In the novel At Bertram's Hotel, Archdeacon Simmons is a friend of Canon Pennyfather. The canon had invited Simmons as a house guest but the Canon had not returned and had been missing for some days.
The Canon's housekeeper Mrs McCrae had grown increasingly worried by her employer's non-appearance. She welcomed the arrival of Simmons as she saw him as a complete contrast to the Canon. Simmons always seemed to know where he was going, and what he was doing. He was "always cheerfully sure of knowing the right thing to be done and doing it".
When the Archdeacon arrived and learned about the Canon's disappearance, he set about trying to locate him by making phone calls, first to the Canon's sister, and then Dr Weissgarten whom he knew was at the same Lucerne conference the Canon was supposed to go to. He also called Bertram's Hotel, the Athenaeum Club and the Kensington Air Terminal. From the details from each of these calls, Simmons was able to piece together what must have happened to the Canon, which was that he had left the hotel, dined at the Athenaeum, proceeded to the air terminal and discovered he was one day late catching his fight. What happened after that was a mystery. From the fact the the Canon would have been carrying cards and letters which would have identified him, Simmons reasoned that he couldn't be in a hospital because they would have certainly gotten in touch. Given all these, Simmons concluded that he and Mrs McCrae had to call the police.
In the BBC 1987 adaptation of the novel, it is Miss Marple who calls Mrs McCrae and tells her to call the police.