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Tess's guilt over having contributed to the death of Prince makes her more open to her mother's proposal that she go to the rich Mrs. D'Urberville.
She's willing to visit her as a distant relation, but reluctant to ask for money.
Tess would rather try to get work somewhere, but since her mother is so set on it, Tess agrees. Still, she tells her mother it is "silly" to think of the rich Mrs. D'Urberville setting Tess up with a rich man.
The next day, Tess takes a passing cart to get to Trantridge, where "the vague and mysterious Mrs. D'Urberville" lived (5.14).
As she leaves the village of Marlott, she looks back, and reflects on the childhood she's spent there.
The narrator describes scenes of Tess with her girlish friends playing in the grass; he then describes Tess's growing "Malthusian vexation" that her parents should continue having so many children (5.17).
Historical side note:
The expression "Malthusian vexation" could use some explanation. Thomas Malthus was a political economist and philosopher who wrote an influential book called Essay on the Principle of Population in 1803. In it, he argues for the control of population growth through celibacy, because if the poorer classes continued to reproduce at the rate they were going, they would just perpetuate the cycle of poverty and starvation—they were reproducing faster than the food supply could support them. So Tess's "Malthusian vexation" refers to this consciousness that her parents were producing more little mouths than they were capable of feeding.
Back to the story:
Tess, the narrator informs us, is better educated and more sensible than either of her parents, and as she has gotten older, more and more of the family responsibilities have fallen to her. So it's a "matter of course" that she should be the one to go on the first visit to the rich D'Urbervilles.
She climbs off of the cart and starts walking in the direction of the D'Urberville house, called The Slopes.
The Slopes is a modern country house, without any farmland associated with it, or any tenants—it is intended for "enjoyment pure and simple" (5.20).
The house itself, she finds, is almost new, but is set within a big piece of forest called The Chase—a reminder of the ancient and "Druidical" (5.21) forest that once covered that whole region.
Everything on the estate, from the stables to the greenhouses, is shiny and new—not at all what Tess expected.
She begins to feel hesitant again.
The narrator explains something of the history of the D'Urbervilles, or Stoke-D'Urbervilles, "as they at first called themselves" (5.25).
Mrs. D'Urberville's husband, Simon Stoke (who is now dead) made his fortune as "an honest merchant (some said money-lender) in the North" of England (5.26). He felt the need to change his name—the narrator doesn't explain why—and spends a while going through old family names in the British Museum before choosing "D'Urberville" as being appropriately old and aristocratic. And, importantly, there were no modern branches of that family—the name had virtually died out.
So the rich branch of the D'Urberville family isn't related to the Durbeyfields at all, but of course Tess's parents don't realize that. They have no idea, the narrator tells us, that it's possible to change your name, or to choose an ancient name because you liked the sound of it at the British Museum.
Tess is standing on the edge of the lawn hesitating when a tall young man comes out of a tent that's pitched on the lawn.
He's smoking a cigarette, and has a curly black moustache (like a stage villain—think Captain Hook or something here).
He greets her with, "Well, my big Beauty, what can I do for you?" (5.30).
Tess doesn't know what to say, so he adds that his name is Mr. D'Urberville, and asks if she's there to see him, or his mother.
She says she'd like to see his mother, but Mr. D'Urberville answers that that would be impossible, as his mother is an invalid and cannot see visitors. He asks what the business is.
Tess becomes embarrassed—her errand seems ridiculous now. She stammers that her mother had sent her to say that they were of the same family.
He at first assumes that she's part of his father's family, the Stokes, but of course she corrects him, and he glosses over his slip.
She says that, since she can't visit his mother, she'll just catch the cart back to Marlott on its way back.
He reminds her that the cart won't be by for some hours, and suggests that he show her around the grounds and garden before she goes.
He calls her his "pretty Coz" (5.53), which is a Shakespearean shortening of "Cousin."
Tess feels encouraged by this—she thinks he's acknowledging her as a relation. But she still wants to cut the visit as short as possible.
But the young man is pushy enough that she feels that it would be rude to refuse.
He takes her through the fruit garden, and feeds her strawberries, much to Tess's embarrassment—she says she would rather feed herself. But he insists.
When she can't eat any more, he fills a basket for her, and then cuts her roses and pins them to her hat and dress, and piles more onto her basket.
Finally, he looks at his watch, and suggests that they have something to eat (besides strawberries) before she has to catch her cart back to Marlott.
They eat in the big tent as though they were at a medieval tournament.
He smokes, and watches her eat with evident enjoyment, and the narrator tells us his first name: Alec.
The narrator describes Tess's "innocence" of the "tragic mischief" Alec would cause her as she sits "munching" (5.63).
As Alec walks Tess back to the road where she'll meet the cart, he asks her name, and for more particulars about her family.
Tess explains about Prince.
Alec says he'll try to do something, and that his mother will surely be able to find work for her. He concludes with the reminder that she is not really a D'Urberville, but a Durbeyfield—"quite another name" (5.69).
Tess proudly answers that she "wishes for no better" name (5.70).
Alec almost kisses her as they part, but thinks better of it, and lets her go.
The narrator says that if Tess had realized the importance of this first meeting, she might have questioned the injustice of her fate, especially since Alec is so clearly the wrong man.
The right man had seen her, but she had left no definite impression on him yet. The narrator doesn't say which man that is, but we're left to guess that it was the young man named Angel who didn't dance with her at the club-walking.
The narrator then questions the bad planning of the universe, and shakes his fist at the tragic frequency of missed connections.
Then Alec D'Urberville went back into his tent on the lawn, looks very pleased, and thinks about what a "charming girl" Tess is.