Etymology
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Wednesday (n.)
fourth day of the week, Old English wodnesdæg "Woden's day," a Germanic loan-translation of Latin dies Mercurii "day of Mercury" (compare Old Norse Oðinsdagr, Swedish Onsdag, Old Frisian Wonsdei, Middle Dutch Wudensdach). For Woden, see Odin.

Contracted pronunciation is recorded from 15c. The Odin-based name is missing in German (mittwoch, from Old High German mittwocha, literally "mid-week"), probably by influence of Gothic, which seems to have adopted a pure ecclesiastical (i.e. non-astrological) week from Greek missionaries. The Gothic model also seems to be the source of Polish środa, Russian sreda "Wednesday," literally "middle."
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shrove (n.)

"shrift, shriving," 1570s, used only in ecclesiastical phrases, shortened from Shrovetide (early 15c., Shrof-tide), "the three days before Ash Wednesday," a time of confession, from schrof-, which is related to schrifen (see shrive). Shrove Tuesday (c. 1500, earlier Shrof-dai, mid-15c.) is from practice of celebration and merrymaking before confession at the start of Lent.

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ember-days (n.)
Old English Ymbrendaeg, Ymbren, 12 days of the year (divided into four seasonal periods, hence Medieval Latin name quatuor tempora) set aside by the Church for fasting and prayers, from Old English ymbren "recurring," corruption of ymbryne "a circuit, revolution, course, anniversary," literally "a running around," from ymb "round" (from Proto-Germanic umbi, from PIE root *ambhi- "around") + ryne "course, running" (from PIE root *rei- "to run, flow"). Perhaps influenced by a corruption of the Latin name (compare German quatember, Danish tamper-dage). The Wednesday, Friday, and Saturday after the first Sunday in Lent, Whit-Sunday, Sept. 14, and Dec. 13, set aside for prayer and fasting.
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hump (n.)

1680s (in hump-backed), of uncertain origin; perhaps from Dutch homp "lump," from Middle Low German hump "bump," from Proto-Germanic *hump-, from PIE *kemb- "to bend, turn, change, exchange" (see change (v.)). Replaced, or perhaps influenced by, crump, from Old English crump.

A meaning attested from 1901 is "mound in a railway yard over which cars must be pushed," which might be behind the figurative sense of "critical point of an undertaking" (1914). By 1957, hump day was in use in reference to the mid-point of a training program or course; it was extended to "Wednesday," as the mid-point of the work-week, by 1987.

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ash (n.1)

"powdery remains of fire," Middle English asshe, from Old English æsce "ash," from Proto-Germanic *askon (source also of Old Norse and Swedish aska, Old High German asca, German asche, Middle Dutch asche, Gothic azgo "ashes"), from PIE root *as- "to burn, glow." Spanish and Portuguese ascua "red-hot coal" are Germanic loan-words.

An ancient symbol of grief or repentance; hence Ash Wednesday (c. 1300), from the custom introduced by Pope Gregory the Great of sprinkling ashes on the heads of penitents on the first day of Lent. Ashes meaning "mortal remains of a person" is attested from late 13c., in reference to the ancient custom of cremation. The meaning "finely pulverized lava thrown from a volcano" is from 1660s.

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quartan (adj.)

"having to do with the fourth," especially of attacks of an intermittent fever, etc., "occurring every fourth day" (by inclusive reckoning; now we would say every third day), early 14c., (feuer) quartain, from Old French (fievre) quartaine or cartaine and directly from Latin (febris) quartana, "quartan (fever)," fem. of quartanus "of or belonging to the fourth; of or occurring on the fourth day," from quartus "the fourth, fourth part" (related to quattuor "four," from PIE root *kwetwer- "four").

Also as a noun, "an ague or fever which recurs on the fourth (third) day," late 14c. Under inclusive reckoning, both days of consecutive occurrence are counted (if you have it on Wednesday and again on Saturday, the ancients would count that as "every four days"). 

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derby (n.)

town and county in England, Old English Deorby "deer village," from deor "deer" (see deer) + by "habitation, homestead," from a Scandinavian source (see first element in bylaw). the annual Derby horse race, the most important in England, was begun 1780 by the 12th Earl of Derby and run at Epsom, Surrey; the name was used for any major horse race after 1875. Hence Derby day (generally the Wednesday before Whitsuntide), etc.

Derby dog, something that "turns up" without fail, as the proverbial dog on the race-course on Derby day, after the track is otherwise cleared for the races. [Century Dictionary; the phrase is attested from 1858] 

The type of stiff, felt hat with a rounded crown and more or less narrow brim was manufactured in U.S. by 1850 and called by that name by 1870; perhaps so called because it was worn in riding. It came in as a fashionable novelty in 1874.

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rogation (n.)

late 14c., rogacioun, in Church use, "a solemn supplication" (especially as said in a procession, a reference to Rogation days), from Old French rogacion and directly from Latin rogationem (nominative rogatio) "an asking, prayer, entreaty," also a specific term in Roman jurisprudence, noun of action from past-participle stem of rogare "to ask, inquire, question," also "to propose (a law, a candidate)," via the notion of "ask" the people; also especially "ask a favor, entreat, request." Apparently this is a figurative use of a PIE verb meaning literally "to stretch out (the hand)," from *rog-, variant of the root *reg- "move in a straight line." Related: Rogations.

Rogation days were the Monday, Tuesday and Wednesday before Ascension Day, a time for processions round fields blessing crops and praying for good harvest, also blessing the boundary markers of each parish. Discouraged by Protestants as superstition, they were continued or revived in modified form as beating the bounds.

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Lent (n.)
"period between Ash Wednesday and Easter," late 14c., short for Lenten (n.) "the forty days of fasting before Easter" in the Christian calendar (early 12c.), from Old English lencten "springtime, spring," the season, also "the fast of Lent," from West Germanic *langitinaz "long-days," or "lengthening of the day" (source also of Old Saxon lentin, Middle Dutch lenten, Old High German lengizin manoth). This prehistoric compound probably refers to increasing daylight in spring and is reconstructed to be from *langaz "long" (source of long (adj.)) + *tina- "day" (compare Gothic sin-teins "daily"), which is cognate with Old Church Slavonic dini, Lithuanian diena, Latin dies "day" (from PIE root *dyeu- "to shine").

Compare similar form evolution in Dutch lente (Middle Dutch lentin), German Lenz (Old High German lengizin) "spring." But the Church sense is peculiar to English. The -en in Lenten (n.) was perhaps mistaken for an affix.
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fourth (adj., n.)

"next in order after the third; an ordinal numeral; being one of four equal parts into which a whole is regarded as divided;" mid-15c., alteration (by influence of four), of ferthe, from Old English feorða "fourth," from Proto-Germanic *feurthan (source also of Old Saxon fiortho, Old Norse fiorðe, Dutch vierde, Old High German fiordo, German vierte); see four + -th (1). As a noun from 1590s, both of fractions and in music.

Among the old Quakers, who rejected the pagan weekday names, fourth day was Wednesday, often a secondary day of meeting for worship. Fourth-dimension attested from 1844. The theatrical fourth wall is from 1807. The celebration of the Fourth of July as the epoch of American independence is attested from 1777.

That there is due to Daniel Smith, of the city tavern, for his bill of expences of Congress, on the 4 of July last, including a balance of an old account, the sum of 729 68/90 dollars; also a bill for materials, workmanship, &c furnished for the fire works on the 4 July, the sum of 102 69/90 dollars .... [Auditor General's report, Aug. 8, 1777, Journals of Congress, vol. VII]
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