Emily's doctor says she died of chronic liver problems. Emily's companion, Minnie Lawson inherits the deceased's house and fortune. In a previous will, the inheritors would have been Emily's nephew, Charles, and nieces, Theresa and Bella. Upon investigation, Poirot discovers a nail with varnish and a string attached to it at the top of the stairs. "Bob...dog...picture...ajar." had been the message that Emily had given before her death. Poirot concludes that Bob the dog, who was outside that night, did not leave the ball on the stairs and that Emily was tripped by the string.
Emily's nephew and nieces talk about contesting the will, but it is not pursued. The gardener reveals that the nephew, Charles, talked to him about his arsenic based week killer. The bottle is almost empty. Minnie Lawson says that on the night of Emily's death she saw someone through her bedroom window wearing a broach with the initials T.A. (possibly Theresa Arundell, Emily's niece).
IN the meantime, Bella reveals her husband Jacob is bullying her and she moves with her children to a hotel, with the help of Minnie. However, for more security Poirot recommends she moves to another hotel. The next day Bella is found dead due to an overdose of chloral, a sleep aid.
Poirot reveals his theory on the murders. Theresa stole the arsenic but could not bring herself to use it. She and her brother suspected each other. Emily, fearing that Charles might be trying to kill her, revealed that she had revised her will. He was satisfied with just stealing some of her money. The brooch which Minnie had seen was really Bella's. The initials TA, reversed in the mirror, stood for Arabella Tanios. She hated her husband and wanted to separate from him and keep the children, but she had no means to do so. Her first attempt with the ball and string failed. Her second attempt involved inserting elemental phosphorous in one of Emily's liver capsules, which succeeded.
Emily was unaware that her aunt had revised her will. When Poirot explained the murder, she took her own life and her children went back to their father. Emily's husband is upset as he did love his wife. However, he finds out she obtained the chloral to kill him. Minnie decides to share her wealth with Charles, Theresa and Bella's children. Theresa marries Dr. Donaldson, Charles squanders his wealth. The terrier goes to live with Poirot but he prefers Captain Hastings.
Dumb Witness, published in 1937, courtesy http://www.agathachristie.com/stories/dumb-witness