Towards zero - Agatha Christie
Lady Tressilian is now confined to her bed, and still invites guests to her seaside home at Gull's Point during the summer. Tennis star Nevile Strange, former ward of Lady Tressilian's deceased husband, incurs her displeasure. He proposes to bring both his new wife, Kay, and his former wife, Audrey, to visit at the same time - a change from past years. Lady Tressilian grudgingly agrees to this set of incompatible guests. Staying in hotels nearby are Kay’s friend, Ted; a long time family friend, Thomas Royde, home after a long stretch working overseas and still faithfully waiting on the sidelines for Audrey; and Mr Treves, an old solicitor and long time friend of the Tressilians.
The dinner party is not so comfortable, as Lady Tressilian had predicted. That night, Mr Treves told a story of an old case, where a child killed another child with an arrow, which was ruled an accident. The child was given a new name and a fresh start, despite a local man having seen the child practising assiduously with a bow and arrow. Mr Treves remembers the case and the child as a result of a distinctive physical feature that he does not describe. Next morning, Treves is found dead in his hotel room, presumed to be heart failure from unnecessary walking up the stairs to his room the previous night, greatly upsetting Lady Tressilian. Thomas and Ted are mystified, as they walked Treves back and saw the note stating that the lift was out of order - they learn from hotel staff that the lift was in working order that night. His death is ruled to be from natural causes.
Lady Tressilian is brutally murdered in her bed, and her maid drugged. Her heirs are Nevile and Audrey. The first evidence points to Nevile Strange as the murderer, including one of his golf clubs with his fingerprints on it. When the maid wakes up, she tells Superintendent Battle that she saw Lady Tressilian alive after Nevile's visit. The evidence then points to Audrey: one of her gloves bloodied and found in the ivy next to her window, and the actual murder weapon. It was fashioned from the handle of a tennis racket and the metal ball from the fireplace fender in Audrey’s room. Then Mary Aldin relates the story narrated by Mr Treves, and his claim that he could recognize that child with certainty; Battle is certain that the lift sign was placed in reaction to that claim.
Angus MacWhirter is standing at the cliff where, a year earlier, he had attempted suicide, when Audrey attempts to run off the same cliff. He grabs her before she can jump. She confesses her fear, and he promises she will be safe. The local cleaners inadvertently give MacWhirter an uncleaned jacket belonging to someone else. Though he is not one of the party at Gull’s House, he is aware of the progress of the investigation, well reported in the local newspapers. He realizes why the jacket has stains in a certain pattern. He visits Gull’s Point, and requests Mary Aldin's help to find a rope in the house. They find a large damp rope in an otherwise dusty attic, and she locks the door until the police come.
Battle arrests Audrey on this evidence. However, Battle's daughter had previously confessed to a theft she never committed due to overwhelming pressure, and so he suspects that Audrey is in a similar situation. MacWhirter meets Battle and tells him what he has learned about this case, including his observation of a man swimming across the creek on the night of the brutal murder, and climbing into the house on a rope. Then, Thomas reveals that Audrey had ended their marriage, not Nevile, as she had grown afraid of him. She was about to marry Adrian Royde, when Adrian was killed in a road accident. With the parties on a motor launch, Battle uses this information to force a confession from Nevile Strange. He had planned events and circumstances to cumulate into his first wife being hanged for the murder of Lady Tressilian – the "Towards Zero" of the title.
Two other deaths (Mr Treves and Adrian Royde) may be due to Nevile, but there is insufficient evidence to prosecute. With his confession, the rope, and the ruse with the bell pull explained, Battle charges him with the murder of Lady Tressilian. Audrey seeks out MacWhirter to thank him, and they decide to marry. They will travel to Chile where he begins his new job. Audrey expects that Thomas will come to realize that he really wants to marry Mary Aldin instead.