Mixer dances, where all the participants shift partners at intervals, are useful icebreakers at dance events. In A Complete Practical Guide to Modern Society Dancing (1903), Philadelphia dancing master Albert W. Newman offers a simple mixer for use with the then-fashionable two-step, asserting hopefully that
The dancers take partners and hold hands in a grand circle, with each gentleman standing to the left of his partner, and all circle to the left (clockwise). The dance leader calls out a number (3, 7, 12, etc.), and all the dancers face their partners and begin a grand chain, giving right hands to their partners and pulling by, left to the next, right to the next, left to the next, etc. As they move, they count people, starting with their partners as "one." When they reach the number called out by the leader, each takes ballroom position with that person and two-step until the leader gives a signal (typically a whistle), at which point all the dancers open up into a grand circle and once again circle to the left.
This sequence is repeated as many times as desired, with the leader calling a different number each time so that the dancers end up with new partners after each grand chain.
Newman suggests that the Round Two Step is not only a standalone mixer but also a suitable final figure for a German, or cotillion, a type of party involving a series of dance games.
This style of circle-and-chain mixer was later known as a Paul Jones, possibly after a piece of popular music. Similar mixers remain current in some living tradition dance forms today.