Gary Roodman
A Square for Four Couples
Historical English Style
Tune: PLAYING (in) THE FIELD

A 1-4 Taking hands-eight circle left halfway around,
  5-8 With partner, gypsy right almost once around (plenty
      of time for this), but 
9-10 M, as you come around in the gypsy, catch your
     corner’s eye, maybe hesitate a moment, and then
     loop out into her partner’s (former) place, while W
     move to the center, stand back-to-back for a
     moment and then turn right back to original
     places. [This is your new partner.]

1-4 INTRODUCTION TO NEW PARTNER:
    Each M in turn (ccw), beginning with the M now
    in 1st position, step into the center of the set to
    face current partner. (At the end, all M have their
    backs to the center, and women should adjust so
    that there are two straight lines of four crossing in
    the center.)

5-12 HEYS FOR FOUR THROUGH THE CENTER:
     (i) Everyone pass partner by the R;
     (ii) W Left hand star halfway in the middle, while M loop
     R on the outside;

     (iii) Everyone pass R with opposite person (who is
      now on your side);

     (iv) M Left hand star halfway in the middle, while W loop
     R on the outside;

    (v) Everyone pass R with partner (you are both now
    crossed over);

    (vi) W Left hand star halfway in the middle, while M loop
    R on the outside and end facing ccw ready to
    receive their opposite person with L hand.
     (All now facing ccw.)

C 1-2 SQUARE LEADS: With this person, lead
      straight out along the side of the the square (not
      around the circle).

  3-4 Face this person and women draw current man to
      new positions along the sides of the set (“heads"
      are now “sides”, and vice versa), wot
  5-8 GRAND SQUARE: Current head couples lead to
      the center, meet partner, turn 1/4 to fall back to the 
      sides with partner, while side couples fall back from
      each other, turn to face partner, and meet in head
      positions.
9-10 Everyone 2HT halfway with partner.
     [W in original places, M progressed one place to the left.] 

MUSIC: “Entree”, Mirtirtillo Suite, from Pastor Fido by G. F. Handel

Video: https://www.youtube.com/watch?v=mf8wQslOsoQ
Teaching Points:
This dance is a bit of a teaching challenge, but in my experience dancers ultimately find it quite logical. (1) The timing of the gypsy and progression in A 9-10 usually requires a bit of practice with the music. (2) The pace in B 5-8 is deliberate without rushing—6 passes over 8 two-beat bars. The women go across the set and come back, while the men go across and stay there.

(3) Orientation at end of the B music: Before teaching the dance, have everyone change places with partner so that they wheel as a couple a quarter turn to the right, so that they are standing like spokes of a wheel facing square.