Exegesis

Setting

Act 1, a park on the island in the Seine just outside Paris

The setting of the first act is the island of IIe de la Jatte which is an island in France, in the river Seine, at the very gates of Paris.

• Page 18, Dot wears a traditional 19^th century outfit: full length dress with bustle, etc.

A bustle is a type of framework used to expand the fullness or support the drapery of the back of a woman's dress.  The time period of the play, a “late bustle” would be worn, which means it is a more exaggerated look than from previous years.  Wikipedia

• Page 24, Dot, “The tip of a stay”

A stay in this case would be the noun, meaning a flat strip of steel, plastic, etc., used especially for stiffening corsets, etc.

• Page 27, Franz, “Jungen!  Nicht so laut!  Ruhe, bitte!”

German for “Boys!  Not so loud! Quiet, please!”  Pronunciation.

• Page 27, An actor recreation of Steuat’s Bathers at Asnières is seen on stage
  
  
• Page 27, The Young Man gives a loud Bronx Cheer

A “Bronx Cheer” is another phrase for “blowing a raspberry.”   Demonstration

• Page 28, Jules, “It’s neither pastoral.  Nor lyrical.  You don’t suppose that it’s satirical?” 

These are references to different types of artistic styles popular at the time of the play.  Pastoral is a form of glorifying the farm life and nature.  Lyrical is in a sense abstract painting, it became more popular in the 1940s.  Satire is a way of using humor and taboo subjects to get ones point across.

• Page 29, Yvonne, “It might be in some dreary Socialistic periodical.”

Socialism is hard to put into one easy definition.  But it was on the rise when the Industrial Revolution kicked in.  To get their views heard they would produce periodicals throughout the year, which in a sense are magazines.  Many people did not take these beliefs seriously.  Wikipedia.

• Page 32, Dot, “We’ll go to the Follies tonight.”

This is most likely referring to the popular French theatre The Folies Bergère.  Famous for its elaborate costumes; the women's were frequently revealing, practically leaving them naked, and shows often contained a good deal of nudity.

• Page 33, It is mentioned in stage directions that Dot sits at her vanity in the style of the painting La Poudreuse (Young Woman With Powder Puff)

• Page 36, Dot, “Fancy young aristocrats with fancy flats…”
  An aristocrat is a nobleman, a member of the elite, has taste, manners, etc.  It is no wonder that Dot thinks of spending time with them.  Pronunciation.