Mrs. Sparsit, Bounderby's housekeeper, is a widow and the proud descendant of two prominent (in her mind anyway) families: her husband was a Powler while she herself is a Scadgers. Bounderby loves having her as a servant – she has fallen from high society and so makes him look even better for climbing as high from the gutter as he has climbed.
Bounderby tells Mrs. Sparsit about Gradgrind's plans for Sissy, and his own worries that she will be a bad influence on "Louisa, Louisa, Louisa."
Mrs. Sparsit praises Bounderby for being "quite another father to Louisa," but he says that if he's another father to anyone it's to Tom. In fact, Tom is coming to work for him at the Bank very soon.
The two banter a bit about how rich and upper class Mrs. Sparsit used to be and how low class and poor Bounderby used to be.
Gradgrind, Louisa, and Sissy come to Bounderby's house. Sissy is shy and confused; she bows a greeting to everyone except (by mistake) Mrs. Sparsit and Bounderby yells at her.
Gradgrind formally offers Sissy a place in his house as a sort of companion and servant to the sickly Mrs. Gradgrind. She accepts, but says that as soon as her father returns, she will leave the Gradgrinds.