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Webster 1913 Edition

Noun.

An end of poorer quality, or in a spoiled condition, as the coarser end of a web of cloth, the untwisted end of a rope, etc.

The refuse or meaner part of anything.

The

fag-end

of business.

Collier.

See also: fag end

fag-end ‎(plural fag-ends)

last remnant
- 1898, Joseph Conrad, Youth
  He was out of his mind; completely and for ever mad, with this sudden shock coming upon the fag-end of his endurance.
- 1981, New Scientist, 22nd Oct. issue, Fresh Air at Brighton, page 265
  But spatchcocked into the proceedings at the fag-end of the morning was a crisp and useful debate on toxic substances.
frayed end of a length of cloth or rope
The unsmoked end of a cigarette or cigar

cigarette butt — see butt