Dance cards or carnets de bals were all the rage in the 19th century whether at a Regency ball or less formal dance events. This pre-1872 sample is from the collection of the State Library of Victoria. You can find a history of the cards and associated protocols over here at Historical Hussies.
This Wikipedia sourced image illustrates a quadrille in action.
If you’re wondering about the “Sir Roger de C” reference, here’s a description of the dance Sir Roger de Coverley in Charles Dickens’ A Christmas Carol. This text and colour illustration is via a Project Gutenberg e-book of the Chapman and Hall edition c 1847 with illustrations by John Leech.
There were more dances, and there were forfeits, and more dances, and there was cake, and there was negus, and there was a great piece of Cold Roast, and there was a great piece of Cold Boiled, and there were mince-pies, and plenty of beer. But the great effect of the evening came after the Roast and Boiled, when the fiddler (an artful dog, mind! The sort of man who knew his business better than you or I could have told it him!) struck up “Sir Roger de Coverley.” Then old Fezziwig stood out to dance with Mrs. Fezziwig. Top couple, too; with a good stiff piece of work cut out for them; three or four and twenty pair of partners; people who were not to be trifled with; people who would dance, and had no notion of walking.
From the Library of Congress Dance Instruction Manual collection (hat tip to librarians for that which they choose to collect and preserve) comes this description of the dance. Click on the link for the complete instructions.
The Project Gutenberg EBook of A Christmas Carol, by Charles Dickens This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.net