A Nutting We Will Go or The Butterfly
Source: Traditional; provided by Rev. Jack Putterill; published in English Dance & Song, April 1941, Volume V, Number 4.
Formation: Longways; Duple Minor; Proper or Sicilian Circle
||Star Right; Star Left
||#1s Face #2s: (#1s Arch, all walk forwards, Turn Alone; #2s Arch, all walk forwards, Turn Alone) x2
||Swing & Change: with your Partner Swing/Polka/Poussette/Promenade 1 & 1/2 times Anti-Clockwise around the other couple
I find it amusing that the notes for one of the figures say "as in Butterfly". The whole dance IS the Butterfly (Hornpipe) as documented in Cecil Sharp's The Country Dance Book Part 1 and in the Community Dances Manual 1!
Cecil Sharp specifies that the dancers should all use the right hand when making the arches. This seems very awkward until you read the footnote: "Traditionally it is customary for partners to hold between them a handkerchief, or two handkerchiefs knotted together, with which they form the arch."
Without the extra space provided by the handkerchiefs the move can be quite rushed; some people only do it once rather than twice. Another variant is to walk backwards to get back to place instead of turning.
Cecil Sharp specifies that the Swing & Change should be done with a Two-Hand Turn hold, but admits that traditional dancers take a waltz hold. That is how I learnt it in the 1960s, polkaing around the other couple. Historically this type of progression was done with a Poussette one and a half times around, but in the second half of the 19th century this evolved into a polka around. If working with dancers who can't polka, a Promenade in a line of four (with the men's left shoulders nearly touching) works well if you use Sicilian Circle or Longways with First Couples Improper. If you do want to actually Swing & Change then I would recommend a hold with the right forearms together, fingertips hookded just above your partner's elbow, and left hands joined underneath. This hold gives lots of connection and control, but has you far enough apart so that you can do any stepping you like and travel easily. Cecil Sharp's description is just a half circle around the other couple, but there is plenty of time to do once and a half.
Thanks to Chloe Metcalfe who pointed out an entry in "Your Questions Answered" in Volume X Number 1. The entry is shown below and explains the change from Longways to Sicilian Circle, plus the change to a hornpipe tune, which I assume means that they slowed it right down so that you could do a strong one-hop-two-hop step.