I finally got to spend some time recently looking through Philadelphia newspaper microfilms, investigating the mysterious (and unlikely) "Cauliflower Chemi" appearing on the 1842 Butchers and Drovers Ball program transcribed by Charles K. Jones in his 2006 biography of Francis Johnson.
I was able to find the newspaper announcement with the ball program in the pages of Philadelphia's Public Ledger (Vol. XII, No. 139, February 28, 1842).
Printing from a very tiny newspaper ad on a low-resolution microfilm which only gets blurrier when enlarged does not produce very good results, so I can see why Jones, lacking a dance background, had trouble figuring out the names of dances. After a lot of squinting, I was able to determine that "Chemi" was actually "Cheat", which makes considerably more sense. The full line reads:
4. Cauliflower. Cheat.
Both are popular "promiscuous figures", which could be substituted in for other figures in a quadrille or, apparently, danced as independent figures one or two at a time. I'm not sure I've ever seen such direct evidence of that on a dance program before.
Since the image from the microfilm is next to useless, I'm going to retranscribe the full program, then talk a little about it below.