Which chapters reveal the mental condition and changing feelings of the governess?
All chapters, if read closely, reveal the mental condition and changing feelings of the governess, but Chapters Two, Three, Six, Nine, and Fifteen are particularly revealing.
In Chapter Two the governess has her first suspicion about Miles when she receives his expulsion letter from his school. In Chapter Three the governess has her first sighting of what she believes to be the apparition of Peter Quint. These chapters are critical to the governess's tailspin into paranoia since they incite the two central mysteries of the novel: Miles's removal from school and the nature of the two "ghosts."
In Chapter Six, after she has seen Peter Quint a second time, the governess starts to fixate on the children's relationship with the ghosts and her role in their safety. She can't seem to make up her mind about the children; sometimes she thinks they are incapable of evil, and other times she believes that they are controlled by Quint and Jessel.
In Chapter Nine the governess becomes almost obsessed with the children's every word, look, and action. Her own visions of the ghosts become more intense, more terrifying, and more personal as the reader approaches the climax at the lake. Her encounter with Miss Jessel in Chapter Fifteen is particularly disturbing and revealing, and the reader can infer that the governess shares Jessel's feelings of loneliness and sexual frustration. These feelings might be the reason for the governess's strange behavior if the ghosts are figments of her imagination.