The London Gentlewoman, or the Hemp-Dresser
Longways for as many as will
Reconstructed by Dafydd Cyhoeddwr
The repeat structure for this dance is very complex.  For part 1, the chorus needs to be repeated once for each couple in the line less 1 (for 3 couples, it is repeated twice, etc). 
Then, this verse + n chorus group needs to be played once for every person in the line, so that everyone gets to switch in their turn, separated by the verse music.
Part 2 simply repeats the chorus a number of times indicated by the (n-1)x3 formula - the verse music is only played once.
And part 3 uses the other formula ((nx3)-1) for its chorus repeats, with only one verse once again
Music: none
Part 1
First progressive figure, part A:
Verse 1, Part A
1&2: Lead up a double, fall back a double
Verse 1, Part B
1&2: Lead up a double, fall back a double
Chorus 1
1&2: Man 1 changes with woman 2 in two doubles
R: Man 1 continues changing places in two doubles, next with man 3, then woman 4, then man 5, and so on, until he has changed places with the appropriate person in the last couple.
First progressive figure, part B:
Verse 1, Part A
1&2: Lead up a double, fall back a double
Verse 1, Part B
1&2: Lead up a double, fall back a double
Chorus 1
1&2: Woman 1 changes with man 2 in two doubles
R: Woman 1 continues changing places down the line until she has changed places into the last couple
First progressive figure, continuing:
The figure continues with the verse, followed by the person in the first man's place changing down the line to the chorus music, then the verse again, followed by the person in the first woman's place changing down the line
When everyone has returned to place, the second part can begin
Note: Playford's instructions are slightly wonky here, giving the men's change and the women's change in separate sections, omitting the "We." in the second of these, not to mention the screwed up "verse"
instructions.  I think that regularizing these two sections as I have done above is not beyond the possibilities, though someone stricter than I might retain the "sides all _._ lead up as before" for the verse.
(There is a subsequent edition of the EDM that includes the "We." back in, but it does not, sadly, correct the mistake in the verse.)
Part 2
Verse 2, Part A
1&2: Side left with your partner (small double to the left to line up right shoulders, double back to place)
Verse 2, Part B
1&2: Side right with your partner (small double to the right to line up left shoulders, double back to place)
Second progressive figure:
1: Couple 1 change places in a double (cross over)
2: Couple 1 fall into the second couple's place (man does a double around behind woman 2 to end up in her place, woman 1 and man 2 the same, couple 2 moving up to make room)
R: The first couple continues crossing and changing to the bottom, each subsequent couple doing the same.  When everyone is back to place, part 3 can begin
Whether the subsequent couples start as soon as there is a couple to "switch" with, or they wait until the previous couple is finished is not clear.
Part 3
Verse 3, Part A
1&2: Arm left with your partner (take right arms and walk two doubles around to the left)
Verse 3, Part B
1&2: Arm right with your partner (take left arms and walk two doubles around to the right)
Third progressive figure:
1: Couple 1 turn each other all the way around in one double
2: Couple 1 switch places in a double
R: The next repeat has man 1 turning and switching with woman 2, and woman 1 doing the same with man 2.  They should turn each other and change back at the bottom of the line.
Each subsequent couple turns and switches themselves, then does down the side of the line to the bottom.  When everyone is back to their starting places, the dance is finished.