Bowline loop may pass around or through an object during the making of the knot. The knot tightens when loaded at (pulled by) the standing part of the line. The bowline is commonly used in sailing small craft, for example to fasten a halyard to the head of a sail or to tie a jib sheet to a clew of a jib. The bowline is well known as a rescue knot for such purposes as rescuing people who might have fallen down a hole, or off a cliff onto a ledge. This knot is particularly useful in such a situation because
Arf invariant of a knot if they are related by a finite sequence of pass-moves, which are illustrated below: (no figure right now) Every knot is pass-equivalent to either the unknot or the trefoil; these two knots are not pass-equivalent and additionally, the right- and left-handed trefoils are pass-equivalent. Now we can define the Arf invariant of a knot to be 0 if it is pass-equivalent to the unknot, or 1 if it is pass-equivalent to the trefoil. This definition is equivalent to the one above. Vaughan Jones showed that the Arf invariant can be obtained by taking the partition function of a signed planar