The girls accompany Father to a meeting of the Antiquarians, hoping it will be a way to meet gentlemen of education and refinement, and possibly, have some fun. They are sporting jaunty caps which must have been a well-accepted style, as Dolly's was featured in Ackermann's Repository in 1809, while Minerva's was in an 1816 issue. I think they are quite cute, and would enjoy wearing the dresses as well.
The Antiquarians meeting reminds me of the old World War II song where the young woman complains about the available men, "They're either too young or too old, they're either too gray or too grassy green". Or really boring. (Says the woman who makes digital pictures out of 200 year old magazines.)