Circassia is (or was) a region on the northeastern shore of the Black Sea.

In Baltimore in 1820 George Willig Jr. published a dance called "The Circassian" in a pamphlet called Admired Cotillions (in the US the distinction between Quadrilles and Cotillions was often lost, and I think this is actually one set of a quadrille. It isn't in a circle and it is not progressive.

Forward two cross over. Chasse. cross. to place. Balance and turn partner. Ladies Chain. promenade and half right and left to place.

The figure for this dance is said to come from Le Pantalon in Payne's 1st Set of Quadrilles. The first 24 bars match and the last 8 have been changed to make the dance progressive. The idea of dancing in a circle, and the name "Circassian" come from G.M.S. Chivers.

In 1822 in his book The Modern Dancing Master, G.M.S. Chivers introduces a style of dancing he calls "Circassian Circle". He then publishes four dances to be done in this style, none of which is called "Circassian Circle" itself.

Chivers's version is different from the modern way of dancing. At the time, in longways sets, only the top two couples would start dancing, in this circle dance only the two couples closest to the music would start, they would pass each other, and then each would dance with the next couple in their direction of motion. And so on.

Any number of persons can join in the Dance, observing that there is an even number of couples; the odd numbers stand on one side, and the even numbers on the other, forming a circle, thus:

The 1st and 2nd couples face each other, who perform the Figure and exchange places: then the 1st and 4th couples, and at the same time, the 2nd and 3rd couples do the same, and so continued all round. Each Dance terminates when all have been through it.

Each lady to stand on the right of her partner throughout the Dance. All the odd numbers face the same as No. 1, and the even numbers face the same as No. 2.

— The Bodleian Libraries, University of Oxford, Harding Mus F 346

Note this is simply a general description of how to dance in a circle. It is followed by four figures for this format. the one which most closely matches the modern version is called "La Daphne":

Right and left set and turn partners ladies chain half pousette into each others place, and turn partners under the arm

— The Bodleian Libraries, University of Oxford, Harding Mus F 346

The next version I can find is Lowes' Ball-Conductor and Assembly Guide (Edinbourgh, ~1831) where they write:

The Circassian Circle

Is a circular Country Dance, for which the party is arranged, as for Quadrilles, across the room; the four at the top commence first, and change sides at the end of the figures, they continue to repeat them with all the couples down the opposite sides of the room, crossing over at the bottom, and continuing till they arrive at their original places; all the other couples must also continue, after they commence, till they make the circuit of the room; and when all have regained their places, the dance is finished

First Circassian Circle

Ladies chain, set and turn partners, right and left, hands four half round, and turn partners, changing places.

I think the Lowes are describing a hall full of two couple quadrille sets (that is improper duple minor lines), lined up along each side wall of a building. As with Chivers, and in keeping with the staggered start in use for country dances at the time, only one set start dancing, the one at the top, they pass each other, and one moves down the right wall, and one down the left, as they move down the lines the dancers behind them will also start, then when they reach the bottom instead of becoming 2s and working their way up, the cross over to the other line, and work their way up. When they reach the top of the other line they stop and wait until everyone else has reached their original position.

In ~1842 Tilt & Bogue published The Ball-Room Preceptor (Third Edition) containing a description of the Circassian Circle very like Chivers's. Only two couples dance at the start, and no specific figure is provided. (In ~1844 Coulon (London), in 1848 George Appleton, Philadelphia, and in ~1850 Kent & Co., Nottingham copy their description word for word)

The next version I've found is Wilson, 1852.

Wilson writes:

Couples vis-a-vis; form a circle round the room; figure, right and left or hands across; set and turn partners; ladies chain; waltz pass on to next couple; repeat.

Wilson defines "Right and Left" on page 15 of The Art of Dancing and it involves no hand clasps.

Sometime between 1850 and 1853 in Lowe's Selection of Popular Country Dances:

Any number of Couples can join in this Dance, the Couples arranging themselves along each side of the room, (the Ladies standing on the right of their partners) and all facing the top of the room, except the first Couples who face each other across the dance.

FIGURE

Ladies chain by top couples. (8 Bars) Balancez and turn partners. (8 bars) Right and left. (8 bars) Hands four half round, then turn parners and face the next couples on the sides of the dance (8 Bars) This figure is repeated with every couple, all down the sides of the dance across the bottom, and up the other sides to places, every couple after they commence keep going on till all have regained their own places.

Courtesy of National Library of Scotland, licensed under:

Joseph Lowe is still recommending the old style progression where only the top couples start. But he now calls this dance "Circassian Circle" rather than one of several dances in that style.

In 1897 in D. Anderson's Ball-Room and Solo Dance Guide, (Dundee)

The couples stand in a circle round the room, two and two, couples facing each other, and backs to other couples. Gentlement have partners always on right hand.

Rights and lefts to places.

Set and turn partners.

Ladies' chain.

Pousette into opposite places.

Repeat figure with next couple round the room.

Courtesy of National Library of Scotland, licensed under:

Given the way he sets up the dance, Anderson must have everyone starting at once.

Note that in Le Pantalon of Payne's 1st Set of Quadrilles the four bars of setting to partner (which come after the rights and lefts) are two different setting steps: Balancé and Sissone Balotté Jetté and Assemblé. The first is an advance and retire movement (toward and away from partner) and the second a side to side movement (to the right, and back to the left).

The RSCDS says "collected in Caithness."

RSCDS Book 6 claims this was "collected in Rothesay, Isle of Bute."

Book 21 contains the note "Collected in Glenesk, Angus".

Book 24 has the comment: "Collected by Miss Jenny MacLaghlan."

Howe in Howe's Drawing-Room Dances (Boston, 1859) published a dance similar to this. It is not a round the room, but it does begin with the 1s improper, starts with balances and turns and includes a ladies chain. Probably not a source for this dance, but likely something derived from the same root.

Book 24 has the comment: "Collected by Miss Jenny MacLaghlan."

Book 24 has the comment: "Collected by Miss Jenny MacLaghlan."

RSCDS Book 26 says "collected from Mr. W Brown, Airdrie, Lanarkshire."

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.

The RSCDS attributes this dance to the New Enlarged and Complete Ball-Room Guide, but when you go to the National Library of Scotland's catalogue and request that book what you get is D. Anderson's Ball-Room and Solo Dance Guide, The Solo Dance Guide appears to have a second title page claiming to be the New Enlarged and Complete Ball-Room Guide. Both are said to have been published in 1897 and I suspect they are indeed the same work. At any rate this dance is in the Solo Dance Guide.

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

Time, 2-4 or 6-8

Stand as for the Quadrille.

Top and bottom couples give right hands across in the centre and go half round.

Give left hand and go back to places.

Top couple and right-hand couple advance and retire to each other. half rights and lefts to each other's places; at the same time bottom couple and left-hand couple advance and retire, half rights and lefts to each others places. Top and bottom couples are now at sides and side couples at top and bottom.

Top and bottom couples half ladies chain.

Side couples half ladies chain.

Top and bottom couples half ladies chain.

Sides half ladies chain, bring ladies back to their own partners.

Top and No. 3 couples again advance and retire, and half rights and lefts; at same time bottom couple and No. 4 couple advance and retire and half rights and lefts, bringing all into their original places.

All promenade half-round with partners.

All walk back to places, the ladies walking behind their partners.

Repeat from beginning — sides taking leading part the second time; top and bottom the third time; sides the fourth time.

Courtesy of National Library of Scotland, licensed under:

The RSCDS attributes this dance to the New Enlarged and Complete Ball-Room Guide, but when you go to the National Library of Scotland's catalogue and request that book what you get is D. Anderson's Ball-Room and Solo Dance Guide, The Solo Dance Guide appears to have a second title page claiming to be the New Enlarged and Complete Ball-Room Guide. Both are said to have been published in 1897 and I suspect they are indeed the same work. At any rate this dance is in the Solo Dance Guide.

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

Time, 2-4 or 6-8

Stand as for the Quadrille.

Top and bottom couples give right hands across in the centre and go half round.

Give left hand and go back to places.

Top couple and right-hand couple advance and retire to each other. half rights and lefts to each other's places; at the same time bottom couple and left-hand couple advance and retire, half rights and lefts to each others places. Top and bottom couples are now at sides and side couples at top and bottom.

Top and bottom couples half ladies chain.

Side couples half ladies chain.

Top and bottom couples half ladies chain.

Sides half ladies chain, bring ladies back to their own partners.

Top and No. 3 couples again advance and retire, and half rights and lefts; at same time bottom couple and No. 4 couple advance and retire and half rights and lefts, bringing all into their original places.

All promenade half-round with partners.

All walk back to places, the ladies walking behind their partners.

Repeat from beginning — sides taking leading part the second time; top and bottom the third time; sides the fourth time.

Courtesy of National Library of Scotland, licensed under:

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.