This is just a punt on the right word - it's a decade or two since I heard the song last - but just by context and fashion, it may be "the Waltz Cotillion" (strictly, the French is "cotillon", more or less the same as petticoat.

As we play it, the Waltz Cotillion should be brisk enough for the petticoats to swing out (yet another sin of the shameful waltz!). The actual dance is rather more complex that a modern round waltz - being a detached figure from a quadrille (The Alberts, offhand). This not only involved moving about the quadrille set searately and in a couple waltz, but has a grand chain in waltz time (which we push to more of a mazurka rhythm).

Regards,

Bob Bolton