Middle English narwe, from Old English nearu "of little width, not wide or broad; constricted, limited; petty; causing difficulty, oppressive; strict, severe," from West Germanic *narwaz "narrowness" (source also of Frisian nar, Old Saxon naru, Middle Dutch nare, Dutch naar) which is not found in other Germanic languages and is of unknown origin.
In reference to railroads, narrow-gauge (also narrow-gage) is by 1841, originally of those less than the standard of 4 feet 8 1/2 inches. The narrow seas (mid-15c.) were the waters between Great Britain and the continent and Ireland, but specifically the Strait of Dover.
word-forming element denoting action, quality, or state, attached to an adjective or past participle to form an abstract noun, from Old English -nes(s), from Proto-Germanic *in-assu- (cognates: Old Saxon -nissi, Middle Dutch -nisse, Dutch -nis, Old High German -nissa, German -nis, Gothic -inassus), from *-in-, originally belonging to the noun stem, + *-assu-, abstract noun suffix, probably from the same root as Latin -tudo (see -tude).
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Definitions of narrowness from WordNet
the property of being narrow; having little width;
the narrowness of the road
an inclination to criticize opposing opinions or shocking behavior;
a restriction of range or scope;
frustrated by the narrowness of people's horizons
the problem with achievement tests is the narrowness they impose on students
the attraction of the book is precisely its narrowness of focus
a small margin;
the landslide he had in the electoral college obscured the narrowness of a victory based on just 43% of the popular vote