Mrs. Sparsit was wrong: Louisa has not gone to Coketown to meet Mr. Harthouse, but rather to Stone Lodge to see her father. As it continues to storm outside, Louisa enters her father's study. She pours out her heart to her shocked father, who is rendered speechless by his eldest child's misery. Louisa reproaches him for never allowing her or Tom to exercise their fancy and imagination, which set them up for their current unhappiness. Mr. Gradgrind groans in sadness to see her present state.
…but in fact Louisa has more strength—and, the novel suggests, more moral goodness—than it appeared. (Whether it is fair, from a modern point of view, to equate Louisa's moral goodness with a refusal to cheat on her awful husband is another issue). Louisa takes the emotion of nearly consummating an affair with Harthouse and finally unleashes it at the source of her problems: her father. Gradgrind's groan indicates his own potential for goodness, and to learn.
Louisa then reveals to him that Mr. Harthouse has declared his love for her, and she doesn't know if she loves him or not—all she knows is that he was the first person to ever show her any affection. She has not disgraced herself, but has brought herself to her father's feet, pleading for him to save her by some other means than his philosophy and education of facts. She then sinks into a dead faint on the floor.
This is a pitiful scene indeed: Louisa reveals how starved she was for affection, something that she felt more strongly than Tom. This, then, is what an education of facts will bring one to.