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The Collaborative International Dictionary
Tripping line

Tripping \Trip"ping\, n.

  1. Act of one who, or that which, trips.

  2. A light dance.

    Other trippings to be trod of lighter toes.
    --Milton.

  3. (Naut.) The loosing of an anchor from the ground by means of its cable or buoy rope.

    Tripping line (Naut.), a small rope attached to the topgallant or royal yard, used to trip the yard, and in lowering it to the deck; also, a line used in letting go the anchor.
    --Luce.

Wiktionary
tripping line

n. (context nautical English) A small rope attached to the topgallant or royal yard, used to trip the yard, and in lowering it to the deck; also, a line used in letting go the anchor.

Wikipedia
Tripping line

On a boat, a tripping line is small rope attached to the topgallant or royal yard, used to trip the yard and lower it to the deck. It's also a line used in releasing the anchor.