At Sir William Lucas's gathering, how does Darcy act around Elizabeth?

Mr. Darcy's behavior at Sir William Lucas's gathering is almost as haughty and proud as it is at the Meryton assembly. For example, when Sir William is attempting to make conversation, engaging Mr. Darcy on the subject of dancing, the older gentleman says that he considers it to be the mark of every polished society. Mr. Darcy rather rudely replies,

Certainly, Sir,—and it has the advantage also of being in vogue amongst the less polished societies of the world.—Every savage can dance.

Whether he is only being contrary or actually saying, in a thinly veiled way, that Sir William's party guests are unpolished savages is unclear. However, in either case, Mr. Darcy is certainly not being as polite as he could or should be. Not only this, but Mr. Darcy's other responses to Sir William are not particularly friendly or warm. They are barely civil at times.
When Sir William spots Elizabeth Bennet walking near to himself and Mr. Darcy, he entreats her to dance with the younger man. Mr. Darcy is "not unwilling to receive" her hand to dance, but Elizabeth declines. Next, "with grave propriety [he] requested to be allowed the honour of her hand, but in vain." After she walks away, Miss Bingley attempts to banter with him, and he admits that he admires Elizabeth's "fine eyes," a comment that sends Miss Bingley (who clearly wants Mr. Darcy for herself) into a tailspin. His behavior, at least toward Elizabeth, is more cordial and less insulting than it is at the Meryton assembly when he flat refuses to ask her to dance when Mr. Bingley suggests it.