What evidence is there to support the interpretation children are being possessed by the ghost, or at least at the governess believes this to be happening?

In Chapter Nineteen, the governess's obsession finally comes into dangerous contact with the children when she can no longer control herself and asks the child about Miss Jessel. Previously, she has always considered the possibility that the children are not haunted and has refrained from mentioning the ghosts. Her mention of Miss Jessel shows her certainty, but her description of her mind before making the statement sounds as if she is describing a mental breakdown. "These three words from her" - asking where Miles was - "were in a flash like the glitter of a drawn blade the jostle of the cup that my hand for weeks and weeks had held high and full to the brim and that now, even before speaking, I felt overflow in a deluge."

It is important to recognize the governess's mental state here, as she is about to see Miss Jessel yet again. In every instance in which she has seen the dead governess before, she has been suffering extreme emotional turmoil.