Etymology
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N 

fourteenth letter of the English alphabet; in chemistry, the symbol for nitrogen.

In late Middle English a and an commonly were joined to the following noun, if that word began with a vowel, which caused confusion over how such words ought to be divided when written separately. In nickname, newt, and British dialectal naunt, the -n- belongs to a preceding indefinite article an or possessive pronoun mine.

Other examples of this from Middle English manuscripts include a neilond ("an island," early 13c.), a narawe ("an arrow," c. 1400), a nox ("an ox," c. 1400), a noke ("an oak," early 15c.), a nappyle ("an apple," early 15c.), a negge ("an egg," 15c.), a nynche ("an inch," c. 1400), a nostryche ("an ostrich," c. 1500). My naunt for mine aunt is recorded from 13c.-17c. None other could be no noder (mid-15c.). My nown (for mine own) was frequent 15c.-18c. In 16c., an idiot sometimes became a nidiot (1530s), which, with still-common casual pronunciation, became nidget (1570s), now, alas, no longer whinnying with us.

It is "of constant recurrence" in the 15c. vocabularies, according to Thomas Wright, their modern editor. One has, among many others, Hoc alphabetum ... a nabse, from misdivision of an ABC (and pronouncing it as a word), and Hic culus ... a ners. Also compare nonce, pigsney. Even in 19c. provincial English and U.S., noration (from an oration) was "a speech; a rumor."

The process also worked in surnames, from oblique cases of Old English at "by, near," as in Nock/Nokes/Noaks from atten Oke "by the oak;" Nye from atten ye "near the lowland;" and see Nashville. (Elision of the vowel of the definite article also took place and was standard in Chancery English of the 15c.: þarchebisshop for "the archbishop," thorient for "the orient.")

But it is more common for an English word to lose an -n- to a preceding a: apron, auger, adder, umpire, humble pie, etc. By a related error in Elizabethan English, natomy or atomy was common for anatomy, noyance (annoyance) and noying (adj.) turn up 14c.-17c., and Marlowe (1590) has Natolian for Anatolian.  The tendency is not limited to English: compare Luxor, jade (n.1), lute, omelet, and Modern Greek mera for hēmera, the first syllable being confused with the article.

The mathematical use of n for "an indefinite number" is attested by 1717 in phrases such as to the nth power (see nth). In Middle English n. was written in form documents to indicate an unspecified name of a person to be supplied by the speaker or reader.

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medium (adj.)

1660s, "average, middling," from medium (n.). The Latin adjective was medius. Meaning "intermediate" is from 1796. As a designation of size or weight, by 1711. As a designation of cooked meat between well-done and rare, it is attested from 1931; earlier was medium-rare (1881).

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medium (n.)

1580s, "a middle ground, quality, or degree; that which holds a middle place or position," from Latin medium "the middle, midst, center; interval," noun use of neuter of adjective medius "in the middle, between; from the middle" (from PIE root *medhyo- "middle").

Many of the secondary senses are via the notion of "intervening substance through which a force or quality is conveyed" (1590s) and "intermediate agency, channel of communication" (c. 1600). From the former, via application to air, etc., comes the sense of "one's environment or conditions" (1865). From the latter comes the sense of "a print publication" (1795) which later grew into the meaning in media.

In spiritualism, "person who conveys spiritual messages," by 1853. In painting, in reference to oil, watercolor, etc., by 1854. The notion is "liquid with which pigments are ground or mixed to give them desired fluidity." Happy medium is the "golden mean," Horace's aurea mediocritas.

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brain-wave (n.)

"apparent telepathic vibration transferring a thought from one person to another without any other medium," 1869, from brain (n.) + wave (n.).

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mass-media (n.)

singular mass-medium, "means of communication that reach large numbers of people," 1923; see mass (n.1) + media (n.).

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pollutant (n.)

polluting agent or medium," "1888, from pollute + -ant. Related: Pollutants.

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milieu (n.)

"surroundings, medium, environment," 1854, from French milieu, "middle, medium, mean," literally "middle place" (12c.), from mi "middle" (from Latin medius, from PIE root *medhyo- "middle") + lieu "place" (see lieu).

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psychic (n.)

"a medium, person susceptible to psychic impressions," 1870; see psychic (adj.).

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average (adj.)

1770, "estimated by averaging," from average (n.). By 1803 as "equal in amount to the sum of all particular quantities divided by the number of them," hence "of medium character."

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middling (adj.)

"medium in rank, condition, or degree; intermediate," 1540s, from Middle English medlinge "intermediate between two things" (late 14c.), from middle (adj.) + present-participle suffix -ing (2). Used in trade to designate the second of three grades of goods. Hence "only medium, neither good nor bad" (1650s). As an adverb, "tolerably, passably," by 1719.

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