Note 1: (tippet)
From the Encycolpedia Britanica Online:
In the 18th-century "tippet" referred to a capelike or scarflike garment worn around the neck and hanging down in front; this tippet could be made of gauze, crepe, lace, velvet, fur, or feathers.
Note 2: (make it at all improper)
Why would it be improper for a brother and sister to dance together?
The reason is that dancing was generally considered to be one of the stages in the courtship between a man and a woman, with the eventual goal being marriage. A ball was one of the few occasions when a man and a woman could flirt with one another and carry on a private conversation--a couple would dance together for perhaps half an hour at time, giving them a fairly good idea of one another.
Because there was no chance that a brother and sister would marry, it was considered improper for them to be engaging in an activity which has the end-goal of marrying your partner.