Etymology
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lynch (v.)

1835, "inflict severe (but not deliberately fatal) bodily punishment (on someone) without legal sanction," from earlier Lynch law (1811), in reference to such activity, which was likely named after William Lynch (1742-1820) of Pittsylvania, Virginia, who c. 1780 led a vigilance committee to keep order there during the Revolution. Other sources trace the name to Charles Lynch (1736-1796) a Virginia magistrate who fined and imprisoned Tories in his district c. 1782, but the connection to him is less likely. The surname is perhaps from Irish Loingseach "sailor."

It implies lawless concert or action among a number of members of the community, to supply the want of criminal justice or to anticipate its delays, or to inflict a penalty demanded by public opinion, though in defiance of the laws. [Century Dictionary, 1895]

Originally any sort of summary justice, done without authority of law, for a crime or public offense; it especially referred to flogging or tarring-and-feathering. At first the act was associated with frontier regions (as in the above citation), though from c. 1835 to the U.S. Civil War it also often was directed against abolitionists. The narrowing of the meaning to "extra-legal execution by hanging" is evident by the 1880s, and after c. 1893 lynching mostly meant killings of blacks by white mobs (especially in retaliation for alleged sexual assaults of white women). This shift in use seems due in part to the work of African-American journalist and activist Ida B. Wells. Lynch mob is attested from 1838. Compare earlier Lydford law, from a place in Dartmoor, England, "where was held a Stannaries Court of summary jurisdiction" [Weekley], hence:

Lydford law: is to hang men first, and indite them afterwards. [Thomas Blount, "Glossographia," 1656]

Also in a similar sense was Jedburgh justice (1706) and, as a verb, to Dewitt (1680s), a reference to two Dutch statesmen of that name, opponents of William of Orange, murdered by a mob in 1672. Related: Lynched; lynching. The city of Lynchburg, Virginia, dates to the 1750s when John Lynch, brother to Charles but a peaceable Quaker, had a ferry landing on the James River there.

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order (n.)

c. 1200, "body of persons living under a religious discipline," from Old French ordre "position, estate; rule, regulation; religious order" (11c.), from earlier ordene, from Latin ordinem (nominative ordo) "row, line, rank; series, pattern, arrangement, routine," originally "a row of threads in a loom," from Proto-Italic *ordn- "row, order" (source also of ordiri "to begin to weave;" compare primordial), which is of uncertain origin. Watkins suggests it is a variant of PIE root *ar- "to fit together," and De Vaan finds this "semantically attractive."

The original English word reflects a medieval notion: "a system of parts subject to certain uniform, established ranks or proportions," and was used of everything from architecture to angels. Old English expressed many of the same ideas with endebyrdnes. From the notion of "formal disposition or array, methodical or harmonious arrangement" comes the meaning "fit or consistent collocation of parts" (late 14c.).

Meaning "a rank in the (secular) community" is first recorded c. 1300. Sense of "a regular sequence or succession" is from late 14c. The meaning "command, directive" is first recorded 1540s, from the notion of "that which keep things in order." Military and honorary orders grew out of the fraternities of Crusader knights.

The business and commerce sense of "a written direction to pay money or deliver property" is attested by 1837; as "a request for food or drink in a restaurant" from 1836. In natural history, as a classification of living things next below class and next above family, it is recorded from 1760. Meaning "condition of a community which is under the rule of law" is from late 15c.

In order "in proper sequence or arrangement" is from c. 1400; out of order "not in proper sequence or orderly arrangement" is from 1540s; since 20c. principally mechanical, but not originally so ("and so home, and there find my wife mightily out of order, and reproaching of Mrs. Pierce and Knipp as wenches, and I know not what," - Pepys, diary, Aug. 6, 1666).

Phrase in order to "for the purpose of" (1650s) preserves etymological notion of "sequence." In short order "without delay" is from 1834, American English; order of battle "arrangement and disposition of an army or fleet for the purposes of engagement" is from 1769. The scientific/mathematical order of magnitude is attested from 1723.

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law (n.)
Origin and meaning of law

Old English lagu (plural laga, combining form lah-) "ordinance, rule prescribed by authority, regulation; district governed by the same laws;" also sometimes "right, legal privilege," from Old Norse *lagu "law," collective plural of lag "layer, measure, stroke," literally "something laid down, that which is fixed or set."

This is reconstructed to be from Proto-Germanic *lagam "put, lay" (from PIE root *legh- "to lie down, lay"). The modern word is thus a twin of lay (n.2) as "that which is set or established."

Rare in Old English, it ousted the more usual ae and also gesetnes, which also were etymologically "something placed or set." 

In physics, "a proposition which expresses the regular order of things," from 1660s. Law and order have been coupled since 1796. To lay down the law (1752) is pleonastic (the "law" in the figure is biblical law, laid down from the pulpit). Poor laws provided for the support of paupers at public expense; sumptuary laws restrained excesses in apparel, food, or luxuries.

It is more common for Indo-European languages to use different words for "a specific law" and for "law" in the general sense of "institution or body of laws," for example Latin lex "a law," ius "a right," especially "legal right, law."

Indo-European words for "a law" are most commonly from verbs for "to put, place, set, lay," such as Greek thesmos (from tithemi "to put, place"), Old English dom (from PIE *dhe- "to put, place, set"), Lithuanian įstatymas (from statyti "cause to stand, set up, establish"), Polish ustawa (from stać "stand"). Also compare Old English gesetnes (above), statute, from Latin statuere; German Gesetz "law," from Old High German gisatzida "a fixing, determination, assessment," with sezzen (modern German setzen) "to make sit, set, put."

Words for "law" in the general sense mostly mean etymologically "what is right" and often are connected with adjectives for "right" (themselves often figurative uses of words for "straight," "upright," "true," "fitting," or "usage, custom." Such are Greek nomos (as in numismatic); French droit, Spanish derecho, from Latin directus; Polish prawo, Russian pravo (from Old Church Slavonic pravŭ "straight," in the daughter languages "right"); also Old Norse rettr, Old English riht, Dutch recht, German Recht (see right (adj.1)).

[L]earn to obey good laws before you seek to alter bad ones [Ruskin, "Fors Clavigera"]
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