Dancers should know that the text for bars 17-20 was changed in 2008.   
 
The original text in Playford (1718) specifes that for [9-12] the M pass their P Rsh, but for [17-20] only says "the women doing the like", leaving unclear which shoulder to use.

RSCDS book 5 (published in 1928), the Pocket Editions of 1954 and 1986, and the 2006 edition of book 5, use the wording “2nd and 1st man stand still while 1st woman dances round and below her partner into 2nd woman’s original place, and 2nd woman dances round and below her partner into 1st woman’s original place. (1st woman dances in front of 2nd woman).”  This is not unambiguous, but seems to imply that the women dance LEFT shoulder round their partner.  TACnotes (5th edition, 2008) says this explicitly.  

The revised “combined A5 edition” of Books 1–6, uses the wording “1st woman dances across the set below her partner, behind him and across to 2nd woman’s original place.  At the same time 2nd woman dances below her partner, behind him and across to  1st woman’s original place.  1st woman dances in front of 2nd woman to begin.” This makes explicit that the women dance RIGHT shoulder round their partner.  This flows far better into the hands round that follow.

This entry to SCDDB (Cribs and diagram) follows the currently official 2008 text.

It has been pointed out that in bars 17-20 both the <<https://my.strathspey.org/dd/dancevideo/7734/|Edinburgh>> and <<https://my.strathspey.org/dd/dancevideo/7313/|Graziani>> videos show 2nd woman passing in front of 1st woman (the opposite of the official Book 5 instructions). This variant seems to work well.