, popular calendars and almanacs continued to begin on January 1. The calendar reform of 1751 restored the Julian New Year in England. New Year's was the main midwinter festival in Scotland from 17c., when Protestant authorities banned Christmas, and continued so after England reverted to Christmas, hence the Scottish flavor ("Auld Lang Syne," etc.). New Year's gathering in public places began 1878 in London, after new bells were installed in St. Paul's.
Old English lang "having a great linear extent, that extends considerably from end to end; tall; lasting," from Proto-Germanic *langa- (source also of Old Frisian and Old Saxon lang, Old High German and German lang, Old Norse langr, Middle Dutch lanc, Dutch lang, Gothic laggs "long").
The Germanic words perhaps are from PIE *dlonghos- (source also of Latin longus "long, extended; further; of long duration; distant, remote," Old Persian darga-, Persian dirang, Sanskrit dirghah "long"), from root *del- (1) "long" (source also of Greek dolikhos "long," endelekhes "perpetual"). Latin longus (source of prolong, elongate, longitude, etc.) thus is probably cognate with, but not the source of, the Germanic words. The word illustrates the Old English tendency for short "a" to become short "o" before -n- (also retained in bond/band and West Midlands dialectal lond from land and hond from hand).
Also in Old English in reference to time, "drawn out in duration," with overtones of "serious." The old sense of "tall" now appears to be dialectal only, or obsolete. For long "during a long time" is from c. 1300. To be long on something, "have a lot" of it, is from 1900, American English slang. A long vowel (c. 1000) originally was pronounced for an extended time. Mathematical long division is from 1808. Sporting long ball is from 1744, originally in cricket. Long jump as a sporting event is attested from 1864. A long face, one drawn downward in expression of sadness or solemnity, is from 1786. Long in the tooth (1841 of persons) is from horses showing age by recession of gums (but not in this sense until 1870). Long knives, name Native Americans gave to white settlers (originally in Virginia/Kentucky) is from 1774, perhaps a reference to their swords. Long time no see, supposedly imitative of American Indian speech, is first recorded 1919 as Chinese English.
Figurative sense of "the distance one goes, extremity to which something is carried" is from 1690s. Phrase at length "to full extent" is attested from c. 1500. As "the length of a swimming pool," 1903. From the notion of "a piece or portion of the extent of anything" come the theater slang sense "a 42-line portion of an actor's part" (1736) and the sporting sense "the length of a horse, car, etc. in a race" used as a unit of measure (1650s).