From two side-by-side files of two facing in opposite directions (This formation has come to be called a four-person "box" because it is the formation from which Box Circulate can be done): Each dancer moves forward to assume the position and facing direction of the dancer ahead in the box. (From two parallel waves, the center people actually do a Box Circulate when they are given the call Centers Circulate; similarly, from parallel waves, on the call "Split Circulate" the two side-by-side tracks of four dancers will each do, in effect, a Box Circulate).
Jim Stewart 1968
This definition is from The Handbook of Modern Square Dancing by Jay King.
It is provided here for informational and educational purposes only.