

In his A Companion to the Ballroom of 1816, Wilson writes:
SINGLE FIGURE1st. strain repeat 2d. played straight thro & D.C.
Set & half right & left with 2d.; set & back again lead don the middle up again · & half poussette with top Cu: ·
OR THUSHands 3 round on the ladies side hand 3 round on the gent: side lead down the middle up again · & set to the top Cu: ·
DOUBLE FIGURE Tune played twice thro' as marked
Swing with right hands round 2d. Cu: then with left set 3 across · set 3 in your places · whole figure contrary corners chain figure four round with top Cu: · & allemande ·
Wilson has a different figure for this tune in his earlier book Treasures of Terpsichore, 1809. Preston has yet another figure in 1796. Cahusac gives two figures in 1795. Campbell has a figure in Campbell's 9th Book of New and Favorite Country Dances & Strathspey Reels from about 1794. While Rutherford, 1756 and Johnson, 1742 give the same figure (Rutherford's compleat Collection of 200 of the most celebrated Country Dances both Old and New, Vol. 1) — but the music they give is a different tune (for one thing it is a jig, not a reel).
This is an attempt to understand the DOUBLE FIGURE which is the basis of the Scottish Country Dance of this name.
In An Analysis of Country Dancing Wilson defines some of the terms he uses. A "whole figure" is just a "full figure eight" (as you might expect, Playford uses the same phrase). Wilson does not explicitly define "whole figure contrary corners" so I'm going to assume it means that the each active does a figure eight around his/her corners, starting with the 1st corner ending around the second, returning where s/he started.
Chain figure is defined: The Ladies and Gentlemen form a circle: when the Lady at A, begins the chain, she gives her right hand to the Gentleman at B, and her left to the Gentlman at C; The Gentleman at B, swings the Lady at D; in short, all the Ladies move one way, and all the Gentlemen another. I think that boils down to a progressive hey with hands, again everyone ending where they began.
Wilson gives a very unclear definition of "allemande" it might be a modern gypsy, or a back to back (he defines neigther of these figures). He says the two people doing the allemande walk in circles around one another, he does not mention taking hands, he does not say how their faces are oriented.
It is tempting to have the 1s become improper after the lines across setting (the RSCDS does this), but Wilson says they are "in your places" for the setting on the sides.
Wilson's 1816 version, as best as I can interpret it
The RSCDS interpreted this dance in 1957 (Book 19).
They changed the progression. They changed the lines of three setting so that the 1s become improper (Wilson says they are proper). They changed the figures of eight into reels, getting everyone involved. The progressive hey gets turned into a reel across. Wilson's non-progressive 4 bar one couple allemande gets turned into the RSCDS's progressive two couple 8 bar allemande, something completely different.
And the music has gone from 32 bars to 40.
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