In 1790 Longman & Broderip published a dance named Duke of Perth's Reel, but it has a different figure.

Rutherford published a dance named "Keep the Country, Bonny Lassie" in 1775, but with a different figure.

Pease Straw has an even longer history with Johnson publishing a dance of that name in 1744, but again with a different figure.

According to the Fletts (Traditional Dancing in Scotland, 1964, p. 247) William Boag was the first to publish this figure under the title "Keep the Country, Bonny Lassie".

First Cu Swing the Right hand and cast off one Cu: Swing the Left hand round Swing the Corners and your Partner each time Set Corners and turn lead outsides.

The Fletts also quote the Blantyre MS. (~1805), titled "Duke of Perth":

Hook right hand with partner — turn round — throw off a couple. Hook with partner with left turn round downmost Ladies with right partner with left uppermost Lady with right partner with left twice round, Sett cross p^r reels.

The (R)SCDS claims this dance comes from J. P. Boulogne's The Ball-Room, or the Juvenile Pupil's Assistant; Containing the Most Fashionable Quadrilles, with Les Lanciers of Sixteen, As Danced in the Public & Private Assemblies in Paris, Glasgow, 1827, titled "Duke of Perth" or "Keep the Country, Bonnie Lassie".

1. The first couple turn by the right hand and pass one couple, they turn left hands, the lady turns the second gentleman, and the gentleman the third lady; the first couple turn again with the left hand, the gentleman the second lady, and the lady the third gentleman, they turn half round. (16)
2. Set at corners and turn. (8)
3. Reel of three. (8)

Kate Hughes (in Ireland) recorded a slightly different version in 1867:

1. The top couple turn by the right hand and pass one couple turn with the left hand
2. The lady turns the seceaond gent and the top gent turn the seceaond ladie
3. The first couple turn agin with the left hand
   The gent turns the seceaond ladie and the top ladie turns third gent
4. Set to corners and turn
5. Reell of three

J. F. Wallace, in ~1872, published:

1. The first couple turn by the right hand and pass one couple; they turn with left hand, the lady turns the second gentleman, and the gentleman the third lady. The first couple turn again with the left hand, the gentleman the second lady, and the lady the third gentleman, turn half round, (16)
2. Set at corners and turn, (8)
3. Reel of three, (8)

D. Anderson, 1897 published something almost word for word from Wallace:

1. The first couple turn by the right hand and pass one couple; they turn with left hands, the lady turns the second gentleman, and the gentleman the third lady. The first couple turn again with the left hand, the gentleman the second lady, and the lady the third gentleman—turn half round. (16)
2. Set at corners and turn. (8)
3. Reel of three. (8)

Note that by Blantyre's time the "lead out sides" has become a reel.

Campbell did publish a dance with this title in his 19th Book, but I do not know whether its figure matches that of the RSCDS dance.

On the other hand, in Thompson's Compleat Collection of 200 Fashionable Country Dances, Vol. III", ~1773, Charles and Samuel Thompson write:

Cast off two Cu. and clap hands cast up and do the same cross over two Cu. lead up to the top and clap hands lead down two Cu. up again and cast off and clap hands

In his A Companion to the Ball Room, 1816, Thomas Wilson published Lady Mary Douglas:, wherein he writes:

SINGLE FIGURE Tune played straight thro and Da Capo
Whole figure at top lead down the middle up again turn your partner & lead outsides

OR THUS Cross over 2 Cu: cross up 1 Cu: towards the top and half figure round the top Cu: & the double triangle

DOUBLE FIGURE Tune played twice thro and Da Capo
Hey on your own sides chain figure 6 round lead down the middle up again lead thro the top Cu: whole figure round the bottom Cu: turn corners whole figure contrary corners

The music consists of 2 eight bar strains. The RSCDS has chosen the DOUBLE FIGURE which means the music should be played ABBABB (I think). "" indicates a strain.

Wilson defines his figures in his An Analysis of Country Dancing.

• Hey on your own sides is only defined as part of "Hey Contrary Sides, and Hey of your own Sides" on page 83 and he shows a mirror/reflection hey.
• Chain figure of six may be found on page 78 of the 3rd edition of the Analysis (1811). The top couple face their partner, as the others face their neighbor then everyone does rights and lefts until they return to where they started. Wilson does not specify how to fit the 6 changes into 8 bars of music.
• lead down the middle up again may be found on pages 10-11 and means: "lead down two couples, turn, lead up to the place of the couple who were below (who move up)" Wilson does not specify a hand hold for the lead, nor whether the 2s take hands.
• lead thro the top Cu: is half of through bottom and top on page 23 and means "the active couple take hands, lead above the top, drop hands, and cast up to their own places.
• whole figure round the bottom Cu: is defined as whole figure at top (that is when the 1s are at top so they figure through the couple below them) may be found on pages 12-13 and means "the active lady starts and crosses down, looping around the man below her then she again cross between the couple below, looping around the woman below and casts up to her own place. The active man starts a little after her and mirrors her motions, looping the woman below and then the man below."
• turn corners may be found on pages 28-32 and appears to mean: the 1s pass partner right shoulder to turn first corners with both hands, then pass each other right shoulder to turn second corners (presumably again with both hands, though Wilson does not specify), finally passing each other left to return to places.
• whole figure contrary corners is found on page 104 of the 3rd edition of the Analysis (1811). Rather awkwardly, Wilson provides two different (contradictory) directions. In the first "the 1s cross down, W1 in front of M1, W1 around M3, M1 around W3, then cross up, W1 around W2, M1 around M2, and return home". In the second the "1s cross up, W1 around M2, M1 around W2, then cross down W1 around W3, M1 around M3, and return home.

RSCDS Book 12 attributes this to Johnson's Caledonian Country Dances of 1748 but it appears earlier.

According to Robert Keller's site this appeared in Walsh's 2nd Edition of Caledonian Country Dances, but I only have access to the 3rd wherein Walsh writes:

The 1st Cu. foots it and casts off then foot it again, and the Man casts off, and the Wo. casts up figure contrary sides figure on your own sides Foot it corners and turn ∴ foot it other corners and turn ∵ Hey contrary sides foot it to your Partner and turn it out.

Johnson published the same figure in about 1742.

The music consists of four 4 bar strains.

There are 8 sub-figures with a mark between them, suggesting that each strain should be repeated. Unfortunately the figures seem take different amounts of time. I'd expect The 1st Cu. foots it and casts off to take 4 bars, but I'd expect figure contrary sides to take 8.

So perhaps Walsh means only half of a figure of eight. That would take 4 bars.

But we still have Hey contrary sides. That takes 8 bars (or maybe 6, but not 4). Could we do half a hey? No, that leaves the corners in the wrong place. Could the 1s do half a hey while everyone else does a full hey? Then we need to make sure the 1s don't bump into the 2s+3s as the 1s set and the corners finish.

This solution does not seem a good one, but I can't think of a better. I doubt it's what Walsh intended.

Could the final strain be played 3 times? Walsh does use a pecular mark at the end of this sub-figure. That just seems worse.

Does Walsh intend the music to be played at four counts per bar rather than two? But most of the sub-figures fit into 4 bars...

The RSCDS attributes this to Bremner's work: A Second Collection of Scots Reels or Country Dances, which they date variously to ~1757 and ~1765. In ~1765 Bremner published A Collection of Scots Reels or Country Dances; a work which only contains tunes with no figures. According to Hugh Thurston the second collection was published in London in 1769. As far as I can tell, what was published in London was actually titled: For the Year 1769. A Collection of Scots Reels or Country Dances. At any rate, that work contains this dance.

Cast off two couples lead up to the Top and cast off set cross corners swing corners and swing your partner and lead outsides

In Treasures of Terpischore, Wilson, 1809, he published a danced called "Wilson's Hornpipe". In his A Companion to the Ball Room, 1816, he published "Mrs. Wilson's Hornpipe." I cannot find any dance of his called "Mr. Wilson's Hornpipe". "Mrs. Wilson's Hornpipe"'s figure is closest to the RSCDS version. Wilson writes:

SINGLE FIGURE Tune played straight thro
Set & change sides with 2^d. Cu: & back again lead down the middle up again & right & left with the top Cu:

OR THUS Cast off 2 Cu: & back again swing with right hands round the 2^d. Cu: & allemande

DOUBLE FIGURE Each strain repeated
Hey contrary sides Hey on your own sides lead down the middle up again lead thro the top Cu: set 3 across & set 3 in your places

OR THUS The 1^st. Cu: cast off at the same time the 3^d Cu: set & lead up then the 3^d cast off & the 1^st set & lead up to places. set & change places with the 2^d. Cu: turn your partner set contrary corners hands 4 round at bottom & half poussette with the top Cu:

The music consists of 2 eight bar strains. The RSCDS figure matches the last figure (the OR THUS of the DOUBLE).

Wilson defines most of his figures in his An Analysis of Country Dancing, 3rd Edition. in this dance all the figures are pretty self-explanatory. The only two I shall reference are:

1. half poussette, as the RSCDS's version of poussette is rather different from Wilson's. It may be found on page 14 and means: "top two couples join hands with partner, circle (as a couple), counter-clockwise, around the other couple returning to their original places."
2. and set contrary corners defined on pages 44-46 "move to 1st corner and set, pass partner right moving to 2nd corner, set, return to places the easiest way". Wilson does not show the corners setting back.

The dance was originally published in 1771, presumably in a "Twenty four country dances for the Year 1771", a work now lost.

Wilson, on page 96, writes:

SINGLE FIGURE Tune played straight thro
Cross over 1 Cu: half figure round the 3^d Cu: & lead outsides
OR THUSCast off 2 Cu: & back again & whole poussette
DOUBLE FIGURE Each strain repeated
Hey on your own sides lead down the middle up again allemande turn corners & the double triangle

This is an interpretation of the DOUBLE FIGURE. The music is two 8 bar strains (jigs) both repeated.

Wilson defines most of his figures in his An Analysis of Country Dancing.
Hey on your own sides is only defined as part of "Hey Contrary Sides, and Hey of your own Sides" on page 83 and he shows a mirror/reflection hey.
lead down the middle up again may be found on pages 10-11 and means: "lead down two couples, turn, lead up to the place of the couple who were below (who move up)" Wilson does not specify a hand hold for the lead, nor whether the 2s take hands.
allemande may be found on page 7 and appears to mean going about your partner in a circle. In a later edition of Analysis Wilson adds the phrase "back to back". Wilson does not define a "back to back" figure. His allemande is a bit rounder than a normal back to back but perhaps that is the closest equivalent.
This is an unusual meaning for "allemande", but, as best as I can understand, that is what Wilson describes.
turn corners may be found on pages 28-32 and appears to mean: the 1s pass partner right shoulder to turn first corners with both hands, then pass each other right shoulder to turn second corners (presumably again with both hands, though Wilson does not specify), finally passing each other left to return to places.
the double triangle does not appear until the 3rd edition of the Analysis on page 113 and means: the middle couple loop first corner right shoulder pass outside partner's place, then loop 2nd corner right shoulder and return to place.
This is completely different from the RSCDS version of double triangles.

Wilson spells the title "Auld Langsyne".

SINGLE FIGURE (Each strain repeated)
The 3 ladies join hands & the 3 gent: join hands set & lead thro' set & back again set & change places with the 2^d. Cu: set & allemande
OR THUS Set & half right & left with 2^d. Cu: set & back again & whole poussette
DOUBLE FIGURE (Tune played twice thro' with repeats)
Cross over 2 Cu: set half figure on your own sides allemande at top whole poussette set contrary corners

Wilson usually gives multiple figures for each tune, the RSCDS appears to be following the DOUBLE FIGURE.

Wilson defines all his figures in his An Analysis of Country Dancing.
Cross over 2 Cu: may be found on page 22 and means "cross go below 2s, cross again, go below 3s".
half figure on your own sides may be found on page 67 and means "weave around the dancers on your own side, move between the couple above, then outside the next couple, finishing at top."
allemande may be found on page 7 and appears to mean a gypsy. This is an unusual meaning for "allemande", but, as best as I can understand, that is what Wilson describes.
poussette may be found on page 53 and means "top two couples join hands with partner, circle, counter-clockwise, one and a half times around the other couple to change places with them.
set contrary corners may be found on pages 55-57 and means "move to 1st corner and set, pass partner right moving to 2nd corner, set, return to places the easiest way". Wilson does not show the corners setting back.

SINGLE FIGURE (Each strain repeated)
Hands 3 round on the ladies side hands 3 round on the gent^ns. side lead down the middle up again & allemande

OR THUS Set & change places with 2^d. Cu: set & back again & whole poussette

DOUBLE FIGURE (Tune played twice thro' with repeats)
Set & hands across quite round with 2^d. Cu: set & back again lead down the middle up again set to top Cu: swing corners chain figure four round with top Cu: & turn your partner

The music consists of two 4 bar strains. Probably played as a reel rather than a strathspey.

The RSCDS is interpretting Wilson's DOUBLE FIGURE

Wilson defines most of his figures in his An Analysis of Country Dancing, 3rd Edition.

1. Set & hands across quite round is one figure which Wilson does not define. However he defines hands across on page 12 where he defines a normal hands across but says they only turn half round (with a footnote saying it is often done by turning completely round and then back again).
   So I'm going to assume that quite round actually means half round. So two bars of setting, followed by two bars to do half a hands across.
2. lead down the middle up again set to the top Cu: may be found on page 8 Top couple leads down to between the third couple, 1s turn and lead up to 2nd place as the second couple move up (Wilson's pictures show them moving up the sidelines and not leading), then actives set (or foot it) to the second couple. (This seems to take 8 bars)
3. swing corners is defined on pages 55-58 and appears to mean: the 1s turn partner by the right hand then 1st corners by the left hand, partner right, 2nd corners left and returning home the shortest way (by the left shoulder).
4. Chain figure for four may be found on page 76 and boils down to what anyone else would call rights and lefts.
5. Turn your partner may be found on page 2 and boils a two hand turn (Wilson calls a right hand turn "swing your partner").

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.