A petition is going around the mill. The girls working there are being asked to sign it, if they want to show their support for a shorter work day. If a girl signs it, she does so knowing that she may be fired and blacklisted from other jobs. Betsy is one of the girls that signs the petition, but she is dismissed because of her cough, which is likely tuberculosis.
Lyddie has become the factory's best worker and consequently has been assigned the task of training a new worker. Lyddie is not happy about her assignment and is not a patient teacher. She would rather be working her own looms. She feels that her student is exceptionally dense and therefore all Irish immigrants must be equally stupid. By the end of the day, Lyddie no longer has the patience to teach her pupil any longer, so she tells the boss to assign the girl to her own loom. Lyddie knows the girl is not ready and is being put into a potentially dangerous situation, but she doesn't care. That act shows how cold and selfish Lyddie has become by this point in the story.