Some notations have a 4, 5 or 6 couple set... each to their own :-) A three couple set means that you 'feel the width' rather than dance up and down a long set... a shorter set also means that you spend more time dancing rather than watching first and second corners enjoying themselves (and in this dance, the first and second corners do do a lot of enjoying themselves).
If you are standing watching people dance, take a step back, keep the set wide and give the active couples a little room.
The first part of the dance is full of things for the first corners and second corners to do alternately, so the sections are addressed alternately ... The first corners are the top man and the bottom lady, the second corners are the top lady and the bottom man. In the first parts of the dance you do not spend much time dancing with your partner...
... Second corners right hand turn
... dance to the top of the set
All face up, first couple continue with their dance up the set and cast out, all follow.
First couple meet with an arch, all pass through ...
As far as I remember this dance has a driving quality that comes with a slip jig, it's fast so a 'running step' works.
As with all dances, It's not possible to take instructions to dance with the 'person of the opposite sex' too literally, most often you'll find people dancing in couples but there's no doubt you'll meet two women dancing together, two men, or a couple with the roles switched over.
Yes, this is more confusing, and it makes the writing down of dances more difficult, but this is what the 'more careful look at the line opposite' is there for. You'll get callers explaining this as 'Sex is not what you are it's where you are...'
Now, if it is you are the couple dancing different roles, expect to have to give more help to confused looking people heading towards you....
If there's a motto for English Ceilidh, Folk Dance, Barn Dance etc it's there's more than one way of doing it... and more than one name for it when you are doing it....
In short, there's no right way, there will be regional variations, there will be different versions depending on who is calling the dance, what the band is and what tunes the band are playing. Long may this remain so...
What might you meet in practice?
A tune by the Old Swan Band, with has a single 'C Music', leads to an more non-stop version. The right hand turn, left hand turn, two hand and back to back. Then straight into a cast from the top, arch at the bottom, all through to place and straight into the right hand turn again. You'll find this in Coulon's Handbook of 1873. Start at page 67
Thanks to Dave Hunt for this...
The dance goes back to Playford and the 'Dancing Master' (1685) in name
The Library of Congress has:
There's a writeup in James Scott Skinner's The People's Ballroom Guide of 1905 (with a long set) which give it the name The Haymakers in Scotland and it appears in the Irish Ceili repertoire under this name. (Watch out though, there is however more than one dance called Haymakers or Haymaker's Jig)
...... when the fiddler (an artful dog, mind. The sort of man who knew his business better than you or I could have told it him.) struck up Sir Roger de Coverley.' Then old Fezziwig stood out to dance with Mrs Fezziwig. Top couple, too; with a good stiff piece of work cut out for them; three or four and twenty pair of partners; people who were not to be trifled with; people who would dance, and had no notion of walking.
But if they had been twice as many -- ah, four times -- old Fezziwig would have been a match for them, and so would Mrs Fezziwig. As to her, she was worthy to be his partner in every sense of the term. If that's not high praise, tell me higher, and I'll use it. A positive light appeared to issue from Fezziwig's calves. They shone in every part of the dance like moons. You couldn't have predicted, at any given time, what would have become of them next. And when old Fezziwig and Mrs Fezziwig had gone all through the dance; advance and retire, both hands to your partner, bow and curtsey, corkscrew, thread-the-needle, and back again to your place; Fezziwig cut -- cut so deftly, that he appeared to wink with his legs, and came upon his feet again without a stagger.
James Prescott has written down the process of reconstructing this and making it danceable. The terms have changed over the years and it's reasonable to assume the 'thread the needle' is not the modern version
... and if you are looking for info about the Cotillion, Coverley and Mazurka WW1 'Dance' class minesweepers (webfeet cache)