In the novel The Mirror Crack'd from Side to Side, Arthur Badcock (real name Alfred Beadle) was the husband of Heather. He works in real estate, at the firm Biddle & Russell. He is a "thin pale man, rather slow in speech".
Arthur lives at No. 3 Arlington Close, at The Development in St. Mary Mead. At the time of the events of the novel, he and his wife had lived there for just about three years.
Arthur tells Inspector Cornish that Heather had never taken Calmo, and that no doctor had ever prescribed it for her. He and Heather had each had a bun and a cup of tea during the fête, and then they were invited up to the house. They met Marina Gregg and her husband. Heather had talked to Marina about how she had met her years before.
Arthur had taken a glass of sherry, while Heather had been offered a daiquiri by Jason Rudd. Someone had jogged Heather's elbow, and her drink was spilled, so Marina gave her her own glass. Heather had drunk it rather quickly. Shortly after that, she sat down, saying she felt "rather queer", and then she died.
After Heather's death, Arthur is described as looking like "a chewed-out bit of string". However, Miss Marple is of the opinion that after the first natural grief, he will not miss her very much. She says that Heather would have been fond of him, look after him when he was sick, prepare meals for him and keep the house well, but she would not know what he might be feeling or thinking, and that makes rather a lonely life for a man.
Miss Marple expects that Arthur will marry again, perhaps quite soon. She also thinks that he will probably marry a woman of much the same type, someone with a personality stronger than his own.
Later in the novel, Cherry Baker wonders whether Arthur and Mrs Bain will "make a match of it".
It is later revealed that Arthur had changed his name from Alfred Beadle when he left America, where he was once briefly married to Marina Gregg, before she became a film star. They were married for a year or two, and then got divorced. He then moved back to England. When this information was brought the attention of the police, they asked Arthur to go to the police station to assist them with their inquiries.
In BBC's 1992 adaptation of the novel, the part of Arthur Badcock was played by Christopher Hancock. His job in real estate is not mentioned, and the sideplot of him once having been the husband of Marina Gregg is eliminated. In this adaptation Arthur and Heather were living in Jersey and not Bermuda when they first met Marina Gregg.
Arthur Badcock does not appear ITV's 2010 adaptation of the novel as in this adaptation, Heather Badcock is portrayed as unmarried.