Etymology
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Walker 

surname, early 13c., probably an agent noun from walk (v.) in the sense "to full cloth." preserves the cloth-fulling sense (walker with this meaning is attested from c. 1300). "Walker" or "Hookey Walker" was a common slang retort of incredulity in early and mid-19c. London, for which "Various problematic explanations have been offered" [Century Dictionary].

"Is it?" said Scrooge. "Go and buy it."
"Walk-ER!" exclaimed the boy.
"No, no," said Scrooge. "I am in earnest" (etc.)
[Dickens, "A Christmas Carol"]
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cakewalk (n.)

"something easy," 1863, American English, from cake (n.) + walk (n.). Probably it is in some way a reference to the cake given as a prize for the fanciest steps in a procession in a Southern black custom (explained by Thornton, 1912, as, "A walking competition among negroes," in which the prize cake goes to "the couple who put on most style"), even though its figurative meaning is recorded before the literal one (1879). As a verb, from 1904. This may also be the source of the verbal phrase take the cake "win all" (1847).

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valgus (adj., n.)

deformity in which a bone or joint is twisted outward from the center of the body; form of club-foot, 1800, from Latin valgus "bandy-legged, bow-legged, having the legs bent outward." Said to be probably related to Sanskrit valgati "to move up and down," Old English wealcan "to roll, move to and fro" (see walk (v.)), perhaps on the notion of "go irregularly or to and fro" [Tucker]. "Yet the main characteristic of 'bow-legged' is the crookedness of the legs, not 'going up and down' or 'to and fro'" [de Vaan] and there are phonetic difficulties. A classical word used in a different sense in modern medicine; also see varus.

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vagrant (n.)
mid-15c., "person who lacks regular employment, one without fixed abode, a tramp," probably from Anglo-French vageraunt, also wacrant, walcrant, which is said in many sources to be a noun use of the past participle of Old French walcrer "to wander," from Frankish (Germanic) *walken, from the same source as Old Norse valka "wander" and English walk (v.).

Under this theory the word was influenced by Old French vagant, vagaunt "wandering," from Latin vagantem (nominative vagans), past participle of vagari "to wander, stroll about" (see vagary). But on another theory the Anglo-French word ultimately is from Old French vagant, with an unetymological -r-. Middle English also had vagaunt "wandering, without fixed abode" (late 14c.), from Old French vagant.
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*wel- (3)
Proto-Indo-European root meaning "to turn, revolve," with derivatives referring to curved, enclosing objects.

It forms all or part of: archivolt; circumvolve; convoluted; convolution; devolve; elytra; evolution; evolve; Helicon; helicopter; helix; helminth; lorimer; ileus; involve; revolt; revolution; revolve; valve; vault (v.1) "jump or leap over;" vault (n.1) "arched roof or ceiling;" volte-face; voluble; volume; voluminous; volute; volvox; volvulus; vulva; wale; walk; wallet; wallow; waltz; well (v.) "to spring, rise, gush;" welter; whelk; willow.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit valate "turns round," ulvam "womb, vulva;" Lithuanian valtis "twine, net," vilnis "wave," apvalus "round;" Old Church Slavonic valiti "roll, welter," vlŭna "wave;" Greek eluein "to roll round, wind, enwrap," eilein "twist, turn, squeeze; revolve, rotate," helix "spiral object;" Latin volvere "to turn, twist;" Gothic walwjan "to roll;" Old English wealwian "roll," weoloc "whelk, spiral-shelled mollusk;" Old High German walzan "to roll, waltz;" Old Irish fulumain "rolling;" Welsh olwyn "wheel."
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obambulation (n.)

"a walking about," c. 1600, from Latin obambulationem (nominative obambulatio) "a going or walking about," noun of action from past-participle stem of obambulare "to go or walk about, walk past, walk near," from ob "about" (see ob-) + ambulare "to walk, go about" (see amble (v.)).

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circumambulate (v.)

"to walk round or about," 1650s, from Latin circumambulatus, past participle of circumambulare "to walk around," from circum "around" (see circum-) + ambulare "to walk, go about" (see amble (v.)). Related: Circumambulated; circumambulating; circumambulation.

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ambulate (v.)
"to walk, move about," 1620s, from Latin ambulatus, past participle of ambulare "to walk, go about" (see amble (v.)). Related: Ambulated; ambulating.
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waddle (v.)
"to walk with short steps, swaying from side to side; to walk as a duck does," 1590s, frequentative of wade. Related: Waddled; waddling. The noun is recorded from 1690s.
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perambulate (v.)

"walk through, about, or over," 1560s, from Latin perambulatus, past participle of perambulare "to walk through, go through, ramble through," from per "through" (from PIE root *per- (1) "forward," hence "through") + ambulare "to walk, go about" (see amble (v.)). Related: Perambulated; perambulating.

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