These are performed by four adjacent dancers on the Side of a Square or other Circular set. The name recognizes that the line joining their initial Places is an arc of a circle (or, more precisely, three adjacent sides of a polygon) but it is somewhat misleading in a Square set in that it implies that the axis of the Reel is similarly distorted whereas the axis is actually the straight line joining the Starting Places of the Middle two dancers.
For example, in bars 25-32 of the Scottish Country Dance Strathspey, Sloane Square, 4th Man, 1st Couple and 2nd Lady perform a Reel whose axis is the extended line joining the 1st Couple's Places in the Square set While 4th Lady, 3rd Couple and 2nd Man perform a Reel whose axis is the line joining the 3rd Couple's Places; the 1st Couple and 3rd Couple start by passing Partners By the left.
Diagram 42 shows the situation about halfway through bar 27, by which time the dancers are equally spaced with 2nd Lady and 4th man Passing By the left in the Top Reel and 2nd Man and 4th Lady Passing By the left in the Bottom Reel. The vertices of the shaded octagon are the Starting Places of the dancers in the 4-Couple Square set, as in Diagram 22.
In a Triangular set, the term Crescent Reel Of Four is commonly used as a synonym for Interlocking reels on the Sides (see Diagram 43); in this case, the axis of each Reel actually is distorted into a crescent shape.
For example, here are some Scottish Country Dances in which the term, Crescent reel of four, is used in either the MiniCrib or the MaxiCrib Dance instructions or both -
Autumn In Pitlochry