Ever since telling her that he was her real father, Henchard has started scolding Elizabeth-Jane over every little thing.
She uses country dialect occasionally and doesn't always know how to act like a fine lady.
She even helps the servants sometimes.
He scolds her for all of this, and it hurts her feelings.
She figures she must be doing something wrong, so she starts studying really hard to make up for her lack of education.
Henchard acts coldly toward her now.
Elizabeth-Jane starts taking walks to the cemetery where her mother is buried.
One day she sees a strange woman there – not much older than herself, but very beautiful and richly dressed. She seems like a fine lady.
They don't speak but they do notice each other.
Elizabeth-Jane goes home and once again faces Henchard's scolding.
Henchard begins to regret having told Farfrae to back off Elizabeth-Jane.
Since he doesn't enjoy having her in the house anymore, he wouldn't mind seeing her married off.
So he sends Farfrae another note, saying that he can talk to Elizabeth-Jane after all.
The next day, Elizabeth-Jane sees the strange woman in the cemetery again.
The woman sees that Elizabeth-Jane looks unhappy and asks her why.
Elizabeth-Jane says her mother is dead (they're sitting by her mother's grave, after all), and that her father is displeased with her.
She says he gets angry with her because of her faults, but that her faults are due to her past and her lack of a formal education.
The woman seems interested, so Elizabeth-Jane briefly tells her her story: how her parents were separated, her mother remarried a sailor, then her parents found each other again.
The woman is sympathetic and Elizabeth-Jane feels better.
The lady says she is a newcomer to Casterbridge. She's renting a big house in the middle of town (most big houses are on the outskirts), and she needs a young woman to live with her as a companion.
Historical Context Note! It was considered improper for a young, unmarried woman (such as this young lady) to live alone, even if their parents had died and they had no living relatives. So it was common for women in that situation to hire a "companion" – or a woman who was reasonably well educated but without a lot of money, to live with them. Basically, a companion is like a friend-for-rent. It's someone you pay to live with you, in some weird position between friend and servant.
She offers to have Elizabeth-Jane come live with her as a companion if her father really seems to want her out of the house.
This sounds like heaven to Elizabeth-Jane. Living with a fine lady like this will give her the opportunity to learn good, aristocratic manners, and Henchard won't be able to make her life quite so miserable.