The Moving Finger

Jerry is injured in a plane crash after which he and his sister, Joanna, take up residence in Mrs. Burton's country house in Lymstock.  They receive an anonymous letter accusing them of being lovers while they are simply siblings.  It turns out many people in town are receiving poison letters.  Mrs. Symmington receives a poison letter claiming that her husband is not the father of her second son; later she is found dead.  Beside her body is a glass containing potassium cyanide and a note stating:  "I can't go on."

Her 20 year old daughter, Megan, stays with the Burton's for awhile.  The Burton's maid receives a call from the distraught maid of the Symmington's.  They plan to meet, but the former never shows up.  The next day her body is found in the cupboard under the stairs by Megan.

An investigator from Scotland Yard concludes that the poison letter writer/murderer is a middle aged, prominent Lymstock resident.  The vicar's wife calls her own expert, Miss Marple.  Elsie Holland, governess to the Symmington boys, receives a poison letter. The police catch Aimee Griffith typing on the same typewriter used by the murderer and arrest her.

Jerry heads to London to see the doctor and takes Megan along.  They stop at the dressmaker to get Megan some clothes.  Jerry realizes he has fallen in love with her and proposes, but she turns him down.  Jerry then asks Mr. Symmington if he can woo Megan.  Megan blackmails her stepfather by saying she has proof that he murdered her mother.  Mr. Symmington pays her off, but does not admit his guilt.  After giving Megan a sleeping drug, he tries to murder her, but Jerry and the police are waiting for him.  Jerry rescues Megan and Mr. Symmington is arrested.

Miss Marple explains that the letters served as a diversion.  Mr. Symmington, in love with Elsie Holland, wanted to get rid of his wife.  He modelled the letters on a case that he worked on as a solicitor.  Miss Marple, knowing that it would be hard to prove his guilt, had Megan lure him into a trap.

Megan realizes she is in love with Jerry who buys Miss Barton's house for them.  His sister Joanna marries a doctor from Lymstock.  Emily and Aimee go on a cruise together.

The Moving Finger, published in 1942, courtesy 

http://www.agathachristie.com/stories/the-moving-finger.