Re:COTILLION; noun
1. a dance with elaborate steps and figures, in particular, an 18th-century French dance based on the contredanse.
US: a quadrille.


which bring us to one of my favorite songs...
http://www-2.cs.cmu.edu/People/rgs/alice-X.html
(scoll down a bit, and you find it the text, just serves as an introduction...) it also seems to suggest that quadrille was also used in the UK.

and neatly answers the question, How far?
the further we are from england, the nearer we are to france!