Sissy leads Mr. Gradgrind and Mr. Bounderby into the pub, called the Pegasus's Arms, where she, her father, and the rest of the circus troupe are staying. She is greatly distressed, however, when she can't find her father there, and runs out to look for him in the circus booth. As Gradgrind and Bounderby wait for her return, they meet some of the other members of the circus: Mr. E. W. B. Childers and Mr. Kidderminster, who speak in an almost incomprehensible slang (to Mr. Gradgrind's confusion and Mr. Bounderby's contempt).
Note that the circus people gather at the Pegasus's Arms—named after a mythological flying horse, and contrast that to Gradgrind's insistence that his students define horses only realistically. This contrast establishes the circus folk as being aligned with "fancy" as opposed to "fact". The circus people's names, containing the words "Child" and "Kid" further emphasizes their connection to "fancy". Gradgrind's confusion and Bounderby's contempt, meanwhile, show both their inability to perceive beyond pure "fact" and how that affects their ability to connect or empathize with others.
The circus people reveal that Sissy's father, Signore Jupe, had not been performing very well lately and that he in fact deserted Sissy, whom he loved dearly, because of his shame in his failure to earn their living. As Gradgrind and Bounderby discuss what they ought to do with this now father-less child (Gradgrind wants to take her in and raise her with his education of facts, while Bounderby doesn't want to do anything for her), the rest of the circus company comes in, including the circus owner, Mr. Sleary. They are dirty, poor, and uncivilized, but they are also kind, gentle, and generous, and are very sad to hear that Sissy might be leaving them.
The circus people have had an education of imagination and fancy rather than facts, but they prove to the better people for it: they know how to love, as their love and care for Sissy demonstrates. Signor Jupe's abandonment of Sissy also comes from love. Again there is a contrast between Gradgrind and Bounderby, with Gradgrind wanting to help Sissy (admittedly in a way that won't actually be that helpful to her), while Bounderby can't be bothered by an abandoned child.
Sissy returns in tears upon discovering her father's desertion, and accepts Mr. Gradgrind's offer to take her into his home and educate her. The circus players, who all loved Sissy dearly, sadly say goodbye to her, and show her a lot of affection in their simple and sincere way.
The circus players prove themselves again to be much more capable of sympathy than Gradgrind or Bounderby as they tearfully say goodbye to Sissy, though Gradgrind's offer to take in Sissy is generous.