The couples stand in fours across the room, all facing the top, except the first two couples, who face down. Women on the right of their partners (See Fig.)

MUSIC	DESCRIPTION
Bars.
1-4	Couples 1 and 4 dance four hands across with right hands.
5-8	And back again with left hands.
9-12	Couples 2 and 3 dance four hands across with right hands.
13-16	And back again with left hands.
17-24	All four couples set twice and turn partners with both hands.
25-28	All four couples, partners facing each other and joining both hands, slip across to one another's places, men passing back to back.
29-32	Slip across back to places, women passing back to back.
33-36	{ First and third couples dance four hands round to the left. Second and fourth couples dance four hands round to the left.
37-40	The same couples giving left hands, dance four hands across back to places.
41-43	All four couples advance (two steps) and retire (one step).
44	Give three claps with the hands.
45-48	Couples 1 and 2 dancing down the dance, pass under the arms of couples 3 and 4, who are dancing up.
	Repeat, with next two couples, and do the same figures with every line until they arrive at the bottom of the dance. As each line reaches top or bottom of the set, change to correct side of partners and stand during one turn of the dance.
	NOTE.— This dance can also be done in groups of four in a circle in which case bars 9-16 are omitted.

Collected locally.

(I believe this to be the original text as printed in 1925, subsequent revisions of the book use different words but describe the same figure.)

If you look at the Scottish Country Dance Database and Dictionary they both claim the four face four version of the dance should be done round the room as well, but the book shows a longways dance with four lines of two couples each, not a round the room dance. In his The Modern Dancing Master, Chivers, London, 1822 describes dancing four face four dances round the room. He calls this a Chivonian Circle.

The (R)SCDS did not say how many times the dance should be repeated. For a four line dance the traditional number would be nine repetitions leaving everyone where they started, but the SCDS is more likely to follow their own methods and only repeat the dance 8 times (leaving the bottom two lines in the wrong places).

In it's 2008 revision of Book 2, the RSCDS attributes this dance to Lowe's Selection of Popular Country Dances, ~1850. Lowe actually publishes two different figures, one which he teaches and which he claims to be the original version, and one which everyone else in Edinburgh dances. Lowe's "Original" version is unlike any other version I've found (nobody else has the dancers clapping, ever), while the other version seems more like the other contemporary versions I've found. The (R)SCDS chose Lowe's "Original" as the basis for their dance.

Lowe writes:

ANY number of couples can join in this Dance, arranging themselves four and four across the room, and all facing the top except the first couple, who face the other way, the Ladies standing on the right of their partners, thus-

1st Couple,	L. G. L. G. 0 + 0 +
2nd Couple,	G. L. G. L. + 0 + 0
3rd Couple,	G. L. G. L. + 0 + 0

Each line as they arrive at the top, face about to be ready to commence.

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Original Figure, as danced by Mr. Lowe's Pupils.

The couples on the right of each line, at angular corners, do hands across and back again to places (8 bar); the couples on the left of each line do the same (8 bars); all eight set and turn partners (8 bars); all eight gallopade across each other, the couples on the right of each line passing in front (4 bars) back again, the other couple passing in front (4 bars). The couples opposite to each other go hands four round (4 bars), all giving left hands, do hands across back again (4 bars); all eight advance and retire, and give three claps with the hands (4 bars); then the couples dancing down the dance pass under the arms of those dancing up (4 bars); then commence the figure with the next couples; then do the same figure with every line till they arrive at the end of the dance, then face about and dance up again.

Courtesy of National Library of Scotland, licensed under:

I think Lowe wants the top couples to pass under the arches made by the bottom as couples, rather than passing by the right, as is the modern method. Lowe also has people do a couples mad robin along their own line, rather than a couples do-si-do with the people opposite.

Joseph Lowe did not suggest dancing it as a round the room dance. The earliest source I have for that is in Albert W. Newman's A Complete Practical Guide to Modern Society Dancing, Philadelphia, 1903 who wrote:

NOTE. — This waiting, however, can be avoided by placing the couples in a complete circle. It is then advisable to arrange but two couples in each set facing each other.

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He, like the (R)SCDS, only recommends the round the room format when the set is a standard improper duple minor rather than a four face four.

Despite the RSCDS's claims, this dance, and the idea of dancing in a four face four (Mescolanze) formation, predate Mr. Lowe.

The earliest version I have found was published by Kattfuß in Germany in 1802.

According to The Regency Dance site Joseph Binns Hart published "Hart's 2nd Set of Quadrilles" sometime between 1818 and 1820. In this work he has a dance called Hart's Tempete Dance which was a dance with two couples facing two other couples (a rare formation for cotillions, but not unknown), however unlike cotilions (or quadrilles) Hart's dance progresses.

In his Hart's Second Set of Quadrilles, Hart writes:

Form a line of 4, the 2 Ladies on the 2 Gentlemens right, 4 more opposite to the first 4, form lines of 4 behind the 2^d. line as many as intend to dance.

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FIGURE

The first 2 lines right and left, chassez across to the right and left with your partner, dechassez, in returning you go behind the 2^d. Couple The Center 4 hands round, the outside couple's turn and back all 8 Set quite round to the right re set to your places, the top four lead through the 2^d. line and begin the same figure with the 3^d. line & so on to the bottom of the dance.

Then in ~1825 GMS Chivers published a dance called La Tempête in his "Dancing Master in Miniature".

The Contrafusion site says the dance was originally European and dates it back to 1802.

In the US, the earliest source I can lay my hands on is from New York in the US in 1851, which was a mescolanze (but not a round the room dance) Mr. Whale & Daughter published La Tempète, as danced at the Queen's Last Ball

This popular Dance is danced by any number of double couples standing as above at commencement. All begin together, — Advance and retire twice, — Partners together gallop across eight steps each way, — Advance and retire twice, — Hand four round in the centre, (as above) Sides the same turning with both hands, — Hands across, (as above) Sides the same, — Advance and retire once, — Go forward to dance with next vis a vis.

Also in 1851, also in New York, Burnton published The Original Tampete

This popular dance is dance by any number of double couples, standing as above at commencement, all begin at once.

1. All forward and back, (4 bars) half right and left, (4 bars) forward and back, (4 bars) half right and left to place (4 bars)
2. Couples Galop eight steps to the left, (4 bars) then eight steps to the right, (4 bars)
3. Small stars (Each double couple form a star, Ladies cross hands, Gents also, round eight steps to the left (4 bars) change eight steps to the right (4 bars)
4. Grand star (Four couples. Ladies take Gents arms & cross hands in centre, eight steps round to the left, (4 bars) change Gentlemen swing in centre and cross hands, Ladies remain on Gents arms outside. eight steps round to the right. (4 bars)
5. Circles (Each double couple form a circle, hands round, eight steps to the left, (4 bars) eight steps to the right (4 bars)

All advance first couple holding hands up, others passing quick through and advance to the new couples. This forms the first figure again, and must therefore be no time lost, when passing through to the next.

These are the original and true figures, as danced in Europe

I have a page devoted to a more complete history of this dance.