Foursome Reel

This dance was probably danced for about a hundred years before anyone bothered to publish it. The earliest Scottish source I can find is Smyth in 1830 who writes:

At the commencement, the Gentlemen place their partners at the end of the room, and stand either before or beside them. — If before them, all the four begin at once, but if otherwise the Ladies must begin first, each person describing the figure eight, and the Gentlemen set to the Ladies alternately.

A year later, the Lowe brothers said the same.

Unfortunately this description is misleading. The figure of a reel for four people is not a figure eight, it's a figure eight with an extra loop. The Fletts kindly point this out.

The Fletts also mention that the reel should be performed "giving shoulders", that is when passing someone of the opposite sex in the reel the shoulder closest to that person should lead (so the dancers are almost back to back), while when passing someone of the same sex the outside shoulder should lead (so the dancers are almost face to face).

Although the glory of the dance is in the various setting steps used, the arms were also involved. The Fletts say that the most common position was for the dancers to hold their arms akimbo. Though the gentlemen often raised their arms (one, or both, or alternating), and the ladies sometimes raised theirs, and sometimes used them to hold their skirts out.

The music was usually a medley of reel tunes, and in later years would start as a strathspey and finish as a reel.

Toward the end of the 19th century, the foursome reel was usually followed immediately by the Reel of Tulloch (in reel time). In the reel of Tulloch when turning someone, the other arm was usually raised.

the Gentlemen set to the Ladies alternately means that the gentlemen finish the reel in each other's places so they are setting to the woman who is not their partner (at least the first time through, they are back with partners after the second time).

Smyth (and the Lowes) seem to suggest that only the Gentlemen set, but the Fletts say all four dancers do.

This was often danced to a strathspey/reel medley.

The earliest written description of the dance actually comes from Thomas Wilson's Analysis of Country Dancing, London, 1808 (page 120). His version is rather different. It starts with two facing couples, each couple turns (I presume a two hand turn), and then everyone turns their opposite, that repeats (turn partner, turn opposite), then the 1st couple crosses in between the second and hey with them. On the second iteration the 2nd couple cross to hey with the 1st.