Etymology
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shire (n.)
Old English scir "administrative office, jurisdiction, stewardship, authority," also in particular use "district, province, country," from Proto-Germanic *skizo (source also of Old High German scira "care, official charge"). Ousted since 14c. by Anglo-French county. The gentrified sense is from The Shires (1796), used by people in other parts of England of those counties that end in -shire; sense transferred to "hunting country of the Midlands" (1860).
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Shropshire 
shortened form of the old spelling of Shrewsbury + shire.
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sheriff (n.)
late Old English scirgerefa "representative of royal authority in a shire," from scir (see shire) + gerefa "chief, official, reeve" (see reeve). As an American county official, attested from 1660s; sheriff's sale first recorded 1798. Sheriff's tooth (late 14c.) was a common name for the annual tax levied to pay for the sheriff's victuals during court sessions.
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Cheshire 

1086, Cestre Scire, from Chester + scir "district" (see shire). Cheshire cat and its proverbial grin are attested from 1770, but the signification is obscure.

I made a pun the other day, and palmed it upon Holcroft, who grinned like a Cheshire cat. (Why do cats grin in Cheshire?—Because it was once a county palatine, and the cats cannot help laughing whenever they think of it, though I see no great joke in it.) I said that Holcroft, on being asked who were the best dramatic writers of the day, replied, "HOOK AND I." Mr Hook is author of several pieces, Tekeli, &c. You know what hooks and eyes are, don't you? They are what little boys do up their breeches with. [Charles Lamb, letter to Thomas Manning, Feb. 26, 1808]
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county (n.)

mid-14c., "a shire, a definite division of a country or state for political and administrative purposes," from Anglo-French counte, from Late Latin comitatus "jurisdiction of a count," from Latin comes (see count (n.1)). It replaced Old English scir "shire."

From late 14c. as "the domain of a count or earl." County palatine, one distinguished by special privileges (Lancaster, Chester, Durham) is from mid-15c. County seat "seat of the government of a county" is by 1848, American English.

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glen (n.)
"narrow valley," late 15c., from Scottish, from Gaelic gleann "mountain valley" (cognate with Old Irish glenn, Welsh glyn). Common in place names such as Glenlivet (1822), a kind of whiskey, named for the place it was first made (literally "the glen of the Livet," a tributary of the Avon); and Glengarry (1841) a kind of men's cap, of Highland origin, named for a valley in Inverness-shire.
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alderman (n.)

Old English aldormonn (Mercian), ealdormann (West Saxon) "Anglo-Saxon ruler, prince, chief; chief officer of a shire," from aldor, ealder "patriarch" (comparative of ald "old;" see old) + monn, mann "man" (from PIE root *man- (1) "man").

Presumably originally of elders of the clan or tribe, but already in Old English used for king's viceroys, regardless of age. In later Old English a more specific title, "chief magistrate of a county," having both civic and military duties. The word yielded under Canute to eorl (see earl), and after the Norman Conquest to count (n.). Having lost its specific sense, alderman was then applied to any head man; meaning "headman of a guild" (early 12c.) passed to "magistrate of a city" (c. 1200) as the guilds became identified with municipal government. Related: Aldermancy; aldermanic.

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parish (n.)

c. 1300, "district with its own church; members of such a church," from Anglo-French paroche, parosse (late 11c.), Old French paroisse, from Late Latin parochia, paroecia "a diocese," an alteration of Late Greek paroikia "a diocese or parish," from paroikos "a sojourner" (in Christian writers), in classical Greek, "neighbor," from para- "near" (see para- (1)) + oikos "house" (from PIE root *weik- (1) "clan").

The sense development of the word in the early Church is unclear, perhaps it is from "sojourner" used as epithet of early Christians as spiritual sojourners in the material world. In early Church writing the word was used in a more general sense than Greek dioikesis, though by 13c. they were synonymous. It replaced Old English preostscyr, literally "priest-shire." In Great Britain (from the 1630s), some southern American colonies, and Louisiana it has been the name for a purely civil division for purposes of local government, with boundaries originally corresponding to an ecclesiastical parish.

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hundred (adj., n.)

"1 more than ninety-nine, ten times ten; the number which is one more than ninety-nine; a symbol representing this number;" Old English hundred "the number of 100, a counting of 100," from Proto-Germanic *hunda-ratha- (source also of Old Frisian hundred, Old Saxon hunderod, Old Norse hundrað, German hundert); first element is Proto-Germanic *hundam "hundred" (cognate with Gothic hund, Old High German hunt), from PIE *km-tom "hundred," reduced from *dkm-tom- (source also of Sanskrit satam, Avestan satem, Greek hekaton, Latin centum, Lithuanian šimtas, Old Church Slavonic suto, Old Irish cet, Breton kant "hundred"), suffixed form of root *dekm- "ten."

The second element is Proto-Germanic *rath "reckoning, number" (as in Gothic raþjo "a reckoning, account, number," garaþjan "to count;" from PIE root *re- "to reason, count"). The common word for the number in Old English was simple hund, and Old English also used hund-teontig.

In Old Norse hundrath meant 120, that is the long hundred of six score, and at a later date, when both the six-score hundred and the five-score hundred were in use, the old or long hundred was styled hundrath tolf-roett ... meaning "duodecimal hundred," and the new or short hundred was called hundrath ti-rætt, meaning "decimal hundred." "The Long Hundred and its use in England" was discussed by Mr W.H. Stevenson, in 1889, in the Archæological Review (iv. 313-27), where he stated that amongst the Teutons, who longest preserved their native customs unimpaired by the influence of Latin Christianity, the hundred was generally the six-score hundred. The short hundred was introduced among the Northmen in the train of Christianity. [Transactions of the Lancashire and Cheshire Antiquarian Society, 1907]

Meaning "division of a county or shire with its own court" (still in some British place names and U.S. state of Delaware) was in Old English and probably represents 100 hides of land. The Hundred Years War (which ran intermittently from 1337 to 1453) was first so called in 1874. The original Hundred Days was the period between Napoleon's restoration and his final abdication in 1815.

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