The dance names mentioned in the song were popular dances of the Nineteenth century; one description is at a Web site here:

Another form of quadrille drew popularity not only because it included familiar figures but also because it provided opportunity to perform the waltz , polka, schottish, Esmerelda, or mazurka. Numerous manuals presented directions for these quadrille variants...The Paris publisher Roret's Nouveau manuel complet de la danse of 1866 also included a Varsovianna Quadrille, after the popular waltz variation of that name. In 1889, Herman A. Strassburg, Jr.'s Call book of modern quadrilles described three waltz quadrilles, including a curious example for three couples (rather than the usual four).

The "Waltz Circassian" may have been a variant of the Circassian Circle Dance - anyway, I liked the way the song gives the actual names of real dances from the 1860's...