16: Tom a Bedlam, or Grayes Inn Maske
longways for 2 or more
mms pages 29 to 32
Playford version: from 1st edition to 10th edition through various names.
Music: Dances Populaires Francaises, by the Broadside Band
Part 1
Verse 1, Part A
1-2: Lead up [a double] and down [a double] again
3-4: Top couple cast off and invert the line [in two doubles]
Verse 1, Part B
1-2: Lead up [a double] from the inverted position, fall back [a double]
3-4: Last couple (at the top of the line) cast off and invert the inverted line 
Chorus 1, Part A
1: The men take their partner by both hands and set them perpendicular to how they were, men above women, forming a single line in the center of the set
2: Return to your normal positions
Chorus 1, Part B
1: The men set to their partner
2: The women set to their partner
Chorus 1, Part C
1: The men congee (bow) to their partner
2: The men salute (kiss (hands of)) their partner
3: The women congee (bow) to their partner
4: The women salute (kiss (hands of)) their partner
Chorus 1, Part D
1-2: Turn your partner all the way around [to the left]
3-4: Turn your partner all the way around in the other direction
Chorus 1, Part E
1: Fall back [a double] from your partner
2-4: Man 1 leads the men through three loops with the result of an inverted line; woman 1 does the same
Chorus 1, Part F
1: Fall back [a double] from your partner
2-4: Man 1 leads the men through three loops with the result of a reverted line; woman 1 does the same
Part 2
Verse 2, Part A
1-2: Side [left to line up right shoulders]
3-4: Invert the line
Verse 2, Part B
1-2: Side [right to line up left shoulders]
3-4: Revert the line
Chorus 2, Part A
1: The women take their partner by both hands and set them perpendicular to how they were, women above men, forming a single line in the center of the set
2: Return to your normal positions
Chorus 2, Part B
1: The women set to their partner
2: The men set to their partner
Chorus 2, Part C
1: The women congee (bow) to their partner
2: The women salute (kiss (hands of)) their partner
3: The men congee (bow) to their partner
4: The men salute (kiss (hands of)) their partner
Chorus 2, Part D
1-2: Turn your partner all the way around [to the left]
3-4: Turn your partner all the way around in the other direction
Chorus 2, Part E
1: Fall back [a double] from your partner
2-4: Man 1 leads the men through three loops with the result of an inverted line; woman 1 does the same
Chorus 2, Part F
1: Fall back [a double] from your partner
2-4: Man 1 leads the men through three loops with the result of a reverted line; woman 1 does the same
Part 3
Verse 3, Part A
1-2: Arm [left (right arms, walk left)]
3-4: Invert the line
Verse 3, Part B
1-2: Arm [right (left arms, walk right)]
3-4: Revert the line
Chorus 3, Part A
1: The men take their partner by both hands and set them perpendicular to how they were, men above women, forming a single line in the center of the set
2: Return to your normal positions
Chorus 3, Part B
1: The men and women set to their partner
2: The men and women set to their partner
Chorus 3, Part C
1: The men and women congee (bow) to their partner
2: The men and women salute (kiss (hands of)) their partner
3: The men and women congee (bow) to their partner
4: The men and women salute (kiss (hands of)) their partner
Chorus 3, Part D
1-2: Turn your partner all the way around [to the left]
3-4: Turn your partner all the way around in the other direction
Chorus 3, Part E
1: Fall back [a double] from your partner
2-4: Man 1 leads the men through three loops with the result of an inverted line; woman 1 does the same
Chorus 3, Part F
1: Fall back [a double] from your partner
2-4: Man 1 leads the men through three loops with the result of a reverted line; woman 1 does the same
Comparison to the Playford version (1st to 10th editions)
Tom a Bedlam, Mad Tom, or Gray's Inn Maske (variously spelled), seems another very popular dance with great logevity.  This pre-Playford version is very clearly of the same family, and will fit easily to the Playford music.
There are specific differences - the inversion of the line, instead of setting and turning, the looping rather than heying, etc - but these are minor variations overall.  It is interesting, though, that each chorus, while substantially the same, is slightly altered in this manuscript's version.
Conclusion:
Very clearly a direct ancestor of the Playford version.
I find it interesting the clear note that is made of the "you only dance with your partner" nature of this dance by having the number of couples go from 1 to as many as you want.