Why do we say "Mind your p's and q's"?

Meaning:

Mind your manners, be on your best behavior

Today, this expression is usually interpreted as a reminder to mind your manners and be on your best behavior, but back in the 18th century it is possible that it had a slightly different meaning given that Francis Grose's 1785 edition of The Dictionary of the Vulgar Tongue, defines it as "to mind one's P's and Q's; to be attentive to the main chance."

Background:

Before getting into the varying origin theories of this expression, first there is the matter of how to spell it: capital letters or lower case, apostrophes or not?

I have gone through life capitalizing Ps and Qs on the basis that less is more when it comes to apostrophes; but, according to the Associated Press Stylebook (the standard style guide for most U.S. newspapers) I am wrong. The correct usage is lower case letter plus apostrophe. In fact, under the section on wrangling apostrophes the AP Stylebook helpfully provides this example: "For plurals of a single letter, add 's: Mind your p's and q's, the Red Sox defeated the Oakland A's."

Incidentally, while endorsing the use of apostrophes for the plurals of single letters such as p's and q's, the AP Stylebook goes on to clarify that apostrophes should not be used in numbers - e.g. 1980s, not 1980's


Having tackled the gritty problem of spelling, what about the source of the expression?

Here, many theories jostle for space, some more plausible than others:

• A literal reminder to distinguish between the lower case letter "p" and its mirror image "q" when writing and typesetting. This is the interpretation used in a letter to the editors of a 1851 edition of Notes and Queries, and by the Oxford English Dictionary in its 2007 edition. It seems particularly credible in the context of printing presses where it would have been very easy to misplace a p for a q, particularly given that the type was set backwards from the point of view of the typesetter. But contrarians argue that, if this is an admonishment to typesetters and children, why choose the letters p and q and not the more frequently used letters b and d?
  
  
• Ps and Qs are short for "pleases" and "thank yous." Given that most people use the expression to mean be on your best behavior, this source would seem to have some validity.
  
  
• A reminder to bartenders to keep track of the pints and quarters that were consumed (and were tracked on a tally sheet using the letters p and q. This seems to be a rather convoluted option, not least because it seems to bear no relationship to how the expression is currently used.
  
  
• French dance instructors cautioned their students to mind their pieds and queues (feet and wigs), but there is no known equivalent expression in French past or present, and why would someone be in danger of confusion something on their head with their feet. In the same light, the theory that sailors were reminded to pay attention to their peas and queues (pea coat and pony tail) seems less than compellling.

The earliest known usage of the expression is also a bit murky as in Thomas Dekker's 1602 play, The Untrussing of the Humorous Poet, 1602 there is a line that reads, "'Troth, so thou'dst need; for now thou art in thy Pee and Kue: thou hast such a villanous broad back..." But the mysterious Pee and Kue in this sounds more like an item of clothing than a metaphor.

Things are a little clearer in 1607 when Dekker teams up with John Webster to write "Westward Ho" in which the expression appears to have been used to mean something similar to its usage today: "At her p. and q. neither Marchantes Daughter, Aldermans Wife, young countrey Gentlewoman, nor Courtiers Mistris, can match her."

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