The RSCDS attributes this to Wallace, ~1880. The Library of Dance dates Wallace's work to ~1900. Perhaps there were multiple publications, or just uncertainty. In any event it appears earlier, in Kate Hughes's manuscript from Dundalk Ireland, 1867:

1. The tow top couples swing (8 bars)
2. First couple down the centre and up (8)
3. Rights and lefts (8)
4. Pousett

At this time the word "swing" was used for almost any circular movement, and could certainly have meant a right hands across/left hands back.

In Wallace's Ball-Room Guide, Glasgow, ~1900, he writes:

1. First and second couples give right hands across and turn round, back to places with left, (Gentleman No. 2 remains beside his partner), 8 bars
2. First couple down the centre and back bringing the Lady into second Gentleman's place, 8 bars
3. First and second couples right and left, 8 bars
4. Pousette, 8 bars

The RSCDS says this was collected in Perthshire and was also found in Allan's Reference Guide to the Ballroom, ~1895, but it appeared elsewhere earlier.

An early version of the dance appears in Kate Hughes's manuscript, the Dancing Book, Dundalk Ireland, 1867. She calls the dance "Torrayburn Lassies".

1. The top gent swing the tow ladies (8 bars)
2. Top gent and his partner swing the second gent (8)
3. Down the centre and up (8)
4. Swing four (8)
5. Pousett (8)

At this time "swing" meant almost any circular movement. The first swing could certainly match the "circle three" of the RSCDS, though presumably followed by a "and back to the right". The "swing four" could be a circle four, or a hands across, or who knows what.

Wallace in his The Excelsior Manual of Dancing, ~1872, calls the dance simply "Torryburn"

1. First couple set and three hands round with second lady, (8 bars)
2. Repeat the same with second gentleman, (8 bars)
3. First couple down the centre and back, (8 bars)
4. Couples No. 1 and 2 Pousette (8 bars)

But in Allan's Reference Guide to the Ball-Room, Glasgow, ~1895, the dance has become Torryburn Lassies.

1. Top couple set, and then three hands round with second lady.
2. Repeat the same with second gentleman.
3. Down the centre and up.
4. Pousette first and second couples.

Courtesy of National Library of Scotland, licensed under:

RSCDS Book 31 attributes this to Thomas Murphy's Aide Memoire, a manuscript from about 1890, but it is clearly derived from Clutha C.D. in Kate Hughes's Dancing Book, ~1867:

1. Top couple swing in the centre
2. Cast a couple and swing
3. Balance four in line with second couple and turn opposite partners
4. Rights and lefts
5. Set and turn opposite partners
6. Half chasie and swing out time
7. Pousette

Hughes's dance is longways, but the figure is closely related.

RSCDS Book 31 says this comes from Allan's Reference Guide to the Ball-Room, ~1880, and it is in that work, but it appears earlier.

In 1852 Seaton published Original Polka Country Dance which also begins with the top couple improper, and contains a lady's chain but there is little similarity beyond that.

In ~1867 Kate Hughes's Dancing Book, Dundalk, 1867 there is an earlier version of the figure:

1. The top couple change places as in the Guaracha first and seceaond couples set at the sides and pass to each others places set to partners and pass repeat.
2. Top couple down the centre and up agin
3. Poussette

Allan's Reference Guide to the Ball-Room, Glasgow, ~1895, says.

1. Top couples change places and face down the dance, the second couple facng up; first and second couple set with two Polka steps and pass to each other's place, set to partners and pass, set again at the sides and pass, and again to partners and resume places.
2. First couple down the centre and up.
3. Pousette.

Courtesy of National Library of Scotland, licensed under:

Kate Hughes writes:

1. The tow top ladies and the tow top gents advance and retire and change places [8]
2. Top ladie and second gent swing in the centre and back to places (8)
3. econd ladie and first gent the same (8)
4. Down the center and up (8)
5. Pousett

While in ~1872 J. F. Wallace wrote in his The "Excelsior" Manual of Dancing:

1. Top four advance and retire, and half right and left, (8)
2. First lady turns the second gentleman by giving right hand and both return to places, (4)
3. Second lady and first gentleman repeat No. 2, (4)
4. First couple down the centre and back, (8)
5. Pousette, (8)

Kate Hughes writes:

1. Top gent cast the second lady down the centre and up (8)
2. Set and turn partners (8)
3. Ladies chain (8)
4. Pousett

J. F. Wallace in his The "Excelsior" Manual of Dancing, ~1872 writes:

1. First gentleman takes the second lady down the centre and up leaving her beside her partner, while he joins his partner, (8)
2. The two couples set and turn partners, (8)
3. Ladies chain, (8)
4. Pousette, (8)

Neither the RSCDS, nor any of the sources specify how L1+M2 cross to opposite sides. The most obvious is for them to cross up at the end of the lead up, but they could simply wheel around at the bottom. I suppose they could even cross over before leading down, but that seems even less likely.

The RSCDS attributes this to D. Anderson's Ball-Room Guide, ~1880, and to Kate Hughes's Dancing Book, ~1867.

Kate Hughes writes:

1. Top couple swing in the centre (8)
2. Balance four in a line with the seceand couple (8)
3. Four arm arm down the centre and up (8)
4. Pousett

J. F. Wallace in his The "Excelsior" Manual of Dancing, ~1872 writes:

1. First couple gives right hands, turns once round, return giving left which is retained and give right hands to partners, (8)
2. The four set in line, using balance step, (4)
3. The gentlemen turns each other's partners (4)
4. The four arm and arm down the centre and back, (8)
5. Pousette (8)

(I think when Wallace says "partner" at the end of 1) that he means "other partner" or what I'd call neighbor.)

D. Anderson's Ball-Room and Solo Dance Guide, he writes:

First gentleman gives right hand to his partner, and turns her in the centre.

Repeat with the left hand.

Set four in a line across the dance with next couple.

All four down the centre and back.

Pousette.

Repeat.

Courtesy of National Library of Scotland, licensed under:

The RSCDS attributes this dance to Mozart Allan's Allan's Reference Guide to the Ball-Room, ~1880 with a note that it may also be found in Kate Hughes's Dancing Book.

1. All the gents set and turn the lady on the right (8)
2. Set and turn the lady on the left (8)
3. Set and turn partners (8)
4. Top couple lead in (8)
5. Top couple poussette in (8)
6. Top and bottom change places bottom open up (8)
7. Back to places and top open up (8)
8. Repeat nos 6 and 7 (16)
9. Eight hands half round and turn partners (8)
10. Poussette to places.
11. Repeated by the other couples.
12. Finish with all promenade

J. F. Wallace also published it in about 1872 in his The "Excelsior" Manual of Dancing:

1. All eight advance (gentlemen to right, ladies to left) balance at corners and turn with both hands, (8)
2. All advance to partners, balance and turn, (8)
3. Couple No. 1 promenade round inside of quadrille, (8)
4. Couple No. 1 poussette or galop round, (8)
5. Couples No. 1 and 2 change places, cross No. 1, passing between couple No. 2; return to places Couple No. 2, passing between couple No. 1, (8)
6. Repeat No. 5, (8)
7. All promenade, (8)
8. All join hands and go half round to left and pousette or promenade back to places (8)

Note: Wallace is using the quadrille system for numbering couples. The second couple is the one directly across from the 1st.

While Allan says:

1. All pass partners, set and turn at the corners.
2. Repass to places, set to partners, and turn
3. Top couple promenade round in the inside of the dance.
4. Then pousette round.
5. First couple cross over to opposite couple's place, the bottom couple passing on the outside to top couple's place.
6. The bottom couple to places, passing in the center, and the first couple repassing on the outside.
7. The top and bottom repeat the same.
8. All join hands and round.
9. All promenade round with partners.

Courtesy of National Library of Scotland, licensed under:

Kate Hughes writes:

1. Top couple swing in the centre (8)
2. Down the centre at the same time the seceaond gent cross over to his partner (8)
3. Top and seceaond couples set in the centre facing each other and turn partners (8)
4. Reel four down the dance (8)
5. Pousett (8)

Bride published a dance with this name in 1768 but it had a different figure. Longman & Broderip republished it in 1781.

Kate Hughes wrote down a dance very similar to the RSCDS version:

1. Top couple turn round to the right and set in the centre of the dance (4)
2. Turn to opposite sides the ladie between the seceaond and third gentlemen the gent between the seceaond and third ladies and set (4)
3. The three on each side join hands advance and retire twice (8)
4. All six join hands in a circle pass half round to the left and back to the right to places.
5. Pousett (8)

And in his The "Excelsior" Manual of Dancing, ~1872, J. F. Wallace writes:

1. First couple turn round to the right and set in the centre of the dance, (4)
2. Turn to opposite side, the lady between the second and third gentlemen, the gentleman between second and third ladies and set, (4)
3. The three on each side advance and retire twice, (8)
4. All six join hands in a circle, pass half round to left, and back to places, (8)
5. Couples No. 1 and 2 Pousette (8)